,,gr[? ,,& ,,=m ,,cambridge ,,univ]sity ,,press ,c4 ,f4 ,,clay1 ,,manag] ,london3 ,,fett] ,,lane1 ,e4,c4 ,ed9burgh3 #ajj ,,pr9ces ,,/reet ,illu/ration ,new ,york3 ,g4 ,p4 ,,putnam',s ,,sons ,bombay1 ,calcutta & ,madras3 ,,macmillan ,,& ,co41 ,,ltd4 ,toronto3 ,j4 ,m4 ,,d5t ,,& ,,sons1 ,,ltd4 ,tokyo3 ,,! ,,m>uz5-,,kabu%iki-,,kai%a ,all rights res]v$ ,,on ,,gr[? ,,& ,,=m ,,by ,d',,arcy ,,w5twor? ,,?ompson ,cambridge3 at ! ,univ]sity ,press #aiag 8,! reason+s ab\t ! wond]ful & intricate op]ations ( nature are s full ( unc]ta9ty1 t1 z ! ,wise-man truly obs]ves1 h>dly d we guess aright at ! ?+s t are ^u e>?1 & ) lab\r d we f9d ! ?+s t are be=e u40 ,/eph5 ,hales1 ,vegetable ,/aticks 7#agbg71 p4 #cah1 #agch4 ,,prefatory ,,note ,?is book ( m9e has little ne$ ( preface1 = inde$ x is 8all preface0 f beg9n+ to end4 ,i h writt5 x z an easy introduction to ! /udy ( organic ,=m1 by me?ods :i* are ! common-places ( physical sci5ce1 :i* are by no means novel 9 _! application to natural hi/ory1 b :i* nev]!less naturali/s are little accu/om$ to employ4 ,x is n ! biologi/ ) an inkl+ ( ma!matics1 b ! skill$ & le>n$ ma!matician :o mu/ ultimately deal ) su* problems z are m]ely sket*$ & adumbrat$ "h4 ,i pret5d to no ma!matical skill1 b ,i h made :at use ,i c\ld ( :at tools ,i _h2 ,i h dealt ) simple cases1 & ! ma!matical me?ods :i* ,i h introduc$ are ( ! easie/ & simple/ k9d4 ,elem5t>y z !y are1 my book has n be5 writt5 )\t ! help--! indisp5sable help--( _m fri5ds4 ,l ,mr ,pope translat+ ,hom]1 :5 ,i felt myself defici5t ,i s\ght assi/ance6 ,& ! exp]i5ce :i* ,johnson attribut$ to ,pope has be5 m9e also1 t m5 ( le>n+ did n refuse to help me4 ,my debts are _m1 & ,i w n try to proclaim !m all3 b ,i beg to record my p>ticul> obligations to ,pr(essor ,claxton ,fidl]1 ,sir ,george ,gre5hill1 ,sir ,joseph ,l>mor1 & ,pr(essor ,a4 ,mc,kenzie2 to a mu* y\ng] b v helpful fri5d1 ,mr ,john ,m>%all1 ,s*ol> ( ,tr9ity2 la/ly1 & 7if ,i may say s7 mo/ ( all1 to my colleague ,pr(essor ,william ,p$die1 ^: advice has made _m useful additions to my book & ^: criticism has sp>$ me _m a fault & blund]4 ,i am "u obligations also to ! au?ors & publi%]s ( _m books f :i* illu/rations h be5 borr[$1 & especially to ! foll[+3 ,to ! ,controll] ( ,h4,m4 ,/ation]y ,(fice1 = leave to reproduce a numb] ( figures1 *iefly ( ,=am9if]a & ( ,radiol>ia1 f ! ,reports ( ! ,*all5g] ,exp$ition4 vi ,to ! ,c\ncil ( ! ,royal ,society ( ,ed9burgh1 & to t ( ! ,zoological ,society ( ,london3--! =m] = lett+ me repr9t f _! ,transactions ! great] "p ( ! text & illu/rations ( my conclud+ *apt]1 ! latt] = ! use ( a numb] ( figures = my *apt] on ,horns4 ,to ,pr(essor ,e4 ,b4 ,wilson1 = 8 well-kn[n & all b indisp5sable figures ( ! cell 7figs4 #db-ea1 #ec72 to ,m4 ,a4 ,pr5ant1 = o!r figures 7#da1 #dh7 9 ! same *apt]2 to ,sir ,donald ,mac,alister & ,mr ,edw9 ,arnold = c]ta9 figures 7#cce-g71 & to ,sir ,edw>d ,s*f] & ,messrs ,longmans = ano!r 7#ccd71 illu/rat+ ! m9ute trabecul> /ructure ( bone4 ,to ,mr ,g]h>d ,heilmann1 ( ,cop5hag51 = 8 beautiful diagrams 7figs4 #chh-ic1 #dja1 #djb7 includ$ 9 my la/ *apt]4 ,to ,pr(essor ,claxton ,fidl] & to ,messrs ,griff91 = lett+ me use1 ) m or less modification or simplification1 a numb] ( illu/rations 7figs4 #cci-cdf7 f ,pr(essor ,fidl]'s ,textbook ( ,bridge ,con/ruction4 ,to ,messrs ,blackwood & ,sons1 = sev]al cuts 7figs4 #abg-i1 #aca1 #agc7 f ,pr(essor ,alleyne ,ni*olson's ,palaeontology2 to ,mr ,he9emann1 = c]ta9 figures 7#eg1 #abb1 #abc1 #bje7 f ,dr ,/phane ,l$uc's ,me*anism ( ,life2 to ,mr ,a4 ,m4 ,wor?+ton & to ,messrs ,longmans1 = figures 7#ga1 #ge7 f ,a ,/udy ( ,spla%es1 & to ,mr ,c4 ,r4 ,d>l+ & to ,messrs ,e4 & ,s4 ,spon = ^? 7fig4 #he7 f ,mr ,d>l+'s ,liquid ,drops & ,globules4 ,to ,messrs ,macmillan & ,co4 = two figures 7#cjd1 #cje7 f ,zittel's ,palaeontology1 to ! ,ox=d ,univ]sity ,press = a diagram 7fig4 #bh7 f ,mr ,j4 ,w4 ,j5k9son's ,exp]im5tal ,embryology2 & to ! ,cambridge ,univ]sity ,press = a numb] ( figures f ,pr(essor ,h5ry ,woods's ,inv]tebrate ,palaeontology1 = "o 7fig4 #baj7 f ,dr ,willey's ,zoological ,results1 & = ano!r 7fig4 #cba7 f 8,?omson & ,tait40 ,_m m1 & by mu* ! great] "p ( my diagrams1 ,i owe to ! untir+ help ( ,dr ,doris ,l4 ,mack9non1 ,d4,sc41 & ( ,miss ,hel5 ,ogilvie1 ,m4,a41 ,b4,sc41 ( ?is ,college4 ,d',,arcy ,,w5twor? ,,?ompson4 ,,univ]sity ,,college1 ,,dundee4 ,decemb]1 #aiaf4 ,,cont5ts ,,*ap4 ,,page ,i4 ,,introductory #a ,,ii4 ,,on ,,magnitude #af ,,iii4 ,,! ,,rate ,,( ,,gr[? #ej ,,iv4 ,,on ,,! ,,int]nal ,,=m ,,& ,,/ructure ,,( ,,! ,,cell #aef ,v4 ,,! ,,=ms ,,( ,,cells #bja ,,vi4 ,a ,,note ,,on ,,adsorption #bgg ,,vii4 ,,! ,,=ms ,,( ,,tissues1 ,,or ,,cell-,,aggregates #bic ,,viii4 ,,! ,,same 7cont9u$7 #cdf ,,ix4 ,,on ,,concretions1 ,,spicules1 ,,& ,,spicul> ,,skeletons #daa ,x4 ,a ,,p>5!tic ,,note ,,on ,,geodetics #dhh ,,xi4 ,,! ,,log>i?mic ,,spiral #dic ,,xii4 ,,! ,,spiral ,,%ells ,,( ,,! ,,=am9if]a #ehg ,,xiii4 ,,! ,,%apes ,,( ,,horns1 ,,& ,,( ,,tee? ,,or ,,tusks3 ,,) ,a ,,note ,,on ,,torsion #fab ,,xiv4 ,,on ,,leaf-,,arrangem5t1 ,,or ,,phyllotaxis #fce ,,xv4 ,,on ,,! ,,%apes ,,( ,,eggs1 ,,& ,,( ,,c]ta9 ,,o!r ,,holl[ ,,/ructures #feb ,,xvi4 ,,on ,,=m ,,& ,,me*anical ,,effici5cy #fgj ,,xvii4 ,,on ,,! ,,!ory ,,( ,,trans=mations1 ,,or ,,! ,,comp>ison ,,( ,,relat$ ,,=ms #gai ,,epilogue #ggh ,,index #ghj ,,li/ ,,( ,,illu/rations #a4 ,n]ve-cells1 f l>g] & small] animals 7,m9ot1 aft] ,irv+ ,h>de/y7 4 4 4 #cg #b4 ,relative magnitudes ( "s m9ute organisms 7,zsigmondy7 4 4 4 #ci #c4 ,curves ( gr[? 9 man 7,quetelet & ,b[dit*7 4 4 4 #fa #d1 #e4 ,mean annual increm5ts ( /ature & weight 9 man 7d47 4 4 4 #ff1 #fi #f4 ,! ratio1 ?r\gh\t life1 ( female weight to male 7d47 4 4 4 #ga #g-i4 ,curves ( gr[? ( *ild1 be=e & aft] bir? 7,8 & ,rss[7 4 4 4 #gd-f #aj4 ,curve ( gr[? ( bamboo 7,o/wald1 aft] ,kraus7 4 4 4 #gg #aa4 ,coeffici5ts ( v>iability 9 human /ature 7,boas & ,wissl]7 4 4 4 #hj #ab4 ,gr[? 9 weight ( m\se 7,wolfgang ,o/wald7 4 4 4 #hc #ac4 ,d4 ( silkworm 7,luciani & ,lo ,monaco7 4 4 4 #hd #ad4 ,d4 ( tadpole 7,o/wald1 aft] ,s*ap]7 4 4 4 #he #ae4 ,l>val eels1 or ,leptocephali1 & "y elv] 7,joh4 ,s*midt7 4 4 4 #hf #af4 ,gr[? 9 l5g? ( ,spirogyra 7,h(mei/]7 4 4 4 #hg #ag4 ,pulsations ( gr[? 9 ,crocus 7,bose7 4 4 4 #hh #ah4 ,relative gr[? ( bra91 he>t & body ( man 7,quetelet7 4 4 4 #ij #ai4 ,ratio ( /ature to span ( arms 7d47 4 4 4 #id #bj4 ,rates ( gr[? ne> ! tip ( a bean-root 7,sa*s7 4 4 4 #if #ba1 #bb4 ,! weight-l5g? ratio ( ! plaice1 & its annual p]iodic *anges 4 4 4 #ii1 #ajj #bc4 ,v>iability ( tail-=ceps 9 e>wigs 7,bateson7 4 4 4 #ajd #bd4 ,v>iability ( body-l5g? 9 plaice 4 4 4 #aje #be4 ,rate ( gr[? 9 plants 9 relation to temp]ature 7,sa*s7 4 4 4 #aji #bf4 ,d4 9 maize1 obs]v$ 7,kpp571 & calculat$ curves 4 4 4 #aab #bg4 ,d4 9 roots ( peas 7,miss ,i4 ,leit*7 4 4 4 #aac #bh1 #bi4 ,rate ( gr[? ( frog 9 relation to temp]ature 7,j5k9son1 aft] ,o4 ,h]twig71 & calculat$ curves ( d4 4 4 4 #aae1 #f #cj4 ,seasonal fluctuation ( rate ( gr[? 9 man 7,daffn]7 4 4 4 #aai #ca4 ,d4 9 ! rate ( gr[? ( trees 7,c4 ,e4 ,hall7 4 4 4 #abj #cb4 ,long-p]iod fluctuation 9 ! rate ( gr[? ( ,arizona trees 7,a4 ,e4 ,d\glass7 4 4 4 #abb #cc1 #cd4 ,! v>y+ =m ( br9e-%rimps 7,artemia71 9 relation to sal9ity 7,abonyi7 4 4 4 #abh1 #i #ce-ci4 ,curves ( reg5]ative gr[? 9 tadpoles' tails 7,m4 ,l4 ,durb97 4 4 4 #adj-ade #dj4 ,relation betwe5 am\nt ( tail remov$1 am\nt re/or$1 & "t requir$ = re/oration 7,m4 ,m4 ,ellis7 4 4 4 #adh #da4 ,c>yok9esis 9 tr\t's egg 7,pr5ant1 aft] ,pr(4 ,p4 ,b\97 4 4 4 #afi #db-ea4 ,diagrams ( mitotic cell-division 7,pr(4 ,e4 ,b4 ,wilson7 4 4 4 #aga-e #eb4 ,*romosomes 9 c\rse ( splitt+ & sep>ation 7,hats*ek & ,flemm+7 4 4 4 #ahj #ec4 ,annul> *romosomes ( mole-cricket 7,wilson1 aft] vom ,ra?7 4 4 4 #aha #ed-ef4 ,diagrams illu/rat+ a hypo!tic field ( =ce 9 c>yok9esis 7,pr(4 ,w4 ,p$die7 4 4 4 #ahb-d #eg4 ,an artificial figure ( c>yok9esis 7,l$uc7 4 4 4 #ahf #eh4 ,a segm5t$ egg ( ,c]ebratulus 7,pr5ant1 aft] ,coe7 4 4 4 #ahi #ei4 ,diagram ( a field ( =ce ) two l poles 4 4 4 #ahi #fj4 ,a budd+ yea/-cell 4 4 4 #bac #fa4 ,! r\lettes ( ! conic sections 4 4 4 #bah #fb4 ,mode ( developm5t ( an unduloid f a cyl9drical tube 4 4 4 #bbj #fc-fe4 ,cyl9drical1 unduloid1 nodoid & cat5oid oil-globules 7,plateau7 4 4 4 #bbb1 #c #ff4 ,diagram ( ! nodoid1 or ela/ic curve 4 4 4 #bbd #fg4 ,diagram ( a cyl9d] capp$ by ! correspond+ portion ( a sph]e 4 4 4 #bbf #fh4 ,a liquid cyl9d] break+ up into sph]es 4 4 4 #bbg #fi4 ,! same ph5om5on 9 a protoplasmic cell ( ,trianea 4 4 4 #bcd #gj4 ,"s phases ( a spla% 7,a4 ,m4 ,wor?+ton7 4 4 4 #bce #ga4 ,a break+ wave 7d47 4 4 4 #bcf #gb4 ,! calycles ( "s campanul>ian zoophytes 4 4 4 #bcg #gc4 ,a flagellate monad1 ,di/igma proteus 7,saville ,k5t7 4 4 4 #bdf #gd4 ,noctiluca mili>is1 diagrammatic 4 4 4 #bdf #ge4 ,v>i\s species ( ,vorticella 7,saville ,k5t & o!rs7 4 4 4 #bdg #gf4 ,v>i\s species ( ,salp+oeca 7d47 4 4 4 #bdh #gg4 ,species ( ,t9t9nus1 ,d9obryon & ,codonella 7d47 4 4 4 #bdh #gh4 ,! tube or cup ( ,vag9icola 4 4 4 #bdh #gi4 ,! same ( ,follicul9a 4 4 4 #bdi #hj4 ,tra*elophyllum 7,wreszni[ski7 4 4 4 #bdi #ha4 ,tri*od9a p$iculus 4 4 4 #beb #hb4 ,d95ymplia gracilis 7,leidy7 4 4 4 #bec #hc4 ,a 8coll>-cell0 ( ,codosiga 4 4 4 #bed #hd4 ,v>i\s species ( ,lag5a 7,brady7 4 4 4 #bef #he4 ,hang+ drops1 to illu/rate ! unduloid =m 7,c4 ,r4 ,d>l+7 4 4 4 #beg #hf4 ,diagram ( a flut$ cyl9d] 4 4 4 #bfj #hg4 ,nodos>ia scal>is 7,brady7 4 4 4 #bfb #hh4 ,flut$ & pleat$ gonangia ( c]ta9 ,campanul>ians 7,allman7 4 4 4 #bfb #hi4 ,v>i\s species ( ,nodos>ia1 ,sagr9a & ,rheophax 7,brady7 4 4 4 #bfc #ij4 ,trypanosoma t9eae & ,spiro*aeta anodontae1 to %ew undulat+ membranes 7,m9*9 & ,fan?am7 4 4 4 #bff #ia4 ,"s species ( ,tri*oma/ix & ,tri*omonas 7,k(oid7 4 4 4 #bfg #ib4 ,h]petomonas assum+ ! undulatory membrane ( a ,trypanosome 7,d4 ,l4 ,mack9non7 4 4 4 #bfh #ic4 ,diagram ( a human blood-corpuscle 4 4 4 #bga #id4 ,sp]m-cells ( decapod cru/acea1 ,ina*us & ,gala!a 7,koltz(f7 4 4 4 #bgc #ie4 ,! same1 9 sal9e solutions ( v>y+ d5sity 7d47 4 4 4 #bgd #if4 ,a sp]m-cell ( ,dromia 7d47 4 4 4 #bge #ig4 ,*ondriosomes 9 cells ( kidney & pancreas 7,b>ratt & ,ma!ws7 4 4 4 #bhe #ih4 ,adsorptive conc5tration ( potassium salts 9 v>i\s plant-cells 7,macallum7 4 4 4 #bij #ii-aja4 ,equilibrium ( surface-t5sion 9 a float+ drop 4 4 4 #bid1 #e #ajb4 ,plateau's 8b\rrelet0 9 plant-cells2 diagrammatic 7,b]?old7 4 4 4 #bih #ajc4 ,p>5*yma ( maize1 %ew+ ! same ph5om5on 4 4 4 #bih #ajd1 #e4 ,diagrams ( ! p>tition-wall betwe5 two soap-bubbles 4 4 4 #bii1 #cjj #ajf4 ,diagram ( a p>tition 9 a conical cell 4 4 4 #cjj #ajg4 ,*a9s ( cells 9 ,no/oc1 ,anaba5a & o!r l[ algae 4 4 4 #cjj #ajh4 ,diagram ( a symmetrically divid$ soap-bubble 4 4 4 #cja #aji4 ,arrangem5t ( p>titions 9 divid+ spores ( ,pellia 7,campbell7 4 4 4 #cjb #aaj4 ,cells ( ,dictyota 7,re9ke7 4 4 4 #cjc #aaa1 #b4 ,t]m9al & o!r cells ( ,*>a1 & "y an!ridium ( d4 4 4 4 #cjc #aac4 ,diagram ( cell-walls & p>titions "u v>i\s conditions ( t5sion 4 4 4 #cjd #aad1 #e4 ,! p>tition-surfaces ( ?ree int]connect$ bubbles 4 4 4 #cjg1 #h #aaf4 ,diagram ( f\r int]connect$ cells or bubbles 4 4 4 #cji #aag4 ,v>i\s configurations ( f\r cells 9 a frog's egg 7,raub]7 4 4 4 #caa #aah4 ,ano!r diagram ( two conjo9$ soap-bubbles 4 4 4 #cac #aai4 ,a fro? ( bubbles1 %ew+ its out] or 8epid]mal0 lay] 4 4 4 #cad #abj4 ,a tetrah$ron1 or tetrah$ral sy/em1 %ew+ its c5tre ( symmetry 4 4 4 #cag #aba4 ,a gr\p ( hexagonal cells 7,bonanni7 4 4 4 #cai #abb1 #c4 ,artificial cellul> tissues 7,l$uc7 4 4 4 #cbj #abd4 ,epid]mis ( ,gir>dia 7,goebel7 4 4 4 #cba #abe4 ,soap-fro?1 & ! same "u compression 7,rhumbl]7 4 4 4 #cbb #abf4 ,epid]mal cells ( ,elodea canad5sis 7,b]?old7 4 4 4 #cbb #abg4 ,li?o/rotion ,m>t9i 7,ni*olson7 4 4 4 #cbe #abh4 ,cya?ophyllum hexagonum 7,ni*olson1 aft] ,zittel7 4 4 4 #cbe #abi4 ,ara*nophyllum p5tagonum 7,ni*olson7 4 4 4 #cbf #acj4 ,heliolites 7,woods7 4 4 4 #cbf #aca4 ,conflu5t septa 9 ,?amna/raea & ,comos]is 7,ni*olson1 aft] ,zittel7 4 4 4 #cbg #acb4 ,geometrical con/ruction ( a bee's cell 4 4 4 #ccj #acc4 ,/ellate cells 9 ! pi? ( a ru%2 diagrammatic 4 4 4 #cce #acd4 ,diagram ( soap-films =m$ 9 a cubical wire skeleton 7,plateau7 4 4 4 #ccg #ace4 ,pol> furr[s 9 sy/ems ( f\r soap-bubbles 7,rob]t7 4 4 4 #cda #acf-h4 ,diagrams illu/rat+ ! division ( a cube by p>titions ( m9imal area 4 4 4 #cdg-ej #aci4 ,cells f hairs ( ,sphacel>ia 7,b]?old7 4 4 4 #cea #adj4 ,! bisection ( an isosceles triangle by m9imal p>titions 4 4 4 #cec #ada4 ,! simil> p>tition+ ( sph]oidal & conical cells 4 4 4 #cec #adb4 ,s-%ap$ p>titions f cells ( algae & mosses 7,re9ke & o!rs7 4 4 4 #cee #adc4 ,diagrammatic explanation ( ! ,s-%ap$ p>titions 4 4 4 #cef #add4 ,developm5t ( ,ery?rotri*ia 7,b]?old7 4 4 4 #cei #ade4 ,p]icl9al1 anticl9al & radial p>tition+ ( a quadrant 4 4 4 #cei #adf4 ,con/ruction = ! m9imal p>tition+ ( a quadrant 4 4 4 #cfa #adg4 ,ano!r diagram ( anticl9al & p]icl9al p>titions 4 4 4 #cfb #adh4 ,mode ( segm5tation ( an artificially flatt5$ frog's egg 7,r\x7 4 4 4 #cfc #adi4 ,! bisection1 by m9imal p>titions1 ( a prism ( small angle 4 4 4 #cfd #aej4 ,comp>ative diagram ( ! v>i\s modes ( bisection ( a prismatic sector 4 4 4 #cfe #aea4 ,diagram ( ! fur!r gr[? ( ! two halves ( a quadrantal cell 4 4 4 #cfg #aeb4 ,diagram ( ! orig9 ( an epid]mic lay] ( cells 4 4 4 #cgj #aec4 ,a discoidal cell divid+ into octants 4 4 4 #cga #aed4 ,a g]m9at+ spore ( ,riccia 7aft] ,campbell71 to %ew ! mann] ( space-p>tition+ 9 ! cellul> tissue 4 4 4 #cgb #aee1 #f4 ,!oretical arrangem5t ( successive p>titions 9 a discoidal cell 4 4 4 #cgc #aeg4 ,sections ( a moss-embryo 7,ki5itz-,g]l(f7 4 4 4 #cgd #aeh4 ,v>i\s possible arrangem5ts ( p>titions 9 gr\ps ( f\r to eight cells 4 4 4 #cge #aei4 ,?ree modes ( p>tition+ 9 a sy/em ( six cells 4 4 4 #cgf #afj1 #a4 ,segm5t+ eggs ( ,tro*us 7,rob]t71 & ( ,cyn?ia 7,conkl97 4 4 4 #cgg #afb4 ,section ( ! apical cone ( ,salv9ia 7,pr+%eim7 4 4 4 #cgg #afc1 #d4 ,segm5t+ eggs ( ,pyrosoma 7,korotneff71 & ( ,e*9us 7,dries*7 4 4 4 #cgg #afe4 ,segm5t+ egg ( a cephalopod 7,watase7 4 4 4 #cgh #aff1 #g4 ,eggs segm5t+ "u pressure3 ( ,e*9us & ,n]eis 7,dries*71 & ( a frog 7,r\x7 4 4 4 #cgh #afh4 ,v>i\s arrangem5ts ( a gr\p ( eight cells on ! surface ( a frog's egg 7,raub]7 4 4 4 #cha #afi4 ,diagram ( ! p>titions & int]facial contacts 9 a sy/em ( eight cells 4 4 4 #chc #agj4 ,v>i\s modes ( aggregation ( eight oil-drops 7,r\x7 4 4 4 #chd #aga4 ,=ms1 or species1 ( ,a/]olampra 7,greville7 4 4 4 #chf #agb4 ,diagrammatic section ( an alcyon>ian polype 4 4 4 #chg #agc1 #d4 ,sections ( ,het]ophyllia 7,ni*olson & ,m>t9 ,duncan7 4 4 4 #chh1 #i #age4 ,diagrammatic section ( a ct5ophore 7,eu*>is7 4 4 4 #cia #agf1 #g4 ,diagrams ( ! con/ruction ( a ,pluteus l>va 4 4 4 #cib1 #c #agh1 #i4 ,diagrams ( ! developm5t ( /omata1 9 ,s$um & 9 ! hyac9? 4 4 4 #cid #ahj4 ,v>i\s spores & poll5-gra9s 7,b]?old & o!rs7 4 4 4 #cif #aha4 ,spore ( ,an?oc]os 7,campbell7 4 4 4 #cig #ahb1 #d1 #i4 ,diagrammatic modes ( division ( a cell "u c]ta9 conditions ( asymmetry 4 4 4 #djj-e #ahc4 ,developm5t ( ! embryo ( ,sphagnum 7,campbell7 4 4 4 #djb #ahe4 ,! gemma ( a moss 7d47 4 4 4 #djc #ahf4 ,! an!ridium ( ,riccia 7d47 4 4 4 #djd #ahg4 ,section ( gr[+ %oot ( ,selag9ella1 diagrammatic 4 4 4 #djd #ahh4 ,an embryo ( ,jung]mannia 7,ki5itz-,g]l(f7 4 4 4 #djd #aij4 ,developm5t ( ! sporangium ( ,osmunda 7,b[]7 4 4 4 #djf #aia4 ,embryos ( ,phascum & ( ,adiantum 7,ki5itz-,g]l(f7 4 4 4 #djh #aib4 ,a section ( ,gir>dia 7,goebel7 4 4 4 #djh #aic4 ,an an!ridium ( ,pt]is 7,/rasburg]7 4 4 4 #dji #aid4 ,spicules ( ,siphonogorgia & ,an?ogorgia 7,/ud]7 4 4 4 #dac #aie-g4 ,calcosph]ites1 deposit$ 9 :ite ( egg 7,h>t+7 4 4 4 #dba1 #b #aih4 ,sections ( ! %ell ( ,mya 7,c>p5t]7 4 4 4 #dbb #aii4 ,concretions1 or spicules1 artificially deposit$ 9 c>tilage 7,h>t+7 4 4 4 #dbc #bjj4 ,fur!r illu/rations ( alcyon>ian spicules3 ,eunicea 7,/ud]7 4 4 4 #dbd #bja-c4 ,associat$1 aggregat$ & composite calcosph]ites 7,h>t+7 4 4 4 #dbe1 #f #bjd4 ,h>t+'s 8cono/ats0 4 4 4 #dbg #bje4 ,liesegang's r+s 7,l$uc7 4 4 4 #dbh #bjf4 ,relay-cry/als ( common salt 7,b[man7 4 4 4 #dbi #bjg4 ,:eel-l cry/als 9 a colloid m$ium 7d47 4 4 4 #dbi #bjh4 ,a conc5trically /riat$ calcosph]ite or sph]ocry/al 7,h>t+7 4 4 4 #dcb #bji4 ,otoli?s ( plaice1 %ew+ 8age-r+s0 7,wallace7 4 4 4 #dcb #baj4 ,spicules1 or calcosph]ites1 ( ,a/roscl]a 7,li/]7 4 4 4 #dcf #baa4 #b4 ,c- & ,s-%ap$ spicules ( sponges & holo?urians 7,sollas & ,?el7 4 4 4 #ddb #bac4 ,an amphidisc ( ,hyalonema 4 4 4 #ddb #bad-g4 ,spicules ( calc>e\s1 tetract9ellid & hexact9ellid sponges1 & ( v>i\s holo?urians 7,haeckel1 ,s*ultze1 ,sollas & ,?el7 4 4 4 #dde-deb #bah4 ,diagram ( a solid body conf9$ by surface-en]gy to a liquid b\nd>y-film 4 4 4 #dfj #bai4 ,a/rorhiza limicola & ar5>ia 7,brady7 4 4 4 #dfd #bbj4 ,a nucle> 8reticulum plasmatique0 7,c>noy7 4 4 4 #dfh #bba4 ,a sph]ical radiol>ian1 ,aulonia hexagona 7,haeckel7 4 4 4 #dfi #bbb4 ,act9omma arcadophorum 7d47 4 4 4 #dfi #bbc4 ,e?mospha]a conosiphonia 7d47 4 4 4 #dgj #bbd4 ,portions ( %ells ( ,c5ospha]a favosa & vesp>ia 7d47 4 4 4 #dgj #bbe4 ,aula/rum tric]os 7d47 4 4 4 #dga #bbf4 ,"p ( ! skeleton ( ,cannorhaphis 7d47 4 4 4 #dgb #bbg4 ,a ,nassell>ian skeleton1 ,callimitra c>olotae 7d47 4 4 4 #dgb #bbh1 #i4 ,portions ( ,dictyo*a /ap$ia 7d47 4 4 4 #dgd #bcj4 ,diagram to illu/rate ! con=mation ( ,callimitra 4 4 4 #dgf #bca4 ,skeletons ( v>i\s radiol>ians 7,haeckel7 4 4 4 #dgi #bcb4 ,diagrammatic /ructure ( ! skeleton ( ,dorataspis 7d47 4 4 4 #dha #bcc1 #d4 ,phatnaspis cri/ata 7,haeckel71 & a diagram ( ! same 4 4 4 #dhc #bce4 ,phractaspis prototypus 7,haeckel7 4 4 4 #dhd #bcf4 ,annul> & spiral ?ick5+s 9 ! walls ( plant-cells 4 4 4 #dhh #bcg4 ,a radiograph ( ! %ell ( ,nautilus 7,gre5 & ,g>d9]7 4 4 4 #did #bch4 ,a spiral =am9if]1 ,globig]9a 7,brady7 4 4 4 #die #bci-db4 ,diagrams to illu/rate ! developm5t or gr[? ( a log>i?mic spiral 4 4 4 #djg-eja #bdc4 ,a helicoid & a scorpioid cyme 4 4 4 #ejb #bdd4 ,an ,ar*im$ean spiral 4 4 4 #ejc #bde-g4 ,m diagrams ( ! developm5t ( a log>i?mic spiral 4 4 4 #eje1 #f #bdh-eg4 ,v>i\s diagrams illu/rat+ ! ma!matical !ory ( gnomons 4 4 4 #ejh-ac #beh4 ,a %ell ( ,haliotis1 to %ew h[ ea* increm5t ( ! %ell con/itutes a gnomon to ! preexi/+ /ructure 4 4 4 #ead #bei1 #fj4 ,spiral =am9if]a1 ,pulv9ul9a & ,cri/ell>ia1 to illu/rate ! same pr9ciple 4 4 4 #ead1 #e #bfa4 ,ano!r diagram ( a log>i?mic spiral 4 4 4 #eag #bfb4 ,a diagram ( ! log>i?mic spiral ( ,nautilus 7,moseley7 4 4 4 #eai #bfc1 #d4 ,op]cula ( ,turbo & ( ,n]ita 7,moseley7 4 4 4 #eba1 #b #bfe4 ,a section ( ! %ell ( ,melo e?iopicus 4 4 4 #ebe #bff4 ,%ells ( ,h>pa & ,dolium1 to illu/rate g5]at+ curves & g5e 4 4 4 #ebf #bfg4 ,d',orbigny's ,helicomet] 4 4 4 #ebi #bfh4 ,section ( a nautiloid %ell1 to %ew ! 8protocon*0 4 4 4 #eca #bfi-gc4 ,diagrams ( log>i?mic spirals1 ( v>i\s angles 4 4 4 #ecb-e #bgd1 #f1 #g4 ,con/ructions = det]m9+ ! angle ( a log>i?mic spiral 4 4 4 #ecg1 #h #bge4 ,an ammonite1 to %ew its corrugat$ surface patt]n 4 4 4 #ecg #bgh-hj4 ,illu/rations ( ! 8angle ( ret>dation0 4 4 4 #edb-d #bha4 ,a %ell ( ,macroscaphites1 to %ew *ange ( curvature 4 4 4 #eej #bhb4 ,con/ruction = det]m9+ ! l5g? ( ! coil$ spire 4 4 4 #eea #bhc4 ,section ( ! %ell ( ,triton corrugatus 7,woodw>d7 4 4 4 #eed #bhd4 ,lamell>ia p]spicua & ,sig>etus haliotoides 7d47 4 4 4 #eee #bhe1 #f4 ,sections ( ! %ells ( ,t]ebra maculata & ,tro*us niloticus 4 4 4 #eei1 #fj #bhg-i4 ,diagrams illu/rat+ ! l9es ( gr[? on a lamellibran* %ell 4 4 4 #efc-e #bij4 ,capr9ella adv]sa 7,woodw>d7 4 4 4 #efg #bia4 ,section ( ! %ell ( ,productus 7,woods7 4 4 4 #efg #bib4 ,! 8skeletal loop0 ( ,t]ebratula 7d47 4 4 4 #efh #bic1 #d4 ,! spiral arms ( ,spirif] & ( ,atrypa 7d47 4 4 4 #efi #bie-g4 ,%ells ( ,cleodora1 ,hyalaea & o!r pt]opods 7,boas7 4 4 4 #egj1 #a #bih1 #i4 ,coord9ate diagrams ( ! %ell-outl9e 9 c]ta9 pt]opods 4 4 4 #egb1 #c #cjj4 ,developm5t ( ! %ell ( ,hyalaea trid5tata 7,tes*7 4 4 4 #egc #cja4 ,pt]opod %ells1 ( ,cleodora & ,hyalaea1 view$ f ! side 7,boas7 4 4 4 #ege #cjb1 #c4 ,diagrams ( septa 9 a conical %ell 4 4 4 #egi #cjd4 ,a section ( ,nautilus1 %ew+ ! log>i?mic spirals ( ! septa to :i* ! %ell-spiral is ! evolute 4 4 4 #eha #cje4 ,ca/ ( ! int]ior ( ! %ell ( ,nautilus1 to %ew ! cont\rs ( ! septa at _! junction ) ! %ell-wall 4 4 4 #ehb #cjf4 ,ammonites ,s[]byi1 to %ew septal outl9es 7,zittel1 aft] ,/e9mann & ,dd]le97 4 4 4 #ehd #cjg4 ,suture-l9e ( ,p9acoc]as 7,zittel1 aft] ,hau]7 4 4 4 #ehd #cjh4 ,%ells ( ,ha/ig]9a1 to %ew ! 8m\?0 7,brady7 4 4 4 #ehh #cji4 ,nummul9a antiquior 7,v4 von ,mll]7 4 4 4 #eia #caj4 ,cornuspira foliacea & ,op]cul9a complanata 7,brady7 4 4 4 #eid #caa4 ,miliol9a pul*ella & l9naeana 7,brady7 4 4 4 #eif #cab1 #c4 ,cyclamm9a cancellata 7d471 & diagrammatic figure ( ! same 4 4 4 #eif1 #g #cad4 ,orbul9a univ]sa 7,brady7 4 4 4 #eih #cae4 ,cri/ell>ia r5i=mis 7d47 4 4 4 #fjj #caf4 ,discorb9a b]!loti 7d47 4 4 4 #fjc #cag4 ,textul>ia tro*us & concava 7d47 4 4 4 #fjd #cah4 ,diagrammatic figure ( a ram's horns 7,sir ,v4 ,brooke7 4 4 4 #fae #cai4 ,head ( an ,arabian wild goat 7,sclat]7 4 4 4 #faf #cbj4 ,head ( ,ovis ,ammon1 %ew+ ,/ ,v5ant's curves 4 4 4 #fba #cba4 ,/ ,v5ant's diagram ( a triangul> prism "u torsion 7,?omson & ,tait7 4 4 4 #fbc #cbb4 ,diagram ( ! same ph5om5on 9 a ram's horn 4 4 4 #fbc #cbc4 ,antl]s ( a ,sw$i% elk 7,lnnb]g7 4 4 4 #fbi #cbd4 ,head & antl]s ( ,c]vus duvauceli 7,lydekk]7 4 4 4 #fcj #cbe1 #f4 ,diagrams ( spiral phyllotaxis 7,p4 ,g4 ,tait7 4 4 4 #fdd1 #e #cbg4 ,fur!r diagrams ( phyllotaxis1 to %ew h[ v>i\s spiral appe>ances may arise out ( "o & ! same angul> leaf-div]g5ce 4 4 4 #fdh #cbh4 ,diagrammatic outl9es ( v>i\s sea-ur*9s 4 4 4 #ffd #cbi1 #cj4 ,diagrams ( ! angle ( bran*+ 9 blood-vessels 7,hess7 4 4 4 #ffg1 #h #cca1 #b4 ,diagrams illu/rat+ ! flexure ( a beam 4 4 4 #fgd1 #h #ccc4 ,an example ( ! mode ( arrangem5t ( ba/-fibres 9 a plant-/em 7,s*w5d5]7 4 4 4 #fhj #ccd4 ,section ( ! head ( a femur1 to %ew its trabecul> /ructure 7,s*f]1 aft] ,rob9son7 4 4 4 #fha #cce4 ,comp>ative diagrams ( a crane-head & ! head ( a femur 7,culmann & ,h4 ,mey]7 4 4 4 #fhb #ccf4 ,diagram ( /ress-l9es 9 ! human foot 7,sir ,d4 ,mac,alister1 aft] ,h4 ,mey]7 4 4 4 #fhd #ccg4 ,trabecul> /ructure ( ! os calcis 7d47 4 4 4 #fhe #cch4 ,diagram ( %e>+-/ress 9 a load$ pill> 4 4 4 #fhf #cci4 ,diagrams ( ti$ ar*1 & b[/r+ gird] 7,fidl]7 4 4 4 #fic #cdj1 #a4 ,diagrams ( a bridge3 %ew+ propos$ span1 ! correspond+ /ress-diagram & reciprocal plan ( con/ruction 7d47 4 4 4 #fif #cdb4 ,a load$ bracket & its reciprocal con/ruction-diagram 7,culmann7 4 4 4 #fig #cdc1 #d4 ,a cantilev] bridge1 ) its reciprocal diagrams 7,fidl]7 4 4 4 #fih #cde4 ,a two-arm$ cantilev] ( ! ,=? ,bridge 7d47 4 4 4 #gjj #cdf4 ,a two-arm$ cantilev] ) load di/ribut$ ov] two pi]-heads1 z 9 ! quadrup$al skeleton 4 4 4 #gjj #cdg-i4 ,/ress-diagrams4 or diagrams ( b5d+ mom5ts1 9 ! backbones ( ! horse1 ( a ,d9osaur1 & ( ,titano!rium 4 4 4 #gja-d #cej4 ,! skeleton ( ,/egosaurus 4 4 4 #gjg #cea4 ,b5d+-mom5ts 9 a beam ) fix$ ends1 to illu/rate ! me*anics ( *evron-bones 4 4 4 #gji #ceb1 #c4 ,coord9ate diagrams ( a circle1 & its de=mation into an ellipse 4 4 4 #gbi #ced4 ,comp>ison1 by means ( ,c>tesian coord9ates1 ( ! cannon-bones ( v>i\s rum9ant animals 4 4 4 #gbi #cee1 #f4 ,log>i?mic coord9ates1 & ! circle ( ,fig4 #ceb inscrib$ !re9 4 4 4 #gbi1 #ca #ceg1 #h4 ,diagrams ( oblique & radial coord9ates 4 4 4 #gca #cei4 ,lanceolate1 ovate & cordate leaves1 comp>$ by ! help ( radial coord9ates 4 4 4 #gcb #cfj4 ,a leaf ( ,begonia da$alea 4 4 4 #gcc #cfa4 ,a network ( log>i?mic spiral coord9ates 4 4 4 #gce #cfb1 #c4 ,feet ( ox1 %eep & giraffe1 comp>$ by means ( ,c>tesian coord9ates 4 4 4 #gch1 #dj #cfd1 #f4 8,proportional diagrams0 ( human physiognomy 7,alb]t ,dr]7 4 4 4 #gdj1 #b #cfe4 ,m$ian & lat]al toes ( a tapir1 comp>$ by means ( rectangul> & oblique coord9ates 4 4 4 #gda #cfg1 #h4 ,a comp>ison ( ! copepods ,oi?ona & ,sapphir9a 4 4 4 #gdb #cfi4 ,! c>apaces ( c]ta9 crabs1 ,g]yon1 ,cory/es & o!rs1 comp>$ by means ( rectil9e> & curvil9e> coord9ates 4 4 4 #gdd #cgj4 ,a comp>ison ( c]ta9 amphipods1 ,h>p9ia1 ,/egocephalus & ,hyp]ia 4 4 4 #gdf #cga4 ,! calycles ( c]ta9 campanul>ian zoophytes1 inscrib$ 9 correspond+ ,c>tesian networks 4 4 4 #gdg #cgb4 ,! calycles ( c]ta9 species ( ,aglaoph5ia1 simil>ly comp>$ by means ( curvil9e> coord9ates 4 4 4 #gdh #cgc1 #d4 ,! fi%es ,argyropelecus & ,/]noptyx1 comp>$ by means ( rectangul> & oblique coord9ate sy/ems 4 4 4 #gdh #cge1 #f4 ,sc>us & ,pomacan?us1 simil>ly comp>$ by means ( rectangul> & coaxial sy/ems 4 4 4 #gdi #cgg-hj4 ,a comp>ison ( ! fi%es ,polyprion1 ,pseudopriacan?us1 ,scorpa5a & ,antigonia 4 4 4 #gej #cha1 #b4 ,a simil> comp>ison ( ,diodon & ,or?agoriscus 4 4 4 #gea #chc4 ,! same ( v>i\s crocodiles3 ,c4 porosus1 ,c4 am]icanus & ,notosu*us t]re/ris 4 4 4 #gec #chd4 ,! pelvic girdles ( ,/egosaurus & ,camptosaurus 4 4 4 #ged #che1 #f4 ,! %\ld]-girdles ( ,cryptocleidus & ( ,i*?yosaurus 4 4 4 #gee #chg4 ,! skulls ( ,dimorphodon & ( ,pt]anodon 4 4 4 #gef #chh-ib4 ,! pelves ( ,ar*aeopt]yx & ( ,apatornis comp>$1 & a me?od illu/rat$ :]eby int]m$iate configurations may be f\nd by int]polation 7,g4 ,heilmann7 4 4 4 #geg-i #cic4 ,! same pelves1 toge!r ) ?ree ( ! int]m$iate or int]polat$ =ms 4 4 4 #gfj #cid1 #e4 ,comp>ison ( ! skulls ( two ext9ct rh9oc]oses1 ,hyra*yus & ,ac]a!rium 7,osborn7 4 4 4 #gfa #cif4 ,occipital views ( v>i\s ext9ct rh9oc]oses 7d47 4 4 4 #gfb #cig-djj4 ,comp>ison ) ea* o!r1 & ) ! skull ( ,hyra*yus1 ( ! skulls ( ,titano!rium1 tapir1 horse & rabbit 4 4 4 #gfc1 #d #dja1 #b4 ,coord9ate diagrams ( ! skulls ( ,eohippus & ( ,equus1 ) v>i\s actual & hypo!tical int]m$iate types 7,heilmann7 4 4 4 #gfe-g #djc4 ,a comp>ison ( v>i\s human scapulae 7,dwight7 4 4 4 #gfi #djd4 ,a human skull1 inscrib$ 9 ,c>tesian coord9ates 4 4 4 #ggj #dje4 ,! same coord9ates on a new projection1 adapt$ to ! skull ( ! *impanzee 4 4 4 #ggj #djf4 ,*impanzee's skull1 inscrib$ 9 ! network ( ,fig4 #dje 4 4 4 #gga #djg1 #h4 ,correspond+ diagrams ( a baboon's skull1 & ( a dog's 4 4 4 #gga1 #c 8,cum =m>um naturalium et corporalium esse non consi/at nisi 9 unione ad mat]iam1 ejusdem ag5tis esse videtur eas produc]e cujus e/ mat]iam transmut>e4 ,secundo1 quia cum hujusmodi =mae non exc$ant virtutem et ord9em et facultatem pr9cipiorum ag5tium 9 natura1 nulla videtur necessitas eorum orig9em 9 pr9cipia r$uc]e altiora40 ,aqu9as1 ,de ,pot4 ,q4 iii1 a1 #aa4 7,quot$ 9 ,brit4 ,assoc4 ,address1 ,section ,d1 #aiaa47 8444,i w\ld t all o!r natural ph5om5a might simil>ly be d$uc$ f me*anical pr9ciples4 ,= _m ?+s move me to suspect t ev]y?+ dep5ds ^u c]ta9 =ces1 9 virtue ( :i* ! p>ticles ( bodies1 ?r\gh =ces n yet und]/ood1 are ei!r impell$ toge!r s z to coh]e 9 regul> figures1 or are repell$ & rec$e f "o ano!r40 ,newton1 9 ,preface to ! ,pr9cipia4 7,quot$ by ,mr ,w4 ,spottiswoode1 ,brit4 ,assoc4 ,presid5tial ,address1 #ahgh47 8,:5 ,sci5ce %all h subject$ all natural ph5om5a to ! laws ( ,!oretical ,me*anics1 :5 %e %all be able to pr$ict ! result ( e comb9ation z un]r+ly z ,hamilton pr$ict$ conical refraction1 or ,adams reveal$ to u ! exi/5ce ( ,neptune1--t we _c say4 ,t day may nev] come1 & x is c]ta9ly f> 9 ! dim future4 ,we may n anticipate x1 we may n ev5 call x possible4 ,b none ! less are we b\nd to look to t day1 & to lab\r = x z ! cr[n+ triumph ( ,sci5ce3--:5 ,!oretical ,me*anics %all be recognis$ z ! key to e physical enigma1 ! *>t = e travell] ?r\gh ! d>k ,inf9ite ( ,nature40 ,j4 ,h4 ,jellett1 9 ,brit4 ,assoc4 ,address1 ,section ,a1 #ahgd4 #a ,,*apt] ,i ,,introductory ,( ! *emi/ry ( 8 day & g5]ation1 ,kant decl>$ t x 0 8a sci5ce1 b n sci5ce10--8e9e ,wiss5s*aft1 ab] ni*t ,wiss5s*aft02 = t ! crit]ion ( physical sci5ce lay 9 its relation to ma!matics4 ,& a hundr$ ye>s lat] ,du ,bois ,reymond1 pr(\nd /ud5t ( ! _m sci5ces on :i* physiology is bas$1 recall$ & reit]at$ ! old say+1 decl>+ t *emi/ry w\ld only rea* ! rank ( sci5ce1 9 ! high & /rict s5se1 :5 x %\ld be f\nd possible to expla9 *emical reactions 9 ! light ( _! causal relation to ! velocities1 t5sions & conditions ( equilibrium ( ! compon5t molecules2 t1 9 %ort1 ! *emi/ry ( ! future mu/ deal ) molecul> me*anics1 by ! me?ods & 9 ! /rict language ( ma!matics1 z ! a/ronomy ( ,newton & ,laplace dealt ) ! />s 9 _! c\rses4 ,we "k h[ great a /ep has be5 made t[>ds ?is di/ant & once hopeless goal1 z ,kant def9$ x1 s9ce van't ,h(f laid ! firm f\ndations ( a ma!matical *emi/ry1 & e>n$ 8 pr\d epitaph1 ,physicam *emiae adiunxit#a4 ,we ne$ n wait = ! full realisation ( ,kant's desire1 9 ord] to apply to ! natural sci5ces ! pr9ciple :i* he urg$4 ,?\gh *emi/ry fall %ort ( its ultimate goal 9 ma!matical me*anics1 nev]!less physiology is va/ly /r5g!n$ & enl>g$ by mak+ use ( ! *emi/ry1 z ( ! physics1 ( ! age4 ,little by little x draws ne>] to our conception ( a true sci5ce1 ) ea* bran* ( physical sci5ce :i* x #b br+s into relation ) itself3 ) e physical law & e ma!matical !orem :i* x le>ns to take into its employ4 ,betwe5 ! physiology ( ,hall]1 f9e z x 01 & t ( ,helmholtz1 ,ludwig1 ,claude ,b]n>d1 !re 0 all ! diff]5ce 9 ! _w4 ,z soon z we adv5ture on ! pa?s ( ! physici/1 we le>n to weigh & to measure1 to deal ) "t & space & mass & _! relat$ concepts1 & to f9d m & m our k express$ & our ne$s satisfi$ ?r\gh ! concept ( numb]1 z 9 ! dreams & visions ( ,plato & ,py?agoras2 = mod]n *emi/ry w\ld h gladd5$ ! he>ts ( ^? great philosophic dream]s4 ,b ! zoologi/ or morphologi/ has be5 sl[1 :]e ! physiologi/ has long be5 eag]1 to invoke ! aid ( ! physical or ma!matical sci5ces2 & ! reasons = ?is diff]5ce lie deep1 & 9 "p are root$ 9 old traditions4 ,! zoologi/ has sc>ce begun to dream ( def9+1 9 ma!matical language1 ev5 ! simpl] organic =ms4 ,:5 he f9ds a simple geometrical con/ruction1 = in/ance 9 ! honey-comb1 he w\ld fa9 ref] x to psy*ical in/9ct or design r ?an to ! op]ation ( physical =ces2 :5 he sees 9 snail1 or nautilus1 or t9y =am9if]al or radiol>ian %ell1 a close approa* to ! p]fect sph]e or spiral1 he is prone1 ( old habit1 to believe t x is aft] all some?+ m ?an a spiral or a sph]e1 & t 9 ?is 8some?+ m0 !re lies :at nei!r physics nor ma!matics c expla94 ,9 %ort he is deeply reluctant to comp>e ! liv+ ) ! dead1 or to expla9 by geometry or by dynamics ! ?+s :i* h _! "p 9 ! my/]y ( life4 ,moreov] he is little incl9$ to feel ! ne$ ( su* explanations or ( su* ext5sion ( 8 field ( ?\ght4 ,he is n )\t "s ju/ification if he feels t 9 admiration ( nature's h&iwork he has an horizon op5 be=e 8 eyes z wide z any man requires4 ,he has ! help ( _m fasc9at+ !ories )9 ! b\nds ( 8 own sci5ce1 :i*1 ?\gh a little lack+ 9 precision1 s]ve ! purpose ( ord]+ 8 ?\ghts & ( sugge/+ new objects ( enquiry4 ,8 art ( classification becomes a ceaseless & an endless se>* aft] ! blood-relation%ips ( ?+s liv+1 & ! p$igrees ( ?+s #c dead & gone4 ,! facts ( embryology become = him1 z ,wolff1 von ,ba] & ,fritz ,mll] proclaim$1 a record n only ( ! life-hi/ory ( ! individual b ( ! annals ( its race4 ,! facts ( geographical di/ribution or ev5 ( ! migration ( birds lead on & on to speculations reg>d+ lo/ cont95ts1 sunk5 isl&s1 or bridges across anci5t seas4 ,e ne/+ bird1 e ant-hill or spid]'s web displays its psy*ological problems ( in/9ct or intellig5ce4 ,above all1 9 ?+s bo? great & small1 ! naturali/ is rightfully impress$1 & f9ally engross$1 by ! peculi> beauty :i* is manife/$ 9 app>5t fitness or 8adaptation10--! fl[] = ! bee1 ! b]ry = ! bird4 ,"t out ( m9d1 x has be5 by way ( ! 8f9al cause10 by ! teleological concept ( 8end10 ( 8purpose10 or ( 8design10 9 "o or ano!r ( its _m =ms 7= its moods are _m71 t m5 h be5 *iefly wont to expla9 ! ph5om5a ( ! liv+ _w2 & x w be s :ile m5 h eyes to see & e>s to he> )al4 ,) ,gal51 z ) ,ari/otle1 x 0 ! physician's way2 ) ,john ,ray1 z ) ,ari/otle1 x 0 ! naturali/'s way2 ) ,kant1 z ) ,ari/otle1 x 0 ! philosoph]'s way4 ,x 0 ! old ,hebrew way1 & has its spl5did sett+ 9 ! /ory t ,god made 8e plant ( ! field be=e x 0 9 ! e>?1 & e h]b ( ! field be=e x grew40 ,x is a common way1 & a great way2 = x br+s ) x a glimpse ( a great vision1 & x lies deep z ! love ( nature 9 ! he>ts ( m54 ,half ov]%ad[+ ! 8effici5t0 or physical cause1 ! argum5t ( ! f9al cause appe>s 9 eighte5? c5tury physics1 9 ! h&s ( su* m5 z ,eul]#b & ,maup]tuis1 to :om ,leibniz#c _h pass$ x on4 ,half ov]%ad[$ by ! me*anical concept1 x runs ?r\gh ,claude ,b]n>d's ,leons sur les #d phnomnes de la ,vie#d1 & abides 9 mu* ( mod]n physiology#e4 ,inh]it$ f ,hegel1 x dom9at$ ,ok5's ,naturphilosophie & l+]$ among 8 lat] disciples1 :o 7 wont to lik5 ! c\rse ( organic evolution n to ! /raggl+ bran*es ( a tree1 b to ! build+ ( a temple1 div9ely plann$1 & ! cr[n+ ( x ) its poli%$ m9>ets#f4 ,x is reta9$1 some:at crudely1 9 mod]n embryology1 by ^? :o see 9 ! e>ly processes ( gr[? a significance 8r prospective ?an retrospective10 su* t ! embryonic ph5om5a mu/ be 8ref]r$ directly to _! usefulness 9 build+ ! body ( ! future animal#g03--:i* is no m1 & no less1 ?an to say1 ) ,ari/otle1 t ! organism is ! 1 or f9al cause1 ( its own processes ( g5]ation & developm5t4 ,x is writ l>ge 9 t ,entele*y#h :i* ,dries* r$iscov]$1 & :i* he made kn[n to _m :o _h nei!r le>n$ ( x f ,ari/otle1 nor /udi$ x ) ,leibniz1 nor laugh$ at x ) ,voltaire4 ,&1 ?\gh x is 9 a v curi\s way1 we are told t teleology 0 8ref\nd$1 re=m$ or rehabilitat$#i0 by ,d>w9's !ory ( natural selection1 :]eby 8e v>iety ( =m & col\r 0 urg5tly & absolutely call$ ^u to produce its title to exi/5ce ei!r z an active useful ag5t1 or z a survival0 ( su* active usefulness 9 ! pa/4 ,b 9 ?is la/1 & v important case1 we h rea*$ a 8teleology0 )\t a 1 #e z m5 l ,butl] & ,janet h be5 prompt to %ew3 a teleology 9 :i* ! f9al cause becomes little m1 if any?+1 ?an ! m]e expression or resultant ( a process ( sift+ out ( ! good f ! bad1 or ( ! bett] f ! worse1 9 %ort ( a process ( me*anism#aj4 ,! app>5t manife/ations ( 8purpose0 or adaptation become "p ( a me*anical philosophy1 accord+ to :i* 8*aque *ose f9it t\j\rs p> s'accommod] son milieu#aa40 ,9 %ort1 by a road :i* resembles b is n ! same z ,maup]tuis's road1 we f9d our way to ! v _w 9 :i* we are liv+1 & f9d t if x be n1 x is ev] t5d+ to become1 8! be/ ( all possible worlds#ab40 ,b ! use ( ! teleological pr9ciple is b "o way1 n ! :ole or ! only way1 by :i* we may seek to le>n h[ ?+s came to be1 & to take _! places 9 ! h>moni\s complexity ( ! _w4 ,to seek n = ends b = 8antec$5ts0 is ! way ( ! physici/1 :o f9ds 8causes0 9 :at he has le>n$ to recognise z fundam5tal prop]ties1 or insep>able concomitants1 or un*ang+ laws1 ( matt] & ( en]gy4 ,9 ,ari/otle's p>able1 ! h\se is !re t m5 may live 9 x2 b x is also !re because ! build]s h laid "o /one ^u ano!r3 & x is z a me*anism1 or a me*anical con/ruction1 t ! physici/ looks ^u ! _w4 ,l w>p & wo(1 me*anism & teleology are int]wov5 toge!r1 & we mu/ n cleave to ! "o & despise ! o!r2 = _! union is 8root$ 9 ! v nature ( totality#ac40 ,nev]!less1 :5 philosophy bids u he>k5 & obey ! lessons bo? ( me*anical & ( teleological int]pretation1 ! precept is h>d to foll[3 s t (t5times x has come to pass1 j z 9 ,bacon's day1 t a lean+ to ! side ( ! f9al cause 8ha? int]cept$ ! sev]e & dilig5t inquiry ( all #f real & physical causes10 & has br\ght x ab\t t 8! se>* ( ! physical cause ha? be5 neglect$ & pass$ 9 sil5ce40 ,s long & s f> z 8=tuit\s v>iation#ad0 & ! 8survival ( ! fitte/0 rema9 engra9$ z fundam5tal & satisfactory hypo!ses 9 ! philosophy ( biology1 s long w ^! 8satisfactory & speci\s causes0 t5d to /ay 8sev]e & dilig5t inquiry10 8to ! great arre/ & prejudice ( future discov]y40 ,! difficulties :i* surr\nd ! concept ( active or 8real0 causation1 9 ,bacon's s5se ( ! ^w1 difficulties ( :i* ,hume & ,locke & ,ari/otle 7 little aw>e1 ne$ sc>cely h9d] u 9 our physical enquiry4 ,z /ud5ts ( ma!matical & ( empirical physics1 we are cont5t to deal ) ^? antec$5ts1 or concomitants1 ( our ph5om5a1 )\t :i* ! ph5om5on does n occur1--) causes1 9 %ort1 :i*1 aliae ex aliis aptae et necessitate nexae1 are no m1 & no less1 ?an conditions s9e qu non4 ,our purpose is /ill adequately fulfill$3 inasmu* z we are /ill enabl$ to correlate1 & to equate1 our p>ticul> ph5om5a ) m & ev] m ( ! physical ph5om5a ar\nd1 & s to weave a web ( connection & int]dep5d5ce :i* %all s]ve our turn1 ?\gh ! metaphysician )hold f t int]dep5d5ce ! title ( causality4 ,we come 9 t\* ) :at ! s*oolm5 call$ a ratio cognosc5di1 ?\gh ! true ratio effici5di is /ill enwrapp$ 9 _m my/]ies4 ,& s h&l$1 ! que/ ( physical causes m]ges ) ano!r great ,ari/otelian !me1--! se>* = relations betwe5 ?+s app>5tly disconnect$1 & = 8similitude 9 ?+s to common view unlike40 ,newton did n %ew ! cause ( ! apple fall+1 b he %ew$ a similitude betwe5 ! apple & ! />s4 ,moreov]1 ! naturali/ & ! physici/ w cont9ue to speak ( 8causes10 j z ( old1 ?\gh x may be ) "s m5tal res]vations3 =1 z a ,fr5* philosoph] said1 9 a k9dr$ difficulty3 8ce sont l des manires de s'exprim]1 #g et si elles sont int]dites il faut r5onc] p>l] de ces *oses40 ,! se>* = diff]5ces or ess5tial contra/s betwe5 ! ph5om5a ( organic & inorganic1 ( animate & inanimate ?+s has occupi$ _m m5s' m9ds1 :ile ! se>* = community ( pr9ciples1 or ess5tial similitudes1 has be5 foll[$ by few2 & ! contra/s are apt to loom too l>ge1 great z !y may be4 ,m4 ,dunan1 discuss+ ! 8,problme de la ,vie#ae0 9 an essay :i* ,m4 ,b]gson greatly comm5ds1 decl>es3 8,les lois physico-*imiques sont aveugles et brutales2 l o elles rgn5t seules1 au lieu d'un ordre et d'un conc]t1 il ne peut y avoir qu'incohr5ce et *aos40 ,b ! physici/ proclaims al\d t ! physical ph5om5a :i* meet u by ! way h _! manife/ations ( =m1 n less beautiful & sc>ce less v>i$ ?an ^? :i* move u to admiration among liv+ ?+s4 ,! waves ( ! sea1 ! little ripples on ! %ore1 ! sweep+ curve ( ! s&y bay betwe5 its headl&s1 ! outl9e ( ! hills1 ! %ape ( ! cl\ds1 all ^! are s _m riddles ( =m1 s _m problems ( morphology1 & all ( !m ! physici/ c m or less easily read & adequately solve3 solv+ !m by ref]5ce to _! antec$5t ph5om5a1 9 ! mat]ial sy/em ( me*anical =ces to :i* !y belong1 & to :i* we int]pret !m z be+ due4 ,!y h also1 d\btless1 _! imman5t teleological significance2 b x is on ano!r plane ( ?\ght f ! physici/'s t we contemplate _! intr9sic h>mony & p]fection1 & 8see t !y are good40 ,nor is x o!rwise ) ! mat]ial =ms ( liv+ ?+s4 ,cell & tissue1 %ell & bone1 leaf & fl[]1 are s _m portions ( matt]1 & x is 9 ob$i5ce to ! laws ( physics t _! p>ticles h be5 mov$1 m\ld$ & con=m$#af4 #h ,!y are no exception to ! rule t 4 ,_! problems ( =m are 9 ! fir/ in/ance ma!matical problems1 & _! problems ( gr[? are ess5tially physical problems2 & ! morphologi/ is1 ipso facto1 a /ud5t ( physical sci5ce4 ,ap>t f ! physico-*emical problems ( mod]n physiology1 ! road ( physico-ma!matical or dynamical inve/igation 9 morphology has _h few to foll[ x2 b ! pa?way is old4 ,! way ( ! old ,ionian physicians1 ( ,anaxagoras#ag1 ( ,emp$ocles & 8 disciples 9 ! days be=e ,ari/otle1 lay j by t highwayside4 ,x 0 ,galileo's & ,borelli's way4 ,x 0 little trodd5 = long aft]w>ds1 b once 9 a :ile ,swamm]dam & ,raumur look$ t way4 ,& ( lat] ye>s1 ,moseley & ,mey]1 ,b]?old1 ,err]a & ,r\x h be5 among ! little b& ( travell]s4 ,we ne$ n wond] if ! way be h>d to foll[1 & if ^! wayf>]s h yet ga!r$ little4 ,a h>ve/ has be5 reap$ by o!rs1 & ! glean+ ( ! grapes is sl[4 ,x behoves u always to rememb] t 9 physics x has tak5 great m5 to discov] simple ?+s4 ,!y are v great names inde$ t we c\ple ) ! explanation ( ! pa? ( a /one1 ! droop ( a *a91 ! t9ts ( a bubble1 ! %ad[s 9 a cup4 ,x is b ! slighte/ adumbration ( a dynamical morphology t we c hope to h1 until ! physici/ & ! ma!matician %all h made ^! problems ( ours _! own1 or till a new ,boscovi* %all h writt5 = ! naturali/ ! new ,!oria ,philosophiae ,naturalis4 ,h[ f>1 ev5 !n1 ma!matics w suffice to describe1 & physics to expla91 ! fabric ( ! body no man c =esee4 ,x may be t all ! laws ( en]gy1 & all ! prop]ties ( matt]1 & all ! *emi/ry ( all ! colloids are z p[]less to expla9 ! body z !y are impot5t to compreh5d ! s\l4 ,= my "p1 ,i ?9k x is n s4 ,( h[ x is t ! s\l in=ms ! body1 physical sci5ce tea*es me no?+3 consci\sness is n expla9$ to my compreh5sion by all ! n]ve-pa?s & 8neurones0 ( ! physiologi/2 nor d ,i ask ( physics h[ goodness %9es 9 "o man's face1 & evil betrays itself 9 ano!r4 ,b ( ! con/ruction & gr[? & work+ #i ( ! body1 z ( all t is ( ! e>? e>?y1 physical sci5ce is1 9 my humble op9ion1 our only tea*] & guide#ah4 ,(t5 & (t5 x happ5s t our physical k is inadequate to expla9 ! me*anical work+ ( ! organism2 ! ph5om5a are sup]latively complex1 ! proc$ure is involv$ & entangl$1 & ! inve/igation has occupi$ b a few %ort lives ( m54 ,:5 physical sci5ce falls %ort ( expla9+ ! ord] :i* reigns ?r\gh\t ^! manifold ph5om5a1--an ord] m *>act]i/ic 9 its totality ?an any ( its ph5om5a 9 !mselves1--m5 ha/5 to invoke a guid+ pr9ciple1 an entele*y1 or call x :at y w4 ,b all ! :ile1 s f> z ,i am aw>e1 no physical law1 any m ?an t ( gravity itself1 n ev5 among ! puzzles ( *emical 8/]eometry10 or ( physiological 8surface-action0 or 8osmosis10 is kn[n to be transgress$ by ! bodily me*anism4 ,"s physici/s decl>e1 z ,maxwell did1 t atoms or molecules m complicat$ by f> ?an ! *emi/'s hypo!ses dem& are requisite to expla9 ! ph5om5a ( life4 ,if :at is impli$ be an explanation ( psy*ical ph5om5a1 let ! po9t be grant$ at once2 we may g yet fur!r1 & decl9e1 ) ,maxwell1 to believe t any?+ ( ! nature ( physical complexity1 h[ev] exalt$1 c\ld ev] suffice4 ,o!r physici/s1 l ,au]ba*#ai1 or ,l>mor#bj1 or ,joly#ba1 assure u t our laws ( !rmodynamics d n suffice1 or are 8inappropriate10 to expla9 ! ma9t5ance or 79 ,joly's phrase7 ! 8accel]ative absorption0 #aj ( ! bodily en]gies1 & ! long battle aga9/ ! cold & d>kness :i* is dea?4 ,) ^! weighty problems ,i am n = ! mom5t conc]n$4 ,my sole purpose is to correlate ) ma!matical /atem5t & physical law c]ta9 ( ! simpl] outw>d ph5om5a ( organic gr[? & /ructure or =m3 :ile all ! :ile reg>d+1 ex hypo!si1 = ! purposes ( ?is correlation1 ! fabric ( ! organism z a mat]ial & me*anical configuration4 ,physical sci5ce & philosophy /& side by side1 & "o upholds ! o!r4 ,)\t some?+ ( ! /r5g? ( physics1 philosophy w\ld be weak2 & )\t some?+ ( philosophy's weal?1 physical sci5ce w\ld be poor4 8,ri5 ne retir]a du tissu de la sci5ce les fils d'or que la ma9 du philosophe y a introduits#bb40 ,b !re are fields :]e ea*1 = a :ile at lea/1 mu/ "w alone2 & :]e physical sci5ce rea*es its limitations1 physical sci5ce itself mu/ help u to discov]4 ,mean:ile ! appropriate & legitimate po/ulate ( ! physici/1 9 approa*+ ! physical problems ( ! body1 is t ) ^! physical ph5om5a no ali5 influ5ce int]f]es4 ,b ! po/ulate1 ?\gh x is c]ta9ly legitimate1 & ?\gh x is ! prop] & necess>y prelude to sci5tific enquiry1 may "s day be prov5 to be untrue2 & its dispro( w n be to ! physici/'s confusion1 b w come z 8 rew>d4 ,9 deal+ ) =ms :i* are s concomitant ) life t !y are seem+ly controll$ by life1 x is 9 no _s ( arrogant ass]tiv5ess t ! physici/ beg9s 8 argum5t1 aft] ! fa%ion ( a mo/ illu/ri\s exempl>1 ) ! old =mul>y ( s*ola/ic *all5ge1--,an ,vita sit8 ,dico quod non4 ,! t]ms ,=m & ,gr[?1 :i* make up ! title ( ?is little book1 are to be und]/ood1 z ,i ne$ h>dly say1 9 _! relation to ! sci5ce ( organisms4 ,we want to see h[1 9 "s cases at lea/1 ! =ms ( liv+ ?+s1 & ( ! p>ts ( liv+ ?+s1 c be expla9$ by physical consid]ations1 & to realise t1 9 g5]al1 no organic =ms exi/ save su* z are 9 con=mity ) ord9>y physical laws4 ,& :ile gr[? is a some:at vague ^w = a complex matt]1 :i* may #aa dep5d on v>i\s ?+s1 f simple imbibition ( wat] to ! complicat$ results ( ! *emi/ry ( nutrition1 x des]ves to be /udi$ 9 relation to =m1 :e!r x proce$ by simple increase ( size )\t obvi\s alt]ation ( =m1 or :e!r x s proce$ z to br+ ab\t a gradual *ange ( =m & ! sl[ developm5t ( a m or less complicat$ /ructure4 ,9 ! ,newtonian language ( elem5t>y physics1 =ce is recognis$ by its action 9 produc+ or 9 *ang+ motion1 or 9 prev5t+ *ange ( motion or 9 ma9ta9+ re/4 ,:5 we deal ) matt] 9 ! concrete1 =ce does n1 /rictly speak+1 ent] into ! "q1 = =ce1 unlike matt]1 has no indep5d5t objective exi/5ce4 ,x is en]gy 9 its v>i\s =ms1 kn[n or unkn[n1 t acts ^u matt]4 ,b :5 we ab/ract our ?\ghts f ! mat]ial to its =m1 or f ! ?+ mov$ to its motions1 :5 we deal ) ! subjective conceptions ( =m1 or movem5t1 or ! movem5ts t *ange ( =m implies1 !n =ce is ! appropriate t]m = our conception ( ! causes by :i* ^! =ms & *anges ( =m are br\ght ab\t4 ,:5 we use ! t]m =ce1 we use x1 z ! physici/ always does1 = ! sake ( brevity1 us+ a symbol = ! magnitude & direction ( an action 9 ref]5ce to ! symbol or diagram ( a mat]ial ?+4 ,x is a t]m z subjective & symbolic z =m itself1 & s is appropriately to be us$ 9 connection !re)4 ,! =m1 !n1 ( any portion ( matt]1 :e!r x be liv+ or dead1 & ! *anges ( =m t are app>5t 9 its movem5ts & 9 its gr[?1 may 9 all cases alike be describ$ z due to ! action ( =ce4 ,9 %ort1 ! =m ( an object is a 8diagram ( =ces10 9 ?is s5se1 at lea/1 t f x we c judge ( or d$uce ! =ces t are act+ or h act$ ^u x3 9 ?is /rict & p>ticul> s5se1 x is a diagram1--9 ! case ( a solid1 ( ! =ces t h be5 impress$ ^u x :5 its con=mation 0 produc$1 toge!r ) ^? t enable x to reta9 its con=mation2 9 ! case ( a liquid 7or ( a gas7 ( ! =ces t are = ! mom5t act+ on x to re/ra9 or balance its own inh]5t mobility4 ,9 an organism1 great or small1 x is n m]ely ! nature ( ! motions ( ! liv+ sub/ance t we mu/ int]pret 9 t]ms ( =ce 7accord+ to k9etics71 b also #ab ! con=mation ( ! organism itself1 ^: p]man5ce or equilibrium is expla9$ by ! int]action or balance ( =ces1 z describ$ 9 /atics4 ,if we look at ! liv+ cell ( an ,amoeba or a ,spirogyra1 we see a some?+ :i* exhibits c]ta9 active movem5ts1 & a c]ta9 fluctuat+1 or m or less la/+1 =m2 & its =m at a giv5 mom5t1 j l its motions1 is to be inve/igat$ by ! help ( physical me?ods1 & expla9$ by ! invocation ( ! ma!matical conception ( =ce4 ,n[ ! /ate1 includ+ ! %ape or =m1 ( a portion ( matt]1 is ! resultant ( a numb] ( =ces1 :i* repres5t or symbolise ! manife/ations ( v>i\s k9ds ( en]gy2 & x is obvi\s1 accord+ly1 t a great "p ( physical sci5ce mu/ be und]/ood or tak5 = grant$ z ! necess>y prelim9>y to ! discussion on :i* we are engag$4 ,b we may at lea/ try to indicate1 v briefly1 ! nature ( ! pr9cipal =ces & ! pr9cipal prop]ties ( matt] ) :i* our subject obliges u to deal4 ,let u imag9e1 = in/ance1 ! case ( a s-call$ 8simple0 organism1 su* z ,amoeba2 & if our %ort li/ ( its physical prop]ties & conditions be helpful to our fur!r discussion1 we ne$ n consid] h[ f> x be complete or adequate f ! wid] physical po9t ( view#bc4 ,?is portion ( matt]1 !n1 is kept toge!r by ! int]molecul> =ce ( cohesion2 9 ! movem5ts ( its p>ticles relatively to "o ano!r1 & 9 its own movem5ts relative to adjac5t matt]1 x meets ) ! oppos+ =ce ( friction4 ,x is act$ on by gravity1 & ?is =ce t5ds 7?\gh slightly1 ow+ to ! ,amoeba's small mass1 & to ! small diff]5ce betwe5 its d5sity & t ( ! surr\nd+ fluid71 to flatt5 x d[n ^u ! solid sub/ance on :i* x may be creep+4 ,our ,amoeba t5ds1 9 ! next place1 to be de=m$ by any pressure f outside1 ev5 ?\gh slight1 :i* may be appli$ to x1 & ?is circum/ance %ews x to consi/ ( matt] 9 a fluid1 or at lea/ semi-fluid1 /ate3 :i* /ate is fur!r indicat$ :5 we obs]ve /ream+ or curr5t motions 9 its int]ior4 #ac ,l o!r fluid bodies1 its surface1 :atsoev] o!r sub/ance1 gas1 liquid or solid1 x be 9 contact )1 & 9 v>y+ degree accord+ to ! nature ( t adjac5t sub/ance1 is ! seat ( molecul> =ce exhibit+ itself z a surface-t5sion1 f ! action ( :i* _m important consequ5ces foll[1 :i* greatly affect ! =m ( ! fluid surface4 ,:ile ! protoplasm ( ! ,amoeba reacts to ! slighte/ pressure1 & t5ds to 8fl[10 & :ile we !re=e speak ( x z a fluid1 x is evid5tly f> less mobile ?an su* a fluid1 = in/ance1 z wat]1 b is r l treacle 9 its sl[ creep+ movem5ts z x *anges its %ape 9 response to =ce4 ,su* fluids are said to h a high viscosity1 & ?is viscosity obvi\sly acts 9 ! way ( ret>d+ *ange ( =m1 or 9 o!r words ( ret>d+ ! effects ( any di/urb+ action ( =ce4 ,:5 ! visc\s fluid is capable ( be+ drawn out into f9e ?reads1 a prop]ty 9 :i* we "k t ! mat]ial ( "s ,amoebae diff]s greatly f t ( o!rs1 we say t ! fluid is also viscid1 or exhibits viscidity4 ,aga91 n by virtue ( our ,amoeba be+ liquid1 b at ! same "t 9 va/ly great] measure ?an if x 7 a solid 7?\gh f> less rapidly ?an if x 7 a gas71 a process ( molecul> diffusion is con/antly go+ on )9 its sub/ance1 by :i* its p>ticles int]*ange _! places )9 ! mass1 :ile surr\nd+ fluids1 gases & solids 9 solution diffuse into & out ( x4 ,9 s f> z ! out] wall ( ! cell is diff]5t 9 "* f ! int]ior1 :e!r x be a m]e pellicle z 9 ,amoeba or a firm cell-wall z 9 ,protococcus1 ! diffusion :i* takes place ?r\gh ?is wall is sometimes di/+ui%$ "u ! t]m osmosis4 ,)9 ! cell1 *emical =ces are at "w1 & s also 9 all probability 7to judge by analogy7 are electrical =ces2 & ! organism reacts also to =ces f )\t1 t h _! orig9 9 *emical1 electrical & !rmal influ5ces4 ,! processes ( diffusion & ( *emical activity )9 ! cell result1 by ! draw+ 9 ( wat]1 salts1 & food-mat]ial ) or )\t *emical trans=mation into protoplasm1 9 gr[?1 & ?is complex ph5om5on we %all usually1 )\t discuss+ its nature & orig91 describe & picture z a =ce4 ,inde$ we %all manife/ly be incl9$ to use ! t]m gr[? 9 two s5ses1 #ad j inde$ z we d 9 ! case ( attraction or gravitation1 on ! "o h& z a process1 & on ! o!r h& z a =ce4 ,9 ! ph5om5a ( cell-division1 9 ! attractions or repulsions ( ! p>ts ( ! divid+ nucleus & 9 ! 8c>yok9etic0 figures t appe> 9 connection ) x1 we seem to see 9 op]ation =ces & ! effects ( =ces1 t h1 to say ! lea/ ( x1 a close analogy ) kn[n physical ph5om5a2 & to ?is matt] we %all aft]w>ds recur4 ,b ?\gh !y resemble kn[n physical ph5om5a1 _! nature is /ill ! subject ( mu* discussion1 & nei!r ! =ms produc$ nor ! =ces at "w c yet be satisfactorily & simply expla9$4 ,we may readily admit1 !n1 t besides ph5om5a :i* are obvi\sly physical 9 _! nature1 !re are actions visible z well z invisible tak+ place )9 liv+ cells :i* our k does n p]mit u to ascribe ) c]ta9ty to any kn[n physical =ce2 & x may or may n be t ^! ph5om5a w yield 9 "t to ! me?ods ( physical inve/igation4 ,:e!r or no1 x is pla9 t we h no cle> rule or guide z to :at is 8vital0 & :at is n2 ! :ole assemblage ( s-call$ vital ph5om5a1 or prop]ties ( ! organism1 _c be cle>ly classifi$ into ^? t are physical 9 orig9 & ^? t are sui g5]is & peculi> to liv+ ?+s4 ,all we c d mean:ile is to analyse1 bit by bit1 ^? p>ts ( ! :ole to :i* ! ord9>y laws ( ! physical =ces m or less obvi\sly & cle>ly & indubitably apply4 ,morphology !n is n only a /udy ( mat]ial ?+s & ( ! =ms ( mat]ial ?+s1 b has its dynamical aspect1 "u :i* we deal ) ! int]pretation1 9 t]ms ( =ce1 ( ! op]ations ( ,en]gy4 ,& "h x is well wor? :ile to rem>k t1 9 deal+ ) ! facts ( embryology or ! ph5om5a ( inh]itance1 ! common language ( ! books seems to deal too mu* ) ! mat]ial elem5ts conc]n$1 z ! causes ( developm5t1 ( v>iation or ( h]$it>y transmission4 ,matt] z su* produces no?+1 *anges no?+1 does no?+2 & h[ev] conv5i5t x may aft]w>ds be to abbreviate our nom5clature & our descriptions1 we mu/ mo/ c>efully realise 9 ! outset t ! sp]matozoon1 ! nucleus1 #ae ! *romosomes or ! g]m-plasm c nev] act z matt] alone1 b only z seats ( en]gy & z c5tres ( =ce4 ,& ?is is b an adaptation 79 ! light1 or r 9 ! conv5tional symbolism1 ( mod]n physical sci5ce7 ( ! old say+ ( ! philosoph]3 4 #af ,,*apt] ,,ii ,,on ,,magnitude ,to t]ms ( magnitude1 & ( direction1 mu/ we ref] all our conceptions ( =m4 ,= ! =m ( an object is def9$ :5 we "k its magnitude1 actual or relative1 9 v>i\s directions2 & gr[? involves ! same conceptions ( magnitude & direction1 ) ?is addition1 t !y are suppos$ to alt] 9 "t4 ,be=e we proce$ to ! consid]ation ( specific =m1 x w be wor? our :ile to consid]1 = a little :ile1 c]ta9 ph5om5a ( spatial magnitude1 or ( ! ext5sion ( a body 9 ! sev]al dim5sions ( space#bd4 ,we are taught by elem5t>y ma!matics t1 9 simil> solid figures1 ! surface increases z ! squ>e1 & ! volume z ! cube1 ( ! l9e> dim5sions4 ,if we take ! simple case ( a sph]e1 ) radius r1 ! area ( its surface is equal to #dr#b1 & its volume to 7#d_/c7r#c2 f :i* x foll[s t ! ratio ( volume to surface1 or ,v_/,s1 is 7#a_/c7r4 ,9 o!r words1 ! great] ! radius 7or ! l>g] ! sph]e7 ! great] w be its volume1 or its mass 7if x be uni=mly d5se ?r\gh\t71 9 comp>ison ) its sup]ficial area4 ,&1 tak+ ,l to repres5t any l9e> dim5sion1 we may write ! g5]al equations 9 ! =m ,s ,l#b1 ,v ,l#c1 or ,s k ,l#b1 & ,v k ,l#c2 & ,v_/,s ,l4 ,f ^! elem5t>y pr9ciples a great numb] ( consequ5ces foll[1 all m or less int]e/+1 & "s ( !m ( great importance4 ,9 ! fir/ place1 ?\gh gr[? 9 l5g? 7let #ag u say7 & gr[? 9 volume 7:i* is usually tantam\nt to mass or weight7 are p>ts ( "o & ! same process or ph5om5on1 ! "o attracts our att5tion by its increase1 v mu* m ?an ! o!r4 ,= in/ance a fi%1 9 d\bl+ its l5g?1 multiplies its weight by no less ?an eight times2 & x all b d\bles its weight 9 gr[+ f f\r in*es long to five4 ,9 ! second place we see t a k ( ! correlation betwe5 l5g? & weight 9 any p>ticul> species ( animal1 9 o!r words a det]m9ation ( k 9 ! =mula ,w k ,l#c1 enables u at any "t to translate ! "o magnitude into ! o!r1 & 7s to speak7 to weigh ! animal ) a measur+-rod2 ?is h[ev] be+ always subject to ! condition t ! animal %all 9 no way h alt]$ its =m1 nor its specific gravity4 ,t its specific gravity or d5sity %\ld mat]ially or rapidly alt] is n v likely2 b z long z gr[? la/s1 *anges ( =m1 ev5 ?\gh inappreciable to ! eye1 are likely to g on4 ,n[ weigh+ is a f> easi] & f> m accurate op]ation ?an measur+2 & ! measurem5ts :i* w\ld reveal slight & o!rwise imp]ceptible *anges 9 ! =m ( a fi%--slight relative diff]5ces betwe5 l5g?1 bread? & dep?1 = in/ance1--w\ld ne$ to be v delicate inde$4 ,b if we c make fairly accurate det]m9ations ( ! l5g?1 :i* is v mu* ! easie/ dim5sion to measure1 & !n correlate x ) ! weight1 !n ! value ( k1 accord+ to :e!r x v>ies or rema9s con/ant1 w tell u at once :e!r !re has or has n be5 a t5d5cy to gradual alt]ation 9 ! g5]al =m4 ,to ?is subject we %all return1 :5 we come to consid] m p>ticul>ly ! rate ( gr[?4 ,b a mu* deep] int]e/ arises out ( ?is *ang+ ratio ( dim5sions :5 we come to consid] ! inevitable *anges ( physical relations ) :i* x is b\nd up4 ,we are apt1 & ev5 accu/om$1 to ?9k t magnitude is s purely relative t diff]5ces ( magnitude make no o!r or m ess5tial diff]5ce2 t ,lilliput & ,brobd+nag are all alike1 accord+ z we look at !m ?r\gh "o end ( ! glass or ! o!r4 ,b ?is is by no means s2 = scale has a v m>k$ effect ^u physical ph5om5a1 & ! effect ( scale con/itutes :at is kn[n z ! pr9ciple ( similitude1 or ( dynamical simil>ity4 #ah ,?is effect ( scale is simply due to ! fact t1 ( ! physical =ces1 "s act ei!r directly at ! surface ( a body1 or o!rwise 9 proportion to ! area ( surface2 & o!rs1 su* z gravity1 act on all p>ticles1 int]nal & ext]nal alike1 & ex]t a =ce :i* is proportional to ! mass1 & s usually to ! volume1 ( ! body4 ,! /r5g? ( an iron gird] obvi\sly v>ies ) ! cross-section ( its memb]s1 & ea* cross-section v>ies z ! squ>e ( a l9e> dim5sion2 b ! weight ( ! :ole /ructure v>ies z ! cube ( its l9e> dim5sions4 ,& x foll[s at once t1 if we build two bridges geometrically simil>1 ! l>g] is ! weak] ( ! two#be4 ,x 0 elem5t>y eng9e]+ exp]i5ce su* z ?is t l$ ,h]b]t ,sp5c]#bf to apply ! pr9ciple ( similitude to biology4 ,! same pr9ciple _h be5 admirably appli$1 9 a few cle> in/ances1 by ,lesage#bg1 a celebrat$ eighte5? c5tury physician ( ,g5eva1 9 an unf9i%$ & unpubli%$ "w#bh4 ,lesage argu$1 = in/ance1 t ! l>g] ratio ( surface to mass w\ld lead 9 a small animal to excessive transpiration1 7 ! sk9 z 8por\s0 z our own2 & t we may h5ce acc\nt = ! h>d5$ or ?ick5$ sk9s ( insects & o!r small t]re/rial animals4 ,aga91 s9ce ! weight ( a fruit increases z ! cube ( its dim5sions1 :ile ! /r5g? ( ! /alk increases z ! squ>e1 x foll[s t ! /alk %\ld gr[ out ( app>5t due proportion to ! fruit2 or alt]natively1 t tall trees %\ld n be> l>ge fruit on sl5d] bran*es1 & t melons & pumpk9s mu/ lie ^u ! gr\nd4 ,& aga91 t 9 quadrup$s a l>ge head mu/ be support$ on a neck :i* is ei!r #ai excessively ?ick & /rong1 l a bull's1 or v %ort l ! neck ( an elephant4 ,b x 0 ,galileo :o1 wellnigh #cjj ye>s ago1 _h fir/ laid d[n ?is g5]al pr9ciple :i* we n[ "k by ! "n ( ! pr9ciple ( similitude2 & he did s ) ! utmo/ possible cle>ness1 & ) a great weal? ( illu/ration1 drawn f /ructures liv+ & dead#bi4 ,he %[$ t nei!r c man build a h\se nor c nature con/ruct an animal beyond a c]ta9 size1 :ile reta9+ ! same proportions & employ+ ! same mat]ials z suffic$ 9 ! case ( a small] /ructure#cj4 ,! ?+ w fall to pieces ( its own weight unless we ei!r *ange its relative proportions1 :i* w at l5g? cause x to become clumsy1 mon/r\s & ineffici5t1 or else we mu/ f9d a new mat]ial1 h>d] & /rong] ?an 0 us$ be=e4 ,bo? processes are famili> to u 9 nature & 9 art1 & practical applications1 undream$ ( by ,galileo1 meet u at e turn 9 ?is mod]n age ( /eel4 ,aga91 z ,galileo 0 also c>eful to expla91 besides ! que/ions ( pure /ress & /ra91 ( ! /r5g? ( muscles to lift an increas+ weight or ( bones to resi/ its cru%+ /ress1 we h ! v important "q ( b5d+ mom5ts4 ,?is "q ent]s1 m or less1 into our :ole range ( problems2 x affects1 z we %all aft]w>ds see1 or ev5 det]m9es ! :ole =m ( ! skeleton1 & is v important 9 su* a case z t ( a tall tree#ca4 ,"h we h to det]m9e ! po9t at :i* ! tree w curve "u its own weight1 if x be ev] s little displac$ f ! p]p5dicul>#cb4 ,9 su* an inve/igation we h to make #bj "s assumptions1--= in/ance1 ) reg>d to ! trunk1 t x tap]s uni=mly1 & ) reg>d to ! bran*es t _! sectional area v>ies accord+ to "s def9ite law1 or 7z ,rusk9 assum$#cc7 t5ds to be con/ant 9 any horizontal plane2 & ! ma!matical treatm5t is apt to be some:at difficult4 ,b ,gre5hill has %ewn t 7on su* assumptions z ! above71 a c]ta9 ,briti% ,columbian p9e-tree1 :i* yield$ ! ,kew flag/aff measur+ #bba ft4 9 height ) a diamet] at ! base ( #ba in*es1 c\ld n possibly1 by !ory1 h gr[n to m ?an ab\t #cjj ft4 ,x is v curi\s t ,galileo sugge/$ precisely ! same height 7dug5to braccia alta7 z ! utmo/ limit ( ! gr[? ( a tree4 ,9 g5]al1 z ,gre5hill %ews1 ! diamet] ( a homog5e\s body mu/ increase z ! p[] #c_/b ( ! height1 :i* acc\nts = ! sl5d] proportions ( "y trees1 comp>$ ) ! /unt$ appe>ance ( old & l>ge ones#cd4 ,9 %ort1 z ,goe! says 9 ,wahrheit und ,di*tung1 8,es i/ dafr gesorgt dass die ,bume ni*t 9 d5 ,himmel wa*s540 ,b ,eiffel's great tree ( /eel 7#ajjj feet high7 is built to a v diff]5t plan2 = "h ! pr(ile ( ! t[] foll[s ! log>i?mic curve1 giv+ equal /r5g? ?r\gh\t1 accord+ to a pr9ciple :i* we %all h occasion to discuss :5 we come to treat ( 8=m & me*anical effici5cy0 9 connection ) ! skeletons ( animals4 ,among animals1 we may see 9 a g5]al way1 )\t ! help ( ma!matics or ( physics1 t exagg]at$ bulk br+s ) x a c]ta9 clums9ess1 a c]ta9 ineffici5cy1 a new elem5t ( risk & haz>d1 a vague prepond]ance ( disadvantage4 ,! case 0 well put by ,ow51 9 a passage :i* has an int]e/ ( its own z a premonition 7some:at l ,de ,c&olle's7 ( ! 8/ruggle = exi/5ce40 ,ow5 wrote z foll[s#ce3 8,9 proportion to ! bulk ( a species is ! difficulty ( ! conte/ :i*1 z a liv+ organis$ :ole1 ! individual ( su* species #ba has to ma9ta9 aga9/ ! surr\nd+ ag5cies t are ev] t5d+ to dissolve ! vital bond1 & subjugate ! liv+ matt] to ! ord9>y *emical & physical =ces4 ,any *anges1 !re=e1 9 su* ext]nal conditions z a species may h be5 orig9ally adapt$ to exi/ 91 w militate aga9/ t exi/5ce 9 a degree proportionate1 p]haps 9 a geometrical ratio1 to ! bulk ( ! species4 ,if a dry season be greatly prolong$1 ! l>ge mammal w suff] f ! dr\ght soon] ?an ! small "o2 if any alt]ation ( climate affect ! quantity ( vegetable food1 ! bulky ,h]bivore w fir/ feel ! effects ( /9t$ n\ri%m5t40 ,b ! pr9ciple ( ,galileo c>ries u mu* fur!r & along m c]ta9 l9es4 ,! t5sile /r5g? ( a muscle1 l t ( a rope or ( our gird]1 v>ies ) its cross-section2 & ! resi/ance ( a bone to a cru%+ /ress v>ies1 aga9 l our gird]1 ) its cross-section4 ,b 9 a t]re/rial animal ! weight :i* t5ds to cru% its limbs or :i* its muscles h to move1 v>ies z ! cube ( its l9e> dim5sions2 & s1 to ! possible magnitude ( an animal1 liv+ "u ! direct action ( gravity1 !re is a def9ite limit set4 ,! elephant1 9 ! dim5sions ( its limb-bones1 is already %ew+ signs ( a t5d5cy to disproportionate ?ickness z comp>$ ) ! small] mammals2 its movem5ts are 9 _m ways hamp]$ & its agility dim9i%$3 x is already t5d+ t[>ds ! maximal limit ( size :i* ! physical =ces p]mit4 ,b1 z ,galileo also saw1 if ! animal be :olly imm]s$ 9 wat]1 l ! :ale1 7or if x be p>tly s1 z 0 9 all probability ! case ) ! giant reptiles ( our second>y rocks71 !n ! weight is c\nt]pois$ to ! ext5t ( an equival5t volume ( wat]1 & is completely c\nt]pois$ if ! d5sity ( ! animal's body1 ) ! includ$ air1 be id5tical 7z 9 a :ale x v ne>ly is7 ) ! wat] ar\nd4 ,"u ^! circum/ances !re is no long] a physical b>ri] to ! indef9ite gr[? 9 magnitude ( ! animal#cf4 ,inde$1 #bb 9 ! case ( ! aquatic animal !re is1 z ,sp5c] po9t$ out1 a di/9ct advantage1 9 t ! l>g] x gr[s ! great] is its velocity4 ,= its available en]gy dep5ds on ! mass ( its muscles2 :ile its motion ?r\gh ! wat] is oppos$1 n by gravity1 b by 8sk9-friction10 :i* increases only z ! squ>e ( its dim5sions2 all o!r ?+s be+ equal1 ! bigg] ! %ip1 or ! bigg] ! fi%1 ! fa/] x t5ds to g1 b only 9 ! ratio ( ! squ>e root ( ! increas+ l5g?4 ,= ! me*anical "w 7,w7 ( :i* ! fi% is capable be+ proportional to ! mass ( its muscles1 or ! cube ( its l9e> dim5sions3 & aga9 ?is "w be+ :olly done 9 produc+ a velocity 7,v7 aga9/ a resi/ance 7,r7 :i* increases z ! squ>e ( ! said l9e> dim5sions2 we h at once ,w l#c1 & also ,w ,r ,v#b l#b ,v#b4 ,!re=e l#c l#b ,v#b1 & ,v l4 ,?is is :at is kn[n z ,fr\de's ,law ( ! correspond5ce ( spe$s4 ,b !re is (t5 ano!r side to ^! que/ions1 :i* makes !m too complicat$ to answ] 9 a ^w4 ,= in/ance1 ! "w 7p] /roke7 ( :i* two simil> eng9es are capable %\ld obvi\sly v>y z ! cubes ( _! l9e> dim5sions1 = x v>ies on ! "o h& ) ! surface ( ! pi/on1 & on ! o!r1 ) ! l5g? ( ! /roke2 s is x likewise 9 ! animal1 :]e ! correspond+ v>iation dep5ds on ! cross-section ( ! muscle1 & on ! space ?r\gh :i* x contracts4 ,b 9 two precisely simil> eng9es1 ! actual available horse-p[] v>ies z ! squ>e ( ! l9e> dim5sions1 & n z ! cube2 & ?is = ! obvi\s reason t ! actual en]gy develop$ dep5ds ^u ! heat+-surface ( ! boil]#cg4 ,s likewise mu/ !re be a simil> t5d5cy1 among animals1 = ! rate ( supply ( k9etic en]gy to v>y ) ! surface ( ! #bc lung1 t is to say 7o!r ?+s be+ equal7 ) ! squ>e ( ! l9e> dim5sions ( ! animal4 ,we may ( c\rse 7dep>t+ f ! condition ( simil>ity7 increase ! heat+-surface ( ! boil]1 by means ( an int]nal sy/em ( tubes1 )\t increas+ its outw>d dim5sions1 & 9 ?is v way nature increases ! respiratory surface ( a lung by a complex sy/em ( bran*+ tubes & m9ute air-cells2 b nev]!less 9 two simil> & closely relat$ animals1 z also 9 two /eam-eng9es ( precisely ! same make1 ! law is b\nd to hold t ! rate ( work+ mu/ t5d to v>y ) ! squ>e ( ! l9e> dim5sions1 accord+ to ,fr\de's law ( /eam%ip comp>ison4 ,9 ! case ( a v l>ge %ip1 built = spe$1 ! difficulty is got ov] by increas+ ! size & numb] ( ! boil]s1 till ! ratio betwe5 boil]-room & eng9e-room is f> beyond :at is requir$ 9 an ord9>y small vessel#ch2 b ?\gh we f9d lung-space increas$ among animals :]e great] rate ( work+ is requir$1 z 9 g5]al among birds1 ,i d n "k t x c be %ewn to increase1 z 9 ! 8ov]-boil]$0 %ip1 ) ! size ( ! animal1 & 9 a ratio :i* out/rips t ( ! o!r bodily dim5sions4 ,if x be ! case !n1 t ! work+ me*anism ( ! muscles %\ld be able to ex]t a =ce proportionate to ! cube ( ! l9e> bodily dim5sions1 :ile ! respiratory me*anism c only supply a /ore ( en]gy at a rate proportional to ! squ>e ( ! said dim5sions1 ! s+ul> result ought to foll[ t1 9 swimm+ = in/ance1 ! l>g] fi% ought to be able to put on a spurt ( spe$ f> 9 excess ( ! small] "o2 b ! di/ance travell$ by ! ye>'s end %\ld be v mu* alike = bo? ( !m4 ,& x %\ld also foll[ t ! curve ( fatigue #bd %\ld be a /eep] "o1 & ! /ay+ p[] %\ld be less1 9 ! small] ?an 9 ! l>g] individual4 ,?is is ! case ( long-di/ance rac+1 :]e ! big w9n] puts on 8 big spurt at ! end4 ,& = an analog\s reason1 wise m5 "k t 9 ! ',v>sity boat-race x is judici\s & prud5t to bet on ! heavi] crew4 ,leav+ aside ! "q ( ! supply ( en]gy1 & keep+ to t ( ! me*anical effici5cy ( ! ma*9e1 we may f9d endless biological illu/rations ( ! pr9ciple ( similitude4 ,9 ! case ( ! fly+ bird 7ap>t f ! initial difficulty ( rais+ itself into ! air1 :i* involves ano!r problem7 x may be %ewn t ! bigg] x gets 7all its proportions rema9+ ! same7 ! m difficult x is = x to ma9ta9 itself al(t 9 flight4 ,! argum5t is z foll[s3 ,9 ord] to keep al(t1 ! bird mu/ communicate to ! air a d[nw>d mom5tum equival5t to its own weight1 & !re=e proportional to ! cube ( its own l9e> dim5sions4 ,b ! mom5tum s communicat$ is proportional to ! mass ( air driv5 d[nw>ds1 & to ! rate at :i* x is driv53 ! mass be+ proportional to ! bird's w+-area1 & also 7) any giv5 slope ( w+7 to ! spe$ ( ! bird1 & ! rate be+ aga9 proportional to ! bird's spe$2 accord+ly ! :ole mom5tum v>ies z ! w+-area1 i4e4 z ! squ>e ( ! l9e> dim5sions1 & also z ! squ>e ( ! spe$4 ,!re=e1 9 ord] t ! bird may ma9ta9 level flight1 its spe$ mu/ be proportional to ! squ>e root ( its l9e> dim5sions4 ,n[ ! rate at :i* ! bird1 9 /eady flight1 has to "w 9 ord] to drive itself =w>d1 is ! rate at :i* x communicates en]gy to ! air2 & ?is is proportional to m ,v#b1 i4e4 to ! mass & to ! squ>e ( ! velocity ( ! air displac$4 ,b ! mass ( air displac$ p] second is proportional to ! w+-area & to ! spe$ ( ! bird's motion1 & !re=e to ! p[] #b ( ! l9e> dim5sions2 & ! spe$ at :i* x is displac$ is proportional to ! bird's spe$1 & !re=e to ! squ>e root ( ! l9e> dim5sions4 ,!re=e ! en]gy communicat$ p] second 7be+ proportional to ! mass & to ! squ>e ( ! spe$7 is jo9tly proportional to ! p[] #b ( ! l9e> dim5sions1 z above1 & to ! fir/ p[] !re(3 #be t is to say1 x increases 9 proportion to ! p[] #c ( ! l9e> dim5sions1 & !re=e fa/] ?an ! weight ( ! bird increases4 ,put 9 ma!matical =m1 ! equations are z foll[s3 7m ! mass ( air ?ru/ d[nw>ds2 ,v its velocity1 proportional to t ( ! bird2 ,m its mom5tum2 l a l9e> dim5sion ( ! bird2 w its weight2 ,w ! "w done 9 mov+ itself =w>d47 ,m w l#c4 ,b ,m m ,v1 & m l#b ,v4 ,!re=e ,m l#b ,v#b1 & l#b ,v#b l#c1 or ,v l4 ,b1 aga91 ,w m ,v#b l#b ,v ,v#b l#b l l l#c4 ,! "w requir+ to be done1 !n1 v>ies z ! p[] #c ( ! bird's l9e> dim5sions1 :ile ! "w ( :i* ! bird is capable dep5ds on ! mass ( its muscles1 & !re=e v>ies z ! cube ( its l9e> dim5sions#ci4 ,! disproportion does n seem at fir/ sight v great1 b x is q en\gh to tell4 ,x is z mu* z to say t1 e "t we d\ble ! l9e> dim5sions ( ! bird1 ! difficulty ( flight is increas$ 9 ! ratio ( #bc 3 #bc1 or #h 3 #aac1 or1 say1 #a 3 #ad4 ,if we take ! o/ri* to exce$ ! sp>r[ 9 l9e> dim5sions z #be 3 #a1 :i* seems well )9 ! m>k1 we h ! ratio betwe5 #bec & #bec1 or betwe5 #eg 3 #ef2 9 o!r words1 flight is j five times m difficult = ! l>g] ?an = ! small] bird#dj4 ,! above inve/igation includes1 besides ! f9al result1 a numb] ( o!rs1 explicit or impli$1 :i* are ( n less importance4 ,( ^! ! simple/ & also ! mo/ important is #bf conta9$ 9 ! equation ,v l1 a result :i* happ5s to be id5tical ) "o we _h also arriv$ at 9 ! case ( ! fi%4 ,9 ! bird's case x has a deep] significance ?an 9 ! o!r2 because x implies "h n m]ely t ! velocity w t5d to increase 9 a c]ta9 ratio ) ! l5g?1 b t x mu/ d s z an ess5tial & prim>y condition ( ! bird's rema9+ al(t4 ,x is accord+ly ( great practical importance 9 a]onautics1 = x %ews h[ a provision ( increas+ spe$ mu/ accompany e enl>gem5t ( our a]oplanes4 ,if a giv5 ma*9e weigh+1 say1 #ejj lbs4 be /able at #dj miles an h\r1 !n "o geometrically simil> :i* weighs1 say1 a c\ple ( tons mu/ h its spe$ det]m9$ z foll[s3 ,w 3 w 33 ,l#c 3 l#c 33 #h 3 #a4 ,!re=e ,l 3 l 33 #b 3 #a4 ,b ,v#b 3 v#b 33 ,l 3 l4 ,!re=e ,v 3 v 33 #b 3 #a #adad 3 #a4 ,t is to say1 ! l>g] ma*9e mu/ be capable ( a spe$ equal to #adad #dj1 or ab\t #ef miles p] h\r4 ,x is highly probable1 z ,lan*e/]#da rem>ks1 t ,lili5?al met 8 untimely dea? n s mu* f any intr9sic fault 9 ! design or con/ruction ( 8 ma*9e1 b simply because 8 eng9e fell some:at %ort ( ! p[] requir$ to give ! spe$ :i* 0 necess>y = /ability4 ,an arr[ is a v imp]fectly design$ a]oplane1 b nev]!less x is evid5tly capable1 to a c]ta9 ext5t & at a high velocity1 ( acquir+ 8/ability0 & h5ce ( actual 8flight03 ! duration & consequ5t range ( its trajectory1 z comp>$ ) a bullet ( simil> initial velocity1 be+ correspond+ly b5efit$4 ,:5 we return to our birds1 & aga9 comp>e ! o/ri* ) ! sp>r[1 we "k little or no?+ ab\t ! spe$ 9 flight ( ! latt]1 b t ( ! swift is e/imat$#db to v>y f a m9imum ( #bj to #ej feet or m p] second1--say f #ad to #ce miles p] h\r4 ,let u take ! same l[] limit z n f> f ! m9imal velocity ( ! sp>r['s flight also2 & x #bg w\ld foll[ t ! o/ri*1 ( #be times ! sp>r['s l9e> dim5sions1 w\ld be compell$ to fly 7if x flew at all7 ) a m9imum velocity ( #e #ad1 or #gj miles an h\r4 ,! same pr9ciple ( necess>y spe$1 or ! indisp5sable relation betwe5 ! dim5sions ( a fly+ object & ! m9imum velocity at :i* x is /able1 acc\nts = a great numb] ( obs]v$ ph5om5a4 ,x tells u :y ! l>g] birds h a m>k$ difficulty 9 ris+ f ! gr\nd1 t is to say1 9 acquir+ to beg9 ) ! horizontal velocity necess>y = _! support2 & :y accord+ly1 z ,m\ill>d#dc & o!rs h obs]v$1 ! heavi] birds1 ev5 ^? weigh+ no m ?an a p\nd or two1 c be effectively 8cag$0 9 a small enclosure op5 to ! sky4 ,x tells u :y v small birds1 especially ^? z small z humm+-birds1 & =tiori ! /ill small] insects1 are capable ( 8/ation>y flight10 a v slight & sc>cely p]ceptible velocity relatively to ! air be+ suffici5t = _! support & /ability4 ,& aga91 s9ce x is 9 all cases velocity relative to ! air t we are speak+ (1 we compreh5d ! reason :y "o may always tell :i* way ! w9d bl[s by wat*+ ! direction 9 :i* a bird />ts to fly4 ,x is n improbable t ! o/ri* has already rea*$ a magnitude1 & we may take x = c]ta9 t ! moa did s1 at :i* flight by muscul> action1 accord+ to ! normal anatomy ( a bird1 has become physiologically impossible4 ,! same reason+ applies to ! case ( man4 ,x w\ld be v difficult1 & probably absolutely impossible1 = a bird to fly 7 x ! bigness ( a man4 ,b ,borelli1 9 discuss+ ?is "q1 laid ev5 great] /ress on ! obvi\s fact t a man's pectoral muscles are s imm5sely less 9 proportion ?an ^? ( a bird1 t h[ev] we may fit ourselves ) w+s we c nev] expect to move !m by any p[] ( our own relatively weak] muscles2 s x is t artificial flight only became possible :5 an eng9e 0 devis$ ^: effici5cy 0 extraord9>ily great 9 comp>ison ) its weight & size4 ,_h ,leon>do da ,v9ci kn[n :at ,galileo knew1 he w\ld n h sp5t a great "p ( 8 life on va9 ef=ts to make to himself w+s4 ,borelli _h le>n$ ! lesson ?or\ghly1 & #bh 9 "o ( 8 *apt]s he deals ) ! proposition1 8,e/ impossible1 ut hom9es propriis viribus artificiose vol>e poss9t#dd40 ,b j z x is easi] to swim ?an to fly1 s is x obvi\s t1 9 a d5s] atmosph]e1 ! conditions ( flight w\ld be alt]$1 & flight facilitat$4 ,we "k t 9 ! c>bonif]\s epo* !re liv$ giant dragon-flies1 ) w+s ( a span f> great] ?an n[adays !y ev] atta92 & ! small bodies & huge ext5d$ w+s ( ! fossil pt]odactyles w\ld seem 9 l mann] to be q abnormal accord+ to our pres5t /&>ds1 & to be beyond ! limits ( me*anical effici5cy "u pres5t conditions4 ,b z ,h>l sugge/s#de1 foll[+ ^u a sugge/ion ( ,arrh5ius1 we h only to suppose t 9 c>bonif]\s & jurassic days ! t]re/rial atmosph]e 0 notably d5s] ?an x is at pres5t1 by reason1 = in/ance1 ( its conta9+ a mu* l>g] proportion ( c>bonic acid1 & we h at once a means ( reconcil+ ! app>5t me*anical discrepancy4 ,v simil> problems1 involv+ 9 v>i\s ways ! pr9ciple ( dynamical similitude1 occur all ?r\gh ! physiology ( locomotion3 z1 = in/ance1 :5 we see t a cock*af] c c>ry a plate1 _m times 8 own weight1 ^u 8 back1 or t a flea c jump _m in*es high4 ,problems ( ?is latt] class h be5 admirably treat$ bo? by ,galileo & by ,borelli1 b _m lat] writ]s h rema9$ ignorant ( _! "w4 ,l9naeus1 = in/ance1 rem>k$ t1 if an elephant 7 z /rong 9 proportion z a /ag-beetle1 x w\ld be able to pull up rocks by ! root1 & to level m\nta9s4 ,& ,kirby & ,sp5ce h a well-kn[n passage direct$ to %ew t su* p[]s z h be5 conf]r$ ^u ! insect h be5 )held f ! high] animals1 = ! reason t _h ^! latt] be5 endu$ !re) !y w\ld h 8caus$ ! e>ly desolation ( ! _w#df40 #bi ,su* problems z t :i* is pres5t$ by ! flea's jump+ p[]s1 ?\gh ess5tially physiological 9 _! nature1 h _! int]e/ = u "h3 because a /eady1 progressive dim9ution ( activity ) increas+ size w\ld t5d to set limits to ! possible gr[? 9 magnitude ( an animal j z surely z ^? factors :i* t5d to break & cru% ! liv+ fabric "u its own weight4 ,9 ! case ( a leap1 we h to d r ) a sudd5 impulse ?an ) a cont9u$ /ra91 & ?is impulse %\ld be measur$ 9 t]ms ( ! velocity imp>t$4 ,! velocity is proportional to ! impulse 7x71 & inv]sely proportional to ! mass 7,m7 mov$3 ,v x_/,m4 ,b1 accord+ to :at we /ill speak ( z 8,borelli's law10 ! impulse 7i4e4 ! "w ( ! impulse7 is proportional to ! volume ( ! muscle by :i* x is produc$#dg1 t is to say 79 simil>ly con/ruct$ animals7 to ! mass ( ! :ole body2 = ! impulse is proportional on ! "o h& to ! cross-section ( ! muscle1 & on ! o!r to ! di/ance ?r\gh :i* x contracts4 ,x foll[s at once f ?is t ! velocity is con/ant1 :atev] be ! size ( ! animals3 9 o!r words1 t all animals1 provid$ always t !y are simil>ly fa%ion$1 ) _! v>i\s lev]s etc41 9 l proportion1 ought to jump1 n to ! same relative1 b to ! same actual height#dh4 ,accord+ to ?is1 !n1 ! flea is n a bett]1 b r a worse jump] ?an a horse or a man4 ,z a matt] ( fact1 ,borelli is c>eful to po9t out t 9 ! act ( leap+ ! impulse is n actually in/antane\s1 z 9 ! bl[ ( a hamm]1 b takes "s little "t1 dur+ :i* ! lev]s are be+ ext5d$ by :i* ! c5tre ( gravity ( ! animal is be+ propell$ =w>ds2 & ?is int]val ( "t w be long] 9 ! case ( ! long] lev]s ( ! l>g] animal4 ,to "s ext5t1 !n1 ?is pr9ciple acts z a corrective to ! m g5]al "o1 #cj & t5ds to leave a c]ta9 balance ( advantage1 9 reg>d to leap+ p[]1 on ! side ( ! l>g] animal#di4 ,b on ! o!r h&1 ! "q ( /r5g? ( mat]ials comes 9 once m1 & ! factors ( /ress & /ra9 & b5d+ mom5t make x1 s to speak1 m & m difficult = nature to end[ ! l>g] animal ) ! l5g? ( lev] ) :i* %e has provid$ ! flea or ! gras%opp]4 ,to ,kirby & ,sp5ce x seem$ t 8,?is wond]ful /r5g? ( insects is d\btless ! result ( some?+ peculi> 9 ! /ructure & arrangem5t ( _! muscles1 & pr9cipally _! extraord9>y p[] ( contraction40 ,?is hypo!sis1 :i* is s easily se51 on physical gr\nds1 to be unnecess>y1 has be5 amply disprov$ 9 a s]ies ( excell5t pap]s by ,f4 ,plateau#ej4 ,a some:at simple problem is pres5t$ to u by ! act ( walk+4 ,x is obvi\s t !re w be a great economy ( "w1 if ! leg sw+ at its normal p5dulum-rate2 &1 ?\gh ?is rate is h>d to calculate1 ow+ to ! %ape & ! jo9t+ ( ! limb1 we may easily conv9ce ourselves1 by c\nt+ our /eps1 t ! leg does actually sw+1 or t5d to sw+1 j z a p5dulum does1 at a c]ta9 def9ite rate#ea4 ,:5 we walk quick]1 we cause ! leg-p5dulum to describe a great] arc1 b we d n appreciably cause x to sw+1 or vibrate1 quick]1 until we %ort5 ! p5dulum & beg9 to run4 ,n[ let two individuals1 ,a & ,b1 walk 9 a simil> fa%ion1 t is to say1 ) a simil> angle ( sw+4 ,! arc ?r\gh :i* ! leg sw+s1 or ! amplitude ( ea* /ep1 w !re=e v>y z ! l5g? ( leg1 or say z a_/b2 b ! "t ( sw+ w v>y z ! squ>e #ca root ( ! p5dulum-l5g?1 or a_/b4 ,!re=e ! velocity1 :i* is measur$ by amplitude_/"t1 w also v>y z ! squ>e-roots ( ! l5g? ( leg3 t is to say1 ! av]age velocities ( ,a & ,b are 9 ! ratio ( a 3 b4 ,! small] man1 or small] animal1 is s f> at a disadvantage comp>$ ) ! l>g] 9 spe$1 b only to ! ext5t ( ! ratio betwe5 ! squ>e roots ( _! l9e> dim5sions3 :]eas1 if ! rate ( movem5t ( ! limb 7 id5tical1 irrespective ( ! size ( ! animal1--if ! limbs ( ! m\se = in/ance swung at ! same rate z ^? ( ! horse1--!n1 z ,f4 ,plateau said1 ! m\se w\ld be z sl[ or sl[] 9 its gait ?an ! tortoise4 ,m4 ,delisle#eb obs]v$ a 8m9ute fly0 walk ?ree in*es 9 half-a-second4 ,?is 0 good /eady walk+4 ,:5 we walk five miles an h\r we g ab\t #hh in*es 9 a second1 or #hh_/f #adg times ! pace ( ,m4 ,delisle's fly4 ,we %\ld walk at j ab\t ! fly's pace if our /ature 7 #a_/7adg7b1 or #a_/baf ( our pres5t height1--say #gb_/baf in*es1 or "o-?ird ( an in* high4 ,b ! leg comprises a complicat$ sy/em ( lev]s1 by ^: v>i\s ex]cise we %all obta9 v diff]5t results4 ,= in/ance1 by be+ c>eful to rise ^u our in/ep1 we consid]ably increase ! l5g? or amplitude ( our /ride1 & v consid]ably increase our spe$ accord+ly4 ,on ! o!r h&1 9 runn+1 we b5d & s %ort5 ! leg1 9 ord] to accommodate x to a quick] rate ( p5dulum-sw+#ec4 ,9 %ort1 ! jo9t$ /ructure ( ! leg p]mits u to use x z ! %orte/ possible p5dulum :5 x is sw++1 & z ! longe/ possible lev] :5 x is ex]t+ its propulsive =ce4 ,ap>t f su* modifications z t describ$ 9 ! la/ p>agraph1--ap>t1 t is to say1 f diff]5ces 9 me*anical con/ruction or 9 ! mann] 9 :i* ! me*anism is us$1--we h n[ arriv$ at a curi\sly simple & uni=m result4 ,= 9 all ! ?ree =ms ( locomotion :i* we h attempt$ #cb to /udy1 alike 9 swimm+1 9 flight & 9 walk+1 ! g5]al result1 atta9$ "u v diff]5t conditions & arriv$ at by v diff]5t modes ( reason+1 is 9 e case t ! velocity t5ds to v>y z ! squ>e root ( ! l9e> dim5sions ( ! organism4 ,f all ! =ego+ discussion we le>n t1 z ,crookes once ^u a "t rem>k$#ed1 ! =m z well z ! actions ( our bodies are entirely condition$ 7save = c]ta9 exceptions 9 ! case ( aquatic animals1 nicely balanc$ ) ! d5sity ( ! surr\nd+ m$ium7 by ! /r5g? ( gravity ^u ?is globe4 ,7 ! =ce ( gravity to be d\bl$1 our bip$al =m w\ld be a failure1 & ! majority ( t]re/rial animals w\ld resemble %ort-legg$ saurians1 or else s]p5ts4 ,birds & insects w\ld also suff]1 ?\gh !re w\ld be "s comp5sation = !m 9 ! increas$ d5sity ( ! air4 ,:ile on ! o!r h& if gravity 7 halv$1 we %\ld get a light]1 m graceful1 m active type1 requir+ less en]gy & less heat1 less he>t1 less lungs1 less blood4 ,?r\gh\t ! :ole field ( morphology we may f9d examples ( a t5d5cy 7ref]able d\btless 9 ea* case to "s def9ite physical cause7 = surface to keep pace ) volume1 ?r\gh "s alt]ation ( its =m4 ,! developm5t ( 8villi0 on ! inn] surface ( ! /oma* & inte/9e 7:i* enl>ge its surface mu* z we enl>ge ! effective surface ( a ba?-t[el71 ! v>i\s valvul> folds ( ! inte/9al l9+1 includ+ ! rem>kable 8spiral fold0 ( ! %>k's gut1 ! convolutions ( ! bra91 ^: complexity is evid5tly correlat$ 79 "p at lea/7 ) ! magnitude ( ! animal1--all ^! & _m m are cases 9 :i* a m or less con/ant ratio t5ds to be ma9ta9$ betwe5 mass & surface1 :i* ratio w\ld h be5 m & m dep>t$ f _h x n be5 = ! alt]ations ( surface-=m#ee4 #cc ,9 ! case ( v small animals1 & ( individual cells1 ! pr9ciple becomes especially important1 9 consequ5ce ( ! molecul> =ces ^: action is /rictly limit$ to ! sup]ficial lay]4 ,9 ! cases j m5tion$1 action is facilitat$ by increase ( surface3 diffusion1 = in/ance1 ( nutri5t liquids or respiratory gases is r5d]$ m rapid by ! great] area ( surface2 b !re are o!r cases 9 :i* ! ratio ( surface to mass may make an ess5tial *ange 9 ! :ole condition ( ! sy/em4 ,we "k1 = in/ance1 t iron ru/s :5 expos$ to moi/ air1 b t x ru/s ev] s mu* fa/]1 & is soon eat5 away1 if ! iron be fir/ r$uc$ to a heap ( small fil+s2 ?is is a m]e diff]5ce ( degree4 ,b ! sph]ical surface ( ! ra9drop & ! sph]ical surface ( ! ocean 7?\gh bo? happ5 to be alike 9 ma!matical =m7 are two totally diff]5t ph5om5a1 ! "o due to surface-en]gy1 & ! o!r to t =m ( mass-en]gy :i* we ascribe to gravity4 ,! contra/ is /ill m cle>ly se5 9 ! case ( waves3 = ! little ripple1 ^: =m & mann] ( propagation are gov]n$ by surface-t5sion1 is f\nd to travel ) a velocity :i* is inv]sely z ! squ>e root ( its l5g?2 :ile ! ord9>y big waves1 controll$ by gravitation1 h a velocity directly proportional to ! squ>e root ( _! wave-l5g?4 ,9 l mann] we %all f9d t ! =m ( all small organisms is l>gely indep5d5t ( gravity1 & l>gely if n ma9ly due to ! =ce ( surface-t5sion3 ei!r z ! direct result ( ! cont9u$ action ( surface t5sion on ! semi-fluid body1 or else z ! result ( its action at a prior /age ( developm5t1 9 br++ ab\t a =m :i* subsequ5t *emical *anges h r5d]$ rigid & la/+4 ,9 ei!r case1 we %all f9d a v great t5d5cy 9 small organisms to assume ei!r ! sph]ical =m or o!r simple =ms relat$ to ord9>y inanimate surface-t5sion ph5om5a2 :i* =ms d n recur 9 ! ext]nal morphology ( l>ge animals1 or if !y 9 "p recur x is = o!r reasons4 #cd ,n[ ?is is a v important matt]1 & is a notable illu/ration ( t pr9ciple ( similitude :i* we h already discuss$ 9 reg>d to sev]al ( its manife/ations4 ,we are com+ easily to a conclusion :i* w affect ! :ole c\rse ( our argum5t ?r\gh\t ?is book1 namely t !re is an ess5tial diff]5ce 9 k9d betwe5 ! ph5om5a ( =m 9 ! l>g] & ! small] organisms4 ,i h call$ ?is book a /udy ( ,gr[? & ,=m1 because 9 ! mo/ famili> illu/rations ( organic =m1 z 9 our own bodies = example1 ^! two factors are insep>ably associat$1 & because we are "h ju/ifi$ 9 ?9k+ ( =m z ! direct resultant & consequ5ce ( gr[?3 ( gr[?1 ^: v>y+ rate 9 "o direction or ano!r has produc$1 by its gradual & unequal increm5ts1 ! successive /ages ( developm5t & ! f9al configuration ( ! :ole mat]ial /ructure4 ,b x is by no means true t =m & gr[? are 9 ?is direct & simple fa%ion correlative or complem5t>y 9 ! case ( m9ute portions ( liv+ matt]4 ,= 9 ! small] organisms1 & 9 ! individual cells ( ! l>g]1 we h rea*$ an ord] ( magnitude 9 :i* ! int]molecul> =ces /rive "u fav\rable conditions )1 & at l5g? altoge!r outweigh1 ! =ce ( gravity1 & also ^? o!r =ces lead+ to movem5ts ( convection :i* are ! prevail+ factors 9 ! l>g] mat]ial aggregate4 ,h[ev] we %all require to deal m fully ) ?is matt] 9 our discussion ( ! rate ( gr[?1 & we may leave x mean:ile1 9 ord] to deal ) o!r matt]s m or less directly conc]n$ ) ! magnitude ( ! cell4 ,! liv+ cell is a v complex field ( en]gy1 & ( en]gy ( _m k9ds1 surface-en]gy includ$4 ,n[ ! :ole surface-en]gy ( ! cell is by no means re/rict$ to its out] surface2 = ! cell is a v het]og5e\s /ructure1 & all its protoplasmic alveoli & o!r visible 7z well z invisible7 het]og5eities make up a great sy/em ( int]nal surfaces1 at e "p ( :i* "o 8phase0 comes 9 contact ) ano!r 8phase10 & surface-en]gy is accord+ly manife/$4 ,b /ill1 ! ext]nal surface is a def9ite portion ( ! sy/em1 ) a def9ite 8phase0 ( its own1 & h[ev] little we may "k ( ! di/ribution ( ! total en]gy ( ! sy/em1 x is at lea/ pla9 t #ce ! conditions :i* fav\r equilibrium w be greatly alt]$ by ! *ang$ ratio ( ext]nal surface to mass :i* a *ange ( magnitude1 unaccompani$ by *ange ( =m1 produces 9 ! cell4 ,9 %ort1 h[ev] x may be br\ght ab\t1 ! ph5om5on ( division ( ! cell w be precisely :at is requir$ to keep approximately con/ant ! ratio betwe5 surface & mass1 & to re/ore ! balance betwe5 ! surface-en]gy & ! o!r en]gies ( ! sy/em4 ,:5 a g]m-cell1 = in/ance1 divides or 8segm5ts0 into two1 x does n increase 9 mass2 at lea/ if !re be "s slight alleg$ t5d5cy = ! egg to increase 9 mass or volume dur+ segm5tation1 x is v slight inde$1 g5]ally imp]ceptible1 & :olly d5i$ by "s#ef4 ,! developm5t or gr[? ( ! egg f a "o-cell$ /age to /ages ( two or _m cells1 is ?us a some:at peculi> k9d ( gr[?2 x is gr[? :i* is limit$ to increase ( surface1 unaccompani$ by gr[? 9 volume or 9 mass4 ,9 ! case ( a soap-bubble1 by ! way1 if x divide into two bubbles1 ! volume is actually dim9i%$#eg :ile ! surface-area is greatly increas$4 ,?is is due to a cause :i* we %all h to /udy lat]1 namely to ! increas$ pressure due to ! great] curvature ( ! small] bubbles4 ,an imm$iate & rem>kable result ( ! pr9ciples j describ$ is a t5d5cy on ! "p ( all cells1 accord+ to _! k9d1 to v>y b little ab\t a c]ta9 mean size1 & to h1 9 fact1 c]ta9 absolute limitations ( magnitude4 ,sa*s#eh po9t$ out1 9 #ahie1 t !re is a t5d5cy = ea* nucleus to be only able to ga!r ar\nd itself a c]ta9 def9ite am\nt ( protoplasm4 ,dries*#ei1 a little lat]1 f\nd t1 by artificial subdivision ( ! egg1 x 0 possible to re> dw>f sea-ur*9 l>vae1 "o-half1 "o-qu>t]1 or ev5 "o-eigh? ( _! #cf normal size2 & t ^! dw>f bodies 7 compos$ ( only a half1 a qu>t] or an eigh? ( ! normal numb] ( cells4 ,simil> obs]vations h be5 (t5 repeat$ & amply confirm$4 ,= in/ance1 9 ! developm5t ( ,crepidula 7a little ,am]ican 8slipp]-limpet10 n[ mu* at home on our own oy/]-b$s71 ,conkl9#fj has succe$$ 9 re>+ dw>f & giant individuals1 ( :i* ! latt] may be z mu* z tw5ty-five times z big z ! =m]4 ,b nev]!less1 ! individual cells1 ( sk91 gut1 liv]1 muscle1 & ( all ! o!r tissues1 are j ! same size 9 "o z 9 ! o!r1--9 dw>f & 9 giant#fa4 ,dries* has laid p>ticul> /ress ^u ?is pr9ciple ( a 8fix$ cell-size40 ,we get an excell5t1 & m famili> illu/ration ( ! same pr9ciple 9 comp>+ ! l>ge bra9-cells or ganglion-cells1 bo? ( ! l[] & ( ! high] animals#fb4 ,illu/ration3 ,fig4 #a4 ,motor ganglion-cells1 f ! c]vical sp9al cord4 7,f ,m9ot1 aft] ,irv+ ,h>de/y47 ,9 ,fig4 #a we h c]ta9 id5tical n]ve-cells tak5 f v>i\s mammals1 f ! m\se to ! elephant1 all repres5t$ on ! same scale ( magnification2 & we see at once t !y are all ( mu* ! same ord] ( magnitude4 ,! n]ve-cell ( ! elephant is ab\t twice t ( ! m\se 9 l9e> dim5sions1 & !re=e ab\t eight times great] 9 volume1 or mass4 ,b mak+ "s all[ance = diff]5ce ( %ape1 ! l9e> dim5sions ( ! elephant are to ^? ( ! m\se 9 a ratio c]ta9ly n less ?an "o to fifty2 f :i* x w\ld foll[ t ! bulk ( ! l>g] animal is some?+ l #abe1jjj times t ( ! less4 ,& x also foll[s1 ! size ( ! n]ve-cells be+ #cg ab\t z eight to "o1 t1 9 correspond+ p>ts ( ! n]v\s sy/em ( ! two animals1 !re are m ?an #ae1jjj times z _m individual cells 9 "o z 9 ! o!r4 ,9 %ort we may 7) ,enriques7 lay x d[n z a g5]al law t among animals1 :e!r l>ge or small1 ! ganglion-cells v>y 9 size )9 n>r[ limits2 & t1 amid/ all ! great v>iety ( /ructural type ( ganglion obs]v$ 9 diff]5t classes ( animals1 x is always f\nd t ! small] species h simpl] ganglia ?an ! l>g]1 t is to say ganglia conta9+ a small] numb] ( cellul> elem5ts#fc4 ,! be>+ ( su* simple facts z ?is ^u ! cell-!ory 9 g5]al is n to be disreg>d$2 & ! w>n+ is especially cle> aga9/ exagg]at$ attempts to correlate physiological processes ) ! visible me*anism ( associat$ cells1 r ?an ) ! sy/em ( en]gies1 or ! field ( =ce1 :i* is associat$ ) !m4 ,= ! life ( #ch ! body is m ?an ! sum ( ! prop]ties ( ! cells ( :i* x is compos$3 z ,goe! said1 8,das ,leb5dige i/ zw> 9 ,elem5te z]legt1 ab] man kann es aus dies5 ni*t wi$] zusamm5/ell5 und beleb540 ,among c]ta9 l[] & microscopic organisms1 su* = in/ance z ! ,rotif]a1 we are /ill m palpably /ruck by ! small numb] ( cells :i* g to con/itute a usually complex organ1 su* z kidney1 /oma*1 ov>y1 etc4 ,we c sometimes numb] !m 9 a few units1 9 place ( ! ?\s&s t make up su* an organ 9 l>g]1 if n always high]1 animals4 ,^! facts con/itute "o among _m argum5ts :i* comb9e to tea* u t1 h[ev] important & advantage\s ! subdivision ( organisms into cells may be f ! con/ructional1 or f ! dynamical po9t ( view1 ! ph5om5on has less ess5tial importance 9 !oretical biology ?an 0 once1 & is (t5 /ill1 assign$ to x4 ,aga91 j z ,sa*s %ew$ t !re 0 a limit to ! am\nt ( cytoplasm :i* c\ld ga!r r\nd a s+le nucleus1 s ,bov]i has demon/rat$ t ! nucleus itself has def9ite limitations ( size1 & t1 9 cell-division aft] f]tilisation1 ea* new nucleus has ! same size z its p>5t-nucleus#fd4 ,9 all ^! cases1 !n1 !re are reasons1 p>tly no d\bt physiological1 b 9 v l>ge "p purely physical1 :i* set limits to ! normal magnitude ( ! organism or ( ! cell4 ,b z we h already discuss$ ! exi/5ce ( absolute & def9ite limitations1 ( a physical k9d1 to ! possible increase 9 magnitude ( an organism1 let u n[ enquire :e!r !re be n also a l[] limit1 bel[ :i* ! v exi/5ce ( an organism is impossible1 or at lea/ :]e1 "u *ang$ conditions1 its v nature mu/ be pr(\ndly modifi$4 ,among ! smalle/ ( kn[n organisms we h1 = in/ance1 ,micromonas mesnili1 ,bonel1 a flagellate infusorian1 :i* measures ab\t #cd 1 or #jjjcd mm41 by #jjjbe mm42 small] ev5 ?an ?is we h a pa?og5ic micrococcus ( ! rabbit1 ,m4 progr$i5s1 ,s*rt]1 ! diamet] ( :i* is said to be only #jjjae mm4 or #ae 1 or #ae #aje cm41--ab\t equal to ! ?ickness ( #ci ! ?9ne/ gold-leaf2 & z small if n small] /ill are a few bact]ia & _! spores4 ,b "h we h rea*$1 or all b rea*$ ! utmo/ limits ( ord9>y microscopic vision2 & !re rema9 /ill small] organisms1 ! s-call$ 8filt]-pass]s10 :i* ! ultra-microscope reveals1 b :i* are ma9ly br\ght )9 our k5 only by ! maladies1 su* z hydrophobia1 foot-&-m\? disease1 or ! 8mosaic0 disease ( ! tobacco-plant1 to :i* ^! invisible micro-organisms give rise#fe4 ,accord+ly1 s9ce x is only by ! diseases :i* !y occasion t ^! t9y bodies are made kn[n to u1 we might be tempt$ to suppose t innum]able o!r invisible organisms1 small] & yet small]1 exi/ unse5 & unrecognis$ by man4 ,illu/ration3 ,fig4 #b4 ,relative magnitudes (3 ,a1 human blood-corpuscle 7#ge 9 diamet]72 ,b1 ,bacillus an?racis 7#d - #ae #a 72 ,c1 v>i\s ,micrococci 7diam4 #je - #a 1 r>ely #b 72 ,d1 ,micromonas progr$i5s1 ,s*rt] 7diam4 #jae 74 ,to illu/rate "s ( ^! small magnitudes ,i h adapt$ ! prec$+ diagram f "o giv5 by ,zsigmondy#ff4 ,^u ! #dj same scale ! m9ute ultramicroscopic p>ticles ( colloid gold w\ld be repres5t$ by ! f9e/ dots :i* we c\ld make visible to ! nak$ eye ^u ! pap]4 ,a bacillus ( ord9>y1 typical size is1 say1 #a 9 l5g?4 ,! l5g? 7or height7 ( a man is ab\t a million & ?ree-qu>t] times z great1 i4e4 #age metres1 or #age #ajf 2 & ! mass ( ! man is 9 ! neighb\rhood ( five million1 million1 million 7#e #ajah7 times great] ?an t ( ! bacillus4 ,if we ask :e!r !re may n exi/ organisms z mu* less ?an ! bacillus z ! bacillus is less ?an ! dim5sions ( a man1 x is v easy to see t ?is is q impossible1 = we are rapidly approa*+ a po9t :]e ! "q ( molecul> dim5sions1 & ( ! ultimate divisibility ( matt]1 beg9s to call = our att5tion1 & to obtrude itself z a crucial factor 9 ! case4 ,cl]k ,maxwell dealt ) ?is matt] 9 8 article 8,atom#fg10 &1 9 some:at great] detail1 ,err]a discusses ! "q on ! foll[+ l9es#fh4 ,! weight ( a hydrog5 molecule is1 accord+ to ! physical *emi/s1 some:]e ab\t #hf #b #ajbb milligrammes2 & t ( any o!r elem5t1 ^: molecul> weight is ,m1 is giv5 by ! equation 7,m7 #hf ,m #ajbb4 ,accord+ly1 ! weight ( ! atom ( sulphur may be tak5 z #hf #cb #ajbb mgm4 #bge #ajbb mgm4 ,! analysis ( ord9>y bact]ia %ews !m to consi/#fi ( ab\t #he ( wat]1 & #ae ( solids2 :ile ! solid residue ( vegetable protoplasm conta9s ab\t "o "p 9 a ?\s& ( sulphur4 ,we may assume1 !re=e1 t ! liv+ protoplasm conta9s ab\t #a_/ajjj #ae_/ajj #ae #aje p>ts ( sulphur1 tak+ ! total weight z #a4 ,b our little micrococcus1 ( #jae 9 diamet]1 w\ld1 if x 7 sph]ical1 h a volume ( _/#f #jaec #ah #ajd cubic microns2 #da & !re=e 7tak+ its d5sity z equal to t ( wat]71 a weight ( #ah #ajd #aji #ah #ajac mgm4 ,b ( ?is total weight1 ! sulphur repres5ts only #ah #ajac #ae #aje #bg #ajag mgm4 ,& if we divide ?is by ! weight ( an atom ( sulphur1 we h 7#bg #ajag7 7#bge #ajbb7 #aj1jjj1 or !reby4 ,accord+ to ?is e/imate1 !n1 our little ,micrococcus progr$i5s %\ld conta9 only ab\t #aj1jjj atoms ( sulphur1 an elem5t indisp5sable to its protoplasmic con/itution2 & x foll[s t an organism ( "o-t5? ! diamet] ( our micrococcus w\ld only conta9 #aj sulphur-atoms1 & !re=e only t5 *emical 8molecules0 or units ( protoplasm6 ,x may be op5 to d\bt :e!r ! pres5ce ( sulphur be really ess5tial to ! con/itution ( ! proteid or 8protoplasmic0 molecule2 b ,err]a gives u yet ano!r illu/ration ( a simil> k9d1 :i* is free f ?is objection or dubiety4 ,! molecule ( album91 z is g5]ally agre$1 c sc>cely be less ?an a ?\s& times ! size ( t ( su* an elem5t z sulphur3 accord+ to "o p>ticul> det]m9ation#gj1 s]um album9 has a con/itution correspond+ to a molecul> weight ( #aj1aff1 & ev5 ?is may be f> %ort ( ! true complexity ( a typical album9oid molecule4 ,! weight ( su* a molecule is #hf #ajaff #ajbb #hg #ajah mgm4 ,n[ ! bact]ia conta9 ab\t #ad ( album9oids1 ^! con/itut+ by f> ! great] "p ( ! dry residue2 & !re=e 7f equation 7#e771 ! weight ( album9 9 our micrococcus is ab\t #ad_/ajj #ah #ajac #be #ajac mgm4 ,if we divide ?is weight by t :i* we h arriv$ at z ! weight ( an album9 molecule1 we h 7#be #ajac7 7#hg #ajah7 #bi #ajd1 9 o!r words1 our micrococcus app>5tly conta9s some?+ less ?an #cj1jjj molecules ( album94 #db ,accord+ to ! mo/ rec5t e/imates1 ! weight ( ! hydrog5 molecule is some:at less ?an t on :i* ,err]a bas$ 8 calculations1 namely ab\t #af #ajbb mgms4 & accord+ to ?is value1 our micrococcus w\ld conta9 j ab\t #bg1jjj album9 molecules4 ,9 o!r words1 :i*ev] det]m9ation we accept1 we see t an organism "o-t5? z l>ge z our micrococcus1 9 l9e> dim5sions1 w\ld only conta9 "s ?irty molecules ( album92 or1 9 o!r words1 our micrococcus is only ab\t ?irty times z l>ge1 9 l9e> dim5sions1 z a s+le album9 molecule#ga4 ,we mu/ d\btless make l>ge all[ances = unc]ta9ty 9 ! assumptions & e/imates ^u :i* ^! calculations are bas$2 & we mu/ also rememb] t ! data ) :i* ! physici/ provides u 9 reg>d to molecul> magnitudes are1 to a v great ext5t1 maximal values1 above :i* ! molecul> magnitude 7or r ! sph]e ( ! molecule's range ( motion7 is n likely to lie3 b bel[ :i* !re is a great] elem5t ( unc]ta9ty z to its possibly great] m9ut5ess4 ,b nev]!less1 :5 we %all h made all reasonable all[ances = unc]ta9ty ^u ! physical side1 x w /ill be cle> t ! smalle/ kn[n bodies :i* are describ$ z organisms draw nigh t[>ds molecul> magnitudes1 & we mu/ recognise t ! subdivision ( ! organism _c proce$ to an indef9ite ext5t1 & 9 all probability _c g v mu* fur!r ?an x appe>s to h done 9 ^! already discov]$ =ms4 ,=1 ev51 aft] giv+ all due reg>d to ! complexity ( our unit 7t is to say ! album9-molecule71 ) all ! increas$ possibilities ( int]relation ) its neighb\rs :i* ?is complexity implies1 we _c b see t physiologically1 & comp>atively speak+1 we h come d[n to a v simple ?+4 ,:ile su* consid]ations z ^!1 bas$ on ! *emical composition ( ! organism1 tea* u t !re mu/ be a def9ite l[] limit to its magnitude1 o!r consid]ations ( a purely physical k9d lead u to ! same conclusion4 ,= our discussion ( ! pr9ciple ( similitude has already taught u t1 long be=e we rea* ^! almo/ inf9itesimal magnitudes1 ! #dc dim9i%+ organism w h greatly *ang$ 9 all its physical relations1 & mu/ at l5g? arrive "u conditions :i* mu/ surely be incompatible ) any?+ su* z we und]/& by life1 at lea/ 9 its full & ord9>y developm5t & manife/ation4 ,we are told1 = in/ance1 t ! p[]ful =ce ( surface-t5sion1 or capill>ity1 beg9s to act )9 a range ( ab\t #a_/ejj1jjj ( an in*1 or say #jje 4 ,a soap-film1 or a film ( oil ^u wat]1 may be att5uat$ to f> less magnitudes ?an ?is2 ! black spots ^u a soap-bubble are kn[n1 by v>i\s concordant me?ods ( measurem5t1 to be only ab\t #f #ajg cm41 or ab\t #jjf ?ick1 & ,"l ,rayleigh & ,m4 ,devaux#gb h obta9$ films ( oil ( #jjb 1 or ev5 #jja 9 ?ickness4 ,b :ile x is possible = a fluid film to exi/ 9 ^! almo/ molecul> dim5sions1 x is c]ta9 t1 long be=e we rea* !m1 !re mu/ arise new conditions ( :i* we h little k & :i* x is n easy ev5 to imag9e4 ,x w\ld seem t1 9 an organism ( #a 9 diamet]1 or ev5 r m1 !re c be no ess5tial di/9ction betwe5 ! int]ior & ! surface lay]s4 ,no holl[ vesicle1 ,i take x1 c exi/ ( ^! dim5sions1 or at lea/1 if x be possible = x to d s1 ! conta9$ gas or fluid mu/ be "u pressures ( a =midable k9d#gc1 & ( :i* we h no k or exp]i5ce4 ,nor1 ,i imag9e1 c !re be any real complexity1 or het]og5eity1 ( its fluid or semi-fluid cont5ts2 !re c be no vacuoles )9 su* a cell1 nor any lay]s def9$ )9 its fluid sub/ance1 = some?+ ( ! nature ( a b\nd>y-film is ! necess>y condition ( ! exi/5ce ( su* lay]s4 ,moreov]1 ! :ole organism1 provid$ t x be fluid or semi-fluid1 c only be sph]ical 9 =m4 ,:at1 !n1 c we attribute1 9 ! way ( prop]ties1 to an organism ( a size z small z1 or small] ?an1 say #je 8 ,x mu/1 9 all probability1 be a homog5e\s1 /ructureless sph]e1 compos$ ( a v small numb] ( album9oid or o!r molecules4 ,its vital prop]ties & functions mu/ be extraord9>ily limit$2 its specific outw>d *>act]s1 ev5 if we c\ld see x1 mu/ be nil2 & its specific prop]ties mu/ be little m ?an ^? ( an ion-lad5 corpuscle1 enabl+ x to p]=m #dd ?is or t *emical reaction1 or to produce ?is or t pa?og5ic effect4 ,ev5 among inorganic1 non-liv+ bodies1 !re mu/ be a c]ta9 grade ( m9ut5ess at :i* ! ord9>y prop]ties become modifi$4 ,= in/ance1 :ile "u ord9>y circum/ances cry/allisation />ts 9 a solution ab\t a m9ute solid fragm5t or cry/al ( ! salt1 ,o/wald has %ewn t we may h p>ticles s m9ute t !y fail to s]ve z a nucleus = cry/allisation1--:i* is z mu* z to say t !y are too m9ute to h ! =m & prop]ties ( a 8cry/al02 & aga91 9 8 ?9 oil-films1 ,"l ,rayleigh has not$ ! /rik+ *ange ( physical prop]ties :i* ensues :5 ! film becomes att5uat$ to some?+ less ?an "o close-pack$ lay] ( molecules#gd4 ,?us1 z ,cl]k ,maxwell put x1 8molecul> sci5ce sets u face to face ) physiological !ories4 ,x =bids ! physiologi/ f imag9+ t /ructural details ( inf9itely small dim5sions su* z ,leibniz assum$1 "o )9 ano!r1 ad inf9itum c furni% an explanation ( ! inf9ite v>iety :i* exi/s 9 ! prop]ties & functions ( ! mo/ m9ute organisms40 ,& = ?is reason he reprobates1 ) n undue sev]ity1 ^? advocates ( pang5esis & simil> !ories ( h]$ity1 :o w\ld place 8a :ole _w ( wond]s )9 a body s small & s devoid ( visible /ructure z a g]m40 ,b inde$ x sc>cely ne$$ ,maxwell's criticism to %ew =? ! imm5se physical difficulties ( ,d>w9's !ory ( ,pang5esis3 :i*1 aft] all1 is z old z ,democritus1 & is no o!r ?an t ,prome!an p>ticulam undique desectam ( :i* we h read1 & at :i* we h smil$1 9 our ,horace4 ,!re are _m o!r ways 9 :i*1 :5 we 8make a long excursion into space10 we f9d our ord9>y rules ( physical behavi\r entirely upset4 ,a v famili> case1 analys$ by ,/okes1 is t ! viscosity ( ! surr\nd+ m$ium has a relatively p[]ful effect ^u bodies bel[ a c]ta9 size4 ,a droplet ( wat]1 a ?\s&? ( an in* 7#be 7 9 diamet]1 _c fall 9 /ill air quick] ?an ab\t an in* & a half p] second2 & z its size decreases1 its resi/ance v>ies z ! diamet]1 & n 7z ) l>g] bodies7 z ! surface ( ! #de drop4 ,?us a drop "o-t5? ( t size 7#be 71 ! size1 app>5tly1 ( ! drops ( wat] 9 a light cl\d1 w fall a hundr$ times sl[]1 or say an in* a m9ute2 & "o aga9 a t5? ( ?is diamet] 7say #be 1 or ab\t twice z big1 9 l9e> dim5sions1 z our micrococcus71 w sc>cely fall an in* 9 two h\rs4 ,by reason ( ?is pr9ciple1 n only d ! small] bact]ia fall v sl[ly ?r\gh ! air1 b all m9ute bodies meet ) great proportionate resi/ance to _! movem5ts 9 a fluid4 ,ev5 su* comp>atively l>ge organisms z ! diatoms & ! =am9if]a1 lad5 ?\gh !y are ) a heavy %ell ( fl9t or lime1 seem to be pois$ 9 ! wat] ( ! ocean1 & fall 9 x ) exce$+ sl[ness4 ,! ,br[nian movem5t has also to be reckon$ )1--t rem>kable ph5om5on /udi$ ne>ly a c5tury ago 7#ahbg7 by ,rob]t ,br[n1 facile pr9ceps botanicorum4 ,x is "o m ( ^? fundam5tal physical ph5om5a :i* ! biologi/s h contribut$1 or help$ to contribute1 to ! sci5ce ( physics4 ,! quiv]+ motion1 accompani$ by rotation1 & ev5 by translation1 manife/$ by ! f9e granul> p>ticles issu+ f a cru%$ poll5-gra91 & :i* ,rob]t ,br[n prov$ to h no vital significance b to be manife/$ also by all m9ute p>ticles :atsoev]1 organic & inorganic1 0 = _m ye>s unexpla9$4 ,ne>ly fifty ye>s aft] ,br[n wrote1 x 0 said to be 8due1 ei!r directly to "s calorical *anges cont9ually tak+ place 9 ! fluid1 or to "s obscure *emical action betwe5 ! solid p>ticles & ! fluid :i* is indirectly promot$ by heat#ge40 ,v %ortly aft] ^! la/ words 7 writt51 x 0 ascrib$ by ,wi5] to molecul> action1 & we n[ "k t x is inde$ due to ! impact or bomb>dm5t ( molecules ^u a body s small t ^! impacts d n = ! mom5t1 z x 71 8av]age out0 to approximate equality on all sides4 ,! movem5t becomes manife/ ) p>ticles ( some:]e ab\t #bj 9 diamet]1 x is admirably display$ by p>ticles ( ab\t #ab 9 diamet]1 & becomes m m>k$ ! small] ! p>ticles are4 ,! bomb>dm5t causes our p>ticles to behave j l molecules ( uncommon size1 & ?is #df behavi\r is manife/$ 9 sev]al ways#gf4 ,fir/ly1 we h ! quiv]+ movem5t ( ! p>ticles2 secondly1 _! movem5t backw>ds & =w>ds1 9 %ort1 /raight1 disjo9t$ pa?s2 ?irdly1 ! p>ticles rotate1 & d s ! m rapidly ! small] !y are1 & by !ory1 confirm$ by obs]vation1 x is f\nd t p>ticles ( #a 9 diamet] rotate on an av]age ?r\gh #ajj p] second1 :ile p>ticles ( #ac 9 diamet] turn ?r\gh only #ad p] m9ute4 ,la/ly1 ! v curi\s result appe>s1 t 9 a lay] ( fluid ! p>ticles are n equally di/ribut$1 nor d !y all ev] fall1 "u ! influ5ce ( gravity1 to ! bottom4 ,b j z ! molecules ( ! atmosph]e are s di/ribut$1 "u ! influ5ce ( gravity1 t ! d5sity 7& !re=e ! numb] ( molecules p] unit volume7 falls (f 9 geometrical progression z we asc5d to high] & high] lay]s1 s is x ) our p>ticles1 ev5 )9 ! n>r[ limits ( ! little portion ( fluid "u our microscope4 ,x is only 9 reg>d to p>ticles ( ! simple/ =m t ^! ph5om5a h be5 !oretically inve/igat$#gg1 & we may take x z c]ta9 t m complex p>ticles1 su* z ! twi/$ body ( a ,spirillum1 w\ld %[ o!r & /ill m complicat$ manife/ations4 ,x is at lea/ cle> t1 j z ! e>ly microscopi/s 9 ! days be=e ,rob]t ,br[n nev] d\bt$ b t ^! ph5om5a 7 purely vital1 s we also may /ill be apt to confuse1 9 c]ta9 cases1 ! "o ph5om5on ) ! o!r4 ,we _c1 inde$1 )\t ! mo/ c>eful scrut9y1 decide :e!r ! movem5ts ( our m9ute/ organisms are intr9sically 8vital0 79 ! s5se ( be+ beyond a physical me*anism1 or work+ model7 or n4 ,= example1 ,s*aud9n has sugge/$ t ! undulat+ movem5ts ( ,spiro*aete pallida mu/ be due to ! pres5ce ( a m9ute1 unse51 8undulat+ membrane02 & ,d(le9 says ( ! same species t 8sie v]h>rt (t mit eig5?mli* zitt]nd5 ,bewegung5 zu e9em ,orte40 ,bo? movem5ts1 ! trembl+ or quiv]+ #dg movem5t describ$ by ,d(le91 & ! undulat+ or rotat+ movem5t describ$ by ,s*aud9n1 are j su* z may be easily & naturally int]pret$ z "p & p>cel ( ! ,br[nian ph5om5on4 ,:ile ! ,br[nian movem5t may ?us simulate 9 a deceptive way ! active movem5ts ( an organism1 ! rev]se /atem5t also to a c]ta9 ext5t holds good4 ,"o sometimes lies awake ( a summ]'s morn+ wat*+ ! flies z !y dance "u ! ceil+4 ,x is a v rem>kable dance4 ,! danc]s d n :irl or gyrate1 ei!r 9 company or alone2 b !y advance & retire2 !y seem to jo/le & reb\nd2 betwe5 ! reb\nds !y d>t hi!r or ?i!r 9 %ort /raight snat*es ( hurri$ flight2 & turn aga9 %>ply 9 a new reb\nd at ! end ( ea* little ru%4 ,_! motions are :olly 8erratic10 indep5d5t ( "o ano!r1 & devoid ( common purpose4 ,?is is no?+ else ?an a va/ly magnifi$ picture1 or simulacrum1 ( ! ,br[nian movem5t2 ! p>allel betwe5 ! two cases lies 9 _! complete irregul>ity1 b ?is 9 itself implies a close resemblance4 ,"o might see ! same ?+ 9 a cr[d$ m>ket-place1 always provid$ t ! bu/l+ cr[d _h no bus9ess :atsoev]4 ,9 l mann] ,lucretius1 & ,epicurus be=e him1 wat*$ ! du/-motes quiv]+ 9 ! beam1 & saw 9 !m a mimic repres5tation1 rei simulacrum et imago1 ( ! et]nal motions ( ! atoms4 ,aga9 ! same ph5om5on may be witness$ "u ! microscope1 9 a drop ( wat] sw>m+ ) ,p>amoecia or su*like ,infusoria2 & "h ! analogy has be5 put to a num]ical te/4 ,foll[+ ) a p5cil ! track ( ea* little swimm]1 & dott+ its place e few seconds 7to ! beat ( a metronome71 ,k>l ,przibram f\nd t ! mean successive di/ances f a common base-l9e obey$ ) great exactitude ! 8,e9/e9 =mula10 t is to say ! p>ticul> =m ( ! 8law ( *ance0 :i* is applicable to ! case ( ! ,br[nian movem5t#gh4 ,! ph5om5on is 7( c\rse7 m]ely analog\s1 & by no means id5tical ) ! ,br[nian movem5t2 = ! range ( motion ( ! little active organisms1 :e!r !y be gnats or infusoria1 is va/ly great] ?an t ( ! m9ute p>ticles :i* are #dh passive "u bomb>dm5t2 b nev]!less ,przibram is incl9$ to ?9k t ev5 8 comp>atively l>ge infusoria are small en\gh = ! molecul> bomb>dm5t to be a /imulus1 ?\gh n ! actual cause1 ( _! irregul> & int]rupt$ movem5ts4 ,!re is yet ano!r v rem>kable ph5om5on :i* may come into play 9 ! case ( ! m9ute/ ( organisms2 & ?is is _! relation to ! rays ( light1 z ,arrh5ius has told u4 ,on ! waves ( a beam ( light1 a v m9ute p>ticle 79 vacuo7 %\ld be actually caught up1 & c>ri$ along ) an imm5se velocity2 & ?is 8radiant pressure0 ex]cises its mo/ p[]ful influ5ce on bodies :i* 7if !y be ( sph]ical =m7 are j ab\t #jjjaf mm41 or #af 9 diamet]4 ,?is is j ab\t ! size1 z we h se51 ( "s ( our smalle/ kn[n protozoa & bact]ia1 :ile we h "s reason to believe t o!rs yet unse51 & p]haps ! spores ( _m1 are small] /ill4 ,n[ we h se5 t su* m9ute p>ticles fall ) extreme sl[ness 9 air1 ev5 at ord9>y atmosph]ic pressures3 our organism measur+ #af w\ld fall b #hc metres 9 a ye>1 :i* is z mu* z to say t its weight (f]s practically no imp$im5t to its transf]5ce1 by ! slighte/ curr5t1 to ! v highe/ regions ( ! atmosph]e4 ,beyond ! atmosph]e1 h[ev]1 x _c g1 until "s new =ce enable x to resi/ ! attraction ( t]re/rial gravity1 :i* ! viscosity ( an atmosph]e is no long] at h& to oppose4 ,b x is conceivable t our p>ticle may g yet f>!r1 & actually break loose f ! bonds ( e>?4 ,= 9 ! upp] regions ( ! atmosph]e1 say fifty miles high1 x w come 9 contact ) ! rays & fla%es ( ! ,nor!rn ,lights1 :i* consi/ 7z ,arrh5ius ma9ta9s7 ( a f9e du/1 or cl\d ( vap\r-drops1 lad5 ) a *>ge ( negative electricity1 & project$ outw>ds f ! sun4 ,z soon z our p>ticle acquires a *>ge ( negative electricity x w beg9 to be repell$ by ! simil>ly lad5 auroral p>ticles1 & ! am\nt ( *>ge necess>y to enable a p>ticle ( giv5 size 7su* z our little monad ( #af 7 to resi/ ! attraction ( gravity may be calculat$1 & is f\nd to be su* z ! actual conditions c easily supply4 ,f9ally1 :5 once set free f ! entanglem5t ( ! e>?'s #di atmosph]e1 ! p>ticle may be propell$ by ! 8radiant pressure0 ( light1 ) a velocity :i* w c>ry x4--l ,uriel glid+ on a sunbeam1--z f> z ! orbit ( ,m>s 9 tw5ty days1 ( ,jupit] 9 eighty days1 & z f> z ! ne>e/ fix$ /> 9 ?ree ?\s& ye>s6 ,?is1 & mu* m1 is ,arrh5ius's contribution t[>ds ! acceptance ( ,"l ,kelv9's hypo!sis t life may be1 & may h be51 dissem9at$ across ! b\nds ( space1 ?r\gh\t ! sol> sy/em & ! :ole univ]se6 ,x may well be t we ne$ atta* no great practical importance to ?is bold conception2 = ev5 ?\gh /ell> space be %ewn to be m>e lib]um to m9ute mat]ial travell]s1 we may be sure t ^? :i* rea* a /ell> or ev5 a planet>y b\rne are inf9itely1 or all b inf9itely1 few4 ,b :e!r or no1 ! remote possibilities ( ! case s]ve to illu/rate 9 a v vivid way ! pr(\nd diff]5ces ( physical prop]ty & pot5tiality :i* are associat$ 9 ! scale ( magnitude ) simple diff]5ces ( degree4 #ej ,,*apt] ,,iii ,,! ,,rate ,,( ,,gr[? ,:5 we /udy magnitude by itself1 ap>t1 t is to say1 f ! gradual *anges to :i* x may be subject1 we are deal+ ) a some?+ :i* may be adequately repres5t$ by a numb]1 or by means ( a l9e ( def9ite l5g?2 x is :at ma!maticians call a scal> ph5om5on4 ,:5 we introduce ! conception ( *ange ( magnitude1 ( magnitude :i* v>ies z we pass f "o direction to ano!r 9 space1 or f "o in/ant to ano!r 9 "t1 our ph5om5on becomes capable ( repres5tation by means ( a l9e ( :i* we def9e bo? ! l5g? & ! direction2 x is 79 ?is p>ticul> aspect7 :at is call$ a vector ph5om5on4 ,:5 we deal ) magnitude 9 relation to ! dim5sions ( space1 ! vector diagram :i* we draw plots magnitude 9 "o direction aga9/ magnitude 9 ano!r1--l5g? aga9/ height1 = in/ance1 or aga9/ bread?2 & ! result is simply :at we call a picture or draw+ ( an object1 or 7m correctly7 a 8plane projection0 ( ! object4 ,9 o!r words1 :at we call ,=m is a ratio ( magnitudes1 ref]r$ to direction 9 space4 ,:5 9 deal+ ) magnitude we ref] its v>iations to successive int]vals ( "t 7or :51 z x is said1 we equate x ) "t71 we are !n deal+ ) ! ph5om5on ( gr[?2 & x is evid5t1 !re=e1 t ?is t]m gr[? has wide mean+s4 ,= gr[? may obvi\sly be positive or negative2 t is to say1 a ?+ may gr[ l>g] or small]1 great] or less2 & by ext5sion ( ! primitive concrete signification ( ! ^w1 we easily & legitimately apply x to non-mat]ial ?+s1 su* z temp]ature1 & say1 = in/ance1 t a body 8gr[s0 hot or cold4 ,:5 9 a two-dim5sional diagram1 we repres5t a magnitude 7= in/ance l5g?7 9 relation to "t 7or 8plot0 #ea l5g? aga9/ "t1 z ! phrase is71 we get t k9d ( vector diagram :i* is commonly kn[n z a 8curve ( gr[?40 ,we p]ceive1 accord+ly1 t ! ph5om5on :i* we are n[ /udy+ is a velocity 7^: 8dim5sions0 are ,space_/,"t or ,l_/,t72 & ?is ph5om5on we %all speak (1 simply1 z a rate ( gr[?4 ,9 v>i\s conv5tional ways we c conv]t a two-dim5sional into a ?ree-dim5sional diagram4 ,we d s1 = example1 by means ( ! geometrical me?od ( 8p]spective0 :5 we repres5t ^u a %eet ( pap] ! l5g?1 bread? & dep? ( an object 9 ?ree-dim5sional space2 b we d x m simply1 z a rule1 by means ( 8cont\r-l9es10 & always :5 "t is "o ( ! dim5sions to be repres5t$4 ,if we sup]impose ^u "o ano!r 7or ev5 set side by side7 pictures1 or plane projections1 ( an organism1 drawn at successive int]vals ( "t1 we h su* a ?ree-dim5sional diagram1 :i* is a p>tial repres5tation 7limit$ to two dim5sions ( space7 ( ! organism's gradual *ange ( =m1 or c\rse ( developm5t2 & 9 su* a case our cont\r-l9es may1 = ! purposes ( ! embryologi/1 be sep>at$ by int]vals repres5t+ a few h\rs or days1 or1 = ! purposes ( ! palaeontologi/1 by int]spaces ( unnumb]$ & innum]able ye>s#gi4 ,su* a diagram repres5ts 9 two ( its ?ree dim5sions =m1 & 9 two1 or ?ree1 ( its dim5sions gr[?2 & s we see h[ intimately ! two conceptions are correlat$ or int]-relat$ to "o ano!r4 ,9 %ort1 x is obvi\s t ! =m ( an animal is det]m9$ by its specific rate ( gr[? 9 v>i\s directions2 accord+ly1 ! ph5om5on ( rate ( gr[? des]ves to be /udi$ z a necess>y prelim9>y to ! !oretical /udy ( =m1 &1 ma!matically speak+1 organic =m itself appe>s to u z a function ( "t#hj4 #eb ,at ! same "t1 we ne$ only consid] ?is "p ( our subject some:at briefly4 ,?\gh x has an ess5tial be>+ on ! problems ( morphology1 x is 9 great] degree involv$ ) physiological problems2 & fur!rmore1 ! /ati/ical or num]ical aspect ( ! "q is peculi>ly adapt$ = ! ma!matical /udy ( v>iation & correlation4 ,on ^! important subjects we %all sc>cely t\*2 = our ma9 purpose w be suffici5tly s]v$ if we consid] ! *>act]i/ics ( a rate ( gr[? 9 a few illu/rative cases1 & recognise t ?is rate ( gr[? is a v important specific prop]ty1 ) its own *>act]i/ic value 9 ?is organism or t1 9 ?is or t "p ( ea* organism1 & 9 ?is or t phase ( its exi/5ce4 ,! /atem5t :i* we h j made t 8! =m ( an organism is det]m9$ by its rate ( gr[? 9 v>i\s directions10 is "o :i* calls 7z we h p>tly se5 9 ! =ego+ *apt]7 = fur!r explanation & = "s measure ( qualification4 ,among organic =ms we %all h frequ5t occasion to see t =m is 9 _m cases due to ! imm$iate or direct action ( c]ta9 molecul> =ces1 ( :i* surface-t5sion is t :i* plays ! greate/ "p4 ,n[ :5 surface-t5sion 7= in/ance7 causes a m9ute semi-fluid organism to assume a sph]ical =m1 or gives ! =m ( a cat5>y or an ela/ic curve to a film ( protoplasm 9 contact ) "s solid skeletal rod1 or :5 x acts 9 v>i\s o!r ways :i* are productive ( def9ite cont\rs1 ?is is a process ( con=mation t1 bo? 9 appe>ance & reality1 is v diff]5t f ! process by :i* an ord9>y plant or animal gr[s into its specific =m4 ,9 bo? cases1 *ange ( =m is br\ght ab\t by ! movem5t ( portions ( matt]1 & 9 bo? cases x is ultimately due to ! action ( molecul> =ces2 b 9 ! "o case ! movem5ts ( ! p>ticles ( matt] lie = ! mo/ "p )9 molecul> range1 :ile 9 ! o!r we h to deal *iefly ) ! transf]5ce ( portions ( matt] into ! sy/em f )\t1 & f "o widely di/ant "p ( ! organism to ano!r4 ,x is to ?is latt] class ( ph5om5a t we usually re/rict ! t]m gr[?2 & x is 9 reg>d to !m t we are 9 a position to /udy ! rate ( action 9 diff]5t directions1 & to see t x is m]ely on a diff]5ce ( velocities t ! modification ( =m ess5tially dep5ds4 #ec ,! diff]5ce betwe5 ! two classes ( ph5om5a is some:at ak9 to ! diff]5ce betwe5 ! =ces :i* det]m9e ! =m ( a ra9-drop & ^? :i*1 by ! fl[+ ( ! wat]s & ! sculptur+ ( ! solid e>?1 h br\ght ab\t ! complex configuration ( a riv]2 molecul> =ces are p>am\nt 9 ! con=mation ( ! "o1 & mol> =ces are dom9ant 9 ! o!r4 ,at ! same "t x is p]fectly true t all *anges ( =m1 inasmu* z !y necess>ily involve *anges ( actual & relative magnitude1 may1 9 a s5se1 be prop]ly look$ ^u z ph5om5a ( gr[?2 & x is also true1 s9ce ! movem5t ( matt] mu/ always involve an elem5t ( "t#ha1 t 9 all cases ! rate ( gr[? is a ph5om5on to be consid]$4 ,ev5 ?\gh ! molecul> =ces :i* play _! "p 9 modify+ ! =m ( an organism ex]t an action :i* is1 !oretically1 all b in/antane\s1 t action is apt to be dragg$ out to an appreciable int]val ( "t by reason ( viscosity or "s o!r =m ( resi/ance 9 ! mat]ial4 ,f ! physical or physiological po9t ( view ! rate ( action ev5 9 su* cases may be well wor? /udy+2 = example1 a /udy ( ! rate ( cell-division 9 a segm5t+ egg may tea* u some?+ ab\t ! "w done1 & ab\t ! v>i\s en]gies conc]n$4 ,b 9 su* cases ! action is1 z a rule1 s homog5e\s1 & ! =m f9ally atta9$ is s def9ite & s little dep5d5t on ! "t tak5 to effect x1 t ! specific rate ( *ange1 or rate ( gr[?1 does n ent] into ! morphological problem4 ,to sum up1 we may lay d[n ! foll[+ g5]al /atem5ts4 ,! =m ( organisms is a ph5om5on to be ref]r$ 9 "p to ! direct action ( molecul> =ces1 9 "p to a m complex & sl[] process1 indirectly result+ f *emical1 osmotic & o!r =ces1 by :i* mat]ial is introduc$ into ! organism & transf]r$ f "o "p ( x to ano!r4 ,x is ?is latt] complex ph5om5on :i* we usually speak ( z 8gr[?40 #ed ,e gr[+ organism1 & e "p ( su* a gr[+ organism1 has its own specific rate ( gr[?1 ref]r$ to a p>ticul> direction4 ,x is ! ratio betwe5 ! rates ( gr[? 9 v>i\s directions by :i* we mu/ acc\nt = ! ext]nal =ms ( all1 save c]ta9 v m9ute1 organisms4 ,?is ratio betwe5 rates ( gr[? 9 v>i\s directions may sometimes be ( a simple k9d1 z :5 x results 9 ! ma!matically def9able outl9e ( a %ell1 or 9 ! smoo? curve ( ! m>g9 ( a leaf4 ,x may sometimes be a v con/ant "o1 9 :i* case ! organism1 :ile gr[+ 9 bulk1 suff]s little or no p]ceptible *ange 9 =m2 b su* equilibrium seldom endures = m ?an a season1 & :5 ! ratio t5ds to alt]1 !n we h ! ph5om5on ( morphological 8developm5t10 or /eady & p]si/5t *ange ( =m4 ,?is elem5t>y concept ( ,=m1 z det]m9$ by v>y+ rates ( ,gr[?1 0 cle>ly appreh5d$ by ! ma!matical m9d ( ,hall]1--:o _h le>n$ 8 ma!matics ( ! great ,john ,b]n\lli1 z ! latt] 9 turn _h le>n$ 8 physiology f ! writ+s ( ,borelli4 ,inde$ x 0 ?is v po9t1 ! app>5tly unlimit$ ext5t to :i*1 9 ! developm5t ( ! *ick1 inequalities ( gr[? c\ld & did produce *anges ( =m & *anges ( anatomical 8/ructure10 t l$ ,hall] to surmise t ! process 0 actually )\t limits1 & t all developm5t 0 b an unfold+1 or 8evolutio10 9 :i* no "p came into be+ :i* _h n ess5tially exi/$ be=e#hb4 ,9 %ort ! celebrat$ doctr9e ( 8pre=mation0 impli$ on ! "o h& a cle> recognition ( :at1 ?r\gh\t ! lat] /ages ( developm5t1 gr[? c d1 by ha/5+ ! increase 9 size ( "o "p1 h9d]+ t ( ano!r1 *ang+ _! relative magnitudes & positions1 & alt]+ _! =ms2 :ile on ! o!r h& x betray$ a failure 7inevitable 9 ^? days7 to recognise ! ess5tial diff]5ce betwe5 ^! movem5ts ( masses & ! molecul> processes :i* prec$e & accompany #ee !m1 & :i* are *>act]i/ic ( ano!r ord] ( magnitude4 ,by o!r writ]s besides ,hall] ! v g5]al1 ?\gh n /rictly univ]sal connection betwe5 =m & rate ( gr[? has be5 cle>ly recognis$4 ,su* a connection is implicit 9 ^? 8proportional diagrams0 by :i* ,dr] & "s ( 8 bro!r arti/s 7 wont to illu/rate ! successive *anges ( =m1 or ( relative dim5sions1 :i* att5d ! gr[? ( ! *ild1 to boyhood & to manhood4 ,! same connection 0 recognis$1 m explicitly1 by "s ( ! old] embryologi/s1 = in/ance by ,p&]#hc1 & appe>s1 z a survival ( ! doctr9e ( pre=mation1 9 8 /udy ( ! developm5t ( ! *ick4 ,& long aft]w>ds1 ! embryological aspect ( ! case 0 emphasis$ by ,81 :o po9t$ out1 = in/ance1 t ! v>i\s fold+s ( ! bla/od]m1 by :i* ! neural & amniotic folds 7 br\ght into be+1 7 ess5tially & obvi\sly ! resultant ( unequal rates ( gr[?1--( local accel]ations or ret>dations ( gr[?1--9 :at to beg9 ) 0 an ev5 & uni=m lay] ( embryonic tissue4 ,if we imag9e a flat %eet ( pap]1 p>ts ( :i* are caus$ 7z by moi/ure or evaporation7 to exp& or to contract1 ! plane surface is at once dimpl$1 or 8buckl$10 or fold$1 by ! resultant =ces ( expansion or contraction3 & ! v>i\s di/ortions to :i* ! plane surface ( ! 8g]m9al disc0 is subject1 z ,8 %ew$ once & = all1 are precisely analog\s4 ,an exp]im5tal demon/ration /ill m closely comp>able to ! actual case ( ! bla/od]m1 is obta9$ by mak+ an 8artificial bla/od]m10 ( little pills or pellets ( d\gh1 :i* are caus$ to gr[1 ) v>y+ velocities1 by ! addition ( v>y+ quantities ( yea/4 ,"h1 z ,r\x is c>eful to po9t out#hd1 we obs]ve t x is n only ! gr[? ( ! individual cells1 b ! traction ex]cis$ ?r\gh _! mutual int]connections1 :i* br+s ab\t ! fold+s & o!r di/ortions ( ! entire /ructure4 #ef ,b ?is aga9 0 cle>ly pres5t to ,hall]'s m9d1 & =m$ an ess5tial "p ( 8 embryological doctr9e4 ,= he has no soon] treat$ ( increm5tum1 or cel]itas increm5ti1 ?an he proce$s to deal ) ! contributory & complem5t>y ph5om5a ( expansion1 traction 7adtractio7#he1 & pressure1 & ! m subtle influ5ces :i* he d5om9ates vis d]ivationis et revulsionis#hf3 ^! latt] be+ ! second>y & correlat$ effects on gr[? 9 "o "p1 br\ght ab\t1 ?r\gh su* *anges z are produc$ 7= in/ance7 9 ! circulation1 by ! gr[? ( ano!r4 ,let u admit t1 on ! physiological side1 ,hall]'s or ,8's me?ods ( explanation c>ry u back b a little way2 yet ev5 ?is little way is some?+ ga9$4 ,nev]!less1 ,i c well rememb] ! h>% criticism1 & ev5 contempt1 :i* ,8's doctr9e met )1 n m]ely on ! gr\nd t x 0 inadequate1 b because su* an explanation 0 deem$ :olly inappropriate1 & 0 utt]ly disav[$#hg4 ,h]twig1 = in/ance1 ass]t$ t1 9 embryology1 :5 we f\nd "o embryonic /age prec$+ ano!r1 ! exi/5ce ( ! =m] 01 = ! embryologi/1 an all-suffici5t 8causal explanation0 ( ! latt]4 8,we consid] 7he says71 t we are /udy+ & expla9+ a causal relation :5 we h demon/rat$ t ! ga/rula arises by invag9ation ( a bla/osph]e1 or ! neural canal by ! infold+ ( a cell plate s z to con/itute a tube#hh40 ,= ,h]twig1 !re=e1 z #eg ,r\x rem>ks1 ! task ( inve/igat+ a physical me*anism 9 embryology1--8d] ,ziel das ,wirk5 zu er=s*510--has no exi/5ce at all4 ,= ,balf\r also1 z = ,h]twig1 ! me*anical or physical aspect ( organic developm5t _h little or no attraction4 ,9 "o notable in/ance1 ,balf\r himself adduc$ a physical1 or quasi-physical1 explanation ( an organic process1 :5 he ref]r$ ! v>i\s modes ( segm5tation ( an ovum1 complete or p>tial1 equal or unequal & s =?1 to ! v>y+ am\nt or ! v>y+ di/ribution ( food yolk 9 association ) ! g]m9al protoplasm ( ! egg#hi4 ,b 9 ! ma91 ,balf\r1 l all ! o!r embryologi/s ( 8 day1 0 engross$ by ! problems ( phylog5y1 & he expressly def9$ ! aims ( comp>ative embryology 7z exemplifi$ 9 8 own textbook7 z be+ 8tw(old3 7#a7 to =m a basis = ,phylog5y4 & 7#b7 to =m a basis = ,organog5y or ! orig9 & evolution ( organs#ij40 ,x has be5 ! great s]vice ( ,r\x & 8 fell[-work]s ( ! s*ool ( 8,entwickelungsme*anik10 & ( _m o!r /ud5ts to ^: "w we %all ref]1 to try1 z ,8 tri$#ia to import into embryology1 :]ev] possible1 ! simpl] concepts ( physics1 to introduce along ) !m ! me?od ( exp]im5t1 & to refuse to be b\nd by ! n>r[ limitations :i* su* tea*+ z t ( ,h]twig w\ld ( necessity impose on ! "w & ! ?\ght & on ! :ole philosophy ( ! biologi/4 ,be=e we pass f ?is g5]al discussion to /udy "s ( ! p>ticul> ph5om5a ( gr[?1 let me give a s+le illu/ration1 f ,d>w91 ( a po9t ( view :i* is 9 m>k$ contra/ to ,hall]'s simple b ess5tially ma!matical conception ( ,=m4 ,!re is a curi\s passage 9 ! ,orig9 ( ,species#ib1 :]e ,d>w9 is discuss+ ! lead+ facts ( embryology1 & 9 p>ticul> ,von ,ba]'s 8law ( embryonic resemblance40 ,"h ,d>w9 says 8,we are s mu* accu/om$ to see a diff]5ce 9 #eh /ructure betwe5 ! embryo & ! adult1 t we are tempt$ to look at ?is diff]5ce z 9 "s necess>y mann] cont+5t on gr[?4 ,b !re is no reason :y1 = in/ance1 ! w+ ( a bat1 or ! f9 ( a porpoise1 %\ld n h be5 sket*$ out ) all _! p>ts 9 prop] proportion1 z soon z any "p became visible40 ,aft] po9t+ out ) 8 habitual c>e v>i\s exceptions1 ,d>w9 proce$s to lay d[n two g5]al pr9ciples1 viz4 8t slight v>iations g5]ally appe> at a n v e>ly p]iod ( life10 & secondly1 t 8at :atev] age a v>iation fir/ appe>s 9 ! p>5t1 x t5ds to reappe> at a correspond+ age 9 ! (fspr+40 ,he !n argues t x is ) nature z ) ! fanci]1 :o does n c>e :at 8 pigeons look l 9 ! embryo1 s long z ! full-gr[n bird possesses ! desir$ qualities2 & t ! process ( selection takes place :5 ! birds or o!r animals are ne>ly gr[n up1--at lea/ on ! "p ( ! bre$]1 & presumably 9 nature z a g5]al rule4 ,! illu/ration ( ^! pr9ciples is set =? z foll[s2 8,let u take a gr\p ( birds1 desc5d$ f "s anci5t =m & modifi$ ?r\gh natural selection = diff]5t habits4 ,!n1 f ! _m successive v>iations hav+ sup]v5$ 9 ! sev]al species at a n v e>ly age1 & hav+ be5 inh]it$ at a correspond+ age1 ! "y w /ill resemble ea* o!r mu* m closely ?an d ! adults1--j z we h se5 ) ! bre$s ( ! pigeon 4444 ,:atev] influ5ce long-cont9u$ use or disuse may h _h 9 modify+ ! limbs or o!r p>ts ( any species1 ?is w *iefly or solely h affect$ x :5 ne>ly mature1 :5 x 0 compell$ to use its full p[]s to ga9 its own liv+2 & ! effects ?us produc$ w h be5 transmitt$ to ! (fspr+ at a correspond+ ne>ly mature age4 ,?us ! "y w n be modifi$1 or w be modifi$ only 9 a slight degree1 ?r\gh ! effects ( ! increas$ use or disuse ( p>ts40 ,?is :ole argum5t is rem>kable1 9 m ways ?an we ne$ try to deal ) "h2 b x is especially rem>kable t ,d>w9 %\ld beg9 by ca/+ d\bt ^u ! broad fact t a 8diff]5ce 9 /ructure betwe5 ! embryo & ! adult0 is 89 "s necess>y mann] cont+5t on gr[?02 & t he %\ld see no reason :y complicat$ /ructures ( ! adult 8%\ld n h be5 sket*$ out #ei ) all _! p>ts 9 prop] proportion1 z soon z any "p became visible40 ,x w\ld seem to me t ev5 ! mo/ elem5t>y att5tion to =m 9 its relation to gr[? w\ld h remov$ mo/ ( ,d>w9's difficulties 9 reg>d to ! p>ticul> ph5om5a :i* he is "h consid]+4 ,= ^! ph5om5a are ph5om5a ( =m1 & !re=e ( relative magnitude2 & ! magnitudes 9 "q are atta9$ by gr[?1 proce$+ ) c]ta9 specific velocities1 & la/+ = c]ta9 long p]iods ( "t4 ,& x is accord+ly obvi\s t 9 any two relat$ individuals 7:e!r specifically id5tical or n7 ! diff]5ces betwe5 !m mu/ manife/ !mselves gradually1 & be b little app>5t 9 ! "y4 ,x is = ! same simple reason t animals :i* are ( v diff]5t sizes :5 adult1 diff] less & less 9 size 7z well z 9 =m7 z we trace !m backw>ds ?r\gh ! foetal /ages4 ,?\gh we /udy ! visible effects ( v>y+ rates ( gr[? ?r\gh\t wellnigh all ! problems ( morphology1 x is n v (t5 t we c directly measure ! velocities conc]n$4 ,b ow+ to ! obvi\s und]ly+ importance :i* ! ph5om5on has to ! morphologi/ we mu/ make %ift to /udy x :]e we c1 ev5 ?\gh our illu/rative cases may seem to h little imm$iate be>+ on ! morphological problem#ic4 ,9 a v simple organism1 ( sph]ical symmetry1 su* z ! s+le sph]ical cell ( ,protococcus or ( ,orbul9a1 gr[? is r$uc$ to its simple/ t]ms1 & inde$ x becomes s simple 9 its outw>d manife/ations t x is no long] ( special int]e/ to ! morphologi/4 ,! rate ( gr[? is measur$ by ! rate ( *ange 9 l5g? ( a radius1 i4e4 ,v 7,r ,r7_/,t1 & f ?is we may calculate1 z already indicat$1 ! rate ( gr[? 9 t]ms ( surface & ( volume4 ,! gr[+ body rema9s ( con/ant =m1 ow+ to ! symmetry ( ! sy/em2 because1 t is to say1 on ! "o h& ! pressure ex]t$ by ! gr[+ protoplasm is ex]t$ equally 9 all directions1 aft] ! mann] ( a hydro/atic pressure1 :i* inde$ x actually is3 :ile on ! o!r h&1 ! 8sk90 or surface lay] ( ! cell is suffici5tly #fj homog5e\s to ex]t at e po9t an approximately uni=m resi/ance4 ,"u ^! conditions !n1 ! rate ( gr[? is uni=m 9 all directions1 & does n affect ! =m ( ! organism4 ,b 9 a l>g] or a m complex organism ! /udy ( gr[?1 & ( ! rate ( gr[?1 pres5ts u ) a v>iety ( problems1 & ! :ole ph5om5on becomes a factor ( great morphological importance4 ,we no long] f9d t x t5ds to be uni=m 9 all directions1 nor h we any "r to expect t x %\ld4 ,! resi/ances :i* x meets ) w no long] be uni=m4 ,9 "o direction b n 9 o!rs x w be oppos$ by ! important resi/ance ( gravity2 & )9 ! gr[+ sy/em itself all mann] ( /ructural diff]5ces w come into play1 sett+ up unequal resi/ances to gr[? by ! v>y+ rigidity or viscosity ( ! mat]ial sub/ance 9 "o direction or ano!r4 ,at ! same "t1 ! actual s\rces ( gr[?1 ! *emical & osmotic =ces :i* lead to ! intussusception ( new matt]1 are n uni=mly di/ribut$2 "o tissue or "o organ may well manife/ a t5d5cy to increase :ile ano!r does n2 a s]ies ( bones1 _! int]v5+ c>tilages1 & _! surr\nd+ muscles1 may all be capable ( v diff]5t rates ( increm5t4 ,! diff]5ces ( =m :i* are ! resultants ( ^! diff]5ces 9 rate ( gr[? are especially manife/$ dur+ t "p ( life :5 gr[? itself is rapid3 :5 ! organism1 z we say1 is und]go+ its developm5t4 ,:5 gr[? 9 g5]al has become sl[1 ! relative diff]5ces 9 rate betwe5 diff]5t p>ts ( ! organism may /ill exi/1 & may be made manife/ by c>eful obs]vation1 b 9 _m1 or p]haps 9 mo/ cases1 ! resultant *ange ( =m does n /rike ! eye4 ,great z are ! diff]5ces betwe5 ! rates ( gr[? 9 diff]5t p>ts ( an organism1 ! m>vel is t ! ratios betwe5 !m are s nicely balanc$ z !y actually are1 & s capable1 accord+ly1 ( keep+ = long p]iods ( "t ! =m ( ! gr[+ organism all b un*ang$4 ,!re is ! nice/ possible balance ( =ces & resi/ances 9 e "p ( ! complex body2 & :5 ?is normal equilibrium is di/urb$1 !n we get abnormal gr[?1 9 ! %ape ( tum\rs1 exo/oses1 & mal=mations ( e k9d4 #fa ,! rate ( gr[? 9 ,man4 ,man w s]ve u z well z ano!r organism = our fir/ illu/rations ( rate ( gr[?2 & we _c d bett] ?an g = our fir/ data conc]n+ him to ,quetelet's ,an?ropomtrie#id1 an epo*-mak+ book = ! biologi/4 ,= n only is x pack$ ) in=mation1 "s ( x /ill unsurpass$1 9 reg>d to human gr[? & =m1 b x also m]its our highe/ admiration z ! fir/ great essay 9 sci5tific /ati/ics1 & ! fir/ "w 9 :i* organic v>iation 0 discuss$ f ! po9t ( view ( ! ma!matical !ory ( probabilities4 ,illu/ration3 ,fig4 #c4 ,curve ( ,gr[? 9 ,man1 f bir? to #bj yrs 772 f ,quetelet's ,belgian data4 ,! upp] curve ( /ature f ,b[dit*'s ,bo/on data4 ,if ! *ild be "s #bj in*es1 or say #ej cm4 tall at bir?1 & ! man "s six feet high1 or say #ahj cm41 at tw5ty1 we may say t 8 av]age rate ( gr[? has be5 7#ahj #ej7_/bj cm41 or #fe c5timetres p] annum4 ,b we "k v well t ?is is #fb b a v r\gh prelim9>y /atem5t1 & t ! boy grew quickly dur+ "s1 & sl[ly dur+ o!r1 ( 8 tw5ty ye>s4 ,x becomes necess>y !re=e to /udy ! ph5om5on ( gr[? 9 successive small portions2 to /udy1 t is to say1 ! successive l5g?s1 or ! successive small diff]5ces1 or increm5ts1 ( l5g? 7or ( weight1 etc471 atta9$ 9 successive %ort increm5ts ( "t4 ,?is we d 9 ! fir/ in/ance 9 ! usual way1 by ! 8graphic me?od0 ( plott+ l5g? aga9/ "t1 & s con/ruct+ our 8curve ( gr[?40 ,our curve ( gr[?1 :e!r ( weight or l5g? 7,fig4 #c71 has always a c]ta9 *>act]i/ic =m1 or *>act]i/ic curvature4 ,?is is our imm$iate pro( ( ! fact t ! rate ( gr[? *anges z "t goes on2 = _h x n be5 s1 _h an equal increm5t ( l5g? be5 add$ 9 ea* equal int]val ( "t1 our 8curve0 w\ld h appe>$ z a /raight l9e4 ,su* z x is1 x tells u n only t ! rate ( gr[? t5ds to alt]1 b t x alt]s 9 a def9ite & ord]ly way2 =1 subject to v>i\s m9or int]ruptions1 due to second>y causes1 our curves ( gr[? are1 on ! :ole1 8smoo?0 curves4 ,! curve ( gr[? = l5g? or /ature 9 man indicates a rapid increase at ! outset1 t is to say dur+ ! quick gr[? ( babyhood2 a long p]iod ( sl[]1 b /ill rapid & almo/ /eady gr[? 9 e>ly boyhood2 z a rule a m>k$ quick5+ soon aft] ! boy is 9 8 te5s1 :5 he comes to 8! gr[+ age02 & f9ally a gradual arre/ ( gr[? z ! boy 8comes to 8 full height10 & rea*es manhood4 ,if we c>ri$ ! curve fur!r1 we %\ld see a v curi\s ?+4 ,we %\ld see t a man's full /ature endures b = a spell2 long be=e fifty#ie x has begun to abate1 by sixty x is notably less5$1 9 extreme old age ! old man's frame is %runk5 & x is b a memory t 8he once 0 tall40 ,we h already se51 & "h we see aga91 t gr[? may h a 8negative value40 ,! ph5om5on ( negative gr[? 9 old age ext5ds to weight also1 & is evid5tly l>gely *emical 9 orig93 ! organism c no long] add new mat]ial to its fabric fa/ en\gh to keep pace ) ! wa/age ( "t4 ,our curve #fc ( gr[? is 9 fact a diagram ( activity1 or 8"t-en]gy0 diagram#if4 ,z ! organism gr[s x is absorb+ en]gy beyond its daily ne$s1 & accumulat+ x at a rate depict$ 9 our ,/ature1 weight1 & span ( out/ret*$ arms4 7,aft] ,quetelet1 pp4 #aic1 #cdf47 ,/ature 9 metres ,weight 9 kgm4 ,span ( ratio arms1 ( /ature ,age ,male ,female ,f_/,m ,male ,female ,f_/,m male to span #j #jejj #jdid #ihh #cb #bi #ijg #jdif #ajjh #a #jfih #jfij #ihh #id #hh #icf #jfie #ajjd #b #jgia #jgha #ihg #aac #ajg #idg #jghi #ajjc #c #jhfd #jhed #ihh #abd #aah #ieb #jhfc #ajja #d #jibg #jiae #ihg #adb #acj #iae #jibg #ajjj #e #jihg #jigd #ihg #aeh #add #iaa #jihh #iii #f #ajdf #ajca #ihe #agb #afj #icj #ajdh #iih #g #aajd #ajhg #ihd #aia #age #iaf #aajg #iig #h #aafb #aadb #ihb #bjh #aia #iah #aaff #iif #i #abah #aaif #ihb #bbf #bad #idg #abbd #iie #aj #abgc #abdi #iha #bde #bce #iei #abha #iid #aa #acbe #acja #ihb #bga #bef #ide #acce #iib #ab #acge #aceb #ihc #bih #bih #ajjj #achh #iia #ac #adbc #adjj #ihd #cdd #cbi #ief #adch #ihi #ad #adfi #addf #ihd #chh #cfg #idf #adhi #ihg #ae #aeac #adhh #ihc #dcf #djd #ibg #aech #iid #af #aeed #aeba #igh #dig #dcf #hgg #aehd #iha #ag #aeid #aedf #igj #ebh #dgc #hif #afcj #igi #ah #afcj #aefc #iei #egh #dij #hdh #afgj #igf #ai #afee #aegj #idi #ehj #eaf #hij #agje #iga #bj #affi #aegd #idc #fja #ebc #hgj #agbh #iff #be #afhb #aegh #ich #fbi #ecc #hdg #agca #igb #cj #afhf #aehj #icg #fcg #edc #hec #agff #iee #dj #afhf #aehj #icg #fcg #eeb #hfg #agff #iee #ej #afhf #aehj #icg #fce #efb #hhd -- -- #fj #afgf #aega #icg #fai #edc #hgg -- -- #gj #affj #aeef #icg #eie #eae #hfe -- -- #hj #afcf #aecd #ich #egh #did #hee -- -- #ij #afaj #aeaj #ich #egh #dic #hec -- -- curve2 b ! "t comes :5 x accumulates no long]1 & at la/ x is con/ra9$ to draw ^u its dw9dl+ /ore4 ,b 9 "p1 ! sl[ decl9e 9 /ature is an expression ( an unequal conte/ betwe5 our bodily p[]s & ! un*ang+ =ce ( gravity1 #fd :i* draws u d[n :5 we w\ld fa9 rise up#ig4 ,= aga9/ gravity we fight all our days1 9 e movem5t ( our limbs1 9 e beat ( our he>ts2 x is ! indomitable =ce t defeats u 9 ! end1 t lays u on our dea?b$1 t l[]s u to ! grave#ih4 ,side by side ) ! curve :i* repres5ts gr[? 9 l5g?1 or /ature1 our diagram %[s ! curve ( weight#ii4 ,t ?is curve is ( a v diff]5t %ape f ! =m] "o1 is acc\nt$ = 9 ! ma9 7?\gh n :olly7 by ! fact :i* we h already dealt )1 t1 :atev] be ! law ( increm5t 9 a l9e> dim5sion1 ! law ( increase 9 volume1 & !re=e 9 weight1 w be t ^! latt] magnitudes t5d to v>y z ! cubes ( ! l9e> dim5sions4 ,?is h[ev] does n acc\nt = ! *ange ( direction1 or 8po9t ( inflection0 :i* we obs]ve 9 ! curve ( weight at ab\t "o or two ye>s old1 nor = c]ta9 o!r diff]5ces betwe5 our two curves :i* ! scale ( our diagram does n yet make cle>4 ,^! diff]5ces are due to ! fact t ! =m ( ! *ild is alt]+ ) gr[?1 t o!r l9e> dim5sions are v>y+ some:at diff]5tly f l5g? or /ature1 & t consequ5tly ! gr[? 9 bulk or weight is foll[+ a m complicat$ law4 ,our curve ( gr[?1 :e!r = weight or l5g?1 is a direct picture ( velocity1 = x repres5ts1 z a connect$ s]ies1 ! successive epo*s ( "t at :i* successive weights or l5g?s are atta9$4 ,b1 z we h already 9 "p se51 a great "p ( ! int]e/ ( our curve lies 9 ! fact t we c see f x1 n only t l5g? 7or "s o!r magnitude7 is *ang+1 b t ! rate ( *ange ( magnitude1 or rate ( gr[?1 is itself *ang+4 ,we h1 9 %ort1 to /udy ! ph5om5on ( accel]ation3 we h begun by /udy+ a velocity1 or rate ( #fe *ange ( magnitude2 we mu/ n[ /udy an accel]ation1 or rate ( *ange ( velocity4 ,! rate1 or velocity1 ( gr[? is measur$ by ! slope ( ! curve2 :]e ! curve is /eep1 x means t gr[? is rapid1 & :5 gr[? ceases ! curve appe>s z a horizontal l9e4 ,if we c f9d a means1 !n1 ( repres5t+ at successive epo*s ! correspond+ slope1 or /eepness1 ( ! curve1 we %all h obta9$ a picture ( ! rate ( *ange ( velocity1 or ! accel]ation ( gr[?4 ,! measure ( ! /eepness ( a curve is giv5 by ! tang5t to ! curve1 or we may e/imate x by tak+ = equal int]vals ( "t 7/rictly speak+1 = ea* inf9itesimal int]val ( "t7 ! actual increm5t add$ dur+ t int]val ( "t3 & 9 practice ?is simply am\nts to tak+ ! successive diff]5ces betwe5 ! values ( l5g? 7or ( weight7 = ! successive ages :i* we h begun by /udy+4 ,if we !n plot ^! successive diff]5ces aga9/ "t1 we obta9 a curve ea* po9t ^u :i* repres5ts a velocity1 & ! :ole curve indicates ! rate ( *ange ( velocity1 & we call x an accel]ation-curve4 ,x conta9s1 9 tru?1 no?+ :atsoev] t 0 n implicit 9 our =m] curve2 b x makes cle> to our eye1 & br+s )9 ! rea* ( fur!r inve/igation1 ph5om5a t 7 h>d to see 9 ! o!r mode ( repres5tation4 ,! accel]ation-curve ( height1 :i* we "h illu/rate1 9 ,fig4 #d1 is v diff]5t 9 =m f ! curve ( gr[? :i* we h j be5 look+ at2 & x happ5s t1 9 ?is case1 !re is a v m>k$ diff]5ce betwe5 ! curve :i* we obta9 f ,quetelet's data ( gr[? 9 height & t :i* we may draw f any o!r s]ies ( obs]vations kn[n to me f ,briti%1 ,fr5*1 ,am]ican or ,g]man writ]s4 ,x beg9s 7z w be se5 f our next table7 at a v high level1 su* z x nev] aft]w>ds atta9s2 & /ill /&s too high1 dur+ ! fir/ ?ree or f\r ye>s ( life1 to be repres5t$ on ! scale ( ! accompany+ diagram4 ,f ^! high velocities x falls away1 on ! :ole1 until ! age :5 gr[? itself ceases1 & :5 ! rate ( gr[?1 accord+ly1 has1 = "s ye>s toge!r1 ! con/ant value ( nil2 b ! rate ( fall1 or rate ( *ange ( velocity1 is subject to sev]al *anges or int]ruptions4 ,dur+ ! fir/ ?ree or f\r ye>s ( life ! fall is cont9u\s & rapid1 #ff b x is some:at arre/$ = a :ile 9 *ildhood1 f ab\t five ye>s old to eight4 ,accord+ to ,quetelet's data1 !re is ano!r slight int]ruption 9 ! fall+ rate betwe5 ! ages ( ab\t f\rte5 & sixte52 b 9 place ( ?is almo/ insignificant int]ruption1 ! ,engli% & o!r /ati/ics indicate a sudd5 ,illu/ration3 ,fig4 #d4 ,mean annual increm5ts ( /ature 771 ,belgian & ,am]ican4 & v m>k$ accel]ation ( gr[? beg9n+ at ab\t twelve ye>s ( age1 & la/+ = ?ree or f\r ye>s2 :5 ?is p]iod ( accel]ation is ov]1 ! rate beg9s to fall aga91 & does s ) great rapidity4 ,we d n "k h[ f> ! abs5ce ( ?is /rik+ feature 9 ! ,belgian curve is due to ! imp]fections ( ,quetelet's data1 or :e!r x is a real & significant feature 9 ! small-/atur$ race :i* he inve/igat$4 ,annual ,increm5t ( ,/ature 79 cm47 f ,belgian & ,am]ican ,/ati/ics4 ,d3 ,belgian 7,quetelet1 p4 #cdd7 ,e3 ,p>is99 7,v>iot et ,*aumet1 p4 #ee7 ,f3 ,toronto 7,boas1 p4 #aedg7 ,g3 ,worce/]1 ,mass4 7,boas1 p4 #aedh7 ,h3 ,ann4 increm5t ,i3 ,increm5t ,j3 ,boys ,k3 ,girls ,v3 ,v>iability ( d4 ,d ,e ,f ,g ,height ,height ,i ,height ,v ,h ,h ,age 7,boys7 ,h ,j ,k ,j ,k 7,boys7 7#f7 ,h 7,j7 ,v 7,k7 ,v #j #ejj -- -- -- -- -- -- -- -- -- -- -- -- #a #fih #aih #gdb #gcf -- -- -- -- -- -- -- -- -- #b #gia #ic #hbg #hah #he #hb -- -- -- -- -- -- -- #c #hfd #gc #hia #hhd #fd #ff -- -- -- -- -- -- -- #d #ibg #fc #ifh #ieh #gg #gd -- -- -- -- -- -- -- #e #ihg #fj #ajcc #ajai #fe #fa #ajeij #ddj -- -- -- -- -- #f #ajdj #ei #ajii #ajhi #ff #gj #aaaeh #dfb #efh #fee #aeg #ege #jhh #g #aajd #eh #aadd #aach #de #di #aafhc #dic #ebe #egj #jfh #eij #jih #h #aafb #eh #aaig #aaie #ec #eg #abbjd #ecd #eba #ecg #jhf #egj #aaj #i #abah #ef #abej #abdg #ec #dh #abfia #edi #dhg #dhi #jif #eej #jig #aj #abgc #ee #acjc #abie #ec #eb #acagh #ege #dhg #eaj #ajc #eig #abc #aa #acbe #eb #accf #acdd #cc #di #acfbj #fai #ddb #ejb #jhh #fag #ahe #ab #acge #ej #acgf #adae #dj #ga #adjgd #fff #ded #dii #abf #fih #ahi #ac #adbc #dh #adea #adhf #ge #ga #adfjj #ged #ebf #eia #ahf #fga #bjf #ad #adfi #df #aech #aebi #hg #dc #aebci #hdi #fci #ghh #bci #edd #bhi #ae #aeac #dd #aeif #aedb #eh #ac #aeigb #hgh #gcc #fbc #bia #ecd #bga #af #aeed #da -- -- -- -- #afdij #ggc #eah #efd #cdf -- -- #ag #aeid #dj -- -- -- -- #afhia #gbb #dja -- -- -- -- #ah #afcj #cf -- -- -- -- #agajg #fgd #baf -- -- -- -- #ai #afee #be -- -- -- -- -- -- -- -- -- -- -- #bj #afgj #ae -- -- -- -- -- -- -- -- -- -- -- 99 ,ages f #a-b1 #b-c1 etc4 ,! epo*s are1 9 ?is table1 #ee1 #fe1 ye>s1 etc4 ,direct obs]vations on actual1 or individualis$1 increase ( /ature f ye> to ye>3 betwe5 ! ages ( #e-f1 #f-g1 etc4 ,ev5 ap>t f ^! data ( ,quetelet's 7:i* seem to con/itute an extreme case71 x is evid5t t !re are v #fh m>k$ diff]5ces betwe5 diff]5t races1 z we %all pres5tly see !re are betwe5 ! two sexes1 9 reg>d to ! epo*s ( accel]ation ( gr[?1 9 o!r words1 9 ! 8phase0 ( ! curve4 ,x is evid5t t1 if we pleas$1 we might repres5t ! rate ( *ange ( accel]ation on yet ano!r curve1 by con/ruct+ a table ( 8second diff]5ces02 ?is w\ld br+ out c]ta9 v int]e/+ ph5om5a1 :i* "h h[ev] we mu/ n /ay to discuss4 ,annual ,increm5t ( ,weight 9 ,man 7kgm474 7,aft] ,quetelet1 ,an?ropomtrie1 p4 #cdf9947 ,increm5t ,age ,male ,female #j-a #ei #ef #a-b #bj #bd #b-c #ae #ad #c-d #ae #ae #d-e #ai #ad #e-f #ai #ad #f-g #ai #aa #g-h #ai #ab #h-i #ai #bj #i-aj #ag #ba #aj-aa #ah #bd #aa-ab #bj #ce #ab-ac #da #ce #ac-ad #dj #ch #ad-ae #da #cg #ae-af #db #ce #af-ag #dc #cc #ag-ah #db #cj #ah-ai #cg #bc #ai-bj #ai #aa #bj-ba #ag #aa #ba-bb #ag #je #bb-bc #af #jd #bc-bd #ji #jb #bd-be #jh #jb 99 ,! values giv5 9 ?is table are n 9 precise accord ) ^? ( ! ,table on p4 #fc4 ,! latt] repres5t ,quetelet's results arriv$ at 9 #ahce2 ! =m] are ! means ( 8 det]m9ations 9 #ahce-dj4 ,! accel]ation-curve = man's weight 7,fig4 #e71 :e!r we draw x f ,quetelet's data1 or f ! ,briti%1 ,am]ican & o!r /ati/ics ( lat] writ]s1 is on ! :ole simil> to t :i* we d$uce f ! /ati/ics ( ^! latt] writ]s 9 reg>d to height or /ature2 t is to say1 x is n a curve :i* cont9ually desc5ds1 b x indicates a rate ( gr[? :i* is subject to important fluctuations at c]ta9 epo*s ( life4 ,we see t x beg9s at a high level1 & falls cont9u\sly & rapidly#ajj #fi dur+ ! fir/ two or ?ree ye>s ( life4 ,aft] a slight recov]y1 x runs ne>ly level dur+ boyhood f ab\t five to twelve ye>s old2 x !n rapidly rises1 9 ! 8gr[+ p]iod0 ( ! e>ly te5s1 & sl[ly & /eadily falls f ab\t ! age ( sixte5 onw>ds4 ,x does n rea* ! base-l9e till ! man is ab\t sev5 or eight & tw5ty1 = normal increase ( weight cont9ues dur+ ! ye>s :5 ! man is 8fill+ out10 long aft] gr[? 9 height has ceas$2 b at la/1 some:]e ab\t ?irty1 ! velocity rea*es z]o1 & ev5 falls bel[ x1 = !n ! man usually beg9s to lose weight a little4 ,! subsequ5t sl[ *anges 9 ?is accel]ation-curve we ne$ n /op to deal )4 ,illu/ration3 ,fig4 #e4 ,mean annual increm5ts ( weight1 9 man & woman2 f ,quetelet's data4 ,9 ! same diagram 7,fig4 #e7 ,i h set =? ! accel]ation-curves 9 respect ( increm5t ( weight = bo? man & woman1 accord+ to ,quetelet4 ,t gr[? 9 boyhood & gr[? 9 girlhood foll[ a v diff]5t c\rse is a matt] ( common k2 b if we simply plot ! ord9>y curve ( gr[?1 or velocity-curve1 ! diff]5ce1 on ! small scale ( our diagrams1 #gj is n v app>5t4 ,x is admirably br\ght out1 h[ev]1 9 ! accel]ation-curves4 ,"h we see t1 aft] infancy1 say f ?ree ye>s old to eight1 ! velocity 9 ! girl is /eady1 j z 9 ! boy1 b x /&s on a l[] level 9 h] case ?an 9 83 ! little maid at ?is age is gr[+ sl[] ?an ! boy4 ,b v soon1 & :ile 8 accel]ation-curve is /ill repres5t$ by a /raight l9e1 h]s has begun to asc5d1 & until ! girl is ab\t ?irte5 or f\rte5 x cont9ues to asc5d rapidly4 ,aft] t age1 z aft] sixte5 or sev5te5 9 ! boy's case1 x beg9s to desc5d4 ,9 %ort1 ?r\gh\t all ?is p]iod1 x is a v simil> curve 9 ! two sexes2 b x has its notable diff]5ces1 9 amplitude & especially 9 phase4 ,la/ ( all1 we may notice t :ile ! accel]ation-curve falls to a negative value 9 ! male ab\t or ev5 a little be=e ! age ( ?irty ye>s1 ?is does n happ5 among wom54 ,!y cont9ue to gr[ 9 weight1 ?\gh sl[ly1 till v mu* lat] 9 life2 until !re comes a f9al p]iod1 9 bo? sexes alike1 dur+ :i* weight1 & height & /r5g? all alike dim9i%4 ,f c]ta9 correct$1 or 8typical0 values1 giv5 = ,am]ican *ildr5 by ,boas & ,wissl] 7l4c4 p4 #db71 we obta9 ! foll[+ /ill cle>] comp>ison ( ! annual increm5ts ( /ature 9 boys & girls3 ! typical /ature at ! comm5cem5t ( ! p]iod1 i4e4 at ! age ( elev51 be+ #acea cm4 & #acfi cm4 = ! boys & girls respectively1 & ! annual increm5ts be+ z foll[s3 ,age #ab #ac #ad #ae #af #ag #ah #ai #bj ,boys 7cm47 #da #fc #hg #gi #eb #cb #ai #ji #jc ,girls 7cm47 #ge #gj #df #ba #ji #jd #ja #jj #jj ,diff]5ce #cd #jg #da #eh #dc #bh #ah #ji #jc ,! result ( ^! diff]5ces 7:i* are ess5tially phase-diff]5ces7 betwe5 ! two sexes 9 reg>d to ! velocity ( gr[? & to ! rate ( *ange ( t velocity1 is to cause ! ratio betwe5 ! weights ( ! two sexes to fluctuate 9 a some:at complicat$ mann]4 ,at bir? ! baby-girl weighs on ! av]age ne>ly #aj p] c5t4 less ?an ! boy4 ,till ab\t two ye>s old %e t5ds to ga9 ^u him1 b %e !n loses aga9 until ! age ( ab\t five2 f five %e ga9s = a few ye>s some:at rapidly1 & ! girl ( t5 to twelve is only "s #c p] c5t4 less 9 weight ?an ! boy4 ,! boy 9 8 te5s ga9s #ga /eadily1 & ! "y woman ( tw5ty is ne>ly #ae p] c5t4 light] ?an ! man4 ,?is ratio ( diff]5ce aga9 sl[ly dim9i%es1 & betwe5 fifty & sixty /&s at ab\t #ab p] c5t41 or n f> f ! mean = all ages2 b once m z old age advances1 ! diff]5ce t5ds1 ?\gh v sl[ly1 to increase 7,fig4 #f74 ,illu/ration3 ,fig4 #f4 ,p]c5tage ratio1 ?r\gh\t life1 ( female weight to male2 f ,quetelet's data4 ,:ile c>eful obs]vations on ! rate ( gr[? 9 o!r animals are some:at scanty1 !y t5d to %[ s f> z !y g t ! g5]al features ( ! ph5om5on are always mu* ! same4 ,:e!r ! animal be long-liv$1 z man or ! elephant1 or %ort-liv$1 l horse or dog1 x passes ?r\gh ! same phases ( gr[?#aja4 ,9 all cases gr[? beg9s sl[ly2 x atta9s a maximum velocity e>ly 9 its c\rse1 & aft]w>ds sl[s d[n 7subject to tempor>y accel]ations7 t[>ds a po9t :]e gr[? ceases altoge!r4 ,b especially 9 ! cold-blood$ animals1 su* z fi%es1 ! sl[+-d[n p]iod is v greatly protract$1 & ! size ( ! creature w\ld seem nev] actually to rea*1 b only to approa* asymptotically1 to a maximal limit4 ,! size ultimately atta9$ is a resultant ( ! rate1 & ( #gb ! duration1 ( gr[?4 ,x is 9 ! ma9 true1 z ,m9ot has said1 t ! rabbit is bigg] ?an ! gu9ea-pig because he gr[s ! fa/]2 b t man is bigg] ?an ! rabbit because he goes on gr[+ = a long] "t4 ,9 ord9>y physical inve/igations deal+ ) velocities1 z = in/ance ) ! c\rse ( a projectile1 we pass at once f ! /udy ( accel]ation to t ( mom5tum & s to t ( =ce2 = *ange ( mom5tum1 :i* is proportional to =ce1 is ! product ( ! mass ( a body into its accel]ation or *ange ( velocity4 ,b we c take no su* easy road ( k9ematical inve/igation 9 ?is case4 ,! 8velocity0 ( gr[? is a v diff]5t ?+ f ! 8velocity0 ( ! projectile4 ,! =ces at "w 9 our case are n susceptible ( direct & easy treatm5t2 !y are too v>i$ 9 _! nature & too indirect 9 _! action = u to be ju/ifi$ 9 equat+ !m directly ) ! mass ( ! gr[+ /ructure4 ,x 0 app>5tly f a feel+ t ! velocity ( gr[? ought 9 "s way to be equat$ ) ! mass ( ! gr[+ /ructure t ,m9ot#ajb introduc$ a curi\s1 & 7z x seems to me7 an unhappy me?od ( repres5t+ gr[?1 9 ! =m ( :at he call$ 8p]c5tage-curves02 a me?od :i* has be5 foll[$ by a numb] ( o!r writ]s & exp]im5t]s4 ,m9ot's me?od 0 to deal1 n ) ! actual increm5ts add$ 9 successive p]iods1 su* z ye>s or days1 b ) ^! increm5ts repres5t$ z p]c5tages ( ! am\nt :i* _h be5 rea*$ at ! end ( ! =m] p]iod4 ,= in/ance1 tak+ ,quetelet's values = ! height 9 c5timetres ( a male infant f bir? to f\r ye>s old1 z foll[s3 ,ye>s #j #a #b #c #d cm4 #ejj #fih #gia #hfd #ibg ,m9ot w\ld /ate ! p]c5tage gr[? 9 ea* ( ! f\r annual p]iods at #cif1 #acc1 #if & #gc p] c5t4 respectively4 ,n[ :5 we plot actual l5g? aga9/ "t1 we h a p]fectly def9ite ?+4 ,:5 we diff]5tiate ?is ,l_/,t1 we h d,l_/d,t1 :i* is 7( c\rse7 velocity2 & f ?is1 by a second diff]5tiation1 we obta9 d#b ,l_/d,t#b1 t is to say1 ! accel]ation4 #gc ,b :5 y take p]c5tages ( y1 y are det]m9+ dy_/y1 & :5 y plot ?is aga9/ dx1 y h 7dy_/y7_/dx1 or dy_/7y dx71 or 7#a_/y7 7dy_/dx71 t is to say1 y are multiply+ ! ?+ y wi% to repres5t by ano!r quantity :i* is itself cont9ually v>y+2 & ! result is t y are deal+ ) some?+ v mu* less easily grasp$ by ! m9d ?an ! orig9al factors4 ,pr(essor ,m9ot is1 ( c\rse1 deal+ ) a p]fectly legitimate function ( x & y2 & 8 me?od is practically tantam\nt to plott+ log y aga9/ x1 t is to say1 ! log>i?m ( ! increm5t aga9/ ! "t4 ,?is c\ld only be def5d$ & ju/ifi$ if x l$ to "s simple result1 = in/ance if x gave u a /raight l9e1 or "s o!r simpl] curve ?an our usual curves ( gr[?4 ,z a matt] ( fact1 x is manife/ t x does no?+ ( ! k9d4 ,pre-natal & po/-natal gr[?4 ,9 ! accel]ation-curves :i* we h %[n above 7,figs4 #b1 #c71 x w be se5 t ! curve />ts at a consid]able int]val f ! actual date ( bir?2 = ! fir/ two increm5ts :i* we c z yet comp>e ) "o ano!r are ^? atta9$ dur+ ! fir/ & second complete ye>s ( life4 ,n[ we c 9 _m cases 8int]polate0 ) safety betwe5 kn[n po9ts ^u a curve1 b x is v mu* less safe1 & is n v (t5 ju/ifiable 7at lea/ until we und]/& ! physical pr9ciple involv$1 & its ma!matical expression71 to 8extrapolate0 beyond ! limits ( our obs]vations4 ,9 %ort1 we d n yet "k :e!r our curve cont9u$ to asc5d z we g backw>ds to ! date ( bir?1 or :e!r x may n h *ang$ its direction1 & desc5d$1 p]haps1 to z]o-value4 ,9 reg>d to l5g?1 or /ature1 h[ev]1 we c obta9 ! requisite in=mation f c]ta9 tables ( ,rss['s#ajc1 :o gives ! /ature ( ! infant mon? by mon? dur+ ! fir/ ye> ( its life1 z foll[s3 ,age 9 mon?s #j #a #b #c #d #e #f #g #h #i #aj #aa #ab ,l5g? 9 cm4 7#ej7 #ed #eh #fj #fb #fd #fe #ff #fge #fh #fi #gje #gb ,diff]5ces 79 cm47 #d #d #b #b #b #a #a #ae #e #a #ae #ae ,if we multiply ^! mon?ly diff]5ces1 or mean mon?ly velocities1 by #ab1 to br+ !m into a =m comp>able ) ! #gd annual velocities already repres5t$ on our accel]ation-curves1 we %all see t ! "o s]ies ( obs]vations jo9s on v well ) ! o!r2 & 9 %ort we see at once t our accel]ation-curve rises /eadily & rapidly z we pass back t[>ds ! date ( bir?4 ,illu/ration3 ,fig4 #g4 ,curve ( gr[? 79 l5g? or /ature7 ( *ild1 be=e & aft] bir?4 7,f ,8 & ,rss['s data47 ,b bir? itself1 9 ! case ( a vivip>\s animal1 is b an unimportant epo* 9 ! hi/ory ( gr[?4 ,x is an epo* ^: relative date v>ies accord+ to ! p>ticul> animal3 ! foal & ! lamb are born relatively lat]1 t is to say :5 developm5t has advanc$ mu* f>!r1 ?an 9 ! case ( man2 ! kitt5 & ! puppy are born e>li] & !re=e m helpless ?an we are2 & ! m\se comes into ! _w /ill e>li] & m in*oate1 s mu* s t ev5 ! little m>supial is sc>cely m un=m$ & embryonic4 ,9 all ^! cases alike1 we mu/1 9 ord] to /udy ! curve ( gr[? 9 its entirety1 take full acc\nt ( pr5atal or intra-ut]9e gr[?4 #ge ,accord+ to ,8#ajd1 ! foll[+ are ! mean l5g?s ( ! unborn human embryo1 f mon? to mon?4 ,mon?s #j #a #b #c #d #e #f #g #h #i #aj 7,bir?7 ,l5g? 9 mm4 #j #ge #dj #hd #afb #bge #ceb #djb #ddc #dgb #dij-ejj ,increm5t p] mon? 9 mm4 -- #ge #cbe #dd #gh #aac #gg #ej #da #bi #ah-bh ,illu/ration3 ,fig4 #h4 ,mean mon?ly increm5ts ( l5g? or /ature ( *ild 79 cms474 ,^! data l9k on v well to ^? ( ,rss[1 :i* we h j consid]$1 & 7?\gh ,8's measurem5ts = ! pre-natal mon?s are m detail$ ?an are ^? ( ,rss[ = ! fir/ ye> ( po/-natal life7 we may draw a cont9u\s curve ( gr[? 7,fig4 #g7 & curve ( accel]ation ( gr[? 7,fig4 #h7 = ! comb9$ p]iods4 ,x w at once be se5 t !re is a 8po9t ( inflection0 some:]e ab\t ! fif? mon? ( intra-ut]9e life#aje3 up to t date gr[? proce$s ) a cont9ually increas+ #gf velocity2 b aft] t date1 ?\gh gr[? is /ill rapid1 its velocity t5ds to fall away4 ,!re is a slight break betwe5 our two sep>ate sets ( /ati/ics at ! date ( bir?1 :ile ?is is ! v epo* reg>d+ :i* we %\ld p>ticul>ly l to h precise & cont9u\s in=mation4 ,und\bt$ly !re is a c]ta9 slight arre/ ( gr[?1 or dim9ution ( ! rate ( gr[?1 ab\t ! epo* ( bir?3 ! sudd5 *ange 9 ! #gg me?od ( nutrition has its inevitable effect2 b ?is slight tempor>y set-back is imm$iately foll[$ by a second>y1 & tempor>y1 accel]ation4 ,illu/ration3 ,fig4 #i4 ,curve ( pre-natal gr[? 7l5g? or /ature7 ( *ild2 & correspond+ curve ( mean mon?ly increm5ts 7mm474 ,illu/ration3 ,fig4 #aj4 ,curve ( gr[? ( bamboo 7f ,o/wald1 aft] ,kraus74 ,x is wor? our :ile to draw a sep>ate curve to illu/rate on a l>g] scale ,8's c>eful data = ! t5 mon?s ( pre-natal life 7,fig4 #i74 ,we see t ?is curve ( gr[? is a beautifully regul> "o1 & is ne>ly symmetrical on ei!r side ( t po9t ( inflection ( :i* we h already spok52 x is a curve = :i* we might well hope to f9d a simple ma!matical expression4 ,! accel]ation-curve %[n 9 ,fig4 #i toge!r ) ! pre-natal curve ( gr[?1 is n tak5 directly f ,8's record$ data1 b is d]iv$ f ! tang5ts drawn to a smoo!d curve1 correspond+ z ne>ly z possible to ! actual curve ( gr[?3 ! rise to a maximal velocity ab\t ! fif? mon? & ! subsequ5t gradual fall are n[ demon/rat$ ev5 m cle>ly ?an be=e4 ,9 ,fig4 #aj1 :i* is a curve ( gr[? ( ! bamboo#ajf1 we see 7s f> z x goes7 ! same ess5tial features1 #gh ! sl[ beg9n+1 ! rapid increase ( velocity1 ! po9t ( inflection1 & ! subsequ5t sl[ negative accel]ation#ajg4 ,v>iability & ,correlation ( ,gr[?4 ,! magnitudes & velocities :i* we are "h deal+ ) are1 ( c\rse1 mean values d]iv$ f a c]ta9 numb]1 sometimes a l>ge numb]1 ( individual cases4 ,b no /ati/ical acc\nt ( mean values is complete unless we also take acc\nt ( ! am\nt ( v>iability among ! individual cases f :i* ! mean value is drawn4 ,to d ?is ?r\gh\t w\ld lead u into detail$ inve/igations :i* lie f> beyond ! scope ( ?is elem5t>y book2 b we may v briefly illu/rate ! nature ( ! process1 9 connection ) ! ph5om5a ( gr[? :i* we h j be5 /udy+4 ,x 0 9 connection ) ^! ph5om5a1 9 ! case ( man1 t ,quetelet fir/ conceiv$ ! /ati/ical /udy ( v>iation1 on l9es :i* 7 aft]w>ds exp\nd$ & develop$ by ,galton1 & :i* h gr[n1 9 ! h&s ( ,k>l ,pe>son & o!rs1 into ! mod]n sci5ce ( ,biometrics4 ,:5 ,quetelet tells u1 = in/ance1 t ! mean /ature ( ! t5-ye> old boy is #abgc metres1 ?is implies1 accord+ to ! law ( error1 or law ( probabilities1 t all ! individual measurem5ts ( t5-ye>-old boys gr\p !mselves 9 an ord]ly way1 t is to say accord+ to a c]ta9 def9ite law1 ab\t ?is mean value ( #abgc4 ,:5 ^! individual measurem5ts are gr\p$ & plott$ z a curve1 s z to %[ ! numb] ( individual cases at ea* individual l5g?1 we obta9 a *>act]i/ic curve ( error or curve ( frequ5cy2 & ! 8spread0 ( ?is curve is a measure ( ! am\nt ( v>iability 9 ?is p>ticul> case4 ,a c]ta9 ma!matical measure ( ?is 8spread10 z describ$ 9 works ^u /ati/ics1 is call$ ! ,index ( ,v>iability1 or ,/&>d ,deviation1 & is usually d5om9at$ by ! lett] 4 ,x is practically equival5t to a det]m9ation ( ! po9t ^u ! frequ5cy curve :]e x *anges its curvature on ei!r side ( ! mean1 & :]e1 f be+ concave t[>ds ! middle l9e1 x spreads out to be convex !reto4 ,:5 we divide ?is #gi value by ! mean1 we get a figure :i* is indep5d5t ( any p>ticul> units1 & :i* is call$ ! ,coeffici5t ( ,v>iability4 7,x is usually multipli$ by #ajj1 to make x ( a m conv5i5t am\nt2 & we may !n def9e ?is coeffici5t1 ,c1 z 7_/,m7 #ajj47 ,9 reg>d to ! gr[? ( man1 ,pe>son has det]m9$ ?is coeffici5t ( v>iability z foll[s3 9 male new-born infants1 ! coeffici5t 9 reg>d to weight is #aeff1 & 9 reg>d to /ature1 #fej2 9 male adults1 = weight #ajhc1 & = /ature1 #cff4 ,! am\nt ( v>iability t5ds1 !re=e1 to decrease ) gr[? or age4 ,simil> det]m9ations h be5 elaborat$ by ,b[dit*1 by ,boas & ,wissl]1 & by o!r writ]s = int]m$iate ages1 especially f ab\t five ye>s old to eighte51 s cov]+ a great "p ( ! :ole p]iod ( gr[? 9 man#ajh4 ,coeffici5t ( ,v>iability 7_/,m #ajj7 9 ,man1 at v>i\s ages4 ,age #e #f #g #h #i ,/ature 7,b[dit*7 #dgf #dfj #ddb #ddi #ddj ,/ature 7,boas & ,wissl]7 #dae #dad #dbb #dcg #dcc ,weight 7,b[dit*7 #aaef #ajbh #aajh #iib #aajd ,age #aj #aa #ab #ac #ad ,/ature 7,b[dit*7 #dee #dgj #dij #edg #egi ,/ature 7,boas & ,wissl]7 #dcf #ded #dgc #eaf #eeg ,weight 7,b[dit*7 #aafj #aagf #acgb #acfj #afhj ,age #ae #af #ag #ah ,/ature 7,b[dit*7 #eeg #dej #dee #cfi ,/ature 7,boas & ,wissl]7 #eej #dfi #dbg #cid ,weight 7,b[dit*7 #aecb #acbh #abif #ajdj ,! result is v curi\s inde$4 ,we see1 f ,fig4 #aa1 t ! curve ( v>iability is v simil> to :at we h call$ ! accel]ation-curve 7,fig4 #d73 t is to say1 x desc5ds :5 ! rate ( gr[? dim9i%es1 & rises v m>k$ly aga9 :51 9 late boyhood1 ! rate ( gr[? is tempor>ily accel]at$4 ,we #hj see1 9 %ort1 t ! am\nt ( v>iability 9 /ature or 9 weight is a function ( ! rate ( gr[? 9 ^! magnitudes1 ?\gh we are n yet 9 a position to equate ! t]ms precisely1 "o ) ano!r4 ,illu/ration3 ,fig4 #aa4 ,coeffici5ts ( v>iability ( /ature 9 ,man 774 f ,boas & ,wissl]'s data4 ,if we take n m]ely ! v>iability ( /ature or weight at a giv5 age1 b ! v>iability ( ! actual successive increm5ts 9 ea* ye>ly p]iod1 we see t ?is latt] coeffici5t ( v>iability t5ds to increase /eadily1 & m & m rapidly1 )9 ! limits ( age = :i* we h in=mation2 & ?is ph5om5on is1 9 ! ma91 easy ( explanation4 ,= a great "p ( ! diff]5ce1 9 reg>d to rate ( gr[?1 betwe5 "o individual & ano!r is a diff]5ce ( phase1--a diff]5ce 9 ! epo*s ( accel]ation & ret>dation1 & f9ally 9 ! epo* :5 gr[? comes to an end4 ,& x foll[s t ! v>iability ( rate w be m & m m>k$1 z we approa* & rea* ! p]iod :5 "s individuals /ill cont9ue1 & o!rs h already ceas$1 to gr[4 ,9 ! foll[+ epitomis$ table1 #ha ,i h tak5 ,boas's det]m9ations ( v>iability 77 7op4 cit4 p4 #aedh71 conv]t$ !m into ! correspond+ coeffici5ts ( v>iability 77_/,m7 #ajj71 & !n smoo!d ! result+ numb]s4 ,coeffici5ts ( ,v>iability 9 ,annual ,increm5t ( ,/ature4 ,age #g #h #i #aj #aa #ab #ac #ad #ae ,boys #agc #aeh #ahf #aia #baj #bdg #bij #cfb #dfa ,girls #aga #agh #aib #bbg #bei #bic #cgj #ddh -- ,! great] v>iability ( annual increm5t 9 ! girls1 z comp>$ ) ! boys1 is v m>k$1 & is easily expla9$ by ! m rapid rate at :i* ! girls run ?r\gh ! sev]al phases ( ! ph5om5on4 ,j z !re is a m>k$ diff]5ce 9 8phase0 betwe5 ! gr[?-curves ( ! two sexes1 t is to say a diff]5ce 9 ! p]iods :5 gr[? is rapid or ! rev]se1 s also1 )9 ea* sex1 w !re be room = simil>1 b individual phase-diff]5ces4 ,?us we may h *ildr5 ( accel]at$ developm5t1 :o at a giv5 epo* aft] bir? are bo? rapidly gr[+ & already 8big = _! age02 & o!rs ( ret>d$ developm5t :o are comp>atively small & h n rea*$ ! p]iod ( accel]ation :i*1 9 great] or less degree1 w come to !m 9 turn4 ,9 o!r words1 !re mu/ "u su* circum/ances be a /rong positive 8coeffici5t ( correlation0 betwe5 /ature & rate ( gr[?1 & also betwe5 ! rate ( gr[? 9 "o ye> & ! next4 ,b x does n by any means foll[ t a *ild :o is precoci\sly big w cont9ue to gr[ rapidly1 & become a man or woman ( exceptional /ature4 ,on ! contr>y1 :5 9 ! case ( ! precoci\s or 8accel]at$0 *ildr5 gr[? has begun to sl[ d[n1 ! backw>d ones may /ill be gr[+ rapidly1 & s mak+ up 7m or less completely7 to ! o!rs4 ,9 o!r words1 ! p]iod ( high positive correlation betwe5 /ature & increm5t w t5d to be foll[$ by "o ( negative correlation4 ,?is int]e/+ & important po9t1 due to ,boas & ,wissl]#aji1 is confirm$ by ! foll[+ table3 ,correlation ( ,/ature & ,increm5t 9 ,boys & ,girls4 7,f ,boas & ,wissl]47 ,age #f #g #h #i #aj #aa #ab #ac #ad #ae ,/ature 7,b7 #aabg #aaee #abcb #abgd #accb #acfh #adbg #adgc #aeei #afbb 7,g7 #aaad #aagg #abad #abgi #acah #acfg #addf #adig #aech #aegb ,increm5t 7,b7 #eg #ec #di #ea #ej #dg #ei #ge #fb #eb 7,g7 #ei #ee #ee #ei #fb #gb #fe #ed #cc #ag ,correlation 7,b7 #be #aa #jh #be #ah #ah #dh #bi #db #dd 7,g7 #dd #ad #bd #dg #ah #ah #db #ci #fc #aa #hb ,a m9or1 b v curi\s po9t br\ght out by ! same inve/igators is t1 if in/ead ( /ature we deal ) height 9 ! sitt+ po/ure 7or1 practically speak+1 ) l5g? ( trunk or back71 !n ! correlations betwe5 ?is height & its annual increm5t are ?r\gh\t negative4 ,9 o!r words1 !re w\ld seem to be a g5]al t5d5cy = ! long trunks to gr[ sl[ly ?r\gh\t ! :ole p]iod "u inve/igation4 ,x is a well-kn[n anatomical fact t tallness is 9 ! ma9 due n to l5g? ( body b to l5g? ( limb4 ,! :ole ph5om5on ( v>iability 9 reg>d to magnitude & to rate ( increm5t is 9 ! highe/ degree sugge/ive3 inasmu* z x helps fur!r to rem9d & to impress ^u u t specific rate ( gr[? is ! real physiological factor :i* we want to get at1 ( :i* specific magnitude1 dim5sions & =m1 & all ! v>iations ( ^!1 are m]ely ! concrete & visible resultant4 ,b ! problems ( v>iability1 ?\gh !y are intimately relat$ to ! g5]al problem ( gr[?1 c>ry u v soon beyond our pres5t limitations4 ,rate ( gr[? 9 o!r organisms#aaj4 ,j z ! human curve ( gr[? has its slight b well-m>k$ int]ruptions1 or v>iations 9 rate1 co9cid+ ) su* epo*s z bir? & pub]ty1 s is x ) o!r animals1 & ?is ph5om5on is p>ticul>ly /rik+ 9 ! case ( animals :i* und]go a regul> metamorphosis4 ,9 ! accompany+ curve ( gr[? 9 weight ( ! m\se 7,fig4 #ab71 bas$ on ,w4 ,o/wald's obs]vations#aaa1 we see a di/9ct slack5+ ( ! rate :5 ! m\se is ab\t a =tnight old1 at :i* p]iod x op5s its eyes & v soon aft]w>ds is wean$4 ,at ab\t six weeks old !re is ano!r well-m>k$ ret>dation ( gr[?1 foll[+ on a v rapid p]iod1 & co9cid+ ) ! epo* ( pub]ty4 #hc ,fig4 #ac %ews ! curve ( gr[? ( ! silkworm#aab1 dur+ its :ole l>val life1 up to ! "t ( its ent]+ ! *rysalis /age4 ,! silkworm m\lts f\r times1 at int]vals ( ab\t a week1 ! fir/ m\lt be+ on ! six? or sev5? day aft] hat*+4 ,a di/9ct ret>dation ( gr[? is exhibit$ on our curve 9 ! case ( ! ?ird & f\r? m\lts2 :ile a simil> ret>dation accompanies ! fir/ & second m\lts also1 b ! scale ( our diagram does n r5d] x visible4 ,:5 ! worm is ab\t sev5 weeks old1 a rem>kable process ( 8purgation0 takes place1 z a prelim9>y to ent]+ on ! pupal1 or *rysalis1 /age2 & ! great & sudd5 loss ( weight :i* accompanies ?is process is ! mo/ m>k$ feature ( our curve4 ,illu/ration3 ,fig4 #ab4 ,gr[? 9 weight ( ,m\se4 7,aft] ,w4 ,o/wald47 ,! rate ( gr[? 9 ! tadpole#aac 7,fig4 #ad7 is likewise m>k$ by epo*s ( ret>dation1 & f9ally by a sudd5 & dra/ic *ange4 ,!re is a slight dim9ution 9 weight imm$iately aft] #hd ! little l>va frees itself f ! egg2 !re is a ret>dation ( gr[? ab\t t5 days lat]1 :5 ! ext]nal gills disappe>2 & f9ally1 ! complete metamorphosis1 ) ! loss ( ! tail1 ! gr[? ( ! legs & ! cessation ( bran*ial respiration1 is accompani$ by a loss ( weight am\nt+ to wellnigh half ! weight ( ! full-gr[n l>va4 #he ,illu/ration3 ,fig4 #ac4 ,gr[? 9 weight ( ,silkworm4 7,f ,o/wald1 aft] ,luciani & ,lo ,monaco47 ,:ile z a g5]al rule1 ! bett] ! animals be f$ ! quick] !y gr[ & ! soon] !y metamorphose1 ,b>fr? has po9t$ out ! curi\s fact t a %ort spell ( />vation1 j be=e metamorphosis is due1 appe>s to ha/5 ! *ange4 ,illu/ration3 ,fig4 #ad4 ,gr[? 9 weight ( ,tadpole4 7,f ,o/wald1 aft] ,s*ap]47 ,! negative gr[?1 or actual loss ( bulk & weight :i* (t51 & p]haps always1 accompanies metamorphosis1 is well %ewn 9 ! case ( ! eel#aad4 ,! contra/ ( size is great betwe5 #hg ! flatt5$1 lancet-%ap$ ,leptocephalus l>va & ! little black cyl9drical1 almo/ ?read-l elv]1 ^: magnitude is less ?an t ( ! ,leptocephalus 9 e dim5sion1 ev51 at fir/1 9 l5g? 7,fig4 #ae74 ,illu/ration3 ,fig4 #ae4 ,developm5t ( ,eel2 f ,leptocephalus l>vae to "y ,elv]4 7,f ,o/wald aft] ,joh4 ,s*midt47 ,illu/ration3 ,fig4 #af4 ,gr[? 9 l5g? ( ,spirogyra4 7,f ,o/wald1 aft] ,h(mei/]47 ,f ! high] /udy ( ! physiology ( gr[? we le>n t su* fluctuations z we h describ$ are b special int]ruptions 9 a process :i* is nev] actually cont9u\s1 b is p]petually int]rupt$ 9 a rhy?mic mann]#aae4 ,h(mei/] %ew$1 = in/ance1 t ! gr[? ( ,spirogyra proce$s by fits & />ts1 by p]iods ( activity & re/1 :i* alt]nate ) "o ano!r at int]vals ( s _m m9utes 7,fig4 #af74 ,& ,bose1 by v ref9$ me?ods ( exp]im5t1 has %ewn t plant-gr[? really proce$s by t9y & p]fectly rhy?mical pulsations recurr+ at regul> int]vals ( a few seconds ( "t4 ,fig4 #ag %ews1 accord+ to ,bose's obs]vations#aaf1 ! gr[? ( a crocus1 "u a v high magnification4 ,! /alk gr[s by little j]ks1 ea* ) an amplitude ( ab\t #jjb mm41 e #hh tw5ty seconds or s1 & aft] ea* little increm5t !re is a p>tial recoil4 ,illu/ration3 ,fig4 #ag4 ,pulsations ( gr[? 9 ,crocus1 9 micro-millimetres4 7,aft] ,bose47 ,! rate ( gr[? ( v>i\s p>ts or organs#aag4 ,! diff]5ces 9 reg>d to rate ( gr[? betwe5 v>i\s p>ts or organs ( ! body1 int]nal & ext]nal1 c be amply illu/rat$ 9 ! case ( man1 & also1 b *iefly 9 reg>d to ext]nal =m1 9 "s few o!r creatures#aah4 ,x is obvi\s t !re lies h]e9 an endless field = ! ma!matical /udy ( correlation & ( v>iability1 b ) ?is aspect ( ! case we _c deal4 ,9 ! accompany+ table1 ,i %ew1 f "s ( ,vi]ordt's data1 ! relative weights1 at v>i\s ages1 comp>$ ) ! weight at bir?1 ( ! entire body1 ( ! bra91 he>t & liv]2 #hi & also ! p]c5tage relation :i* ea* ( ^! organs be>s1 at ! sev]al ages1 to ! weight ( ! :ole body4 ,weight ( ,v>i\s ,organs1 comp>$ ) ! ,total ,weight ( ! ,human ,body 7male74 7,aft] ,vi]ordt1 ,anatom4 ,tabell51 pp4 #ch1 #ci47 ,p]c5tage weights comp>$ ,weight ,relative weights ( ) total body-weights ( body ,age 9 kg4 ,body ,bra9 ,he>t ,liv] ,body ,bra9 ,he>t ,liv] #j #ca #a #a #a #a #ajj #abbi #jgf #deg #a #ij #bij #bdh #age #bce #ajj #ajej #jdf #cgj #b #aaj #cee #bfi #bbj #cjb #ajj #icb #jdg #chi #c #abe #djc #bia #bge #cdb #ajj #hhf #jeb #chh #d #adj #deb #cdi #cad #dae #ajj #iej #jec #dbj #e #aei #eac #ccb #cdc #chj #ajj #gid #jea #cci #f #agh #egd #ceg #cfj #dcd #ajj #gfc #jdh #cde #g #aig #fce #ced #cie #dhf #ajj #fhd #jdg #cdi #h #baf #fig #cfb #djb #dei #ajj #fch #jdd #cja #i #bce #geh #cgd #dei #die #ajj #fjf #jdf #bii #aj #beb #hac #cgj #eda #eij #ajj #eei #jea #ccb #aa #bgj #hga #ceg #eig #fad #ajj #ejd #jeb #cbb #ab #bij #ice #cgh 7#dac7 #fba #ajj #dhh 7#jcd7 #cjc #ac #cca #ajfh #cij #fie #gca #ajj #ddi #jej #cac #ad #cga #aaig #cch #iaf #hci #ajj #cdg #jeh #cbj #ae #dab #acbi #cia #hde #ibb #ajj #cfb #jdh #cag #af #dei #adha #cgg #igf #ide #ajj #caf #jea #bie #ag #dig #afjc #cgj #ajfc #ajdf #ajj #bhd #jea #bih #ah #eci #agci #cgc #ajcc #ajfe #ajj #bfd #jdf #bhj #ai #egf #aheh #cfg #aadb #aafa #ajj #bdc #jea #bhf #bj #eie #aiai #cgi #abid #aaja #ajj #bdc #jea #bfb #ba #fab #aigd #cga #abei #aadh #ajj #bca #jdi #bff #bb #fbi #bjbi #ced #acbd #aahb #ajj #bad #jej #bff #bc #fde #bjha #cff #abdb #ajgi #ajj #baf #jdf #bcg #bd -- -- #cgd #acji #acjd #ajj -- -- -- #be #ffb #bacf #cgf #abgd #abhd #ajj #baf #jdf #bge ,f ,quetelet4 ,f ! fir/ portion ( ! table1 x w be se5 t none ( ^! organs by any means keep pace ) ! body z a :ole 9 reg>d to gr[? 9 weight2 9 o!r words1 !re mu/ be "s o!r "p ( ! fabric1 d\btless ! muscles & ! bones1 :i* increase m rapidly ?an ! av]age increase ( ! body4 ,he>t & liv] bo? gr[ ne>ly at ! same rate1 & by ! #ij age ( tw5ty-five !y h multipli$ _! weight at bir? by ab\t ?irte5 times1 :ile ! weight ( ! entire body has be5 multipli$ by ab\t tw5ty-"o2 b ! weight ( ! bra9 has mean:ile be5 multipli$ only ab\t ?ree & a qu>t] times4 ,9 ! next place1 we see ! v rem>kable ph5om5on t ! bra91 gr[+ rapidly till ! *ild is ab\t f\r ye>s old1 !n gr[s m mu* sl[ly till ab\t eight or n9e ye>s old1 & aft] t "t !re is sc>cely any fur!r p]ceptible increase4 ,^! ph5om5a are diagrammatically illu/rat$ 9 ,fig4 #ah4 ,illu/ration3 ,fig4 #ah4 ,relative gr[? 9 weight 79 ,man7 ( ,bra91 ,he>t1 & :ole ,body4 ,_m /ati/ics indicate a decrease ( bra9-weight dur+ adult life4 ,boas#aai 0 incl9$ to attribute ?is app>5t ph5om5on to our /ati/ical me?ods1 & to hold t x c\ld 8h>dly be expla9$ 9 any o!r way ?an by assum+ an increas$ dea?-rate among m5 ) v l>ge bra9s1 at an age ( ab\t tw5ty ye>s40 ,b ,raymond ,pe>l has %ewn t !re is evid5ce ( a /eady & v gradual decl9e 9 ! weight ( ! bra9 ) advanc+ age1 beg9n+ at or be=e ! tw5tie? ye>1 & cont9u+ ?r\gh\t adult life#abj4 #ia ,! second "p ( ! table %ews ! /eadily decreas+ weights ( ! organs 9 "q z comp>$ ) ! body2 ! bra9 fall+ f ov] #ab p] c5t4 at bir? to little ov] #b p] c5t4 at five & tw5ty2 ! he>t f #ge to #df p] c5t42 & ! liv] f #deg to #bge p] c5t4 ( ! :ole bodily weight4 ,x is pla91 !n1 t !re is no simple & direct relation1 hold+ good ?r\gh\t life1 betwe5 ! size ( ! body z a :ole & t ( ! organs we h j discuss$2 & ! *ang+ ratio ( magnitude is especially m>k$ 9 ! case ( ! bra91 :i*1 z we h j se51 con/itutes ab\t "o-eigh? ( ! :ole bodily weight at bir?1 & b "o-fiftie? at five & tw5ty4 ,! same *ange ( ratio is obs]v$ 9 o!r animals1 9 equal or ev5 great] degree4 ,= in/ance1 ,max ,web]#aba tells u t 9 ! lion1 at five weeks1 f\r mon?s1 elev5 mon?s1 & la/ly :5 full-gr[n1 ! bra9-weight repres5ts ! foll[+ fractions ( ! weight ( ! :ole body1 viz4 #a_/ah1 #a_/hj1 #a_/ahd1 & #a_/edf4 ,& ,kellicott has1 9 l mann]1 %ewn t 9 ! dogfi%1 :ile "s organs 7e4g4 rectal gl&1 pancreas1 etc47 increase /eadily & v ne>ly proportionately to ! body z a :ole1 ! bra91 & "s o!r organs also1 gr[ 9 a dim9i%+ ratio1 :i* is capable ( repres5tation1 approximately1 by a log>i?mic curve#abb4 ,b if we conf9e ourselves to ! adult1 !n1 z ,raymond ,pe>l has %ewn 9 ! case ( man1 ! relation ( bra9-weight to age1 to /ature1 or to weight1 becomes a comp>atively simple "o1 & may be s5sibly express$ by a /raight l9e1 or simple equation4 ,?us1 if ,w be ! bra9-weight 79 grammes71 & ,a be ! age1 or ,s ! /ature1 ( ! individual1 !n 79 ! case ( ,sw$i% males7 ! foll[+ simple equations suffice to give ! requir$ ratios3 ,w #adhgh #aid ,a #iaejf #bhf ,s4 #ib ,^! equations are applicable to ages betwe5 fifte5 & eighty2 if we take n>r[] limits1 say betwe5 fifte5 & fifty1 we c get a clos] agreem5t by us+ some:at alt]$ con/ants4 ,9 ! two sexes1 & 9 diff]5t races1 ^! empirical con/ants w be greatly *ang$#abc4 ,donaldson has fur!r %ewn t ! correlation betwe5 bra9-weight & body-weight is v mu* clos] 9 ! rat ?an 9 man#abd4 ,! fall+ ratio ( weight ( bra9 to body ) increase ( size or age f9ds its p>allel 9 comp>ative anatomy1 9 ! g5]al law t ! l>g] ! animal ! less is ! relative weight ( ! bra94 ,weight ( ,weight ( entire animal bra9 gms4 gms4 ,ratio ,m>moset #cce #abe #a 3 #bf ,spid] monkey #ahde #abf #a 3 #ae ,felis m9uta #abcd #bcf #a 3 #ef ,f4 dome/ica #ccjj #ca #a 3 #ajg ,leop>d #bg1gjj #afd #a 3 #afh ,lion #aai1ejj #bai #a 3 #edf ,elephant #c1jdh1jjj #edcj #a 3 #efj ,:ale 7,globiocephalus7 #a1jjj1jjj #beaa #a 3 #djj ,= mu* in=mation on ?is subject1 see ,dubois1 8,abhngigkeit des ,hirngewi*tes von d] ,krp]grsse bei d5 ,suge?i]510 ,ar*4 f4 ,an?ropol4 ,,xxv1 #ahig4 ,dubois has attempt$1 b ,i ?9k ) v d\btful success1 to equate ! weight ( ! bra9 ) t ( ! animal4 ,we may d ?is1 9 a v simple way1 by repres5t+ ! weight ( ! body z a p[] ( t ( ! bra92 ?us1 9 ! above table ( ! weights ( bra9 & body 9 f\r species ( cat1 if we call ,w ! weight ( ! body 79 grammes71 & w ! weight ( ! bra91 !n if 9 all f\r cases we express ! ratio by ,w wn1 we f9d t n is almo/ con/ant1 & diff]s little f #bbd 9 all f\r species3 ! values be+ respectively1 9 ! ord] ( ! table #bcf1 #bbd1 #bah1 & #bag4 ,b ?is evid5tly am\nts to no m ?an an empirical rule2 = we c easily see t x dep5ds on ! p>ticul> scale :i* we h us$1 & t if ! weights _h be5 tak51 = in/ance1 9 kilogrammes or 9 milligrammes1 ! agreem5t or co9cid5ce w\ld n h occurr$#abe4 #ic ,! ,l5g? ( ! ,head 9 ,man at v>i\s ,ages4 7,aft] ,quetelet1 p4 #bjg47 ,m5 ,wom5 ,age ,total height ,head ,ratio ,height ,head ,ratio m4 m4 m4 m4 ,bir? #jejj #jaaa #dej #jdid #jaaa #dde #a ye> #jfih #jaed #dec #jfij #jaed #ddh #b ye>s #jgia #jagc #deg #jgha #jagb #ded #c ye>s #jhfd #jahb #dgd #jhed #jahj #dgd #e ye>s #jihg #jaib #ead #jigd #jahh #eah #aj ye>s #abgc #jbje #fba #abdi #jbja #fba #ae ye>s #aeac #jbae #gjd #adhh #jbac #fii #bj ye>s #affi #jbbg #gce #aegd #jbbj #gae #cj ye>s #afhf #jbbh #gci #aehj #jbba #gae #dj ye>s #afhf #jbbh #gci #aehj #jbba #gae ,a smoo? curve1 v simil> to ?is1 = ! gr[? 9 8auricul> height0 ( ! girl's head1 is giv5 by ,pe>son1 9 ,biometrika1 ,,iii1 p4 #ada4 #aijd4 ,z reg>ds ext]nal =m1 v simil> diff]5ces exi/1 :i* h[ev] we mu/ express 9 t]ms n ( weight b ( l5g?4 ,?us ! annex$ table %ews ! *ang+ ratios ( ! v]tical l5g? ( ! head to ! entire /ature2 & :ile ?is ratio con/antly dim9i%es1 x w be se5 t ! rate ( *ange is greate/ 7or ! coeffici5t ( accel]ation highe/7 betwe5 ! ages ( ab\t two & five ye>s4 ,9 "o ( ,quetelet's tables 7supra1 p4 #fc71 he gives measurem5ts ( ! total span ( ! out/ret*$ arms 9 man1 f ye> to ye>1 comp>$ ) ! v]tical /ature4 ,! two measurem5ts are s ne>ly id5tical 9 actual magnitude t a direct comp>ison by means ( curves becomes unsatisfactory2 b ,i h r$uc$ ,quetelet's data to p]c5tages1 & x w be se5 f ,fig4 #ai t ! p]c5tage proportion ( span to height und]goes a rem>kable & /eady *ange f bir? to ! age ( tw5ty ye>s2 ! man gr[s m rapidly 9 /ret* ( arms ?an he does 9 height1 & ! span :i* 0 less ?an #id ! /ature at bir? by ab\t #a p] c5t4 exce$s x at ! age ( tw5ty by ab\t #d p] c5t4 ,aft] ! age ( tw5ty1 ,quetelet's data are few & irregul>1 b x is cle> t ! span goes on = a long :ile increas+ 9 proportion to ! /ature4 ,h[ f> ! ph5om5on is due to actual gr[? ( ! arms & h[ f> to ! increas+ bread? ( ! *e/ is n yet asc]ta9$4 ,illu/ration3 ,fig4 #ai4 ,ratio ( /ature 9 ,man1 to span ( out/ret*$ arms4 7,f ,quetelet's data47 ,! diff]5ces ( rate ( gr[? 9 diff]5t p>ts ( ! body are v simply br\ght out by ! foll[+ table1 :i* %ews ! relative gr[? ( c]ta9 p>ts & organs ( a "y tr\t1 at int]vals ( a few days dur+ ! p]iod ( mo/ rapid developm5t4 ,x w\ld n be difficult1 f a picture ( ! little tr\t at any "o ( ^! /ages1 to draw its approximate =m at any o!r1 by ! help ( ! num]ical data "h set =?#abf4 #ie ,tr\t 7,salmo f>io73 proportionate gr[? ( v>i\s organs4 7,f ,j5k9son's data47 ,days ,total #a/ ,v5tral #bnd ,bread? old l5g? ,eye ,head dorsal f9 dorsal ,tail-f9 ( tail #di #ajj #ajj #ajj #ajj #ajj #ajj #ajj #ajj #fc #abii #abid #adhc #adhf #adhe #ajhd #agch #aeei #gg #aedi #adgc #ahib 7#bjcf7 7#aicf7 #acib #begi #bbjd #ib #agcd #agid #bbjj 7#aicb7 7#ahba7 #aede #cjgf #bgbb #ajf #aidf #aibe #bdbe #agcb #afec #agcd #ccgc #bhgg ,:ile x is inequality ( gr[? 9 diff]5t directions t we c mo/ easily compreh5d z a ph5om5on lead+ to gradual *ange ( outw>d =m1 we %all see 9 ano!r *apt]#abg t diff]5ces ( rate at diff]5t p>ts ( a longitud9al sy/em1 ?\gh always 9 ! same direction1 also lead to v notable & regul> trans=mations4 ,( ?is ph5om5on1 ! diff]5ce 9 rate ( longitud9al gr[? betwe5 head & body is a simple case1 & ! diff]5ce :i* accompanies & results f x 9 ! bodily =m ( ! *ild & ! man is easy to see4 ,a l ph5om5on has be5 /udi$ 9 mu* great] detail 9 ! case ( plants1 by ,sa*s & c]ta9 o!r botani/s1 aft] a me?od 9 use by ,/eph5 ,hales a hundr$ & fifty ye>s be=e#abh4 ,on ! gr[+ root ( a bean1 t5 n>r[ zones 7 m>k$ (f1 />t+ f ! apex1 ea* zone a millimetre 9 bread?4 ,aft] tw5ty-f\r h\rs' gr[?1 at a c]ta9 con/ant temp]ature1 ! :ole m>k$ portion _h gr[n f #aj mm4 to #cc mm4 9 l5g?2 b ! individual zones _h gr[n at v unequal rates1 z %ewn 9 ! annex$ table#abi4 ,zone ,increm5t mm4 ,apex #ae #bnd #eh #crd #hb #d? #ce #e? #af #f? #ac #g? #je #h? #jc #i? #jb #aj? #ja #if ,illu/ration3 ,fig4 #bj4 ,rate ( gr[? 9 successive zones ne> ! tip ( ! bean-root4 ,! sev]al values 9 ?is table lie v ne>ly 7z we see by ,fig4 #bj7 9 a smoo? curve2 9 o!r words a def9ite law1 or pr9ciple ( cont9uity1 connects ! rates ( gr[? at successive po9ts along ! gr[+ axis ( ! root4 ,moreov] ?is curve1 9 its g5]al features1 is s+ul>ly l ^? accel]ation-curves :i* we h already /udi$1 9 :i* we plott$ ! rate ( gr[? aga9/ successive int]vals ( "t1 z "h we h plott$ x aga9/ successive spatial int]vals ( an actual gr[+ /ructure4 ,if we suppose = a mom5t t ! velocities ( gr[? _h be5 transv]se to ! axis1 in/ead (1 z 9 ?is case1 longitud9al & p>allel ) x1 x is obvi\s t ^! same velocities w\ld h giv5 u a leaf-%ap$ /ructure1 ( :i* our curve 9 ,fig4 #bj 7if drawn to a suitable scale7 w\ld repres5t ! actual outl9e on ei!r side ( ! m$ian axis2 or1 aga91 if gr[? _h be5 n conf9$ to "o plane b symmetrical ab\t ! axis1 we %\ld h _h a sort ( turnip-%ap$ root1 #ig hav+ ! =m ( a surface ( revolution g5]at$ by ! same curve4 ,?is !n is a simple & n unimportant illu/ration ( ! direct & easy passage f velocity to =m4 ,a k9dr$ problem occurs :51 in/ead ( 8zones0 artificially m>k$ out 9 a /em1 we deal ) ! rates ( gr[? 9 successive actual 8int]nodes02 & an int]e/+ v>iation ( ?is problem occurs :5 we consid]1 n ! actual gr[? ( ! int]nodes1 b ! v>y+ numb] ( leaves :i* !y successively produce4 ,:]e we h :orls ( leaves at ea* node1 z 9 ,equisetum & 9 _m wat]-we$s1 !n ! problem pres5ts itself 9 a simple =m1 & 9 "o su* case1 namely 9 ,c]atophyllum1 x has be5 c>efully inve/igat$ by ,mr ,raymond ,pe>l#acj4 ,x is f\nd t ! mean numb] ( leaves p] :orl increases ) ea* successive :orl2 b t ! rate ( increm5t dim9i%es f :orl to :orl1 z we asc5d ! axis4 ,9 o!r words1 ! increase 9 ! numb] ( leaves p] :orl foll[s a log>i?mic ratio2 & if y be ! mean numb] ( leaves p] :orl1 & x ! successional numb] ( ! :orl f ! root or ma9 /em upw>ds1 !n y ,a ,c log7x a71 :]e ,a1 ,c1 & a are c]ta9 specific con/ants1 v>y+ ) ! "p ( ! plant :i* we happ5 to be consid]+4 ,on ! ma9 /em1 ! rate ( *ange 9 ! numb] ( leaves p] :orl is v sl[2 :5 we come to ! small twigs1 or 8t]ti>y bran*es10 x has become rapid1 z we see f ! foll[+ abbreviat$ table3 ,numb] ( leaves p] :orl on ! t]ti>y bran*es ( ,c]atophyllum4 ,position ( :orl #a #b #c #d #e #f ,mean numb] ( leaves #fee #hjg #ijj #ibj #ige #ajjj ,increm5t -- #aeb #ic #bj 7#ee7 7#be7 ,we h se5 t a sl[ b def9ite *ange ( =m is a common accompanim5t ( increas+ age1 & is br\ght ab\t z ! simple & natural result ( an alt]$ ratio betwe5 ! rates ( gr[? 9 diff]5t dim5sions3 or r by ! progressive *ange necess>ily br\ght ab\t by ! diff]5ce 9 _! accel]ations4 ,!re are _m cases h[ev] 9 :i* ! *ange is all b imp]ceptible to ord9>y measurem5t1 & _m o!rs 9 :i* "s "o dim5sion is easily measur$1 b o!rs are h>d to measure ) correspond+ accuracy4 #ih ,= in/ance1 9 any ord9>y fi%1 su* z a plaice or a haddock1 ! l5g? is n difficult to measure1 b measurem5ts ( bread? or dep? are v mu* m unc]ta94 ,9 cases su* z ^!1 :ile x rema9s difficult to def9e ! precise nature ( ! *ange ( =m1 x is easy to %ew t su* a *ange is tak+ place if we make use ( t ratio ( l5g? to weight :i* we h spok5 ( 9 ! prec$+ *apt]4 ,assum+1 z we may fairly d1 t weight is directly proportional to bulk or volume1 we may express ?is relation 9 ! =m ,w_/,l#c k1 :]e k is a con/ant1 to be det]m9$ = ea* p>ticul> case4 7,w & ,l are express$ 9 grammes & c5timetres1 & x is usual to multiply ! result by "s figure1 su* z #ajjj1 s z to give ! con/ant k a value ne> to unity47 ,plaice caught 9 a c]ta9 area1 ,m>*1 #aijg4 ,v>iation ( k 7! weight-l5g? coeffici5t7 ) size4 7,data tak5 f ! ,dep>tm5t ( ,agriculture & ,fi%]ies' ,plaice-,report1 vol4 ,i1 p4 #ajg1 #aijh47 ,size 9 cm4 ,weight 9 gm4 ,w_/,l#c #aj1jjj ,w_/,l#c 7smoo!d7 #bc #aac #ibh -- #bd #abh #ibf #idc #be #aeb #igc #ifa #bf #agc #ihd #igi #bg #aic #iha #iij #bh #bba #ajjf #ajjd #bi #bej #ajbe #ajab #cj #bga #ajjd #ajab #ca #cjj #ajjg #ajjd #cb #cbh #ajja #iih #cc #ced #ihe #ihh #cd #chd #igg #ihj #ce #dai #igg #igf #cf #ded #igc #ifg #cg #dib #ieb #ifc #ch #ebi #ifd #ief #ci #efd #iea #iej #dj #fad #iei #iej #da #fdg #ici #ich #db #fgi #iaf #ibe #dc #gcb #iba #ibe #dd #hjj #ici #idj #de #hge #ifj -- #ii ,n[ :ile ?is k may be spok5 ( z a 8con/ant10 hav+ a c]ta9 mean value specific to ea* species ( organism1 & dep5d+ on ! =m ( ! organism1 any *ange to :i* x may be subject w be a v delicate index ( progressive *anges ( =m2 = we "k t our measurem5ts ( l5g? are1 on ! av]age1 v accurate1 & weigh+ is a /ill m delicate me?od ( comp>ison ?an any l9e> measurem5t4 ,illu/ration3 ,fig4 #ba4 ,*anges 9 ! weight-l5g? ratio ( ,plaice1 ) increas+ size4 ,?us1 9 ! case ( plaice1 :5 we deal ) ! mean values = a l>ge numb] ( specim5s1 & :5 we are c>eful to deal only ) su* z are caught 9 a p>ticul> locality & at a p>ticul> "t1 we see t k is by no means con/ant1 b /eadily increases to a maximum1 & aft]w>ds sl[ly decl9es ) ! increas+ size ( ! fi% 7,fig4 #ba74 ,to beg9 )1 !re=e1 ! weight is increas+ m rapidly ?an ! cube ( ! l5g?1 & x foll[s t ! l5g? itself is increas+ less rapidly ?an "s o!r l9e> dim5sion2 :ile 9 lat] life ?is condition is rev]s$4 ,! maximum is rea*$ :5 ! l5g? ( ! fi% is some:]e ne> to #cj cm41 & x is tempt+ to suppose t ) ?is 8po9t ( inflection0 !re is associat$ "s well-m>k$ epo* 9 ! fi%'s life4 ,z a matt] ( fact1 ! size ( #cj cm4 is approximately t at :i* sexual maturity may be said to beg91 or is at lea/ ne> en\gh to sugge/ a close connection betwe5 ! two ph5om5a4 ,! fir/ /ep t[>ds fur!r inve/igation ( ! #ajj app>5t co9cid5ce w\ld be to det]m9e ! coeffici5t k ( ! two sexes sep>ately1 & to discov] :e!r or n ! po9t ( inflection is rea*$ 7or sexual maturity is rea*$7 at a small] size 9 ! male ?an 9 ! female plaice2 b ! mat]ial = ?is inve/igation is at pres5t scanty4 ,illu/ration3 ,fig4 #bb4 ,p]iodic annual *ange 9 ! weight-l5g? ratio ( ,plaice4 ,a /ill m curi\s & m unexpect$ result appe>s :5 we comp>e ! values ( k = ! same fi% at diff]5t seasons ( ! ye>#aca4 ,:5 = simplicity's sake 7z 9 ! accompany+ table & ,fig4 #bb7 we re/rict ourselves to fi% ( "o p>ticul> size1 x is n necess>y to det]m9e ! value ( k1 because a *ange 9 ! ratio ( l5g? to weight is obvi\s en\gh2 b :5 we h small numb]s1 & v>i\s sizes1 to deal )1 ! det]m9ation ( k may help u v mu*4 ,x w be se51 !n1 t 9 ! case ( plaice ! ratio ( weight to l5g? exhibits a regul> p]iodic v>iation ) ! c\rse ( ! seasons4 #aja ,relation ( ,weight to ,l5g? 9 ,plaice ( #ee cm4 long1 f ,mon? to ,mon?4 7,data tak5 f ! ,dep>tm5t ( ,agriculture & ,fi%]ies ,plaice-,report1 vol4 ,,ii1 p4 #ib1 #aiji47 ,av]age weight 9 grammes ,w_/,l#c #ajj ,w_/,l#c 7smoo!d7 ,jan4 #bjci #abbf #aaeg ,feb4 #agce #ajdc #ajhj ,m>* #afaf #jiga #jihi ,april #aehe #jiec #jifg ,may #afbd #jigf #jihe ,june #agjg #ajbf #ajje ,july #afhf #ajac #ajcg ,augu/ #aghc #ajgb #ajdb ,sept4 #agcc #ajdb #aaaa ,oct4 #bjbi #abbj #aafj ,nov4 #bjbf #abah #abac ,dec4 #aiih #abja #abae ,) un*ang+ l5g?1 ! weight & !re=e ! bulk ( ! fi% falls (f f ab\t ,novemb] to ,m>* or ,april1 & aga9 betwe5 ,may or ,june & ,novemb] ! bulk & weight are gradually re/or$4 ,! explanation is simple1 & dep5ds :olly on ! process ( spawn+1 & on ! subsequ5t build+ up aga9 ( ! tissues & ! reproductive organs4 ,x foll[s t1 by ?is me?od1 )\t ev] see+ a fi% spawn1 & )\t ev] dissect+ "o to see ! /ate ( its reproductive sy/em1 we c asc]ta9 its spawn+ season1 & det]m9e ! beg9n+ & end !re(1 ) great accuracy4 ,z a f9al illu/ration ( ! rate ( gr[?1 & ( unequal gr[? 9 v>i\s directions1 ,i give ! foll[+ table ( data reg>d+ ! ox1 ext5d+ ov] ! fir/ ?ree ye>s1 or ne>ly s1 ( ! animal's life4 ,! obs]v$ data are 7#a7 ! weight ( ! animal1 mon? by mon?1 7#b7 ! l5g? ( ! back1 f ! occiput to ! root ( ! tail1 & 7#c7 ! height to ! )]s4 ,to ^! data ,i h add$ 7#a7 ! ratio ( l5g? to height1 7#b7 ! coeffici5t 7k7 express+ ! ratio ( weight to ! cube ( ! l5g?1 & 7#c7 a simil> coeffici5t 7k7 = ! height ( ! animal4 ,x w be se5 t1 :ile all ^! ratios t5d to alt] cont9u\sly1 %ew+ t ! animal's =m is /eadily alt]+ z x approa*es maturity1 ! ratio betwe5 l5g? & weight #ajb *anges comp>atively little4 ,! simple ratio betwe5 l5g? & height increases consid]ably1 z inde$ we %\ld expect2 = we "k t 9 all ,ungulate animals ! legs are rem>kably ,relations betwe5 ! ,weight & c]ta9 ,l9e> ,dim5sions ( ! ,ox4 7,data f ,przibram1 aft] ,cornev947 k k ,age 9 ,w1 wt4 ,l1 l5g? ,h1 ,w_/,l#c ,w_/,h#c mon?s 9 kg4 ( back height ,l_/,h #aj #aj #j #cg #gh #gj #aaad #ggi #ajgi #a #eec #id #gg #abba #ffe #abaj #b #hfc #aji #he #abhb #fff #adjf #c #abac #abjg #id #abhd #fij #adfj #d #aejc #acad #ie #achc #ffb #aged #e #agic #adjd #ajdj #acej #fdi #afjj #f #bajc #adhd #ajhg #acfe #fdd #afch #g #bdgc #aebd #aabb #aceh #fii #agea #h #bfgc #aeha #aadg #acgh #fgg #agia #i #bhbh #afba #aafb #acie #ffd #ahjb #aj #cjcg #afea #aaib #ache #fge #agic #aa #cbgg #afid #abae #acid #fgd #agid #ab #cejg #agdj #abch #adje #fff #ahdi #ac #cgdg #agfe #abed #adjg #fhb #aijj #ad #ciac #aghe #abfd #adab #fhh #aich #ae #djei #ahjd #abgj #adbj #fib #aihb #af #dagi #ahad #abhj #adag #gjj #bjib #ag #dbci #ahcb #abij #adbj #fhi #aigd #ah #dbci #ahei #abig #adcc #ffj #aidc #ai #dbgi #ahge #acjg #adce #fdi #aiaf #bj #dcgi #ahhd #acaa #adcg #fee #aidd #ba #ddgi #ahic #acba #adcc #ffa #aidc #bb #dfdd #aija #accc #adbf #fgf #aifj #bc #dhji #aiji #acde #adai #fia #aigg #bd #ejji #aiad #aceb #adaf #gad #bjbg #be #ebji #aiai #acei #adab #gcg #bjge #bf #ecda #aibd #acfa #adad #gej #baai #bg #edgc #aibi #acfc #adae #gfb #bafb #bh #eede #aibi #acfc #adae #ggb #baij #bi #efag #aibi #acfc #adae #ghb #bbah #cj #ehfb #aidi #achc #adji #gib #bbaf #ca #fajg #aifi #adjc #adjc #hjj #bbaa #cb #fbeg #aihc #adbj #acif #hjc #bahf #cc #fdjg #aiig #adcg #acij #hje #baei #cd #feeg #bjaa #aded #achc #hjf #bacc ,cornev91 ,*41 tudes sur la croissance1 ,ar*4 de ,physiol4 norm4 et pa?ol4 7#e71 ,,iv1 p4 #dgg1 #ahib4 #ajc long at bir? 9 comp>ison ) o!r dim5sions ( ! body4 ,x is some:at curi\s1 h[ev]1 t ?is ratio seems to fall (f a little 9 ! ?ird ye> ( gr[?1 ! animal cont9u+ to gr[ 9 height to a m>k$ degree aft] gr[? 9 l5g? has become v sl[4 ,! ratio betwe5 height & weight is by mu* ! mo/ v>iable ( our ?ree ratios2 ! coeffici5t ,w_/,h#c /eadily increases1 & is m ?an twice z great at ?ree ye>s old z x 0 at bir?4 ,?is illu/rates ! important1 b obvi\s fact1 t ! coeffici5t k is mo/ v>iable 9 ! case ( t dim5sion :i* gr[s mo/ uni=mly1 t is to say mo/ ne>ly 9 proportion to ! g5]al bulk ( ! animal4 ,9 %ort1 ! successive values ( k1 z det]m9$ 7at successive epo*s7 = "o dim5sion1 are a measure ( ! v>iability ( ! o!rs4 ,f ! :ole ( ! =ego+ discussion we see t a c]ta9 def9ite rate ( gr[? is a *>act]i/ic or specific ph5om5on1 deep-seat$ 9 ! physiology ( ! organism2 & t a v l>ge "p ( ! specific morphology ( ! organism dep5ds ^u ! fact t !re is n only an av]age1 or aggregate1 rate ( gr[? common to ! :ole1 b also a v>iation ( rate 9 diff]5t p>ts ( ! organism1 t5d+ t[>ds a specific rate *>act]i/ic ( ea* diff]5t "p or organ4 ,! smalle/ *ange 9 ! relative magnitudes ( ^! p>tial or localis$ velocities ( gr[? w be soon manife/$ 9 m & m /rik+ diff]5ces ( =m4 ,?is is z mu* z to say t ! "t-elem5t1 :i* is implicit 9 ! idea ( gr[?1 c nev] 7or v seldom7 be :olly neglect$ 9 our consid]ation ( =m#acb4 ,x is sc>cely necess>y to enl>ge "h ^u our /atem5t1 = n only is ! tru? ( x self-evid5t1 b x w f9d illu/ration aga9 & aga9 ?r\gh\t ?is book4 ,nev]!less1 let u g out ( our way = a mom5t to consid] x 9 ref]5ce to a p>ticul> case1 & to enquire :e!r x helps to remove any ( ! difficulties :i* t case appe>s to pres5t4 #ajd ,illu/ration3 ,fig4 #bc4 ,v>iability ( l5g? ( tail-=ceps 9 a sample ( ,e>wigs4 7,aft] ,bateson1 ,p4 ,z4 ,s4 #ahib1 p4 #ehh47 ,9 a v well-kn[n pap]1 ,bateson %ew$ t1 among a l>ge numb] ( e>wigs1 collect$ 9 a p>ticul> locality1 ! males fell into two gr\ps1 *>act]is$ by l>ge or by small tail-=ceps1 ) v few in/ances ( int]m$iate magnitude4 ,?is di/ribution into two gr\ps1 accord+ to magnitude1 is illu/rat$ 9 ! accompany+ diagram 7,fig4 #bc72 & ! ph5om5on 0 describ$1 & has be5 (t5 quot$1 z "o ( dimorphism1 or discont9u\s v>iation4 ,9 ?is diagram ! "t-elem5t does n appe>2 b x is c]ta91 & evid5t1 t x lies close beh9d4 ,suppose we take "s organism :i* is born n at all times ( ! ye> 7z man is7 b at "s "o p>ticul> season 7= in/ance a fi%71 !n any r&om sample w consi/ ( individuals ^: ages1 & !re=e ^: magnitudes1 w =m a discont9u\s s]ies2 & by plott+ ^! magnitudes on a curve 9 relation to ! numb] ( individuals ( ea* p>ticul> magnitude1 we obta9 a curve su* z t %ewn 9 ,fig4 #bd1 ! fir/ practical use ( :i* is to enable u to analyse our sample into its con/itu5t 8age-gr\ps10 or 9 o!r words to det]m9e approximately ! age1 or ages ( ! fi%4 ,& if1 in/ead ( measur+ ! :ole l5g? ( our fi%1 we _h conf9$ ourselves to p>ticul> p>ts1 su* z head1 or #aje tail or f91 we %\ld h obta9$ discont9u\s curves ( di/ribution1 precisely analog\s to ^? = ! entire animal4 ,n[ we "k t ! diff]5ces ) :i* ,bateson 0 deal+ 7 entirely a "q ( magnitude1 & we _c help see+ t ! discont9u\s di/ributions ( magnitude repres5t$ by 8 e>wigs' tails are j su* z are illu/rat$ by ! magnitudes ( ! old] & y\ng] fi%2 we may inde$ g s f> z to say t ! curves are precisely comp>able1 = 9 bo? cases we see a *>act]i/ic feature ( detail1 namely t ! 8spread0 ( ! curve is great] 9 ! second wave ?an 9 ! fir/1 t is to say 79 ! case ( ! fi%7 9 ! old] z well z l>g] s]ies4 ,ov] ! reason = ?is ph5om5on1 :i* is simple & all b obvi\s1 we ne$ n pause4 ,illu/ration3 ,fig4 #bd4 ,v>iability ( l5g? ( body 9 a sample ( ,plaice4 ,x is evid5t1 !n1 t 9 ?is case ( 8dimorphism10 ! tails ( ! "o gr\p ( e>wigs 7:i* ,bateson calls ! 8high males07 h ei!r gr[n fa/]1 or h be5 gr[+ = a long] p]iod ( "t1 ?an ^? ( ! 8l[ males40 ,if we c\ld be c]ta9 t ! :ole r&om sample ( e>wigs 7 ( "o & ! same age1 !n we %\ld h to ref] ! ph5om5on ( dimorphism to a physiological ph5om5on1 simple 9 k9d 7h[ev] rem>kable & unexpect$72 viz4 t !re 7 two alt]native #ajf values1 v diff]5t f "o ano!r1 = ! mean velocity ( gr[?1 & t ! individual e>wigs v>i$ ar\nd "o or o!r ( ^! mean values1 9 ea* case accord+ to ! law ( probabilities4 ,b on ! o!r h&1 if we c\ld believe t ! two gr\ps ( e>wigs 7 ( diff]5t ages1 !n ! ph5om5on w\ld be simplicity itself1 & !re w\ld be no m to be said ab\t x#acc4 ,be=e we pass f ! subject ( ! relative rate ( gr[? ( diff]5t p>ts or organs1 we may take brief note ( ! fact t v>i\s exp]im5ts h be5 made to det]m9e :e!r ! normal ratios are ma9ta9$ "u alt]$ circum/ances ( nutrition1 & especially 9 ! case ( p>tial />vation4 ,= in/ance1 x has be5 f\nd possible to keep "y rats alive = _m weeks on a diet su* z is j suffici5t to ma9ta9 life )\t p]mitt+ any increase ( weight4 ,! rat ( ?ree weeks old weighs ab\t #be gms41 & "u a normal diet %\ld weigh at t5 weeks old ab\t #aej gms41 9 ! male1 or #aae gms4 9 ! female2 b ! und]f$ rat is /ill kept at t5 weeks old to ! weight ( #be gms4 ,"u normal diet ! proportions ( ! body *ange v consid]ably betwe5 ! ages ( ?ree & t5 weeks4 ,= in/ance ! tail gets relatively long]2 & ev5 :5 ! total gr[? ( ! rat is prev5t$ by und]fe$+1 ! =m cont9ues to alt] s t ?is increas+ l5g? ( ! tail is /ill manife/#acd4 #ajg ,full-f$ ,rats4 ,age 9 ,l5g? ( ,l5g? ( ,total weeks body 7mm47 tail 7mm47 l5g? ( tail #j #dhg #afi #fef #beh #a #fde #bid #ici #cac #c #ijd #eia #adie #cie #f #abhj #aajj #bchj #dfb #aj #agcj #aejj #cbcj #dfd ,und]f$ ,rats4 #f #ihj #gbc #agjc #dbe #aj #iif #hci #ahce #deg ,aga9 z physiologi/s h long be5 aw>e1 !re is a m>k$ diff]5ce 9 ! v>iation ( weight ( ! diff]5t organs1 accord+ to :e!r ! animal's total weight rema9 con/ant1 or be caus$ to dim9i% by actual />vation2 & fur!r /rik+ diff]5ces appe> :5 ! diet is n only scanty1 b ill-balanc$4 ,b ^! ph5om5a ( abnormal gr[?1 h[ev] int]e/+ f ! physiological view1 are ( little practical importance to ! morphologi/4 ,! effect ( temp]ature#ace4 ,! rates ( gr[? :i* we h hi!rto dealt ) are bas$ on special inve/igations1 conduct$ "u p>ticul> local conditions4 ,= in/ance1 ,quetelet's data1 s f> z we h us$ !m to illu/rate ! rate ( gr[? 9 man1 are drawn f 8 /udy ( ! population ( ,belgium4 ,b ap>t f t 8=tuit\s0 individual v>iation :i* we h already consid]$1 x is obvi\s t ! normal rate ( gr[? w be f\nd to v>y1 9 man & 9 o!r animals1 j z ! av]age /ature v>ies1 9 diff]5t localities1 & 9 diff]5t 8races40 ,?is ph5om5on is a v complex "o1 & is d\btless a resultant ( _m undef9$ contributory causes2 b we at lea/ ga9 some?+ 9 reg>d to x1 :5 we discov] t ! rate ( gr[? is directly affect$ by temp]ature1 & probably by o!r physical #ajh conditions4 ,raumur 0 ! fir/ to %ew1 & ! obs]vation 0 repeat$ by ,bonnet#acf1 t ! rate ( gr[? or developm5t ( ! *ick 0 dep5d5t on temp]ature1 be+ ret>d$ at temp]atures bel[ & some:at accel]at$ at temp]atures above ! normal temp]ature ( incubation1 t is to say ! temp]ature ( ! sitt+ h54 ,9 ! case ( plants ! fact t gr[? is greatly affect$ by temp]ature is a matt] ( famili> k2 ! subject 0 fir/ c>efully /udi$ by ,alphonse ,de ,c&olle1 & 8 results & ^? ( 8 foll[]s are discuss$ 9 ! textbooks ( ,botany#acg4 ,t v>iation ( temp]ature con/itutes only "o factor 9 det]m9+ ! rate ( gr[? is admirably illu/rat$ 9 ! case ( ! ,bamboo4 ,x has be5 /at$ 7by ,lock7 t 9 ,ceylon ! rate ( gr[? ( ! ,bamboo is directly proportional to ! humidity ( ! atmosph]e3 & aga9 7by ,%ibata7 t 9 ,japan x is directly proportional to ! temp]ature4 ,! two /atem5ts h be5 +5i\sly & satisfactorily reconcil$ by ,blackman#ach1 :o sugge/s t 9 ,ceylon ! temp]ature-conditions are all t c be desir$1 b moi/ure is apt to be defici5t3 :ile 9 ,japan !re is ra9 9 abundance b ! av]age temp]ature is some:at too l[4 ,s t 9 ! "o c\ntry x is ! "o factor1 & 9 ! o!r c\ntry x is ! o!r1 :i* is ess5tially v>iable4 ,! annex$ diagram 7,fig4 #be71 %ew+ ! gr[? 9 l5g? ( ! roots ( "s common plants dur+ an id5tical p]iod ( =ty-eight h\rs1 at temp]atures v>y+ f ab\t #ad to #cg ,c41 is a suffici5t illu/ration ( ! ph5om5on4 ,we see t 9 all cases !re is a c]ta9 optimum temp]ature at :i* ! rate ( gr[? is a maximum1 & we c also see t on ei!r side ( ?is optimum temp]ature ! accel]ation ( gr[?1 positive or negative1 ) increase ( temp]ature is rapid1 :ile at a di/ance f ! optimum x is v sl[4 ,f ! data giv5 by ,sa*s & o!rs1 we see fur!r t ?is optimum temp]ature is v mu* ! same = all ! common plants ( our own climate :i* h z yet be5 /udi$2 9 !m x is #aji some:]e ab\t #bf ,c4 7or say #gg ,f471 or ab\t ! temp]ature ( a w>m summ]'s day2 :ile x is f\nd1 v naturally1 to be consid]ably high] 9 ! case ( plants su* z ! melon or ! maize1 :i* are at home 9 w>m] regions t our own4 ,illu/ration3 ,fig4 #be4 ,relation ( rate ( gr[? to temp]ature 9 c]ta9 plants4 7,f ,sa*s's data47 ,9 a l>ge numb] ( physical ph5om5a1 & 9 a v m>k$ degree 9 all *emical reactions1 x is f\nd t rate ( action is affect$1 & = ! mo/ "p accel]at$1 by rise ( temp]ature2 & ?is effect ( temp]ature t5ds to foll[ a def9ite 8expon5tial0 law1 :i* holds good )9 a consid]able range ( temp]ature1 b is alt]$ or dep>t$ f :5 we pass beyond c]ta9 normal limits4 ,! law1 z laid d[n by van't ,h(f = *emical reactions1 is1 t = an int]val ( n degrees ! velocity v>ies z xn1 x be+ call$ ! 8temp]ature coeffici5t0#aci = ! reaction 9 "q4 #aaj ,van't ,h(f's law1 :i* has become a fundam5tal pr9ciple ( *emical me*anics1 is likewise applicable 7) c]ta9 qualifications7 to ! ph5om5a ( vital *emi/ry2 & x foll[s t1 on v mu* ! same l9es1 we may speak ( ! 8temp]ature coeffici5t0 ( gr[?4 ,at ! same "t we mu/ rememb] t !re is a v important diff]5ce 7?\gh we c sc>cely call x a fundam5tal "o7 betwe5 ! purely physical & ! physiological ph5om5on1 9 t 9 ! =m] we /udy 7or seek & pr(ess to /udy7 "o ?+ at a "t1 :ile 9 ! latt] we h always to d ) v>i\s factors :i* int]sect & int]f]e2 increase 9 ! "o case 7or *ange ( any k9d7 t5ds to be cont9u\s1 9 ! o!r case x t5ds to be br\ght to arre/4 ,?is is ! simple mean+ ( t ,law ( ,optimum1 laid d[n by ,err]a & by ,sa*s z a g5]al pr9ciple ( physiology3 namely t e physiological process :i* v>ies 7l gr[? itself7 ) ! am\nt or int5sity ( "s ext]nal influ5ce1 does s accord+ to a law 9 :i* progressive increase is foll[$ by progressive decrease2 9 o!r words ! function has its optimum condition1 & its curve %ews a def9ite maximum4 ,9 ! case ( temp]ature1 z ,jo/ puts x1 x has on ! "o h& its accel]at+ effect :i* t5ds to foll[ van't ,h(f's law4 ,b x has also ano!r & a cumulative effect ^u ! organism3 8,sie s*digt od] sie ermdet ihn1 und je hh] sie /eigt1 de/o ras*] ma*t sie die ,s*digung gelt5d und de/o s*nell] s*reitet sie voran40 ,x w\ld seem to be ?is d\ble effect ( temp]ature 9 ! case ( ! organism :i* gives u our 8optimum0 curves1 :i* are ! expression1 accord+ly1 n ( a prim>y ph5om5on1 b ( a m or less complex resultant4 ,moreov]1 z ,blackman & o!rs h po9t$ out1 our 8optimum0 temp]ature is v ill-def9$ until we take acc\nt also ( ! duration ( our exp]im5t2 = obvi\sly1 a high temp]ature may lead to a %ort1 b exhau/+1 spell ( rapid gr[?1 :ile ! sl[] rate manife/$ at a l[] temp]ature may be ! be/ 9 ! end4 #aaa ,! mile & ! hundr$ y>ds are won by diff]5t runn]s2 & maximum rate ( work+1 & maximum am\nt ( "w done1 are two v diff]5t ?+s#adj4 ,9 ! case ( maize1 a c]ta9 s]ies ( exp]im5ts %ew$ t ! gr[? 9 l5g? ( ! roots v>i$ ) ! temp]ature z foll[s#ada3 ,temp]ature ,gr[? 9 #dh h\rs ,c4 mm4 #ahj #aa #bce #ajh #bff #bif #bhe #bfe #cjb #fdf #cce #fie #cfe #bjg ,let u write our =mula 9 ! =m ,v7tn7_/,vt xn4 ,!n *oos+ two values out ( ! above exp]im5tal s]ies 7say ! second & ! second-la/71 we h t #bce1 n #aj1 & ,v1 ,v #ajh & #fie respectively4 ,accord+ly #fie_/ajh #fd x#aj4 ,!re=e 7log #fd7_/aj1 or #jhjf log x4 ,&1 x #abjd 7= an int]val ( #a ,c474 ,?is fir/ approximation might be consid]ably improv$ by tak+ acc\nt ( all ! exp]im5tal values1 two only ( :i* we h z yet made use (2 b ev5 z x is1 we see by ,fig4 #bf t x is 9 v fair accordance ) ! actual results ( obs]vation1 )9 ^? p>ticul> limits ( temp]ature to :i* ! exp]im5t is conf9$4 #aab ,= an exp]im5t on ,lup9us albus1 quot$ by ,asa ,gray#adb1 ,i h work$ out ! correspond+ coeffici5t1 b a little m c>efully4 ,its value ,i f9d to be #aaf1 or v ne>ly id5tical ) t we h j f\nd = ! maize2 & ! correspond5ce betwe5 ! calculat$ curve & ! actual obs]vations is n[ a close "o4 ,illu/ration3 ,fig4 #bf4 ,relation ( rate ( gr[? to temp]ature 9 ,maize4 ,obs]v$ values 7aft] ,kpp571 & calculat$ curve4 ,s9ce ! above p>agraphs 7 writt51 new data h come to h&4 ,miss ,i4 ,leit* has made c>eful obs]vations ( ! rate ( gr[? ( rootlets ( ! ,pea2 & ,i h attempt$ a fur!r analysis ( h] pr9cipal results#adc4 ,9 ,fig4 #bg are %ewn ! mean rates ( gr[? 7bas$ on ab\t a hundr$ exp]im5ts7 at "s ?irty-f\r diff]5t temp]atures betwe5 #jh & #bic1 ea* exp]im5t la/+ r less ?an tw5ty-f\r h\rs4 ,work+ out ! mean temp]ature coeffici5t = a great _m comb9ations ( ^! values1 ,i obta9 a value ( #ajib p] ,c41 or #bda = an int]val ( #aj1 & a mean value = ! :ole s]ies %[+ a rate ( gr[? ( j ab\t #a mm4 p] h\r at a temp]ature ( #bj4 ,my curve 9 ,fig4 #bg is drawn f ^! det]m9ations2 & x w be se5 t1 :ile x is by no means exact at ! l[] temp]atures1 & w ( c\rse fail u altoge!r at v high #aac temp]atures1 yet x s]ves z a v satisfactory guide to ! relations betwe5 rate & temp]ature )9 ! ord9>y limits ( heal?y gr[?4 ,miss ,leit* holds t ! curve is n a van't ,h(f curve2 & ?is1 9 /rict accuracy1 we ne$ n dispute4 ,b ! ph5om5on seems to me to be "o into :i* ! van't ,h(f ratio ent]s l>gely1 ?\gh d\btless comb9$ ) o!r factors :i* we _c at pres5t det]m9e or elim9ate4 ,illu/ration3 ,fig4 #bg4 ,relation ( rate ( gr[? to temp]ature 9 rootlets ( ,pea4 7,f ,miss ,i4 ,leit*'s data47 ,:ile ! above results con=m fairly well to ! law ( ! temp]ature coeffici5t1 x is evid5t t ! imbibition ( wat] plays s l>ge a "p 9 ! process ( elongation ( ! root or /em t ! ph5om5on is r a physical ?an a *emical "o3 & on ?is acc\nt1 z ,blackman has rem>k$1 ! data commonly giv5 = ! rate ( gr[? 9 plants are apt to be #aad irregul>1 & sometimes 7we might ev5 say7 mislead+#add4 ,! fact also1 :i* we h already le>n$1 t ! elongation ( a %oot t5ds to proce$ by j]ks1 r ?an smoo?ly1 is ano!r indication t ! ph5om5on is n purely & simply a *emical "o4 ,we h abundant illu/rations1 h[ev]1 among animals1 9 :i* we may /udy ! temp]ature coeffici5t "u circum/ances :]e1 ?\gh ! ph5om5on is always complicat$ by osmotic factors1 true metabolic gr[? or *emical comb9ation plays a l>g] role4 ,?us ,mlle4 ,maltaux & ,pr(essor ,mass>t#ade h /udi$ ! rate ( division 9 a c]ta9 flagellate1 ,*ilomonas p>amoecium1 & f\nd ! process to take #bi m9utes at #ae ,c41 #ab at #be1 & only #e m9utes at #ce ,c4 ,^! velocities are 9 ! ratio ( #a 3 #bd 3 #egf1 :i* ratio corresponds precisely to a temp]ature coeffici5t ( #bd = ea* rise ( #aj1 or ab\t #ajib = ea* degree c5tigrade4 ,by means ( ?is pr9ciple we may ?r[ light on ! app>5tly complicat$ results ( _m exp]im5ts4 ,= in/ance1 ,fig4 #bh is an illu/ration1 :i* has be5 (t5 copi$1 ( ,o4 ,h]twig's "w on ! effect ( temp]ature on ! rate ( developm5t ( ! tadpole#adf4 ,f inspection ( ?is diagram1 we see t ! "t tak5 to atta9 c]ta9 /ages ( developm5t 7d5ot$ by ! numb]s ,,iii-,,vii7 0 z foll[s1 at #bj & at #aj ,c41 respectively4 ,at #bj ,at #aj ,/age ,,iii #bj #fe days ,/age ,,iv #bg #ha days ,/age ,v #cj #ajg days ,/age ,,vi #dj #ace days ,/age ,,vii #ej #afh days ,total #afg #eef days ,t is to say1 ! "t tak5 to produce a giv5 result at #aae #aj 0 7on ! av]age7 some:]e ab\t #eef_/afg1 or #ccc1 times z long z 0 requir$ at #bj4 ,illu/ration3 ,fig4 #bh4 ,diagram %ew+ "t tak5 79 days71 at v>i\s temp]atures 7,c471 to rea* c]ta9 /ages ( developm5t 9 ! ,frog3 viz4 ,i1 ga/rula2 ,,ii1 m$ull>y plate2 ,,iii1 closure ( m$ull>y folds2 ,,iv1 tail-bud2 ,v1 tail & gills2 ,,vi1 tail-f92 ,,vii1 op]culum beg9n+2 ,,viii1 d4 clos+2 ,,ix1 fir/ appe>ance ( h9d-legs4 7,f ,j5k9son1 aft] ,o4 ,h]twig1 #ahih47 ,we may !n put our equation aga9 9 ! simple =m1 #aaf x#aj #ccc4 ,or1 #aj log x log #ccc #ebbdd4 ,!re=e log x #jebbd1 & x #aabh4 ,t is to say1 betwe5 ! int]vals ( #aj & #bj ,c41 if x take m days1 at a c]ta9 giv5 temp]ature1 = a c]ta9 /age ( developm5t to be atta9$1 x w take m #aabhn days1 :5 ! temp]ature is n degrees less1 = ! same /age to be arriv$ at4 ,illu/ration3 ,fig4 #bi4 ,calculat$ values1 correspond+ to prec$+ figure4 ,fig4 #bi is calculat$ ?r\gh\t f ?is value2 & x w be se5 t x is extremely concordant ) ! orig9al diagram1 z reg>ds all ! /ages ( developm5t & ! :ole range ( temp]atures %ewn3 9 spite ( ! fact t ! coeffici5t on :i* x is bas$ 0 d]iv$ by an easy me?od f a v few po9ts 9 ! orig9al curves4 #aag ,k>l ,pet]#adg1 exp]im5t+ *iefly on e*9od]m eggs1 & also mak+ use ( ,h]twig's exp]im5ts on "y tadpoles1 gives ! normal temp]ature coeffici5ts = int]vals ( #aj ,c4 7commonly writt5 ,q#aj7 z foll[s4 ,spha]e*9us #bae1 ,e*9us #bac1 ,rana #bhf4 ,^! values are n only concordant1 b are evid5tly ( ! same ord] ( magnitude z ! temp]ature-coeffici5t 9 ord9>y *emical reactions4 ,pet] has also discov]$ ! v int]e/+ fact t ! temp]ature-coeffici5t alt]s ) age1 usually b n always becom+ small] z age increases4 ,spha]e*9us2 ,segm5tation ,q#aj #bbi1 ,lat] /ages ,q#aj #bjc4 ,e*9us2 ,segm5tation ,q#aj #bcj1 ,lat] /ages ,q#aj #bjh4 ,rana2 ,segm5tation ,q#aj #bbc1 ,lat] /ages ,q#aj #ccd4 ,fur!rmore1 ! temp]ature coeffici5t v>ies ) ! temp]ature1 dim9i%+ z ! temp]ature rises1--a rule :i* van't ,h(f has %ewn to hold 9 ord9>y *emical op]ations4 ,?us1 9 ,rana ! temp]ature coeffici5t at l[ temp]atures may be z high z #ef3 :i* is j ano!r way ( say+ t at l[ temp]atures developm5t is exceptionally ret>d$4 ,9 c]ta9 fi%1 su* z plaice & haddock1 ,i & o!rs h f\nd cle> evid5ce t ! asc5d+ curve ( gr[? is subject to seasonal int]ruptions1 ! rate dur+ ! w9t] mon?s be+ always sl[] ?an 9 ! mon?s ( summ]3 x is z ?\gh we sup]impos$ a p]iodic1 annual1 s9e-curve ^u ! cont9u\s curve ( gr[?4 ,& fur!r1 z gr[? itself gr[s less & less f ye> to ye>1 s w ! diff]5ce betwe5 ! w9t] & ! summ] rate also gr[ less & less4 ,! fluctuation 9 rate #aah w repres5t a vibration :i* is gradually dy+ out2 ! amplitude ( ! s9e-curve w gradually dim9i% till x disappe>s2 9 %ort1 our ph5om5on is simply express$ by :at is kn[n z a 8damp$ s9e-curve40 ,exactly ! same ?+ occurs 9 man1 ?\gh nei!r 9 8 case nor 9 t ( ! fi% h we suffici5t data = its complete illu/ration4 ,we c demon/rate ! fact1 h[ev]1 9 ! case ( man by ! help ( c]ta9 v int]e/+ measurem5ts :i* h be5 record$ by ,daffn]#adh1 ( ! height ( ,g]man cadets1 measur$ at half-ye>ly int]vals4 ,gr[? 9 height ( ,g]man milit>y ,cadets1 9 half-ye>ly p]iods4 7,daffn]47 ,height 9 c5t4 ,increm5t 9 cm4 ,numb] ,w9t] ,summ] obs]v$ ,age ,octob] ,april ,octob] -ye> -ye> ,ye> #ab #aa-ab #acid #adaj #adcc #af #bc #ci #hj #ab-ac #adcj #adde #adgd #ae #bi #dd #adf #ac-ad #adge #adie #aebe #bj #cj #ej #afb #ad-ae #aebb #aeej #aehe #be #ce #fj #afb #ae-af #aehe #afjh #afch #bc #cj #ec #aej #af-ag #afce #afed #afgg #ai #bc #db #hb #ag-ah #afgg #afhi #agjd #ab #ae #bg #bb #ah-ai #afih #agjf #agae #jh #ji #ag #f #ai-bj #agjg #agaa #agae #jd #jd #jh ,9 ! accompany+ diagram 7,fig4 #cj7 ! half-ye>ly increm5ts are set =?1 f ! above table1 & x w be se5 t !y =m two ev5 & entirely sep>ate s]ies4 ,! curve jo9+ up ea* s]ies ( po9ts is an accel]ation-curve2 & ! comp>ison ( ! two curves gives a cle> view ( ! relative rates ( gr[? dur+ w9t] & summ]1 & ! fluctuation :i* ^! velocities und]go dur+ ! ye>s 9 "q4 ,! dott$ l9e repres5ts1 approximately1 ! accel]ation-curve 9 its cont9u\s fluctuation ( alt]nate seasonal decrease & increase4 ,9 ! case ( trees1 ! seasonal fluctuations ( gr[?#adi admit #aai ( easy det]m9ation1 & x is a po9t ( consid]able int]e/ to comp>e ! ph5om5on 9 ev]gre5 & 9 decidu\s trees4 ,i happ5 to h no measurem5ts at h& ) :i* to make ?is comp>ison 9 ! case ( our native trees1 b f a pap] by ,mr ,*>les ,e4 ,hall#aej ,i h compil$ c]ta9 mean values = gr[? 9 ! climate ( ,uruguay4 ,illu/ration3 ,fig4 #cj4 ,half-ye>ly increm5ts ( gr[?1 9 cadets ( v>i\s ages4 7,f ,daffn]'s data47 ,mean mon?ly increase 9 ,gir? ( ,ev]gre5 & ,decidu\s ,trees1 at ,san ,jorge1 ,uruguay4 7,aft] ,c4 ,e4 ,hall47 ,values express$ z p]c5tages ( total annual increase4 ,jan4 ,feb4 ,m>4 ,apr4 ,may ,june ,july ,aug4 ,sept4 ,oct4 ,nov4 ,dec4 ,ev]gre5s #ia #hh #hf #hi #gg #ed #dc #fj #ia #aaa #ajh #ajb ,decidu\s trees #bjc #adf #ij #bc #jh #jc #jg #ac #ce #ii #afg #baj ,! measurem5ts tak5 7 ^? ( ! gir? ( ! tree1 9 mm41 at ?ree feet f ! gr\nd4 ,! ev]gre5s includ$ species ( ,p9us1 ,eucalyptus & ,acacia2 ! decidu\s trees includ$ ,qu]cus1 ,populus1 ,rob9ia & ,melia4 ,i h m]ely tak5 mean values = ^! two gr\ps1 & express$ ! mon?ly values z p]c5tages ( ! mean annual increase4 ,! result 7z %ewn by ,fig4 #ca7 is v mu* :at we might h expect$4 ,! gr[? ( ! decidu\s trees is completely arre/$ 9 w9t]-"t1 & ! arre/ is all b complete ov] #abj a consid]able p]iod ( "t2 moreov]1 dur+ ! w>m season1 ! mon?ly values are regul>ly grad$ 7approximately 9 a s9e-curve7 ) a cle> maximum 79 ! s\!rn hemisph]e7 ab\t ! mon? ( ,decemb]4 ,9 ! ev]gre5 trees1 on ! o!r h&1 ! amplitude ( ! p]iodic wave is v mu* less2 !re is a notable am\nt ( gr[? all ! ye> r\nd1 &1 :ile !re is a m>k$ dim9ution 9 rate dur+ ! colde/ mon?s1 !re is a t5d5cy t[>ds equality ov] a consid]able "p ( ! w>m] season4 ,x is probable t "s ( ! species exam9$1 & especially ! p9es1 7 def9itely ret>d$ 9 gr[?1 ei!r by a temp]ature above _! optimum1 or by defici5cy ( moi/ure1 dur+ ! hotte/ p]iod ( ! ye>2 ) ! result t ! seasonal curve 9 our diagram has 7z x 77 its region ( maximum cut (f4 ,illu/ration3 ,fig4 #ca4 ,p]iodic annual fluctuation 9 rate ( gr[? ( trees 79 ! s\!rn hemisph]e74 ,9 ! case ( trees1 ! seasonal p]iodicity ( gr[? is s well m>k$ t we are entitl$ to make use ( ! ph5om5on 9 a conv]se way1 & to draw d$uctions z to v>iations 9 #aba climate dur+ pa/ ye>s f ! record ( v>y+ rates ( gr[? :i* ! tree1 by ! ?ickness ( its annual r+s1 has pres]v$ = u4 ,mr4 ,a4 ,e4 ,d\glass1 ( ! ,univ]sity ( ,arizona1 has made a c>eful /udy ( ?is "q#aea1 & ,i h receiv$ 7?r\gh ,pr(essor ,h4 ,h4 ,turn] ( ,ox=d7 "s measurem5ts ( ! av]age wid? ( ! successive annual r+s 9 8yell[ p9e10 #ejj ye>s old1 f ,arizona1 9 :i* trees ! annual r+s are v cle>ly di/+ui%$4 ,f ! ye> #acia to #aeah1 ! mean ( two trees 0 us$2 f #aeai to #aiab1 ! mean ( five2 & ! means ( ^!1 & sometimes ( l>g] numb]s1 7 f\nd to be v concordant4 ,a correction 0 appli$ by draw+ a long1 ne>ly /raight l9e ?r\gh ! curve = ! :ole p]iod1 :i* l9e 0 assum$ to repres5t ! sl[ly dim9i%+ mean wid? ( r+ accompany+ ! increase ( size1 or age1 ( ! tree2 & ! actual gr[? z measur$ 0 equat$ ) ?is dim9i%+ mean4 ,! figures us$ give1 accord+ly1 ! ratio ( ! actual gr[? 9 ea* ye> to ! mean gr[? correspond+ to ! age or magnitude ( ! tree at t epo*4 ,x 0 at once manife/ t ! rate ( gr[? s det]m9$ %ew$ a t5d5cy to fluctuate 9 a long p]iod ( betwe5 #ajj & #bjj ye>s4 ,i !n smoo!d 9 gr\ps ( #ajj 7accord+ to ,gauss's me?od7 ! ye>ly values1 s t ea* numb] ?us f\nd repres5t$ ! mean annual increase dur+ a c5tury3 t is to say1 ! value ascrib$ to ! ye> #aejj repres5t$ ! av]age annual gr[? dur+ ! :ole p]iod betwe5 #adej & #aeej1 & s on4 ,^! values give u a curve ( beautiful & surpris+ smoo?ness1 f :i* we seem compell$ to draw ! direct conclusion t ! climate ( ,arizona1 dur+ ! la/ #ejj ye>s1 has fluctuat$ ) a regul> p]iodicity ( almo/ precisely #aej ye>s4 ,"h aga9 we %\ld be left 9 d\bt 7s f> z ^! #abc obs]vations g7 :e!r ! ess5tial factor be a fluctuation ( temp]ature or an alt]nation ( moi/ure & aridity2 b ! "* ( ! ,arizona climate1 & ! kn[n facts ( rec5t ye>s1 enc\rage ! belief t ! latt] is ! m direct & m important factor4 ,illu/ration3 ,fig4 #cb4 ,long-p]iod fluctuation 9 rate ( gr[? ( ,arizona trees 7smoo!d 9 #ajj-ye> p]iods71 f ,a4,d4 #acij-adij to ,a4,d4 #ahaj-aiaj4 ,x has be5 (t5 rem>k$ t our common ,european trees1 su* = in/ance z ! elm or ! *]ry1 t5d to h l>g] leaves ! fur!r nor? we g2 b 9 ?is case ! ph5om5on is to be ascrib$ r to ! long] h\rs ( daylight ?an to any diff]5ce ( temp]ature#aeb4 ,! po9t is a physiological "o1 & consequ5tly ( little importance to u "h#aec2 ! ma9 po9t = ! morphologi/ is ! v simple "o t physical or climatic conditions h greatly influ5c$ ! rate ( gr[?4 ,! case is analog\s to ! direct influ5ce ( temp]ature 9 modify+ ! col\ration ( organisms1 su* z c]ta9 butt]flies4 ,n[ if temp]ature affects ! rate ( gr[? 9 /rict uni=mity1 alike 9 all directions & 9 all p>ts or organs1 its direct effect mu/ be limit$ to ! production ( local races or v>ieties diff]+ f "o ano!r 9 actual magnitude1 z ! ,sib]ian goldf9* or bullf9*1 = in/ance1 diff] f our own4 ,b if !re be ev5 ev] s little ( a discrim9at+ action 9 ! enhancem5t ( gr[? by temp]ature1 su* t x accel]ates ! gr[? ( "o tissue or "o organ m ?an ano!r1 !n x is evid5t t x mu/ at once lead to an actual diff]5ce ( racial1 or ev5 8specific0 =m4 ,x is n to be d\bt$ t ! v>i\s factors ( climate h "s su* discrim9at+ influ5ce4 ,! leaves ( our nor!rn trees may !mselves be an in/ance ( x2 & we h1 #abd probably1 a /ill bett] in/ance ( x 9 ! case ( ,alp9e plants#aed1 ^: g5]al habit is dw>f$1 ?\gh _! floral organs suff] little or no r$uction4 ,! subject1 h[ev]1 has be5 little inve/igat$1 & great z its !oretic importance w\ld be to u1 we mu/ mean:ile leave x alone4 ,osmotic factors 9 gr[?4 ,! curves ( gr[? :i* we h n[ be5 /udy+ repres5t ph5om5a :i* h at lea/ a two-fold int]e/1 morphological & physiological4 ,to ! morphologi/1 :o recognises t =m is a 8function0 ( gr[?1 ! important facts are ma9ly ^!3 7#a7 t ! rate ( gr[? is an ord]ly ph5om5on1 ) g5]al features common to v v>i\s organisms1 :ile ea* p>ticul> organism has its own *>act]i/ic ph5om5a1 or 8specific con/ants02 7#b7 t rate ( gr[? v>ies ) temp]ature1 t is to say ) season & ) climate1 & ) v>i\s o!r physical factors1 ext]nal & int]nal2 7#c7 t x v>ies 9 diff]5t p>ts ( ! body1 & accord+ to v>i\s directions or axes2 su* v>iations be+ def9itely correlat$ ) "o ano!r1 & ?us giv+ rise to ! *>act]i/ic proportions1 or =m1 ( ! organism1 & to ! *anges 9 =m :i* x und]goes 9 ! c\rse ( its developm5t4 ,b to ! physiologi/1 ! ph5om5on sugge/s _m o!r important consid]ations1 & ?r[s mu* light on ! v nature ( gr[? itself1 z a manife/ation ( *emical & physical en]gies4 ,to be cont5t to %ew t a c]ta9 rate ( gr[? occurs 9 a c]ta9 organism "u c]ta9 conditions1 or to speak ( ! ph5om5on z a 8reaction0 ( ! liv+ organism to its environm5t or to c]ta9 /imuli1 w\ld be b an example ( t 8lack ( p>ticul>ity#aee0 9 reg>d to ! actual me*anism ( physical cause & effect ) :i* we are apt 9 biology to be too easily satisfi$4 ,b 9 ! case ( rate ( gr[? we pass some:at #abe beyond ^! limitations2 = ! aff9ity ) c]ta9 types ( *emical reaction is pla91 & has be5 recognis$ by a great numb] ( physiologi/s4 ,a l>ge "p ( ! ph5om5on ( gr[?1 bo? 9 animals & /ill m conspicu\sly 9 plants1 is associat$ ) 8turgor10 t is to say1 is dep5d5t on osmotic conditions2 9 o!r words1 ! velocity ( gr[? dep5ds 9 great measure 7z we h already se51 p4 #aac7 on ! am\nt ( wat] tak5 up into ! liv+ cells1 z well z on ! actual am\nt ( *emical metabolism p]=m$ by !m#aef4 ,( ! *emical ph5om5a :i* result 9 ! actual increase ( protoplasm we %all speak pres5tly1 b ! rle ( wat] 9 gr[? des]ves also a pass+ ^w1 ev5 9 our morphological enquiry4 ,x has be5 %ewn by ,loeb t 9 ,c]ian?us or ,tubul>ia1 = in/ance1 ! cells 9 ord] to gr[ mu/ be turgesc5t2 & ?is turgesc5ce is only possible s long z ! salt wat] 9 :i* ! cells lie does n ov]/ep a c]ta9 limit ( conc5tration4 ,! limit1 9 ! case ( ,tubul>ia1 is pass$ :5 ! salt am\nts to ab\t #ed p] c5t4 ,sea-wat] conta9s "s #cj to #ce p4c4 ( salts2 b x is :5 ! sal9ity falls mu* bel[ ?is normal1 to ab\t #bb p4c41 t ,tubul>ia exhibits its maximal turgesc5ce1 & maximal gr[?4 ,a fur!r dilution is said to act z a poison to ! animal4 ,loeb has also %ewn#aeg t 9 c]ta9 eggs 7e4g4 ^? ( ! little fi% ,fundulus7 an increas+ conc5tration ( ! sea-wat] 7lead+ to a dim9i%+ 8wat]-cont5t0 ( ! egg7 ret>ds ! rate ( segm5tation & at l5g? r5d]s segm5tation impossible2 ?\gh nucle> division1 by ! way1 goes on = "s "t long]4 ,among _m o!r obs]vations ( ! same k9d1 ^? ( ,bialaszewicz#aeh1 on ! e>ly gr[? ( ! frog1 are notable4 ,he %ews t ! gr[? ( ! embryo :ile /ill )9 ! #abf vitell9e membrane dep5ds :olly on ! absorption ( wat]2 t :e!r rate ( gr[? be fa/ or sl[ 79 accordance ) temp]ature7 ! quantity ( wat] absorb$ is con/ant2 & t successive *anges ( =m correspond to def9ite quantities ( wat] absorb$4 ,! solid residue1 z ,dav5port has also %ewn1 may actually & notably dim9i%1 :ile ! embryo organism is increas+ rapidly 9 bulk & weight4 ,on ! o!r h&1 9 lat] /ages & especially 9 ! high] animals1 ! p]c5tage ( wat] t5ds to dim9i%4 ,?is has be5 %ewn by ,dav5port 9 ! frog1 by ,potts 9 ! *ick1 & p>ticul>ly by ,fehl+ 9 ! case ( man#aei4 ,fehl+'s results are epitomis$ z foll[s3 ,age 9 weeks #f #ag #bb #bd #bf #cj #ce #ci ,p]c5tage ( wat] #ige #iah #ibj #hii #hfd #hcg #hbi #gdb ,& ! foll[+ illu/rate ,dav5port's results = ! frog3 ,age 9 weeks #a #b #e #g #i #ad #da #hd ,p]c5tage ( wat] #efc #ehe #gfg #hic #ica #iej #ijb #hge ,to su* ph5om5a ( osmotic balance z ! above1 or 9 o!r words to ! dep5d5ce ( gr[? on ! uptake ( wat]1 ,hb]#afj & also ,loeb are incl9$ to ref] ! modifications ( =m :i* c]ta9 phyllopod cru/acea und]go1 :5 ! highly sal9e wat]s :i* !y inhabit are fur!r conc5trat$1 or are abnormally dilut$4 ,_! gr[?1 accord+ to ,s*mankewits*1 is ret>d$ by increase ( conc5tration1 s t ! individuals f ! m sal9e wat]s appe> /unt$ & dw>fi%2 & !y become alt]$ or trans=m$ 9 o!r ways1 :i* = ! mo/ "p sugge/ 8deg5]ation10 or a failure to atta9 full & p]fect developm5t#afa4 ,important physiological *anges also ensue4 ,! rate ( multiplication is increas$1 & p>!nog5etic reproduction is enc\rag$4 ,male individuals become pl5tiful 9 ! less sal9e wat]s1 & "h ! females br+ =? #abg _! "y alive2 males disappe> altoge!r 9 ! m conc5trat$ br9es1 & !n ! females lay eggs1 :i*1 h[ev]1 only beg9 to develop :5 ! sal9ity is some:at r$uc$4 ,! be/-kn[n case is ! little 8br9e-%rimp10 ,artemia sal9a1 f\nd1 9 "o =m or ano!r1 all ! _w ov]1 & fir/ discov]$ m ?an a c5tury & a half ago 9 ! salt-pans at ,lym+ton4 ,among _m alli$ =ms1 "o1 ,a4 milhaus5ii1 inhabits ! natron-lakes ( ,egypt & ,arabia1 :]e1 "u ! "n ( 8l\l10 or 8,fezzan-worm10 x is eat5 by ! ,arabs#afb4 ,?is fact is int]e/+1 because x indicates 7& inve/igation has app>5tly confirm$7 t ! tissues ( ! creature are n impregnat$ ) salt1 z is ! m$ium 9 :i* x lives4 ,! fluids ( ! body1 ! milieu int]ne 7z ,claude ,b]n>d call$ !m#afc71 are no m salt ?an are ^? ( any ord9>y cru/acean or o!r animal1 b conta9 only "s #jh p] c5t4 ( ,na,cl#afd1 :ile ! milieu ext]ne may conta9 #aj1 #bj1 or m p] c5t4 ( ?is & o!r salts2 :i* is z mu* z to say t ! sk91 or body-wall1 ( ! creature acts z a 8semi-p]meable membrane10 ?r\gh :i* ! dissolv$ salts are n p]mitt$ to diffuse1 ?\gh wat] passes ?r\gh freely3 until a /atical equilibrium 7d\btless ( a complex k9d7 is at l5g? atta9$4 ,among ! /ructural *anges :i* result f increas$ conc5tration ( ! br9e 7p>tly dur+ ! life-"t ( ! individual1 b m m>k$ly dur+ ! %ort season :i* suffices = ! developm5t ( ?ree or f\r1 or p]haps m1 successive g5]ations71 x is f\nd t ! tail comes to be> few] & few] bri/les1 & ! tail-f9s !mselves t5d at la/ to disappe>2 ^! *anges correspond+ to :at h be5 #abh describ$ z ! specific *>act]s ( ,a4 milhaus5ii1 & ( a /ill m extreme =m1 ,a4 kpp5iana2 :ile on ! o!r h&1 progressive dilution ( ! wat] t5ds to precisely opposite conditions1 result+ 9 =ms :i* h also be5 describ$ z sep>ate species1 & ev5 ref]r$ to a sep>ate g5us1 ,callaonella1 closely ak9 to ,bran*ipus 7,fig4 #cc74 ,p>i passu ) ^! *anges1 !re is a m>k$ *ange 9 ! relative l5g?s ( ! =e & h9d portions ( ! body1 t is to say1 ( ! 8cephalo?orax0 & abdom53 ! latt] gr[+ relatively long]1 ! salt] ! wat]4 ,9 o!r words1 n only is ! rate ( gr[? ( ! :ole ,illu/ration3 ,fig4 #cc4 ,br9e-%rimps 7,artemia71 f m or less sal9e wat]4 ,upp] figures %ew tail-segm5t & tail-f9s2 l[] figures1 relative l5g? ( cephalo?orax & abdom54 7,aft] ,abonyi47 animal less5$ by ! sal9e conc5tration1 b ! specific rates ( gr[? 9 ! p>ts ( its body are relatively *ang$4 ,?is latt] ph5om5on l5ds itself to num]ical /atem5t1 & ,abonyi has lately %ewn t we may con/ruct a v regul> curve1 by plott+ ! proportionate l5g? ( ! creature's abdom5 aga9/ ! sal9ity1 or d5sity1 ( ! wat]2 & ! sev]al species ( ,artemia1 ) all _! o!r correlat$ specific *>act]s1 are !n f\nd to occupy successive1 m or less well-def9$1 & m or less ext5d$1 regions ( ! curve 7,fig4 #cc74 ,9 %ort1 ! d5sity ( ! wat] is s cle>ly a 8function0 ( ! specific #abi "*1 t we may briefly def9e ! species ,artemia 7,callaonella7 ,jelskii1 = in/ance1 z ! ,artemia ( d5sity #ajjj-ajaj 7,na,cl71 or ! typical ,a4 sal9a1 or pr9cipalis1 z ! ,artemia ( d5sity #ajah-ajbe1 & s =?4 ,x is a mo/ int]e/+ fact t ^! ,artemiae1 "u ! protection ( _! semi-p]meable sk9s1 are capable ( liv+ 9 wat]s n only ( great d5sity1 b ( v v>i$ *emical composition4 ,! natron-lakes1 = in/ance1 conta9 l>ge quantities ( magnesium ,illu/ration3 ,fig4 #cd4 ,p]c5tage ratio ( l5g? ( abdom5 to cephalo?orax 9 br9e-%rimps1 at v>i\s sal9ities4 7,aft] ,abonyi47 sulphate2 & ! ,artemiae cont9ue to live equally well 9 artificial solutions :]e ?is salt1 or :]e calcium *loride1 has l>gely tak5 ! place ( sodium *loride 9 ! m common habitat4 ,fur!rmore1 su* wat]s z ^? ( ! natron-lakes are subject to v great *anges ( *emical composition z conc5tration proce$s1 ow+ to ! diff]5t solubilities ( ! con/itu5t salts4 ,x appe>s t ! =ms :i* ! ,artemiae assume1 & ! *anges :i* !y und]go1 are id5tical or #acj indi/+ui%able1 :i*ev] ( ! above salts happ5 to exi/1 or to pr$om9ate1 9 _! sal9e habitat4 ,at ! same "t we /ill lack 7s f> z ,i "k7 ! simple1 b crucial exp]im5ts :i* %all tell u :e!r1 9 solutions ( diff]5t *emical composition1 x is at equal d5sities1 or at 8isotonic0 conc5trations 7t is to say1 "u conditions :]e ! osmotic pressure1 & consequ5tly ! rate ( diffusion1 is id5tical71 t ! same /ructural *anges are produc$1 or correspond+ phases ( equilibrium atta9$4 ,:ile ,hb] & o!rs#afe h ref]r$ all ^! ph5om5a to osmosis1 ,abonyi is incl9$ to believe t ! viscosity1 or me*anical resi/ance1 ( ! fluid also reacts ^u ! organism2 & o!r possible modes ( op]ation h be5 sugge/$4 ,b we may take x = c]ta9 t ! ph5om5on z a :ole is n a simple "o2 & t x includes besides ! passive ph5om5a ( int]molecul> diffusion1 "s o!r =m ( activity :i* plays ! "p ( a regulatory me*anism#aff4 ,gr[? & catalytic action4 ,9 ord9>y *emical reactions we h to deal 7#a7 ) a specific velocity prop] to ! p>ticul> reaction1 7#b7 ) v>iations due to temp]ature & o!r physical conditions1 7#c7 accord+ to van't ,h(f's 8,law ( ,mass10 ) v>iations due to ! actual quantities pres5t ( ! react+ sub/ances1 & 7#d7 9 c]ta9 cases1 ) v>iations due to ! pres5ce ( 8catalys+ ag5ts40 ,9 ! simpl] reactions1 ! law ( mass involves a /eady1 gradual sl[+-d[n ( ! process1 accord+ to a log>i?mic ratio1 z ! reaction proce$s & z ! initial am\nt ( sub/ance dim9i%es2 a ph5om5on1 h[ev]1 :i* ne$ n necess>ily #aca occur 9 ! organism1 "p ( ^: en]gies are devot$ to ! cont9ual br++-up ( fre% supplies4 ,catalytic action occurs :5 "s sub/ance1 (t5 9 v m9ute quantity1 is pres5t1 & by its pres5ce produces or accel]ates an action1 by op5+ 8a way r\nd10 )\t ! catalytic ag5t itself be+ dim9i%$ or us$ up#afg4 ,"h ! velocity curve1 ?\gh quick5$1 is n necess>ily alt]$ 9 =m1 = gradually ! law ( mass ex]ts its effect & ! rate ( ! reaction gradually dim9i%es4 ,b 9 c]ta9 cases we h ! v rem>kable ph5om5on t a body act+ z a catalys] is necess>ily =m$ z a product1 or bye-product1 ( ! ma9 reaction1 & 9 su* a case z ?is ! reaction-velocity w t5d to be /eadily accel]at$4 ,in/ead ( dw9dl+ away1 ! reaction w cont9ue ) an ev]-increas+ velocity3 always subject to ! res]vation t limit+ conditions w 9 "t make !mselves felt1 su* z a failure ( "s necess>y +r$i5t1 or a developm5t ( "s sub/ance :i* %all antagonise or f9ally de/roy ! orig9al reaction4 ,su* an action z ?is we h le>n$1 f ,o/wald1 to describe z 8autocatalysis40 ,n[ we "k t c]ta9 products ( protoplasmic metabolism1 su* z ! enzymes1 are v p[]ful catalys]s1 & we are entitl$ to speak ( an autocatalytic action on ! "p ( protoplasm itself4 ,?is catalytic activity ( protoplasm is a v important ph5om5on4 ,z ,blackman says1 9 ! address already quot$1 ! botani/s 7or ! zoologi/s7 8call x gr[?1 attribute x to a specific p[] ( protoplasm = assimilation1 & leave x alone z a fundam5tal ph5om5on2 b !y are mu* conc]n$ z to ! di/ribution ( new gr[? 9 innum]able specifically di/9ct =ms40 ,:ile ! *emi/1 on ! o!r h&1 recognises x z a famili> ph5om5on1 & ref]s x to ! same category z 8 o!r kn[n examples ( autocatalysis4 #acb ,?is v important1 & p]haps ev5 fundam5tal ph5om5on ( gr[? w\ld seem to h be5 fir/ recognis$ by ,pr(essor ,*odat ( ,g5eva1 z we are told by 8 pupil ,monni]#afh4 8,on peut bi51 a9si que ,m4 ,*odat l'a propos1 considr] l'accroissem5t comme une raction *imique complexe1 dans laquelle le catalysateur e/ la cellule vivante1 et les corps en prs5ce sont l'eau1 les sels1 et l'acide c>bonique40 ,v soon aft]w>ds a simil> sugge/ion 0 made by ,loeb#afi1 9 connection ) ! syn!sis ( nucle9 or nucle> protoplasm2 = he rem>k$ t1 z 9 an autocatalys$ *emical reaction1 ! velocity ( ! syn!sis increases dur+ ! initial /age ( cell-division 9 proportion to ! am\nt ( nucle> matt] already syn!sis$4 ,9 o!r words1 "o ( ! products ( ! reaction1 i4e4 "o ( ! con/itu5ts ( ! nucleus1 accel]ates ! production ( nucle> f cytoplasmic mat]ial4 ,! ph5om5on ( autocatalysis is by no means conf9$ to liv+ or protoplasmic *emi/ry1 b at ! same "t x is *>act]i/ically1 & app>5tly con/antly1 associat$ !re)4 ,& x w\ld seem t to x we may ascribe a consid]able "p ( ! diff]5ce betwe5 ! gr[? ( ! organism & ! simpl] gr[? ( ! cry/al#agj3 ! fact1 = in/ance1 t ! cell c gr[ 9 a v l[ conc5tration ( its nutritive solution1 :ile ! cry/al gr[s only 9 a sup]saturat$ "o2 & ! fundam5tal fact t ! nutritive solution ne$ only conta9 ! m or less raw mat]ials ( ! complex con/itu5ts ( ! cell1 :ile ! cry/al gr[s only 9 a solution ( its own actual sub/ance#aga4 ,z ,f4 ,f4 ,blackman has po9t$ out1 ! multiplication ( an organism1 = in/ance ! prodigi\sly rapid increase ( a bact]ium1 #acc :i* t5ds to d\ble its numb]s e few m9utes1 till 77 x n = limit+ factors7 its numb]s w\ld be all b incalculable 9 a day#agb1 is a simple b mo/ /rik+ illu/ration ( ! pot5tialities ( protoplasmic catalysis2 & 7ap>t f ! l>ge %>e tak5 by m]e 8turgesc5ce0 or imbibition ( wat]7 ! same is true ( ! gr[?1 or cell-multiplication1 ( a multicellul> organism 9 its fir/ /age ( rapid accel]ation4 ,x is n necess>y = u to pursue ?is subject mu* fur!r1 = x is suffici5tly cle> t ! normal 8curve ( gr[?0 ( an organism1 9 all its g5]al features1 v closely resembles ! velocity-curve ( *emical autocatalysis4 ,we see 9 x ! fir/ & mo/ typical phase ( great] & great] accel]ation2 ?is is foll[$ by a phase 9 :i* limit+ conditions 7^: details are practically unkn[n7 lead to a fall+ (f ( ! =m] accel]ation2 & 9 mo/ cases we come at l5g? to a ?ird phase1 9 :i* ret>dation ( gr[? is succe$$ by actual dim9ution ( mass4 ,"h we may recognise ! influ5ce ( processes1 or ( products1 :i* h become actually delet]i\s2 _! delet]i\s influ5ce is /av$ (f = a :ile1 z ! organism draws on its accumulat$ res]ves1 b !y lead ere long to ! /oppage ( all activity1 & to ! physical ph5om5on ( dea?4 ,b :5 we h once admitt$ t ! limit+ conditions ( gr[?1 :i* cause a phase ( ret>dation to foll[ a phase ( accel]ation1 are v imp]fectly kn[n1 x is pla9 t1 ipso facto1 we mu/ admit t a resemblance r ?an an id5tity betwe5 ?is ph5om5on & t ( *emical autocatalysis is all t we c safely ass]t mean:ile4 ,inde$1 z ,enriques has %ewn1 po9ts ( contra/ betwe5 ! two ph5om5a are n lack+2 = in/ance1 z ! *emical reaction draws to a close1 x is by ! gradual atta9m5t ( *emical equilibrium3 b :5 organic gr[? draws to a close1 x is by reason ( a v diff]5t k9d ( equilibrium1 due 9 ! ma9 to ! gradual diff]5tiation ( ! organism into p>ts1 among ^: peculi> #acd & specialis$ functions t ( cell-multiplication t5ds to fall into abeyance#agc4 ,x w\ld seem to foll[1 z a natural consequ5ce1 f :at has be5 said1 t we c\ld )\t mu* difficulty r$uce our curves ( gr[? to log>i?mic =mulae#agd ak9 to ^? :i* ! physical *emi/ f9ds applicable to 8 autocatalytic reactions4 ,?is has be5 dilig5tly attempt$ by v>i\s writ]s#age2 b ! results1 :ile n de/ructive ( ! hypo!sis itself1 are only p>tially successful4 ,! difficulty arises ma9ly f ! fact t1 9 ! life-hi/ory ( an organism1 we h usually to deal 7z inde$ we h se57 ) sev]al recurr5t p]iods ( relative accel]ation & ret>dation4 ,x is easy to f9d a =mula :i* %all satisfy ! conditions dur+ any "o ( ^! p]iodic phases1 b x is v difficult to frame a compreh5sive =mula :i* %all apply to ! entire p]iod ( gr[?1 or to ! :ole duration ( life4 ,b if x be mean:ile impossible to =mulate or to solve 9 precise ma!matical t]ms ! equation to ! gr[? ( an organism1 we h yet gone a v long way t[>ds ! solution ( su* problems :5 we h f\nd a 8qualitative expression10 z ,po9c> puts x2 t is to say1 :5 we h ga9$ a fair approximate k ( ! g5]al curve :i* repres5ts ! unkn[n function4 ,z soon z we h t\*$ on su* matt]s z ! *emical ph5om5on ( catalysis1 we are on ! ?re%old ( a subject :i*1 if we 7 able to pursue x1 w\ld soon lead u f> into ! special doma9 ( physiology2 & !re x w\ld be necess>y to foll[ x if we 7 deal+ ) gr[? z a ph5om5on 9 itself1 in/ead ( m]ely z a help to our /udy & compreh5sion ( =m4 ,= in/ance ! :ole "q ( diet1 ( ov]fe$+ & und]fe$+1 w\ld pres5t itself = discussion#agf4 ,b )\t attempt+ to op5 up ?is l>ge subject1 we may say a #ace fur!r pass+ ^w ^u ! ess5tial fact t c]ta9 *emical sub/ances h ! p[] ( accel]at+ or ( ret>d+1 or 9 "s way regulat+1 gr[?1 & ( s influ5c+ directly ! morphological features ( ! organism4 ,?us leci?9 has be5 %ewn by ,hatai#agg1 ,danilewsky#agh & o!rs to h a rem>kable p[] ( /imulat+ gr[? 9 v>i\s animals2 & ! s-call$ 8auximones10 :i* ,pr(essor ,bottomley prep>es by ! action ( bact]ia ^u peat appe> to be1 aft] a some:at simil> fa%ion1 pot5t accel]ators ( ! gr[? ( plants4 ,b by mu* ! mo/ int]e/+ cases1 f our po9t ( view1 are ^? :]e a p>ticul> sub/ance appe>s to ex]t a diff]5tial effect1 /imulat+ ! gr[? ( "o "p or organ ( ! body m ?an ano!r4 ,x has be5 kn[n = a numb] ( ye>s t a diseas$ condition ( ! pituit>y body accompanies ! ph5om5on kn[n z 8acromegaly10 9 :i* ! bones are v>i\sly enl>g$ or elongat$1 & :i* is m or less exemplifi$ 9 e skeleton ( a 8giant02 :ile on ! o!r h&1 disease or extirpation ( ! ?yroid causes an arre/ ( skeletal developm5t1 &1 if x take place e>ly1 ! subject rema9s a dw>f4 ,^!1 !n1 are well-kn[n illu/rations ( ! regulation ( function by "s int]nal gl&ul> secretion1 "s enzyme or 8hormone0 7z ,bayliss & ,/>l+ call x71 or 8h>mozone10 z ,gley calls x 9 ! p>ticul> case :]e ! function regulat$ is t ( gr[?1 ) its consequ5t influ5ce on =m4 ,among o!r illu/rations 7:i* are pl5tiful7 we h1 = in/ance ! gr[? ( ! plac5tal decidua1 :i* ,loeb has %ewn to be due to a sub/ance giv5 (f by ! corpus luteum ( ! ov>y1 giv+ to ! ut]9e tissues an abnormal capacity = gr[?1 :i* 9 turn is call$ into action by ! contact ( ! ovum1 or ev5 ( any =eign body4 ,& v>i\s sexual *>act]s1 su* z ! plumage1 comb & spurs ( ! cock1 are believ$ 9 l mann] to arise 9 response to "s p>ticul> int]nal secretion4 ,:5 ! s\rce ( su* a secretion is remov$ by ca/ration1 well-kn[n morphological *anges take place 9 v>i\s animals2 & :5 a conv]se *ange takes place1 ! female acquires1 9 great] or less degree1 *>act]s :i* are #acf prop] to ! male1 z 9 c]ta9 extreme cases1 kn[n f "t immemorial1 :5 late 9 life a h5 assumes ! plumage ( ! cock4 ,!re are "s v rem>kable exp]im5ts by ,gud]nats*1 9 :i* he has %ewn t by fe$+ tadpoles 7:e!r ( frogs or toads7 on ?yroid gl& sub/ance1 _! legs may be made to gr[ out at any "t1 days or weeks be=e ! normal date ( _! appe>ance#agi4 ,no o!r organic food 0 f\nd to produce ! same effect2 b s9ce ! ?yroid gl& is kn[n to conta9 iod9e#ahj1 ,morse exp]im5t$ ) ?is latt] sub/ance1 & f\nd t if ! tadpoles 7 f$ ) iodis$ am9o-acids ! legs develop$ precoci\sly1 j z :5 ! ?yroid gl& itself 0 us$4 ,we may take x1 !n1 z an e/abli%$ fact1 ^: full ext5t & be>+s are /ill await+ inve/igation1 t !re exi/ sub/ances bo? )9 & )\t ! organism :i* h a m>vell\s p[] ( accel]at+ gr[?1 & ( do+ s 9 su* a way z to affect n only ! size b ! =m or proportions ( ! organism4 ,if we once admit1 z we are n[ b\nd to d1 ! exi/5ce ( su* factors z ^!1 :i*1 by _! physiological activity & ap>t f any direct action ( ! n]v\s sy/em1 t5d t[>ds ! accel]ation ( gr[? & consequ5t modification ( =m1 we are l$ into wide fields ( speculation by an easy & a legitimate pa?way4 ,pr(essor ,gley c>ries su* speculations a long1 long way3 = he says#aha t by ^! *emical influ5ces 8,t\te une p>tie de la con/ruction des tres p>ait s'expliqu] d'une faon t\te mcanique4 ,la =t]esse1 si longtemps inaccessible1 du vitalisme e/ entame4 ,c> la notion morphognique tait1 suivant le mot de ,da/re#ahb1 comme #8le d]ni] rduit de la =ce vitale4' 0 ,! physiological speculations we ne$ n discuss3 b1 to take a s+le example f morphology1 we beg9 to und]/& ! possibility1 & to compreh5d ! probable mean+1 ( ! #acg all b sudd5 appe>ance on ! e>? ( su* exagg]at$ & almo/ mon/r\s =ms z ^? ( ! great second>y reptiles & ! great t]ti>y mammals#ahc4 ,we beg9 to see t x is 9 ord] to acc\nt1 n = ! appe>ance1 b = ! disappe>ance ( su* =ms z ^! t natural selection mu/ be invok$4 ,& we !n1 ,i ?9k1 draw ne> to ! conclusion t :at is true ( ^! is univ]sally true1 & t ! great function ( natural selection is n to orig9ate1 b to remove3 donec ad int]itum g5us id natura r$egit#ahd4 ,! _w ( ?+s liv+1 l ! _w ( ?+s inanimate1 gr[s ( itself1 & pursues its ceaseless c\rse ( creative evolution4 ,x has room1 wide b n unb\nd$1 = v>iety ( liv+ =m & /ructure1 z ^! t5d t[>ds _! seem+ly endless1 b yet /rictly limit$1 possibilities ( p]mutation & degree3 x has room = ! great & = ! small1 room = ! weak & = ! /rong4 ,environm5t & circum/ance d n always make a prison1 :]e9 p]=ce ! organism mu/ ei!r live or die2 = ! ways ( life may be *ang$1 & _m a refuge f\nd1 be=e ! s5t5ce ( unfitness is pron\nc$ & ! p5alty ( ext]m9ation paid4 ,b !re comes a "t :5 8v>iation10 9 =m1 dim5sions1 or o!r qualities ( ! organism1 goes f>!r ?an is compatible ) all ! means at h& ( heal? & welf>e = ! individual & ! /ock2 :51 "u ! active & creative /imulus ( =ces f )9 & f )\t1 ! active & creative en]gies ( gr[? pass ! b\nds ( physical & physiological equilibrium3 & s rea* ! limits :i*1 z aga9 ,lucretius tells u1 natural law has set betwe5 :at may & :at may n be1 8et quid quaeque queant p] fo$]a naturai quid porro nequeant40 ,!n1 at la/1 we are entitl$ to use ! cu/om>y metaphor1 & to see 9 natural selection an inexorable =ce1 ^: function #ach is n to create b to de/roy1--to we$1 to prune1 to cut d[n & to ca/ into ! fire#ahe4 ,reg5]ation1 or gr[? & repair4 ,! ph5om5on ( reg5]ation1 or ! re/oration ( lo/ or amputat$ p>ts1 is a p>ticul> case ( gr[? :i* des]ves sep>ate consid]ation4 ,z we are all aw>e1 ?is prop]ty is manife/$ 9 a high degree among inv]tebrates & _m cold-blood$ v]tebrates1 dim9i%+ z we asc5d ! scale1 until at l5g?1 9 ! w>m-blood$ animals1 x less5s d[n to no m ?an t vis m$icatrix :i* heals a w\nd4 ,ev] s9ce ! days ( ,ari/otle1 & especially s9ce ! exp]im5ts ( ,trembley1 ,raumur & ,spallanzani 9 ! middle ( ! eighte5? c5tury1 ! physiologi/ & ! psy*ologi/ h alike recognis$ t ! ph5om5on is bo? p]plex+ & important4 ,! g5]al ph5om5on is amply discuss$ else:]e1 & we ne$ only deal ) x 9 its imm$iate relation to gr[?#ahf4 ,reg5]ation1 l gr[? 9 o!r cases1 proce$s ) a velocity :i* v>ies accord+ to a def9ite law2 ! rate v>ies ) ! "t1 & we may /udy x z velocity & z accel]ation4 ,let u take1 z an in/ance1 ,miss ,m4 ,l4 ,durb9's measurem5ts ( ! rate ( reg5]ation ( tadpoles' tails3 ! rate be+ "h measur$ 9 t]ms1 n ( mass1 b ( l5g?1 or longitud9al increm5t#ahg4 ,f a numb] ( tadpoles1 ^: av]age l5g? 0 #cdb mm41 _! tails be+ on an av]age #bab mm4 long1 ab\t half ! tail #aci 7#aae mm47 0 cut (f1 & ! am\nts reg5]at$ 9 successive p]iods are %ewn z foll[s3 ,days aft] op]ation #c #g #aj #ad #ah #bd #cj 7#a7 ,am\nt reg5]at$ 9 mm4 #ad #cd #dc #eb #ee #fb #fe 7#b7 ,increm5t dur+ ea* p]iod #ad #bj #ji #ji #jc #jg #jc 7#c7 787 ,rate p] day dur+ ea* p]iod #jdf #jej #jcj #jbe #jjg #jab #jje ,! fir/ l9e ( numb]s 9 ?is table1 if plott$ z a curve aga9/ ! numb] ( days1 w give u a v satisfactory view ( ! 8curve ( gr[?0 )9 ! p]iod ( ! obs]vations3 t is to say1 ( ! successive relations ( l5g? to "t1 or ! velocity ( ! process4 ,b ! ?ird l9e is n s satisfactory1 & mu/ n be plott$ directly z an accel]ation curve4 ,= x is evid5t t ! 8rates0 "h det]m9$ d n correspond to velocities at ! dates to :i* !y are ref]r$1 b are ! mean velocities ov] a prec$+ p]iod2 & moreov] ! p]iods ov] :i* ^! means are tak5 are "h ( v unequal l5g?4 ,b we may draw a good deal m in=mation f ?is exp]im5t1 if we beg9 by draw+ a smoo? curve1 z ne>ly z possible ?r\gh ! po9ts correspond+ to ! am\nts reg5]at$ 7accord+ to ! fir/ l9e ( ! table72 & if we !n int]polate f ?is smoo? curve ! actual l5g?s atta9$1 day by day1 & d]ive f ^!1 by subtraction1 ! successive daily increm5ts1 :i* are ! measure ( ! daily mean velocities 7,table1 p4 #ada74 7,! m accurate & /rictly correct me?od w\ld be to draw successive tang5ts to ! curve47 ,9 our curve ( gr[? 7,fig4 #ce7 we _c safely int]polate values = ! fir/ ?ree days1 t is to say = ! dates betwe5 amputation & ! fir/ actual measurem5t ( ! reg5]at$ "p4 ,:at goes on 9 ^! ?ree days is v important2 b we "k no?+ ab\t x1 save t our curve desc5d$ to z]o some:]e or o!r )9 t p]iod4 ,z we h already le>n$1 we c m or less safely int]polate betwe5 kn[n po9ts1 or actual obs]vations2 b "h we h no kn[n />t+-po9t4 ,9 %ort1 = all t ! obs]vations tell u1 & = all t ! appe>ance ( ! curve c sugge/1 ! curve ( gr[? may h desc5d$ ev5ly to ! base-l9e1 :i* x w\ld !n h rea*$ ab\t ! end ( ! second #adj day2 or x may h _h )9 ! fir/ ?ree days a *ange ( direction1 or 8po9t ( inflection10 & may !n h sprung at once f ! base-l9e at z]o4 ,t is to say1 !re may ,illu/ration3 ,fig4 #ce4 ,curve ( reg5]ative gr[? 9 tadpoles' tails4 7,f ,m4 ,l4 ,durb9's data47 h be5 an int]v5+ 8lat5t p]iod10 dur+ :i* no gr[? ,illu/ration3 ,fig4 #cf4 ,mean daily increm5ts1 correspond+ to ,fig4 #ce4 #ada occurr$1 betwe5 ! "t ( injury & ! fir/ measurem5t ( reg5]ative gr[?2 or1 = all we yet "k1 reg5]ation may h begun at once1 b ) a velocity mu* less ?an t :i* x aft]w>ds atta9$4 ,?is app>5tly trifl+ diff]5ce w\ld correspond to a v great diff]5ce 9 ! nature ( ! ph5om5on1 & w\ld lead to a v /rik+ diff]5ce 9 ! curve :i* we h next to draw4 ,! curve already drawn 7,fig4 #ce7 illu/rates1 z we h se51 ! relation ( l5g? to "t1 i4e4 ,l_/,t ,v4 ,! second 7,fig4 #cf7 repres5ts ! rate ( *ange ( velocity2 x sets ,v aga9/ ,t2 ,! =ego+ table1 ext5d$ by graphic int]polation4 ,total ,daily ,days increm5t increm5t ,logs ( d4 #a -- -- -- #b -- -- -- #c #adj #fj #agh #d #bjj #eb #agb #e #beb #de #afe #f #big #dc #afc #g #cdj #cb #aea #h #cgb #cj #adh #i #djb #bh #ade #aj #dcj #bb #acd #aa #deb #ba #acb #ab #dgc #ai #abh #ac #dib #ah #abf #ad #eaj #ag #abc #ae #ebg #ac #aaa #af #edj #ad #aae #ag #eed #ac #aaa #ah #efg #aa #ajd #ai #egh #aj #ajj #bj #ehh #aj #ajj #ba #eih #ji #ie #bb #fjg #jg #he #bc #fad #jg #hd #bd #fba #jh #ij #be #fbi #jf #gh #bf #fce #jf #gh #bg #fda #je #gj #bh #fdf #jd #fj #bi #fej #jc #dh #cj #fec #adb & ,v_/,t or ,l_/,t#b1 repres5ts 7z we h le>n$7 ! accel]ation ( gr[?1 ?is be+ simply ! 8diff]5tial coeffici5t10 ! fir/ d]ivative ( ! =m] curve4 ,illu/ration3 ,fig4 #cg4 ,log>i?ms ( values %ewn 9 ,fig4 #cf4 ,n[1 plott+ ?is accel]ation curve f ! date ( ! fir/ measurem5t made ?ree days aft] ! amputation ( ! tail 7,fig4 #cf71 we see t x has no po9t ( inflection1 b falls /eadily1 only m & m sl[ly1 till at la/ x comes d[n ne>ly to ! base-l9e4 ,! velocities ( gr[? are cont9ually dim9i%+4 ,z reg>ds ! miss+ portion at ! beg9n+ ( ! curve1 we _c be sure :e!r x b5t r\nd & came d[n to z]o1 or :e!r1 z 9 our ord9>y accel]ation curves ( gr[? f bir? onw>ds1 x />t$ f a maximum4 ,! =m] is1 9 ?is case1 obvi\sly ! m probable1 b we _c be sure4 ,z reg>ds t l>ge portion ( ! curve :i* we are acqua9t$ )1 we see t x resembles ! curve kn[n z a rectangul> hyp]bola1 :i* is ! =m assum$ :5 two v>iables 79 ?is case ,v & ,t7 v>y inv]sely z "o ano!r4 ,if we take ! log>i?ms ( ! velocities 7z giv5 9 ! table7 & plot !m aga9/ "t 7,fig4 #cg71 we see t !y fall1 approximately1 into a /raight l9e2 & if ?is curve be plott$ on ! #adc prop] scale we %all f9d t ! angle :i* x makes ) ! base is ab\t #be1 ( :i* ! tang5t is #df1 or 9 r\nd numb]s 4 ,_h ! angle be5 #de 7tan #de #a71 ! curve w\ld h be5 actually a rectangul> hyp]bola1 ) ,v ,t con/ant4 ,z x is1 we may assume1 provisionally1 t x belongs to ! same family ( curves1 s t ,vm ,tn1 or ,vm_/n ,t1 or ,v ,tn_/m1 are all sev]ally con/ant4 ,9 o!r words1 ! velocity v>ies inv]sely z "s p[] ( ! "t1 or vice v]sa4 ,& 9 ?is p>ticul> case1 ! equation ,v ,t#b con/ant1 holds v ne>ly true2 t is to say ! velocity v>ies1 or t5ds to v>y1 inv]sely z ! squ>e ( ! "t4 ,if "s g5]al law ak9 to ?is c\ld be e/abli%$ z a g5]al law1 or ev5 z a common rule1 x w\ld be ( great importance4 ,illu/ration3 ,fig4 #ch4 ,rate ( reg5]ative gr[? 9 l>g] tadpoles4 ,b ?\gh nei!r 9 ?is case nor 9 any o!r c ! m9ute increm5ts ( gr[? dur+ ! fir/ few h\rs1 or ! fir/ c\ple ( days1 aft] injury1 be directly measur$1 yet ! mo/ important po9t is q capable ( solution4 ,:at ! =ego+ curve leaves u 9 ignorance (1 is simply :e!r gr[? />ts at z]o1 ) z]o velocity1 & works up quickly to a maximum velocity f :i* x aft]w>ds gradually falls away2 or :e!r aft] a lat5t p]iod1 x beg9s1 s to speak1 9 full =ce4 ,! answ] #add to ?is "q-dep5ds on :e!r1 9 ! days foll[+ ! fir/ actual measurem5t1 we c or _c detect a daily increm5t 9 velocity1 be=e t velocity beg9s its normal c\rse ( dim9ution4 ,n[ ?is prelim9>y asc5t to a maximum1 or po9t ( inflection ( ! curve1 ?\gh n %ewn 9 ! above-quot$ exp]im5t1 has be5 (t5 obs]v$3 z = in/ance1 9 ano!r simil> exp]im5t by ! au?or ( ! =m]1 ! tadpoles be+ 9 ?is case ( l>g] size 7av]age #dia mm47#ahh4 ,days #c #e #g #aj #ab #ad #ag #bd #bh #ca ,increm5t #jhf #bae #cff #ebj #eie #fch #gaj #gfj #hbj #hdj ,or1 by graphic int]polation1 ,total ,daily ,days increm5t d4 #a #bc #bc #b #ec #cj #c #hf #cc #d #acj #dd #e #bjj #gj #f #bgh #gh #g #ceh #hj #h #dcj #gb #i #dij #fj #aj #ebi #ci #aa #efb #cc #ab #eij #bh #ac #fac #bc #ad #fch #be #ae #ffa #bc #af #fha #bj #ag #gjj #ai etc4 ,! accel]ation curve is drawn 9 ,fig4 #ci4 ,"h we h j :at we lack$ 9 ! =m] case1 namely a visible po9t ( inflection 9 ! curve ab\t ! sev5? day 7,figs4 #ch1 #ci71 ^: exi/5ce is confirm$ by successive obs]vations on ! #crd1 #e?1 #g? & #aj? days1 & :i* ju/ifies to "s ext5t our extrapolation = ! o!rwise unkn[n p]iod up to & end+ ) ! ?ird day2 b ev5 "h !re is a %ort space ne> ! v beg9n+ dur+ :i* we are n q sure ( ! precise slope ( ! curve4 ,we h n[ le>n$ t1 accord+ to ^! exp]im5ts1 ) :i* _m o!rs are 9 sub/antial agreem5t1 ! rate ( gr[? 9 ! reg5]ative process is z foll[s4 ,aft] a v %ort lat5t p]iod1 n yet actually prov$ b ^: exi/5ce is highly probable1 gr[? comm5ces ) a velocity :i* v #ade rapidly increases to a maximum4 ,! curve quickly1--almo/ sudd5ly1--*anges its direction1 z ! velocity beg9s to fall2 & ! rate ( fall1 t is1 ! negative accel]ation1 proce$s at a sl[] & sl[] rate1 :i* rate v>ies inv]sely z "s p[] ( ! "t1 & is f\nd 9 bo? ( ! above-quot$ exp]im5ts to be v approximately z #a_/,t#b4 ,b x is obvi\s t ! value :i* we h f\nd = ! latt] portion ( ! curve 7h[ev] closely x be con=m$ to7 is only an empirical value2 x has only a tempor>y usefulness1 & mu/ 9 "t give place to a =mula :i* %all repres5t ! entire ph5om5on1 f />t to f9i%4 ,illu/ration3 ,fig4 #ci4 ,daily increm5t1 or am\nt reg5]at$1 correspond+ to ,fig4 #ch4 ,:ile ! curve ( reg5]ative gr[? is app>5tly diff]5t f ! curve ( ord9>y gr[? z usually drawn 7& :ile ?is app>5t diff]5ce has be5 comm5t$ on & treat$ z valid by c]ta9 writ]s7 we are n[ 9 a position to see t x only looks diff]5t because we are able to /udy x1 if n f ! beg9n+1 at lea/ v ne>ly s3 :ile an ord9>y curve ( gr[?1 z x is usually pres5t$ to u1 is "o :i* dates1 n #adf f ! beg9n+ ( gr[?1 b f ! comp>atively late1 & unimportant1 & ev5 fallaci\s epo* ( bir?4 ,a complete curve ( gr[?1 />t+ f z]o1 has ! same ess5tial *>act]i/ics z ! reg5]ation curve4 ,inde$ ! m we consid] ! ph5om5on ( reg5]ation1 ! m pla9ly does x %ew itself to u z b a p>ticul> case ( ! g5]al ph5om5on ( gr[?#ahi1 foll[+ ! same l9es1 obey+ ! same laws1 & m]ely />t$ into activity by ! special /imulus1 direct or indirect1 caus$ by ! infliction ( a w\nd4 ,nei!r m nor less ?an 9 o!r problems ( physiology are we call$ ^u1 9 ! case ( reg5]ation1 to indulge 9 metaphysical speculation1 or to dwell ^u ! b5efic5t purpose :i* seem+ly und]lies ?is process ( heal+ & re/oration4 ,x is a v g5]al rule1 ?\gh app>5tly n a univ]sal "o1 t reg5]ation t5ds to fall some:at %ort ( a complete re/oration ( ! lo/ "p2 a c]ta9 p]c5tage only ( ! lo/ tissues is re/or$4 ,?is fact 0 well kn[n to "s ( ^? old inve/igators1 :o1 l ! ,abb ,trembley & l ,voltaire1 f\nd a fasc9ation 9 ! /udy ( artificial injury & ! reg5]ation :i* foll[$ x4 ,sir ,john ,graham ,dalyell1 = in/ance1 says1 9 ! c\rse ( an admirable p>agraph on reg5]ation#aij3 8,! reproductive faculty 444 is n conf9$ to "o portion1 b may ext5d ov] _m2 & x may ensue ev5 9 relation to ! reg5]at$ portion m ?an once4 ,nev]!less1 ! faculty gradually weak5s1 s t 9 g5]al e successive reg5]ation is small] & m imp]fect ?an ! organisation prec$+ x2 & at l5g? x is exhau/$40 ,9 c]ta9 m9ute animals1 su* z ! ,infusoria1 9 :i* ! capacity = 8reg5]ation0 is s great t ! entire animal may be re/or$ f ! m]e/ fragm5t1 x becomes ( great int]e/ to discov] :e!r !re be "s def9ite size at :i* ! fragm5t ceases to display ?is p[]4 ,?is "q has #adg be5 /udi$ by ,lillie#aia1 :o f\nd t 9 ,/5tor1 :ile /ill small] fragm5ts 7 capable ( surviv+ = days1 ! smalle/ portions capable ( reg5]ation 7 ( a size equal to a sph]e ( ab\t #hj 9 diamet]1 t is to say ( a volume equal to ab\t "o tw5ty-sev5? ( ! av]age entire animal4 ,he arrives at ! rem>kable conclusion t = ?is1 & = all o!r species ( animals1 !re is a 8m9imal organisation mass10 t is to say a 8m9imal mass ( def9ite size consi/+ ( nucleus & cytoplasm )9 :i* ! organisation ( ! species c j f9d its lat5t expression40 ,& 9 l mann]1 ,bov]i#aib has %ewn t ! fragm5t ( a sea-ur*9's egg capable ( gr[+ up into a new embryo1 & s dis*>g+ ! complete functions ( an entire & un9jur$ ovum1 rea*es its limit at ab\t "o-tw5tie? ( ! orig9al egg1--o!r writ]s hav+ f\nd a limit at ab\t "o-f\r?4 ,^! magnitudes1 small z !y are1 repres5t objects easily visible "u a l[ p[] ( ! microscope1 & s /& 9 a v diff]5t category to ! m9imal magnitudes 9 :i* life itself c be manife/$1 & :i* we h discuss$ 9 *apt] ,,ii4 ,a numb] ( ph5om5a connect$ ) ! l9e> rate ( reg5]ation are illu/rat$ & epitomis$ 9 ! accompany+ diagram 7,fig4 #dj71 :i* ,i h con/ruct$ f c]ta9 data giv5 by ,ellis 9 a pap] on ! relation ( ! am\nt ( tail reg5]at$ to ! am\nt remov$1 9 ,tadpoles4 ,^! data are summ>is$ 9 ! next ,table4 ,! tadpoles 7 all v mu* ( a size1 ab\t #dj mm42 ! av]age l5g? ( tail 0 v ne> to #bf mm41 or #fe p] c5t4 ( ! :ole body-l5g?2 & 9 f\r s]ies ( exp]im5ts ab\t #aj1 #bj1 #dj & #fj p] c5t4 ( ! tail 7 sev]ally remov$4 ,! am\nt reg5]at$ 9 successive int]vals ( ?ree days is %ewn 9 our table4 ,by plott+ ! actual am\nts reg5]at$ aga9/ ^! ?ree-day int]vals ( "t1 we may int]polate values = ! "t tak5 to reg5]ate def9ite p]c5tage am\nts1 #e p] c5t41 #aj p] c5t41 etc4 ( ! #adh ,illu/ration3 ,fig4 #dj4 ,relation betwe5 ! p]c5tage am\nt ( tail remov$1 ! p]c5tage re/or$1 & ! "t requir$ = its re/oration4 7,f ,m4 ,m4 ,ellis's data47 ,! ,rate ( ,reg5]ative ,gr[? 9 ,tadpoles' ,tails4 7,aft] ,m4 ,m4 ,ellis1 ,j4 ,exp4 ,zool4 ,,vii1 p4 #dba1 #aiji47 ,body ,tail ,am\nt ,p] c5t4 am\nt reg5]at$ 9 days l5g? l5g? remov$ ( tail ,s]ies mm4 mm4 mm4 remov$ #c #f #i #ab #ae #ah #cb ,o #ciege #behie #cb #abcf #ac #ca #dd #dd #dd #dd #dd ,p #djba #bfac #ebh #bjbj #aj #bi #dj #dd #dd #dd #dd ,r #cihf #begj #ajd #djej #f #bj #ca #dj #dh #dh #dh ,s #djcd #bfaa #adh #efg #j #af #cc #ci #de #dh #dh ,ea* s]ies gives ! mean ( #bj exp]im5ts4 am\nt remov$2 & my diagram is con/ruct$ f ! f\r sets ( values ?us obta9$1 t is to say f ! f\r sets ( exp]im5ts :i* diff]$ f "o ano!r 9 ! am\nt ( tail amputat$4 ,to ^! we h to add ! g5]al result ( a fif? s]ies ( exp]im5ts1 :i* %ew$ t :5 z mu* z #ge p] c5t4 ( ! tail 0 cut (f1 no reg5]ation took place at all1 b ! animal pres5tly di$4 ,9 our diagram1 !n1 ea* #adi curve indicates ! "t tak5 to reg5]ate n p] c5t4 ( ! am\nt remov$4 ,all ! curves conv]ge t[>ds inf9ity1 :5 ! am\nt remov$ 7z %ewn by ! ord9ate7 approa*es #ge p] c5t42 & all ( ! curves />t f z]o1 = no?+ is reg5]at$ :]e no?+ _h be5 remov$4 ,ea* curve approximates 9 =m to a cubic p>abola4 ,! am\nt reg5]at$ v>ies also ) ! age ( ! tadpole & ) o!r factors1 su* z temp]ature2 9 o!r words1 = any giv5 age1 or size1 ( tadpole & also = v>i\s specific temp]atures1 a simil> diagram might be con/ruct$4 ,! p[] ( reproduc+1 or reg5]at+1 a lo/ limb is p>ticul>ly well develop$ 9 ar?ropod animals1 & is sometimes accompani$ by rem>kable modification ( ! =m ( ! reg5]at$ limb4 ,a case 9 po9t1 :i* has attract$ mu* att5tion1 occurs 9 connection ) ! claws ( c]ta9 ,cru/acea#aic4 ,9 _m ,cru/acea we h an asymmetry ( ! great claws1 "o be+ l>g] ?an ! o!r & also m or less diff]5t 9 =m4 ,= in/ance1 9 ! common lob/]1 "o claw1 ! l>g] ( ! two1 is provid$ ) a few great 8cru%+0 tee?1 :ile ! small] claw has m num]\s tee?1 small & s]rat$4 ,?\gh ,ari/otle ?\ght o!rwise1 x appe>s t ! cru%+-claw may be on ! "r or left side1 indiff]5tly2 :e!r x be on "o or ! o!r is a problem ( 8*ance40 ,x is o!rwise 9 _m o!r ,cru/acea1 :]e ! l>g] & m p[]ful claw is always left or "r1 z ! case may be1 accord+ to ! species3 :]e1 9 o!r words1 ! 8probability0 ( ! l>ge or ! small claw be+ left or be+ "r is tantam\nt to c]ta9ty#aid4 ,! "o claw is ! l>g] because x has gr[n ! fa/]2 #aej x has a high] 8coeffici5t ( gr[?10 & accord+ly1 z age advances1 ! disproportion betwe5 ! two claws becomes m & m evid5t4 ,moreov]1 we mu/ assume t ! *>act]i/ic =m ( ! claw is a 8function0 ( its magnitude2 ! knobb9ess is a ph5om5on co9cid5t ) gr[?1 & we nev]1 "u any circum/ances1 f9d ! small] claw ) big cru%+ tee? & ! big claw ) little s]rat$ ones4 ,!re are _m o!r some:at simil> cases :]e size & =m are manife/ly correlat$1 & we h already se51 to "s ext5t1 t ! ph5om5on ( gr[? is accompani$ by c]ta9 ratios ( velocity t lead inevitably to *anges ( =m4 ,mean:ile1 !n1 we mu/ simply assume t ! ess5tial diff]5ce betwe5 ! two claws is "o ( magnitude1 ) :i* a c]ta9 diff]5tiation ( =m is insep>ably associat$4 ,if we amputate a claw1 or if1 z (t5 happ5s1 ! crab 8ca/s x (f10 x und]goes a process ( reg5]ation1--x gr[s anew1 & evid5tly does s ) an accel]at$ velocity1 :i* accel]ation w cease :5 equilibrium ( ! p>ts is once m atta9$3 ! accel]at$ velocity be+ a case 9 po9t to illu/rate t vis revulsionis ( ,hall]1 to :i* we h already ref]r$4 ,) ! help ( ?is pr9ciple1 ,przibram acc\nts = c]ta9 curi\s ph5om5a :i* accompany ! process ( reg5]ation4 ,z 8 exp]im5ts & ^? ( ,morgan %ew1 if ! l>ge or knobby claw 7,a7 be remov$1 !re are c]ta9 cases1 e4g4 ! common lob/]1 :]e x is directly reg5]at$4 ,9 o!r cases1 e4g4 ,alpheus#aie1 ! o!r claw 7,b7 assumes ! size & =m ( t :i* 0 amputat$1 :ile ! latt] reg5]ates itself 9 ! =m ( ! o!r & weak] "o2 ,a & ,b h app>5tly *ang$ places4 ,9 a ?ird case1 z 9 ! crabs1 ! ,a-claw reg5]ates itself z a small or ,b-claw1 b ! ,b-claw rema9s = a "t unalt]$1 ?\gh sl[ly & 9 ! c\rse ( repeat$ m\lts x lat] on assumes ! l>ge & heavily too!d ,a-=m4 ,mu* has be5 writt5 on ?is ph5om5on1 b 9 ess5ce x is v simple4 ,x dep5ds ^u ! respective rates ( gr[?1 ^u a ratio betwe5 ! rate ( reg5]ation & ! rate ( gr[? ( ! un9jur$ limb3 complicat$ a little1 h[ev]1 by #aea ! possibility ( ! un9jur$ limb gr[+ all ! fa/] = a "t aft] ! animal has be5 reliev$ ( ! o!r4 ,f ! "t ( amputation1 say ( ,a1 ,a beg9s to gr[ f z]o1 ) a high 8reg5]ative0 velocity2 :ile ,b1 />t+ f a def9ite magnitude1 cont9ues to increase1 ) its normal or p]haps some:at accel]at$ velocity4 ,! ratio betwe5 ! two velocities ( gr[? w det]m9e :e!r1 by a giv5 "t1 ,a has equall$1 out/ripp$1 or /ill fall5 %ort ( ! magnitude ( ,b4 ,t ?is is ! gi/ ( ! :ole problem is confirm$ 7if confirmation be necess>y7 by c]ta9 exp]im5ts ( ,wilson's4 ,x is kn[n t by section ( ! n]ve to a crab's claw1 its gr[? is ret>d$1 & z ! g5]al gr[? ( ! animal proce$s ! claw comes to appe> /unt$ or dw>f$4 ,n[ 9 su* a case z t ( ,alpheus1 we h se5 t ! rate ( reg5]ative gr[? 9 an amputat$ l>ge claw fails to let x rea* or ov]take ! magnitude ( ! gr[+ little claw3 :i* latt]1 9 %ort1 n[ appe>s z ! big "o4 ,b if at ! same "t z we amputate ! big claw we also sev] ! n]ve to ! less] "o1 we s f> sl[ d[n ! latt]'s gr[? t ! o!r is able to make up to x1 & 9 ?is case ! two claws cont9ue to gr[ at approximately equal rates1 or 9 o!r words cont9ue ( coequal size4 ,! ph5om5on ( reg5]ation goes "s way t[>ds help+ u to compreh5d ! ph5om5on ( 8multiplication by fission10 z x is exemplifi$ at lea/ 9 its simpl] cases 9 _m worms & worm-l animals4 ,= physical reasons :i* we %all h to /udy 9 ano!r *apt]1 !re is a natural t5d5cy = any tube1 if x h ! prop]ties ( a fluid or semi-fluid sub/ance1 to break up into segm5ts aft] x comes to a c]ta9 l5g?2 & no?+ c prev5t its do+ s1 except ! pres5ce ( "s controll+ =ce1 su* = in/ance z may be due to ! pressure ( "s ext]nal support1 or "s sup]ficial ?ick5+ or o!r intr9sic rigidity ( its own sub/ance4 ,if we add to ?is natural t5d5cy t[>ds fission ( a cyl9drical or tubul> worm1 ! ord9>y ph5om5on ( reg5]ation1 we h all t is ess5tially impli$ 9 8reproduction by fission40 ,& 9 s f> #aeb z ! process re/s ^u a physical pr9ciple1 or natural t5d5cy1 we may acc\nt = its occurr5ce 9 a great v>iety ( animals1 zoologically dissimil>2 & also = its pres5ce "h & abs5ce !re1 9 =ms :i*1 ?\gh mat]ially diff]5t 9 a physical s5se1 are zoologically speak+ v closely alli$4 ,,conclusion ,,& ,,summ>y4 ,b ! ph5om5a ( reg5]ation1 l all ! o!r ph5om5a ( gr[?1 soon c>ry u f> afield1 & we mu/ draw ?is brief discussion to a close4 ,= ! ma9 features :i* appe> to be common to all curves ( gr[? we may hope to h1 "s day1 a physical explanation4 ,9 p>ticul> we %\ld l to "k ! mean+ ( t po9t ( inflection1 or abrupt *ange f an increas+ to a decreas+ velocity ( gr[? :i* all our curves1 & especially our accel]ation curves1 demon/rate ! exi/5ce (1 provid$ only t !y include ! initial /ages ( ! :ole ph5om5on3 j z we %\ld also l to h a full physical or physiological explanation ( ! gradually dim9i%+ velocity ( gr[? :i* foll[s1 & :i* 7?\gh subject to tempor>y int]ruption or abeyance7 is on ! :ole *>act]i/ic ( gr[? 9 all cases :atsoev]4 ,9 %ort1 ! *>act]i/ic =m ( ! curve ( gr[? 9 l5g? 7or any o!r l9e> dim5sion7 is a ph5om5on :i* we are at pres5t unable to expla91 b :i* pres5ts u ) a def9ite & attractive problem = future solution4 ,x w\ld seem evid5t t ! abrupt *ange 9 velocity mu/ be due1 ei!r to a *ange 9 t pressure outw>ds f )91 by :i* ! 8=ces ( gr[?0 make !mselves manife/1 or to a *ange 9 ! resi/ances aga9/ :i* !y act1 t is to say ! t5sion ( ! surface2 & ?is latt] =ce we d n by any means limit to 8surface-t5sion0 prop]1 b may ext5d to ! developm5t ( a m or less resi/ant membrane or 8sk910 or ev5 to ! resi/ance ( fibres or o!r hi/ological elem5ts1 b9d+ ! b\nd>y lay]s to ! p>ts )94 ,i take x t ! sudd5 arre/ ( velocity is mu* m likely to be due to a sudd5 increase ( resi/ance ?an to a sudd5 dim9ution ( int]nal en]gies3 9 o!r words1 ,i suspect t x is co9cid5t ) "s notable ev5t ( hi/ological diff]5tiation1 su* z #aec ! rapid =mation ( a comp>atively firm sk92 & t ! dw9dl+ ( velocities1 or ! negative accel]ation1 :i* foll[s1 is ! resultant or composite effect ( wan+ =ces ( gr[? on ! "o h&1 & increas+ sup]ficial resi/ance on ! o!r4 ,?is is z mu* z to say t gr[?1 :ile its own en]gy t5ds to increase1 leads also1 aft] a :ile1 to ! e/abli%m5t ( resi/ances :i* *eck its own fur!r increase4 ,our k ( ! :ole complex ph5om5on ( gr[? is s scanty t x may seem ra% to advance ev5 ?is t5tative sugge/ion4 ,b yet !re are "o or two kn[n facts :i* seem to be> ^u ! "q1 & to indicate at lea/ ! mann] 9 :i* a v>y+ resi/ance to expansion may affect ! velocity ( gr[?4 ,= in/ance1 x has be5 %ewn by ,frazee#aif t electrical /imulation ( tadpoles1 ) small curr5t d5sity & l[ voltage1 increases ! rate ( reg5]ative gr[?4 ,z j su* an electrification w\ld t5d to l[] ! surface-t5sion1 & accord+ly decrease ! ext]nal resi/ance1 ! exp]im5t w\ld seem to support1 9 "s slight degree1 ! sugge/ion :i* ,i h made4 ,delage#aig has lately made use ( ! pr9ciple ( specific rate ( gr[?1 9 consid]+ ! "q ( h]$ity itself4 ,we "k t ! *romat9 ( ! f]tilis$ egg comes f ! male & female p>5t alike1 9 equal or ne>ly equal %>es2 we "k t ! initial *romat91 s contribut$1 multiplies _m ?\s&-fold1 to supply ! *romat9 = e cell ( ! (fspr+'s body2 & x has1 !re=e1 a high 8coeffici5t ( gr[?40 ,if we admit1 ) ,van ,b5$5 & o!rs1 t ! initial contributions ( male & female *romat9 cont9ue to be transmitt$ to ! succe$+ g5]ations ( cells1 we may !n conceive ^! *romat9s to reta9 ea* its own coeffici5t ( gr[?2 & if ^! diff]$ ev] s little1 a gradual prepond]ance ( "o or o!r w\ld make itself felt 9 "t1 & might conceivably expla9 ! prepond]at+ influ5ce ( "o p>5t or ! o!r ^u ! *>act]s ( ! (fspr+4 ,inde$ ,o4 ,h]twig is said 7accord+ to ,delage's int]pretation7 to h actually %ewn t we c artificially modify ! rate ( gr[? ( "o or o!r *romat91 & s increase or dim9i% ! influ5ce ( ! mat]nal or pat]nal h]$ity4 ,?is !ory ( ,delage's has its fasc9ation1 b x calls = some:at l>ge assumptions2 & 9 p>ticul>1 x seems 7l s _m o!r !ories relat+ to ! *romosomes7 to re/ f> too mu* ^u mat]ial elem5ts1 r ?an on ! impond]able dynamic factors ( ! cell4 #aed ,we may summ>ise1 z foll[s1 ! ma9 results ( ! =ego+ discussion3 7#a7 ,except 9 c]ta9 m9ute organisms & m9ute p>ts ( organisms1 ^: =m is due to ! direct action ( molecul> =ces1 we may look ^u ! =m ( ! organism z a 8function ( gr[?10 or a direct expression ( a rate ( gr[? :i* v>ies accord+ to its diff]5t directions4 7#b7 ,rate ( gr[? is subject to def9ite laws1 & ! velocities 9 diff]5t directions t5d to ma9ta9 a ratio :i* is m or less con/ant = ea* specific organism2 & to ?is regul>ity is due ! fact t ! =m ( ! organism is 9 g5]al regul> & con/ant4 7#c7 ,nev]!less1 ! ratio ( velocities 9 diff]5t directions is n absolutely con/ant1 b t5ds to alt] or fluctuate 9 a regul> way2 & to ^! progressive *anges are due ! *anges ( =m :i* accompany 8developm5t10 & ! sl[] *anges ( =m :i* cont9ue p]ceptibly 9 aft] life4 7#d7 ,! rate ( gr[? is a function ( ! age ( ! organism1 x has a maximum some:at e>ly 9 life1 aft] :i* epo* ( maximum x sl[ly decl9es4 7#e7 ,! rate ( gr[? is directly affect$ by temp]ature1 & by o!r physical conditions4 7#f7 ,x is m>k$ly affect$1 9 ! way ( accel]ation or ret>dation1 at c]ta9 physiological epo*s ( life1 su* z bir?1 pub]ty1 or metamorphosis4 7#g7 ,"u c]ta9 circum/ances1 gr[? may be negative1 ! organism gr[+ small]3 & su* negative gr[? is a common accompanim5t ( metamorphosis1 & a frequ5t accompanim5t ( old age4 7#h7 ,! ph5om5on ( reg5]ation is associat$ ) a l>ge tempor>y increase 9 ! rate ( gr[? 7or 8accel]ation0 ( gr[?7 ( ! injur$ surface2 9 o!r respects1 reg5]ative gr[? is simil> to ord9>y gr[? 9 all its ess5tial ph5om5a4 ,9 ?is discussion ( gr[?1 we h left out ( acc\nt a va/ numb] ( processes1 or ph5om5a1 by :i*1 9 ! physiological me*anism ( ! body1 gr[? is effect$ & controll$4 ,we h dealt ) gr[? 9 its relation to magnitude1 & to #aee t relativity ( magnitudes :i* con/itutes =m2 & s we h /udi$ x z a ph5om5on :i* /&s at ! beg9n+ ( a morphological1 r ?an at ! end ( a physiological enquiry4 ,"u ^! re/rictions1 we h treat$ x z f> z possible1 or 9 su* fa%ion z our pres5t k p]mits1 on /rictly physical l9es4 ,9 all its aspects1 & n lea/ 9 its relation to =m1 ! gr[? ( organisms has _m analogies1 "s close & "s p]haps m remote1 among inanimate ?+s4 ,z ! waves gr[ :5 ! w9ds /rive ) ! o!r =ces :i* gov]n ! movem5ts ( ! surface ( ! sea1 z ! heap gr[s :5 we p\r corn out ( a sack1 z ! cry/al gr[s :5 f ! surr\nd+ solution ! prop] molecules fall into _! appropriate places3 s 9 all ^! cases1 v mu* z 9 ! organism itself1 is gr[? accompani$ by *ange ( =m1 & by a developm5t ( def9ite %apes & cont\rs4 ,& 9 ^! cases 7z 9 all o!r me*anical ph5om5a71 we are l$ to equate our v>i\s magnitudes ) "t1 & s to recognise t gr[? is ess5tially a "q ( rate1 or ( velocity4 ,! diff]5ces ( =m1 & *anges ( =m1 :i* are br\ght ab\t by v>y+ rates 7or 8laws07 ( gr[?1 are ess5tially ! same ph5om5on :e!r !y be1 s to speak1 episodes 9 ! life-hi/ory ( ! individual1 or manife/ !mselves z ! normal & di/9ctive *>act]i/ics ( :at we call sep>ate species ( ! race4 ,f "o =m1 or ratio ( magnitude1 to ano!r !re is b "o /raight & direct road ( trans=mation1 be ! j\rney tak5 fa/ or sl[2 & if ! trans=mation take place at all1 x w 9 all likelihood proce$ 9 ! self-same way1 :e!r x occur )9 ! life-"t ( an individual or dur+ ! long ance/ral hi/ory ( a race4 ,no small "p ( :at is kn[n z ,wolff's or von ,ba]'s law1 t ! individual organism t5ds to pass ?r\gh ! phases *>act]i/ic ( its ance/ors1 or t ! life-hi/ory ( ! individual t5ds to recapitulate ! ance/ral hi/ory ( its race1 lies wrapp$ up 9 ?is simple acc\nt ( ! relation betwe5 rate ( gr[? & =m4 ,b en\gh ( ?is discussion4 ,let u leave = a :ile ! subject ( ! gr[? ( ! organism1 & attempt to /udy ! con=mation1 )9 & )\t1 ( ! individual cell4 #aef ,,*apt] ,,iv ,,on ,,! ,,int]nal ,,=m ,,& ,,/ructure ,,( ,,! ,,cell ,9 ! e>ly days ( ! cell-!ory1 m ?an sev5ty ye>s ago1 ,goodsir 0 wont to speak ( cells z 8c5tres ( gr[?0 or 8c5tres ( nutrition10 & to consid] !m z ess5tially 8c5tres ( =ce40 ,he look$ =w>d to a "t :5 ! =ces connect$ ) ! cell %\ld be p>ticul>ly inve/igat$3 :51 t is to say1 m9ute anatomy %\ld be /udi$ 9 its dynamical aspect4 8,:5 ?is bran* ( enquiry10 he says 8%all h be5 op5$ up1 we %all expect to h a sci5ce ( organic =ces1 hav+ direct relation to anatomy1 ! sci5ce ( organic =ms#aih40 ,& likewise1 long aft]w>ds1 ,gi>d contemplat$ a sci5ce ( morphodynamique1--b /ill look$ ^u x z =m+ s gu>d$ & hidd5 a 8t]ritoire sci5tifique1 que la plup>t des naturali/es de nos j\rs ne le v]ront que comme ,mose vit la t]re promise1 seulem5t de lo9 et sans p\voir y entr]#aii40 ,to ! ext]nal =ms ( cells1 & to ! =ces :i* produce & modify ^! =ms1 we %all pay att5tion 9 a lat] *apt]4 ,b !re are =ms & configurations ( matt] )9 ! cell1 :i* also des]ve to be /udi$ ) due reg>d to ! =ces1 kn[n or unkn[n1 ( ^: resultant !y are ! visible expression4 ,9 ! long int]val s9ce ,goodsir's day1 ! visible /ructure1 ! con=mation & configuration1 ( ! cell1 has be5 /udi$ f> m abundantly ?an ! purely dynamic problems t are associat$ !re)4 ,! ov]:elm+ progress ( microscopic obs]vation has multipli$ our k ( cellul> & intracellul> /ructure2 & to ! multitude ( visible /ructures x #aeg has be5 (t5 easi] to attribute virtues ?an to ascribe intelligible functions or modes ( action4 ,b "h & !re nev]!less1 ?r\gh\t ! :ole lit]ature ( ! subject1 we f9d recognition ( ! inevitable fact t dynamical problems lie beh9d ! morphological problems ( ! cell4 ,bts*li po9t$ out =ty ye>s ago1 ) emphatic cle>ness1 ! failure ( morphological me?ods1 & ! ne$ = physical me?ods1 if we 7 to p5etrate deep] into ! ess5tial nature ( ! cell#bjj4 ,& su* m5 z ,loeb & ,:itman1 ,dries* & ,r\x1 & n a few besides1 h pursu$ ! same tra9 ( ?\ght & simil> me?ods ( enquiry4 ,:itman#bja1 = in/ance1 puts ! case 9 a nut%ell :51 9 speak+ ( ! s-call$ 8c>yok9etic0 ph5om5a ( nucle> division1 he rem9ds u t ! lead+ idea 9 ! t]m 8c>yok9esis0 is motion1--8motion view$ z an expon5t ( =ces resid+ 91 or act+ ^u1 ! nucleus4 ,x reg>ds ! nucleus z a seat ( en]gy1 :i* displays itself 9 ph5om5a ( motion#bjb40 ,9 %ort x w\ld seem evid5t t1 except 9 relation to a dynamical inve/igation1 ! m]e /udy ( cell /ructure has b little value ( its own4 ,t a giv5 cell1 an ovum = in/ance1 conta9s ?is or t visible sub/ance or /ructure1 g]m9al vesicle or g]m9al spot1 *romat9 or a*romat91 *romosomes or c5trosomes1 obvi\sly gives no explanation ( ! activities ( ! cell4 ,& 9 all su* hypo!ses z t ( 8pang5esis10 9 all ! !ories :i* attribute specific prop]ties to micellae1 #aeh idiopla/s1 ids1 or o!r con/itu5t p>ticles ( protoplasm or ( ! cell1 we are apt to fall into ! error ( attribut+ to matt] :at is due to en]gy & is manife/$ 9 =ce3 or1 m /rictly speak+1 ( attribut+ to mat]ial p>ticles individually :at is due to ! en]gy ( _! collocation4 ,! t5d5cy is a v natural "o1 z k ( /ructure increases1 to ascribe p>ticul> virtues to ! mat]ial /ructures !mselves1 & ! error is "o into :i* ! disciple is likely to fall1 b ( :i* we ne$ n suspect ! ma/]-m9d4 ,! dynamical aspect ( ! case 0 9 all probability kept well 9 view by ^? :o1 l ,goodsir himself1 fir/ attack$ ! problem ( ! cell & orig9at$ our conceptions ( its nature & functions4 ,b if we speak1 z ,weismann & o!rs speak1 ( an 8h]$it>y sub/ance10 a sub/ance :i* is split (f f ! p>5t-body1 & :i* h&s on to ! new g5]ation ! *>act]i/ics ( ! old1 we c only ju/ify our mode ( spee* by ! assumption t t p>ticul> portion ( matt] is ! ess5tial vehicle ( a p>ticul> *>ge or di/ribution ( en]gy1 9 :i* is involv$ ! capability ( produc+ motion1 or ( do+ 8"w40 ,=1 z ,newton said1 to tell u t a ?+ 8is end[$ ) an occult specific quality1 by :i* x acts & produces manife/ effects1 is to tell u no?+2 b to d]ive two or ?ree g5]al pr9ciples ( motion#bjc f ph5om5a w\ld be a v great /ep 9 philosophy1 ?\gh ! causes ( ^! pr9ciples 7 n yet discov]$40 ,! ?+s :i* we see 9 ! cell are less important ?an ! actions :i* we recognise 9 ! cell2 & ^! latt] we mu/ especially scrut9ize1 9 ! hope ( discov]+ h[ f> !y may be attribut$ to ! simple & well-kn[n physical =ces1 & h[ f> !y be relevant or irrelevant to ! ph5om5a :i* we associate )1 & deem ess5tial to1 ! manife/ation ( life4 ,x may be t 9 ?is way we %all 9 "t draw nigh to ! recognition ( a specific & ultimate residuum4 #aei ,& lack+1 z we /ill d lack1 direct k ( ! actual =ces inh]5t 9 ! cell1 we may yet le>n some?+ ( _! di/ribution1 if n also ( _! nature1 f ! outw>d & inw>d configuration ( ! cell1 & f ! *anges tak+ place 9 ?is configuration2 t is to say f ! movem5ts ( matt]1 ! k9etic ph5om5a1 :i* ! =ces 9 action set up4 ,! fact t ! g]m-cell develops into a v complex /ructure1 is no absolute pro( t ! cell itself is /ructurally a v complicat$ me*anism3 nor yet1 ?\gh ?is is some:at less obvi\s1 is x suffici5t to prove t ! =ces at "w1 or lat5t1 )9 x are especially num]\s & complex4 ,if we bl[ into a b[l ( soapsuds & raise a great mass ( _m-hu$ & v>i\sly %ap$ bubbles1 if we explode a rocket & wat* ! regul> & beautiful configuration ( its fall+ /ream]s1 if we consid] ! wond]s ( a lime/one cav]n :i* a filt]+ /ream has fill$ ) /alactites1 we soon p]ceive t 9 all ^! cases we h begun ) an initial sy/em ( v slight complexity1 ^: /ructure 9 no way =e%ad[$ ! result1 & ^: comp>atively simple intr9sic =ces only play _! "p by complex int]action ) ! equally simple =ces ( ! surr\nd+ m$ium4 ,9 an e>li] age1 m5 s\ght = ! visible embryo1 ev5 = ! homunculus1 )9 ! reproductive cells2 & to ?is day1 we scrut9ize ^! cells = visible /ructure1 unable to free ourselves f t old doctr9e ( 8pre-=mation#bjd40 ,moreov]1 ! microscope seem$ to sub/antiate ! idea 7:i* we may trace back to ,leibniz#bje & to ,hobbes#bjf71 t !re is no limit to ! me*anical complexity :i* we may po/ulate 9 an organism1 & no limit1 !re=e1 to ! hypo!ses :i* we may re/ !reon4 ,b no microscopical exam9ation ( a /ick ( seal+-wax1 no /udy ( ! mat]ial ( :i* x is compos$1 c enlight5 #afj u z to its electrical manife/ations or prop]ties4 ,matt] ( itself has no p[] to d1 to make1 or to become3 x is 9 en]gy t all ^! pot5tialities reside1 en]gy invisibly associat$ ) ! mat]ial sy/em1 & 9 int]action ) ! en]gies ( ! surr\nd+ univ]se4 ,t 8function presupposes /ructure0 has be5 decl>$ an accept$ axiom ( biology4 ,:o x 0 t s =mulat$ ! aphorism ,i d n "k2 b z reg>ds ! /ructure ( ! cell x h>ks back to ,brcke1 ) ^: dem& = a me*anism1 or organisation1 )9 ! cell hi/ologi/s h ev] s9ce be5 attempt+ to comply#bjg4 ,b unless we mean to include !reby invisible1 & m]ely *emical or molecul>1 /ructure1 we come at once on dang]\s gr\nd4 ,= we h se51 9 a =m] *apt]1 t "s m9ute 8organisms0 are already kn[n ( su* all b inf9itesimal magnitudes t ev]y?+ :i* ! morphologi/ is accu/om$ to conceive z 8/ructure0 has become physically impossible2 & moreov] rec5t rese>* t5ds g5]ally to r$uce1 r ?an to ext5d1 our conceptions ( ! visible /ructure necess>ily inh]5t 9 liv+ protoplasm4 ,! microscopic /ructure :i*1 9 ! la/ resort or 9 ! simple/ cases1 x seems to %ew1 is t ( a m or less visc\s colloid1 or r mixture ( colloids1 & no?+ m4 ,n[1 z ,cl]k ,maxwell puts x1 9 discuss+ ?is v problem1 8"o mat]ial sy/em c diff] f ano!r only 9 ! configuration & motion :i* x has at a giv5 in/ant#bjh40 ,if we _c assume diff]5ces 9 /ructure1 we mu/ assume diff]5ces 9 motion1 t is to say1 9 en]gy4 ,& if we _c d ?is1 !n inde$ we are ?r[n back ^u modes ( reason+ unau?oris$ 9 physical sci5ce1 & %all f9d ourselves con/ra9$ to assume1 or to 8admit1 t ! prop]ties ( a g]m are n ^? ( a purely mat]ial sy/em40 #afa ,b we are by no means necess>ily 9 ?is dilemma4 ,= ?\gh we come p]il\sly ne> to x :5 we contemplate ! l[e/ ord]s ( magnitude to :i* life has be5 attribut$1 yet 9 ! case ( ! ord9>y cell1 or ord9>y egg or g]m :i* is go+ to develop into a complex organism1 if we h no reason to assume or to believe t x comprises an intricate 8me*anism10 we may be q sure1 bo? on direct & indirect evid5ce1 t1 l ! p[d] 9 our rocket1 x is v het]og5e\s 9 its /ructure4 ,x is a mixture ( sub/ances ( v>i\s k9ds1 m or less fluid1 m or less mobile1 influ5c$ 9 v>i\s ways by *emical1 electrical1 osmotic1 & o!r =ces1 & 9 _! admixture sep>at$ by a multitude ( surfaces1 or b\nd>ies1 at :i* ^!1 or c]ta9 ( ^! =ces are made manife/4 ,inde$1 su* an arrangem5t z ?is is already en\gh to con/itute a 8me*anism02 = we mu/ be v c>eful n to let our physical or physiological concept ( me*anism be n>r[$ to an int]pretation ( ! t]m d]iv$ f ! delicate & complicat$ contrivances ( human skill4 ,f ! physical po9t ( view1 we und]/& by a 8me*anism0 :atsoev] *ecks or controls1 & guides into det]m9ate pa?s1 ! work+s ( en]gy2 9 o!r words1 :atsoev] leads 9 ! degradation ( en]gy to its manife/ation 9 "s det]m9ate =m ( "w1 at a /age %ort ( t ultimate degradation :i* lapses 9 uni=mly diffus$ heat4 ,?is1 z ,w>burg has well expla9$1 is ! g5]al effect or function ( ! physiological ma*9e1 & 9 p>ticul> ( t "p ( x :i* we call 8cell-/ructure#bji40 ,! normal muscle-cell is some?+ :i* turns en]gy1 d]iv$ f oxidation1 into "w2 x is a me*anism :i* arre/s & utilises ! *emical en]gy ( oxidation 9 its d[nw>d c\rse2 b ! same cell :5 injur$ or dis9tegrat$1 loses its 8usefulness10 & sets free a greatly increas$ proportion ( its en]gy 9 ! =m ( heat4 ,b v great & wond]ful ?+s are done aft] ?is mann] by means ( a me*anism 7:e!r natural or artificial7 ( extreme simplicity4 ,a pool ( wat]1 by virtue ( its surface1 #afb is an admirable me*anism = ! mak+ ( waves2 ) a lump ( ice 9 x1 x becomes an effici5t & self-conta9$ me*anism = ! mak+ ( curr5ts4 ,! great cosmic me*anisms are /up5d\s 9 _! simplicity2 &1 9 po9t ( fact1 e great or little aggregate ( het]og5e\s matt] 7n id5tical 9 8phase07 involves1 ipso facto1 ! ess5tials ( a me*anism4 ,ev5 a non-liv+ colloid1 f its intr9sic het]og5eity1 is 9 ?is s5se a me*anism1 & "o 9 :i* en]gy is manife/$ 9 ! movem5t & ceaseless re>rangem5t ( ! con/itu5t p>ticles4 ,= ?is reason ,graham 7if ,i rememb] rightly7 speaks some:]e or o!r ( ! colloid /ate z 8! dynamic /ate ( matt]02 or 9 ! same philosoph]'s phrase 7( :i* ,mr ,h>dy#baj has lately rem9d$ u71 x possesses 8en]gia#baa40 ,let u turn !n to consid]1 briefly & diagrammatically1 ! /ructure ( ! cell1 a f]tilis$ g]m-cell or ovum = in/ance1 n 9 any va9 attempt to correlate ?is /ructure ) ! /ructure or prop]ties ( ! result+ & yet di/ant organism2 b m]ely to see h[ f>1 by ! /udy ( its =m & its *ang+ int]nal configuration1 we may ?r[ light on c]ta9 =ces :i* are = ! "t be+ at "w )9 x4 ,we may say at once t we c sc>cely hope to le>n m ( ^! =ces1 9 ! fir/ in/ance1 ?an a few facts reg>d+ _! direction & magnitude2 ! nature & specific id5tity ( ! =ce or =ces is a v diff]5t matt]4 ,?is latt] problem is likely to be v difficult ( elucidation1 = ! reason1 among o!rs1 t v diff]5t =ces are (t5 v mu* alike 9 _! outw>d & visible manife/ations4 ,s x has come to pass t we h a multitude ( discordant hypo!ses z to ! nature ( ! =ces act+ )9 ! cell1 & produc+1 9 cell division1 ! 8c>yok9etic0 figures ( :i* we are ab\t to speak4 ,"o /ud5t may1 l ,rhumbl]1 *oose to acc\nt = !m by an hypo!sis ( me*anical traction1 act+ on a reticul> web ( protoplasm#bab2 ano!r1 l ,l$uc1 may %ew u h[ 9 #afc _m ( _! mo/ /rik+ features !y may be admirably simulat$ by ! diffusion ( salts 9 a colloid m$ium2 o!rs aga91 l ,gall>do#bac & ,h>tog1 & ,rhumbl] 79 8 e>li] pap]s7#bad1 insi/ on _! resemblance to ! ph5om5a ( electricity & magnetism#bae2 :ile ,h>tog believes t ! =ce 9 "q is only analog\s to ^!1 & has a specific id5tity ( its own#baf4 ,all ^! conflict+ views are ( second>y importance1 s long z we seek only to acc\nt = c]ta9 configurations :i* reveal ! direction1 r ?an ! nature1 ( a =ce4 ,"o & ! same sy/em ( l9es ( =ce may appe> 9 a field ( magnetic or ( electrical en]gy1 ( ! osmotic en]gy ( diffusion1 ( ! gravitational en]gy ( a fl[+ /ream4 ,9 %ort1 we may expect to le>n some?+ ( ! pure or ab/ract dynamics1 long be=e we c deal ) ! special physics ( ! cell4 ,= inde$ 7z ,maill>d has sugge/$71 j z uni=m expansion ab\t a s+le c5tre1 to :atsoev] physical cause x may be due w lead to ! configuration ( a sph]e1 s w any two c5tres or foci ( pot5tial 7( :atsoev] k9d7 lead to ! configurations ) :i* ,f>aday made u famili> "u ! "n ( 8l9es ( =ce#bag02 & ?is is z mu* z to say t ! ph5om5on1 #afd ?\gh physical 9 ! concrete1 is 9 ! ab/ract purely ma!matical1 & 9 its v ess5ce is nei!r m nor less ?an a prop]ty ( ?ree-dim5sional space4 ,b z a matt] ( fact1 9 ?is in/ance1 t is to say 9 try+ to expla9 ! lead+ ph5om5a ( ! c>yok9etic division ( ! cell1 we %all soon p]ceive t any explanation :i* is bas$1 l ,rhumbl]'s1 on m]e me*anical traction1 is obvi\sly inadequate1 & we %all f9d ourselves limit$ to ! hypo!sis ( "s pol>is$ & pol>is+ =ce1 su* z we deal )1 = in/ance1 9 ! ph5om5a ( magnetism or electricity4 ,let u speak fir/ ( ! cell itself1 z x appe>s 9 a /ate ( re/1 & let u proce$ aft]w>ds to /udy ! m active ph5om5a :i* accompany its division4 ,our typical cell is a sph]ical body2 t is to say1 ! uni=m surface-t5sion at its b\nd>y is balanc$ by ! outw>d resi/ance ( uni=m =ces )94 ,b at times ! surface-t5sion may be a fluctuat+ quantity1 z :5 x produces ! rhy?mical contractions or 8,ransom's waves0 on ! surface ( a tr\t's egg2 or aga91 :ile ! egg is 9 contact ) o!r bodies1 ! surface-t5sion may be locally unequal & v>iable1 giv+ rise to an amoeboid figure1 z 9 ! egg ( ,hydra#bah4 ,)9 ! ovum is a nucleus or g]m9al vesicle1 also sph]ical1 & consi/+ z a rule ( portions ( 8*romat910 aggregat$ toge!r )9 a m fluid drop4 ,! fact has (t5 be5 comm5t$ ^u t1 9 cells g5]ally1 !re is no correlation ( =m 7?\gh !re app>5tly is ( size7 betwe5 ! nucleus & ! 8cytoplasm10 or ma9 body ( ! cell4 ,s ,:itman#bai rem>ks t 8except dur+ ! process ( division ! nucleus seldom dep>ts f its typical sph]ical =m4 ,x divides & sub-divides1 ev] return+ to ! same r\nd or oval =m 4444 ,h[ diff]5t ) ! cell4 ,x pres]ves ! sph]ical =m z r>ely z ! nucleus dep>ts f x4 ,v>iation 9 =m m>ks ! beg9n+ & ! end ( e important *apt] 9 its #afe hi/ory40 ,on simple dynamical gr\nds1 ! contra/ is easily expla9$4 ,s long z ! fluid sub/ance ( ! nucleus is qualitatively diff]5t f1 & incapable ( mix+ )1 ! fluid or semi-fluid protoplasm :i* surr\nds x1 we %all expect x to be1 z x almo/ always is1 ( sph]ical =m4 ,=1 on ! "o h&1 x is b\nd$ by a liquid film1 ^: surface-t5sion is uni=m2 & on ! o!r1 x is imm]s$ 9 a m$ium :i* transmits on all sides a uni=m fluid pressure#bbj4 ,= a simil> reason ! contractile vacuole ( a ,protozoon is sph]ical 9 =m3 x is j a 8drop0 ( fluid1 b\nd$ by a uni=m surface-t5sion & ?r\gh ^: b\nd>y-film diffusion is tak+ place4 ,b "h1 own+ to ! small diff]5ce betwe5 ! fluid con/itut+1 & t surr\nd+1 ! drop1 ! surface-t5sion equilibrium is un/able2 x is apt to vani%1 & ! r\nd$ outl9e ( ! drop1 l a bur/ bubble1 disappe>s 9 a mom5t#bba4 ,! case ( ! sph]ical nucleus is closely ak9 to ! sph]ical =m ( ! yolk )9 ! bird's egg#bbb4 ,b if ! sub/ance ( ! cell acquire a great] solidity1 z = in/ance 9 a muscle #aff cell1 or by reason ( muc\s accumulations 9 an epi!lium cell1 !n ! laws ( fluid pressure no long] apply1 ! ext]nal pressure on ! nucleus t5ds to become unsymmetrical1 & its %ape is modifi$ accord+ly4 8,amoeboid0 movem5ts may be set up 9 ! nucleus by any?+ :i* di/urbs ! symmetry ( its own surface-t5sion4 ,& ! cases1 z 9 _m ,rhizopods1 :]e 8nucle> mat]ial0 is scatt]$ 9 small portions ?r\gh\t ! cell in/ead ( be+ aggregat$ 9 a s+le nucleus1 are probably capable ( v simple explanation by suppos+ t ! 8phase diff]5ce0 7z ! *emi/s say7 betwe5 ! nucle> & ! protoplasmic sub/ance is comp>atively slight1 & ! surface-t5sion :i* t5ds to keep !m sep>ate is correspond+ly small#bbc4 ,x has be5 %ewn t ord9>y nuclei1 isolat$ 9 a liv+ or fre% /ate1 easily fl[ toge!r2 & ?is fact is en\gh to sugge/ t !y are aggregations ( a p>ticul> sub/ance r ?an bodies des]v+ ! "n ( p>ticul> organs4 ,x is by reason ( ! same t5d5cy to conflu5ce or aggregation ( p>ticles t ! ord9>y nucleus is itself =m$1 until ! imposition ( a new =ce leads to its disruption4 ,ap>t f t invisible or ultra-microscopic het]og5eity :i* is insep>able f our notion ( a 8colloid10 !re is a visible het]og5eity ( /ructure )9 bo? ! nucleus & ! out] protoplasm4 ,! =m]1 = in/ance1 conta9s a r\nd$ nucleolus or 8g]m9al spot10 c]ta9 conspicu\s granules or /r&s ( ! peculi> sub/ance call$ *romat91 & a co>se me%work ( a protoplasmic mat]ial kn[n z 8l990 or a*romat92 ! out] protoplasm1 or cytoplasm1 is g5]ally believ$ to consi/ ?r\gh\t ( a sponge-"w1 or r alveol> me%work1 ( m & less fluid sub/ances2 & la/ly1 !re are g5]ally to be detect$ "o or m v m9ute bodies1 usually 9 ! cytoplasm1 sometimes )9 ! nucleus1 kn[n z ! c5trosome or c5trosomes4 ,! morphologi/ is accu/om$ to speak ( a 8pol>ity0 ( #afg ! cell1 mean+ !reby a symmetry ( visible /ructure ab\t a p>ticul> axis4 ,= in/ance1 :5ev] we c recognise 9 a cell bo? a nucleus & a c5trosome1 we may consid] a l9e drawn ?r\gh ! two z ! morphological axis ( pol>ity2 9 an epi!lium cell1 x is obvi\s t ! cell is morphologically symmetrical ab\t a m$ian axis pass+ f its free surface to its atta*$ base4 ,aga91 by an ext5sion ( ! t]m 8pol>ity10 z is cu/om>y 9 dynamics1 we may h a 8radial0 pol>ity1 betwe5 c5tre & p]iph]y2 & la/ly1 we may h sev]al app>5tly indep5d5t c5tres ( pol>ity )9 ! s+le cell4 ,only 9 cells ( q irregul>1 or amoeboid =m1 d we fail to recognise a def9ite & symmetrical 8pol>ity40 ,! morphological 8pol>ity0 is accompani$ by1 & is b ! outw>d expression 7or "p ( x7 ( a true dynamical pol>ity1 or di/ribution ( =ces2 & ! 8l9es ( =ce0 are r5d]$ visible by concat5ation ( p>ticles ( matt]1 su* z come "u ! influ5ce ( ! =ces 9 action4 ,:5 ! l9es ( =ce /ream inw>ds f ! p]iph]y t[>ds a po9t 9 ! int]ior ( ! cell1 ! p>ticles susceptible ( attraction ei!r cr[d t[>ds ! surface ( ! cell1 or1 :5 ret>d$ by friction1 are se5 =m+ l9es or 8fibrillae0 :i* radiate outw>ds f ! c5tre & con/itute a s-call$ 8a/]40 ,9 ! cells ( column> or ciliat$ epi!lium1 :]e ! sides ( ! cell are symmetrically dispos$ to _! neighb\rs b ! free & atta*$ surfaces are v div]se f "o ano!r 9 _! ext]nal relations1 x is ^! latt] surfaces :i* con/itute ! opposite poles2 & 9 accordance ) ! p>allel l9es ( =ce s set up1 we v frequ5tly see p>allel l9es ( granules :i* h rang$ !mselves p]p5dicul>ly to ! free surface ( ! cell 7cf4 fig4 #ig74 ,a simple manife/ation ( 8pol>ity0 may be well illu/rat$ by ! ph5om5on ( diffusion1 :]e we may conceive1 & may automatically reproduce1 a 8field ( =ce10 ) its poles & visible l9es ( equipot5tial1 v mu* z 9 ,f>aday's conception ( ! field ( =ce ( a magnetic sy/em4 ,?us1 9 "o ( ,l$uc's exp]im5ts#bbd1 if we spread a lay] ( salt solution ov] a level #afh plate ( glass1 & let fall into ! middle ( x a drop ( indian ink1 or ( blood1 we %all f9d ! col\r$ p>ticles travell+ outw>ds f ! c5tral 8pole ( conc5tration0 along ! l9es ( diffusive =ce1 & s mapp+ out = u a 8monopol> field0 ( diffusion3 & if we set two su* drops side by side1 _! l9es ( diffusion w oppose1 & repel1 "o ano!r4 ,or1 in/ead ( ! uni=m lay] ( salt solution1 we may place at a little di/ance f "o ano!r a gra9 ( salt & a drop ( blood1 repres5t+ two opposite poles3 & s obta9 a picture ( a 8bipol> field0 ( diffusion4 ,9 ei!r case1 we obta9 results closely analog\s to ! 8morphological10 b really dynamical1 pol>ity ( ! organic cell4 ,b 9 all probability1 ! dynamical pol>ity1 or asymmetry ( ! cell is a v complicat$ ph5om5on3 = ! obvi\s reason t1 9 any sy/em1 "o asymmetry w t5d to beget ano!r4 ,a *emical asymmetry w induce an inequality ( surface-t5sion1 :i* w lead directly to a modification ( =m2 ! *emical asymmetry may 9 turn be due to a process ( electrolysis 9 a pol>is$ electrical field2 & aga9 ! *emical het]og5eity may be int5sifi$ into a *emical 8pol>ity10 by ! t5d5cy ( c]ta9 sub/ances to seek a locus ( great] or less surface-en]gy4 ,we ne$ n attempt to grapple ) a subject s complicat$1 & lead+ to s _m problems :i* lie beyond ! sph]e ( int]e/ ( ! morphologi/4 ,b yet ! morphologi/1 9 8 /udy ( ! cell1 _c q evade ^! important issues2 & we %all return to !m aga9 :5 we h dealt some:at ) ! =m ( ! cell1 & h tak5 acc\nt ( "s ( ! simpl] ph5om5a ( surface-t5sion4 ,we are n[ ready1 & 9 "s measure prep>$1 to /udy ! num]\s & complex ph5om5a :i* usually accompany ! division ( ! cell1 = in/ance ( ! f]tilis$ egg4 ,division ( ! cell is ess5tially accompani$1 & prec$$1 by a *ange f radial or monopol> to a def9itely bipol> pol>ity4 ,9 ! hi!rto quiesc5t1 or app>5tly quiesc5t cell1 we p]ceive c]ta9 movem5ts1 :i* correspond precisely to :at mu/ accompany & result f a 8pol>isation0 ( =ces )9 ! #afi cell3 ( =ces :i*1 :atev] may be _! specific nature1 at lea/ are capable ( pol>isation1 & ( produc+ consequ5t attraction or repulsion betwe5 *>g$ p>ticles ( matt]4 ,! oppos+ =ces :i* 7 di/ribut$ 9 equilibrium ?r\gh\t ! sub/ance ( ! cell become focuss$ at two 8c5trosomes10 :i* may or may n be already di/+ui%$ z visible portions ( matt]2 9 ! egg1 "o ( ^! is always ne> to1 & ! o!r remote f1 ! 8animal pole0 ( ! egg1 :i* pole is visibly z well z *emically diff]5t f ! o!r1 & is ! region 9 :i* ! m rapid & conspicu\s developm5tal *anges w pres5tly beg94 ,betwe5 ! two c5trosomes1 a sp9dle-%ap$ ,illu/ration3 ,fig4 #da4 ,c>yok9etic figure 9 a divid+ cell 7or bla/om]e7 ( ! ,tr\t's egg4 7,aft] ,pr5ant1 f a prep>ation by ,pr(4 ,p4 ,b\947 figure appe>s1 ^: /rik+ resemblance to ! l9es ( =ce made visible by iron-fil+s betwe5 ! poles ( a magnet1 0 at once recognis$ by ,h]mann ,fol1 :5 9 #ahgc he witness$ = ! fir/ "t ! ph5om5on 9 "q4 ,on ! f>!r side ( ! c5trosomes are se5 />-l figures1 or 8a/]s10 9 :i* we c )\t difficulty recognise ! brok5 l9es ( =ce :i* run ext]nally to ^? /rong] l9es :i* lie ne>] to ! pol> axis & :i* con/itute ! 8sp9dle40 ,! l9es ( =ce are r5d]$ visible or 8mat]ial10 j z 9 ! exp]im5t ( ! iron-fil+s1 by ! fact t1 9 ! het]og5e\s sub/ance ( ! cell1 c]ta9 portions ( matt] are m 8p]meable0 to ! act+ =ce ?an ! re/1 become !mselves pol>is$ aft] ! #agj fa%ion ( a magnetic or 8p>amagnetic0 body1 arrange !mselves 9 an ord]ly way betwe5 ! two poles ( ! field ( =ce1 cl+ to "o ano!r z x 7 9 ?reads#bbe1 & are only prev5t$ by ! friction ( ! surr\nd+ m$ium f approa*+ & congregat+ ar\nd ! adjac5t poles4 ,z ! field ( =ce /r5g!ns1 ! m w ! l9es ( =ce be drawn 9 t[>ds ! int]pol> axis1 & ! less evid5t w be ^? remot] l9es :i* con/itute ! t]m9al1 or extrapol>1 a/]s3 a cle> space1 free f mat]ialis$ l9es ( =ce1 may ?us t5d to be set up on ei!r side ( ! sp9dle1 ! s-call$ 8,bts*li space0 ( ! hi/ologi/s#bbf4 ,on ! o!r h&1 ! l9es ( =ce con/itut+ ! sp9dle w be less conc5trat$ if !y f9d a pa? ( less resi/ance at ! p]iph]y ( ! cell3 z happ5s1 9 our exp]im5t ( ! iron-fil+s1 :5 we encircle ! field ( =ce ) an iron r+4 ,on ?is pr9ciple1 ! diff]5ces obs]v$ betwe5 cells 9 :i* ! sp9dle is well develop$ & ! a/]s small1 & o!rs 9 :i* ! sp9dle is weak & ! a/]s enorm\sly develop$1 c be easily expla9$ by v>iations 9 ! pot5tial ( ! field1 ! l>ge1 conspicu\s a/]s be+ probably correlat$ ) a m>k$ p]meability ( ! surface ( ! cell4 ,! visible field ( =ce1 ?\gh (t5 call$ ! 8nucle> sp9dle10 is =m$ outside (1 b usually ne> to1 ! nucleus4 ,let u look a little m closely into ! /ructure ( ?is body1 & into ! *anges :i* x pres5tly und]goes4 ,)9 its sph]ical outl9e 7,fig4 #db71 x conta9s an 8alveol>0 #aga me%work 7(t5 describ$1 f its appe>ance 9 optical section1 z a 8reticulum071 consi/+ ( m solid sub/ances1 ) m fluid matt] fill+ up ! int]alveol> me%es4 ,?is ph5om5on is no?+ else ?an :at we call 9 ord9>y language1 a 8fro?0 or a 8foam40 ,x is a surface-t5sion ph5om5on1 due to ! int]act+ surface-t5sions ( two int]mix$ fluids1 n v diff]5t 9 d5sity1 z !y /rive to sep>ate4 ,( precisely ! same k9d 7z ,bts*li 0 ! fir/ to %ew7 are ! m9ute alveol> networks :i* are to be disc]n$ 9 ! cytoplasm ( ! cell#bbg1 & :i* we n[ "k to be n inh]5t 9 ! nature ( protoplasm1 or ( liv+ matt] 9 g5]al1 b to be due to v>i\s causes1 natural z well z artificial4 ,! microscopic honeycomb /ructure ( ca/ metal "u v>i\s conditions ( cool+1 ev5 on a gr& scale ! column> /ructure ( basaltic rock1 is an example ( ! same surface-t5sion ph5om5on4 #agb ,illu/ration3 ,fig4 #db4 ,illu/ration3 ,fig4 #dc4 ,b "h we t\* ! br9k ( a subject s important t we mu/ n pass x by )\t a ^w1 & yet s cont5ti\s t we mu/ n ent] into its details4 ,! "q involv$ is simply :e!r ! great mass ( record$ obs]vations & accept$ beliefs ) reg>d to ! visible /ructure ( protoplasm & ( ! cell con/itute a fair picture ( ! actual liv+ cell1 or be bas$ on appe>ances :i* are incid5t to dea? itself & to ! artificial treatm5t :i* ! microscopi/ is accu/om$ to apply4 ,! great bulk ( hi/ological "w is done by me?ods :i* involve ! sudd5 kill+ ( ! cell or organism by /rong reag5ts1 ! assumption be+ t dea? is s rapid t ! visible ph5om5a exhibit$ dur+ life are reta9$ or 8fix$0 9 our prep>ations4 ,:ile ?is assumption is reasonable & ju/ifi$ z reg>ds ! g5]al outw>d =m ( small organisms or ( individual cells1 en\gh has be5 done ( late ye>s to %ew t ! case is totally diff]5t 9 ! case ( ! m9ute int]nal networks1 granules1 etc41 :i* repres5t ! alleg$ /ructure ( protoplasm4 ,=1 z ,h>dy puts x1 8,x is notori\s t ! v>i\s fix+ reag5ts are coagulants ( organic colloids1 & t !y produce precipitates :i* h a c]ta9 figure or /ructure1 444 & t ! figure v>ies1 o!r ?+s be+ equal1 accord+ to ! reag5t us$40 ,s x comes to pass t "s writ]s#bbh h altoge!r d5i$ ! exi/5ce 9 ! liv+ cell-protoplasm ( a network or alveol> 8foam02 o!rs#bbi h ca/ d\bts on ! ma9 t5ets ( rec5t hi/ology reg>d+ nucle> /ructure2 & ,h>dy1 discuss+ ! /ructure ( c]ta9 gl&-cells1 decl>es t 8!re is no evid5ce t ! /ructure discov]able 9 ! cell-sub/ance ( ^! cells aft] fixation has any c\nt]p>t 9 ! cell :5 liv+40 8,a l>ge "p ( x0 he goes on to say 8is an artefact4 ,! pr(\nd diff]5ce 9 ! m9ute /ructure ( a secretory cell ( a muc\s gl& accord+ to ! reag5t :i* is us$ to fix x w\ld1 x seems to me1 almo/ suffice to e/abli% ?is /atem5t 9 ! abs5ce ( o!r evid5ce40 ,nev]!less1 hi/ological /udy proce$s1 especially on ! "p ( ! morphologi/s1 ) b little *ange 9 !ory or 9 me?od1 9 spite ( ^! & _m o!r w>n+s4 ,t c]ta9 visible /ructures1 nucleus1 vacuoles1 8attraction-sph]es0 or c5trosomes1 etc41 are actually pres5t 9 ! liv+ cell1 we "k = c]ta92 & to ?is class belong ! great majority ( /ructures 7includ+ ! nucle> 8sp9dle0 itself7 ) :i* we are at pres5t conc]n$4 ,t _m o!r alleg$ /ructures are artificial has also be5 plac$ beyond a d\bt2 b :]e to draw ! divid+ l9e we (t5 d n "k#bcj4 #agc ,! foll[+ is a brief epitome ( ! visible *anges und]gone by a typical cell1 lead+ up to ! act ( segm5tation1 & con/itut+ ! ph5om5on ( mitosis or c>yok9etic division4 ,9 ! egg ( a sea-ur*91 we see ) almo/ diagrammatic complet5ess :at is set =? "h#bca4 ,illu/ration3 ,fig4 #dd4 ,illu/ration3 ,fig4 #de4 #a4 ,! *romat91 :i* to beg9 ) 0 di/ribut$ 9 granules on ! o!rwise a*romatic reticulum 7,fig4 #db71 conc5trates to =m a ske9 or spireme1 :i* may be a cont9u\s ?read f ! fir/ 7,figs4 #dc1 #dd71 or f ! fir/ segm5t$4 ,9 any case x divides transv]sely soon] or lat] into a numb] ( *romosomes 7,fig4 #de71 :i* z a rule h ! %ape ( little rods1 /raight or curv$1 (t5 b5t into a ,v1 b :i* may also be ovoid1 or r\nd1 or ev5 annul>4 ,c]ta9 deeply /a9+ masses1 ! nucleoli1 :i* may be pres5t 9 ! re/+ nucleus1 d n take "p 9 ! process ( *romosome =mation2 !y are ei!r ca/ out ( ! nucleus & are dissolv$ 9 ! cytoplasm1 or fade away 9 situ4 #b4 ,mean:ile1 ! deeply /a9+ granule 7"h extra-nucle>71 kn[n z ! c5trosome1 has divid$ 9 two4 ,! two result+ granules travel to opposite poles ( ! nucleus1 & #agd !re ea* becomes surr\nd$ by a sy/em ( radiat+ l9es1 ! a/]s2 imm$iately ar\nd ! c5trosome is a cle> space1 ! c5trosph]e 7,figs4 #dc-de74 ,betwe5 ! two c5trosomes ) _! a/]s /ret*es a bundle ( a*romatic fibres1 ! sp9dle4 #c4 ,! surface-film b\nd+ ! nucleus has brok5 d[n1 ! def9ite nucle> b\nd>ies are lo/1 & ! sp9dle n[ /ret*es ?r\gh ! nucle> mat]ial1 9 :i* lie ! *romosomes 7,figs4 #de1 #df74 ,^! *romosomes n[ arrange !mselves midway betwe5 ! poles ( ! sp9dle1 :]e !y =m :at is call$ ! equatorial plate 7,fig4 #dg74 ,illu/ration3 ,fig4 #df4 ,illu/ration3 ,fig4 #dg4 #d4 ,ea* *romosome splits longitud9ally into two3 usually at ?is /age1--b x is to be notic$ t ! splitt+ may h tak5 place s e>ly z ! spireme /age 7,fig4 #dh74 #e4 ,! halves ( ! split *romosomes n[ sep>ate f "o ano!r1 & travel 9 opposite directions t[>ds ! two poles 7,fig4 #di74 ,z !y move1 x becomes app>5t t ! sp9dle consi/s ( a m$ian bundle ( 8fibres10 ! c5tral sp9dle1 runn+ f pole to pole1 & a m sup]ficial %ea? ( 8mantle-fibres10 to :i* ! *romosomes seem to be atta*$1 & by :i* !y seem to be drawn t[>ds ! a/]s4 #f4 ,! daught] *romosomes1 arrang$ n[ 9 two gr\ps1 become closely cr[d$ 9 a mass ne> ! c5tre ( ea* a/] #age 7,fig4 #ej74 ,!y fuse toge!r & =m once m an alveol> reticulum & may occasionally at ?is /age =m ano!r spireme4 ,illu/ration3 ,fig4 #dh4 ,illu/ration3 ,fig4 #di4 ,a b\nd>y or surface wall is n[ develop$ r\nd ea* recon/ruct$ nucle> mass1 & ! sp9dle-fibres disappe> 7,fig4 #ea74 ,! c5trosome rema9s1 z a rule1 outside ! nucleus4 ,illu/ration3 ,fig4 #ej4 ,illu/ration3 ,fig4 #ea4 #g4 ,on ! c5tral sp9dle1 9 ! position ( ! equatorial plate1 !re has appe>$ dur+ ! migration ( ! *romosomes1 a 8cell-plate0 ( deeply /a9+ ?ick5+s 7,figs4 #ej1 #ea74 ,?is is m conspicu\s 9 plant-cells4 #agf #h4 ,a con/riction has mean:ile appe>$ 9 ! cytoplasm1 & ! cell divides ?r\gh ! equatorial plane4 ,9 plant-cells ! l9e ( ?is division is =e%ad[$ by ! 8cell-plate10 :i* ext5ds f ! sp9dle across ! entire cell1 & splits into two lay]s1 betwe5 :i* appe>s ! membrane by :i* ! daught] cells are cleft asund]4 ,9 animal cells ! cell-plate does n atta9 su* dim5sions1 & no cell-wall is =m$4 ,! :ole1 or v ne>ly ! :ole ( ^! nucle> ph5om5a may be br\ght into relation ) t pol>isation ( =ces1 9 ! cell z a :ole1 ^: field is made manife/ by ! 8sp9dle0 & 8a/]s0 ( :i* we h already spok53 c]ta9 p>ticul> ph5om5a1 directly attributable to surface-t5sion & diffusion1 tak+ place 9 m or less obvi\s & inevitable dep5d5ce ^u ! pol> sy/em4 ,! ref]5ce numb]s 9 ! foll[+ acc\nt ref] to ! p>agraphs & figures ( ! prec$+ summ>y ( visible nucle> ph5om5a4 ,at ! same "t1 9 attempt+ to expla9 ! ph5om5a1 we _c say too cle>ly1 or too (t51 t all t we are mean:ile ju/ifi$ 9 do+ is to try to %ew t su* & su* actions lie )9 ! range ( kn[n physical actions & ph5om5a1 or t kn[n physical ph5om5a produce effects simil> to !m4 ,we want to feel sure t ! :ole ph5om5on is n sui g5]is1 b is someh[ or o!r capable ( be+ ref]r$ to dynamical laws1 & to ! g5]al pr9ciples ( physical sci5ce4 ,b :5 we speak ( "s p>ticul> =ce or mode ( action1 us+ x z an illu/rative hypo!sis1 we mu/ /op f> %ort ( ! implication t ?is or t =ce is necess>ily ! v "o :i* is actually at "w )9 ! liv+ cell2 & c]ta9ly we ne$ n attempt ! =midable task ( try+ to reconcile1 or to *oose betwe51 ! v>i\s hypo!ses :i* h already be5 enunciat$1 or ! sev]al assumptions on :i* !y dep5d4 ,any region ( space )9 :i* action is manife/$ is a field ( =ce2 & a simple example is a bipol> field1 9 :i* ! action is symmetrical ) ref]5ce to ! l9e jo9+ two po9ts1 or poles1 & also ) ref]5ce to ! 8equatorial0 plane equidi/ant f bo?4 ,we h su* a 8field ( =ce0 9 #agg ! neighb\rhood ( ! c5trosome ( ! ripe cell or ovum1 :5 x is ab\t to divide2 & by ! "t ! c5trosome has divid$1 ! field is def9itely a bipol> "o4 ,! quality ( a m$ium fill+ ! field ( =ce may be uni=m1 or x may v>y f po9t to po9t4 ,9 p>ticul>1 x may dep5d ^u ! magnitude ( ! field2 & ! quality ( "o m$ium may diff] f t ( ano!r4 ,su* v>iation ( quality1 )9 "o m$ium1 or f "o m$ium to ano!r1 is capable ( diagrammatic repres5tation by a v>iation ( ! direction or ! /r5g? ( ! field 7o!r conditions be+ ! same7 f ! /ate manife/$ 9 "s uni=m m$ium tak5 z a /&>d4 ,! m$ium is said to be p]meable to ! =ce1 9 great] or less degree ?an ! /&>d m$ium1 accord+ z ! v>iation ( ! d5sity ( ! l9es ( =ce f ! /&>d case1 "u o!rwise id5tical conditions1 is 9 excess or defect4 ,a body plac$ 9 ! m$ium w t5d to move t[>ds regions ( great] or less =ce accord+ z its p]meability is great] or less ?an t ( ! surr\nd+ m$ium#bcb4 ,9 ! common exp]im5t ( plac+ iron-fil+s betwe5 ! two poles ( a magnetic field1 ! fil+s h a v high p]meability2 & n only d !y !mselves become pol>is$ s z to attract "o ano!r1 b !y t5d to be attract$ f ! weak] to ! /rong] p>ts ( ! field1 & z we h se51 7 x n = friction or "s o!r resi/ance1 !y w\ld soon ga!r toge!r ar\nd ! ne>e/ pole4 ,b if we repeat ! same exp]im5t ) su* a metal z bismu?1 :i* is v little p]meable to ! magnetic =ce1 !n ! conditions are rev]s$1 & ! p>ticles1 be+ repell$ f ! /rong] to ! weak] p>ts ( ! field1 t5d to take up _! position z f> f ! poles z possible4 ,! p>ticles h become pol>is$1 b 9 a s5se opposite to t ( ! surr\nd+1 or adjac5t1 field4 ,n[1 9 ! field ( =ce ^: opposite poles are m>k$ by #agh ! c5trosomes ! nucleus appe>s to act z a m or less p]meable body1 z a body m p]meable ?an ! surr\nd+ m$ium1 t is to say ! 8cytoplasm0 ( ! cell4 ,x is accord+ly attract$ by1 & drawn into1 ! field ( =ce1 & tries1 z x 71 to set itself betwe5 ! poles & z f> z possible f bo? ( !m4 ,9 o!r words1 ! c5trosome-foci w be app>5tly drawn ov] its surface1 until ! nucleus z a :ole is involv$ )9 ! field ( =ce1 :i* is visibly m>k$ out by ! 8sp9dle0 7p>4 #c1 ,figs4 #dd1 #de74 ,if ! field ( =ce be electrical1 or act 9 a fa%ion analog\s to an electrical field1 ! *>g$ nucleus w h its surface-t5sions dim9i%$#bcc3 ) ! d\ble result t ! inn] alveol> me%work w be brok5 up 7p>4 #a71 & t ! sph]ical b\nd>y ( ! :ole nucleus w disappe> 7p>4 #b74 ,! break-up ( ! alveoli 7by ?9n+ & rupture ( _! p>tition walls7 leads to ! =mation ( a net1 & ! fur!r break-up ( ! net may lead to ! unravell+ ( a ?read or 8spireme0 7,figs4 #dc1 #dd74 ,"h !re comes into play a fundam5tal pr9ciple :i*1 9 s f> z we require to und]/& x1 c be expla9$ 9 simple words4 ,! effect 7& we might ev5 say ! object7 ( draw+ ! m p]meable body 9 betwe5 ! poles1 is to obta9 an 8easi] pa?0 by :i* ! l9es ( =ce may travel2 b x is obvi\s t a long] r\te ?r\gh ! m p]meable body may at l5g? be f\nd less advantage\s ?an a %ort] r\te ?r\gh ! less p]meable m$ium4 ,t is to say1 ! m p]meable body w only t5d to be drawn 9 to ! field ( =ce until a po9t is rea*$ :]e 7s to speak7 ! way r\nd & ! way ?r\gh are equally advantage\s4 ,we %\ld accord+ly expect t 7on our hypo!sis7 !re w\ld be f\nd cases 9 :i* ! nucleus 0 :olly1 & o!rs 9 :i* x 0 only p>tially1 & 9 great] or less degree1 drawn 9 to ! field betwe5 ! c5trosomes4 ,?is is precisely :at is f\nd to occur 9 actual fact4 ,figs4 #dd & #de repres5t two s-call$ 8types10 ( a phase :i* foll[s t repres5t$ 9 ,fig4 #dc4 ,accord+ to ! usual descriptions 7& 9 p>ticul> to ,pr(essor #agi ,e4 ,b4 ,wilson's#bcd71 we are told t1 9 su* a case z ,fig4 #dd1 ! 8prim>y sp9dle0 disappe>s & ! c5trosomes div]ge to opposite poles ( ! nucleus2 su* a condition be+ f\nd 9 _m plant-cells1 & 9 ! cleavage-/ages ( _m eggs4 ,9 ,fig4 #de1 on ! o!r h&1 ! prim>y sp9dle p]si/s1 & subsequ5tly comes to =m ! ma9 or 8c5tral0 sp9dle2 :ile at ! same "t we see ! fad+ away ( ! nucle> membrane1 ! break+ up ( ! spireme into sep>ate *romosomes1 & an +r[? into ! nucle> area ( ! 8a/ral rays10--all z 9 ,fig4 #df1 :i* repres5ts ! next succe$+ phase ( ,fig4 #de4 ,?is condition1 ( ,fig4 #df1 occurs 9 a v>iety ( cases2 x is well se5 9 ! epid]mal cells ( ! salam&]1 & is also on ! :ole *>act]i/ic ( ! mode ( =mation ( ! 8pol> bodies40 ,x is cle> & obvi\s t ! two 8types0 correspond to m]e diff]5ces ( degree1 & are su* z w\ld naturally be br\ght ab\t by diff]5ces 9 ! relative p]meabilities ( ! nucle> mass & ( ! surr\nd+ cytoplasm1 or ev5 by diff]5ces 9 ! magnitude ( ! =m] body4 ,b n[ an important *ange takes place1 or r an important diff]5ce appe>s2 =1 :]eas ! nucleus z a :ole t5d$ to be drawn 9 to ! /rong] p>ts ( ! field1 :5 x comes to break up we f9d1 on ! contr>y1 t its conta9$ spireme-?read or sep>ate *romosomes t5d to be repell$ to ! weak] p>ts4 ,:atev] ?is diff]5ce may be due to1--:e!r1 = in/ance1 to actual diff]5ces ( p]meability1 or possibly to diff]5ces 9 8surface-*>ge10--! fact is t ! *romat9 sub/ance n[ behaves aft] ! fa%ion ( a 8diamagnetic0 body1 & is repell$ f ! /rong] to ! weak] p>ts ( ! field4 ,9 o!r words1 its p>ticles1 ly+ 9 ! int]-pol> field1 t5d to travel t[>ds ! equatorial plane !re( 7,figs4 #dg1 #dh71 & fur!r t5d to move outw>ds t[>ds ! p]iph]y ( t plane1 t[>ds :at ! hi/ologi/ calls ! 8mantle-fibres10 or out]mo/ ( ! l9es ( =ce ( :i* ! sp9dle is made up 7p>4 #e1 ,fig4 #dg74 ,& if ?is comp>atively non-p]meable *romat9 sub/ance come to consi/ ( sep>ate portions1 m or less elongat$ 9 =m1 ^! portions1 or sep>ate 8*romosomes10 w adju/ !mselves longitud9ally1 #ahj 9 a p]iph]al equatorial circle 7,figs4 #dh1 #di74 ,?is is precisely :at actually takes place4 ,moreov]1 be=e ! break+ up ( ! nucleus1 long be=e ! *romat9 mat]ial has brok5 up into sep>ate *romosomes1 & at ! v "t :5 x is be+ fa%ion$ into a 8spireme10 ?is body already lies 9 a pol> field1 & mu/ already h a t5d5cy to set itself 9 ! equatorial plane !re(4 ,b ! long1 cont9u\s spireme ?read is unable1 s long z ! nucleus reta9s its sph]ical b\nd>y wall1 to adju/ itself 9 a simple equatorial annulus2 9 /riv+ to d s1 x mu/ t5d to coil & 8k9k0 itself1 & 9 s do+ 7if all ?is be s71 x mu/ t5d to assume ! *>act]i/ic convolutions ( ! 8spireme40 ,illu/ration3 ,fig4 #eb4 ,*romosomes1 und]go+ splitt+ & sep>ation4 7,aft] ,hats*ek & ,flemm+1 diagrammatis$47 ,aft] ! spireme has brok5 up into sep>ate *romosomes1 ^! p>ticles come into a position ( tempor>y1 & un/able1 equilibrium ne> ! p]iph]y ( ! equatorial plane1 & "h !y t5d to place !mselves 9 a symmetrical arrangem5t 7,fig4 #eb74 ,! p>ticles are r\nd$1 l9e>1 sometimes annul>1 simil> 9 =m & size to "o ano!r2 & ly+ z !y d 9 a fluid1 & subject to a symmetrical sy/em ( =ces1 x is n surpris+ t !y arrange !mselves 9 a symmetrical mann]1 ! precise arrangem5t dep5d+ on ! =m ( ! p>ticles !mselves4 ,?is symmetry may p]haps be due1 z has already be5 sugge/$1 to induc$ electrical *>ges4 ,9 discuss+ ,brau]'s obs]vations on ! splitt+ ( ! *romatic filam5t1 & ! symmetrical arrangem5t ( ! sep>ate granules1 9 ,asc>is megalocephala1 ,lillie#bce #aha rem>ks3 8,?is behavi\r is /rongly sugge/ive ( ! division ( a colloidal p>ticle "u ! influ5ce ( its surface electrical *>ge1 & ( ! effects ( mutual repulsion 9 keep+ ! products ( division ap>t40 ,x is also probable t surface-t5sions betwe5 ! p>ticles & ! surr\nd+ protoplasm w\ld br+ ab\t an id5tical result1 & w\ld suffici5tly acc\nt = ! obvi\s1 & at fir/ sight1 v curi\s1 symmetry4 ,we "k t if we float a c\ple ( mat*es 9 wat] !y t5d to approa* "o ano!r1 till !y lie close toge!r1 side by side2 &1 if we lay ^u a smoo? wet plate f\r mat*es1 half brok5 across1 a precisely simil> attraction br+s ! f\r mat*es toge!r 9 ! =m ( a symmetrical cross4 ,:e!r "o ( ^!1 or "s o!r1 be ! actual explanation ( ! ph5om5on1 x is at lea/ pla9 t by "s physical cause1 "s mutual & symmetrical attraction or repulsion ( ! p>ticles1 we mu/ seek to acc\nt = ! curi\s symmetry ( ^! s-call$ 8tetrads40 ,! rem>kable annul> *romosomes1 %ewn 9 ,fig4 #ec1 c also be easily imitat$ by means ( loops ( ?read ^u a soapy film :5 ! film )9 ! annulus is brok5 or its t5sion r$uc$4 ,illu/ration3 ,fig4 #ec4 ,annul> *romosomes1 =m$ 9 ! sp]matog5esis ( ! ,mole-cricket4 7,f ,wilson1 aft] ,vom ,ra?47 ,s f> z we h n[ gone1 !re is no great difficulty 9 po9t+ to simple & famili> ph5om5a ( a field ( =ce :i* are simil>1 or comp>able1 to ! ph5om5a :i* we witness )9 ! cell4 ,b among ^! latt] ph5om5a !re are o!rs = :i* x is n s easy to sugge/1 9 accordance ) kn[n laws1 a simple mode ( physical causation4 ,x is n at once obvi\s h[1 9 any simple sy/em ( symmetrical =ces1 #ahb ! *romosomes1 :i* _h at fir/ be5 app>5tly repell$ f ! poles t[>ds ! equatorial plane1 %\ld !n be split asund]1 & %\ld pres5tly be attract$ 9 opposite directions1 "s to "o pole & "s to ! o!r4 ,rememb]+ t x is n our purpose to ass]t t "s "o p>ticul> mode ( action is at "w1 b m]ely to %ew t !re d exi/ physical =ces1 or di/ributions ( =ce1 :i* are capable ( produc+ ! requir$ result1 ,i give ! foll[+ sugge/ive hypo!sis1 :i* ,i owe to my colleague ,pr(essor ,w4 ,p$die4 ,z we h begun by suppos+ t ! nucle>1 or *romosomal matt] diff]s 9 p]meability f ! m$ium1 t is to say ! cytoplasm1 9 :i* x lies1 let u n[ make ! fur!r assumption t its p]meability is v>iable1 & dep5ds ^u ! /r5g? ( ! field4 ,illu/ration3 ,fig4 #ed4 ,9 ,fig4 #ed1 we h a field ( =ce 7repres5t+ our cell71 consi/+ ( a homog5e\s m$ium1 & includ+ two opposite poles3 l9es ( =ce are indicat$ by full l9es1 & loci ( con/ant magnitude ( =ce are %ewn by dott$ l9es4 ,let u n[ consid] a body ^: p]meability 77 dep5ds on ! /r5g? ( ! field ,f4 ,at two field-/r5g?s1 su* z ,fa1 ,fb1 let ! p]meability ( ! body be equal to t ( ! #ahc m$ium1 & let ! curv$ l9e 9 ,fig4 #ee repres5t g5]ally its p]meability at o!r field-/r5g?s2 & let ! out] & inn] dott$ curves 9 ,fig4 #ed repres5t respectively ! loci ( ! field-/r5g?s ,fb & ,fa4 ,! body if x be plac$ 9 ! m$ium )9 ei!r bran* ( ! inn] curve1 or outside ! out] curve1 w t5d to move into ! neighb\rhood ( ! adjac5t pole4 ,if x be plac$ 9 ! region int]m$iate to ! two dott$ curves1 x w t5d to move t[>ds regions ( weak] field-/r5g?4 ,illu/ration3 ,fig4 #ee4 ,! locus ,fb is !re=e a locus ( /able position1 t[>ds :i* ! body t5ds to move2 ! locus ,fa is a locus ( un/able position1 f :i* x t5ds to move4 ,if ! body 7 plac$ across ,fa1 x might be torn asund] into two portions1 ! split co9cid+ ) ! locus ,fa4 ,suppose a numb] ( su* bodies to be scatt]$ ?r\gh\t ! m$ium4 ,let at fir/ ! regions ,fa & ,fb be entirely outside ! space :]e ! bodies are situat$3 &1 9 mak+ ?is supposition we may1 if we please1 suppose t ! loci :i* we are call+ ,fa & ,fb are mean:ile situat$ some:at f>!r f ! axis ?an 9 our figure1 t 7= in/ance7 ,fa is situat$ :]e we h drawn ,fb1 & t ,fb is /ill fur!r out4 ,! bodies !n t5d t[>ds ! poles2 b ! t5d5cy may be v small if1 9 ,fig4 #ee1 ! curve & its int]sect+ /raight l9e d n div]ge v f> f "o ano!r beyond ,fa2 9 o!r #ahd words1 if1 :5 situat$ 9 ?is region1 ! p]meability ( ! bodies is n v mu* 9 excess ( t ( ! m$ium4 ,let ! poles n[ t5d to sep>ate f>!r & f>!r f "o ano!r1 ! /r5g? ( ea* pole rema9+ unalt]$2 9 o!r words1 let ! c5trosome-foci rec$e f "o ano!r1 z !y actually d1 draw+ out ! sp9dle-?reads betwe5 !m4 ,! loci ,fa1 ,fb1 w close 9 to ne>] relative di/ances f ! poles4 ,9 do+ s1 :5 ! locus ,fa crosses "o ( ! bodies1 ! body may be torn asund]2 if ! body be ( elongat$ %ape1 & be cross$ at m po9ts ?an "o1 ! =ces at "w w t5d to exagg]ate its fold+s1 & ! t5d5cy to rupture is greate/ :5 ,fa is 9 "s m$ian position 7,fig4 #ef74 ,illu/ration3 ,fig4 #ef4 ,:5 ! locus ,fa has pass$ entirely ov] ! body1 ! body t5ds to move t[>ds regions ( weak] =ce2 b :51 9 turn1 ! locus ,fb has cross$ x1 !n ! body aga9 moves t[>ds regions ( /rong] =ce1 t is to say1 t[>ds ! ne>e/ pole4 ,&1 9 ?us mov+ t[>ds ! pole1 x w d s1 z appe>s actually to be ! case 9 ! divid+ cell1 along ! c\rse ( ! out] l9es ( =ce1 ! s-call$ 8mantle-fibres0 ( ! hi/ologi/#bcf4 ,su* consid]ations z ^! give g5]al results1 easily op5 to modification 9 detail by a *ange ( any ( ! arbitr>y po/ulates :i* h be5 made = ! sake ( simplicity4 ,d\btless !re are _m o!r assumptions :i* w\ld m or less meet ! case2 = in/ance1 t ( ,ida ,h4 ,hyde t1 #ahe dur+ ! active phase ( ! *romat9 molecule 7dur+ :i* x decomposes & sets free nucleic acid7 x c>ries a *>ge opposite to t :i* x be>s dur+ its re/+1 or alkal9e phase2 & t x w\ld accord+ly move t[>ds diff]5t poles "u ! influ5ce ( a curr5t1 w&]+ ) its negative *>ge 9 an alkal9e fluid dur+ its acid phase to ! anode1 & to ! ka?ode dur+ its alkal9e phase4 ,a :ole field ( speculation is op5$ up :5 we beg9 to consid] ! cell n m]ely z a pol>is$ electrical field1 b also z an electrolytic field1 full ( w&]+ ions4 ,inde$ x is high "t we rem9d$ ourselves t we h p]haps be5 deal+ too mu* ) ord9>y physical analogies3 & t our :ole field ( =ce )9 ! cell is ( an ord] ( magnitude :]e ^! gross] analogies may fail to s]ve u1 & might ev5 play u false1 or lead u a/ray4 ,b our sole object mean:ile1 z ,i h said m ?an once1 is to demon/rate1 by su* illu/rations z ^!1 t1 :atev] be ! actual & z yet unkn[n modus op]&i1 !re are physical conditions & di/ributions ( =ce :i* c\ld produce j su* ph5om5a ( movem5t z we see tak+ place )9 ! liv+ cell4 ,?is1 & no m1 is precisely :at ,desc>tes is said to h claim$ = 8 description ( ! human body z a 8me*anism#bcg40 ,! =ego+ acc\nt is bas$ on ! provisional assumption t ! ph5om5a ( c>yok9esis are analog\s to1 if n id5tical ) ^? ( a bipol> electrical field2 & ?is comp>ison1 9 my op9ion1 (f]s )\t d\bt ! be/ available s]ies ( analogies4 ,b we mu/ on no acc\nt omit to m5tion ! fact t "s ( ,l$uc's diffusion-exp]im5ts (f] v rem>kable analogies to ! diagrammatic ph5om5a ( c>yok9esis1 z %ewn 9 ! annex$ figure#bch4 ,"h we h two id5tical 7n opposite7 poles ( osmotic conc5tration1 =m$ by plac+ a drop ( indian ink 9 salt wat]1 & !n on ei!r side ( ?is c5tral drop1 a hyp]tonic drop ( salt solution m lightly col\r$4 ,on ei!r side ! pigm5t ( ! c5tral drop has be5 drawn t[>ds ! focus ne>e/ to x2 b 9 ! middle l9e1 ! pigm5t #ahf is drawn 9 opposite directions by equal =ces1 & s t5ds to rema9 undi/urb$1 9 ! =m ( an 8equatorial plate40 ,nor %\ld we omit to take acc\nt 7h[ev] briefly & inadequately7 ( a novel & elegant hypo!sis put =w>d by ,a4 ,b4 ,lamb4 ,?is hypo!sis makes use ( a !orem ( ,bj]knes1 to ! effect t syn*ron\sly vibrat+ or pulsat+ bodies 9 a liquid field attract or repel "o ano!r accord+ z _! oscillations are id5tical or opposite 9 phase4 ,"u su* circum/ances1 true curr5ts1 or hydrodynamic l9es ( =ce1 are produc$1 id5tical 9 =m ) ! l9es ( =ce ( a magnetic field2 & o!r p>ticles float+1 ?\gh n necess>ily pulsat+1 9 ! liquid field1 t5d to be attract$ or repell$ by ! pulsat+ bodies accord+ z !y are light] or heavi] ?an ! surr\nd+ fluid4 ,moreov] 7& ?is is ! mo/ rem>kable po9t ( all71 ! l9es ( =ce set up by ! oppositely pulsat+ bodies are ! same z ^? :i* are produc$ by opposite magnetic poles3 ?\gh 9 ! =m] case repulsion1 & 9 ! latt] case attraction1 takes place betwe5 ! two poles#bci4 ,illu/ration3 ,fig4 #eg4 ,artificial c>yok9esis 7aft] ,l$uc71 = comp>ison ) ,fig4 #da1 p4 #afi4 ,b to return to our g5]al discussion4 ,:ile x c sc>cely be too (t5 repeat$ t our enquiry is n direct$ t[>ds ! solution ( physiological problems1 save #ahg only 9 s f> z !y are insep>able f ! problems pres5t$ by ! visible configurations ( =m & /ructure1 & :ile we try1 z f> z possible1 to evade ! difficult "q ( :at p>ticul> =ces are at "w :5 ! m]e visible =ms produc$ are su* z to leave ?is an op5 "q1 yet 9 ?is p>ticul> case we h be5 drawn into ! use ( electrical analogies1 & we are b\nd to ju/ify1 if possible1 our resort to ?is p>ticul> mode ( physical action4 ,!re is an important pap] by ,r4 ,s4 ,lillie1 on ! 8,electrical ,convection ( c]ta9 ,free ,cells & ,nuclei#bdj10 :i*1 :ile ,i _c quote x 9 direct support ( ! sugge/ions :i* ,i h made1 yet gives j ! evid5ce we ne$ 9 ord] to %ew t electrical =ces act ^u ! con/itu5ts ( ! cell1 & t _! action discrim9ates betwe5 ! two species ( colloids repres5t$ by ! cytoplasm & ! nucle> *romat94 ,& ! diff]5ce is su* t1 9 ! pres5ce ( an electrical curr5t1 ! cell sub/ance & ! nuclei 7includ+ sp]m-cells7 t5d to migrate1 ! =m] on ! :ole ) ! positive1 ! latt] ) ! negative /ream3 a diff]5ce ( electrical pot5tial be+ ?us indicat$ betwe5 ! p>ticle & ! surr\nd+ m$ium1 j z 9 ! case ( m9ute susp5d$ p>ticles ( v>i\s k9ds 9 v>i\s feebly conduc+ m$ia#bda4 ,& ! electrical diff]5ce is d\btless greate/1 9 ! case ( ! cell con/itu5ts1 j at ! p]iod ( mitosis3 :5 ! *romat9 is inv>iably 9 its mo/ deeply /a9+1 mo/ /rongly acid1 & !re=e1 presumably1 9 its mo/ electrically negative phase4 ,9 %ort1 #ahh ,lillie comes easily to ! conclusion t 8electrical !ories ( mitosis are entitl$ to m c>eful consid]ation ?an !y h hi!rto receiv$40 ,among o!r inve/igations1 all lead+ t[>ds ! same g5]al conclusion1 namely t diff]5ces ( electric pot5tial play a great "p 9 ! ph5om5on ( cell division1 ,i w\ld m5tion a v notewor?y pap] by ,ida ,h4 ,hyde#bdb1 9 :i* ! writ] %ews 7among o!r important obs]vations7 t n only is !re a measurable diff]5ce ( pot5tial betwe5 ! animal & vegetative poles ( a f]tilis$ egg 7,fundulus1 toad1 turtle1 etc471 b t ?is diff]5ce is n con/ant1 b fluctuates1 or actually rev]ses its direction1 p]iodically1 at epo*s co9cid+ ) successive acts ( segm5tation or o!r important phases 9 ! developm5t ( ! egg#bdc2 j z o!r physical rhy?ms1 = in/ance 9 ! production ( ,,co#b1 _h already be5 %ewn to d4 ,h5ce we %all be by no means surpris$ to f9d t ! 8mat]ialis$0 l9es ( =ce1 :i* 9 ! e>li] /ages =m ! conv]g5t curves ( ! sp9dle1 are replac$ 9 ! lat] phases ( c>yok9esis by div]g5t curves1 indicat+ t ! two foci1 :i* are m>k$ out )9 ! field by ! divid$ & recon/itut$ nuclei1 are n[ alike 9 _! pol>ity 7,figs4 #eh1 #ei74 ,x is c]ta91 to my m9d1 t ^! obs]vations ( ,miss ,hyde's1 & ( ,lillie's1 tak5 toge!r ) ^? ( _m writ]s on ! behavi\r ( colloid p>ticles g5]ally 9 _! relation to an electrical field1 h a close be>+ ^u ! physiological side ( our problem1 ! full discussion ( :i* lies outside our pres5t field4 ,! break-up ( ! nucleus1 already ref]r$ to & ascrib$ to a dim9ution ( its surface-t5sion1 is accompani$ by c]ta9 diffusion ph5om5a :i* are sometimes visible to ! eye2 & we are rem9d$ ( ,"l ,kelv9's view t diffusion is implicitly #ahi associat$ ) surface-t5sion *anges1 ( :i* ! fir/ /ep is a m9ute puck]+ ( ! surface-sk91 a sort ( int]digitation ) ! surr\nd+ m$ium4 ,= in/ance1 ,s*ewiak(f has obs]v$ 9 ,euglypha#bdd t1 j be=e ! break-up ( ! nucleus1 a sy/em ( rays appe>s1 conc5tr$ ab\t x1 b hav+ no?+ to d ) ! pol> a/]s3 & dur+ ! exi/5ce ( ?is /riation1 ! nucleus enl>ges v consid]ably1 evid5tly by imbibition ( fluid f ! surr\nd+ protoplasm4 ,9 %ort1 diffusion is at "w1 h& 9 h& )1 & z x 7 9 opposition to1 ! surface-t5sions :i* def9e ! nucleus4 ,by diffusion1 h& 9 h& ) surface-t5sion1 ! alveoli ( ! nucle> me%work are =m$1 enl>g$1 & f9ally ruptur$3 diffusion sets up ! movem5ts :i* give rise to ! appe>ance ( rays1 or /riae1 ar\nd ! nucleus3 & ?r\gh increas+ diffusion1 & weak5+ surface-t5sion1 ! r\nd$ outl9e ( ! nucleus f9ally disappe>s4 #aij ,illu/ration3 ,fig4 #eh4 ,f9al /age 9 ! fir/ segm5tation ( ! egg ( ,c]ebratulus4 7,f ,pr5ant1 aft] ,coe47#bde ,illu/ration3 ,fig4 #ei4 ,diagram ( field ( =ce ) two simil> poles4 ,z we /udy ^! manifold ph5om5a1 9 ! individual cases ( p>ticul> plants & animals1 we recognise a close id5tity ( type1 c\pl$ ) almo/ endless v>iation ( specific detail2 & 9 p>ticul>1 ! ord] ( succession 9 :i* c]ta9 ( ! ph5om5a occur is v>iable & irregul>4 ,! precise ord] ( ! ph5om5a1 ! "t ( longitud9al & ( transv]se fission ( ! *romat9 ?read1 ( ! break-up ( ! nucle> wall1 & s =?1 w dep5d ^u v>i\s m9or cont+5cies & 8int]f]5ces40 ,& x is wor?y ( p>ticul> note t ^! v>iations1 9 ! ord] ( ev5ts & 9 o!r subord9ate details1 :ile d\btless attributable to specific physical conditions1 w\ld seem to be )\t any obvi\s classificatory value or o!r biological significance#bdf4 ,z reg>ds ! actual me*anical division ( ! cell into two halves1 we %all see pres5tly t1 9 c]ta9 cases1 su* z t ( a long cyl9drical filam5t1 surface-t5sion1 & :at is kn[n z ! pr9ciple ( 8m9imal area10 g a long way to expla9 ! me*anical process ( division2 & 9 all cells :atsoev]1 ! process ( division mu/ someh[ be expla9$ z ! result ( a conflict betwe5 surface-t5sion & its oppos+ =ces4 ,b 9 su* a case z our sph]ical cell1 x is n v easy to see :at physical cause is at "w to di/urb its equilibrium & its integrity4 ,! fact t1 :5 actual division ( ! cell takes place1 x does s at "r angles to ! pol> axis & precisely 9 ! direction ( ! equatorial plane1 w\ld lead u to suspect t ! new surface =m$ 9 ! equatorial plane sets up an annul> t5sion1 direct$ inw>ds1 :]e x meets ! out] surface lay] ( ! cell itself4 ,b at ?is po9t1 ! problem becomes m complicat$4 ,be=e we c\ld hope to compreh5d x1 we %\ld h n only to enquire into ! pot5tial di/ribution at ! surface ( ! cell 9 relation to t :i* we h se5 to exi/ 9 its int]ior1 b we %\ld probably also h to take acc\nt ( ! diff]5ces ( pot5tial :i* ! mat]ial arrangem5ts along ! l9es ( =ce mu/ !mselves t5d to produce4 ,only #aia ?us c\ld we approa* a compreh5sion ( ! balance ( =ces :i* cohesion1 friction1 capill>ity & electrical di/ribution comb9e to set up4 ,! mann] 9 :i* we reg>d ! ph5om5on w\ld seem to turn1 9 great measure1 ^u :e!r or no we are ju/ifi$ 9 assum+ t1 9 ! liquid surface-film ( a m9ute sph]ical cell1 local1 & symmetrically localis$1 diff]5ces ( surface-t5sion are likely to occur4 ,if n1 !n *anges 9 ! con=mation ( ! cell su* z lead imm$iately to its division mu/ be ascrib$ n to local *anges 9 its surface-t5sion1 b r to direct *anges 9 int]nal pressure1 or to me*anical =ces due to an induc$ surface-di/ribution ( electrical pot5tial4 ,x has seem$ o!rwise to _m writ]s1 & we h a numb] ( !ories ( cell division :i* are all bas$ directly on inequalities or asymmetry ( surface-t5sion4 ,= in/ance1 ,bts*li sugge/$1 "s =ty ye>s ago#bdg1 t cell division is br\ght ab\t by an increase ( surface-t5sion 9 ! equatorial region ( ! cell4 ,?is explanation1 h[ev]1 c sc>cely hold2 = x w\ld seem t su* an increase ( surface-t5sion 9 ! equatorial plane w\ld lead to ! cell becom+ flatt5$ out into a disc1 ) a %>ply curv$ equatorial edge1 & to a /ream+ ( mat]ial t[>ds ! equator4 ,9 #ahie1 ,loeb %ew$ t ! /ream+ w5t on f ! equator t[>ds ! divid$ nuclei1 & he suppos$ t ! viol5ce ( ^! /ream+ movem5ts br\ght ab\t actual division ( ! cell3 a hypo!sis :i* 0 adopt$ by _m o!r physiologi/s#bdh4 ,?is /ream+ movem5t w\ld sugge/1 z ,rob]tson has po9t$ out1 a dim9ution ( surface-t5sion 9 ! region ( ! equator4 ,n[ ,qu9cke has %ewn t ! =mation ( soaps at ! surface ( an oil-droplet results 9 a dim9ution ( ! surface-t5sion ( ! latt]2 & t if ! saponification be local1 t "p ( ! surface t5ds to spread4 ,by lay+ a ?read moi/5$ ) a dilute solution ( cau/ic alkali1 or ev5 m]ely sme>$ ) soap1 across a drop ( oil1 ,rob]tson has fur!r %ewn t ! drop at once divides into two3 ! edges ( ! drop1 t is to say ! ends ( ! #aib diamet] across :i* ! ?read lies1 rec$e f ! ?read1 s =m+ a not* at ea* end ( ! diamet]1 :ile viol5t /ream+ motions are set up at ! surface1 away f ! ?read 9 ! direction ( ! two opposite poles4 ,rob]tson#bdi sugge/s1 accord+ly1 t ! division ( ! cell is actually br\ght ab\t by a l[]+ ( ! equatorial surface-t5sion1 & t ?is 9 turn is due to a *emical action1 su* z a lib]ation ( *ol91 or ( soaps ( *ol91 ?r\gh ! splitt+ ( leci?9 9 nucle> syn!sis4 ,b purely *emical *anges are n ( necessity ! fundam5tal cause ( alt]ation 9 ! surface-t5sion ( ! egg1 = ! action ( electrolytes on surface-t5sion is n[ well kn[n & easily demon/rat$4 ,s1 accord+ to o!r views ?an ^? ) :i* we h be5 deal+1 electrical *>ges are suffici5t 9 !mselves to acc\nt = alt]ations ( surface-t5sion2 :ile ^! 9 turn acc\nt = t protoplasmic /ream+ :i*1 z s _m inve/igators agree1 initiates ! segm5tation ( ! egg#bej4 ,a great "p ( our difficulty arises f ! fact t 9 su* a case z ?is ! v>i\s ph5om5a are s entangl$ & app>5tly concurr5t t x is h>d to say :i* initiates ano!r1 & to :i* ?is or t second>y ph5om5on may be consid]$ due4 ,( rec5t ye>s ! ph5om5on ( adsorption has be5 adduc$ 7z we h already briefly said7 9 ord] to acc\nt = _m ( ! ev5ts & appe>ances :i* are associat$ ) ! asymmetry1 & lead t[>ds ! division1 ( ! cell4 ,b our %ort discussion ( ?is ph5om5on may be res]v$ = ano!r *apt]4 ,h[ev]1 we are n directly conc]n$ "h ) ! ph5om5a ( segm5tation or cell division 9 !mselves1 except only 9 s f> z visible *anges ( =m are capable ( easy & obvi\s correlation ) ! play ( =ce4 ,! v fact ( 8developm5t0 indicates t1 :ile x la/s1 ! equilibrium ( ! egg is nev] complete#bea4 ,& we may simply conclude ! #aic matt] by say+ t1 if y h c>yok9etic figures develop+ inside ! cell1 t ( itself indicates t ! dynamic sy/em & ! localis$ =ces aris+ f x are 9 cont9ual alt]ation2 &1 consequ5tly1 *anges 9 ! outw>d configuration ( ! sy/em are b\nd to take place4 ,z reg>ds ! ph5om5a ( f]tilisation1--( ! union ( ! sp]matozoon ) ! 8pronucleus0 ( ! egg1--we might /udy ^! also 9 illu/ration1 up to a c]ta9 po9t1 ( ! pol>is$ =ces :i* are manife/ly at "w4 ,b we %all m]ely take1 z a s+le illu/ration1 ! pa?s ( ! male & female pronuclei1 z !y travel to _! ultimate meet+ place4 ,! sp]matozoon1 :5 )9 a v %ort di/ance ( ! egg-cell1 is attract$ by x4 ,( ! nature ( ?is attractive =ce we h no c]ta9 k1 ?\gh we w\ld seem to h a pregnant h9t 9 ,loeb's discov]y t1 9 ! neighb\rhood ( o!r sub/ances1 su* ev5 z a fragm5t1 or bead1 ( glass1 ! sp]matozoon und]goes a simil> attraction4 ,b1 :atev] ! =ce may be1 x is "o act+ normally to ! surface ( ! ovum1 & accord+ly1 aft] entry1 ! sp]m-nucleus po9ts /raight t[>ds ! c5tre ( ! egg2 f ! fact t o!r sp]matozoa1 subsequ5t to ! fir/1 fail to effect an entry1 we may safely conclude t an imm$iate consequ5ce ( ! entry ( ! sp]matozoon is an increase 9 ! surface-t5sion ( ! egg#beb4 ,some:]e or o!r1 ne> or f> away1 )9 ! egg1 lies its own nucle> body1 ! s-call$ female pronucleus1 & we f9d aft] a :ile t ?is has fus$ ) ! head ( ! sp]matozoon 7or male pronucleus71 & t ! body result+ f _! fusion has come to occupy ! c5tre ( ! egg4 ,?is mu/ be due 7z ,:itman po9t$ out long ago7 to a =ce ( attraction act+ betwe5 ! two bodies1 & ano!r =ce act+ ^u "o or o!r or bo? 9 ! direction ( ! c5tre ( ! cell4 ,did we "k ! magnitude ( ^! sev]al =ces1 x w\ld be a v easy task to calculate ! precise pa? :i* ! two pronuclei w\ld foll[1 lead+ to conjugation & ! c5tral #aid position4 ,z we d n "k ! magnitude1 b only ! direction1 ( ^! =ces we c only make a g5]al /atem5t3 7#a7 ! pa?s ( bo? mov+ bodies w lie :olly )9 a plane triangle drawn betwe5 ! two bodies & ! c5tre ( ! cell2 7#b7 unless ! two bodies happ5 to lie1 to beg9 )1 precisely on a diamet] ( ! cell1 _! pa?s until !y meet "o ano!r w be curv$ pa?s1 ! convexity ( ! curve be+ t[>ds ! /raight l9e jo9+ ! two bodies2 7#c7 ! two bodies w meet a little be=e !y rea* ! c5tre2 &1 hav+ met & fus$1 w travel on to rea* ! c5tre 9 a /raight l9e4 ,! actual /udy & obs]vation ( ! pa? foll[$ is n v easy1 ow+ to ! fact t :at we usually see is n ! pa? itself1 b only a projection ( ! pa? ^u ! plane ( ! microscope2 b ! curv$ pa? is p>ticul>ly well se5 9 ! frog's egg1 :]e ! pa? ( ! sp]matozoon is m>k$ by a little /reak ( br[n pigm5t1 & ! fact ( ! meet+ ( ! pronuclei be=e rea*+ ! c5tre has be5 repeat$ly se5 by _m obs]v]s4 ,! problem is no?+ else ?an a p>ticul> case ( ! fam\s problem ( ?ree bodies1 :i* has s occupi$ ! a/ronom]s2 & x is obvi\s t ! =ego+ brief description is v f> f includ+ all possible cases4 ,_m ( ^! are p>ticul>ly describ$ 9 ! works ( ,fol1 ,r\x1 ,:itman & o!rs#bec4 ,! intracellul> ph5om5a ( :i* we h n[ spok5 h assum$ imm5se importance 9 biological lit]ature & discussion dur+ ! la/ =ty ye>s2 b x is op5 to u to d\bt :e!r !y w be f\nd 9 ! end to possess m ?an a remote & second>y biological significance4 ,mo/1 if n all ( !m1 w\ld seem to foll[ imm$iately & inevitably f v simple assumptions z to ! physical con/itution ( ! cell1 & f an extremely simple di/ribution ( pol>is$ =ces )9 x4 ,we h already se5 t h[ a ?+ gr[s1 & :at x gr[s into1 is a dynamic & n a m]ely mat]ial problem2 s f> z ! mat]ial sub/ance is conc]n$1 x is s only by reason #aie ( ! *emical1 electrical or o!r =ces :i* are associat$ ) x4 ,b !re is ano!r consid]ation :i* w\ld lead u to suspect t _m features 9 ! /ructure & configuration ( ! cell are ( v second>y biological importance2 & t is1 ! great v>iation to :i* ^! ph5om5a are subject 9 simil> or closely relat$ organisms1 & ! app>5t impossibility ( correlat+ !m ) ! peculi>ities ( ! organism z a :ole4 8,comp>ative /udy has %ewn t almo/ e detail ( ! processes 7( mitosis7 describ$ above is subject to v>iation 9 diff]5t =ms ( cells#bed40 ,a multitude ( cells divide to ! accompanim5t ( c>yok9etic ph5om5a2 b o!rs d s )\t any visible c>yok9esis at all4 ,sometimes ! pol>is$ field ( =ce is )91 sometimes x is adjac5t to1 & at o!r times x lies remote f ! nucleus4 ,! di/ribution ( pot5tial is v (t5 symmetrical & bipol>1 z 9 ! case describ$2 b a less symmetrical di/ribution (t5 occurs1 ) ! result t we h1 = a "t at lea/1 num]\s c5tres ( =ce1 in/ead ( ! two ma9 correlat$ poles3 ?is is ! simple explanation ( ! num]\s /ellate figures1 or 8,/rahlung510 :i* h be5 describ$ 9 c]ta9 eggs1 su* z ^? ( ,*aetopt]us4 ,9 "o & ! same species ( worm 7,asc>is megalocephala71 "o gr\p or two gr\ps ( *romosomes may be pres5t4 ,& rem>kably con/ant1 9 g5]al1 z ! numb] ( *romosomes 9 any "o species und\bt$ly is1 yet we mu/ n =get t1 9 plants & animals alike1 ! :ole range ( obs]v$ numb]s is b a small "o2 = 7z reg>ds ! g]m-nuclei7 few organisms h less ?an six *romosomes1 & few] /ill h m ?an sixte5#bee4 ,9 closely relat$ animals1 su* z v>i\s species ( ,copepods1 & ev5 9 ! same species ( worm or insect1 ! =m ( ! *romosomes1 & _! arrangem5t 9 relation to ! nucle> sp9dle1 h be5 f\nd to diff] 9 ! v>i\s ways allud$ to above4 ,9 %ort1 !re seem to be /rong gr\nds = believ+ t ^! & _m simil> ph5om5a are 9 no way specifically relat$ to ! p>ticul> organism 9 :i* !y h #aif be5 obs]v$1 & are n ev5 specially & indisputably connect$ ) ! organism z su*4 ,!y include su* manife/ations ( ! physical =ces1 9 _! v>i\s p]mutations & comb9ations1 z may also be witness$1 "u appropriate conditions1 9 non-liv+ ?+s4 ,:5 we attempt to sep>ate our purely morphological or 8purely embryological0 /udies f physiological & physical inve/igations1 we t5d ipso facto to reg>d ea* p>ticul> /ructure & configuration z an attribute1 or a p>ticul> 8"*10 ( ?is or t p>ticul> organism4 ,f ?is assumption we are apt to g on to ! draw+ ( new conclusions or ! fram+ ( new !ories z to ! ance/ral hi/ory1 ! classificatory position1 ! natural aff9ities ( ! sev]al organisms3 9 fact1 to apply our embryological k ma9ly1 & at times exclusively1 to ! /udy ( phylog5y4 ,:5 we f9d1 z we are n long ( f9d+1 t our phylog5etic hypo!ses1 z drawn f embryology1 become complex & unwieldy1 we are nev]!less reluctant to admit t ! :ole me?od1 ) its fundam5tal po/ulates1 is at fault4 ,& yet no?+ %ort ( ?is w\ld seem to be ! case1 9 reg>d to ! e>li] phases at lea/ ( embryonic developm5t4 ,all ! evid5ce at h& goes1 z x seems to me1 to %ew t embryological data1 prior to & ev5 long aft] ! epo* ( segm5tation1 are ess5tially a subject = physiological & physical inve/igation & h b ! v slighte/ l9k ) ! problems ( sy/ematic or zoological classification4 ,comp>ative embryology has its own facts to classify1 & its own me?ods & pr9ciples ( classification4 ,?us we may classify eggs accord+ to ! pres5ce or abs5ce1 ! paucity or abundance1 ( _! associat$ food-yolk1 ! *romosomes accord+ to _! =m & _! numb]1 ! segm5tation accord+ to its v>i\s 8types10 radial1 bilat]al1 spiral1 & s =?4 ,b we h little "r to expect1 & 9 po9t ( fact we %all v seldom & 7z x 77 only accid5tally f9d1 t ^! embryological categories co9cide ) ! l9es ( 8natural0 or 8phylog5etic0 classification :i* h be5 arriv$ at by ! sy/ematic zoologi/4 ,! cell1 :i* ,goodsir spoke ( z a 8c5tre ( =ce10 is 9 #aig reality a 8sph]e ( action0 ( c]ta9 m or less localis$ =ces2 & ( ^!1 surface-t5sion is ! p>ticul> =ce :i* is especially responsible = giv+ to ! cell its outl9e & its morphological individuality4 ,! p>tially segm5t$ diff]s f ! totally segm5t$ egg1 ! unicellul> ,infusorian f ! m9ute multicellul> ,turbell>ian1 9 ! int5sity & ! range ( ^? surface-t5sions :i* 9 ! "o case succe$ & 9 ! o!r fail to =m a visible sep>ation betwe5 ! 8cells40 ,adam ,s$gwick us$ to call att5tion to ! fact t v (t51 ev5 9 eggs t appe> to be totally segm5t$1 x is yet impossible to discov] an actual sep>ation or cleavage1 ?r\gh & ?r\gh betwe5 ! cells :i* on ! surface ( ! egg are s cle>ly delimit$2 s f> & no f>!r h ! physical =ces effectuat$ a visible 8cleavage40 ,! vacuolation ( ! protoplasm 9 ,act9ophrys or ,act9ospha]ium is due to localis$ surface-t5sions1 q irrespective ( ! mult9ucle> nature ( ! latt] organism4 ,9 %ort1 ! b\nd>y walls due to surface-t5sion may be pres5t or may be abs5t ) or )\t ! delim9ation ( ! o!r specific fields ( =ce :i* are usually correlat$ ) ^! b\nd>ies & ) ! indep5d5t individuality ( ! cells4 ,:at we may safely admit1 h[ev]1 is t "o effect ( ^! circumscrib$ fields ( =ce is usually su* a sep>ation or segregation ( ! protoplasmic con/itu5ts1 ! m fluid f ! less fluid & s =?1 z to give a field :]e surface-t5sion may d its "w & br+ a visible b\nd>y into be+4 ,:5 ! =mation ( a 8surface0 is once effect$1 its physical condition1 or phase1 w be b\nd to diff] notably f t ( ! int]ior ( ! cell1 & "u appropriate *emical conditions ! =mation ( an actual cell-wall1 cellulose or o!r1 is easily intelligible4 ,to ?is subject we %all return aga91 9 ano!r *apt]4 ,f ! mom5t t we ent] on a dynamical conception ( ! cell1 we p]ceive t ! old debates 7 9 va9 z to :at visible portions ( ! cell 7 active or passive1 liv+ or non-liv+4 ,= ! manife/ations ( =ce c only be due to ! int]action ( ! v>i\s p>ts1 to ! transf]5ce ( en]gy f "o to ano!r4 ,c]ta9 prop]ties may be manife/$1 c]ta9 functions may be c>ri$ on1 by ! protoplasm ap>t #aih f ! nucleus2 b ! int]action ( ! two is necess>y1 t o!r & m important prop]ties or functions may be manife/$4 ,we "k1 = in/ance1 t portions ( an ,infusorian are incapable ( reg5]at+ lo/ p>ts 9 ! abs5ce ( a nucleus1 :ile nucleat$ pieces soon rega9 ! specific =m ( ! organism3 & we are told t reproduction by fission _c be initiat$1 ?\gh app>5tly all its lat] /eps c be c>ri$ on1 indep5d5tly ( nucle> action4 ,nor1 z ,v]worn po9t$ out1 c ! nucleus possibly be reg>d$ z ! 8sole vehicle ( inh]itance10 s9ce only 9 ! conjunction ( cell & nucleus d we f9d ! ess5tials ( cell-life4 8,k]n und ,protoplasma s9d nur v]e9t leb5sfhig10 z ,nussbaum said4 ,inde$ we may1 ) ,e4 ,b4 ,wilson1 g fur!r1 & say t 8! t]ms #8nucleus' & #8cell-body' %\ld probably be reg>d$ z only topographical expressions d5ot+ two diff]5tiat$ areas 9 a common /ructural basis40 ,endless discussion has tak5 place reg>d+ ! c5trosome1 "s hold+ t x is a specific & ess5tial /ructure1 a p]man5t corpuscle d]iv$ f a simil> pre-exi/+ corpuscle1 a 8f]tilis+ elem5t0 9 ! sp]matozoon1 a special 8organ ( cell-division10 a mat]ial 8dynamic c5tre0 ( ! cell 7z ,van ,b5$5 & ,bov]i call x72 :ile on ! o!r h&1 x is po9t$ out t _m cells live & multiply )\t any visible c5trosomes1 t a c5trosome may disappe> & be creat$ anew1 & ev5 t "u artificial conditions abnormal *emical /imuli may lead to ! =mation ( new c5trosomes4 ,we may safely take x t ! c5trosome1 or ! 8attraction sph]e10 is ess5tially a 8c5tre ( =ce10 & t ?is dynamic c5tre may or may n be con/itut$ by 7b w be v apt to produce7 a concrete & visible conc5tration ( matt]4 ,x is f> f correct to say1 z is (t5 done1 t ! cell-wall1 or cell-membrane1 belongs 8to ! passive products ( protoplasm r ?an to ! liv+ cell itself02 or to say t 9 ! animal cell1 ! cell-wall1 because x is 8slightly develop$10 is relatively unimportant comp>$ ) ! important role :i* x assumes 9 plants4 ,on ! contr>y1 x is q c]ta9 t1 :e!r visibly diff]5tiat$ into a semi-p]meable membrane1 or m]ely con/itut$ by a liquid film1 ! surface ( ! cell is ! seat ( #aii important =ces1 capill>y & electrical1 :i* play an ess5tial "p 9 ! dynamics ( ! cell4 ,ev5 9 ! ?ick5$1 l>gely solidifi$ cellulose wall ( ! plant-cell1 ap>t f ! me*anical resi/ances :i* x af=ds1 ! osmotic =ces develop$ 9 connection ) x are ( ess5tial importance4 ,b if ! cell acts1 aft] ?is fa%ion1 z a :ole1 ea* "p int]act+ ( necessity ) ! re/1 ! same is c]ta9ly true ( ! entire multicellul> organism3 z ,s*wann said ( old1 9 v precise & adequate words1 8! :ole organism subsi/s only by means ( ! reciprocal action ( ! s+le elem5t>y p>ts#bef40 ,z ,wilson says aga91 8! physiological autonomy ( ! individual cell falls into ! backgr\nd 444 & ! app>5tly composite "* :i* ! multicellul> organism may exhibit is ow+ to a second>y di/ribution ( its en]gies among local c5tres ( action#beg40 ,x is "h t ! homology breaks d[n :i* is s (t5 drawn1 & ov]drawn1 betwe5 ! unicellul> organism & ! individual cell ( ! metazoon#beh4 ,:itman1 ,adam ,s$gwick#bei1 & o!rs h lo/ no opportunity ( w>n+ u aga9/ a too lit]al acceptation ( ! cell-!ory1 aga9/ ! view t ! multicellul> organism is a colony 7or1 z ,haeckel call$ x 79 ! case ( ! plant71 a 8republic07 ( indep5d5t units ( life#bfj4 ,z ,goe! said long ago1 8,das leb5dige i/ zw> 9 ,elem5te #bjj z]legt1 ab] man kann es aus dies5 ni*t wi$] zusamm5/ell5 und beleb520 ! dictum ( ! ,cellul>pa?ologie be+ j ! opposite1 8,j$es ,?i] ers*e9t als e9e ,summe vital] ,e9heit51 von d55 j$e d5 voll5 ,*>akt] des ,leb5s an si* trgt40 ,h(mei/] & ,sa*s h taught u t 9 ! plant ! gr[? ( ! mass1 ! gr[? ( ! organ1 is ! prim>y fact1 t 8cell =mation is a ph5om5on v g5]al 9 organic life1 b /ill only ( second>y significance40 8,comp>ative embryology0 says ,:itman1 8rem9ds u at e turn t ! organism dom9ates cell-=mation1 us+ = ! same purpose "o1 sev]al1 or _m cells1 mass+ its mat]ial & direct+ its movem5ts & %ap+ its organs1 z if cells did n exi/#bfa40 ,s ,raub] decl>$ t1 9 ! :ole _w ( organisms1 8das ,ganze lief]t die ,!ile1 ni*t die ,!ile das ,ganze3 letzt]es setzt die ,!ile zusamm51 ni*t diese j5es#bfb40 ,& on ! botanical side ,de ,b>y has summ$ up ! matt] 9 an aphorism1 8,die ,pflanze bildet ,zell51 ni*t die ,zelle bildet ,pflanz540 ,discuss$ almo/ :olly f ! concrete1 or morphological po9t ( view1 ! "q has = ! mo/ "p be5 made to turn on :e!r actual protoplasmic cont9uity c be demon/rat$ betwe5 "o cell & ano!r1 :e!r ! organism be an actual reticulum1 or syncytium4 ,b f ! dynamical po9t ( view ! "q is mu* simpl]4 ,we !n deal n ) mat]ial cont9uity1 n ) little bridges ( connect+ protoplasm1 b ) a cont9uity ( =ces1 a compreh5sive field ( =ce1 :i* runs ?r\gh & ?r\gh ! entire organism & is by no means re/rict$ 9 its passage to a protoplasmic cont9uum4 ,& su* a cont9u\s field ( =ce1 someh[ %ap+ ! :ole organism1 indep5d5tly ( ! numb]1 magnitude & =m ( ! individual cells1 :i* ent]1 l a fro?1 into its fabric1 seems to me c]ta9ly & obvi\sly to exi/4 ,z ,:itman says1 8! fact t physiological unity is n brok5 by cell-b\nd>ies is confirm$ 9 s _m ways t x mu/ be accept$ z "o ( ! fundam5tal tru?s ( biology#bfc40 #bja ,,*apt] ,v ,,! ,,=ms ,,( ,,cells ,protoplasm1 z we h already said1 is a fluid or r a semifluid sub/ance1 & we ne$ n pause "h to attempt to describe ! p>ticul> prop]ties ( ! semifluid1 colloid1 or jelly-l sub/ances to :i* x is alli$2 we %\ld f9d x no easy matt]4 ,nor ne$ we appeal to precise !oretical def9itions ( fluidity1 le/ we come into a debateable l&4 ,x is 9 ! mo/ g5]al s5se t protoplasm is 8fluid40 ,z ,graham said 7( colloid matt] 9 g5]al71 8its s(tness p>takes ( fluidity1 & enables ! colloid to become a vehicle = liquid diffusion1 l wat] itself#bfd40 ,:5 we c deal ) protoplasm 9 suffici5t quantity we see x fl[2 p>ticles move freely ?r\gh x1 air-bubbles & liquid droplets %ew r\nd or sph]ical )9 x2 & we %all h mu* to say ab\t o!r ph5om5a manife/$ by its own surface1 :i* are ^? especially *>act]i/ic ( liquids4 ,x may encompass & conta9 solid bodies1 & x may 8secrete0 )9 or ar\nd itself solid sub/ances2 & v (t5 9 ! complex liv+ organism ^! solid sub/ances =m$ by ! liv+ protoplasm1 l %ell or nail or horn or fea!r1 may rema9 :5 ! protoplasm :i* =m$ !m is dead & gone2 b ! protoplasm itself is fluid or semifluid1 & accord+ly p]mits ( free 7?\gh n necess>ily rapid7 diffusion & easy convection ( p>ticles )9 itself4 ,?is simple fact is ( elem5t>y importance 9 connection ) =m1 & ) :at appe> at fir/ sight to be common *>act]i/ics or peculi>ities ( ! =ms ( liv+ ?+s4 ,! old] naturali/s1 9 discuss+ ! diff]5ces betwe5 inorganic & organic bodies1 laid /ress ^u ! fact or /atem5t t ! =m] gr[ by 8agglut9ation10 & ! latt] by #bjb :at !y t]m$ 8intussusception40 ,! contra/ is true1 r1 ( solid z comp>$ ) jelly-l bodies ( all k9ds1 liv+ or dead1 ! great majority ( :i* z x s happ5s1 b by no means all1 are ( organic orig94 ,a cry/al 8gr[s0 by deposition ( new molecules1 "o by "o & lay] by lay]1 sup]impos$ or aggregat$ ^u ! solid sub/ratum already =m$4 ,ea* p>ticle w\ld seem to be influ5c$1 practically speak+1 only by ! p>ticles 9 its imm$iate neighb\rhood1 & to be 9 a /ate ( fre$om & indep5d5ce f ! influ5ce1 ei!r direct or indirect1 ( its remot] neighb\rs4 ,z ,"l ,kelv9 & o!rs h expla9$ ! =mation & ! result+ =ms ( cry/als1 s we believe t ea* add$ p>ticle takes up its position 9 relation to its imm$iate neighb\rs already arrang$1 g5]ally 9 ! holes & corn]s t _! arrangem5t leaves1 & 9 close/ contact ) ! greate/ numb]#bfe4 ,& h5ce we may repeat or imitate ?is process ( arrangem5t1 ) great or app>5tly ev5 ) precise accuracy 79 ! case ( ! simpl] cry/all9e sy/ems71 by pil+ up sph]ical pills or gra9s ( %ot4 ,9 s do+1 we mu/ h reg>d to ! fact t ea* p>ticle mu/ drop into ! place :]e x c g mo/ easily1 or :]e no easi] place (f]s4 ,9 m te*nical language1 ea* p>ticle is free to take up1 & does take up1 its position ( lea/ pot5tial en]gy relative to ^? already deposit$2 9 o!r words1 = ea* p>ticle motion is induc$ until ! en]gy ( ! sy/em is s di/ribut$ t no t5d5cy or resultant =ce rema9s to move x m4 ,! application ( ?is pr9ciple has be5 %ewn to lead to ! production ( planes#bff 79 all cases :]e by ! limitation ( mat]ial1 surfaces mu/ occur72 & :]e we h planes1 /raight edges & solid angles mu/ obvi\sly also occur2 &1 if equilibrium is #bjc to foll[1 mu/ occur symmetrically4 ,our pil+ up ( %ot1 or manufacture ( mimic cry/als1 gives u visible demon/ration t ! result is actually to obta91 z 9 ! natural cry/al1 plane surfaces & %>p angles1 symmetrically dispos$4 ,b ! liv+ cell gr[s 9 a totally diff]5t way1 v mu* z a piece ( glue swells up 9 wat]1 by 8imbibition10 or by int]p5etration into & ?r\gh\t its entire sub/ance4 ,! semifluid colloid mass takes up wat]1 p>tly to comb9e *emically ) its individual molecules#bfg1 p>tly by physical diffusion into ! int]/ices betwe5 ^! molecules1 & p>tly1 z x w\ld seem1 9 o!r ways2 s t ! entire ph5om5on is a v complex & ev5 an obscure "o4 ,b1 s f> z we are conc]n$1 ! net result is a v simple "o4 ,= ! equilibrium or t5d5cy to equilibrium ( fluid pressure 9 all p>ts ( its int]ior :ile ! process ( imbibition is go+ on1 ! con/ant re>rangem5t ( its fluid mass1 ! contra/ 9 %ort ) ! cry/all9e me?od ( gr[? :]e ea* p>ticle comes to re/ to move 7relatively to ! :ole7 no m1 lead ! mass ( jelly to swell up1 v mu* z a bladd] into :i* we bl[ air1 & s1 by a grad$ & h>moni\s di/ribution ( =ces1 to assume ev]y:]e a r\nd$ & m or less bubble-l ext]nal =m#bfh4 ,s1 :5 ! same s*ool ( old] naturali/s call$ att5tion to a new di/9ction or contra/ ( =m betwe5 ! organic & inorganic objects1 9 t ! cont\rs ( ! =m] t5d$ to r\ndness & curvature1 & ^? ( ! latt] to be b\nd$ by /raight l9es1 planes & %>p angles1 we see t ?is contra/ 0 n a new & diff]5t "o1 b only ano!r aspect ( _! =m] /atem5t1 & an imm$iate consequ5ce ( ! diff]5ce betwe5 ! processes ( agglut9ation & intussusception4 ,?is common & g5]al contra/ betwe5 ! =m ( ! cry/al on ! "o h&1 & ( ! colloid or ( ! organism on ! o!r1 mu/ by no means be press$ too f>4 ,= ,lehmann1 #bjd 9 8 great "w on s-call$ ,fluid ,cry/als#bfi1 to :i* we %all aft]w>ds return1 has %ewn h[1 "u c]ta9 circum/ances1 surface-t5sion ph5om5a may coexi/ ) cry/allisation1 & produce a =m ( m9imal pot5tial :i* is a resultant ( bo?3 ! fact be+ t ! bonds ma9ta9+ ! cry/all9e arrangem5t are n[ s mu* loos] ?an 9 ! solid condition t ! t5d5cy to lea/ total surface-area is capable ( be+ satisfi$4 ,?us ! ph5om5on ( 8liquid cry/allisation0 does n de/roy ! di/9ction betwe5 cry/all9e & colloidal =ms1 b gives add$ unity & cont9uity to ! :ole s]ies ( ph5om5a#bgj4 ,lehmann has also demon/rat$ ph5om5a )9 ! cry/al1 kn[n = in/ance z transcry/allisation1 :i* %ew u t we mu/ n speak ungu>d$ly ( ! gr[? ( cry/als z limit$ to deposition ^u a surface1 & ,bts*li has already po9t$ out ! possible great importance to ! biologi/ ( ! v>i\s ph5om5a :i* ,lehmann has describ$#bga4 ,s f> !n1 z gr[? goes on1 unaffect$ by pressure or o!r ext]nal =ce1 ! fluidity ( protoplasm1 its mobility int]nal & ext]nal1 & ! mann] 9 :i* p>ticles move ) comp>ative fre$om f place to place )91 all manife/ly t5d to ! production ( swell+1 r\nd$ surfaces1 & to _! great pr$om9ance ov] plane surfaces 9 ! cont\r ( ! organism4 ,^! r\nd$ cont\rs w t5d to be pres]v$1 = a :ile1 9 ! case ( nak$ protoplasm by its viscosity1 & 9 ! pres5ce ( a cell-wall by its v lack ( fluidity4 ,9 a g5]al way1 ! pres5ce ( curv$ b\nd>y surfaces w be especially obvi\s 9 ! unicellul> organisms1 & /ill m g5]ally 9 ! ext]nal =ms ( all organisms2 & :]ev] mutual pressure betwe5 adjac5t cells1 or o!r adjac5t p>ts1 has n come into play to flatt5 ! r\nd$ surfaces into planes4 ,b ! r\nd$ cont\rs t are assum$ & exhibit$ by #bje a piece ( h>d glue1 :5 we ?r[ x into wat] & see x exp& z x sucks ! wat] up1 are n ne>ly s regul> or s beautiful z are ^? :i* appe> :5 we bl[ a bubble1 or =m a drop1 or p\r wat] into a m or less ela/ic bag4 ,= ^! curv+ cont\rs dep5d ^u ! prop]ties ( ! bag itself1 ( ! film or membrane t conta9s ! mobile gas1 or t conta9s or b\nds ! mobile liquid mass4 ,& h]eby1 9 ! case ( ! fluid or semifluid mass1 we are introduc$ to ! subject ( surface t5sion3 ( :i* inde$ we h spok5 9 ! prec$+ *apt]1 b :i* we mu/ n[ exam9e ) great] c>e4 ,among ! =ces :i* det]m9e ! =ms ( cells1 :e!r !y be solit>y or arrang$ 9 contact ) "o ano!r1 ?is =ce ( surface-t5sion is c]ta9ly ( great1 & is probably ( p>am\nt importance4 ,b :ile we %all try to sep>ate out ! ph5om5a :i* are directly due to x1 we mu/ n =get t1 9 ea* p>ticul> case1 ! actual con=mation :i* we /udy may be1 & usually is1 ! m or less complex resultant ( surface t5sion act+ toge!r ) gravity1 me*anical pressure1 osmosis1 or o!r physical =ces4 ,surface t5sion is t =ce by :i* we expla9 ! =m ( a drop or ( a bubble1 ( ! surfaces ext]nal & int]nal ( a 8fro?0 or collocation ( bubbles1 & ( _m o!r ?+s ( l nature & 9 l circum/ances#bgb4 ,x is a prop]ty ( liquids 79 ! s5se at lea/ ) :i* our subject is conc]n$71 & x is manife/$ at or v ne> ! surface1 :]e ! liquid comes into contact ) ano!r liquid1 a solid or a gas4 ,we note "h t ! t]m surface is to be int]pret$ 9 a wide s5se2 = :]ev] we h solid p>ticles imb$d$ 9 a fluid1 :]ev] we h a non-homog5e\s fluid or semi-fluid su* z a p>ticle #bjf ( protoplasm1 :]ev] we h ! pres5ce ( 8impurities10 z 9 a mass ( molt5 metal1 !re we h always to be> 9 m9d ! exi/5ce ( 8surfaces0 & ( surface t5sions1 n only on ! ext]ior ( ! mass b also ?r\gh\t its int]/ices1 :]ev] l meets unlike4 ,surface t5sion is due to molecul> =ce1 to =ce t is to say aris+ f ! action ( "o molecule ^u ano!r1 & x is accord+ly ex]t$ ?r\gh\t a small ?ickness ( mat]ial1 comp>able to ! range ( ! molecul> =ces4 ,we imag9e t )9 ! int]ior ( ! liquid mass su* molecul> int]actions negative "o ano!r3 b t at & ne> ! free surface1 )9 a lay] or film approximately equal to ! range ( ! molecul> =ce1 !re mu/ be a lack ( su* equilibrium & consequ5tly a manife/ation ( =ce4 ,! action ( ! molecul> =ces has be5 v>i\sly expla9$4 ,b "o simple explanation 7or mode ( /atem5t7 is t ! molecules ( ! surface lay] 7^: ?ickness is def9ite & con/ant7 are be+ con/antly attract$ into ! int]ior by ^? :i* are m deeply situat$1 & t consequ5tly1 z molecules keep quitt+ ! surface = ! int]ior1 ! bulk ( ! latt] increases :ile ! surface dim9i%es2 & ! process cont9ues till ! surface itself has become a m9imum1 ! surface-%r9kage exhibit+ itself z a surface-t5sion4 ,?is is a suffici5t description ( ! ph5om5on 9 cases :]e a portion ( liquid is subject to no o!r ?an its own molecul> =ces1 & 7s9ce ! sph]e has1 ( all solids1 ! smalle/ surface = a giv5 volume7 x acc\nts = ! sph]ical =m ( ! ra9drop1 ( ! gra9 ( %ot1 or ( ! liv+ cell 9 _m simple organisms4 ,x acc\nts also1 z we %all pres5tly see1 = a great numb] ( mu* m complicat$ =ms1 manife/$ "u less simple conditions4 ,let u "h briefly note t surface t5sion is1 9 itself1 a comp>atively small =ce1 & easily measurable3 = in/ance t ( wat] is equival5t to b a few gra9s p] l9e> in*1 or a few grammes p] metre4 ,b ?is small t5sion1 :5 x exi/s 9 a curv$ surface ( v great curvature1 gives rise to a v great pressure direct$ t[>ds ! c5tre ( curvature4 ,we c easily calculate ?is pressure1 & s satisfy ourselves t1 :5 ! radius ( curvature is ( molecul> dim5sions1 ! #bjg pressure is ( ! magnitude ( ?\s&s ( atmosph]es1--a conclusion :i* is support$ by o!r physical consid]ations4 ,! contraction ( a liquid surface & o!r ph5om5a ( surface t5sion involve ! do+ ( "w1 & ! p[] to d "w is :at we call en]gy4 ,x is obvi\s1 9 su* a simple case z we h j consid]$1 t ! :ole en]gy ( ! sy/em is diffus$ ?r\gh\t its molecules2 b ( ?is :ole /ock ( en]gy x is only t "p :i* comes into play at or v ne> to ! surface :i* normally manife/s itself 9 "w1 & h5ce we may speak 7?\gh ! t]m is op5 to "s objections7 ( a specific surface en]gy4 ,! consid]ation ( surface en]gy1 & ( ! mann] 9 :i* its am\nt is increas$ & multipli$ by ! multiplication ( surfaces due to ! subdivision ( ! organism into cells1 is ( ! highe/ importance to ! physiologi/2 & ev5 ! morphologi/ _c :olly pass x by1 if he desires to /udy ! =m ( ! cell 9 its relation to ! ph5om5a ( surface t5sion or 8capill>ity40 ,! case has be5 set =? ) ! utmo/ possible lucidity by ,tait & by ,cl]k ,maxwell1 on ^: tea*+ ! foll[+ p>agraphs are bas$3 !y hav+ bas$ _! tea*+ ^u t ( ,gauss1--:o re/$ on ,laplace4 ,let ,e be ! :ole pot5tial en]gy ( a mass ,m ( liquid2 let e#j be ! en]gy p] unit mass ( ! int]ior liquid 7we may call x ! int]nal en]gy72 & let e be ! en]gy p] unit mass = a lay] ( ! sk91 ( surface ,s1 ( ?ickness t1 & d5sity 7e be+ :at we call ! surface en]gy74 ,x is obvi\s t ! total en]gy consi/s ( ! int]nal plus ! surface en]gy1 & t ! =m] is di/ribut$ ?r\gh ! :ole mass1 m9us its surface lay]s4 ,t is to say1 9 ma!matical language1 ,e 7,m ,s t 7 e#j ,s t e4 ,b ?is is equival5t to writ+3 ,m e#j ,s t 7e e#j72 & ?is is z mu* z to say t ! total en]gy ( ! sy/em may be tak5 to consi/ ( two portions1 "o uni=m ?r\gh\t ! :ole mass1 & ano!r1 :i* is proportional on ! "o h& to ! am\nt ( surface1 & on ! o!r h& is proportional to ! diff]5ce betwe5 e & e#j1 t is to say to ! diff]5ce betwe5 ! unit values ( ! int]nal & ! surface en]gy4 #bjh ,x 0 ,gauss :o fir/ %ew$ aft] ?is fa%ion h[1 f ! mutual attractions betwe5 all ! p>ticles1 we are l$ to an expression :i* is :at we n[ call ! pot5tial en]gy ( ! sy/em2 & we "k1 z a fundam5tal !orem ( dynamics1 t ! pot5tial en]gy ( ! sy/em t5ds to a m9imum1 & 9 t m9imum f9ds1 z a matt] ( c\rse1 its /able equilibrium4 ,we see 9 our la/ equation t ! t]m ,m e#j is irr$ucible1 save by a r$uction ( ! mass itself4 ,b ! o!r t]m may be dim9i%$ 7#a7 by a r$uction 9 ! area ( surface1 ,s1 or 7#b7 by a t5d5cy t[>ds equality ( e & e#j1 t is to say by a dim9ution ( ! specific surface en]gy1 e4 ,^! !n are ! two me?ods by :i* ! en]gy ( ! sy/em w manife/ itself 9 "w4 ,! "o1 :i* is mu* ! m important = our purposes1 leads always to a dim9ution ( surface1 to ! s-call$ 8pr9ciple ( m9imal areas02 ! o!r1 :i* leads to ! l[]+ 7"u c]ta9 circum/ances7 ( surface t5sion1 is ! basis ( ! !ory ( ,adsorption1 to :i* we %all h "s occasion to ref] z ! modus op]&i 9 ! developm5t ( a cell-wall1 & 9 a v>iety ( o!r hi/ological ph5om5a4 ,9 ! te*nical phraseology ( ! day1 ! 8capacity factor0 is involv$ 9 ! "o case1 & ! 8int5sity factor0 9 ! o!r4 ,inasmu* z we are conc]n$ ) ! =m ( ! cell x is ! =m] :i* becomes our ma9 po/ulate3 tell+ u t ! en]gy equations ( ! surface ( a cell1 or ( ! free surfaces ( cells p>tly 9 contact1 or ( ! p>tition-surfaces ( cells 9 contact ) "o ano!r or ) an adjac5t solid1 all indicate a m9imum ( pot5tial en]gy 9 ! sy/em1 by :i* ! sy/em is br\ght1 ipso facto1 into equilibrium4 ,& we %all n fail to obs]ve1 ) some?+ m ?an m]e hi/orical int]e/ & curiosity1 h[ deeply & intr9sically !re ent] into ?is :ole class ( problems ! 8pr9ciple ( lea/ action0 ( ,maup]tuis1 ! 8l9eae curvae maximi m9imive proprietate gaud5tes0 ( ,eul]1 by :i* pr9ciples ^! old natural philosoph]s expla9$ correctly a multitude ( ph5om5a1 & drew ! l9es :]eon ! f\ndations ( great "p ( mod]n physics are well & truly laid4 #bji ,9 all cases :]e ! pr9ciple ( maxima & m9ima comes into play1 z x conspicu\sly does 9 ! sy/ems ( liquid films :i* are gov]n$ by ! laws ( surface-t5sion1 ! figures & con=mations produc$ are *>act]is$ by obvi\s & rem>kable symmetry4 ,su* symmetry is 9 a high degree *>act]i/ic ( organic =ms1 & is r>ely abs5t 9 liv+ ?+s1--save 9 su* cases z amoeba1 :]e ! equilibrium on :i* symmetry dep5ds is likewise lack+4 ,& if we ask :at physical equilibrium has to d ) =mal symmetry & regul>ity1 ! reason is n f> to seek2 nor c x be put bett] ?an 9 ! foll[+ words ( ,ma*'s#bgc4 8,9 e symmetrical sy/em e de=mation t t5ds to de/roy ! symmetry is complem5t$ by an equal & opposite de=mation t t5ds to re/ore x4 ,9 ea* de=mation positive & negative "w is done4 ,"o condition1 !re=e1 ?\gh n an absolutely suffici5t "o1 t a maximum or m9imum ( "w corresponds to ! =m ( equilibrium1 is ?us suppli$ by symmetry4 ,regul>ity is successive symmetry4 ,!re is no reason1 !re=e1 to be a/oni%$ t ! =ms ( equilibrium are (t5 symmetrical & regul>40 ,z we proce$ 9 our enquiry1 & especially :5 we approa* ! subject ( tissues1 or agglom]ations ( cells1 we %all h f "t to "t to call 9 ! help ( elem5t>y ma!matics4 ,b already1 ) v little ma!matical help1 we f9d ourselves 9 a position to deal ) "s simple examples ( organic =ms4 ,:5 we melt a /ick ( seal+-wax 9 ! flame1 surface t5sion 7:i* 0 ineffectively pres5t 9 ! solid b f9ds play 9 ! n[ fluid mass71 r\nds (f its %>p edges into curves1 s /riv+ t[>ds a surface ( m9imal area2 & 9 l mann]1 by melt+ ! tip ( a ?9 rod ( glass1 ,leeuw5hoek made ! little sph]ical beads :i* s]v$ him = a microscope#bgd4 ,:5 any drop ( protoplasm1 ei!r ov] all its surface or at "s free end1 z at ! extremity ( ! pseudopodium ( an amoeba1 is #baj se5 likewise to 8r\nd itself (f10 t is n an effect ( 8vital contractility10 b 7z ,h(mei/] %ew$ s long ago z #ahfg7 a simple consequ5ce ( surface t5sion2 & almo/ imm$iately aft]w>ds ,engelmann#bge argu$ on ! same l9es1 t ! =ces :i* cause ! contraction ( protoplasm 9 g5]al may 8be j ! same z ^? :i* t5d to make e non-sph]ical drop ( fluid become sph]ical60 ,we are n conc]n$ "h ) ! _m !ories & speculations :i* w\ld connect ! ph5om5a ( surface t5sion ) contractility1 muscul> movem5t or o!r special physiological functions1 b we f9d ample room to trace ! op]ation ( ! same cause 9 produc+1 "u conditions ( re/ & equilibrium1 c]ta9 def9ite & inevitable =ms ( surface4 ,x is h[ev] ( great importance to obs]ve t ! liv+ cell is "o ( ^? cases :]e ! ph5om5a ( surface t5sion are by no means limit$ to ! out] surface2 = )9 ! het]og5e\s sub/ance ( ! cell1 betwe5 ! protoplasm & its nucle> & o!r cont5ts1 & 9 ! alveol> network ( ! cytoplasm itself 7s f> z t 8alveol> /ructure0 is actually pres5t 9 life71 we h a multitude ( int]ior surfaces2 &1 especially among plants1 we may h a l>ge inn] surface ( 8int]facial0 contact1 :]e ! protoplasm conta9s cavities or 8vacuoles0 fill$ ) a diff]5t & m fluid mat]ial1 ! 8cell-sap40 ,"h we h a great field = ! developm5t ( surface t5sion ph5om5a3 & s long ago z #ahfe1 ,ngeli & ,s*w5d5] %ew$ t ! /ream+ curr5ts ( plant cells might be v plausibly expla9$ by ?is ph5om5on4 ,ev5 t5 ye>s e>li]1 ,web] _h rem>k$ ^u ! resemblance betwe5 ^! protoplasmic /ream+s & ! /ream+s to be obs]v$ 9 c]ta9 inanimate drops1 = :i* no cause b surface t5sion c\ld be assign$#bgf4 ,! case ( amoeba1 ?\gh x is an elem5t>y case1 is at ! same "t a complicat$ "o4 ,:ile x rema9s 8amoeboid10 x is nev] at re/ or 9 equilibrium2 x is always mov+1 f "o to ano!r ( its protean *anges ( configuration2 its surface t5sion is con/antly v>y+ f po9t to po9t4 ,:]e ! #baa surface t5sion is great]1 t portion ( ! surface w contract into sph]ical or sph]oidal =ms2 :]e x is less ! surface w correspond+ly ext5d4 ,:ile g5]ally speak+ ! surface en]gy has a m9imal value1 x is n necess>ily con/ant4 ,x may be dim9i%$ by a rise ( temp]ature2 x may be alt]$ by contact ) adjac5t sub/ances#bgg1 by ! transport ( con/itu5t mat]ials f ! int]ior to ! surface1 or aga9 by actual *emical & f]m5tative *ange4 ,)9 ! cell1 ! surface en]gies develop$ ab\t its het]og5e\s cont5ts w con/antly v>y z ^! cont5ts are affect$ by *emical metabolism4 ,z ! colloid mat]ials are brok5 d[n & z ! p>ticles 9 susp5sion are dim9i%$ 9 size ! 8free surface en]gy0 w be increas$1 b ! osmotic en]gy w be dim9i%$#bgh4 ,?us arise ! v>i\s fluctuations ( surface t5sion & ! v>i\s ph5om5a ( amoeboid =m & motion1 :i* ,bts*li & o!rs h reproduc$ or imitat$ by means ( ! f9e emulsions :i* con/itute _! 8artificial amoebae40 ,a multitude ( exp]im5ts %ew h[ extraord9>ily delicate is ! adju/m5t ( ! surface t5sion =ces1 & h[ s5sitive !y are to ! lea/ *ange ( temp]ature or *emical /ate4 ,?us1 on a plate :i* we h w>m$ at "o side1 a drop ( alcohol runs t[>ds ! w>m area1 a drop ( oil away f x2 & a drop ( wat] on ! glass plate exhibits lively movem5ts :5 #bab we br+ into its neighb\rhood a heat$ wire1 or a glass rod dipp$ 9 e!r4 ,:5 we f9d t a plasmodium ( ,ae?alium1 = in/ance1 creeps t[>ds a damp spot1 or t[>ds a w>m spot1 or t[>ds sub/ances t happ5 to be nutriti\s1 & aga9 creeps away f solutions ( sug> or ( salt1 we seem to be deal+ ) ph5om5a e "o ( :i* c be p>allel$ by ord9>y ph5om5a ( surface t5sion#bgi4 ,ev5 ! soap-bubble itself is imp]fectly 9 equilibrium1 = ! reason t its film1 l ! protoplasm ( amoeba or ,ae?alium1 is an excessively het]og5e\s sub/ance4 ,its surface t5sions v>y f po9t to po9t1 & *emical *anges & *anges ( temp]ature increase & magnify ! v>iation4 ,! :ole surface ( ! bubble is 9 con/ant movem5t z ! conc5trat$ portions ( ! soapy fluid make _! way outw>ds f ! deep] lay]s2 x ?9s & x ?ick5s1 its col\rs *ange1 curr5ts are set up 9 x1 & little bubbles glide ov] x2 x cont9ues 9 ?is /ate ( con/ant movem5t1 z its p>ts /rive "o ) ano!r 9 all _! int]actions t[>ds equilibrium#bhj4 ,9 ! case ( ! nak$ protoplasmic cell1 z ! amoeboid phase is emphatically a phase ( fre$om & activity1 ( *emical & physiological *ange1 s1 on ! o!r h&1 is ! sph]ical =m indicative ( a phase ( re/ or comp>ative inactivity4 ,9 ! "o phase we see unequal surface t5sions manife/$ 9 ! creep+ movem5ts ( ! amoeboid body1 9 ! r\nd+ (f ( ! ends ( ! pseudopodia1 9 ! fl[+ out ( its sub/ance ov] a p>ticle ( 8food10 & 9 ! curr5t-motions 9 ! int]ior ( its mass2 till f9ally1 9 ! o!r phase1 :5 int]nal homog5eity & equilibrium h be5 atta9$ & ! pot5tial #bac en]gy ( ! sy/em is = ! "t be+ at a m9imum1 ! cell assumes a r\nd$ or sph]ical =m1 pass+ into a /ate ( 8re/10 & 7= a reason :i* we %all pres5tly see7 becom+ at ! same "t 8ency/$40 ,illu/ration3 ,fig4 #fj4 ,9 a budd+ yea/-cell 7,fig4 #fj71 we see a m def9ite & re/rict$ *ange ( surface t5sion4 ,:5 a 8bud0 appe>s1 :e!r ) or )\t actual gr[? by osmosis or o!rwise ( ! mass1 x does s because at a c]ta9 "p ( ! cell-surface ! surface t5sion has m or less sudd5ly dim9i%$1 & ! area ( t portion exp&s accord+ly2 b 9 turn ! surface t5sion ( ! exp&$ area w make itself felt1 & ! bud w be r\nd$ (f into a m or less sph]ical =m4 ,! yea/-cell ) its bud is a simple example ( a pr9ciple :i* we %all f9d to be v important4 ,our :ole treatm5t ( cell-=m 9 relation to surface-t5sion dep5ds on ! fact 7:i* ,err]a 0 ! fir/ to po9t out1 or to give cle> expression to7 t ! incipi5t cell-wall reta9s ) b little impairm5t ! prop]ties ( a liquid film#bha1 & t ! gr[+ cell1 9 spite ( ! membrane by :i* x has already begun to be surr\nd$1 behaves v mu* l a fluid drop4 ,b ev5 ! ord9>y yea/-cell %[s1 by its ovoid & non-sph]ical =m1 t x has acquir$ its %ape "u ! influ5ce ( "s =ce o!r ?an t uni=m & symmetrical surface-t5sion :i* w\ld be productive ( a sph]e2 & ?is or any o!r asymmetrical =m1 once acquir$1 may be reta9$ by virtue ( ! solidification & consequ5t rigidity ( ! membran\s wall ( ! cell4 ,unless su* rigidity ensue1 x is pla9 t su* a con=mation z t ( ! cell ) its atta*$ bud c\ld n be long reta9$1 amid/ ! con/antly v>y+ conditions1 z a figure ( ev5 p>tial equilibrium4 ,b z a matt] ( fact1 ! cell 9 ?is case is n 9 equilibrium at all2 x is 9 process ( budd+1 & is sl[ly alt]+ its %ape by r\nd+ (f ! bud4 ,x is pla9 t ov] its surface ! surface-en]gies are unequally di/ribut$1 ow+ to "s het]og5eity ( ! sub/ance2 & to ?is matt] we %all aft]w>ds return4 ,9 l mann] ! develop+ egg #bad ?r\gh all its successive phases ( =m is nev] 9 complete equilibrium2 b is m]ely respond+ to con/antly *ang+ conditions1 by phases ( p>tial1 transitory1 un/able & conditional equilibrium4 ,x is obvi\s t !re are innum]able solit>y plant-cells1 & unicellul> organisms 9 g5]al1 :i*1 l ! yea/-cell1 d n correspond to any ( ! simple =ms t may be g5]at$ "u ! influ5ce ( simple & homog5e\s surface-t5sion2 & 9 _m cases ^! =ms1 :i* we %\ld expect to be un/able & transitory1 h become fix$ & /able by reason ( ! comp>atively sudd5 or rapid solidification ( ! envelope4 ,?is is ! case1 = in/ance1 9 _m ( ! m complicat$ =ms ( diatoms or ( desmids1 :]e we are deal+1 9 a less /rik+ b ev5 m curi\s way ?an 9 ! budd+ yea/-cell1 n ) "o simple act ( =mation1 b ) a complicat$ result ( successive /ages ( localis$ gr[?1 int]rupt$ by phases ( p>tial consolidation4 ,! orig9al cell has acquir$ or assum$ a c]ta9 =m1 & !n1 "u alt]+ conditions & new di/ributions ( en]gy1 has ?ick5$ "h or weak5$ !re1 & has gr[n out or t5d$ 7z x 77 to bran*1 at p>ticul> po9ts4 ,we c (t51 or inde$ g5]ally1 trace 9 ea* p>ticul> /age ( gr[? or at ea* p>ticul> tempor>y gr[+ po9t1 ! laws ( surface t5sion manife/+ !mselves 9 :at is = ! "t be+ a fluid surface2 nay m1 ev5 9 ! adult & complet$ /ructure1 we h little difficulty 9 trac+ & recognis+ 7= in/ance 9 ! outl9e ( su* a desmid z ,eua/rum7 ! r\nd$ lobes t h successively gr[n or fl[$ out f ! orig9al r\nd$ & flatt5$ cell4 ,:at we see 9 a _m *amb]$ =am9if]1 su* z ,globig]9a or ,rotalia1 is j ! same ?+1 save t x is c>ri$ out 9 great] complet5ess & p]fection4 ,! little organism z a :ole is n a figure ( equilibrium or ( m9imal area2 b ea* new bud or sep>ate *amb] is su* a figure1 condition$ by ! =ces ( surface t5sion1 & sup]pos$ ^u ! complex aggregate ( simil> bubbles aft] ^! latt] h become consolidat$ "o by "o into a rigid sy/em4 ,let u n[ make "s enquiry reg>d+ ! v>i\s =ms #bae :i*1 "u ! influ5ce ( surface t5sion1 a surface c possibly assume4 ,9 do+ s1 we are obvi\sly limit$ to conditions "u :i* o!r =ces are relatively unimportant1 t is to say :]e ! 8surface en]gy0 is a consid]able fraction ( ! :ole en]gy ( ! sy/em2 & ?is 9 g5]al w be ! case :5 we are deal+ ) portions ( liquid s small t _! dim5sions come )9 :at we h call$ ! molecul> range1 or1 m g5]ally1 9 :i* ! 8specific surface0 is l>ge#bhb3 9 o!r words x w be small or m9ute organisms1 or ! small cellul> elem5ts ( l>g] organisms1 ^: =ms w be gov]n$ by surface-t5sion2 :ile ! g5]al =ms ( ! l>g] organisms w be due to o!r & non-molecul> =ces4 ,= in/ance1 a l>ge surface ( wat] sets itself level because "h gravity is pr$om9ant2 b ! surface ( wat] 9 a n>r[ tube is manife/ly curv$1 = ! reason t we are "h deal+ ) p>ticles :i* are mutually )9 ! range ( ea* o!r's molecul> =ces4 ,! same is ! case ) ! cell-surfaces & cell-p>titions :i* we are pres5tly to /udy1 & ! effect ( gravity w be especially c\nt]act$ & conceal$ :51 z 9 ! case ( protoplasm 9 a wat]y fluid1 ! object is imm]s$ 9 a liquid ( ne>ly its own specific gravity4 ,we h already le>n$1 z a fundam5tal law ( surface-t5sion ph5om5a1 t a liquid film 9 equilibrium assumes a =m :i* gives x a m9imal area "u ! conditions to :i* x is subject4 ,& ^! conditions include 7#a7 ! =m ( ! b\nd>y1 if su* exi/1 & 7#b7 ! pressure1 if any1 to :i* ! film is subject2 :i* pressure is closely relat$ to ! volume1 ( air or ( liquid1 :i* ! film 7if x be a clos$ "o7 may h to conta94 ,9 ! simple/ ( cases1 :5 we take up a soap-film on a plane wire r+1 ! film is expos$ to equal atmosph]ic pressure on bo? sides1 & x obvi\sly has its m9imal area 9 ! =m ( a plane4 ,s long z our wire r+ lies 9 "o plane 7h[ev] irregul> 9 outl9e71 ! film /ret*$ across x w /ill be 9 a plane2 b if we b5d ! r+ s t x lies no long] 9 a plane1 !n our film w become curv$ into a surface :i* may be extremely complicat$1 b is /ill ! smalle/ possible #baf surface :i* c be drawn cont9u\sly across ! unev5 b\nd>y4 ,! "q ( pressure involves n only ext]nal pressures act+ on ! film1 b also t :i* ! film itself is capable ( ex]t+4 ,= we h se5 t ! film is always contract+ to its smalle/ limits2 & :5 ! film is curv$1 ?is obvi\sly leads to a pressure direct$ inw>ds1--p]p5dicul>1 t is to say1 to ! surface ( ! film4 ,9 ! case ( ! soap-bubble1 ! uni=m contraction ( ^: surface has l$ to its sph]ical =m1 ?is pressure is balanc$ by ! pressure ( ! air )92 & if an outlet be giv5 = ?is air1 !n ! bubble contracts ) p]ceptible =ce until x /ret*es across ! m\? ( ! tube1 = in/ance ! m\? ( ! pipe ?r\gh :i* we h bl[n ! bubble4 ,a precisely simil> pressure1 direct$ inw>ds1 is ex]cis$ by ! surface lay] ( a drop ( wat] or a globule ( m]cury1 or by ! surface pellicle on a portion or 8drop0 ( protoplasm4 ,only we mu/ always rememb] t 9 ! soap-bubble1 or ! bubble :i* a glass-bl[] bl[s1 !re is a tw(old pressure z comp>$ ) t :i* ! surface-film ex]cises on ! drop ( liquid ( :i* x is a "p2 = ! bubble consi/s 7unless x be s ?9 z to consi/ ( a m]e lay] ( molecules#bhc7 ( a liquid lay]1 ) a free surface )9 & ano!r )\t1 & ea* ( ^! two surfaces ex]cises its own indep5d5t & coequal t5sion1 & correspond+ pressure#bhd4 ,if we /ret* a tape ^u a flat table1 :atev] be ! t5sion ( ! tape x obvi\sly ex]cises no pressure ^u ! table bel[4 ,b if we /ret* x ov] a curv$ surface1 a cyl9d] = in/ance1 x does ex]cise a d[nw>d pressure2 & ! m curv$ ! surface ! great] is ?is pressure1 t is to say ! great] is ?is %>e ( ! entire =ce ( t5sion :i* is resolv$ 9 ! d[nw>d direction4 ,9 ma!matical language1 ! pressure 7p7 v>ies directly z ! t5sion 7,t71 & inv]sely z ! radius ( curvature 7,r73 t is to say1 p ,t_/,r1 p] unit ( surface4 #bag ,if in/ead ( a cyl9d]1 :i* is curv$ only 9 "o direction1 we take a case :]e !re are curvatures 9 two dim5sions 7z = in/ance a sph]e71 !n ! effects ( ^! mu/ be simply add$ to "o ano!r1 & ! result+ pressure p is equal to ,t_/,r ,t_/,r or p ,t7#a_/,r #a_/,r7#bhe4 ,& if 9 addition to ! pressure p1 :i* is due to surface t5sion1 we h to take into acc\nt o!r pressures1 p1 p1 etc41 :i* are due to gravity or o!r =ces1 !n we may say t ! total pressure1 ,p p p ,t7#a_/,r #a_/,r74 ,:ile 9 "s cases1 = in/ance 9 speak+ ( ! %ape ( a bird's egg1 we %all h to take acc\nt ( ^! extrane\s pressures1 9 ! pres5t "p ( our subject we %all = ! mo/ "p be able to neglect !m4 ,our equation is an equation ( equilibrium4 ,! resi/ance to compression1--! pressure outw>ds1--( our fluid mass1 is a con/ant quantity 7,p72 ! pressure inw>ds1 ,t7#a_/,r #a_/,r71 is also con/ant2 & if 7unlike ! case ( ! mobile amoeba7 ! surface be homog5e\s1 s t ,t is ev]y:]e equal1 x foll[s t ?r\gh\t ! :ole surface #a_/,r #a_/,r ,c 7a con/ant74 ,n[ equilibrium is atta9$ aft] ! surface contraction has done its utmo/1 t is to say :5 x has r$uc$ ! surface to ! smalle/ possible area2 & s we arrive1 f ! physical side1 at ! conclusion t a surface su* t #a_/,r #a_/,r ,c1 9 o!r words a surface :i* has ! same mean curvature at all po9ts1 is equival5t to a surface ( m9imal area3 & to ! same conclusion we may also arrive ?r\gh purely analytical ma!matics4 ,x is obvi\s t ! plane & ! sph]e are two examples ( su* surfaces1 = 9 bo? cases ! radius ( curvature is ev]y:]e con/ant1 be+ equal to inf9ity 9 ! case ( ! plane1 & to "s def9ite magnitude 9 ! case ( ! sph]e4 ,f ! fact t we may ext5d a soap-film across a r+ ( wire h[ev] fanta/ically ! latt] may be b5t1 we realise t !re is no limit to ! numb] ( surfaces ( m9imal area :i* may be con/ruct$ or may be imag9$2 & :ile "s ( ^! are v complicat$ inde$1 "s1 = in/ance a spiral helicoid screw1 are relatively v simple4 ,b if we limit ourselves to #bah surfaces ( revolution 7t is to say1 to surfaces symmetrical ab\t an axis71 we f9d1 z ,plateau 0 ! fir/ to %ew1 t ^? :i* meet ! case are v few 9 numb]4 ,!y are six 9 all1 namely ! plane1 ! sph]e1 ! cyl9d]1 ! cat5oid1 ! unduloid1 & a curi\s surface :i* ,plateau call$ ! nodoid4 ,^! sev]al surfaces are all closely relat$1 & ! passage f "o to ano!r is g5]ally easy4 ,_! ma!matical int]relation is express$ by ! fact 7fir/ %ewn by ,delaunay#bhf1 9 #ahda7 t ! plane curves by ^: rotation !y are g5]at$ are !mselves g5]at$ z 8r\lettes0 ( ! conic sections4 ,let u imag9e a /raight l9e ^u :i* a circle1 an ellipse or o!r conic section rolls2 ! focus ( ! conic section w describe a l9e 9 "s relation to ! fix$ axis1 & ?is l9e 7or r\lette71 rotat+ ar\nd ! axis1 w describe 9 space "o or o!r ( ! six surfaces ( revolution ) :i* we are deal+4 ,illu/ration3 ,fig4 #fa4 ,if we imag9e an ellipse s to roll ov] a l9e1 ei!r ( its foci w describe a s9u\s or wavy l9e 7,fig4 #fa;,b7 at a di/ance alt]nately maximal & m9imal f ! axis2 & ?is wavy l9e1 by rotation ab\t ! axis1 becomes ! m]idional l9e ( ! surface :i* we call ! unduloid4 ,! m unequal ! two axes are ( our ellipse1 ! m pron\nc$ w be ! s9uosity ( ! describ$ r\lette4 ,if ! two axes be equal1 !n our ellipse becomes a circle1 & ! pa? describ$ by its roll+ c5tre is a /raight l9e p>allel to ! axis 7,a72 & obvi\sly ! solid ( revolution g5]at$ !refrom w be a cyl9d]4 ,if "o axis ( our ellipse vani%1 :ile ! o!r rema9 ( f9ite l5g?1 !n ! ellipse is r$uc$ to a /raight l9e1 & its r\lette w appe> z a succession ( semicircles t\*+ "o ano!r ^u ! axis 7,c72 ! solid ( revolution w be a s]ies ( equal sph]es4 ,if z be=e "o axis ( ! ellipse vani%1 b ! o!r be inf9itely long1 !n ! curve describ$ by ! rotation #bai ( ?is latt] w be a circle ( inf9ite radius1 i4e4 a /raight l9e inf9itely di/ant f ! axis2 & ! surface ( rotation is n[ a plane4 ,if we imag9e "o focus ( our ellipse to rema9 at a giv5 di/ance f ! axis1 b ! o!r to become inf9itely remote1 t is tantam\nt to say+ t ! ellipse becomes trans=m$ into a p>abola2 & by ! roll+ ( ?is curve along ! axis !re is describ$ a cat5>y 7,d71 ^: solid ( revolution is ! cat5oid4 ,la/ly1 b ?is is a little m difficult to imag9e1 we h ! case ( ! hyp]bola4 ,we _c well imag9e ! hyp]bola roll+ ^u a fix$ /raight l9e s t its focus %all describe a cont9u\s curve4 ,b let u suppose t ! fix$ l9e is1 to beg9 )1 asymptotic to "o bran* ( ! hyp]bola1 & t ! roll+ proce$ until ! l9e is n[ asymptotic to ! o!r bran*1 t is to say t\*+ x at an inf9ite di/ance2 !re w !n be ma!matical cont9uity if we recomm5ce roll+ ) ?is second bran*1 & s 9 turn ) ! o!r1 :5 ea* has run its c\rse4 ,we %all see1 on reflection1 t ! l9e trac$ by "o & ! same focus w be an 8ela/ic curve0 describ+ a succession ( k9ks or knots 7,e71 & ! solid ( revolution describ$ by ?is m]idional l9e ab\t ! axis is ! s-call$ nodoid4 ,! physical transition ( "o ( ^! surfaces into ano!r c be exp]im5tally illu/rat$ by means ( soap-bubbles1 or bett] /ill1 aft] ! me?od ( ,plateau1 by means ( a l>ge globule ( oil1 support$ :5 necess>y by wire r+s1 )9 a fluid ( specific gravity equal to its own4 ,to prep>e a mixture ( alcohol & wat] ( a d5sity precisely equal to t ( ! oil-globule is a tr\blesome matt]1 & a me?od devis$ by ,mr ,c4 ,r4 ,d>l+ is a great improvem5t on ,plateau's#bhg4 ,mr ,d>l+ uses ! oily liquid or?otoluid5e1 :i* does n mix ) wat]1 has a beautiful & conspicu\s r$ col\r1 & has precisely ! same d5sity z wat] :5 bo? are kept at a temp]ature ( #bd ,c4 ,we h !re=e only to run ! liquid into wat] at ?is temp]ature 9 ord] to produce beautifully sph]ical drops ( any requir$ size3 & by add+ #bbj a little salt to ! l[] lay]s ( wat]1 ! drop may be made to float or re/ ^u ! d5s] liquid4 ,we h already se5 t ! soap-bubble1 sph]ical to beg9 )1 is trans=m$ into a plane :5 we relieve its int]nal pressure & let ! film %r9k back ^u ! orifice ( ! pipe4 ,if we bl[ a small bubble & !n cat* x up on a second pipe1 s t x /ret*es betwe51 we may gradually draw ! two pipes ap>t1 ) ! result t ! sph]oidal surface w be gradually flatt5$ 9 a longitud9al direction1 & ! bubble w be trans=m$ into a cyl9d]4 ,b if we draw ! pipes yet f>!r ap>t1 ! cyl9d] w n>r[ 9 ! middle into a sort ( h\rglass =m1 ! increas+ curvature ( its transv]se section be+ balanc$ by a gradually increas+ negative curvature 9 ! longitud9al section4 ,! cyl9d] has1 9 turn1 be5 conv]t$ into an unduloid4 ,:5 we hold a portion ( a s(t glass tube 9 ! flame1 & 8draw x out10 we are 9 ! same id5tical fa%ion conv]t+ a cyl9d] into an unduloid 7,fig4 #fb;,a72 :5 on ! o!r h& we /op ! end & bl[1 we aga9 conv]t ! cyl9d] into an unduloid 7,b71 b into "o :i* is n[ positively1 :ile ! =m] 0 negatively curv$4 ,! two figures are ess5tially ! same1 save t ! two halves ( ! "o are rev]s$ 9 ! o!r4 ,illu/ration3 ,fig4 #fb4 ,t sph]es1 cyl9d]s & unduloids are ( ! commone/ occurr5ce among ! =ms ( small unicellul> organism1 or ( individual cells 9 ! simpl] aggregates1 & t 9 ! processes ( gr[?1 reproduction & developm5t transitions are frequ5t f "o ( ^! =ms to ano!r1 is obvi\s to ! naturali/1 & we %all deal pres5tly ) a few illu/rations ( ^! ph5om5a4 ,b be=e we g fur!r 9 ?is enquiry1 x w be necess>y to consid]1 to "s small ext5t at lea/1 ! curvatures ( ! six diff]5t surfaces1 t is to say1 to det]m9e :at modification #bba is requir$1 9 ea* case1 ( ! g5]al equation :i* applies to !m all4 ,we %all f9d t ) ?is "q is closely connect$ ! "q ( ! pressures ex]cis$ by1 or imp++ on ! film1 & also ! v important "q ( ! limitations :i*1 f ! nature ( ! case1 exi/ to prev5t ! ext5sion ( c]ta9 ( ! figures beyond c]ta9 b\nds4 ,! :ole subject is ma!matical1 & we %all only deal ) x 9 ! mo/ elem5t>y way4 ,we h se5 t1 9 our g5]al =mula1 ! expression #a_/,r #a_/,r ,c1 a con/ant2 & t ?is is1 9 all cases1 ! condition ( our surface be+ "o ( m9imal area4 ,9 o!r words1 x is always true = "o & all ( ! six surfaces :i* we h to consid]4 ,b ! con/ant ,c may h any value1 positive1 negative1 or nil4 ,9 ! case ( ! plane1 :]e ,r & ,r are bo? inf9ite1 x is obvi\s t #a_/,r #a_/,r #j4 ,! expression !re=e vani%es1 & our dynamical equation ( equilibrium becomes ,p p4 ,9 %ort1 we c only h a plane film1 or we %all only f9d a plane surface 9 our cell1 :5 on ei!r side !re( we h equal pressures or no pressure at all4 ,a simple case is ! plane p>tition betwe5 two equal & simil> cells1 z 9 a filam5t ( spirogyra4 ,9 ! case ( ! sph]e1 ! radii are all equal1 ,r ,r2 !y are also positive1 & ,t 7#a_/,r #a_/,r71 or #b ,t_/,r1 is a positive quantity1 involv+ a positive pressure ,p1 on ! o!r side ( ! equation4 ,9 ! cyl9d]1 "o radius ( curvature has ! f9ite & positive value ,r2 b ! o!r is inf9ite4 ,our =mula becomes ,t_/,r1 to :i* corresponds a positive pressure ,p1 suppli$ by ! surface-t5sion z 9 ! case ( ! sph]e1 b evid5tly ( j half ! magnitude develop$ 9 ! latt] case = a giv5 value ( ! radius ,r4 ,! cat5oid has ! rem>kable prop]ty t its curvature 9 "o direction is precisely equal & opposite to its curvature 9 ! o!r1 ?is prop]ty hold+ good = all po9ts ( ! surface4 ,t is to say1 ,r ,r2 & ! expression becomes 7#a_/,r #a_/,r7 7#a_/,r #a_/,r7 #j2 9 o!r words1 ! surface1 z 9 ! case ( ! plane1 has no #bbb curvature1 & ex]cises no pressure4 ,!re are no o!r surfaces1 save ^! two1 :i* %>e ?is rem>kable prop]ty2 & x foll[s1 z a simple coroll>y1 t we may expect at times to h ! cat5oid & ! plane coexi/+1 z p>ts ( "o & ! same b\nd>y sy/em2 j z1 9 a cyl9drical drop or cell1 ! cyl9d] is capp$ by portions ( sph]es1 su* t ! cyl9drical & sph]ical portions ( ! wall ex]t equal positive pressures4 ,9 ! unduloid1 unlike ! f\r surfaces :i* we h j be5 consid]+1 x is obvi\s t ! curvatures *ange f "o po9t to ano!r4 ,at ! middle ( "o ( ! swoll5 portions1 or 8beads10 ! two curvatures are bo? positive2 ! expression 7#a_/,r #a_/,r7 is !re=e positive1 & x is also f9ite4 ,! film1 accord+ly1 ex]cises a positive t5sion inw>ds1 :i* mu/ be comp5sat$ by a f9ite & positive outw>d pressure ,p4 ,at ! middle ( "o ( ! n>r[ necks1 betwe5 two adjac5t beads1 !re is obvi\sly1 9 ! transv]se direction1 a mu* /rong] curvature ?an 9 ! =m] case1 & ! curvature :i* balances x is n[ a negative "o4 ,b ! sum ( ! two mu/ rema9 positive1 z well z con/ant2 & we !re=e see t ! convex or positive curvature mu/ always be great] ?an ! concave or negative curvature at ! same po9t4 ,?is is pla9ly ! case 9 our figure ( ! unduloid4 ,! nodoid is1 l ! unduloid1 a cont9u\s curve :i* keeps alt]+ its curvature z x alt]s its di/ance f ! axis2 b 9 ?is case ! resultant pressure inw>ds is negative in/ead ( positive4 ,b ?is curve is a complicat$ "o1 & a full discussion ( x w\ld c>ry u beyond our scope4 ,illu/ration3 ,fig4 #fc4 ,9 "o ( ,plateau's exp]im5ts1 a bubble ( oil 7protect$ f gravity by ! specific gravity ( ! surr\nd+ fluid be+ id5tical ) its own7 is balanc$ betwe5 two annuli4 ,x may !n be br\ght to assume ! =m ( ,fig4 #fc1 t is to say ! =m ( a cyl9d] ) sph]ical ends2 & !re is !n ev]y:]e1 ow+ to ! convexity ( ! surface film1 a pressure inw>ds ^u ! fluid cont5ts ( ! bubble4 ,if ! surr\nd+ liquid be ev] s little heavi] or light] ?an t :i* con/itutes ! drop1 !n ! conditions ( equilibrium w be accord+ly #bbc modifi$1 & ! cyl9drical drop w assume ! =m ( an unduloid 7,fig4 #fd ,a1 ,b71 ) its dilat$ portion bel[ or above1 ,illu/ration3 ,fig4 #fd4 z ! case may be2 & our cyl9d] may also1 ( c\rse1 be conv]t$ into an unduloid ei!r by elongat+ x fur!r1 or by ab/ract+ a portion ( its oil1 until at l5g? rupture ensues & ! cyl9d] breaks up into two new sph]ical drops4 ,9 all cases alike1 ! unduloid1 l ! orig9al cyl9d]1 w be capp$ by sph]ical ends1 :i* are ! sign1 & ! consequ5ce1 ( ! positive pressure produc$ by ! curv$ walls ( ! unduloid4 ,b if our initial cyl9d]1 in/ead ( be+ tall1 be a flat or dumpy "o 7) c]ta9 def9ite relations ( height to bread?71 !n new ph5om5a may be exhibit$4 ,= n[1 if a little oil be cauti\sly )drawn f ! mass by help ( a small syr+e1 ! cyl9d] may be made to flatt5 d[n s t its upp] & l[] surfaces become plane2 :i* is ( itself an indication t ! pressure inw>ds is n[ nil4 ,b at ! v mom5t :5 ! upp] & l[] surfaces become plane1 x w be f\nd t ! sides curve inw>ds1 9 ! fa%ion %ewn 9 ,fig4 #fe;,b4 ,?is figure is a cat5oid1 :i*1 z ,illu/ration3 ,fig4 #fe4 we h already se51 is1 l ! plane itself1 a surface ex]cis+ no pressure1 & :i* !re=e may coexi/ ) ! plane z "p ( "o & ! same sy/em4 ,we may cont9ue to )draw m oil f our bubble1 drop by drop1 & n[ ! upp] & l[] surfaces dimple d[n into concave portions ( sph]es1 z ! result ( ! negative int]nal pressure2 & !reupon ! p]iph]al cat5oid surface alt]s its =m 7p]haps1 on ?is small scale1 imp]ceptibly71 & becomes a portion ( a nodoid 7,fig4 #fe;,a74 #bbd ,x repres5ts1 9 fact1 t portion ( ! nodoid1 :i* 9 ,fig4 #ff lies betwe5 su* po9ts z ,o1 ,p4 ,:ile x is easy to ,illu/ration3 ,fig4 #ff4 draw ! outl9e1 or m]idional section1 ( ! nodoid 7z 9 ,fig4 #ff71 x is obvi\s t ! solid ( revolution to be d]iv$ f x1 c nev] be realis$ 9 its entirety3 = "o "p ( ! solid figure w\ld cut1 or entangle )1 ano!r4 ,all t we c ev] d1 accord+ly1 is to realise isolat$ portions ( ! nodoid4 ,if1 9 a sequel to ! prec$+ exp]im5t ( ,plateau's1 we use solid discs in/ead ( annuli1 s z to enable u to ex]t direct me*anical pressure ^u our globule ( oil1 we aga9 beg9 by adju/+ ! pressure ( ^! discs s t ! oil assumes ! =m ( a cyl9d]3 our discs1 t is to say1 are adju/$ to ex]cise a me*anical pressure equal to :at 9 ! =m] case 0 suppli$ by ! surface-t5sion ( ! sph]ical caps or ends ( ! bubble4 ,if we n[ increase ! pressure slightly1 ! p]iph]al walls w become convexly curv$1 ex]cis+ a precisely correspond+ pressure4 ,"u ^! circum/ances ! =m assum$ by ! sides ( our figure w be t ( a portion ( an unduloid4 ,if we increase ! pressure betwe5 ! discs1 ! p]iph]al surface ( oil w bulge out m & m1 & w pres5tly con/itute a portion ( a sph]e4 ,b we may cont9ue ! process yet fur!r1 & )9 c]ta9 limits we %all f9d t ! sy/em rema9s p]fectly /able4 ,:at is ?is new curv$ surface :i* has aris5 out ( ! sph]e1 z ! latt] 0 produc$ f ! unduloid8 ,x is no o!r ?an a portion ( a nodoid1 t "p :i* 9 ,fig4 #ff lies betwe5 su* limits z ,m & ,n4 ,b ?is surface1 :i* is concave 9 bo? directions t[>ds ! surface ( ! oil )91 is ex]t+ a pressure ^u ! latt]1 j z did ! sph]e out ( :i* a mom5t ago x 0 trans=m$2 & we _h j /at$1 9 consid]+ ! previ\s exp]im5t1 t ! pressure inw>ds ex]t$ by ! nodoid 0 a negative "o4 ,! explanation ( ?is seem+ discrepancy lies 9 ! simple fact t1 if we foll[ ! outl9e #bbe ( our nodoid curve 9 ,fig4 #ff f ,o1 ,p1 ! surface conc]n$ 9 ! =m] case1 to ,m1 ,n1 t conc]n$ 9 ! pres5t1 we %all see t 9 ! two exp]im5ts ! surface ( ! liquid is n homolog\s1 b lies on ! positive side ( ! curve 9 ! "o case & on ! negative side 9 ! o!r4 ,( all ! surfaces :i* we h be5 describ+1 ! sph]e is ! only "o :i* c enclose space2 ! o!rs c only help to d s1 9 comb9ation ) "o ano!r or ) ! sph]e itself4 ,?us we h se5 t1 9 normal equilibrium1 ! cyl9drical vesicle is clos$ at ei!r end by a portion ( a sph]e1 & s on4 ,moreov] ! sph]e is n only ! only "o ( our figures :i* c enclose a f9ite space2 x is also1 ( all possible figures1 t :i* encloses ! greate/ volume ) ! lea/ area ( surface2 x is /rictly & absolutely ! surface ( m9imal area1 & x is !re=e ! =m :i* w be naturally assum$ by a unicellul> organism 7j z by a ra9drop71 :5 x is practically homog5e\s & :51 l ,orbul9a float+ 9 ! ocean1 its surr\nd+s are likewise practically homog5e\s & symmetrical4 ,x is only relatively speak+ t all ! re/ are surfaces m9imae areae2 !y are s1 t is to say1 "u ! giv5 conditions1 :i* involve v>i\s =ms ( pressure or re/ra9t4 ,su* re/ra9ts are impos$1 = in/ance1 by ! pipes or annuli ) ! help ( :i* we draw out our cyl9drical or unduloid oil-globule or soap-bubble2 & 9 ! case ( ! organic cell1 simil> re/ra9ts are con/antly suppli$ by solidification1 p>tial or complete1 local or g5]al1 ( ! cell-wall4 ,be=e we pass to biological illu/rations ( our surface-t5sion figures1 we h /ill ano!r prelim9>y matt] to deal )4 ,we h se5 f our description ( two ( ,plateau's classical exp]im5ts1 t at "s p>ticul> po9t "o type ( surface gives place to ano!r2 & aga91 we "k t1 :5 we draw out our soap-bubble into & !n beyond a cyl9d]1 !re comes a c]ta9 def9ite po9t at :i* our bubble breaks 9 two1 & leaves u ) two bubbles ( :i* ea* is a sph]e1 or a portion ( a sph]e4 ,9 %ort !re are c]ta9 def9ite limits to ! dim5sions ( our figures1 )9 :i* limits equilibrium is /able b at :i* x becomes un/able1 & above :i* x #bbf breaks d[n4 ,moreov] 9 our composite surfaces1 :5 ! cyl9d] = in/ance is capp$ by two sph]ical cups or l5ticul> discs1 !re is a well-def9$ ratio :i* regulates _! respective curvatures1 & !re=e _! respective dim5sions4 ,^! two matt]s we may deal ) toge!r4 ,let u imag9e a liquid drop :i* by appropriate conditions has be5 made to assume ! =m ( a cyl9d]2 we h already se5 t its ends w be t]m9at$ by portions ( sph]es4 ,s9ce "o & ! same liquid film cov]s ! sides & ends ( ! drop 7or s9ce "o & ! same delicate membrane encloses ! sides & ends ( ! cell71 we assume ! surface-t5sion 7,t7 to be ev]y:]e id5tical2 & x foll[s1 s9ce ! int]nal fluid-pressure is also ev]y:]e id5tical1 t ! expression 7#a_/,r #a_/,r7 = ! cyl9d] is equal to ! correspond+ expression1 :i* we may call 7#a_/r #a_/r71 9 ! case ( ! t]m9al sph]es4 ,b 9 ! cyl9d] #a_/,r #j1 & 9 ! sph]e #a_/r #a_/r4 ,!re=e our relation ( equality becomes #a_/,r #b_/r1 or r #b ,r2 t is to say1 ! sph]e 9 "q has j twice ! radius ( ! cyl9d] ( :i* x =ms a cap4 ,illu/ration3 ,fig4 #fg4 ,& if ,ob1 ! radius ( ! sph]e1 be equal to twice ! radius 7,oa7 ( ! cyl9d]1 x foll[s t ! angle a,ob is an angle ( #fj1 & b,oc is also an angle ( #fj2 t is to say1 ! arc bc is equal to 7#a_/c7 4 ,9 o!r words1 ! sph]ical disc :i* 7"u ! giv5 conditions7 caps our cyl9d]1 is n a portion tak5 at haphaz>d1 b is nei!r m nor less ?an t portion ( a sph]e :i* is subt5d$ by a cone ( #fj4 ,moreov]1 x is pla9 t ! height ( ! sph]ical cap1 de1 ,ob ab ,r 7#b #c7 #jbg ,r1 :]e ,r is ! radius ( our cyl9d]1 or "o-half ! radius ( our sph]ical cap3 9 o!r words ! normal height ( ! sph]ical cap ov] ! end ( ! cyl9drical cell is j a v little m ?an "o-eigh? ( ! diamet] ( ! cyl9d]1 or ( ! radius ( ! #bbg sph]e4 ,& ^! are ! proportions :i* we recognise1 "u normal circum/ances1 9 su* a case z ! cyl9drical cell ( ,spirogyra :]e its free end is capp$ by a portion ( a sph]e4 ,among ! _m important !oretical discov]ies :i* we owe to ,plateau1 "o to :i* we h j ref]r$ is ( peculi> importance3 namely t1 ) ! exception ( ! sph]e & ! plane1 ! surfaces ) :i* we h be5 deal+ are only 9 complete equilibrium )9 c]ta9 dim5sional limits1 or 9 o!r words1 h a c]ta9 def9ite limit ( /ability2 only ! plane & ! sph]e1 or any portions ( a sph]e1 are p]fectly /able1 because !y are p]fectly symmetrical1 figures4 ,= exp]im5tal demon/ration1 ! case ( ! cyl9d] is ! simple/4 ,if we produce a liquid film hav+ ! =m ( a cyl9d]1 ei!r by ,illu/ration3 ,fig4 #fh4 draw+ out a bubble or by support+ betwe5 two r+s a globule ( oil1 ! exp]im5t proce$s easily until ! l5g? ( ! cyl9d] becomes j ab\t ?ree times z great z its diamet]4 ,b some:]e ab\t ?is limit ! cyl9d] alt]s its =m2 x beg9s to n>r[ at ! wai/1 s pass+ into an unduloid1 & ! de=mation progresses quickly until at la/ our cyl9d] breaks 9 two1 & its two halves assume a sph]ical =m4 ,x is f\nd1 by !oretical consid]ations1 t ! precise limit ( /ability is at ! po9t :5 ! l5g? ( ! cyl9d] is exactly equal to its circumf]5ce1 t is to say1 :5 ,l #b,r1 or :5 ! ratio ( l5g? to diamet] is repres5t$ by 4 ,9 ! case ( ! cat5oid1 ,plateau's exp]im5tal proc$ure 0 z foll[s4 ,to support 8 globule ( oil 791 z usual1 a mixture ( alcohol & wat] ( its own specific gravity71 he us$ #bbh a pair ( metal r+s1 :i* happ5$ to h a diamet] ( #ga millimetres2 &1 9 a s]ies ( exp]im5ts1 he set ^! r+s ap>t at di/ances ( #ee1 #di1 #dg1 #de1 & #dc mm4 successively4 ,9 ea* case he began by br++ 8 oil-globule into a cyl9drical =m1 by suck+ sup]flu\s oil out ( ! drop until ?is result 0 atta9$2 & always1 = ! reason ) :i* we are n[ acqua9t$1 ! cyl9drical sides 7 associat$ ) sph]ical ends to ! cyl9d]4 ,on cont9u+ to )draw oil 9 ! hope ( conv]t+ ^! sph]ical ends into planes1 he f\nd1 naturally1 t ! sides ( ! cyl9d] drew 9 to =m a concave surface2 b x 0 by no means easy to get ! extremities actually plane3 & unless !y 7 s1 ?us indicat+ t ! surface-pressure ( ! drop 0 nil1 ! curvature ( ! sides c\ld n be t ( a cat5oid4 ,= 9 ! fir/ exp]im5t1 :5 ! r+s 7 #ee mm4 ap>t1 z soon z ! convexity ( ! ends 0 to a c]ta9 ext5t dim9i%$1 x spontane\sly increas$ aga92 & ! transv]se con/riction ( ! globule correspond+ly deep5$1 until at a c]ta9 po9t equilibrium set 9 anew4 ,inde$1 ! m oil he remov$1 ! m convex became ! ends1 until at la/ ! increas+ transv]se con/riction l$ to ! break+ ( ! oil-globule into two4 ,9 ! ?ird exp]im5t1 :5 ! r+s 7 #dg mm4 ap>t1 x 0 easy to obta9 end-surfaces t 7 actually plane1 & !y rema9$ s ev5 ?\gh m oil 0 )drawn1 ! transv]se con/riction deep5+ accord+ly4 ,only aft] a consid]able am\nt ( oil _h be5 suck$ up did ! plane t]m9al surface become gradually convex1 & pres5tly ! n>r[ wai/1 n>r[+ m & m1 broke across 9 ! usual way4 ,f9ally 9 ! fif? exp]im5t1 :]e ! r+s 7 /ill ne>] toge!r1 x 0 aga9 possible to br+ ! ends ( ! oil-globule to a plane surface1 z 9 ! ?ird & f\r? exp]im5ts1 & to keep ?is surface plane 9 spite ( "s cont9u$ )drawal ( oil4 ,b v soon ! ends became gradually concave1 & ! concavity deep5$ z m & m oil 0 )drawn1 until at a c]ta9 limit1 ! :ole oil-globule broke up 9 g5]al disruption4 ,we le>n f ?is t ! limit+ size ( ! cat5oid 0 rea*$ :5 ! di/ance ( ! support+ r+s 0 to _! diamet] z #dg to #ga1 or1 z ne>ly z possible1 z two to ?ree2 #bbi & z a matt] ( fact x c be %ewn t #b_/c is ! true !oretical value4 ,above ?is limit ( #b_/c1 ! inevitable convexity ( ! end-surfaces %[s t a positive pressure inw>ds is be+ ex]t$ by ! surface film1 & ?is tea*es u t ! sides ( ! figure actually con/itute n a cat5oid b an unduloid1 ^: spontane\s *anges t5d to a =m ( great] /ability4 ,bel[ ! #b_/c limit ! cat5oid surface is ess5tially un/able1 & ! =m into :i* x passes "u c]ta9 conditions ( di/urbance su* z t ( ! excessive )drawal ( oil1 is t ( a nodoid 7,fig4 #fe;,a74 ,! unduloid has c]ta9 peculi> prop]ties z reg>ds its limitations ( /ability4 ,b z to ^! we ne$ m5tion two facts only3 7#a7 t :5 ! unduloid1 :i* we produce ) our soap-bubble or our oil-globule1 consi/s ( ! figure conta9+ a complete con/riction1 x has some:at wide limits ( /ability2 b 7#b7 if x conta9 ! swoll5 portion1 !n equilibrium is limit$ to ! condition t ! figure consi/s simply ( "o complete unduloid1 t is to say t its ends are con/itut$ by ! n>r[e/ portions1 & its middle by ! wide/ portion ( ! entire curve4 ,! !oretical pro( ( ?is latt] fact is difficult1 b if we take ! pro( = grant$1 ! fact w s]ve to ?r[ light on :at we h le>n$ reg>d+ ! /ability ( ! cyl9d]4 ,=1 :5 we rememb] t ! m]idional section ( our unduloid is g5]at$ by ! roll+ ( an ellipse ^u a /raight l9e 9 its own plane1 we %all easily see t ! l5g? ( ! entire unduloid is equal to ! circumf]5ce ( ! g5]at+ ellipse4 ,z ! unduloid becomes less & less s9u\s 9 outl9e1 x gradually approa*es1 & 9 "t rea*es1 ! =m ( a cyl9d]2 & correspond+ly1 ! ellipse :i* g5]at$ x has its foci m & m approximat$ until x passes into a circle4 ,! cyl9d] ( a l5g? equal to ! circumf]5ce ( its g5]at+ circle is !re=e precisely homolog\s to an unduloid ^: l5g? is equal to ! circumf]5ce ( its g5]at+ ellipse2 & ?is is j :at we recognise z con/itut+ "o complete segm5t ( ! unduloid4 ,:ile ! figures ( equilibrium :i* are at ! same "t surfaces ( revolution are only six 9 numb]1 !re is an inf9ite #bcj numb] ( figures ( equilibrium1 t is to say ( surfaces ( con/ant mean curvature1 :i* are n surfaces ( revolution2 & x c be %ewn ma!matically t any giv5 cont\r c be occupi$ by a f9ite portion ( "s "o su* surface1 9 /able equilibrium4 ,! exp]im5tal v]ification ( ?is !orem lies 9 ! simple fact 7already not$7 t h[ev] we may b5d a wire into a clos$ curve1 plane or n plane1 we may always1 "u appropriate precautions1 fill ! entire area ) an unbrok5 film4 ,( ! regul> figures ( equilibrium1 t is to say surfaces ( con/ant mean curvature1 ap>t f ! surfaces ( revolution :i* we h discuss$1 ! helicoid spiral is ! mo/ int]e/+ to ! biologi/4 ,?is is a helicoid g5]at$ by a /raight l9e p]p5dicul> to an axis1 ab\t :i* x turns at a uni=m rate :ile at ! same "t x slides1 also uni=mly1 along ?is same axis4 ,at any po9t 9 ?is surface1 ! curvatures are equal & ( opposite sign1 & ! sum ( ! curvatures is accord+ly nil4 ,among :at are call$ 8rul$ surfaces0 7:i* we may describe z surfaces capable ( be+ def9$ by a sy/em ( /ret*$ /r+s71 ! plane & ! helicoid are ! only two ^: mean curvature is null1 :ile ! cyl9d] is ! only "o ^: curvature is f9ite & con/ant4 ,z ?is simple/ ( helicoids corresponds1 9 ?ree dim5sions1 to :at 9 two dim5sions is m]ely a plane 7! latt] be+ g5]at$ by ! rotation ( a /raight l9e ab\t an axis )\t ! sup]add$ glid+ motion :i* g5]ates ! helicoid71 s !re are o!r & mu* m complicat$ helicoids :i* correspond to ! sph]e1 ! unduloid & ! re/ ( our figures ( revolution1 ! g5]at+ planes ( ^! latt] be+ suppos$ to w9d spirally ab\t an axis4 ,9 ! case ( ! cyl9d] x is obvi\s t ! result+ figure is indi/+ui%able f ! cyl9d] itself4 ,9 ! case ( ! unduloid we obta9 a groov$ spiral1 su* z we may meet ) 9 nature 7= in/ance 9 ,spiro*tes1 ,bodo gracilis1 etc471 & :i* accord+ly x is ( int]e/ to u to be able to recognise z a surface ( m9imal area or con/ant curvature4 ,! =ego+ consid]ations deal ) a small "p only ( ! !ory ( surface t5sion1 or ( capill>ity3 ) t "p1 namely1 :i* relates to ! =ms ( surface :i* are #bca capable ( subsi/+ 9 equilibrium "u ! action ( t =ce1 ei!r ( itself or subject to c]ta9 simple con/ra9ts4 ,& z yet we h limit$ ourselves to ! case ( a s+le surface1 or ( a s+le drop or bubble1 leav+ to ano!r occasion a discussion ( ! =ms assum$ :5 su* drops or vesicles meet & comb9e toge!r4 ,9 %ort1 :at we h said may help u to und]/& ! =m ( a cell1--consid]$1 z ) c]ta9 limitations we may legitimately consid] x1 z a liquid drop or liquid vesicle2 ! con=mation ( a tissue or cell-aggregate mu/ be dealt ) 9 ! light ( ano!r s]ies ( !oretical consid]ations4 ,9 bo? cases1 we c d no m ?an t\* ^u ! fr+e ( a l>ge & difficult subject4 ,!re are _m =ms capable ( realisation "u surface t5sion1 & _m ( !m d\btless to be recognis$ among organisms1 :i* we _c t\* ^u 9 ?is elem5t>y acc\nt4 ,! subject is a v g5]al "o2 x is1 9 its ess5ce1 m ma!matical ?an physical2 x is "p ( ! ma!matics ( surfaces1 & only comes into relation ) surface t5sion1 because ?is physical ph5om5on illu/rates & exemplifies1 9 a concrete way1 mo/ ( ! simple & symmetrical conditions ) :i* ! g5]al ma!matical !ory is capable ( deal+4 ,& be=e we pass to illu/rate by biological examples ! physical ph5om5a :i* we h describ$1 we mu/ be c>eful to rememb] t ! physical conditions :i* we h hi!rto presuppos$ w nev] be :olly realis$ 9 ! organic cell4 ,its sub/ance w nev] be a p]fect fluid1 & h5ce equilibrium w be m or less sl[ly rea*$2 its surface w seldom be p]fectly homog5e\s1 & !re=e equilibrium w 79 ! fluid condition7 seldom be p]fectly atta9$2 x w v (t51 or g5]ally1 be ! seat ( o!r =ces1 symmetrical or unsymmetrical2 & all ^! causes w m or less p]turb ! effects ( surface t5sion act+ by itself4 ,b we %all f9d t1 on ! :ole1 ^! effects ( surface t5sion ?\gh modifi$ are n oblit]at$ nor ev5 mask$2 & accord+ly ! ph5om5a to :i* ,i h devot$ ! =ego+ pages w be f\nd manife/ly recurr+ & repeat+ !mselves among ! ph5om5a ( ! organic cell4 ,9 a spid]'s web we f9d exemplifi$ sev]al ( ! pr9ciples #bcb ( surface t5sion :i* we h n[ expla9$4 ,! ?read is =m$ out ( ! fluid secretion ( a gl&1 & issues f ! body z a semi-fluid cyl9d]1 t is to say 9 ! =m ( a surface ( equilibrium1 ! =ce ( expulsion giv+ x its elongation & t ( surface t5sion giv+ x its circul> section4 ,x is prev5t$1 by almo/ imm$iate solidification on exposure to ! air1 f break+ up into sep>ate drops or sph]ules1 z x w\ld o!rwise t5d to d z soon z ! l5g? ( ! cyl9d] _h pass$ its limit ( /ability4 ,b x is o!rwise ) ! /icky secretion :i*1 com+ f ano!r gl&1 is simultane\sly p\r$ ov] ! issu+ ?read :5 x is to =m ! spiral portion ( ! web4 ,?is latt] secretion is m fluid ?an ! fir/1 & reta9s its fluidity = a v mu* long] "t1 f9ally dry+ up aft] sev]al h\rs4 ,by capill>ity x 8wets0 ! ?read1 spread+ itself ov] x 9 an ev5 film1 :i* film is n[ itself a cyl9d]4 ,b ?is liquid cyl9d] has its limit ( /ability :5 its l5g? equals its own circumf]5ce1 & !re=e j at ! po9ts s def9$ x t5ds to disrupt into sep>ate segm5ts3 or r1 9 ! actual case1 at po9ts some:at m di/ant1 ow+ to ! imp]fect fluidity ( ! visc\s film1 & /ill m to ! frictional drag ^u x ( ! inn] solid cyl9d]1 or ?read1 ) :i* x is 9 contact4 ,! cyl9d] disrupts 9 ! usual mann]1 pass+ fir/ into ! wavy outl9e ( an unduloid1 ^: swoll5 portions swell m & m till ! contract$ p>ts break asund]1 & we arrive at a s]ies ( sph]ical drops or beads1 ( equal size1 /rung at equal int]vals along ! ?read4 ,if we try to spread v>ni% ov] a ?9 /ret*$ wire1 we produce automatically ! same id5tical result#bhh2 unless our v>ni% be su* z to dry almo/ in/antane\sly1 x ga!rs into beads1 & d :at we c1 we fail to spread x smoo?4 ,x foll[s t1 accord+ to ! viscidity & dry+ p[] ( ! v>ni%1 ! process may /op or seem to /op at any po9t %ort ( ! =mation ( ! p]fect sph]ules2 x is q possible1 !re=e1 t z our f9al /age we may only obta9 half-=m$ beads1 or ! wavy outl9e ( an unduloid4 ,! =mation ( ! beads may be facilitat$ or ha/5$ by j]k+ ! /ret*$ ?read1 z ! spid] actually does3 ! #bcc effect ( ! j]k be+ to di/urb & de/roy ! un/able equilibrium ( ! viscid cyl9d]#bhi4 ,ano!r v curi\s ph5om5on "h pres5ts itself4 ,9 ,plateau's exp]im5tal sep>ation ( a cyl9d] ( oil into two sph]ical portions1 x 0 notic$ t1 :5 contact 0 ne>ly brok51 t is to say :5 ! n>r[ neck ( ! unduloid _h become v ?91 ! two sph]ical bullae1 in/ead ( absorb+ ! fluid out ( ! n>r[ neck into !mselves z !y _h done ) ! prec$+ portion1 drew out ?is small rema9+ "p ( ! liquid into a ?9 ?read z !y complet$ _! sph]ical =m & consequ5tly rec$$ f "o ano!r3 ! reason be+ t1 aft] ! ?read or 8neck0 has rea*$ a c]ta9 t5uity1 ! int]nal friction ( ! fluid prev5ts or ret>ds its rapid exit f ! little ?read to ! adjac5t sph]ule4 ,x is = ! same reason t we are able to draw a glass rod or tube1 :i* we h heat$ 9 ! middle1 into a long & uni=m cyl9d] or ?read1 by quickly sep>at+ ! two ends4 ,b 9 ! case ( ! glass rod1 ! long ?9 int]m$iate cyl9d] quickly cools & solidifies1 :ile 9 ! ord9>y sep>ation ( a liquid cyl9d] ! correspond+ int]m$iate cyl9d] rema9s liquid2 & !re=e1 l any o!r liquid cyl9d]1 x is liable to break up1 provid$ t its dim5sions exce$ ! normal limit ( /ability4 ,& its l5g? is g5]ally su* t x breaks at two po9ts1 ?us leav+ two t]m9al portions cont9u\s ) ! sph]es & becom+ conflu5t ) ^!1 & "o m$ian portion :i* resolves itself into a comp>atively t9y sph]ical drop1 midway betwe5 ! orig9al & l>g] two4 ,occasionally1 ! same process ( =mation ( a connect+ ?read repeats itself a second "t1 betwe5 ! small int]m$iate sph]ule & ! l>ge sph]es2 & 9 ?is case we obvi\sly obta9 two additional sph]ules1 /ill small] 9 size1 & ly+ "o on ei!r side ( our fir/ little "o4 ,?is :ole ph5om5on1 ( equal & regul>ly int]spac$ beads1 (t5 ) little beads regul>ly int]spac$ betwe5 ! l>g] ones1 & possibly also ev5 a ?ird s]ies ( /ill small] beads regul>ly int]calat$1 may be easily obs]v$ 9 a spid]'s web1 su* z t ( ,epeira1 v (t5 ) beautiful regul>ity1--:i* #bcd naturally1 h[ev]1 is sometimes int]rupt$ & di/urb$ ow+ to a slight want ( homog5eity 9 ! secret$ fluid2 & ! same ph5om5on is repeat$ on a gross] scale :5 ! web is bespangl$ ) dew1 & e ?read be/rung ) pe>ls innum]able4 ,to ! old] naturali/s1 ^! regul>ly arrang$ & beautifully =m$ globules on ! spid]'s web 7 a cause ( great wond] & admiration4 ,blackwall1 c\nt+ "s tw5ty globules 9 a t5? ( an in*1 calculat$ t a l>ge g>d5-spid]'s web compris$ ab\t #abj1jjj globules2 ! net 0 spun & f9i%$ 9 ab\t =ty m9utes1 & ,blackwall 0 evid5tly fill$ ) a/oni%m5t at ! skill & quickness ) :i* ! spid] manufactur$ ^! little beads4 ,& no wond]1 = accord+ to ! above e/imate !y _h to be made at ! rate ( ab\t #ej p] second#bij4 ,illu/ration3 ,fig4 #fi4 ,hair ( ,trianea1 9 glyc]9e4 7,aft] ,b]?old47 ,! little delicate beads :i* /ud ! long ?9 pseudopodia ( a =am9if]1 su* z ,gromia1 or :i* 9 l mann] appe> ^u ! cyl9drical film ( protoplasm :i* cov]s ! long radiat+ spicules ( ,globig]9a1 repres5t an id5tical ph5om5on4 ,inde$ !re are _m cases1 9 :i* we may /udy 9 a protoplasmic filam5t ! :ole process ( =mation ( su* beads4 ,if we squeeze out on to a slide ! viscid cont5ts ( a mi/letoe b]ry1 ! long /icky ?reads into :i* ! sub/ance runs %ew ! :ole ph5om5on p>ticul>ly well4 ,ano!r way to demon/rate x 0 notic$ _m ye>s ago by ,h(mei/] & aft]w>ds expla9$ by ,b]?old4 ,! hairs ( c]ta9 wat]-plants1 su* z ,hydro*>is or ,trianea1 con/itute v long cyl9drical cells1 ! protoplasm be+ support$1 & ma9ta9$ 9 equilibrium by its contact ) ! cell-wall4 ,b if we imm]se ! filam5t 9 "s d5se fluid1 a little sug>-solution = in/ance1 or dilute glyc]9e1 ! cell-sap t5ds to diffuse outw>ds1 ! protoplasm p>ts company ) its surr\nd+ & support+ wall1 #bce & lies free z a protoplasmic cyl9d] 9 ! int]ior ( ! cell4 ,!reupon x imm$iately %ews signs ( in/ability1 & comm5ces to disrupt4 ,x t5ds to ga!r into sph]es1 :i* h[ev]1 z 9 our illu/ration1 may be prev5t$ by _! n>r[ qu>t]s f assum+ ! complete sph]ical =m2 & 9 betwe5 ^! sph]es1 we h m or less regul>ly alt]nate ones1 ( small] size#bia4 ,simil>1 b less regul>1 beads or droplets may be caus$ to appe>1 "u /imulation by an alt]nat+ curr5t1 9 ! protoplasmic ?reads )9 ! liv+ cells ( ! hairs ( ,tradescantia4 ,! explanation usually giv5 is1 t ! viscosity ( ! protoplasm is r$uc$1 or its fluidity increas$2 b an increase ( ! surface t5sion w\ld seem a m likely reason#bib4 ,illu/ration3 ,fig4 #gj4 ,phases ( a ,spla%4 7,f ,wor?+ton47 ,we may take note "h ( a rem>kable s]ies ( ph5om5a1 :i*1 ?\gh !y seem at fir/ sight to be ( a v diff]5t ord]1 are closely relat$ to ! ph5om5a :i* att5d & :i* br+ ab\t ! break+-up ( a liquid cyl9d] or ?read4 ,9 "s ( ,mr ,wor?+ton's mo/ beautiful exp]im5ts on #bcf spla%es1 x 0 f\nd t ! fall ( a r\nd pebble into wat] f a consid]able height1 caus$ ! rise ( a filmy %eet ( wat] 9 ! =m ( a cup or cyl9d]2 & ! edge ( ?is cyl9drical film t5d$ to be cut up into alt]nate lobes & not*es1 & ! prom95t lobes or 8jets0 t5d$1 9 m extreme cases1 to break (f or to break up into sph]ical beads 7,fig4 #gj7bic4 ,a precisely simil> appe>ance is se51 on a great scale1 9 ! ?9 edge ( a break+ wave3 :5 ! smoo? cyl9drical edge1 at a giv5 mom5t1 %oots out an array ( t9y jets :i* break up into ! droplets :i* con/itute 8spray0 7,fig4 #ga1 a1 b74 ,we are at once rem9d$ ( ! beautifully symmetrical not*+ on ! calycles ( _m hydroids1 :i* little cups be=e !y became /iff & rigid _h begun _! exi/5ce z liquid or semi-liquid films4 ,illu/ration3 ,fig4 #ga4 ,a break+ wave4 7,f ,wor?+ton47 ,! ph5om5on is two-fold4 ,9 ! fir/ place1 ! edge ( our tubul> or crat]-l film =ms a liquid r+ or annulus1 :i* is closely comp>able ) ! liquid ?read or cyl9d] :i* we h j be5 consid]+1 if only we conceive ! ?read to be b5t r\nd into ! r+4 ,& accord+ly1 j z ! ?read spontane\sly segm5ts1 fir/ into an unduloid1 & !n into sep>ate sph]ical drops1 s likewise w ! edge ( our annulus t5d to d4 ,?is phase ( not*+1 or bead+1 ( ! edge ( ! film is beautifully se5 9 _m ( ,wor?+ton's exp]im5ts#bid4 ,9 ! second place1 ! v fact ( ! ris+ ( ! crat] means t liquid is fl[+ up f bel[ t[>ds ! rim2 & ! segm5tation ( ! rim means t *annels ( easi] fl[ are #bcg creat$1 along :i* ! liquid is l$1 or is driv51 into ! protub]ances3 & ^! are ?us exagg]at$ into ! jets or arms :i* are sometimes s conspicu\s at ! edge ( ! crat]4 ,9 %ort1 any film or film-l cup1 fluid or semi-fluid 9 its consi/5cy1 w1 l ! /raight liquid cyl9d]1 be un/able3 & its in/ability w manife/ itself 7among o!r ways7 9 a t5d5cy to segm5tation or not*+ ( ! edge2 & j su* a p]iph]al not*+ is a conspicu\s feature ( _m m9ute organic cup-l /ructures4 ,9 ! case ( ! hydroid calycle 7,fig4 #gb71 we are l$ to ! conclusion t ! two common & conspicu\s features ( not*+ or ind5tation ( ! cup1 & ( con/riction or annulation ( ! long cyl9drical /em1 are ph5om5a ( ! same ord] & are due to surface-t5sion 9 bo? cases alike4 ,illu/ration3 ,fig4 #gb4 ,calycles ( ,campanul>ian zoophytes4 7,a7 ,c4 integra2 7,b7 ,c4 gro5l&ica2 7,c7 ,c4 bisp9osa2 7,d7 ,c4 r>id5tata4 ,ano!r ph5om5on display$ 9 ! same exp]im5ts is ! =mation ( a rope-l or cord-l ?ick5+ ( ! edge ( ! annulus4 ,?is is due to ! m or less sudd5 *eck+ at ! rim ( ! fl[ ( liquid ris+ f bel[3 & a simil> p]iph]al ?ick5+ is frequ5tly se51 n only 9 "s ( our hydroid cups1 b 9 _m ,vorticellas 7cf4 ,fig4 #ge71 & o!r organic cup-l con=mations4 ,a p]usal ( ,mr ,wor?+ton's book w soon sugge/ t ^! are n ! only manife/ations ( surface-t5sion 9 connection ) spla%es :i* pres5t curi\s resemblances & analogies to ph5om5a ( organic =m4 ,! ph5om5a ( an ord9>y liquid spla% are s swiftly #bch transitory t _! /udy is only r5d]$ possible by 8in/antane\s0 photography3 b ?is excessive rapidity is n an ess5tial "p ( ! ph5om5on4 ,= in/ance1 we c repeat & demon/rate _m ( ! simpl] ph5om5a1 9 a p]man5t or quasi-p]man5t =m1 by spla%+ wat] on to a surface ( dry s&1 or by fir+ a bullet into a s(t metal t>get4 ,!re is no?+1 !n1 to prev5t a sl[ & la/+ manife/ation1 9 a visc\s m$ium su* z a protoplasmic organism1 ( ph5om5a :i* appe> & disappe> ) prodigi\s rapidity 9 a m mobile liquid4 ,nor is !re any?+ peculi> 9 ! 8spla%0 itself2 x is simply a conv5i5t me?od ( sett+ up c]ta9 motions or curr5ts1 & produc+ c]ta9 surface-=ms1 9 a liquid m$ium1--or ev5 9 su* an extremely imp]fect fluid z is repres5t$ 79 ano!r s]ies ( exp]im5ts7 by a b$ ( s&4 ,accord+ly1 we h a l>ge range ( possible conditions "u :i* ! organism might conceivably display configurations analog\s to1 or id5tical )1 ^? :i* ,mr ,wor?+ton has %ewn u h[ to exhibit by "o p>ticul> exp]im5tal me?od4 ,to "o :o has wat*$ ! pott] at 8 :eel1 x is pla9 t ! pott]'s ?umb1 l ! glass-bl[]'s bla/ ( air1 dep5ds = its efficacy ^u ! physical prop]ties ( ! m$ium on :i* x op]ates1 :i* = ! "t be+ is ess5tially a fluid4 ,! cup & ! sauc]1 l ! tube & ! bulb1 display 79 _! simple & primitive =ms7 beautiful surfaces ( equilibrium z manife/$ "u c]ta9 limit+ conditions4 ,!y are nei!r m nor less ?an glorifi$ 8spla%es10 =m$ sl[ly1 "u conditions ( re/ra9t :i* enhance or reveal _! ma!matical symmetry4 ,we h se51 & we %all see aga9 be=e we are done1 t ! art ( ! glass-bl[] is full ( lessons = ! naturali/ z also = ! physici/3 illu/rat+ z x does ! developm5t ( a ho/ ( ma!matical configurations & organic con=mations :i* dep5d ess5tially on ! e/abli%m5t ( a con/ant & uni=m pressure )9 a clos$ ela/ic %ell or fluid envelope4 ,9 l mann] ! pott]'s art illu/rates ! some:at obscur] & m complex problems 7sc>cely less frequ5t 9 biology7 ( a figure ( equilibrium :i* is an op5 surface1 or solid1 ( revolution4 ,x is cle>1 at ! same "t1 t ! two s]ies ( problems are closely ak92 = ! #bci glass-bl[] c make mo/ ?+s t ! pott] makes1 by cutt+ (f portions ( 8 holl[ w>e4 ,& besides1 :5 ?is fails1 & ! glass-bl[]1 ceas+ to bl[1 beg9s to use 8 rod to trim ! sides or turn ! edges ( w9eglass or ( beak]1 he is m]ely borr[+ a trick f ! craft ( ! pott]4 ,x w\ld be v5turesome inde$ to ext5d our comp>ison ) ^! liquid surface-t5sion ph5om5a f ! cup or calycle ( ! hydrozoon to ! little hydroid polype )93 & yet ,i feel conv9c$ t !re is some?+ to be le>n$ by su* a comp>ison1 ?\gh n )\t mu* detail$ consid]ation & ma!matical /udy ( ! surfaces conc]n$4 ,! cyl9drical body ( ! t9y polype1 ! jet-l r[ ( t5tacles1 ! bead$ annulations :i* ^! t5tacles exhibit1 ! web-l film :i* sometimes 7:5 !y /& a little way ap>t7 conjo9s _! bases1 ! ?9 annul> film ( tissue :i* surr\nds ! little organism's m\?1 & ! mann] 9 :i* ?is annul> 8p]i/ome0 contracts#bie1 l a %r9k+ soap-bubble1 to close ! ap]ture1 are e "o ( !m features to :i* we may f9d a s+ul> & /rik+ p>allel 9 ! surface-t5sion ph5om5a :i* ,mr ,wor?+ton has illu/rat$ & demon/rat$ 9 ! case ( ! spla%4 ,"h h[ev]1 we may freely confess t we are = ! pres5t on ! unc]ta9 gr\nd ( sugge/ion & conjecture2 & s mu/ we rema91 9 reg>d to _m o!r simple & symmetrical organic =ms1 until _! =m & dynamical /ability %all h be5 inve/igat$ by ! ma!matician3 9 o!r words1 until ! ma!maticians %all h become p]suad$ t !re is an imm5se unwork$ field :]e9 !y may lab\r1 9 ! detail$ /udy ( organic =m4 ,accord+ to ,plateau1 ! viscidity ( ! liquid1 :ile x helps to ret>d ! break+ up ( ! cyl9d] & s increases ! l5g? ( ! segm5ts beyond t :i* !ory dem&s1 has nev]!less less influ5ce 9 ?is direction ?an we might h expect$4 ,on ! o!r h&1 any ext]nal support or adhesion1 su* z contact ) a solid body1 w be equival5t to a r$uction ( surface-t5sion & s w v greatly increase ! #bdj /ability ( our cyl9d]4 ,x is = ?is reason t ! m]cury 9 our !rmomet] tubes does n z a rule sep>ate into drops1 ?\gh x occasionally does s1 mu* to our inconv5i5ce4 ,& aga9 x is = ?is reason t ! protoplasm 9 a long & gr[+ tubul> or cyl9drical cell does n necess>ily divide into sep>ate cells & int]nodes1 until ! l5g? ( ^! f> exce$s ! !oretic limits4 ,( c\rse h[ev] & :5ev] x does s1 we mu/1 )\t ev] exclud+ ! ag5cy ( surface t5sion1 rememb] t !re may be o!r =ces affect+ ! latt]1 & accel]at+ or ret>d+ t manife/ation ( surface t5sion by :i* ! cell is actually r\nd$ (f & divid$4 ,9 mo/ liquids1 ,plateau ass]ts t1 on ! av]age1 ! influ5ce ( viscosity is su* z to cause ! cyl9d] to segm5t :5 its l5g? is ab\t f\r times1 or at mo/ f f\r to six times t ( its diamet]3 in/ead ( a fraction ov] ?ree times z1 9 a p]fect fluid1 !ory w\ld dem&4 ,if we take x at f\r times1 x may !n be %ewn t ! result+ sph]es w\ld h a diamet] ( ab\t #ah times1 & _! di/ance ap>t w\ld be equal to ab\t #bb times ! diamet] ( ! orig9al cyl9d]4 ,! calculation is n difficult :i* w\ld %ew h[ ^! numb]s are alt]$ 9 ! case ( a cyl9d] =m$ ar\nd a solid core1 z 9 ! case ( ! spid]'s web4 ,plateau has also made ! int]e/+ obs]vation t ! "t tak5 9 ! process ( division ( ! cyl9d] is directly proportional to ! diamet] ( ! cyl9d]1 :ile v>y+ consid]ably ) ! nature ( ! liquid4 ,?is "q1 ( ! "t occupi$ 9 ! division ( a cell or filam5t1 9 relation to ! dim5sions ( ! latt]1 has n s f> z ,i "k be5 enquir$ into by biologi/s4 ,f ! simple fact t ! sph]e is ( all surfaces t ^: surface-area = a giv5 volume is an absolute m9imum1 we h already se5 x to be pla9 t x is ! "o & only figure ( equilibrium :i* w be assum$ "u surface-t5sion by a drop or vesicle1 :5 no o!r di/urb+ factors are pres5t4 ,"o ( ! mo/ important ( ^! di/urb+ factors w be introduc$1 9 ! =m ( complicat$ t5sions & pressures1 :5 "o drop is 9 contact ) ano!r drop & :5 a sy/em ( int]m$iate films or p>tition walls is develop$ betwe5 !m4 #bda ,?is subject we %all discuss lat]1 9 connection ) cell-aggregates or tissues1 & we %all f9d t fur!r !oretical consid]ations are ne$$ z a prelim9>y to any su* enquiry4 ,mean:ile let u consid] a few cases ( ! =ms ( cells1 ei!r solit>y1 or 9 su* simple aggregates t _! individual =m is little di/urb$ !reby4 ,let u cle>ly und]/& t ! cases we are ab\t to consid] are ^? cases :]e ! p]fect symmetry ( ! sph]e is replac$ by ano!r symmetry1 less complete1 su* z t ( an ellipsoidal or cyl9drical cell4 ,! cases ( asymmetrical de=mation or displacem5t1 su* z is illu/rat$ 9 ! production ( a bud or ! developm5t ( a lat]al bran*1 are mu* simpl]4 ,= "h we ne$ only assume a slight & localis$ v>iation ( surface-t5sion1 su* z may be br\ght ab\t 9 v>i\s ways ?r\gh ! het]og5e\s *emi/ry ( ! cell2 to ?is po9t we %all return 9 our *apt] on ,adsorption4 ,b ! diffus$ & grad$ asymmetry ( ! sy/em1 :i* br+s ab\t = in/ance ! ellipsoidal %ape ( a yea/-cell1 is ano!r matt]4 ,if ! sph]e be ! "o surface ( complete symmetry & !re=e ( indep5d5t equilibrium1 x foll[s t 9 e cell :i* is o!rwise con=m$ !re mu/ be "s def9ite =ce to cause its dep>ture f sph]icity2 & if ?is cause be ! v simple & obvi\s "o ( ! resi/ance (f]$ by a solidifi$ envelope1 su* z an egg-%ell or firm cell-wall1 we mu/ /ill seek = ! de=m+ =ce :i* 0 9 action to br+ ab\t ! giv5 %ape1 prior to ! assumption ( rigidity4 ,su* a cause may be ei!r ext]nal to1 or may lie )91 ! cell itself4 ,on ! "o h& x may be due to ext]nal pressure or to "s =m ( me*anical re/ra9t3 z x is 9 all our exp]im5ts 9 :i* we submit our bubble to ! p>tial re/ra9t ( discs or r+s or m complicat$ cages ( wire2 & on ! o!r h& x may be due to intr9sic causes1 :i* mu/ come "u ! head ei!r ( diff]5ces ( int]nal pressure1 or ( lack ( homog5eity or isotropy 9 ! surface itself#bif4 #bdb ,our full =mula ( equilibrium1 or equation to an ela/ic surface1 is ,p pe 7,t_/,r ,t_/,r71 :]e ,p is ! int]nal pressure1 pe any extrane\s pressure normal to ! surface1 ,r1 ,r ! radii ( curvature at a po9t1 & ,t1 ,t1 ! correspond+ t5sions1 normal to "o ano!r1 ( ! envelope4 ,n[ 9 any giv5 =m :i* we are seek+ to acc\nt =1 ,r1 ,r are kn[n quantities2 b all ! o!r factors ( ! equation are unkn[n & subject to enquiry4 ,& someh[ or o!r1 by ?is =mula1 we mu/ acc\nt = ! =m ( any solit>y cell :atsoev] 7provid$ always t x be n =m$ by successive /ages ( solidification71 ! cyl9drical cell ( ,spirogyra1 ! ellipsoidal yea/-cell1 or 7z we %all see 9 ano!r *apt]7 ! %ape ( ! egg ( any bird4 ,9 us+ ?is =mula hi!rto1 we h tak5 x 9 a simplifi$ =m1 t is to say we h made sev]al limit+ assumptions4 ,we h assum$ t ,p 0 simply ! uni=m hydro/atic pressure1 equal 9 all directions1 ( a body ( liquid2 we h assum$ t ! t5sion ,t 0 simply due to surface-t5sion 9 a homog5e\s liquid film1 & 0 !re=e equal 9 all directions1 s t ,t ,t2 & we h only dealt ) surfaces1 or p>ts ( a surface1 :]e extrane\s pressure1 pn1 0 non-exi/5t4 ,n[ 9 ! case ( a bird's egg1 ! ext]nal pressure pn1 t is to say ! pressure ex]cis$ by ! walls ( ! oviduct1 w be f\nd to be a v important factor2 b 9 ! case ( ! yea/-cell or ! ,spirogyra1 :olly imm]s$ 9 wat]1 no su* ext]nal pressure comes into play4 ,we are accord+ly left1 9 su* cases z ^! la/1 ) two hypo!ses1 namely t ! dep>ture f a sph]ical =m is due to inequalities 9 ! int]nal pressure ,p1 or else to inequalities 9 ! t5sion ,t1 t is to say to a diff]5ce betwe5 ,t & ,t4 ,9 o!r words1 x is !oretically possible t ! oval =m ( a yea/-cell is due to a great] int]nal pressure1 a great] 8t5d5cy to gr[10 9 ! direction ( ! long] axis ( ! ellipse1 or alt]natively1 t ) equal & symmetrical t5d5cies to gr[? !re is associat$ a diff]5ce ( ext]nal resi/ance 9 #bdc respect ( ! t5sion ( ! cell-wall4 ,n[ ! =m] hypo!sis is n impossible2 ! protoplasm is f> f be+ a p]fect fluid2 x is ! seat ( v>i\s int]nal =ces1 sometimes manife/ly pol>2 & accord+ly x is q possible t ! int]nal =ces1 osmotic & o!r1 :i* lead to an increase ( ! cont5t ( ! cell & are manife/$ 9 pressure outw>dly direct$ ^u its wall may be unsymmetrical1 & su* z to lead to a de=mation ( :at w\ld o!rwise be a simple sph]e4 ,b :ile ?is hypo!sis is n impossible1 x is n v easy ( acceptance4 ,! protoplasm1 ?\gh n a p]fect fluid1 has yet on ! :ole ! prop]ties ( a fluid2 )9 ! small compass ( ! cell !re is little room = ! developm5t ( unsymmetrical pressures2 &1 9 su* a case z ,spirogyra1 :]e a l>ge "p ( ! cavity is fill$ by a fluid & wat]y cell-sap1 ! conditions are /ill m obvi\sly ^? "u :i* a uni=m hydro/atic pressure is to be expect$4 ,b 9 v>iations ( ,t1 t is to say ( ! specific surface-t5sion p] unit area1 we h an ample field = all ! v>i\s de=mations ) :i* we %all h to deal4 ,our condition n[ is1 t 7,t_/,r ,t_/,r7 a con/ant2 b x no long] foll[s1 ?\gh x may /ill (t5 be ! case1 t ?is w repres5t a surface ( absolute m9imal area4 ,z soon z ,t & ,t become unequal1 x is obvi\s t we are no long] deal+ ) a p]fectly liquid surface film2 b its dep>ture f a p]fect fluidity may be ( all degrees1 f t ( a slight non-isotropic viscosity to ! /ate ( a firm ela/ic membrane#big4 ,& x matt]s little :e!r ?is viscosity or semi-rigidity be manife/$ 9 ! self-same lay] :i* is /ill a "p ( ! protoplasm ( ! cell1 or 9 a lay] :i* is completely diff]5tiat$ into a di/9ct & sep>ate membrane4 ,z soon z1 by secretion or 8adsorption10 ! molecul> con/itution ( ! surface lay] is alt]$1 x is cle>ly conceivable t ! alt]ation1 or ! second>y *emical *anges :i* foll[ x1 may be su* z to produce an anisotropy1 & to r5d] ! molecul> =ces less capable 9 "o direction ?an ano!r ( ex]t+ t contractile =ce by :i* !y are /riv+ to r$uce to an absolute m9imum ! #bdd surface area ( ! cell4 ,a slight inequality 9 two opposite directions w produce ! ellipsoid cell1 & a v great inequality w give rise to ! cyl9drical cell#bih4 ,i take x !re=e1 t ! cyl9drical cell ( ,spirogyra1 or any o!r cyl9drical cell :i* gr[s 9 fre$om f any manife/ ext]nal re/ra9t1 has assum$ t p>ticul> =m simply by reason ( ! molecul> con/itution ( its develop+ surface-membrane2 & t ?is molecul> con/itution 0 anisotrop\s1 9 su* a way z to r5d] ext5sion easi] 9 "o direction ?an ano!r4 ,su* a lack ( homog5eity or ( isotropy1 9 ! cell-wall is (t5 r5d]$ visible1 especially 9 plant-cells1 9 v>i\s ways1 9 ! =m ( conc5tric lamellae1 annul> & spiral /riations1 & ! l4 ,b ?is ph5om5on1 :ile x br+s ab\t a c]ta9 dep>ture f complete symmetry1 is /ill compatible )1 & coexi/5t )1 _m ( ! ph5om5a :i* we h se5 to be associat$ ) surface-t5sion4 ,! symmetry ( t5sions /ill leaves ! cell a solid ( revolution1 & its surface is /ill a surface ( equilibrium4 ,! fluid pressure )9 ! cyl9d] /ill causes ! film or membrane :i* caps its ends to be ( a sph]ical =m4 ,& 9 ! "y cell1 :]e ! surface pellicle is abs5t or b little diff]5tiat$1 z = in/ance 9 ! ogonium ( ,a*lya1 or 9 ! "y zygospore ( ,spirogyra1 we always see ! t5d5cy ( ! entire /ructure t[>ds a sph]ical =m reass]t+ itself3 unless1 z 9 ! latt] case1 x be ov]come by direct compression )9 ! cyl9drical "m-cell4 ,moreov]1 9 ^? cases :]e ! adult filam5t consi/s ( cyl9drical cells1 we see t ! "y1 g]m9at+ spore1 at fir/ sph]ical1 v soon assumes ) gr[? an elliptical or ovoid =m3 ! direct result ( an incipi5t anisotropy ( its envelope1 :i* :5 m develop$ w conv]t ! ovoid into a cyl9d]4 ,we may also notice t a truly cyl9drical cell is comp>atively r>e2 = 9 mo/ cases1 :at we call a cyl9drical cell %ews a di/9ct bulg+ ( its sides2 x is n truly a cyl9d]1 b a portion ( a sph]oid or ellipsoid4 #bde ,unicellul> organisms 9 g5]al1 includ+ ! protozoa1 ! unicellul> cryptogams1 ! v>i\s bact]ia1 & ! free1 isolat$ cells1 spores1 ova1 etc4 ( high] organisms1 are ref]able = ! mo/ "p to a v small numb] ( typical =ms2 b besides a c]ta9 numb] ( o!rs :i* may be s ref]able1 ?\gh obscurely1 !re are obvi\sly _m o!rs 9 :i* ei!r no symmetry is to be recogniz$1 or 9 :i* ! =m is cle>ly n "o ( equilibrium4 ,among ^! latt] we h ,amoeba itself1 & all mann] ( amoeboid organisms1 & also _m curi\sly %ap$ cells1 su* z ! ,trypanosomes & v>i\s o!r ab]rant ,infusoria4 ,we %all return to ! consid]ation ( ^!2 b 9 ! mean:ile x w suffice to say t1 z _! surfaces are n equilibrium-surfaces1 s nei!r are ! liv+ cells !mselves 9 any /able equilibrium4 ,on ! contr>y1 !y are 9 cont9ual flux & movem5t1 ea* portion ( ! surface con/antly *ang+ its =m1 & pass+ f "o phase to ano!r ( an equilibrium :i* is nev] /able = m ?an a mom5t4 ,! =m] class1 :i* re/ 9 /able equilibrium1 mu/ fall 7z we h se57 into two classes1--^? ^: equilibrium arises f liquid surface-t5sion alone1 & ^? 9 ^: con=mation "s o!r pressure or re/ra9t has be5 sup]impos$ ^u ord9>y surface-t5sion4 ,to ! fact t ^! little organisms belong to an ord] ( magnitude 9 :i* =m is ma9ly1 if n :olly1 condition$ & controll$ by molecul> =ces1 is due ! limit$ range ( =ms :i* !y actually exhibit4 ,^! =ms v>y accord+ to v>y+ physical conditions4 ,sometimes !y d s 9 s regul> & ord]ly a way t we in/9ctively expla9 !m m]ely z 8phases ( a life-hi/ory10 & leave physical prop]ties & physical causation alone3 b _m ( _! v>iations ( =m we treat z exceptional1 abnormal1 decad5t or morbid1 & are apt to pass ^! ov] 9 neglect1 :ile we give our att5tion to :at we suppose to be ! typical or 8*>act]i/ic0 =m or attitude4 ,9 ! case ( ! smalle/ organisms1 ! bact]ia1 micrococci1 & s =?1 ! range ( =m is especially limit$1 ow+ to _! m9ut5ess1 ! p[]ful pressure :i* _! highly curv$ surfaces ex]t1 & ! comp>atively homog5e\s nature ( _! sub/ance4 ,b )9 _! n>r[ range ( possible div]sity #bdf ^! m9ute organisms are protean 9 _! *anges ( =m4 ,a c]ta9 species w n only *ange its %ape f /age to /age ( its little 8cycle0 ( life2 b x w be rem>kably diff]5t 9 outw>d =m accord+ to ! circum/ances "u :i* we f9d x1 or ! hi/ological treatm5t to :i* we submit x4 ,h5ce ! pa?ological /ud5t1 comm5c+ ! /udy ( bact]iology1 is e>ly w>n$ to pay little he$ to diff]5ces ( =m1 = purposes ( recognition or specific id5tification4 ,:atev] gr\nds we may h = attribut+ to ^! organisms a p]man5t or /able specific id5tity 7aft] ! fa%ion ( ! high] plants & animals71 we c seldom safely d s on ! gr\nd ( def9ite & always recognisable =m3 we may (t5 be incl9$1 9 %ort1 to ascribe to !m a physiological 7sometimes a 8pa?og5ic071 r ?an a morphological specificity4 ,illu/ration3 ,fig4 #gc4 ,a flagellate 8monad10 ,di/igma proteus1 ,ehr4 7,aft] ,saville ,k5t47 ,illu/ration3 ,fig4 #gd4 ,noctiluca mili>is4 ,among ! ,infusoria1 we h a small numb] ( =ms ^: symmetry is di/9ctly sph]ical1 = in/ance among ! small flagellate monads2 b ev5 ^! are seldom actually sph]ical except :5 we see !m 9 a non-flagellate & m or less ency/$ or 8re/+0 /age4 ,9 ?is condition1 x ne$ h>dly be rem>k$ t ! sph]ical =m is common & g5]al among a great v>iety ( unicellul> organisms4 ,:5 our little monad developes a flagellum1 t is 9 itself an indication ( 8pol>ity0 or symmetrical non-homog5eity ( ! cell2 & accord+ly1 we #bdg usually see signs ( an unequal t5sion ( ! membrane 9 ! neighb\rhood ( ! base ( ! flagellum4 ,"h ! t5sion is usually less ?an else:]e1 & ! radius ( curvature is accord+ly less3 9 o!r words t end ( ! cell is drawn out to a tap]+ po9t 7,fig4 #gc74 ,b sometimes x is ! o!r way1 z 9 ,noctiluca1 :]e ! l>ge flagellum spr+s f a depression 9 ! o!rwise uni=mly r\nd$ cell4 ,9 ?is case ! explanation seems to lie 9 ! _m /r&s ( radiat+ protoplasm :i* conv]ge ^u ?is po9t1 & may be suppos$ to keep x relatively fix$ by _! viscosity1 :ile ! re/ ( ! cell-surface is free to exp& 7,fig4 #gd74 ,illu/ration3 ,fig4 #ge4 ,v>i\s species ( ,vorticella4 7,mo/ly aft] ,saville ,k5t47 ,a v l>ge numb] ( ,infusoria repres5t unduloids1 or portions ( unduloids1 & ?is type ( surface appe>s & reappe>s 9 a great v>iety ( =ms4 ,! cups ( ! v>i\s species ( ,vorticella 7,fig4 #ge7 are no?+ 9 ! _w b a beautiful s]ies ( unduloids1 or p>tial unduloids1 9 e gradation f a =m t is all b cyl9drical to "o t is all b a p]fect sph]e4 ,^! unduloids are n completely symmetrical1 b !y are su* unduloids z develop !mselves :5 we susp5d an oil-globule betwe5 two unequal r+s1 or bl[ a soap-bubble betwe5 two unequal pipes2 =1 j z 9 ^! cases1 ! surface ( our ,vorticella bell f9ds its t]m9al supports1 on ! "o h& 9 its atta*m5t to its n>r[ /alk1 & on ! o!r 9 ! ?ick5$ r+ f :i* spr+ its circumoral cilia4 ,& "h let me say1 t a po9t or zone f :i* cilia arise w\ld seem always to h a peculi> relation to ! surr\nd+ t5sions4 ,x usually =ms a %>p sali5t1 a prom95t po9t or ridge1 z 9 our little monads ( ,fig4 #gc2 %ew+ t1 9 its =mation1 ! surface t5sion _h "h locally dim9i%$4 ,b if su* a ridge or fillet consolidate 9 ! lea/ degree1 x becomes a s\rce ( /r5g?1 & a po9t d'appui = ! adjac5t film4 ,we %all deal ) ?is po9t aga9 9 ! next *apt]4 #bdh ,illu/ration3 ,fig4 #gf4 ,v>i\s species ( ,salp+oeca4 ,illu/ration3 ,fig4 #gg4 ,v>i\s species ( ,t9t9nus1 ,d9obryon & ,codonella4 7,aft] ,saville ,k5t & o!rs47 ,illu/ration3 ,fig4 #gh4 ,vag9icola4 ,illu/ration3 ,fig4 #gi4 ,follicul9a4 ,illu/ration3 ,fig4 #hj4 ,tra*elophyllum4 7,aft] ,wreszni[ski47 ,precisely ! same s]ies ( unduloid =ms may be trac$ 9 ev5 great] v>iety among v>i\s o!r families or g5]a ( ! ,infusoria4 ,sometimes1 z 9 ,vorticella itself1 ! unduloid is se5 m]ely 9 ! cont\r ( ! s(t semifluid body ( ! liv+ animal4 ,at o!r times1 z 9 ,salp+oeca1 ,t9t9nus1 & _m o!r g5]a1 we h a di/9ct membran\s cup1 sep>ate f ! animal1 b orig9ally secret$ by1 & m\ld$ ^u1 its semifluid liv+ surface4 ,"h we h an excell5t illu/ration ( ! contra/ betwe5 ! diff]5t ways 9 :i* su* a /ructure may be reg>d$ & int]pret$4 ,! teleological explanation is t x is develop$ = ! sake ( protection1 z a domicile & %elt] = ! little organism )94 ,! me*anical explanation ( ! physici/ 7seek+ only aft] ! 8effici5t10 & n ! 8f9al0 cause71 is t x is #bdi pres5t1 & has its actual con=mation1 by reason ( c]ta9 *emico-physical conditions3 t x 0 inevitable1 "u ! giv5 conditions1 t c]ta9 con/itu5t sub/ances actually pres5t 9 ! protoplasm %\ld be aggregat$ by molecul> =ces 9 its surface lay]2 t "u ?is adsorptive process1 ! conditions cont9u+ fav\rable1 ! p>ticles %\ld accumulate & conc5trate till !y =m$ 7) ! help ( ! surr\nd+ m$ium7 a pellicle or membrane1 ?ick] or ?9n] z ! case might be2 t ?is surface pellicle or membrane 0 inevitably b\nd1 by molecul> =ces1 to become a surface ( ! lea/ possible area :i* ! circum/ances p]mitt$2 t 9 ! pres5t case1 ! symmetry & 8fre$om0 ( ! sy/em p]mitt$1 & ipso facto caus$1 ?is surface to be a surface ( revolution2 & t ( ! few surfaces ( revolution :i*1 z be+ also surfaces m9imae areae1 7 available1 ! unduloid 0 manife/ly ! "o p]mitt$1 & ipso facto caus$1 by ! dim5sions ( ! organisms & o!r circum/ances ( ! case4 ,& j z ! ?ickness or ?9ness ( ! pellicle 0 obvi\sly a subord9ate matt]1 a m]e matt] ( degree1 s we also see t ! actual outl9e ( ?is or t p>ticul> unduloid is also a v subord9ate matt]1 su* z physico-*emical v>iants ( a m9ute k9d w\ld suffice to br+ ab\t2 = betwe5 ! v>i\s unduloids :i* ! v>i\s species ( ,vorticella repres5t1 !re is no m real diff]5ce ?an t diff]5ce ( ratio or degree :i* exi/s betwe5 two circles ( diff]5t diamet]1 or two l9es ( unequal l5g?4 #bej ,9 v _m cases 7( :i* ,fig4 #hj is an example71 we h an unduloid =m exhibit$1 n by a surr\nd+ pellicle or %ell1 b by ! s(t1 protoplasmic body ( a ciliat$ organism4 ,9 su* cases ! =m is mobile1 & cont9ually *anges f "o to ano!r unduloid cont\r1 accord+ to ! movem5ts ( ! animal4 ,we h "h1 app>5tly1 to deal ) an un/able equilibrium1 & also sometimes ) ! m complicat$ problem ( 8/ream-l9es10 z 9 ! difficult problems sugge/$ by ! =m ( a fi%4 ,b ?is :ole class ( cases1 & ( problems1 we c m]ely take note ( 9 pass+1 = _! treatm5t is too h>d = u4 ,9 consid]+ su* s]ies ( =ms z ! v>i\s unduloids :i* we h j be5 reg>d+1 we are br\ght %>ply up 7z 9 ! case ( our ,bact]ia or ,micrococci7 aga9/ ! biological concept ( organic species4 ,9 ! int5se classificatory activity ( ! la/ hundr$ ye>s1 x has come ab\t t e =m :i* is app>5tly *>act]i/ic1 t is to say :i* is capable ( be+ describ$ or portray$1 & capable ( be+ recognis$ :5 met ) aga91 has be5 record$ z a species1--= we ne$ n conc]n ourselves ) ! occasional discussions1 or individual op9ions1 z to :e!r su* & su* a =m des]ve 8specific rank10 or be 8only a v>iety40 ,& ?is secul> lab\r is pursu$ 9 direct ob$i5ce to ! precept ( ! ,sy/ema ,naturae1--8ut sic 9 summa confusione r]um app>5ti1 summus conspiciatur ,naturae ordo40 ,9 l mann] ! physici/ records1 & is entitl$ to record1 8 _m hundr$ 8species0 ( sn[-cry/als#bii1 or ( cry/als ( calcium c>bonate4 ,b reg>d+ ^! latt] species1 ! physici/ makes no assumptions3 he records !m simplicit]1 z specific 8=ms02 he notes1 z be/ he c1 ! circum/ances 7su* z temp]ature or humidity7 "u :i* !y occur1 9 ! hope ( elucidat+ ! conditions det]m9+ _! =mation2 b above all1 he does n introduce #bea ! elem5t ( "t1 & ( succession1 or discuss _! orig9 & affiliation z an hi/orical sequ5ce ( ev5ts4 ,b 9 biology1 ! t]m species c>ries ) x _m l>ge1 ?\gh (t5 vague assumptions4 ,?\gh ! doctr9e or concept ( ! 8p]man5ce ( species0 is dead & gone1 yet a c]ta9 def9ite value1 or sort ( quasi-p]man5cy1 is /ill connot$ by ! t]m4 ,?us if a t9y =am9if]al %ell1 a ,lag5a = in/ance1 be f\nd liv+ to-day1 & a %ell indi/+ui%able f x to ! eye be f\nd fossil 9 ! ,*alk or "s o!r remote geological =mation1 ! assumption is deem$ legitimate t t species has 8surviv$10 & has h&$ d[n its m9ute specific "* or *>act]s1 f g5]ation to g5]ation1 un*ang$ = untold myriads ( ye>s#cjj4 ,or if ! anci5t =ms be l to1 r ?an id5tical ) ! rec5t1 we /ill assume an unbrok5 desc5t1 accompani$ by ! h]$it>y transmission ( common *>act]s & progressive v>iations4 ,& if two id5tical =ms be discov]$ at ! ends ( ! e>?1 /ill 7) occasional slight res]vations on ! score ( possible 8homoplasy071 we build hypo!ses on ?is fact ( id5tity1 tak+ x = grant$ t ! two app]ta9 to a common /ock1 ^: disp]sal 9 space mu/ someh[ be acc\nt$ =1 its r\te trac$1 its epo* det]m9$1 & its causes discuss$ or discov]$4 ,9 %ort1 ! naturali/ admits no exception to ! rule t a 8natural classification0 c only be a g5ealogical "o1 nor ev] d\bts t 8,! fact t we are able to classify organisms at all 9 accordance ) ! /ructural *>act]i/ics :i* !y pres5t1 is due to ! fact ( _! be+ relat$ by desc5t#cja40 ,b ?is great g5]alisation is apt 9 my op9ion1 to c>ry u too f>4 ,x may be safe & sure & helpful & illum9at+ :5 we apply x to su* complex entities1--su* ?\s&-fold resultants ( ! comb9ation & p]mutation ( _m v>iable *>act]s1--z a horse1 a lion or an eagle2 b 7to my m9d7 x has a v diff]5t look1 & a f> less firm f\ndation1 :5 we attempt to ext5d x to m9ute organisms ^: specific *>act]s are few & simple1 ^: simplicity #beb becomes mu* m manife/ :5 we reg>d x f ! po9t ( view ( physical & ma!matical description & analysis1 & ^: =m is ref]able1 or 7to say ! lea/ ( x7 is v l>gely ref]able1 to ! direct & imm$iate action ( a p>ticul> physical =ce4 ,:5 we come to deal ) ! m9ute skeletons ( ! ,radiol>ia we %all aga9 f9d ourselves deal+ ) endless modifications ( =m1 9 :i* x becomes /ill m difficult to disc]n1 or to apply1 ! guid+ pr9ciple ( affiliation or g5ealogy4 ,illu/ration3 ,fig4 #ha4 ,among ! m ab]rant =ms ( ,infusoria is a little species kn[n z ,tri*od9a p$icidus1 a p>asite on ! ,hydra1 or fre%-wat] polype 7,fig4 #ha47 ,?is ,tri*od9a has ! =m ( a m or less flatt5$ circul> disc1 ) a r+ ( cilia ar\nd bo? its upp] & l[] m>g9s4 ,! sali5t ridge f :i* ^! cilia spr+ may be tak51 z we h already said1 to play ! "p ( a /r5g!n+ 8fillet40 ,! circul> base ( ! animal is flatt5$1 9 contact ) ! flatt5$ surface ( ! ,hydra ov] :i* x creeps1 & ! opposite1 upp] surface may be flatt5$ ne>ly to a plane1 or may at o!r times appe> slightly convex or slightly concave4 ,! sides ( ! little organism are contract$1 =m+ a symmetrical equatorial groove betwe5 ! upp] & l[] discs2 &1 on acc\nt ( ! m9ute size ( ! animal & its con/ant movem5ts1 we _c submit ! curvature ( ?is concavity to measurem5t1 nor recognise by ! eye its exact cont\r4 ,b x is evid5t t ! conditions are precisely simil> to ^? describ$ on p4 #bbc1 :]e we 7 consid]+ ! conditions ( /ability ( ! cat5oid4 ,& x is fur!r evid5t t1 :5 ! upp] disc is actually plane1 ! equatorial groove is /rictly a cat5oid surface ( revolution2 & :5 on ! o!r h& x is depress$1 !n ! equatorial groove w t5d to assume ! =m ( a nodoidal surface4 ,ano!r curi\s type is ! flatt5$ spiral ( ,d95ympha#cjb #bec :i* rem9ds u ( ! cyl9drical spiral ( a ,spirillum among ! bact]ia4 ,9 ,d95ympha we h a symmetrical figure1 ^: two opposite surfaces ea* con/itute a surface ( con/ant mean curvature2 x is evid5tly a figure ( equilibrium "u c]ta9 special conditions ( re/ra9t4 ,! cyl9drical coil ( ! ,spirillum1 on ! o!r h&1 is a surface ( con/ant mean curvature1 & !re=e ( equilibrium1 z truly1 & 9 ! same s5se1 z ! cyl9d] itself4 ,illu/ration3 ,fig4 #hb4 ,d95ympha gracilis1 ,leidy4 ,illu/ration3 ,fig4 #hc4 ,a v curi\s con=mation is t ( ! vibratile 8coll>10 f\nd 9 ,codosiga & ! o!r 8,*oan(lagellates10 & :i* we also meet ) 9 ! 8coll>-cells0 :i* l9e ! int]ior cavities ( a sponge4 ,su* coll>-cells are always v m9ute1 & ! coll> is con/itut$ ( a v delicate film1 :i* %ews an undulatory or rippl+ motion4 ,x is a surface ( revolution1 & z x ma9ta9s itself 9 equilibrium 7?\gh a some:at un/able & fluctuat+ "o71 x mu/ be1 "u ! re/rict$ circum/ances ( its case1 a surface ( m9imal area4 ,b x is n s easy to see :at ^! special circum/ances are2 & x is obvi\s t ! coll>1 if left to itself1 mu/ at once #bed contract d[nw>ds t[>ds its base1 & become conflu5t ) ! g5]al surface ( ! cell2 = x has no longitud9al supports & no /r5g!n+ r+ at its p]iph]y4 ,b 9 all ^! coll>-cells1 !re /&s )9 ! annulus ( ! coll> a l>ge & p[]ful cilium or flagellum1 9 con/ant movem5t2 & by ! action ( ?is flagellum1 & d\btless 9 "p also by ! intr9sic vibrations ( ! coll> itself1 !re is set up a con/ant /eady curr5t 9 ! surr\nd+ wat]1 ^: direction w\ld seem to be su* t x passes up ! outside ( ! coll>1 d[n its inn] side1 & out 9 ! middle 9 ! direction ( ! flagellum2 & !re is a di/9ct eddy1 9 :i* =eign p>ticles t5d to be caught1 ar\nd ! p]iph]al m>g9 ( ! coll>4 ,:5 ! cell dies1 t is to say :5 motion ceases1 ! coll> imm$iately %rivels away & disappe>s4 ,x is notable1 by ! way1 t ! edge ( ?is little mobile cup is always smoo?1 nev] not*$ or lob$ z 9 ! cases we h discuss$ on p4 #bcf3 ?is latt] condition be+ ! outcome ( a def9ite in/ability1 m>k+ ! close ( a p]iod ( equilibrium2 :ile 9 ! vibratile coll> ( ,codosiga ! equilibrium1 su* z x is1 is be+ con/antly r5ew$ & p]petuat$ l t ( a juggl]'s pole1 by ! motions ( ! sy/em4 ,i take x t1 someh[1 its exi/5ce 79 a /ate ( p>tial equilibrium7 is due to ! curr5t motions1 & to ! traction ex]t$ ^u x ?r\gh ! friction ( ! /ream :i* is con/antly pass+ by4 ,i ?9k1 9 %ort1 t x is =m$ v mu* 9 ! same way z ! cup-l r+ ( /ream+ ribbons1 :i* we see flutt]+ & vibrat+ 9 ! air-curr5t ( a v5tilat+ fan4 ,x is likely en\gh1 h[ev]1 t a diff]5t & mu* bett] explanation may yet be f\nd2 & if we turn once m to ,mr ,wor?+ton's ,/udy ( ,spla%es1 we may f9d a curi\s sugge/ion ( analogy 9 ! beautiful crat]s encircl+ a c5tral jet 7z ! coll> ( ,codosiga encircles ! flagellum71 :i* we see produc$ 9 ! lat] /ages ( ! spla% ( a pebble#cjc4 #bee ,among ! ,=am9if]a we h an imm5se v>iety ( =ms1 :i*1 9 ! light ( surface t5sion & ( ! pr9ciple ( m9imal area1 are capable ( explanation & ( r$uction to a small numb] ( *>act]i/ic types4 ,_m ( ! ,=am9if]a are composite /ructures1 =m$ by ! successive imposition ( cell ^u cell1 & ^! we %all deal ) lat] on2 let u glance "h at ! simpl] con=mations exhibit$ by ! s+le *amb]$ or 8mono?alamic0 g5]a1 & p]haps "o or two ( ! simple/ composites4 ,we beg9 ) =ms1 l ,a/rorhiza 7,fig4 #bai1 p4 #dfd71 :i* are 9 a high degree irregul>1 & end ) o!rs :i* manife/ a p]fect & ma!matical regul>ity4 ,! broad diff]5ce betwe5 ^! two types is t ! =m] are *>act]is$1 l ,amoeba1 by a v>iable surface t5sion1 & consequ5tly by un/able equilibrium2 b ! /rong contra/ betwe5 ^! & ! regul> =ms is bridg$ ov] by v>i\s transition-/ages1 or diff]5ces ( degree4 ,inde$1 z 9 all o!r ,rhizopods1 ! v fact ( ! emission ( pseudopodia1 :i* rea* _! highe/ developm5t 9 ?is gr\p ( animals1 is a sign ( un/able surface-equilibrium2 & we mu/ !re=e consid] t ^? =ms :i* indicate symmetry & equilibrium 9 _! %ells h secret$ ^! dur+ p]iods :5 re/ & uni=mity ( surface conditions alt]nat$ ) ! phases ( pseudopodial activity4 ,! irregul> =ms are 9 almo/ all cases ar5ace\s1 t is to say !y h no solid %ells =m$ by /eady adsorptive secretion1 b only a loos] cov]+ ( s& gra9s ) :i* ! protoplasmic body has come 9 contact & coh]$4 ,sometimes1 z 9 ,ramul9a1 we h a calc>e\s %ell comb9$ ) irregul>ity ( =m2 b "h we c easily see a p>tial & z x 7 a brok5 regul>ity1 ! regul> =ms ( sph]e & cyl9d] be+ repeat$ 9 v>i\s p>ts ( ! ramifi$ mass4 ,:5 we look m closely at ! ar5ace\s =ms1 we f9d t ! same ?+ is true ( !m2 !y repres5t1 ei!r 9 :ole or "p1 approximations to ! =m ( surfaces ( equilibrium1 sph]es1 cyl9d]s & s =?4 ,9 ,as*emonella we h a precise replica ( ! calc>e\s ,ramul9a2 & 9 ,a/rorhiza itself1 9 ! =ms di/+ui%$ by naturali/s z ,a4 crassat9a1 :at is describ$ z ! 8subsegm5t$ int]ior#cjd0 #bef seems to %ew ! natural1 physical t5d5cy ( ! long semifluid cyl9d] ( protoplasm to contract1 at its limit ( /ability1 into unduloid con/rictions1 z a /ep t[>ds ! break+ up into sep>ate sph]es3 ! completion ( :i* process is re/ra9$ or prev5t$ by ! rigidity & friction ( ! ar5ace\s cov]+4 ,illu/ration3 ,fig4 #hd4 ,v>i\s species ( ,lag5a4 7,aft] ,brady47 ,pass+ to ! typical1 calc>e\s-%ell$ ,=am9if]a1 we h ! mo/ symmetrical ( all possible types 9 ! p]fect sph]e ( ,orbul9a2 ?is is a pelagic organism1 ^: float+ habitat places x 9 a position ( p]fect symmetry t[>ds all ext]nal =ces4 ,save = "o or two o!r =ms :i* are also sph]ical1 or approximately s1 l ,?uramm9a1 ! re/ ( ! mono?alamic calc>e\s ,=am9if]a are all compris$ by naturali/s )9 ! g5us ,lag5a4 ,?is l>ge & v>i$ g5us consi/s ( 8flask-%ap$0 %ells1 ^: surface is simply t ( an unduloid1 or m frequ5tly1 l t ( a flask itself1 an unduloid comb9$ ) a portion ( a sph]e4 ,we d n "k ! circum/ances #beg "u :i* ! %ell ( ,lag5a is =m$1 nor ! nature ( ! =ce by :i*1 dur+ its =mation1 ! surface is /ret*$ out into ! unduloid =m2 b we may be pretty sure t x is susp5d$ v]tically 9 ! sea1 t is to say 9 a position ( symmetry z reg>ds its v]tical axis1 ab\t :i* ! unduloid surface ( revolution is symmetrically =m$4 ,at ! same "t we h o!r types ( ! same %ell 9 :i* ! =m is m or less flatt5$2 & ^! are d\btless ! cases 9 :i* su* symmetry ( position 0 n pres5t1 or 0 replac$ by a broad]1 lat]al contact ) ! surface pellicle#cje4 ,illu/ration3 ,fig4 #he4 7,aft] ,d>l+47 ,:ile ,orbul9a is a simple sph]ical drop1 ,lag5a sugge/s to our m9ds a 8hang+ drop10 drawn out to a long & sl5d] neck by its own weight1 aid$ by ! viscosity ( ! mat]ial4 ,inde$ ! v>i\s hang+ drops1 su* z ,mr ,c4 ,r4 ,d>l+ %ews u1 are ! mo/ beautiful & p]fect unduloids1 ) sph]ical ends1 t x is possible to conceive4 ,a suitable liquid1 a little d5s] ?an wat] & incapable ( mix+ ) x 7su* z e?yl b5zoate71 is p\r$ on a surface ( wat]4 ,x spreads #beh ov] ! surface & gradually =ms a hang+ drop1 approximately hemisph]ical2 b z m liquid is add$ ! drop s9ks or r gr[s d[nw>ds1 /ill adh]+ to ! surface film2 & ! balance ( =ces betwe5 gravity & surface t5sion results 9 ! unduloid cont\r1 z ! increas+ weight ( ! drop t5ds to /ret* x out & f9ally break x 9 two4 ,at ! mom5t ( rupture1 by ! way1 a t9y droplet is =m$ 9 ! att5uat$ neck1 su* z we describ$ 9 ! normal division ( a cyl9drical ?read 7p4 #bcc74 ,to pass to a mu* m highly organis$ class ( animals1 we f9d ! unduloid beautifully exemplifi$ 9 ! little flask-%ap$ %ells ( c]ta9 ,pt]opod mollusca1 e4g4 ,cuvi]9a#cjf4 ,"h aga9 ! symmetry ( ! figure w\ld at once lead u to suspect t ! creature liv$ 9 a position ( symmetry to ! surr\nd+ =ces1 z = in/ance if x float$ 9 ! ocean 9 an erect position1 t is to say ) its long axis co9cid5t ) ! direction ( gravity2 & ?is we "k to be actually ! mode ( life ( ! little ,pt]opod4 ,_m species ( ,lag5a are complicat$ & beautifi$ by a patt]n1 & "s by ! sup]addition to ! %ell ( plane ext5sions or 8w+s40 ,^! latt] give a second>y1 bilat]al symmetry to ! little %ell1 & are /rongly sugge/ive ( a phase or p]iod ( gr[? 9 :i* x lay horizontally on ! surface1 in/ead ( hang+ v]tically f ! surface-film3 9 :i*1 t is to say1 x 0 a float+ & n a hang+ drop4 ,! patt]n is ( two k9ds4 ,sometimes x consi/s ( a sort ( f9e reticulation1 ) r\nd$ or m or less hexagonal int]spaces3 9 o!r cases x is produc$ by a symmetrical s]ies ( ridges or folds1 usually longitud9al1 on ! body ( ! flask-%ap$ cell1 b occasionally transv]sely arrang$ ^u ! n>r[ neck4 ,! reticulat$ & fold$ patt]ns we may consid] sep>ately4 ,! nett$ patt]n is v simil> to ! wr9kl$ surface ( a dri$ pea1 or to ! m regul> wr9kl$ patt]ns ^u _m o!r se$s & ev5 poll5-gra9s4 ,if a sph]ical body aft] develop+ a 8sk90 beg9 to %r9k a little1 & if ! sk9 h s f> lo/ its ela/icity z to be unable to keep pace ) ! %r9kage ( ! inn] mass1 x w t5d to fold or wr9kle2 & if ! %r9kage be uni=m1 & ! ela/icity & flexibility ( ! sk9 be also uni=m1 !n ! am\nt ( #bei fold+ w be uni=mly di/ribut$ ov] ! surface4 ,little concave depressions w appe>1 regul>ly int]spac$1 & sep>at$ by convex folds4 ,! little concavities be+ ( equal size 7unless ! sy/em be o!rwise p]turb$7 ea* "o w t5d to be surr\nd$ by six o!rs2 & :5 ! process has rea*$ its limit1 ! int]m$iate b\nd>y-walls1 or rais$ folds1 w be f\nd conv]t$ into a regul> patt]n ( hexagons4 ,b ! analogy ( ! me*anical wr9kl+ ( ! coat ( a se$ is b a r\gh & di/ant "o2 = we are evid5tly deal+ ) molecul> r ?an ) me*anical =ces4 ,9 "o ( ,d>l+'s exp]im5ts1 a little heavy t>-oil is dropp$ onto a sauc] ( wat]1 ov] :i* x spreads 9 a ?9 film %[+ beautiful int]f]5ce col\rs aft] ! fa%ion ( ^? ( a soap-bubble4 ,pres5tly t9y holes appe> 9 ! film1 :i* gradually increase 9 size till !y =m a cellul> patt]n or honeycomb1 ! oil ga!r+ toge!r 9 ! me%es or walls ( ! cellul> net4 ,"s action ( ?is sort is 9 all probability at "w 9 a surface-film ( protoplasm cov]+ ! %ell4 ,z a physical ph5om5on ! actions involv$ are by no means fully und]/ood1 b surface-t5sion1 diffusion & cohesion d\btless play _! respective p>ts !re9#cjg4 ,! v p]fect cellul> patt]ns obta9$ by ,l$uc 7to :i* we %all h occasion to ref] 9 a subsequ5t *apt]7 are diffusion patt]ns on a l>g] scale1 b n ess5tially diff]5t4 ,illu/ration3 ,fig4 #hf4 ,! fold$ or pleat$ patt]n is d\btless to be expla9$1 9 a g5]al way1 by ! %r9kage ( a surface-film "u c]ta9 #bfj conditions ( visc\s or frictional re/ra9t4 ,a case :i* 7z x seems to me7 is closely analog\s to t ( our =am9if]al %ells is describ$ by ,qu9cke#cjh1 :o let a film ( album9 or ( res9 set & h>d5 ^u a surface ( quicksilv]1 & f\nd t ! little solid pellicle _h be5 ?r[n into a patt]n ( symmetrical folds4 ,if ! surface ?us ?r[n into folds be t ( a cyl9d]1 or any o!r figure ) "o pr9cipal axis ( symmetry1 su* z an ellipsoid or unduloid1 ! direction ( ! folds w t5d to be relat$ to ! axis ( symmetry1 & we might expect accord+ly to f9d regul> longitud9al1 or regul> transv]se wr9kl+4 ,n[ z a matt] ( fact we almo/ inv>iably f9d 9 ! ,lag5a ! =m] condition3 t is to say1 9 our ellipsoid or unduloid cell1 ! puck]+ takes ! =m ( ! v]tical flut+ on a column1 r ?an t ( ! transv]se pleat+ ( an accordion4 ,& fur!r1 !re is (t5 a t5d5cy = su* longitud9al flut+s to be m or less localis$ at ! end ( ! ellipsoid1 or 9 ! region :]e ! unduloid m]ges into its sph]ical base4 ,9 ?is latt] region we (t5 meet ) a regul> s]ies ( %ort longitud9al folds1 z we d 9 ! =ms ( ,lag5a d5om9at$ ,l4 semi/riata4 ,all ^! v>i\s =ms ( surface c be imitat$1 or r c be precisely reproduc$1 by ! art ( ! glass-bl[]#cji4 ,fur!rmore1 !y rem9d "o1 9 a /rik+ way1 ( ! regul> ribs or flut+s 9 ! film or %ea? :i* spla%es up to envelop a smoo? ball :i* has be5 dropp$ into a liquid1 z ,mr ,wor?+ton has s beautifully %ewn#caj4 #bfa ,9 ,mr ,wor?+ton's exp]im5t1 !re appe>s to be some?+ ( ! nature ( a visc\s drag 9 ! surface-pellicle2 b :atev] be ! actual cause ( v>iation ( t5sion1 x is n difficult to see t !re mu/ be 9 g5]al a t5d5cy t[>ds longitud9al puck]+ or 8flut+0 9 ! case ( a ?9-wall$ cyl9drical or o!r elongat$ body1 r ?an a t5d5cy t[>ds transv]se puck]+1 or 8pleat+40 ,= let u suppose t "s *ange takes place involv+ an increase ( surface-t5sion 9 "s small area ( ! curv$ wall1 & lead+ !re=e to an increase ( pressure3 t is to say let ,t become ,t t1 & ,p become ,p p4 ,our new equation ( equilibrium1 !n1 9 place ( ,p ,t_/r ,t_/r becomes ,p p 7,t t7_/r 7,t t7_/r1 & by subtraction1 p t_/r t_/r4 ,n[ if r r1 t_/r t_/r4 ,!re=e1 9 ord] to produce ! small increm5t ( pressure p1 x is easi] to d s by increas+ t_/r ?an t_/r2 t is to say1 ! easi] way is to alt]1 or dim9i% r4 ,& ! same w hold good if ! t5sion & pressure be dim9i%$ in/ead ( increas$4 ,?is is z mu* z to say t1 :5 corrugation or 8rippl+0 ( ! walls takes place ow+ to small *anges ( surface-t5sion1 & consequ5tly ( pressure1 su* corrugation is m likely to take place 9 ! plane ( r1--t is to say1 9 ! plane ( greate/ curvature4 ,& x foll[s t 9 su* a figure z an ellipsoid1 wr9kl+ w be mo/ likely to take place n only 9 a longitud9al direction b ne> ! extremities ( ! figure1 t is to say aga9 9 ! region ( greate/ curvature4 ,illu/ration3 ,fig4 #hg4 ,nodos>ia scal>is1 ,bats*4 ,illu/ration3 ,fig4 #hh4 ,gonangia ( ,campanul>ians4 7a7 ,c4 gracilis2 7b7 ,c4 gr&is4 7,aft] ,allman47 ,! longitud9al wr9kl+ ( ! flask-%ap$ bodies ( our ,lag5ae1 & ( ! m or less cyl9drical cells ( _m o!r ,=am9if]a 7,fig4 #hg71 is 9 complete accord ) ! above !oretical consid]ations2 b nev]!less1 we soon f9d t our result is n a g5]al "o1 b is def9$ by c]ta9 limit+ conditions1 & is accord+ly subject to :at are1 at fir/ sight1 important exceptions4 ,= in/ance1 :5 we turn to ! n>r[ neck ( ! ,lag5a we see at once t our !ory no long] holds2 = #bfb ! wr9kl+ :i* 0 inv>iably longitud9al 9 ! body ( ! cell is z inv>iably transv]se 9 ! n>r[ neck4 ,! reason = ! diff]5ce is n f> to seek4 ,! conditions 9 ! neck are v diff]5t f ^? 9 ! exp&$ portion ( ! cell3 ! ma9 diff]5ce be+ t ! ?ickness ( ! wall is no long] insignificant1 b is ( consid]able magnitude z comp>$ ) ! diamet]1 or circumf]5ce1 ( ! neck4 ,we mu/ accord+ly take x into acc\nt 9 consid]+ ! b5d+ mom5ts at any po9t 9 ?is region ( ! %ell-wall4 ,& x is at once obvi\s t1 9 any portion ( ! n>r[ neck1 flexure ( a wall 9 a transv]se direction w be v difficult1 :ile flexure 9 a longitud9al direction w be comp>atively easy2 j z1 9 ! case ( a long n>r[ /rip ( iron1 we may easily b5d x into folds runn+ transv]sely to its long axis1 b n ! o!r way4 ,! mann] 9 :i* our little ,lag5a-%ell t5ds to fold or wr9kle1 longitud9ally 9 its wid] "p1 & transv]sely or annul>ly 9 its n>r[ neck1 is ?us completely & easily expla9$4 ,an id5tical ph5om5on is apt to occur 9 ! little flask-%ap$ gonangia1 or reproductive capsules1 ( "s ( ! hydroid zoophytes4 ,9 ! annex$ draw+s ( ^! gonangia 9 two species ( ,campanul>ia1 we see t 9 "o case ! little vesicle #bfc has ! flask-%ap$ or unduloid configuration ( a ,lag5a2 & "h ! walls ( ! flask are longitud9ally flut$1 j aft] ! mann] we h witness$ 9 ! latt] g5us4 ,b 9 ! o!r ,campanul>ian ! vesicles are long1 n>r[ & tubul>1 & "h a transv]se fold+ or pleat+ takes ! place ( ! longitud9ally flut$ patt]n4 ,& ! v =m ( ! folds or pleats is en\gh to sugge/ t we are n deal+ "h ) a simple ph5om5on ( surface-t5sion1 b ) a condition 9 :i* surface-t5sion & /iffness are bo? pres5t1 & play _! p>ts 9 ! resultant =m4 ,illu/ration3 ,fig4 #hi4 ,v>i\s ,=am9if]a 7aft] ,brady71 a1 ,nodos>ia simplex2 b1 ,n4 pygmaea2 c1 ,n4 co/ulata2 e1 ,n4 hispida2 f1 ,n4 elata2 d1 ,rheophax 7,lituola7 di/ans2 g1 ,sagr9a virgata4 ,pass+ f ! solit>y flask-%ap$ cell ( ,lag5a1 we h1 9 ano!r s]ies ( =ms1 a con/rict$ cyl9d]1 or succession ( unduloids2 su* z are repres5t$ 9 ,fig4 #hi1 illu/rat+ c]ta9 species ( ,nodos>ia1 ,rheophax & ,sagr9a4 ,9 "s ( ^! cases1 & c]ta9ly 9 t ( ! ar5ace\s g5us ,rheophax1 we h to d ) ! ord9>y ph5om5on ( a segm5t+ or p>tially segm5t+ cyl9d]4 ,b 9 o!rs1 ! /ructure is n develop$ out ( a cont9u\s protoplasmic cyl9d]1 b z we c see by exam9+ ! int]ior ( ! %ell1 x has be5 =m$ 9 successive /ages1 beg9n+ ) a simple unduloid 8,lag5a10 ab\t ^: neck1 aft] its solidification1 ano!r drop ( protoplasm accumulat$1 & 9 turn assum$ ! unduloid1 or lag5oid1 =m4 ,! *a9s ( int]connect$ bubbles :i* #bfd ,morey & ,drap] made _m ye>s ago ( melt$ res9 are a v simil> if n id5tical ph5om5on#caa4 ,!re n[ rema9 = our consid]ation1 among ! ,protozoa1 ! great oceanic gr\p ( ! ,radiol>ia1 & ! little gr\p ( _! fre%wat] allies1 ! ,heliozoa4 ,9 ne>ly all ^! =ms we h ?is specific *emical diff]5ce f ! ,=am9if]a1 t :5 !y secrete1 z !y g5]ally d secrete1 a h>d skeleton1 x is compos$ ( silica in/ead ( lime4 ,^! organisms & ! v>i\s beautiful & highly complicat$ skeletal fabrics :i* !y develop give u _m int]e/+ illu/rations ( physical ph5om5a1 among :i* ! manife/ations ( surface-t5sion are v prom95t4 ,b ! *ief ph5om5a connect$ ) _! skeletons we %all deal ) 9 ano!r place1 "u ! head ( spicul> concretions4 ,9 a simple & typical ,heliozoan1 su* z ! ,sun-animalcule1 ,act9ophrys sol1 we h a 8drop0 ( protoplasm1 contract$ by its surface t5sion into a sph]ical =m4 ,)9 ! het]og5e\s protoplasmic mass are m fluid portions1 & at ! surface :i* sep>ates ^! f ! surr\nd+ protoplasm a simil> surface t5sion causes !m also to assume ! =m ( sph]ical 8vacuoles10 :i* 9 reality are little cle> drops )9 ! big "o2 unless inde$ !y become num]\s & closely pack$1 9 :i* case1 in/ead ( isolat$ sph]es or droplets !y w con/itute a 8fro?10 _! mutual pressures & t5sions giv+ rise to regul> configurations su* z we %all /udy 9 ! next *apt]4 ,"o or m ( su* cle> spaces may be :at is call$ a 8contractile vacuole03 t is to say1 a droplet ^: surface t5sion is 9 un/able equilibrium & is apt to vani% altoge!r1 s t ! def9ite outl9e ( ! vacuole sudd5ly disappe>s#cab4 ,aga91 )9 ! protoplasm are "o or m nuclei1 ^: own surface t5sion 7at ! surface betwe5 ! nucleus & ! surr\nd+ protoplasm71 has drawn !m 9 turn into ! %ape #bfe ( sph]es4 ,outw>ds ?r\gh ! protoplasm1 & /ret*+ f> beyond ! sph]ical surface ( ! cell1 !re run /iff l9e> ?reads ( modifi$ or diff]5tiat$ protoplasm1 replac$ or re9=c$ 9 "s cases by delicate silice\s ne$les4 ,9 ei!r case we "k little or no?+ ab\t ! =ces :i* lead to _! production1 & we d n hide our ignorance :5 we ascribe _! developm5t to a 8radial pol>isation0 ( ! cell4 ,9 ! case ( ! protoplasmic filam5t1 we may 7if we seek = a hypo!sis71 suppose t x is someh[ comp>able to a viscid /ream1 or 8liquid ve910 ?ru/ or squirt$ out f ! body ( ! cell4 ,b :5 x is once =m$1 ?is long & comp>atively rigid filam5t is sep>at$ by a di/9ct surface f ! neighb\r+ protoplasm1 t is to say f ! m fluid surface-protoplasm ( ! cell2 & ! latt] beg9s to creep up ! filam5t1 j z wat] w\ld creep up ! int]ior ( a glass tube1 or ! sides ( a glass rod imm]s$ 9 ! liquid4 ,x is ! simple case ( a balance betwe5 ?ree sep>ate t5sions3 7#a7 t betwe5 ! filam5t & ! adjac5t protoplasm1 7#b7 t betwe5 ! filam5t & ! adjac5t wat]1 & 7#c7 t betwe5 ! wat] & ! protoplasm4 ,call+ ^! t5sions respectively ,tfp1 ,tfw1 & ,twp1 equilibrium w be atta9$ :5 ! angle ( contact betwe5 ! fluid protoplasm & ! filam5t is su* t cos 7,tfw ,twp7_/,tfp4 ,x is evid5t 9 ?is case t ! angle is a v small "o4 ,! precise =m ( ! curve is some:at diff]5t f t :i*1 "u ord9>y circum/ances1 is assum$ by a liquid :i* creeps up a solid surface1 z wat] 9 contact ) air creeps up a surface ( glass2 ! diff]5ce be+ due to ! fact t "h1 ow+ to ! d5sity ( ! protoplasm be+ practically id5tical ) t ( ! surr\nd+ m$ium1 ! :ole sy/em is practically immune f gravity4 ,"u normal circum/ances ! curve is "p ( ! 8ela/ic curve0 by :i* t surface ( revolution is g5]at$ :i* we h call$1 aft] ,plateau1 ! nodoid2 b 9 ! pres5t case x is app>5tly a cat5>y4 ,:atev] curve x be1 x obvi\sly =ms a surface ( revolution ar\nd ! filam5t4 ,s9ce ! attraction ex]cis$ by ?is surface t5sion is symmetrical ar\nd ! filam5t1 ! latt] w be pull$ equally #bff 9 all directions2 9 o!r words x w t5d to be set normally to ! surface ( ! sph]e1 t is to say radiat+ directly outw>ds f ! c5tre4 ,if ! di/ance betwe5 two adjac5t filam5ts be consid]able1 ! curve w simply meet ! filam5t at ! angle already ref]r$ to2 b if !y be suffici5tly ne> toge!r1 we %all h a cont9u\s cat5>y curve =m+ a hang+ loop betwe5 "o filam5t & ! o!r4 ,& :5 ?is is s1 & ! radial filam5ts are m or less symmetrically int]spac$1 we may h a beautiful sy/em ( honeycomb-l depressions ov] ! surface ( ! organism1 ea* cell ( ! honeycomb hav+ a /rictly def9$ geometric configuration4 ,illu/ration3 ,fig4 #ij4 ,a1 ,trypanosoma t9eae 7aft] ,m9*972 ,b1 ,spiro*aeta anodontae 7aft] ,fan?am74 ,9 ! simpl] ,radiol>ia1 ! sph]ical =m ( ! entire organism is equally well-m>k$2 & "h1 z also 9 ! m complicat$ ,heliozoa 7su* z ,act9ospha]ium71 ! organism is diff]5tiat$ into sev]al di/9ct lay]s1 ea* b\nd>y surface t5d+ to be sph]ical1 & s con/itut+ sph]e )9 sph]e4 ,"o ( ^! lay]s at lea/ is close pack$ ) vacuoles1 =m+ an 8alveol> me%work10 ) ! configurations ( :i* we %all attempt 9 ano!r *apt] to correlate ! *>act]i/ic /ructure ( c]ta9 complex types ( skeleton4 ,an exceptional =m ( cell1 b a beautiful manife/ation ( surface-t5sion 7or s ,i take x to be71 occurs 9 ,trypanosomes1 ^? t9y p>asites ( ! blood t are associat$ ) sleep+-sickness & _m o!r grave or dire maladies4 ,^! t9y organisms consi/ ( elongat$ solit>y cells d[n "o side ( :i* runs a v delicate frill1 or 8undulat+ membrane10 ! free edge ( :i* is se5 to be slightly ?ick5$1 & ! :ole ( #bfg :i* und]goes rhy?mical & beautiful wavy movem5ts4 ,:5 c]ta9 ,trypanosomes are artificially cultivat$ 7= in/ance ,t4 rotatorium1 f ! blood ( ! frog71 phases ( gr[? are witness$ 9 :i* ! organism has no undulat+ membrane1 b possesses a long cilium or 8flagellum10 spr++ f ne> ! front end1 & exce$+ ! :ole body 9 l5g?#cac4 ,aga91 9 ,t4 lewisii1 :5 x reproduces by 8multiple fission10 ! products ( ?is division are likewise devoid ( an undulat+ membrane1 b are provid$ ) a long free flagellum#cad4 ,x is a plausible assumption to suppose t1 z ! flagellum waves ab\t1 x comes to lie ne> & p>allel to ! body ( ! cell1 & t ! frill or undulat+ membrane is =m$ by ! cle>1 fluid protoplasm ( ! surface lay] spr++ up 9 a film to run up & along ! flagellum1 j z a soap-film w\ld be =m$ 9 simil> circum/ances4 ,illu/ration3 ,fig4 #ia4 ,a1 ,tri*omonas muris1 ,h>tmann2 ,b1 ,tri*oma/ix s]p5tis1 ,dobell2 ,c1 ,tri*omonas angu/a1 ,alexeieff4 7,aft] ,k(oid47 ,?is mode ( =mation ( ! undulat+ membrane or frill appe>s to be confirm$ by ! appe>ances %ewn 9 ,fig4 #ia4 #bfh ,"h we h ?ree little organisms closely alli$ to ! ord9>y ,trypanosomes1 ( :i* "o1 ,tri*oma/ix 7,b71 possesses f\r flagella1 & ! o!r two1 ,tri*omonas1 app>5tly ?ree only3 ! two latt] possess ! frill1 :i* is lack+ 9 ! fir/#cae4 ,b x is impossible to d\bt t :5 ! frill is pres5t 7z 9 ,a & ,c71 its out] edge is con/itut$ by ! app>5tly miss+ flagellum 7a71 :i* has become atta*$ to ! body ( ! creature at ! po9t c1 ne> its po/]ior end2 & all along its c\rse1 ! sup]ficial protoplasm has be5 drawn out into a film1 betwe5 ! flagellum 7a7 & ! adjac5t surface or edge ( ! body 7b74 ,illu/ration3 ,fig4 #ib4 ,h]petomonas assum+ ! undulatory membrane ( a ,trypanosome4 7,aft] ,d4 ,l4 ,mack9non47 ,moreov]1 ?is mode ( =mation has be5 actually witness$ & describ$1 ?\gh 9 a some:at exceptional case4 ,! little flagellate monad ,h]petomonas is normally de/itute ( an undulat+ membrane1 b possesses a s+le long t]m9al flagellum4 ,accord+ to ,dr ,d4 ,l4 ,mack9non1 ! cytoplasm 9 a c]ta9 /age ( gr[? becomes some:at 8/icky10 a phrase :i* we may 9 all probability int]pret to mean t its surface t5sion is be+ r$uc$4 ,= ?is /ick9ess is %ewn 9 two ways4 ,9 ! fir/ place1 ! long body1 9 ! c\rse ( its v>i\s b5d+ movem5ts1 is apt to adh]e head to tail 7s to speak71 giv+ a r\nd$ or sometimes annul> =m to ! organism1 su* z has also be5 describ$ 9 c]ta9 species or /ages ( ,trypanosomes4 ,b aga91 ! long flagellum1 if x get b5t backw>ds ^u ! body1 t5ds to adh]e to its surface4 8,:]e ! flagellum 0 pretty long & active1 its ef=ts to cont9ue movem5t "u ^! abnormal conditions result$ 9 ! gradual lift+ up f ! cytoplasm ( ! body ( a sort ( pseudo-undulat+ membrane 7,fig4 #ib74 ,! movem5ts ( ?is /ructure 7 s exactly ^? ( a true undulat+ membrane t x 0 #bfi difficult to believe "o 0 n deal+ ) a small1 blunt trypanosome#caf40 ,?is 9 %ort is a precise description ( ! mode ( developm5t :i*1 f !oretical consid]ations alone1 we %\ld conceive to be ! natural if n ! only possible way 9 :i* ! undulat+ membrane c\ld come into exi/5ce4 ,!re is a g5us closely alli$ to ,trypanosoma1 viz4 ,trypanoplasma1 :i* possesses "o free flagellum1 toge!r ) an undulat+ membrane2 & x resembles ! neighb\r+ g5us ,bodo1 save t ! latt] has two flagella & no undulat+ membrane4 ,9 l mann]1 ,trypanosoma s closely resembles ,h]petomonas t1 :5 individuals ascrib$ to ! =m] g5us exhibit a free flagellum only1 !y are said to be 9 ! 8,h]petomonas /age40 ,9 %ort all ?r\gh ! ord]1 we h pairs ( g5]a1 :i* are presum$ to be sep>ate & di/9ct1 viz4 ,trypanosoma-,h]petomonas1 ,trypanoplasma-,bodo1 ,tri*oma/ix-,tri*omonas1 9 :i* "o diff]s f ! o!r ma9ly if n solely 9 ! fact t a free flagellum 9 ! "o is replac$ by an undulat+ membrane 9 ! o!r4 ,we c sc>cely d\bt t ! two /ructures are ess5tially "o & ! same4 ,! undulat+ membrane ( a ,trypanosome1 !n1 accord+ to our int]pretation ( x1 is a liquid film & mu/ obey ! law ( con/ant mean curvature4 ,x is "u curi\s limitations ( fre$om3 = by "o bord] x is atta*$ to ! comp>atively motionless body1 :ile its free bord] is con/itut$ by a flagellum :i* reta9s its activity & is be+ con/antly ?r[n1 l ! la% ( a :ip1 into wavy curves4 ,x foll[s t ! membrane1 = e alt]ation ( its longitud9al curvature1 mu/ at ! same in/ant become curv$ 9 a direction p]p5dicul> !reto2 x b5ds1 n z a tape b5ds1 b ) ! accompanim5t ( beautiful b t9y waves ( d\ble curvature1 all t5d+ t[>ds ! e/abli%m5t ( an 8equipot5tial surface02 & its *>act]i/ic undulations are n orig9at$ by an active mobility ( ! membrane b are due to ! molecul> t5sions :i* produce ! v same result 9 a soap-film "u simil> circum/ances4 ,9 c]ta9 ,spiro*aetes1 ,s4 anodontae 7,fig4 #ij7 & ,s4 balbiani #bgj 7:i* we f9d 9 oy/]s71 a v simil> undulat+ membrane exi/s1 b x is coil$ 9 a regul> spiral r\nd ! body ( ! cell4 ,x =ms a 8screw-surface10 or helicoid1 &1 ?\gh we might ?9k t no?+ c\ld well be m curv$1 yet its ma!matical prop]ties are su* t x con/itutes a 8rul$ surface0 ^: 8mean curvature0 is ev]y:]e nil2 & ?is prop]ty 7z we h se57 x %>es ) ! plane1 & ) ! plane alone4 ,precisely su* a surface1 & ( exquisite beauty1 may be produc$ by b5d+ a wire ^u itself s t "p =ms an axial rod & "p a spiral wrapp+ r\nd ! axis1 & !n dipp+ ! :ole into a soapy solution4 ,^! undulat+ & helicoid surfaces are exactly reproduc$ among c]ta9 =ms ( sp]matozoa4 ,! tail ( a sp]matozoon consi/s normally ( an axis surr\nd$ by cle>] & m fluid protoplasm1 & ! axis sometimes splits up into two or m sl5d] filam5ts4 ,to surface t5sion op]at+ betwe5 ^! & ! surface ( ! fluid protoplasm 7j z 9 ! case ( ! flagellum ( ! ,trypanosome71 ,i ascribe ! =mation ( ! undulat+ membrane :i* we f9d1 = in/ance1 9 ! sp]matozoa ( ! newt or salam&]2 & ( ! helicoid membrane1 wrapp$ 9 a f> clos] & m beautiful spiral ?an t :i* we saw 9 ,spiro*aeta1 :i* is *>act]i/ic ( ! sp]matozoa ( _m birds4 ,be=e we pass f ! subject ( ! con=mation ( ! solit>y cell we mu/ take "s acc\nt ( c]ta9 o!r exceptional =ms1 less easy ( explanation1 & /ill less p]fectly und]/ood4 ,su* is ! case1 = in/ance1 ) ! r$ blood-corpuscles ( man & o!r v]tebrates2 & among ! sp]m-cells ( ! decapod cru/acea we f9d =ms /ill m ab]rant & n less p]plex+4 ,^! are among ! comp>atively few cells or cell-l /ructures ^: =m seems to be incapable ( explanation by !ories ( surface-t5sion4 ,9 all ! mammalia 7save a v few7 ! r$ blood-corpuscles are flatt5$ circul> discs1 dimpl$ 9 ^u _! two opposite sides4 ,?is configuration closely resembles t ( an india-rubb] ball :5 we p9* x tightly betwe5 f+] & ?umb2 & we may also comp>e x ) t exp]im5t ( ,plateau's #bga 7describ$ on p4 #bbc71 :]e a flat cyl9drical oil-drop1 ( c]ta9 relative dim5sions1 c1 by suck+ away a little ( ! conta9$ oil1 be made to assume ! =m ( a biconcave disc1 ^: p]iph]y is "p ( a nodoidal surface4 ,f ! relation ( ! nodoid to ! 8ela/ic curve10 we p]ceive t ^! two examples are closely ak9 "o to ! o!r4 ,illu/ration3 ,fig4 #ic4 ,! =m ( ! corpuscle is symmetrical1 & its surface is a surface ( revolution2 b x is obvi\sly n a surface ( con/ant mean curvature1 nor ( con/ant pressure4 ,= we see at once t1 9 ! sectional diagram 7,fig4 #ic71 ! pressure inw>ds due to surface t5sion is positive at ,a1 & negative at ,c2 at ,b !re is no curvature 9 ! plane ( ! pap]1 :ile p]p5dicul> to x ! curvature is negative1 & ! pressure !re=e is also negative4 ,accord+ly1 f ! po9t ( view ( surface t5sion alone1 ! blood-corpuscle is n a surface ( equilibrium2 or 9 o!r words1 x is n a fluid drop susp5d$ 9 ano!r liquid4 ,x is obvi\s !re=e t "s o!r =ce or =ces mu/ be at "w1 & ! simple effect ( me*anical pressure is "h exclud$1 because ! blood-corpuscle exhibits its *>act]i/ic %ape :ile float+ freely 9 ! blood4 ,9 ! l[] v]tebrates ! blood-corpuscles h ! =m ( a flatt5$ oval disc1 ) r %>p edges & ellipsoidal surfaces1 & ?is aga9 is manife/ly n a surface ( equilibrium4 ,two facts are especially notewor?y 9 connection ) ! =m ( ! blood-corpuscle4 ,9 ! fir/ place1 its =m is only ma9ta9$1 t is to say x is only 9 equilibrium1 9 relation to c]ta9 prop]ties ( ! m$ium 9 :i* x floats4 ,if we add a little wat] to ! blood1 ! corpuscle quickly loses its *>act]i/ic %ape & becomes a sph]ical drop1 t is to say a true surface ( m9imal area & ( /able equilibrium4 ,if on ! o!r h& we add a /rong solution ( salt1 or a little glyc]9e1 ! corpuscle contracts1 & its surface becomes puck]$ & unev54 ,9 ^! ph5om5a x is s f> obey+ ! laws ( diffusion & ( surface t5sion4 #bgb ,9 ! second place1 x c be exactly imitat$ artificially by means ( o!r colloid sub/ances4 ,_m ye>s ago ,norris made ! v int]e/+ obs]vation t 9 an emulsion ( glue ! drops assum$ a biconcave =m resembl+ t ( ! mammalian corpuscles#cag4 ,! glue 0 impure1 & d\btless conta9$ leci?92 & x is possible 7z ,pr(essor ,waym\? ,reid tells me7 to make a simil> emulsion ) c]ebrosides & *ole/]9 oleate1 9 :i* ! same con=mation ( ! drops or p>ticles is beautifully %ewn4 ,n[ su* *ole/]9 bodies h an important place among ^? 9 :i* ,lehmann & o!rs h %ewn & /udi$ ! =mation ( fluid cry/als1 t is to say ( bodies 9 :i* ! =ces ( cry/allisation & ! =ces ( surface t5sion are battl+ ) "o ano!r#cah2 &1 = want ( a bett] explanation1 we may 9 ! mean:ile sugge/ t "s su* cause is at ! bottom ( ! con=mation ! explanation ( :i* pres5ts s _m difficulties4 ,b we mu/ n1 p]haps1 pass f ?is subject )\t add+ t ! case is a difficult & complex "o f ! physiological po9t ( view4 ,= ! surface ( a blood-corpuscle consi/s ( a 8semi-p]meable membrane10 ?r\gh :i* c]ta9 sub/ances pass freely & n o!rs 7= ! mo/ "p anions & n cations71 & x may be1 accord+ly1 t we h 9 life a cont9ual /ate ( osmotic inequilibrium1 ( negative osmotic t5sion )91 to :i* comp>atively simple cause ! imp]fect di/5sion ( ! corpuscle may be also due#cai4 ,! :ole ph5om5on w\ld be comp>atively easy to und]/& if we might po/ulate a /iff] p]iph]al region to ! corpuscle1 9 ! =m = in/ance ( a p]iph]al ela/ic r+4 ,su* an annul> ?ick5+ or /iff5+1 l ! 8collapse-r+s0 :i* an eng9e] ins]ts 9 a boil]1 has be5 actually ass]t$ to exi/1 b its pres5ce is n au!nticat$4 ,b x is n at all improbable t we h /ill mu* to le>n ab\t ! ph5om5a ( osmosis itself1 z manife/$ 9 ! case ( m9ute bodies su* z a blood-corpuscle2 & 7z ,pr(essor ,p$die sugge/s to me7 x is by no means impossible t curvature #bgc ( ! surface may itself modify ! osmotic or p]haps ! adsorptive action4 ,if x %\ld be f\nd t osmotic action t5d$ to /op1 or to rev]se1 on *ange ( curvature1 x w\ld foll[ t ?is ph5om5on w\ld give rise to int]nal curr5ts2 & ! *ange ( pressure consequ5t on ^! w\ld t5d to int5sify ! *ange ( curvature :5 once />t$#cbj4 ,illu/ration3 ,fig4 #id4 ,sp]m-cells ( ,decapod ,cru/acea 7aft] ,koltz(f74 a1 ,ina*us scorpio2 b1 ,gala!a squamif]a2 c1 d4 aft] mac]ation1 to %ew spiral fibrillae4 ,! sp]m-cells ( ! ,decapod cru/acea exhibit v>i\s s+ul> %apes4 ,9 ! ,crayfi% !y are flatt5$ cells ) /iff curv$ processes radiat+ outw>ds l a ,/ ,ca!r9e's :eel2 9 ,ina*us !re are two su* circles ( /iff processes2 9 ,gala!a we h a /ill m complex =m1 ) long & slightly twi/$ processes4 ,9 all ^! cases1 j z 9 ! case ( ! blood-corpuscle1 ! /ructure alt]s1 & f9ally loses1 its *>act]i/ic =m :5 ! nature or con/itution 7or z we may assume 9 p>ticul>--! d5sity7 ( ! surr\nd+ m$ium is *ang$4 ,"h aga91 z 9 ! blood-corpuscle1 we h to d ) a v important =ce1 :i* we _h n hi!rto consid]$ 9 ?is connection1--! =ce ( osmosis1 manife/$ "u conditions simil> to ^? ( ,pfeff]'s classical exp]im5ts on ! plant-cell4 ,! surface ( ! cell acts z a 8semi-p]meable membrane10 #bgd p]mitt+ ! passage ( c]ta9 dissolv$ sub/ances 7or _! 8ions07 & includ+ or exclud+ o!rs2 & ?us r5d]+ manife/ & measurable ! exi/5ce ( a def9ite 8osmotic pressure40 ,9 ! case ( ! sp]m-cells ( ,ina*us1 c]ta9 quantitative exp]im5ts h be5 p]=m$#cba4 ,! sp]m-cell exhibits its *>act]i/ic con=mation :ile ly+ 9 ! s]\s fluid ( ! animal's body1 9 ord9>y sea-wat]1 or 9 a #e p] c5t4 solution ( potassium nitrate2 ^! ?ree fluids be+ all 8isotonic0 ) "o ano!r4 ,z we alt] ! conc5tration ( potassium nitrate1 ! cell assumes c]ta9 def9ite =ms correspond+ to def9ite conc5trations ( ! salt2 &1 z a fur!r & f9al pro( t ! ph5om5on is entirely physical1 x is f\nd t o!r salts produce an id5tical effect :5 _! conc5tration is proportionate to _! molecul> weight1 & :atev] id5tical effect is produc$ by v>i\s salts 9 _! respective conc5trations1 a simil>ly id5tical effect is produc$ :5 ^! conc5trations are d\bl$ or o!rwise proportionately *ang$#cbb4 ,illu/ration3 ,fig4 #ie4 ,sp]m-cells ( ,ina*us1 z !y appe> 9 sal9e solutions ( v>y+ d5sity4 7,aft] ,koltz(f47 ,?us ! foll[+ table %ews ! p]c5tage conc5trations ( c]ta9 salts necess>y to br+ ! cell into ! =ms a & c ( ,fig4 #ie2 9 ea* case ! quantities are proportional to ! molecul> weights1 & 9 ea* case twice ! quantity is necess>y to produce ! effect ( ,fig4 #ie;c comp>$ ) t :i* gives rise to ! all b sph]ical =m ( ,fig4 #ie;a4 #bge conc5tration ( salts 9 :i* ! sp]m-cell ( ,ina*us assumes ! =m ( fig4 a fig4 c ,sodium *loride #jf #ab ,sodium nitrate #jhe #ag ,potassium nitrate #aj #bj ,acetic acid #bb #de ,cane sug> #ej #ajj ,illu/ration3 ,fig4 #if4 ,sp]m-cell ( ,dromia4 7,aft] ,koltz(f47 ,if we look !n1 ^u ! sph]ical =m ( ! cell z its true condition ( symmetry & ( equilibrium1 we see t :at we call its normal appe>ance is j "o ( _m int]m$iate phases ( %r9kage1 br\ght ab\t by ! ab/raction ( fluid f its int]ior z ! result ( an osmotic pressure great] outside ?an inside ! cell1 & :]e ! %r9kage ( volume is n kept pace ) by a contraction ( ! surface-area4 ,9 ! case ( ! blood-corpuscle1 ! %r9kage is ( no great am\nt1 & ! result+ de=mation is symmetrical2 su* /ructural inequality z may be necess>y to acc\nt = x ne$ be b small4 ,b 9 ! case ( ! sp]m-cells1 we mu/ h1 & we actually d f9d1 a some:at complicat$ arrangem5t ( m or less rigid or ela/ic /ructures 9 ! wall ( ! cell1 :i* l ! wire framework 9 ,plateau's exp]im5ts1 re/ra9 & modify ! =ces act+ on ! drop4 ,9 "o =m ( ,plateau's exp]im5ts1 in/ead ( support+ 8 drop on r+s or frames ( wire1 he laid ^u its surface "o or m ela/ic coils2 & !n1 on )draw+ oil f ! c5tre ( 8 globule1 he saw its uni=m %r9kage c\nt]act$ by ! spiral spr+s1 ) ! result t ! c5tre ( ea* ela/ic coil seem$ to %oot out into a prom95ce4 ,j su* spiral coils are figur$ 7aft] ,koltz(f7 9 ,fig4 #if2 & !y may be reg>d$ z precisely ak9 to ^? local ?ick5+s1 spiral & o!r1 to :i* we h already ascrib$ ! cyl9drical =m ( ! ,spirogyra cell4 ,9 all probability we mu/ 9 l mann] attribute ! peculi> spiral & o!r =ms1 = in/ance ( _m ,infusoria1 to ! #bgf pres5ce1 among ! multitud9\s o!r diff]5tiations ( _! protoplasmic sub/ance1 ( su* m or less ela/ic fibrillae1 :i* play z x 7 ! "p ( a microscopic skeleton#cbc4 ,b ^! cases :i* we h j dealt )1 lead u to ano!r consid]ation4 ,9 a semi-p]meable membrane1 ?r\gh :i* wat] passes freely 9 & out1 ! conditions ( a liquid surface are greatly modifi$2 &1 9 ! ideal or ultimate case1 !re is nei!r surface nor surface t5sion at all4 ,& ?is w\ld lead u some:at to reconsid] our position1 & to enquire :e!r ! true surface t5sion ( a liquid film is actually responsible = all t we h ascrib$ to x1 or :e!r c]ta9 ( ! ph5om5a :i* we h assign$ to t cause may n 9 "p be due to ! contractility ( def9ite & ela/ic membranes4 ,b to inve/igate ?is "q1 9 p>ticul> cases1 is r = ! physiologi/3 & ! morphologi/ may g on 8 way1 pay+ little he$ to :at is no d\bt a difficulty4 ,9 surface t5sion we h ! production ( a film ) ! prop]ties ( an ela/ic membrane1 & ) ! special peculi>ity t contraction cont9ues ) ! same en]gy h[ev] f> ! process may h already gone2 :ile ! ord9>y ela/ic membrane contracts to a c]ta9 ext5t1 & contracts no m4 ,b )9 wide limits ! ess5tial ph5om5a are ! same 9 bo? cases4 ,our fundam5tal equations apply to bo? cases alike4 ,& accord+ly1 s long z our purpose is morphological1 s long z :at we seek to expla9 is regul>ity & def9it5ess ( =m1 x matt]s little if we %\ld happ51 "h or !re1 to confuse surface t5sion ) ela/icity1 ! contractile =ces manife/$ at a liquid surface ) ^? :i* come into play at ! complex int]nal surfaces ( an ela/ic solid4 #bgg ,,*apt] ,,vi ,a ,,note ,,on ,,adsorption ,a v important coroll>y to1 or amplification ( ! !ory ( surface t5sion is to be f\nd 9 ! mod]n *emico-physical doctr9e ( ,adsorption#cbd4 ,9 its full /atem5t ?is subject soon becomes complicat$1 & involves physical conceptions & ma!matical treatm5t :i* g beyond our range4 ,b x is necess>y = u to take acc\nt ( ! ph5om5on1 ?\gh x be 9 ! mo/ elem5t>y way4 ,9 ! brief acc\nt ( ! !ory ( surface t5sion ) :i* our la/ *apt] began1 x 0 po9t$ out t1 9 a drop ( liquid1 ! pot5tial en]gy ( ! sy/em c\ld be dim9i%$1 & "w manife/$ accord+ly1 9 two ways4 ,9 ! fir/ place we saw t1 at our liquid surface1 surface t5sion t5ds to set up an equilibrium ( =m1 9 :i* ! surface is r$uc$ or contract$ ei!r to ! absolute m9imum ( a sph]e1 or at any rate to ! lea/ possible area :i* is p]mitt$ by ! v>i\s circum/ances & conditions2 & if ! two bodies :i* comprise our sy/em1 namely ! drop ( liquid & its surr\nd+ m$ium1 be simple sub/ances1 & ! sy/em be uncomplicat$ by o!r di/ributions ( =ce1 !n ! en]gy ( ! sy/em w h done its "w :5 ?is equilibrium ( =m1 ?is m9imal area ( surface1 is once atta9$4 ,?is ph5om5on ( ! production ( a m9imal surface-area we h n[ se5 to be ( fundam5tal importance 9 ! ext]nal morphology ( ! cell1 & especially 7s f> z we h yet gone7 ( ! solit>y cell or unicellul> organism4 #bgh ,b we also saw1 accord+ to ,gauss's equation1 t ! pot5tial en]gy ( ! sy/em w be dim9i%$ 7& its dim9ution w accord+ly be manife/$ 9 "w7 if f any cause ! specific surface en]gy be dim9i%$1 t is to say if x be br\ght m ne>ly to an equality ) ! specific en]gy ( ! molecules 9 ! int]ior ( ! liquid mass4 ,?is latt] is a ph5om5on ( great mom5t 9 mod]n physiology1 &1 :ile we ne$ n attempt to deal ) x 9 detail1 x has a be>+ on cell-=m & cell-/ructure :i* we _c af=d to ov]look4 ,9 v>i\s ways a dim9ution ( ! surface en]gy may be br\ght ab\t4 ,= in/ance1 x is kn[n t e isolat$ drop ( fluid has1 "u normal circum/ances1 a surface-*>ge ( electricity3 9 su* a way t a positive or negative *>ge 7z ! case may be7 is inh]5t 9 ! surface ( ! drop1 :ile a correspond+ *>ge1 ( contr>y sign1 is inh]5t 9 ! imm$iately adjac5t molecul> lay] ( ! surr\nd+ m$ium4 ,n[ ! effect ( ?is di/ribution1 by :i* all ! surface molecules ( our drop are simil>ly *>g$1 is t by virtue ( ?is *>ge !y t5d to repel "o ano!r1 & possibly also to draw o!r molecules1 ( opposite *>ge1 f ! int]ior ( ! mass2 ! result be+ 9 ei!r case to antagonise or cancel1 m or less1 t normal t5d5cy ( ! surface molecules to attract "o ano!r :i* is manife/$ 9 surface t5sion4 ,9 o!r words1 an increas$ electrical *>ge conc5trat+ at ! surface ( a drop t5ds1 :e!r x be positive or negative1 to l[] ! surface t5sion4 ,b a /ill m important case has next to be consid]$4 ,let u suppose t our drop consi/s no long] ( a s+le *emical sub/ance1 b conta9s o!r sub/ances ei!r 9 susp5sion or 9 solution4 ,suppose 7z a v simple case7 t x be a wat]y fluid1 expos$ to air1 & conta9+ droplets ( oil3 we "k t ! specific surface t5sion ( oil 9 contact ) air is mu* less ?an t ( wat]1 & x foll[s t1 if ! wat]y surface ( our drop be replac$ by an oily surface ! specific surface en]gy ( ! sy/em w be notably dim9i%$4 ,n[ "u ^! circum/ances x is f\nd t 7q ap>t f gravity1 by :i* ! oil might float to ! surface7 ! oil has a t5d5cy to be drawn to ! surface2 & ?is ph5om5on ( molecul> attraction #bgi or 8adsorption0 repres5ts ! "w done1 equival5t to ! dim9i%$ pot5tial en]gy ( ! sy/em#cbe4 ,9 m g5]al t]ms1 if a liquid 7or "o or o!r ( two adjac5t liquids7 be a *emical mixture1 "s "o con/itu5t 9 :i*1 if x ent]$ into or increas$ 9 am\nt 9 ! surface lay]1 w\ld h ! effect ( dim9i%+ its surface t5sion1 !n t con/itu5t w h a t5d5cy to accumulate or conc5trate at ! surface3 ! surface t5sion may be said1 z x 71 to ex]cise an attraction on ?is con/itu5t sub/ance1 draw+ x into ! surface lay]1 & ?is t5d5cy w proce$ until at a c]ta9 8surface conc5tration0 equilibrium is rea*$1 its oppon5t be+ t osmotic =ce :i* t5ds to keep ! sub/ance 9 uni=m solution or diffusion4 ,9 ! complex mixtures :i* con/itute ! protoplasm ( ! liv+ cell1 ?is ph5om5on ( 8adsorption0 has abundant play3 = _m ( ^! con/itu5ts1 su* z oils1 soaps1 album5s1 etc4 possess ! requir$ prop]ty ( dim9i%+ surface t5sion4 ,moreov]1 ! m a sub/ance has ! p[] ( l[]+ ! surface t5sion ( ! liquid 9 :i* x happ5s to be dissolv$1 ! m w x t5d to displace ano!r & less effective sub/ance f ! surface lay]4 ,?us we "k t protoplasm always conta9s fats or oils1 n only 9 visible drops1 b also 9 ! f9e/ susp5sion or 8colloidal solution40 ,if "u any impulse1 su* = in/ance z might arise f ! ,br[nian movem5t1 a droplet ( oil be br\ght close to ! surface1 x is at once drawn into t surface1 & t5ds to spread itself 9 a ?9 lay] ov] ! :ole surface ( ! cell4 ,b a soapy surface 7= in/ance7 w\ld h 9 contact ) ! surr\nd+ wat] a surface t5sion ev5 less ?an t ( ! film ( oil3 & consequ5tly1 if soap be pres5t 9 ! wat] x w 9 turn be adsorb$1 & w t5d to displace ! oil f ! surface pellicle#cbf4 ,& ?is is all z #bhj mu* z to say t ! molecules ( ! dissolv$ or susp5d$ sub/ance or sub/ances w s di/ribute !mselves ?r\gh\t ! drop z to lead t[>ds an equilibrium1 = ea* small unit ( volume1 betwe5 ! sup]ficial & int]nal en]gy2 or s1 9 o!r words1 z to lead t[>ds a r$uction to a m9imum ( ! pot5tial en]gy ( ! sy/em4 ,?is t5d5cy to conc5tration at ! surface ( any sub/ance )9 ! cell by :i* ! surface t5sion t5ds to be dim9i%$1 or vice v]sa1 con/itutes1 !n1 ! ph5om5on ( ,adsorption2 & ! g5]al /atem5t by :i* x is def9$ is kn[n z ! ,will>d-,gibbs1 or ,gibbs-,?omson law#cbg4 ,among ! _m important physical features or concomitants ( ?is ph5om5on1 let u take note at pres5t t we ne$ n conceive ( a /rictly sup]ficial di/ribution ( ! adsorb$ sub/ance1 t is to say ( its direct association ) ! surface lay] ( molecules su* z we imag9$ 9 ! case ( ! electrical *>ge2 b r ( a progressive t5d5cy to conc5trate1 m & m1 z ! surface is ne>ly approa*$4 ,inde$ we may conceive ! colloid or gelat9\s precipitate 9 :i*1 9 ! case ( our protoplasmic cell1 ! dissolv$ sub/ance t5ds (t5 to be ?r[n d[n1 to con/itute "o b\nd>y lay] aft] ano!r1 ! g5]al effect be+ int5sifi$ & multipli$ by ! repeat$ addition ( ^! new surfaces4 ,moreov]1 x is n less important to obs]ve t ! process ( adsorption1 9 ! neighb\rhood ( ! surface ( a het]og5e\s liquid mass1 is a process :i* takes "t2 ! t5d5cy to surface conc5tration is a gradual & progressive "o1 & w fluctuate ) e m9ute *ange 9 ! composition ( our sub/ance & ) e *ange 9 ! area ( its surface4 ,9 o!r words1 x involves 79 e het]og5e\s sub/ance7 a cont9ual in/ability ( equilibrium3 & a con/ant manife/ation #bha ( motion1 sometimes 9 ! m]e invisible transf] ( molecules b (t5 9 ! production ( visible curr5ts ( fluid or manife/ alt]ations 9 ! =m or outl9e ( ! sy/em4 ,! physiologi/1 z we h already rem>k$1 takes acc\nt ( ! g5]al ph5om5on ( adsorption 9 _m ways3 p>ticul>ly 9 connection ) v>i\s results & consequ5ces ( osmosis1 inasmu* z ?is process is dep5d5t on ! pres5ce ( a membrane1 or membranes1 su* z ! ph5om5on ( adsorption br+s into exi/5ce4 ,= in/ance x plays a lead+ "p 9 all mod]n !ories ( muscul> contraction1 9 :i* ph5om5on a connection ) surface t5sion 0 fir/ indicat$ by ,fitz,gerald & d',arsonval ne>ly =ty ye>s ago#cbh4 ,&1 z ,w4 ,o/wald 0 ! fir/ to %ew1 x gives u an entirely new conception ( ! relation ( gases 7t is to say1 ( oxyg5 & c>bon dioxide7 to ! r$ corpuscles ( ! blood#cbi4 ,b re/rict+ ourselves1 z mu* z may be1 to our morphological aspect ( ! case1 !re are sev]al ways 9 :i* adsorption beg9s at once to ?r[ light ^u our subject4 ,9 ! fir/ place1 our prelim9>y acc\nt1 su* z x is1 is already tantam\nt to a description ( ! process ( developm5t ( a cell-membrane1 or cell-wall4 ,! s-call$ 8secretion0 ( ?is cell-wall is no?+ m ?an a sort ( exudation1 or /riv+ t[>ds ! surface1 ( c]ta9 con/itu5t molecules or p>ticles )9 ! cell2 & ! ,gibbs-,?omson law =mulates1 9 "p at lea/1 ! conditions "u :i* !y d s4 ,! adsorb$ mat]ial may range f ! almo/ unrecognisable pellicle ( a blood-corpuscle to ! di/9ctly diff]5tiat$ 8ectos>c0 ( a protozoan1 & aga9 to ! developm5t ( a fully =m$ cell-wall1 z 9 ! cellulose p>titions ( a vegetable tissue4 ,9 su* cases1 ! dissolv$ & adsorbable mat]ial has n only ! prop]ty ( l[]+ ! surface t5sion1 & h5ce #bhb ( itself accumulat+ at ! surface1 b has also ! prop]ty ( increas+ ! viscosity & me*anical rigidity ( ! mat]ial 9 :i* x is dissolv$ or susp5d$1 & s ( con/itut+ a visible & tangible 8membrane#ccj40 ,! 8zoogloea0 ar\nd a gr\p ( bact]ia is probably a ph5om5on ( ! same ord]4 ,9 ! sup]ficial deposition ( inorganic mat]ials we see ! same process abundantly exemplifi$4 ,n only d we h ! simple case ( ! build+ ( a %ell or 8te/0 ^u ! outw>d surface ( a liv+ cell1 z = in/ance 9 a ,=am9if]1 b 9 a subsequ5t *apt]1 :5 we come to deal ) v>i\s spicules & spicul> skeletons su* z ^? ( ! sponges & ( ! ,radiol>ia1 we %all see t x is highly *>act]i/ic ( ! :ole process ( spicule-=mation = ! deposits to be laid d[n j 9 ! 8int]facial0 b\nd>ies betwe5 cells or vacuoles1 & t ! =m ( ! spicul> /ructures t5ds 9 _m cases to be regulat$ & det]m9$ by ! arrangem5t ( ^! b\nd>ies4 ,9 physical *emi/ry1 an important di/9ction is drawn betwe5 adsorption & pseudo-adsorption#cca1 ! =m] be+ a rev]sible1 ! latt] an irrev]sible or p]man5t ph5om5on4 ,t is to say1 adsorption1 /rictly speak+1 implies ! surface-conc5tration ( a dissolv$ sub/ance1 "u circum/ances :i*1 if !y be alt]$ or rev]s$1 w cause ! conc5tration to dim9i% or disappe>4 ,b pseudo-adsorption includes cases1 d\btless orig9at+ 9 adsorption prop]1 :]e subsequ5t *anges leave ! conc5trat$ sub/ance incapable ( re-ent]+ ! liquid sy/em4 ,x is obvi\s t _m 7?\gh n all7 ( our biological illu/rations1 = in/ance ! =mation ( spicules or ( p]man5t cell-membranes1 belong to ! class ( s-call$ pseudo-adsorption ph5om5a4 ,b ! app>5t contra/ betwe5 ! two is 9 ! ma9 a second>y "o1 & h[ev] important to ! *emi/ is ( little consequ5ce to u4 #bhc ,:ile ?is brief sket* ( ! !ory ( membrane-=mation is cursory & inadequate1 x is en\gh to %ew t ! physical !ory ( adsorption t5ds 9 "p to ov]turn1 9 "p to simplify enorm\sly1 ! old] hi/ological descriptions4 ,we c no long] be cont5t ) su* /atem5ts z t ( ,/rasbrg]1 t membrane-=mation 9 g5]al is associat$ ) ! 8activity ( ! k9oplasm10 or t ( ,h>p] t a c]ta9 spore-membrane arises directly f ! a/ral rays#ccb4 ,9 %ort1 we h easily rea*$ ! g5]al conclusion t1 ! =mation ( a cell-wall or cell-membrane is a *emico-physical ph5om5on1 :i* ! purely objective me?ods ( ! biological microscopi/ d n suffice to int]pret4 ,if ! process ( adsorption1 on :i* ! =mation ( a membrane dep5ds1 be itself dep5d5t on ! p[] ( ! adsorb$ sub/ance to l[] ! surface t5sion1 x is obvi\s t adsorption c only take place :5 ! surface t5sion already pres5t is great] ?an z]o4 ,x is = ?is reason t films or ?reads ( creep+ protoplasm %ew little t5d5cy1 or none1 to cov] !mselves ) an ency/+ membrane2 & t x is only :51 9 an alt]$ phase1 ! protoplasm has develop$ a positive surface t5sion1 & has accord+ly ga!r$ itself up into a m or less sph]ical body1 t ! t5d5cy to =m a membrane is manife/$1 & ! organism develops its 8cy/0 or cell-wall4 ,x is f\nd t a rise ( temp]ature greatly r$uces ! adsorbability ( a sub/ance1 & ?is d\btless comes1 ei!r 9 "p or :ole1 f ! fact t a rise ( temp]ature is itself a cause ( ! l[]+ ( surface t5sion4 ,we may 9 all probability ascribe to ?is fact & to its conv]se1 or at lea/ associate ) x1 su* ph5om5a z ! ency/m5t ( unicellul> organisms at ! approa* ( w9t]1 or ! frequ5t =mation ( /rong %ells or membran\s capsules 9 8w9t]-eggs40 ,aga91 s9ce a film or a fro? 7:i* is a sy/em ( films7 c only be ma9ta9$ by virtue ( a c]ta9 viscosity or rigidity ( #bhd ! liquid1 x may be quickly caus$ to disappe> by ! pres5ce 9 its neighb\rhood ( "s sub/ance capable ( r$uc+ ! surface t5sion2 = ?is sub/ance1 be+ adsorb$1 may displace f ! adsorptive lay] a mat]ial to :i* 0 due ! rigidity ( ! film4 ,9 ?is way a 8ba?ytonic0 sub/ance su* z e!r causes mo/ foams to subside1 & ! p\r+ oil on tr\bl$ wat]s n only /ills ! waves b /ill m quickly dissipates ! foam ( ! break]s4 ,! process ( break+ up an alveol> network1 su* z occurs at a c]ta9 /age 9 ! nucle> division ( ! cell1 may p]haps be ascrib$ 9 "p to su* a cause1 z well z to ! direct l[]+ ( surface t5sion by electrical ag5cy4 ,our la/ illu/ration has l$ u back to ! subject ( a previ\s *apt]1 namely to ! visible configuration ( ! int]ior ( ! cell2 & 9 connection ) ?is wide subject !re are _m ph5om5a on :i* light is app>5tly ?r[n by our k ( adsorption1 & ( :i* we took little or no acc\nt 9 our =m] discussion4 ,"o ( ^! ph5om5a is t visible or concrete 8pol>ity10 :i* we h already se5 to be 9 "s way associat$ ) a dynamical pol>ity ( ! cell4 ,?is morphological pol>ity may be ( a v simple k9d1 z :51 9 an epi!lial cell1 x is manife/$ by ! outw>d %ape ( ! elongat$ or column> cell itself1 by ! ess5tial diff]5ce betwe5 its free surface & its atta*$ base1 or by ! pres5ce 9 ! neighb\rhood ( ! =m] ( muc\s or o!r products ( ! cell's activity4 ,b 9 a great _m cases1 ?is 8pol>is$0 symmetry is supplem5t$ by ! pres5ce ( v>i\s fibrillae1 or ( l9e> arrangem5ts ( p>ticles1 :i* 9 ! elongat$ or 8monopol>0 cell run p>allel ) its axis1 & :i* t5d to a radial arrangem5t 9 ! m or less r\nd$ or sph]ical cell4 ,( late ye>s especially1 an imm5se importance has be5 atta*$ to ^! v>i\s l9e> or fibrill> arrangem5ts1 z !y occur 7aft] /a9+7 9 ! cell-sub/ance ( inte/9al epi!lium1 ( sp]matocytes1 ( ganglion cells1 & mo/ abundantly & mo/ frequ5tly ( all 9 gl& cells4 ,v>i\s functions1 :i* seem some:at arbitr>ily *os51 h be5 assign$1 & _m h>d names giv5 to !m2 = ^! /ructures n[ include y\r mito*ondria & y\r *ondriokonts 7bo? ( ^! be+ v>ieties #bhe ( *ondriosomes71 y\r ,altmann's granules1 y\r microsomes1 pseudo-*romosomes1 epid]mal fibrils & basal filam5ts1 y\r ar*eoplasm & erga/oplasm1 & probably y\r idiozomes1 plasmosomes1 & _m o!r hi/ological m9utiae#ccc4 ,illu/ration3 ,fig4 #ig4 ,a1 ,b1 ,*ondriosomes 9 kidney-cells1 prior to & dur+ secretory activity 7aft] ,b>ratt72 ,c1 d4 9 pancreas ( frog 7aft] ,ma!ws74 ,! position ( ^! bodies ) reg>d to ! o!r cell-/ructures is c>efully describ$4 ,sometimes !y lie 9 ! neighb\rhood ( ! nucleus itself1 t is to say 9 proximity to ! fluid b\nd>y surface :i* sep>ates ! nucleus f ! cytoplasm2 & 9 ?is position !y (t5 =m a some:at cl\dy sph]e :i* con/itutes ! ,neb5k]n4 ,9 ! majority ( cases1 z 9 ! epi!lial cells1 !y =m filam5t\s /ructures1 & r[s ( granules1 ^: ma9 direction is p>allel to ! axis ( ! cell1 & :i* may1 9 "s cases1 & 9 "s =ms1 be conspicu\s at ! "o end1 & 9 "s cases at ! o!r end ( ! cell4 ,b ,i d n f9d t ! hi/ologi/s attempt to expla91 or to correlate ) o!r ph5om5a1 ! t5d5cy ( ^! bodies to lie p>allel ) ! axis1 & p]p5dicul> to ! extremities ( ! cell2 x is m]ely not$ z a peculi>ity1 or a specific "*1 ( ^! p>ticul> /ructures4 ,extraord9>ily complicat$ & div]se functions h be5 ascrib$ to !m4 ,engelmann's 8,fibrill5konus10 :i* 0 almo/ c]ta9ly ano!r aspect ( ! same ph5om5on1 0 held by him & by cytologi/s l ,br$a & ,heid5ha91 to be an app>atus connect$ 9 "s #bhf unexpla9$ way ) ! me*anism ( cili>y movem5t4 ,meves look$ ^u ! *ondriosomes z ! actual c>ri]s or transmitt]s ( h]$ity#ccd4 ,altmann inv5t$ a new aphorism1 ,omne granulum e granulo1 z a ref9em5t ( ,vir*['s omnis cellula e cellula2 & _m o!r hi/ologi/s1 m or less 9 accord1 accept$ ! *ondriosomes z important entities1 sui g5]is1 int]m$iate 9 grade betwe5 ! cell itself & its ultimate molecul> compon5ts4 ,! extreme cytologi/s ( ! ,muni* s*ool1 ,pop(f1 ,golds*midt & o!rs1 foll[+ ,ri*>d ,h]twig1 decl>+ ^! /ructures to be id5tical ) 8*romidia0 7"u :i* "n ,h]twig rank$ all extra-nucle> *romat971 w\ld assign !m complex functions 9 ma9ta9+ ! balance betwe5 nucle> & cytoplasmic mat]ial2 & ! 8*romidial hypo!sis10 z e read] ( rec5t cytological lit]ature kn[s1 has become a v ab/ruse & complicat$ ?+#cce4 ,) ! help ( ! 8b9ucle>ity hypo!sis0 ( ,s*aud9n & 8 s*ool1 x has giv5 u ! *romidial net1 ! *romidial app>atus1 ! tropho*romidia1 idio*romidia1 gameto*romidia1 ! protogonoplasm1 & _m o!r novel & orig9al conceptions4 ,! names are apt to v>y some:at 9 significance f "o writ] to ano!r4 ,! out/&+ fact1 z x seems to me1 is t physiological sci5ce has be5 heavily burd5$ 9 ?is matt]1 ) a j>gon ( names & a ?ick cl\d ( hypo!ses2 :ile1 f ! physical po9t ( view we are tempt$ to see b little my/]y 9 ! :ole ph5om5on1 & to ascribe x1 9 all probability & 9 g5]al t]ms1 to ! ga!r+ or 8clump+0 toge!r1 "u surface t5sion1 ( v>i\s con/itu5ts ( ! het]og5e\s cell-cont5t1 & to ! draw+ out ( ^! little clumps along ! axis ( ! cell t[>ds "o or o!r ( its extremities1 9 relation to osmotic curr5ts1 z ^! 9 turn are set up 9 direct relation #bhg to ! ph5om5a ( surface en]gy & ( adsorption#ccf4 ,& all ?is implies t ! /udy ( ^! m9ute /ructures1 if x tea* u no?+ else1 at lea/ surely & c]ta9ly reveals to u ! pres5ce ( a def9ite 8field ( =ce10 & a dynamical pol>ity )9 ! cell4 ,our next & la/ illu/ration ( ! effects ( adsorption1 :i* we owe to ! inve/igations ( ,pr(essor ,macallum1 is ( great importance2 = x introduces u to a s]ies ( ph5om5a 9 reg>d to :i* we seem n[ to /& on firm] gr\nd ?an 9 "s ( ! =ego+ cases1 ?\gh we _c yet consid] t ! :ole /ory has be5 told4 ,9 our la/ *apt] we 7 re/rict$ ma9ly1 ?\gh n entirely1 to a consid]ation ( figures ( equilibrium1 su* z ! sph]e1 ! cyl9d] or ! unduloid2 & we began at once to f9d ourselves 9 difficulties :5 we 7 confront$ by dep>tures f symmetry1 z = in/ance 9 ! simple case ( ! ellipsoidal yea/-cell & ! production ( its bud4 ,we f\nd ! cyl9drical cell ( ,spirogyra1 ) its plane or sph]ical ends1 a comp>atively simple matt] to und]/&2 b :5 ?is uni=m cyl9d] puts out a lat]al outgr[?1 9 ! act ( conjugation1 we h a new & v diff]5t sy/em ( =ces to expla94 ,! analogy ( ! soap-bubble1 or ( ! simple liquid drop1 0 apt to lead u to suppose t ! surface t5sion 01 on ! :ole1 uni=m ov] ! surface ( our cell2 & t its dep>tures f symmetry ( =m 7 !re=e likely to be due to v>iations 9 ext]nal resi/ance4 ,b if we h be5 incl9$ to make su* an assumption we mu/ n[ #bhh reconsid] x1 & be prep>$ to deal ) important localis$ v>iations 9 ! surface t5sion ( ! cell4 ,=1 z a matt] ( fact1 ! simple case ( a p]fectly symmetrical drop1 ) uni=m surface1 at :i* adsorption takes place ) simil> uni=mity1 is probably r>e 9 physics1 & r>] /ill 7if x exi/ at all7 9 ! fluid or fluid-conta9+ sy/em :i* we call 9 biology a cell4 ,we h mo/ly to d ) cells ^: g5]al het]og5eity ( sub/ance leads to qualitative diff]5ces ( surface1 & h5ce to v>y+ di/ributions ( surface t5sion4 ,we mu/ accord+ly inve/igate ! case ( a cell :i* displays "s def9ite & regul> het]og5eity ( its liquid surface1 j z ,amoeba displays a het]og5eity :i* is complex1 irregul> & cont9ually fluctuat+ 9 am\nt & di/ribution4 ,su* het]og5eity z we are speak+ ( mu/ be ess5tially *emical1 & ! prelim9>y problem is to devise me?ods ( 8micro*emical0 analysis1 :i* %all reveal localis$ accumulations ( p>ticul> sub/ances )9 ! n>r[ limits ( a cell1 9 ! hope t1 _! normal effect on surface t5sion be+ asc]ta9$1 we may !n correlate ) _! pres5ce & di/ribution ! actual indications ( v>y+ surface t5sion :i* ! =m or movem5t ( ! cell displays4 ,9 !ory ! me?od is all t we c\ld wi%1 b 9 practice we mu/ be cont5t ) a v limit$ application ( x2 = ! sub/ances :i* may h su* action z we are look+ =1 & :i* are also actual or possible con/itu5ts ( ! cell1 are v num]\s1 :ile ! means are v seldom at h& to demon/rate _! precise di/ribution & localisation4 ,b 9 "o or two cases we h su* means1 & ! mo/ notable is 9 connection ) ! elem5t potassium4 ,z ,pr(essor ,macallum has %ewn1 ?is elem5t c be reveal$1 9 v m9ute quantities1 by means ( a c]ta9 salt1 a nitrite ( cobalt & sodium#ccg4 ,?is salt p5etrates readily into ! tissues & into ! int]ior ( ! cell2 x comb9es ) potassium to =m a sp>+ly soluble nitrite ( cobalt1 sodium & potassium2 & ?is1 on subsequ5t treatm5t ) ammonium sulphide1 is conv]t$ into a *>act]i/ic black precipitate ( cobaltic sulphide#cch4 #bhi ,by ?is means ,macallum demon/rat$ "s ye>s ago ! unexpect$ pres5ce ( accumulations ( potassium 7i4e4 ( *loride or o!r salts ( potassium7 localis$ 9 p>ticul> p>ts ( v>i\s cells1 bo? solit>y cells & tissue cells2 & he arriv$ at ! conclusion t ! localis$ accumulations 9 "q 7 simply evid5ces ( conc5tration ( ! dissolv$ potassium salts1 =m$ & localis$ 9 accordance ) ! ,gibbs-,?omson law4 ,9 o!r words1 ^! accumulations1 occurr+ z !y actually d 9 connection ) v>i\s b\nd>y surfaces1 are evid5ce1 :5 !y appe> irregul>ly di/ribut$ ov] su* a surface1 ( inequalities 9 its surface t5sion#cci2 & we may safely take x t our potassium salts1 l inorganic sub/ances 9 g5]al1 t5d to raise ! surface t5sion1 & w !re=e be f\nd conc5trat+ at a portion ( ! surface ^: t5sion is weak#cdj4 ,9 ,pr(essor ,macallum's figure 7,fig4 #ih1 #a7 ( ! little gre5 alga ,pleuroc>pus1 we see t "o side ( ! cell is beg9n+ to bulge out 9 a wide convexity4 ,?is bulge is1 9 ! fir/ place1 a sign ( weak5$ surface t5sion on "o side ( ! cell1 :i* z a :ole _h hi!rto be5 a symmetrical cyl9d]2 9 ! second place1 we see t ! bulg+ area corresponds to ! position ( a great conc5tration ( ! potassic salt2 :ile 9 ! ?ird place1 f ! physiological po9t ( view1 we call ! ph5om5on ! fir/ /age 9 ! process ( conjugation4 ,9 ,fig4 #ih1 #b1 ( ,mesoc>pus 7a close ally ( ,spirogyra71 we see ! same ph5om5on admirably exemplifi$ 9 a lat] /age4 ,f ! adjac5t cells di/9ct outgr[?s are be+ emitt$1 :]e ! surface t5sion has be5 weak5$3 j z ! glass-bl[] w>ms & s(t5s a small "p ( 8 tube to bl[ out ! s(t5$ area into a bubble or div]ticulum2 & 9 our ,mesoc>pus cells 7besides a c]ta9 am\nt ( potassium r5d]$ visible ov] ! b\nd>y :i* #bij sep>ates ! gre5 protoplasm f ! cell-sap71 !re is a v l>ge accumulation precisely at ! po9t :]e ! t5sion ( ! orig9ally cyl9drical cell is weak5+ to produce ! bulge4 ,b 9 a /ill lat] /age1 :5 ! b\nd>y betwe5 ! two conjugat+ cells is lo/ & ! cytoplasm ( ! two cells becomes fus$ toge!r1 !n ! signs ( potassic conc5tration quickly disappe>1 ! salt becom+ g5]ally diffus$ ?r\gh ! n[ symmetrical & sph]ical 8zygospore40 ,illu/ration3 ,fig4 #ih4 ,adsorptive conc5tration ( potassium salts 9 7#a7 cell ( ,pleuroc>pus ab\t to conjugate2 7#b7 conjugat+ cells ( ,mesoc>pus2 7#c7 spr\t+ spores ( ,equisetum4 7,aft] ,macallum47 ,9 a spore ( ,equisetum 7,fig4 #ih1 #c71 :ile x is /ill a s+le cell1 no localis$ conc5tration ( potassium is to be disc]n$2 b z soon z ! spore has divid$1 by an int]nal p>tition1 into two cells1 ! potassium salt is f\nd to be conc5trat$ 9 ! small] "o1 & especially t[>ds its out] wall1 :i* is m>k$ by a pron\nc$ convexity4 ,& z ?is convexity 7:i* corresponds to "o pole ( ! n[ asymmetrical1 or quasi-ellipsoidal spore7 gr[s out into ! root-hair1 ! potassium salt accompanies its gr[?1 & is conc5trat$ "u its wall4 ,! conc5tration is1 #bia accord+ly1 a concomitant ( ! dim9i%$ surface t5sion :i* is manife/$ 9 ! alt]$ configuration ( ! sy/em4 ,9 ! case ( ciliate or flagellate cells1 !re is to be f\nd a *>act]i/ic accumulation ( potassium at & ne> ! base ( ! cilia4 ,! relation ( cili>y movem5t to surface t5sion lies beyond our range1 b ! fact :i* we h j m5tion$ ?r[s light ^u ! frequ5t or g5]al pres5ce ( a little protub]ance ( ! cell-surface j :]e a flagellum is giv5 (f 7cf4 p4 #bdg71 & ( a little project+ ridge or fillet at ! base ( an isolat$ r[ ( cilia1 su* z we f9d 9 ,vorticella4 ,yet ano!r ( ,pr(essor ,macallum's demon/rations1 ?\gh its int]e/ is ma9ly physiological1 w help u some:at fur!r to compreh5d :at is impli$ 9 our ph5om5on4 ,9 a normal cell ( ,spirogyra1 a conc5tration ( potassium is reveal$ along ! :ole surface ( ! spiral coil ( *lorophyll-be>+1 or 8*romatophoral10 protoplasm1 ! re/ ( ! cell be+ :olly de/itute ( ! =m] sub/ance3 ! indication be+ t1 at ?is p>ticul> b\nd>y1 betwe5 *romatophore & cell-sap1 ! surface t5sion is small 9 comp>ison ) any o!r int]facial surface )9 ! sy/em4 ,n[ z ,macallum po9ts out1 ! pres5ce ( potassium is kn[n to be a factor1 9 connection ) ! *lorophyll-be>+ protoplasm1 9 ! syn!tic production ( />* f ,,co#b "u ! influ5ce ( sunlight4 ,b we are left 9 "s d\bt z to ! consecutive ord] ( ! ph5om5a4 ,= ! l[]$ surface t5sion1 indicat$ by ! pres5ce ( ! potassium1 may be itself a cause ( ! c>bohydrate syn!sis2 :ile on ! o!r h&1 ?is syn!sis may be att5d$ by ! production ( sub/ances 7e4g4 =maldehyde7 :i* l[] ! surface t5sion1 & s conduce to ! conc5tration ( potassium4 ,all we "k = c]ta9 is t ! sev]al ph5om5a are associat$ ) "o ano!r1 z app>5tly insep>able p>ts or inevitable concomitants ( a c]ta9 complex action4 ,& n[ to return1 = a mom5t1 to ! "q ( cell-=m4 ,:5 we ass]t t ! =m ( a cell 79 ! abs5ce ( me*anical pressure7 is ess5tially dep5d5t on surface t5sion1 & ev5 :5 we make ! prelim9>y assumption t protoplasm is ess5tially #bib a fluid1 we are re/+ our belief on a g5]al cons5sus ( evid5ce1 r ?an on compliance ) any "o crucial def9ition4 ,! simple fact is t ! agreem5t ( cell-=ms ) ! =ms :i* physical exp]im5t & ma!matical !ory assign to liquids "u ! influ5ce ( surface t5sion1 is s frequ5tly & (t5 s typically manife/$1 t we are l$1 or driv51 to accept ! surface t5sion hypo!sis z g5]ally applicable & z equival5t to a univ]sal law4 ,! occasional difficulties or app>5t exceptions are su* z call = fur!r enquiry1 b fall %ort ( ?r[+ d\bt ^u our hypo!sis4 ,macallum's rese>*es introduce a new elem5t ( c]ta9ty1 a 8nail 9 a sure place10 :5 !y demon/rate t1 9 c]ta9 movem5ts or *anges ( =m :i* we %\ld naturally attribute to weak5$ surface t5sion1 a *emical conc5tration :i* w\ld naturally accompany su* weak5+ actually takes place4 ,!y fur!r tea* u t 9 ! cell a *emical het]og5eity may exi/ ( a v m>k$ k9d1 c]ta9 sub/ances be+ accumulat$ "h & abs5t !re1 )9 ! n>r[ b\nds ( ! sy/em4 ,su* localis$ accumulations c z yet only be demon/rat$ 9 ! case ( a v few sub/ances1 & ( a s+le "o 9 p>ticul>2 & ^! are sub/ances ^: pres5ce does n produce1 b ^: conc5tration t5ds to foll[1 a weak5+ ( surface t5sion4 ,! physical cause ( ! localis$ inequalities ( surface t5sion rema9s unkn[n4 ,we may assume1 if we please1 t x is due to ! prior accumulation1 or local production1 ( *emical bodies :i* w\ld h ?is direct effect2 ?\gh we are by no means limit$ to ?is hypo!sis4 ,b 9 spite ( "s rema9+ difficulties & unc]ta9ties1 we h arriv$ at ! conclusion1 z reg>ds unicellul> organisms1 t n only _! g5]al configuration b also _! dep>tures f symmetry may be correlat$ ) ! molecul> =ces manife/$ 9 _! fluid or semi-fluid surfaces4 #bic ,,*apt] ,,vii ,,! ,,=ms ,,( ,,tissues ,,or ,,cell-,,aggregates ,we n[ pass f ! consid]ation ( ! solit>y cell to t ( cells 9 contact ) "o ano!r1--to :at we may call 9 ! fir/ in/ance 8cell-aggregates10--?r\gh :i* we %all be l$ ultimately to ! /udy ( complex tissues4 ,9 ?is "p ( our subject1 z 9 ! prec$+ *apt]s1 we %all h to give "s consid]ation to ! effects ( v>i\s =ces2 b1 z 9 ! case ( ! con=mation ( ! solit>y cell1 we %all probably f9d1 & we may at lea/ beg9 by assum+1 t ! ag5cy ( surface t5sion is especially manife/ & important4 ,! effect ( ?is surface t5sion w *iefly manife/ itself 9 ! production ( surfaces m9imae areae3 :]e1 z ,plateau 0 always c>eful to po9t out1 we mu/ und]/& by ?is expression n an absolute1 b a relative m9imum1 an area1 t is to say1 :i* approximates to an absolute m9imum z ne>ly z circum/ances & ! conditions ( ! case p]mit4 ,!re are c]ta9 fundam5tal pr9ciples1 or fundam5tal equations1 besides ^? :i* we h already consid]$1 :i* we %all ne$ 9 our enquiry4 ,= in/ance ! case :i* we briefly t\*$ ^u 7on p4 #bfe7 ( ! angle ( contact betwe5 ! protoplasm & ! axial filam5t 9 a ,heliozoan we %all n[ f9d to be b a p>ticul> case ( a g5]al & elem5t>y !orem4 ,let u re-/ate z foll[s1 9 t]ms ( ,en]gy1 ! g5]al pr9ciple :i* und]lies ! !ory ( surface t5sion or capill>ity4 ,:5 a fluid is 9 contact ) ano!r fluid1 or ) a solid or a gas1 a portion ( ! en]gy ( ! sy/em 7t1 namely1 :i* we call surface en]gy71 is proportional to ! area ( ! surface ( contact3 x is also proportional to a coeffici5t :i* is specific = ea* p>ticul> pair ( sub/ances1 & :i* is con/ant = ^!1 save only 9 s f> z x may be modifi$ by #bid *anges ( temp]ature or ( electric *>ge4 ,! condition ( m9imum pot5tial en]gy 9 ! sy/em1 :i* is ! condition ( equilibrium1 w accord+ly be obta9$ by ! utmo/ possible dim9ution 9 ! area ( ! surfaces 9 contact4 ,:5 we h ?ree bodies 9 contact1 ! case becomes a little m complex4 ,suppose = in/ance we h a drop ( "s fluid1 ,a1 float+ on ano!r fluid1 ,b1 & expos$ to air1 ,c4 ,! :ole surface en]gy ( ! sy/em may n[ be consid]$ z divid$ into two p>ts1 "o at ! surface ( ! drop1 & ! o!r outside ( ! same2 ! latt] portion is inh]5t 9 ! surface ,,bc1 betwe5 ! mass ( fluid ,b & ! sup]9cumb5t air1 ,c2 b ! =m] portion consi/s ( two p>ts1 = x is divid$ betwe5 ! two surfaces ,,ab & ,,ac1 t namely :i* sep>ates ! drop f ! surr\nd+ fluid & t :i* sep>ates x f ! atmosph]e4 ,s f> z ,illu/ration3 ,fig4 #ii4 ! drop is conc]n$1 !n1 equilibrium dep5ds on a prop] balance betwe5 ! en]gy1 p] unit area1 :i* is resid5t 9 its own two surfaces1 & t :i* is ext]nal !reto3 t is to say1 if we call ,ebc ! en]gy at ! surface betwe5 ! two fluids1 & s on ) ! o!r two pairs ( surface en]gies1 ! condition ( equilibrium1 or ( ma9t5ance ( ! drop1 is t ,ebc ,eab ,eac4 ,if1 on ! o!r h&1 ! fluid ,a happ5s to be oil & ! fluid ,b1 wat]1 !n ! en]gy p] unit area ( ! wat]-air surface is great] ?an t ( ! oil-air surface & t ( ! oil-wat] surface toge!r2 i4e4 ,ewa ,eoa ,eow4 ,"h !re is no equilibrium1 & 9 ord] to obta9 x ! wat]-air surface mu/ always t5d to decrease & ! o!r two int]facial surfaces to increase2 :i* is z mu* z to say t ! wat] t5ds to become cov]$ by a spread+ film ( oil1 & ! wat]-air surface to be aboli%$4 #bie ,! surface en]gy ( :i* we h "h spok5 is manife/$ 9 t contractile =ce1 or 8t5sion10 ( :i* we h already _h s mu* to say#cda4 ,9 any "p ( ! free wat] surface1 = in/ance1 "o surface p>ticle attracts ano!r surface p>ticle1 & ! resultant ( ^! multitud9\s attractions is an equilibrium ( t5sion ?r\gh\t ?is p>ticul> surface4 ,9 ! case ( our ?ree bodies 9 contact ) "o ano!r1 & )9 a small area v ne> to ! po9t ( contact1 a wat] p>ticle 7= in/ance7 w be pull$ outw>ds by ano!r wat] p>ticle2 b on ! opposite side1 s to speak1 !re w be no wat] surface1 & no wat] p>ticle1 to furni% ! c\nt]balanc+ pull2 ?is c\nt]pull1 ,illu/ration3 ,fig4 #ajj4 ,illu/ration3 ,fig4 #aja4 :i* is necess>y = equilibrium1 mu/ !re=e be provid$ by ! t5sions exi/+ 9 ! o!r two surfaces ( contact4 ,9 %ort1 if we c\ld imag9e a s+le p>ticle plac$ at ! v po9t ( contact1 x w\ld be drawn ^u by ?ree diff]5t =ces1 ^: directions w\ld lie 9 ! ?ree surface planes1 & ^: magnitude w\ld be proportional to ! specific t5sions *>act]i/ic ( ! two bodies :i* 9 ea* case comb9e to =m ! 8int]facial0 surface4 ,n[ = ?ree =ces act+ at a po9t to be 9 equilibrium1 !y mu/ be capable ( repres5tation1 9 magnitude & direction1 by ! ?ree sides ( a triangle1 tak5 9 ord]1 9 accordance ) ! elem5t>y !orem ( ! ,triangle ( ,=ces4 ,s1 if we "k ! =m ( our float+ drop 7,fig4 #ajj71 !n by draw+ tang5ts f ,o 7! po9t ( mutual contact71 #bif we det]m9e ! ?ree angles ( our triangle 7,fig4 #aja71 & we !re=e "k ! relative magnitudes ( ! ?ree surface t5sions1 :i* magnitudes are proportional to its sides2 & conv]sely1 if we "k ! magnitudes1 or relative magnitudes1 ( ! ?ree sides ( ! triangle1 we also "k its angles1 & ^! det]m9e ! =m ( ! section ( ! drop4 ,x is sc>cely necess>y to m5tion t1 s9ce all po9ts on ! edge ( ! drop are "u simil> conditions1 "o ) ano!r1 ! =m ( ! drop1 z we look d[n ^u x f above1 mu/ be circul>1 & ! :ole drop mu/ be a solid ( revolution4 ,! pr9ciple ( ! ,triangle ( ,=ces is exp&$1 z foll[s1 by an old sev5te5?-c5tury !orem1 call$ ,lami's ,!orem3 8,if ?ree =ces act+ at a po9t be 9 equilibrium1 ea* =ce is proportional to ! s9e ( ! angle conta9$ betwe5 ! directions ( ! o!r two40 ,t is to say ,p 3 ,q 3 ,r 3 s9 ,,qor 3 s9 ,,por 3 s9 ,,poq4 or ,p_/s9 ,,qor ,q_/s9 ,,rop ,r_/s9 ,,poq4 ,& f ?is1 9 turn1 we d]ive ! equival5t =mulae1 by :i* ea* =ce is express$ 9 t]ms ( ! o!r two1 & ( ! angle betwe5 !m3 ,p#b ,q#b ,r#b #b,q ,r cos7,,qor71 etc4 ,f ?is & ! =ego+1 we le>n ! foll[+ important & useful d$uctions3 7#a7 ,! ?ree =ces c only be 9 equilibrium :5 any "o ( !m is less ?an ! sum ( ! o!r two3 = o!rwise1 ! triangle is impossible4 ,n[ 9 ! case ( a drop ( olive-oil ^u a clean wat] surface1 ! relative magnitudes ( ! ?ree t5sions 7at #ae ,c47 h be5 det]m9$ z foll[s3 ,wat]-air surface #ge ,oil-air surface #cb ,oil-wat] surface #ba ,no triangle hav+ sides ( ^! relative magnitudes is possible2 & no su* drop !re=e c rema9 9 equilibrium4 #big 7#b7 ,! ?ree surfaces may be all alike3 z :5 a soap-bubble floats ^u soapy wat]1 or :5 two soap-bubbles are jo9$ toge!r1 on ei!r side ( a p>tition-film4 ,9 ?is case1 ! ?ree t5sions are all equal1 & !re=e ! ?ree angles are all equal2 t is to say1 :5 ?ree simil> liquid surfaces meet toge!r1 !y always d s at an angle ( #abj4 ,:e!r our two conjo9$ soap-bubbles be equal or unequal1 ?is is /ill ! inv>iable rule2 because ! specific t5sion ( a p>ticul> surface is unaffect$ by any *anges ( magnitude or =m4 7#c7 ,if two only ( ! surfaces be alike1 !n two ( ! angles w be alike1 & ! o!r w be unlike2 & ?is la/ w be ! diff]5ce betwe5 #cfj & ! sum ( ! o!r two4 ,a p>ticul> case is :5 a film is /ret*$ betwe5 solid & p>allel walls1 l a soap-film )9 a cyl9drical tube4 ,"h1 s long z !re is no ext]nal pressure appli$ to ei!r side1 s long z bo? ends ( ! tube are op5 or clos$1 ! angles on ei!r side ( ! film w be equal1 t is to say ! film w set itself at "r angles to ! sides4 ,_m ye>s ago ,sa*s laid x d[n z a pr9ciple1 :i* has become celebrat$ 9 botany "u ! "n ( ,sa*s's ,rule1 t "o cell-wall always t5ds to set itself at "r angles to ano!r cell-wall4 ,?is rule applies to ! case :i* we h j illu/rat$2 & su* validity z ! rule possesses is due to ! fact t among plant-tissues x v frequ5tly happ5s t "o cell-wall has become solid & rigid be=e ano!r & lat] p>tition-wall is develop$ 9 connection ) x4 7#d7 ,!re is ano!r important pr9ciple :i* arises n out ( our equations b out ( ! g5]al consid]ations by :i* we 7 l$ to !m4 ,we h se5 t1 at & ne> ! po9t ( contact betwe5 our sev]al surfaces1 !re is a cont9u$ balance ( =ces1 c>ri$1 s to speak1 across ! int]val2 9 o!r words1 !re is physical cont9uity betwe5 "o surface & ano!r4 ,x foll[s necess>ily f ?is t ! surfaces m]ge "o into ano!r by a cont9u\s curve4 ,:atev] be ! =m ( our surfaces & :atev] ! angle betwe5 !m1 ?is small int]v5+ surface1 approximately sph]ical1 is always !re to bridge ov] ! l9e ( contact#cdb2 & ?is little fillet1 or 8b\rrelet10 #bih z ,plateau call$ x1 is l>ge en\gh to be a common & conspicu\s feature 9 ! microscopy ( tissues 7,fig4 #ajb74 ,= in/ance1 ! s-call$ 8splitt+0 ( ! cell-wall1 :i* is conspicu\s at ! angles ( ! l>ge 8p>5*ymat\s0 cells 9 ! succul5t tissues ( all high] plants 7,fig4 #ajc71 is no?+ m ?an a manife/ation ( ,plateau's 8b\rrelet10 or surface ( cont9uity#cdc4 ,we may n[ illu/rate "s ( ! =ego+ pr9ciples1 be=e we proce$ to ! m complex cases 9 :i* m bodies ?an ?ree are 9 mutual contact4 ,b 9 do+ s1 we mu/ con/antly be> 9 m9d ! pr9ciples set =? 9 our *apt] on ! =ms ( cells1 & especially ^? relat+ to ! pressure ex]cis$ by a curv$ film4 ,illu/ration3 ,fig4 #ajb4 7,aft] ,b]?old47 ,illu/ration3 ,fig4 #ajc4 ,p>5*yma ( ,maize4 ,let u look = a mom5t at ! case pres5t$ by ! p>tition-wall 9 a d\ble soap-bubble4 ,z we h j se51 ! ?ree films 9 contact 7viz4 ! out] walls ( ! two bubbles & ! p>tition-wall betwe57 be+ all compos$ ( ! same sub/ance #bii & all alike 9 contact ) air1 ! ?ree surface t5sions mu/ be equal2 & ! ?ree films mu/ !re=e1 9 all cases1 meet at an angle ( #abj4 ,b1 unless ! two bubbles be ( precisely equal size 7& !re=e ( equal curvature7 x is obvi\s t ! tang5ts to ! sph]es w n meet ! plane ( _! circle ( contact at equal angles1 & !re=e t ! p>tition-wall mu/ be a curv$ surface3 x is only plane :5 x divides two equal & symmetrical cells4 ,x is also obvi\s1 f ! symmetry ( ! figure1 t ! c5tres ( ! sph]es1 ! c5tre ( ! p>tition1 & ! c5tres ( ! two sph]ical surfaces are all on "o & ! same /raight l9e4 ,illu/ration3 ,fig4 #ajd4 ,n[ ! surfaces ( ! two bubbles ex]t a pressure inw>ds :i* is inv]sely proportional to _! radii3 t is to say p 3 p 33 #a_/r 3 #a_/r2 & ! p>tition wall mu/1 = equilibrium1 ex]t a pressure 7,p7 :i* is equal to ! diff]5ce betwe5 ^! two pressures1 t is to say1 ,p #a_/,r #a_/r #a_/r 7r r7_/r r4 ,x foll[s t ! curvature ( ! p>tition wall mu/ be j su* a curvature z is capable ( ex]t+ ?is pressure1 t is to say1 ,r r r_/7r r74 ,! p>tition wall1 !n1 is always a portion ( a sph]ical surface1 ^: radius is equal to ! product1 divid$ by ! diff]5ce1 ( ! radii ( ! two vesicles4 ,x foll[s at once f ?is t if ! two bubbles be equal1 ! radius ( curvature ( ! p>tition is inf9itely great1 t is to say ! p>tition is 7z we h already se57 a plane surface4 ,! geometrical con/ruction by :i* we obta9 ! position ( ! c5tres ( ! two sph]es & also ( ! p>tition surface is v simple1 always provid$ t ! surface t5sions are uni=m ?r\gh\t ! sy/em4 ,if p be a po9t ( contact betwe5 ! two sph]es1 & cp be a radius ( "o ( !m1 !n make ! angle cpm #fj1 & m>k (f on pm1 pc equal to ! #cjj radius ( ! o!r sph]e2 9 l mann]1 make ! angle cpn #fj1 cutt+ ! l9e cc 9 c2 !n c w be ! c5tre ( ! second sph]e1 & c t ( ! sph]ical p>tition4 ,illu/ration3 ,fig4 #aje4 ,illu/ration3 ,fig4 #ajf4 ,:e!r ! p>tition be or be n a plane surface1 x is obvi\s t its l9e ( junction ) ! re/ ( ! sy/em lies 9 a plane1 & is at "r angles to ! axis ( symmetry4 ,! actual curvature ( ! p>tition-wall is easily se5 9 optical section2 b 9 surface view1 ! l9e ( junction is project$ z a plane 7,fig4 #ajf71 p]p5dicul> to ! axis1 & ?is appe>ance has also help$ to l5d support & au?ority to 8,sa*s's ,rule40 ,illu/ration3 ,fig4 #ajg4 ,filam5ts1 or *a9s ( cells1 9 v>i\s l[] ,algae4 7,a7 ,no/oc2 7,b7 ,anaba5a2 7,c7 ,rivul>ia2 7,d7 ,oscillatoria4 ,_m sph]ical cells1 su* z ,protococcus1 divide into two equal halves1 :i* are !re=e sep>at$ by a plane p>tition4 ,among ! o!r l[] ,algae1 ak9 to ,protococcus1 su* z ! ,no/ocs & ,oscillatoriae1 9 :i* ! cells are imb$d$ 9 a gelat9\s matrix1 we f9d a s]ies ( =ms su* z are repres5t$ 9 ,fig4 #ajg4 ,sometimes ! cells are solit>y or disunit$2 sometimes !y run 9 pairs or 9 r[s1 sep>at$ "o f ano!r by flat p>titions2 & sometimes ! conjo9$ cells are approximately hemisph]ical1 b at o!r times ea* half is m ?an a hemisph]e4 ,^! v>i\s conditions dep5d1 #cja accord+ to :at we h already le>n$1 ^u ! relative magnitudes ( ! t5sions at ! surface ( ! cells & at ! b\nd>y betwe5 !m#cdd4 ,9 ! typical case ( an equally divid$ cell1 su* z a d\ble & co-equal soap-bubble1 :]e ! p>tition-wall & ! out] walls are simil> to "o ano!r & 9 contact ) simil> sub/ances1 we c easily det]m9e ! =m ( ! sy/em4 ,=1 at any po9t ( ! b\nd>y ( ! p>tition-wall1 ,o1 ! t5sions be+ equal1 ! angles ,,qop1 ,,rop1 ,,qor are all equal1 & ea* is1 !re=e1 an angle ( #abj4 ,b ,,oq1 ,,or be+ tang5ts1 ! c5tres ( ! two sph]es 7or circul> arcs 9 ! figure7 lie on p]p5dicul>s to !m2 !re=e ! radii ,,co1 ,c,o meet at an ,illu/ration3 ,fig4 #ajh4 angle ( #fj1 & ,,coc is an equilat]al triangle4 ,t is to say1 ! c5tre ( ea* circle lies on ! circumf]5ce ( ! o!r2 ! p>tition lies midway betwe5 ! two c5tres2 & ! l5g? 7i4e4 ! diamet]7 ( ! p>tition-wall1 ,,po1 is #b s9 #fj #agcb times ! radius1 or #hff times ! diamet]1 ( ea* ( ! cells4 ,?is gives u1 !n1 ! =m ( an aggregate ( two equal cells "u uni=m conditions4 ,z soon z ! t5sions become unequal1 :e!r f *anges 9 _! own sub/ance or f diff]5ces 9 ! sub/ances ) :i* !y are 9 contact1 !n ! =m alt]s4 ,if ! t5sion #cjb along ! p>tition1 ,p1 dim9i%es1 ! p>tition itself enl>ges1 & ! angle ,,qor increases3 until1 :5 ! t5sion ,p is v small comp>$ to ,q or ,r1 ! :ole figure becomes a circle1 & ! p>tition-wall1 divid+ x into two hemisph]es1 /&s at "r angles to ! out] wall4 ,?is is ! case :5 ! out] wall ( ! cell is practically solid4 ,on ! o!r h&1 if ,p beg9s to increase relatively to ,q & ,r1 !n ! p>tition-wall contracts1 & ! two adjac5t cells become l>g] & l>g] segm5ts ( a sph]e1 until at l5g? ! sy/em becomes divid$ into two sep>ate cells4 ,illu/ration3 ,fig4 #aji4 ,spore ( ,pellia4 7,aft] ,campbell47 ,9 ! spores ( ,liv]worts 7su* z ,pellia71 ! fir/ p>tition-wall 7! equatorial p>tition 9 ,fig4 #aji1 a7 divides ! spore into two equal halves1 & is !re=e a plane surface1 normal to ! surface ( ! cell2 b ! next p>titions arise ne> to ei!r end ( ! orig9al sph]ical or elliptical cell4 ,ea* ( ^! latt] p>titions w 7l ! fir/7 t5d to set itself normally to ! cell-wall2 at lea/ ! angles on ei!r side ( ! p>tition w be id5tical1 & _! magnitude w dep5d ^u ! t5sion exi/+ betwe5 ! cell-wall & ! surr\nd+ m$ium4 ,!y w only be "r angles if ! cell-wall is already practically solid1 & 9 all probability 7rigidity ( ! cell-wall n be+ q atta9$7 !y w be some:at great]4 ,9 ei!r case ! p>tition itself w be a portion ( a sph]e1 ^: curvature w n[ d5ote a diff]5ce ( pressures 9 ! two *amb]s or cells1 :i* x s]ves to sep>ate4 7,! lat] /ages ( cell-division1 repres5t$ 9 ! figures b & c1 we are n yet 9 a position to deal )47 ,we h innum]able cases1 ne> ! tip ( a gr[+ filam5t1 :]e 9 l mann] ! p>tition-wall :i* cuts (f ! t]m9al #cjc cell con/itutes a sph]ical l5s-%ap$ surface1 set normally to ! adjac5t walls4 ,at ! tips ( ! bran*es ( _m ,florideae1 = in/ance1 we f9d su* a l5ticul> p>tition4 ,9 ,dictyota di*otoma1 z figur$ by ,re9ke1 we h a succession ( su* p>titions2 &1 by ! way1 9 su* cases z ^!1 :]e ! tissues are v transp>5t1 we h (t5 9 optical section a puzzl+ confusion ( l9es2 "o be+ ! optical section ( ! curv$ p>tition-wall1 ! o!r be+ ! /raight l9e> projection ( its out] edge to :i* we h already ref]r$4 ,9 ! conical t]m9al cell ( ,*>a1 we h ! same l5s-%ap$ curve1 b a little l[] d[n1 :]e ! sides ( ! %oot are approximately p>allel1 we h flat transv]se p>titions1 at ! edges ( :i*1 h[ev]1 we recognise a convexity ( ! out] cell-wall & a def9ite angle ( contact1 equal on ! two sides ( ! p>tition4 ,illu/ration3 ,fig4 #aaj4 ,cells ( ,dictyota4 7,aft] ,re9ke47 ,illu/ration3 ,fig4 #aaa4 ,t]m9al & o!r cells ( ,*>a4 ,illu/ration3 ,fig4 #aab4 ,"y an!ridium ( ,*>a4 ,9 ! "y an!ridia ( ,*>a 7,fig4 #aab71 & 9 ! n dissimil> case ( ! sporangium 7or conidiophore7 ( ,mucor1 we easily recognise ! hemisph]ical =m ( ! septum :i* %uts (f ! l>ge sph]ical cell f ! cyl9drical filam5t4 ,"h1 9 ! fir/ phase ( developm5t1 we %\ld h to take into consid]ation ! diff]5t pressures ex]t$ by ! s+le curvature ( ! cyl9d] & ! d\ble curvature ( its sph]ical cap 7p4 #bba72 & we %\ld f9d t ! p>tition w\ld h a some:at l[ curvature1 ) a radius less ?an ! diamet] ( ! cyl9d]2 :i* x w\ld h exactly equall$ b = ! additional pressure inw>ds :i* x receives #cjd f ! curvature ( ! l>ge surr\nd+ sph]e4 ,b z ! latt] cont9ues to gr[1 its curvature decreases1 & s likewise does ! inw>d pressure ( its surface2 & accord+ly ! little convex p>tition bulges out m & m4 ,9 ord] to epitomise ! =ego+ facts let ! annex$ diagrams 7,fig4 #aac7 repres5t a sy/em ( ?ree films1 ( :i* "o is a p>tition-wall betwe5 ! o!r two2 & let ! t5sions at ! ?ree surfaces1 or ! tractions ex]cis$ ^u a po9t at _! meet+-place1 be proportional to ,t1 ,t & t4 ,let 1 1 be1 z 9 ! figure1 ! opposite angles4 ,!n3 7#a7 ,if ,t be equal to ,t1 & t be relatively insignificant1 ! angles 1 w be ( #ij4 ,illu/ration3 ,fig4 #aac4 7#b7 ,if ,t ,t1 b be a little great] ?an t1 !n t w ex]t an appreciable traction1 & 1 w be m ?an #ij1 say1 = in/ance1 #ajj4 7#c7 ,if ,t ,t t1 !n 1 1 w all equal #abj4 ,! m complicat$ cases1 :5 t1 ,t & ,t are all unequal1 are already suffici5tly expla9$4 ,! biological facts :i* ! =ego+ consid]ations g a long way to expla9 & acc\nt = h be5 ! subject ( mu* argum5t & discussion1 especially on ! "p ( ! botani/s4 ,let me recapitulate1 9 a v few words1 ! hi/ory ( ?is long discussion4 ,"s fifty ye>s ago1 ,h(mei/] laid x d[n z a g5]al law t 8,! p>tition-wall /&s always p]p5dicul> to :at 0 previ\sly ! pr9cipal direction ( gr[? 9 ! cell10--or1 9 o!r words1 p]p5dicul> to ! long axis ( ! cell#cde4 ,t5 #cje ye>s lat]1 ,sa*s =mulat$ 8 rule1 or pr9ciple1 ( 8rectangul> section10 decl>+ t 9 all tissues1 h[ev] complex1 ! cell-walls cut "o ano!r 7at ! "t ( _! =mation7 at "r angles#cdf4 ,ye>s be=e1 ,s*w5d5] _h f\nd1 9 ! f9al results ( cell-division1 a univ]sal sy/em ( 8or?ogonal trajectories#cdg02 & ?is idea ,sa*s fur!r develop$1 introduc+ complicat$ sy/ems ( confocal ellipses & hyp]bol1 & di/+ui%+ betwe5 p]icl9al walls1 ^: curves approximate to ! p]iph]al cont\rs1 radial p>titions1 :i* cut ^! at an angle ( #ij1 & f9ally anticl9es1 :i* /& at "r angles to ! o!r two4 ,re9ke1 9 #ahhj1 0 ! fir/ to ?r[ "s d\bt ^u ?is explanation4 ,he po9t$ out v>i\s cases :]e ! angle 0 n a "r angle1 b 0 v def9itely an acute "o2 & he saw1 app>5tly1 9 ! m common rectangul> symmetry m]ely :at he calls a necess>y1 b second>y1 result ( gr[?#cdh4 ,)9 ! next few ye>s1 a numb] ( botanical writ]s 7 cont5t to po9t out fur!r exceptions to ,sa*s's ,rule#cdi2 & 9 "s cases to %[ t ! curvatures ( ! p>tition-walls1 especially su* cases ( l5ticul> curvature z we h describ$1 7 by no means acc\nt$ = by ei!r ,h(mei/] or ,sa*s2 :ile )9 ! same p]iod1 ,sa*s himself1 & also ,raub]1 attempt$ to ext5d ! ma9 g5]alisation to animal tissues#cej4 ,:ile ^! writ]s reg>d$ ! =m & arrangem5t ( ! cell-walls z a biological ph5om5on1 ) little if any direct relation to ord9>y physical laws1 or ) b a vague ref]5ce to 8me*anical conditions10 ! physical side ( ! case 0 soon urg$ by o!rs1 ) m or less =ce & cog5cy4 ,inde$ ! g5]al resemblance betwe5 a cellul> tissue & a 8fro?0 #cjf _h be5 po9t$ out long be=e1 by ,mels5s1 :o _h made an 8artificial tissue0 by bl[+ into a solution ( :ite ( egg#cea4 ,9 #ahhf1 ,b]?old publi%$ 8 ,protoplasmame*anik1 9 :i* he def9itely adopt$ ! pr9ciple ( 8m9imal areas10 &1 foll[+ on ! l9es ( ,plateau1 comp>$ ! =ms ( _m cell-surfaces & ! arrangem5t ( _! p>titions ) ^? assum$ "u surface t5sion by a sy/em ( 8weightless films40 ,b1 z ,klebs#ceb po9ts out 9 review+ ,b]?old's book1 ,b]?old 0 c>eful to /op %ort ( attribut+ ! biological ph5om5a to a def9ite me*anical cause4 ,!y rema9$ = him1 z !y _h done = ,sa*s1 s _m 8ph5om5a ( gr[?10 or 8prop]ties ( protoplasm40 ,9 ! same ye>1 b :ile /ill app>5tly unacqua9t$ ) ,b]?old's "w1 ,err]a#cec publi%$ a %ort b v lucid article1 9 :i* he def9itely ascrib$ to ! cell-wall 7z ,h(mei/] _h already done7 ! prop]ties ( a semi-liquid film & drew f ?is z a logical consequ5ce ! d$uction t x mu/ assume ! v>i\s configurations :i* ! law ( m9imal areas imposes on ! soap-bubble4 ,s :at we may call ,err]a's ,law is =mulat$ z foll[s3 ,a cellul> membrane1 at ! mom5t ( its =mation1 t5ds to assume ! =m :i* w\ld be assum$1 "u ! same conditions1 by a liquid film de/itute ( weight4 ,soon aft]w>ds ,*abry1 9 discuss+ ! embryology ( ! ,ascidians1 indicat$ _m ( ! po9ts 9 :i* ! contacts betwe5 cells repeat ! surface-t5sion ph5om5a ( ! soap-bubble1 & came to ! conclusion t "p1 at lea/1 ( ! embryological ph5om5a 7 purely physical#ced2 & ! same l9e ( inve/igation & ?\ght 7 pursu$ & develop$ by ,rob]t1 9 connection ) ! embryology ( ! ,mollusca#cee4 ,dries* aga91 9 a s]ies ( pap]s1 cont9u$ to draw att5tion to ! pres5ce ( capill>y ph5om5a 9 ! segm5t+ cells #cjg ( v>i\s embryos1 & came to ! conclusion t ! mode ( segm5tation 0 ( little importance z reg>ds ! f9al result#cef4 ,la/ly de ,wildeman#ceg1 9 a some:at wid]1 b also vagu] g5]alisation ?an ,err]a's1 decl>$ t 8,! =m ( ! cellul> framework ( vegetables1 & also ( animals1 9 its ess5tial features1 dep5ds ^u ! =ces ( molecul> physics40 ,illu/ration3 ,fig4 #aad4 ,let u return to our problem ( ! arrangem5t ( p>tition films4 ,:5 we h ?ree bubbles 9 contact1 in/ead ( two z 9 ! case already consid]$1 ! ph5om5on is /rictly analog\s to our =m] case4 ,! ?ree bubbles w be sep>at$ by ?ree p>tition surfaces1 ^: curvature w dep5d ^u ! relative size ( ! sph]es1 & :i* w be plane if ! latt] are all ( ! same dim5sions2 b :e!r plane or curv$1 ! ?ree p>titions w meet "o ano!r at an angle ( #abj1 9 an axial l9e4 ,v>i\s pretty geometrical coroll>ies accompany ?is arrangem5t4 ,= in/ance1 if ,fig4 #aad repres5t ! ?ree associat$ bubbles 9 a plane drawn ?r\gh _! c5tres1 c1 c1 c 7or :at is ! same ?+1 if x repres5t ! base ( ?ree bubbles re/+ on a plane71 !n ! l9es uc1 uc1 or sc1 sc1 etc41 drawn to ! #cjh c5tres f ! po9ts ( int]section ( ! circul> arcs1 w always enclose an angle ( #fj4 ,aga9 7,fig4 #aae71 if we make ! angle cuf equal to #fj1 & produce uf to meet cc 9 f1 f w be ! c5tre ( ! circul> arc :i* con/itutes ! p>tition ,ou2 & fur!r1 ! ?ree po9ts f1 g1 h1 successively det]m9$ 9 ?is ,illu/ration3 ,fig4 #aae4 mann]1 w lie on "o & ! same /raight l9e4 ,9 ! case ( coequal bubbles or cells 7z 9 ,fig4 #aad1 ,b71 x is obvi\s t ! l9es jo9+ _! c5tres =m an equilat]al triangle2 & consequ5tly1 t ! c5tre ( ea* circle 7or sph]e7 lies on ! circumf]5ce ( ! o!r two2 x is also obvi\s t uf is n[ #cji p>allel to cc1 & accord+ly t ! c5tre ( curvature ( ! p>tition is n[ inf9itely di/ant1 or 7z we h already said71 t ! p>tition itself is plane4 ,illu/ration3 ,fig4 #aaf4 ,:5 we h f\r bubbles 9 conjunction1 !y w\ld seem to be capable ( arrangem5t 9 two symmetrical ways3 ei!r1 z 9 ,fig4 #aaf 7,a71 ) ! f\r p>tition-walls meet+ at "r angles1 or1 z 9 7,b71 ) five p>titions meet+1 ?ree & ?ree1 at angles ( #abj4 ,?is latt] arrangem5t is /rictly analog\s to ! arrangem5t ( ?ree bubbles 9 ,fig4 #aad4 ,n[1 ?\gh bo? ( ^! figures1 f _! symmetry1 are app>5tly figures ( equilibrium1 yet1 physically1 ! =m] turns out to be ( un/able & ! latt] ( /able equilibrium4 ,if we try to br+ our f\r bubbles into ! =m ( ,fig4 #aaf1 ,a1 su* an arrangem5t endures only = an in/ant2 ! p>titions glide ^u ea* o!r1 a m$ian wall spr+s into exi/5ce1 & ! sy/em at once assumes ! =m ( our second figure 7,b74 ,?is is a direct consequ5ce ( ! law ( m9imal areas3 = x c be %ewn1 by some:at difficult ma!matics 7z 0 fir/ done by ,lam>le71 t1 9 divid+ a clos$ space into a giv5 numb] ( *amb]s by means ( p>tition-walls1 ! lea/ possible area ( ^! p>tition-walls1 tak5 toge!r1 c only be atta9$ :5 !y meet toge!r 9 gr\ps ( ?ree1 at equal angles1 t is to say at angles ( #abj4 #caj ,:]ev] we h a true cellul> complex1 an arrangem5t ( cells 9 actual physical contact by means ( a b\nd>y film1 we f9d ?is g5]al pr9ciple 9 =ce2 we mu/ only be> 9 m9d t1 = its p]fect recognition1 we mu/ be able to view ! object 9 a plane at "r angles to ! b\nd>y walls4 ,= in/ance1 9 any ord9>y section ( a vegetable p>5*yma1 we recognise ! appe>ance ( a 8fro?10 precisely resembl+ t :i* we c con/ruct by imprison+ a mass ( soap-bubbles 9 a n>r[ vessel ) flat sides ( glass2 9 bo? cases we see ! cell-walls ev]y:]e meet+1 by ?rees1 at angles ( #abj1 irrespective ( ! size ( ! individual cells3 ^: relative size1 on ! o!r h&1 det]m9es ! curvature ( ! p>tition-walls4 ,on ! surface ( a honey-comb we h precisely ! same conjunction1 betwe5 cell & cell1 ( ?ree b\nd>y walls1 meet+ at #abj4 ,9 embryology1 :5 we exam9e a segm5t+ egg1 ( f\r 7or m7 segm5ts1 we f9d 9 l mann]1 9 ! great majority ( cases1 if n 9 all1 t ! same pr9ciple is /ill exemplifi$2 ! f\r segm5ts d n meet 9 a common c5tre1 b ea* cell is 9 contact ) two o!rs1 & ! ?ree1 & only ?ree1 common b\nd>y walls meet at ! normal angle ( #abj4 ,a s-call$ pol> furr[#ceh1 ! visible edge ( a v]tical p>tition-wall1 jo9s 7or sep>ates7 ! two triple contacts1 precisely z 9 ,fig4 #aaf1 ,b4 ,9 ! f\r-cell$ /age ( ! frog's egg1 ,raub] 7an exceptionally c>eful obs]v]7 %ews u ?ree alt]native modes 9 :i* ! f\r cells may be f\nd to be conjo9$ 7,fig4 #aag74 ,9 7,a7 we h ! commone/ arrangem5t1 :i* is t :i* we h j /udi$ & f\nd to be ! simple/ !oretical "o2 t namely :]e a /raight 8pol> furr[0 int]v5es1 & :]e1 at its extremities1 ! p>tition-walls are conjo9$ ?ree by ?ree4 ,9 7,b71 we h aga9 a pol> furr[1 :i* is n[ se5 to be a portion ( ! fir/ 8segm5tation-furr[0 7cf4 ,fig4 #aee etc47 by :i* ! egg 0 orig9ally divid$ into two2 ! f\r-cell$ /age be+ rea*$ by ! appe>ance ( ! transv]se furr[s #caa & _! correspond+ p>titions4 ,9 ?is case1 ! pol> furr[ is se5 to be s9u\sly curv$1 & ,raub] tells u t its curvature gradually alt]s3 z a matt] ( fact1 x 7or r ! p>tition-wall correspond+ to x7 is gradually sett+ itself into a position ( equilibrium1 t is to say ( equiangul> contact ) its neighb\rs1 :i* position ( equilibrium is already atta9$ or ne>ly s 9 ,fig4 #aag1 ,a4 ,9 ,fig4 #aag1 ,c1 we h a v diff]5t condition1 ) :i* we %all deal 9 a mom5t4 ,illu/ration3 ,fig4 #aag4 ,v>i\s ways 9 :i* ! f\r cells are co-arrang$ 9 ! f\r-cell$ /age ( ! frog's egg4 7,aft] ,raub]47 ,accord+ to ! relative magnitude ( ! bodies 9 contact1 ?is 8pol> furr[0 may be long] or %ort]1 & x may be s m9ute z to be n easily disc]nible2 b x is q c]ta9 t no simple & homog5e\s sy/em ( fluid films su* z we are deal+ ) is 9 equilibrium )\t its pres5ce4 ,9 ! acc\nts giv51 h[ev]1 by embryologi/s ( ! segm5tation ( ! egg1 :ile ! pol> furr[ is depict$ 9 ! great majority ( cases1 !re are o!rs 9 :i* x has n be5 se5 & "s 9 :i* its abs5ce is def9itely ass]t$#cei4 ,! cases :]e f\r cells1 ly+ 9 "o plane1 meet 9 a po9t1 su* z 7 frequ5tly figur$ by ! old] embryologi/s1 are v difficult to v]ify1 & ,i h n come across a s+le cle> case 9 rec5t lit]ature4 ,consid]+ ! physical /ability ( ! o!r arrangem5t1 ! great prepond]ance ( cases 9 :i* x is kn[n to occur1 ! difficulty ( recognis+ ! pol> furr[ 9 cases :]e x is v small & unless x be specially look$ =1 & ! natural t5d5cy ( ! draughtsman to make an all b symmetrical /ructure appe> :olly s1 ,i am mu* incl9$ to attribute to #cab error or imp]fect obs]vation all ^? cases :]e ! junction-l9es ( f\r cells are repres5t$ 7aft] ! mann] ( ,fig4 #aaf1 ,a7 z a simple cross#cfj4 ,b :ile a true f\r-ray$ int]section1 or simple cross1 is !oretically impossible 7save z a transitory & highly un/able condition71 !re is ano!r condition :i* may closely simulate x1 & :i* is common en\gh4 ,!re are pl5ty ( repres5tations ( segm5t+ eggs1 9 :i*1 in/ead ( ! triple junction & pol> furr[1 ! f\r cells 7& 9 l mann] _! m num]\s successors7 are repres5t$ z r\nd$ (f1 & sep>at$ f "o ano!r by an empty space1 or by a little drop ( an extrane\s fluid1 evid5tly n directly miscible ) ! fluid surfaces ( ! cells4 ,su* is ! case 9 ! obvi\sly accurate figure :i* ,raub] gives 7,fig4 #aag1 ,c7 ( ! ?ird mode ( conjunction 9 ! f\r-cell$ /age ( ! frog's egg4 ,"h ,raub] is mo/ c>eful to po9t out t ! furr[s d n simply 8cross10 or meet 9 a po9t1 b are sep>at$ by a little space1 :i* he calls ! ,polgrb*51 & ass]ts to be con/antly pres5t :5soev] ! pol> furr[1 or ,bre*ungsl9ie1 is n to be disc]n$4 ,?is little int]pos$ space1 ) its conta9$ drop ( fluid1 mat]ially alt]s ! case1 & implies a new condition ( !oretical & actual equilibrium4 ,=1 on ! "o h&1 we see t n[ ! f\r int]cellul> p>titions d n meet "o ano!r at all2 b really imp+e ^u f\r new & sep>ate p>titions1 :i* con/itute int]facial contacts1 n betwe5 cell & cell1 b betwe5 ! respective cells & ! int]calat$ drop4 ,& secondly1 ! angles at :i* ^! f\r little surfaces w meet ! f\r cell-p>titions1 w be det]m9$1 9 ! usual way1 by ! balance betwe5 ! respective t5sions ( ^! sev]al surfaces4 ,9 an extreme case 7z 9 "s poll5-gra9s7 x may be f\nd t ! cells "u ! obs]v$ circum/ances are n truly 9 surface contact3 t !y are s _m drops :i* t\* b d n 8wet0 "o ano!r1 & :i* are m]ely held toge!r by ! pressure ( ! surr\nd+ envelope4 ,b ev5 suppos+1 #cac z is 9 all probability ! actual case1 t !y are 9 actual fluid contact1 ! case f ! po9t ( view ( surface t5sion pres5ts no difficulty4 ,9 ! case ( ! conjo9$ soap-bubbles1 we 7 deal+ ) simil> contacts & ) equal surface t5sions ?r\gh\t ! sy/em2 b 9 ! sy/em ( protoplasmic cells :i* con/itute ! segm5t+ egg we mu/ make all[ance = an inequality ( t5sions1 betwe5 ! surfaces :]e cell meets cell1 & :]e on ! o!r h& cell-surface is 9 contact ) ! surr\nd+ m$ium1--9 ?is case g5]ally wat] or "o ( ! fluids ( ! body4 ,rememb] t our g5]al condition is t1 9 our ,illu/ration3 ,fig4 #aah4 entire sy/em1 ! sum ( ! surface en]gies is a m9imum2 &1 :ile ?is is atta9$ by ! sum ( ! surfaces be+ a m9imum 9 ! case :]e ! en]gy is uni=mly di/ribut$1 x is n necess>ily s "u non-uni=m conditions4 ,9 ! diagram 7,fig4 #aah7 if ! en]gy p] unit area be great] along ! contact surface cc1 :]e cell meets cell1 ?an along ca or cb1 :]e cell-surface is 9 contact ) ! surr\nd+ m$ium1 ^! latt] surfaces w t5d to increase & ! surface ( cell-contact to dim9i%4 ,9 %ort !re w be ! usual balance ( =ces betwe5 ! t5sion along ! surface cc1 & ! two oppos+ t5sions along ca & cb4 ,if ! =m] be great] ?an ei!r ( ! o!r two1 ! outside angle w be less ?an #abj2 & if ! t5sion along ! surface cc be z mu* or m ?an ! sum ( ! o!r two1 !n ! drops w /& 9 contact only1 save = ! possible effect ( ext]nal pressure1 at a po9t4 ,?is is ! explanation1 9 g5]al t]ms1 ( ! peculi> conditions obta9+ 9 ,no/oc & its allies 7p4 #cjj71 & x also leads u to a consid]ation ( ! g5]al prop]ties & *>act]s ( an 8epid]mal0 lay]4 ,:ile ! inn] cells ( ! honey-comb are symmetrically situat$1 %>+ ) _! neighb\rs 9 equally di/ribut$ pressures or t5sions1 & !re=e all t5d+ ) great accuracy #cad to id5tity ( =m1 ! case is obvi\sly diff]5t ) ! cells at ! bord]s ( ! sy/em4 ,s x is1 9 l mann]1 ) our fro? ( soap-bubbles4 ,! bubbles1 or cells1 9 ! int]ior ( ! mass are all alike 9 g5]al "*1 & if !y be equal 9 size are alike 9 e respect3 _! sides are uni=mly flatt5$#cfa1 & t5d to meet at equal angles ( #abj4 ,b ! bubbles :i* con/itute ! out] lay] reta9 _! sph]ical surfaces1 :i* h[ev] /ill t5d to meet ! p>tition-walls connect$ ) !m at con/ant angles ( #abj4 ,?is out] lay] ( bubbles1 :i* =ms ! surface ( our fro?1 con/itutes aft] a fa%ion :at we %\ld call 9 botany an 8epid]mal0 lay]4 ,b 9 our fro? ( soap-bubbles we h1 z a rule1 ! same k9d ( contact 7t is to say1 contact ) air7 bo? )9 & )\t ! bubbles2 :ile 9 our liv+ cell1 ! out] wall ( ! epid]mal cell is expos$ to air on ! "o side1 b is 9 contact ) ! ,illu/ration3 ,fig4 #aai4 protoplasm ( ! cell on ! o!r3 & ?is involves a diff]5ce ( t5sions1 s t ! out] walls & _! adjac5t p>titions are no long] likely to meet at equal angles ( #abj4 ,moreov]1 a *emical *ange1 due = in/ance to oxidation or possibly also to adsorption1 is v likely to affect ! ext]nal wall1 & may t5d to its consolidation2 & ?is process1 z we h se51 is tantam\nt to a l>ge increase1 & at ! same "t an equalisation1 ( t5sion 9 t out] wall1 & w lead ! adjac5t p>titions to imp+e ^u x at angles m & m ne>ly approximat+ to #ij3 ! bubble-l1 or sph]ical1 surfaces ( ! individual cells be+ m & m flatt5$ 9 consequ5ce4 ,la/ly1 ! *emical *anges :i* affect ! out] walls ( ! sup]ficial cells may ext5d1 9 great] or less degree1 to _! inn] walls also3 ) ! result t ^! #cae cells w t5d to become m or less rectangul> ?r\gh\t1 & w cease to dovetail into ! int]/ices ( ! next subjac5t lay]4 ,^! !n are ! g5]al *>act]s :i* we recognise 9 an epid]mis2 & we p]ceive t ! fundam5tal "* ( an epid]mis simply is t x lies on ! outside1 & t its ma9 physical *>act]i/ics foll[1 z a matt] ( c\rse1 f ! position :i* x occupies & f ! v>i\s consequ5ces :i* t situation entails4 ,we h h[ev] by no means exhau/$ ! subject 9 ?is %ort acc\nt2 = ! botani/ is accu/om$ to draw a %>p di/9ction betwe5 a true epid]mis & :at is call$ epid]mal tissue4 ,! latt]1 :i* is f\nd 9 su* a sea-we$ z ,lam9>ia & 9 v _m o!r cryptogamic plants1 consi/s1 z 9 ! hypo!tical case we h describ$1 ( a m or less simple & direct modification ( ! g5]al or fundam5tal tissue4 ,b a 8true epid]mis10 su* z we h x 9 ! high] plants1 is some?+ ) a long morphological hi/ory1 some?+ :i* has be5 laid d[n or diff]5tiat$ 9 an e>ly /age ( ! plant's gr[?1 & :i* aft]w>ds reta9s its sep>ate & indep5d5t "*4 ,we %all see pres5tly t a physical reason is aga9 at h& to acc\nt1 "u c]ta9 circum/ances1 = ! e>ly p>tition+ (f1 f a mass ( embryonic tissue1 ( an out] lay] ( cells :i* f _! fir/ appe>ance are m>k$ (f f ! re/ by _! rectangul> & flatt5$ =m4 ,we h hi!rto consid]$ our cells1 or bubbles1 z ly+ 9 a plane ( symmetry1 & fur!r1 we h only consid]$ ! appe>ance :i* !y pres5t z project$ on t plane3 9 simpl] words1 we h be5 consid]+ _! appe>ance 9 surface or 9 sectional view4 ,b we h fur!r to consid] !m z solids1 :e!r !y be /ill gr\p$ 9 relation to a s+le plane 7l ! f\r cells 9 ,fig4 #aaf7 or heap$ ^u "o ano!r1 z = in/ance 9 a tetrah$ral =m l f\r cannon-balls2 & 9 ei!r case we h to pass f ! problems ( plane to ^? ( solid geometry4 ,9 %ort1 ! fur!r developm5t ( our !me mu/ lead u along two pa?s ( enquiry1 :i* cont9ually int]cross1 namely 7#a7 ! /udy ( m complex cases ( p>tition & ( contact 9 a plane1 & 7#b7 ! :ole "q ( ! surfaces #caf & angles pres5t$ by solid figures 9 symmetrical juxtaposition4 ,let u take a simple case ( ! latt] k9d1 & aga9 aft]w>ds1 s f> z possible1 let u try to keep ! two !mes sep>ate4 ,:]e we h ?ree sph]es 9 contact1 z 9 ,fig4 #aad or 9 ei!r half ( ,fig4 #aaf1 ,b1 let u consid] ! po9t ( contact 7,o1 ,fig4 #aad7 n z a po9t 9 ! plane section ( ! diagram1 b z a po9t :]e ?ree furr[s meet on ! surface ( ! sy/em4 ,at ?is po9t1 ?ree cells meet2 b x is also obvi\s t !re meet "h six surfaces1 namely ! out]1 sph]ical walls ( ! ?ree bubbles1 & ! ?ree p>tition-walls :i* divide !m1 two & two4 ,also1 f\r l9es or edges meet "h2 viz4 ! ?ree ext]nal arcs :i* =m ! out] b\nd>ies ( ! p>tition-walls 7& :i* correspond to :at we commonly call ! 8furr[s0 9 ! segm5t+ egg72 & z a f\r? edge1 ! 8arris0 or junction ( ! ?ree p>titions 7p]p5dicul> to ! plane ( ! pap]71 :]e !y all ?ree meet toge!r1 z we h se51 at equal angles ( #abj4 ,la/ly1 !re meet at ! po9t f\r solid angles1 ea* b\nd$ by ?ree surfaces3 to wit1 )9 ea* bubble a solid angle b\nd$ by two p>tition-walls & by ! surface wall2 & 7f\r?ly7 an ext]nal solid angle b\nd$ by ! out] surfaces ( all ?ree bubbles4 ,n[ 9 ! case ( ! soap-bubbles 7^: surfaces are all 9 contact ) air1 bo? outside & 971 ! six films meet+ at ! po9t1 :e!r surface films or p>tition films1 are all simil>1 ) simil> t5sions4 ,9 o!r words ! t5sions1 or =ces1 act+ at ! po9t are all simil> & symmetrically arrang$1 & x at once foll[s f ?is t ! angles1 solid z well z plane1 are all equal4 ,x is also obvi\s t1 z reg>ds ! po9t ( contact1 ! sy/em w /ill be symmetrical1 & its symmetry w be q un*ang$1 if we add a f\r? bubble 9 contact ) ! o!r ?ree3 t is to say1 if :]e we _h m]ely ! out] air be=e1 we n[ replace x by ! air 9 ! int]ior ( ano!r bubble4 ,! only diff]5ce w be t ! pressure ex]cis$ by ! walls ( ?is f\r? bubble w alt] ! curvature ( ! surfaces ( ! o!rs1 s f> z x encloses !m2 &1 if all f\r bubbles be id5tical 9 size1 ^! surfaces :i* =m]ly we call$ ext]nal & :i* h n[ come to be int]nal p>titions1 w1 l ! o!rs1 be flatt5$ by equal & opposite pressure1 into planes4 ,we are n[ deal+1 9 %ort1 #cag ) six planes1 meet+ symmetrically 9 a po9t1 & con/itut+ !re f\r equal solid angles4 ,illu/ration3 ,fig4 #abj4 ,if we make a wire cage1 9 ! =m ( a regul> tetrah$ron1 & dip x into soap-solution1 !n :5 we )draw x we see t to ea* "o ( ! six edges ( ! tetrah$ron1 i4e4 to ea* "o ( ! six wires :i* con/itute ! little cage1 a film has atta*$ itself2 & ^! six films meet int]nally at a po9t1 & con/itute 9 e respect ! symmetrical figure :i* we h j be5 describ+4 ,9 %ort1 ! sy/em ( films we h h]eby automatically produc$ is precisely ! sy/em ( p>tition-walls :i* exi/ 9 our tetrah$ral aggregation ( f\r sph]ical bubbles3--precisely ! same1 t is to say1 9 ! neighb\rhood ( ! meet+-po9t1 & only diff]+ 9 t we h made ! wires ( our tetrah$ron /raight1 in/ead ( imitat+ ! circul> arcs :i* actually =m ! int]sections ( our bubbles4 ,?is detail we c easily introduce 9 our wire model if we please4 ,let u look = a mom5t at ! geometry ( our figure4 ,let o 7,fig4 #abj7 be ! c5tre ( ! tetrah$ron1 i4e4 ! c5tre ( symmetry :]e our films meet2 & let oa1 ob1 oc1 od1 be l9es drawn to ! f\r corn]s ( ! tetrah$ron4 ,produce ao to meet ! base 9 p2 !n apd is a "r-angl$ triangle4 ,x is n difficult to prove t 9 su* a figure1 o 7! c5tre ( gravity ( ! sy/em7 #cah lies j ?ree-qu>t]s ( ! way betwe5 an apex1 a1 & a po9t1 p1 :i* is ! c5tre ( gravity ( ! opposite base4 ,!re=e op oa_/#c od_/#c4 ,!re=e cos dop #a_/c & cos aod #a_/c4 ,t is to say1 ! angle aod is j1 z ne>ly z possible1 #aji #bh #af4 ,?is angle1 !n1 ( #aji #bh #af1 or v ne>ly #aji degrees & a half1 is ! angle at :i*1 9 ?is & e o!r solid sy/em ( liquid films1 ! edges ( ! p>tition-walls meet "o ano!r at a po9t4 ,x is ! fundam5tal angle 9 ! solid geometry ( our sy/ems1 j z #abj 0 ! fundam5tal angle ( symmetry s long z we consid]$ only ! plane projection1 or plane section1 ( ?ree films meet+ 9 an edge4 ,out ( ^! two angles1 we may con/ruct a great v>iety ( figures1 plane & solid1 :i* become all ! m v>i$ & complex :51 by consid]+ ! case ( unequal z well z equal cells1 we admit curv$ 7e4g4 sph]ical7 z well z plane b\nd>y surfaces4 ,let u consid] "s examples & illu/rations ( ^!1 beg9n+ ) ^? :i* we ne$ only consid] 9 ref]5ce to a plane4 ,let u imag9e a sy/em ( equal cyl9d]s1 or equal sph]es1 9 contact ) "o ano!r 9 a plane1 & repres5t$ 9 section by ! equal & contigu\s circles ( ,fig4 #aba4 ,i borr[ my figure1 by ! way1 f an old ,italian naturali/1 ,bonanni 7a contempor>y ( ,borelli1 ( ,hay & ,will\ghby & ( ,m>t9 ,li/]71 :o dealt ) ?is matt] 9 a book *iefly devot$ to molluscan %ells#cfb4 ,x is obvi\s1 z a simple geometrical fact1 t ea* ( ^! equal circles is 9 contact ) six surr\nd+ circles4 ,imag9e n[ t ! :ole sy/em comes "u "s uni=m /ress4 ,x may be ( uni=m surface t5sion at ! b\nd>ies ( all ! cells2 x may be ( pressure caus$ by uni=m gr[? or expansion )9 ! cells2 or x may be due to "s uni=mly appli$ con/rict+ pressure f )\t4 ,9 all ( ^! cases ! po9ts ( contact betwe5 ! circles 9 ! diagram w be ext5d$ into #cai l9es ( contact1 repres5t+ surfaces ( contact 9 ! actual sph]es or cyl9d]s2 & ! equal circles ( our diagram w be conv]t$ into regul> & equal hexagons4 ,! angles ( ^! hexagons1 at ea* ( :i* ?ree hexagons meet1 are ( c\rse angles ( #abj4 ,s f> z ! =m is conc]n$1 s long z we are conc]n$ only ) a morphological result & n ) a physiological process1 ! result is precisely ! same :atev] be ! =ce :i* br+s ! bodies toge!r 9 symmetrical apposition2 x is by no means necess>y = u1 9 ! fir/ in/ance1 ev5 to enquire :e!r x be surface t5sion or me*anical pressure or "s o!r physical =ce :i* is ! cause1 or ! ma9 cause1 ( ! ph5om5on4 ,illu/ration3 ,fig4 #aba4 ,diagram ( hexagonal cells4 7,aft] ,bonanni47 ,! production by mutual int]action ( polyh$ral cells1 :i*1 "u conditions ( p]fect symmetry1 become regul> hexagons1 is v beautifully illu/rat$ by ,pr(4 ,bn>d's 8t\rbillons cellulaires0 7cf4 p4 #bei71 & also 9 "s ( ,l$uc's diffusion exp]im5ts4 ,a weak 7#e p] c5t47 solution ( gelat9e is all[$ to set on a plate ( glass1 & little drops ( a #e or #aj p] c5t4 solution ( f]rocyanide ( potassium are !n plac$ at regul> int]vals ^u ! gelat9e4 ,imm$iately ea* little drop becomes ! c5tre1 or pole1 ( a sy/em ( diffusion curr5ts1 #cbj & ! sev]al sy/ems conflict ) & repel "o ano!r1 s t pres5tly ea* little area becomes ! seat ( a d\ble curr5t sy/em1 f its c5tre outw>ds & back aga92 until at l5g? ! conc5tration ( ! field becomes equalis$ & ! curr5ts #cba ,illu/ration3 ,fig4 #abb4 ,an 8artificial tissue10 =m$ by col\r$ drops ( sodium *loride solution diffus+ 9 a less d5se solution ( ! same salt4 7,aft] ,l$uc47 ,illu/ration3 ,fig4 #abc4 ,an artificial cellul> tissue1 =m$ by ! diffusion 9 gelat9e ( drops ( a solution ( potassium f]rocyanide4 7,aft] ,l$uc47 cease4 ,aft] equilibrium is atta9$1 & :5 ! gelat9\s mass is p]mitt$ to dry1 we h an artificial tissue ( m or less regul>ly hexagonal 8cells10 :i* simulate 9 ! close/ way an organic p>5*yma4 ,& by v>y+ ! exp]im5t1 9 ways :i* ,l$uc describes1 we may simulate v>i\s =ms ( tissue1 & produce cells ) ?ick walls or ) ?91 cells 9 close contact or ) wide int]cellul> spaces1 cells ) plane or ) curv$ p>titions1 & s =?4 ,illu/ration3 ,fig4 #abd4 ,epid]mis ( ,gir>dia4 7,aft] ,goebel47 ,! hexagonal patt]n is illu/rat$ among organisms 9 c\ntless cases1 b ^? 9 :i* ! patt]n is p]fectly regul>1 by reason ( p]fect uni=mity ( =ce & p]fect equality ( ! individual cells1 are n s num]\s4 ,! hexagonal epi!lium-cells ( ! pigm5t lay] ( ! eye1 ext]nal to ! ret9a1 are a good example4 ,"h we h a s+le lay] ( uni=m cells1 repos+ on ! "o h& ^u a basem5t membrane1 support$ beh9d by ! solid wall ( ! scl]otic1 & expos$ on ! o!r h& to ! uni=m fluid pressure ( ! vitre\s hum\r4 ,! conditions all po9t1 & lead1 to a p]fectly symmetrical result3 t is to say1 ! cells1 uni=m 9 size1 are flatt5$ out to a uni=m ?ickness by ! fluid pressure act+ radially2 & _! reaction on ea* o!r conv]ts ! flatt5$ discs into regul> hexagons4 ,9 an ord9>y column> epi!lium1 su* z t ( ! inte/9e1 we see aga9 t ! column> cells h be5 compress$ into hexagonal prisms2 b "h z a rule ! cells are less uni=m 9 size1 small cells are apt to be int]calat$ among ! l>g]1 & ! p]fect symmetry is accord+ly lo/4 ,! same is true ( ord9>y vegetable p>5*yma2 ! orig9ally sph]ical cells are approximately equal 9 size1 b only approximately2 & !re are accord+ly all degrees 9 ! regul>ity & symmetry ( ! result+ tissue4 ,b obvi\sly1 :]ev] we #cbb h1 9 addition to ! =ces :i* t5d to produce ! regul> hexagonal symmetry1 "s o!r asymmetrical compon5t aris+ f gr[? or traction1 !n our regul> hexagons w be di/ort$ 9 v>i\s simple ways4 ,?is condition is illu/rat$ 9 ! accompany+ diagram ( ! epid]mis ( ,gir>dia2 x also acc\nts = ! m or less po9t$ or fusi=m cells1 ea* /ill 9 contact 7z a rule7 ) six o!rs1 :i* =m ! epi!lial l9+ ( ! blood-vessels3 & o!r simil>1 or analog\s1 in/ances are v common4 ,illu/ration3 ,fig4 #abe4 ,soap-fro? "u pressure4 7,aft] ,rhumbl]47 ,9 a soap-fro? imprison$ betwe5 two glass plates1 we h a symmetrical sy/em ( cells1 :i* appe> 9 optical section 7z 9 ,fig4 #abe1 ,b7 z regul> hexagons2 b if we press ! plates a little clos] toge!r1 ! hexagons become de=m$ or flatt5$ 7,fig4 #abe1 ,a74 ,9 ?is case1 h[ev]1 if we cease to apply fur!r pressure1 ! t5sion ( ! films ?r\gh\t ! sy/em soon adju/s itself aga91 & 9 a %ort "t ! sy/em has rega9$ ! =m] symmetry ( ,fig4 #abe1 ,b4 ,illu/ration3 ,fig4 #abf4 ,f leaf ( ,elodea canad5sis4 7,aft] ,b]?old47 ,9 ! gr[? ( an ord9>y dicotyl$on\s leaf1 we once m see reflect$ 9 ! =m ( its epid]mal cells ! tractions1 irregul> b on ! :ole longitud9al1 :i* gr[? has sup]pos$ on ! t5sions ( ! p>tition-walls 7,fig4 #abf74 ,9 ! n>r[ elongat$ leaf ( a ,monocotyl$on1 su* z a hyac9?1 ! elongat$1 app>5tly quadrangul> #cbc cells ( ! epid]mis appe> z a necess>y consequ5ce ( ! simpl] laws ( gr[? :i* gave its simple =m to ! leaf z a :ole4 ,9 ?is la/ case1 h[ev]1 z 9 all ! o!rs1 ! rule /ill holds t only ?ree p>titions 79 surface view7 meet 9 a po9t2 & at _! po9t ( meet+ ! walls are = a %ort di/ance manife/ly curv$1 s z to p]mit ! junction to take place at or ne>ly at ! normal angle ( #abj4 ,briefly speak+1 :]ev] we h a sy/em ( cyl9d]s or sph]es1 associat$ toge!r ) suffici5t mutual int]action to br+ !m into complete surface contact1 !re1 9 section or 9 surface view1 we t5d to get a patt]n ( hexagons4 ,:ile ! =mation ( an hexagonal patt]n on ! basis ( ready-=m$ & symmetrically arrang$ mat]ial units is a v common1 & inde$ ! g5]al way1 x does n foll[ t !re are n o!rs by :i* su* a patt]n c be obta9$4 ,= in/ance1 if we take a little triangul> di% ( m]cury & set x vibrat+ 7ei!r by help ( a tun+-=k1 or by simply tapp+ on ! sides7 we %all h a s]ies ( little waves or ripples />t+ inw>ds f ea* ( ! ?ree faces2 & ! int]cross+1 or int]f]5ce ( ^! ?ree sets ( waves produces cre/s & holl[s1 & int]m$iate po9ts ( no di/urbance1 ^: loci are se5 z a beautiful patt]n ( m9ute hexagons4 ,x is possible t ! v m9ute & a/oni%+ly regul> patt]n ( hexagons :i* we see1 = in/ance1 on ! surface ( _m diatoms1 may be a ph5om5on ( ?is ord]#cfc4 ,! same may be ! case also 9 ,arcella1 :]e an app>5tly hexagonal patt]n is f\nd n to consi/ ( simple hexagons1 b ( 8/raight l9es 9 ?ree sets ( p>allels1 ! l9es ( ea* set mak+ an angle ( sixty degrees ) ^? ( ! o!r two sets#cfd40 ,we mu/ also be> 9 m9d1 9 ! case ( ! m9ut] =ms1 ! l>ge possibilities ( optical illusion4 ,= in/ance1 9 "o ( ,abbe's 8diffraction-plates10 a patt]n ( dots1 set at equal int]spaces1 is reproduc$ on a v m9ute scale by photography2 b "u c]ta9 conditions ( microscopic illum9ation & focuss+1 ^! isolat$ dots appe> z a patt]n ( hexagons4 ,a symmetrical arrangem5t ( hexagons1 su* z we h j be5 /udy+1 sugge/s v>i\s simple geometrical coroll>ies1 ( :i* ! foll[+ may p]haps be a useful "o4 ,we may sometimes desire to e/imate ! numb] ( hexagonal areas or facets 9 "s /ructure :]e ^! are num]\s1 su* = in/ance z ! #cbd cornea ( an insect's eye1 or 9 ! m9ute patt]n ( hexagons on _m diatoms4 ,an approximate enum]ation is easily made z foll[s4 ,= ! area ( a hexagon 7if we call ! %ort diamet]1 t namely :i* bisects two ( ! opposite sides7 is #b 7#c7_/b1 ! area ( a circle be+ d#b _/#d4 ,!n1 if ! diamet] 7d7 ( a circul> area include n hexagons1 ! area ( t circle equals 7n 7#b _/#d4 ,&1 divid+ ?is numb] by ! area ( a s+le hexagon1 we obta9 = ! numb] ( areas 9 ! circle1 ea* equal to a hexagonal facet1 ! expression n#b _/#d #b_/7c7 #jijgn#b1 or 7#i_/aj7 n#b1 ne>ly4 ,?is calculation deals1 n only ) ! complete facets1 b ) ! areas ( ! brok5 hexagons at ! p]iph]y ( ! circle4 ,if we neglect ^! latt]1 & consid] our :ole field z consi/+ ( successive r+s ( hexagons ab\t a c5tral "o1 we may obta9 a /ill simpl] rule#cfe4 ,= obvi\sly1 ar\nd our c5tral hexagon !re /&s a zone ( six1 & ar\nd ^! a zone ( twelve1 & ar\nd ^! a zone ( eighte51 & s on4 ,& ! total numb]1 exclud+ ! c5tral hexagon1 is accord+ly3 ,= "o zone #f #b #c #c #a #b1 ,= two zones #ah #c #f #c #b #c1 ,= ?ree zones #cf #d #i #c #c #d1 ,= f\r zones #fj #e #ab #c #d #e1 ,= five zones #ij #f x #ae #c #e #f1 & s =?4 ,if ,n be ! numb] ( zones1 & if we add "o to ! above numb]s = ! odd c5tral hexagon1 ! rule evid5tly is1 t ! total numb]1 ,h1 #c,n7,n #a7 #a4 ,?us1 if 9 a prep>ation ( a fly's cornea1 ,i c c\nt tw5ty-five facets 9 a l9e f a c5tral "o1 ! total numb] 9 ! entire circul> field is 7#c #be #bf7 #a #aieacff4 ,! same pr9ciples :i* acc\nt = ! developm5t ( hexagonal symmetry hold true1 z a matt] ( c\rse1 n only ( individual cells 79 ! biological s5se71 b ( any close-pack$ bodies ( uni=m size & orig9ally circul> outl9e2 & ! hexagonal patt]n is !re=e ( v common occurr5ce1 "u widely diff]5t circum/ances4 ,! curi\s read] may consult ,sir ,?omas ,br[ne's qua9t & beautiful acc\nt1 9 ! ,g>d5 ( ,cyrus1 ( hexagonal 7& also ( qu9cuncial7 symmetry 9 plants & animals1 :i* 8do? neatly decl>e h[ nature ,geometrize?1 & obs]ve? ord] 9 all ?+s40 #cbe ,we h _m v>i$ examples ( ?is pr9ciple among corals1 :]ev] ! polypes are 9 close juxtaposition1 ) nei!r empty space nor accumulations ( matrix betwe5 _! adjac5t walls4 ,favosites go?l&ica1 = in/ance1 furni%es u ) an excell5t example4 ,9 ! great g5us ,li?o/rotion we h "s species t are 8massive0 & o!rs t are 8fasciculate02 9 o!r words 9 "s ! long cyl9drical corallites are 9 close contact ) "o ano!r1 & 9 o!rs !y are sep>ate & loosely bundl$ 7,fig4 #abg74 ,accord+ly 9 ! =m] ! corallites are ,illu/ration3 ,fig4 #abg4 ,li?o/rotion ,m>t9i4 7,aft] ,ni*olson47 ,illu/ration3 ,fig4 #abh4 ,cya?ophyllum hexagonum4 7,f ,ni*olson1 aft] ,zittel47 squeez$ into hexagonal prisms1 :ile 9 ! latt] !y reta9 _! cyl9drical =m4 ,:]e ! polypes are comp>atively few1 & s h room to spread1 ! mutual pressure ceases to "w or only t5ds to pu% !m asund]1 lett+ !m rema9 circul> 9 outl9e 7e4g4 ,!cosmilia74 ,:]e !y v>y gradually 9 size1 z = in/ance 9 ,cya?ophyllum hexagonum1 !y are m or less hexagonal b are n regul> hexagons2 & :]e !re is great] & m irregul> v>iation 9 size1 ! cells w be on ! av]age hexagonal1 b "s w h few] & "s m sides ?an six1 z 9 ! annex$ figure ( ,ara*nophyllum 7,fig4 #abi74 #cbf ,:]e l>g] & small] cells1 correspond+ to two diff]5t k9ds ( zooids1 are mix$ toge!r1 we may get v>i\s results4 ,if ! l>g] cells are num]\s en\gh to be m or less 9 contact ) "o ano!r 7e4g4 v>i\s ,monticuliporae7 !y w be irregul> hexagons1 :ile ! small] cells betwe5 !m w be cru%$ into all mann] ( irregul> angul> =ms4 ,if on ! o!r h& ! l>ge cells are comp>atively few & are l>ge & /rong-wall$ comp>$ ) _! small] neighb\rs1 !n ! latt] alone w be squeez$ into hexagons1 :ile ! l>g] ones w t5d to reta9 _! circul> outl9e undi/urb$ 7e4g4 ,heliopora1 ,heliolites1 etc474 ,illu/ration3 ,fig4 #abi4 ,ara*nophyllum p5tagonum4 7,aft] ,ni*olson47 ,illu/ration3 ,fig4 #acj4 ,heliolites4 7,aft] ,woods47 ,:51 z happ5s 9 c]ta9 corals1 ! p]iph]al walls or 8!cae0 ( ! individual polypes rema9 undevelop$ b ! radiat+ septa are =m$ & calcifi$1 !n we obta9 new & beautiful ma!matical configurations 7,fig4 #aca74 ,= ! radiat+ septa are no long] conf9$ to ! circul> or hexagonal b\nds ( a polypite1 b t5d to meet & become conflu5t ) _! neighb\rs on e side2 &1 t5d+ to assume positions ( equilibrium1 or ( m9imal area1 "u ! re/ra9ts to :i* !y are subject1 !y fall into congru5t curves2 & ^! correspond1 9 a /rik+ mann]1 to ! l9es ( =ce runn+1 9 a common field ( =ce1 betwe5 a numb] ( second>y c5tres4 ,simil> patt]ns may be produc$ 9 v>i\s ways1 by ! play ( osmotic or magnetic =ces2 & a p>ticul> & v curi\s case is to be f\nd 9 ^? complicat$ =ms ( nucle> division #cbg kn[n z tria/]s1 polya/]s1 etc41 ^: relation to a field ( =ce ,h>tog has expla9$#cfg4 ,x is obvi\s t1 9 our corals1 ^! curv+ septa are all or?ogonal to ! non-exi/5t hexagonal b\nd>ies4 ,z ! ph5om5on is :olly due to ! imp]fect developm5t or non-exi/5ce ( a !cal wall1 x is n surpris+ t we f9d id5tical configurations among v>i\s corals1 or families ( corals1 n o!rwise relat$ to "o ano!r2 we f9d ! same or v simil> patt]ns display$1 = in/ance1 9 ,synhelia 7,ocul9idae71 9 ,phillipsa/raea 7,rugosa71 9 ,?amna/raea 7,fungida71 & 9 _m m4 ,illu/ration3 ,fig4 #aca4 ,surface-views ( ,corals ) undevelop$ !cae & conflu5t septa4 ,a1 ,?amna/raea2 ,b1 ,comos]is4 7,f ,ni*olson1 aft] ,zittel47 ,! mo/ fam\s ( all hexagonal con=mations & p]haps ! mo/ beautiful is t ( ! bee's cell4 ,"h we h1 z 9 our la/ examples1 a s]ies ( equal cyl9d]s1 compress$ by symmetrical =ces into regul> hexagonal prisms4 ,b 9 ?is case we h two r[s ( su* cyl9d]s1 set opposite to "o ano!r1 end to end2 & we h accord+ly to consid] also ! con=mation ( _! ends4 ,we may suppose our orig9al cyl9drical cells to h sph]ical ends1 :i* is _! normal & symmetrical mode ( t]m9ation2 &1 = close/ pack+1 x is obvi\s t ! end ( any "o cyl9d] w t\*1 & fit 9 betwe51 ! ends ( ?ree cyl9d]s 9 ! opposite r[4 ,x is j z :5 we pile r\nd-%ot 9 a heap2 ea* sph]e t we #cbh set d[n fits into its ne/ betwe5 ?ree o!rs1 & ! f\r =m a regul> tetrah$ral arrangem5t4 ,j z x 0 obvi\s1 !n1 t by mutual pressure f ! six lat]ally adjac5t cells1 any "o cell w\ld be squeez$ into a hexagonal prism1 s is x also obvi\s t1 by mutual pressure aga9/ ! ?ree t]m9al neighb\rs1 ! end ( any "o cell w be compress$ into a solid trih$ral angle ^: edges w meet1 z 9 ! analog\s case already describ$ ( a sy/em ( soap-bubbles1 at a plane angle ( #aji & s _m m9utes & seconds4 ,:at we h to compreh5d1 !n1 is h[ ! six sides ( ! cell are to be comb9$ ) its ?ree t]m9al facets4 ,?is is done by bevell+ (f ?ree alt]nate angles ( ! prism1 9 a uni=m mann]1 until we h tap]$ ! prism to a po9t2 & by s do+1 we evid5tly produce ?ree rhombic surfaces1 ea* ( :i* is d\ble ( ! triangle =m$ by jo9+ ! apex to ! ?ree unt\*$ angles ( ! prism4 ,if we exp]im5t1 n ) cyl9d]s1 b ) sph]es1 if = in/ance we pile toge!r a mass ( bread-pills 7or pills ( pla/ic9e71 & !n submit ! :ole to a uni=m pressure1 x is obvi\s t ea* ball 7l ! se$s 9 a pomegranate1 z ,kepl] said71 w be 9 contact ) twelve o!rs1--six 9 its own plane1 ?ree bel[ & ?ree above1 & 9 compression x w !re=e develop twelve plane surfaces4 ,x w 9 %ort repeat1 above & bel[1 ! conditions to :i* ! bee's cell is subject at "o end only2 &1 s9ce ! sph]e is symmetrically situat$ t[>ds its neighb\rs on all sides1 x foll[s t ! twelve plane sides to :i* its surface has be5 r$uc$ w be all simil>1 equal & simil>ly situat$4 ,moreov]1 s9ce we h produc$ ?is result by squeez+ our orig9al sph]es close toge!r1 x is evid5t t ! bodies s =m$ completely fill space4 ,! regul> solid :i* fulfils all ^! conditions is ! rhombic dodecah$ron4 ,! bee's cell1 !n1 is ?is figure incompletely =m$3 x is a hexagonal prism ) "o op5 or unf9i%$ end1 & "o trih$ral apex ( a rhombic dodecah$ron4 ,! geometrical =m ( ! bee's cell mu/ h attract$ ! att5tion & excit$ ! admiration ( ma!maticians f "t immemorial4 ,pappus ! ,alex&r9e has left u 79 ! introduction to ! ,fif? ,book ( 8 ,collections7 an acc\nt ( its hexagonal plan1 & he drew f its ma!matical symmetry ! #cbi conclusion t ! bees 7 end[$ ) reason3 8,!re be+1 !n1 ?ree figures :i* ( !mselves c fill up ! space r\nd a po9t1 viz4 ! triangle1 ! squ>e & ! hexagon1 ! bees h wisely select$ = _! /ructure t :i* conta9s mo/ angles1 suspect+ inde$ t x c\ld hold m honey ?an ei!r ( ! o!r two40 ,erasmus ,b>?ol9us 0 app>5tly ! fir/ to sugge/ t ?is hypo!sis 0 n w>rant$1 & t ! hexagonal =m 0 no m ?an ! necess>y result ( equal pressures1 ea* bee /riv+ to make its own little circle z l>ge z possible4 ,! inve/igation ( ! ends ( ! cell 0 a m difficult matt]1 & came lat]1 ?an t ( its sides4 ,9 g5]al t]ms ?is arrangem5t 0 d\btless (t5 /udi$ & describ$3 z = in/ance1 9 ! ,g>d5 ( ,cyrus3 8,& ! ,combes !mselves s regul>ly contriv$ t _! mutual int]sections make ?ree ,loz5ges at ! bottom ( e ,cell2 :i* sev]ally reg>d$ make ?ree ,r[s ( neat ,rhomboidall ,figures1 connect$ at ! angles1 & s cont9ue ?ree sev]al *a9s ?r\gh\t ! :ole comb40 ,b ,m>aldi#cfh 7,cass9i's nephew7 0 ! fir/ to measure ! t]m9al solid angle or det]m9e ! =m ( ! rhombs 9 ! pyramidal end+ ( ! cell4 ,he tells u t ! angles ( ! rhomb are #aaj & #gj3 8,*aque base d'alvole e/ =me p> trois rhombes presque t\j\rs gaux et semblables1 qui1 suivant les mesures que n\s avons prises1 ont les deux angles obtus *acun de #aaj degrs1 et p> consqu5t les deux aigus *acun de #gj40 ,he also /at$ t ! angles ( ! trapeziums :i* =m ! sides ( ! body ( ! cell 7 id5tical angles1 ( #aaj & #gj2 b 9 ! same pap] he speaks ( ! angles z be+1 respectively1 #aji #bh & #gj #cb4 ,"h a s+ul> confusion at once arose1 & has be5 p]petuat$ 9 ! books#cfi4 8,un=tunately ,raumur *ose to look ^u ?is second det]m9ation ( ,m>aldi's z be+1 z well z ! fir/1 a direct result ( measurem5t1 :]eas x is 9 reality !oretical4 ,he speaks ( x z ,m>aldi's m precise measurem5t1 & ?is error has be5 repeat$ 9 spite ( its absurdity to ! pres5t day2 nobody #ccj appe>s to h ?\ght ( ! impossibility ( measur+ su* a ?+ z ! end ( a bee's cell to ! ne>e/ m9ute40 ,at any rate1 x n[ occurr$ to ,raumur 7z curi\sly en\gh1 x _h n done to ,m>aldi7 t1 j z ! closely pack$ hexagons gave ! m9imal ext5t ( b\nd>y 9 a plane1 s ! actual solid figure1 z det]m9$ by ,m>aldi1 might be t :i*1 = a giv5 solid cont5t1 gives ! m9imum ( surface3 or :i*1 9 o!r words1 w\ld hold ! mo/ honey = ! lea/ wax4 ,he set ?is problem be=e ,ko5ig1 & ! geomet] confirm$ 8 conjecture1 ! result ( 8 calculations agree+ )9 two m9utes 7#aji #bf & #gj #cd7 ) ,m>aldi's det]m9ation4 ,b aga91 ,maclaur9#cgj & ,lhuili]#cga1 by diff]5t me?ods1 obta9$ a result id5tical ) ,m>aldi's2 & 7 able to %ew t ! discrepancy ( #b 0 due to an error 9 ,ko5ig's calculation 7( tan #b71--t is to say to ! imp]fection ( 8 log>i?mic tables1--n 7z ! books say#cgb7 8to a mi/ake on ! "p ( ! ,bee40 8,n to a mi/ake on ! "p ( ,m>aldi0 is1 ( c\rse1 all t we are entitl$ to say4 ,illu/ration3 ,fig4 #acb4 ,! !orem may be prov$ z foll[s3 ,,abcdef1 abcdef1 is a "r prism ^u a regul> hexagonal base4 ,! corn]s ,,bdf are cut (f by planes ?r\gh ! l9es ,,ac1 ,,ce1 ,,ea1 meet+ 9 a po9t ,v on ! axis ,,vn ( ! prism1 & int]sect+ ,bb1 ,dd1 ,ff1 at ,x1 ,y1 ,z4 ,x is evid5t t ! volume ( ! figure ?us =m$ is ! same z t ( ! orig9al prism ) hexagonal ends4 ,=1 if ! axis cut ! hexagon ,,abcdef 9 ,n1 ! volumes ,,acvn1 ,,acbx are equal4 #cca ,x is requir$ to f9d ! incl9ation ( ! faces =m+ ! trih$ral angle at ,v to ! axis1 su* t ! surface ( ! figure may be a m9imum4 ,let ! angle ,,nvx1 :i* is half ! solid angle ( ! prism1 2 ! side ( ! hexagon1 z ,,ab1 a2 & ! height1 z ,aa1 h4 ,!n1 ,,ac #b;a cos #cj a#c4 ,& ,,vx a_/s9 7f inspection ( ! triangle ,,lxb7 ,!re=e ! area ( ! rhombus ,,vaxc 7a#b #c7_/7b s9 74 ,& ! area ( ,aab,x 7a_/#b77b;h ,,vx cos 7 7a_/#b77b;h a_/#b cot 74 ,!re=e ! total area ( ! figure hexagon abcdef #c;a7#b;h 7a_/#b7 cot 7 #c77;a#b #c7_/7b s9 774 ,!re=e d7,area7_/d 7#c;a#b_/b777a_/s9#b 7 7#c cos 7_/7s9#b 774 ,b ?is expression vani%es1 t is to say1 d7,area7_/d #j1 :5 cos #a_/c1 t is :5 #ed #dd #h 7#aji #bh #af74 ,?is !n is ! condition "u :i* ! total area ( ! figure has its m9imal value4 ,t ! beautiful regul>ity ( ! bee's ar*itecture is due to "s automatic play ( ! physical =ces1 & t x 7 fanta/ic to assume 7) ,pappus & ,raumur7 t ! bee int5tionally seeks = a me?od ( economis+ wax1 is c]ta91 b ! precise mann] ( ?is automatic action is n s cle>4 ,:5 ! hive-bee builds a solit>y cell1 or a small clu/] ( cells1 z x does = ^? eggs :i* are to develop into que5s1 x makes b a rude production4 ,! que5-cells are lumps ( co>se wax holl[$ out & r\ghly bitt5 into %ape1 be>+ ! m>ks ( ! bee's jaws1 l ! m>ks ( a blunt adze on a r\gh-hewn log4 ,omitt+ ! simple/ ( all cases1 :5 7z among "s humble-bees7 ! old cocoons are us$ to hold honey1 ! cells built by ! 8solit>y0 wasps & bees are ( v>i\s k9ds4 ,!y may be =m$ by p>tition+ (f little *amb]s 9 a holl[ /em2 #ccb !y may be r\nd$ or oval capsules1 (t5 v neatly con/ruct$1 out ( mud1 or vegetable fibre or little /ones1 agglut9at$ toge!r ) a saliv>y glue2 b !y %ew1 except = _! r\nd$ or tubul> =m1 no ma!matical symmetry4 ,! social wasps & _m bees build1 usually out ( vegetable matt] *ew$ into a pa/e ) saliva1 v beautiful ne/s ( 8combs02 & ! close-set pap]y cells :i* con/itute ^! combs are j z regul>ly hexagonal z are ! wax5 cells ( ! hive-bee4 ,b 9 ^! cases 7or ne>ly all ( !m7 ! cells are 9 a s+le r[2 _! sides are regul>ly hexagonal1 b _! ends1 f ! want ( oppon5t =ces1 rema9 simply sph]ical4 ,9 ,melipona dome/ica 7( :i* ,d>w9 epitomises ,pi]re ,hub]'s description7 8! l>ge wax5 honey-cells are ne>ly sph]ical1 ne>ly equal 9 size1 & are aggregat$ into an irregul> mass40 ,b ! sph]ical =m is only se5 on ! outside ( ! mass2 = inw>dly ea* cell is flatt5$ into 8two1 ?ree or m flat surfaces1 accord+ z ! cell adjo9s two1 ?ree or m o!r cells4 ,:5 "o cell re/s on ?ree o!r cells1 :i* f ! sph]es be+ ne>ly ( ! same size is v frequ5tly & necess>ily ! case1 ! ?ree flat surfaces are unit$ into a pyramid2 & ?is pyramid1 z ,hub] has rem>k$1 is manife/ly a gross imitation ( ! ?ree-sid$ pyramidal base ( ! cell ( ! hive-bee#cgc40 ,! "q is1 to :at p>ticul> =ce are we to ascribe ! plane surfaces & def9ite angles :i* def9e ! sides ( ! cell 9 all ^! cases1 & ! ends ( ! cell 9 cases :]e "o r[ meets & opposes ano!r4 ,we h se5 t ,b>?ol9 sugge/$1 & x is /ill commonly believ$1 t ?is result is due to simple physical pressure1 ea* bee enl>g+ z mu* z x c ! cell :i* x is a-build+1 & nudg+ its wall outw>ds till x fills e int]v5+ gap & presses h>d aga9/ ! simil> ef=ts ( its neighb\r 9 ! cell next door#cgd4 ,b x is v d\btful #ccc :e!r su* physical or me*anical pressure1 m or less int]mitt5tly ex]cis$1 c\ld produce ! all b p]fectly smoo?1 plane surfaces & ! all b p]fectly def9ite & con/ant angles :i* *>act]ise ! cell1 :e!r x be con/ruct$ ( wax or pap]y pulp4 ,x seems m likely t we h to d ) a true surface-t5sion effect2 9 o!r words1 t ! walls assume _! configuration :5 9 a semi-fluid /ate1 :ile ! pap]y pulp is /ill liquid1 or :ile ! wax is w>m "u ! high temp]ature ( ! cr[d$ hive#cge4 ,"u ^! circum/ances1 ! direct ef=ts ( ! wasp or bee may be suppos$ to be limit$ to ! mak+ ( a tubul> cell1 z ?9 z ! nature ( ! mat]ial p]mits1 & pack+ ^! little cells z close z possible toge!r4 ,x is !n easily conceivable t ! symmetrical t5sions ( ! adjac5t films 7?\gh some:at ret>d$ by viscosity7 %\ld suffice to br+ ! :ole sy/em into equilibrium1 t is to say into ! precise configuration :i* ! comb actually pres5ts4 ,9 %ort1 ! ,m>aldi pyramids :i* t]m9ate ! bee's cell are precisely id5tical ) ! facets ( a rhombic dodecah$ron1 su* z we h assum$ to con/itute 7& :i* d\btless "u c]ta9 conditions d con/itute7 ! surfaces ( contact 9 ! int]ior ( a mass ( soap-bubbles or ( uni=m p>5*ymat\s cells2 & !re is e reason to believe t ! physical explanation is id5tical1 & n m]ely ma!matically analog\s4 ,! rem>kable passage 9 :i* ,buffon discusses ! bee's cell & ! hexagonal configuration 9 g5]al is ( su* hi/orical importance1 & tallies s closely ) ! :ole tr5d ( our enquiry1 t ,i w quote x 9 full3 8,dirai-je encore un mot2 ces cellules des abeilles1 tant vantes1 tant admires1 me f\rniss5t une preuve de plus contre l'en?\siasme et l'admiration2 cette figure1 t\te gomtrique et t\te rgulire qu'elle n\s p>at1 et qu'elle e/ en effet dans la spculation1 n'e/ ici qu'un rsultat mcanique et assez imp>fait qui se tr\ve s\v5t dans la nature1 #ccd et que l'on rem>que mme dans les productions les plus brutes2 les cri/aux et plusieurs autres pi]res1 quelques sels1 etc41 pr5n5t con/amm5t cette figure dans leur =mation4 ,qu'on obs]ve les petites cailles de la peau d'une r\ssette1 on v]ra qu'elles sont hexagones1 p>ce que *aque caille croissant en mme temps se fait ob/acle1 et t5d occup] le plus d'espace qu'il e/ possible dans un espace donn3 on voit ces mmes hexagones dans le second e/omac des animaux rum9ans1 on les tr\ve dans les gra9es1 dans leurs capsules1 dans c]ta9es fleurs1 etc4 ,qu'on remplisse un vaisseau de pois1 ou pltot de quelque autre gra9e cyl9drique1 et qu'on le f]me exactem5t aprs y avoir v]s autant d'eau que les int]valles qui re/5t entre ces gra9es peuv5t en recevoir2 qu'on fasse b\illir cette eau1 t\s ces cyl9dres devi5dront de colonnes six pans#cgf4 ,on y voit clairem5t la raison1 qui e/ purem5t mcanique2 *aque gra9e1 dont la figure e/ cyl9drique1 t5d p> son r5flem5t occup] le plus d'espace possible dans un espace donn1 elles devi5n5t donc t\tes ncessairem5t hexagones p> la compression rciproque4 ,*aque abeille *]*e occup] de mme le plus d'espace possible dans un espace donn1 il e/ donc ncessaire aussi1 puisque le corps des abeilles e/ cyl9drique1 que leurs cellules sont hexagones1--p> la mme raison des ob/acles rciproques4 ,on donne plus d'esprit aux m\*es dont les ouvrages sont les plus rguli]s2 les abeilles sont1 dit-on1 plus +nieuses que les gupes1 que les frlons1 etc41 qui sav5t aussi l'ar*itecture1 mais dont les con/ructions sont plus grossires et plus irrgulires que celles des abeilles3 on ne veut pas voir1 ou l'on ne se d\te pas que cette rgul>it1 plus ou mo9s gr&e1 dp5d uniquem5t du nombre et de la figure1 et nullem5t de l'intellig5ce de ces petites btes2 plus elles sont nombreuses1 plus il y a des =ces qui agiss5t galem5t et s'oppos5t de mme1 plus il y a p> consqu5t de contra9te mcanique1 de rgul>it =ce1 et de p]fection app>5te dans leurs productions#cgg40 #cce ,a v beautiful hexagonal symmetry1 z se5 9 section1 or dodecah$ral1 z view$ 9 ! solid1 is pres5t$ by ! cells :i* =m ! pi? ( c]ta9 ru%es 7e4g4 ,juncus effusus71 & some:at less diagrammatically by ^? :i* make ! pi? ( ! banana4 ,^! cells are /ellate 9 =m1 & ! tissue pres5ts 9 section ! appe>ance ( a network ( six-ray$ />s 7,fig4 #acc1 c71 l9k$ toge!r by ! tips ( ! rays1 & sep>at$ by symmetrical1 air-fill$1 int]cellul> spaces4 ,9 ?ick sections1 ! solid twelve-ray$ />s may be v beautifully se5 "u ! b9ocul> microscope4 ,illu/ration3 ,fig4 #acc4 ,diagram ( developm5t ( 8/ellate cells10 9 pi? ( ,juncus4 7,! d>k1 or %ad$1 areas repres5t ! cells2 ! light areas be+ ! gradually enl>g+ 8int]cellul> spaces407 ,:at has happ5$ "h is n difficult to und]/&4 ,imag9e1 z be=e1 a sy/em ( equal sph]es all 9 contact1 ea* "o !re=e t\*+ six o!rs 9 an equatorial plane2 & let ! cells be n only 9 contact1 b become atta*$ at ! po9ts ( contact4 ,!n in/ead ( ea* cell exp&+1 s z to encroa* on & fill up ! int]cellul> spaces1 let ea* cell t5d to contract or %rivel up1 by ! )drawal ( fluid f its int]ior4 ,! #ccf result w obvi\sly be t ! int]cellul> spaces w increase2 ! six equatorial atta*m5ts ( ea* cell 7,fig4 #acc1 a7 7or its twelve atta*m5ts 9 all1 to adjac5t cells7 w rema9 fix$1 & ! portions ( cell-wall betwe5 ^! po9ts ( atta*m5t w be )drawn 9 a symmetrical fa%ion 7b7 t[>ds ! c5tre4 ,z ! f9al result 7c7 we %all h a 8dodecah$ral />0 or />-polygon1 :i* appe>s 9 section z a six-ray$ figure4 ,x is obvi\sly necess>y t ! pi?-cells %\ld n only be atta*$ to "o ano!r1 b t ! out]mo/ lay] %\ld be firmly atta*$ to a b\nd>y wall1 s z to pres]ve ! symmetry ( ! sy/em4 ,:at actually occurs 9 ! ru% is tantam\nt to ?is1 b n absolutely id5tical4 ,"h x is n s mu* ! pi?-cells :i* t5d to %rivel )9 a b\nd>y ( con/ant size1 b r ! b\nd>y wall 7t is1 ! p]iph]al r+ ( woody & o!r tissues7 :i* cont9ues to exp& aft] ! pi?-cells :i* x encloses h ceas$ to gr[ or to multiply4 ,! twelve po9ts ( atta*m5t on ! sph]ical surface ( ea* little pi?-cell are uni=mly drawn asund]2 b ! cont5t1 or volume1 ( ! cell does n increase correspond+ly2 & ! rema9+ portions ( ! surface1 accord+ly1 %r9k inw>ds & gradually con/itute ! complicat$ surface ( a twelve-po9t$ />1 :i* is /ill a symmetrical figure & is /ill also a surface ( m9imal area "u ! new conditions4 ,a few ye>s aft] ! publication ( ,plateau's book1 ,"l ,kelv9 %ew$1 9 a %ort b v beautiful pap]#cgh1 t we mu/ n ha/ily assume f su* argum5ts z ! =ego+1 t a close-pack$ assemblage ( rhombic dodecah$ra w be ! true & g5]al solution ( ! problem ( divid+ space ) a m9imum p>titional area1 or w be pres5t 9 a cellul> liquid 8foam10 9 :i* x is manife/ t ! problem is actually & automatically solv$4 ,! g5]al ma!matical solution ( ! problem 7z we h already indicat$7 is1 t e int]face or p>tition-wall mu/ h con/ant curvature ?r\gh\t2 t :]e su* p>titions meet 9 an edge1 !y mu/ int]sect at angles su* t equal =ces1 9 planes p]p5dicul> to ! l9e #ccg ( int]section1 %all balance2 & f9ally1 t no m ?an ?ree su* int]faces may meet 9 a l9e or edge1 :5ce x foll[s t ! angle ( int]section ( ! film-surfaces mu/ be exactly #abj4 ,an assemblage ( equal & simil> rhombic dodecah$ra goes f> to meet ! case3 x completely fills up space2 all its surfaces or int]faces are planes1 t is to say1 surfaces ( con/ant curvature ?r\gh\t2 & ^! surfaces all meet toge!r at angles ( #abj4 ,nev]!less1 ! pro( t our rhombic dodecah$ron 7su* z we f9d exemplifi$ 9 ! bee's cell7 is a surface ( m9imal area1 is n a compreh5sive pro(2 x is limit$ to c]ta9 conditions1 & practically am\nts to no m ?an ?is1 t ( ! regul> solids1 ) all sides plane & simil>1 ?is "o has ! lea/ surface = its solid cont5t4 ,illu/ration3 ,fig4 #acd4 ,! rhombic dodecah$ron has six tetrah$ral angles1 & eight trih$ral angles2 & x is obvi\s1 on consid]ation1 t at ea* ( ! =m] six dodecah$ra meet 9 a po9t1 & t1 :]e ! f\r tetrah$ral facets ( ea* coalesce ) _! neighb\rs1 we h twelve plane films1 or int]faces1 meet+ 9 a po9t4 ,9 a precisely simil> fa%ion1 we may imag9e twelve plane films1 drawn inw>ds f ! twelve edges ( a cube1 to meet at a po9t 9 ! c5tre ( ! cube4 ,b1 z ,plateau discov]$#cgi1 :5 we dip a cubical wire skeleton into soap-solution & take x out aga91 ! twelve films :i* are ?us g5]at$ d n meet 9 a po9t1 b are gr\p$ ar\nd a small c5tral1 plane1 quadrilat]al film 7,fig4 #acd74 ,9 o!r words1 twelve plane films1 meet+ 9 a po9t1 are ess5tially un/able4 ,if we bl[ ^u our artificial film-sy/em1 ! little quadrilat]al alt]s its place1 sett+ itself p>allel n[ to "o & n[ to ano!r ( ! pair$ faces ( ! cube2 b we nev] get rid ( x4 ,moreov]1 ! size & %ape ( ! quadrilat]al1 z ( all ! o!r films 9 ! sy/em1 are p]fectly def9ite4 ,( ! twelve films 7:i* we _h #cch expect$ to f9d all plane & all simil>7 f\r are plane isosceles triangles1 & eight are slightly curv$ quadrilat]al figures4 ,! =m] h two curv$ sides1 meet+ at an angle ( #aji #bh1 & _! apices co9cide ) ! corn]s ( ! c5tral quadrilat]al1 ^: sides are also curv$1 & also meet at ?is id5tical angle2--:i* 7z we obs]ve7 is likewise an angle :i* we h be5 deal+ ) 9 ! simpl] case ( ! bee's cell1 & inde$ 9 all ! regul> solids ( :i* we h yet treat$4 ,by complet+ ! assemblage ( polyh$ra ( :i* ,plateau's skeleton-cube gives a "p1 ,"l ,kelv9 %ew$ t we %\ld obta9 a set ( equal & simil> f\rte5-sid$ figures1 or 8tetrakaidecah$ra02 & t by means ( an assemblage ( ^! figures space is homog5e\sly p>tition$--t is to say1 into equal1 simil> & simil>ly situat$ cells--) an economy ( surface 9 relation to area ev5 great] ?an 9 an assemblage ( rhombic dodecah$ra4 ,9 ! mo/ g5]alis$ case1 ! tetrakaidecah$ron is b\nd$ by ?ree pairs ( equal & p>allel quadrilat]al faces1 & f\r pairs ( equal & p>allel hexagonal faces1 nei!r ! quadrilat]als nor ! hexagons be+ necess>ily plane4 ,9 a c]ta9 p>ticul> case1 ! quadrilat]als are plane surfaces1 b ! hexagons slightly curv$ 8anticla/ic0 surfaces2 & ^! latt] h at e po9t equal & opposite curvatures1 & are surfaces ( m9imal curvature = a b\nd>y ( six curv$ edges4 ,! figure has ! rem>kable prop]ty t1 l ! plane rhombic dodecah$ron1 x s p>titions space t ?ree faces meet+ 9 an edge d s ev]y:]e at equal angles ( #abj #chj4 ,we may take x z c]ta9 t1 9 a sy/em ( p]fectly fluid films1 l ! int]ior ( a mass ( soap-bubbles1 :]e ! films are p]fectly free to glide or to rotate ov] "o ano!r1 ! mass is actually divid$ into cells ( ?is rem>kable con=mation4 #cci ,& x is q possible1 also1 t 9 ! cells ( a vegetable p>5*yma1 by c>efully mac]at+ !m ap>t1 ! same con=mation may yet be demon/rat$ "u suitable conditions2 t is to say :5 ! :ole tissue is highly symmetrical1 & ! individual cells are z ne>ly z possible equal 9 size4 ,b 9 an ord9>y microscopic section1 x w\ld seem practically impossible to di/+ui% ! f\rte5-sid$ figure f ! twelve-sid$4 ,moreov]1 if we h any?+ :atsoev] int]pos$ s z to prev5t our twelve films meet+ 9 a po9t1 & 7s to speak7 to take ! place ( our little c5tral quadrilat]al1--if we h1 = in/ance1 a t9y bead or droplet 9 ! c5tre ( our artificial sy/em1 or ev5 a little ?ick5+1 or 8b\rrelet0 z ,plateau call$ x1 ( ! cell-wall1 !n x is no long] necess>y t ! tetrakaidecah$ron %\ld be =m$4 ,accord+ly1 x is v probably ! case t1 9 ! p>5*ymat\s tissue1 "u ! actual conditions ( re/ra9t & ( v imp]fect fluidity1 x is aft] all ! rhombic dodecah$ral configuration :i*1 ev5 "u p]fectly symmetrical conditions1 is g5]ally assum$4 ,x foll[s f all t we h said1 t ! problems connect$ ) ! con=mation ( cells1 & ) ! mann] 9 :i* a giv5 space is p>tition$ by !m1 soon become exce$+ly complex4 ,& :ile ?is is s ev5 :5 all our cells are equal & symmetrically plac$1 x becomes va/ly m s :5 cells v>y+ ev5 slightly 9 size1 9 h>dness1 rigidity or o!r qualities1 are pack$ toge!r4 ,! ma!matics ( ! case v soon become too h>d = u2 b 9 its ess5ce1 ! ph5om5on rema9s ! same4 ,we h little reason to d\bt1 & no j cause to disbelieve1 t ! :ole configuration1 = in/ance ( an egg 9 ! advanc$ /ages ( segm5tation1 is accurately det]m9$ by simple physical laws1 j z mu* z 9 ! e>ly /ages ( two or f\r cells1 dur+ :i* e>ly /ages we are able to recognise & demon/rate ! =ces & _! resultant effects4 ,b :5 ma!matical inve/igation has become too difficult1 x (t5 happ5s t physical exp]im5t c reproduce = u ! ph5om5a :i* ,nature exhibits to u1 & :i* we are /riv+ to compreh5d4 ,= in/ance1 9 an admirable rese>*1 ,m4 ,rob]t %ew$1 "s ye>s ago1 n only t ! e>ly segm5tation ( #cdj ! egg ( ,tro*us 7a m>9e univalve mollusc7 proce$$ 9 accordance ) ! laws ( surface t5sion1 b he also succe$$ 9 imitat+ by means ( soap-bubbles1 sev]al /ages1 "o aft] ano!r1 ( ! develop+ egg4 ,illu/ration3 ,fig4 #ace4 ,aggregations ( f\r soap-bubbles1 to %ew v>i\s arrangem5ts ( ! int]m$iate p>tition & pol> furr[s4 7,aft] ,rob]t47 ,m4 ,rob]t c>ri$ 8 exp]im5ts z f> z ! /age ( sixte5 cells1 or bubbles4 ,x is n easy to c>ry ! artificial sy/em q s f>1 b 9 ! e>li] /ages ! exp]im5t is easy2 we h m]ely to bl[ our bubbles 9 a little di%1 add+ "o to ano!r1 & adju/+ _! sizes to produce a symmetrical sy/em4 ,"o ( ! simple/ & prettie/ p>ts ( 8 inve/igation conc]n$ ! 8pol> furr[0 ( :i* we h spok5 on p4 #caj4 ,on bl[+ f\r little contigu\s bubbles he f\nd 7z we may all f9d ) ! greate/ ease7 t !y =m a symmetrical sy/em1 two 9 contact ) "o ano!r by a lam9> film1 & two1 :i* are elevat$ a little above ! o!rs1 & :i* are sep>at$ by ! l5g? ( ! a=esaid lam9a4 ,! bubbles are ?us 9 contact ?ree by ?ree1 _! p>tition-walls mak+ ) "o ano!r equal angles ( #abj4 ,! upp] & l[] edges ( ! int]m$iate lam9a 7! l[] "o visible ?r\gh ! transp>5t sy/em7 con/itute ! two pol> furr[s ( ! embryologi/ 7,fig4 #ace1 #a-c74 ,! lam9a itself is plane :5 ! sy/em is symmetrical1 b x responds by a correspond+ curvature to ! lea/ inequality ( ! bubbles on ei!r side4 ,9 ! exp]im5t1 ! upp] pol> furr[ is usually a little %ort] ?an ! l[]1 b p>allel to x2 t is to say1 ! lam9a is ( trapezoidal =m3 ?is lack ( p]fect symmetry be+ due 79 ! exp]im5tal case7 to ! l[] portion ( ! bubbles be+ some:at drawn asund] by ! t5sion ( _! atta*m5ts to ! sides ( ! di% 7,fig4 #ace1 #d74 ,a simil> ph5om5on is usually f\nd 9 ,tro*us1 accord+ to ,rob]t1 & _m o!r obs]v]s h likewise f\nd ! upp] furr[ to be %ort] ?an ! "o bel[4 ,9 ! v>i\s species ( ! g5us ,crepidula1 ,conkl9 ass]ts t ! two furr[s are equal 9 ,c4 convexa1 t ! upp] "o is ! %ort] 9 ,c4 =nicata1 & t ! upp] "o all b disappe>s 9 ,c4 plana2 b we may well be p]mitt$ to d\bt1 )\t ! evid5ce ( v special inve/igations1 :e!r ^! slight physical diff]5ces are actually *>act]i/ic (1 & con/ant 91 p>ticul> alli$ species4 #cda ,return+ to ! exp]im5tal case1 ,rob]t f\nd t by )draw+ a little air f1 & s dim9i%+ ! bulk ( ! two t]m9al bubbles 7i4e4 ^? at ! ends ( ! int]m$iate lam9a71 ! upp] pol> furr[ 0 caus$ to elongate1 till x became equal 9 l5g? to ! l[]2 & by cont9u+ ! process x became ! long] 9 its turn4 ,^! two conditions h aga9 be5 describ$ by inve/igators z *>act]i/ic ( ?is embryo or t2 = in/ance 9 ,unio1 ,lillie has describ$ ! two furr[s z gradually alt]+ _! respective l5g?s#cha2 & ,wilson 7z ,lillie rem>ks7 _h already po9t$ out t 8! r$uction ( ! apical cross-furr[1 z comp>$ ) t at ! vegetative pole #cdb 9 molluscs & annelids #8/&s 9 obvi\s relation to ! diff]5t size ( ! cells produc$ at ! two poles#chb4' 0 ,:5 ! two lat]al bubbles are gradually r$uc$ 9 size1 or ! two t]m9al ones enl>g$1 ! upp] furr[ becomes %ort] & %ort]2 & at ! mom5t :5 x is ab\t to vani%1 a new furr[ makes its in/antane\s appe>ance 9 a direction p]p5dicul> to ! old "o2 b ! inf]ior furr[1 con/ra9$ by its atta*m5t to ! base1 rema9s un*ang$1 & accord+ly our two pol> furr[s1 :i* 7 =m]ly p>allel1 are n[ at "r angles to "o ano!r4 ,in/ead ( a s+le plane quadrilat]al p>tition1 we h n[ two triangul> ones1 meet+ 9 ! middle ( ! sy/em by _! apices1 & ly+ 9 planes at "r angles to "o ano!r 7,fig4 #ace1 #e-g7chc4 ,two su* pol> furr[s1 equal 9 l5g? & arrang$ 9 a cross1 h aga9 be5 frequ5tly describ$ by ! embryologi/s4 ,rob]t himself f\nd ?is condition 9 ,tro*us1 z an occasional or exceptional occurr5ce3 x has be5 describ$ z normal 9 ,a/]9a by ,ludwig1 9 ,bran*ipus by ,spang5b]g1 & 9 ,podocoryne & ,hydract9ia by ,bunt+4 ,x is evid5t t x repres5ts a /ate ( un/able equilibrium1 only to be ma9ta9$ "u c]ta9 conditions ( re/ra9t )9 ! sy/em4 ,s1 by slight & delicate modifications 9 ! relative size ( ! cells1 we may pass ?r\gh all ! possible arrangem5ts ( ! m$ian p>tition1 & ( ! 8furr[s0 :i* correspond to its upp] & l[] edges2 & e "o ( ^! arrangem5ts has be5 frequ5tly obs]v$ 9 ! f\r-cell$ /age ( v>i\s embryos4 ,z ! phases pass "o into ! o!r1 !y are accompani$ by *anges 9 ! curvature ( ! p>tition1 :i* 9 l mann] correspond precisely to ph5om5a :i* ! embryologi/s h witness$ & describ$4 ,& all ^! configurations belong to t l>ge class ( ph5om5a ^: di/ribution among embryos1 or among organisms 9 g5]al1 be>s no relation to ! b\nd>ies ( zoological classification2 ?r\gh molluscs1 worms1 #cdc coel5t]ates1 v]tebrates & :at n1 we meet ) n[ "o & n[ ano!r1 9 a m$ley :i* defies classification4 ,!y are n 8vital ph5om5a10 or 8functions0 ( ! organism1 or special *>act]i/ics ( ?is or t organism1 b purely physical ph5om5a4 ,! k9dr$ b m complicat$ ph5om5a :i* correspond to ! pol> furr[ :5 a l>g] numb] ( cells ?an f\r are associat$ toge!r1 we %all deal ) 9 ! next *apt]4 ,hav+ %ewn t ! capill>y ph5om5a are pat5t & unmi/akable dur+ ! e>li] /ages ( embryonic developm5t1 b soon become m obscure & incapable ( exp]im5tal reproduction 9 ! lat] /ages1 :5 ! cells h increas$ 9 numb]1 v>i\s writ]s includ+ ,rob]t himself h be5 incl9$ to argue t ! physical ph5om5a die away1 & are ov]p[]$ & cancell$ by ag5cies ( a v diff]5t ord]4 ,"h we pass into a region :]e direct obs]vation & exp]im5t are n at h& to guide u1 & :]e a man's tr5d ( ?\ght1 & way ( judg+ ! :ole evid5ce 9 ! case1 mu/ %ape 8 philosophy4 ,we mu/ rememb] t1 ev5 9 a fro? ( soap-bubbles1 we c apply an exact analysis only to ! simple/ cases & conditions ( ! ph5om5on2 we _c describe1 b c only imag9e1 ! =ces :i* 9 su* a fro? control ! respective sizes1 positions & curvatures ( ! innum]able bubbles & films ( :i* x consi/s2 b our k is en\gh to leave u assur$ t :at we h le>n$ by inve/igation ( ! simple/ cases includes ! pr9ciples :i* det]m9e ! mo/ complex4 ,9 ! case ( ! gr[+ embryo we "k f ! beg9n+ t surface t5sion is only "o ( ! physical =ces at "w2 & t o!r =ces1 includ+ ^? display$ )9 ! int]ior ( ea* liv+ cell1 play _! "p 9 ! det]m9ation ( ! sy/em4 ,b we h no evid5ce :atsoev] t at ?is po9t1 or t po9t1 or at any1 ! dom9ion ( ! physical =ces ov] ! mat]ial sy/em gives place to a new condition :]e ag5cies at pres5t unkn[n to ! physici/ impose !mselves on ! liv+ matt]1 & become responsible = ! con=mation ( its mat]ial fabric4 ,be=e we leave = ! pres5t ! subject ( ! segm5t+ #cdd egg1 we mu/ take brief note ( two associat$ problems3 viz4 7#a7 ! =mation & enl>gem5t ( ! segm5tation cavity1 or c5tral int]space ar\nd :i* ! cells t5d to gr\p !mselves 9 a s+le lay]1 & 7#b7 ! =mation ( ! ga/rula1 t is to say 79 a typical case7 ! conv]sion 8by invag9ation10 ( ! "o-lay]$ ball into a two-lay]$ cup4 ,nei!r problem is free f difficulty1 & all we c d mean:ile is to /ate !m 9 g5]al t]ms1 introduc+ "s m or less plausible assumptions4 ,! =m] problem is comp>atively easy1 z reg>ds ! t5d5cy ( a segm5tation cavity to enl>ge1 :5 once x has be5 e/abli%$4 ,we may !n assume t subdivision ( ! cells is due to ! appe>ance ( a new-=m$ septum )9 ea* cell1 t ?is septum has a t5d5cy to %r9k "u surface t5sion1 & t ^! *anges w be accompani$ on ! :ole by a dim9ution ( surface en]gy 9 ! sy/em4 ,?is be+ s1 x may be %ewn t ! volume ( ! divid$ cells mu/ be less ?an x 0 prior to division1 or 9 o!r words t "p ( _! cont5ts mu/ exude dur+ ! process ( segm5tation#chd4 ,accord+ly1 ! case :]e ! segm5tation cavity enl>ges & ! embryo developes into a holl[ bla/osph]e may1 "u ! circum/ances1 be simply describ$ z ! case :]e t outfl[ or exudation f ! cells ( ! bla/od]m is direct$ on ! :ole inw>ds4 ,! physical =ces involv$ 9 ! invag9ation ( ! cell-lay] to =m ! ga/rula h be5 repeat$ly discuss$#che1 b ! true explanation seems z yet to be by no means cle>4 ,! case1 h[ev]1 is probably n a v difficult "o1 provid$ t we may assume a diff]5ce ( osmotic pressure at ! two poles ( ! bla/osph]e1 t is to say betwe5 ! cells :i* are be+ diff]5tiat$ into out] & inn]1 into epibla/ & hypobla/4 ,x is pla9 t a bla/osph]e1 or holl[ vesicle b\nd$ by a lay] ( vesicles1 is "u v diff]5t physical conditions f a s+le1 simple vesicle or bubble4 ,! bla/osph]e has no effective surface t5sion ( its own1 su* z to ex]t pressure on #cde its cont5ts or br+ ! :ole into a sph]ical =m2 nor w local v>iations ( surface en]gy be directly capable ( affect+ ! =m ( ! sy/em4 ,b if ! sub/ance ( our bla/osph]e be suffici5tly visc\s1 !n osmotic =ces may set up curr5ts :i*1 react+ on ! ext]nal fluid pressure1 may easily cause modifications ( %ape2 & ! p>ticul> case ( invag9ation itself w n be difficult to acc\nt = on ?is assumption ( non-uni=m exudation & imbibition4 #cdf ,,*apt] ,,viii ,,! ,,=ms ,,( ,,tissues ,,or ,,cell-,,aggregates 7cont9u$7 ,! problems :i* we h be5 consid]+1 & especially t ( ! bee's cell1 belong to a class ( 8isop]imetrical0 problems1 :i* deal ) figures ^: surface is a m9imum = a def9ite cont5t or volume4 ,su* problems soon become difficult1 b we may f9d _m easy examples :i* lead u t[>ds ! explanation ( biological ph5om5a2 & ! p>ticul> subject :i* we %all f9d mo/ easy ( approa* is t ( ! division1 9 def9ite proportions1 ( "s def9ite portion ( space1 by a p>tition-wall ( m9imal area4 ,! !oretical pr9ciples s arriv$ at we %all !n attempt to apply1 aft] ! mann] ( ,b]?old & ,err]a1 to ! actual biological ph5om5a ( cell-division4 ,?is inve/igation we may approa* 9 two ways3 by consid]+1 namely1 ! p>tition+ (f f "s giv5 space or area ( "o-half 7or "s o!r fraction7 ( its cont5t2 or aga91 by deal+ simultane\sly ) ! p>titions necess>y = ! break+ up ( a giv5 space into a def9ite numb] ( comp>tm5ts4 ,if we take1 to beg9 )1 ! simple case ( a cubical cell1 x is obvi\s t1 to divide x into two halves1 ! smalle/ possible p>tition-wall is "o :i* runs p>allel to1 & midway betwe51 two ( its opposite sides4 ,if we call a ! l5g? ( "o ( ! edges ( ! cube1 !n a#b is ! area1 alike ( "o ( its sides1 & ( ! p>tition :i* we h int]pos$ p>allel1 or normal1 !reto4 ,b if we n[ consid] ! bisect$ cube1 & wi% to divide ! "o-half ( x aga91 x is obvi\s t ano!r p>tition p>allel to ! fir/1 s f> f be+ ! smalle/ possible1 is precisely twice ! size ( a cross-p>tition p]p5dicul> to x2 #cdg = ! area ( ?is new p>tition is a a_/#b4 ,& aga91 = a ?ird bisection1 our next p>tition mu/ be p]p5dicul> to ! o!r two1 & x is obvi\sly a little squ>e1 ) an area ( 7a7#b 7a#b74 ,f ?is we may draw ! simple rule t1 = a rectangul> body or p>allelopip$ to be divid$ equally by means ( a p>tition ( m9imal area1 7#a7 ! p>tition mu/ cut across ! longe/ axis ( ! figure2 & 7#b7 9 ! ev5t ( successive bisections1 ea* p>tition mu/ run at "r angles to its imm$iate pr$ecessor4 ,illu/ration3 ,fig4 #acf4 7,aft] ,b]?old47 ,we h already spok5 ( 8,sa*s's ,rules10 :i* are an empirical /atem5t ( ! me?od ( cell-division 9 plant-tissues2 & we may n[ set !m =? 9 full4 7#a7 ,! cell typically t5ds to divide into two co-equal p>ts4 7#b7 ,ea* new plane ( division t5ds to int]sect at "r angles ! prec$+ plane ( division4 ,! fir/ ( ^! rules is a /atem5t ( physiological fact1 n )\t its exceptions1 b s g5]ally true t x w ju/ify u 9 limit+ our enquiry1 = ! mo/ "p1 to cases ( equal subdivision4 ,t x is by no means univ]sally true = cells g5]ally is %ewn1 = in/ance1 by su* well-kn[n cases #cdh z ! unequal segm5tation ( ! frog's egg4 ,x is true :5 ! divid+ cell is homog5e\s1 & "u ! influ5ce ( symmetrical =ces2 b x ceases to be true :5 ! field is no long] dynamically symmetrical1 = in/ance1 :5 ! p>ts diff] 9 surface t5sion or int]nal pressure4 ,?is latt] condition1 ( asymmetry ( field1 is frequ5t 9 segm5t+ eggs#chf1 & is !n equival5t to ! pr9ciple ^u :i* ,balf\r laid /ress1 z lead+ to 8unequal0 or to 8p>tial0 segm5tation ( ! egg1--viz4 ! unequal or asymmetrical di/ribution ( protoplasm & ( food-yolk4 ,! second rule1 :i* also has its exceptions1 is true 9 a l>ge numb] ( cases2 & x owes its validity1 z we may judge f ! illu/ration ( ! repeat$ly bisect$ cube1 solely to ! guid+ pr9ciple ( m9imal areas4 ,x is 9 %ort subord9ate to1 & cov]s c]ta9 cases includ$ "u1 a mu* m important & fundam5tal rule1 due n to ,sa*s b to ,err]a2 t 7#c7 ! incipi5t p>tition-wall ( a divid+ cell t5ds to be su* t its area is ! lea/ possible by :i* ! giv5 space-cont5t c be enclos$4 ,let u return to ! case ( our cube1 & let u suppose t1 in/ead ( bisect+ x1 we desire to %ut (f "s small portion only ( its volume4 ,x is f\nd 9 ! c\rse ( exp]im5ts ^u soap-films1 t if we try to br+ a p>tition-film too ne> to "o side ( a cubical 7or rectangul>7 space1 x becomes un/able2 & is easily %ift$ to a totally new position1 9 :i* x con/itutes a curv$ cyl9drical wall1 cutt+ (f "o corn] ( ! cube4 ,x meets ! sides ( ! cube at "r angles 7= reasons :i* we h already consid]$72 &1 z we may see f ! symmetry #cdi ( ! case1 x con/itutes precisely "o-qu>t] ( a cyl9d]4 ,our plane transv]se p>tition1 :]ev] x 0 plac$1 _h always ! same area1 viz4 a#b2 & x is obvi\s t a cyl9drical wall1 if x cut (f a small corn]1 may be mu* less ?an ?is4 ,we want1 accord+ly1 to det]m9e :at is ! p>ticul> volume :i* might be p>tition$ (f ) equal economy ( wall-space 9 "o way z ! o!r1 t is to say1 :at area ( cyl9drical wall w\ld be nei!r m nor less ?an ! area a#b4 ,! calculation is v easy4 ,! surface-area ( a cyl9d] ( l5g? a is #br a1 & t ( our qu>t]-cyl9d] is1 !re=e1 a r_/#b2 & ?is be+1 by hypo!sis1 a#b1 we h a r_/#b1 or r #b;a_/4 ,! volume ( a cyl9d]1 ( l5g? a1 is ar#b1 & t ( our qu>t]-cyl9d] is 7a r#b7_/d1 :i* 7by sub/itut+ ! value ( r7 is equal to 7a#c7_/4 ,n[ precisely ?is same volume is1 obvi\sly1 %ut (f by a transv]se p>tition ( area a#b1 if ! ?ird side ( ! rectangul> space be equal to a_/4 ,& ?is fraction1 if we take a #a1 is equal to #jcah4441 or r less ?an "o-?ird4 ,&1 z we h j se51 ! radius1 or side1 ( ! correspond+ qu>t]-cyl9d] w be twice t fraction1 or equal to #fcf times ! side ( ! cubical cell4 ,illu/ration3 ,fig4 #acg4 ,if !n1 9 ! process ( division ( a cubical cell1 x s divide t ! two portions be n equal 9 volume b t "o portion by any?+ less ?an ab\t ?ree-t5?s ( ! :ole1 or ?ree-sev5?s ( ! o!r portion1 !re w be a t5d5cy = ! cell to divide1 n by means ( a plane transv]se p>tition1 b by means ( a curv$1 cyl9drical wall cutt+ (f "o corn] ( ! orig9al cell2 & ! "p s cut (f w be "o-qu>t] ( a cyl9d]4 ,by a simil> calculation we c %ew t a sph]ical wall1 cutt+ (f "o solid angle ( ! cube1 & con/itut+ an octant ( a sph]e1 w\ld likewise be ( less area ?an a plane p>tition z soon z ! volume to be enclos$ 0 n great] ?an ab\t #cej "o-qu>t] ( ! orig9al cell#chg4 ,b :ile bo? ! cyl9drical wall & ! sph]ical wall w\ld be ( less area ?an ! plane transv]se p>tition aft] t limit 7( "o-qu>t] volume7 0 pass$1 ! cyl9drical w\ld /ill be ! bett] ( ! two up to a fur!r limit4 ,x is only :5 ! volume to be p>tition$ (f #cea is no great] ?an ab\t #jae1 or some:]e ab\t "o-sev5?1 ( ! :ole1 t ! sph]ical cell-wall 9 an angle ( ! cubical cell1 t is to say ! octant ( a sph]e1 is def9itely ( less area ?an ! qu>t]-cyl9d]4 ,9 ! accompany+ diagram 7,fig4 #ach7 ! relative areas ( ! ?ree p>titions are %ewn = all fractions1 less ?an "o-half1 ( ! divid$ cell4 ,illu/ration3 ,fig4 #ach4 ,9 ?is figure1 we see t ! plane transv]se p>tition1 :atev] fraction ( ! cube x cut (f1 is always ( ! same dim5sions1 t is to say is always equal to a#b1 or #a4 ,if "o-half ( ! cube h to be cut (f1 ?is plane transv]se p>tition is mu* ! be/1 = we see by ! diagram t a cyl9drical p>tition cutt+ (f an equal volume w\ld h an area ab\t #be1 & a sph]ical p>tition w\ld h an area ab\t #ej great]4 ,! po9t ,a 9 ! diagram corresponds to ! po9t :]e ! cyl9drical p>tition w\ld beg9 to h an advantage ov] ! plane1 t is to say 7z we h se57 :5 ! fraction to be cut (f is ab\t "o-?ird1 or #cah ( ! :ole4 ,9 l mann]1 at ,b ! sph]ical octant beg9s to h an advantage ov] ! plane2 & x is n till we rea* ! po9t ,c t ! sph]ical octant becomes ( less area ?an ! qu>t]-cyl9d]4 ,illu/ration3 ,fig4 #aci4 ,! case we h dealt ) is ( little practical importance to ! biologi/1 because ! cases 9 :i* a cubical1 or rectangul>1 cell divides unequally1 & unsymmetrically1 are app>5tly few2 b we c f9d1 z ,b]?old po9t$ out1 a few examples1 = in/ance 9 ! hairs )9 ! reproductive 8conceptacles0 ( c]ta9 ,fuci 7,sphacel>ia1 etc41 ,fig4 #aci71 or 9 ! 8p>aphyses0 ( mosses 7,fig4 #adb74 ,b x is ( great !oretical importance3 z s]v+ to introduce u to a l>ge class ( cases1 9 :i* ! %ape & ! relative dim5sions ( ! orig9al cavity lead1 accord+ to ! pr9ciple ( m9imal areas1 to cell-division 9 v def9ite & sometimes unexpect$ ways4 ,x is n easy1 nor inde$ possible1 to give a g5]alis$ acc\nt ( ^! cases1 = ! limit+ conditions are some:at complex1 & ! ma!matical treatm5t soon becomes difficult4 ,b x is easy to compreh5d a few simple cases1 :i* ( !mselves w c>ry u a good long way2 & :i* w g f> to conv9ce ! /ud5t t1 9 o!r cases #ceb :i* we _c fully ma/]1 ! same guid+ pr9ciple is at ! root ( ! matt]4 ,! bisection ( a solid 7or ! subdivision ( its volume 9 o!r def9ite proportions7 soon leads u into a geometry :i*1 if n necess>ily difficult1 is apt to be unfamili>2 b 9 su* problems we c g a long way1 & (t5 f> en\gh = our p>ticul> purpose1 if we m]ely consid] ! plane geometry ( a side or section ( our figure4 ,= in/ance1 9 ! case ( ! cube :i* we h be5 j consid]+1 & 9 ! case ( ! plane & cyl9drical p>titions by :i* x has be5 divid$1 x is obvi\s t1 s9ce ^! two p>titions ext5d symmetrically f top to bottom ( our cube1 t we ne$ only consid] 7s f> z !y are conc]n$7 ! mann] 9 :i* !y subdivide ! base ( ! cube4 ,! :ole problem ( ! solid1 up to a c]ta9 po9t1 is conta9$ 9 our plane diagram ( ,fig4 #ach4 ,& :5 our p>ticul> solid is a solid ( revolution1 !n x is obvi\s t a /udy ( its plane ( symmetry 7t is to say any plane pass+ ?r\gh its axis ( rotation7 gives u ! solution ( ! :ole problem4 ,! "r cone is a case 9 po9t1 = "h ! inve/igation ( its modes ( symmetrical subdivision is completely met by an exam9ation ( ! isosceles triangle :i* con/itutes its plane ( symmetry4 ,! bisection ( an isosceles triangle by a l9e :i* %all be ! %orte/ possible is a v easy problem4 ,let ,,abc be su* a triangle ( :i* ,a is ! apex2 x may be %ewn t1 = its %orte/ l9e ( bisection1 we are limit$ to ?ree cases3 viz4 to a v]tical l9e ,,ad1 bisect+ ! angle at ,a & ! side ,,bc2 to a transv]se l9e p>allel to ! base ,,bc2 or to an oblique l9e p>allel to ,,ab or to ,,ac4 ,! respective magnitudes1 or l5g?s1 ( ^! p>tition l9es foll[ at once f ! magnitudes ( ! angles ( our triangle4 ,= we "k1 to beg9 )1 s9ce ! areas ( simil> figures v>y z ! squ>es ( _! l9e> dim5sions1 t1 9 ord] to bisect ! area1 a l9e p>allel to "o side ( our triangle mu/ always h a l5g? equal to #a_/b ( t side4 ,if !n1 we take our base1 ,,bc1 9 all cases ( a l5g? #b1 ! transv]se p>tition drawn p>allel to x w always h a l5g? equal to #b_/b1 or #b4 ,! v]tical #cec p>tition1 ,,ad1 s9ce ,,bd #a1 w always equal tan 7 be+ ! angle ,,abc74 ,& ! oblique p>tition1 ,,gh1 be+ equal to ,,ab_/#b #a_/7b cos 74 ,if !n we call our v]tical1 transv]se ,illu/ration3 ,fig4 #adj4 & oblique p>titions1 ,v1 ,t1 & ,o1 we h ,v tan 2 ,t #b2 & ,o #a_/7b cos 71 or ,v 3 ,t 3 ,o tan _/#b 3 #a 3 #a_/7b cos 74 ,&1 work+ out ^! equations = v>i\s values ( 1 we v soon see t ! v]tical p>tition 7,v7 is ! lea/ ( ! ?ree until #de1 at :i* limit ,v & ,o are ea* equal to #a_/b #gjg2 & t aga91 :5 #fj1 ,o & ,t are ea* #a1 aft] :i* ,t 7^: value always #a7 is ! %orte/ ( ! ?ree p>titions4 ,&1 z we h se51 ^! results are at once applicable1 n only to ! case ( ! plane triangle1 b also to t ( ! conical cell4 ,illu/ration3 ,fig4 #ada4 ,9 l mann]1 if we h a sph]oidal body1 less ?an a hemisph]e1 su* = in/ance z a l[1 wat*-glass %ap$ cell 7,fig4 #ada1 a71 x is obvi\s t ! smalle/ possible p>tition by :i* we c divide x into two equal halves #ced is 7z 9 our flatt5$ disc7 a m$ian v]tical "o4 ,& likewise1 ! hemisph]e itself c be bisect$ by no small] p>tition meet+ ! walls at "r angles ?an t m$ian "o :i* divides x into two simil> quadrants ( a sph]e4 ,b if we produce our hemisph]e into a m elevat$1 conical body1 or into a cyl9d] ) sph]ical cap1 x is obvi\s t !re comes a po9t :]e a transv]se1 horizontal p>tition w bisect ! figure ) less area ( p>tition-wall ?an a m$ian v]tical "o 7c74 ,& fur!rmore1 !re w be an int]m$iate region1 a region :]e height & base h _! relative dim5sions ne>ly equal 7z 9 b71 :]e an oblique p>tition w be bett] ?an ei!r ! v]tical or ! transv]se1 ?\gh "h ! analogy ( our triangle does n suffice to give u ! precise limit+ values4 ,we ne$ n exam9e ^! limitations 9 detail1 b we mu/ look at ! curvatures :i* accompany ! sev]al conditions4 ,we h se5 t a film t5ds to set itself at equal angles to ! surface :i* x meets1 & !re=e1 :5 t surface is a solid1 to meet x 7or its tang5t if x be a curv$ surface7 at "r angles4 ,our v]tical p>tition is1 !re=e1 ev]y:]e normal to ! orig9al cell-walls1 & con/itutes a plane surface4 ,b 9 ! tall]1 conical cell ) transv]se p>tition1 ! latt] /ill meets ! opposite sides ( ! cell at "r angles1 & x foll[s t x mu/ itself be curv$2 moreov]1 s9ce ! t5sion1 & !re=e ! curvature1 ( ! p>tition is ev]y:]e uni=m1 x foll[s t its curv$ surface mu/ be a portion ( a sph]e1 concave t[>ds ! apex ( ! orig9al1 n[ divid$1 cell4 ,9 ! int]m$iate case1 :]e we h an oblique p>tition1 meet+ bo? ! base & ! curv$ sides ( ! "m-cell1 ! contact mu/ /ill be ev]y:]e at "r angles3 provid$ we cont9ue to suppose t ! walls ( ! "m-cell 7l ^? ( our diagrammatic cube7 h become practically rigid be=e ! p>tition appe>s1 & are !re=e n affect$ & de=m$ by ! t5sion ( ! latt]4 ,9 su* a case1 & especially :5 ! cell is elliptical 9 cross-section1 or is /ill m complicat$ 9 =m1 x is evid5t t ! p>tition1 9 adapt+ itself to circum/ances & 9 ma9ta9+ itself z a surface ( m9imal area subject to all ! conditions ( ! case1 may h to assume a complex curvature4 #cee ,illu/ration3 ,fig4 #adb4 ,s-%ap$ p>titions3 ,a1 f ,taonia atom>ia 7aft] ,re9ke72 ,b1 f p>aphyses ( ,fucus2 ,c1 f rhizoids ( ,moss2 ,d1 f p>aphyses ( ,polytri*um4 ,:ile 9 v _m cases ! p>titions 7l ! walls ( ! orig9al cell7 w be ei!r plane or sph]ical1 a m complex curvature w be assum$ "u a v>iety ( conditions4 ,x w be apt to occur1 = in/ance1 :5 ! "m-cell is irregul> 9 %ape1 & "o p>ticul> case ( su* asymmetry w be t 9 :i* 7z 9 ,fig4 #adc7 ! cell has begun to bran*1 or give (f a div]ticulum1 be=e division takes place4 ,a v complicat$ case ( a diff]5t k9d1 ?\gh n )\t its analogies to ! cases we are consid]+1 w occur 9 ! p>titions ( m9imal area :i* subdivide ! spiral tube ( a nautilus1 z we %all pres5tly see4 ,& aga91 :5ev] we h a m>k$ int]nal asymmetry ( ! cell1 lead+ to irregul> & anomal\s modes ( division1 9 :i* ! cell is n necess>ily divid$ into two equal halves & 9 :i* ! p>tition-wall may assume an oblique position1 !n app>5tly anomal\s curvatures w t5d to make _! appe>ance#chh4 ,suppose t a m or less oblong cell h a t5d5cy to divide by means ( an oblique p>tition 7z may happ5 ?r\gh v>i\s causes or conditions ( asymmetry71 su* a p>tition w /ill h a t5d5cy to set itself at "r angles to ! rigid walls #cef ( ! "m-cell3 & x w at once foll[ t our oblique p>tition1 ?r\gh\t its :ole ext5t1 w assume ! =m ( a complex1 saddle-%ap$ or anticla/ic surface4 ,illu/ration3 ,fig4 #adc4 ,diagrammatic explanation ( ,s-%ap$ p>tition4 ,_m su* cases ( p>titions ) complex or d\ble curvature exi/1 b !y are n always easy ( recognition1 nor is ! p>ticul> case :]e !y appe> 9 a t]m9al cell a common "o4 ,we may see !m1 = in/ance1 9 ! roots 7or rhizoids7 ( ,mosses1 especially at ! po9t ( developm5t ( a new rootlet 7,fig4 #adb1 ,c72 & aga9 among ,mosses1 9 ! 8p>aphyses0 ( ! male pro?alli 7e4g4 9 ,polytri*um71 we f9d m or less simil> p>titions 7,d74 ,!y are frequ5t also among _m ,fuci1 z 9 ! hairs or p>aphyses ( ,fucus itself 7,b74 ,9 ,taonia atom>ia1 z figur$ 9 ,re9ke's memoir on ! ,dictyotaceae ( ! ,gulf ( ,naples#chi1 we see1 9 l mann]1 oblique p>titions1 :i* on m c>eful exam9ation are se5 to be curves ( d\ble curvature 7,fig4 #adb1 ,a74 ,! physical cause & orig9 ( ^! ,s-%ap$ p>titions is some:at obscure1 b we may attempt a t5tative explanation4 ,:5 we ass]t a t5d5cy = ! cell to divide transv]sely to its long axis1 we are n only /at+ empirically t ! p>tition t5ds to appe> 9 a small1 r ?an a l>ge cross-section ( ! cell3 b we are also implicitly ascrib+ to ! cell a longitud9al pol>ity 7,fig4 #adc1 ,a71 & implicitly ass]t+ t x t5ds to #ceg divide 7j z ! segm5t+ egg does71 by a p>tition transv]se to its pol> axis4 ,su* a pol>ity may conceivably be due to a *emical asymmetry1 or anisotropy1 su* z we h le>n$ ( 7f ,pr(essor ,macallum's exp]im5ts7 9 our *apt] on ,adsorption4 ,n[ if ! *emical conc5tration1 on :i* ?is anisotropy or pol>ity 7by hypo!sis7 dep5ds1 be unsymmetrical1 "o ( its poles be+ z x 7 deflect$ to "o side1 :]e a little bran* or bud is be+ 7or ab\t to be7 giv5 (f1--all 9 precise accordance ) ! adsorption ph5om5a describ$ on p4 #bhi1--!n our 8pol> axis0 w\ld necess>ily be a curv$ axis1 & ! p>tition1 be+ con/ra9$ 7aga9 ex hypo!si7 to arise transv]sely to ! pol> axis1 w\ld lie obliquely to ! app>5t axis ( ! cell 7,fig4 #adc1 ,b1 ,c74 ,& if ! oblique p>tition be s situat$ t x has to meet ! opposite walls 7z 9 ,c71 !n1 9 ord] to d s symmetrically 7i4e4 ei!r p]p5dicul>ly1 z :5 ! cell-wall is already solidifi$1 or at lea/ at equal angles on ei!r side71 x is evid5t t ! p>tition1 9 its c\rse f "o side ( ! cell to ! o!r1 mu/ necess>ily assume a m or less ,s-%ap$ curvature 7,fig4 #adc1 ,d74 ,z a matt] ( fact1 :ile we h abundant simple illu/rations ( ! pr9ciples :i* we h n[ begun to /udy1 app>5t exceptions to ?is simplicity1 due to an asymmetry ( ! cell itself1 or ( ! sy/em ( :i* ! s+le cell is b a "p1 are by no means r>e4 ,= example1 we "k t 9 cambium-cells1 division frequ5tly takes place p>allel to ! long axis ( ! cell1 :5 a p>tition ( mu* less area w\ld suffice if x 7 set cross-ways3 & x is only :5 a consid]able disproportion has be5 set up betwe5 ! l5g? & bread? ( ! cell1 t ! balance is 9 "p r$ress$ by ! appe>ance ( a transv]se p>tition4 ,x 0 ow+ to su* exceptions t ,b]?old 0 l$ to qualify & ev5 to depreciate ! importance ( ! law ( m9imal areas z a factor 9 cell-division1 aft] he himself _h done s mu* to demon/rate & elucidate x#cij4 ,he 0 deeply & rightly impress$ by ! fact t o!r =ces besides surface #ceh t5sion1 bo? ext]nal & int]nal to ! cell1 play _! "p 9 ! det]m9ation ( its p>titions1 & t ! answ] to our problem is n to be giv5 9 a ^w4 ,h[ fundam5tally important x is1 h[ev]1 9 spite ( all conflict+ t5d5cies & app>5t exceptions1 we %all see bett] & bett] z we proce$4 ,b let u leave ! exceptions & return to a consid]ation ( ! simpl] & m g5]al ph5om5a4 ,& 9 s do+1 let u leave ! case ( ! cubical1 quadrangul> or cyl9drical cell1 & exam9e ! case ( a sph]ical cell & ( its successive divisions1 or ! /ill simpl] case ( a circul>1 discoidal cell4 ,:5 we attempt to inve/igate ma!matically ! position & =m ( a p>tition ( m9imal area1 x is pla9 t we %all be deal+ ) comp>atively simple cases :]ev] ev5 "o dim5sion ( ! cell is mu* less ?an ! o!r two4 ,:]e two dim5sions are small comp>$ ) ! ?ird1 z 9 a ?9 cyl9drical filam5t l t ( ,spirogyra1 we h ! problem at its simple/2 = x is at once obvi\s1 !n1 t ! p>tition mu/ lie transv]sely to ! long axis ( ! ?read4 ,b ev5 :]e "o dim5sion only is relatively small1 z = in/ance 9 a flatt5$ plate1 our problem is s f> simplifi$ t we see at once t ! p>tition _c be p>allel to ! ext5d$ plane1 b mu/ cut ! cell1 someh[1 at "r angles to t plane4 ,9 %ort1 ! problem ( divid+ a mu* flatt5$ solid becomes id5tical ) t ( divid+ a simple surface ( ! same =m4 ,!re are a numb] ( small ,algae1 gr[+ 9 ! =m ( small flatt5$ discs1 consi/+ 7= a "t at any rate7 ( b a s+le lay] ( cells1 :i*1 z ,b]?old %ew$1 exemplify ?is comp>atively simple problem2 & we %all f9d pres5tly t x is also admirably illu/rat$ 9 ! cell-divisions :i* occur 9 ! egg ( a frog or a sea-ur*91 :5 ! egg = ! sake ( exp]im5t is flatt5$ out "u artificial pressure4 ,illu/ration3 ,fig4 #add4 ,developm5t ( ,ery?rotri*ia4 7,aft] ,b]?old47 ,illu/ration3 ,fig4 #ade4 ,fig4 #add 7tak5 f ,b]?old's ,monograph ( ! ,naples ,bangiaciae7 repres5ts y\ng] & old] discs ( ! little alga ,ery?rotri*ia discig]a2 & x w be se5 t1 9 all /ages save ! fir/1 we h an arrangem5t ( cell-p>titions :i* looks some:at complex1 b into :i* we mu/ attempt to ?r[ "s light & ord]4 ,/>t+ ) ! orig9al s+le1 & flatt5$1 #cei cell1 we h no difficulty ) ! fir/ two cell-divisions2 = we "k t no bisect+ p>titions c possibly be %ort] ?an ! two diamet]s1 :i* divide ! cell into halves & into qu>t]s4 ,we h only to rememb] t1 = ! sum total ( p>titions to be a m9imum1 ?ree only mu/ meet 9 a po9t2 & !re=e1 ! f\r quadrantal walls mu/ %ift a little1 produc+ ! usual little m$ian p>tition1 or cross-furr[1 in/ead ( "o common1 c5tral po9t ( junction4 ,?is little int]m$iate wall1 h[ev]1 w be v small1 & to all int5ts & purposes we may deal ) ! case z ?\gh we _h n[ to d ) f\r equal cells1 ea* "o ( !m a p]fect quadrant4 ,& s our problem is1 to f9d ! %orte/ l9e :i* %all divide ! quadrant ( a circle into two halves ( equal area4 ,a radial p>tition 7,fig4 #ade1 ,a71 />t+ f ! apex ( ! quadrant1 is at once exclud$1 = a reason simil> to t j ref]r$ to2 our *oice mu/ lie !re=e betwe5 two modes ( division su* z are illu/rat$ 9 ,fig4 #ade1 :]e ! p>tition is ei!r 7z 9 ,b7 #cfj conc5tric ) ! out] bord] ( ! cell1 or else 7z 9 ,c7 cuts t out] bord]2 9 o!r words1 our p>tition may 7,b7 cut bo? radial walls1 or 7,c7 may cut "o radial wall & ! p]iph]y4 ,^! are ! two me?ods ( division :i* ,sa*s call$1 respectively1 7,b7 p]icl9al1 & 7,c7 anticl9al#cia4 ,we may ei!r treat ! walls ( ! divid+ quadrant z already solidifi$1 or at lea/ z hav+ a t5sion comp>$ ) :i* t ( ! incipi5t p>tition film is inconsid]able4 ,9 ei!r case ! p>tition mu/ meet ! cell-wall1 on ei!r side1 at "r angles1 & 7its own t5sion & curvature be+ ev]y:]e uni=m7 x mu/ take ! =m ( a circul> arc4 ,n[ we f9d t a flatt5$ cell :i* is approximately a quadrant ( a circle inv>iably divides aft] ! mann] ( ,fig4 #ade1 ,c1 t is to say1 by an approximately circul>1 anticl9al wall1 su* z we n[ recognise 9 ! eight-cell$ /age ( ,ery?rotri*ia 7,fig4 #add72 let u !n consid] t ,nature has solv$ our problem = u1 & let u "w out ! actual geometric conditions4 ,let ! quadrant ,,oab 79 ,fig4 #adf7 be divid$ into two p>ts ( equal area1 by ! circul> arc ,,mp4 ,x is requir$ to det]m9e 7#a7 ! position ( ,p ^u ! arc ( ! quadrant1 t is to say ! angle ,,bop2 7#b7 ! position ( ! po9t ,m on ! side ,,oa2 & 7#c7 ! l5g? ( ! arc ,,mp 9 t]ms ( a radius ( ! quadrant4 7#a7 ,draw ,,op2 also ,,pc a tang5t1 meet+ ,,oa 9 ,c2 & ,,pn1 p]p5dicul> to ,,oa4 ,let u call a a radius2 & ! angle at ,c1 :i* is obvi\sly equal to ,,opn1 or ,,pob4 ,!n ,,cp a cot 2 ,,pn a cos 2 ,,nc ,,cp cos a 7cos#b 7_/7s9 74 ,! area ( ! portion ,,pmn ,c7,p#b7 ,,pn ,,nc a#b7;cot#b 7 a7cos 7 a7cos#b 7_/7s9 7 a#b7;cot#b 7cos#c 7_/7s9 774 #cfa ,& ! area ( ! portion ,,pna a#b7_/b 7 ,,on ,,np a#b7_/b 7 a7s9 7 a7cos 7 a#b7_/b s9 cos 74 ,!re=e ! area ( ! :ole portion ,,pma 7a#b7_/b 7_/#b cot#b 7cos#c 7_/s9 s9 cos 7 7a#b7_/b 7_/#b cot#b cot 71 & also1 by hypo!sis1 area ( ! quadrant1 7a#b7_/h4 ,illu/ration3 ,fig4 #adf4 ,h5ce is def9$ by ! equation a#b_/b 7_/#b cot#b cot 7 7a#b7_/h1 or _/#d cot#b cot #j4 ,we may solve ?is equation by con/ruct+ a table 7( :i* ! foll[+ is a small portion7 = v>i\s values ( 4 _/#d cot cot#b x #cd #cd #ghed #fjcc #adead #abgji #jjaf #ce #ghed #fjcf #adeje #abgjj #jjac #cf #ghed #fjci #addif #abfij #jjji #cg #ghed #fjdb #addhg #abfhj #jjje #ch #ghed #fjde #addgh #abfga #jjjb #ci #ghed #fjdh #addfi #abffa #jjjb #dj #ghed #fjea #addfj #abfeb #jjje #cfb ,we see accord+ly t ! equation is solv$ 7z accurately z ne$ be7 :5 is an angle some:at ov] #cd #ch1 or say #cd #ch4 ,t is to say1 a quadrant ( a circle is bisect$ by a circul> arc cutt+ ! side & ! p]iph]y ( ! quadrant at "r angles1 :5 ! arc is su* z to include 7#ij #cd #ch71 i4e4 #ee #bb ( ! quadrantal arc4 ,?is det]m9ation ( ours is practically id5tical ) t :i* ,b]?old arriv$ at by a r\gh & ready me?od1 )\t ! use ( ma!matics4 ,he simply tri$ v>i\s ways ( divid+ a quadrant ( pap] by means ( a circul> arc1 & w5t on do+ s till he got ! weights ( 8 two pieces ( pap] approximately equal4 ,! angle1 z he ?us det]m9$ x1 0 #cdf1 or say #cd #cf4 7#b7 ,! position ( ,m on ! side ( ! quadrant ,,oa is giv5 by ! equation ,,om a cosec a cot 2 ! value ( :i* expression1 = ! angle :i* we h j discov]$1 is #cjbh4 ,t is to say1 ! radius 7or side7 ( ! quadrant w be divid$ by ! new p>tition into two p>ts1 9 ! proportions ( ne>ly ?ree to sev54 7#c7 ,! l5g? ( ! arc ,,mp is equal to a cot 2 & ! value ( ?is = ! giv5 angle is #hgea4 ,?is is z mu* z to say t ! curv$ p>tition-wall :i* we are consid]+ is %ort] ?an a radial p>tition 9 ! proportion ( #h to #aj1 or sev5-eights almo/ exactly4 ,b we mu/ also comp>e ! l5g? ( ?is curv$ 8anticl9al0 p>tition-wall 7,,mp7 ) t ( ! conc5tric1 or p]icl9al1 "o 7,,rs1 ,fig4 #adg7 by :i* ! quadrant might also be bisect$4 ,! l5g? ( ?is p>tition is obvi\sly equal to ! arc ( ! quadrant 7i4e4 ! p]iph]al wall ( ! cell7 divid$ by #b2 or1 9 t]ms ( ! radius1 _/#bb #aaaa4 ,s t1 n only is ! anticl9al p>tition 7su* z we actually f9d 9 nature7 notably ! be/1 b ! p]icl9al "o1 :5 x comes to divid+ an entire quadrant1 is v consid]ably l>g] ev5 ?an a radial p>tition4 ,illu/ration3 ,fig4 #adg4 ,! two cells into :i* our orig9al quadrant is n[ divid$1 :ile !y are equal 9 volume1 are ( v diff]5t %apes2 ! #cfc "o is a triangle 7,,map7 ) two sides =m$ ( circul> arcs1 & ! o!r is a f\r-sid$ figure 7,,mobp71 :i* we may call approximately oblong4 ,we _c say z yet h[ ! triangul> portion ought to divide2 b x is obvi\s t ! lea/ possible p>tition-wall :i* %all bisect ! o!r mu/ run across ! long axis ( ! oblong1 t is to say p]icl9ally4 ,?is1 also1 is precisely :at t5ds actually to take place4 ,9 ! foll[+ diagrams 7,fig4 #adh7 ( a frog's egg divid+ "u pressure1 t is to say :5 r$uc$ to ! =m ( a flatt5$ plate1 we see1 fir/ly1 ! division into f\r quadrants 7by ! p>titions #a1 #b72 secondly1 ! division ( ea* quadrant by means ( an anticl9al circul> arc 7#c1 #c71 cutt+ ! p]iph]al wall ( ! quadrant approximately 9 ! proportions ( ?ree to sev52 & ?irdly1 we see t ( ! eight cells 7f\r triangul> & f\r oblong7 into :i* ! :ole egg is n[ divid$1 ! f\r :i* we h call$ oblong n[ proce$ to divide by p>titions transv]se to _! long axes1 or r\ghly p>allel to ! p]iph]y ( ! egg4 ,illu/ration3 ,fig4 #adh4 ,segm5tation ( frog's egg1 "u artificial compression4 7,aft] ,r\x47 ,! "q h[ ! o!r1 or triangul>1 portion ( ! divid$ quadrant w next divide leads u to ano!r well-def9$ problem1 :i* is only a slight ext5sion1 mak+ all[ance = ! circul> arcs1 ( t elem5t>y problem ( ! triangle we h already consid]$4 ,we "k n[ t an entire quadrant mu/ divide 7s t its bisect+ wall %all h ! lea/ possible area7 by means ( an anticl9al p>tition1 b h[ ab\t any small] sectors ( circles8 ,x is obvi\s 9 ! case ( a small prismatic #cfd sector1 su* z t %ewn 9 ,fig4 #adi1 t a p]icl9al p>tition is ! smalle/ by :i* we c possibly bisect ! cell2 we want1 accord+ly1 to "k ! limits bel[ :i* ! p]icl9al p>tition is always ! be/1 & above :i* ! anticl9al arc1 z 9 ! case ( ! :ole quadrant1 has ! advantage 9 reg>d to smallness ( surface area4 ,?is may be easily det]m9$2 = ! prec$+ inve/igation is a p]fectly g5]al "o1 & ! results hold good = sectors ( any o!r arc1 z well z = ! quadrant1 or arc ( #ij4 ,t is to say1 ! l5g? ( ! p>tition-wall ,,mp is always det]m9$ by ! angle 1 accord+ to our equation ,,mp a cot 2 & ! angle has a def9ite relation to 1 ! angle ( arc4 ,illu/ration3 ,fig4 #adi4 ,moreov]1 9 ! case ( ! p]icl9al b\nd>y1 ,,rs 7,fig4 #adg7 7or ab1 ,fig4 #adi71 we "k t1 if x bisect ! cell1 ,,rs a _/#b4 ,accord+ly1 ! arc ,,rs w be j equal to ! arc ,,mp :5 cot _/#b4 ,:5 cot _/#b or ,,mp ,,rs1 !n division w take place z 9 ,,rs4 ,:5 cot _/#b1 or ,,mp ,,rs1 !n division w take place z 9 ,,mp4 ,9 ! accompany+ diagram 7,fig4 #aej71 ,i h plott$ ! v>i\s magnitudes ) :i* we are conc]n$1 9 ord] to exhibit ! sev]al limit+ values4 ,"h we see1 9 ! fir/ place1 ! curve m>k$ 1 :i* %ews on ! 7left-h&7 v]tical scale ! v>i\s possible magnitudes ( t angle 7viz4 ! angle #cfe ( arc ( ! :ole sector :i* we wi% to divide71 & on ! horizontal scale ! correspond+ values ( 1 or ! angle :i* ,illu/ration3 ,fig4 #aej4 det]m9es ! po9t on ! p]iph]y :]e x is cut by ! p>tition-wall1 ,,mp4 ,two limit+ cases are to be notic$ "h3 7#a7 at #ij 7po9t ,a 9 diagram71 because we are at pres5t only #cff deal+ ) arcs no great] ?an a quadrant2 & 7#b71 ! po9t 7,b7 :]e ! angle comes to equal ! angle 1 = aft] t po9t ! con/ruction becomes impossible1 s9ce an anticl9al bisect+ p>tition-wall w\ld be p>tly outside ! cell4 ,! only p>tition :i*1 aft] ! po9t1 c possibly exi/1 is a p]icl9al "o4 ,?is po9t1 z our diagram %ews u1 occurs :5 ! angles 7 & 7 are ea* r "u #eb4 ,next ,i h plott$1 on ! same diagram1 & 9 relation to ! same scales ( angles1 ! correspond+ l5g?s ( ! two p>titions1 viz4 ,,rs & ,,mp1 _! l5g?s be+ express$ 7on ! "r-h& side ( ! diagram7 9 relation to ! radius ( ! circle 7a71 t is to say ! side wall1 ,,oa1 ( our cell4 ,! limit+ values "h are 7#a71 ,c1 ,c1 :]e ! angle ( arc is #ij1 & :]e1 z we h already se51 ! two p>tition-walls h ! relative magnitudes ( ,,mp 3 ,,rs #jhge 3 #aaaa2 7#b7 ! po9t ,d1 :]e ,,rs equals unity1 t is to say :]e ! p]icl9al p>tition has ! same l5g? z a radial "o2 ?is occurs :5 is r "u #hb 7cf4 ! po9ts ,d1 ,d72 7#c7 ! po9t ,e1 :]e ,,rs & ,,mp int]sect2 t is to say ! po9t at :i* ! two p>titions1 p]icl9al & anticl9al1 are ( ! same magnitude2 ?is is ! case1 accord+ to our diagram1 :5 ! angle ( arc is j ov] #fb4 ,we see f ?is1 !n1 t :at we h call$ an anticl9al p>tition1 z ,,mp1 is only likely to occur 9 a triangul> or prismatic cell ^: angle ( arc lies betwe5 #ij & #fb4 ,9 all n>r[] or m tap]+ cells1 ! p]icl9al p>tition w be ( less area1 & w !re=e be m & m likely to occur4 ,! case 7,f7 :]e ! angle is j #fj is ( "s int]e/4 ,"h1 ow+ to ! curvature ( ! p]iph]al bord]1 & ! consequ5t fact t ! p]iph]al angles are some:at great] ?an ! apical angle 1 ! p]icl9al p>tition has a v slight & almo/ imp]ceptible advantage ov] ! anticl9al1 ! relative proportions be+ ab\t z ,,mp 3 ,,rs #jgc 3 #jgb4 ,b if ! equilat]al triangle be a plane sph]ical triangle1 i4e4 a plane triangle b\nd$ by circul> arcs1 !n we see t !re is no long] any di/9ction at all betwe5 our two p>titions2 ,,mp & ,,rs are n[ id5tical4 ,on ! same diagram1 ,i h ins]t$ ! curve = values ( #cfg cosec cot ,,om1 t is to say ! di/ances f ! c5tre1 along ! side ( ! cell1 ( ! />t+-po9t 7,m7 ( ! anticl9al p>tition4 ,! po9t ,c repres5ts its position 9 ! case ( a quadrant1 & %ews x to be 7z we h already said7 ab\t #c_/aj ( ! l5g? ( ! radius f ! c5tre4 ,if1 on ! o!r h&1 our cell be an equilat]al triangle1 !n we h to read (f ! po9t on ?is curve correspond+ to #fj1 & we f9d x at ! po9t ,f 7v]tically "u ,f71 :i* tells u t ! p>tition n[ />ts #de_/aj1 or ne>ly halfway1 along ! radial wall4 ,! =ego+ consid]ations c>ry u a long way 9 our inve/igations ( _m ( ! simpl] =ms ( cell-division4 ,/rictly speak+ !y are limit$ to ! case ( flatt5$ cells1 9 :i* we c treat ! problem z ?\gh we 7 simply p>tition+ a plane surface4 ,b x is obvi\s t1 ?\gh !y d n tea* u ! :ole con=mation ( ! p>tition :i* divides a m complicat$ solid into two halves1 yet !y d1 ev5 9 su* a case1 enlight5 u s f>1 t !y tell u ! appe>ance pres5t$ 9 "o plane ( ! actual solid4 ,& z ?is is all t we see 9 a microscopic section1 x foll[s t ! results we h arriv$ at w greatly help u 9 ! int]pretation ( microscopic appe>ances1 ev5 9 comp>atively complex cases ( cell-division4 ,illu/ration3 ,fig4 #aea4 ,let u n[ return to our quadrant cell 7,,oapb71 :i* we h f\nd to be divid$ into a triangul> & a quadrilat]al portion1 z 9 ,fig4 #adg or ,fig4 #aea2 & let u n[ suppose ! :ole sy/em to gr[1 9 a uni=m fa%ion1 z a prelude to fur!r subdivision4 ,! :ole quadrant1 gr[+ uni=mly 7or ) equal radial increm5ts71 w /ill rema9 a quadrant1 & x is obvi\s1 !re=e1 t = e new increm5t ( size1 m w be add$ to ! m>g9 ( its triangul> portion ?an to ! #cfh n>r[] m>g9 ( its quadrilat]al portion2 & ^! increm5ts w be 9 proportion to ! angles ( arc1 viz4 #ee #bb 3 #cd #ch1 or z #if 3 #fj1 i4e4 z #h 3 #e4 ,& accord+ly1 if we may assume 7& ! assumption is a v plausible "o71 t1 j z ! quadrant itself divid$ into two halves aft] x got to a c]ta9 size1 s ea* ( its two halves w rea* ! same size be=e aga9 divid+1 x is obvi\s t ! triangul> portion w be d\bl$ 9 size1 & !re=e ready to divide1 a consid]able "t be=e ! quadrilat]al "p4 ,to "w out ! problem 9 detail w\ld lead u into tr\blesome ma!matics2 b if we simply assume t ! increm5ts are proportional to ! increas+ radii ( ! circle1 we h ! foll[+ equations3 ,let u call ! triangul> cell ,t1 & ! quadrilat]al1 ,q 7,fig4 #aea72 let ! radius1 ,,oa1 ( ! orig9al quadrantal cell a #a2 & let ! increm5t :i* is requir$ to add on a portion equal to ,t 7su* z ,,pp,a,a7 be call$ x1 & let t requir$1 simil>ly1 = ! d\bl+ ( ,q be call$ x4 ,!n we see t ! area ( ! orig9al quadrant ,t ,q a#b #ghed;a#b1 :ile ! area ( ,t ,q #cibg;a#b4 ,! area ( ! enl>g$ sector1 p,,oa1 7a x7#b 7#ee #bb7 #b #dhca7;a x7#b1 & ! area ,,opa a#b 7#ee #bb7 #b #dhca;a#b4 ,!re=e ! area ( ! add$ portion1 ,t1 #dhca 77a x7#b a#b74 ,& ?is1 by hypo!sis1 ,t #cibg;a#b4 ,we get1 accord+ly1 s9ce a #a1 x#b #bx #cibg_/dhca #haj1 &1 solv+1 x #a #aha #acde1 or x #jcde4 ,work+ out x 9 ! same way1 we arrive at ! approximate value1 x #a #aeag4 #cfi ,?is is z mu* z to say t1 suppos+ ea* cell t5ds to divide into two halves :5 7& n be=e7 its orig9al size is d\bl$1 !n1 9 our flatt5$ disc1 ! triangul> cell ,t w t5d to divide :5 ! radius ( ! disc has increas$ by ab\t a ?ird 7f #a to #acde71 b ! quadrilat]al cell1 ,q1 w n t5d to divide until ! l9e> dim5sions ( ! disc h increas$ by ab\t a half 7f #a to #aeag74 ,! case "h illu/rat$ is ( no small g5]al importance4 ,= x %ews u t a uni=m & symmetrical gr[? ( ! organism 7symmetrical1 t is to say1 "u ! limitations ( a plane surface1 or plane section7 by no means involves a uni=m or symmetrical gr[? ( ! individual cells1 b may1 "u c]ta9 conditions1 actually lead to inequality among ^!2 & ?is inequality may be fur!r emphasis$ by diff]5ces :i* arise out ( x1 9 reg>d to ! ord] ( frequ5cy ( fur!r subdivision4 ,?is ph5om5on 7or to be q c&id1 ?is hypo!sis1 :i* is due to ,b]?old7 is entirely indep5d5t ( any *ange or v>iation 9 individual surface t5sions2 & accord+ly x is ess5tially diff]5t f ! ph5om5on ( unequal segm5tation 7z /udi$ by ,balf\r71 to :i* we h ref]r$ on p4 #cdh4 ,9 ?is fa%ion1 we might g on to consid] ! mann]1 & ! ord] ( succession1 9 :i* ! subsequ5t cell-divisions w\ld t5d to take place1 z gov]n$ by ! pr9ciple ( m9imal areas4 ,b ! calculations w\ld gr[ m difficult1 or ! results got by simple me?ods w\ld gr[ less & less exact4 ,at ! same "t1 "s ( ^! results w\ld be ( great int]e/1 & well wor? ! tr\ble ( obta9+4 ,= in/ance1 ! precise mann] 9 :i* our triangul> cell1 ,t1 w\ld next divide w\ld be int]e/+ to "k1 & a g5]al solution ( ?is problem is c]ta9ly tr\blesome to calculate4 ,b 9 ?is p>ticul> case we c see t ! wid? ( ! triangul> cell ne> ,p is s obvi\sly less ?an t ne> ei!r ( ! o!r two angles1 t a circul> arc cutt+ (f t angle is b\nd to be ! %orte/ possible bisect+ l9e2 & t1 9 %ort1 our triangul> cell w t5d to subdivide1 j l ! orig9al quadrant1 into a triangul> & a quadrilat]al portion4 ,b ! case w be diff]5t next "t1 because 9 ?is new #cgj triangle1 ,,prq1 ! lea/ wid? is ne> ! inn]mo/ angle1 t at ,q2 & ! bisect+ circul> arc w !re=e be opposite to ,q1 or 7approximately7 p>allel to ,,pr4 ,! importance ( ?is fact is at once evid5t2 = x means to say t !re soon comes a "t :51 :e!r by ! division ( triangles or ( quadrilat]als1 we f9d only quadrilat]al cells adjo9+ ! p]iph]y ( our circul> disc4 ,9 ! subsequ5t division ( ^! quadrilat]als1 ! p>titions w arise transv]sely to _! long axes1 t is to say1 radially 7z ,u1 ,v72 & we %all consequ5tly h a sup]ficial or p]iph]al lay] ( quadrilat]al cells1 ) sides approximately p>allel1 t is to say :at we are accu/om$ to call an epid]mis4 ,& ?is epid]mis or sup]ficial lay] w be 9 cle> contra/ ) ! m irregul>ly %ap$ cells1 ! products ( triangles & quadrilat]als1 :i* make up ! deep]1 und]ly+ lay]s ( tissue4 ,illu/ration3 ,fig4 #aeb4 ,9 foll[+ out ^! !oretic pr9ciples & o!rs l to !m1 9 ! actual division ( liv+ cells1 we mu/ always be> 9 m9d c]ta9 conditions & qualifications4 ,9 ! fir/ place1 ! law ( m9imal area & ! o!r rules :i* we h arriv$ at are n absolute b relative3 !y are l9ks1 & v important l9ks1 9 a *a9 ( physical causation2 !y are always at "w1 b _! effects may be ov]ridd5 & conceal$ by ! op]ation ( o!r =ces4 ,secondly1 we mu/ rememb] t1 9 ! great majority ( cases1 ! cell-sy/em :i* we h 9 view is con/antly increas+ 9 magnitude by active gr[?2 & by ?is means ! =m & also ! proportions ( ! cells are cont9ually liable to alt]ation1 ( :i* ph5om5on we h already _h an example4 ,?irdly1 we mu/ c>efully rememb] t1 until our cell-walls become absolutely solid & rigid1 !y are always apt to be modifi$ 9 =m ow+ to ! t5sion ( ! adjac5t #cga walls2 & aga91 t s long z our p>tition films are fluid or semifluid1 _! po9ts & l9es ( contact ) "o ano!r may %ift1 l ! %ift+ outl9es ( a sy/em ( soap-bubbles4 ,?is is ! physical cause ( ! movem5ts frequ5tly se5 among segm5t+ cells1 l ^? to :i* ,raub] call$ att5tion 9 ! segm5t+ ovum ( ! frog1 & l ^? m /rik+ movem5ts or accommodations :i* give rise to a s-call$ 8spiral0 type ( segm5tation4 ,illu/ration3 ,fig4 #aec4 ,diagram ( flatt5$ or discoid cell divid+ into octants3 to %ew gradual t5d5cy t[>ds a position ( equilibrium4 ,be>+ 9 m9d1 !n1 ^! consid]ations1 let u see :at our flatt5$ disc is likely to look l1 aft] a few successive divisions into compon5t cells4 ,9 ,fig4 #aec1 a1 we h a diagrammatic repres5tation ( our disc1 aft] x has divid$ into f\r quadrants1 & ea* ( ^! 9 turn into a triangul> & a quadrilat]al portion2 b z yet1 ?is figure sc>cely sugge/s to u any?+ l ! normal look ( an aggregate ( liv+ cells4 ,b let u g a little fur!r1 /ill limit+ ourselves1 h[ev]1 to ! consid]ation ( ! eight-cell$ /age4 ,:]ev] "o ( our radiat+ p>titions meets ! p]iph]al wall1 !re w 7z we "k7 be a mutual t5sion betwe5 ! ?ree conv]g5t films1 :i* w t5d to set _! edges at equal angles to "o ano!r1 angles t is to say ( #abj4 ,9 consequ5ce ( ?is1 ! out] wall ( ea* individual cell w 79 ?is surface view ( our disc7 #cgb be an arc ( a circle ( :i* we c det]m9e ! c5tre by ! me?od us$ on p4 #cjg2 &1 fur!rmore1 ! n>r[] cells1 t is to say ! quadrilat]als1 w h ?is out] bord] some:at m curv$ ?an _! broad] neighb\rs4 ,we arrive1 !n1 at ! condition %ewn 9 ,fig4 #aec1 b4 ,)9 ! cell1 also1 :]ev] wall meets wall1 ! angle ( contact mu/ t5d1 9 e case1 to be an angle ( #abj2 & 9 no case may m ?an ?ree films 7z se5 9 section7 meet 9 a po9t 7c72 & ?is condition1 ( ! p>titions meet+ ?ree by ?ree1 & at co-equal angles1 w obvi\sly involve ! curvature ( "s1 if n all1 ( ! p>titions 7d7 :i* 9 our prelim9>y inve/igation we treat$ z plane4 ,to solve ?is problem 9 a g5]al way is no easy matt]2 b x is a problem :i* ,nature solves 9 e case :]e1 z 9 ! case we are consid]+1 eight bubbles1 or eight cells1 meet toge!r 9 a 7plane or curv$7 surface4 ,an approximate solution has be5 giv5 9 ,fig4 #aec1 d2 & x w n[ at once be recognis$ t ?is figure has va/ly m resemblance to an aggregate ( liv+ cells ?an _h ! diagram ( ,fig4 #aec1 a ) :i* we began4 ,illu/ration3 ,fig4 #aed4 ,j z we h con/ruct$ 9 ?is case a s]ies ( purely diagrammatic or s*ematic figures1 s x w be z a rule possible to diagrammatise1 ) b little alt]ation1 ! complicat$ appe>ances pres5t$ by any ord9>y aggregate ( cells4 ,! accompany+ little figure 7,fig4 #aed71 ( a g]m9at+ spore ( a ,liv]wort 7,riccia71 aft] a draw+ ( ,pr(essor ,campbell's1 sc>cely ne$s fur!r explanation3 = x is well-nigh a typical diagram ( ! me?od ( space-p>tition+ :i* we are n[ consid]+4 ,let u look aga9 at our figures 7on p4 #cei7 ( ! disc ( ,ery?rotri*ia1 f ,b]?old's ,monograph ( ! ,bangiaceae & r$raw ! e>li] /ages 9 diagrammatic fa%ion4 ,9 ! foll[+ s]ies ( diagrams ! new p>titions1 or ^? j ab\t to =m1 are 9 ea* case outl9$2 & 9 ! next succe$+ /age !y are %ewn aft] settl+ d[n into position1 & aft] ex]cis+ _! respective tractions on ! walls previ\sly laid d[n4 ,x is cle>1 ,i ?9k1 t ^! f\r diagrammatic figures repres5t all t is %ewn 9 ! fir/ five /ages drawn by ,b]?old f ! plant itself2 b ! correspond5ce _c #cgc 9 ?is case be precisely accurate1 = ! simple reason t ,b]?old's figures are tak5 f diff]5t individuals1 & are !re=e only approximately consecutive & n /rictly cont9u\s4 ,! la/ ( ! six draw+s 9 ,fig4 #add is already too ,illu/ration3 ,fig4 #aee4 ,!oretical arrangem5t ( successive p>titions 9 a discoid cell2 = comp>ison ) ,fig4 #add4 complicat$ = diagrammatisation1 t is to say x is too complicat$ = u to deciph] ) c]ta9ty ! precise ord] ( appe>ance ( ! num]\s p>titions :i* x conta9s4 ,b 9 ,fig4 #aef ,i %ew "o m diagrammatic figure1 ( a disc :i* ,illu/ration3 ,fig4 #aef4 ,!oretical division ( a discoid cell into sixty-f\r *amb]s3 no all[ance be+ made = ! mutual tractions ( ! cell-walls4 has divid$1 accord+ to ! !oretical plan1 into ab\t sixty-f\r cells2 & mak+ due all[ance = ! successive *anges :i* ! mutual t5sions & tractions ( ! p>titions mu/ #cgd br+ ab\t1 increas+ 9 complexity ) ea* succe$+ /age1 we c see1 ev5 at ?is advanc$ & complicat$ /age1 a v consid]able resemblance betwe5 ! actual picture 7,fig4 #add7 & ! diagram :i* we h "h con/ruct$ 9 ob$i5ce to a few simple rules4 ,9 l mann]1 9 ! annex$ figures1 repres5t+ sections ?r\gh a "y embryo ( a ,moss1 we h v little difficulty 9 disc]n+ ! successive /ages t mu/ h int]v5$ betwe5 ! two /ages %ewn3 s z to lead f ! j divid$ quadrants 7"o ( :i*1 by ! way1 has n yet divid$ 9 our figure 7a77 to ! /age 7b7 9 :i* a well-m>k$ epid]mal lay] surr\nds an at fir/ sight irregul> agglom]ation ( 8fundam5tal0 tissue4 ,illu/ration3 ,fig4 #aeg4 ,sections ( embryo ( a moss4 7,aft] ,ki5itz-,g]l(f47 ,9 ! la/ p>agraph b "o1 ,i h spok5 ( ! difficulty ( s arrang+ ! meet+-places ( a numb] ( cells t at ea* junction only ?ree cell-walls %all meet 9 a l9e1 & all ?ree %all meet x at equal angles ( #abj4 ,z a matt] ( fact1 ! problem is soluble 9 a numb] ( ways2 t is to say1 :5 we h a numb] ( cells1 say eight z 9 ! case consid]$1 enclos$ 9 a common b\nd>y1 !re are v>i\s ways 9 :i* _! walls c be made to meet int]nally1 ?ree by ?ree1 at equal angles2 & ^! diff]5ces w entail diff]5ces also 9 ! curvature ( ! walls1 & consequ5tly 9 ! %ape ( ! cells4 ,! "q is some:at complex2 x has be5 dealt ) by ,plateau1 & treat$ ma!matically by ,m4 ,van ,rees#cib4 ,illu/ration3 ,fig4 #aeh4 ,v>i\s possible arrangem5ts ( int]m$iate p>titions1 9 gr\ps ( #d1 #e1 #f1 #g or #h cells4 ,if )9 our b\nd>y we h ?ree cells all meet+ #cge int]nally1 !y mu/ meet 9 a po9t2 fur!rmore1 !y t5d to d s at equal angles ( #abj1 & !re is an end ( ! matt]4 ,if we h f\r cells1 !n1 z we h already se51 ! conditions are satisfi$ by int]pos+ a little int]m$iate wall1 ! two extremities ( :i* con/itute ! meet+-po9ts ( ?ree cells ea*1 & ! upp] edge ( :i* m>ks ! 8pol> furr[40 ,simil>ly1 9 ! case ( five cells1 we require two little int]m$iate walls1 & two pol> furr[s2 & we soon arrive at ! rule t1 = n cells1 we require n #c little longitud9al p>titions 7& correspond+ pol> furr[s71 connect+ ! triple junctions ( ! cells2 & ^! little walls1 l all ! re/ )9 ! sy/em1 mu/ be incl9$ to "o ano!r at angles ( #abj4 ,:]e we h only "o su* wall 7z 9 ! case ( f\r cells71 or only two 7z 9 ! case ( five cells71 !re is no room = ambiguity4 ,b :]e we h ?ree little connect+-walls1 z 9 ! case ( six cells1 x is obvi\s t we c arrange !m 9 ?ree diff]5t ways1 z 9 ! annex$ ,fig4 #aei4 ,9 ! sy/em ( sev5 cells1 ! f\r p>titions c be arrang$ 9 f\r ways2 & ! five p>titions requir$ 9 ! case ( eight cells c be arrang$ 9 no less ?an ?irte5 diff]5t ways1 ( :i* ,fig4 #aeh %ews "s half-doz5 only4 ,x does n foll[ t1 s to speak1 ^! v>i\s #cgf arrangem5ts are all equally good2 "s are kn[n to be mu* m /able ?an o!rs1 & "s h nev] yet be5 realis$ 9 actual exp]im5t4 ,! conditions :i* lead to ! pres5ce ( any "o ( !m1 9 pref]5ce to ano!r1 are z yet1 s f> z ,i am aw>e1 undet]m9$1 b to ?is po9t we %all return4 ,examples ( ^! v>i\s arrangem5ts meet u at e turn1 & n only 9 cell-aggregates1 b 9 v>i\s cases :]e non-rigid & semi-fluid p>titions 7or p>titions t 7 s to beg9 )7 meet toge!r4 ,& x is a necess>y consequ5ce ( ?is physical ph5om5on1 & ( ! limit$ & v small numb] ( possible arrangem5ts1 t we get simil> appe>ances1 capable ( repres5tation by ! same diagram1 9 ! mo/ div]se fields ( biology#cic4 ,illu/ration3 ,fig4 #aei4 ,among ! publi%$ figures ( embryonic /ages & o!r cell aggregates1 we only disc]n ^! little int]m$iate p>titions 9 cases :]e ! inve/igator has drawn c>efully j :at lay be=e him1 )\t any preconceiv$ notions z to radial or o!r symmetry2 b ev5 9 o!r cases we c g5]ally recognise1 )\t mu* difficulty1 :at ! actual arrangem5t 0 :]eby ! cell-walls met toge!r 9 equilibrium4 ,i h a /rong suspicion t a lean+ t[>ds ,sa*s's ,rule1 t "o cell-wall t5ds to set itself at "r angles to ano!r cell-wall 7a rule ^: /rict limitations1 & n>r[ range ( application1 we h already #cgg consid]$7 is responsible = _m inaccurate or incomplete repres5tations ( ! mutual arrangem5t ( aggregat$ cells4 ,illu/ration3 ,fig4 #afj4 ,segm5t+ egg ( ,tro*us4 7,aft] ,rob]t47 ,illu/ration3 ,fig4 #afa4 ,two views ( segm5t+ egg ( ,cyn?ia p>tita4 7,aft] ,conkl947 ,illu/ration3 ,fig4 #afb4 7a7 ,section ( apical cone ( ,salv9ia4 7,aft] ,pr+%eim#cid47 7b7 ,diagram ( probable actual arrangem5t4 ,illu/ration3 ,fig4 #afc4 ,egg ( ,pyrosoma4 7,aft] ,korotneff74 ,illu/ration3 ,fig4 #afd4 ,egg ( ,e*9us1 segm5t+ "u pressure4 7,aft] ,dries*47 ,9 ! accompany+ s]ies ( figures 7,figs4 #afj-afg7 ,i h #cgh set =? a few aggregates ( eight cells1 mo/ly f draw+s ( segm5t+ eggs4 ,9 "s cases !y %ew cle>ly ! mann] 9 :i* ! cells meet "o ano!r1 always at angles ( #abj1 & always ) ! help ( five int]m$iate b\nd>y walls )9 ! eight-cell$ sy/em2 9 o!r cases ,i h add$ a slightly alt]$ draw+1 s z to %ew1 ) z little *ange z #cgi possible1 ! arrangem5t ( b\nd>ies :i* probably actually exi/$1 & gave rise to ! appe>ance :i* ! obs]v] drew4 ,^! draw+s may be comp>$ ) ! v>i\s diagrams ( ,fig4 #aeh1 9 :i* "s sev5 out ( ! possible ?irte5 arrangem5ts ( five int]m$iate p>titions 7= a sy/em ( eight cells7 h be5 already set =?4 ,illu/ration3 ,fig4 #afe4 7a7 ,"p ( segm5t+ egg ( ,cephalopod 7aft] ,watase72 7b7 probable actual arrangem5t4 ,illu/ration3 ,fig4 #aff4 7a7 ,egg ( ,e*9us2 7b7 d4 ( ,n]eis1 "u pressure4 7,aft] ,dries*74 ,illu/ration3 ,fig4 #afg4 7a7 ,egg ( frog1 "u pressure 7aft] ,r\x72 7b7 probable actual arrangem5t4 ,x w be se5 t ,m4 ,rob]t-,torn['s figure ( ! segm5t+ egg ( ,tro*us 7,fig4 #afj7 cle>ly %ews ! cells gr\p$ aft] ! fa%ion ( ,fig4 #aeh1 a4 ,9 l mann]1 ,mr ,conkl9's figure ( ! ascidian egg 7,cyn?ia7 %ews equally cle>ly ! arrangem5t g4 ,a sea-ur*9 egg1 segm5t+ "u pressure1 z figur$ by ,dries*1 sc>cely requires any modification ( ! draw+ to appe> z a diagram ( ! type d4 ,turn+ = a mom5t to a botanical illu/ration1 we h a figure ( ,pr+%eim's %ew+ an eight-cell$ /age 9 ! apex ( ! "y cone ( ,salv9ia2 x is 9 all probability ref]able1 z 9 my modifi$ diagram1 to type c4 ,beside x is figur$ a v diff]5t object1 a segm5t+ egg ( ! ,ascidian ,pyrosoma1 aft] ,korotneff2 x may be t ?is also is to be ref]r$ to type c1 b ,i ?9k x is m easily ref]able to type b4 ,= !re is a diff]5ce betwe5 ?is diagram & t ( ,salv9ia1 9 t "h app>5tly1 ( ! pairs ( lat]al cells1 ! upp] & ! l[] cell are alt]nately ! l>g]1 :ile 9 ! diagram ( ,salv9ia ! l[] lat]al cells bo? appe> mu* l>g] ?an ! upp] ones2 & ?is diff]5ce tallies ) ! appe>ance produc$ if we fill 9 ! eight cells accord+ to ! type b or ! type c4 ,9 ! segm5t+ cuttlefi% egg1 !re is aga9 a slight dubiety z to :i* type x %\ld be ref]r$ to1 b x is 9 all probability ref]able1 l ,dries*'s ,e*9us egg1 to d4 ,la/ly1 ,i h copi$ f ,r\x a curi\s figure ( ! egg ( ,rana escul5ta1 view$ f ! animal pole1 :i* appe>s to me ref]able1 9 all probability1 to type g4 ,( type f1 9 :i* ! five p>titions =m a figure ) f\r re-entrant angles1 t is to say a figure repres5t+ ! five sides ( a hexagon1 ,i h f\nd no examples among segm5t+ eggs1 & t arrangem5t 9 all probability is a v un/able "o4 ,x is obvi\s en\gh1 )\t m ado1 t ^! ph5om5a are 9 ! /ricte/ & complete/ way common to bo? plants #chj & animals4 ,9 o!r words !y tally )1 & !y fur!r ext5d1 ! g5]al & fundam5tal conclusions laid d[n by ,s*wann1 9 8 ,mikroskopis*e ,unt]su*ung5 b] die ,ueb]e9/immung 9 d] ,/ruktur und dem ,wa*/hum d] ,?i]e und ,pflanz54 ,b n[ t we h se5 h[ a c]ta9 limit$ numb] ( types ( eight-cell$ segm5tation 7or ( arrangem5ts ( eight cell-p>titions7 appe> & reappe>1 "h & !re1 ?r\gh\t ! :ole _w ( organisms1 !re /ill rema9s ! v important "q1 :e!r 9 ea* p>ticul> organism ! conditions are su* z to lead to "o p>ticul> arrangem5t be+ pr$om9ant1 *>act]i/ic1 or ev5 inv>iable4 ,9 %ort1 is a p>ticul> arrangem5t ( cell-p>titions to be look$ ^u 7z ! publi%$ figures ( ! embryologi/ are apt to sugge/7 z a specific "*1 or at lea/ a con/ant or normal "*1 ( ! p>ticul> organism8 ,! answ] to ?is "q is a direct negative1 b x is only 9 ! "w ( ! mo/ c>eful & accurate obs]v]s t we f9d x reveal$4 ,raub] 7:om we h m ?an once _h occasion to quote7 0 "o ( ^? embryologi/s :o record$ j :at he saw1 )\t prejudice or preconception2 z ,bo]haave said ( ,swamm]dam1 quod vidit id ass]uit4 ,n[ ,raub] has put on record a consid]able numb] ( v>iations 9 ! arrangem5t ( ! fir/ eight cells1 :i* =m a discoid surface ab\t ! dorsal 7or 8animal07 pole ( ! frog's egg4 ,9 a c]ta9 numb] ( cases ^! figures are id5tical ) "o ano!r 9 type1 id5tical 7t is to say7 save = slight diff]5ces 9 magnitude1 relative proportions1 or ori5tation4 ,b ,i h select$ 7,fig4 #afh7 six diagrammatic figures1 :i* are all ess5tially diff]5t1 & ^! diagrams seem to me to be> intr9sic evid5ce ( _! accuracy3 ! curvatures ( ! p>tition-walls1 & ! angles at :i* !y meet agree closely ) ! requirem5ts ( !ory1 & :5 !y dep>t f !oretical symmetry !y d s only to ! slight ext5t :i* we %\ld naturally expect 9 a mat]ial & imp]fectly homog5e\s sy/em#cie4 #cha ,illu/ration3 ,fig4 #afh4 ,v>i\s modes ( gr\p+ ( eight cells1 at ! dorsal or epibla/ic pole ( ! frog's egg4 7,aft] ,raub]47 ,( ^! six illu/rations1 two are exceptional4 ,9 ,fig4 #afh1 #e1 we obs]ve t "o ( ! eight cells is surr\nd$ on all sides by ! o!r sev54 ,?is is a p]fectly natural condition1 & repres5ts1 l ! re/1 a phase ( p>tial or conditional equilibrium4 ,b x is n includ$ 9 ! s]ies we are n[ consid]+1 :i* is re/rict$ to ! case ( eight cells ext5d+ outw>ds to a common b\nd>y4 ,! condition %ewn 9 ,fig4 #afh1 #f1 is aga9 peculi>1 & is probably r>e2 b x is includ$ "u ! cases consid]$ on p4 #cab1 9 :i* ! cells are n 9 complete fluid contact1 b are sep>at$ by little droplets ( extrane\s matt]2 x ne$s no fur!r comm5t4 ,b ! o!r f\r cases are beautiful diagrams ( space-p>tition+1 simil> to ^? we h j be5 consid]+1 b s exquisitely cle> t !y ne$ no modification1 no 8t\*+-up10 to exhibit _! ma!matical regul>ity4 ,x w easily be recognis$ t 9 ,fig4 #afh1 #a & #b1 we h ! arrangem5ts correspond+ to a & d ( our diagram 7,fig4 #aeh73 b ! o!r two 7i4e4 #c & #d7 repres5t o!r ( ! ?irte5 possible arrangem5ts1 :i* are n includ$ 9 t #chb diagram4 ,x w\ld be a curi\s & int]e/+ inve/igation to asc]ta91 9 a l>ge numb] ( frogs' eggs1 all at ?is /age ( developm5t1 ! p]c5tage ( cases 9 :i* ^! v>i\s arrangem5ts occur1 ) a view ( correlat+ _! frequ5cy ) ! !oretical conditions 7s f> z !y are kn[n1 or c be asc]ta9$7 ( relative /ability4 ,"o ?+ /&s out z v c]ta9 inde$3 t ! elem5t>y diagram ( ! frog's egg commonly giv5 9 text-books ( embryology1--9 :i* ! cells are depict$ z uni=mly symmetrical quadrangul> bodies1--is entirely inaccurate & grossly mislead+#cif4 ,we n[ beg9 to realise ! rem>kable fact1 :i* may ev5 appe> a />tl+ "o to ! biologi/1 t all possible gr\p+s or arrangem5ts :atsoev] ( eight cells 7:]e all take "p 9 ! surface ( ! gr\p1 none be+ subm]g$ or :olly envelop$ by ! re/7 are ref]able to "s "o or o!r ( ?irte5 types or =ms4 ,& t all ! ?\s&s & ?\s&s ( draw+s :i* dilig5t obs]v]s h made ( su* eight-cell$ /ructures1 animal or vegetable1 anatomical1 hi/ological or embryological1 are "o & all repres5tations ( "s "o or ano!r ( ^! ?irte5 types3--or r inde$ ( some:at less ?an ! :ole ?irte51 = !re is reason to believe t1 out ( ! total numb] ( possible gr\p+s1 a c]ta9 small numb] are ess5tially un/able1 & h at be/1 9 ! concrete1 b a transitory & evanesc5t exi/5ce4 ,be=e we leave ?is subject1 on :i* a va/ deal m might be said1 !re are "o or two po9ts :i* we mu/ n omit to consid]4 ,let u note1 9 ! fir/ place1 t ! appe>ance :i* our plane diagrams sugge/ ( inequality ( ! sev]al cells is apt to be deceptive2 = ! diff]5ces ( magnitude app>5t 9 "o plane may well be1 & probably g5]ally are1 balanc$ by equal & opposite diff]5ces 9 ano!r4 ,secondly1 let u rem>k t ! rule :i* we are consid]+ ref]s only #chc to angles1 & to ! numb]1 n to ! l5g? ( ! int]m$iate p>titions2 x is to a great ext5t by v>iations 9 ! l5g? ( ^! t ! magnitudes ( ! cells may be equalis$1 or o!rwise balanc$1 & ! :ole sy/em br\ght into equilibrium4 ,la/ly1 !re is a curi\s po9t to consid]1 9 reg>d to ! numb] ( actual contacts1 9 ! v>i\s cases1 betwe5 cell & cell4 ,if we inspect ! diagrams 9 ,fig4 #afi 7:i* repres5t ?ree out ( our ?irte5 possible arrangem5ts ( eight cells7 we %all see t1 9 ! case ( type b1 two cells are ea* 9 contact ) two o!rs1 two cells ) ?ree o!rs1 & f\r cells ea* ) f\r o!r cells4 ,9 type a f\r cells are ea* 9 contact ) two1 two ) f\r1 & two ) five4 ,9 type f1 two are 9 contact ) two1 f\r ) ?ree1 & "o ) no less ?an sev54 ,9 all cases ! ,illu/ration3 ,fig4 #afi4 numb] ( contacts is tw5ty-six 9 all2 or1 9 o!r words1 !re are ?irte5 int]nal p>titions1 besides ! eight p]iph]al walls4 ,= x is easy to see t1 9 all cases ( n cells ) a common ext]nal b\nd>y1 ! numb] ( int]nal p>titions is #bn #c2 or ! numb] ( :at we call ! int]nal or int]facial contacts is #b7bn #c74 ,b x w\ld appe> t ! mo/ /able arrangem5ts are ^? 9 :i* ! total numb] ( contacts is mo/ ev5ly divid$1 & ! lea/ /able are ^? 9 :i* "s "o cell has1 z 9 type f1 a pr$om9ant numb] ( contacts4 ,9 a well-kn[n s]ies ( exp]im5ts1 ,r\x has %ewn h[1 by means ( oil-drops1 v>i\s arrangem5ts1 or aggregations1 ( cells c be simulat$2 & 9 ,fig4 #agj ,i %ew a numb] ( ,r\x's figures1 & h ascrib$ !m to :at seem to be _! appropriate 8types0 among ^? :i* we h j be5 consid]+2 b #chd x w be obs]v$ t 9 ^! figures ( ,r\x's ! drops are n always 9 complete contact1 a little air-bubble (t5 keep+ !m ap>t at _! apical junctions1 s t we see ! configuration t[>ds :i* ! sy/em is t5d+ r ?an t :i* x has fully atta9$#cig4 ,! type :i* we h call$ f 0 f\nd by ,r\x to be un/able1 ! l>ge 7or app>5tly l>ge7 drop a quickly pass+ into ! c5tre ( ! sy/em1 & "h tak+ up a position ( equilibrium 9 :i*1 z usual1 ?ree cells meet ?r\gh\t 9 a po9t1 at equal angles1 & 9 :i*1 9 ?is case1 all ! cells h an equal numb] ( 8int]facial0 contacts4 ,illu/ration3 ,fig4 #agj4 ,aggregations ( oil-drops4 7,aft] ,r\x47 ,figs4 #d-f repres5t successive *anges 9 a s+le sy/em4 ,we ne$ by no means be surpris$ to f9d t1 9 su* arrangem5ts1 ! commone/ & mo/ /able di/ributions are ^? 9 :i* ! cell-contacts are di/ribut$ z uni=mly z possible betwe5 ! sev]al cells4 ,we always expect to f9d "s su* t5d5cy to equality 9 cases :]e we h to d ) small oscillations on ei!r side ( a symmetrical condition4 #che ,! rules & pr9ciples :i* we h arriv$ at f ! po9t ( view ( surface t5sion h a mu* wid] be>+ ?an is at once sugge/$ by ! problems to :i* we h appli$ !m2 = 9 ?is elem5t>y /udy ( ! cell-b\nd>ies 9 a segm5t+ egg or tissue we are on ! v]ge ( a difficult & important subject 9 pure ma!matics4 ,x is a subject adumbrat$ by ,leibniz1 /udi$ some:at m deeply by ,eul]1 & greatly develop$ ( rec5t ye>s4 ,x is ! ,geometria ,situs ( ,gauss1 ! ,analysis ,situs ( ,riemann1 ! ,!ory ( ,p>titions ( ,cayley1 & ( ,spatial ,complexes ( ,li/+#cih4 ,! crucial po9t = ! biologi/ to compreh5d is1 t 9 a clos$ surface divid$ into a numb] ( faces1 ! arrangem5t ( all ! faces1 l9es & po9ts 9 ! sy/em is capable ( analysis1 & t1 :5 ! numb] ( faces or areas is small1 ! numb] ( possible arrangem5ts is small also4 ,?is is ! simple reason :y we meet 9 su* a case z we h be5 discuss+ 7viz4 ! arrangem5t ( a gr\p or sy/em ( eight cells7 ) ! same few types recurr+ aga9 & aga9 9 all sorts ( organisms1 plants z well z animals1 & ) no relation to ! l9es ( biological classification3 & :y1 fur!r1 we f9d simil> configurations occurr+ to m>k ! symmetry1 n ( cells m]ely1 b ( ! p>ts & organs ( entire animals4 ,! ph5om5a are n 8functions10 or specific *>act]s1 ( ?is or t tissue or organism1 b involve g5]al pr9ciples :i* lie )9 ! prov9ce ( ! ma!matician4 ,! !ory ( space-p>tition+1 to :i* ! segm5tation ( ! egg gives u an easy practical introduction1 is illu/rat$ 9 mu* m complex ways 9 o!r fields ( natural hi/ory4 ,a v beautiful b imm5sely complicat$ case is furni%$ by ! 8v5ation0 ( ! w+s ( insects4 ,"h we h sometimes 7z 9 ! dragon-flies71 a g5]al reticulum ( small1 m or less hexagonal 8cells03 b 9 mo/ o!r cases1 9 flies1 bees1 butt]flies1 etc41 we h a mod]ate numb] ( cells1 ^: p>titions always imp+e ^u "o ano!r ?ree by ?ree1 & ^: arrangem5t1 !re=e1 includes ( necessity a numb] ( small int]m$iate p>titions1 analog\s to our pol> furr[s4 ,i ?9k #chf t a ma!matical /udy ( ^!1 includ+ an inve/igation ( ! 8de=mation0 ( ! w+ 7t is to say1 ( ! *anges 9 %ape & *anges 9 ! =m ( its 8cells0 :i* x und]goes dur+ ! life ( ! individual1 & f "o species to ano!r7 w\ld be ( great int]e/4 ,9 v _m cases1 ! entomologi/ relies ^u ?is v5ation1 & ^u ! occurr5ce ( ?is or t int]m$iate ve91 = 8 classification1 & !re=e = 8 hypo!tical phylog5y ( p>ticul> gr\ps2 :i* latt] proc$ure h>dly comm5ds itself to ! physici/ or ! ma!matician4 ,illu/ration3 ,fig4 #aga4 7,a7 ,a/]olampra m>yl&ica1 ,ehr42 7,b1 ,c7 ,a4 v>iabilis1 ,grev4 7,aft] ,greville47 ,ano!r case1 geometrically ak9 b biologically v diff]5t1 is to be f\nd 9 ! little diatoms ( ! g5us ,a/]olampra1 & _! imm$iate cong5]s#cii4 ,9 ,a/]olampra we h a little disc1 9 :i* we see 7z x 77 radiat+ spokes ( "o mat]ial1 alt]nat+ ) int]vals occupi$ on ! flatt5$ :eel-l disc by ano!r 7,fig4 #aga74 ,! spokes v>y 9 numb]1 b ! g5]al appe>ance is 9 a high degree sugge/ive ( ! ,*ladni figures produc$ by ! vibration ( a circul> plate4 ,! spokes broad5 out t[>ds ! c5tre1 & int]lock by visible junctions1 :i* obey ! rule ( triple int]section1 & accord+ly exemplify ! p>tition-figures ) :i* we are deal+4 ,b :]eas we h f\nd ! p>ticul> arrangem5t 9 :i* "o cell is 9 contact ) all ! re/ to be un/able1 accord+ to ,r\x's oil-drop exp]im5ts1 & to be conspicu\s #chg by its abs5ce f our diagrams ( segm5t+ eggs1 "h 9 ,a/]olampra1 on ! o!r h&1 x occurs frequ5tly1 & is inde$ ! commone/ arrangem5t#djj 7,fig4 #aga1 ,b74 ,9 all probability1 we are entitl$ to consid] ?is m>k$ diff]5ce natural en\gh4 ,= we may suppose t 9 ,a/]olampra 7unlike ! case ( ! segm5t+ egg7 ! t5d5cy is to p]fect radial symmetry1 all ! spokes emanat+ f a po9t 9 ! c5tre3 su* a condition w\ld be em95tly un/able1 & w\ld break d[n "u ! lea/ asymmetry4 ,a v simple1 p]haps ! simple/ case1 w\ld be t "o s+le spoke %\ld diff] slightly f ! re/1 & %\ld s t5d to be drawn 9 amid ! o!rs1 ^! latt] rema9+ simil> & symmetrical among !mselves4 ,su* a configuration w\ld be va/ly less un/able ?an ! orig9al "o 9 :i* all ! b\nd>ies meet 9 a po9t2 & ! fact t fur!r progress is n made t[>ds o!r configurations ( /ill great] /ability may be suffici5tly acc\nt$ = by viscosity1 rapid solidification1 or o!r conditions ( re/ra9t4 ,a p]fectly /able condition w\ld ( c\rse be obta9$ if1 z 9 ! case ( ,r\x's oil-drop 7,fig4 #agj1 #f71 "o ( ! cellul> spaces pass$ into ! c5tre ( ! sy/em1 ! o!r p>titions radiat+ outw>ds f its circul> wall to ! p]iph]y ( ! :ole sy/em4 ,precisely su* a condition occurs among our diatoms2 b :5 x does s1 x is look$ ^u z ! m>k & *>act]isation ( ! alli$ g5us ,ara*noidiscus4 ,illu/ration3 ,fig4 #agb4 ,section ( ,alcyon>ian polype4 ,9 a diagrammatic section ( an ,alcyon>ian polype 7,fig4 #agb71 we h eight *amb]s set1 symmetrically1 ab\t a n9?1 :i* con/itutes ! 8/oma*40 ,9 ?is arrangem5t !re is no difficulty1 = x is obvi\s t1 ?r\gh\t ! sy/em1 ?ree b\nd>ies meet 79 plane section7 9 a po9t4 ,9 _m corals we h z #chh simple1 or ev5 simpl] conditions1 = ! radiat+ calcifi$ p>titions ei!r conv]ge ^u a c5tral *amb]1 or fail to meet x & end freely4 ,b 9 a few cases1 ! p>titions or 8septa0 conv]ge to meet "o ano!r1 !re be+ no c5tral *amb] on :i* !y may imp+e2 & "h ! mann] 9 :i* contact is effect$ becomes complicat$1 & involves problems id5tical ) ^? :i* we are n[ /udy+4 ,illu/ration3 ,fig4 #agc4 ,het]ophyllia angulata4 7,aft] ,ni*olson47 ,9 ! great majority ( corals we h z simple or ev5 simpl] conditions ?an ^? ( ,alcyonium2 = z a rule ! calcifi$ p>titions or septa ( ! coral ei!r conv]ge ^u a c5tral *amb] 7or c5tral 8columella071 or else fail to meet x & end freely4 ,9 ! latt] case ! problem ( space-p>tition+ does n arise2 9 ! =m]1 h[ev] num]\s ! septa be1 _! sep>ate contacts ) ! wall ( ! c5tral *amb] comply ) our fundam5tal rule accord+ to :i* ?ree l9es & no m meet 9 a po9t1 & f ?is simple & symmetrical arrangem5t !re is little t5d5cy to v>iation4 ,b 9 a few cases1 ! septal p>titions conv]ge to meet "o ano!r1 !re be+ no c5tral *amb] on :i* !y may imp+e2 & "h ! mann] 9 :i* contact is effect$ becomes complicat$1 & involves problems ( space-p>tition+ id5tical ) ^? :i* we are n[ /udy+4 ,9 ! g5us ,het]ophyllia & 9 a few alli$ =ms we h su* conditions1 & /ud5ts ( ! ,coel5t]ata h f\nd !m v puzzl+4 ,mc,coy#dja1 _! fir/ discov]]1 pron\nc$ ^! corals to be 8totally unlike0 any o!r gr\p1 rec5t or fossil2 & ,pr(essor ,m>t9 ,duncan1 writ+ a memoir on ,het]ophyllia & its allies#djb1 describ$ !m z 8p>adoxical 9 _! anatomy40 ,illu/ration3 ,fig4 #agd4 ,het]ophyllia sp4 7,aft] ,m>t9 ,duncan47 ,! simple/ or y\nge/ ,het]ophylliae kn[n h six septa 7z 9 ,fig4 #agd1 a72 9 ! case figur$1 f\r ( ^! septa are conjo9$ two & two1 ?us =m+ ! usual triple junctions toge!r ) _! int]m$iate p>tition-walls3 & 9 ! #chi case ( ! o!r two we may fairly assume t _! prop] & orig9al arrangem5t 0 t ( our type #f;b 7,fig4 #aeh71 ?\gh ! c5tral int]m$iate p>tition has be5 cr[d$ out by p>tial coalesc5ce4 ,:5 ) increas+ age ! septa become m num]\s1 _! arrangem5t becomes exce$+ly v>iable2 = ! simple reason t1 f ! ma!matical po9t ( view1 ! numb] ( possible arrangem5ts1 ( #aj1 #ab or m cellul> p>titions 9 triple contact1 t5ds to increase ) great rapidity1 & !re is little to *oose betwe5 _m ( !m 9 reg>d to symmetry & equilibrium4 ,b :ile1 ma!matically speak+1 ea* p>ticul> case among ! multitude ( possible cases is an ord]ly & def9ite arrangem5t1 f ! purely biological po9t ( view on ! o!r h& no law or ord] is recognisable2 & s ,mc,coy describ$ ! g5us z be+ *>act]is$ by ! possession ( septa 8de/itute ( any ord] ( arrangem5t1 b irregul>ly bran*+ & coalesc+ 9 _! passage f ! solid ext]nal walls t[>ds "s indef9ite po9t ne> ! c5tre :]e ! few ma9 lamellae irregul>ly ana/omose40 #cij ,9 ! two examples figur$ 7,fig4 #agd71 bo? comp>atively simple ones1 x w be se5 t1 ( ! ma9 *amb]s1 "o is 9 ea* case an unsymmetrical "o2 t is to say1 !re is "o *amb] :i* is 9 contact ) a great] numb] ( its neighb\rs ?an any o!r1 & :i* at an e>li] /age mu/ h _h contact ) !m all2 ?is 0 ! case ( our type f1 9 ! eight-cell$ sy/em 7,fig4 #aeh74 ,su* an asymmetrical *amb] 7:i* may occur 9 a sy/em ( any numb] ( cells great] ?an six71 con/itutes :at is kn[n to /ud5ts ( ! ,coel5t]ata z a 8fossula02 & we may recognise x n only "h1 b also 9 ,zaphr5tis & its allies1 & 9 a good _m o!r corals besides4 ,moreov] c]ta9 corals are describ$ z hav+ m ?an "o fossula3 ?is appe>ance be+ naturally produc$ "u c]ta9 ( ! o!r asymmetrical v>iations ( normal space-p>tition+4 ,:]e a s+le fossula occurs1 we are usually told t x is a symptom ( 8bilat]ality02 & ?is is 9 turn int]pret$ z an indication ( a high] grade ( organisation ?an is impli$ 9 ! purely 8radial symmetry0 ( ! common] types ( coral4 ,! ma!matical aspect ( ! case gives no w>rant = ?is int]pretation4 ,let u c>efully notice 7le/ we run ! risk ( confus+ two di/9ct problems7 t ! space-p>tition+ ( ,het]ophyllia by no means agrees ) ! details ( t :i* we h /udi$ 9 7= in/ance7 ! case ( ! develop+ disc ( ,ery?rotri*ia3 ! diff]5ce simply be+ t ,het]ophyllia illu/rates ! g5]al case ( cell-p>tition+ z ,plateau & ,van ,rees /udi$ x1 :ile 9 ,ery?rotri*ia1 & 9 our o!r embryological & hi/ological in/ances1 we h f\nd ourselves ju/ifi$ 9 mak+ ! additional assumption t ea* new p>tition divid$ a cell into co-equal p>ts4 ,no su* law holds 9 ,het]ophyllia1 ^: case is ess5tially diff]5t f ! o!rs3 inasmu* z ! *amb]s ^: p>tition we are discuss+ 9 ! coral are m]e empty spaces 7empty save = ! m]e access ( sea-wat]72 :ile 9 our hi/ological & embryological in/ances1 we 7 speak+ ( ! division ( a cellul> unit ( liv+ protoplasm4 ,accord+ly1 among o!r diff]5ces1 ! 8transv]se0 or 8p]icl9al0 p>titions1 :i* 7 b\nd to appe> at regul> int]vals & 9 def9ite positions1 :5 co-equal bisection 0 a feature ( ! #cia case1 are comp>atively few & irregul> 9 ! e>li] /ages ( ,het]ophyllia1 ?\gh !y beg9 to appe> 9 numb]s aft] ! ma91 m or less radial1 p>titions h become num]\s1 & :5 accord+ly ^! radiat+ p>titions come to b\nd n>r[ & almo/ p>allel-sid$ int]spaces2 !n x is t ! transv]se or p]icl9al p>titions beg9 to come 91 & =m :at ! /ud5t ( ! ,coel5t]ata calls ! 8dissepim5ts0 ( ! coral4 ,we ne$ g no fur!r into ! configuration & anatomy ( ! corals2 b x seems to me beyond a d\bt t ! :ole "q ( ! complicat$ arrangem5t ( septa & dissepim5ts ?r\gh\t ! gr\p 7includ+ ! curi\s vesicul> or bubble-l tissue ( ! ,cya?ophyllidae & ! g5]al /ructural plan ( ! ,tetracoralla1 su* z ,/reptoplasma & its allies7 is well wor? inve/igation f ! physical & ma!matical po9t ( view1 aft] ! fa%ion :i* is "h slightly adumbrat$4 ,illu/ration3 ,fig4 #age4 ,diagrammatic section ( a ,ct5ophore 7,eu*>is74 ,! me?od ( divid+ a circul>1 or sph]ical1 sy/em into eight p>ts1 equal z to _! areas b unequal 9 _! p]iph]al b\nd>ies1 is probably ( wide biological application2 t is to say1 )\t necess>ily suppos+ x to be rigor\sly foll[$1 ! typical configuration :i* x yields seems to recur aga9 & aga91 ) m or less approximation to precision1 & "u widely diff]5t circum/ances4 ,i am incl9$ to ?9k1 = in/ance1 t ! unequal division ( ! surface ( a ,ct5ophore by its #cib m]idian-l ciliat$ b&s is a case 9 po9t 7,fig4 #age74 ,"h1 if we imag9e ea* quadrant to be twice bisect$ by a curv$ anticl9e1 we %all get :at is app>5tly a close approximation to ! actual position ( ! ciliat$ b&s4 ,! case h[ev] is complicat$ by ! fact t ! sectional plan ( ! organism is nev] q circul>1 b always m or less elliptical4 ,"o po9t1 at lea/1 is cle>ly se5 9 ! symmetry ( ! ,ct5ophores2 & t is t ! radiat+ canals :i* pass outw>ds to correspond 9 position ) ! ciliat$ b&s1 h no common c5tre1 b div]ge f "o ano!r by repeat$ bifurcations1 9 a mann] comp>able to ! conjunctions ( our cell-walls4 ,9 l mann] ,i am incl9$ to sugge/ t ! same pr9ciple may help u to und]/& ! app>5tly complex arrangem5t ( ! skeletal rods ( a l>val ,e*9od]m1 & ! v complex con=mation ( ! l>va :i* is br\ght ab\t by ! pres5ce ( ^! long1 sl5d] skeletal radii4 ,illu/ration3 ,fig4 #agf4 ,diagrammatic arrangem5t ( p>titions1 repres5t$ by skeletal rods1 9 l>val ,e*9od]m 7,ophiura74 ,9 ,fig4 #agf ,i h divid$ a circle into its f\r quadrants1 & h bisect$ ea* quadrant by a circul> arc 7,,bc71 pass+ f radius to p]iph]y1 z 9 ! =ego+ cases ( cell-division2 & ,i h aga9 bisect$1 9 a simil> way1 ! triangul> halves ( ea* quadrant 7,,dd74 ,i h also ins]t$ a small circle 9 ! middle ( ! figure1 conc5tric ) ! l>ge "o4 ,if n[ we imag9e ^? l9es 9 ! figure :i* ,i h drawn black to be replac$ by solid rods we %all h at once ! frame-"w ( an ,ophiurid 7,pluteus7 l>va4 ,let u imag9e all ^! arms to be #cic b5t symmetrically d[nw>ds1 s t ! plane ( ! pap] is trans=m$ into a sph]oidal surface1 su* z t ( a hemisph]e1 or t ( a tall conical figure ) curv$ sides2 let a membrane be spread1 umbrella-l1 betwe5 ! out/ret*$ skeletal rods1 & let its m>g9 loop f rod to rod 9 curves :i* are possibly cat5>ies1 b are m probably portions ( an 8ela/ic curve10 & ! outw>d resemblance to a ,pluteus l>va is n[ complete4 ,by v>i\s slight modifications1 by alt]+ ! relative l5g?s ( ! rods1 by modify+ _! curvature or by replac+ ! curv$ rod by a tang5t to itself1 we c r+ ! *anges :i* lead u f "o kn[n type ( ,pluteus to ano!r4 ,! case ( ! ,bip9n>ia l>vae ( ,e*9ids is c]ta9ly analog\s1 b x becomes v mu* m complicat$2 we h to d ) a m complex p>tition+ ( space1 & ,i confess t ,i am n yet able to repres5t ! m complicat$ =ms 9 s simple a way4 ,illu/ration3 ,fig4 #agg4 ,pluteus-l>va ( ,ophiurid4 ,illu/ration3 ,fig4 #agh4 ,diagrammatic developm5t ( ,/omata 9 ,s$um4 7,cf4 fig4 9 ,sa*s's ,botany1 #ahhb1 p4 #ajc47 ,!re are a few notable exceptions 7besides ! v>i\s unequally segm5t+ eggs7 to ! g5]al rule t 9 cell-division ! "m-cell t5ds to divide into equal halves2 & "o ( ^! exceptional cases is to be f\nd 9 connection ) ! developm5t ( 8/omata0 9 ! leaves ( plants4 ,! epid]mal cells by :i* ! leaf is cov]$ may be ( v>i\s %apes2 sometimes1 z 9 a hyac9?1 !y are oblong1 b m (t5 !y h an irregul> %ape 9 :i* we c recognise1 m or less cle>ly1 a di/ort$ or imp]fect hexagon4 ,9 ! case ( ! oblong cells1 a transv]se p>tition w be ! lea/ possible1 :e!r ! cell be equally or unequally divid$1 unless 7z we h already se57 #cid ! space to be cut (f be a v small "o1 n m ?an ab\t ?ree-t5?s ! area ( a squ>e bas$ on ! %ort side ( ! orig9al rectangul> cell4 ,z ! portion usually cut (f is n ne>ly s small z ?is1 we get ! =m ( p>tition %ewn 9 ,fig4 #agi1 & ! cell s cut (f is next bisect$ by a p>tition at "r angles to ! fir/2 ?is latt] p>tition splits1 & ! two la/-=m$ cells con/itute ! s-call$ 8gu>d-cells0 ( ! ,illu/ration3 ,fig4 #agi4 ,diagrammatic developm5t ( /omata 9 ,hyac9?4 /oma4 ,9 o!r cases1 z 9 ,fig4 #agh1 !re w come a po9t :]e ! m9imal p>tition necess>y to cut (f ! requir$ fraction ( ! cell-cont5t is no long] a transv]se "o1 b is a portion ( a cyl9drical wall 7#b7 cutt+ (f "o corn] ( ! "m-cell4 ,! cell s cut (f is n[ a c]ta9 segm5t ( a circle1 ) an arc ( approximately #abj2 & its next division w be by means ( a curv$ wall cutt+ x into a triangul> & a quadrangul> portion 7#c74 ,! triangul> portion w cont9ue to divide 9 a simil> way 7#d1 #e71 & at l5g? 7= a reason :i* is n yet cle>7 ! p>tition wall #cie betwe5 ! new-=m$ cells splits1 & aga9 we h ! ph5om5on ( a 8/oma0 ) its att5dant gu>d-cells4 ,9 ,fig4 #agi are %ewn ! successive /ages ( division1 & ! *ang+ curvatures ( ! v>i\s walls :i* ensue z ea* subsequ5t p>tition appe>s1 introduc+ a new t5sion into ! sy/em4 ,x is obvi\s t 9 ! case ( ! oblong cells ( ! epid]mis 9 ! hyac9? ! /omata w be f\nd arrang$ 9 regul> r[s1 :ile !y w be irregul>ly di/ribut$ ov] ! surface ( ! leaf 9 su* a case z we h depict$ 9 ,s$um4 ,:ile1 z ,i h said1 ! me*anical cause ( ! split :i* con/itutes ! orifice ( ! /oma is n q cle>1 yet !re c be little or no d\bt t x1 l ! re/ ( ! ph5om5on1 is relat$ to surface t5sion4 ,x might well be t x is directly due to ! pres5ce und]nea? ?is portion ( epid]mis ( ! holl[ air-space :i* ! /oma is app>5tly develop$ 8= ! purpose0 ( communicat+ )2 ?is air-surface on bo? sides ( ! delicate epid]mis might well cause su* an alt]ation ( t5sions t ! two halves ( ! divid+ cell w\ld t5d to "p company4 ,9 %ort1 if ! surface-en]gy 9 a cell-air contact 7 half or less ?an half t 9 a contact betwe5 cell & cell1 !n x is obvi\s t our p>tition w\ld t5d to split1 & give u a two-fold surface 9 contact ) air1 in/ead ( ! orig9al b\nd>y or int]face betwe5 "o cell & ! o!r4 ,9 ,pr(essor ,macallum's exp]im5ts1 :i* we h briefly discuss$ 9 our %ort *apt] on ,adsorption1 x 0 f\nd t l>ge quantities ( potassium ga!r$ toge!r along ! out] walls ( ! gu>d-cells ( ! /oma1 !reby indicat+ a l[ surface-t5sion along ^! out] walls4 ,! t5d5cy ( ! gu>d-cells to bulge outw>ds is s f> expla9$1 & x is possible t1 "u ! exi/+ conditions ( re/ra9t1 we may h "h a =ce t5d+1 or help+1 to split ! two cells asund]4 ,x is cle> en\gh1 h[ev]1 t ! la/ /age 9 ! developm5t ( a /oma1 is1 f ! physical po9t ( view1 n yet prop]ly und]/ood4 ,illu/ration3 ,fig4 #ahj4 ,v>i\s poll5-gra9s & spores 7aft] ,b]?old1 ,campbell1 ,goebel & o!rs74 7#a7 ,epilobium2 7#b7 ,passiflora2 7#c7 ,neottia2 7#d7 ,p]iploca graeca2 7#e7 ,apocynum2 7#f7 ,erica2 7#g7 ,spore ( ,osmunda2 7#h7 ,tetraspore ( ,calli?amnion4 ,illu/ration3 ,fig4 #aha4 ,divid+ spore ( ,an?oc]os4 7,aft] ,campbell47 ,9 all our =ego+ examples ( ! developm5t ( a 8tissue0 we h se5 t ! process consi/s 9 ! successive division ( cells1 ea* act ( division be+ accompani$ by ! =mation #cif ( a b\nd>y-surface1 :i*1 :e!r x become at once a solid or semi-solid p>tition or :e!r x rema9 semi-fluid1 ex]cises 9 all cases an effect on ! position & ! =m ( ! b\nd>y :i* comes into be+ ) ! next act ( division4 ,9 contra/ to ?is g5]al process /&s ! ph5om5on kn[n z 8free cell-=mation10 9 :i*1 out ( a common mass ( protoplasm1 a numb] ( sep>ate cells are simultane\sly1 or all b simultane\sly1 diff]5tiat$4 ,9 a numb] ( cases x happ5s t1 to beg9 )1 a numb] ( 8"m-cells0 are =m$ simultane\sly1 & ea* ( ^! divides1 by two successive divisions1 into f\r 8daught]-cells40 ,^! daught]-cells w t5d to gr\p !mselves1 j z w\ld f\r soap-bubbles1 into a 8tetrad10 ! f\r cells correspond+ to ! angles ( a regul> tetrah$ron4 ,= ! sy/em ( f\r bodies is evid5tly "h 9 p]fect symmetry2 ! p>tition-walls & _! respective edges meet at equal angles3 ?ree walls ev]y:]e meet+ 9 an edge1 & ! f\r edges conv]g+ to a po9t 9 ! geometrical c5tre ( ! sy/em4 ,?is is ! typical mode ( developm5t ( poll5-gra9s1 common among ,monocotyl$ons & all b univ]sal among ,dicotyl$on\s plants4 ,by a loos5+ ( ! surr\nd+ tissue & an expansion ( ! cavity1 or an!r-cell1 9 :i* #cig !y lie1 ! poll5-gra9s aft]w>ds fall ap>t1 & _! individual =m w dep5d ^u :e!r or no _! walls h solidifi$ be=e ?is lib]ation takes place4 ,= if n1 !n ! sep>ate gra9s w be free to assume a sph]ical =m z a consequ5ce ( _! own individual & unre/rict$ gr[?2 b if !y become solid or rigid prior to ! sep>ation ( ! tetrad1 !n !y w cons]ve m or less completely ! plane int]faces & %>p angles ( ! elem5ts ( ! tetrah$ron4 ,! latt] is ! case1 = in/ance1 9 ! poll5-gra9s ( ,epilobium 7,fig4 #ahj1 #a7 & 9 _m o!rs4 ,9 ! ,passion-fl[] 7#b7 we h an int]m$iate condition3 :]e we c /ill see an indication ( ! facets :]e ! gra9s abutt$ on "o ano!r 9 ! tetrad1 b ! plane faces h be5 swoll5 by gr[? into sph]oidal or sph]ical surfaces4 ,x is obvi\s t !re may easily be cases :]e ! tetrads ( daught]-cells are prev5t$ f assum+ ! tetrah$ral =m3 cases1 t is to say1 :]e ! f\r cells are =c$ & cru%$ into "o plane4 ,! figures giv5 by ,goebel ( ! developm5t ( ! poll5 ( ,neottia 7#c1 a-e3 all ! figures ref]r+ to gra9s tak5 f a s+le an!r71 illu/rate ?is to p]fection2 & x w be se5 t1 :5 ! f\r cells lie 9 a plane1 !y con=m exactly to our typical diagram ( ! fir/ f\r cells 9 a segm5t+ ovum4 ,occasionally1 ?\gh ! f\r cells lie 9 a plane1 ! diagram seems to fail u1 = ! cells appe> to meet 9 a simple cross 7z 9 #e72 b "h we soon p]ceive t ! cells are n 9 complete int]facial contact1 b are kept ap>t by a little int]v5+ drop ( fluid or bubble ( air4 ,! spores ( f]ns 7#g7 develop 9 v mu* ! same way z poll5-gra9s2 & !y also v (t5 reta9 traces ( ! %ape :i* !y assum$ z memb]s ( a tetrah$ral figure4 ,among ! 8tetraspores0 7#h7 ( ! ,florideae1 or ,r$ ,seawe$s1 we h a ph5om5on :i* is 9 e respect analog\s4 ,"h aga9 x is obvi\s t1 ap>t f diff]5ces 9 actual magnitude1 & ap>t f sup]ficial or 8accid5tal0 diff]5ces 7ref]able to o!r physical ph5om5a7 9 ! way ( col\r1 #cih texture & m9ute sculpture or patt]n1 x comes to pass1 ?r\gh ! laws ( surface-t5sion & ! pr9ciples ( ! geometry ( position1 t a v small numb] ( diagrammatic figures w suffici5tly repres5t ! outw>d =ms ( all ! tetraspores1 f\r-cell$ poll5-gra9s1 & o!r f\r-cell$ aggregates :i* are kn[n or are ev5 capable ( exi/5ce4 ,we h be5 deal+ hi!rto 7save = "s slight exceptions7 ) ! p>tition+ ( cells on ! assumption t ! sy/em ei!r rema9s unalt]$ 9 size or else t gr[? has proce$$ uni=mly 9 all directions4 ,b we ext5d ! scope ( our enquiry v greatly :5 we beg9 to deal ) unequal gr[?1 ) gr[?1 t is to say1 :i* produces a great] ext5sion along "s "o axis ?an ano!r4 ,& "h we come close 9 t\* ) t great & /ill 7z ,i ?9k7 insuffici5tly appreciat$ g5]alisation ( ,sa*s1 t ! mann] 9 :i* ! cells divide is ! result1 & n ! cause1 ( ! =m ( ! divid+ /ructure3 t ! =m ( ! mass is caus$ by its gr[? z a :ole1 & is n a resultant ( ! gr[? ( ! cells individually consid]$#djc4 ,su* asymmetry ( gr[? may be easily imag9$1 & may conceivably arise f a v>iety ( causes4 ,9 any individual cell1 = in/ance1 x may arise f molecul> asymmetry ( ! /ructure ( ! cell-wall1 giv+ x great] rigidity 9 "o direction ?an ano!r1 :ile all ! :ile ! hydro/atic pressure )9 ! cell rema9s con/ant & uni=m4 ,9 an aggregate ( cells1 x may v well arise f a great] *emical1 or osmotic1 activity 9 "o ?an ano!r1 lead+ to a localis$ increase 9 ! fluid pressure1 & to a correspond+ bulge ov] a c]ta9 area ( ! ext]nal surface4 ,x might conceivably occur z a direct result ( ! prec$+ cell-divisions1 :5 ^! are su* z to produce _m p]iph]al or conc5tric walls 9 "o "p & few or none 9 ano!r1 ) ! obvi\s result ( /r5g!n+ ! common b\nd>y wall & resi/+ ! outw>d pressure ( gr[? 9 p>ts :]e ! =m] is ! case2 t is to say1 9 our divid+ quadrant1 if #cii its quadrangul> portion subdivide by p]icl9es1 & ! triangul> portion by oblique anticl9es 7z we h se5 to be ! natural t5d5cy71 !n we might expect t ext]nal gr[? w\ld be m manife/ ov] ! latt] ?an ov] ! =m] areas4 ,z a direct & imm$iate consequ5ce ( ?is we might expect a t5d5cy = special outgr[?s1 or 8buds10 to arise f ! triangul> r ?an f ! quadrangul> cells2 & ?is turns out to be n m]ely a t5d5cy t[>ds :i* !oretical consid]ations po9t1 b a widespread & important factor 9 ! morphology ( ! cryptogams4 ,b mean:ile1 )\t enquir+ fur!r into ?is complicat$ "q1 let u simply take x t1 if we />t f su* a simple case z a r\nd cell :i* has divid$ into two halves1 or f\r qu>t]s 7z ! case may be71 we %all at once get bilat]al symmetry ab\t a ma9 axis1 & o!r second>y results aris+ !refrom1 z soon z "o ( ! halves1 or "o ( ! qu>t]s1 beg9s to %ew a rate ( gr[? 9 advance ( ! o!rs2 = ! m rapidly gr[+ cell1 or ! p]iph]al wall common to two or m su* rapidly gr[+ cells1 w bulge out into an ellipsoid =m1 & may f9ally ext5d into a cyl9d] ) r\nd$ or ellipsoid end4 ,?is latt] v simple case is illu/rat$ 9 ! developm5t ( a poll5-tube1 :]e ! rapidly gr[+ cell develops into ! elongat$ cyl9drical tube1 & ! sl[-gr[+ or quiesc5t "p rema9s beh9d z ! s-call$ 8vegetative0 cell or cells4 ,j z we h f\nd x easi] to /udy ! segm5tation ( a circul> disc ?an t ( a sph]ical cell1 s let u beg9 9 ! same way1 by enquir+ into ! divisions :i* w ensue if ! disc t5d to gr[1 or elongate1 9 "s "o p>ticul> direction1 in/ead ( 9 radial symmetry4 ,! figures :i* we %all !n obta9 w n only apply to ! disc1 b w also repres5t1 9 all ess5tial features1 a projection or longitud9al section ( a solid body1 sph]ical to beg9 )1 pres]v+ its symmetry z a solid ( revolution1 & subject to ! same g5]al laws z we h /udi$ 9 ! disc#djd4 #djj 7#a7 ,suppose1 9 ! fir/ place1 t ! axis ( gr[? lies symmetrically 9 "o ( ! orig9al quadrantal cells ( a segm5t+ disc2 & let ?is gr[+ cell elongate ) comp>ative rapidity be=e x subdivides4 ,:5 x does divide1 x w necess>ily d s by a transv]se p>tition1 concave t[>ds ! apex ( ! cell3 &1 z fur!r elongation takes place1 ! cyl9drical /ructure :i* w be develop$ !reby w t5d to be aga9 & aga9 subdivid$ by simil> concave transv]se p>titions4 ,if at any "t1 ?r\gh ?is process ( concurr5t elongation & subdivision1 ! apical cell become equival5t to1 or less ?an1 a hemisph]e1 x w next divide by means ( a longitud9al1 or v]tical p>tition2 & simil> longitud9al p>titions w arise 9 ! o!r segm5ts ( ! cyl9d]1 z soon z x comes ab\t t _! l5g? 79 ! direction ( ! axis7 is less ?an _! bread?4 ,illu/ration3 ,fig4 #ahb4 ,b :5 we ?9k ( ?is /ructure 9 ! solid1 we at once p]ceive t ea* ( ^! flatt5$ segm5ts ( ! cyl9d]1 into :i* our cyl9d] has divid$1 is equival5t to a flatt5$ circul> disc2 & its fur!r division w accord+ly t5d to proce$ l any o!r flatt5$ disc1 namely into f\r quadrants1 & aft]w>ds by anticl9es & p]icl9es 9 ! usual way4 #dja ,a section across ! cyl9d]1 !n1 w t5d to %ew u precisely ! same arrangem5ts z we h already s fully /udi$ 9 connection ) ! typical division ( a circul> cell into quadrants1 & ( ^! quadrants into triangul> & quadrangul> portions1 & s on4 ,b !re are o!r possibilities to be consid]$1 9 reg>d to ! mode ( division ( ! elongat+ quasi-cyl9drical portion1 z x gradually develops out ( ! gr[+ & bulg+ quadrantal cell2 = ! mann] 9 :i* ?is latt] cell divides w simply dep5d ^u ! =m x has assum$ be=e ea* successive act ( division takes place1 t is to say ^u ! ratio betwe5 its rate ( gr[? & ! frequ5cy ( its successive divisions4 ,=1 z we h already se51 if ! gr[+ cell atta9 a m>k$ly oblong or cyl9drical =m be=e division ensues1 !n ! p>tition w arise transv]sely to ! long axis2 if x be b a little m ?an a hemisph]e1 x w divide by an oblique p>tition2 & if x be less ?an a hemisph]e 7z x may come to be aft] successive transv]se divisions7 x w divide by a v]tical p>tition1 t is to say by "o co9cid+ ) its axis ( gr[?4 ,an imm5se numb] ( p]mutations & comb9ations may arise 9 ?is way1 & we mu/ conf9e our illu/rations to a small numb] ( cases4 ,! important ?+ is n s mu* to trace out ! v>i\s con=mations :i* may arise1 b to grasp ! fundam5tal pr9ciple3 :i* is1 t ! =ces :i* dom9ate ! =m ( ea* cell regulate ! mann] ( its subdivision1 t is to say ! =m ( ! new cells into :i* x subdivides2 or 9 o!r words1 ! =m ( ! gr[+ organism regulates ! =m & numb] ( ! cells :i* ev5tually con/itute x4 ,! complex cell-network is n ! cause b ! result ( ! g5]al configuration1 :i* latt] has its ess5tial cause 9 :atsoev] physical & *emical processes h l$ to a v>y+ velocity ( gr[? 9 "o direction z comp>$ ) ano!r4 ,illu/ration3 ,fig4 #ahc4 ,developm5t ( ,sphagnum4 7,aft] ,campbell47 ,9 ! annex$ figure ( an embryo ( ,sphagnum we see a mode ( developm5t almo/ precisely correspond+ to ! hypo!tical case :i* we h j describ$1--! case1 t is to say1 :]e "o ( ! f\r orig9al quadrants ( ! "m-cell is ! *ief ag5t 9 future gr[? & developm5t4 ,we see at ! base ( our fir/ figure 7a71 ! ?ree /ation>y1 or #djb undivid$ quadrants1 "o ( :i* has fur!r sl[ly divid$ 9 ! /age b4 ,! active quadrant has gr[n quickly into a cyl9drical /ructure1 :i* inevitably divides1 9 ! next place1 into a s]ies ( transv]se p>titions2 & accord+ly1 ?is mode ( developm5t c>ries ) x ! pres5ce ( a s+le 8apical cell10 ^: l[] wall is a sph]ical surface ) its convexity d[nw>ds4 ,ea* cell ( ! subdivid$ cyl9d] n[ appe>s z a m or less flatt5$ disc1 ^: mode ( fur!r sub-division we may progno/icate accord+ to our =m] inve/igation1 to :i* subject we %all pres5tly return4 ,illu/ration3 ,fig4 #ahd4 7#b7 ,9 ! next place1 /ill keep+ to ! case :]e only "o ( ! orig9al quadrant-cells cont9ues to gr[ & develop1 let u suppose t ?is gr[+ cell falls to be divid$ :5 by gr[? x has become j a little great] ?an a hemisph]e2 x w !n divide1 z 9 ,fig4 #ahd1 #b1 by an oblique p>tition1 9 ! usual way1 ^: precise position & incl9ation to ! base w dep5d entirely on ! configuration ( ! cell itself1 save only1 ( c\rse1 t we may h also to take into acc\nt ! possibility ( ! division be+ into two unequal halves4 ,by our hypo!sis1 #djc ! gr[? ( ! :ole sy/em is ma9ly 9 a v]tical direction1 :i* is z mu* z to say t ! m actively gr[+ protoplasm1 or at lea/ ! /ronge/ osmotic =ce1 w be f\nd ne> ! apex2 :]e inde$ !re is obvi\sly m ext]nal surface = osmotic action4 ,x w !re=e be t "o ( ! two cells :i* conta9s1 or con/itutes1 ! apex :i* w gr[ m rapidly ?an ! o!r1 & :i* !re=e w be ! fir/ to divide1 & inde$ 9 any case1 x w usually be ?is "o ( ! two :i* w t5d to divide fir/1 inasmu* z ! triangul> & n ! quadrangul> half is b\nd to con/itute ! apex#dje4 ,x is obvi\s t 7unless ! act ( division be s long po/pon$ t ! cell has become quasi-cyl9drical7 x w divide by ano!r oblique p>tition1 />t+ f1 & runn+ at "r angles to1 ! fir/4 ,& s division w proce$1 ,illu/ration3 ,fig4 #ahe4 ,gemma ( ,moss4 7,aft] ,campbell47 by oblique alt]nate p>titions1 ea* "o t5d+ to be1 at fir/1 p]p5dicul> to t on :i* x is bas$ & also to ! p]iph]al wall2 b all ^! po9ts ( contact soon t5d+1 by reason ( ! equal t5sions ( ! ?ree films or surfaces :i* meet !re1 to =m angles ( #abj4 ,!re w always be1 9 su* a case1 a s+le apical cell1 ( a m or less di/9ctly triangul> =m4 ,! annex$ figure ( ! develop+ an!ridium ( a ,liv]wort 7,riccia7 is a typical example ( su* a case4 ,9 ,fig4 #ahe :i* repres5ts a 8gemma0 ( a ,moss1 we see j ! same ?+2 ) ?is addition1 t "h ! l[] ( ! two orig9al cells has gr[n ev5 m quickly ?an ! o!r1 con/itut+ a long cyl9drical /alk1 & divid+ 9 accordance ) its %ape1 by means ( transv]se septa4 ,9 all su* cases z ^!1 ! cells ^: developm5t we h /udi$ w 9 turn t5d to subdivide1 & ! mann] 9 :i* !y w d s mu/ dep5d ^u _! own proportions2 & 9 all cases1 z we h already se51 !re w soon] or lat] be a t5d5cy to ! =mation ( p]icl9al walls1 cutt+ (f an 8epid]mal lay] ( cells10 z ,fig4 #ahf illu/rates v well4 ,illu/ration3 ,fig4 #ahf4 ,developm5t ( an!ridium ( ,riccia4 7,aft] ,campbell47 ,illu/ration3 ,fig4 #ahg4 ,section ( gr[+ %oot ( ,selag9ella1 diagrammatic4 ,illu/ration3 ,fig4 #ahh4 ,embryo ( ,jung]mannia4 7,aft] ,ki5itz-,g]l(f47 ,! me?od ( division by means ( oblique p>titions is a common "o 9 ! case ( #8gr[+ po9ts'2 = x evid5tly #djd includes all cases 9 :i* ! act ( cell-division does n lag f> beh9d t elongation :i* is det]m9$ by ! specific rate ( gr[?4 ,& x is also obvi\s t1 "u a common type1 !re mu/ "h be includ$ a v>iety ( cases :i* w1 at fir/ sight1 pres5t a v diff]5t appe>ance "o f ano!r4 ,= in/ance1 9 ,fig4 #ahg :i* repres5ts a gr[+ %oot ( ,selag9ella1 & some:at less diagrammatically 9 ! "y embryo ( ,jung]mannia 7,fig4 #ahh71 we h ! appe>ance ( an almo/ /raight v]tical p>tition runn+ up 9 ! axis ( ! sy/em1 & ! prim>y cell-walls are set almo/ at "r angles to x1--almo/ transv]sely1 t is to say to ! out] walls & to ! long axis ( ! /ructure4 ,we soon recognise1 h[ev]1 #dje t ! diff]5ce is m]ely a diff]5ce ( degree4 ,! m remote ! p>titions are1 t is to say ! great] ! velocity ( gr[? relatively to division1 ! less abrupt w be ! alt]nate k9ks or curvatures ( ! portions :i* lie 9 ! neighb\rhood ( ! axis1 & ! m w ^! portions appe> to con/itute a s+le unbrok5 wall4 ,illu/ration3 ,fig4 #ahi4 7#c7 ,b an appe>ance ne>ly1 if n q1 indi/+ui%able f ?is may be got 9 ano!r way1 namely1 :5 ! orig9al gr[+ cell is s ne>ly hemisph]ical t x is actually divid$ by a v]tical p>tition1 into two quadrants2 & f ?is v]tical p>tition1 z x elongates1 lat]al p>tition-walls w arise on ei!r side4 ,& by ! t5sions ex]cis$ by ^!1 ! v]tical p>tition w be b5t into little portions set at #abj "o to ano!r1 & ! :ole w come to look j l t :i*1 9 ! =m] case1 0 made up ( portions ( _m successive oblique p>titions4 ,let u n[1 9 "o or two cases1 foll[ out a little fur!r ! /ages ( cell-division ^: beg9n+ we h /udi$ 9 ! la/ p>agraphs4 ,9 ! an!ridium ( ,riccia1 aft] ! successive oblique p>titions h produc$ ! longitud9al s]ies ( cells %ewn 9 ,fig4 #ahf1 x is pla9 t ! next p>titions w arise p]icl9ally1 t is to say p>allel to ! out] wall1 :i* 9 ?is p>ticul> case repres5ts ! %ort axis ( ! oblong cells4 ,! effect is at once to produce an epid]mal lay]1 ^: cells w t5d to subdivide fur!r by means ( p>titions p]p5dicul> to ! free surface1 t is to say cross+ ! flatt5$ cells by _! %orte/ diamet]4 ,! inn] mass1 b5ea? ! epid]mis1 consi/s ( cells :i* are /ill m or less oblong1 or :i* become #djf def9itely s 9 process ( gr[?2 & ^! aga9 divide1 p>allel to _! %ort axes1 into squ>i% cells1 :i* z usual1 by ! mutual t5sion ( _! walls1 become hexagonal1 z se5 9 a plane section4 ,!re is a cle> di/9ction1 !n1 9 =m z well z 9 position1 betwe5 ! out] cov]+-cells & ^? :i* lie )9 ?is envelope2 ! latt] are r$uc$ to a condition :i* m]ely fulfils ! me*anical function ( a protective coat1 :ile ! =m] und]go less modification1 & give rise to ! actively liv+1 reproductive elem5ts4 ,illu/ration3 ,fig4 #aij4 ,developm5t ( sporangium ( ,osmunda4 7,aft] ,b[]47 ,9 ,fig4 #aij is %ewn ! developm5t ( ! sporangium ( a f]n 7,osmunda74 ,we may trace "h ! common ph5om5on ( a s]ies ( oblique p>titions1 built alt]nately on "o ano!r1 & cutt+ (f a conspicu\s triangul> apical cell4 ,ov] ! :ole sy/em an epid]mal lay] has be5 =m$1 9 ! mann] we h describ$2 & 9 ?is case x cov]s ! apical cell also1 ow+ to ! fact t x 0 ( su* dim5sions t1 at "o /age ( gr[?1 a p]icl9al p>tition wall1 cutt+ (f its out] end1 0 indicat$ z ( less area ?an an anticl9al "o4 ,?is p]icl9al wall cuts d[n ! apical cell to ! proportions1 v ne>ly1 ( an equilat]al triangle1 b ! solid =m ( ! cell is obvi\sly t ( a tetrah$ron ) curv$ faces2 & accord+ly1 ! lea/ possible p>titions by :i* fur!r subdivision c be effect$ w run successively p>allel to its f\r sides 7or its ?ree sides :5 we conf9e ourselves to ! appe>ances z se5 9 #djg section74 ,! effect1 z se5 9 section1 is to cut (f on ea* side a *>act]i/ically flatt5$ cell1 oblong z se5 9 section1 /ill leav+ a triangul> 7or /rictly speak+1 a tetrah$ral7 "o 9 ! c5tre4 ,! =m] cells1 :i* con/itute no specific /ructure or p]=m no specific physiological function1 b :i* m]ely repres5t c]ta9 directions 9 space t[>ds :i* ! :ole sy/em ( p>tition+ has gradually l$1 are call$ by botani/s ! 8tapetum40 ,! active gr[+ tetrah$ral cell :i* lies betwe5 !m1 & f :i* 9 a s5se e o!r cell 9 ! sy/em has be5 ei!r directly or indirectly segm5t$ (f1 /ill manife/s1 z x 71 its vig\r & activity1 & n[1 by int]nal subdivision1 becomes ! "m-cell ( ! spores4 ,9 all ^! cases1 = simplicity's sake1 we h m]ely consid]$ ! appe>ances pres5t$ 9 a s+le1 longitud9al1 plane ( optical section4 ,b x is n difficult to int]pret f ^! appe>ances :at w\ld be se5 9 ano!r plane1 = in/ance 9 a transv]se section4 ,9 our fir/ example1 = in/ance1 t ( ! develop+ embryo ( ,sphagnum 7,fig4 #ahc71 we c see t1 at appropriate levels1 ! cells ( ! orig9al cyl9drical r[ h divid$ into transv]se r[s ( f\r1 & !n ( eight cells4 ,we may be sure t ! f\r cells repres5t1 approximately1 quadrants ( a cyl9drical disc1 ! f\r cells1 z usual1 n meet+ 9 a po9t1 b int]cept$ by a small int]m$iate p>tition4 ,aga91 :]e we h a plate ( eight cells1 we may well imag9e t ! eight octants are arrang$ 9 :at we h f\nd to be ! way naturally result+ f ! division ( f\r quadrants1 t is to say into alt]nately triangul> & quadrangul> portions2 & ?is is f\nd by means ( sections to be ! case4 ,! accompany+ figure is precisely comp>able to our previ\s diagrams ( ! arrangem5t ( an aggregate ( eight cells 9 a divid+ disc1 save only t1 9 two cases1 ! cells h already und]gone a fur!r subdivision4 ,illu/ration3 ,fig4 #aia4 7,a1 ,b17 ,sections ( y\ng] & old] embryos ( ,phascum2 7,c7 d4 ( ,adiantum4 7,aft] ,ki5itz-,g]l(f47 ,illu/ration3 ,fig4 #aib4 ,section ?r\gh frond ( ,gir>dia sphacel>ia4 7,aft] ,goebel47 ,x foll[s 9 l mann]1 t 9 a ho/ ( cases we meet ) ?is *>act]i/ic figure1 9 "o or o!r ( its possible1 & /rictly limit$1 v>iations1--9 ! cross sections ( gr[+ embryonic /ructures1 j z we h already se5 t x appe>s 9 a ho/ ( cases :]e ! entire sy/em 7or a portion ( its #djh surface7 consi/s ( eight cells only4 ,= example1 9 ,fig4 #aia1 we h x aga91 9 a section ( a "y embryo ( a moss 7,phascum71 & 9 a section ( an embryo ( a f]n 7,adiantum74 ,9 ,fig4 #aib %ew+ a section ?r\gh a gr[+ frond ( a sea-we$ 7,gir>dia7 we h a case :]e ! p>titions =m+ ! eight octants h con=m$ to ! usual type2 b in/ead ( ! usual division by p]icl9es ( ! f\r quadrangul> spaces1 ^! latt] are divid+ by means ( oblique septa1 app>5tly ow+ to ! fact t ! cell is n divid+ into two equal1 b into two unequal portions4 ,9 ?is la/ figure we h a peculi> look ( /iffness or =mality1 su* t x appe>s at fir/ to be> little resemblance to ! re/4 ,! explanation is ( ! simple/4 ,! mode ( p>tition+ diff]s little 7except to "s slight ext5t 9 ! way already m5tion$7 f ! normal type2 b 9 ?is case ! p>tition walls are s ?ick & become s quickly comp>atively solid & rigid1 t ! second>y curvatures due to _! successive mutual tractions are "h imp]ceptible4 ,illu/ration3 ,fig4 #aic4 ,developm5t ( an!ridium ( ,pt]is4 7,aft] ,/rasbrg]47 ,a curi\s & beautiful case1 app>5tly ab]rant b :i* w\ld d\btless be f\nd con=m+ /rictly to physical laws1 if #dji only we cle>ly und]/ood ! actual conditions1 is indicat$ 9 ! developm5t ( ! an!ridium ( a f]n1 z describ$ by ,/rasbrg]4 ,"h ! an!ridium develops f a s+le cell1 ^: =m has gr[n to be some?+ m ?an a hemisph]e2 & ! fir/ p>tition1 in/ead ( /ret*+ transv]sely across ! cell1 z we %\ld expect x to d if ! cell 7 actually sph]ical1 has z x 7 sagg$ d[n to come 9 contact ) ! base1 & s to develop into an annul> p>tition1 runn+ r\nd ! l[] m>g9 ( ! cell4 ,! ph5om5on is ak9 to t cutt+ (f ( ! corn] ( a cubical cell by a sph]ical p>tition1 ( :i* we h spok5 on p4 #cdi1 & ! annul> film is v easy to reproduce by means ( a soap-bubble 9 ! bottom ( a cyl9drical di% or beak]4 ,! next p>tition is a p]icl9al "o1 conc5tric ) ! out] surface ( ! "y an!ridium2 & ?is 9 turn is foll[$ by a concave p>tition :i* cuts (f ! apex ( ! orig9al cell3 b :i* becomes connect$ ) ! second1 or p]icl9al p>tition 9 precisely ! same annul> fa%ion z ! fir/ p>tition did ) ! base ( ! little an!ridium4 ,! result is t1 at ?is /age1 we h f\r cell-cavities 9 ! little an!ridium3 7#a7 a c5tral cavity2 7#b7 an annul> space ar\nd ! l[] m>g92 7#c7 a n>r[ annul> or cyl9drical space ar\nd ! sides ( ! an!ridium2 & 7#d7 a small t]m9al or apical cell4 ,x is evid5t t ! t5d5cy1 9 ! next place1 w be to subdivide ! flatt5$ ext]nal cells by means ( anticl9al p>titions1 & s to conv]t ! :ole /ructure into a s+le lay] ( epid]mal cells1 surr\nd+ a c5tral cell )9 :i*1 9 c\rse ( "t1 ! an!rozoids are develop$4 ,! =ego+ acc\nt deals only ) a few elem5t>y ph5om5a1 & may seem to fall f> %ort ( an attempt to deal 9 g5]al ) 8! =ms ( tissues40 ,b x is ! pr9ciple involv$1 & n its ultimate & v complex results1 t we c alone #daj attempt to grapple )4 ,! /ock-9-trade ( ma!matical physics1 9 all ! subjects ) :i* t sci5ce deals1 is = ! mo/ "p made up ( simple1 or simplifi$1 cases ( ph5om5a :i* 9 _! actual & concrete manife/ations are usually too complex = ma!matical analysis2 & :5 we attempt to apply its me?ods to our biological & hi/ological ph5om5a1 9 a prelim9>y & elem5t>y way1 we ne$ n wond] if we be limit$ to illu/rations :i* are obvi\sly ( a simple k9d1 & :i* cov] b a small "p ( ! ph5om5a ) :i* ! hi/ologi/ has become famili>4 ,b x is only relatively t ^! ph5om5a to :i* we h f\nd ! me?od applicable are to be deem$ simple & few4 ,!y g already f> beyond ! simple/ ph5om5a ( all1 su* z we see 9 ! divid+ ,protococcus1 & 9 ! fir/ /ages1 two-cell$ or f\r-cell$1 ( ! segm5t+ egg4 ,!y c>ry u into /ages :]e ! cells are already num]\s1 & :]e ! :ole con=mation has become by no means easy to depict or visualise1 )\t ! help & guidance :i* ! ph5om5a ( surface-t5sion1 ! laws ( equilibrium & ! pr9ciple ( m9imal areas are at h& to supply4 ,& s f> z we h gone1 & s f> z we c disc]n1 we see no sign ( ! guid+ pr9ciples fail+ u1 or ( ! simple laws ceas+ to hold good4 #daa ,,*apt] ,,ix ,,on ,,concretions1 ,,spicules1 ,,& ,,spicul> ,,skeletons ,! deposition ( inorganic mat]ial 9 ! liv+ body1 usually 9 ! =m ( calcium salts or ( silica1 is a v common & wide-spread ph5om5on4 ,x beg9s 9 simple ways1 by ! appe>ance ( small isolat$ p>ticles1 cry/all9e or non-cry/all9e1 ^: =m has little relation or sometimes none to ! /ructure ( ! organism2 x culm9ates 9 ! complex skeletons ( ! v]tebrate animals1 9 ! massive skeletons ( ! corals1 or 9 ! poli%$1 sculptur$ & ma!matically regul> molluscan %ells4 ,ev5 among _m v simple organisms1 su* z ! ,diatoms1 ! ,radiol>ians1 ! ,=am9if]a1 or ! ,sponges1 ! skeleton displays extraord9>y v>iety & beauty1 :e!r by reason ( ! intr9sic =m ( its elem5t>y con/itu5ts or ! geometric symmetry ) :i* ^! are arrang$ & int]connect$4 ,) reg>d to ! =m ( ^! v>i\s /ructures 7& ?is is all t imm$iately conc]ns u "h71 x is pla9 t we h to d ) two di/9ct problems1 :i* h[ev]1 ?\gh !oretically di/9ct1 may m]ge ) "o ano!r4 ,= ! =m ( ! spicule or o!r skeletal elem5t may dep5d simply ^u its *emical nature1 z = in/ance1 to take a simple b n ! only case1 :5 ! =m is purely cry/all9e2 or ! inorganic solid mat]ial may be laid d[n 9 con=mity ) ! %apes assum$ by ! cells1 tissues or organs1 & s be1 z x 71 m\ld$ to ! %ape ( ! liv+ organism2 & aga91 !re may well be int]m$iate /ages 9 :i* bo? ph5om5a may be simultane\sly recognis$1 ! molecul> =ces play+ _! "p 9 conjunction )1 & "u ! re/ra9t (1 ! o!r =ces inh]5t 9 ! sy/em4 #dab ,s f> z ! problem is a purely *emical "o1 we mu/ deal ) x v briefly inde$2 & all ! m because special inve/igations reg>d+ x h z yet be5 few1 & ev5 ! ma9 facts ( ! case are v imp]fectly kn[n4 ,?is at lea/ is evid5t1 t ! :ole s]ies ( ph5om5a ) :i* we are ab\t to deal g deep into ! subject ( colloid *emi/ry1 & especially ) t bran* ( ! sci5ce :i* deals ) ! prop]ties ( colloids 9 connection ) capill>y or surface ph5om5a4 ,x is to ! special /ud5t ( colloid *emi/ry t we mu/ ultimately & *iefly look = ! elucidation ( our problem#djf4 ,9 ! fir/ & simple/ "p ( our subject1 ! ess5tial problem is ! problem ( cry/allisation 9 pres5ce ( colloids4 ,9 ! cells ( plants1 true cry/als are f\nd 9 comp>ative abundance1 & !y consi/1 9 ! great majority ( cases1 ( calcium oxalate4 ,9 ! /em & root ( ! rhub>b1 = in/ance1 9 ! leaf-/alk ( ,begonia1 & 9 c\ntless o!r cases1 sometimes )9 ! cell1 sometimes 9 ! sub/ance ( ! cell-wall1 we f9d l>ge & well-=m$ cry/als ( ?is salt2 _! v>ieties ( =m1 :i* are extremely num]\s1 are simply ! cry/all9e =ms prop] to ! salt itself1 & belong to ! two sy/ems1 cubic & monocl9ic1 9 "o or o!r ( :i*1 accord+ to ! am\nt ( wat] ( cry/allisation1 ?is salt is kn[n to cry/allise4 ,:5 calcium oxalate cry/allises accord+ to ! latt] sy/em 7z x does :5 its molecule is comb9$ ) two molecules ( wat] ( cry/allisation71 ! microscopic cry/als h ! =m ( f9e ne$les1 or 8raphides10 su* z are v common 9 plants2 & x has be5 f\nd t ^! are artificially produc$ :5 ! salt is cry/allis$ out 9 pres5ce ( glucose or ( dextr9#djg4 ,illu/ration3 ,fig4 #aid4 ,alcyon>ian spicules3 ,siphonogorgia & ,an?ogorgia4 7,aft] ,/ud]47 ,calcium c>bonate1 on ! o!r h&1 :5 x occurs 9 plant-cells 7z x does abundantly1 = in/ance 9 ! 8cy/oli?s0 ( ! ,urticaceae & ,acan?aceae1 & 9 great quantities 9 ,melobesia #dac & ! o!r calc>e\s or 8/ony0 algae71 appe>s 9 ! =m ( f9e r\nd$ granules1 ^: inh]5t cry/all9e /ructure is n outw>dly visible1 b is only reveal$ 7l t ( a molluscan %ell7 "u pol>is$ light4 ,among animals1 a skeleton ( c>bonate ( lime occurs "u a multitude ( =ms1 ( :i* we ne$ only m5tion n[ a v few ( ! mo/ conspicu\s4 ,! spicules ( ! calc>e\s sponges are triradiate1 occasionally quadriradiate1 bodies1 ) po9t$ rays1 n cry/all9e 9 outw>d =m b ) a def9itely cry/all9e int]nal /ructure4 ,we %all return aga9 to ^!1 & f9d = !m :at w\ld seem to be a satisfactory explanation ( _! =m4 ,among ! ,alcyon>ian zoophytes we h a great v>iety ( spicules#djh1 :i* are sometimes /raight & sl5d] rods1 sometimes flatt5$ & m or less /riat$ plates1 & /ill m (t5 r\nd$ or bran*$ concretions ) r\gh or knobby surfaces 7,figs4 #aid1 #bjj74 ,a ?ird type1 pres5t$ by sev]al v diff]5t ?+s1 su* z a pe>l1 or ! e>-bone ( a bony fi%1 consi/s ( a m or less #dad r\nd$ body1 sometimes sph]ical1 sometimes flatt5$1 9 :i* ! calc>e\s matt] is laid d[n 9 conc5tric zones1 d5s] & cle>] lay]s alt]nat+ ) "o ano!r4 ,9 ! developm5t ( ! molluscan %ell & 9 ! calcification ( a bird's egg or ! %ell ( a crab1 = in/ance1 sph]oidal bodies ) simil> conc5tric /riation make _! appe>ance2 b in/ead ( rema9+ sep>ate !y become cr[d$ toge!r1 & z !y coalesce !y comb9e to =m a patt]n ( hexagons4 ,9 "s cases1 ! c>bonate ( lime on be+ dissolv$ away by acid leaves beh9d x a c]ta9 small am\nt ( organic residue2 9 mo/ cases o!r salts1 su* z phosphates ( lime1 ammonia or magnesia are pres5t 9 small quantities2 & 9 mo/ cases if n all ! develop+ spicule or concretion is someh[ or o!r s associat$ ) liv+ cells t we are apt to take x = grant$ t x owes its peculi>ities ( =m to ! con/ructive or pla/ic ag5cy ( ^!4 ,! appe>ance ( direct association ) liv+ cells1 h[ev]1 is apt to be fallaci\s2 = ! actual precipitation takes place1 z a rule1 n 9 actively liv+1 b 9 dead or at lea/ inactive tissue#dji3 t is to say 9 ! 8=m$ mat]ial0 or matrix :i* 7z = in/ance 9 c>tilage7 accumulates r\nd ! liv+ cells1 9 ! int]spaces betwe5 ^! latt]1 or at lea/1 z (t5 happ5s1 9 connection ) ! cell-wall or cell-membrane r ?an )9 ! sub/ance ( ! protoplasm itself4 ,we ne$ n g ! l5g? ( ass]t+ t ?is is a rule )\t exception2 b1 s f> z x goes1 x is ( great importance & to its consid]ation we %all pres5tly return#daj4 ,cognate ) ?is is ! fact t x is kn[n1 at lea/ 9 "s cases1 t ! organism c g on liv+ & multiply+ ) app>5tly unimpair$ heal?1 :5 /9t$ or ev5 :olly depriv$ ( ! mat]ial ( :i* x is wont to make its spicules #dae or its %ell4 ,?us1 ,p\*et & ,*abry#daa h %[n t ! eggs ( sea-ur*9s re>$ 9 lime-free wat] develop 9 app>5t heal?1 into l>vae entirely de/itute ( ! usual skeleton ( calc>e\s rods1 & 9 :i*1 accord+ly1 ! long arms ( ! ,pluteus l>va1 :i* ! rods support & di/5d1 are entirely suppress$4 ,& aga91 :5 ,=am9if]a are kept = g5]ations 9 wat] f :i* !y gradually exhau/ ! lime1 _! %ells gr[ hyal9e & transp>5t1 & seem to consi/ only ( *it9\s mat]ial4 ,on ! o!r h&1 9 ! pres5ce ( excess ( lime1 ! %ells become mu* alt]$1 /r5g!n$ ) v>i\s 8ornam5ts10 & assum+ *>act]s describ$ z prop] to o!r v>ieties & ev5 species#dab4 ,! crucial exp]im5t1 !n1 is to attempt ! =mation ( simil> /ructures or =ms1 ap>t f ! liv+ organism3 b1 h[ev] feasible ! attempt may be 9 !ory1 we %all be prep>$ f ! fir/ to enc\nt] difficulties1 & to realise t1 ?\gh ! actions involv$ may be :olly )9 ! range ( *emi/ry & physics1 yet ! actual conditions ( ! case may be s complex1 subtle & delicate1 t only n[ & !n1 & 9 ! simple/ ( cases1 %all we f9d ourselves 9 a position to imitate !m completely & successfully4 ,su* an inve/igation is only "p ( t mu* wid] field ( enquiry ?r\gh :i* ,/ephane ,l$uc & _m o!r work]s#dac h s\ght to produce1 by syn!tic means1 =ms simil> to ^? ( liv+ ?+s2 b x is a well-def9$ & circumscrib$ "p ( t wid] inve/igation4 ,:5 by *emical or physical exp]im5t we obta9 configurations simil>1 = in/ance1 to ! ph5om5a ( nucle> division1 or con=mations simil> to a patt]n ( hexagonal cells1 or a gr\p ( vesicles :i* resemble "s p>ticul> tissue or cell-aggregate1 we inde$ prove :at x is ! ma9 object ( ?is book to illu/rate1 namely1 t ! physical =ces are capable ( produc+ p>ticul> organic =ms4 ,b x is by no means always t we c feel p]fectly assur$ t ! physical =ces :i* we deal ) 9 our exp]im5t are id5tical )1 & n m]ely analog\s to1 #daf ! physical =ces :i*1 at "w 9 nature1 are br++ ab\t ! result :i* we h succe$$ 9 imitat+4 ,9 ! pres5t case1 h[ev]1 our enquiry is re/rict$ & app>5tly simplifi$2 we are seek+ 9 ! fir/ in/ance to obta9 by purely *emical means a purely *emical result1 & !re is little room = ambiguity 9 our int]pretation ( ! exp]im5t4 ,:5 we f9d ourselves inve/igat+ ! =ms assum$ by *emical comp\nds "u ! peculi> circum/ances ( association ) a liv+ body1 & :5 we f9d ^! =ms to be *>act]i/ic or recognisable1 & someh[ diff]5t f ^? :i*1 "u o!r circum/ances1 ! same sub/ance is wont to assume1 an analogy pres5ts itself to our m9ds1 captivat+ ?\gh p]haps some:at remote1 betwe5 ?is subject ( ours & c]ta9 syn!tic problems ( ! organic *emi/4 ,!re is d\btless an ess5tial diff]5ce1 z well z a diff]5ce ( scale1 betwe5 ! visible =m ( a spicule or concretion & ! hypo!tical =m ( an individual molecule2 b molecul> =m is a v important concept2 & ! *emi/ has n only succe$$1 s9ce ! days ( ,whl]1 9 syn!sis+ _m sub/ances :i* are *>act]i/ically associat$ ) liv+ matt]1 b 8 task has includ$ ! attempt to acc\nt = ! molecul> =ms ( c]ta9 8asymmetric0 sub/ances1 glucose1 malic acid & _m m1 z !y occur 9 nature4 ,^! are bodies :i*1 :5 artificially syn!sis$1 h no optical activity1 b :i*1 z we actually f9d !m 9 organisms1 turn 7:5 9 solution7 ! plane ( pol>is$ light 9 "o direction or ! o!r2 ?us dextro-glucose & laevomalic acid are common products ( plant metabolism2 b dextromalic acid & laevo-glucose d n occur 9 nature at all4 ,! optical activity ( ^! bodies dep5ds1 z ,pa/eur %ew$ m ?an fifty ye>s ago#dad1 ^u ! =m1 "r-h&$ or left-h&$1 ( _! molecules1 :i* molecul> asymmetry fur!r gives rise to a correspond+ "r or left-h&$ness 7or enantiomorphism7 9 ! cry/all9e aggregates4 ,x is a di/9ct problem 9 organic or physiological *emi/ry1 #dag & by no means )\t its int]e/ = ! morphologi/1 to discov] h[ x is t nature1 = ea* p>ticul> sub/ance1 habitually builds up1 or at lea/ selects1 its molecules 9 a "o-sid$ fa%ion1 "r-h&$ or left-h&$ z ! case may be4 ,x w s]ve u no bett] to ass]t t ?is ph5om5on has its orig9 9 8=tuity10 ?an to repeat ! ,abb ,galiani's say+1 8les ds de la nature sont pips40 ,! problem is n s closely relat$ to our imm$iate subject t we ne$ discuss x at l5g?2 b at ! same "t x has its cle> relation to ! g5]al "q ( =m 9 relation to vital ph5om5a1 & moreov] x has acquir$ int]e/ z a !me ( long-cont9u$ discussion & new importance f "s comp>atively rec5t discov]ies4 ,accord+ to ,pa/eur1 !re lay 9 ! molecul> asymmetry ( ! natural bodies & ! symmetry ( ! artificial products1 "o ( ! mo/ deep-seat$ diff]5ces betwe5 vital & non-vital ph5om5a3 he w5t fur!r1 & decl>$ t 8?is 0 p]haps ! only well-m>k$ l9e ( dem>cation t c at pres5t #ahfj be drawn betwe5 ! *emi/ry ( dead & ( liv+ matt]40 ,ne>ly =ty ye>s aft]w>ds ! same !me 0 pursu$ & elaborat$ by ,japp 9 a celebrat$ lecture#dae1 & ! di/9ction /ill has its weight1 ,i believe1 9 ! m9ds ( _m if n mo/ *emi/s4 8,we arrive at ! conclusion10 said ,pr(essor ,japp1 8t ! production ( s+le asymmetric comp\nds1 or _! isolation f ! mixture ( _! enantiomorphs1 is1 z ,pa/eur firmly held1 ! pr]ogative ( life4 ,only ! liv+ organism1 or ! liv+ intellig5ce ) its conception ( asymmetry1 c produce ?is result4 ,only asymmetry c beget asymmetry40 ,9 ^! la/ words 7:i*1 s f> z ! *emi/ & ! biologi/ are conc]n$1 we may ackn[l$ge to be p]fectly true#daf7 lies ! #dah crux ( ! difficulty2 = !y at once bid u enquire :e!r 9 nature1 ext]nal to & antec$5t to life1 !re be n "s asymmetry to :i* we may ref] ! fur!r propagation or 8begett+0 ( ! new asymmetries3 or :e!r 9 default !re(1 we be rigor\sly conf9$ to ! conclusion1 f :i* ,japp 8saw no escape10 t 8at ! mom5t :5 life fir/ arose1 a directive =ce came into play1--a =ce ( precisely ! same "* z t :i* enables ! intellig5t op]ator1 by ! ex]cise ( 8 w1 to select "o cry/allis$ enantiomorph & reject its asymmetric opposite#dag40 ,obs]ve t x is only ! fir/ beg9n+s ( *emical asymmetry t we ne$ to discov]2 = :5 asymmetry is once manife/$1 x is n disput$ t x w cont9ue 8to beget asymmetry40 ,a plausible sugge/ion is n[ at h&1 :i* if x be confirm$ & ext5d$ w supply or at lea/ suffici5tly illu/rate ! k9d ( explanation :i* is requir$#dah4 ,we "k 9 ! fir/ place t 9 cases :]e ord9>y non-pol>is$ light acts ^u a *emical sub/ance1 ! am\nt ( *emical action is proportionate to ! am\nt ( light absorb$4 ,we "k 9 ! second place#dai1 9 c]ta9 cases1 t light circul>ly pol>is$ is absorb$ 9 diff]5t am\nts by ! "r-h&$ or left-h&$ v>ieties1 z ! case may be1 ( an asymmetric sub/ance4 ,& ?irdly1 we "k t a portion ( ! light :i* comes to u f ! sun is already plane-pol>is$ light1 :i* becomes 9 "p circul>ly pol>is$1 by reflection 7accord+ to ,jam97 at ! surface ( ! sea1 & !n rotat$ 9 a p>ticul> direction "u ! influ5ce ( t]re/rial magnetism4 ,we only require to be assur$ t ! relation betwe5 absorption ( light & *emical activity w cont9ue to hold good 9 ! case ( circul>ly pol>is$ light2 t is to say #dai t ! =mation ( "s new sub/ance or o!r1 "u ! influ5ce ( light s pol>is$1 w proce$ asymmetrically 9 consonance ) ! asymmetry ( ! light itself2 or conv]sely1 t ! asymmetrically pol>is$ light w t5d to m rapid decomposition ( ^? molecules by :i* x is *iefly absorb$4 ,?is latt] pro( is n[ said to be furni%$ by ,byk#dbj1 :o ass]ts t c]ta9 t>trates become unsymmetrical "u ! cont9u$ influ5ce ( ! asymmetric rays4 ,"h !n we seem to h an example1 ( a p>ticul> k9d & 9 a p>ticul> in/ance1 an example limit$ b yet crucial 7if confirm$71 ( an asymmetric =ce1 non-vital 9 its orig91 :i* might conceivably be ! />t+-po9t ( t asymmetry :i* is *>act]i/ic ( s _m organic products4 ,! my/]ies ( organic *emi/ry are great1 & ! diff]5ces betwe5 its processes or reactions z !y are c>ri$ out 9 ! organism & 9 ! laboratory are _m#dba4 ,! actions1 catalytic & o!r1 :i* g on 9 ! liv+ cell are ( extraord9>y complexity4 ,b ! cont5tion t !y are diff]5t 9 k9d f :at we t]m ord9>y *emical op]ations1 or t 9 ! production ( s+le asymmetric comp\nds !re is actually to be witness$1 z ,pa/eur ma9ta9$1 a 8pr]ogative ( life10 w\ld seem to be no long] safely t5able4 ,& fur!rmore1 x behoves u to rememb] t1 ev5 ?\gh failure cont9u$ to att5d all artificial attempts to orig9ate ! asymmetric or optically active comp\nds :i* organic nature produces 9 abundance1 ?is w\ld only prove t a c]ta9 physical =ce1 or mode ( physical action1 is at "w among liv+ ?+s ?\gh unkn[n else:]e4 ,x is a mode ( action :i* we c easily imag9e1 ?\gh ! actual me*anism we _c set ago+ :5 we please4 ,& x foll[s t su* a diff]5ce betwe5 liv+ matt] & dead w\ld c>ry u b a little way1 = x w\ld /ill be conf9$ /rictly to ! physical or me*anical plane4 ,our hi/oric int]e/ 9 ! :ole "q is increas$ by ! #dbj fact1 or ! great probability1 t 8! t5acity ) :i* ,pa/eur f\ght aga9/ ! doctr9e ( spontane\s g5]ation 0 n unconnect$ ) 8 belief t *emical comp\nds ( "o-sid$ symmetry c\ld n arise save "u ! influ5ce ( life#dbb40 ,b ! "q :e!r spontane\s g5]ation be a fact or n does n dep5d ^u !oretical consid]ations2 our negative response is bas$1 & is s f> s\ndly bas$1 on repeat$ failures to demon/rate its occurr5ce4 ,_m a great law ( physical sci5ce1 n except+ gravitation itself1 has no high] claim on our acceptance4 ,let u return !n1 aft] ?is digression1 to ! g5]al subject ( ! =ms assum$ by c]ta9 *emical bodies :5 deposit$ or precipitat$ )9 ! organism1 & to ! "q ( h[ f> ^! =ms may be artificially imitat$ or !oretically expla9$4 ,mr ,george ,ra9ey1 ( ,/ ,b>?olomew's ,hospital 7to :om we h already ref]r$71 & ,pr(essor ,p4 ,h>t+1 ( ,utre*t1 7 ! fir/ to deal ) ?is specific problem4 ,mr ,ra9ey publi%$1 betwe5 #aheg & #ahfa1 a s]ies ( valuable & ?\ghtful pap]s to %ew t %ell & bone & c]ta9 o!r organic /ructures 7 =m$ 8by a process ( molecul> coalesc5ce1 demon/rable 9 c]ta9 artificially-=m$ products#dbc40 ,pr(essor ,h>t+1 aft] ?irty ye>s ( exp]im5tal "w1 publi%$ 9 #ahgb a pap]1 :i* has become classical1 entitl$ ,re*]*es de ,morphologie ,syn?tique1 sur la production artificielle de quelques =mations calcaires organiques2 8 aim 0 to pave ! way = a 8morphologie syn?tique10 z ,whl] _h laid ! f\ndations ( a 8*imie syn?tique10 by 8 classical discov]y =ty ye>s be=e4 #dba ,illu/ration3 ,fig4 #aie4 ,calcosph]ites1 or concretions ( calcium c>bonate1 deposit$ 9 :ite ( egg4 7,aft] ,h>t+47 ,illu/ration3 ,fig4 #aif4 ,a s+le calcosph]ite1 ) c5tral 8nucleus10 & /riat$1 iridesc5t bord]4 7,aft] ,h>t+47 ,illu/ration3 ,fig4 #aig4 ,lat] /ages 9 ! same exp]im5t4 ,illu/ration3 ,fig4 #aih1 ,a4 ,section ( %ell ( ,mya2 ,b4 ,section ( h+e-too? ( d4 7,aft] ,c>p5t]47 ,ra9ey & ,h>t+ us$ simil> me?ods1 & ^! 7 su* z _m o!r work]s h cont9u$ to employ1--p>tly ) ! direct object ( expla9+ ! g5esis ( organic =ms & p>tly z an integral "p ( :at is n[ kn[n z ,colloid ,*emi/ry4 ,! :ole gi/ ( ! me?od 0 to br+ "s soluble salt ( lime1 su* z ! *loride or nitrate1 into solution )9 a colloid m$ium1 su* z gum1 gelat9e or album92 & !n to precipitate x out 9 ! =m ( "s insoluble comp\nd1 su* z ! c>bonate or oxalate4 ,h>t+ f\nd t1 :5 he add$ a little sodium or potassium c>bonate to a conc5trat$ solution ( calcium *loride 9 album91 he got at fir/ a gelat9\s mass1 or 8colloid precipitate03 :i* sl[ly trans=m$ by ! appe>ance ( t9y microscopic p>ticles1 at fir/ motionless1 b aft]w>ds z !y grew l>g] %ew+ ! typical ,br[nian movem5t4 ,s f>1 v mu* ! same ph5om5a 7 witness$ :e!r ! solution 7 album9\s or n1 & simil> appe>ances inde$ _h be5 witness$ & record$ by ,gu/av ,rose1 s f> back z #ahcgdbd2 b 9 ! lat] /ages ! pres5ce ( album9oid matt] made a great diff]5ce4 ,n[1 aft] a few days1 ! calcium c>bonate 0 se5 to be deposit$ 9 ! =m ( l>ge r\nd$ concretions1 ) a m or less di/9ct c5tral nucleus1 & ) a surr\nd+ /ructure at once radiate & #dbb conc5tric2 ! pres5ce ( conc5tric zones or lamellae1 alt]nately d>k & cle>1 0 especially *>act]i/ic4 ,^! r\nd 8calcosph]ites0 %ew$ a t5d5cy to aggregate toge!r 9 lay]s1 & !n to assume polyh$ral1 or (t5 regul>ly hexagonal1 outl9es4 ,9 ?is latt] condition !y closely resemble ! e>ly /ages ( calcification 9 a molluscan 7,fig4 #aih71 or /ill m 9 a cru/acean %ell#dbe2 :ile 9 _! isolat$ condition #dbc !y v closely resemble ! little calc>e\s bodies 9 ! tissues ( a trematode or a ce/ode worm1 or 9 ! oesophageal gl&s ( an e>?worm#dbf4 ,illu/ration3 ,fig4 #aii4 ,l>ge irregul> calc>e\s concretions1 or spicules1 deposit$ 9 a piece ( dead c>tilage1 9 pres5ce ( calcium phosphate4 7,aft] ,h>t+47 ,:5 ! album9 0 some:at scanty1 or :5 x 0 mix$ ) gelat9e1 & especially :5 a little phosphate ( lime 0 #dbd add$ to ! mixture1 ! sph]oidal globules t5d$ to become r\gh1 by an outgr[? ( sp9\s or digiti=m projections2 & 9 "s cases1 b n )\t ! pres5ce ( ! phosphate1 ! result 0 an irregul>ly %ap$ knobby spicule1 precisely simil> to ^? :i* are *>act]i/ic ( ! ,alcyon>ia#dbg4 ,illu/ration3 ,fig4 #bjj4 ,additional illu/rations ( ,alcyon>ian spicules3 ,eunicea4 7,aft] ,/ud]47 ,! r\gh spicules ( ! ,alcyon>ia are extraord9>ily v>iable 9 %ape & size1 z1 look+ at !m f ! *emi/'s or ! physici/'s po9t ( view1 we %\ld expect !m to be4 ,p>tly ^u ! =m ( ^! spicules1 & p>tly on ! g5]al =m or mode ( bran*+ ( ! entire colony ( polypes1 a va/ numb] ( sep>ate 8species0 h be5 bas$ by sy/ematic zoologi/s4 ,b x is n[ admitt$ t ev5 9 specim5s ( a s+le species1 f "o & ! same locality1 ! spicules may v>y imm5sely 9 %ape & size3 & ,pr(essor ,hickson decl>es 79 a pap] publi%$ :ile ^! %eets are pass+ ?r\gh ! press7 t aft] _m ye>s ( labori\s "w 9 /riv+ to det]m9e species ( ^! animal colonies1 he feels 8q conv9c$ t we h be5 engag$ 9 a m or less fruitless task#dbh04 ,! =mation ( a too? has v lately be5 %[n to be a ph5om5on ( ! same ord]4 ,t is to say1 8calcification 9 bo? d5t9e & enamel #dbe is 9 great "p a physical ph5om5on2 ! actual deposit 9 bo? tissues occurs 9 ! =m ( calcosph]ites1 & ! process 9 mammalian tissue is id5tical 9 e po9t ) ! same process occurr+ 9 l[] organisms#dbi40 ,! ossification ( bone1 we may be sure1 is 9 ! same s5se & to ! same ext5t a physical ph5om5on4 ,! typical /ructure ( a calcosph]ite is no o!r ?an t ( a pe>l1 nor does x diff] ess5tially f t ( ! otoli? ( a mollusc or ( a bony fi%4 7,! otoli?s1 by ! way1 ( ! elasmobran* fi%es1 l ^? ( reptiles & birds1 are n develop$ aft] ?is fa%ion1 b are true cry/als ( calc-sp>47 ,illu/ration3 ,fig4 #bja4 ,a 8cru/0 ( close-pack$ calc>e\s concretions1 precipitat$ at ! surface ( an album9\s solution4 7,aft] ,h>t+47 ,?r\gh\t ^! ph5om5a1 ! effect ( surface-t5sion is manife/4 ,x is by surface-t5sion t ultra-microscopic p>ticles are br\ght toge!r 9 ! fir/ floccul> precipitate or coagulum2 by ! same ag5cy1 ! co>s] p>ticles are 9 turn agglut9at$ into visible lumps2 & ! =m ( ! calcosph]ites1 :e!r x be t ( ! solit>y sph]es or t assum$ 9 v>i\s /ages ( aggregation 7e4g4 ,fig4 #bjb7dcj1 is likewise due to ! same ag5cy4 ,illu/ration3 ,fig4 #bjb4 ,aggregat$ calcosph]ites4 7,aft] ,h>t+47 ,f ! po9t ( view ( colloid *emi/ry ! :ole ph5om5on is v important & significant2 & n ! lea/ significant "p is ?is t5d5cy ( ! solidifi$ deposits to assume ! =m ( 8sph]ulites10 & o!r r\nd$ cont\rs4 ,9 ! phraseology ( t sci5ce1 we are deal+ ) a two-phase sy/em1 :i* f9ally consi/s ( solid p>ticles 9 susp5sion 9 a liquid 7! =m] be+ /yl$ ! disp]se phase1 ! latt] ! #dbf disp]sion m$ium74 ,9 accordance ) a rule fir/ recognis$ by ,o/wald#dca1 :5 a sub/ance beg9s to sep>ate out f a solution1 s mak+ its appe>ance z a new phase1 x always makes its appe>ance fir/ z a liquid#dcb4 ,"h is a case 9 po9t4 ,! m9ute quantities ( mat]ial1 on _! way f a /ate ( solution to a /ate ( 8susp5sion10 pass ?r\gh a liquid to a solid =m2 & _! tempor>y soj\rn 9 ! =m] leaves its impress 9 ! r\nd$ cont\rs :i* surface-t5sion br\ght ab\t :ile ! little aggregate 0 /ill labile or fluid3 :ile co9cid5tly ) ?is surface-t5sion effect ^u ! surface1 cry/allisation t5d$ to take place ?r\gh\t ! little liquid mass1 or 9 su* portion ( x z _h n yet consolidat$ & cry/allis$4 ,illu/ration3 ,fig4 #bjc4 7,aft] ,h>t+47 ,:]e we h simple aggregates ( two or ?ree calcosph]ites1 ! result+ figure is precisely t ( s _m contigu\s soap-bubbles4 ,9 o!r cases1 composite =ms result :i* are n s easily expla9$1 b :i*1 if we c\ld only acc\nt = !m1 w\ld be ( v great int]e/ to ! biologi/4 ,= in/ance1 :5 small] calcosph]es seem1 z x 71 to invade ! sub/ance ( a l>g] "o1 we get curi\s con=mations :i* 9 ! close/ possible way resemble ! outl9es ( c]ta9 ( ! ,diatoms 7,fig4 #bjc74 ,ano!r v curi\s =mation1 :i* ,h>t+ calls a 8cono/at10 is ( frequ5t occurr5ce1 & 9 x we see at lea/ a sugge/ion ( analogy ) ! configuration :i*1 9 a protoplasmic /ructure1 we h spok5 ( z a 8coll>-cell40 ,! #dbg cono/ats1 :i* are =m$ 9 ! surface lay] ( ! solution1 consi/ ( a portion ( a sph]oidal calcosph]ite1 ^: upp] "p is cont9u$ into a ?9 sph]oidal coll>1 ( some:at l>g] radius ?an ! solid sph]e2 b ! precise mann] 9 :i* ! coll> is =m$1 possibly ar\nd a bubble ( gas1 possibly ab\t a vortex-l diffusion-curr5t#dcc is n obvi\s4 ,among ^! v>i\s ph5om5a1 ! conc5tric /riation obs]v$ 9 ! calcosph]ite has acquir$ a special int]e/ & importance#dcd4 ,x is "p ( a ph5om5on n[ widely kn[n1 & recognis$ z an important factor 9 colloid *emi/ry1 "u ! "n ( 8,liesegang's ,r+s#dce40 ,illu/ration3 ,fig4 #bjd4 ,cono/ats4 7,aft] ,h>t+47 ,if we dissolve1 = in/ance1 a little bi*romate ( pota% 9 gelat9e1 p\r x on to a glass plate1 & aft] x is set place ^u x a drop ( silv] nitrate solution1 !re appe>s 9 ! c\rse ( a few h\rs ! ph5om5on ( ,liesegang's r+s4 ,at fir/ ! silv] =ms a c5tral pat* ( abundant r$di% br[n *romate precipitate2 b ar\nd ?is1 z ! silv] nitrate diffuses sl[ly ?r\gh ! gelat9e1 ! precipitate no long] comes d[n 9 a cont9u\s1 uni=m lay]1 b =ms a s]ies ( zones1 beautifully regul>1 :i* alt]nate ) cle> int]spaces ( jelly1 & :i* /& f>!r & f>!r ap>t1 9 log>i?mic ratio1 z !y rec$e f ! c5tre4 ,= a discussion ( ! raison d'tre ( #dbh ?is ph5om5on1 /ill some:at problematic1 ! /ud5t mu/ consult ! text-books ( physical & colloid *emi/ry#dcf4 ,b1 speak+ v g5]ally1 we may say ! appe>ance ( ,liesegang's r+s is b a p>ticul> & /rik+ case ( a m g5]al ph5om5on1 namely ! influ5ce on cry/allisation ( ! pres5ce ( =eign bodies or 8impurities10 repres5t$ 9 ?is case by ! 8gel0 or colloid matrix#dcg4 ,f>aday %ew$ long ago t to ! pres5ce ( slight impurities might be ascrib$ ! b&$ /ructure ( ice1 ( b&$ qu>tz or agate1 onyx1 etc42 & ,qu9cke & ,toml9son h add$ to our scanty k ( ! same ph5om5on#dch4 ,illu/ration3 ,fig4 #bje4 ,liesegang's ,r+s4 7,aft] ,l$uc47 ,besides ! t5d5cy to rhy?mic action1 z manife/$ 9 ,liesegang's r+s1 ! association ( colloid matt] ) a cry/alloid 9 solution may lead to o!r well-m>k$ effects4 ,^!1 accord+ to ,pr(essor ,j4 ,h4 ,b[man#dci1 may be gr\p$ some:at z foll[s3 7#a7 total prev5tion ( cry/allisation2 7#b7 suppression ( c]ta9 ( ! l9es ( cry/all9e gr[?2 7#c7 ext5sion ( ! cry/al to abnormal proportions1 ) a t5d5cy = x to become a comp\nd cry/al2 7#d7 a curv+ or gyrat+ ( ! cry/al or its p>ts4 #dbi ,illu/ration3 ,fig4 #bjf4 ,relay-cry/als ( common salt4 7,aft] ,b[man47 ,illu/ration3 ,fig4 #bjg4 ,:eel-l cry/als 9 a colloid4 7,aft] ,b[man47 ,= in/ance1 x w\ld seem t1 if ! supply ( mat]ial to ! gr[+ cry/al be n =?com+ 9 suffici5t quantity 7z may well happ5 9 a colloid m$ium1 = lack ( convection-curr5ts71 !n gr[? w foll[ only ! /ronge/ l9es ( cry/allis+ =ce1 & w be suppress$ or p>tially suppress$ along o!r axes4 ,! cry/al w h a t5d5cy to become fili=m1 or 8fibr\s02 & ! raphides ( our plant-cells are a case 9 po9t4 ,aga91 ! long sl5d] cry/al s =m$1 pu%+ its way into new mat]ial1 may initiate a new c5tre ( cry/allisation3 we get ! ph5om5on kn[n z a 8relay10 along ! pr9cipal l9es ( =ce1 & sometimes along subord9ate axes z well4 ,?is ph5om5on is illu/rat$ 9 ! accompany+ figure ( cry/allisation 9 a colloid m$ium ( common salt2 & x may possibly be t we h "h an explanation1 or "p ( an explanation1 ( ! comp\nd silice\s spicules ( ! ,hexact9ellid sponges4 ,la/ly1 :5 ! cry/allis+ =ce is ne>ly equall$ by ! resi/ance ( ! visc\s m$ium1 ! cry/al takes ! l9e ( lea/ resi/ance1 ) v v>i\s results4 ,"o ( ^! results w\ld seem to be a gyratory c\rse1 giv+ to ! cry/al a curi\s :eel-l %ape1 z 9 ,fig4 #bjg2 & o!r results are ! fea!ry1 f]n-l #dcj or arboresc5t %apes s frequ5tly se5 9 microscopic cry/allisation4 ,to return to ,liesegang's r+s1 ! typical appe>ance ( conc5tric r+s ^u a gelat9\s plate may be modifi$ 9 v>i\s exp]im5tal ways4 ,= in/ance1 our gelat9\s m$ium may be plac$ 9 a capill>y tube imm]s$ 9 a solution ( ! precipitat+ salt1 & 9 ?is case we %all obta9 a v]tical succession ( b&s or zones regul>ly int]spac$3 ! result be+ v closely comp>able to ! b&$ pigm5tation :i* we see 9 ! hair ( a rabbit or a rat4 ,9 ! ord9>y plate prep>ation1 ! free surface ( ! gelat9e is "u diff]5t conditions to ! l[] lay]s & especially to ! l[e/ lay] 9 contact ) ! glass2 & !re=e x (t5 happ5s t we obta9 a d\ble s]ies ( r+s1 "o deep & ! o!r sup]ficial1 :i* by occasional bl5d+ or int]lac+1 may produce a nett$ patt]n4 ,9 "s cases1 z :5 only ! inn] surface ( our capill>y tube is cov]$ ) a lay] ( gelat9e1 !re is a t5d5cy = ! deposit to take place 9 a cont9u\s spiral l9e1 r ?an 9 conc5tric & sep>ate zones4 ,by su* means1 accord+ to ,k/]#ddj v>i\s =ms ( annul>1 spiral & reticulat$ ?ick5+s 9 ! vascul> tissue ( plants may be closely imitat$2 & he & c]ta9 o!r writ]s h ( late be5 incl9$ to c>ry ! same *emico-physical ph5om5on a v long way1 9 ! explanation ( v>i\s b&$1 /rip$1 & o!r rhy?mically successional types ( /ructure or pigm5tation4 ,= example1 ! /rip$ pigm5tation ( ! leaves 9 _m plants 7su* z ,eulalia japonica71 ! /rip$ or cl\d$ col\r+ ( _m fea!rs or ( a cat's sk91 ! patt]ns ( _m fi%es1 su* = in/ance z ! brightly col\r$ tropical ,*aetodonts & ! l1 are all reg>d$ by him z s _m in/ances ( 8diffusion-figures0 closely relat$ to ! typical ,liesegang ph5om5on4 ,gebh>dt has made a p>ticul> /udy ( ! same subject 9 ! case ( insects#dda4 ,he decl>es1 = in/ance1 t ! b&$ w+s ( ,papilio podalirius are precisely imitat$ 9 ,liesegang's exp]im5ts2 t ! f9] m>k+s on ! w+s ( ! ,goatmo? 7,cossus lignip]da7 %ew ! d\ble arrangem5t ( l>g] & ( #dca small] int]m$iate rhy?ms1 likewise manife/$ 9 c]ta9 cases ( ! same k9d2 t ! alt]nate b&+ ( ! ant5nae 7= in/ance 9 ,sesia spheci=mis71 a pigm5tation n concurr5t ) ! segm5t$ /ructure ( ! ant5na1 is explicable 9 ! same way2 & t ! 8ocelli10 = in/ance ( ! ,emp]or mo?1 are typical illu/rations ( ! common conc5tric type4 ,d>w9's well-kn[n disquisition#ddb on ! ocell> patt]n ( ! fea!rs ( ! ,argus ,pheasant1 z a result ( sexual selection1 w occur to ! read]'s m9d1 9 /rik+ contra/ to ?is or to any o!r direct physical explanation#ddc4 ,to turn f ! di/ribution ( pigm5t to m deeply seat$ /ructural *>act]s1 ,l$uc has %ewn h[1 = in/ance1 ! lam9> /ructure ( ! cornea or ! l5s is aga91 app>5tly1 a simil> ph5om5on4 ,9 ! l5s ( ! fi%'s eye1 we h a v curi\s appe>ance1 ! consecutive lamellae be+ r\gh5$ or not*$ by close-set1 int]lock+ s9uosities2 & precisely ! same appe>ance1 save t x is n q s regul>1 is pres5t$ 9 "o ( ,k/]'s figures z ! effect ( precipitat+ a little sodium phosphate 9 a gelat9\s m$ium4 ,bi$]mann has /udi$1 f ! same po9t ( view1 ! /ructure & developm5t ( ! molluscan %ell1 ! problem :i* ,ra9ey _h fir/ attack$ m ?an fifty ye>s be=e#ddd2 & ,liesegang himself has appli$ 8 results to ! =mation ( pe>ls1 & to ! developm5t ( bone#dde4 #dcb ,among all ! _m cases :]e ?is ph5om5on ( ,liesegang's comes to ! naturali/'s aid 9 explanation ( rhy?mic or zon>y configurations 9 organic =ms1 x has a special int]e/ :]e ! pres5ce ( conc5tric zones or r+s appe>s1 at fir/ sight1 z a sure & c]ta9 sign ( p]iodicity ( gr[?1 dep5d+ on ! seasons1 & capable !re=e ( s]v+ z a m>k & record ( ! creature's age4 ,?is is ! case1 = in/ance1 ) ! scales1 bones & otoli?s ( fi%es2 & a k9dr$ ph5om5a 9 />*-gra9s has giv5 rise1 9 l mann]1 to ! belief t !y indicate a diurnal & nocturnal p]iodicity ( activity & re/#ddf4 ,illu/ration3 ,fig4 #bjh4 ,t ?is is actually ! case 9 gr[+ />*-gra9s is g5]ally believ$1 on ! au?ority ( ,mey]#ddg2 b :ile "u c]ta9 circum/ances a m>k$ alt]nation ( gr[+ & re/+ p]iods may occur1 & may leave its impress on ! /ructure ( ! gra91 !re is n[ great reason to believe t1 ap>t f su* ext]nal influ5ces1 ! int]nal ph5om5a ( diffusion may1 j z 9 ! typical ,liesegang exp]im5t1 produce ! well-kn[n conc5tric r+s4 ,! sph]ocry/als ( inul91 9 l mann]1 %ew1 l ! 8calcosph]ites0 ( ,h>t+ 7,fig4 #bjh71 a conc5tric /ructure :i* 9 all likelihood has _h no causative impulse save f )94 ,illu/ration3 ,fig4 #bji4 ,otoli?s ( ,plaice1 %[+ f\r zones or 8age-r+s40 7,aft] ,wallace47 ,! /riation1 or conc5tric lamellation1 ( ! scales & otoli?s ( fi%es has be5 mu* employ$ ( rec5t ye>s z a tru/wor?y & unmi/akeable m>k ( ! fi%'s age4 ,!re are difficulties 9 ! way ( accept+ ?is hypo!sis1 n ! lea/ ( :i* is ! fact t ! otoli?-zones1 = in/ance1 are extremely well m>k$ ev5 9 ! case ( "s fi%es :i* sp5d _! lives 9 deep wat]1 #dcc :]e ! temp]ature & o!r physical conditions %ew little or no appreciable fluctuation ) ! seasons ( ! ye>4 ,!re are1 on ! o!r h&1 ph5om5a :i* seem /rongly confirmatory ( ! hypo!sis3 = in/ance ! fact 7if x be fully e/abli%$7 t 9 su* a fi% z ! cod1 zones ( gr[?1 id5tical 9 numb]1 are f\nd bo? on ! scales & 9 ! otoli?s#ddh4 ,! subject has become a mu* debat$ "o1 & ?is is n ! place = its discussion2 b x is at lea/ obvi\s1 ) ! ,liesegang ph5om5on 9 view1 t we h no "r to assume t an appe>ance ( rhy?m & p]iodicity 9 /ructure & gr[? is necess>ily b\nd up )1 & indubitably br\ght ab\t by1 a p]iodic recurr5ce ( p>ticul> ext]nal conditions4 ,b :ile 9 ! ,liesegang ph5om5on we h rhy?mic precipitation :i* dep5ds only on =ces intr9sic to ! sy/em1 & is indep5d5t ( any correspond+ rhy?mic *anges 9 temp]ature or o!r ext]nal conditions1 we h n f> to seek = in/ances ( *emico-physical ph5om5a :]e rhy?mic alt]nations ( appe>ance or /ructure are produc$ 9 close relation to p]iodic fluctuations ( temp]ature4 ,a well-kn[n in/ance is t ( ! ,/assfurt deposits1 :]e ! rock-salt alt]nates regul>ly ) ?9 lay]s ( 8anhydrite10 or 79 ano!r s]ies ( b$s7 ) 8polyhalite#ddi03 & :]e ^! zones are commonly reg>d$ z m>k+ ye>s1 & _! alt]nate b&s z hav+ be5 =m$ 9 connection ) ! seasons4 ,a discussion1 h[ev]1 ( ?is rem>kable & significant ph5om5on1 & ( h[ ! *emi/ expla9s x1 by help ( ! 8phase-rule10 9 connection ) temp]ature conditions1 w\ld lead u f> beyond our scope#dej4 ,we n[ see t ! me?ods by :i* we attempt to /udy ! *emical or *emico-physical ph5om5a :i* accompany ! developm5t ( an inorganic concretion or spicule )9 ! #dcd body ( an organism soon introduce u to a multitude ( k9dr$ ph5om5a1 ( :i* our k is /ill scanty1 & :i* we mu/ n attempt to discuss at great] l5g?4 ,z reg>ds our ma9 po9t1 namely ! =mation ( spicules & o!r elem5t>y skeletal =ms1 we h se5 t c]ta9 ( !m may be safely ascrib$ to simple precipitation or cry/allisation ( inorganic mat]ials1 9 ways m or less modifi$ by ! pres5ce ( album9\s or o!r colloid sub/ances4 ,! effect ( ^! latt] is f\nd to be mu* great] 9 ! case ( "s cry/allisable bodies ?an 9 o!rs4 ,= in/ance1 ,h>t+1 & ,ra9ey also1 f\nd z a rule t calcium oxalate 0 mu* less affect$ by a colloid m$ium ?an 0 calcium c>bonate2 x %ew$ 9 _! h&s no t5d5cy to =m r\nd$ concretions or 8calcosph]ites0 9 pres5ce ( a colloid1 b cont9u$ to cry/allise1 ei!r normally1 or ) a t5d5cy to =m ne$les or raphides4 ,x is d\btless = ?is reason t1 z we h se51 cry/als ( calcium oxalate are s common 9 ! tissues ( plants1 :ile ^? ( o!r calcium salts are r>e4 ,b true calcosph]ites1 or sph]ocry/als1 ( ! oxalate are occasionally f\nd1 = in/ance 9 c]ta9 ,cacti1 & ,bts*li#dea has succe$$ 9 mak+ !m artificially 9 ,h>t+'s usual way1 t is to say by cry/allisation 9 a colloid m$ium4 ,!re l9k on to ^! latt] obs]vations1 & to ! /atem5t already quot$ t calc>e\s deposits are associat$ ) ! dead products r ?an ) ! liv+ cells ( ! organism1 c]ta9 v int]e/+ facts 9 reg>d to ! solubility ( salts 9 colloid m$ia1 :i* h be5 made kn[n to u ( late1 & :i* g f> to acc\nt = ! pres5ce 7ap>t f ! =m7 ( calc>e\s precipitates )9 ! organism#deb4 ,x has be5 %ewn1 9 ! fir/ place1 t ! pres5ce ( album9 has a notable effect on ! solubility 9 a wat]y solution ( calcium salts1 increas+ ! solubility ( ! phosphate 9 a m>k$ degree1 & t ( ! c>bonate 9 /ill great] proportion2 b ! #dce sulphate is only v little m soluble 9 pres5ce ( album9 ?an 9 pure wat]1 & ! r>ity ( its occurr5ce )9 ! organism is s f> acc\nt$ =4 ,on ! o!r h&1 ! bodies d]iv$ f ! break+ d[n ( ! album9s1 _! 8catabolic0 products1 su* z ! peptones1 etc41 dissolve ! calcium salts to a mu* less degree ?an album9 itself2 & 9 ! case ( ! phosphate1 its solubility 9 !m is sc>cely great] ?an 9 wat]4 ,! probability is1 !re=e1 t ! actual precipitation ( ! calcium salts is n due to ! direct action ( c>bonic acid1 etc4 on a m soluble salt 7z 0 at "o "t believ$72 b to catabolic *anges 9 ! proteids ( ! organism1 :i* t5d to ?r[ d[n ! salts already =m$1 :i* _h rema9$ hi!rto 9 album9\s solution4 ,! v slight solubility ( calcium phosphate "u su* circum/ances acc\nts = its pr$om9ance 91 = in/ance1 mammalian bone#dec2 & :]ev]1 9 %ort1 ! supply ( ?is salt has be5 available to ! organism4 ,to sum up1 we see t1 :e!r f food or f sea-wat]1 calcium sulphate w t5d to pass b little into solution 9 ! album9oid sub/ances ( ! body3 calcium c>bonate w ent] m freely1 b a consid]able "p ( x w t5d to rema9 9 solution3 :ile calcium phosphate w pass into solution 9 consid]able am\nt1 b w be almo/ :olly precipitat$ aga91 z ! album9 becomes brok5 d[n 9 ! normal process ( metabolism4 ,we h /ill to wait = a simil> & equally illum9at+ /udy ( ! solution & precipitation ( silica1 9 pres5ce ( organic colloids4 ,f ! comp>atively small gr\p ( inorganic =mations :i*1 aris+ )9 liv+ organisms1 owe _! =m solely to precipitation or to cry/allisation1 t is to say to *emical or o!r molecul> =ces1 we %all pres5tly pass to t o!r & l>g] gr\p :i* appe> to be con=m$ 9 direct relation to ! =ms & ! arrangem5t ( ! cells or o!r protoplasmic elem5ts#ded4 #dcf ,! two pr9ciples ( con=mation are bo? illu/rat$ 9 ! spicul> skeletons ( ! ,sponges4 ,illu/ration3 ,fig4 #baj4 ,close-pack$ calcosph]ites1 or s-call$ 8spicules10 ( ,a/roscl]a4 7,aft] ,li/]47 ,9 a consid]able numb]1 b )al a m9ority ( cases1 ! =m ( ! sponge-spicule may be deem$ suffici5tly expla9$ on ! l9es ( ,h>t+'s & ,ra9ey's exp]im5ts1 t is to say z ! direct result ( *emical or physical ph5om5a associat$ ) ! deposition ( lime or ( silica 9 pres5ce ( colloids#dee4 ,?is is ! case1 = in/ance1 ) v>i\s small spicules ( a globul> or sph]oidal =m1 =m$ ( amorph\s silica1 conc5trically /riat$ )91 & (t5 develop+ irregul> knobs or t9y tub]cles ov] _! surfaces4 ,9 ! ab]rant sponge ,a/roscl]a#def1 we h1 to beg9 )1 r\nd$1 /riat$ discs or globules1 :i* 9 l mann] are no?+ m or less ?an ! #dcg 8calcosph]ites0 ( ,h>t+'s exp]im5ts2 & z ^! gr[ !y become closely aggregat$ toge!r 7,fig4 #baj71 & assume an angul>1 polyh$ral =m1 once m 9 complete accordance ) ! results ( exp]im5t#deg4 ,aga91 9 _m ,monaxonid sponges1 we h irregul>ly %ap$1 or bran*$ spicules1 r\gh5$ or tub]culat$ by second>y sup]ficial deposits1 & rem9d+ "o ( ! spicules ( "s ,alcyon>ia4 ,^! also mu/ be look$ ^u z ! simple result ( *emical deposition1 ! =m ( ! deposit be+ some:at modifi$ 9 con=mity ) ! surr\nd+ tissues1 j z 9 ! simple exp]im5t ! =m ( ! concretion>y precipitate is affect$ by ! het]og5eity1 visible or invisible1 ( ! matrix4 ,la/ly1 ! simple ne$les ( amorph\s silica1 :i* con/itute "o ( ! commone/ types ( spicule1 call = little 9 ! way ( explanation2 !y are accretions or deposits ab\t a l9e> axis1 or f9e ?read ( organic mat]ial1 j z ! ord9>y r\nd$ calcosph]ite is deposit$ ab\t "s m9ute po9t or c5tre ( cry/allisation1 & z ord9>y cry/allisation is (t5 />t$ by a p>ticle ( atmosph]ic du/2 9 "s cases !y also1 l ! o!rs1 are apt to be r\gh5$ by m irregul> second>y deposits1 :i* probably1 z 9 ,h>t+'s exp]im5ts1 appe> 9 ?is irregul> =m :5 ! supply ( mat]ial has become relatively scanty4 ,our few =ego+ examples1 div]se z !y are 9 look & k9d & rang+ f ! spicules ( ,a/roscl]a or ,alcyonium to ! otoli?s ( a fi%1 seem all to h _! free orig9 9 "s l>g] or small] fluid-conta9+ space1 or cavity ( ! body3 pretty mu* z ,h>t+'s calcosph]es made _! appe>ance 9 ! album9\s cont5t ( a di%4 ,b we n[ come at la/ to a mu* l>g] class ( spicul> & skeletal /ructures1 = ^: regul> & (t5 complex =ms "s o!r explanation ?an ! intr9sic =ces ( cry/allisation or molecul> adhesion is manife/ly necess>y4 ,z we ent] on ?is subject1 :i* is c]ta9ly no small or easy "o1 x may conduce to simplicity1 & to brevity1 #dch if we try to make a r\gh classification1 by way ( =eca/1 ( ! *ief conditions :i* we are likely to meet )4 ,j z we look ^u animals z con/itut$1 "s ( a va/ numb] ( cells1 & o!rs ( a s+le cell or ( a v few1 & j z ! %ape ( ! =m] has no long] a visible relation to ! individual %apes ( its con/itu5t cells1 :ile 9 ! latt] x is cell-=m :i* dom9ates or is actually equival5t to ! =m ( ! organism1 s %all we f9d x to be1 ) m or less exact analogy1 9 ! case ( ! skeleton4 ,= example1 our own skeleton consi/s ( bones1 9 ! =mation ( ea* ( :i* a va/ numb] ( m9ute liv+ cellul> elem5ts are necess>ily conc]n$2 b ! =m & ev5 ! arrangem5t ( ^! bone-=m+ cells or corpuscles are monoton\sly simple1 & we _c f9d 9 ^! a physical explanation ( ! outw>d & visible configuration ( ! bone4 ,x is z "p ( a f> l>g] field ( =ce1--9 :i* we mu/ consid] gravity1 ! action ( v>i\s muscles1 ! compressions1 t5sions & b5d+ mom5ts due to v>i\sly di/ribut$ loads1 ! :ole int]action ( a v complex me*anical sy/em1--t we mu/ expla9 7if we are to expla9 at all7 ! configuration ( a bone4 ,9 contra/ to ^! massive skeletons1 or con/itu5ts ( a skeleton1 we h o!r skeletal elem5ts ^: :ole magnitude1 or ^: magnitude 9 "s dim5sion or ano!r1 is comm5surate ) ! magnitude ( a s+le liv+ cell1 or 7z comes to v mu* ! same ?+7 is comp>able to ! range ( action ( ! molecul> =ces4 ,su* is ! case ) ! ord9>y spicules ( a sponge1 ) ! delicate skeleton ( a ,radiol>ian1 or ) ! d5s] & robu/] %ells ( ! ,=am9if]a4 ,! effect ( scale1 !n1 ( :i* we _h s mu* to say 9 our introductory *apt] on ,magnitude1 is b\nd to be app>5t 9 ! /udy ( skeletal fabrics1 & to lead to ess5tial diff]5ces betwe5 ! big & ! little1 ! massive & ! m9ute1 9 reg>d to _! controll+ =ces & _! resultant =ms4 ,& if all ?is be s1 & if ! range ( action ( ! molecul> =ces be 9 tru? ! important & fundam5tal ?+1 !n we may some:at ext5d our /atem5t ( ! case1 & include 9 x n only association ) ! liv+ cellul> elem5ts ( ! body1 b also association ) any bubbles1 drops1 vacuoles or vesicles :i* #dci may be compris$ )9 ! b\nds ( ! organism1 & :i* are 7z _! names & *>act]s connote7 ( ! ord] ( magnitude ( :i* we are speak+4 ,proce$+ a little f>!r 9 our classification1 we may conceive ea* little skeletal elem5t to be associat$1 9 "o case1 ) a s+le cell or vesicle1 & 9 ano!r ) a clu/] or 8sy/em0 ( consociat$ cells4 ,9 ei!r case !re are v>i\s possibilities4 ,= in/ance1 ! calcifi$ or o!r skeletal mat]ial may t5d to ov]spread ! entire out] surface ( ! cell or clu/] ( cells1 & s t5d accord+ly to assume "s configuration comp>able to t ( a fluid drop or ( an aggregation ( drops2 ?is1 9 brief1 is ! gi/ & ess5ce ( our /ory ( ! =am9if]al %ell4 ,ano!r common1 b v diff]5t condition w arise if1 9 ! case ( ! cell-aggregates1 ! skeletal mat]ial t5ds to accumulate 9 ! int]/ices betwe5 ! cells1 9 ! p>tition-walls :i* sep>ate !m1 or 9 ! /ill m re/rict$ di/ribution indicat$ by ! l9es ( junction betwe5 ^! p>tition-walls4 ,conditions su* z ^! w g a v long way to help u 9 our und]/&+ ( _m sponge-spicules & ( an imm5se v>iety ( radiol>ian skeletons4 ,& la/ly 7= ! pres5t71 !re is a possible & v int]e/+ case ( a skeletal elem5t associat$ ) ! surface ( a cell1 n s z to cov] x l a %ell1 b only s z to pursue a c\rse ( its own )9 x1 & subject to ! re/ra9ts impos$ by su* conf9em5t to a curv$ & limit$ surface4 ,) ?is curi\s condition we %all deal imm$iately4 ,?is prelim9>y & mu* simplifi$ classification ( skeletal =ms 7z is evid5t en\gh7 does n pret5d to complet5ess4 ,x leaves out ( acc\nt "s k9ds ( con=mation & configuration ) :i* we %all attempt to deal1 & o!rs :i* we mu/ p]=ce omit4 ,b nev]!less x may help to cle> or to m>k our way t[>ds ! subjects :i* ?is *apt] has to consid]1 & ! conditions by :i* !y are at lea/ p>tially def9$4 ,among ! sev]al possible1 or conceivable1 types ( microscopic skeletons let u *oose1 to beg9 )1 ! case ( a spicule1 m or less simply l9e> z f> z its intr9sic p[]s ( gr[? are #ddj conc]n$1 b :i* owes its n[ some:at complicat$ =m to a re/ra9t impos$ by ! individual cell to :i* x is conf9$1 & )9 ^: b\nds x is g5]at$4 ,! conception ( a spicule develop$ "u su* conditions we owe to a di/+ui%$ physici/1 ! late ,pr(essor ,g4 ,f4 ,fitz,gerald4 ,_m ye>s ago1 ,sollas po9t$ out t if a spicule beg9 to gr[ 9 "s p>ticul> way1 presumably "u ! control or con/ra9t impos$ by ! organism1 x cont9ues to gr[ by fur!r *emical deposition 9 ! same =m or direction ev5 aft] x has got beyond ! b\nd>ies ( ! organism or its cells4 ,?is ph5om5on is :at we see 91 & ?is imp]fect explanation goes s f> to acc\nt =1 ! cont9u$ gr[? 9 /raight l9es ( ! long calc>e\s sp9es ( ,globig]9a or ,ha/ig]9a1 or ! simil>ly radiat+ b silice\s spicules ( _m ,radiol>ia4 ,9 physical language1 if our cry/all9e /ructure has once begun to be laid d[n 9 a def9ite ori5tation1 fur!r additions t5d to accrue 9 a l regul> fa%ion & 9 an id5tical direction2 & ?is corresponds to ! ph5om5on ( s-call$ 8ori5tirte ,adsorption10 z describ$ by ,lehmann4 ,9 ,globig]9a or 9 ,acan?ocy/is ! long ne$les gr[ out freely into ! surr\nd+ m$ium1 ) no?+ to imp$e _! rectil9e> gr[? & _! approximately radiate di/ribution4 ,b let u consid] "s simple cases to illu/rate ! =ms :i* a spicule w t5d to assume :51 /riv+ 7z x 77 to gr[ /raight1 x comes "u ! influ5ce ( "s simple & con/ant re/ra9t or compulsion4 ,if we take any two po9ts on "s curv$ surface1 su* z t ( a sph]e or an ellipsoid1 & imag9e a /r+ /ret*$ betwe5 !m1 we obta9 :at is kn[n 9 ma!matics z a 8geodetic0 curve4 ,x is ! %orte/ l9e :i* c be trac$ betwe5 ! two po9ts1 ^u ! surface itself2 & ! mo/ famili> ( all cases1 f :i* ! "n is d]iv$1 is t curve ^u ! e>?'s surface :i* ! navigator le>ns to foll[ 9 ! practice ( 8great-circle sail+40 ,:]e ! surface is sph]ical1 ! geodetic is always lit]ally a 8great circle10 a circle1 t is to say1 ^: c5tre is ! c5tre ( ! sph]e4 ,if in/ead ( a sph]e we be deal+ ) an ellipsoid1 ! geodetic becomes a v>iable figure1 accord+ to ! position ( our two po9ts4 #dda ,= obvi\sly1 if !y lie 9 a l9e p]p5dicul> to ! long axis ( ! ellipsoid1 ! geodetic :i* connects !m is a circle1 also p]p5dicul> to t axis2 & if !y lie 9 a l9e p>allel to ! axis1 _! geodetic is a portion ( t ellipse ab\t :i* ! :ole figure is a solid ( revolution4 ,b if our two po9ts lie1 relatively to "o ano!r1 9 any o!r direction1 !n _! geodetic is "p ( a spiral curve 9 space1 w9d+ ov] ! surface ( ! ellipsoid4 ,to say1 z we h done1 t ! geodetic is ! %orte/ l9e betwe5 two po9ts ^u ! surface1 is z mu* z to say t x is a projection ( "s p>ticul> /raight l9e ^u ! surface 9 "q2 & x foll[s t1 if any l9e> body be conf9$ to t surface1 :ile reta9+ a t5d5cy to gr[ by successive increm5ts always 7save only = its conf9em5t to t surface7 9 a /raight l9e1 ! resultant =m :i* x w assume w be t ( a geodetic4 ,9 ma!matical language1 x is a prop]ty ( a geodetic t ! plane ( any two consecutive elem5ts is a plane p]p5dicul> to t 9 :i* ! geodetic lies2 or1 9 simpl] words1 any two consecutive elem5ts lie 9 a /raight l9e 9 ! plane ( ! surface1 & only div]ge f a /raight l9e 9 space by ! actual curvature ( ! surface to :i* !y are re/ra9$4 ,illu/ration3 ,fig4 #baa4 ,sponge & ,holo?urian spicules4 ,illu/ration3 ,fig4 #bab4 ,illu/ration3 ,fig4 #bac4 ,an 8amphidisc0 ( ,hyalonema4 ,let u n[ imag9e a spicule1 ^: natural t5d5cy is to gr[ into a /raight l9e> elem5t1 ei!r by reason ( its own molecul> anisotropy1 or because x is deposit$ ab\t a ?read-l axis2 & let u suppose t x is conf9$ ei!r )9 a cell-wall or 9 adhesion !reto2 x at once foll[s t its l9e ( gr[? w be simply a geodetic to ! surface ( ! cell4 ,& if ! cell be an imp]fect sph]e1 or a m or less regul> ellipsoid1 ! spicule w t5d to gr[ into "o or o!r ( ?ree =ms3 ei!r a plane curve ( circul> arc2 or1 m commonly1 a plane curve :i* is a portion ( an ellipse2 or1 mo/ commonly ( all1 a curve :i* is a portion ( a spiral 9 space4 ,9 ! latt] case1 ! numb] ( turns ( ! spiral w dep5d1 n only on ! l5g? ( ! spicule1 b on ! relative dim5sions ( ! ellipsoidal cell1 z well z ^u ! angle by :i* ! spicule is incl9$ to ! ellipsoid axes2 b a v common case w probably be t 9 :i* ! spicule looks at fir/ sight to be #ddb a plane ,c-%ap$ figure1 b is discov]$1 on m c>eful inspection1 to lie n 9 "o plane b 9 a m complicat$ spiral twi/4 ,?is inve/igation includes a s]ies ( =ms :i* are abundantly repres5t$ among actual sponge-spicules1 z illu/rat$ 9 ,figs4 #baa & #bab4 ,if ! spicule be n re/rict$ to l9e> gr[?1 b h a t5d5cy to exp&1 or to bran* out f a ma9 axis1 we %all obta9 a s]ies ( m complex figures1 all relat$ to ! geodetic sy/em ( curves4 ,a v simple case w arise :]e ! spicule occupies1 9 ! fir/ in/ance1 ! axis ( ! conta9+ cell1 & !n1 on rea*+ its b\nd>y1 t5ds to bran* or spread outw>ds4 ,we %all n[ get v>i\s figures1 9 "s ( :i* ! spicule w appe> z an axis exp&+ into a disc or :eel at ei!r end2 & 9 o!r cases1 ! t]m9al disc w be replac$1 or repres5t$1 by a s]ies ( rays or spokes1 ) a reflex curvature1 correspond+ to ! sph]ical or ellipsoid curvature ( ! surface ( ! cell4 ,su* spicules z ^! are aga9 exce$+ly common among v>i\s sponges 7,fig4 #bac74 ,fur!rmore1 if ^! me*anical me?ods ( con=mation1 & o!rs l to ^!1 be ! true cause ( ! %apes :i* ! spicules assume1 x is pla9 t ! production ( ^! spicul> %apes is n a specific function ( sponges or ( any p>ticul> sponge1 b t we %\ld expect #ddc ! same or v simil> ph5om5a to occur 9 o!r organisms1 :]ev] ! conditions ( inorganic secretion )9 clos$ cells 0 v mu* ! same4 ,z a matt] ( fact1 9 ! gr\p ( ,holo?uroidea1 :]e ! =mation ( intracellul> spicules is a *>act]i/ic feature ( ! gr\p1 all ! pr9cipal types ( con=mation :i* we h j describ$ c be closely p>allel$4 ,inde$ 9 _m cases1 ! =ms ( ! ,holo?urian spicules are id5tical & indi/+ui%able f ^? ( ! sponges#deh4 ,b ! ,holo?urian spicules are compos$ ( calcium c>bonate :ile ^? :i* we h j describ$ 9 ! case ( sponges are usually1 if n always1 silice\s3 ?is be+ j ano!r pro( ( ! fact t 9 su* cases ! =m ( ! spicule is n due to its *emical nature or molecul> /ructure1 b to ! ext]nal =ces to :i*1 dur+ its gr[?1 ! spicule is submitt$4 ,s mu* = t comp>atively limit$ class ( sponge-spicules ^: =ms seem capable ( explanation on ! hypo!sis t !y are develop$ )91 or "u ! re/ra9t impos$ by1 ! surface ( a cell or vesicle4 ,su* spicules are usually ( small size1 z well z ( comp>atively simple =m2 & !y are greatly out/ripp$ 9 numb]1 9 size1 & 9 suppos$ importance z guides to zoological classification1 by ano!r class ( spicules4 ,?is new class includes su* z we h suppos$ to be capable ( explanation on ! assumption t !y develop 9 association 7( "s sort or ano!r7 ) ! l9es ( junction ( contigu\s cells4 ,!y include ! triradiate spicules ( ! calc>e\s sponges1 ! quadriradiate or 8tetract9ellid0 spicules :i* occur 9 ! same gr\p1 b m *>act]i/ically 9 c]ta9 silice\s sponges kn[n z ! ,tetract9ellidae1 & la/ly p]haps 7?\gh ^! la/ are admitt$ly some:at h>d] to und]/&7 ! six-ray$ spicules ( ! ,hexact9ellids4 ,! spicules ( ! calc>e\s sponges are commonly triradiate1 & ! ?ree radii are usually incl9$ to "o ano!r at equal1 or ne>ly equal angles2 9 c]ta9 cases1 two ( ! ?ree rays are ne>ly 9 a /raight l9e1 & at "r angles to ! #ddd ?ird#dei4 ,!y are seldom 9 a plane1 b are usually incl9$ to "o ano!r 9 a solid1 trih$ral angle1 n easy ( precise measurem5t "u ! microscope4 ,! ?ree rays are v (t5 supplem5t$ by a f\r?1 :i* is set tetrah$rally1 mak+1 t is to say1 coequal angles ) ! o!r ?ree4 ,! calc>e\s spicule consi/s ma9ly ( c>bonate ( lime1 9 ! =m ( calcite1 ) 7accord+ to von ,ebn]7 "s admixture ( soda & magnesia1 ( sulphates & ( wat]4 ,accord+ to ! same writ] 7b ! fact1 ?\gh x w\ld seem easy to te/1 is /ill disput$7 !re is no organic matt] 9 ! spicule1 ei!r 9 ! =m ( an axial filam5t or o!rwise1 & ! appe>ance ( /ratification1 (t5 simulat+ ! pres5ce ( an axial fibre1 is due to 8mix$ cry/allisation0 ( ! v>i\s con/itu5ts4 ,! spicule is a true cry/al1 & !re=e its exi/5ce & its =m are prim>ily due to ! molecul> =ces ( cry/allisation2 moreov] x is a s+le cry/al & n a gr\p ( cry/als1 z is at once se5 by its behavi\r 9 pol>is$ light4 ,b its axes are n cry/all9e axes1 & its =m nei!r agrees )1 nor 9 any way resembles1 any "o ( ! _m polymorphic =ms 9 :i* calcite is capable ( cry/allis+4 ,x is z ?\gh x 7 c>v$ out ( a solid cry/al2 x is1 9 fact1 a cry/al "u re/ra9t1 a cry/al gr[+1 z x 71 9 an artificial m\ld2 & ?is m\ld is con/itut$ by ! surr\nd+ cells1 or /ructural vesicles ( ! sponge4 ,illu/ration3 ,fig4 #bad4 ,spicules ( ,grantia & o!r calc>e\s sponges4 7,aft] ,haeckel47 ,we h already /udi$ 9 an elem5t>y way1 b amply = our pres5t purpose1 ! mann] 9 :i* ?ree or m cells1 or bubbles1 t5d to meet toge!r "u ! influ5ce ( surface-t5sion1 & also ! outw>dly simil> ph5om5a :i* may be br\ght ab\t by a uni=m di/ribution ( me*anical pressure4 ,we h se5 t :5 we conf9e ourselves to a plane assemblage ( su* bodies1 we f9d !m meet+ "o ano!r 9 ?rees2 t 9 a section or plane projection ( su* an assemblage we see ! p>tition-walls meet+ "o ano!r at equal angles ( #abj2 t :5 ! bodies are uni=m 9 size1 ! p>titions are /raight l9es1 :i* comb9e to =m regul> hexagons2 & t :5 #dde ! bodies are unequal 9 size1 ! p>titions are curv$1 & comb9e to =m o!r & less regul> polygons4 ,x is pla91 accord+ly1 t 9 any flatt5$ or /ratifi$ assemblage ( su* cells1 a solidifi$ skeletal deposit :i* orig9ates or accumulates ei!r betwe5 ! cells or )9 ! ?ickness ( _! mutual p>titions1 w t5d to take ! =m ( triradiate bodies1 ^: rays 79 a typical case7 w be set at equal angles ( #abj 7,fig4 #bad1 ,f74 ,& ?is latt] condition ( equality w be op5 to modification 9 v>i\s ways4 ,x w be modifi$ by any inequality 9 ! specific t5sions ( adjac5t cells2 z a special case1 x w be apt to be greatly modifi$ at ! surface ( ! sy/em1 :]e a spicule happ5s to be =m$ 9 a plane p]p5dicul> to ! cell-lay]1 s t "o ( its ?ree rays lies betwe5 two adjac5t cells & ! o!r two are associat$ ) ! surface ( contact betwe5 ! cells & ! surr\nd+ m$ium2 9 su* a case 7z 9 ! cases consid]$ 9 connection ) ! =ms ( ! cells !mselves #ddf on p4 #cad71 we %all t5d to obta9 a spicule ) two equal angles & "o unequal 7,fig4 #bad1 ,a1 ,c74 ,9 ! la/ case1 ! two out]1 or sup]ficial rays1 w t5d to be m>k$ly curv$4 ,aga91 ! equiangul> condition w be dep>t$ f1 & m or less curvature w be imp>t$ to ! rays1 :]ev] ! cells ( ! sy/em cease to be uni=m 9 size1 & :5 ! hexagonal symmetry ( ! sy/em is lo/ accord+ly4 ,la/ly1 al?\gh we speak ( ! rays z meet+ at c]ta9 def9ite angles1 ?is /atem5t applies to _! axes1 r ?an to ! rays !mselves4 ,=1 if ! triradiate spicule be develop$ 9 ! int]space betwe5 ?ree juxtapos$ cells1 x is obvi\s t its sides w t5d to be concave1 = ! int]space betwe5 our ?ree contigu\s equal circles is an equilat]al1 curvil9e> triangle2 & ev5 if our spicule be deposit$1 n 9 ! space betwe5 our ?ree cells1 b 9 ! ?ickness ( ! int]v5+ wall1 !n we may recollect 7f p4 #big7 t ! sev]al p>titions nev] actually meet at %>p angles1 b ! angle ( contact is always bridg$ ov] by a small accumulation ( mat]ial 7v>y+ 9 am\nt accord+ to its fluidity7 ^: b\nd>y takes ! =m ( a circul> arc1 & :i* con/itutes ! 8b\rrelet0 ( ,plateau4 ,9 any sample ( ! triradiate spicules ( ,grantia1 or 9 any s]ies ( c>eful draw+s1 su* z ^? ( ,haeckel among o!rs1 we %all f9d t all ^! v>i\s configurations are precisely & completely illu/rat$4 ,! tetrah$ral1 or r tetract9ellid1 spicule ne$s no explanation 9 detail 7,fig4 #bad1 ,d1 ,e74 ,= j z a triradiate spicule corresponds to ! case ( ?ree cells 9 mutual contact1 s does ! f\r-ray$ spicule to t ( a solid aggregate ( f\r cells3 ^! latt] t5d+ to meet "o ano!r 9 a tetrah$ral sy/em1 %ew+ f\r edges1 at ea* ( :i* f\r surfaces meet1 ! edges be+ incl9$ to "o ano!r at equal angles ( ab\t #aji4 ,& ev5 9 ! case ( a s+le lay]1 or sup]ficial lay]1 ( cells1 if ! skeleton orig9ate 9 connection ) all ! edges ( mutual contact1 we %all1 9 complete & typical cases1 h a f\r-ray$ spicule1 ( :i* "o /raight limb w correspond to ! l9e ( junction betwe5 ! ?ree cells1 & ! o!r ?ree limbs 7:i* w !n be curv$ limbs7 w correspond to ! edges :]e two cells meet "o ano!r on ! surface ( ! sy/em4 #ddg ,b if su* a physical explanation ( ! =ms ( our spicules is to be accept$1 we mu/ seek at once = "s physical ag5cy by :i* we may expla9 ! pres5ce ( ! solid mat]ial j at ! junctions or int]faces ( ! cells1 & = ! =ces by :i* x is conf9$ to1 & m\ld$ to ! =m (1 ^! int]cellul> or int]facial contacts4 ,x is to ,drey] t we *iefly owe ! physical or me*anical !ory ( spicul> con=mation :i* ,i h j describ$1--a !ory :i* ultimately re/s on ! =m assum$1 "u surface-t5sion1 by an aggregation ( cells or vesicles4 ,b ?is fundam5tal po9t be+ grant$1 we h /ill sev]al possible alt]natives by :i* to expla9 ! details ( ! ph5om5on4 ,drey]1 if ,i und]/& him aright1 0 cont5t to assume t ! solid mat]ial1 secret$ or excret$ by ! organism1 accumulat$ 9 ! int]/ices betwe5 ! cells1 & 0 !re subject$ to me*anical pressure or con/ra9t z ! cells got m & m cr[d$ toge!r by _! own gr[? & t ( ! sy/em g5]ally4 ,z f> z ! g5]al =m ( ! spicules goes1 su* explanation is n inadequate1 ?\gh "u x we may h to r5\nce "s ( our assumptions z to :at takes place at ! out] surface ( ! sy/em4 ,b 9 all 7or mo/7 cases :]e1 b a few ye>s ago1 ! concepts ( secretion or excretion seem$ precise en\gh1 we are n[-a-days incl9$ to turn to ! ph5om5on ( adsorption z a fur!r /age t[>ds ! elucidation ( our facts4 ,"h we h a case 9 po9t4 ,9 ! tissues ( our sponge1 :]ev] two cells meet1 !re we h a def9ite surface ( contact1 & !re accord+ly we h a manife/ation ( surface-en]gy2 & ! conc5tration ( surface-en]gy w t5d to be a maximum at ! l9es or edges :]eby ! ?ree1 or f\r1 su* surfaces are conjo9$4 ,( ! micro-*emi/ry ( ! sponge-cells our ignorance is great2 b 7)\t v5tur+ on any hypo!sis involv+ ! *emical details ( ! process7 we may safely ass]t t !re is an inh]5t probability t c]ta9 sub/ances w t5d to be conc5trat$ & ultimately deposit$ j 9 ^! l9es ( int]cellul> contact & conjunction4 ,9 o!r words1 adsorptive conc5tration1 "u osmotic pressure1 at & 9 ! surface-film :i* con/itutes ! mutual b\nd>y betwe5 contigu\s #ddh cells1 em]ges z an alt]native 7&1 z x seems to me1 a highly pref]able alt]native7 to ,drey]'s conception ( an accumulation "u me*anical pressure 9 ! vacant spaces left betwe5 "o cell & ano!r4 ,b a purely *emical1 or purely molecul> adsorption1 is n ! only =m ( ! hypo!sis on :i* we may rely4 ,= f ! purely physical po9t ( view1 angles & edges ( contact betwe5 adjac5t cells w be loci 9 ! field ( di/ribution ( surface-en]gy1 & any mat]ial p>ticles :atsoev] w t5d to und]go a dim9ution ( fre$om on ent]+ "o ( ^? b\nd>y regions4 ,9 a v simple case1 let u imag9e a c\ple ( soap bubbles 9 contact ) "o ano!r4 ,ov] ! surface ( ea* bubble !re glide 9 e direction1 z usual1 a multitude ( t9y bubbles & droplets2 b z soon z ^! f9d _! way into ! groove or re-entrant angle betwe5 ! two bubbles1 !re _! fre$om ( movem5t is s f> re/ra9$1 & out ( t groove !y h little or no t5d5cy to em]ge4 ,a cognate ph5om5on is to be witness$ 9 microscopic sections ( /eel or o!r metals4 ,"h1 amid ! 8cry/all9e0 /ructure ( ! metal 7:]e 9 cool+ its imp]fectly homog5e\s mat]ial has develop$ a cellul> /ructure1 %ew+ 79 section7 hexagonal or polygonal cont\rs71 we c easily obs]ve1 z ,pr(essor ,p$die has %ewn me1 t ! little p>ticles ( graphite & o!r =eign bodies common 9 ! matrix1 h t5d$ to aggregate !mselves 9 ! walls & at ! angles ( ! polygonal cells--?is be+ a direct result ( ! dim9i%$ fre$om :i* ! p>ticles und]go on ent]+ "o ( ^! b\nd>y regions#dfj4 ,x is by a comb9ation ( ^! two pr9ciples1 *emical adsorption on ! "o h&1 & physical quasi-adsorption or conc5tration ( gross] p>ticles on ! o!r1 t ,i conceive ! sub/ance ( ! sponge-spicule to be conc5trat$ & aggregat$ at ! cell b\nd>ies2 & ! =ms ( ! triradiate & tetract9ellid spicules are 9 precise con=mity ) ?is hypo!sis4 ,a few g5]al matt]s1 & a few p>ticul> cases1 rema9 to be consid]$4 ,x matt]s little or n at all1 = ! ph5om5on 9 "q1 #ddi :at is ! hi/ological nature or 8grade0 ( ! vesicul> /ructures on :i* x dep5ds4 ,9 "s cases 7ap>t f sponges71 !y may be no m ?an ! little alveoli ( ! intracellul> protoplasmic network1 & ?is w\ld seem to be ! case at lea/ 9 "o kn[n case1 t ( ! protozoan ,entosol5ia asp]a1 9 :i*1 )9 ! vesicul> protoplasm ( ! s+le cell1 ,mbius has describ$ t9y spicules 9 ! %ape ( little tetrah$ra ) concave sides4 ,x is probably also ! case 9 ! small beg9n+s ( ! ,e*9od]m spicules1 :i* are likewise intracellul>1 & are ( simil> %ape4 ,9 ! case ( our sponges we h _m v>y+ conditions1 :i* we ne$ n attempt to exam9e 9 detail4 ,9 "s cases !re is evid5ce = believ+ t ! spicule is =m$ at ! b\nd>ies ( true cells or hi/ological units4 ,b 9 ! case ( ! l>g] triradiate or tetract9ellid spicules ( ! sponge-body1 !y f> surpass 9 size ! actual 8cells02 we f9d !m ly+1 regul>ly & symmetrically arrang$1 betwe5 ! 8pore-canals0 or 8ciliat$ *amb]s10 & x is 9 con=mity ) ! %ape & arrangem5t ( ^! r\nd$ or sph]oidal /ructures t _! %ape is assum$4 ,aga91 x is n necess>ily at v>iance ) our hypo!sis to f9d t1 9 ! adult sponge1 ! l>g] spicules may greatly outgr[ ! b\nds n only ( actual cells b also ( ! ciliat$ *amb]s1 & may ev5 appe> to project freely f ! surface ( ! sponge4 ,= we h already se5 t ! spicule is capable ( gr[+1 )\t m>k$ *ange ( =m1 by fur!r deposition1 or cry/allisation1 ( lay] ^u lay] ( calc>e\s molecules1 ev5 9 an artificial solution2 & we are entitl$ to believe t ! same process may be c>ri$ on 9 ! tissues ( ! sponge1 )\t greatly alt]+ ! symmetry ( ! spicule1 long aft] x has e/abli%$ its *>act]i/ic =m ( a sy/em ( sl5d] trih$ral or tetrah$ral rays4 ,nei!r is x ( great importance to our hypo!sis :e!r ! ray$ spicule necess>ily arises z a s+le /ructure1 or does s f sep>ate m9ute c5tres ( aggregation4 ,m9*9 has %ewn t1 9 "s cases at lea/1 ! latt] is ! case2 ! spicule beg9s1 he tells u1 z ?ree t9y rods1 sep>ate f "o ano!r1 ea* develop$ 9 ! int]space betwe5 two si/]-cells1 :i* are !mselves ! results ( ! division ( "o ( a #dej little trio ( cells2 & ! little rods meet & fuse toge!r :ile /ill v m9ute1 :5 ! :ole spicule is only ab\t #a_/bjj ( a millimetre long4 ,at ?is /age1 x is int]e/+ to le>n t ! spicule is non-cry/all9e2 b ! new accretions ( calc>e\s matt] are soon deposit$ 9 cry/all9e =m4 ,?is obs]vation ?rew consid]able difficulties 9 ! way ( =m] me*anical !ories ( ! con=mation ( ! spicule1 & 0 q at v>iance ) ,drey]'s !ory1 accord+ to :i* ! spicule 0 b\nd to beg9 f a c5tral nucleus co9cid+ ) ! meet+-place ( ! ?ree contigu\s cells1 or r ! int]space betwe5 !m4 ,b ! difficulty is remov$ :5 we import ! concept ( adsorption2 = by ?is ag5cy x is natural en\gh1 or conceivable en\gh1 t ! process ( deposition %\ld g on at sep>ate p>ts ( a common sy/em ( surfaces2 & if ! cells t5d to meet "o ano!r by _! int]faces be=e ^! int]faces ext5d to ! angles & s complete ! polygonal cell1 x is aga9 conceivable & natural t ! spicule %\ld fir/ arise 9 ! =m ( sep>ate & deta*$ limbs or rays4 ,illu/ration3 ,fig4 #bae4 ,spicules ( tetract9ellid sponges 7aft] ,sollas74 a-e1 anatria5es2 d-f1 protria5es4 ,among ! tetract9ellid sponges1 ^: spicules are compos$ ( amorph\s silica or opal1 all or mo/ ( ! above-describ$ ma9 types ( spicule occur1 &1 z ! "n ( ! gr\p implies1 ! f\r-ray$1 tetrah$ral spicules are especially repres5t$4 ,a some:at frequ5t type ( spicule is "o 9 :i* "o ( ! f\r rays is greatly develop$1 & ! o!r ?ree con/itute small prongs div]g+ at equal angles f ! ma9 or axial ray4 ,9 all probability1 z ,drey] sugge/s1 we h "h _h to d ) a gr\p ( f\r vesicles1 ( :i* ?ree 7 l>ge & co-equal1 :ile a f\r? & v mu* small] "o lay above & betwe5 ! o!r ?ree4 ,9 c]ta9 cases :]e we h likewise "o l>ge & ?ree mu* small] #dea rays1 ! latt] are recurv$1 z 9 ,fig4 #bae4 ,?is type1 save = ! con/ancy ( ! numb] ( rays1 & ! limitation ( ! t]m9al ones to ?ree1 & save also = ! m important diff]5ce t !y occur only at "o & n at bo? ends ( ! long axis1 is simil> to ! type ( spicule illu/rat$ 9 ,fig4 #bac1 :i* we h expla9$ z be+ probably develop$ )9 an oval cell1 by ^: walls its bran*es h be5 con=m$ to geodetic curves4 ,b x is mu* m probable t we h "h to d ) a spicule develop$ 9 ! mid/ ( a gr\p ( ?ree coequal & m or less elongat$ or cyl9drical cells or vesicles1 ! long axial ray correspond+ to _! common l9e ( contact1 & ! ?ree %ort rays hav+ ea* la9 9 ! surface furr[ betwe5 two out ( ! ?ree adjac5t cells4 ,illu/ration3 ,fig4 #baf4 ,v>i\s holo?urian spicules4 7,aft] ,?el47 ,j z 9 ! case ( ! little curv$ or ,s-%ap$ spicules1 =m$ app>5tly )9 ! b\nds ( a s+le cell1 s also 9 ! case ( ! l>g] tetract9ellid & analog\s types d we f9d among ! ,holo?uroidea ! same configurations reproduc$ z we h dealt ) 9 ! sponges4 ,! holo?urian spicules are a little less neatly =m$1 a little r\gh]1 ?an ! sponge-spicules2 & c]ta9 =ms occur among ! =m] gr\p :i* d n pres5t !mselves among ! latt]2 b = ! mo/ "p a community ( type is obvi\s & /rik+ 7,fig4 #baf74 ,a curi\s &1 physically speak+1 /rictly analog\s =mation to ! tetrah$ral spicules ( ! sponges is f\nd 9 ! #deb spores ( a c]ta9 little gr\p ( p>asitic protozoa1 ! ,act9omyxidia4 ,^! spores are =m$ f clu/]s ( six cells1 ( :i* ?ree come to con/itute ! capsule ( ! spore2 & ?is capsule1 always triradiate 9 its symmetry1 is 9 "s species drawn out into long rays1 ( :i* "o con/itutes a /raight c5tral axis1 :ile ! o!rs1 com+ (f f x at equal angles1 are recurv$ 9 wide circul> arcs4 ,! acc\nt giv5 ( ! developm5t ( ?is /ructure by its discov]]s#dfa is some:at obscure to me1 b ,i ?9k t1 on physical gr\nds1 !re c be no d\bt :atev] t ! quadriradiate capsule has be5 someh[ modell$ ^u a gr\p ( ?ree surr\nd+ cells1 its axis ly+ betwe5 ! ?ree1 & its ?ree radial arcs occupy+ ! furr[s betwe5 adjac5t pairs4 ,illu/ration3 ,fig4 #bag4 ,spicules ( hexact9ellid sponges4 7,aft] ,f4 ,e4 ,s*ultze47 ,! typically six-ray$ silice\s spicules ( ! hexact9ellid sponges1 :ile !y are p]haps ! mo/ regul> & beautifully =m$ spicules to be f\nd )9 ! entire gr\p1 h be5 f\nd v difficult to expla91 & ,drey] has confess$ 8 complete inability to acc\nt = _! con=mation4 ,b1 ?\gh x is d\btless only ?r[+ ! difficulty a little fur!r back1 we may s f> acc\nt = !m by consid]+ t ! cells or vesicles by :i* !y are con=m$ are n arrang$ 9 #dec :at is kn[n z 8close/ pack+10 b 9 l9e> s]ies2 s t 9 _! arrangem5t1 & by _! mutual compression1 we t5d to get a patt]n1 n ( hexagons1 b ( squ>es3 or1 look+ to ! solid1 n ( dodecah$ra b ( cubes or p>allelopip$a4 ,?is inde$ appe>s to be ! case1 n ) ! individual cells 79 ! hi/ological s5se71 b ) ! l>g] units or vesicles :i* make up ! body ( ! hexact9ellid4 ,& ?is be+ s1 ! spicules =m$ betwe5 ! l9e>1 or cubical s]ies ( vesicles1 w h ! same t5d5cy t[>ds a 8hexact9ellid0 %ape1 correspond+ to ! angles & adjac5t edges ( a sy/em ( cubes1 z 9 our =m] case !y _h to a triradiate or a tetract9ellid =m1 :5 develop$ 9 connection ) ! angles & edges ( a sy/em ( hexagons1 or a sy/em ( dodecah$ra4 ,hi/ologically1 ! case is illu/rat$ by a well-kn[n ph5om5on 9 embryology4 ,9 ! segm5t+ ovum1 !re is a t5d5cy = ! cells to be budd$ (f 9 l9e> s]ies2 & s !y (t5 rema91 9 r[s side by side1 at lea/ = a consid]able "t & dur+ ! c\rse ( sev]al consecutive cell divisions4 ,su* an arrangem5t con/itutes :at ! embryologi/s call ! 8radial type0 ( segm5tation#dfb4 ,b 9 :at is describ$ z ! 8spiral type0 ( segm5tation1 x is /at$ t1 z soon z ! fir/ horizontal furr[ has divid$ ! cells into an upp] & a l[] lay]1 ^? ( 8! upp] lay] are %ift$ 9 respect to ! l[] lay]1 by means ( a rotation ab\t ! v]tical axis#dfc40 ,x is1 ( c\rse1 evid5t t ! :ole process is m]ely t :i* is famili> to physici/s z 8close pack+40 ,x is a v simple case ( :at ,"l ,kelv9 us$ to call 8a problem 9 tactics40 ,x is a m]e "q ( ! rigidity ( ! sy/em1 ( ! fre$om ( movem5t on ! "p ( its con/itu5t cells1 :e!r or at :at /age ?is t5d5cy to slip into ! close/ prop9quity1 or position ( m9imum pot5tial1 w be f\nd to manife/ itself4 ,h[ev] ! hexact9ellid spicules be arrang$ 7& ?is is #ded n at all easy to det]m9e7 9 relation to ! tissues & *amb]s ( ! sponge1 x is at lea/ cle> t1 :e!r !y be sep>ate or be fus$ toge!r 7z (t5 happ5s7 9 a composite skeleton1 !y effect a symmetrical p>tition+ ( space accord+ to ! cubical sy/em1 9 contra/ to t clos] pack+ :i* is repres5t$ & effect$ by ! tetrah$ral sy/em#dfd4 ,?is "q ( ! orig9 & causation ( ! =ms ( sponge-spicules1 ) :i* we h n[ briefly dealt1 is all ! m important & all ! m int]e/+ because x has be5 discuss$ "t & aga91 f po9ts ( view :i* are *>act]i/ic ( v diff]5t s*ools ( ?\ght 9 biology4 ,haeckel f\nd 9 ! =m ( ! sponge-spicule a typical illu/ration ( 8 !ory ( 8bio-cry/allisation02 he consid]$ t ^! 8biocry/als0 repres5t$ 8some?+ midway--e9 ,mitteld+--betwe5 an inorganic cry/al & an organic secretion02 t !re 0 a 8compromise betwe5 ! cry/allis+ ef=ts ( ! calcium c>bonate & ! =mative activity ( ! fus$ cells ( ! syncytium02 & t ! semi-cry/all9e secretions ( calcium c>bonate 87 utilis$ by natural selection z #8spicules' = build+ up a skeleton1 & aft]w>ds1 by ! int]action ( adaptation & h]$ity1 became modifi$ 9 =m & diff]5tiat$ 9 a va/ v>iety ( ways 9 ! /ruggle = exi/5ce#dfe40 ,:at ,haeckel precisely signifi$ by ^! words is n cle> to me4 ,f4 ,e4 ,s*ultze1 p]ceiv+ t id5tical =ms ( spicule 7 develop$ :e!r ! mat]ial 7 cry/all9e or non-cry/all9e1 ab&on$ all !ories bas$ ^u cry/allisation2 he simply saw 9 ! =m & arrangem5t ( ! spicules some?+ :i* 0 8be/ fitt$0 = its purpose1 t is to say = ! support & /r5g!n+ ( ! por\s walls ( ! sponge1 & f\nd cle> evid5ce ( 8utility0 9 ! specific /ructure ( ^! skeletal elem5ts4 #dee ,sollas & ,drey]1 z we h se51 introduc$ 9 v>i\s ways ! conception ( physical causation1--z inde$ ,haeckel himself _h done 9 reg>d to "o p>ticul>1 :5 he suppos$ ! position ( ! spicules to be due to ! con/ant passage ( ! wat]-curr5ts4 ,?\gh ev5 "h1 by ! way1 if ,i und]/& ,haeckel aright1 he 0 ?9k+ n m]ely ( a direct or imm$iate physical causation1 b ( "o manife/+ itself ?r\gh ! ag5cy ( natural selection#dff4 ,sollas laid /ress ^u ! 8pa? ( lea/ resi/ance0 z det]m9+ ! direction ( gr[?2 :ile ,drey] dealt 9 great] detail ) ! v>i\s t5sions & pressures to :i* ! gr[+ spicule 0 expos$1 amid ! alveol> or vesicul> /ructure :i* 0 repres5t$ alike by ! *amb]s ( ! sponge1 by ! reticulum ( con/itu5t cells1 or by ! m9ute /ructure ( ! intracellul> protoplasm4 ,b nei!r ( ^! writ]s1 s f> z ,i c discov]1 0 incl9$ to d\bt = a mom5t ! receiv$ canon ( biology1 :i* sees 9 su* /ructures z ^! ! *>act]i/ics ( true organic species1 & ! indications ( an h]$it>y aff9ity by :i* blood-relation%ip & ! succession ( evolution>y desc5t ?r\gh\t geologic "t c be ultimately d$uc$4 ,la/ly1 ,m9*91 9 a well-kn[n pap]#dfg1 took sides ) ,s*ultze1 & gave reasons = diss5t+ f su* me*anical !ories z ^? ( ,sollas & ( ,drey]4 ,= example1 aft] po9t+ out t all protoplasm conta9s a numb] ( 8granules0 or microsomes1 conta9$ 9 ! alveol> framework & lodg$ at ! nodes ( ! reticulum1 he argu$ t ^! also ought to acquire a =m su* z ! spicules possess1 if x 7 ! case t ^! latt] ow$ _! =m to _! v simil> or id5tical position4 8,if vesicul> t5sion _c 9 any o!r in/ance cause ! granules at ! nodes to assume a tetraxon =m1 :y %\ld x d s = ! scl]ites80 ,9 all probability ! answ] to ?is "q is n f> to seek4 ,if ! =ce :i* ! 8me*anical0 hypo!sis has 9 view 7 simply t ( me*anical pressure1 #def z betwe5 solid bodies1 !n inde$ we %\ld expect t any sub/ances :atsoev]1 ly+ betwe5 ! imp++ sph]es1 w\ld t5d 7unless !y 7 inf9itely h>d7 to assume ! quadriradiate or 8tetraxon0 =m2 b ?is conclusion does n foll[ at all1 9 s f> z x is to surface-en]gy t we ascribe ! ph5om5on4 ,"h ! specific nature ( ! sub/ances involv$ makes all ! diff]5ce4 ,we _c argue f "o sub/ance to ano!r2 adsorptive attraction %ews its effect on "o & n on ano!r2 & we h n ! lea/ reason to be surpris$ if we f9d t ! little granules ( protoplasmic mat]ial1 :i* z !y lie ba!d 9 ! m fluid protoplasm h 7presumably1 & z _! %ape indicates7 a /rong surface-t5sion ( _! own1 behave t[>ds ! adjac5t vesicles 9 a v diff]5t fa%ion to ! incipi5t aggregations ( calc>e\s or silice\s matt] 9 a colloid m$ium4 8,! ontog5y ( ! spicules10 says ,pr(essor ,m9*91 8po9ts cle>ly to _! regul> =m be+ a phylog5etic adaptation1 :i* has become fix$ & h&$ on by h]$ity1 appe>+ 9 ! ontog5y z a prophetic adaptation40 ,& aga91 8,! =ms ( ! spicules are ! result ( adaptation to ! requirem5ts ( ! sponge z a :ole1 produc$ by ! action ( natural selection ^u v>iation 9 e direction40 ,x w\ld sc>cely be possible to illu/rate m briefly & m cog5tly ?an by ^! few words 7or ! simil> words ( ,haeckel quot$ on p4 #ded71 ! fundam5tal diff]5ce betwe5 ! ,d>w9ian conception ( ! causation & det]m9ation ( ,=m1 & t :i* is *>act]i/ic ( ! physical sci5ces4 ,if ,i h dealt comp>atively briefly ) ! inorganic skeleton ( sponges1 9 spite ( ! obvi\s importance ( ?is "p ( our subject f ! physical or me*anical po9t ( view1 x has be5 ow+ to sev]al reasons4 ,9 ! fir/ place1 ?\gh ! g5]al tr5d ( ! ph5om5a is cle>1 x mu/ be at once admitt$ t _m po9ts are obscure1 & c\ld only be discuss$ at ! co/ ( a long argum5t4 ,9 ! second place1 ! physical !ory is 7z ,i h %ewn7 9 manife/ conflict ) ! acc\nts giv5 by v>i\s embryologi/s ( ! developm5t ( ! spicules1 & ( ! curr5t biological !ories :i* _! descriptions embody2 x is beyond our scope to deal ) su* descriptions #deg 9 detail4 ,la/ly1 we f9d ourselves able to illu/rate ! same physical pr9ciples ) great] cle>ness & great] c]titude 9 ano!r gr\p ( animals1 namely ! ,radiol>ia4 ,9 our description ( ! skeletons occurr+ )9 ?is gr\p we %all by no means ab&on ! prelim9>y classification ( microscopic skeletons :i* we h laid d[n2 b we %all h occasion to bl5d ) x ! consid]ation ( c]ta9 o!r m or less correlat$ ph5om5a4 ,! gr\p ( microscopic organisms kn[n z ! ,radiol>ia is extraord9>ily ri* 9 div]se =ms1 or 8species40 ,i d n "k h[ _m ( su* species h be5 describ$ & def9$ by naturali/s1 b "s ?irty ye>s ago ! numb] 0 said to be ov] f\r ?\s&1 arrang$ 9 m ?an sev5 hundr$ g5]a#dfh4 ,( late ye>s !re has be5 a t5d5cy to r$uce ! numb]1 x be+ f\nd t "s ( ! e>li] species & ev5 g5]a are b gr[?-/ages ( "o & ! same =m1 sometimes m]e fragm5ts or 8fission-products0 common to sev]al species1 or sometimes =ms s simil> & s int]connect$ by int]m$iate =ms t ! naturali/ d5om9ates !m n 8species0 b 8v>ieties40 ,x has to be admitt$1 9 %ort1 t ! conception ( species among ! ,radiol>ia has n hi!rto be51 & is n yet1 on ! same foot+ z t among mo/ o!r gr\ps ( animals4 ,b ap>t f ! extraord9>y multiplicity ( =ms among ! ,radiol>ia1 !re are c]ta9 o!r features 9 ?is multiplicity :i* arre/ our att5tion4 ,= in/ance1 ! di/ribution ( species 9 space is curi\s & vague2 _m species are f\nd all ov] ! _w1 or at lea/ e "h & !re1 ) no evid5ce ( specific limitations ( geographical habitat2 o!rs occur 9 ! neighb\rhood ( ! two poles2 "s are conf9$ to w>m & o!rs to cold curr5ts ( ! ocean4 ,9 "t also _! di/ribution is n less vague3 s mu* s t x has be5 ass]t$ ( !m t 8f ! ,cambrian age d[nw>ds1 ! families & ev5 g5]a appe> id5tical ) ^? n[ liv+40 ,la/ly1 except p]haps 9 ! case ( a few l>ge 8colonial =ms10 we seldom if ev] f9d1 z is usual #deh 9 mo/ animals1 a local pr$om9ance ( "o p>ticul> species4 ,on ! contr>y1 9 a little p9* ( deep-sea mud or ( "s fossil 8,radiol>ian e>?10 we %all probably f9d scores1 & x may be ev5 hundr$s1 ( diff]5t =ms4 ,moreov]1 ! radiol>ian skeletons are ( q extraord9>y delicacy & complexity1 9 spite ( _! m9ut5ess & ! comp>ative simplicity ( ! 8unicellul>0 organisms )9 :i* !y gr[2 & ^! complex con=mations h a wond]ful & unusual appe>ance ( geometric regul>ity4 ,all ^! g5]al consid]ations seem su* z to prep>e u = ! special ne$ ( "s physical hypo!sis ( causation4 ,! little skeletal fabrics rem9d u ( su* objects z sn[-cry/als 7!mselves almo/ endless 9 _! div]sity71 r ?an ( a collection ( di/9ct animals1 con/ruct$ 9 app>5t accordance ) functional ne$s1 & di/ribut$ 9 accordance ) _! fitness = p>ticul> situations4 ,nev]!less great ef=ts h be5 made ( rec5t ye>s to atta* 8a biological mean+0 to ^! elaborate /ructures2 & 8to ju/ify ! hope t 9 "t ! utilit>ian "* ( ! skeleton w be m completely recognis$#dfi40 ,9 ! majority ( cases1 ! skeleton ( ! ,radiol>ia is compos$1 l t ( s _m sponges1 ( silica2 9 "o l>ge family1 ! ,acan?>ia 7& p]haps 9 "s o!rs71 x is compos$1 9 great "p at lea/1 ( a v unusual con/itu5t1 namely /rontium sulphate#dgj4 ,!re is no fundam5tal or important morphological "* 9 :i* ! %ells =m$ ( ^! two con/itu5ts diff] f "o ano!r2 & 9 no case c ! *emical prop]ties ( ^! inorganic mat]ials be said to influ5ce ! =m ( ! complex skeleton or %ell1 save only 9 ?is g5]al way t1 by _! rigidity & t\ghness1 !y may give rise to a fabric f> m delicate & sl5d] ?an we f9d develop$ among calc>e\s organisms4 ,a slight exception to ?is rule is f\nd 9 ! pres5ce ( true cry/als1 :i* occur )9 ! c5tral capsules ( c]ta9 #dei ,radiol>ia1 = in/ance ! g5us ,collospha]a#dga4 ,johannes ,mll] 7^: k & insight nev] fail to a/oni% u7 rem>k$ t ^! 7 id5tical 9 =m ) cry/als ( cele/9e1 a sulphate ( /rontium & b>ium2 & ,bts*li's discov]y ( sulphates ( /rontium & ( b>ium 9 k9dr$ =ms r5d] x all b c]ta9 t !y are actually true cry/als ( cele/9e#dgb4 ,9 its typical =m1 ! ,radiol>ian body consi/s ( a sph]ical mass ( protoplasm1 ar\nd :i*1 & sep>at$ f x by "s sort ( por\s 8capsule10 lies a fro?y mass1 compos$ ( protoplasm honeycomb$ into a multitude ( alveoli or vacuoles1 fill$ ) a fluid :i* c sc>cely diff] mu* f sea-wat]#dgc4 ,accord+ to _! surface-t5sion conditions1 ^! vacuoles may appe> m or less isolat$ & sph]ical1 or jo9+ toge!r 9 a 8fro?0 ( polygonal cells2 & 9 ! latt]1 :i* is ! common] condition1 ! cells t5d to be ( equal size1 & ! result+ polygonal me%work beautifully regul>4 ,9 _m cases1 a l>ge numb] ( su* simple individual organisms are associat$ toge!r1 =m+ a float+ colony1 & x is highly probable t _m o!r =ms1 ) ^: scatt]$ skeletons we are alone acqua9t$1 _h 9 life =m$ "p likewise ( a colonial organism4 ,9 contradi/9ction to ! sponges1 9 :i* ! skeleton always beg9s z a loose mass ( isolat$ spicules1 :i* only 9 a few exceptional cases 7su* z ,euplectella & ,f>rea7 fuse into a cont9u\s network1 ! *>act]i/ic feature ( ! ,radiol>ians lies 9 ! possession ( a cont9u\s skeleton1 9 ! =m ( a nett$ me% or p]=at$ lacework1 sometimes h[ev] replac$ by & (t5 associat$ ) m9ute indep5d5t spicules4 ,be=e we proce$ to treat ( ! m complex skeletons1 we may beg91 !n1 by deal+ ) ^! comp>atively simple cases :]e ei!r ! entire skeleton or a consid]able "p ( x is repres5t$1 n by a cont9u\s fabric1 b by a quantity ( loose1 sep>ate spicules1 or aciculae1 :i* seem1 l ! spicules ( ,alcyonium1 #dfj to be develop$ z free & isolat$ =mations or deposits1 precipitat$ 9 ! colloid matrix1 ) no relation ( =m to ! cellul> or vesicul> b\nd>ies4 ,^! simple acicul> spicules occupy a def9ite position 9 ! organism4 ,sometimes1 z = in/ance among ! fre%-wat] ,heliozoa 7e4g4 ,raphidiophrys71 !y lie on ! out] surface ( ! organism1 & n infrequ5tly 7:5 ! spicules are few 9 numb]7 !y t5d to collect r\nd ! bases ( ! pseudopodia1 or ar\nd ! l>ge radiat+ spicules1 or axial rays1 9 ! cases :]e ^! latt] are pres5t4 ,:5 ! spicules are ?us localis$ ar\nd "s prom95t c5tre1 !y t5d to take up a position ( symmetry 9 reg>d to x2 in/ead ( =m+ a tangl$ or felt$ lay]1 !y come to lie side by side1 9 a radiat+ clu/] r\nd ! focus4 ,9 o!r cases 7z = in/ance 9 ! well-kn[n ,radiol>ian ,aulacan?a scolyman?a7 ! felt$ lay] ( aciculae lies at "s dep? bel[ ! surface1 =m+ a sph]e conc5tric ) ! entire sph]ical organism4 ,9 ei!r case1 :e!r ! lay] ( spicules be deep or be sup]ficial1 x t5ds to m>k a 8surface ( discont9uity10 a meet+ place betwe5 two di/9ct lay]s ( protoplasm or betwe5 ! protoplasm & ! wat] ar\nd2 & x is obvi\s t1 9 ei!r case1 !re are manife/ations ( surface-en]gy at ! b\nd>y1 :i* cause ! spicules to be reta9$ !re1 & to take up _! position 9 its plane4 ,! case is some:at1 ?\gh n directly1 analog\s to t ( a cirrus cl\d1 :i* m>ks ! place ( a surface ( discont9uity 9 a /ratifi$ atmosph]e4 ,illu/ration3 ,fig4 #bah4 ,we h1 !n1 to enquire :at are ! conditions :i* %all1 ap>t f gravity1 conf9e an extrane\s body to a surface-film2 & we may d ?is v simply1 by consid]+ ! surface-en]gy ( ! entire sy/em4 ,9 ,fig4 #bah we h two fluids 9 contact ) "o ano!r 7let u call !m wat] & protoplasm71 & a body 7b7 :i* may be imm]s$ 9 ei!r1 or may be re/rict$ to ! b\nd>y #dfa betwe54 ,we h "h ?ree possible 8int]facial contacts0 ea* ) its own specific surface-en]gy1 p] unit ( surface area3 namely1 t betwe5 our p>ticle & ! wat] 7let u call x 71 t betwe5 ! p>ticle & ! protoplasm 771 & t betwe5 wat] & protoplasm 774 ,:5 ! body lies 9 ! b\nd>y ( ! two fluids1 let u say half 9 "o & half 9 ! o!r1 ! surface-en]gies conc]n$ are equival5t to 7,s_/#b7 7,s_/#b72 b we mu/ also rememb] t1 by ! pres5ce ( ! p>ticle1 a small portion 7equal to its sectional area s7 ( ! orig9al contact-surface betwe5 wat] & protoplasm has be5 oblit]at$1 & ) x a proportionate quantity ( en]gy1 equival5t to s1 has be5 set free4 ,:51 on ! o!r h&1 ! body lies entirely )9 "o or o!r fluid1 ! surface-en]gies ( ! sy/em 7s f> z we are conc]n$7 are equival5t to ,s s1 or ,s s1 z ! case may be4 ,accord+ z be less or great] ?an 1 ! p>ticle w h a t5d5cy to rema9 imm]s$ 9 ! wat] or 9 ! protoplasm2 b if 7,s_/#b77 7 s be less ?an ei!r ,s or ,s1 !n ! condition ( m9imal pot5tial w be f\nd :5 ! p>ticle lies1 z we h said1 9 ! b\nd>y zone1 half 9 "o fluid & half 9 ! o!r2 &1 if we 7 to attempt a m g5]al solution ( ! problem1 we %\ld evid5tly h to deal ) possible conditions ( equilibrium "u :i* ! necess>y balance ( en]gies w\ld be atta9$ by ! p>ticle ris+ or s9k+ 9 ! b\nd>y zone1 s z to adju/ ! relative magnitudes ( ! surface-areas conc]n$4 ,x is obvi\s t ?is pr9ciple may1 9 c]ta9 cases1 help u to expla9 ! position ev5 ( a radial spicule1 :i* is j a case :]e ! surface ( ! solid spicule is di/ribut$ betwe5 ! fluids ) a m9imal di/urbance1 or m9imal replacem5t1 ( ! orig9al surface ( contact betwe5 ! "o fluid & ! o!r4 ,9 l mann] we may provide = ! case 7a common & an important "o7 :]e ! protoplasm 8creeps up0 ! spicule1 cov]+ x ) a delicate film4 ,9 ,acan?ocy/is we h yet ano!r special case1 :]e ! radial spicules plunge only a c]ta9 di/ance into ! protoplasm ( ! cell1 be+ arre/$ at a b\nd>y-surface betwe5 an inn] & an out] lay] ( cytoplasm2 "h we h only to assume t !re is a t5sion #dfb at ?is surface1 betwe5 ! two lay]s ( protoplasm1 suffici5t to balance ! t5sions :i* act directly on ! spicule#dgd4 ,9 v>i\s ,acan?ometridae1 besides su* typical *>act]s z ! radial symmetry1 ! conc5tric lay]s ( protoplasm1 & ! capill>y surfaces 9 :i* ! out]1 vacuolat$ protoplasm is fe/oon$ ^u ! project+ radii1 we h ano!r curi\s feature4 ,on ! surface ( ! protoplasm :]e x creeps up ! sides ( ! long radial spicules1 we f9d a numb] ( elongat$ bodies1 =m+ 9 ea* case "o or sev]al little gr\ps1 & ly+ neatly arrang$ 9 p>allel bundles4 ,a ,russian naturali/1 ,s*ewiak(f1 ^: views h be5 accept$ 9 ! text-books1 tells u t ^! are muscul> /ructures1 s]v+ to raise or l[] ! conical masses ( protoplasm ab\t ! radial spicules1 :i* latt] s]ve z s _m 8t5t-poles0 or ma/s1 on :i* ! protoplasmic membranes are hoi/$ up2 & ! little elongat$ bodies are dignifi$ ) v>i\s names1 su* z 8myonemes0 or 8myophriscs10 9 allusion to _! suppos$ muscul> nature#dge4 ,?is explanation is by no means conv9c+4 ,to beg9 )1 we h precisely simil> fe/oons ( protoplasm 9 a multitude ( o!r cases :]e ! 8myonemes0 are lack+2 f _! m9ute size 7#jjf-jab mm47 & ! am\nt ( contraction !y are said to be capable (1 ! myonemes c h>dly be v effici5t in/rum5ts ( traction2 & fur!r1 = !m to act 7z is alleg$7 = a specific purpose1 namely ! 8hydro/atic regulation0 ( ! organism giv+ x p[] to s9k or to swim1 w\ld seem to imply a me*anism ( action & ( coord9ation :i* is difficult to conceive 9 ^! m9ute & simple organisms4 ,! fact is 7z x seems to me71 t ! :ole me?od ( explanation is unnecess>y4 ,j z ! suppos$ 8haul+ up0 ( ! protoplasmic fe/oons is at once expla9$ by capill>y ph5om5a1 s also1 9 all probability1 is ! position & arrangem5t ( ! little elongat$ bodies4 ,:atev] ! actual nature ( ^! bodies may be1 :e!r !y are truly portions ( diff]5tiat$ protoplasm1 or :e!r !y are =eign bodies or spicul> /ructures 7z bodies occupy+ a simil> position 9 o!r cases und\bt$ly are71 we c expla9 _! situation on ! surface #dfc ( ! protoplasm1 & _! arrangem5t ar\nd ! radial spicules1 all on ! pr9ciples ( surface-t5sion#dgf4 ,?is la/ case is n ( ! simple/2 & ,i d n =get t my explanation ( x1 :i* is :olly !oretical1 implies a d\bt ( ,s*ewiak(f's /atem5ts1 :i* are f\nd$ on direct p]sonal obs]vation4 ,?is ,i am none too will+ to d2 b :e!r x be ju/ly done 9 ?is case or n1 ,i hold t x is 9 pr9ciple ju/ifiable to look ) great suspicion ^u a numb] ( k9dr$ /atem5ts :]e x is obvi\s t ! obs]v] has left out ( acc\nt ! purely physical aspect ( ! ph5om5on1 & all ! opportunities ( simple explanation :i* ! consid]ation ( t aspect might af=d4 ,:e!r x be :olly applicable to ?is p>ticul> & complex case or no1 our g5]al !orem ( ! localisation & arre/m5t ( solid p>ticles 9 a surface-film is ( v great biological importance2 = on x dep5ds ! p[] display$ by _m little nak$ protoplasmic organisms ( cov]+ !mselves ) an 8agglut9at$0 %ell4 ,sometimes1 z 9 ,difflugia1 ,a/rorhiza 7,fig4 #bai7 & o!rs1 ?is cov]+ consi/s ( s&-gra9s pick$ up f ! surr\nd+ m$ium1 & sometimes1 on ! o!r h&1 z 9 ,quadrula1 x consi/s ( solid p>ticles :i* are said to arise1 z inorganic deposits or concretions1 )9 ! protoplasm itself1 & :i* f9d _! way outw>ds to a position ( equilibrium 9 ! surface-lay]2 & 9 bo? cases1 ! mutual capill>y attractions betwe5 ! p>ticles1 conf9$ to ! b\nd>y-lay] b enjoy+ a c]ta9 measure ( fre$om !re91 t5ds to ! ord]ly arrangem5t ( ! p>ticles "o ) ano!r1 & ev5 to ! appe>ance ( a regul> 8patt]n0 z ! result ( ?is arrangem5t4 ,illu/ration3 ,fig4 #bai4 ,ar5ace\s ,=am9if]a2 ,a/rorhiza limicola & ar5>ia4 7,f ,brady's ,*all5g] ,monograph47 ,! 8pick+ up0 by ! protoplasmic organism ( a solid p>ticle ) :i* 8to build its h\se0 7= x is h>d to avoid ?is cu/om>y use ( an?ropomorphic figures ( spee*1 mislead+ ?\gh !y be71 is a physical ph5om5on k9dr$ to t by :i* an ,amoeba 8swall[s0 a p>ticle ( food4 ,?is latt] process has be5 reproduc$ or imitat$ 9 v>i\s pretty exp]im5tal #dfe ways4 ,= in/ance1 ,rhumbl] has %ewn t if a ?read ( glass be cov]$ ) %ellac & br\ght ne> a drop ( *lor(orm susp5d$ 9 wat]1 ! drop takes 9 ! spicule1 robs x ( its %ellac cov]+1 & !n passes x out aga9#dgg4 ,x is all a "q ( relative surface-en]gies1 lead+ to diff]5t degrees ( 8adhesion0 betwe5 ! *lor(orm & ! glass or its cov]+4 ,?us x is t ! ,amoeba takes 9 ! diatom1 dissolves (f its proteid cov]+1 & ca/s out ! %ell4 ,fur!rmore1 z ! :ole ph5om5on dep5ds on a di/ribution ( surface-en]gy1 ! am\nt ( :i* is specific to c]ta9 p>ticul> sub/ances 9 contact ) "o ano!r1 we h no difficulty 9 und]/&+ ! selective action1 :i* is v (t5 a conspicu\s feature 9 ! ph5om5on#dgh4 ,j z "s caddis-worms make _! h\ses ( twigs1 & o!rs ( %ells & aga9 o!rs ( /ones1 s "s ,rhizopods con/ruct _! agglut9at$ 8te/0 out ( /ray sponge-spicules1 or fru/ules ( diatoms1 or aga9 ( t9y mud p>ticles or ( l>g] gra9s ( s&4 ,9 all ^! cases1 we h app>5tly to deal ) diff]5ces 9 specific #dff surface-en]gies1 & also d\btless ) diff]5ces 9 ! total available am\nt ( surface-en]gy 9 relation to gravity or o!r extrane\s =ces4 ,9 my e>ly /ud5t days1 ,wyville ,?omson us$ to tell u t c]ta9 deep-sea 8,difflugias10 aft] con/ruct+ a %ell out ( p>ticles ( ! black volcanic s& common 9 p>ts ( ! ,nor? ,atlantic1 f9i%$ x (f ) 8a clean :ite coll>0 ( little gra9s ( qu>tz4 ,ev5 ?is ph5om5on may be acc\nt$ = on surface-t5sion pr9ciples1 if we assume t ! surface-en]gy ratios h t5d$ to *ange1 ei!r ) ! gr[? ( ! protoplasm or by reason ( ext]nal v>iation ( temp]ature or ! l2 & we are by no means oblig$ to attribute ! ph5om5on to a manife/ation ( volition1 or ta/e1 or ae/hetic skill1 on ! "p ( ! microscopic organism4 ,nor1 :5 c]ta9 ,radiol>ia t5d m ?an o!rs to attract into _! own sub/ance diatoms & su*-l =eign bodies1 is x sci5tifically correct to speak1 z "s text-books d1 ( species 89 :i* diatom selection has become a regul> habit40 ,to d s is an exagg]at$ misuse ( an?ropomorphic phraseology4 ,! =mation ( an 8agglut9at$0 %ell is ?us se5 to be a purely physical ph5om5on1 & inde$ a special case ( a m g5]al physical ph5om5on :i* has _m o!r important consequ5ces 9 biology4 ,= ! %ell to assume ! solid & p]man5t "* :i* x acquires1 = in/ance1 9 ,difflugia1 we h only to make ! additional assumption t "s small quantities ( a cem5t+ sub/ance are secret$ by ! animal1 & t ?is sub/ance fl[s or creeps by capill>y attraction betwe5 all ! int]/ices ( ! little qu>tz gra9s1 & ends by b9d+ !m all firmly toge!r4 ,rhumbl]#dgi has %ewn u h[ ^! agglut9at$ te/s1 ( spicules or ( s&-gra9s1 c be precisely imitat$1 & h[ !y are =m$ ) great] or less ease1 & great] or less rapidity1 accord+ to ! nature ( ! mat]ials employ$1 t is to say1 accord+ to ! specific surface-t5sions :i* are involv$4 ,= in/ance if we mix up a little p[d]$ glass ) *lor(orm1 & set a drop ( ! mixture 9 wat]1 ! glass p>ticles ga!r neatly r\nd ! surface ( ! drop s quickly t ! eye _c foll[ ! #dfg op]ation4 ,if we p]=m ! same exp]im5t ) oil & f9e s&1 dropp$ into #gj p] c5t4 alcohol1 a /ill m beautiful artificial ,rhizopod %ell is =m$1 b x takes "s ?ree h\rs to d4 ,x is curi\s t1 j at ! v "t :5 ,rhumbl] 0 ?us demon/rat+ ! purely physical nature ( ! ,difflugian %ell1 ,v]worn 0 /udy+ ! same & k9dr$ organisms f ! old] /&po9t ( an incipi5t psy*ology#dhj4 ,b1 z ,rhumbl] himself admits1 ,v]worn 0 v c>eful n to ov]e/imate ! app>5t signs ( volition1 or selective *oice1 9 ! little organism's use ( ! mat]ial ( its dwell+4 ,?is long p>5!sis has l$ u away1 = ! "t be+1 f ! subject ( ! ,radiol>ian skeleton1 & to t subject we mu/ n[ return4 ,leav+ aside1 !n1 ! loose & scatt]$ spicules1 :i* we h suffici5tly discuss$1 ! m p]fect ,radiol>ian skeletons consi/ ( a cont9u\s & regul> /ructure2 & ! silice\s 7or o!r inorganic7 mat]ial ( :i* ?is framework is compos$ t5ds to be deposit$ 9 "o or o!r ( two ways or 9 bo? comb9$3 7#a7 9 ! =m ( long spicul> axes1 usually conjo9$ at1 or emanat+ f1 ! c5tre ( ! protoplasmic body1 & =m+ a symmetric radial sy/em2 7#b7 9 ! =m ( a cru/1 develop$ 9 v>i\s ways1 ei!r on ! out] surface ( ! organism or 9 relation to ! v>i\s int]nal surfaces :i* sep>ate its conc5tric lay]s or its compon5t vesicles4 ,n unfrequ5tly1 ?is sup]ficial skeleton comes to con/itute a sph]ical %ell1 or a sy/em ( conc5tric or o!rwise associat$ sph]es4 ,illu/ration3 ,fig4 #bbj4 8,reticulum plasmatique40 7,aft] ,c>noy47 ,we h already le>n$ t a great "p ( ! body ( ! ,radiol>ian1 & especially t out] portion to :i* ,haeckel has giv5 ! "n ( ! 8calymma10 is built up ( a great mass ( 8vesicles10 =m+ a sort ( /iff fro?1 & equival5t 9 ! physical s5se 7?\gh n necess>ily 9 ! biological s5se7 to 8cells10 inasmu* z ! little vesicles h _! own well-def9$ b\nd>ies1 & _! own surface ph5om5a4 ,9 %ort1 all t we h said ( cell-surfaces1 & cell con=mations1 9 our discussion ( cells & ( tissues1 w apply 9 l mann]1 & "u appropriate conditions1 to ^!4 ,9 c]ta9 cases1 ev5 9 #dfh s common & simple a "o z ! vacuolat$ sub/ance ( an ,act9ospha]ium1 we may see a v close resemblance1 or =mal analogy1 to an ord9>y cellul> or 8p>5*ymat\s0 tissue1 9 ! close-pack$ arrangem5t & consequ5t configuration ( ^! vesicles1 & ev5 at times 9 a slight membran\s h>d5+ ( _! walls4 ,leidy has figur$#dha "s curi\s little bodies1 l small masses ( consolidat$ fro?1 :i* seem to be no?+ else ?an ! dead & empty husks1 or filmy skeletons1 ( ,act9ospha]ium4 ,& ,c>noy#dhb has demon/rat$ 9 c]ta9 cell-nuclei an all b precisely simil> framework1 ( extreme delicacy & m9ut5ess1 z ! result ( p>tial solidification ( int]/itial matt] 9 a close-pack$ sy/em ( alveoli 7,fig4 #bbj74 ,illu/ration3 ,fig4 #bba4 ,aulonia hexagona1 ,hkl4 ,illu/ration3 ,fig4 #bbb4 ,act9omma arcadophorum1 ,hkl4 ,let u n[ suppose t1 9 our ,radiol>ian1 ! out] surface ( ! animal is cov]$ by a lay] ( fro?-l vesicles1 uni=m or ne>ly s 9 size4 ,we "k t _! t5sions w t5d to con=m !m into a 8honeycomb10 or regul> me%work ( hexagons1 & t ! free end ( ea* hexagonal prism w be a little sph]ical cap4 ,suppose n[ t x be at ! out] surface ( ! protoplasm 7t namely :i* is 9 contact ) ! surr\nd+ sea-wat]71 t ! silice\s p>ticles h a t5d5cy to be secret$ or adsorb$2 x w at once foll[ t !y w %[ a t5d5cy to aggregate 9 ! grooves :i* sep>ate ! vesicles1 & ! result w be ! developm5t ( a mo/ delicate sph]e compos$ ( t9y rods arrang$ 9 a regul> hexagonal network 7e4g4 ,aulonia74 ,su* a con=mation is #dfi extremely common1 & among its _m v>iants may be f\nd cases 9 :i* 7e4g4 ,act9omma71 ! vesicles h be5 less regul> 9 size1 & "s 9 :i* ! hexagonal me%work has be5 develop$ n only on "o out] surface1 b at successive #dgj surfaces1 produc+ a sy/em ( conc5tric sph]es4 ,if ! silice\s mat]ial be n limit$ to ! l9e> junctions ( ! cells1 b spread ov] a portion ( ! out] sph]ical surfaces or caps1 !n we %all h ! condition repres5t$ 9 ,fig4 #bbc 7,e?mospha]a71 :]e ! %ell appe>s p]=at$ by circul> in/ead ( hexagonal ap]tures1 & ! circul> pores are set on slight sph]oidal em95ces2 &1 int]connect$ ) su* types z ?is1 we h o!rs 9 :i* ! accumulat+ pellicles ( skeletal matt] h ext5d$ f ! edges into ! sub/ance ( ! b\nd>y walls & h s produc$ a sy/em ( films1 normal to ! surface ( ! sph]e1 con/itut+ a v p]fect honeycomb1 z 9 ,c5ospha]a favosa & vesp>ia#dhc4 ,illu/ration3 ,fig4 #bbc4 ,e?mospha]a conosiphonia1 ,hkl4 ,illu/ration3 ,fig4 #bbd4 ,portions ( %ells ( two 8species0 ( ,c5ospha]a3 upp] figure1 ,c4 favosa1 l[]1 ,c4 vesp>ia1 ,hkl4 ,9 "o or two v simple =ms1 su* z ! fre%-wat] ,cla?rul9a1 j su* a sph]ical p]=at$ %ell is produc$ out ( "s organic1 acan?9-l sub/ance2 & 9 "s examples ( ,cla?rul9a ! *it9\s lattice-"w ( ! %ell is j z #dga regul> & delicate1 ) ! me%es j z beautifully hexagonal1 z 9 ! silice\s %ells ( ! oceanic ,radiol>ia4 ,?is is only ano!r pro( 7if pro( be ne$$7 t ! peculi> con=mation ( ^! little skeletons is n due to ! mat]ial ( :i* !y are compos$1 b to ! m\ld+ ( t mat]ial ^u an und]ly+ vesicul> /ructure4 ,illu/ration3 ,fig4 #bbe4 ,aula/rum tric]os1 ,hkl4 ,let u next suppose t1 ^u "s su* lattice-"w z has j be5 describ$1 ano!r & ext]nal lay] ( cells or vesicles is develop$1 & t in/ead ( 7or p]haps only 9 addition to7 a second hexagonal lattice-"w1 :i* might develop conc5trically to ! fir/ 9 ! b\nd>y-furr[s ( ?is new lay] ( cells1 ! silice\s matt] n[ t5ds to be deposit$ radially1 or normally to ! surface ( ! sph]e1 j 9 ! l9es :]e ! ext]nal lay] ( vesicles meet "o ano!r1 ?ree by ?ree4 ,! result w be t1 :5 ! vesicles !mselves are remov$1 a s]ies ( radiat+ spicules w be reveal$1 direct$ outw>ds f ea* ( ! angles ( ! orig9al hexagon2 z is se5 9 ,fig4 #bbe4 ,& x may fur!r happ5 t ^! radiat+ skeletal rods are cont9u$ at _! di/al ends into div]g5t rays1 =m+ a triple =k1 & correspond+ 7aft] a fa%ion #dgb :i* we h already describ$ z occurr+ 9 c]ta9 sponge-spicules7 to ! ?ree sup]ficial furr[s betwe5 ! adjac5t cells4 ,?is la/ is1 z x 71 an int]m$iate /age betwe5 ! simple rods & ! complete =mation ( ano!r conc5tric sph]e ( lattic$ hexagons4 ,ano!r possible case is :5 ! l>ge & uni=m vesicles ( ! out] protoplasm are mix$ )1 or replac$ by1 mu* small] vesicles1 pil$ on "o ano!r 9 m or less conc5tric lay]s2 9 ?is case ! radiat+ rods w no long] be /raight1 b w be b5t into a zig-zag patt]n1 ) angles 9 ?ree v]tical planes1 correspond+ to ! successive contacts ( ! gr\ps ( cells ar\nd ! axis 7,fig4 #bbf74 ,illu/ration3 ,fig4 #bbf4 ,illu/ration3 ,fig4 #bbg4 ,a ,nassell>ian skeleton1 ,callimitra c>olotae1 ,hkl4 ,among a c]ta9 gr\p call$ ! ,nassell>ia1 we f9d geometrical =ms ( peculi> simplicity & beauty1--su* = in/ance z t :i* ,i h repres5t$ 9 ,fig4 #bbg4 ,x is obvi\s at a glance t ?is is su* a skeleton z may h be5 =m$ #dgc 7,i ?9k we may g s f> z to say mu/ h be5 =m$7 at ! int]faces ( a little tetrah$ral gr\p ( cells1 ! f\r equal cells ( ! tetrah$ron be+ 9 ?is p>ticul> case supplem5t$ by a little "o 9 ! c5tre ( ! sy/em4 ,we see1 precisely z 9 ! int]nal b\nd>y-sy/em ( an artificial gr\p ( f\r soap-bubbles1 ! plane surfaces ( contact1 six 9 numb]2 ! relation to "o ano!r ( ea* triple set ( int]facial planes1 meet+ "o ano!r at equal angles ( #abj2 & f9ally ! relation ( ! f\r l9es or edges ( triple contact1 :i* t5d 7b = ! little c5tral vesicle7 to meet at co-equal solid angles 9 ! c5tre ( ! sy/em1 all z we h describ$ on p4 #cah4 ,9 %ort1 ea* triple-wall$ re-entrant angle ( ! little %ell has ess5tially ! configuration 7or a "p !re(7 ( :at we h call$ a 8,m>aldi pyramid0 9 our acc\nt ( ! ar*itecture ( ! honeycomb1 on p4 #cbidhd4 ,!re are /ill two or ?ree rem>kable or peculi> features 9 ?is all b ma!matically p]fect %ell1 & !y are 9 "p easy & 9 "p !y seem m difficult ( int]pretation4 ,illu/ration3 ,fig4 #bbh4 ,an isolat$ portion ( ! skeleton ( ,dictyo*a4 ,illu/ration3 ,fig4 #bbi4 ,dictyo*a /ap$ia1 ,hkl4 ,we notice t ! am\nt ( solid matt] deposit$ 9 ! plane int]facial b\nd>ies is greatly increas$ at ! out] m>g9 ( ea* b\nd>y wall1 :]e x m]ges or co9cides ) ! sup]ficial furr[ :i* sep>ates ! free1 sph]ical surfaces ( ! bubbles f "o ano!r2 & we may sometimes f9d t1 along ^! edges1 ! skeleton rema9s complete & /rong1 :ile x %[s signs ( imp]fect developm5t or ( break+ away ov] great "p ( ! re/ ( ! int]facial surfaces4 ,9 ?is !re is no?+ anomal\s1 = we h already recognis$ t x is at ! edges or m>g9s ( ! int]facial p>tition-walls t ! manife/ation ( surface-en]gy w t5d to rea* its maximum4 ,& j z we h se5 t1 9 c]ta9 ( our 8multicellul>0 sph]ical ,radiol>ians1 x is at ! sup]ficial #dgd edges or bord]s ( ! p>titions1 & "h only1 t skeletal =mation occurs 7giv+ rise to ! nett$ %ell ) its hexagonal me%es ( ,fig4 #bba71 s also at times1 9 ! case ( su* little aggregates ( cells or vesicles z ! f\r-cell$ sy/em ( ,callimitra1 x may happ5 t ab\t ! ext]nal b\nd>y-l9es1 & n 9 ! int]ior b\nd>y-planes1 ! :ole ( ! skeletal matt] is aggregat$4 ,9 ,fig4 #bbh we see a curi\s little skeletal /ructure or complex spicule1 ^: con=mation is easily acc\nt$ = aft] ?is fa%ion4 ,little spicules su* z ?is =m isolat$ portions ( ! skeleton 9 ! g5us ,dictyo*a1 & occur scatt]$ ov] ! sph]ical surface ( ! organism 7,fig4 #bbi74 ,! m or less basket-%ap$ spicule has evid5tly be5 develop$ ab\t a little clu/] ( f\r cells or vesicles1 ly+ 9 or on ! plane ( ! surface ( ! organism1 & !re=e arrang$1 n 9 ! tetrah$ral =m ( ,callimitra1 b 9 ! mann] 9 :i* f\r contigu\s cells ly+ side by side normally set !mselves1 l ! f\r cells ( a segm5t+ egg3 t is to say ) an int]v5+ 8pol> furr[10 ^: ends m>k ! meet+ place1 at equal angles1 ( ! cells 9 gr\ps ( ?ree4 ,! little project+ spokes1 or spikes1 :i* are set normally to ! ma9 basket-"w1 seem to be incomplet$ portions ( a l>g] basket1 or 9 o!r words imp]fectly =m$ elem5ts correspond+ to ! int]facial contacts 9 ! surr\nd+ p>ts #dge ( ! sy/em4 ,simil> b m complex =mations1 all explicable z basket-l frameworks develop$ ar\nd a clu/] ( cells1 are kn[n 9 great v>iety4 ,9 our ,nassell>ian itself1 & 9 _m o!r cases :]e ! plane int]facial b\nd>y-walls are skeletonis$1 we see t ! silice\s matt] is n deposit$ 9 an ev5 & cont9u\s lay]1 l ! wax5 walls ( a bee's cell1 b con/itutes a me%work ( f9e curvil9e> ?reads2 & ! curves seem to run1 on ! :ole1 isogonally1 & to =m ?ree ma9 s]ies1 "o approximately p>allel to1 or conc5tric )1 ! out] or free edge ( ! p>tition1 & ! o!r two relat$ sev]ally to its two edges ( atta*m5t4 ,sometimes 7z may also be se5 9 our figure71 ! sy/em is /ill fur!r complicat$ by a f\r? s]ies ( l9e> elem5ts1 :i* t5d to run radially f ! c5tre ( ! sy/em to ! free edge ( ea* p>tition4 ,z reg>ds ! =m]1 _! arrangem5t is su* z w\ld result if deposition or solidification _h proce$$ 9 waves1 />t+ indep5d5tly f ea* ( ! ?ree b\nd>ies ( ! little p>tition-wall2 & some?+ ( ?is k9d is d\btless :at has happ5$4 ,we are rem9d$ at once ( ! wave-l p]iodicity ( ! ,liesegang ph5om5on4 ,b ap>t f ?is we might conceive ( o!r explanations4 ,= in/ance1 ! liquid film :i* orig9ally con/itutes ! p>tition mu/ easily be ?r[n into vibrations1 & 7l ! du/ ^u a ,*ladni's plate7 m9ute p>ticles ( matt] 9 contact ) ! film w\ld t5d to take up _! position 9 a symmetrical arrangem5t1 9 direct relation to ! nodal po9ts or l9es ( ! vibrat+ surface#dhe4 ,"s su* explanation z ?is 7to my ?9k+7 mu/ be invok$ to acc\nt = ! m9ute & v>i$ & v beautiful patt]ns ^u _m diatoms1 ! resemblance ( :i* patt]ns 79 c]ta9 ( _! simpl] cases7 to ! ,*ladni figures is sometimes /rik+ & obvi\s4 ,b ! _m special problems :i* ! diatom skeleton sugge/s ,i h n attempt$ to consid]4 ,illu/ration3 ,fig4 #bcj4 ,! la/ peculi>ity ( our ,nassell>ian lies 9 an app>5t dep>ture f :at we %\ld at fir/ expect 9 ! way ( its #dgf ext]nal symmetry4 ,7 ! sy/em actually compos$ ( f\r sph]ical vesicles 9 mutual contact1 ! out] m>g9 ( ea* ( ! six int]facial planes w\ld obvi\sly be a circul> arc2 & accord+ly1 at ea* angle ( ! tetrah$ron1 we %\ld expect to h a depress$1 or re-entrant angle1 in/ead ( a prom95t cusp4 ,?is is all d\btless due to "s simple balance ( t5sions1 ^: precise nature & di/ribution is mean:ile a matt] ( conjecture4 ,b x seems z ?\gh an extremely simple explanation w\ld g a long way1 & possibly ! :ole way1 to meet ?is p>ticul> case4 ,9 our ord9>y plane diagram ( ?ree cells1 or soap-bubbles1 9 contact1 we "k 7& we h j said7 t ! t5sions ( ! ?ree p>titions draw inw>ds ! out] walls ( ! sy/em1 till at ea* po9t ( triple contact 7,p7 we t5d to get a triradiate1 equiangul> junction4 ,b if we introduce ano!r bubble into ! c5tre ( ! sy/em 7,fig4 #bcj71 !n1 z ,plateau %ew$1 ! t5sions ( its walls & ^? ( ! ?ree p>titions by :i* x is n[ susp5d$1 aga9 balance "o ano!r1 & ! c5tral bubble appe>s 79 plane projection7 z a curvil9e>1 equilat]al triangle4 ,we h only got to conv]t ?is plane diagram into t ( a tetrah$ral solid to obta9 almo/ precisely ! configuration :i* we are seek+ to expla94 ,n[ we obs]ve t1 s f> z our figure ( ,callimitra in=ms u1 ?is is j ! %ape ( ! little bubble :i* occupies ! c5tre ( ! tetrah$ral sy/em 9 t ,radiol>ian skeleton4 ,& ,i conceive1 accord+ly1 t ! entire organism 0 n limit$ to ! f\r cells or vesicles 7toge!r ) ! little c5tral #dgg fif?7 :i* we h hi!rto be5 imag9+1 b !re mu/ h be5 an out] tetrah$ral sy/em1 enclos+ ! cells :i* fabricat$ ! skeleton1 j z ^! latt] enclos$1 & de=m$1 ! little bubble 9 ! c5tre ( all4 ,we h only to suppose t ?is hypo!tical tetrah$ral s]ies1 =m+ ! out] lay] or surface ( ! :ole sy/em1 0 = "s *emico-physical reason incapable ( secret+ at its int]facial contacts a skeletal fabric#dhf4 ,9 ?is hypo!tical case1 ! edges ( ! skeletal sy/em w\ld be circul> arcs1 meet+ "o ano!r at an angle ( #abj1 or1 9 ! solid pyramid1 ( #aji3 & ?is latt] is v ne>ly ! condition :i* our little skeleton actually displays4 ,b we obs]ve 9 ,fig4 #bbg t1 9 ! imm$iate neighb\rhood ( ! tetrah$ral angle1 ! circul> arcs are slightly drawn out into project+ cusps 7cf4 ,fig4 #bcj1 ,b74 ,!re is no ,s-%ap$ curvature ( ! tetrah$ral edges z a :ole1 b a v slight "o1 a v slight *ange ( curvature2 close to ! apex4 ,?is1 ,i conceive1 is no?+ m ?an :at1 9 a mat]ial sy/em1 we are b\nd to h1 to repres5t a 8surface ( cont9uity40 ,x is a ph5om5on precisely analog\s to ,plateau's 8b\rrelet10 :i* we h already se5 to be a con/ant feature ( all cellul> sy/ems1 r\nd+ (f ! %>p angul> contacts by :i* 79 our m elem5t>y treatm5t7 we expect "o film to make its junction ) ano!r#dhg4 ,9 ! =ego+ examples ( ,radiol>ia1 ! symmetry :i* ! organism displays w\ld seem to be id5tical ) t symmetry ( =ces :i* is due to ! assemblage ( surface-t5sions 9 ! :ole sy/em2 ?is symmetry be+ display$1 9 "o class ( cases1 9 a complex sph]ical mass ( fro?1 & 9 #dgh ano!r class 9 a simpl] aggregate ( a few1 o!rwise isolat$1 vesicles4 ,b among ! va/ numb] ( o!r kn[n ,radiol>ia1 !re are c]ta9 =ms 7especially among ! ,phaeod>ia & ,acan?>ia7 :i* display a /ill m rem>kable symmetry1 ! orig9 ( :i* is by no means cle>1 ?\gh surface-t5sion d\btless plays a "p 9 its causation4 ,^! are cases 9 :i* 7z 9 "s ( ^? already describ$7 ! skeleton consi/s 7#a7 ( radiat+ spicul> rods1 def9ite 9 numb] & position1 & 7#b7 ( int]connect+ rods or plates1 tang5tial to ! m or less sph]ical body ( ! organism1 ^: =m becomes1 accord+ly1 t ( a geometric1 polyh$ral solid4 ,x may be t !re is no ma!matical diff]5ce1 save "o ( degree1 betwe5 su* a hexagonal polyh$ron z we h se5 9 ,aulacan?a1 & ^? :i* we are ab\t to describe2 b ! great] regul>ity1 ! num]ical symmetry1 & ! app>5t simplicity ( ^! latt]1 makes ( !m a class ap>t1 & sugge/s problems :i* h n be5 solv$ nor ev5 inve/igat$4 ,illu/ration3 ,fig4 #bca4 ,skeletons ( v>i\s ,radiol>ians1 aft] ,haeckel4 #a4 ,circoporus sexfurcus2 #b4 ,c4 octah$rus2 #c4 ,circogonia icosah$ra2 #d4 ,circospa?is nov5a2 #e4 ,circorrhegma dodecah$ra4 ,! matt] is suffici5tly illu/rat$ by ! accompany+ figures1 all drawn f ,haeckel's ,monograph ( ! ,*all5g] ,radiol>ia#dhh4 ,9 "o ( ^! we see a regul> octah$ron1 9 ano!r a regul>1 or p5tagonal dodecah$ron1 9 a ?ird a regul> icosah$ron4 ,9 all cases ! figure appe>s to be p]fectly symmetrical1 ?\gh nei!r ! triangul> facets ( ! octah$ron & icosah$ron1 nor ! p5tagonal facets ( ! dodecah$ron1 are necess>ily plane surfaces4 ,9 all ( ^! cases1 ! radial spicules correspond to ! solid angles ( ! figure2 & !y are1 accord+ly1 six 9 numb] 9 ! octah$ron1 tw5ty 9 ! dodecah$ron1 & twelve 9 ! icosah$ron4 ,if we add to ^! ?ree figures ! regul> tetrah$ron1 :i* we h _h frequ5t occasion to /udy1 & ! cube 7:i* is repres5t$1 at lea/ 9 outl9e1 9 ! skeleton ( ! hexact9ellid sponges71 we h complet$ ! s]ies ( ! five regul> polyh$ra kn[n to geomet]s1 ! ,platonic bodies#dhi ( ! old] ma!maticians4 ,x is at fir/ sight all ! m rem>kable t we %\ld "h meet #dhj ) ! :ole five regul> polyh$ra1 :5 we rememb] t1 among ! va/ v>iety ( cry/all9e =ms kn[n among m9]als1 ! regul> dodecah$ron & icosah$ron1 simple z !y are f ! ma!matical po9t ( view1 nev] occur4 ,n only d ^! latt] nev] occur 9 ,cry/allography1 b 7z is expla9$ 9 text-books ( t sci5ce7 x has be5 %ewn t !y _c occur1 ow+ to ! fact t _! indices 7or numb]s express+ ! relation ( ! faces to ! ?ree prim>y axes7 involve an irrational quantity3 :]eas x is a fundam5tal law ( cry/allography1 involv$ 9 ! :ole !ory ( space-p>tition+1 t 8! indices ( any & e face ( a cry/al are small :ole numb]s#dij40 ,at ! same "t1 an imp]fect p5tagonal dodecah$ron1 ^: p5tagonal sides are non-equilat]al1 is common among cry/als4 ,if we may safely judge f ,haeckel's figures1 ! p5tagonal dodecah$ron ( ! ,radiol>ian is p]fectly regul>1 & we mu/ presume1 accord+ly1 t x is n br\ght ab\t by pr9ciples ( space-p>tition+ simil> to ^? :i* manife/ !mselves 9 ! ph5om5on ( cry/allisation4 ,x w be obs]v$ t 9 all ^! radiol>ian polyh$ral %ells1 ! surface ( ea* ext]nal facet is =m$ ( a m9ute hexagonal network1 ^: probable orig91 9 relation to a vesicul> /ructure1 is su* z we h already discuss$4 ,illu/ration3 ,fig4 #bcb4 ,dorataspis sp42 diagrammatic4 ,9 c]ta9 alli$ ,radiol>ia 7,fig4 #bcb71 :i*1 l ! dodecah$ral =m figur$ 9 ,fig4 #bca1 #e1 h tw5ty radial sp9es1 ^! latt] are commonly describ$ z be+ arrang$ 9 a c]ta9 v s+ul> way4 ,x is /at$ t _! arrangem5t may be ref]r$ #dha to a s]ies ( five p>allel circles on ! sph]e1 correspond+ to ! equator 7c71 ! tropics 7b1 d7 & ! pol> circles 7a1 e72 & t beg9n+ ) f\r equidi/ant sp9es 9 ! equator1 we h alt]nat+ :orls ( f\r1 radiat+ outw>ds f ! sph]e 9 ea* ( ! o!r p>allel zones4 ,?is rule 0 laid d[n by ! celebrat$ ,johannes ,mll]1 & has ev] s9ce be5 us$ & quot$ z ,mll]'s law4 ,! *ief po9t 9 ?is alleg$ arrangem5t :i* /rikes u at fir/ sight z v curi\s1 is t !re is said to be no sp9e at ei!r pole2 & :5 we come to exam9e c>efully ! figure ( ! organism1 we f9d t ! receiv$ description does n d ju/ice to ! facts4 ,we see1 9 ! fir/ place1 f su* figures z ,figs4 #bcb1 #bcd1 t "h1 unlike our =m] cases1 ! radial sp9es issue ?r\gh ! facets 7& ?r\gh all ! facets7 ( ! polyh$ron1 in/ead ( ?r\gh its solid angles2 & accord+ly1 t our tw5ty sp9es correspond 7n1 z be=e1 to a dodecah$ron7 b to "s sort ( an icosah$ron4 ,we see 9 ! next place1 t ?is icosah$ron is compos$ ( faces1 or plates1 ( two diff]5t k9ds1 "s hexagonal & "s p5tagonal2 & :5 we look clos]1 we discov] t ! :ole figure is t ( a hexagonal prism1 ^: twelve solid angles are replac$ by p5tagonal facets4 ,bo? hexagons & p5tagons #dhb appe> to be p]fectly equilat]al1 b if we try to con/ruct a plane-sid$ polyh$ron ( ?is k9d1 we soon f9d t x is impossible2 = into ! angles betwe5 ! six equatorial hexagons ^? ( ! six unit$ p5tagons w n fit4 ,! figure h[ev] c be easily con/ruct$ if we replace ! /raight edges 7or "s ( !m7 by curves1 & ! plane facets by correspond+1 slightly curv$1 surfaces4 ,! true symmetry ( ?is figure1 !n1 is hexagonal1 ) a pol> axis1 produc$ into two pol> spicules2 ) six equatorial spicules1 or rays2 & ) two sets ( six spicul> rays1 int]pos$ betwe5 ! pol> axis & ! equatorial rays1 & alt]nat+ 9 position ) ! latt]4 ,mll]'s description 0 em5d$ by ,br&t1 & :at is n[ kn[n z 8,br&t's law10 viz4 t ! symmetry consi/s ( two pol> rays1 & ?ree :orls ( six ea*1 co9cides ) ! above description s f> z ! spicul> axes g3 save only t ,br&t specifically /ates t ! int]m$iate :orls /& equidi/ant betwe5 ! equator & ! poles1 i4e4 9 latitude #de4 ,:ile n f> f ! tru?1 ?is /atem5t is n exact2 = accord+ to ! geometry ( ! figure1 ! int]m$iate cycles obvi\sly /& 9 a slightly high] latitude1 b ?is latitude ,i h n attempt$ to det]m9e2 = ! calculation seems to be a little tr\blesome ow+ to ! curvature ( ! sides ( ! figure1 & ! enquir+ ma!matician w p]=m x m easily ?an ,i4 ,br&t1 if ,i und]/& him rightly1 did n propose 8 8law0 z a sub/itute = ,mll]'s law1 b z a second law applicable to a few p>ticul> cases4 ,i on ! o!r h& c f9d no case to :i* ,mll]'s law prop]ly applies4 ,if we con/ruct su* a polyh$ron1 & set x 9 ! position ( ,fig4 #bcb1 ,b1 we %all easily see t x is capable ( explanation 7?\gh improp]ly7 9 accordance ) ,mll]'s law2 = ! f\r equatorial rays ( ,mll] 7c7 n[ correspond to ! two pol> & to two opposite equatorial facets ( our polyh$ron3 ! f\r 8pol>0 rays ( ,mll] 7a or e7 correspond to two adjac5t hexagons & two int]m$iate p5tagons ( ! figure3 & ,mll]'s 8tropical0 rays 7b or d7 are ^? :i* emanate f ! rema9+ f\r p5tagonal facets1 9 ea* half ( ! figure4 ,9 "s cases1 su* z ,haeckel's ,phatnaspis cri/ata 7,fig4 #bcc71 we h an ellipsoidal body1 f :i* ! sp9es em]ge 9 ! ord] describ$1 b :i* is n obvi\sly divid$ by facets4 ,9 ,fig4 #bcd ,i h indicat$ ! facets correspond+ to ! rays1 & divid+ ! surface 9 ! usual symmetrical way4 #dhc ,illu/ration3 ,fig4 #bcc4 ,phatnaspis cri/ata1 ,hkl4 ,illu/ration3 ,fig4 #bcd4 ,! same1 diagrammatic4 #dhd ,)9 any polyh$ron we may always inscribe ano!r polyh$ron1 ^: corn]s correspond 9 numb] to ! sides or facets ( ! orig9al figure1 or 79 alt]native cases7 to a c]ta9 numb] ( ^! sides2 & a simil> result is obta9$ by bevell+ (f ! corn]s ( ! orig9al polyh$ron4 ,we may obta9 a precisely simil> symmetrical result if 79 su* a case z ^! ,radiol>ians :i* we are describ+71 we imag9e ! radial sp9es to be int]connect$ by tang5tial rods1 in/ead ( by ! complete facets :i* we h j be5 deal+ )4 ,9 our complicat$ polyh$ron ) its tw5ty radial sp9es arrang$ 9 ! mann] describ$ !re are v>i\s symmetrical ways 9 :i* we may imag9e ^! int]connect+ b>s to be arrang$4 ,! mo/ symmetrical ( ^! is "o 9 :i* ! :ole surface is divid$ into eighte5 rhomboidal areas1 obta9$ by sy/ematically connect+ ea* gr\p ( f\r adjac5t radii4 ,?is figure has eighte5 faces 7,f71 tw5ty corn]s 7,c71 & !re=e ?irty-six edges 7,e71 9 con=mity ) ,eul]'s !orem1 ,f ,c ,e #b4 ,illu/ration3 ,fig4 #bce4 ,phractaspis prototypus1 ,hkl4 ,ano!r symmetrical arrangem5t w divide ! surface into f\rte5 rhombs & eight triangles4 ,?is latt] arrangem5t is obta9$ by l9k+ up ! radial rods z foll[s3 aaaa1 aba1 abcb1 bcdc1 etc4 ,"h we h aga9 tw5ty corn]s1 b we h tw5ty-two faces2 ! numb] ( edges1 or tang5tial spicul> b>s1 w be f\nd1 !re=e1 by ! above =mula1 to be =ty4 ,9 ,haeckel's figure ( ,phractaspis prototypus we h a spicul> skeleton :i* appe>s to be con/ruct$ precisely ^u ?is plan1 & to be d]ivable f ! facet$ polyh$ron precisely aft] ?is mann]4 ,9 all ^! latt] cases x is ! arrangem5t ( ! axial rods1 or 9 o!r words ! 8pol> symmetry0 ( ! entire organism1 :i* lies at ! root ( ! matt]1 & :i*1 if only #dhe we c\ld acc\nt = x1 w\ld make x comp>atively easy to expla9 ! sup]ficial configuration4 ,b !re are no obvi\s me*anical =ces by :i* we c s expla9 ?is peculi> pol>ity4 ,?is at lea/ is evid5t1 t x arises 9 ! c5tral mass ( protoplasm1 :i* is ! ess5tial liv+ portion ( ! organism z di/+ui%$ f t fro?y p]iph]al mass ^: /ructure has help$ u to expla9 s _m ph5om5a ( ! sup]ficial or ext]nal skeleton4 ,to say t ! arrangem5t dep5ds ^u a specific pol>isation ( ! cell is m]ely to ref] ! problem to o!r t]ms1 & to set x aside = future solution4 ,b x is possible t we may le>n some?+ ab\t ! l9es 9 :i* to seek = su* a solution by consid]+ ! case ( ,lehmann's 8fluid cry/als10 & ! light :i* !y ?r[ ^u ! ph5om5a ( molecul> aggregation4 ,! ph5om5on ( 8fluid cry/allisation0 is f\nd 9 a numb] ( *emical bodies2 x is exhibit$ at a specific temp]ature = ea* sub/ance2 & x w\ld seem to be limit$ to bodies 9 :i* !re is a m or less elongat$1 or 8*a9-l0 arrangem5t ( ! atoms 9 ! molecule4 ,su* bodies1 at ! appropriate temp]ature1 t5d to aggregate !mselves into masses1 :i* are sometimes sph]ical drops or globules 7! s-call$ 8sph]ulites071 & sometimes h ! def9ite =m ( ne$le-l or prismatic cry/als4 ,9 ei!r case !y rema9 liquid1 & are also d\bly refractive1 pol>is+ light 9 brilliant col\rs4 ,toge!r ) !m are =m$ ord9>y solid cry/als1 also ) *>act]i/ic pol>isation1 & into su* solid cry/als all ! fluid mat]ial ultimately turns4 ,x is evid5t t 9 ^! liquid cry/als1 ?\gh ! molecules are freely mobile1 j z are ^? ( wat]1 !y are yet subject to1 or end[$ )1 a 8directive =ce10 a =ce :i* conf]s ^u !m a def9ite configuration or 8pol>ity10 ! ,ge/altungskraft ( ,lehmann4 ,su* an hypo!sis z ?is _h be5 gradually extrud$ f ! !ories ( ma!matical cry/allography#dia2 & x _h come to be believ$ t ! symmetrical con=mation ( a homog5e\s cry/all9e /ructure 0 suffici5tly expla9$ by ! m]e me*anical fitt+ toge!r ( appropriate /ructural units along ! easie/ & simple/ l9es ( 8close pack+03 j z #dhf a pile ( oranges becomes def9ite1 bo? 9 outw>d =m & inw>d /ructural arrangem5t1 )\t ! play ( any specific directive =ce4 ,b :ile our conceptions ( ! tactical arrangem5t ( cry/all9e molecules rema9 ! same z be=e1 & our hypo!ses ( 8modes ( pack+0 or ( 8space-lattices0 rema9 z useful z ev] = ! def9ition & explanation ( ! molecul> arrangem5ts1 an entirely new !oretical conception is introduc$ :5 we f9d su* space-lattices ma9ta9$ 9 :at has hi!rto be5 consid]$ ! molecul> fre$om ( a liquid field2 & we are con/ra9$1 accord+ly1 to po/ulate a specific molecul> =ce1 or 8,ge/altungskraft0 7n unlike ,kepl]'s 8facultas =matrix071 to acc\nt = ! ph5om5on4 ,n[ j z "s sort ( specific 8,ge/altungskraft0 _h be5 ( old ! deus ex ma*9a acc\nt+ = all cry/all9e ph5om5a 7gn>a totius geometri1 et 9 ea ex]cita1 z ,kepl] said71 & z su* an hypo!sis1 aft] be+ de?ron$ & repudiat$1 has n[ f\ght its way back & has made good its "r to be he>d1 s x may be also 9 biology4 ,we beg9 by an easy & g5]al assumption ( specific prop]ties1 by :i* ea* organism assumes its own specific =m2 we le>n lat] 7z x is ! purpose ( ?is book to %ew7 t ?r\gh\t ! :ole range ( organic morphology !re are innum]able ph5om5a ( =m :i* are n peculi> to liv+ ?+s1 b :i* are m or less simple manife/ations ( ord9>y physical law4 ,b e n[ & !n we come to c]ta9 deep-seat$ signs ( protoplasmic symmetry or pol>isation1 :i* seem to lie beyond ! rea* ( ! ord9>y physical =ces4 ,x by no means foll[s t ! =ces 9 "q are n ess5tially physical =ces1 m obscure & less famili> to u ?an ! re/2 & ?is w\ld seem to be ! crucial lesson = u to draw f ,lehmann's surpris+ & mo/ beautiful discov]y4 ,= ,lehmann seems actually to h demon/rat$1 9 non-liv+1 *emical bodies1 ! exi/5ce ( j su* a det]m9ant1 j su* a 8,ge/altungskraft10 z w\ld be ( inf9ite help to u if we might po/ulate x = ! explanation 7= in/ance7 ( our ,radiol>ian's axial symmetry4 ,b fur!r ?an ?is we _c g2 = su* analogy z we seem to see 9 ! ,lehmann ph5om5on soon evades u1 & refuses to be press$ home4 ,n only is x ! case1 z we h already #dhg se51 t c]ta9 ( ! geometric =ms assum$ by ! symmetrical ,radiol>ian %ells are j su* z ! 8space-lattice0 !ory w\ld seem to be inapplicable to1 b x is 9 o!r ways obvi\s t symmetry ( cry/allisation1 :e!r liquid or solid1 has no close p>allel1 b only a s]ies ( analogies1 9 ! protoplasmic symmetry ( ! liv+ cell4 #dhh ,,*apt] ,x ,a ,,p>5!tic ,,note ,,on ,,geodetics ,we h made use 9 ! la/ *apt] ( ! ma!matical pr9ciple ( ,geodetics 7or ,geodesics7 9 ord] to expla9 ! con=mation ( a c]ta9 class ( sponge-spicules2 b ! pr9ciple is ( mu* wid] application 9 morphology1 & w\ld seem to des]ve att5tion :i* x has n yet receiv$4 ,illu/ration3 ,fig4 #bcf4 ,annul> & spiral ?ick5+s 9 ! walls ( plant-cells4 ,def9+1 mean:ile1 our geodetic l9e 7z we h already done7 z ! %orte/ di/ance betwe5 two po9ts on ! surface ( a solid ( revolution1 we f9d t ! geodetics ( ! cyl9d] give u "o ( ! simple/ ( cases4 ,"h x is pla9 t ! geodetics are ( ?ree k9ds3 7#a7 a s]ies ( annuli ar\nd ! cyl9d]1 t is to say1 a sy/em ( circles1 9 planes p>allel to "o ano!r & at "r angles to ! axis ( ! cyl9d] 7,fig4 #bcf1 a72 7#b7 a s]ies ( /raight l9es p>allel to ! axis2 & 7#c7 a s]ies ( spiral curves w9d+ r\nd ! wall ( ! cyl9d] 7b1 c74 ,^! ?ree sy/ems are all ( frequ5t occurr5ce1 & are all illu/rat$ 9 ! local ?ick5+s ( ! wall ( ! cyl9drical cells or vessels ( plants4 ,! spiral1 or r helicoid1 geodetic is p>ticul>ly common 9 cyl9drical /ructures1 & is beautifully %ewn = in/ance 9 ! spiral coil :i* /iff5s ! tra*eal tubes ( an insect1 or ! s-call$ 8tra*eides0 ( a woody /em4 ,a simil> #dhi ph5om5on is (t5 witness$ 9 ! splitt+ ( a glass tube4 ,if a crack appe> 9 a ?9 tube1 su* z a te/-tube1 x has a t5d5cy to be prolong$ 9 its own direction1 & ! m p]fectly homog5e\s & isotropic be ! glass ! m ev5ly w ! split t5d to foll[ ! /raight c\rse 9 :i* x began4 ,z a result1 ! crack 9 our te/-tube is (t5 se5 to cont9ue till ! tube is split into a cont9u\s spiral ribbon4 ,9 a "r cone1 ! spiral geodetic falls into clos] & clos] coils z ! diamet] ( ! cone n>r[s2 & a v beautiful geodetic ( ?is k9d is exemplifi$ 9 ! sutural l9e ( a spiral %ell1 su* z ,turritella1 or 9 ! /riations :i* run p>allel ) ! spiral suture4 ,simil>ly1 9 an ellipsoidal surface1 we h a spiral geodetic1 ^: coils get clos] toge!r z we approa* ! ends ( ! long axis ( ! ellipse2 9 ! splitt+ ( ! integum5t ( an ,equisetum-spore1 by :i* are =m$ ! spiral 8elat]s0 ( ! spore1 we h a case ( ?is k9d1 ?\gh ! spiral is n suffici5tly prolong$ to %ew all its features 9 detail4 ,we h se5 9 ^! v>i\s cases1 t our orig9al def9ition ( a geodetic requires to be modifi$2 = x is only subject to conditions t x is 8! %orte/ di/ance betwe5 two po9ts on ! surface ( ! solid10 & "o ( ! commone/ ( ^! re/rict+ conditions is t our geodetic may be con/ra9$ to g twice1 or _m times1 r\nd ! surface on its way4 ,9 %ort1 we mu/ r$ef9e our geodetic1 z a curve drawn ^u a surface1 su* t1 if we take any two adjac5t po9ts on ! curve1 ! curve gives ! %orte/ di/ance betwe5 !m4 ,aga91 9 ! geodetic sy/ems :i* we meet ) 9 morphology1 x sometimes happ5s t we h two opposite sy/ems ( geodetic spirals sep>ate & di/9ct f "o ano!r1 z 9 ,fig4 #bcf1 c2 & x is also common to f9d ! two sy/ems int]f]+ ) "o ano!r1 & =m+ a criss-cross1 or reticulat$ arrangem5t4 ,?is is a v common s\rce ( reticulat$ patt]ns4 ,among ! ciliat$ ,infusoria1 we h 9 ! spiral l9es along :i* _! cilia are arrang$ a great v>iety ( beautiful geodetic curves2 ?\gh x is probable en\gh t 9 "s complicat$ cases ^! are n simple geodetics1 b projections ( curves o!r ?an a /raight l9e ^u ! surface ( ! solid4 #dij ,la/ly1 a v in/ructive case is furni%$ by ! arrangem5t ( ! muscul> fibres on ! surface ( a holl[ organ1 su* z ! he>t or ! /oma*4 ,"h we may consid] ! ph5om5on f ! po9t ( view ( me*anical effici5cy1 z well z f t ( purely descriptive or objective anatomy4 ,9 fact we h an a priori "r to expect t ! muscul> fibres cov]+ su* holl[ or tubul> organs w co9cide ) geodetic l9es1 9 ! s5se 9 :i* we are n[ us+ ! t]m4 ,= if we imag9e a contractile fibre1 or ela/ic b&1 to be fix$ by its two ends ^u a curv$ surface1 x is obvi\s t its fir/ ef=t ( contraction w t5d to exp5d itself 9 accommodat+ ! b& to ! =m ( ! surface1 9 8/ret*+ x tight10 or 9 o!r words 9 caus+ x to assume a direction :i* is ! %orte/ possible l9e ^u ! surface betwe5 ! two extremes3 & x is only !n t fur!r contraction w h ! effect ( con/rict+ ! tube & s ex]cis+ pressure on its cont5ts4 ,?us ! muscul> fibres1 z !y w9d ov] ! curv$ surface ( an organ1 arrange !mselves automatically 9 geodesic curves3 9 precisely ! same mann] z we also automatically con/ruct complex sy/ems ( geodesics :5ev] we w9d a ball ( wool or a sp9dle ( t[1 or :5 ! skilful surgeon b&ages a limb4 ,9 ^! latt] cases we see ! production ( ^? 8figures-(-eight10 to :i*1 9 ! case = in/ance ( ! he>t-muscles1 ,pettigrew & o!r anatomi/s h ascrib$ peculi> importance4 ,9 ! case ( bo? he>t & /oma* we mu/ look ^u ^! organs z develop$ f a simple cyl9drical tube1 aft] ! fa%ion ( ! glass-bl[]1 z is fur!r discuss$ on p4 #gcg ( ?is book1 ! modification ( ! simple cyl9d] consi/+ ( v>i\s degrees ( dilatation & ( twi/+4 ,9 ! primitive undi/ort$ cyl9d]1 z 9 an art]y or 9 ! inte/9e1 ! muscul> fibres run 9 geodetic l9es1 :i* z a rule are n spiral1 b are m]ely ei!r annul> or longitud9al2 ^! are ! ord9>y 8circul> & longitud9al coats10 :i* =m ! normal musculature ( all tubul> organs1 or ( ! body-wall ( a cyl9drical worm#dib4 ,if we consid] ea* muscul> fibre z an ela/ic /r&1 imb$d$ 9 ! ela/ic membrane :i* con/itutes ! wall ( ! organ1 x #dia is evid5t t1 :atev] be ! di/ortion suff]$ by ! entire organ1 ! individual fibre w foll[ ! same c\rse1 :i* w /ill1 9 a s5se1 be a geodetic4 ,b if ! di/ortion be consid]able1 z = in/ance if ! tube become b5t ^u itself1 or if at "s po9t its walls bulge outw>ds 9 a div]ticulum or p\*1 x is obvi\s t ! old sy/em ( geodetics w only m>k ! %orte/ di/ance betwe5 two po9ts m or less approximate to "o ano!r1 & t new sy/ems ( geodetics w t5d to appe>1 peculi> to ! new surface1 & l9k+ up po9ts m remote f "o ano!r4 ,?is is evid5tly ! case 9 ! human /oma*4 ,we /ill h ! sy/ems1 or _! unoblit]at$ rema9s1 ( circul> & longitud9al muscles2 b we also see two new sy/ems ( fibres1 bo? obvi\sly geodetic 7or r1 :5 we look m closely1 bo? p>ts ( "o & ! same geodetic sy/em71 9 ! =m ( annuli encircl+ ! p\* or div]ticulum at ! c>diac end ( ! /oma*1 & ( oblique fibres tak+ a spiral c\rse f ! neighb\rhood ( ! oesophagus ov] ! sides ( ! organ4 ,9 ! he>t we h a simil>1 b m complicat$ ph5om5on4 ,its musculature consi/s1 9 great "p1 ( ! orig9al simple sy/em ( circul> & longitud9al muscles :i* envelop$ ! orig9al art]ial tubes1 :i* tubes1 aft] a process ( local ?ick5+1 expansion1 & especially twi/+1 came toge!r to con/itute ! composite1 or d\ble1 mammalian he>t2 & ^! sy/ems ( muscul> fibres1 geodetic to beg9 )1 rema9 geodetic 79 ! s5se 9 :i* we are us+ ! ^w7 aft] all ! twi/+ to :i* ! primitive cyl9drical tube or tubes h be5 subject$4 ,t is to say1 ^! fibres /ill run _! %orte/ possible c\rse1 f />t to f9i%1 ov] ! complicat$ curv$ surface ( ! organ2 & x is only because !y d s t _! contraction1 or longitud9al %ort5+1 is able to produce its direct effect1 z ,borelli well und]/ood1 9 ! contraction or sy/ole ( ! he>t#dic4 #dib ,z a p>5!tic coroll>y to ! case ( ! spiral patt]n ^u ! wall ( a cyl9drical cell1 we may consid] = a mom5t ! spiral l9e :i* _m small organisms t5d to foll[ 9 _! pa? ( locomotion#did4 ,! helicoid spiral1 trac$ ar\nd ! wall ( our cyl9d]1 may be expla9$ z a composition ( two velocities1 "o a uni=m velocity 9 ! direction ( ! axis ( ! cyl9d]1 ! o!r a uni=m velocity 9 a circle p]p5dicul> to ! axis4 ,9 a some:at analog\s fa%ion1 ! small] ciliat$ organisms1 su* z ! ciliate & flagellate ,infusoria1 ! ,rotif]s1 ! sw>m-spores ( v>i\s ,proti/s1 & s =?1 h a t5d5cy to comb9e a direct ) a revolv+ pa? 9 _! ord9>y locomotion4 ,! means ( locomotion :i* !y possess 9 _! cilia are at be/ some:at primitive & ineffici5t2 !y h no app>5t means ( /e]+1 or modify+ _! direction2 &1 if _! c\rse t5d$ to sw]ve ev] s little to "o side1 ! result w\ld be to br+ !m r\nd & r\nd aga9 9 an approximately circul> pa? 7su* z a man a/ray on ! prairie is said to foll[71 ) little or no progress 9 a def9ite longitud9al direction4 ,b z a matt] ( fact1 ei!r ?r\gh ! direct action ( _! cilia or by reason ( a m or less unsymmetrical =m ( ! body1 all ^! creatures t5d m or less to rotate ab\t _! long axis :ile !y swim4 ,& ?is axial rotation1 j z 9 ! case ( a rifle-bullet1 causes _! natural sw]ve1 :i* is always 9 ! same direction z reg>ds _! own bodies1 to be 9 a cont9ually *ang+ direction z reg>ds space3 9 %ort1 to make a spiral c\rse ar\nd1 & m or less approximate to1 a /raight axial l9e4 #dic ,,*apt] ,,xi ,,! ,,log>i?mic ,,spiral ,! v num]\s examples ( spiral con=mation :i* we meet ) 9 our /udies ( organic =m are peculi>ly adapt$ to ma!matical me?ods ( inve/igation4 ,b ere we beg9 to /udy !m1 we mu/ take c>e to def9e our t]ms1 & we _h bett] also attempt "s r\gh prelim9>y classification ( ! objects ) :i* we %all h to deal4 ,9 g5]al t]ms1 a ,spiral ,curve is a l9e :i*1 />t+ f a po9t ( orig91 cont9ually dim9i%es 9 curvature z x rec$es f t po9t2 or1 9 o!r words1 ^: radius ( curvature cont9ually increases4 ,?is def9ition is wide en\gh to include a numb] ( diff]5t curves1 b on ! o!r h& x excludes at lea/ "o :i* 9 popul> spee* we are apt to confuse ) a true spiral4 ,?is latt] curve is ! simple ,screw1 or cyl9drical ,helix1 :i* curve1 z is v evid5t1 nei!r />ts f a def9ite orig91 nor v>ies 9 its curvature z x proce$s4 ,! 8spiral0 ?ick5+ ( a woody plant-cell1 ! 8spiral0 ?read )9 an insect's tra*eal tube1 or ! 8spiral0 twi/ & tw9e ( a climb+ /em are n1 ma!matically speak+1 spirals at all1 b screws or helices4 ,!y belong to a di/9ct1 ?\gh by no means v remote1 family ( curves4 ,"s ( ^! helical =ms we h j n[ treat$ (1 briefly & p>5!tically1 "u ! subject ( ,geodetics4 ,illu/ration3 ,fig4 #bcg4 ,! %ell ( ,nautilus pompilius1 f a radiograph3 to %ew ! log>i?mic spiral ( ! %ell1 toge!r ) ! arrangem5t ( ! int]nal septa4 7,f ,messrs ,gre5 & ,g>d9]1 9 ,proc4 ,malacol4 ,soc4 ,,ii1 #ahig47 ,( true organic spirals we h no lack#die4 ,we ?9k at once ( ! beautiful spiral curves ( ! horns ( rum9ants1 & ( ! /ill m v>i$1 if n m beautiful1 spirals ( molluscan %ells4 ,closely relat$ spirals may be trac$ 9 ! arrangem5t #did ( ! florets 9 ! sunfl[]2 a true spiral1 ?\gh n1 by ! way1 s easy ( inve/igation1 is pres5t$ to u by ! outl9e ( a cordate leaf2 & yet aga91 we c recognise typical ?\gh transitory spirals 9 ! coil ( an elephant's trunk1 9 ! 8circl+ #die spires0 ( a snake1 9 ! coils ( a cuttle-fi%'s arm1 or ( a monkey's or a *ameleon's tail4 ,among su* =ms z ^!1 & ! _m o!rs :i* we might easily add to !m1 x is obvi\s t we h to d ) ?+s :i*1 ?\gh ma!matically simil>1 are biologically speak+ fundam5tally diff]5t4 ,& n only are !y biologically remote1 b !y are also physically diff]5t1 9 reg>d to ! nature ( ! =ces to :i* !y are sev]ally due4 ,= 9 ! fir/ place1 ! spiral coil ( ! elephant's trunk or ( ! *ameleon's tail is1 z we h said1 b a transitory configuration1 & is pla9ly ! result ( c]ta9 muscul> =ces act+ ^u a /ructure ( a def9ite1 & normally an ess5tially diff]5t1 =m4 ,x is r a position1 or an attitude1 ?an a =m1 9 ! s5se 9 :i* we h be5 us+ ?is latt] t]m2 &1 unlike mo/ ( ! =ms :i* we h be5 /udy+1 x has little or no direct relation to ! ph5om5on ( ,gr[?4 ,illu/ration3 ,fig4 #bch4 ,a ,=am9if]al %ell 7,globig]9a74 ,aga91 !re is a manife/ & n unimportant diff]5ce betwe5 su* a spiral con=mation z is built up by ! sep>ate & successive florets 9 ! sunfl[]1 & t :i*1 9 ! snail or ,nautilus %ell1 is app>5tly a s+le & indivisible unit4 ,& a simil>1 if n id5tical diff]5ce is app>5t betwe5 ! ,nautilus %ell & ! m9ute %ells ( ! ,=am9if]a1 :i* s closely simulate x2 inasmu* z ! spiral %ells ( ^! latt] are ess5tially composite /ructures1 comb9$ out ( successive & sep>ate *amb]s1 :ile ! molluscan %ell1 ?\gh x may 7z 9 ,nautilus7 become second>ily subdivid$1 has gr[n z "o cont9u\s tube4 ,x foll[s f all ?is t !re _c #dif possibly be a physical or dynamical1 ?\gh !re may well be a ma!matical ,law ( ,gr[?1 :i* is common to1 & :i* def9es1 ! spiral =m 9 ! ,nautilus1 9 ! ,globig]9a1 9 ! ram's horn1 & 9 ! disc ( ! sunfl[]4 ,( ! spiral =ms :i* we h n[ m5tion$1 e "o 7) ! s+le exception ( ! outl9e ( ! cordate leaf7 is an example ( ! rem>kable curve kn[n z ! ,log>i?mic ,spiral4 ,b be=e we ent] ^u ! ma!matics ( ! log>i?mic spiral1 let u c>efully obs]ve t ! :ole ( ! organic =ms 9 :i* x is cle>ly & p]man5tly exhibit$1 h[ev] diff]5t !y may be f "o ano!r 9 outw>d appe>ance1 9 nature & 9 orig91 nev]!less all belong1 9 a c]ta9 s5se1 to "o p>ticul> class ( con=mations4 ,9 ! great majority ( cases1 :5 we consid] an organism 9 "p or :ole1 :5 we look 7= in/ance7 at our own h& or foot1 or contemplate an insect or a worm1 we h no reason 7or v little7 to consid] "o "p ( ! exi/+ /ructure z old] ?an ano!r2 ?r\gh & ?r\gh1 ! new] p>ticles h be5 m]g$ & comm+l$1 by intussusception1 among ! old2 ! :ole outl9e1 su* z x is1 is due to =ces :i* = ! mo/ "p are /ill at "w to %ape x1 & :i* 9 %ap+ x h %ap$ x z a :ole4 ,b ! horn1 or ! snail-%ell1 is curi\sly diff]5t2 = 9 ea* ( ^!1 ! pres5tly exi/+ /ructure is1 s to speak1 p>tly old & p>tly new2 x has be5 con=m$ by successive & cont9u\s increm5ts2 & ea* successive /age ( gr[?1 />t+ f ! orig91 rema9s z an integral & un*ang+ portion ( ! /ill gr[+ /ructure1 & s cont9ues to repres5t :at at "s e>li] epo* con/itut$ = ! "t be+ ! /ructure 9 its entirety4 ,9 a slightly diff]5t1 b closely cognate way1 ! same is true ( ! spirally arrang$ florets ( ! sunfl[]4 ,= "h aga9 we are reg>d+ s]ially arrang$ portions ( a composite /ructure1 :i* portions1 simil> to "o ano!r 9 =m1 diff] 9 age2 & !y diff] also 9 magnitude 9 a /rict ratio accord+ to _! age4 ,someh[ or o!r1 9 ! log>i?mic spiral ! "t-elem5t always ent]s 92 & to ?is important fact1 full ( curi\s biological z well z ma!matical significance1 we %all aft]w>ds return4 #dig ,x is1 z we h s (t5 se51 an ess5tial "p ( our :ole problem1 to try to und]/& :at di/ribution ( =ces is capable ( produc+ ?is or t organic =m1--to give1 9 %ort1 a dynamical expression to our descriptive morphology4 ,n[ ! g5]al di/ribution ( =ces :i* lead to ! =mation ( a spiral 7:e!r log>i?mic or o!r7 is v easily und]/ood2 & ne$ n c>ry u beyond ! use ( v elem5t>y ma!matics4 ,illu/ration3 ,fig4 #bci4 ,if we imag9e gr[? to act 9 a p]p5dicul> direction1 z = example ! upw>d =ce ( gr[? 9 a gr[+ /em 7,,oa71 !n1 9 ! abs5ce ( o!r =ces1 elongation w z a matt] ( c\rse proce$ 9 an un*ang+ direction1 t is to say ! /em w gr[ /raight upw>ds4 ,suppose n[ t !re be "s con/ant ext]nal =ce1 su* z ! w9d1 imp++ on ! gr[+ /em2 & suppose 7= simplicity's sake7 t ?is ext]nal =ce be 9 a con/ant direction 7,,ab7 p]p5dicul> to ! intr9sic =ce ( gr[?4 ,! direction ( actual gr[? w be 9 ! l9e ( ! resultant ( ! two =ces3 &1 s9ce ! ext]nal =ce is 7by hypo!sis7 con/ant 9 direction1 :ile ! int]nal =ce t5ds always to act 9 ! l9e ( actual gr[?1 x is obvi\s t our gr[+ organism w t5d to be b5t into a curve1 to :i*1 = ! "t be+1 #dih ! actual =ce ( gr[? w be act+ at a tang5t4 ,s long z ! two =ces cont9ue to act1 ! curve w approa*1 b w nev] atta91 ! direction ( ,,ab1 p]p5dicul> to ! orig9al direction ,,oa4 ,if ! ext]nal =ce be con/ant 9 am\nt ! curve w approximate to ! =m ( a hyp]bola2 &1 at any rate1 x is obvi\s t x w nev] t5d to assume a spiral =m4 ,9 l mann]1 if we consid] a horizontal beam1 fix$ at "o end1 ! imposition ( a weight at ! o!r w b5d ! beam into a curve1 :i*1 z ! beam elongates or ! weight increases1 w br+ ! weight$ end ne>] & ne>] to ! v]tical4 ,b su* a =ce1 con/ant 9 direction1 w obvi\sly nev] curve ! beam into a spiral1--a fact s pat5t & obvi\s t x w\ld be sup]flu\s to /ate x1 7 x n t "s naturali/s h be5 9 ! habit ( invok+ gravity z ! =ce to :i* may be attribut$ ! spiral flexure ( ! %ell4 ,b if1 on ! o!r h&1 ! deflect+ =ce be inh]5t 9 ! gr[+ body1 or s connect$ ) x 9 a sy/em t its direction 7in/ead ( be+ con/ant1 z 9 ! =m] case7 *anges ) ! direction ( gr[?1 & is p]p5dicul> 7or incl9$ at "s con/ant angle7 to ?is *ang+ direction ( ! gr[+ =ce1 !n x is pla9 t !re is no su* limit to ! deflection f ! normal1 b ! gr[+ curve w t5d to w9d r\nd & r\nd its po9t ( orig94 ,9 ! typical case ( ! snail-%ell1 su* an intr9sic =ce is manife/ly pres5t 9 ! action ( ! columell> muscle4 ,_m o!r simple illu/rations c be giv5 ( a spiral c\rse be+ impress$ ^u :at is prim>ily rectil9e> motion1 by any /eady deflect+ =ce :i* ! mov+ body c>ries1 s to speak1 along ) x1 & :i* cont9ually gives a lop-sid$ t5d5cy to its =w>d movem5t4 ,= in/ance1 we h be5 told t a man or a horse1 travell+ ov] a great prairie1 is v apt to f9d himself1 aft] a long day's j\rney1 back aga9 ne> to 8 />t+ po9t4 ,"h "s small & imp]ceptible bias1 su* z might = in/ance be caus$ by "o leg be+ 9 a m9ute degree long] or /rong] ?an ! o!r1 has /eadily deflect$ ! =w>d movem5t to "o side2 & has gradually br\ght ! travell] back1 p]haps 9 a circle to ! v po9t f :i* he set out1 #dii or else by a spiral curve1 some:]e )9 rea* & recognition ( x4 ,illu/ration3 ,fig4 #bdj4 ,we come to a simil> result :5 we consid]1 = in/ance1 a cyl9drical body 9 :i* =ces ( gr[? are at "w t5d+ to its elongation1 b ^! =ces are unsymmetrically di/ribut$4 ,let ! t5d5cy to elongation along ,,ab be ( a magnitude proportional to ,,bb1 & t along ,,cd be ( a magnitude proportional to ,,dd2 & 9 ea* elem5t p>allel to ,,ab & ,,cd1 let a p>allel =ce ( gr[?1 proportionately int]m$iate 9 magnitude1 be at "w3 & let ,,eff be ! middle l9e4 ,!n at any cross-section ,,bfd1 if we d$uct ! mean =ce ,,ff1 we h a c]ta9 positive =ce at ,b1 equal to ,bb1 & an equal & opposite =ce at ,d1 equal to ,dd4 ,b ,,ab & ,,cd are n sep>ate /ructures1 b are connect$ toge!r1 ei!r by a solid core1 or by ! walls ( a tubul> %ell2 & ! =ces :i* t5d to sep>ate ,b & ,d are oppos$1 accord+ly1 by a t5sion 9 ,,bd4 ,x foll[s !re=e1 t !re w be a resultant =ce ,,bg1 act+ 9 a direction int]m$iate betwe5 ,bb & ,,bd1 & also a resultant1 ,,dh1 act+ at ,d 9 an opposite direction2 & accord+ly1 aft] a small increm5t ( gr[?1 ! gr[+ end ( ! cyl9d] w come to lie1 n 9 ! direction ,,bd1 b 9 ! direction ,,gh4 ,! problem is !re=e analog\s to t ( a beam to :i* we apply a b5d+ mom5t2 & x is pla9 t ! unequal =ce ( gr[? is equival5t to a 8c\ple0 :i* w imp>t to our /ructure a curv$ =m4 ,=1 if we reg>d ! "p ,,abdc z practically rigid1 & ! "p ,,bb,d,d z pliable1 ?is c\ple #ejj w t5d to turn /rips su* z ,b,d ab\t an axis p]p5dicul> to ! plane ( ! diagram1 & pass+ ?r\gh an int]m$iate po9t ,f4 ,x is pla91 also1 s9ce all ! =ces "u consid]ation are intr9sic to ! sy/em1 t ?is t5d5cy w be cont9u\s1 & t z gr[? proce$s ! curv+ body w assume ei!r a circul> or a spiral =m4 ,b ! t5sion :i* we h "h assum$ to exi/ 9 ! direction ,,bd w obvi\sly disappe> if we suppose a suffici5tly rapid rate ( gr[? 9 t direction4 ,= if we may reg>d ! m\? ( our tubul> %ell z p]fectly ext5sible 9 its own plane1 s t x ex]ts no traction :atsoev] on ! sides1 !n x w be drawn out into m & m elongat$ ellipses1 =m+ ! m & m oblique orifices ( a /raight tube4 ,9 o!r words1 9 su* a /ructure z we h presuppos$1 ! exi/5ce or ma9t5ance ( a con/ant ratio betwe5 ! rates ( ext5sion or gr[? 9 ! v]tical & transv]se directions w lead1 9 g5]al1 to ! developm5t ( a log>i?mic spiral2 ! magnitude ( t ratio w det]m9e ! "* 7t is to say1 ! con/ant angle7 ( ! spiral2 & ! spirals s produc$ w include1 z special or limit+ cases1 ! circle & ! /raight l9e4 ,illu/ration3 ,fig4 #bda4 ,illu/ration3 ,fig4 #bdb4 ,we may disp5se ) ! hypo!sis ( b5d+ mom5ts1 if we simply presuppose t ! increm5ts ( gr[? take place at a con/ant angle to ! gr[+ surface 7z ,,ab71 b m rapidly at ,a 7:i* we %all call ! 8out] edge07 ?an at ,b1 & t ?is diff]5ce ( velocity ma9ta9s a con/ant ratio4 ,let u also assume t ! :ole /ructure is rigid1 ! new accretions solidify+ z soon z !y are laid on4 ,= example1 #eja let ,fig4 #bdb repres5t 9 section ! e>ly gr[? ( a ,nautilus-%ell1 & let ! "p ,,arb repres5t ! e>lie/ /age ( all1 :i* 9 ,nautilus is ne>ly semicircul>4 ,we h to f9d a law gov]n+ ! gr[? ( ! %ell1 su* t ea* edge %all develop into an equiangul> spiral2 & ?is law1 accord+ly1 mu/ be ! same = ea* edge1 namely t at ea* in/ant ! direction ( gr[? makes a con/ant angle ) a l9e drawn f a fix$ po9t 7call$ ! pole ( ! spiral7 to ! po9t at :i* gr[? is tak+ place4 ,?is gr[?1 we n[ f9d1 may be consid]$ z effect$ by ! cont9u\s addition ( simil> quadrilat]als4 ,?us1 9 ,fig4 #bda1 ,,a$b is a quadrilat]al ) ,,ae1 ,,db p>allel1 & ) ! angle ,,eab ( a c]ta9 def9ite magnitude1 4 ,let ,,ab & ,,ed meet1 :5 produc$1 9 ,c2 & call ! angle ,,ace 7or x,cy7 4 ,make ! angle y,cz angle x,cy1 4 ,draw ,,eg1 s t ! angle y,e,g 1 meet+ ,cz 9 ,g2 & draw ,,df p>allel to ,,eg4 ,x is !n easy to %[ t ,,a$b & ,,egfd are simil> quadrilat]als4 ,&1 :5 we consid] ! quadrilat]al ,,a$b z hav+ inf9itesimal sides1 ,,ae & ,,bd1 ! angle t5ds to 1 ! con/ant angle ( an equiangul> spiral :i* passes ?r\gh ! po9ts ,,aeg1 & ( a simil> spiral :i* passes ?r\gh ! po9ts ,,bdf2 & ! po9t ,c is ! pole ( bo? ( ^! spirals4 ,9 a p>ticul> limit+ case1 :5 our quadrilat]als are all equal z well z simil>1--:i* w be ! case :5 ! angle 7or ! angles ,,eac1 etc47 is a #ejb "r angle1--! 8spiral0 curve w be a circul> arc1 ,c be+ ! c5tre ( ! circle4 ,ano!r1 & a v simple illu/ration may be drawn f ! 8cymose infloresc5ces0 ( ! botani/s1 ?\gh ! actual mode ( developm5t ( "s ( ^! /ructures is op5 to dispute1 & _! nom5clature is involv$ 9 extraord9>y hi/orical confusion#dif4 ,illu/ration3 ,fig4 #bdc4 ,a1 a helicoid1 ,b1 a scorpioid cyme4 ,9 ,fig4 #bdc;,b 7:i* repres5ts ! ,cic9nus ( ,s*imp]1 or cyme unip>e scorpioide ( ,bravais1 z se5 9 ! ,borage71 we beg9 ) a prim>y %oot f :i* is giv5 (f1 at a c]ta9 def9ite angle1 a second>y %oot3 & f t 9 turn1 on ! same side & at ! same angle1 ano!r %oot1 & s on4 ,! deflection1 or curvature1 is cont9u\s & progressive1 = x is caus$ by no ext]nal =ce b only by causes intr9sic 9 ! sy/em4 ,& ! :ole sy/em is symmetrical3 ! angles at :i* ! successive %oots are giv5 (f be+ all equal1 & ! l5g?s ( ! %oots dim9i%+ 9 con/ant ratio4 ,! result is t ! successive %oots1 or successive increm5ts ( gr[?1 are tang5ts to a curve1 & ?is curve is a true log>i?mic spiral4 ,b :ile1 9 ?is simple case1 ! successive %oots are depict$ z ly+ 9 a plane1 x may also happ5 t1 9 addition to _! successive angul> div]g5ce f "o ano!r )9 t plane1 !y also t5d to div]ge by successive equal angles f t plane ( ref]5ce2 & by ?is means1 !re w be sup]pos$ ^u ! log>i?mic spiral a helicoid twi/ or screw4 ,&1 9 ! p>ticul> case :]e ?is latt] angle ( div]g5ce is j equal to #ahj1 or two "r angles1 ! successive %oots w once m come to lie 9 a plane1 b !y w appe> to come (f f "o ano!r on alt]nate sides1 z 9 ,fig4 #bdc ,a4 ,?is is ! ,s*raubel or ,bo/ryx ( ,s*imp]1 ! cyme unip>e hlicoide ( ,bravais4 ,! log>i?mic spiral is /ill lat5t 9 x1 z 9 ! o!r2 b is conceal$ f view by ! de=mation result+ f ! helicoid4 ,! confusion ( nom5clature w\ld seem to h aris5 f ! fact t _m botani/s did n recognise 7z ! bro!rs ,bravais did7 ! ma!matical significance ( ! latt] case2 b 7 l$1 by ! snail-l spiral ( ! scorpioid cyme1 to transf] ! "n 8helicoid0 to x4 ,9 ! /udy ( su* curves z ^!1 !n1 we speak ( ! po9t ( orig9 z ! pole 7,o72 a /raight l9e hav+ its extremity 9 ! pole & revolv+ ab\t x1 is call$ ! radius vector2 #ejc & a po9t 7,p7 :i* is conceiv$ z travell+ along ! radius vector "u def9ite conditions ( velocity1 w !n describe our spiral curve4 ,( sev]al ma!matical curves ^: =m & developm5t may be s conceiv$1 ! two mo/ important 7& ! only two ) :i* we ne$ deal71 are ^? :i* are kn[n z 7#a7 ! equable spiral1 or spiral ( ,ar*im$es1 & 7#b7 ! log>i?mic1 or equiangul> spiral4 ,illu/ration3 ,fig4 #bdd4 ,! =m] may be illu/rat$ by ! spiral coil 9 :i* a sailor coils a rope ^u ! deck2 z ! rope is ( uni=m ?ickness1 s 9 ! :ole spiral coil is ea* :orl ( ! same bread? z t :i* prec$es & z t :i* foll[s x4 ,us+ its anci5t def9ition1 we may def9e x by say+1 t 8,if a /raight l9e revolve uni=mly ab\t its extremity1 a po9t :i* likewise travels uni=mly along x w describe ! equable spiral#dig40 ,or1 putt+ ! same ?+ into our m mod]n words1 8,if1 :ile ! radius vector revolve uni=mly ab\t ! pole1 a po9t 7,p7 travel ) uni=m velocity along x1 ! curve describ$ w be t call$ ! equable spiral1 or spiral ( ,ar*im$es40 #ejd ,x is pla9 t ! spiral ( ,ar*im$es may be comp>$ to a cyl9d] coil$ up4 ,& x is pla9 also t a radius 7r ,,op71 made up ( ! successive & equal :orls1 w increase 9 ari?metical progression3 & w equal a c]ta9 con/ant quantity 7a7 multipli$ by ! :ole numb] ( :orls1 or 7m /rictly speak+7 multipli$ by ! :ole angle 77 ?r\gh :i* x has revolv$3 s t r a4 ,b1 9 contra/ to ?is1 9 ! log>i?mic spiral ( ! ,nautilus or ! snail-%ell1 ! :orls gradually increase 9 bread?1 & d s 9 a /eady & un*ang+ ratio4 ,our def9ition is z foll[s3 8,if1 in/ead ( travell+ ) a uni=m velocity1 our po9t move along ! radius vector ) a velocity increas+ z its di/ance f ! pole1 !n ! pa? describ$ is call$ a log>i?mic spiral40 ,ea* :orl :i* ! radius vector int]sects w be broad] ?an its pr$ecessor 9 a def9ite ratio2 ! radius vector w increase 9 l5g? 9 geometrical progression1 z x sweeps ?r\gh successive equal angles2 & ! equation to ! spiral w be r a4 ,z ! spiral ( ,ar*im$es1 9 our example ( ! coil$ rope1 might be look$ ^u z a coil$ cyl9d]1 s may ! log>i?mic spiral1 9 ! case ( ! %ell1 be pictur$ z a cone coil$ ^u itself4 ,n[ x is obvi\s t if ! :orls increase v sl[ly inde$1 ! log>i?mic spiral w come to look l a spiral ( ,ar*im$es1 ) :i* h[ev] x nev] becomes id5tical2 = x is incorrect to say1 z is sometimes done1 t ! ,ar*im$ean spiral is a 8limit+ case0 ( ! log>i?mic spiral4 ,! ,nummulite is a case 9 po9t4 ,"h we h a l>ge numb] ( :orls1 v n>r[1 v close toge!r1 & app>5tly ( equal bread?1 :i* give rise to an appe>ance simil> to t ( our coil$ rope4 ,&1 9 a case ( ?is k9d1 we might actually f9d t ! :orls 7 ( equal bread?1 be+ produc$ 7z is app>5tly ! case 9 ! ,nummulite7 n by any v sl[ & gradual gr[? 9 ?ickness ( a cont9u\s tube1 b by a succession ( simil> cells or *amb]s laid on1 r\nd & r\nd1 det]m9$ z to _! size by con/ant surface-t5sion conditions & !re=e ( unv>y+ dim5sions4 ,b ev5 9 ?is case we %\ld h no ,ar*im$ean spiral1 b only a log>i?mic spiral 9 :i* ! con/ant angle approximat$ to #ij4 #eje ,=1 9 ! log>i?mic spiral1 :5 t5ds to #ij1 ! expression r a cot t5ds to r a7#a cot 72 :ile ! equation to ! ,ar*im$ean spiral is r b4 ,! nummulite mu/ always h a c5tral core1 or initial cell1 ar\nd :i* ! coil is n only wrapp$1 b out ( :i* x spr+s2 & ?is initial *amb] corresponds to our a 9 ! expression r a a cot 4 ,! out] :orls resemble ^? ( an ,ar*im$ean spiral1 because ( ! o!r t]m a cot 9 ! same expression4 ,x foll[s f ?is t 9 all su* cases ! :orls mu/ be ( excessively small bread?4 ,!re are _m o!r specific prop]ties ( ! log>i?mic spiral1 s int]relat$ to "o ano!r t we may *oose pretty well any "o ( !m z ! basis ( our def9ition1 & d$uce ! o!rs f x ei!r by analytical me?ods or by ! me?ods ( elem5t>y geometry4 ,= in/ance1 ! equation r a may be writt5 9 ! =m log r log a1 or 7log r7_/7log a71 or 7s9ce a is a con/ant71 k log r4 ,:i* is z mu* z to say t ! vector angles ab\t ! pole are proportional to ! log>i?ms ( ! successive radii2 f :i* circum/ance ! "n ( ! 8log>i?mic spiral0 is d]iv$4 ,illu/ration3 ,fig4 #bde4 ,let u next reg>d our log>i?mic spiral f ! dynamical po9t ( view1 z :5 we consid] ! =ces conc]n$ 9 ! gr[? ( a mat]ial1 concrete spiral4 ,9 a gr[+ /ructure1 let ! =ces ( gr[? ex]t$ at any po9t ,p be a =ce ,f act+ along ! l9e jo9+ ,p to a pole ,o & a =ce ,t act+ 9 a direction p]p5dicul> to ,,op2 & let ! magnitude ( ^! =ces be 9 ! same con/ant ratio at all po9ts4 ,x foll[s t ! resultant ( ! =ces ,f & ,t 7z ,,pq7 makes a con/ant angle ) ! radius vector4 ,b ! con/ancy ( ! angle betwe5 tang5t & radius vector at any po9t is a fundam5tal prop]ty ( ! log>i?mic spiral1 & may be %ewn to foll[ f our def9ition ( ! curve3 x gives to ! curve its alt]native "n ( equiangul> spiral4 ,h5ce 9 a /ructure gr[+ "u ! above conditions ! =m ( ! b\nd>y w be a log>i?mic spiral4 #ejf ,illu/ration3 ,fig4 #bdf4 ,9 su* a spiral1 radial gr[? & gr[? 9 ! direction ( ! curve be> a con/ant ratio to "o ano!r4 ,=1 if we consid] a consecutive radius vector1 ,,op1 ^: increm5t z comp>$ ) ,,op is dr1 :ile ds is ! small arc ,,pp1 !n dr_/ds cos con/ant4 ,illu/ration3 ,fig4 #bdg4 ,9 ! concrete case ( ! %ell1 ! di/ribution ( =ces w be1 orig9ally1 a little m complicat$ ?an ?is1 ?\gh by resolv+ ! =ces 9 "q1 ! sy/em may be r$uc$ to ?is simple =m4 ,& fur!rmore1 ! actual di/ribution ( =ces w n always be id5tical2 = example1 !re is a di/9ct diff]5ce betwe5 ! cases 7z 9 ! snail7 :]e a columell> muscle ex]ts a def9ite traction 9 ! direction ( ! pole1 & ^? 7su* z ,nautilus7 :]e !re is no columell> muscle1 & :]e "s o!r =ce mu/ be discov]$1 or po/ulat$1 to acc\nt = ! flexure4 ,9 ! mo/ frequ5t case1 we h1 z 9 ,fig4 #bdg1 ?ree =ces to deal )1 act+ at a po9t1 p3 ,l1 act+ 9 ! direction ( ! tang5t to ! curve1 & repres5t+ ! =ce ( longitud9al gr[?2 ,t1 p]p5dicul> to ,l1 & repres5t+ ! organism's t5d5cy to gr[ 9 bread?2 & ,p1 ! traction ex]cis$1 9 ! direction ( ! pole1 by ! columell> muscle4 ,let u resolve ,l & ,t into compon5ts along ,p 7namely ,a1 ,b71 & p]p5dicul> to ,p 7namely ,a1 ,b72 we h n[ only two =ces to consid]1 viz4 ,p ,a ,b1 & ,a ,b4 ,& ^! two latt] we c aga9 resolve1 if we please1 s z to deal only ) =ces 9 ! direction ( ,p & ,t4 ,n[1 ! ratio ( ^! =ces rema9+ con/ant1 ! locus ( ! po9t p is an equiangul> spiral4 #ejg ,fur!rmore we see h[ any slight *ange 9 any "o ( ! =ces ,p1 ,t1 ,l w t5d to modify ! angle 1 & produce a slight dep>ture f ! absolute regul>ity ( ! log>i?mic spiral4 ,su* slight dep>tures f ! absolute simplicity & uni=mity ( ! !oretic law we %all n be surpris$ to f9d1 m or less frequ5tly1 9 ,nature1 9 ! complex sy/em ( =ces pres5t$ by ! liv+ organism4 ,9 ! gr[? ( a %ell1 we c conceive no simpl] law ?an ?is1 namely1 t x %all wid5 & l5g!n 9 ! same unv>y+ proportions3 & ?is simple/ ( laws is t :i* ,nature t5ds to foll[4 ,! %ell1 l ! creature )9 x1 gr[s 9 size b does n *ange its %ape2 & ! exi/5ce ( ?is con/ant relativity ( gr[?1 or con/ant simil>ity ( =m1 is ( ! ess5ce1 & may be made ! basis ( a def9ition1 ( ! log>i?mic spiral4 ,su* a def9ition1 ?\gh n commonly us$ by ma!maticians1 has be5 occasionally employ$2 & x is "o f :i* ! o!r prop]ties ( ! curve c be d$uc$ ) great ease & simplicity4 ,9 ma!matical language x w\ld run z foll[s3 8,any plane curve proce$+ f a fix$ po9t 7:i* is call$ ! pole71 & su* t ! arc int]cept$ betwe5 ?is po9t & any o!r :atsoev] on ! curve is always simil> to itself1 is call$ an equiangul>1 or log>i?mic1 spiral#dih40 ,9 ?is def9ition1 we h :at is probably ! mo/ fundam5tal & 8intr9sic0 prop]ty ( ! curve1 namely ! prop]ty ( cont9ual simil>ity3 & ?is is inde$ ! v prop]ty by reason ( :i* x is peculi>ly associat$ ) organic gr[? 9 su* /ructures z ! horn or ! %ell1 or ! scorpioid cyme :i* is describ$ on p4 #ejb4 ,= x is peculi>ly *>act]i/ic ( ! spiral ( a %ell1 = in/ance1 t 7"u all normal circum/ances7 x does n alt] its %ape z x gr[s2 ea* increm5t is geometrically simil> to its pr$ecessor1 & ! :ole1 at any epo*1 is simil> to :at con/itut$ ! :ole at ano!r & an e>li] epo*4 ,we feel no surprise :5 ! animal :i* secretes ! %ell1 or any o!r animal :atsoev]1 gr[s by su* #ejh symmetrical expansion z to pres]ve its =m un*ang$2 ?\gh ev5 !re1 z we h already se51 ! un*ang+ =m d5otes a nice balance betwe5 ! rates ( gr[? 9 v>i\s directions1 :i* is b seldom accurately ma9ta9$ = long4 ,b ! %ell reta9s its un*ang+ =m 9 spite ( its asymmetrical gr[?2 x gr[s at "o end only1 & s does ! horn4 ,& ?is rem>kable prop]ty ( increas+ by t]m9al gr[?1 b nev]!less reta9+ un*ang$ ! =m ( ! entire figure1 is *>act]i/ic ( ! log>i?mic spiral1 & ( no o!r ma!matical curve4 ,illu/ration3 ,fig4 #bdh4 ,we may at once illu/rate ?is curi\s ph5om5on by draw+ ! outl9e ( a little ,nautilus %ell )9 a big "o4 ,we "k1 or we may see at once1 t !y are ( precisely ! same %ape2 s t1 if we look at ! little %ell ?r\gh a magnify+ glass1 x becomes id5tical ) ! big "o4 ,b we "k1 on ! o!r h&1 t ! little ,nautilus %ell gr[s into ! big "o1 n by uni=m gr[? or magnification 9 all directions1 z is 7?\gh only approximately7 ! case :5 ! boy gr[s into ! man1 b by gr[+ at "o end only4 ,?\gh ( all curves1 ?is prop]ty ( cont9u$ simil>ity is f\nd only 9 ! log>i?mic spiral1 !re are v _m rectil9e> figures 9 :i* x may be obs]v$4 ,= in/ance1 z we may easily see1 x holds good ( any "r cone2 = evid5tly1 9 ,fig4 #bdh1 ! little inn] cone 7repres5t$ 9 its triangul> section7 may become id5tical ) ! l>g] "o ei!r by magnification all r\nd 7z 9 a71 or simply by an increm5t at "o end 7z 9 b72 inde$1 9 ! case ( ! cone1 we h yet a ?ird possibility1 = ! same result is atta9$ :5 x increases all r\nd1 save only at ! base1 t is to say :5 ! triangul> section increases #eji on two ( its sides1 z 9 c4 ,all ?is is closely associat$ ) ! fact1 :i* we h already not$1 t ! ,nautilus %ell is b a cone roll$ up2 9 o!r words1 ! cone is b a p>ticul> v>iety1 or 8limit+ case10 ( ! spiral %ell4 ,?is prop]ty1 :i* we s easily recognise 9 ! cone1 w\ld seem to h engag$ ! p>ticul> att5tion ( ! mo/ anci5t ma!maticians ev5 f ! days ( ,py?agoras1 & s1 ) little d\bt1 f ! m anci5t days ( t ,egyptian s*ool :5ce he d]iv$ ! f\ndations ( 8 le>n+#dii2 & its be>+ on our biological problem ( ! %ell1 ?\gh app>5tly indirect1 is yet s close t x des]ves our fur!r consid]ation4 ,illu/ration3 ,fig4 #bdi4 ,illu/ration3 ,fig4 #bej4 ,if1 z 9 ,fig4 #bdi1 we add to two sides ( a squ>e a symmetrical ,l-%ap$ portion1 simil> 9 %ape to :at we call a 8c>p5t]'s squ>e10 ! result+ figure is /ill a squ>e2 & ! portion :i* we h add$ is call$1 by ,ari/otle 7,phys4 ,,iii1 #d71 a 8gnomon40 ,euclid ext5ds ! t]m to include ! case ( any p>allelogram#ejj1 :e!r rectangul> or n 7,fig4 #bej72 & ,h]o ( ,alex&ria specifically def9es a 8gnomon0 7z inde$ ,ari/otle implicitly def9es x71 z any figure :i*1 be+ add$ to any figure :atsoev]1 leaves ! resultant figure simil> to ! orig9al4 ,includ$ 9 ?is important def9ition is ! case ( numb]s1 consid]$ geometrically2 t is to say1 ! 1 :i* c be translat$ into =m1 by means ( r[s ( dots or o!r signs 7cf4 ,ari/4 ,metaph4 #ajib b #ab71 or 9 ! patt]n ( a til$ floor3 all accord+ to 8! my/ical way ( #eaj ,py?agoras1 & ! secret magick ( numb]s40 ,?us = example1 ! odd numb]s are 8gnomonic numb]s10 because #j #a #ab1 #ab #c #bb1 #bb #e #cb1 #cb #g #db etc41 :i* relation we may illu/rate graphically by ! successive numb]s ( dots :i* keep ! annex$ figure a p]fect squ>e#eja3 z foll[s3 ,illu/ration3 ,fig4 #bea4 ,illu/ration3 ,fig4 #beb4 ,!re are o!r gnomonic figures m curi\s /ill4 ,= in/ance1 if we make a rectangle 7,fig4 #bea7 su* t ! two sides are 9 ! ratio ( #a 3 #b1 x is obvi\s t1 on d\bl+ x1 we obta9 a precisely simil> figure2 = #a 3 #b 33 #b 3 #b2 & #eaa ea* half ( ! figure1 accord+ly1 is n[ a gnomon to ! o!r4 ,ano!r elegant example is :5 we />t ) a rectangle 7,a7 ^: sides are 9 ! proportion ( #a 3 7#e #a71 or1 approximately1 #a 3 #jfah4 ,! gnomon to ?is figure is a squ>e 7,b7 erect$ on its long] side1 & s on successively 7,fig4 #beb74 ,illu/ration3 ,fig4 #bec4 ,illu/ration3 ,fig4 #bed4 ,9 any triangle1 z ,ari/otle tells u1 "o "p is always a gnomon to ! o!r "p4 ,= in/ance1 9 ! triangle ,,abc 7,fig4 #bec71 let u draw ,,cd1 s z to make ! angle ,,bcd equal to ! angle ,a4 ,!n ! "p ,,bcd is a triangle simil> to ! :ole triangle ,,abc1 & ,,adc is a gnomon to ,,bcd4 ,a v elegant case is :5 ! orig9al triangle ,,abc is an isosceles triangle hav+ "o angle ( #cf1 & ! o!r two angles1 !re=e1 ea* equal to #gb 7,fig4 #bed74 ,!n1 by bisect+ "o ( ! angles ( ! base1 we subdivide ! l>ge isosceles triangle into two isosceles triangles1 ( :i* "o is simil> to ! :ole figure & ! o!r is its gnomon#ejb4 ,!re is good reason to believe t ?is triangle 0 especially /udi$ by ! ,py?agoreans2 = x lies at ! root ( _m int]e/+ geometrical con/ructions1 su* z ! regul> p5tagon1 & ! my/ical 8p5talpha10 & a :ole range ( o!r curi\s figures belov$ ( ! anci5t ma!maticians#ejc4 #eab ,illu/ration3 ,fig4 #bee4 ,if we take any "o ( ^! figures1 = in/ance ! isosceles triangle :i* we h j describ$1 & add to x 7or subtract f x7 9 succession a s]ies ( gnomons1 s conv]t+ x into l>g] & l>g] 7or small] & small]7 triangles all simil> to ! fir/1 we f9d t ! apices 7or o!r correspond+ po9ts7 ( all ^! triangles h _! locus ^u a log>i?mic spiral3 a result :i* foll[s directly f t alt]native def9ition ( ! log>i?mic spiral :i* ,i h quot$ f ,:itwor? 7p4 #ejg74 ,illu/ration3 ,fig4 #bef4 ,log>i?mic spiral d]iv$ f correspond+ po9ts 9 a sy/em ( squ>es4 ,aga91 we may build up a s]ies ( "r-angl$ triangles1 ea* ( :i* is a gnomon to ! prec$+ figure2 & "h aga91 a log>i?mic spiral is ! locus ( correspond+ po9ts 9 ^! successive triangles4 ,& la/ly1 :5soev] we fill up space ) a #eac collection ( ei!r equal or simil> figures1 simil>ly situat$1 z 9 ,figs4 #bef1 #beg1 !re we c always discov] a s]ies ( inscrib$ or escrib$ log>i?mic spirals4 ,illu/ration3 ,fig4 #beg4 ,! same 9 a sy/em ( hexagons4 ,once m1 !n1 we may modify our def9ition1 & say t3 8,any plane curve proce$+ f a fix$ po9t 7or pole71 & su* t ! vectorial area ( any sector is always a gnomon to ! :ole prec$+ figure1 is call$ an equiangul>1 or log>i?mic1 spiral40 ,& we may n[ introduce ?is new concept & nom5clature into our description ( ! ,nautilus %ell & o!r relat$ organic =ms1 by say+ t3 7#a7 if a gr[+ /ructure be built up ( successive p>ts1 simil> & simil>ly situat$1 we c always trace ?r\gh correspond+ po9ts a s]ies ( log>i?mic spirals 7,figs4 #beh1 #bei1 etc472 7#b7 x is *>act]i/ic ( ! gr[? ( ! horn1 ( ! %ell1 & ( all o!r organic =ms 9 :i* a log>i?mic spiral c be recognis$1 t ea* successive increm5t ( gr[? is a gnomon to ! entire pre-exi/+ /ructure4 ,& conv]sely 7#c7 x foll[s obvi\sly1 t 9 ! log>i?mic spiral outl9e ( ! %ell or ( ! horn we c always inscribe an endless v>iety ( o!r gnomonic figures1 hav+ no necess>y relation1 save z a #ead ma!matical accid5t1 to ! nature or mode ( developm5t ( ! actual /ructure#ejd4 #eae ,illu/ration3 ,fig4 #beh4 ,a %ell ( ,haliotis1 ) two ( ! _m l9es ( gr[?1 or g5]at+ curves1 m>k$ out 9 black3 ! areas b\nd$ by ^! l9es ( gr[? be+ 9 all cases 8gnomons0 to ! pre-exi/+ %ell4 ,illu/ration3 ,fig4 #bei4 ,a spiral =am9if] 7,pulv9ul9a71 to %[ h[ ea* successive *amb] cont9ues ! symmetry (1 or con/itutes a gnomon to1 ! re/ ( ! /ructure4 ,illu/ration3 ,fig4 #bfj4 ,ano!r spiral =am9if]1 ,cri/ell>ia4 ,( ^! ?ree propositions1 ! second is ( v great use & advantage = our easy und]/&+ & simple description ( ! molluscan %ell1 & ( a great v>iety ( o!r /ructures ^: mode ( gr[? is analog\s1 & ^: ma!matical prop]ties are !re=e id5tical4 ,we see at once t ! successive *amb]s ( a spiral ,nautilus 7,fig4 #bcg7 or ( a /raight ,or?oc]as 7,fig4 #cjj71 ea* :orl or "p ( a :orl ( a p]iw9kle or o!r ga/ropod 7,fig4 #beh71 ea* new increm5t ( ! op]culum ( a ga/ropod 7,fig4 #bfc71 ea* additional increm5t ( an elephant's tusk1 or ea* new *amb] ( a spiral =am9if] 7,figs4 #bei & #bfj71 has its lead+ *>act]i/ic at once describ$ & its =m s f> expla9$ by ! simple /atem5t t x con/itutes a gnomon to ! :ole previ\sly exi/+ /ructure4 ,& h]e9 lies ! explanation ( t 8"t-elem5t0 9 ! developm5t ( organic spirals ( :i* we h spok5 already1 9 a prelim9>y & empirical way4 ,= x foll[s z a simple coroll>y to ?is !orem ( gnomons t we mu/ n expect to f9d ! log>i?mic spiral manife/$ 9 a /ructure ^: p>ts are simultane\sly produc$1 z = in/ance 9 ! m>g9 ( a leaf1 or among ! _m curves t make ! cont\r ( a fi%4 ,b we mu/ r look = x :]ev] ! organism reta9s = u1 & /ill pres5ts to u at a s+le view1 ! successive phases ( prec$+ gr[?1 ! successive magnitudes atta9$1 ! successive outl9es occupi$1 z ! organism or a "p !re( pursu$ ! ev5 t5\r ( its gr[?1 ye> by ye> & day by day4 ,& x easily foll[s f ?is1 t x is 9 ! h>d p>ts ( organisms1 & n ! s(t1 fle%y1 actively gr[+ p>ts1 t ?is spiral is commonly & *>act]i/ically f\nd2 n 9 ! fre% mobile tissues ^: =m is con/ra9$ m]ely by ! active =ces ( ! mom5t2 b 9 ?+s l %ell & tusk1 & horn & claw1 :]e ! object is visibly compos$ ( p>ts #eaf successively1 & p]man5tly1 laid d[n4 ,9 ! ma91 ! log>i?mic spiral is *>act]i/ic1 n ( ! liv+ tissues1 b ( ! dead4 ,& = ! same reason1 x w always or ne>ly always be accompani$1 & adorn$1 by a patt]n =m$ ( 8l9es ( gr[?10 ! la/+ record ( e>li] & successive /ages ( =m & magnitude4 ,x is evid5t t ! spiral curve ( ! %ell is1 9 a s5se1 a vector diagram ( its own gr[?2 = x %ews at ea* in/ant ( "t1 ! direction1 radial & tang5tial1 ( gr[?1 & ! un*ang+ ratio ( velocities 9 ^! directions4 ,reg>d+ ! actual velocity ( gr[? 9 ! %ell1 we "k v little 7or practically no?+71 by way ( exp]im5tal measurem5t2 b if we make a c]ta9 simple assumption1 !n we may g a good deal fur!r 9 our description ( ! log>i?mic spiral z x appe>s 9 ?is concrete case4 ,let u make ! assumption t simil> increm5ts are add$ to ! %ell 9 equal times2 t is to say1 t ! am\nt ( gr[? 9 unit "t is measur$ by ! areas subt5d$ by equal angles4 ,?us1 9 ! out] :orl ( a spiral %ell a def9ite area m>k$ out by ridges1 tub]cles1 etc41 has v diff]5t l9e> dim5sions to ! correspond+ areas ( ! inn] :orl1 b ! symmetry ( ! figure implies t x subt5ds an equal angle ) ^!2 & x is reasonable to suppose t ! successive regions1 m>k$ out 9 ?is way by successive natural b\nd>ies or patt]ns1 are produc$ 9 equal int]vals ( "t4 ,if ?is be s1 ! radii measur$ f ! pole to ! b\nd>y ( ! %ell w 9 ea* case be proportional to ! velocity ( gr[? at ?is po9t ^u ! circumf]5ce1 & at ! "t :5 x correspond$ ) ! out] lip1 or region ( active gr[?2 & :ile ! direction ( ! radius vector corresponds ) ! direction ( gr[? 9 ?ickness ( ! animal1 s does ! tang5t to ! curve correspond ) ! direction1 = ! "t be+1 ( ! animal's gr[? 9 l5g?4 ,! successive radii are a measure ( ! accel]ation ( gr[?1 & ! spiral curve ( ! %ell itself is no o!r ?an ! hodograph ( ! gr[? ( ! conta9$ organism4 #eag ,s f> z we h n[ gone1 we h /udi$ ! elem5t>y prop]ties ( ! log>i?mic spiral1 includ+ its fundam5tal prop]ty ( cont9u$ simil>ity2 & we h accord+ly le>n$ t ! %ell or ! horn t5ds necess>ily to assume ! =m ( ?is ma!matical figure1 because 9 ^! /ructures gr[? proce$s by successive increm5ts1 :i* are always simil> 9 =m1 simil>ly situat$1 & ( con/ant relative magnitude "o to ano!r4 ,our *ief objects 9 enquir+ fur!r into ! ma!matical prop]ties ( ! log>i?mic spiral w be3 7#a7 to f9d means ( confirm+ & v]ify+ ! fact t ! %ell 7or o!r organic curve7 is actually a log>i?mic spiral2 7#b7 to le>n h[1 by ! prop]ties ( ! curve1 we may fur!r ext5d our k or simplify our descriptions ( ! %ell2 & 7#c7 to und]/& ! factors by :i* ! *>act]i/ic =m ( any p>ticul> log>i?mic spiral is det]m9$1 & s to compreh5d ! nature ( ! specific or g5]ic *>act]s by :i* "o spiral %ell is f\nd to diff] f ano!r4 ,( ! elem5t>y prop]ties ( ! log>i?mic spiral1 s f> z we h n[ enum]at$ !m1 ! foll[+ are ^? :i* we may mo/ easily inve/igate 9 ! concrete case1 su* z we h to d ) 9 ! molluscan %ell3 7#a7 t ! pol> radii ( po9ts ^: vectorial angles are 9 ari?metical progression1 are !mselves 9 geometrical progression2 & 7#b7 t ! tang5t at any po9t ( a log>i?mic spiral makes a con/ant angle 7call$ ! angle ( ! spiral7 ) ! pol> radius vector4 ,illu/ration3 ,fig4 #bfa4 ,! =m] ( ^! two propositions may be writt5 9 :at is1 p]haps1 a simpl] =m1 z foll[s3 radii :i* =m equal angles ab\t ! pole ( ! log>i?mic spiral1 are !mselves cont9u$ proportionals4 ,t is to say1 9 ,fig4 #bfa1 :5 ! angle ,,roq is equal to ! angle ,,qop1 !n ,,or 3 ,,oq 33 ,,oq 3 ,,op4 ,a p>ticul> case ( ?is proposition is :5 ! equal angles are ea* angles ( #cfj3 t is to say :5 9 ea* case ! radius vector makes a complete revolution1 & :51 !re=e ,p1 ,q & ,r all lie ^u ! same radius4 #eah ,x 0 by obs]v+1 ) ! help ( v c>eful measurem5t1 ?is cont9u$ proportionality1 t ,moseley 0 enabl$ to v]ify 8 fir/ assumption1 bas$ on ! g5]al appe>ance ( ! %ell1 t ! %ell ( ,nautilus 0 actually a log>i?mic spiral1 & ?is demon/ration he 0 imm$iately aft]w>ds 9 a position to g5]alise by ext5d+ x to all ! spiral ,ammonitoid & ,ga/ropod mollusca#eje4 ,=1 tak+ a m$ian transv]se section ( a ,nautilus pompilius1 & c>efully measur+ ! successive bread?s ( ! :orls 7f ! d>k l9e :i* m>ks :at 0 orig9ally ! out] surface1 be=e x 0 cov]$ up by fre% deposits on ! "p ( ! gr[+ & advanc+ %ell71 ,moseley f\nd t 8! di/ance ( any two ( its :orls measur$ ^u a radius vector is "o-?ird t ( ! two next :orls measur$ ^u ! same radius vector#ejf4 ,?us 79 ,fig4 #bfb71 ab is "o-?ird ( bc1 de ( ef1 gh ( hi1 & kl ( lm4 ,! curve is !re=e a log>i?mic spiral40 ,! num]ical ratio 9 ! case ( ! ,nautilus happ5s to be "o ( unusual simplicity4 ,let u take1 ) ,moseley1 a some:at m complicat$ example4 ,f ! apex ( a l>ge specim5 ( ,turbo duplicatus#ejg a #eai l9e 0 drawn across its :orls1 & _! wid?s 7 measur$ ^u x 9 succession1 beg9n+ ) ! la/ b "o4 ,! measurem5ts 71 z be=e1 made ) a f9e pair ( compasses & a diagonal scale4 ,! sight 0 assi/$ by a magnify+ glass4 ,9 a p>allel column to ! foll[+ admeasurem5ts are ! t]ms ( a geometric progression1 ^: fir/ t]m is ! wid? ( ! wide/ :orl measur$1 & ^: common ratio is #aahjd4 ,illu/ration3 ,fig4 #bfb4 ,wid?s ( successive ,t]ms ( a geometrical progression1 :orls measur$ 9 in*es ^: fir/ t]m is ! wid? ( & p>ts ( an in* ! wide/ :orl1 & ^: common ratio is #aahjd #aca #aca #aab #aajih #id #idjah #hj #gifea #fg #fgdgf #eg #egafd #dh #dhdbg #da #dajbf ,! close co9cid5ce betwe5 ! obs]v$ & ! calculat$ figures is v rem>kable1 & is amply suffici5t to ju/ify ! conclusion t we are "h deal+ ) a true log>i?mic spiral4 ,nev]!less1 9 ord] to v]ify 8 conclusion /ill fur!r1 & to get p>tially rid ( ! inaccuracies due to successive small #ebj measurem5ts1 ,moseley proce$$ to inve/igate ! same %ell1 measur+ n s+le :orls1 b gr\ps ( :orls1 tak5 sev]al at a "t3 mak+ use ( ! foll[+ prop]ty ( a geometrical progression1 t 8if repres5t ! ratio ( ! sum ( e ev5 numb] 7m7 ( its t]ms to ! sum ( half t numb] ( t]ms1 !n ! common ratio 7r7 ( ! s]ies is repres5t$ by ! =mula r 7 #a7b_/m 40 ,accord+ly1 ,moseley made ! foll[+ measurem5ts1 beg9n+ f ! second & ?ird :orls respectively3 ,wid? ( ,six :orls ,?ree :orls ,ratio #ecg #bjc #bfde #dee #agb #bfde ,f\r :orls ,two :orls #dae #agd #bche #ceb #adg #bcid 8,by ! ratios ( ! two fir/ admeasurem5ts1 ! =mula gives r 7#afde7a_/c #aahjd4 ,by ! mean ( ! ratios d$uc$ f ! second two admeasurem5ts1 x gives r 7#achi7 #aahjf4 8,x is sc>cely possible to imag9e a m accurate v]ification ?an is d$uc$ f ^! l>g] admeasurem5ts1 & we may ) safety annex to ! species ,turbo duplicatus ! *>act]i/ic numb] #aah40 ,by simil> & equally concordant obs]vations1 ,moseley f\nd = ,turbo phasianus ! *>act]i/ic ratio1 #age2 & = ,bucc9um subulatum t ( #aac4 ,f ! table ref]r+ to ,turbo duplicatus1 on page #eai1 x is p]haps wor? :ile to illu/rate ! log>i?mic /atem5t ( ! same facts3 t is to say1 ! elem5t>y coroll>y to ! fact t ! successive radii are 9 geometric progression1 t _! log>i?ms diff] f "o ano!r by a con/ant am\nt4 #eba ,turbo duplicatus4 ,relative wid?s ( ,log>i?ms ( ,diff]5ce ( successive :orls successive :orls successive log>i?ms #aca #baagbg -- #aab #bjdibb #jfhje #id #aigcac #jgfji #hj #aijcji #jgjjd #fg #ahbfjg #jggjb #eg #ageehg #jgjbj #dh #afhabd #jgdfc #da #aafabgh #jfhdf ,mean diff]5ce #jgbjg ,& #jgbjg is ! log>i?m ( #aahje4 ,illu/ration3 ,fig4 #bfc4 ,op]culum ( ,turbo4 ,! log>i?mic spiral is n only v beautifully manife/$ 9 ! molluscan %ell1 b also1 9 c]ta9 cases1 9 ! little lid or 8op]culum0 by :i* ! entrance to ! tubul> %ell is clos$ aft] ! animal has )drawn itself )94 ,9 ! spiral %ell ( ,turbo1 = in/ance1 ! op]culum is a ?ick calc>e\s /ructure1 ) a beautifully curv$ outl9e1 :i* gr[s by successive increm5ts appli$ to "o portion ( its edge1 & %ews1 accord+ly1 a spiral l9e ( gr[? ^u its surface4 ,! successive increm5ts leave _! traces on ! surface ( ! op]culum #ebb 7,fig4 #bfd1 #a71 :i* traces h ! =m ( curv$ l9es 9 ,turbo1 & ( /raight l9es 9 7e4g47 ,n]ita 7,fig4 #bfd1 #b72 t is to say1 ap>t f ! side con/itut+ ! out] edge ( ! op]culum 7:i* side is always & ( necessity curv$7 ! successive increm5ts con/itute curvil9e> triangles 9 ! "o case1 & rectil9e> triangles 9 ! o!r4 ,! sides ( ^! triangles are tang5ts to ! spiral l9e ( ! op]culum1 & may be suppos$ to g5]ate x by _! consecutive int]sections4 ,illu/ration3 ,fig4 #bfd4 ,op]cula ( 7#a7 ,turbo1 7#b7 ,n]ita4 7,aft] ,moseley47 ,9 a numb] ( su* op]cula1 ,moseley measur$ ! bread?s ( ! successive :orls along a radius vector#ejh1 j 9 ! same way z he did ) ! entire %ell 9 ! =ego+ cases2 & "h is "o example ( 8 results4 ,op]culum ( ,turbo sp42 bread? 79 in*es7 ( successive :orls1 measur$ f ! pole4 ,di/ance ,ratio ,di/ance ,ratio ,di/ance ,ratio ,di/ance ,ratio #bd #af #b #ah #bbh #bca #bcj #bcj #ee #cg #f #db #bcb #bcj #bcj #bbd #abh #he #ach #id #ebc ,! ratio is approximately con/ant1 & ?is spiral also is1 !re=e1 a log>i?mic spiral4 ,b "h comes 9 a v beautiful illu/ration ( t prop]ty ( ! log>i?mic spiral :i* causes its :ole %ape to rema9 un*ang$1 9 spite ( its app>5tly unsymmetrical1 or unilat]al1 mode ( gr[?4 ,= ! m\? ( ! tubul> %ell1 into :i* ! op]culum has to fit1 is gr[+ or wid5+ on all sides3 :ile ! op]culum is increas+1 n by additions made at ! same "t all r\nd its m>g91 b by additions made only on "o side ( x at ea* successive /age4 ,"o edge ( ! op]culum ?us rema9s unalt]$ z x is advanc$ into ea* new position1 & z x is plac$ 9 a newly =m$ section ( ! tube1 simil> to b great] ?an ! la/4 ,nev]!less1 ! two appos$ /ructures1 ! *amb] & its plug1 at all times fit "o ano!r to p]fection4 ,! me*anical problem 7by no means an easy "o71 is ?us solv$3 8,h[ to %ape a tube ( a v>iable section1 s t a pi/on driv5 along x %all1 by "o side ( its m>g91 co9cide cont9ually ) its surface z x advances1 provid$ only t ! pi/on be made at ! same "t cont9ually to revolve 9 its own plane40 ,z ,moseley puts x3 8,t ! same edge :i* fitt$ a portion ( ! fir/ less section %\ld be capable ( adju/m5t1 s z to fit a portion ( ! next simil> b great] section1 supposes a geometrical provision 9 ! curv$ =m ( ! *amb] ( great app>5t complication & difficulty4 ,b ,god ha? be/[$ ^u ?is humble ar*itect ! practical skill ( a le>n$ geometrician1 & he makes ?is provision ) admirable precision 9 t curvature ( ! log>i?mic spiral :i* he gives to ! section ( ! %ell4 ,?is curvature obta9+1 he has only to turn 8 op]culum slightly r\nd 9 its own plane z he advances x into ea* newly =m$ portion ( 8 *amb]1 to adapt "o m>g9 ( x to a new & l>g] surface & a diff]5t curvature1 leav+ ! space to be fill$ up by increas+ ! op]culum :olly on ! o!r m>g940 ,b 9 _m1 & inde$ m num]\s ,ga/ropod mollusca1 ! op]culum does n gr[ 9 ?is rem>kable spiral fa%ion1 b by ! app>5tly mu* simpl] process ( accretion by conc5tric r+s4 ,?is sugge/s to u ano!r ma!matical #ebd feature ( ! log>i?mic spiral4 ,we h already se5 t ! log>i?mic spiral has a numb] ( 8limit+ cases10 app>5tly v div]se f "o ano!r4 ,?us ! "r cone is a log>i?mic spiral 9 :i* ! revolution ( ! radius vector is inf9itely sl[2 &1 9 ! same s5se1 ! /raight l9e itself is a limit+ case ( ! log>i?mic spiral4 ,! spiral ( ,ar*im$es1 ?\gh n a limit+ case ( ! log>i?mic spiral1 closely resembles "o 9 :i* ! angle ( ! spiral is v ne> to #ij1 & ! spiral is coil$ ar\nd a c5tral core4 ,b if ! angle ( ! spiral 7 actually #ij1 ! radius vector w\ld describe a circle1 id5tical ) ! 8core0 ( :i* we h j spok52 & accord+ly x may be said t ! circle is1 9 ?is s5se1 a true limit+ case ( ! log>i?mic spiral4 ,9 ?is s5se1 !n1 ! circul> conc5tric op]culum1 = in/ance ( ,turritella or ,littor9a1 does n repres5t a brea* ( cont9uity1 b a 8limit+ case0 ( ! spiral op]culum ( ,turbo2 ! successive 8gnomons0 are n[ n lat]al or t]m9al additions1 b complete conc5tric r+s4 ,view$ 9 reg>d to its own fundam5tal prop]ties & to ^? ( its limit+ cases1 ! log>i?mic spiral is ! simple/ ( all kn[n curves2 & ! rigid uni=mity ( ! simple laws1 or =ces1 by :i* x is develop$ suffici5tly acc\nt = its frequ5t manife/ation 9 ! /ructures built up by ! sl[ & /eady gr[? ( organisms4 ,9 ord] to translate into precise t]ms ! :ole =m & gr[? ( a spiral %ell1 we %\ld h to employ a ma!matical notation1 consid]ably m complicat$ ?an any t ,i h attempt$ to make use ( 9 ?is book4 ,b1 9 ! mo/ elem5t>y language1 we may n[ at lea/ attempt to describe ! g5]al me?od1 & "s ( ! v>iations1 ( ! ma!matical developm5t ( ! %ell4 ,let u imag9e a clos$ curve 9 space1 :e!r circul> or elliptical or ( "s o!r & m complex specific =m1 n necess>ily 9 a plane3 su* a curve z we see be=e u :5 we consid] ! m\?1 or t]m9al orifice1 ( our tubul> %ell2 & let u imag9e "s "o *>act]i/ic po9t )9 ?is clos$ curve1 su* z its c5tre ( gravity4 ,!n1 />t+ f a fix$ #ebe orig91 let ?is c5tre ( gravity describe an equiangul> spiral 9 space1 ab\t a fix$ axis 7namely ! axis ( ! %ell71 :ile at ! same "t ! g5]at+ curve gr[s1 ) ea* angul> increm5t ( rotation1 9 su* a way z to pres]ve ! symmetry ( ! entire figure1 ) or )\t a simultane\s movem5t ( translation along ! axis4 ,illu/ration3 ,fig4 #bfe4 ,melo e?iopicus1 ,l4 ,x is pla9 t ! entire result+ %ell may n[ be look$ ^u 9 ei!r ( two ways4 ,x is1 on ! "o h&1 an ensemble ( simil> clos$ curves spirally arrang$ 9 space1 gradually increas+ 9 dim5sions1 9 proportion to ! increase ( _! vectorial angle f ! pole4 ,9 o!r words1 we c imag9e our %ell cut up into a sy/em ( r+s1 foll[+ "o ano!r 9 cont9u\s spiral succession f t t]m9al & l>ge/ "o1 :i* con/itutes ! lip ( ! orifice ( ! %ell4 ,or1 on ! o!r h&1 we may figure to ourselves ! :ole %ell z made up ( an ensemble ( spiral l9es 9 space1 ea* spiral hav+ be5 #ebf trac$ out by ! gradual gr[? & revolution ( a radius vector f ! pole to a giv5 po9t ( ! g5]at+ curve4 ,bo? sy/ems ( l9es1 ! g5]at+ spirals 7z ^! latt] may be call$71 & ! clos$ g5]at+ curves correspond+ to successive m>g9s or lips ( ! %ell1 may be easily trac$ 9 a great v>iety ( cases4 ,?us1 = example1 9 ,dolium1 ,eburnea1 & a ho/ ( o!rs1 ! g5]at+ spirals are beautifully m>k$ out by ridges1 tub]cles or b&s ( col\r4 ,9 ,trophon1 ,scal>ia1 & 7among c\ntless o!rs7 9 ! ,ammonites1 x is ! successive g5]at+ curves :i* m conspicu\sly leave _! impress on ! %ell4 ,& 9 n a few cases1 z 9 ,h>pa1 ,dolium p]dix1 etc41 bo? alike are conspicu\s1 ridges & col\r-b&s int]sect+ "o ano!r 9 a beautiful isogonal sy/em4 #ebg ,illu/ration3 ,fig4 #bff4 #a1 ,h>pa2 #b1 ,dolium4 ,! ridges on ! %ell correspond 9 7#a7 to g5]at+ curves1 9 7#b7 to g5]at+ spirals4 ,9 ! complete ma!matical =mula 7su* z ,i h n v5tur$ to set =?#eji7 = any giv5 turb9ate %ell1 we %\ld h1 accord+ly1 to include factors = at lea/ ! foll[+ elem5ts3 7#a7 = ! specific =m ( ! section ( ! tube1 :i* we h call$ ! g5]at+ curve2 7#b7 = ! specific rate ( gr[? ( ?is g5]at+ curve2 7#c7 = its specific rate ( angul> rotation ab\t ! pole1 p]p5dicul> to ! axis2 7#d7 9 turb9ate 7z oppos$ to nautiloid7 %ells1 = its rate ( %e>1 or screw-translation p>allel to ! axis4 ,!re are also o!r factors ( :i* we %\ld h to take acc\nt1 & :i* w\ld help to make our :ole expression a v complicat$ "o4 ,we %\ld f9d1 = in/ance1 7#e7 t 9 v _m cases our g5]at+ curve 0 n a plane curve1 b a s9u\s curve 9 ?ree dim5sions2 & we %\ld also h to take acc\nt 7#f7 ( ! incl9ation ( ! plane ( ?is g5]at+ curve to ! axis1 a factor :i* w h a v important influ5ce on ! =m & appe>ance ( ! %ell4 ,= in/ance 9 ,haliotis x is obvi\s t ! g5]at+ curve lies 9 a plane v oblique to ! axis ( ! %ell4 ,la/ly1 we at once p]ceive t ! ratios :i* happ5 to exi/ betwe5 ^! v>i\s factors1 ! ratio = in/ance betwe5 ! gr[?-factor & ! rate ( angul> revolution1 w give u endless possibilities ( p]mutation ( =m4 ,= in/ance 7#g7 ) a giv5 velocity ( vectorial rotation1 a c]ta9 rate ( gr[? 9 ! g5]at+ curve w give u a spiral %ell ( :i* ea* successive :orl w j t\* its pr$ecessor & no m2 ) a sl[] gr[?-factor1 ! :orls w /& asund]1 z 9 a ram's horn2 ) a quick] gr[?-factor1 ea* :orl w cut or int]sect its pr$ecessor1 z 9 an ,ammonite or ! majority ( ga/ropods1 & s on 7cf4 p4 #eda74 ,9 l mann] 7#h7 ! ratio betwe5 ! gr[?-factor & ! rate ( screw-translation p>allel to ! axis w det]m9e ! apical angle ( ! result+ conical /ructure3 w give u ! diff]5ce1 = example1 betwe5 ! %>p1 po9t$ cone ( ,turritella1 ! less acute "o ( ,fusus or ,bucc9um1 & ! #ebh obtuse "o ( ,h>pa or ,dolium4 ,9 %ort x is obvi\s t all ! diff]5ces ( =m :i* we obs]ve betwe5 "o %ell & ano!r are ref]able to matt]s ( degree1 dep5d+1 "o & all1 ^u ! relative magnitudes ( ! v>i\s factors 9 ! complex equation to ! curve4 ,! pap] 9 :i*1 ne>ly eighty ye>s ago1 ,canon ,moseley ?us gave a simple ma!matical expression to ! spiral =ms ( univalve %ells1 is "o ( ! classics ( ,natural ,hi/ory4 ,b o!r /ud5ts be=e him _h come v ne> to recognis+ ?is ma!matical simplicity ( =m & /ructure4 ,ab\t ! ye> #ahah1 ,re9ecke _h sugge/$ t ! relative bread?s ( ! adjac5t :orls 9 an ,ammonite =m$ a con/ant & diagno/ic "*2 & ,leopold von ,bu* accept$ & develop$ ! idea#eaj4 ,b long be=e1 ,swamm]dam1 ) a deep] insight1 _h grasp$ ! root ( ! :ole matt]3 =1 tak+ a few div]se examples1 su* z ,helix & ,spirula1 he %ew$ t !y & all o!r spiral %ells :atsoev] 7 ref]able to "o common type1 namely to t ( a simple tube1 v>i\sly curv$ accord+ to def9ite ma!matical laws2 t all mann] ( ornam5tation1 9 ! way ( sp9es1 tub]osities1 col\r-b&s & s =?1 might be sup]pos$ ^u !m1 b ! type 0 "o ?r\gh\t1 & specific diff]5ces 7 ( a geometrical k9d4 8,omnis enim quae int] eas animadv]titur diff]5tia ex sola nascitur div]sitate gyrationum3 quibus si insup] ext]na qua$am adjunguntur ornam5ta p9n>um1 s9uum1 anfractuum1 planiti]um1 em95ti>um1 pr(unditatum1 ext5sionum1 impressionum1 circumvolutionum1 colorumque3 444 tunc de9ceps facile e/1 qu>umcumque ,co*le>um figuras geometricas1 curvosque1 obliquos atque rectos angulos1 ad unicam omnes speciem r$ig]e3 ad oblongum videlicet tubulum1 qui v>io modo curvatus1 crispatus1 extrorsum et introrsum flexus1 ita concrevit#eaa40 #ebi ,= "s ye>s aft] ! appe>ance ( ,moseley's pap]1 a numb] ( writ]s foll[$ 9 8 foot/eps1 & attempt$1 9 v>i\s ways1 to put 8 conclusions to practical use4 ,= in/ance1 ,d',orbigny devis$ a v simple protractor1 :i* he call$ a ,helicomet]#eab1 & :i* is repres5t$ 9 ,fig4 #bfg4 ,by means ( ?is little in/rum5t1 ! apical angle ( ! turb9ate %ell 0 imm$iately read (f1 & c\ld !n be us$ z a specific & diagno/ic "*4 ,by keep+ "o limb ( ! protractor p>allel to ! side ( ! cone :ile ! o!r 0 br\ght into l9e ) ! suture betwe5 two adjac5t :orls1 ano!r specific angle1 ! 8sutural angle10 c\ld 9 l mann] be record$4 ,&1 by ! l9e> scale ^u ! in/rum5t1 ! relative bread?s ( ! consecutive :orls1 & t ( ! t]m9al *amb] to ! re/ ( ! %ell1 might also1 ?\gh some:at r\ghly1 be det]m9$4 ,= in/ance1 9 ,t]ebra dimidiata1 ! apical angle 0 f\nd to be #ac1 ! sutural angle #aji1 & s =?4 ,illu/ration3 ,fig4 #bfg4 ,d',orbigny's ,helicomet]4 ,x 0 at once obvi\s t1 9 su* a %ell z is repres5t$ 9 ,fig4 #bfg ! entire outl9e ( ! %ell 7always except+ t ( ! imm$iate neighb\rhood ( #ecj ! m\?7 c\ld be re/or$ f a brok5 fragm5t4 ,= if we draw our tang5ts to ! cone1 x foll[s f ! symmetry ( ! figure t we c cont9ue ! projection ( ! sutural l9e1 & s m>k (f ! successive :orls1 by simply draw+ a s]ies ( consecutive p>allels1 & by !n fill+ into ! quadrilat]als s m>k$ (f a s]ies ( curves simil> to "o ano!r1 & to ! :orls :i* are /ill intact 9 ! brok5 %ell4 ,b ! use ( ! helicomet] soon %ew$ t x 0 by no means univ]sally ! case t "o & ! same "r cone 0 tang5t to all ! turb9ate :orls2 9 o!r words1 !re 0 n always "o specific apical angle :i* held good = ! entire sy/em4 ,9 ! great majority ( cases1 x is true1 ! same tang5t t\*es all ! :orls1 & is a /raight l9e4 ,b 9 o!rs1 z 9 ! l>ge ,c]i?ium nodosum1 su* a l9e is slightly convex to ! axis ( ! %ell2 & 9 ! %ort spire ( ,dolium1 = in/ance1 ! convexity is m>k$1 & ! apex ( ! spire is a di/9ct cusp4 ,on ! o!r h&1 9 ,pupa & ,clausilia1 ! common tang5t is concave to ! axis ( ! %ell4 ,s also is x1 z we %all pres5tly see1 among ! ,ammonites3 :]e !re are "s species 9 :i* ! ratio ( :orl to :orl rema9s1 to all appe>ance1 p]fectly con/ant2 o!rs 9 :i* x gradually1 ?\gh only slightly increases2 & o!rs aga9 9 :i* x slightly & gradually falls away4 ,x is obvi\s t1 among ! manifold possibilities ( gr[?1 su* conditions z ^! are v easily conceivable4 ,x is mu* m rem>kable t1 among ^! %ells1 ! relative velocities ( gr[? 9 v>i\s dim5sions %\ld be z con/ant z x is1 ?an t !re %\ld be an occasional dep>ture f p]fect regul>ity4 ,9 su* cases z ^! latt]1 ! log>i?mic law ( gr[? is only approximately true4 ,! %ell is no long] to be repres5t$ z a "r cone :i* has be5 roll$ up1 b z a cone :i* _h gr[n trumpet-%ap$1 or conv]sely ^: m\? _h n>r[$ 91 & :i* 9 section is a curvil9e> in/ead ( a rectil9e> triangle4 ,b all t has happ5$ is t a new factor1 usually ( small or all b imp]ceptible magnitude1 has be5 introduc$ into ! case2 s t ! ratio1 log r log 1 is no long] con/ant1 b v>ies slightly1 & 9 accordance ) "s simple law4 #eca ,"s writ]s1 su* z ,naumann & ,grabau1 ma9ta9$ t ! molluscan spiral 0 no true log>i?mic spiral1 b diff]$ f x specifically1 & !y gave to x ! "n ( ,con*ospiral4 ,!y po9t$ out t ! log>i?mic spiral orig9ates 9 a ma!matical po9t1 :ile ! molluscan %ell />ts ) a little embryonic %ell1 or c5tral *amb] 7! 8protocon*0 ( ! con*ologi/s71 ar\nd :i* ! spiral is subsequ5tly wrapp$4 ,x is pla9 t ?is und\bt$ & obvi\s fact ne$ n affect ! log>i?mic law ( ! %ell z a :ole2 we h only to add a small con/ant to our equation1 :i* becomes r m a4 ,!re w\ld seem1 by ! way1 to be consid]able confusion 9 ! books ) reg>d to ! s-call$ 8protocon*40 ,9 _m cases x is a def9ite /ructure1 ( simple =m1 repres5t+ ! m or less globul> embryonic %ell be=e x began to elongate into its conical or spiral =m4 ,b 9 _m cases :at is describ$ z ! 8protocon*0 is m]ely an empty space 9 ! middle ( ! spiral coil1 result+ f ! fact t ! actual spiral %ell has a def9ite magnitude to beg9 )1 & t we _c foll[ x d[n to its vani%+ po9t 9 inf9ity4 ,= in/ance1 9 ! accompany+ figure1 ! l>ge space a is /yl$ ! protocon*1 b x is ! little bulb\s or hemisph]ical *amb] )9 x1 at ! end ( ! spire1 :i* is ! real beg9n+ ( ! tubul> %ell4 ,! =m & magnitude ( ! space a are det]m9$ by ! 8angle ( ret>dation10 or ratio ( rate ( gr[? betwe5 ! inn] & out] curves ( ! spiral %ell4 ,!y are indep5d5t ( ! %ape & size ( ! embryo1 & dep5d only 7z we %all see bett] pres5tly7 on ! direction & relative rate ( gr[? ( ! d\ble cont\r ( ! %ell4 ,illu/ration3 ,fig4 #bfh4 ,n[ t we h dealt1 9 a v g5]al way1 ) "s ( ! m obvi\s prop]ties ( ! log>i?mic spiral1 let u consid] c]ta9 ( !m a little m p>ticul>ly1 keep+ 9 #ecb view z our *ief object ! inve/igation 7on elem5t>y l9es7 ( ! possible mann] & range ( v>iation ( ! molluscan %ell4 ,illu/ration3 ,fig4 #bfi4 ,!re is yet ano!r equation to ! log>i?mic spiral1 v commonly employ$1 & )\t ! help ( :i* we %all f9d t we _c get f>4 ,x is z foll[s3 r cot 4 ,?is foll[s directly f ! fact t ! angle 7! angle betwe5 ! radius vector & ! tang5t to ! curve7 is con/ant4 ,=1 !n1 tan 7 tan 7 r d_/dr1 !re=e dr_/r d cot 1 &1 integrat+1 log r cot 1 or r cot 4 ,z we h se5 ?r\gh\t our prelim9>y discussion1 ! two mo/ important con/ants 7or *ief 8specific *>act]s10 z ! naturali/ w\ld say7 9 any giv5 log>i?mic spiral1 are 7#a7 ! magnitude ( ! angle ( ! spiral1 or 8con/ant angle10 1 & 7#b7 ! rate ( increase ( ! radius vector = any giv5 angle ( revolution1 4 ,( ?is latt]1 ! simple/ case is :5 #b1 or #cfj2 t is to say :5 we comp>e ! bread?s1 along ! same radius vector1 ( two successive :orls4 ,z our two magnitudes1 t ( ! con/ant angle1 & t ( ! ratio ( ! radii or bread?s ( :orl1 are relat$ to "o ano!r1 we may det]m9e ei!r ( !m by actual measurem5t & proce$ to calculate ! o!r4 ,9 any complete spiral1 su* z t ( ,nautilus1 x is 7z we h se57 easy to measure any two radii 7r71 or ! bread?s 9 #ecc a radial direction ( any two :orls 7,w74 ,we h !n m]ely to apply ! =mula rn #a_/rn e cot 1 or ,wn #a_/,wn e cot 1 :i* we may simply write r e cot 1 etc42 s9ce our fir/ radius or :orl is reg>d$1 = ! purpose ( comp>ison1 z be+ equal to unity4 ,?us1 9 ! diagram1 ,,oc_/,,oe1 or ,,ef_/,,bd1 or ,,dc_/,,ef1 be+ 9 ea* case radii1 or diamet]s1 at "r angles to "o ano!r1 are all equal to e_/#b cot 4 ,:ile 9 l mann]1 ,,eo_/,,(1 ,,eg_/,,fh1 or ,,g_/,,ho1 all equal e cot 2 & ,,bc_/,,ba1 or ,,co_/,,ob e#b cot 4 ,illu/ration3 ,fig4 #bgj4 ,z soon1 !n1 z we h prep>$ tables = ^! values1 ! det]m9ation ( ! con/ant angle 9 a p>ticul> %ell becomes a v simple matt]4 ,a complete table w\ld be cumbr\s1 & x w be suffici5t to deal ) ! simple case ( ! ratio betwe5 ! bread?s ( adjac5t1 or imm$iately succe$+1 :orls4 ,"h we h r e#b cot 1 or log r log e #b cot 1 f :i* we obta9 ! foll[+ figures#eac3 #ecd ,ratio ( bread? ( ea* :orl to ! next prec$+ ,con/ant angle r_/#a #aa #hi #h #abe #hg #eh #ae #hf #ah #bj #hc #db #be #ha #db #cj #hj #e #ce #gh #dc #dj #gg #cd #de #gf #cb #ej #ge #ch #ajj #fi #ec #bjj #fd #ca #ejj #eh #e #ajjj #ec #df #a1jjjj #db #ag #aj1jjj #cd #ai #ajj1jjj #bh #cg #a1jjj1jjj #bd #bh #aj1jjj1jjj #ba #ah #ajj1jjj1jjj #ah #ej #a1jjj1jjj1jjj #af #eb ,illu/ration3 ,fig4 #bga4 ,we le>n sev]al int]e/+ ?+s f ?is %ort table4 ,we see1 9 ! fir/ place1 t :]e ea* :orl is ab\t ?ree times ! bread? ( its neighb\r & pr$ecessor1 z is ! case 9 ,nautilus1 ! con/ant angle is 9 ! neighb\rhood ( #hj2 & h5ce also t1 9 all ! ord9>y ,ammonitoid %ells1 & 9 all ! typically spiral %ells ( ! ,ga/ropods#ead1 ! con/ant angle is also a l>ge "o1 be+ v seldom less ?an #hj1 & usually betwe5 #hj & #he4 ,9 ! next place1 we see t ) small] angles ! app>5t =m ( ! spiral is greatly alt]$1 & ! v fact ( its be+ a spiral soon ceases to be app>5t 7,figs4 #bga1 #bgb74 ,suppose "o :orl to be an in* 9 bread?1 !n1 if ! angle ( ! spiral 7 #hj1 ! #ece next :orl w\ld 7z we h j se57 be ab\t ?ree in*es broad2 if x 7 #gj1 ! next :orl w\ld be ne>ly t5 in*es1 & if x 7 #fj1 ! next :orl w\ld be ne>ly f\r feet broad4 ,if ! angle 7 #bh1 ! next :orl w\ld be a mile & a half 9 bread?2 & if x 7 #ag1 ! next w\ld be "s #ae1jjj miles broad4 ,illu/ration3 ,fig4 #bgb4 ,9 o!r words1 ! spiral %ells ( g5tle curvature1 or ( small con/ant angle1 su* z ,d5talium or ,nodos>ia1 are true log>i?mic spirals1 j z are ^? ( ,nautilus or ,rotalia3 f :i* !y diff] only 9 degree1 9 ! magnitude ( an angul> con/ant4 ,b ?is dim9i%$ magnitude ( ! angle causes ! spiral to dilate ) su* imm5se rapidity t1 s to speak1 8x nev] comes r\nd02 & s1 9 su* a %ell z ,d5talium1 we nev] see b a small portion ( ! initial :orl4 ,illu/ration3 ,fig4 #bgc4 ,we might p]haps be incl9$ to suppose t1 9 su* a %ell z ,d5talium1 ! lack ( a visible spiral convolution 0 only due to our see+ b a small portion ( ! curve1 at a di/ance f ! pole1 & :51 !re=e1 its #ecf curvature _h already greatly dim9i%$4 ,t is to say we might suppose t1 h[ev] small ! angle a1 & h[ev] rapidly ! :orls accord+ly increas$1 !re w\ld nev]!less be a manife/ spiral convolution 9 ! imm$iate neighb\rhood ( ! pole1 z ! />t+ po9t ( ! curve4 ,b x may be %ewn t ?is is n s4 ,=1 tak+ ! =mula r a cot 1 ?is1 = any giv5 spiral1 is equival5t to ak4 ,!re=e log7r_/a7 k1 or1 #a_/k _/log7r_/a74 ,!n1 if increase by #b1 :ile r increases to r#a1 #a_/k 7 #b7_/log7r#a_/;a71 :i* leads1 by subtraction to #a_/k log7r#a_/r7 #b4 ,n[1 z t5ds to #j1 k 7i4e4 cot 7 t5ds to 1 & !re=e1 z k 1 log7r#a_/r7 & also r#a_/r 4 ,!re=e if "o :orl exi/s1 ! radius vector ( ! o!r is inf9ite2 9 o!r words1 !re is n[h]e1 ev5 9 ! ne> neighb\rhood ( ! pole1 a complete revolution ( ! spire4 ,our spiral %ells ( small con/ant angle1 su* z ,d5talium1 may accord+ly be consid]$ to repres5t suffici5tly well ! true comm5cem5t ( _! respective spirals4 ,let u return to ! problem ( h[ to asc]ta91 by direct measurem5t1 ! spiral angle ( any p>ticul> %ell4 ,! me?od already employ$ is only applicable to complete spirals1 t is to say to ^? 9 :i* ! angle ( ! spiral is l>ge1 & fur!rmore x is inapplicable to portions1 or brok5 fragm5ts1 ( a %ell4 ,9 ! case ( ! brok5 fragm5t1 x is pla9 t ! det]m9ation ( ! angle is n m]ely ( !oretic int]e/1 b may be ( great practical use to ! con*ologi/ z be+ ! "o & only way by :i* he may re/ore ! outl9e ( ! miss+ portions4 ,we h a consid]able *oice ( me?ods1 :i* h be5 summ>is$ by1 & are p>tly due to1 a v c>eful /ud5t ( ! ,cephalopoda1 ! late ,rev4 ,j4 ,f4 ,blake#eae4 #ecg 7#a7 ,! foll[+ me?od is useful & easy :5 we h a portion ( a s+le :orl1 su* z to %ew bo? its inn] & its out] edge4 ,a brok5 :orl ( an ,ammonite1 a curv$ %ell su* z ,d5talium1 or a horn ( simil> =m to ! latt]1 w fall "u ?is head4 ,we h m]ely to draw a tang5t1 ,,geh1 to ! out] :orl at any po9t ,e2 !n draw to ! inn] :orl a tang5t p>allel to ,,geh1 t\*+ ! curve 9 "s po9t ,f4 ,! /raight l9e jo9+ ! po9ts ( contact1 ,,ef1 mu/ evid5tly pass ?r\gh ! pole3 &1 accord+ly1 ! angle ,,gef is ! angle requir$4 ,9 %ells :i* be> longitud9al /riae or o!r ornam5ts1 any pair ( ^! w suffice = our purpose1 in/ead ( ! actual b\nd>ies ( ! :orl4 ,b x is obvi\s t ?is me?od w be apt to fail u :5 ! angle is v small2 & :51 consequ5tly1 ! po9ts ,e & ,f are v remote4 ,illu/ration3 ,fig4 #bgd4 7#b7 ,9 %ells 7or horns7 %ew+ r+s1 or o!r transv]se ornam5tation1 we may take x t ^! ornam5ts are set at a con/ant angle to ! spire1 & !re=e to ! radii4 ,! angle 77 betwe5 two ( !m1 z ,,ac1 ,,bd1 is !re=e equal to ! angle betwe5 ! pol> radii f ,a & ,b1 or f ,c & ,d2 & !re=e ,,bd_/,,ac e cot 1 :i* gives u ! angle 9 t]ms ( kn[n quantities4 #ech ,illu/ration3 ,fig4 #bge4 ,an ,ammonite1 to %ew corrugat$ surface-patt]n4 ,illu/ration3 ,fig4 #bgf4 7#c7 ,if only ! out] edge be available1 we h ! ord9>y geometrical problem1--giv5 an arc ( an equiangul> spiral1 to f9d its pole & spiral angle4 ,! me?ods we may employ dep5d 7#a7 on det]m9+ directly ! position ( ! pole1 & 7#b7 on det]m9+ ! radius ( curvature4 ,illu/ration3 ,fig4 #bgg4 ,! fir/ me?od is !oretically simple1 b difficult 9 practice2 = x requires great accuracy 9 det]m9+ ! po9ts4 ,let ,,ad1 ,,db1 be two tang5ts drawn to ! curve4 ,!n a circle drawn ?r\gh ! po9ts ,,abd w pass ?r\gh ! pole ,o2 s9ce ! angles ,,oad1 ,,obe 7! supplem5t ( ,,obd71 are equal4 ,! po9t ,o may be det]m9$ by ! int]section ( two su* circles2 & ! angle ,,dbo is !n ! angle1 1 requir$4 ,or we may det]m9e1 graphically1 at two po9ts1 ! radii ( curvature1 #a #b4 ,!n1 if s be ! l5g? ( ! arc betwe5 !m 7:i* may be det]m9$ ) fair accuracy by roll+ ! m>g9 ( ! %ell along a rul]7 cot 7#a #b7_/s4 ,! foll[+ me?od#eaf1 giv5 by ,blake1 w save actual det]m9ation ( ! radii ( curvature4 ,measure along a tang5t to ! curve1 ! di/ance1 ,,ac1 at :i* a c]ta9 small (fset1 ,,cd1 is made by ! curve2 & f ano!r po9t ,b1 measure ! di/ance at :i* ! curve makes an equal (fset4 ,!n1 call+ ! (fset 2 ! arc ,,ab1 s2 & ,,ac1 ,,be1 respectively x#a1 x#b1 we h #a 7x#ab #b7_/b1 approximately1 & cot 7x#bb x#ab7_/bs4 ,( all ^! me?ods by :i* ! ma!matical con/ants1 or specific *>act]s1 ( a giv5 spiral %ell may be det]m9$1 ! only "o ( :i* mu* use has be5 made is t :i* ,moseley fir/ employ$1 namely1 ! simple me?od ( det]m9+ #eci ! relative bread?s ( ! :orl at di/ances sep>at$ by "s conv5i5t vectorial angle 7su* z #ij1 #ahj1 or #cfj74 ,v elaborate measurem5ts ( a numb] ( ,ammonites h be5 made by ,naumann#eag1 by ,s&b]g]#eah1 & by ,grabau#eai1 among :i* we may *oose a c\ple ( cases = consid]ation4 ,9 ! foll[+ table ,i h tak5 a portion ( ,grabau's det]m9ations ( ! bread? ( ! :orls 9 ,ammonites 7,arce/es7 ,ammonites intuslabiatus4 ,ratio ( bread? ( ,bread? ( :orls successive :orls ,! angle 77 7#ahj ap>t7 7#cfj ap>t7 z calculat$ #jcj mm4 -- -- -- #jcj #accc #hg #bc #jdj #aejj #hf #ai #jde #aejj #hf #ai #jfj #addd #hf #ci #jfe #adag #hf #di #jhe #afib #he #ac #aaj #aehh #he #dg #ace #aede #hf #b #agj #afcj #he #cc #bbj #adda #hf #dj #bde #adcb #hf #dc #cae #agce #he #j #dbe #afhc #he #af #ecj #adhb #hf #be #fcj #aeai #hf #ab #hje #afce #he #cb #ajcj #adaf #hf #ej #aadj #abeb #hg #eg #abij -- -- -- ,mean #hf #ae #edj intuslabiatus2 ^! measurem5ts ,grabau gives = e #de ( arc1 b ,i h only set =? "o qu>t] ( ^! measurem5ts1 t is to say1 ! bread?s ( successive :orls measur$ along "o diamet] on bo? sides ( ! pole4 ,! ratio betwe5 alt]nate measurem5ts is !re=e ! same ratio z ,moseley adopt$1 namely ! ratio ( bread? betwe5 contigu\s :orls along a radius vector4 ,i h !n add$ to ^! obs]v$ values ! correspond+ calculat$ values ( ! angle 1 z obta9$ f our usual =mula4 ,!re is consid]able irregul>ity 9 ! ratios d]iv$ f ^! measurem5ts1 b x w be se5 t ?is irregul>ity only implies a v>iation ( ! angle ( ! spiral betwe5 ab\t #he & #hg2 & ! values fluctuate pretty regul>ly ab\t ! mean1 :i* is #hf #ae4 ,consid]+ ! difficulty ( measur+ ! :orls1 especially t[>ds ! c5tre1 & 9 p>ticul> ! difficulty ( det]m9+ ) precise accuracy ! position ( ! pole1 x is cle> t 9 su* a case z ?is we are sc>cely ju/ifi$ 9 ass]t+ t ! law ( ! log>i?mic spiral is dep>t$ f4 ,9 "s cases1 h[ev]1 x is und\bt$ly dep>t$ f4 ,"h = in/ance is ano!r table f ,grabau1 %ew+ ! correspond+ ratios 9 an ,ammonite ( ! gr\p ( ,arce/es tornatus4 ,9 ?is case we see a di/9ct t5d5cy ( ! ratios to ,ammonites tornatus4 ,ratio ( bread? ( ,bread? ( :orls successive :orls ,! spiral angle 7#ahj ap>t7 7#cfj ap>t7 77 z calculat$ #jbe mm4 -- -- -- #jcj #adjj #hf #ef #jce #affg #he #ba #jej #bjjj #hc #db #jgj #bjjj #hc #db #ajj #bjjj #hc #db #adj #bajj #hc #af #baj #bagi #hb #ef #cje #bbch #hb #db #dgj #bdib #ha #dd #gfj #begd #ha #bg #abaj #bedf #ha #cc #aice -- -- -- ,mean #hc #bb #eda increase z we pass f ! c5tre ( ! coil outw>ds1 & consequ5tly = ! values ( ! angle to dim9i%4 ,! case is precisely comp>able to t ( a cone ) slightly curv+ sides3 9 :i*1 t is to say1 !re is a slight accel]ation ( gr[? 9 a transv]se z comp>$ ) ! longitud9al direction4 ,9 a tubul> spiral1 :e!r plane or helicoid1 ! consecutive :orls may ei!r be 7#a7 isolat$ & remote f "o ano!r2 or 7#b7 !y may precisely meet1 s t ! out] bord] ( "o & ! inn] bord] ( ! next j co9cide2 or 7#c7 !y may ov]lap1 ! vector plane ( ea* out] :orl cutt+ t ( its imm$iate pr$ecessor or pr$ecessors4 ,look+1 z we h done1 ^u ! spiral %ell z be+ ess5tially a cone roll$ up1 x is pla9 t1 = a giv5 spiral angle1 int]section or non-int]section ( ! successive :orls w dep5d ^u ! apical angle ( ! orig9al cone4 ,= ! wid] ! cone1 ! m rapidly w its inn] bord] t5d to encroa* on ! out] bord] ( ! prec$+ :orl4 ,b x is also pla9 t ! great] be ! apical angle ( ! cone1 & ! broad]1 consequ5tly1 ! cone itself be1 ! great] diff]5ce w !re be betwe5 ! total l5g?s ( its inn] & out] bord]1 "u giv5 conditions ( flexure4 ,&1 s9ce ! inn] & out] bord]s are describ+ precisely ! same spiral ab\t ! pole1 x is pla9 t we may consid] ! inn] bord] z be+ ret>d$ 9 gr[? z comp>$ ) ! out]1 & z be+ always id5tical ) a small] & e>li] "p ( ! latt]4 ,if be ! ratio ( gr[? betwe5 ! out] & ! inn] curve1 !n1 ! out] curve be+ repres5t$ by r a e cot 1 ! equation to ! inn] "o w be r ae cot 1 or r a e7 7cot 1 & may !n be call$ ! angle ( ret>dation1 to :i* ! inn] curve is subject by virtue ( its sl[] rate ( gr[?4 #edb ,disp5s+ ) ma!matical =mulae1 ! sev]al conditions may be illu/rat$ z foll[s3 ,illu/ration3 ,fig4 #bgh4 ,9 ! diagrams 7,fig4 #bgh71 ,o ,p#a ,p#b ,p#c1 etc4 repres5ts a radius1 on :i* ,p#a1 ,p#b1 ,p#c1 are ! po9ts atta9$ by ! out] bord] ( ! tubul> %ell aft] z _m entire consecutive revolutions4 ,& ,p#a1 ,p#b1 ,p#c1 are ! po9ts simil>ly int]sect$ by ! inn] bord]2 ,,op_/,,op be+ always 1 :i* is ! ratio ( gr[?1 or 8cutt+-d[n factor40 ,!n1 obvi\sly1 :5 ,o ,p#a is less ?an ,o ,p#b ! :orls w be sep>at$ by an int]space 7a72 7#b7 :5 ,o ,p#a ,o ,p#b !y w be 9 contact 7b71 & 7#c7 :5 ,o ,p#a is great] ?an ,o ,p#b !re w a great] or less ext5t ( ov]lapp+1 t is to say ( concealm5t ( ! surfaces ( ! e>li] by ! lat] :orls 7c74 ,& z a fur!r case 7#d71 x is pla9 t if be v l>ge1 t is to say if ,o ,p#a be great]1 n only ?an ,o ,p#b b also ?an ,o ,p#c1 ,o ,p#d1 etc41 we %all h complete1 or all b complete concealm5t by ! la/ =m$ :orl1 ( ! :ole ( its pr$ecessors4 ,?is latt] condition is completely atta9$ 9 ,nautilus pompilius1 & approa*$1 ?\gh n q atta9$1 9 ,n4 umbilicatus2 & ! diff]5ce betwe5 ^! two =ms1 or 8species10 is con/itut$ accord+ly by a diff]5ce 9 ! value ( 4 7#e7 ,!re is also a f9al case1 n easily di/+ui%able ext]nally f 7#d71 :]e ,p lies on #edc ! opposite side ( ! radius vector to ,p1 & is !re=e imag9>y4 ,?is f9al condition is exhibit$ 9 ,argonauta4 ,! limit+ values ( are easily asc]ta9$4 ,illu/ration3 ,fig #bgi ,9 ,fig4 #bgi we h portions ( two successive :orls1 ^: correspond+ po9ts on ! same radius vector 7z ,r & ,r7 are1 !re=e1 at a di/ance ap>t correspond+ to #b4 ,let r & r ref] to ! inn]1 & ,r1 ,r to ! out] sides ( ! two :orls4 ,!n1 if we consid] ,r a e cot 1 x foll[s t ,r a e7 #b7;cot 1 r a e cot a e7 7cot 1 & r a e7 #b7;cot a e7 #b 7cot 4 ,n[ 9 ! ?ree cases 7a1 b1 c7 repres5t$ 9 ,fig4 #bgh1 x is pla9 t r ,r1 respectively4 ,t is to say1 a e7 #b7;cot a e cot 1 & e#b cot #a4 ,! case 9 :i* e#b cot #a1 or log #b cot log 1 is ! case repres5t$ 9 ,fig4 #bgh1 b3 t is to say1 ! p>ticul> case1 = ea* value ( 1 :]e ! consecutive :orls j t\*1 )\t int]space or ov]lap4 ,= su* cases1 !n1 we may tabulate ! values ( 1 z foll[s3 ,con/ant angle ,ratio 77 ( rate ( gr[? ( inn] bord] ( tube1 ( spiral z comp>$ ) t ( ! out] bord] #hi #hif #hh #hjc #hg #gbj #hf #fde #he #egg #hj #ccj #ge #bcd #gj #ajaf #fe #jecd #edd ,we see1 accord+ly1 t 9 plane spirals ^: con/ant angle lies1 say1 betwe5 #fe & #gj1 we c only obta9 contact betwe5 consecutive :orls if ! rate ( gr[? ( ! inn] bord] ( ! tube be a small fraction1--a t5? or a tw5tie?--( t ( ! out] bord]4 ,9 spirals ^: con/ant angle is #hj1 contact is atta9$ :5 ! respective rates ( gr[? are1 approximately1 z #c to #a2 :ile 9 spirals ( con/ant angle f ab\t #he to #hi1 contact is atta9$ :5 ! rates ( gr[? are 9 ! ratio ( f ab\t #c_/e to #i_/aj4 ,illu/ration3 ,fig4 #bhj4 ,if on ! o!r h& we h1 = any giv5 value ( 1 a value ( great] or less ?an ! value giv5 9 ! above table1 !n we h1 respectively1 ! conditions ( sep>ation or ( ov]lap :i* are exemplifi$ 9 ,fig4 #bgh1 a & c4 ,&1 j z we h con/ruct$ ?is table ( values ( = ! p>ticul> case ( simple contact betwe5 ! :orls1 s we c\ld con/ruct simil> tables = v>i\s degrees ( sep>ation1 or degrees ( ov]lap4 ,= in/ance1 a case :i* admits ( simple solution is t 9 :i* ! int]space betwe5 ! :orls is ev]y:]e a mean proportional betwe5 ! bread?s ( ! :orls !mselves 7,fig4 #bhj74 #ede ,9 ?is case1 let u call ,,oa ,r1 ,,oc ,r#a & ,,ob r4 ,we !n h ,r#a ,,oa a e cot 1 ,r#b ,,oc a e7 #b7 cot 1 ,r#a ,r#b a e#b7 7 cot r#b #ebj4 ,& r#b 7#a_/7b #b cot 1 :5ce1 equat+1 #a_/ e cot 4 ,! correspond+ values ( are z foll[s3 ,ratio 77 ( rates ( gr[? ( out] & inn] bord]1 su* z to produce a spiral ) int]spaces betwe5 ! :orls1 ! bread? ( :i* int]spaces is a mean proportional betwe5 ! ,con/ant angle 77 bread?s ( ! :orls !mselves #ij #ajj 7imag9>y7 #hi #ie #hh #hi #hg #he #hf #ha #he #gf #hj #eg #ge #dc #gj #cb #fe #bc #fj #ah #ee #ac #ej #jij #de #jfc #dj #jdb #ce #jbf #cj #jaf ,z reg>ds ! angle ( ret>dation1 1 9 ! =mula r e cot 1 or r e7 7cot 1 & 9 ! case r e7#b 7cot 1 or log 7#b 7cot 1 #edf x is evid5t t :5 #b1 t w mean t #a4 ,9 o!r words1 ! out] & inn] bord]s ( ! tube are id5tical1 & ! tube is con/itut$ by "o cont9u\s l9e4 ,:5 is a v small fraction1 t is to say :5 ! rates ( gr[? ( ! two bord]s ( ! tube are v div]se1 !n w t5d t[>ds inf9ity--t5d t is to say t[>ds a condition 9 :i* ! inn] bord] ( ! tube nev] gr[s at all4 ,?is condition is n infrequ5tly approa*$ 9 nature4 ,! ne>ly p>allel-sid$ cone ( ,d5talium1 or ! widely sep>at$ :orls ( ,lituites1 are evid5tly cases :]e ne>ly approa*es unity 9 ! "o case1 & is /ill l>ge 9 ! o!r1 be+ correspond+ly small2 :ile we c easily f9d cases :]e is v l>ge1 & is a small fraction1 = in/ance 9 ,haliotis1 or 9 ,gryphaea4 ,= ! purposes ( ! morphologi/1 !n1 ! ma9 result ( ?is la/ g5]al inve/igation is to %ew t all ! v>i\s types ( 8op50 & 8clos$0 spirals1 all ! v>i\s degrees ( sep>ation or ov]lap ( ! successive :orls1 are simply ! outw>d expression ( a v>y+ ratio 9 ! rate ( gr[? ( ! out] z comp>$ ) ! inn] bord] ( ! tubul> %ell4 ,! =ego+ problem ( contact1 or int]section1 ( ! successive :orls1 is a v simple "o 9 ! case ( ! discoid %ell b a m complex "o 9 ! turb9ate4 ,= 9 ! discoid %ell contact w evid5tly take place :5 ! ret>dation ( ! inn] z comp>$ ) ! out] :orl is j #cfj1 & ! %ape ( ! :orls ne$ n be consid]$4 ,z ! angle ( ret>dation dim9i%es f #cfj1 ! :orls w /& fur!r & fur!r ap>t 9 an op5 coil2 z x increases beyond #cfj1 !y w m & m ov]lap2 & :5 ! angle ( ret>dation is inf9ite1 t is to say :5 ! true inn] edge ( ! :orl does n gr[ at all1 !n ! %ell is said to be completely involute4 ,( ?is latt] condition we h a /rik+ example 9 ,argonauta1 & "o a little m obscure 9 ,nautilus pompilius4 ,9 ! turb9ate %ell1 ! problem ( contact is tw(old1 = we h to deal ) ! possibilities ( contact on ! same side ( ! axis 7:i* is :at we h dealt ) 9 ! discoid7 & #edg also ) ! new possibility ( contact or int]section on ! opposite side2 x is ?is latt] case :i* w det]m9e ! pres5ce or abs5ce ( an umbilicus1 & :e!r1 if pres5t1 x w be an op5 conical space or a twi/$ cone4 ,x is fur!r obvi\s t1 9 ! case ( ! turb9ate1 ! "q ( contact or no contact w dep5d on ! %ape ( ! g5]at+ curve2 & if we take ! simple case :]e ?is g5]at+ curve may be consid]$ z an ellipse1 !n contact w be f\nd to dep5d on ! angle :i* ! major axis ( ?is ellipse makes ) ! axis ( ! %ell4 ,! "q becomes a complicat$ "o1 & ! /ud5t w f9d x treat$ 9 ,blake's pap] already ref]r$ to4 ,:5 "o :orl ov]laps ano!r1 s t ! g5]at+ curve cuts its pr$ecessor 7at a di/ance ( #b7 on ! same radius vector1 ! locus ( int]section w foll[ a spiral l9e ^u ! %ell1 :i* is call$ ! 8suture0 by con*ologi/s4 ,x is evid5tly "o ( t ensemble ( spiral l9es 9 space ( :i*1 z we h se51 ! :ole %ell may be conceiv$ to be con/itut$2 & we might call x a 8contact-spiral10 or 8spiral ( int]section40 ,9 discoid %ells1 su* z an ,ammonite or a ,planorbis1 or 9 ,nautilus umbilicatus1 !re are obvi\sly two su* contact-spirals1 "o on ea* side ( ! %ell1 t is to say "o on ea* side ( a plane p]p5dicul> to ! axis4 ,9 turb9ate %ells su* a condition is also possible1 b is some:at r>e4 ,we h x = in/ance1 9 ,sol>ium p]spectivum1 :]e ! "o contact-spiral is visible on ! ext]ior ( ! cone1 & ! o!r lies int]nally1 w9d+ r\nd ! op5 cone ( ! umbilicus#eba2 b ?is second contact-spiral is usually imag9>y1 or conceal$ )9 ! :orls ( ! turb9at$ %ell4 ,aga91 9 ,haliotis1 "o ( ! contact-spirals is non-exi/5t1 because ( ! extreme obliquity ( ! plane ( ! g5]at+ curve4 ,9 ,scal>ia pretiosa & 9 ,spirula !re is no contact-spiral1 because ! gr[? ( ! g5]at+ curve has be5 too sl[1 9 comp>ison ) ! vector rotation ( its plane4 ,9 ,argonauta & 9 ,cypraea1 !re is no contact-spiral1 because ! gr[? ( ! g5]at+ curve has be5 too quick4 ,nor1 ( c\rse1 is !re any contact-spiral 9 ,patella or 9 ,d5talium1 because ! angle is too small ev] to give u a complete revolution ( ! spire4 #edh ,! v>i\s =ms ( /raight or spiral %ells among ! ,cephalopods1 :i* we h se5 to be capable ( complete def9ition by ! help ( elem5t>y ma!matics1 h receiv$ a v complicat$ descriptive nom5clature f ! palaeontologi/s4 ,= in/ance1 ! /raight cones are spok5 ( z or?oc]acones or bactriticones1 ! loosely coil$ =ms z gyroc]acones or mimoc]acones1 ! m closely coil$ %ells1 9 :i* "o :orl ov]laps ! o!r1 z nautilicones or ammoniticones1 & s =?4 ,9 su* a succession ( =ms ! biologi/ sees und\bt$ & unque/ion$ evid5ce ( ance/ral desc5t4 ,= in/ance we read 9 ,zittel's ,palaeontology#ebb3 8,! bactriticone obvi\sly repres5ts ! primitive or prim>y radical ( ! ,ammonoidea1 & ! mimoc]acone ! next or second>y radical ( ?is ord]02 :ile precisely ! opposite conclusion 0 drawn by ,ow51 :o suppos$ t ! /raight *amb]$ %ells ( su* fossil cephalopods z ,or?oc]as _h be5 produc$ by ! gradual unw9d+ ( a coil$ nautiloid %ell#ebc4 ,to su* phylog5etic hypo!ses ! ma!matical or dynamical /udy ( ! =ms ( %ells l5ds no valid support4 ,if we h two %ells 9 :i* ! con/ant angle ( ! spire be respectively #hj & #fj1 t fact 9 itself does n at all ju/ify an ass]tion t ! "o is m primitive1 m anci5t1 or m 8ance/ral0 ?an ! o!r4 ,nor1 if we f9d a ?ird 9 :i* ! angle happ5s to be #gj1 does t fact entitle u to say t ?is %ell is int]m$iate betwe5 ! o!r two1 9 "t1 or 9 blood relation%ip1 or 9 any o!r s5se :atsoev] save only ! /rictly =mal & ma!matical "o4 ,= x is evid5t t1 ?\gh ^! p>ticul> ari?metical con/ants manife/ !mselves 9 visible & recognisable diff]5ces ( =m1 yet !y are n necess>ily m deep-seat$ or significant ?an are ^? :i* manife/ !mselves only 9 diff]5ce ( magnitude2 & ! /ud5t ( phylog5y sc>cely v5tures to draw conclusions z to ! relative antiquity ( two alli$ organisms on ! gr\nd t "o happ5s to be bigg] or less1 or long] or %ort]1 ?an ! o!r4 #edi ,at ! same "t1 :ile x is obvi\sly unsafe to re/ conclusions ^u su* features z ^!1 unless !y be /rongly support$ & corroborat$ 9 o!r ways1--= ! simple reason t !re is unlimit$ room = co9cid5ce1 or sep>ate & indep5d5t atta9m5t ( ?is or t magnitude or num]ical ratio1--yet on ! o!r h& x is c]ta9 t1 9 p>ticul> cases1 ! evolution ( a race has actually involv$ gradual increase or decrease 9 "s "o or m num]ical factors1 magnitude itself includ$1--t is to say increase or decrease 9 "s "o or m ( ! actual & relative velocities ( gr[?4 ,:5 we d meet ) a cle> & unmi/akable s]ies ( su* progressive magnitudes or ratios1 manife/+ !mselves 9 a progressive s]ies ( 8alli$0 =ms1 !n we h ! ph5om5on ( 8or?og5esis40 ,= or?og5esis is simply t ph5om5on ( cont9u\s l9es or s]ies ( =m 7& also ( functional or physiological capacity71 :i* 0 ! f\ndation ( ! ,!ory ( ,evolution1 alike to ,lam>ck & to ,d>w9 & ,wallace2 & :i* we see to exi/ :atev] be our ideas ( ! 8orig9 ( species10 or ( ! nature & orig9 ( 8functional adaptations40 ,& to my m9d1 ! ma!matical 7z di/+ui%$ f ! purely physical7 /udy ( morphology bids fair to help u to recognise ?is ph5om5on ( or?og5esis 9 _m cases :]e x is n at once pat5t to ! eye2 & also1 on ! o!r h&1 to w>n u1 9 _m o!r cases1 t ev5 /rong & app>5tly complex resemblances 9 =m may be capable ( aris+ indep5d5tly1 & may sometimes signify no m ?an ! equally accid5tal num]ical co9cid5ces :i* are manife/$ 9 id5tity ( l5g? or weight1 or any o!r simple magnitudes4 ,illu/ration3 ,fig4 #bha4 ,an ammonitoid %ell 7,macroscaphites7 to %ew *ange ( curvature4 ,i h already ref]r$ to ! fact t1 :ile 9 g5]al a v great & rem>kable regul>ity ( =m is *>act]i/ic ( ! molluscan %ell1 t complete regul>ity is apt to be dep>t$ f4 ,we h cle> cases ( su* a dep>ture 9 ,pupa1 ,clausilia1 & v>i\s ,bulimi1 :]e ! envelop+ cone ( ! spire is n a "r cone b a cone ^: sides are curv$4 ,x is pla9 t ?is condition may arise 9 two ways3 ei!r by a gradual *ange 9 ! ratio ( gr[? ( ! :orls1 t is to say 9 ! log>i?mic spiral itself1 or by a *ange 9 ! velocity ( #eej translation along ! axis1 t is to say 9 ! helicoid :i*1 9 all turb9ate %ells1 is sup]pos$ ^u ! spiral4 ,v c>eful measurem5ts w be necess>y to det]m9e to :i* ( ^! factors1 or 9 :at proportions to ea*1 ! ph5om5on is due4 ,b 9 _m ,ammonitoidea :]e ! helicoid factor does n ent] into ! case1 we h a cle> illu/ration ( gradual & m>k$ *anges 9 ! spiral angle itself1 t is to say ( ! ratio ( gr[? correspond+ to increase ( vectorial angle4 ,we h se5 f "s ( ,naumann's & ,grabau's measurem5ts t su* a t5d5cy to v>y1 su* an accel]ation or ret>dation1 may be detect$ ev5 9 ,ammonites :i* pres5t no?+ abnormal to ! eye4 ,b let u suppose t ! spiral angle increases some:at rapidly2 we %all !n get a spiral ) gradually n>r[+ :orls1 & ?is condition is *>act]i/ic ( ,oekotrau/es1 a subg5us ( ,ammonites4 ,if on ! o!r h&1 ! angle gradually dim9i%es1 & ev5 falls away to z]o1 we %all h ! spiral curve op5+ out1 z x does 9 ,scaphites1 ,ancyloc]as & ,lituites1 until ! spiral coil is replac$ by a spiral curve s g5tle z to seem all b /raight4 ,la/ly1 !re are a few cases1 su* z ,bell]ophon expansus & "s ,goniatites1 :]e ! out] spiral does n p]ceptibly *ange1 b ! :orls become m 8embrac+0 or ! :ole %ell m involute4 ,"h x is ! angle ( ret>dation1 ! ratio ( gr[? betwe5 ! out] & inn] p>ts ( ! :orl1 :i* und]goes a gradual *ange4 ,9 ord] to und]/& ! relation ( a close-coil$ %ell to "o ( its /raight] cong5]s1 to comp>e 7= example7 an #eea ,ammonite ) an ,or?oc]as1 x is necess>y to e/imate ! l5g? ( ! "r cone :i* has1 s to speak1 be5 coil$ up into ! spiral %ell4 ,our problem !n is1 ,to f9d ! l5g? ( a plane log>i?mic spiral1 9 t]ms ( ! radius & ! con/ant angle 4 ,9 ! annex$ diagram1 if ,,op be a radius vector1 ,,oq a l9e ( ref]5ce p]p5dicul> to ,,op1 & ,,pq a tang5t to ! curve1 ,,pq1 or sec 1 is equal 9 l5g? to ! spiral arc ,,op4 ,& ?is is practically obvi\s3 = ,,pp_/,,pr ds_/dr sec 1 & !re=e sec s_/r1 or ! ratio ( arc to radius vector4 ,illu/ration3 ,fig4 #bhb4 ,accord+ly1 ! ratio ( l1 ! total l5g?1 to r1 ! radius vector up to :i* ! total l5g? is to be measur$1 is express$ by a simple table ( secants2 z foll[s3 l_/r #e #ajjd #aj #ajae #bj #ajfd #cj #aafe #dj #acje #ej #aef #fj #bj #gj #bi #ge #ci #hj #eh #he #aae #hf #adc #hg #aia #hh #bhg #hi #egc #hi #aj #fhh #bj #hei #cj #aadf #dj #agai #ej #cdch #ee #fhge #ei #cdcgg #ij ,inf9ite ,putt+ ! same table inv]sely1 s z to %ew ! total #eeb l5g? 9 :ole numb]s1 9 t]ms ( ! radius1 we h z foll[s3 ,total l5g? 79 t]ms ( ! radius7 ,con/ant angle #b #fj #c #gj #ca #d #ge #cb #e #gh #bh #aj #hd #af #bj #hg #h #cj #hh #f #dj #hh #cd #ej #hh #ea #ajj #hi #bf #ajjj #hi #ef #cf #aj1jjj #hi #ei #cj ,accord+ly1 we see t 7#a71 :5 ! con/ant angle ( ! spiral is small1 ! spiral itself is sc>cely di/+ui%able f a /raight l9e1 & its l5g? is b v little great] ?an t ( its own radius vector4 ,?is rema9s pretty mu* ! case = a consid]able increase ( angle1 say f #j to #bj or m2 7#b7 = a v consid]ably great] increase ( ! con/ant angle1 say to #ej or m1 ! %ell w\ld only h ! appe>ance ( a g5tle curve2 7#c7 ! *>act]i/ic close coils ( ! ,nautilus or ,ammonite w\ld be typically repres5t$ only :5 ! con/ant angle lies )9 a few degrees on ei!r side ( ab\t #hj4 ,! coil$ up spiral ( a ,nautilus1 ) a con/ant angle ( ab\t #hj1 is ab\t six times ! l5g? ( its radius vector1 or r m ?an ?ree times its own diamet]2 :ile t ( an ,ammonite1 ) a con/ant angle (1 say1 f #he to #hh1 is f ab\t six to fifte5 times z long z its own diamet]4 ,& 7#d7 z we approa* an angle ( #ij 7at :i* po9t ! spiral vani%es 9 a circle71 ! l5g? ( ! coil increases ) enorm\s rapidity4 ,our spiral w\ld soon assume ! appe>ance ( ! close coils ( a ,nummulite1 & ! successive increm5ts ( bread? 9 ! successive :orls w\ld become inappreciable to ! eye4 ,! log>i?mic spiral ( high con/ant angle w\ld1 z we h already se51 t5d to become indi/+ui%able1 )\t ! mo/ c>eful measurem5t1 f an ,ar*im$ean spiral4 ,& x is obvi\s1 moreov]1 t our ord9>y me?ods ( #eec det]m9+ ! con/ant angle ( ! spiral w\ld n 9 ^! cases be accurate en\gh to enable u to measure ! l5g? ( ! coil3 we %\ld h to devise a new me?od1 bas$ on ! measurem5t ( radii or diamet]s ov] a l>ge numb] ( :orls4 ,! geometrical =m ( ! %ell involves _m o!r beautiful prop]ties1 ( great int]e/ to ! ma!matician1 b :i* x is n possible to r$uce to su* simple expressions z we h be5 cont5t to use4 ,= in/ance1 we may obta9 an equation :i* %all express completely ! surface ( any %ell1 9 t]ms ( pol> or ( rectangul> coord9ates 7z has be5 done by ,moseley & by ,blake71 or 9 ,hamiltonian vector notation4 ,x is likewise possible 7?\gh ( little int]e/ to ! naturali/7 to det]m9e ! area ( a con*oidal surface1 or ! volume ( a con*oidal solid1 & to f9d ! c5tre ( gravity ( ei!r surface or solid#ebd4 ,& ,blake has fur!r %ewn1 ) consid]able elaboration1 h[ we may deal ) ! symmetrical di/ortion1 due to pressure1 :i* fossil %ells are (t5 f\nd to h und]gone1 & h[ we may recon/itute by calculation _! orig9al undi/ort$ =m1--a problem :i*1 7 ! available me?ods only a little easi]1 w\ld be v helpful to ! palaeontologi/2 =1 z ,blake himself has %ewn1 x is easy to mi/ake a symmetrically di/ort$ specim5 ( 7= in/ance7 an ,ammonite1 = a new & di/9ct species ( ! same g5us4 ,b x is evid5t t to deal fully ) ! ma!matical problems conta9$ 91 or sugge/$ by1 ! spiral %ell1 w\ld require a :ole treatise1 r ?an a s+le *apt] ( ?is elem5t>y book4 ,let u !n1 leav+ ma!matics aside1 attempt to summ>ise1 & p]haps to ext5d1 :at has be5 said ab\t ! g5]al possibilities ( =m 9 ?is class ( organisms4 ,! ,univalve ,%ell3 a summ>y4 ,! surface ( any %ell1 :e!r discoid or turb9ate1 may be imag9$ to be g5]at$ by ! revolution ab\t a fix$ axis ( a clos$ curve1 :i*1 rema9+ always geometrically simil> to itself1 increases cont9ually its dim5sions3 &1 s9ce ! rate ( gr[? ( ! g5]at+ curve & its velocity ( rotation foll[ ! same law1 ! curve trac$ 9 space by correspond+ po9ts #eed 9 ! g5]at+ curve is1 9 all cases1 a log>i?mic spiral4 ,9 discoid %ells1 ! g5]at+ figure revolves 9 a plane p]p5dicul> to ! axis1 z 9 ,nautilus1 ! ,argonaut & ! ,ammonite4 ,9 turb9ate %ells1 x slides cont9ually along ! axis ( revolution1 & ! curve 9 space g5]at$ by any giv5 po9t p>takes1 !re=e1 ( ! "* ( a helix1 z well z ( a log>i?mic spiral2 x may be /rictly entitl$ a helico-spiral4 ,su* turb9ate or helico-spiral %ells include ! snail1 ! p]iw9kle & all ! common typical ,ga/ropods4 ,illu/ration3 ,fig4 #bhc4 ,section ( a spiral1 or turb9ate1 univalve1 ,triton corrugatus1 ,lam4 7,f ,woodw>d47 ,! g5]at+ figure1 z repres5t$ by ! m\? ( ! %ell1 is sometimes a plane curve1 ( simple =m2 9 o!r & m num]\s cases1 x becomes m complicat$ 9 =m & its b\nd>ies d n lie 9 "o plane3 b 9 su* cases z ^! we may replace x by its 8trace10 on a plane at "s def9ite angle to ! direction ( gr[?1 = in/ance by its =m z x appe>s 9 a section ?r\gh ! axis ( ! helicoid %ell4 ,! g5]at+ curve is ( v v>i\s %apes4 ,x is circul> 9 ,scal>ia or ,cyclo/oma1 & 9 ,spirula2 x may be consid]$ z a segm5t ( a circle 9 ,natica or 9 ,planorbis4 ,x is approximately triangul> 9 ,conus1 & rhomboidal 9 ,sol>ium or ,potamides4 ,x is v commonly m or less elliptical3 ! long axis ( ! ellipse be+ p>allel to ! axis ( ! %ell 9 ,oliva & ,cypraea2 all b p]p5dicul> to x 9 _m ,tro*i2 & oblique to x 9 _m well-m>k$ cases1 su* z ,/omatella1 ,lamell>ia1 ,sig>etus haliotoides 7,fig4 #bhd7 & ,haliotis4 ,9 ,nautilus pompilius x is approximately a semi-ellipse1 & 9 ,n4 umbilicatus r m ?an a semi-ellipse1 ! long axis ly+ 9 bo? cases p]p5dicul> to ! axis ( ! %ell#ebe4 ,its #eee =m is seldom op5 to easy ma!matical expression1 save :5 x is an actual circle or ellipse2 b an exception to ?is rule may be f\nd 9 c]ta9 ,ammonites1 =m+ ! gr\p 8,cordati10 :]e 7z ,blake po9ts out7 ! curve is v ne>ly repres5t$ by a c>dioid1 ^: equation is r a7#a cos 74 ,! g5]at+ curve may gr[ sl[ly or quickly2 its gr[?-factor is v sl[ 9 ,d5talium or ,turritella1 v rapid 9 ,n]ita1 or ,pileopsis1 or ,haliotis or ! ,limpet4 ,x may conta9 ! axis 9 its plane1 z 9 ,nautilus2 x may be p>allel to ! axis1 z 9 ! majority ( ,ga/ropods2 or x may be incl9$ to ! axis1 z x is 9 a v m>k$ degree 9 ,haliotis4 ,9 fact1 9 ,haliotis ! g5]at+ curve is s oblique to ! axis ( ! %ell t ! latt] appe>s to gr[ by additions to "o m>g9 only 7cf4 ,fig4 #beh71 z 9 ! case ( ! op]cula ( ,turbo & ,n]ita ref]r$ to on p4 #ebb2 & ?is is :at ,moseley suppos$ x to d4 ,illu/ration3 ,fig4 #bhd4 ,a1 ,lamell>ia p]spicua2 ,b1 ,sig>etus haliotoides4 7,aft] ,woodw>d47 ,! g5]al appe>ance ( ! entire %ell is det]m9$ 7ap>t f ! =m ( its g5]at+ curve7 by ! magnitude ( ?ree angles2 & ^! 9 turn are det]m9$1 z has be5 suffici5tly expla9$1 by ! ratios ( c]ta9 velocities ( gr[?4 ,^! angles are 7#a7 ! con/ant angle ( ! log>i?mic spiral 772 7#b7 9 turb9ate %ells1 ! envelop+ angle ( ! cone1 or 7tak+ half t angle7 ! angle 77 :i* a tang5t to ! :orls makes ) ! axis ( ! %ell2 & 7#c7 an angle call$ ! 8angle ( ret>dation0 771 :i* expresses ! ret>dation 9 gr[? ( #eef ! inn] z comp>$ ) ! out] "p ( ea* :orl1 & !re=e measures ! ext5t to :i* "o :orl ov]laps1 or ! ext5t to :i* x is sep>at$ f1 ano!r4 ,! spiral angle 77 is v small 9 a limpet1 :]e x is usually tak5 z #j2 b x is evid5tly ( a significant am\nt1 ?\gh obscur$ by ! %ortness ( ! tubul> %ell4 ,9 ,d5talium x is /ill small1 b suffici5t to give ! appe>ance ( a regul> curve2 x am\nts "h probably to ab\t #cj to #dj4 ,9 ,haliotis x is f ab\t #gj to #ge2 9 ,nautilus ab\t #hj2 & x lies betwe5 #hj & #he1 or ev5 m1 9 ! majority ( ,ga/ropods4 ,! case ( ,fissurella is curi\s4 ,"h we h1 app>5tly1 a conical %ell ) no trace ( spiral curvature1 or 79 o!r words7 ) a spiral angle :i* approximates to #j2 b 9 ! m9ute embryonic %ell 7z 9 t ( ! limpet7 a spiral convolution is di/9ctly to be se54 ,x w\ld seem1 !n1 t :at we h to d ) "h is an unusually l>ge gr[?-factor 9 ! g5]at+ curve1 :i* causes ! %ell to dilate into a cone ( v wide angle1 ! apical portion ( :i* has become lo/ or absorb$1 & ! rema9+ "p ( :i* is too %ort to %[ cle>ly its intr9sic curvature4 ,9 ! closely alli$ ,em>g9ula1 !re is likewise a well-m>k$ spiral 9 ! embryo1 :i* h[ev] is /ill manife/$ 9 ! curvature ( ! adult1 ne>ly conical1 %ell4 ,9 bo? cases we h to d ) a v wide-angl$ cone1 & ) a high ret>dation-factor = its inn]1 or po/]ior1 bord]4 ,! s]ies is cont9u$1 f ! app>5tly simple cone to ! complete spiral1 ?r\gh su* =ms z ,calyptraea4 ,! angle 1 z we h se51 is n always1 nor rigor\sly1 a con/ant angle4 ,9 "s ,ammonites x may increase ) age1 ! :orls becom+ clos] & clos]2 9 o!rs x may decrease rapidly1 & ev5 fall to z]o1 ! coil$ %ell !n /raight5+ out1 z 9 ,lituites & simil> =ms4 ,x dim9i%es some:at1 also1 9 _m ,or?oc]ata1 :i* are slightly curv$ 9 y\?1 b /raight 9 age4 ,x t5ds to increase notably 9 "s common l&-%ells1 ! ,pupae & ,bulimi2 & x decreases 9 ,succ9ea4 ,directly relat$ to ! angle is ! ratio :i* subsi/s betwe5 ! bread?s ( successive :orls4 ,! foll[+ table gives a few illu/rations ( ?is ratio 9 p>ticul> cases1 9 addition to ^? :i* we h already /udi$4 #eeg ,ratio ( bread? ( consecutive :orls4 ,po9t$ ,turb9ates ,telescopium fuscum #aad ,acus subulatus #aaf 99,turritella t]ebellata #aah 99,turritella imbricata #abj ,c]i?ium palu/re #abb ,turritella duplicata #abc ,melanopsis t]ebralis #abc ,c]i?ium nodulosum #abd 99,turritella c>9ata #abe ,acus cr5ulatus #abe ,t]ebra maculata 7,fig4 #bhe7 #abe 99,c]i?ium lignit>um #abf ,acus dimidiatus #abh ,c]i?ium sulcatum #acb ,fusus longissimus #acd 99,pleurotom>ia conoidea #acd ,tro*us niloticus 7,fig4 #bhf7 #ada ,mitra episcopalis #adc ,fusus antiquus #aej ,scal>ia pretiosa #aef ,fusus colosseus #aga ,phasianella bulloides #ahj ,helico/yla poly*roa #bjj ,obtuse ,turb9ates & ,discoids ,conus virgo #abe ,conus litt]atus #adj ,conus betul9a #adc 99,helix nemoralis #aej 99,sol>ium p]spectivum #aej ,sol>ium tro*le>e #afb ,sol>ium magnificum #age 99,natica ap]ta #bjj ,euomphalus p5tangulatus #bjj ,planorbis corneas #bjj ,sol>opsis pellis-s]p5tis #bjj ,dolium zonatum #baj 99,natica glauc9a #cjj ,nautilus pompilius #cjj ,haliotis excavatus #dbj ,haliotis p>vus #fjj ,delph9ula atrata #fjj ,haliotis rugoso-plicata #icj ,haliotis viridis #ajjj ,^? m>k$ 99 f ,naumann2 ! re/ f ,macali/]#ebf4 ,9 ! case ( turb9ate %ells1 we require to take into acc\nt ! angle 1 9 ord] to det]m9e ! spiral angle f ! ratio ( ! bread?s ( consecutive :orls2 = ! %ort table giv5 on p4 #ecd is only applicable to discoid %ells1 9 :i* ! angle is an angle ( #ij4 ,our =mula1 z m5tion$ on p4 #eah n[ becomes ,r #b s9 cot 4 ,= ?is =mula ,i h work$ out ! foll[+ table4 #eeh ,table %ew+ values ( ! spiral angle correspond+ to c]ta9 ratios ( bread? ( successive :orls ( ! %ell1 = v>i\s values ( ! apical semi-angle 4 ,ratio ,r_/#a #e #aj #ae #bj #cj #dj #ej #fj #gj #hj #ij #aa #hj #h #he #j #hf #dd #hg #bh #hh #af #hh #ci #hh #eb #hi #j #hi #d #hi #g #hi #h #abe #fg #ea #gh #bg #hb #aa #hd #e #he #ef #hf #ej #hg #ba #hg #ci #hg #ej #hg #ef #hg #eh #ae #ec #cj #fi #cg #gf #j #gi #ba #hb #ci #hd #af #he #ac #he #dd #hf #d #hf #ae #hf #ah #bj #ch #bj #eg #ce #ff #ee #gc #aa #gg #cd #hj #af #ha #eb #hb #de #hc #ah #hc #cg #hc #db #be #cj #ec #ej #j #fj #ce #fg #j #gc #de #gg #ac #gi #ai #hj #bf #ha #aa #ha #ce #ha #db #cj #bf #cb #dd #ej #ef #j #fc #j #gj #de #gd #de #gg #ag #gh #ce #gi #bh #gi #ef #hj #e #ce #bc #cg #da #e #eb #be #ei #ej #fh #ae #gb #de #ge #ce #gg #b #gh #a #gh #cc #gh #dc #dj #ba #ce #ch #aj #di #ce #eg #ae #ff #aj #ga #c #gd #i #ge #db #gf #dg #gg #bb #gg #cd #de #bj #j #cf #j #dg #ae #ee #e #fd #be #fi #ce #gb #ed #gd #cc #ge #dc #gf #bj #gf #ce #ej #ah #de #cd #aj #de #bj #ec #ae #fb #ee #fh #ae #ga #dh #gc #ca #gd #de #ge #be #ge #ch #ajj #ac #be #be #bj #ce #ae #dc #e #ec #de #fj #bj #fd #eg #fg #d #fh #db #fi #ce #fi #ec #bjj #aj #be #bj #j #bh #cj #ce #de #df #be #ec #be #eh #eb #fa #aj #fc #f #fd #aj #fd #ca #ejj #h #j #ae #ce #bb #ce #bh #ej #ch #de #de #ee #eb #a #ed #ah #ef #bh #eg #db #eh #f #ajjj #f #ej #ac #bj #ai #cj #be #e #cd #bj #da #ae #dg #ce #di #de #eb #c #ec #bj #ec #df #eei ,f ?is table1 by int]polation1 we may easily fill 9 ! approximate values ( 1 z soon z we h det]m9$ ! apical angle & measur$ ! ratio ,r2 z foll[s3 ,r ,turritella sp4 #aab #g #ha ,c]i?ium nodulosum #abd #ae #hb ,conus virgo #abe #gj #hh ,mitra episcopalis #adc #af #gh ,scal>ia pretiosa #aef #bf #ha ,phasianella bulloides #ahj #bf #hj ,sol>ium p]spectivum #aej #ec #he ,natica ap]ta #bjj #gj #hc ,planorbis corneus #bjj #ij #hd ,euomphalus p5tangulatus #bjj #ij #hd ,we see f ?is t %ells s diff]5t 9 appe>ance z ,c]i?ium1 ,sol>ium1 ,natica & ,planorbis diff] v little inde$ 9 ! magnitude ( ! spiral angle 1 t is to say 9 ! relative velocities ( radial & tang5tial gr[?4 ,x is ^u ! angle t ! diff]5ce 9 _! =m ma9ly dep5ds3 t is to say ! am\nt ( longitud9al %e>+1 or displacem5t p>allel to ! axis ( ! %ell4 ,illu/ration3 ,fig4 #bhe4 ,t]ebra maculata1 ,l4 ,! envelop+ angle1 or r semi-angle 771 ( ! cone may be tak5 z #ij 9 ! discoid %ells1 su* z ,nautilus & ,planorbis4 ,x is /ill a l>ge angle1 ( #gj or #ge1 9 ,conus or 9 ,cymba1 some:at less 9 ,cassis1 ,h>pa1 ,dolium or ,natica2 x is ab\t #ej to #ee 9 ! v>i\s species ( ,sol>ium1 ab\t #ce 9 ! typical ,tro*i1 su* z ,t4 niloticus or ,t4 zizyph9us1 & ab\t #be or #bf 9 ,scal>ia pretiosa & ,phasianella bulloides2 x becomes a v acute angle1 ( #ae1 #aj1 or ev5 less1 9 ,eulima1 ,turritella or ,c]i?ium4 ,! co/ly ,conus gloria-m>is1 "o ( ! #efj great treasures ( ! con*ologi/1 diff]s f its cong5]s 9 no important p>ticul> save 9 ! some:at 8produc$0 spire1 t is to say 9 ! comp>atively l[ value ( ! angle 4 ,illu/ration3 ,fig4 #bhf4 ,tro*us niloticus1 ,l4 ,a v>iation ) advanc+ age ( is common1 b 7z ,blake po9ts out7 x is (t5 n to be di/+ui%$ or dis5tangl$ f an alt]ation ( 4 ,:e!r alone1 or comb9$ ) a *ange 9 1 we f9d x 9 all ^? _m ,ga/ropods ^: :orls _c all be t\*$ by ! same envelop+ cone1 & ^: spire is accord+ly describ$ z concave or convex4 ,! =m] condition1 z we h x 9 ,c]i?ium1 & 9 ! cusp-l spire ( ,cassis1 ,dolium & "s ,cones1 is mu* ! common] ( ! two4 ,& su* t5d5cy to decrease may lead to becom+ a negative angle2 9 :i* case we h a depress$ spire1 z 9 ! ,cypraeae4 ,:5 we f9d a 8rev]s$ %ell10 a :elk or a snail = in/ance ^: spire w9ds to ! left in/ead ( to ! "r1 we may describe x ma!matically by ! simple /atem5t t ! angle has *ang$ sign4 ,9 ! g5us ,ampull>ia1 or ,apple-snails1 inhabit+ tropical or sub-tropical riv]s1 we h a rem>kable condition2 = 9 c]ta9 8species0 ! spiral turns to ! "r1 9 o!rs to ! left1 & 9 o!rs aga9 we h a flatt5$ #efa 8discoid0 %ell2 & fur!rmore we h num]\s int]m$iate /ages1 on ei!r side1 %ew+ "r & left-h&$ spirals ( v>y+ degrees ( acut5ess#ebg4 ,9 ?is case1 ! angle may be said to v>y1 )9 ! limits ( a g5us1 f some:]e ab\t #ce to some:]e ab\t #abe4 ,! angle ( ret>dation 77 is v small 9 ,d5talium & ,patella2 x is v l>ge 9 ,haliotis4 ,x becomes inf9ite 9 ,argonauta & 9 ,cypraea4 ,connect$ ) ! angle ( ret>dation are ! v>i\s possibilities ( contact or sep>ation1 9 v>i\s degrees1 betwe5 adjac5t :orls 9 ! discoid1 & betwe5 bo? adjac5t & opposite :orls 9 ! turb9at$ %ell4 ,b ) ^! ph5om5a we h already dealt suffici5tly4 ,( ,bivalve ,%ells4 ,hi!rto we h dealt only ) univalve %ells1 & x is 9 ^! t all ! ma!matical problems connect$ ) ! spiral1 or helico-spiral1 are be/ illu/rat$4 ,b ! case ( ! bivalve %ell1 ( ,lamellibran*s or ( ,bra*iopods1 pres5ts no ess5tial diff]5ce1 save only t we h "h to d ) two conjugate spirals1 ^: two axes h a def9ite relation to "o ano!r1 & "s fre$om ( rotatory movem5t relatively to "o ano!r4 ,! g5]at+ curve is p>ticul>ly well se5 9 ! bivalve1 :]e x simply con/itutes :at we call 8! outl9e ( ! %ell40 ,x is = ! mo/ "p a plane curve1 b n always2 = !re are =ms1 su* z ,hippopus1 ,tridacna & _m ,cockles1 or ,rhyn*onella & ,spirif] among ! ,bra*iopods1 9 :i* ! edges ( ! two valves int]lock1 & o!rs1 su* z ,pholas1 ,mya1 etc41 :]e 9 "p !y fail to meet4 ,9 su* cases z ^! ! g5]at+ curves are conjugate1 hav+ a simil> relation1 b ( opposite sign1 to a m$ian plane ( ref]5ce4 ,a great v>iety ( =m is exhibit$ by ^! g5]at+ curves among ! bivalves4 ,9 a good _m cases ! curve is approximately circul>1 z 9 ,anomia1 ,cyclas1 ,artemis1 ,isoc>dia2 x is ne>ly semi-circul> 9 ,argiope4 ,x is approximately elliptical 9 ,or?is & 9 ,anodon2 x may be call$ semi-elliptical 9 ,spirif]4 ,x is a ne>ly rectil9e> #efb triangle 9 ,li?oc>dium1 & a curvil9e> triangle 9 ,mactra4 ,_m app>5tly div]se b m or less relat$ =ms may be %ewn to be de=mations ( a common type1 by a simple application ( ! ma!matical !ory ( 8,trans=mations10 :i* we %all h to /udy 9 a lat] *apt]4 ,9 su* a s]ies z is furni%$1 = in/ance1 by ,g]villea1 ,p]na1 ,avicula1 ,modiola1 ,mytilus1 etc41 a 8simple %e>0 acc\nts = mo/1 if n all1 ( ! app>5t diff]5ces4 ,^u ! surface ( ! bivalve %ell we usually see ) great cle>ness ! 8l9es ( gr[?0 :i* repres5t ! successive m>g9s ( ! %ell1 or 9 o!r words ! successive positions assum$ dur+ gr[? by ! gr[+ g5]at+ curve2 & we h a good illu/ration1 accord+ly1 ( h[ x is *>act]i/ic ( ! g5]at+ curve t x %\ld con/antly increase1 :ile nev] alt]+ its geometric simil>ity4 ,und]ly+ ^! 8l9es ( gr[?10 :i* are s *>act]i/ic ( a molluscan %ell 7& ( n a few o!r organic =mations71 !re is1 !n1 a 8law ( gr[?0 :i* we may attempt to enquire into & :i* may be illu/rat$ 9 v>i\s ways4 ,! simple/ cases are ^? 9 :i* we c /udy ! l9es ( gr[? on a m or less flatt5$ %ell1 su* z ! "o valve ( an oy/]1 a ,pect5 or a ,tell9a1 or "s su* bivalve mollusc4 ,"h ar\nd an orig91 ! s-call$ 8umbo0 ( ! %ell1 we h a s]ies ( curves1 sometimes ne>ly circul>1 sometimes elliptical1 & (t5 asymmetrical2 & su* curves are obvi\sly n 8conc5tric10 ?\gh we are (t5 apt to call !m s1 b are always 8co-axial40 ,?is mann] ( arrangem5t may be illu/rat$ by v>i\s analogies4 ,we might = in/ance comp>e x to a s]ies ( waves1 radiat+ outw>ds f a po9t1 ?r\gh a m$ium :i* (f]$ a resi/ance increas+1 ) ! angle ( div]g5ce1 accord+ to "s simple law4 ,we may f9d ano!r1 & p]haps a simpl] illu/ration z foll[s3 ,9 a v simple & beautiful !orem1 ,galileo %ew$ t1 if we imag9e a numb] ( incl9$ planes1 or gutt]s1 slop+ d[nw>ds 79 a v]tical plane7 at v>i\s angles f a common />t+-po9t1 & if we imag9e a numb] ( balls roll+ ea* d[n its own gutt] "u ! influ5ce ( gravity 7& )\t h9drance f friction71 !n1 at any giv5 in/ant1 ! locus ( #efc all ^! mov+ bodies is a circle pass+ ?r\gh ! po9t ( orig94 ,= ! accel]ation along any "o ( ! slop+ pa?s1 = in/ance ,,ab 7,fig4 #bhg71 is su* t ,,ab g cos t#b g ,,ab_/,,ac t#b4 ,!re=e t#b #b_/;g ,,ac4 ,illu/ration3 ,fig4 #bhg4 ,t is to say1 all ! balls rea* ! circumf]5ce ( ! circle at ! same mom5t z ! ball :i* drops v]tically f ,a to ,c4 ,:]e1 !n1 z (t5 happ5s1 ! g5]at+ curve ( ! %ell is approximately a circle pass+ ?r\gh ! po9t ( orig91 we may consid] ! accel]ation ( gr[? along v>i\s radiants to be gov]n$ by a simple ma!matical law1 closely ak9 to t simple law ( accel]ation :i* gov]ns ! movem5ts ( a fall+ body4 ,&1 mutatis mut&is1 a simil> def9ite law und]lies ! cases :]e ! g5]at+ curve is cont9ually elliptical1 or :]e x assumes "s m complex1 b /ill regul> & con/ant =m4 ,x is easy to ext5d ! proposition to ! p>ticul> case :]e ! l9es ( gr[? may be consid]$ elliptical4 ,9 su* a case we h x#b_/;a#b y#b_/;b#b #a1 :]e a & b are ! major & m9or axes ( ! ellipse4 ,or1 *ang+ ! orig9 to ! v]tex ( ! figure x#b_/;a#b #bx_/a y#b_/;b#b #j1 giv+ 7x a7#b_/;a#b y#b_/;b#b #a4 ,!n1 transf]r+ to pol> coord9ates1 :]e r cos x1 r s9 y1 we h 7r cos#b 7_/a#b 7#b cos 7_/a 7r s9 7_/b#b #j1 #efd :i* is equival5t to r 7#b;a b#b cos 7_/77b#b cos#b 7 7a#b s9#b 771 or1 elim9at+ ! s9e-function1 r 7#b;a b#b cos 7_/77b#b a#b7 cos#b a#b74 ,obvi\sly1 9 ! case :5 a b1 ?is gives u ! circul> sy/em :i* we h already consid]$4 ,= o!r values1 or ratios1 ( a & b1 & = all values ( 1 we c easily con/ruct a table1 ( :i* ! foll[+ is a sample3 ,*ords ( an ellipse1 ^: major & m9or axes 7a1 b7 are 9 c]ta9 giv5 ratios4 a_/b #a_/c #a_/b #b_/c #a_/a #c_/b #b_/a #c_/a #j #aj #aj #aj #aj #aj #aj #aj #aj #aja #aja #ajjb #ihe #idh #ijb #gic #bj #aje #ajc #ajje #idj #hbj #fie #dhe #cj #aaae #ajfe #ajje #hff #fff #die #bhi #dj #aba #aaa #iie #gff #eje #cdb #agh #ej #acd #aade #ieb #fdc #cgb #bcb #aac #fj #aej #aadb #heg #ejj #beh #aeb #jga #gj #aei #ajae #fgj #cdb #afc #jib #jdb #hj #abce #fce #cge #agd #jgh #jde #jbj #ij #jj #jj #jj #jj #jj #jj #jj ,illu/ration3 ,fig4 #bhh4 ,! coaxial ellipses :i* we !n draw1 f ! values giv5 9 ! table1 are su* z are %ewn 9 ,fig4 #bhh = ! ratio a_/b #c_/a1 & 9 ,fig4 #bhi = ! ratio a_/b 2 ^! are fair approximations to ! actual outl9es1 & to ! actual arrangem5t ( ! l9es ( gr[?1 9 su* =ms z ,solecurtus or ,cultellus1 & 9 ,tell9a or ,psammobia4 ,x is n difficult to introduce a con/ant into our equation to meet ! case ( a %ell :i* is some:at unsymmetrical on ei!r side ( ! m$ian axis4 ,x is a some:at m tr\blesome matt]1 h[ev]1 to br+ ^! configurations into relation ) a 8law ( gr[?10 z 0 s easily done 9 ! case ( ! circul> figure3 9 o!r words1 to #efe =mulate a law ( accel]ation accord+ to :i* po9ts />t+ f ! orig9 ,o1 & mov+ along radial l9es1 w\ld all lie1 at any future epo*1 on an ellipse pass+ ?r\gh ,o2 & ?is calculation we ne$ n ent] into4 ,illu/ration3 ,fig4 #bhi4 ,all t we are imm$iately conc]n$ ) is ! simple fact t :]e a velocity1 su* z our rate ( gr[?1 v>ies ) its direction1--v>ies t is to say z a function ( ! angul> div]g5ce f a c]ta9 axis1--!n1 9 a c]ta9 simple case1 we get l9es ( gr[? laid d[n z a sy/em ( coaxial circles1 &1 :5 ! function is a m complex "o1 z a sy/em ( ellipses or ( o!r m complicat$ coaxial figures1 :i* figures may or may n be symmetrical on ei!r side ( ! axis4 ,among our bivalve mollusca we %all f9d ! l9es ( gr[? to be approximately circul> 91 = in/ance1 ,anomia2 9 ,lima 7e4g4 ,l4 subauriculata7 we h a sy/em ( ne>ly symmetrical ellipses ) ! v]tical axis ab\t twice ! transv]se2 9 ,sol5 pellucidus1 we h aga9 a sy/em ( l9es ( gr[? :i* are n f> f be+ symmetrical ellipses1 9 :i* h[ev] ! transv]se is betwe5 ?ree & f\r times z great z ! v]tical axis4 ,9 ! great majority ( cases1 we h a simil> ph5om5on ) ! fur!r complication ( slight1 b occasionally v consid]able1 lat]al asymmetry4 ,9 c]ta9 little ,cru/acea 7( ! g5us ,e/h]ia7 ! c>apace takes ! =m ( a bivalve %ell1 closely simulat+ t ( a #eff lamellibran*iate mollusc1 & be>+ l9es ( gr[? 9 all respects analog\s to or ev5 id5tical ) ^? ( ! latt]4 ,! explanation is v curi\s & int]e/+4 ,9 ord9>y ,cru/acea ! c>apace1 l ! re/ ( ! *it9is$ & calcifi$ integum5t1 is %$ (f 9 successive m\lts1 & is re/or$ aga9 z a :ole4 ,b 9 ,e/h]ia 7& "o or two o!r small cru/acea7 ! m\lt is incomplete3 ! old c>apace is reta9$1 & ! new1 gr[+ up und]nea? x1 adh]es to x l a l9+1 & projects beyond its edge3 s t 9 c\rse ( "t ! m>g9s ( successive old c>apaces appe> z 8l9es ( gr[?0 ^u ! surface ( ! %ell4 ,9 ?is mode ( =mation1 !n 7b n 9 ! usual "o71 we obta9 a /ructure :i* 8is p>tly old & p>tly new10 & ^: successive increm5ts are all simil>1 simil>ly situat$1 & enl>g$ 9 a cont9u$ progression4 ,we h1 9 %ort1 all ! conditions appropriate & necess>y = ! developm5t ( a log>i?mic spiral2 & ?is log>i?mic spiral 7?\gh x is "o ( small angle7 gives its own "* to ! /ructure1 & causes ! little c>apace to p>take ( ! *>act]i/ic con=mation ( ! molluscan %ell4 ,! ess5tial simplicity1 z well z ! great regul>ity ( ! 8curves ( gr[?0 :i* result 9 ! famili> configurations ( our bivalve %ells1 suffici5tly expla91 9 a g5]al way1 ! ease ) :i* !y may be imitat$1 z = in/ance 9 ! s-call$ 8artificial %ells0 :i* ,kapp]s has produc$ f ! con*oidal =m & lam9ation ( lumps ( melt$ & quickly cool$ p>aff9#ebh4 ,9 ! above acc\nt ( ! ma!matical =m ( ! bivalve %ell1 we h suppos$1 = simplicity's sake1 t ! pole or orig9 ( ! sy/em is at a po9t :]e all ! successive curves t\* "o ano!r4 ,b su* an arrangem5t is nei!r !oretically probable1 nor is x actually ! case2 = x w\ld mean t 9 a c]ta9 direction gr[? fell1 n m]ely to a m9imum1 b to z]o4 ,z a matt] ( fact1 ! c5tre ( ! sy/em 7! 8umbo0 ( ! con*ologi/s7 lies n at ! edge ( ! sy/em1 b v ne> to x2 9 o!r words1 !re is a c]ta9 am\nt ( gr[? all r\nd4 ,b to take acc\nt ( ?is condition w\ld involve m tr\blesome ma!matics1 & x is obvi\s t ! =ego+ illu/rations are a suffici5tly ne> approximation to ! actual case4 #efg ,among ! bivalves ! spiral angle 77 is v small 9 ! flatt5$ %ells1 su* z ,or?is1 ,l+ula or ,anomia4 ,x is l>g]1 z a rule1 9 ! ,lamellibran*s ?an 9 ! ,bra*iopods1 b 9 ! latt] x is ( consid]able magnitude among ! ,p5tam]i4 ,among ! ,lamellibran*s x is l>ge/ 9 su* =ms z ,isoc>dia & ,dic]as1 & 9 ! v curi\s g5us ,capr9ella2 9 all ( ^! la/-nam$ g5]a its magnitude leads to ! production ( a spiral %ell ( sev]al :orls1 precisely z 9 ! univalves4 ,! angle is usually equal1 b ( opposite sign1 9 ! two valves ( ! ,lamellibran*1 & usually ( opposite sign b unequal 9 ! two valves ( ! ,bra*iopod4 ,x is v unequal 9 _m ,o/reidae1 & especially 9 su* =ms z ,gryphaea1 or 9 ,capr9ella1 :i* is a k9d ( exagg]at$ ,gryphaea4 ,occasionally x is ( ! same sign 9 bo? valves 7t is to say1 bo? valves curve ! same way7 z we see sometimes 9 ,anomia1 & mu* bett] 9 ,productus or ,/rophom5a4 ,illu/ration3 ,fig4 #bij4 ,capr9ella adv]sa4 7,aft] ,woodw>d47 ,illu/ration3 ,fig4 #bia4 ,section ( ,productus 7,/rophom5a7 sp4 7,f ,woods47 ,ow+ to ! l>ge gr[?-factor ( ! g5]at+ curve1 & ! comp>atively small angle ( ! spiral1 ! :ole %ell seldom assumes a spiral =m s conspicu\s z to manife/ 9 a typical way ! helical twi/ or %e> :i* is s conspicu\s 9 ! #efh majority ( univalves1 or to let u measure or e/imate ! magnitude ( ! apical angle 77 ( ! envelop+ cone4 ,?is h[ev] we c d 9 =ms l ,isoc>dia & ,dic]as2 :ile 9 ,capr9ella we see t ! :orls lie 9 a plane p]p5dicul> to ! axis1 =m+ a discoidal spire4 ,z 9 ! latt] %ell1 s also univ]sally among ! ,bra*iopods1 !re is no lat]al asymmetry 9 ! plane ( ! g5]at+ curve su* z to lead to ! developm5t ( a helix2 b 9 ! majority ( ! ,lamellibran*iata x is obvi\s1 f ! obliquity ( ! l9es ( gr[?1 t ! angle is significant 9 am\nt4 ,illu/ration3 ,fig4 #bib4 ,skeletal loop ( ,t]ebratula4 7,f ,woods47 ,! s-call$ 8spiral arms0 ( ,spirif] & _m o!r ,bra*iopods are n difficult to expla94 ,!y beg9 z a s+le /ructure1 9 ! =m ( a loop ( %elly sub/ance1 atta*$ to ! dorsal valve ( ! %ell1 9 ! neighb\rhood ( ! h+e4 ,?is loop has a curvature ( its own1 simil> to b n necess>ily id5tical ) t ( ! valve to :i* x is atta*$2 & ?is curvature w t5d to be develop$1 by cont9u\s & symmetrical gr[?1 into a fully =m$ log>i?mic spiral1 s f> z x is p]mitt$ to d s "u ! con/ra9t ( ! %ell 9 :i* x is conta9$4 ,9 v>i\s ,t]ebratulae we see ! spiral gr[? ( ! loop1 m or less flatt5$ & di/ort$ by ! re/ra9+ pressure ( ! v5tral valve4 ,9 a numb] ( cases ! loop rema9s small1 b gives (f two ne>ly p>allel bran*es or (f%oots1 :i* cont9ue to gr[4 ,& ^!1 />t+ ) j su* a slight curvature z ! loop itself possess$1 gr[ on & on till !y may =m close-w\nd spirals1 always provid$ t ! 8spiral angle0 ( ! curve is su* t ! result+ spire c be freely conta9$ )9 ! cavity ( ! %ell4 ,ow+ to ! bilat]al symmetry ( ! :ole sy/em1 ! case w be r>e1 & unlikely to occur1 9 :i* ea* sep>ate arm w coil /rictly 9 a plane1 s z to con/itute a discoid spiral2 = ! orig9al #efi direction ( ea* ( ! two bran*es1 p>allel to ! valve 7or ne>ly s7 & outw>ds f ! middle l9e1 w t5d to con/itute a curve ( d\ble curvature1 & s1 on fur!r gr[?1 to develop into a helicoid4 ,?is is :at actually occurs1 9 ! great majority ( cases4 ,b ! curvature may be su* t ! helicoid gr[s outw>ds f ! middle l9e1 or inw>ds t[>ds ! middle l9e1 a v slight diff]5ce 9 ! initial curvature be+ suffici5t to direct ! spire ! "o way or ! o!r2 ! middle c\rse ( an undeviat+ discoid spire w be r>e1 f ! usual lack ( any obvi\s controll+ =ce to prev5t its deviation4 ,! cases 9 :i* ! helicoid spires po9t t[>ds1 or po9t away f1 ! middle l9e are ascrib$1 9 zoological classification1 to p>ticul> 8families0 ( ,bra*iopods1 ! =m] ,illu/ration3 ,fig4 #bic4 ,spiral arms ( ,spirif]4 7,f ,woods47 ,illu/ration3 ,fig4 #bid4 ,inw>dly direct$ spiral arms ( ,atrypa4 condition def9+ 7or help+ to def9e7 ! ,atrypidae & ! latt] ! ,spirif]idae & ,a?yridae4 ,x is obvi\s t ! incipi5t curvature ( ! arms1 & consequ5tly ! =m & direction ( ! spirals1 w be influ5c$ by ! surr\nd+ pressures1 & ^! 9 turn by ! g5]al %ape ( ! %ell4 ,we %all expect1 accord+ly1 to f9d ! long outw>dly direct$ spirals associat$ ) %ells :i* are transv]sely elongat$1 z ,spirif] is2 :ile ! m r\nd$ ,atrypas w t5d to ! opposite condition4 ,9 a few cases1 z 9 ,cyrt9a or ,reticul>ia1 :]e ! %ell is comp>atively n>r[ b long1 & :]e ! uncoil$ basal support ( ! arms is long also1 ! spiral coils into :i* ! latt] gr[ are turn$ backw>ds1 9 ! direction :]e !re is room = !m4 ,& 9 ! few cases :]e ! %ell is v consid]ably flatt5$1 ! spirals 7if !y f9d room #egj to gr[ at all7 w be con/ra9$ to d s 9 a discoid or ne>ly discoid fa%ion1 & ?is is actually ! case 9 su* flatt5$ =ms z ,kon9ck9a or ,!cidium4 ,! ,%ells ( ,pt]opods4 ,:ile ma!matically speak+ we are entitl$ to look ^u ! bivalve %ell ( ! ,lamellibran* z consi/+ ( two di/9ct elem5ts1 ea* comp>able to ! entire %ell ( ! univalve1 we h no biological gr\nds = su* a /atem5t2 = ! %ell arises f a s+le embryonic orig91 & aft]w>ds becomes split into portions :i* con/itute ! two sep>ate valves4 ,we c p]haps ?r[ "s indirect light ^u ?is ph5om5on1 & ^u sev]al o!r ph5om5a connect$ ) %ell-gr[?1 by a consid]ation ( ! simple conical or tubul> %ells ( ! ,pt]opods4 ,! %ells ( ! latt] are 9 few cases suitable = simple ma!matical inve/igation1 b nev]!less !y are ( v consid]able int]e/ 9 connection ) our g5]al problem4 ,! morphology ( ! ,pt]opods is by no means well und]/ood1 & 9 speak+ ( !m ,i w assume t !re are /ill gr\nds = believ+ 79 spite ( ,boas' & ,pels5e]'s argum5ts7 t !y are directly relat$ to1 or may at lea/ be directly comp>$ )1 ! ,cephalopoda#ebi4 ,illu/ration3 ,fig4 #bie4 ,pt]opod %ells3 7#a7 ,cuvi]9a columnella2 7#b7 ,cleodora *i]*iae2 7#c7 ,c4 pygmaea4 7,aft] ,boas47 ,! simple/ %ells among ! ,pt]opods h ! =m ( a tube1 m or less cyl9drical 7,cuvi]9a71 m (t5 conical 7,creseis1 ,clio72 & ?is tubul> %ell 7z we h already _h occasion to rem>k1 on p4 #beh71 frequ5tly t5ds1 :5 x is v small & delicate1 to assume ! "* ( an unduloid4 7,9 su* a case x is m ?an likely t ! t9y %ell1 or t portion ( x :i* con/itutes ! unduloid1 has n gr[n by successive #ega increm5ts or 8r+s ( gr[?10 b has develop$ z a :ole47 ,a ?ick5$ 8rib0 is (t51 p]haps g5]ally1 pres5t on ! dorsal side ( ! little conical %ell4 ,9 a few cases 7,limac9a1 ,p]aclis7 ! tube becomes spirally coil$1 9 a normal log>i?mic spiral or helico-spiral4 ,illu/ration3 ,fig4 #bif4 ,diagrammatic transv]se sections1 or outl9es ( ! m\?1 9 c]ta9 ,pt]opod %ells3 ,a1 ,b1 ,cleodora au/ralis2 ,c1 ,c4 pyramidalis2 ,d1 ,c4 balantium2 ,e1 ,c4 cuspidata4 7,aft] ,boas47 ,illu/ration3 ,fig4 #big4 ,%ells ( !cosome ,pt]opods 7aft] ,boas74 7#a7 ,cleodora cuspidata2 7#b7 ,hyalaea trisp9osa2 7#c7 ,h4 globulosa2 7#d7 ,h4 unc9ata2 7#e7 ,h4 inflexa4 ,9 c]ta9 cases 7e4g4 ,cleodora1 ,hyalaea7 ! tube or cone is curi\sly modifi$4 ,9 ! fir/ place1 its cross-section1 orig9ally #egb circul> or ne>ly s1 becomes flatt5$ or compress$ dorso-v5trally2 & ! angle1 or r edge1 :]e dorsal & v5tral walls meet1 becomes m & m drawn out into a ridge or keel4 ,along ! free m>g91 bo? ( ! dorsal & ! v5tral portion ( ! %ell1 gr[? proce$s ) a regul>ly v>y+ velocity1 s t ^! m>g9s1 or lips1 ( ! %ell become regul>ly curv$ or m>k$ly s9u\s4 ,at ! same "t1 gr[? 9 a transv]se direction proce$s ) an accel]ation :i* manife/s itself 9 a curvature ( ! sides1 replac+ ! /raight bord]s ( ! orig9al cone4 ,9 o!r words1 ! cross-section ( ! cone1 or :at we h be5 call+ ! g5]at+ curve1 increases its dim5sions m rapidly ?an its di/ance f ! pole4 ,illu/ration3 ,fig4 #bih4 ,cleodora cuspidata4 ,9 ! above figures1 = in/ance 9 t ( ,cleodora cuspidata1 ! m>k+s ( ! %ell :i* repres5t ! successive edges ( ! lip at =m] /ages ( gr[?1 furni% u at once ) a 8graph0 ( ! v>y+ velocities ( gr[? z measur$1 radially1 f ! apex4 ,we c reveal m cle>ly ! nature ( ^! v>iations 9 ! foll[+ way :i* is simply tantam\nt to conv]t+ our radial into rectangul> coord9ates4 ,neglect+ curvature 7if any7 ( ! sides & treat+ ! %ell 7= simplicity's sake7 z a "r cone1 we lay (f equal angles f ! apex ,o1 along ! radii ,oa1 ,ob1 etc4 ,if we !n plot1 z v]tical equidi/ant ord9ates1 ! magnitudes ,oa1 ,ob 444 ,,oy1 & aga9 on to ,oa1 we obta9 a diagram su* z ! foll[+ 7,fig4 #bii72 by #egc help ( :i* we n only see m cle>ly ! way 9 :i* ! gr[?-rate v>ies f po9t to po9t1 b we also recognise mu* bett] ?an be=e1 ! simil> nature ( ! law :i* gov]ns ?is v>iation 9 ! diff]5t species4 ,illu/ration3 ,fig4 #bii4 ,curves obta9$ by trans=m+ radial ord9ates1 z 9 ,fig4 #bih1 into v]tical equidi/ant ord9ates4 #a1 ,hyalaea trisp9osa2 #b1 ,cleodora cuspidata4 ,illu/ration3 ,fig4 #cjj4 ,developm5t ( ! %ell ( ,hyalaea 7,cavol9ia7 trid5tata1 ,=skal3 ! e>li] /ages be+ ! 8,pleuropus longifilis0 ( ,tros*el4 7,aft] ,tes*47 ,fur!rmore1 ! "y %ell hav+ become diff]5tiat$ into a dorsal & a v5tral "p1 m>k$ (f f "o ano!r by a lat]al edge or keel1 & ! inequality ( gr[? be+ su* z to cause ea* portion to increase mo/ rapidly 9 ! m$ian l9e1 x foll[s t ! entire %ell w appe> to h be5 split into a dorsal & a v5tral plate1 bo? connect$ )1 & project+ f1 #egd :at rema9s ( ! orig9al undivid$ cone4 ,putt+ ! same ?+ 9 o!r words1 we may say t ! g5]at+ figure1 :i* lay at fir/ 9 a plane p]p5dicul> to ! axis ( ! cone1 has n[1 by unequal gr[?1 be5 %>ply b5t or fold$1 s z to lie approximately 9 two planes1 p>allel to ! ant]ior & po/]ior faces ( ! cone4 ,we h only to imag9e ! apical connect+ portion to be fur!r r$uc$1 & f9ally to disappe> or rupture1 & we %\ld h a bivalve %ell develop$ out ( ! orig9al simple cone4 ,9 its out] & gr[+ portion1 ! %ell ( our ,pt]opod n[ consi/s ( two p>ts :i*1 ?\gh /ill connect$ toge!r at ! apex1 may be treat$ z gr[+ practically indep5d5tly4 ,! %ell is no long] a simple tube1 or simple cone1 9 :i* regul> inequalities ( gr[? w lead to ! developm5t ( a spiral2 & ?is = ! simple reason t we h n[ two opposite maxima ( gr[?1 in/ead ( a maximum on ! "o side & a m9imum on ! o!r side ( our tubul> %ell4 ,z a matt] ( fact1 ! dorsal & ! v5tral plate t5d to curve 9 opposite directions1 t[>ds ! middle l9e1 ! dorsal curv+ v5trally & ! v5tral curv+ t[>ds ! dorsal side4 ,9 ! case ( ! ,lamellibran* or ! ,bra*iopod1 x is q possible = bo? valves to gr[ into m or less pron\nc$ spirals1 = ! simple reason t !y are h+$ ^u "o ano!r2 & ea* gr[+ edge1 in/ead ( be+ br\ght to a /&/ill by ! gr[? ( its opposite neighb\r1 is free to move out ( ! way1 by ! rotation ab\t ! h+e ( ! plane 9 :i* x lies4 ,illu/ration3 ,fig4 #cja4 ,pt]opod %ells1 f ! side3 7#a7 ,cleodora cuspidata2 7#b7 ,hyalaea longiro/ris2 7#c7 ,h4 trisp9osa4 7,aft] ,boas47 ,b :]e1 z 9 ! ,pt]opod1 !re is no su* h+e1 ! dorsal & v5tral halves ( ! %ell 7or dorsal & v5tral valves1 if we may call !m s71 if !y curv$ t[>ds "o ano!r 7z !y d 9 a cockle71 w\ld soon int]f]e ) "o ano!r's progress1 & ! developm5t ( a pair ( conjugate spirals w\ld become impossible4 ,nev]!less1 !re is obvi\sly1 9 bo? dorsal & v5tral valve1 a t5d5cy to ! developm5t ( a spiral curve1 t ( ! v5tral valve be+ m m>k$ ?an t ( ! l>g] & ov]lapp+ dorsal "o1 exactly z 9 ! two unequal valves ( ,t]ebratula4 ,9 _m cases 7e4g4 ,cleodora cuspidata71 ! dorsal valve or plate1 #ege /r5g!n$ & /iff5$ by its midrib1 is ne>ly /raight1 :ile ! curvature ( ! o!r is well display$4 ,b ! case w be mat]ially alt]$ & simplifi$ if gr[? be arre/$ or ret>d$ 9 ei!r half ( ! %ell4 ,suppose = in/ance t ! dorsal valve grew s sl[ly t aft] a :ile1 9 comp>ison ) ! o!r1 we might speak ( x z be+ abs5t altoge!r3 or suppose t x m]ely became s r$uc$ 9 relative size z to =m no imp$im5t to ! cont9u$ gr[? ( ! v5tral "o2 ! latt] w\ld cont9ue to gr[ 9 ! direction ( its natural curvature1 & w\ld end by =m+ a complete & coil$ log>i?mic spiral4 ,x w\ld be precisely analog\s to ! spiral %ell ( ,nautilus1 &1 9 reg>d to its v5tral position1 concave t[>ds ! dorsal side1 x w\ld ev5 des]ve to be call$ directly homolog\s ) x4 ,suppose1 on ! o!r h&1 t ! v5tral valve 7 to be greatly r$uc$1 & ev5 to disappe>1 ! dorsal valve w\ld !n pursue its unoppos$ gr[?2 &1 7 x to be m>k$ly curv$1 x w\ld come to =m a log>i?mic spiral1 concave t[>ds ! v5tral side1 z is ! case 9 ! %ell ( ,spirula#ecj4 ,7 ! dorsal valve to be de/itute ( any m>k$ curvature 7or 9 o!r words1 to h b a l[ spiral angle71 x w\ld =m a simple plate1 z 9 ! %ells ( ,sepia or ,loligo4 ,inde$1 9 ! %ells ( ^! latt]1 & especially 9 t ( ,sepia1 we seem to recognise a manife/ resemblance to ! dorsal plate ( ! ,pt]opod %ell1 z we h x 7e4g47 9 ,cleodora or ,hyalaea2 #egf ! little 8ro/rum0 ( ,sepia is b ! apex ( ! primitive cone1 & ! r\nd$ ant]ior extremity has gr[n accord+ to a law precisely su* z t :i* has produc$ ! curv$ m>g9 ( ! dorsal valve 9 ! ,pt]opod4 ,! v5tral portion ( ! orig9al cone is ne>ly1 b n :olly1 want+4 ,x is repres5t$ by ! s-call$ po/]ior wall ( ! 8siphuncul> space40 ,9 _m decapod cuttle-fi%es also 7e4g4 ,tod>odes1 ,illex1 etc47 we /ill see at ! po/]ior end ( ! 8p510 a ve/ige ( ! primitive cone1 ^: dorsal m>g9 only has cont9u$ to gr[2 & ! same ph5om5on1 on an exagg]at$ scale1 is repres5t$ 9 ! ,belemnites4 ,x is n at all impossible t we may expla9 on ! same l9es ! developm5t ( ! curi\s 8op]culum0 ( ! ,ammonites4 ,?is consi/s ( a s+le horny plate 7,anapty*us71 or ( a ?ick]1 m calcifi$ plate divid$ into two symmetrical halves 7,apty*i71 (t5 f\nd inside ! t]m9al *amb] ( ! ,ammonite1 & occasionally to be se5 ly+ 9 situ1 z an op]culum :i* p>tially closes ! m\? ( ! %ell2 ?is /ructure is kn[n to exi/ ev5 9 connection ) ! e>ly embryonic %ell4 ,9 =m ! ,anapty*us1 or ! pair ( conjo9$ ,apty*i1 %ew an upp] & a l[] bord]1 ! latt] /rongly convex1 ! =m] sometimes slightly concave1 sometimes slightly convex1 & usually %ew+ a m$ian projection or slightly develop$ ro/rum4 ,f ?is 8ro/ral0 bord] ! curves ( gr[? />t1 & c\rse r\nd p>allel to1 f9ally con/itut+1 ! convex bord]4 ,x is ?is convex bord] :i* fits into ! free m>g9 ( ! m\? ( ! ,ammonite's %ell1 :ile ! o!r is appli$ to & ov]laps ! prec$+ :orl ( ! spire4 ,n[ ?is relation%ip is precisely :at we %\ld expect1 7 we to imag9e z our />t+-po9t a %ell simil> to t ( ,hyalaea1 9 :i* h[ev] ! dorsal "p ( ! split cone _h become sep>ate f ! v5tral half1 _h rema9$ flat1 & _h gr[n comp>atively sl[ly1 :ile at ! same "t x kept slipp+ =w>d ov] ! gr[+ & coil+ spire into :i* ! v5tral half ( ! orig9al %ell develops#eca4 ,9 %ort1 ,i ?9k !re is reason to believe1 or at lea/ to suspect1 t we #egg h 9 ! %ell & ,apty*us ( ! ,ammonites1 two portions ( a once unit$ /ructure2 ( :i* o!r ,cephalopods reta9 n bo? p>ts b only "o or o!r1 "o z ! v5trally situat$ %ell ( ,nautilus1 ! o!r z ! dorsally plac$ %ell = example ( ,sepia or ( ,spirula4 ,9 ! case ( ! bivalve %ells ( ! ,lamellibran*s or ( ! ,bra*iopods1 we h to deal ) a ph5om5on precisely analog\s to ! split & flatt5$ cone ( our ,pt]opods1 save only t ! primitive cone has be5 split into two portions1 n incompletely z 9 ! ,pt]opod 7,hyalaea71 b completely1 s z to =m two sep>ate valves4 ,?\gh some:at great] fre$om is giv5 to gr[? n[ t ! two valves are sep>ate & h+$1 yet /ill ! two valves oppose & hamp] "o ano!r1 s t 9 ! longitud9al direction ea* is capable ( only a mod]ate curvature4 ,?is curvature1 z we h se51 is recognisable z a log>i?mic spiral1 b only n[ & !n does ! gr[? ( ! spiral cont9ue s f> z to develop successive coils3 z x does 9 a few symmetrical =ms su* z ,isoc>dia cor2 & z x does /ill m conspicu\sly 9 a few o!rs1 su* z ,gryphaea & ,capr9ella1 :]e "o ( ! two valves is /unt$1 & ! gr[? ( ! o!r is 7relatively speak+7 unoppos$4 ,( ,septa4 ,be=e we leave ! subject ( ! molluscan %ell1 we h /ill ano!r problem to deal )1 9 reg>d to ! =m & arrangem5t ( ! septa :i* divide up ! tubul> %ell into *amb]s1 9 ! ,nautilus1 ! ,ammonite & _! allies 7,fig4 #cjd1 etc474 ,! exi/5ce ( septa 9 a ,nautiloid %ell may probably be acc\nt$ = z foll[s4 ,we h se5 t x is a prop]ty ( a cone t1 :ile gr[+ by increm5ts at "o end only1 x cons]ves its orig9al %ape3 !re=e ! animal )91 :i* 7?\gh gr[+ by a diff]5t law7 also cons]ves its %ape1 w cont9ue to fill ! %ell if x actually fills x to beg9 )3 z does a snail or o!r ,ga/ropod4 ,b suppose t our mollusc fills a "p only ( a conical %ell 7z x does 9 ! case ( ,nautilus72 !n1 unless x alt] its %ape1 x mu/ move upw>d z x gr[s 9 ! gr[+ cone1 until x come to occupy a space simil> 9 =m #egh to t :i* x occupi$ be=e3 j1 inde$1 z a little ball drops f> d[n into ! cone1 b a big "o mu/ /ay f>!r up4 ,!n1 :5 ! animal aft] a p]iod ( gr[? has mov$ f>!r up 9 ! %ell1 ! mantle-surface cont9ues its normal secretory activity1 & t portion :i* _h be5 9 contact ) ! =m] septum secretes a septum anew4 ,9 %ort1 at any giv5 epo*1 ! creature is n secret+ a tube & a septum by sep>ate op]ations1 b is secret+ a %elly case ab\t its r\nd$ body1 ( :i* case "o "p appe>s to u z ! cont9uation ( ! tube1 & ! o!r "p1 m]g+ ) x by indi/+ui%able b\nd>ies1 appe>s to u z ! septum#ecb4 ,! v>i\s =ms assum$ by ! septa 9 spiral %ells#ecc pres5t u ) a numb] ( problems ( great beauty1 simple 9 _! ess5ce1 b ^: full inve/igation w\ld soon lead u into ma!matics ( a v high ord]4 ,we d n "k 9 great detail h[ ^! septa are laid d[n2 b ! ess5tial facts are cle>#ecd4 ,! septum beg9s z a v ?9 cuticul> membrane 7compos$ app>5tly ( a sub/ance call$ con*yol971 :i* is secret$ by ! sk91 or mantle-surface1 ( ! animal2 & ^u ?is membrane nacre\s matt] is gradually laid d[n on ! mantle-side 7t is to say betwe5 ! animal's body & ! cuticul> membrane :i* has be5 ?r[n (f f x71 s t ! membrane rema9s z a ?9 pellicle ov] ! h9d] surface ( ! septum1 & s t1 to beg9 )1 ! membran\s septum is m\ld$ on ! flexible & ela/ic surface ( ! animal1 )9 :i* ! fluids ( ! body mu/ ex]cise a uni=m1 or ne>ly uni=m pressure4 ,let u ?9k1 !n1 ( ! septa z !y w\ld appe> 9 _! uncalcifi$ condition1 =m$ (1 or at lea/ sup]pos$ ^u1 an #egi ela/ic membrane4 ,!y mu/ !n foll[ ! g5]al law1 applicable to all ela/ic membranes "u uni=m pressure1 t ! t5sion v>ies inv]sely z ! radius ( curvature2 & we come back once m to our old equation ( ,laplace1 t ,p ,t7#a_/r #a_/r74 ,moreov]1 s9ce ! cavity bel[ ! septum is practically clos$1 & is fill$ ei!r ) air or ) wat]1 ,p w be con/ant ov] ! :ole area ( ! septum4 ,& fur!r1 we mu/ assume1 at lea/ to beg9 )1 t ! membrane con/itut+ ! incipi5t septum is homog5e\s or isotropic4 ,let u take fir/ ! case ( a /raight cone1 ( circul> section1 m or less l an ,or?oc]as2 & let u suppose t ! septum is atta*$ to ! %ell 9 a plane p]p5dicul> to its axis4 ,! septum itself mu/ !n obvi\sly be sph]ical4 ,moreov] ! ext5t ( ! sph]ical surface is con/ant1 & easily det]m9$4 ,= obvi\sly1 9 ,fig4 #cjb1 ! angle ,,lcl equals ! supplem5t ( ! angle 7,,lol7 ( ! cone2 t is to say1 ! circle ( contact subt5ds an angle at ! c5tre ( ! sph]ical surface1 :i* is con/ant1 & :i* is equal to #b4 ,! case is n exclud$ :]e1 ow+ to an asymmetry ( t5sions1 ! septum meets ! side walls ( ! cone at o!r ?an a "r angle1 z 9 ,fig4 #cjc2 & "h1 :ile ! septa /ill rema9 portions ( sph]es1 ! geometrical con/ruction = ! position ( _! c5tres is equally easy4 ,illu/ration3 ,fig4 #cjb4 ,illu/ration3 ,fig4 #cjc4 ,if1 on ! o!r h&1 ! atta*m5t ( ! septum to ! inn] walls ( ! cone be 9 a plane oblique to ! axis1 !n x is evid5t t ! outl9e ( ! septum w be an ellipse1 & its surface an #ehj ellipsoid4 ,if ! atta*m5t ( ! septum be n 9 "o plane1 b =m a s9u\s l9e ( contact ) ! cone1 !n ! septum w be a saddle-%ap$ surface1 ( great complexity & beauty4 ,9 all cases1 provid$ only t ! membrane be isotropic1 ! =m assum$ w be precisely t ( a soap-bubble "u simil> conditions ( atta*m5t3 t is to say1 x w be 7) ! usual limitations or conditions7 a surface ( m9imal area4 ,if our cone be no long] /raight1 b curv$1 !n ! septa w be symmetrically de=m$ 9 consequ5ce4 ,a beautiful & int]e/+ case is af=d$ u by ,nautilus itself4 ,"h ! outl9e ( ! septum1 ref]r$ to a plane1 is approximately b\nd$ by two elliptic curves1 simil> & simil>ly situat$1 ^: areas are to "o ano!r 9 a def9ite ratio1 namely z ,a#a_/;,a#b 7r#a r#a7_/7r#b r#b7 #d cot 1 & a simil> ratio exi/s 9 ,ammonites & all o!r close-:orl$ spirals1 9 :i* h[ev] we _c always make ! simple assumption ( elliptical =m4 ,9 a m$ian section ( ,nautilus1 we see ea* septum =m+ a tang5t to ! inn] & to ! out] wall1 j z x did 9 a section ( ! /raight ,or?oc]as2 b ! curvatures 9 ! neighb\rhood ( ^! two po9ts ( contact are n id5tical1 = !y n[ v>y inv]sely z ! radii1 drawn f ! pole ( ! spiral %ell4 ,! cont\r ( ! septum 9 ?is m$ian plane is a spiral curve id5tical ) ! orig9al log>i?mic spiral4 ,( ?is x is ! 8inv]t10 & ! fact t ! orig9al curve & its inv]t are bo? id5tical is "o ( ! mo/ beautiful prop]ties ( ! log>i?mic spiral#ece4 ,illu/ration3 ,fig4 #cjd4 ,section ( ,nautilus1 %ew+ ! cont\r ( ! septa 9 ! m$ian plane3 ! septa be+ 79 ?is plane7 log>i?mic spirals1 ( :i* ! %ell-spiral is ! evolute4 ,b :ile ! outl9e ( ! septum 9 m$ian section is simple & easy to det]m9e1 ! curv$ surface ( ! septum 9 its entirety is a v complicat$ matt]1 ev5 9 ,nautilus :i* is "o ( ! simple/ ( actual cases4 ,=1 9 ! fir/ place1 s9ce ! =m ( ! septum1 z se5 9 m$ian section1 is t ( a log>i?mic spiral1 & z !re=e its curvature is con/antly alt]+1 x foll[s t1 9 successive transv]se sections1 ! #eha curvature is also con/antly alt]+4 ,b 9 ! case ( ,nautilus1 !re are o!r aspects ( ! ph5om5on1 :i* we c illu/rate1 b only 9 "p1 9 ! foll[+ simple mann]4 ,let u imag9e a pack ( c>ds1 9 :i* we h cut out ( ea* c>d a simil> concave arc ( a log>i?mic spiral1 su* z we actually see 9 ! m$ian section ( ! septum ( a ,nautilus4 ,!n1 :ile we hold ! c>ds toge!r1 f\rsqu>e1 9 ! ord9>y position ( ! #ehb pack1 we h a simple 8rul$0 surface1 :i* 9 any longitud9al section has ! =m ( a log>i?mic spiral b 9 any transv]se section is a /raight horizontal l9e4 ,if we %e> or slide ! c>ds ^u "o ano!r1 ?ru/+ ! middle c>ds ( ! pack =w>d 9 advance ( ! o!rs1 till ! "o end ( ! pack is a convex1 & ! o!r a concave1 ellipse1 ! cut edges :i* comb9e to repres5t our septum w n[ =m a curv$ surface ,illu/ration3 ,fig4 #cje4 ,ca/ ( ! int]ior ( ,nautilus3 to %ew ! cont\rs ( ! septa at _! junction ) ! %ell-wall4 ( mu* great] complexity2 & ?is is "p1 b n by any means all1 ( ! de=mation produc$ z a direct consequ5ce ( ! =m 9 ,nautilus ( ! section ( ! tube )9 :i* ! septum has to lie4 ,& ! complex curvature ( ! surface w be manife/$ 9 a s9u\s outl9e ( ! edge1 or l9e ( atta*m5t ( ! septum to ! tube1 & w v>y accord+ to ! configuration ( ! latt]4 ,9 ! case ( ,nautilus1 x is easy to %ew empirically 7?\gh n p]haps easy to demon/rate #ehc ma!matically7 t ! s9u\s or saddle-%ap$ =m ( ! 8suture0 7or l9e ( atta*m5t ( ! septum to ! tube7 is su* z c be precisely acc\nt$ = 9 ?is mann]4 ,x is also easy to see t1 :5 ! section ( ! tube 7or 8g5]at+ curve07 is m complicat$ 9 =m1 :5 x is flatt5$1 groov$1 or o!rwise ornam5t$1 ! curvature ( ! septum & ! outl9e ( its sutural atta*m5t w become v complicat$ inde$#ecf2 b x w be comp>atively simple 9 ! case ( ! fir/ few sutures ( ! "y %ell1 laid d[n be=e any ov]lapp+ ( :orls has tak5 place1 & ?is comp>ative simplicity ( ! fir/-=m$ sutures is a m>k$ feature among ,ammonites#ecg4 ,we h o!r s\rces ( complication1 besides ^? :i* are at once introduc$ by ! sectional =m ( ! tube4 ,= in/ance1 ! siphuncle1 or little inn] tube :i* p]=ates ! septa1 ex]cises a c]ta9 am\nt ( t5sion1 sometimes evid5tly consid]able1 ^u ! latt]2 s t we c no long] consid] ea* septum z an isotropic surface1 "u uni=m pressure2 & !re may be o!r /ructural modifications1 or inequalities1 9 t portion ( ! animal's body ) :i* ! septum is 9 contact1 & by :i* x is con=m$4 ,x is h>dly likely1 = all ^! reasons1 t we %all ev] atta9 to a full & p>ticul> explanation ( ! septal surfaces & _! sutural outl9es ?r\gh\t ! :ole range ( ,cephalopod %ells2 b 9 g5]al t]ms1 ! problem is probably n beyond ! rea* ( ma!matical analysis4 ,! problem might be approa*$ exp]im5tally1 aft] ! mann] ( ,plateau's exp]im5ts1 by b5d+ #ehd a wire into ! complicat$ =m ( ! suture-l9e1 & /udy+ ! =m ( ! liquid film :i* con/itutes ! correspond+ surface m9imae areae4 ,illu/ration3 ,fig4 #cjf4 ,ammonites 7,sonn9ia7 ,s[]byi4 7,f ,zittel1 aft] ,/e9mann & ,dd]le947 ,illu/ration3 ,fig4 #cjg4 ,suture-l9e ( a ,triassic ,ammonite 7,p9acoc]as74 7,f ,zittel1 aft] ,hau]47 ,9 c]ta9 ,ammonites ! septal outl9e is fur!r complicat$ 9 ano!r way4 ,sup]pos$ ^u ! usual s9u\s outl9e1 ) its 8lobes0 & 8saddles10 we h "h a m9utely ramifi$1 or arboresc5t outl9e1 9 :i* all ! bran*es t]m9ate 9 wavy1 m or less circul> arcs1--look+ j l ! #8l&scape m>ble' f ! ,bri/ol ,rhaetic4 ,we h no difficulty 9 recognis+ 9 ?is a surface-t5sion ph5om5on4 ,! figures are precisely su* z we c imitate 7= in/ance7 by p\r+ a #ehe few drops ( milk ^u a greasy plate1 or ( oil ^u an alkal9e solution4 ,we h v f> f exhau/$1 we h p]haps little m ?an begun1 ! /udy ( ! log>i?mic spiral & ! associat$ curves :i* f9d exemplification 9 ! multitud9\s div]sities ( molluscan %ells4 ,b1 ) a clos+ ^w or two1 we mu/ n[ br+ ?is *apt] to an end4 ,9 ! spiral %ell we h a problem1 or a ph5om5on1 ( gr[?1 imm5sely simplifi$ by ! fact t ea* successive increm5t is irrevocably fix$ 9 reg>d to magnitude & position1 in/ead1 ( rema9+ 9 a /ate ( flux & %>+ 9 ! fur!r *anges :i* ! organism und]goes4 ,9 su* a /ructure1 !n1 we h c]ta9 prim>y ph5om5a ( gr[? manife/$ 9 _! orig9al simplicity1 undi/urb$ by second>y & conflict+ ph5om5a4 ,:at actually gr[s is m]ely ! lip ( an orifice1 :]e !re is produc$ a r+ ( solid mat]ial1 ^: =m we h treat$ ( "u ! "n ( ! g5]at+ curve2 & ?is g5]at+ curve gr[s 9 magnitude )\t alt]ation ( its =m4 ,besides its increase 9 areal magnitude1 ! gr[+ curve has c]ta9 /rictly limit$ degrees ( fre$om1 :i* def9e its motions 9 space3 t is to say1 x has a vector motion at "r angles to ! axis ( ! %ell2 & x has a slid+ motion along t axis4 ,&1 ?\gh we may "k no?+ :atsoev] ab\t ! actual velocities ( any ( ^! motions1 we d "k t !y are s correlat$ toge!r t _! relative velocities rema9 con/ant1 & accord+ly ! =m & symmetry ( ! :ole sy/em rema9 9 g5]al un*ang$4 ,b !re is a va/ range ( possibilities 9 reg>d to e "o ( ^! factors3 ! g5]at+ curve may be ( v>i\s =ms1 & ev5 :5 ( simple =m1 su* z an ellipse1 its axes may be set at v>i\s angles to ! sy/em2 ! plane also 9 :i* x lies may v>y1 almo/ indef9itely1 9 its angle relatively to t ( any plane ( ref]5ce 9 ! sy/em2 & 9 ! sev]al velocities ( gr[?1 ( rotation & ( translation1 & !re=e 9 ! ratios betwe5 all ^!1 we h aga9 a va/ range ( possibilities4 ,we h !n a c]ta9 def9ite type1 or gr\p ( =ms1 ma!matically isomorph\s1 b pres5t+ inf9ite div]sities ( outw>d appe>ance3 :i* div]sities1 z ,swamm]dam #ehf said1 ex sola nascuntur div]sitate gyrationum2 & :i* accord+ly are se5 to h _! orig9 9 diff]5ces ( rate1 or ( magnitude1 & s to be1 ess5tially1 nei!r m nor less ?an diff]5ces ( degree4 ,9 nature1 we f9d ^! =ms pres5t+ !mselves ) b little relation to ! "* ( ! creature by :i* !y are produc$4 ,spiral =ms ( c]ta9 p>ticul> k9ds are common to ,ga/ropods & to ,cephalopods1 & to div]se families ( ea*2 :ile outside ! class ( molluscs altoge!r1 among ! ,=am9if]a & among ! worms 7z 9 ,spirorbis1 ,spirographis1 & 9 ! ,d5talium-l %ell ( ,ditrupa71 we aga9 meet ) simil> & correspond+ =ms4 ,aga91 we f9d ! same =ms1 or =ms :i* 7save = ext]nal ornam5t7 are ma!matically id5tical1 repeat+ !mselves 9 all p]iods ( ! _w's geological hi/ory2 &1 irrespective ( climate or local conditions1 we see !m mix$ up1 "o ) ano!r1 9 ! dep?s & on ! %ores ( e sea4 ,x is h>d inde$ 7to my m9d7 to see :]e ,natural ,selection necess>ily ent]s 91 or to admit t x has _h any %>e :atsoev] 9 ! production ( ^! v>i$ con=mations4 ,unless inde$ we use ! t]m ,natural ,selection 9 a s5se s wide z to deprive x ( any purely biological significance2 & s recognise z a sort ( natural selection :atsoev] nexus ( causes suffices to diff]5tiate betwe5 ! likely & ! unlikely1 ! sc>ce & ! frequ5t1 ! easy & ! h>d3 & leads accord+ly1 "u ! peculi> conditions1 limitations & re/ra9ts :i* we call 8ord9>y circum/ances10 "o type ( cry/al1 "o =m ( cl\d1 "o *emical comp\nd1 to be ( frequ5t occurr5ce & ano!r to be r>e4 #ehg ,,*apt] ,,xii ,,! ,,spiral ,,%ells ,,( ,,! ,,=am9if]a ,we h already dealt 9 a few simple cases ) ! %ells ( ! ,=am9if]a#ech2 & we h se5 t :]ev] ! %ell is b a s+le unit or s+le *amb]1 its =m may be expla9$ 9 g5]al by ! laws ( surface t5sion3 ! assumption be+ t ! little mass ( protoplasm :i* makes ! simple %ell behaves z a fluid drop1 ! =m ( :i* is p]petuat$ :5 ! protoplasm acquires its solid cov]+4 ,?us ! sph]ical ,orbul9ae & ! flask-%ap$ ,lag5ae repres5t drops 9 equilibrium1 "u v>i\s conditions ( fre$om or con/ra9t2 :ile ! irregul>1 amoeboid body ( ,a/rorhiza is a manife/ation n ( equilibrium1 b ( a v>y+ & fluctuat+ di/ribution ( surface en]gy4 ,:5 ! =am9if]al %ell becomes multilocul>1 ! same g5]al pr9ciples cont9ue to hold2 ! gr[+ protoplasm increases drop by drop1 & ea* successive drop has its p>ticul> ph5om5a ( surface en]gy1 manife/$ at its fluid surface1 & t5d+ to conf] ^u x a c]ta9 place 9 ! sy/em & a c]ta9 %ape ( its own4 ,x is *>act]i/ic & ev5 diagno/ic ( ?is p>ticul> gr\p ( ,protozoa 7#a7 t developm5t proce$s by a well-m>k$ alt]nation ( re/ & ( activity--( activity dur+ :i* ! protoplasm increases1 & ( re/ dur+ :i* ! %ell is =m$2 7#b7 t ! %ell is =m$ at ! out] surface ( ! protoplasmic organism1 & t5ds to con/itute a cont9u\s or all b cont9u\s cov]+2 & x foll[s 7#c7 f ^! two factors tak5 toge!r t ea* successive increm5t is add$ on outside ( & di/9ct f its pr$ecessors1 t ! successive p>ts or *amb]s ( #ehh ! %ell are ( diff]5t & successive ages1 t "o "p ( ! %ell is always relatively new1 & ! re/ old 9 v>i\s grades ( s5iority4 ,! =ms :i* we set toge!r 9 ! si/]-gr\p ( ,radiol>ia are v diff]5tly *>act]is$4 ,"h ! cells or vesicles ( :i* ea* little composite organism is made up are b little sep>at$1 & 9 no way wall$ (f1 f "o ano!r2 ! h>d skeletal matt] t5ds to be deposit$ 9 ! =m ( isolat$ spicules or ( little connect$ rods or plates1 at ! angles1 ! edges or ! int]faces ( ! vesicles2 ! cells or vesicles =m a coord9at$ & cotemporane\s r ?an a successive s]ies4 ,9 a ^w1 ! :ole quasi-fluid protoplasmic body may be lik5$ to a little mass ( fro? or foam3 t is to say1 to an aggregation ( simultane\sly =m$ drops or bubbles1 ^: physical prop]ties & geometrical relations are v diff]5t f ^? ( a sy/em ( drops or bubbles :i* are =m$ "o aft] ano!r1 ea* solidify+ be=e ! next is =m$4 ,illu/ration3 ,fig4 #cjh4 ,ha/ig]9a sp42 to %ew ! 8m\?40 ,) ! actual orig9 or mode ( developm5t ( ! =am9if]al %ell we are n[ b little conc]n$4 ,! ma9 factor is ! adsorption1 & subsequ5t precipitation at ! surface ( ! organism1 ( calcium c>bonate1--! %ell s =m$ be+ int]rupt$ by pores or by "s l>g] int]space or 8m\?0 7,fig4 #cjh71 :i* int]ruptions we may d\btless int]pret z be+ due to unequal di/ributions ( surface en]gy4 ,9 _m #ehi cases ! fluid protoplasm 8picks up0 s&-gra9s & o!r =eign p>ticles1 aft] a fa%ion :i* we h already describ$ 7p4 #dfc72 & x cem5ts ^! toge!r ) m or less ( calc>e\s mat]ial4 ,! calc>e\s %ell is a cry/all9e /ructure1 & ! micro-cry/als ( calcium c>bonate are s set t _! little prisms radiate outw>ds 9 ea* *amb] ?r\gh ! ?ickness ( ! wall3--:i* symmetry is subject to correspond+ modification :5 ! sph]ical *amb]s are m or less symmetrically de=m$#eci4 ,9 v>i\s ways ! r\nd$1 drop-l %ells ( ! ,=am9if]a1 bo? simple & comp\nd1 h be5 artificially imitat$4 ,?us1 if small globules ( m]cury be imm]s$ 9 wat] 9 :i* a little *romic acid is all[$ to dissolve1 z ! little beads ( quicksilv] become sl[ly cov]$ ) a cry/all9e coat ( m]curic *romate !y assume v>i\s =ms rem9isc5t ( ! mono?alamic ,=am9if]a4 ,! m]curic *romate has a high] atomic volume ?an ! m]cury :i* x replaces1 & !re=e ! fluid cont5ts ( ! drop are "u pressure1 :i* increases ) ! ?ickness ( ! pellicle2 h5ce at "s weak spot 9 ! latt] ! cont5ts w pres5tly bur/ =?1 s =m+ a m\? to ! little %ell4 ,sometimes a long ?read is =m$1 j z 9 ,rhabdamm9a l9e>is2 & sometimes unduloid swell+s make _! appe>ance on su* a ?read1 j z 9 ,r4 discreta4 ,& aga91 by appropriate modifications ( ! exp]im5tal conditions1 x is possible 7z ,rhumbl] has %ewn7 to build up a *amb]$ %ell#edj4 ,9 a few =ms1 su* z ,globig]9a & its close allies1 ! %ell is beset dur+ life ) excessively long & delicate calc>e\s sp9es or ne$les4 ,x is only 9 oceanic =ms t ^! are pres5t1 because only :5 pois$ 9 wat] c su* #eij delicate /ructures endure2 9 dead %ells1 su* z we are mu* m famili> )1 e trace ( !m is brok5 & rubb$ away4 ,! gr[? ( ^! long ne$les is expla9$ 7z we h already briefly m5tion$1 on p4 #ddj7 by ! ph5om5on :i* ,lehmann calls ori5tirte ,adsorption--! t5d5cy = a cry/all9e /ructure to gr[ by accretion1 n necess>ily 9 ! outw>d =m ( a 8cry/al10 b cont9u+ 9 any direction or ori5tation :i* has once be5 impress$ ^u x3 9 ?is case ! spicul> gr[? is simply 9 direct cont9uation ( ! radial symmetry ( ! micro-cry/all9e elem5ts ( ! %ell-wall4 ,ov] ! surface ( ! %ell ! radiat+ spicules t5d to occur 9 a hexagonal patt]n1 symmetrically gr\p$ ar\nd ! pores :i* p]=ate ! %ell4 ,rhumbl] has sugge/$ t ?is arrangem5t is due to diffusion-curr5ts1 =m+ little eddies ab\t ! base ( ! pseudopodia issu+ f ! pores3 ! idea be+ borr[$ f ,bn>d1 to :om is due ! discov]y ( ?is type or ord] ( vortices#eda4 ,9 "o ( ,bn>d's exp]im5ts a ?9 lay] ( p>aff9 is /rewn ) p>ticles ( graphite1 !n w>m$ to melt+1 :]eupon ea* little solid granule becomes ! c5tre ( a vortex2 by ! int]action ( ^! vortices ! p>ticles t5d to be repell$ to equal di/ances f "o ano!r1 & 9 ! end !y are f\nd to be arrang$ 9 a hexagonal patt]n#edb4 ,! analogy is pla9 betwe5 ?is exp]im5t & ^? diffusion exp]im5ts by :i* ,l$uc produces 8 beautiful hexagonal sy/ems ( artificial cells1 ) :i* we h dealt 9 a previ\s *apt] 7p4 #cbj74 ,b let u come back to ! %ell itself1 & consid] p>ticul>ly its spiral =m4 ,t ! %ell 9 ! ,=am9if]a %\ld t5d t[>ds a spiral =m ne$ n surprise u2 = we h le>n$ t "o ( ! fundam5tal conditions ( ! production ( a concrete spiral is j precisely :at we h "h1 namely ! gradual developm5t ( a /ructure by means ( successive increm5ts sup]add$ to its ext]ior1 :i* !n =m "p1 successively1 ( a p]man5t & rigid /ructure4 ,?is condition #eia is obvi\sly =?com+ 9 ! =am9if]al1 b n at all 9 ! radiol>ian1 %ell4 ,our second fundam5tal condition ( ! production ( a log>i?mic spiral is t ea* successive increm5t %all be s posit$ & s con=m$ t its addition to ! sy/em leaves ! =m ( ! :ole sy/em un*ang$4 ,we h n[ to enquire into ?is latt] condition2 & to det]m9e :e!r ! successive increm5ts1 or successive *amb]s1 ( ! =am9if]al %ell actually con/itute gnomons to ! entire /ructure4 ,x is obvi\s en\gh t ! spiral %ells ( ! ,=am9if]a closely resemble true log>i?mic spirals4 ,inde$ s precisely d ! m9ute %ells ( _m ,=am9if]a repeat or simulate ! spiral %ells ( ,nautilus & its allies t to ! naturali/s ( ! e>ly n9ete5? c5tury !y 7 kn[n z ! ,cphalopodes microscopiques#edc1 until ,duj>d9 %ew$ t _! little bodies compris$ no complex anatomy ( organs1 b consi/$ m]ely ( t slime-l organic matt] :i* he taught u to call 8s>code10 & :i* we le>n$ aft]w>ds f ,s*wann to speak ( z 8protoplasm40 ,illu/ration3 ,fig4 #cji4 ,nummul9a antiquior1 ,r4 & ,v4 7,aft] ,v4 von ,mll]47 ,"o /rik+ diff]5ce1 h[ev]1 is app>5t betwe5 ! %ell ( ,nautilus & ! little nautiloid or rotal9e %ells ( ! ,=am9if]a3 namely t ! septa 9 ^! latt]1 & 9 all o!r #eib *amb]$ ,=am9if]a1 are convex outw>ds 7,fig4 #cjh71 :]eas !y are concave outw>ds 9 ,nautilus 7,fig4 #cjd7 & 9 ! re/ ( ! *amb]$ molluscan %ells4 ,! reason is p]fectly simple4 ,9 bo? cases ! curvature ( ! septum 0 det]m9$ be=e x became rigid1 & at a "t :5 x _h ! prop]ties ei!r ( a fluid film or an ela/ic membrane4 ,9 bo? cases ! actual curvature is det]m9$ by ! t5sions ( ! membrane & ! pressures to :i* x 0 expos$4 ,n[ x is obvi\s t ! extr9sic pressure :i* ! t5sion ( ! membrane has to )/& is on opposite sides 9 ! two cases4 ,9 ,nautilus1 ! pressure to be resi/$ is t produc$ by ! gr[+ body ( ! animal1 ly+ to ! out] side ( ! septum1 9 ! out]1 wid] portion ( ! tubul> %ell4 ,9 ! ,=am9if] ! septum at ! "t ( its =mation 0 no septum at all2 x 0 b a portion ( ! convex surface ( a drop-t portion namely :i* aft]w>ds became ov]lapp$ & enclos$ by ! succe$+ drop2 & ! curvature ( ! septum is concave t[>ds ! pressure to be resi/$1 :i* latt] is inside ! septum1 be+ simply ! hydro/atic pressure ( ! fluid cont5ts ( ! drop4 ,! "o septum is1 speak+ g5]ally1 ! rev]se ( ! o!r2 ! organism1 s to speak1 is outside ! "o & inside ! o!r2 & 9 bo? cases alike1 ! septum t5ds to assume ! =m ( a surface ( m9imal area1 z p]mitt$1 or z def9$1 by all ! circum/ances ( ! case4 ,! log>i?mic spiral is easily recognisable 9 typical cases#edd 7& especially :]e ! spire makes m ?an "o visible revolution ab\t ! pole71 by its fundam5tal prop]ty ( cont9u$ simil>ity3 t is to say1 by reason ( ! fact t ! big _m-*amb]$ %ell is ( j ! same %ape z ! small] & y\ng] %ell--:i* ph5om5on is app>5t & ev5 obvi\s 9 ! nautiloid ,=am9if]a1 z 9 ,nautilus itself3 b nev]!less ! nature ( ! curve mu/ be v]ifi$ by c>eful measurem5t1 j z ,moseley det]m9$ or v]ifi$ x 9 8 #eic orig9al /udy ( nautilus 7cf4 p4 #eah74 ,?is has accord+ly be5 done1 by v>i\s writ]s3 & 9 ! fir/ in/ance by ,val]ian von ,mll]1 9 an elaborate /udy ( ,fusul9a--a palaeozoic g5us ^: little %ells h built up va/ tracts ( c>bonif]\s lime/one ov] great "p ( ,european ,russia#ede4 ,9 ?is g5us a gr[+ surface ( protoplasm may be conceiv$ z wrapp+ r\nd & r\nd a small initial *amb]1 9 su* a way z to produce a fusi=m or ellipsoidal %ell--a transv]se section ( :i* reveals ! close-w\nd spiral coil4 ,! foll[+ are examples ( measurem5ts ( ! successive :orls 9 a c\ple ( species ( ?is g5us4 ,f4 cyl9drica1 ,fis*] ,f4 ,bcki1 v4 ,mll] ,bread? 79 millimetres74 ,:orl ,obs]v$ ,calculat$ ,obs]v$ ,calculat$ ,i #acb -- #jgi -- ,,ii #aie #aih #abj #aai ,,iii #cjj #big #ahj #agi ,,iv #ddi #dde #bfd #bfg ,v -- -- #cif #dja ,9 bo? cases ! successive :orls are v ne>ly 9 ! ratio ( #a 3 #ae2 & on ?is ratio ! calculat$ values are bas$4 ,"h is ano!r ( von ,mll]'s s]ies ( measurem5ts ( ,f4 cyl9drica1 ! measurem5ts be+ ^? ( opposite :orls--t is to say ( :orls #ahj ap>t3 ,bread? 9 mm4 #jif #aag #add #agf #baf #bfd #cbc #cie ,log4 ( mm4 #ihb #jfh #aeh #bdf #ccd #dbb #eji #eig ,diff4 ( logs4 -- #jhf #jij #jhh #jhh #jhh #jhg #jhh ,! mean log>i?mic diff]5ce is "h #jhh1 log #abbe2 or ! mean diff]5ce ( alt]nate logs 7correspond+ to a vector angle ( #b1 i4e4 to consecutive measurem5ts along ! same radius7 is #agf1 log #ae1 ! same value z be=e4 ,& ?is ratio ( #ae betwe5 ! bread?s ( successive :orls corresponds 7z we see by our table on p4 #ecd7 to a con/ant angle ( ab\t #eid #hf1 or j su* a spiral z we commonly meet ) 9 ! ,ammonites#edf 7cf4 p4 #eci74 ,9 ,fusul9a1 & 9 "s few o!r ,=am9if]a 7cf4 ,fig4 #caj1 ,a71 ! spire seems to w9d ev5ly on1 ) little or no ext]nal sign ( ! successive p]iods ( gr[?1 or successive *amb]s ( ! %ell4 ,! septa :i* m>k (f ! *amb]s1 & correspond to ret>dations or cessations 9 ! p]iodicity ( gr[?1 are /ill to be f\nd 9 sections ( ! %ell ( ,fusul9a2 b !y are some:at irregul> & comp>atively inconspicu\s2 ! measurem5ts we h j spok5 ( are tak5 )\t ref]5ce to ! segm5ts or *amb]s1 b only ) ref]5ce to ! :orls1 or 9 o!r words ) direct ref]5ce to ! vectorial angle4 ,illu/ration3 ,fig4 #caj4 ,a1 ,cornuspira foliacea1 ,phil42 ,b1 ,op]cul9a complanata1 ,defr4 ,! l9e> dim5sions ( successive *amb]s h be5 #eie measur$ 9 a numb] ( cases4 ,van ,it]son#edg has done s 9 v>i\s ,miliol9idae1 ) su* results z ! foll[+3 ,trilocul9a rotunda1 d',orb4 ,no4 ( *amb] #a #b #c #d #e #f #g #h #i #aj ,bread? ( *amb] 9 -- #cd #de #fa #hd #aad #adb #ahb #bdf #cai ,bread? ( *amb] 9 1 calculat$ -- #cd #de #fj #gi #aje #adj #ahg #bdc #cai ,"h ! mean ratio ( bread? ( consecutive *amb]s may be tak5 z #acbc 7t is to say1 ! eigh? root ( #cai_/cd72 & ! calculat$ values1 z giv5 above1 are bas$ on ?is det]m9ation4 ,aga91 ,rhumbl] has measur$ ! l9e> dim5sions ( a numb] ( rotal9e =ms1 = in/ance ,pulv9ul9a m5>di 7,fig4 #bei73 9 :i* common species he f9ds ! mean l9e> ratio ( consecutive *amb]s to be ab\t #aahg4 ,9 bo? cases1 & especially 9 ! latt]1 ! ratio is n /rictly con/ant f *amb] to *amb]1 b is subject to a small second>y fluctuation#edh4 ,illu/ration3 ,fig4 #caa4 #a1 #b1 ,miliol9a pul*ella1 d',orb42 #c-e1 ,m4 l9naeana1 d',orb4 7,aft] ,brady47 ,illu/ration3 ,fig4 #cab4 ,cyclamm9a cancellata1 ,brady4 ,:5 ! l9e> dim5sions ( successive *amb]s are 9 cont9u$ proportion1 !n1 9 ord] t ! :ole %ell may con/itute a log>i?mic spiral1 x is necess>y t ! sev]al *amb]s %\ld subt5d equal angles ( revolution at ! pole4 ,9 ! case ( ! ,miliolidae ?is is obvi\sly ! case 7,fig4 #caa72 = 9 ?is family ! *amb]s lie 9 two r[s 7,bilocul9a71 or ?ree r[s 7,trilocul9a71 or 9 "s o!r small numb] ( s]ies3 s t ! angles subt5d$ by !m are l>ge1 simple fractions ( ! circul> arc1 su* z #ahj or #abj4 ,9 _m ( ! nautiloid =ms1 su* z ,cyclamm9a 7,fig4 #cab71 ! angles subt5d$1 ?\gh ( less magnitude1 are /ill rem>kably con/ant1 z we #eig may see by ,fig4 #cac2 :]e ! angle subt5d$ by ea* *amb] is made equal to #bj1 & ?is diagrammatic figure is n p]ceptibly diff]5t f ! o!r4 ,9 "s cases ! subt5d$ angle is less con/ant2 & 9 ^! x w\ld be necess>y to equate ! sev]al l9e> dim5sions ) ! correspond+ vector angles1 accord+ to our equation r e cot 4 ,x is probable t1 by s tak+ acc\nt ( v>iations ( 1 su* v>iations ( r z 7accord+ to ,rhumbl]'s measurem5ts7 ,pulv9ul9a & o!r g5]a appe> to %ew1 w\ld be f\nd to dim9i% or ev5 to disappe>4 ,illu/ration3 ,fig4 #cac4 ,cyclamm9a sp4 7,diagrammatic47 ,! law ( increase by :i* ea* *amb] be>s a con/ant ratio ( magnitude to ! next may be look$ ^u z a simple consequ5ce ( ! /ructural uni=mity or homog5eity ( ! organism2 we h m]ely to suppose 7z ?is uni=mity w\ld naturally lead u to d7 t ! rate ( increase is at ea* in/ant proportional to ! :ole exi/+ mass4 ,= if ,v#j1 ,v#a etc41 be ! volumes ( ! successive *amb]s1 let ,v#a be> a con/ant proportion to ,v#j1 s t ,v#a q ,v#j1 & let ,v#b be> ! same proportion to ! :ole pre-exi/+ volume3 !n ,v#b q7,v#j ,v#a7 q7,v#j q ,v#j7 q ,v#j7a q7 & ,v#b_/,v#a #a q4 #eih ,?is ratio ( #a_/7a q7 is easily %ewn to be ! con/ant ratio runn+ ?r\gh ! :ole s]ies1 f *amb] to *amb]2 & if ?is ratio ( volumes be con/ant1 s also are ! ratios ( correspond+ surfaces1 & ( correspond+ l9e> dim5sions1 provid$ always t ! successive increm5ts1 or successive *amb]s1 are simil> 9 =m4 ,we h /ill to discuss ! simil>ity ( =m & ! symmetry ( position :i* *>act]ise ! successive *amb]s1 & :i*1 toge!r ) ! law ( cont9u$ proportionality ( size1 are ! di/9ctive *>act]s & ! indisp5sable conditions ( a s]ies ( 8gnomons40 ,! m9ute size ( ! =am9if]al %ell or at lea/ ( ea* successive increm5t !re(1 tak5 9 connection ) ! fluid or semi-fluid nature ( ! protoplasmic sub/ance1 is en\gh to sugge/ t ! molecul> =ces1 & especially ! =ce ( surface-t5sion1 mu/ ex]cise a controll+ influ5ce ov] ! =m ( ! :ole /ructure2 & ?is sugge/ion1 or belief1 is already impli$ 9 our /atem5t t ea* successive increm5t ( gr[+ protoplasm con/itutes a sep>ate drop4 ,^! 8drops10 p>tially conceal$ by _! successors1 b /ill %ew+ 9 "p _! r\nd$ outl9es1 are easily recognisable 9 ! v>i\s =am9if]al %ells :i* are illu/rat$ 9 ?is *apt]4 ,illu/ration3 ,fig4 #cad4 ,orbul9a univ]sa1 d',orb4 ,! accompany+ figure repres5ts1 to beg9 )1 ! sph]ical %ell *>act]i/ic ( ! common1 float+1 oceanic ,orbul9a4 ,9 ! specim5 illu/rat$1 a second *amb]1 sup]add$ to ! #eii fir/1 has aris5 z a drop ( protoplasm :i* exud$ ?r\gh ! pores ( ! fir/ *amb]1 accumulat$ on its surface1 & spread ov] ! latt] till x came to re/ 9 a position ( equilibrium4 ,we may take x t ?is position ( equilibrium is det]m9$1 at lea/ 9 ! fir/ in/ance1 by ! 8law ( ! con/ant angle10 :i* holds1 or t5ds to hold1 9 all cases :]e ! free surface ( a giv5 liquid is 9 contact ) a giv5 solid1 9 pres5ce ( ano!r liquid or a gas4 ,! correspond+ equations are precisely ! same z ^? :i* we h us$ 9 discuss+ ! =m ( a drop 7on p4 #bid72 ?\gh "s slight modification mu/ be made 9 our def9itions1 inasmu* z ! consid]ation ( surface-t5sion is no long] appropriate at ! solid surfaces1 & ! concept ( surface-en]gy mu/ take its place4 ,be t z x may1 x is en\gh = u to obs]ve t1 9 su* a case z ours1 :5 a giv5 fluid 7namely protoplasm7 is 9 surface contact ) a solid 7viz4 a calc>e\s %ell71 9 pres5ce ( ano!r fluid 7sea-wat]71 !n ! angle ( contact1 or angle by :i* ! common surface 7or int]face7 ( ! two liquids abuts aga9/ ! solid wall1 t5ds to be con/ant3 & t be+ s1 ! drop w h a c]ta9 def9ite =m1 dep5d+ 7int] alia7 on ! =m ( ! surface ) :i* x is 9 contact4 ,aft] a p]iod ( re/1 dur+ :i* ! surface ( our second drop becomes rigid by calcification1 a new p]iod ( gr[? w recur & a new drop ( protoplasm be accumulat$4 ,circum/ances rema9+ ! same1 ?is new drop w meet ! solid surface ( ! %ell at ! same angle z did ! =m] "o2 &1 ! o!r =ces at "w on ! sy/em rema9+ ! same1 ! =m ( ! :ole drop1 or *amb]1 w be ! same z be=e4 ,accord+ to ,rhumbl]1 ?is 8law ( ! con/ant angle0 is ! fundam5tal pr9ciple 9 ! me*anical con=mation ( ! =am9if]al %ell1 & provides = ! symmetry ( =m z well z ( position 9 ea* succe$+ drop ( protoplasm3 :i* =m & position1 once acquir$1 become rigid & fix$ ) ! onset ( calcification4 ,b ,rhumbl]'s explanation br+s ) x its own difficulties4 ,x is by no means easy ( v]ification1 = on ! v complicat$ curv$ surfaces ( ! %ell x seems to me extraord9>ily difficult to measure1 or ev5 to recognise1 ! actual angle ( contact3 ( :i* angle ( contact1 by ! way1 #fjj b little is kn[n1 save only 9 ! p>ticul> case :]e "o ( ! ?ree bodies is air1 z :5 a surface ( wat] is expos$ to air & 9 contact ) glass4 ,x is easy moreov] to see t 9 _m ( our ,=am9if]a ! angle ( contact1 ?\gh x may be con/ant 9 homolog\s positions f *amb] to *amb]1 is by no means con/ant at all po9ts along ! b\nd>y ( ea* *amb]4 ,9 ,cri/ell>ia1 = in/ance 7,fig4 #cae71 x w\ld seem to be 7& ,rhumbl] ass]ts t x actually is7 ab\t #ij on ! out] side & only ab\t #ej on ! inn] side ( ea* septal p>tition2 9 ,pulv9ul9a 7,fig4 #bei71 accord+ to ,rhumbl]1 ! angles adjac5t to ! m\? are ( #ij1 & ! opposite angles are ( #fj1 9 ea* *amb]4 ,= ^! & o!r simil> discrepancies ,rhumbl] w\ld acc\nt by simply invok+ ! het]og5eity ( ! protoplasmic drop3 t is to say1 by assum+ t ! protoplasm has a diff]5t composition & diff]5t prop]ties 7includ+ a v diff]5t di/ribution ( surface-en]gy71 at po9ts ne> to & remote f ! m\? ( ! %ell4 ,:e!r ! diff]5ces 9 angle ( contact be z great z ,rhumbl] takes !m to be1 :e!r m>k$ het]og5eities ( ! protoplasm occur1 & :e!r ^! be en\gh to acc\nt = ! diff]5ces ( angle1 ,i _c tell4 ,b x seems to me t we _h bett] re/ cont5t ) a g5]al /atem5t1 & t ,rhumbl] has tak5 too precise & n>r[ a view4 ,illu/ration3 ,fig4 #cae4 ,cri/ell>ia r5i=mis1 d',orb4 #fja ,9 ! molecul> gr[? ( a cry/al1 al?\gh we mu/ ( necessity assume t ea* molecule settles d[n 9 a position ( m9imum pot5tial en]gy1 we f9d x v h>d inde$ to expla9 precisely1 ev5 9 simple cases & aft] all ! lab\rs ( mod]n cry/allograph]s1 :y ?is or t position is actually a place ( m9imum pot5tial4 ,9 ! case ( our little ,=am9if] 7j z 9 ! case ( ! cry/al71 let u !n be cont5t to ass]t t ea* drop or bead ( protoplasm takes up a position ( m9imum pot5tial en]gy1 9 relation to all ! circum/ances ( ! case2 & let u n attempt1 9 ! pres5t /ate ( our k1 to def9e t position ( m9imum pot5tial by ref]5ce to angle ( contact or any o!r p>ticul> condition ( equilibrium4 ,9 mo/ cases ! :ole expos$ surface1 on "s portion ( :i* ! drop mu/ come to re/1 is an extremely complicat$ "o1 & ! =ces involv$ con/itute a sy/em :i*1 9 its entirety1 is m complicat$ /ill2 b f ! symmetry ( ! case & ! cont9uity ( ! :ole ph5om5on1 we are entitl$ to believe t ! conditions are j ! same1 or v ne>ly ! same1 "t aft] "t1 f "o *amb] to ano!r3 z ! "o *amb] is con=m$ s w ! next t5d to be1 & z ! "o is situat$ relatively to ! sy/em s w its successor t5d to be situat$ 9 turn4 ,! physical law ( m9imum pot5tial 7includ+ also ! law ( m9imal area7 is all t we ne$ 9 ord] to expla91 9 g5]al t]ms1 ! cont9u$ simil>ity ( "o *amb] to ano!r2 & ! physiological law ( gr[?1 by :i* a cont9u$ proportionality ( size t5ds to run ?r\gh ! s]ies ( successive *amb]s1 impresses ^u ?is s]ies ( simil> increm5ts ! =m ( a log>i?mic spiral4 ,9 ea* p>ticul> case ! nature ( ! log>i?mic spiral1 z def9$ by its con/ant angle1 w be *iefly det]m9$ by ! rate ( gr[?2 t is to say by ! p>ticul> ratio 9 :i* ea* new *amb] exce$s its pr$ecessor 9 magnitude4 ,b %ells hav+ ! same con/ant angle 77 may /ill diff] f "o ano!r 9 _m ways--9 ! g5]al =m & relative position ( ! *amb]s1 9 _! ext5t ( ov]lap1 & h5ce 9 ! actual cont\r & appe>ance ( ! %ell2 & ^! v>iations mu/ correspond to p>ticul> di/ributions ( en]gy )9 ! sy/em1 :i* is gov]n$ z a :ole by ! law ( m9imum pot5tial4 #fjb ,our problem1 !n1 becomes r$uc$ to t ( inve/igat+ ! possible configurations :i* may be d]iv$ f ! successive symmetrical apposition ( simil> bodies ^: magnitudes are 9 cont9u$ proportion2 & x is obvi\s1 ma!matically speak+1 t ! v>i\s possible arrangem5ts all come "u ! head ( ! log>i?mic spiral1 toge!r ) ! limit+ cases :i* x includes4 ,s9ce ! diff]5ce betwe5 "o su* =m & ano!r dep5ds ^u ! num]ical value ( c]ta9 coeffici5ts ( magnitude1 x is pla9 t any "o mu/ t5d to pass into any o!r by small & cont9u\s gradations2 9 o!r words1 t a classification ( ^! =ms mu/ 7l any classification :atsoev] ( log>i?mic spirals or ( any o!r ma!matical curves71 be !oretic or 8artificial40 ,b we may easily make su* an artificial classification1 & %all probably f9d x to agree1 m or less1 ) ! usual me?ods ( classification recognis$ by biological /ud5ts ( ! ,=am9if]a4 ,fir/ly we h ! typically spiral %ells1 :i* occur 9 great v>iety1 & :i* 7= our pres5t purpose7 we ne$ h>dly describe fur!r4 ,we may m]ely notice h[ 9 c]ta9 cases1 = in/ance ,globig]9a1 ! individual *amb]s are little remov$ f sph]es2 9 o!r words1 ! area ( contact betwe5 ! adjac5t *amb]s is small4 ,9 su* =ms z ,cyclamm9a & ,pulv9ul9a1 on ! o!r h&1 ea* *amb] is greatly ov]lapp$ by its successor1 & ! sph]ical =m ( ea* is lo/ 9 a m>k$ asymmetry4 ,fur!rmore1 9 ,globig]9a & "s o!rs we h a t5d5cy to ! developm5t ( a helicoid spiral 9 space1 z 9 s _m ( our univalve molluscan %ells4 ,! ma!matical problem ( h[ a %ell %\ld gr[1 "u ! assumptions :i* we h made1 w\ld probably f9d its mo/ g5]al /atem5t 9 su* a case z t ( ,globig]9a1 :]e ! :ole organism lives & gr[s freely pois$ 9 a m$ium ^: d5sity is little diff]5t f its own4 ,! majority ( spiral =ms1 on ! o!r h&1 are plane or discoid spirals1 & we may take x t 9 ^! cases "s =ce has ex]cis$ a controll+ influ5ce1 s z to keep all ! *amb]s 9 a plane4 ,?is is especially ! case 9 =ms l ,rotalia or ,discorb9a 7,fig4 #caf71 :]e ! organism lives atta*$ to a rock or a frond ( sea-we$2 = "h 7j z 9 ! case ( #fjc ! coil$ tubes :i* little worms su* z ,s]pula & ,spirorbis make1 "u simil> conditions7 ! spiral disc is itself asymmetrical1 its :orls be+ m>k$ly flatt5$ on _! atta*$ surfaces4 ,illu/ration3 ,fig4 #caf4 ,discorb9a b]!loti1 d',orb4 ,we may also conceive1 among o!r conditions1 ! v curi\s case 9 :i* ! protoplasm may entirely ov]spread ! surface ( ! %ell )\t rea*+ a position ( equilibrium2 9 :i* case a new %ell w be =m$ enclos+ ! old "o1 #fjd :e!r ! old "o be 9 ! =m ( a s+le1 solit>y *amb]1 or h already atta9$ to ! =m ( a *amb]$ or spiral %ell4 ,?is is precisely :at (t5 happ5s 9 ! case ( ,orbul9a1 :5 )9 ! sph]ical %ell we f9d a small1 b p]fectly =m$1 spiral 8,globig]9a#edi40 ,! v>i\s ,miliolidae 7,fig4 #caa71 only diff] f ! typical spiral1 or rotal9e =ms1 9 ! l>ge angle subt5d$ by ea* *amb]1 & ! consequ5t abruptness ( _! incl9ation to ea* o!r4 ,9 ^! cases ! outw>d appe>ance ( a spiral t5ds to be lo/2 & x behoves u to recollect1 all ! m1 t our spiral curve is n necess>ily id5tical ) ! outl9e ( ! %ell1 b is always a l9e drawn ?r\gh correspond+ po9ts 9 ! successive *amb]s ( ! latt]4 ,illu/ration3 ,fig4 #cag4 ,a1 ,t]tul>ia tro*us1 d',orb4 ,b1 ,t4 concava1 ,k>r]4 ,we rea* a limit+ case ( ! log>i?mic spiral :5 ! *amb]s are arrang$ 9 a /raight l9e2 & ! eye w t5d to associate ) ?is limit+ case ! mu* m num]\s =ms 9 :i* ! spiral angle is small1 & ! %ell only exhibits a g5tle curve ) no succession ( envelop+ :orls4 ,?is con/itutes ! ,nodos>ian type 7,fig4 #hg1 p4 #bfb72 & "h aga91 we mu/ po/ulate "s =ce :i* has t5d$ to keep ! *amb]s 9 a rectil9e> s]ies3 su* = in/ance z gravity1 act+ on a sy/em ( 8hang+ drops40 #fje ,9 ,textul>ia & its allies 7,fig4 #cag71 we h a precise p>allel to ! helicoid cyme ( ! botani/s 7cf4 p4 #ejb73 t is to say we h a screw translation1 p]p5dicul> to ! plane ( ! und]ly+ log>i?mic spiral4 ,9 o!r words1 9 trac+ a g5etic spiral ?r\gh ! :ole succession ( *amb]s1 we d s by a cont9u\s vector rotation1 ?r\gh successive angles ( #ahj 7or #abj 9 "s cases71 :ile ! pole moves along an axis p]p5dicul> to ! orig9al plane ( ! spiral4 ,ano!r type is furni%$ by ! 8cyclic0 %ells ( ! ,orbitolitidae1 :]e small & num]\s *amb]s t5d to be add$ on r\nd & r\nd ! sy/em1 s build+ up a circul> flatt5$ disc4 ,?is aga9 we p]ceive to be1 ma!matically1 a limit+ case ( ! log>i?mic spiral1 :]e ! spiral has become a circle & ! con/ant angle is n[ an angle ( #ij4 ,la/ly !re are a c]ta9 numb] ( ,=am9if]a 9 :i*1 )\t m ado1 we may simply say t ! arrangem5t ( ! *amb]s is irregul>1 nei!r ! law ( con/ant ratio ( magnitude nor t ( con/ant =m be+ obey$4 ,! *amb]s are heap$ pell-mell ^u "o ano!r1 & su* =ms are kn[n to naturali/s z ! ,ac]vul>idae4 ,:ile 9 ^! la/ we h an extreme lack ( regul>ity1 we mu/ n exagg]ate ! regul>ity or con/ancy :i* ! m ord9>y =ms display4 ,we may ?9k x h>d to believe t ! simple causes1 or simple laws1 :i* we h describ$ %\ld op]ate1 & op]ate aga9 & aga91 9 millions ( individuals to produce ! same delicate & complex con=mations4 ,b we are tak+ a good deal = grant$ if we ass]t t !y d s1 & 9 p>ticul> we are assum+1 ) v little pro(1 ! 8con/ancy ( species0 9 ?is gr\p ( animals4 ,j z ,v]worn has %ewn t ! typical ,amoeba proteus1 :5 a trace ( alkali is add$ to ! wat] 9 :i* x lives1 t5ds1 by alt]ation ( surface t5sions1 to protrude ! m delicate pseudopodia *>act]i/ic ( ,a4 radiosa1--& aga9 :5 ! wat] is r5d]$ a little m alkal9e1 to turn app>5tly into ! s-call$ ,a4 limax1--s x is evid5t t a v slight modification 9 ! surface-en]gies conc]n$1 might t5d to turn "o s-call$ species into ano!r among ! ,=am9if]a4 ,to :at ext5t ?is process actually occurs1 we d n "k4 #fjf ,b t ?is1 or some?+ ( ! k9d1 does actually occur we c sc>cely d\bt4 ,= example 9 ! g5us ,p5]oplis1 ! fir/ portion ( ! %ell consi/s ( a s]ies ( *amb]s arrang$ 9 a spiral or nautiloid s]ies2 b z age advances ! spiral is apt to be modifi$ 9 v>i\s ways#eej4 ,sometimes ! successive *amb]s gr[ rapidly broad]1 ! :ole %ell becom+ fan-%ap$4 ,sometimes ! *amb]s become n>r[]1 till !y no long] enfold ! e>li] *amb]s b only come 9 contact ea* ) its imm$iate pr$ecessor3 ! result be+ t ! %ell /raight5s out1 & 7tak+ into acc\nt ! e>li] spiral portion7 may be describ$ z crozi]-%ap$4 ,betwe5 ^! extremes ( %ape1 & 9 reg>d to o!r v>iations ( ?ickness or ?9ness1 r\ghness or smoo?ness1 & s on1 !re are innum]able gradations pass+ "o into ano!r & int]mix$ )\t reg>d to geographical di/ribution3--8:]ev] ,p5]oplides ab\nd ?is wide v>iation exi/s1 & no?+ c be m easy ?an to pick out a numb] ( /rik+ specim5s & give to ea* a di/9ctive "n1 b 9 no o!r way c !y be divid$ into #8species4'#eea0 ,"s writ]s h wond]$ at ! peculi> v>iability ( ?is p>ticul> %ell#eeb2 b = all we "k ( ! life-hi/ory ( ! ,=am9if]a1 x may well be t a great numb] ( ! o!r =ms :i* we di/+ui% z sep>ate species & ev5 g5]a are no m ?an tempor>y manife/ations ( ! same v>iability#eec4 #fjg ,conclusion4 ,if we c compreh5d & int]pret on "s su* l9es z ^! ! =m & mode ( gr[? ( ! =am9if]al %ell1 we may also beg9 to und]/& two /rik+ features ( ! gr\p1 namely1 on ! "o h& ! l>ge numb] ( div]se types or families :i* exi/ & ! l>ge numb] ( species & v>ieties )9 ea*1 & on ! o!r ! p]si/5ce ( =ms :i* 9 _m cases seem to h und]gone little *ange or none at all f ! ,cretace\s or ev5 f e>li] p]iods to ! pres5t day4 ,9 few o!r gr\ps1 p]haps only among ! ,radiol>ia1 d we seem to possess s ne>ly complete a picture ( all possible transitions betwe5 =m & =m1 & ( ! :ole bran*+ sy/em ( ! evolution>y tree3 z ?\gh little or no?+ ( x _h ev] p]i%$1 & ! :ole web ( life1 pa/ & pres5t1 7 z complete z ev]4 ,x leads "o to imag9e t ^! %ells h gr[n accord+ to laws s simple1 s mu* 9 h>mony ) _! mat]ial1 ) _! environm5t1 & ) all ! =ces int]nal & ext]nal to :i* !y are expos$1 t none is bett] ?an ano!r & none fitt] or less fit to survive4 ,x invites "o also to contemplate ! possibility ( ! l9es ( possible v>iation be+ "h s n>r[ & det]m9ate t id5tical =ms may h come indep5d5tly into be+ aga9 & aga94 ,:ile we c trace 9 ! mo/ complete & beautiful mann] ! passage ( "o =m into ano!r among ^! little %ells1 & ascribe !m all at la/ 7if we please7 to a s]ies :i* />ts ) ! simple sph]e ( ,orbul9a or ) ! amoeboid body ( ,a/rorhiza1 ! "q />es u 9 ! face :e!r ?is be an 8evolution0 :i* we h any "r to correlate ) hi/oric "t4 ,! ma!matician c trace "o conic section into ano!r1 & 8evolve0 = example1 ?r\gh innum]able grad$ ellipses1 ! circle f ! /raight l9e3 :i* trac+ ( cont9u\s /eps is a true 8evolution10 ?\gh "t has no "p !re94 ,x 0 aft] ?is fa%ion t ,hegel1 & = t matt] ,ari/otle himself1 0 an evolutioni/--to :om evolution 0 #fjh a m5tal concept1 involv+ ord] & cont9uity 9 ?\ght1 b n an actual sequ5ce ( ev5ts 9 "t4 ,su* a conception ( evolution is n easy = ! mod]n biologi/ to grasp1 & h>d] /ill to appreciate4 ,& s x is t ev5 ^? :o1 l ,drey]#eed & l ,rhumbl]1 /udy ! =am9if]al %ell z a physical sy/em1 :o recognise t its :ole plan & mode ( gr[? is closely ak9 to ! ph5om5a exhibit$ by fluid drops "u p>ticul> conditions1 & :o expla9 ! con=mation ( ! %ell by help ( ! same physical pr9ciples & ma!matical laws--yet all ! :ile abate no jot or tittle ( ! ord9>y po/ulates ( mod]n biology1 nor d\bt ! validity & univ]sal applicability ( ! concepts ( ,d>w9ian evolution4 ,= ^! writ]s ! biog5etis*es ,grundgesetz rema9s impregnable4 ,! ,=am9if]a rema9 = !m a great family tree1 ^: actual p$igree is traceable to ! remote/ ages2 9 :i* hi/orical evolution has co9cid$ ) progressive *ange2 & 9 :i* /ructural fitness = a p>ticul> function 7or functions7 has ex]cis$ its selective action & ensur$ 8! survival ( ! fitte/40 ,by successive /ages ( hi/oric evolution we are suppos$ to pass f ! irregul> ,a/rorhiza to a ,rhabdamm9a ) its m conc5trat$ disc2 to ! =ms ( ! same g5us :i* consi/ ( b a s+le tube ) c5tral *amb]2 to ^? :]e ?is *amb] is m & m di/9ctly segm5t$2 s to ! typical _m-*amb]$ ,nodos>iae2 & f ^!1 by ano!r def9ite advance & lat] evolution to ! spiral ,tro*amm9ae4 ,aft] ?is fa%ion1 ?r\gh\t ! :ole v>i$ s]ies ( ! ,=am9if]a1 ,drey] & ,rhumbl] 7foll[+ ,neumayr7 recognise s _m successions ( relat$ =ms1 "o pass+ into ano!r1 & /&+ t[>ds x 9 a def9ite relation%ip ( ance/ry or desc5t4 ,ea* evolution ( =m1 f simpl] to m complex1 is deem$ to h be5 att5d$ by an advantage to ! organism1 an enhancem5t ( its *ances ( survival or p]petuation2 h5ce ! hi/orically old] =ms are1 on ! :ole1 /ructurally ! simpl]2 or conv]sely ! simpl] =ms1 su* z ! simple sph]e1 7 ! fir/ to come into be+ 9 primeval seas2 & f9ally1 ! gradual developm5t & increas+ #fji complication ( ! individual )9 its own lifetime is held to be at lea/ a p>tial recapitulation ( ! unkn[n hi/ory ( its race & dyna/y#eee4 ,we enc\nt] _m difficulties :5 we try to ext5d su* concepts z ^! to ! ,=am9if]a4 ,we are l$ = in/ance to ass]t1 z ,rhumbl] does1 t ! increas+ complexity ( ! %ell1 & ( ! mann] 9 :i* "o *amb] is fitt$ on ano!r1 makes = advantage2 & ! p>ticul> advantage on :i* ,rhumbl] re/s 8 argum5t is /r5g?4 ,increase ( /r5g?1 die ,fe/igkeits/eig]ung1 is accord+ to him ! guid+ pr9ciple 9 =am9if]al evolution1 & m>ks ! hi/oric /ages ( _! developm5t 9 geologic "t4 ,b 9 days gone by ,i us$ to see ! bea* ( a little ,connem>a bay be/rewn ) millions ^u millions ( =am9if]al %ells1 simple ,lag5ae1 less simple ,nodos>iae1 m complex ,rotaliae3 all drift$ by wave & g5tle curr5t f _! sea-cradle to _! s&y grave3 all ly+ blea*$ & dead3 "o m delicate ?an ano!r1 b all 7or va/ multitudes ( !m7 p]fect & unbrok54 ,& s ,i am n incl9$ to believe t niceties ( =m affect ! case v mu*3 nor 9 g5]al t =am9if]al life involves a /ruggle = exi/5ce :]e9 breakage is a con/ant dang] to be av]t$1 & increas$ /r5g? an advantage to be ensur$#eef4 ,9 ! c\rse ( ! same argum5t ,rhumbl] rem>ks t ,=am9if]a are abs5t f ! co>se s&s & gravels#eeg1 z ,williamson inde$ _h obs]v$ _m ye>s ago3 s av]t+1 or #faj at lea/ escap+1 ! dang]s ( concussion4 ,b ?is is aft] all a v simple matt] ( me*anical analysis4 ,! co>s5ess or f95ess ( ! s$im5t on ! sea-bottom is a measure ( ! curr5t3 :]e ! curr5t is /rong ! l>g] /ones are wa%$ clean1 :]e !re is p]fect /illness ! f9e/ mud settles d[n2 & ! light1 fragile %ells ( ! ,=am9if]a f9d _! appropriate place1 l e o!r grad$ s$im5t1 9 ?is spontane\s ord] ( lixiviation4 ,! !orem ( ,organic ,evolution is "o ?+2 ! problem ( deciph]+ ! l9es ( evolution1 ! ord] ( phylog5y1 ! degrees ( relation%ip & consangu9ity1 is q ano!r4 ,among ! high] organisms we arrive at conclusions reg>d+ ^! ?+s by weigh+ mu* circum/antial evid5ce1 by deal+ ) ! resultant ( _m v>iations1 & by consid]+ ! probability or improbability ( _m co9cid5ces ( cause & effect2 b ev5 !n our conclusions are at be/ unc]ta91 our judgm5ts are cont9ually op5 to revision & subject to appeal1 & all ! pro( & confirmation we c ev] h is t :i* comes f ! direct1 b fragm5t>y evid5ce ( palaeontology#eeh4 ,b 9 s f> z =ms c be %ewn to dep5d on ! play ( physical =ces1 & ! v>iations ( =m to be directly due to simple quantitative v>iations 9 ^!1 j s f> are we ?r[n back on our gu>d be=e ! biological conception ( consangu9ity1 & compell$ to revise ! vague canons :i* connect classification ) phylog5y4 ,! physici/ expla9s 9 t]ms ( ! prop]ties ( matt]1 & classifies accord+ to a ma!matical analysis1 all ! drops & =ms ( drops & associations ( drops1 all ! k9ds ( fro? & foam1 :i* he may discov] among inanimate ?+s2 & 8 task ends !re4 ,b :5 su* =ms1 su* con=mations & configurations1 occur among liv+ ?+s1 !n at once ! biologi/ introduces 8 concepts ( h]$ity1 ( hi/orical evolution1 ( succession 9 "t1 ( recapitulation ( remote ance/ry 9 individual gr[?1 ( common orig9 7unless contradict$ by direct evid5ce7 ( simil> =ms remotely sep>at$ by geographic space or geologic "t1 ( fitness = a function1 ( #faa adaptation to an environm5t1 ( high] & l[]1 ( 8bett]0 & 8worse40 ,?is is ! fundam5tal diff]5ce betwe5 ! 8explanations0 ( ! physici/ & ^? ( ! biologi/4 ,9 ! ord] ( physical & ma!matical complexity !re is no "q ( ! sequ5ce ( hi/oric "t4 ,! =ces t br+ ab\t ! sph]e1 ! cyl9d] or ! ellipsoid are ! same ye/]day & to-morr[4 ,a sn[-cry/al is ! same to-day z :5 ! fir/ sn[s fell4 ,! physical =ces :i* m\ld ! =ms ( ,orbul9a1 ( ,a/rorhiza1 ( ,lag5a or ( ,nodos>ia to-day 7 /ill ! same1 & = aught we h reason to believe ! physical conditions "u :i* !y work$ 7 n appreciably diff]5t1 9 t ye/]day :i* we call ! ,cretace\s epo*2 or1 = aught we "k1 ?r\gh\t all t duration ( "t :i* is m>k$1 b n measur$1 by ! geological record4 ,9 a ^w1 ! m9ut5ess ( our organism br+s its con=mation z a :ole )9 ! range ( ! molecul> =ces2 ! laws ( its gr[? & =m appe> to lie on simple l9es2 :at ,b]gson calls#eei ! 8ideal k9%ip0 is pla9 & c]ta91 b ! 8mat]ial affiliation0 is problematic & obscure2 &1 9 ! end & up%ot1 x seems to me by no means c]ta9 t ! biologi/'s usual mode ( reason+ is appropriate to ! case1 or t ! concept ( cont9u\s hi/orical evolution mu/ necess>ily1 or may safely & legitimately1 be employ$4 #fab ,,*apt] ,,xiii ,,! ,,%apes ,,( ,,horns1 ,,& ,,( ,,tee? ,,or ,,tusks3 ,,) ,a ,,note ,,on ,,torsion ,we h _h s mu* to say on ! subject ( %ell-spirals t we mu/ deal briefly ) ! analog\s problems :i* are pres5t$ by ! horns ( %eep1 goats1 antelopes & o!r horn$ quadrup$s2 & all ! m1 because ^! horn-spirals are on ! :ole less symmetrical1 less easy ( measurem5t ?an ^? ( ! %ell1 & 9 o!r ways also are less easy ( inve/igation4 ,let u disp5se altoge!r 9 ?is case ) ma!matics2 & be cont5t ) a v simple acc\nt ( ! configuration ( a horn4 ,!re are ?ree types ( horn :i* des]ve sep>ate consid]ation3 fir/ly1 ! horn ( ! rh9oc]os2 secondly ! horns ( ! %eep1 ! goat1 ! ox or ! antelope1 t is to say1 ( ! s-call$ holl[-horn$ rum9ants2 & ?irdly1 ! solid bony horns1 or 8antl]s10 :i* are *>act]i/ic ( ! de]4 ,! horn ( ! rh9oc]os pres5ts no difficulty4 ,x is physiologically equival5t to a mass ( consolidat$ hairs1 &1 l ord9>y hair1 x consi/s ( non-liv+ or 8=m$0 mat]ial1 cont9ually add$ to by ! liv+ tissues at its base4 ,9 section1 t is to say 9 ! =m ( its 8g5]at+ curve10 ! horn is approximately elliptical1 ) ! long axis =e-&-aft1 or1 9 "s species1 ne>ly circul>4 ,its longitud9al gr[? proce$s ) a maximum velocity ant]iorly1 & a m9imum po/]iorly2 & ! ratio ( ^! velocities be+ con/ant1 ! horn curves into ! =m ( a log>i?mic spiral 9 ! mann] t we h already /udi$4 ,! spiral is ( small angle1 b 9 ! long]-horn$ species1 su* z ! great :ite rh9oc]os 7,c]atorh9us71 ! spiral =m is di/9ctly to be recognis$4 ,z ! horn #fac occupies a m$ian position on ! head1--a position1 t is to say1 ( symmetry 9 respect to ! field ( =ce on ei!r side1--!re is no t5d5cy t[>ds a lat]al twi/1 & ! horn accord+ly develops z a plane log>i?mic spiral4 ,:5 two horns coexi/1 ! h9d] "o is mu* ! small] ( ! two3 :i* is z mu* z to say t ! =ce1 or rate1 ( gr[? dim9i%es z we pass backw>ds1 j z x does )9 ! limits ( ! s+le horn4 ,& accord+ly1 :ile bo? horns h ess5tially ! same %ape1 ! spiral curvature is less manife/ 9 ! second "o1 simply by reason ( its comp>ative %ortness4 ,! pair$ horns ( ! ord9>y holl[-horn$ rum9ants1 su* z ! %eep or ! goat1 gr[ "u conditions :i* are 9 "s respects simil>1 b :i* diff] 9 o!r & important respects f ! conditions "u :i* ! horn gr[s 9 ! rh9oc]os4 ,z reg>ds its /ructure1 ! entire horn n[ consi/s ( a bony core ) a cov]+ ( sk92 ! inn]1 or d]mal1 lay] ( ! latt] is ri*ly suppli$ ) nutri5t blood-vessels1 :ile ! out] lay]1 or epid]mis1 develops ! fibr\s or *it9\s mat]ial1 *emically & morphologically ak9 to a mass ( cem5t$ or consolidat$ hairs1 :i* con/itutes ! 8%ea?0 ( ! horn4 ,a zone ( active gr[? at ! base ( ! horn keeps add+ to ?is %ea?1 r+ by r+1 & ! specific =m ( ?is annul> zone is1 accord+ly1 t ( ! 8g5]at+ curve0 ( ! horn4 ,ea* horn no long] lies1 z x does 9 ! rh9oc]os1 9 ! plane ( symmetry ( ! animal ( :i* x =ms a "p2 & ! limit$ field ( =ce conc]n$ 9 ! g5esis & gr[? ( ! horn is b\nd1 accord+ly1 to be m or less lat]ally asymmetrical4 ,b ! two horns are 9 symmetry "o ) ano!r2 !y =m 8conjugate0 spirals1 "o be+ ! 8mirror-image0 ( ! o!r4 ,j z 9 ! hairy coat ( ! animal ea* hair1 on ei!r side ( ! m$ian 8p>t+10 t5ds to h a c]ta9 def9ite direction ( its own axis1 incl9$ away f ! m$ian axial plane ( ! :ole sy/em1 s is x bo? ) ! bony core ( ! horn & ) ! consolidat$ mass ( hairs or hair-l sub/ance :i* con/itutes its %ea?2 ! prim>y axis ( ! horn is m or less incl9$ to1 & may ev5 be ne>ly p]p5dicul> to1 ! axial plane ( ! animal4 ,! gr[? ( ! horny %ea? is n cont9u\s1 b m or #fad less def9itely p]iodic3 sometimes1 z 9 ! %eep1 ?is p]iodicity is p>ticul>ly well-m>k$1 & causes ! horny %ea? to be compos$ ( a s]ies ( all b sep>ate r+s1 :i* are suppos$ to be =m$ ye> by ye>1 & s to record ! age ( ! animal#efj4 ,j z we s\ght = ! true g5]at+ curve 9 ! orifice1 or 8lip10 ( ! molluscan %ell1 s we might be apt to assume t 9 ! spiral horn ! g5]at+ curve correspond$ to ! lip or m>g9 ( "o ( ! horny r+s or annuli4 ,?is annul> m>g91 or b\nd>y ( ! r+1 is usually a s9u\s curve1 n ly+ 9 a plane1 b su* z w\ld =m ! b\nd>y ( an anticla/ic surface ( great complexity3 to ! mean+ & orig9 ( :i* ph5om5on we %all return pres5tly4 ,b1 z we h already se5 9 ! case ( ! molluscan %ell1 ! complexities ( ! lip itself1 or ( ! correspond+ l9es ( gr[? ^u ! %ell1 ne$ n conc]n u 9 our /udy ( ! developm5t ( ! spiral3 inasmu* z we may sub/itute = ^! actual b\nd>y l9es1 _! 8trace10 or projection on a plane p]p5dicul> to ! axis--9 o!r words ! simple outl9e ( a transv]se section ( ! :orl4 ,9 ! horn1 ?is transv]se section is (t5 circul> or ne>ly s1 z 9 ! ox5 & _m antelopes3 x n[ & !n becomes ( some:at complicat$ polygonal outl9e1 z 9 a highl& ram2 b 9 _m antelopes1 & 9 mo/ ( ! %eep1 ! outl9e is t ( an isosceles1 or sometimes ne>ly equilat]al triangle1 a =m :i* is typically display$1 = in/ance1 9 ,ovis ,ammon4 ,! horn 9 ?is latt] case is a trih$ral prism1 ^: ?ree faces are1 7#a7 an upp]1 or frontal face1 9 cont9uation ( ! plane ( ! frontal bone2 7#b7 an out]1 or orbital1 />t+ f ! upp] m>g9 ( ! orbit2 & 7#c7 an inn]1 or 8nu*al10 abutt+ on ! p>ietal bone#efa4 ,along ^! ?ree faces1 & _! correspond+ angles or edges1 we c trace 9 ! fibr\s sub/ance ( ! horn a s]ies ( homolog\s spirals1 su* z we #fae h call$ 9 a prec$+ *apt] ! 8ensemble ( g5]at+ spirals0 :i* con/itute ! surface4 ,illu/ration3 ,fig4 #cah4 ,diagram ( ,ram's horns4 7,aft] ,sir ,v9c5t ,brooke1 f ,p4,z4,s47 a1 frontal2 b1 orbital2 c1 nu*al surface4 ,9 "s few cases1 ( :i* ! male musk ox is "o ( ! mo/ notable1 ! horn is n develop$ 9 a cont9u\s spiral curve4 ,x *anges its %ape z gr[? proce$s2 & ?is1 z we h se51 is en\gh to %[ t x does n con/itute a log>i?mic spiral4 ,! reason is t ! bony exo/oses1 or horn-cores1 ab\t :i* ! horny %ea? is %ap$ & m\ld$1 nei!r gr[ cont9u\sly nor ev5 rema9 ( con/ant size aft] atta9+ _! full gr[?4 ,b z ! horns gr[ heavy ! bony core is b5t d[nw>ds by _! weight1 & s guides ! gr[? ( ! horn 9 a new direction4 ,moreov] z age advances1 ! horn-core is fur!r weak5$ & to a great ext5t absorb$3 & ! horny %ea? or horn prop]1 depriv$ ( its support1 cont9ues to gr[1 b 9 a flatt5$ curve v diff]5t f its orig9al spiral#efb4 ,! *amois is a some:at analog\s case4 ,"h ! t]m9al1 or olde/1 "p ( ! horn is curv$2 x t5ds to assume a spiral =m1 ?\gh f its comp>ative %ortness x seems m]ely to be b5t into a hook4 ,b lat] on1 ! bony core )91 z x gr[s & /r5g!ns1 /iff5s ! horn1 & guides x into a /raight] c\rse or =m4 ,! same ph5om5on #faf ( *ange ( curvature1 manife/+ itself at ! "t :51 or ! place :]e1 ! horn is fre$ f ! support ( ! int]nal core1 is se5 9 a good _m o!r antelopes 7su* z ! h>tebee/7 & 9 _m buffaloes2 & ! cases :]e x is mo/ manife/ appe> to be ^? :]e ! bony core is relatively %ort1 or relatively weak4 ,illu/ration3 ,fig4 #cai4 ,head ( ,arabian ,wild ,goat1 ,capra s9aitica4 7,aft] ,sclat]1 f ,p4,z4,s47 ,b 9 ! great majority ( horns1 we h no difficulty 9 recognis+ a cont9u\s log>i?mic spiral1 nor 9 ref]r+ x1 z be=e1 to an unequal rate ( gr[? 7p>allel to ! axis7 on two opposite sides ( ! horn1 ! inequality ma9ta9+ a con/ant ratio z long z gr[? proce$s4 ,9 c]ta9 antelopes1 su* z ! gemsbok1 ! spiral angle is v small1 or 9 o!r words ! horn is v ne>ly /raight2 9 o!r species ( ! same g5us ,oryx1 su* z ! ,beisa antelope & ! ,leucoryx1 a g5tle #fag curve 7n unlike ?\gh g5]ally less ?an t ( a ,d5talium %ell7 is evid5t2 & ! spiral angle1 accord+ to ! few measurem5ts ,i h made1 is f\nd to measure f ab\t #bj to ne>ly #dj4 ,9 "s ( ! l>ge wild goats1 su* z ! ,sc9de wild goat1 we h a beautiful log>i?mic spiral1 ) a con/ant angle ( r less ?an #gj2 & we may easily arrange a s]ies ( =ms1 su* = example z ! ,sib]ian ibex1 ! m\fflon1 ,ovis ,ammon1 etc41 & end+ ) ! long-horn$ ,highl& ram3 9 :i*1 z we pass f "o to ano!r1 we recognise precisely homolog\s spirals1 ) an increas+ angul> con/ant1 ! spiral angle be+1 = in/ance1 ab\t #ge or r less 9 ,ovis ,ammon1 & 9 ! ,highl& ram a v little m4 ,we h already se5 t 9 ! neighb\rhood ( #gj or #hj a small *ange ( angle makes a m>k$ diff]5ce 9 ! appe>ance ( ! spire2 & we "k also t ! actual l5g? ( ! horn makes a v /rik+ diff]5ce1 = ! spiral becomes especially conspicu\s to ! eye :5 a horn or %ell is long en\gh to %ew sev]al :orls1 or at lea/ a consid]able "p ( "o entire :orl4 ,ev5 9 ! simple/ cases1 su* z ! wild goats1 ! spiral is nev] 7/rictly speak+7 a plane or discoid spiral3 b 9 great] or less degree !re is always sup]pos$ ^u ! plane log>i?mic spiral a helical spiral 9 space4 ,sometimes ! latt] is sc>cely app>5t1 = ! helical curvature is comp>atively small1 & ! horn 7?\gh long1 z 9 ! said wild goats7 is n ne>ly long en\gh to %ew a complete convolution3 at o!r times1 z 9 ! ram1 & /ill bett] 9 _m antelopes1 su* z ! koodoo1 ! helicoid or corkscrew curve ( ! horn is its mo/ *>act]i/ic feature4 ,accord+ly we may /udy1 z 9 ! molluscan %ell1 ! helicoid compon5t ( ! spire--9 o!r words ! v>iation 9 :at we h call$ 7on p4 #eee7 ! angle 4 ,?is factor x is :i*1 m ?an ! con/ant angle ( ! log>i?mic spiral1 imp>ts a *>act]i/ic appe>ance to ! v>i\s species ( %eep1 = in/ance to ! v>i\s closely alli$ species ( ,asiatic wild %eep1 or ,argali4 ,9 all ( ^! ! con/ant angle ( ! log>i?mic spiral is v mu* ! same1 b ! %e>+ compon5t diff]s greatly4 ,& ?us ! long drawn out horns ( #fah ,ovis ,poli1 f\r feet or m f tip to tip1 diff] conspicu\sly f ^? ( ,ovis ,ammon or ,o4 hodgsoni1 9 :i* a v simil> log>i?mic spiral is w\nd 7z x 77 r\nd a mu* blunt] cone4 ,! ram's horn !n1 l ! snail's %ell1 is a curve ( d\ble curvature1 9 :i* "o compon5t has impos$ ^u ! /ructure a plane log>i?mic spiral1 & ! o!r has produc$ a cont9u\s displacem5t1 or 8%e>10 proportionate 9 magnitude to1 & p]p5dicul> or o!rwise incl9$ 9 direction to1 ! axis ( ! =m] spiral curvature4 ,! result is precisely analog\s to t :i* we h /udi$ 9 ! snail & o!r spiral univalves2 b :ile ! =m1 & !re=e ! resultant =ces1 are simil>1 ! orig9al di/ribution ( =ce is n ! same3 = we h n "h1 z we _h 9 ! snail-%ell1 a 8columell>0 muscle1 to introduce ! compon5t act+ 9 ! direction ( ! axis4 ,we h1 x is true1 ! c5tral bony core1 :i* 9 "p p]=ms an analog\s function2 b ! ma9 ph5om5on "h is app>5tly a complex di/ribution ( rates ( gr[?1 p]p5dicul> to ! plane ( ! g5]at+ curve4 ,let u cont9ue to disp5se ) ma!matics1 = ! ma!matical treatm5t ( a curve ( d\ble curvature is nev] v simple1 & let u deal ) ! matt] by exp]im5t4 ,we h se5 t ! g5]at+ curve1 or transv]se section1 ( a typical ram's horn is triangul> 9 =m4 ,measur+ 7along ! curve ( ! horn7 ! l5g? ( ! ?ree edges ( ! trih$ral /ructure 9 a specim5 ( ,ovis ,ammon1 & call+ !m respectively ! out]1 inn]1 & h9d] edges 7f _! position at ! base ( ! horn1 relatively to ! skull71 ,i f9d ! out] edge to measure #hj cm41 ! inn] #gd cm41 & ! po/]ior #de cm42 let u say t1 r\ghly1 !y are 9 ! ratio ( #i 3 #h 3 #e4 ,!n1 if we make a numb] ( little c>dbo>d triangles1 equip ea* ) ?ree little legs 7,i make !m ( cork71 ^: relative l5g?s are z #i 3 #h 3 #e1 & pile !m up & /ick !m all toge!r1 we /raightway build up a curve ( d\ble curvature precisely analog\s to ! ram's horn3 except only t1 9 ?is fir/ approximation1 we h n all[$ = ! gradual increm5t 7or decrem5t7 ( ! triangul> surfaces1 t is to say1 = ! tap]+ ( ! horn due to ! gr[? 9 its own plane ( ! g5]at+ curve4 #fai ,9 ?is case !n1 & 9 mo/ o!r trih$ral or ?ree-sid$ horns1 "o ( ! ?ree compon5ts1 or ?ree unequal velocities ( gr[?1 is ( relatively small magnitude1 b ! o!r two are ne>ly equal "o to ! o!r4 ,x w\ld involve b little *ange = ^! latt] to become precisely equal2 & aga9 b little to turn ! balance ( inequality ! o!r way4 ,b ! imm$iate consequ5ce ( ?is alt]$ ratio ( gr[? w\ld be t ! horn w\ld appe> to w9d ! o!r way1 z x does 9 ! antelopes1 & also 9 c]ta9 goats1 e4g4 ! m>khor1 ,capra falcon]i4 ,= ^! two opposite directions ( twi/ ,dr ,:]ry has introduc$ a conv5i5t nom5clature4 ,:5 ! horn w9ds s t we foll[ x f base to apex 9 ! direction ( ! h&s ( a wat*1 x is cu/om>y to call x a 8left-h&$0 spiral4 ,su* a spiral we h 9 ! horn on ! left-h& side ( a ram's head4 ,accord+ly1 ,dr ,:]ry calls ! condition homonym\s1 :]e1 z 9 ! %eep1 a "r-h&$ spiral is on ! "r side ( ! head1 & a left-h&$ spiral on ! left side2 :ile he calls ! opposite condition het]onym\s1 z we h x 9 ! antelopes1 :]e ! "r-h&$ twi/ is on ! left side ( ! head1 & ! left-h&$ twi/ on ! "r-h& side4 ,among ! goats1 we may h ei!r condition4 ,?us ! dome/ic & mo/ ( ! wild goats agree ) ! %eep2 b 9 ! m>khor ! twi/$ horns are het]onym\s1 z 9 ! antelopes4 ,! diff]5ce1 z we h se51 is easily expla9$2 & 7v mu* z 9 ! case ( our opposite spirals 9 ! apple-snail1 ref]r$ to on p4 #efj71 x has no v deep importance4 ,summ>is$ !n1 9 a v few words1 ! argum5t by :i* we acc\nt = ! spiral con=mation ( ! horn is z foll[s3 ,! horn elongates by d9t ( cont9ual gr[? )9 a n>r[ zone1 or annulus1 at its base4 ,if ! rate ( gr[? be id5tical on all sides ( ?is zone1 ! horn w gr[ /raight2 if x be great] on "o side ?an on ! o!r1 ! horn w become curv$3 & x probably w be great] on "o side ?an on ! o!r1 because ea* s+le horn occupies an unsymmetrical field ) ref]5ce to ! plane ( symmetry ( ! animal4 ,if ! maximal & m9imal velocities ( gr[? be precisely at opposite sides ( ! zone ( gr[?1 ! resultant spiral w be a plane spiral2 b if !y be n precisely or diametrically opposite1 !n ! spiral w be a spiral 9 space1 ) a w9d+ or helical compon5t2 & x is by no means likely t ! maximum & m9imum w occur at precisely opposite ends ( a diamet]1 = #fbj no su* plane ( symmetry is manife/$ 9 ! field ( =ce to :i* ! gr[+ annulus corresponds or app]ta9s4 ,n[ we mu/ c>efully rememb] t ! rates ( gr[? ( :i* we are "h speak+ are ! net rates ( longitud9al increm5t1 9 :i* increm5t ! activity ( ! liv+ cells 9 ! zone ( gr[? at ! base ( ! horn is only "o 7?\gh x is ! fundam5tal7 factor4 ,9 o!r words1 if ! horny %ea? 7 cont9ually be+ add$ to ) equal rapidity all r\nd its zone ( active gr[?1 b at ! same "t _h its elongation m ret>d$ on "o side ?an ! o!r 7prior to its complete solidification7 by v>y+ degrees ( adhesion or membran\s atta*m5t to ! bone core )91 !n ! net result w\ld be a spiral curve precisely su* z w\ld h aris5 f initial inequalities 9 ! rate ( gr[? itself4 ,x seems highly probable t ?is is a v important factor1 & sometimes ev5 ! *ief factor 9 ! case4 ,! same ph5om5on ( atta*m5t to ! bony core1 & ! consequ5t friction or ret>dation ) :i* ! %ea? slides ov] its surface1 w lead to v>i\s subsidi>y ph5om5a3 among o!rs to ! pres5ce ( transv]se folds or corrugations ^u ! horn1 & to _! unequal di/ribution ^u its sev]al faces or edges4 ,& :ile x is p]fectly true t ne>ly all ! *>act]s ( ! horn c be acc\nt$ = by unequal velocities ( longitud9al gr[? ^u its diff]5t sides1 x is also pla9 t ! actual field ( =ce is a v complicat$ "o inde$4 ,= example1 we c easily see t 7at lea/ 9 ! great majority ( cases7 ! direction ( gr[? ( ! horny fibres ( ! %ea? is by no means p>allel to ! axis ( ! core )92 accord+ly ^! fibres w t5d to w9d 9 a sy/em ( helicoid curves ar\nd ! core1 & n only ?is helicoid twi/ b any o!r t5d5cy to spiral curvature on ! "p ( ! %ea? w t5d to be oppos$ or modifi$ by ! resi/ance ( ! core )94 ,b on ! o!r h& liv+ bone is a v pla/ic /ructure1 & yields easily ?\gh sl[ly to any =ces t5d+ to its de=mation2 & s1 to a consid]able ext5t1 ! bony core itself w t5d to be modell$ by ! curvature :i* ! gr[+ %ea? assumes1 & ! f9al result w be det]m9$ by an equilibrium betwe5 ^! two sy/ems ( =ces4 #fba ,:ile x is n v safe1 p]haps1 to lay d[n any g5]al rule z to :at horns are m1 & :at are less spirally curv$1 ,i ?9k x may be said t1 on ! :ole1 ! ?ick] ! horn1 ! great] is its spiral curvature4 ,x is ! sl5d] horns1 ( su* =ms z ! ,beisa antelope1 :i* are g5tly curv$1 & x is ! robu/ horns ( goats or ( %eep 9 :i* ! curvature is m pron\nc$4 ,o!r ?+s be+ ! same1 ?is is :at we %\ld expect to f9d2 = x is :]e ! transv]se section ( ! horn is l>ge t we may expect to f9d ! m m>k$ diff]5ces 9 ! int5sity ( ! field ( =ce1 :e!r ( active gr[? or ( ret>dation1 on opposite sides or 9 diff]5t sectors !re(4 ,illu/ration3 ,fig4 #cbj4 ,head ( ,ovis ,ammon1 %ew+ ,/ ,v5ant's curves4 ,b !re is yet ano!r & a v rem>kable ph5om5on :i* we may disc]n 9 ! gr[? ( a horn1 :5 x takes ! =m ( a curve ( d\ble curvature1 namely1 an effect ( torsional /ra92 & ?is x is :i* gives rise to ! s9u\s 8l9es ( gr[?10 or s9u\s b\nd>ies ( ! sep>ate horny r+s1 ( :i* we h already spok54 ,x is n at fir/ sight obvi\s t a me*anical /ra9 ( torsion is necess>ily involv$ 9 ! gr[? ( ! horn4 ,9 our exp]im5tal illu/ration 7p4 #fah71 we built up a twi/$ coil ( sep>ate elem5ts1 & no torsional /ra9 att5d$ ! developm5t ( ! sy/em4 ,s w\ld x be if ! horny %ea? grew by successive annul> increm5ts1 free save = _! relation to "o ano!r1 & hav+ no atta*m5t to ! solid core )94 ,b z a matt] ( fact !re is #fbb su* an atta*m5t1 by subcutane\s connective tissue1 to ! bony core2 & accord+ly a torsional /ra9 w be set up 9 ! gr[+ horny %ea?1 aga9 provid$ t ! =ces ( gr[? !re9 be direct$ m or less obliquely to ! axis ( ! core2 = a 8c\ple0 is ?us introduc$1 giv+ rise to a /ra9 :i* ! %ea? w\ld n exp]i5ce 7 x free 7s to speak7 to slip along1 impell$ only by ! pressure ( its own gr[? f bel[4 ,& fur!rmore1 ! successive small increm5ts ( ! gr[+ horn 7t is to say1 ( ! horny %ea?7 are n in/antane\sly conv]t$ f liv+ to solid & rigid sub/ance2 b !re is an int]m$iate /age1 probably long-cont9u$1 dur+ :i* ! new-=m$ horny sub/ance 9 ! neighb\rhood ( ! zone ( active gr[? is /ill pla/ic & capable ( de=mation4 ,n[ we "k1 f ! celebrat$ exp]im5ts ( ,/ ,v5ant#efc1 t 9 ! torsion ( an ela/ic body1 o!r ?an a cyl9d] ( circul> section1 a v rem>kable /ate ( /ra9 is introduc$4 ,if ! body be ?us cyl9drical 7:e!r solid or holl[71 !n a twi/ leaves ea* circul> section un*ang$1 9 dim5sions & 9 figure4 ,b 9 all o!r cases1 su* z an elliptic rod or a prism ( any p>ticul> sectional =m1 =ces are introduc$ :i* act p>allel to ! axis ( ! /ructure1 & :i* w>p ea* section into a complex anticla/ic surface4 ,?us 9 ! case ( a triangul> & equilat]al prism1 su* z is %ewn 9 section 9 ,fig4 #cba1 if ! "p ( ! rod repres5t$ 9 ! section be twi/$ by a =ce act+ 9 ! direction ( ! arr[1 !n ! orig9ally plane section w be w>p$ z indicat$ 9 ! diagram3--:]e ! full cont\r-l9es repres5t elevation above1 & ! dott$ l9es repres5t depression bel[1 ! orig9al level4 ,on ! ext]nal surface ( ! prism1 !n1 cont\r-l9es :i* 7 orig9ally p>allel & horizontal1 w be f\nd w>p$ into s9u\s curves1 su* t1 on ea* ( ! ?ree faces1 ! curve w be convex upw>ds on "o half1 & concave upw>ds on ! o!r half ( ! face4 ,! ram's horn1 & /ill bett] t ( ,ovis ,ammon1 is comp>able to su* a prism1 save t 9 section x is n q equilat]al1 & t its ?ree faces are n plane4 ,! w>p+ is !re=e n precisely id5tical on ! ?ree faces #fbc ( ! horn2 b1 9 ! g5]al di/ribution ( ! curves1 x is 9 complete accordance ) !ory4 ,simil> anticla/ic curves are well se5 9 _m antelopes2 b !y are conspicu\s by _! abs5ce 9 ! cyl9drical horns ( ox54 ,illu/ration3 ,fig4 #cba4 ,illu/ration3 ,fig4 #cbb4 ,! bett] to illu/rate ?is ph5om5on1 ! nature ( :i* is inde$ obvi\s en\gh f a sup]ficial exam9ation ( ! horn1 ,i made a pla/] ca/ ( "o ( ! horny r+s 9 a horn ( ,ovis ,ammon1 s z to get an accurate patt]n ( its s9u\s edge3 & !n1 fill+ ! m\ld up ) wet clay1 ,i modell$ an anticla/ic surface1 su* z to correspond z ne>ly z possible ) ! s9u\s outl9e#efd4 ,f9ally1 aft] mak+ a pla/] ca/ ( ?is sectional surface1 ,i drew its cont\r-l9es 7z %ewn 9 ,fig4 #cbb71 ) ! help ( a simple =m ( sph]omet]4 ,x w be se5 t 9 great "p ?is diagram is precisely simil> to ,/ ,v5ant's diagram ( ! cross-section ( a twi/$ triangul> prism2 & ?is is especially ! case 9 ! neighb\rhood ( ! %>p angle ( our prismatic section4 ,t 9 p>ts ! diagram is some:at asymmetrical is n to be wond]$ at3 & 7ap>t f inaccuracies due to ! some:at r\gh means by :i* x 0 made7 ?is asymmetry c be suffici5tly acc\nt$ = by anisotropy ( ! mat]ial1 by inequalities 9 ?ickness ( diff]5t p>ts ( ! horny %ea?1 & especially 7,i ?9k7 by unequal di/ributions ( rigidity due to ! pres5ce ( ! small] corrugations ( ! #fbd horn4 ,x is app>5tly on acc\nt ( ^! m9or corrugations t1 9 su* horns z ! ,highl& ram's1 :]e !y are /rongly m>k$1 ! ma9 ,/ ,v5ant effect is n ne>ly s well %ewn z 9 ! smoo!r horns su* z ^? ( ,o4 ,ammon & its imm$iate cong5]s#efe4 ,a fur!r ,note ^u ,torsion4 ,! ph5om5on ( torsion1 to :i* we h be5 ?us introduc$1 op5s up _m wide que/ions 9 connection ) =m4 ,"s ( ! associat$ ph5om5a are admirably illu/rat$ 9 ! case ( climb+ plants2 b we c only deal ) ^! /ill m briefly & p>5!tically4 ,! subject ( climb+ plants has be5 elaborately dealt ) n only 9 ,d>w9's books#eff1 b also by a v l>ge numb] ( e>li] & lat] writ]s4 ,9 8tw9+0 plants1 :i* con/itute ! great] numb] ( 8climb]s10 ! ess5tial ph5om5on is a t5d5cy ( ! gr[+ %oot to revolve ab\t a v]tical axis--a t5d5cy long ago discuss$ & inve/igat$ by su* writ]s z ,palm1 ,h4 von ,mohl & ,dutro*et#efg4 ,?is t5d5cy to revolution--8circumvolution10 z ,d>w9 calls x1 8revolv+ nutation10 z ,sa*s puts x--is v closely comp>able to ! process by :i* an antelope's horn 7su* z ! koodoo's7 gr[s into its spiral or r helicoid =m2 & x is simply due1 9 l mann]1 to inequalities 9 ! rate ( gr[? on diff]5t sides ( ! gr[+ /em4 ,!re is only ?is diff]5ce betwe5 ! two cases1 t 9 ! antelope's horn ! zone ( active gr[? is conf9$ to ! base ( ! horn1 :ile 9 ! climb+ /em ! same ph5om5on is at "w ?r\gh\t ! :ole l5g? ( ! gr[+ /ructure4 ,?is gr[? is 9 ! ma9 due to 8turgesc5ce10 t is to ! ext5sion1 or elongation1 ( ready-=m$ cells ?r\gh ! imbibition ( wat]2 x is a ph5om5on due to osmotic pressure4 ,! p>ticul> /imuli to :i* ^! movem5ts 7t is to say1 ^! inequalities ( gr[?7 h be5 #fbe ascrib$1 su* z contact 7?igmotaxis71 exposure to light 7heliotropism71 & s =?1 ne$ n be discuss$ "h#efh4 ,a simple /em gr[+ upright 9 ! d>k1 or 9 uni=mly diffus$ light1 w\ld be 9 a position ( equilibrium to a field ( =ce radially symmetrical ab\t its v]tical axis4 ,b ?is complete radial symmetry w n (t5 occur2 & ! radial anomalies may be su* z arise intr9sically f /ructural peculi>ities 9 ! /em itself1 or ext]nally to x by reason ( unequal illum9ation or ?r\gh v>i\s o!r localis$ =ces4 ,! ess5tial fact1 s f> z we are conc]n$1 is t 9 tw9+ plants we h a v m>k$ t5d5cy to inequalities 9 longitud9al gr[? on diff]5t aspects ( ! /em--a t5d5cy :i* is b an exagg]at$ manife/ation ( "o :i* is m or less pres5t1 "u c]ta9 conditions1 9 all plants :atsoev]4 ,j z 9 ! case ( ! rum9ants' horns s we f9d "h1 t ?is inequality may be1 s to speak1 positive or negative1 ! maximum ly+ to ! "o side or ! o!r ( ! tw9+ /em2 & s x comes to pass t "s climb]s tw9e to ! "o side & "s to ! o!r3 ! hop & ! honeysuckle foll[+ ! sun1 & ! field-convolvulus tw9+ 9 ! rev]se direction2 !re are also "s1 l ! woody night%ade 7,solanum ,dulcam>a7 :i* tw9e indiff]5tly ei!r way4 ,toge!r ) ?is circumnutatory movem5t1 !re is v g5]ally to be se5 an actual torsion ( ! tw9+ /em--a twi/1 t is to say1 ab\t its own axis2 & ,mohl made ! curi\s obs]vation1 confirm$ by ,d>w91 t :5 a /em tw9es ar\nd a smoo? cyl9drical /ick ! torsion does n take place1 save 8only 9 t degree :i* foll[s z a me*anical necessity f ! spiral w9d+03 b t /ems :i* _h climb$ ar\nd a r\gh /ick 7 all m or less1 & g5]ally mu*1 twi/$4 ,"h ,d>w9 did n refra9 f introduc+ t teleological argum5t :i* p]vades 8 :ole tra9 ( reason+3 8,! /em10 he says1 8probably ga9s rigidity by be+ twi/$ 7on ! same pr9ciple t a mu* twi/$ rope #fbf is /iff] ?an a slackly twi/$ "o71 & is ?us indirectly b5efit$ s z to be able to pass ov] inequalities 9 its spiral asc5t1 & to c>ry its own weight :5 all[$ to revolve freely40 ,! me*anical explanation w\ld appe> to be v simple1 & su* z to r5d] ! teleological hypo!sis unnecess>y4 ,9 ! case ( ! r\gh5$ support1 !re is a tempor>y adhesion or 8cl++0 betwe5 x & ! gr[+ /em :i* tw9es ar\nd x2 & a sy/em ( =ces is ?us set up1 produc+ a 8c\ple10 j z x 0 9 ! case ( ! ram's or antelope's horn ?r\gh direct adhesion ( ! bony core to ! surr\nd+ %ea?4 ,! twi/ is ! direct result ( ?is c\ple1 & x disappe>s :5 ! support is s smoo? t no su* =ce comes to be ex]t$4 ,ano!r important class ( climb]s includes ! s-call$ 8leaf-climb]s40 ,9 ^!1 "s portion ( ! leaf1 g5]ally ! petiole1 sometimes 7z 9 ! fumitory7 ! elongat$ midrib1 curls r\nd a support2 & a ph5om5on ( l nature occurs 9 _m1 ?\gh n all1 ( ! s-call$ 8t5dril-be>]s40 ,except t a diff]5t "p ( ! plant1 leaf or t5dril in/ead ( /em1 is conc]n$ 9 ! tw9+ process1 ! ph5om5on "h is /rictly analog\s to our =m] case2 b 9 ! result+ helix !re is1 z a rule1 ?is obvi\s diff]5ce1 t1 :ile ! tw9+ /em1 = in/ance ( ! hop1 makes a sl[ revolution ab\t its support1 ! typical leaf-climb] makes a close1 firm coil3 ! axis ( ! latt] is ne>ly p]p5dicul> & p>allel to ! axis ( its support1 :ile 9 ! tw9+ /em ! angle betwe5 ! two axes is comp>atively small4 ,ma!matically speak+1 ! diff]5ce m]ely am\nts to ?is1 t ! compon5t 9 ! direction ( ! v]tical axis is l>ge 9 ! "o case1 & ! correspond+ compon5t is small1 if n abs5t1 9 ! o!r2 9 o!r words1 we h 9 ! climb+ /em a consid]able v]tical compon5t1 due to its own t5d5cy to gr[ 9 height1 :ile ?is longitud9al or v]tical ext5sion ( ! :ole sy/em is n app>5t1 or little app>5t1 9 ! o!r cases4 ,b f ! fact t ! tw9+ /em t5ds to run obliquely to its support1 & ! coil+ petiole ( ! leaf-climb] t5ds to run transv]sely to ! axis ( its support1 !re imm$iately foll[s ?is m>k$ diff]5ce1 t ! ph5om5on #fbg ( torsion1 s manife/ 9 ! =m] case1 w be abs5t 9 ! latt]4 ,!re is "o o!r ph5om5on :i* meets u 9 ! tw9+ & twi/$ /em1 & :i* is d\btless illu/rat$ also1 ?\gh n s well1 9 ! antelope's horn2 x is a ph5om5on :i* =ms ! subject ( a second *apt] ( ,/ ,v5ant's rese>*es on ! effects ( torsional /ra9 9 ela/ic bodies4 ,we h already se5 h[ "o effect ( torsion1 9 = in/ance a prism1 is to produce /ra9s p>allel to ! axis1 elevat+ p>ts & depress+ o!r p>ts ( ea* transv]se section4 ,b 9 addition to ?is1 ! same torsion has ! effect ( mat]ially alt]+ ! =m ( ! section itself1 z we may easily see by twi/+ a squ>e or oblong piece ( india-rubb]4 ,if we />t ) a cyl9d]1 su* z a r\nd piece ( catapult india-rubb]1 & twi/ x on its own long axis1 we h already se5 t x suff]s no o!r di/ortion2 x /ill rema9s a cyl9d]1 t is to say1 x is /ill 9 section ev]y:]e circul>4 ,b if x be ( any o!r %ape ?an cyl9drical ! case is q diff]5t1 = n[ ! sectional %ape t5ds to alt] "u ! /ra9 ( torsion4 ,?us1 if our rod be elliptical 9 section to beg9 )1 x w1 "u torsion1 become a m elongat$ ellipse2 if x be squ>e1 its angles w become m prom95t1 & its sides w curve inw>ds1 till at l5g? ! squ>e assumes ! appe>ance ( a f\r-po9t$ />1 ) r\nd$ angles4 ,fur!rmore1 look+ at ! results ( ?is process ( modification1 we f9d exp]im5tally t ! resultant figures are m easily twi/$1 less resi/ant to torsion1 ?an 7 ^? f :i* we evolv$ !m2 & ?is is a v curi\s physical or ma!matical fact4 ,s a cyl9d]1 :i* is especially resi/ant to torsion1 is v easily b5t or flex$2 :ile project+ ribs or angles1 su* z an eng9e] makes 9 a b> or pill> ( iron = ! purpose ( greatly increas+ its /r5g? 9 ! way ( resi/ance to b5d+1 actually make x mu* weak] ?an be=e 7= ! same am\nt ( metal p] unit l5g?7 9 ! way ( resi/ance to torsion4 ,9 ! hop itself1 & 9 a v consid]able numb] ( o!r tw9+ & twi/+ /ems1 ! ribb$ or *annell$ =m ( ! /em is a conspicu\s feature4 ,we may safely take x1 7#a7 t #fbh su* /ems are especially susceptible ( torsion2 & 7#b7 t ! effect ( torsion w be to int5sify any su* peculi>ities ( sectional outl9e :i* !y may possess1 ?\gh n to initiate !m 9 an orig9ally cyl9drical /ructure4 ,9 ! leaf-climb]s ! case does n pres5t itself1 = !re1 z we h se51 torsion itself is n1 or is v slightly1 manife/$4 ,!re are v di/9ct traces ( ! ph5om5on 9 ! horns ( c]ta9 antelopes1 b ! reason :y x is n a m conspicu\s feature ( ! antelope's horn or ( ! ram's is app>5tly a v simple "o3 namely1 t ! pres5ce ( ! bony core )9 t5ds to *eck t de=mation :i* is p]p5dicul>1 :ile x p]mits t :i* is p>allel1 to ! axis ( ! horn4 ,( ,de]'s ,antl]s4 ,b let u return to our subject ( ! %apes ( horns1 & consid] briefly our la/ class ( ^! /ructures1 namely ! bony antl]s ( ! v>i\s species ( elk & de]#efi4 ,! problems :i* ^! pres5t to u are v diff]5t f ^? :i* we h _h to d ) 9 ! antelope or ! %eep4 ,illu/ration3 ,fig4 #cbc4 ,antl]s ( ,sw$i% ,elk4 7,aft] ,lnnb]g1 f ,p4,z4,s47 ,) reg>d to its /ructure1 x is pla9 t ! bony antl] corresponds1 ^u ! :ole1 to ! bony core ( ! antelope's horn2 :ile 9 place ( ! h>d horny %ea? ( ! latt]1 we h ! s(t 8velvet10 :i* e season cov]s ! new gr[+ antl]1 & protects ! l>ge nutri5t blood-vessels by help ( :i* ! antl] gr[s#egj4 ,! ma9 diff]5ce lies 9 ! fact t1 9 ! "o case1 ! bony core1 imprison$ )9 its %ea?1 is r5d]$ incapable ( bran*+ & incapable also ( lat]al expansion1 & ! :ole horn is only p]mitt$ to gr[ 9 l5g?1 :ile reta9+ a sectional cont\r t is id5tical ) 7or b little alt]$ f7 t :i* x possesses at its gr[+ base3 #fbi b 9 ! antl]1 on ! o!r h&1 no su* re/ra9t is impos$1 & ! liv+1 gr[+ fabric ( bone may exp& into a broad flatt5$ plate ov] :i* ! blood-vessels run4 ,9 ! imm$iate neighb\rhood ( ! ma9 blood-vessels gr[? w be mo/ active2 9 ! int]spaces betwe51 x may :olly fail3 ) ! result t we may h great not*es cut out ( ! flatt5$ plate1 or may at l5g? f9d x r$uc$ to ! =m ( a simple bran*+ /ructure4 ,! ma9 po9t1 z x seems to me1 is t ! 8horn0 is ess5tially an axial rod1 :ile ! 8antl]0 is ess5tially an outspread surface#ega4 ,9 o!r words1 ,i believe t ! :ole configuration ( an antl] is m easily und]/ood by conceiv+ x z a plate or a surface1 m & m not*$ & scollop$ till b a sl5d] skeleton may rema91 ?an to look ^u x ! o!r way1 namely z an axial /em 7or beam7 giv+ #fcj (f bran*es 7or t9es71 ! int]spaces betwe5 :i* latt] may sometimes be fill$ up to =m a cont9u\s plate4 ,illu/ration3 ,fig4 #cbd4 ,head & antl]s ( a ,/ag 7,c]vus ,duvauceli74 7,aft] ,lydekk]1 f ,p4,z4,s47 ,9 a s5se x matt]s v little :e!r we reg>d ! broad plate-l antl]s ( ! elk or ! sl5d] bran*+ antl]s ( ! /ag z ! m primitive type2 = we are n conc]n$ "h ) ! "q ( hypo!tical phylog5y4 ,& ev5 f ! ma!matical po9t ( view x makes little or no diff]5ce :e!r we describe ! plate z con/itut$ by ! int]connection ( ! bran*es1 or ! bran*es d]iv$ by a process ( not*+ or incision f ! plate4 ,! important po9t = u is to recognise t 7save = occasional slight irregul>ities7 ! bran*+ sy/em 9 ! "o con=ms ess5tially to ! curv$ plate or surface :i* we see pla9ly 9 ! o!r4 ,9 %ort ! arrangem5t ( ! bran*es is m or less comp>able to t ( ! ve9s 9 a leaf1 or to t ( ! blood-vessels z !y c\rse ov] ! curv$ surface ( an organ4 ,x is a process ( ramification1 n1 l t ( a tree1 9 v>i\s planes1 b /rictly limit$ #fca to a s+le surface4 ,& j z ! ve9s )9 a leaf are n necess>ily conf9$ 7z !y happ5 to be 9 mo/ ord9>y leaves7 to a plane surface1 b1 z 9 ! petal ( a tulip or ! capsule ( a poppy1 may h to run _! c\rse )9 a curv$ surface1 s does ! analogy ( ! leaf lead u directly to ! mode ( bran*+ :i* is *>act]i/ic ( ! antl]4 ,! surface to :i* ! bran*es ( ! antl] t5d to be conf9$ is a m or less sph]oidal1 or occasionally an ellipsoidal "o2 & fur!rmore1 :5 we inspect any well-develop$ pair ( antl]s1 su* z ^? ( a r$ de]1 a sambur or a wapiti1 we h no difficulty 9 see+ t ! two antl]s make up betwe5 !m a s+le surface1 & con/itute a symmetrical figure1 ea* half be+ ! mirror-image ( ! o!r4 ,to put ! case 9 ano!r way1 a pair ( antl]s 7ap>t f occasional slight irregul>ities7 t5ds to con/itute a figure su* t we c\ld conceive an ela/ic %eet /ret*$ ov] or r\nd ! entire sy/em1 s z to =m "o cont9u\s & ev5 surface2 & n only w\ld ! surface curvature be on ! :ole smoo? & ev51 b ! b\nd>y ( ! surface w\ld also t5d to be an ev5 curve3 t is to say ! tips ( all ! t9es w\ld approximately h _! locus 9 a cont9u\s curve4 ,x foll[s f ?is t if we want to make a simple model ( a set ( antl]s1 we %all be v greatly help$ by tak+ "s appropriate sph]oidal surface z our gr\ndwork or scaffold+4 ,! be/ =m ( surface is a matt] = trial & inve/igation 9 ea* p>ticul> case2 b ev5 9 a sph]e1 by select+ appropriate areas !re(1 we c obta9 suffici5t v>ieties ( surface to meet all ord9>y cases4 ,) m]ely a bit ( sculptor's clay or pla/ic9e1 we %\ld be put h>d to x to model ! horns ( a wapiti or a re9de]3 b if we />t ) an orange 7or a r\nd flor5ce flask7 & lay our little tap]$ rolls ( pla/ic9e ^u x1 9 simple natural curves1 x is surpris+ to see h[ quickly & successfully we c imitate "o type ( antl] aft] ano!r4 ,9 do+ s1 we %all be /ruck by ! fact t our model may v>y 9 its mode ( bran*+ )9 v consid]able limits1 & yet look p]fectly natural4 ,= ! same wide range ( v>iation is *>act]i/ic ( ! natural antl]s !mselves4 ,z ,sir ,v4 ,brooke says 7op4 cit4 p4 #hib71 8,no two antl]s are ev] exactly alike2 & ! #fcb v>iation to :i* ! antl]s are subject is s great t 9 ! abs5ce ( a l>ge s]ies !y w\ld be held to be indicative ( sev]al di/9ct species#egb40 ,b all ^! _m v>iations lie )9 a limit$ range1 = !y are all subject to our g5]al rule t ! entire /ructure is ess5tially conf9$ to a s+le curv$ surface4 ,x is pla9 t 9 ! curvatures bo? ( ! beam & ( its t9es1 9 ! angles by :i* ^! latt] meet ! beam1 & 9 ! cont\rs ( ! entire sy/em1 !re are involv$ _m elegant ma!matical problems ) :i* we _c at pres5t attempt to deal4 ,nor mu/ we attempt mean:ile to enquire into ! physical mean+ or orig9 ( ^! ph5om5a1 = z yet ! clue seems to be lack+ & we %\ld only heap "o hypo!sis ^u ano!r4 ,t !re is a complete contra/ ( ma!matical prop]ties betwe5 ! horn & ! antl] is ! ma9 lesson ) :i*1 9 ! meantime1 we mu/ re/ cont5t4 ,( ,tee?1 & ( ,beak & ,claw4 ,9 a fa%ion simil> to t manife/$ 9 ! %ell or ! horn1 we f9d ! log>i?mic spiral to be implicit 9 a great _m o!r organic /ructures :]e ! ph5om5a ( gr[? proce$ 9 a simil> way3 t is to say1 :]e ab\t an axis !re is "s asymmetry lead+ to unequal rates ( longitud9al gr[?1 & :]e ! /ructure is ( su* a k9d t ea* new increm5t is add$ on z a p]man5t & un*ang+ "p ( ! entire con=mation4 ,nail & claw1 beak & too?1 all come "u ?is category4 ,! log>i?mic spiral always t5ds to manife/ itself 9 su* /ructures z ^!1 ?\gh x usually only attracts our att5tion 9 elongat$ /ructures1 :]e 7t is to say7 ! radius vector has describ$ a consid]able angle4 ,:5 ! can>y-bird's claws gr[ long f lack ( use1 or :5 ! incisor too? ( a rabbit or a rat gr[s long by reason ( an injury to ! oppon5t too? aga9/ :i* x 0 wont to bite1 we "k t ! too? or claw t5ds to gr[ into a spiral curve1 & we speak ( x z a mal=mation4 ,b !re has be5 no fundam5tal *ange ( =m1 save only an abnormal increase 9 l5g?2 #fcc ! elongat$ too? or claw has ! selfsame curvature t x _h :5 x 0 %ort1 b ! spiral curvature becomes m & m manife/ ! long] x gr[s4 ,a curi\s analog\s case is t ( ! ,new ,zeal& huia bird1 9 :i* ! beak ( ! female is describ$ z be+ comp>atively %ort & /raight1 :ile t ( ! male is long & curv$2 x is easy to see t !re is a slight curvature also 9 ! beak ( ! female1 & t ! beak ( ! male %[s no?+ b ! same curve produc$4 ,9 ! case ( ! m curv$ beaks1 su* z ^? ( an eagle or a p>rot1 we may1 if we please1 det]m9e ! con/ant angle ( ! log>i?mic spiral1 j z we h done 9 ! case ( ! ,nautilus %ell2 & "h aga91 z ! bird gr[s old] or ! beak long]1 ! spiral nature ( ! curve becomes m & m app>5t1 z 9 ! hook$ beak ( an old eagle1 or z 9 ! great beak ( "s l>ge p>rot su* z a hyac9?9e macaw4 ,let u glance at "o or two in/ances to illu/rate ! spiral curvature ( tee?4 ,a d5ti/ kn[s t e too? has a curvature ( its own1 & t 9 pull+ ! too? he mu/ foll[ ! direction ( ! curve2 b 9 an ord9>y too? ?is curvature is sc>cely visible1 & is lea/ s :5 ! diamet] ( ! too? is l>ge comp>$ ) its l5g?4 ,9 ! simply =m$1 m or less conical tee?1 su* z are ^? ( ! dolph91 & 9 ! m or less simil>ly %ap$ can9es & incisors ( mammals 9 g5]al1 ! curvature ( ! too? is p>ticul>ly well se54 ,we see x 9 ! little tee? ( a h$gehog1 & 9 ! can9es ( a dog or a cat x is v obvi\s inde$4 ,:5 ! great can9e ( ! c>nivore becomes /ill fur!r enl>g$ or elongat$1 z 9 ,ma*airodus1 x gr[s into ! /rongly curv$ sabre-too? ( t great ext9ct tig]4 ,9 rod5ts1 x is ! incisors :i* und]go a great elongation2 _! rate ( gr[? diff]s1 ?\gh b slightly1 on ! two sides1 ant]ior & po/]ior1 ( ! axis1 & by summation ( ^! slight diff]5ces 9 ! rapid gr[? ( ! too? an unmi/akeable log>i?mic spiral is gradually built up4 ,we see x admirably 9 ! beav]1 or 9 ! great gr\nd-rat1 ,geomys4 ,! elephant is a simil> case1 save t ! too?1 or tusk1 rema9s1 ow+ to comp>ative lack ( we>1 9 a m p]fect condition4 ,9 ! rod5t 7save only 9 ^? abnormal cases m5tion$ on ! la/ page7 ! #fcd ant]ior1 fir/-=m$1 "p ( ! too? we>s away z fa/ z x is add$ to f beh9d2 & 9 ! gr[n animal1 all ^? portions ( ! too? ne> to ! pole ( ! log>i?mic spiral h long disappe>$4 ,9 ! elephant1 on ! o!r h&1 we see1 practically speak+1 ! :ole unworn too?1 f po9t to root2 & its actual tip ne>ly co9cides ) ! pole ( ! spiral4 ,if we assume 7z ) no great inaccuracy we may d7 t ! tip actually co9cides ) ! pole1 !n we may v easily con/ruct ! cont9u\s spiral ( :i* ! exi/+ tusk con/itutes a "p2 & by s do+1 we see ! %ort1 g5tly curv$ tusk ( our ord9>y elephant gr[+ gradually into ! spiral tusk ( ! mammo?4 ,no d\bt1 j z 9 ! case ( our molluscan %ells1 we h a t5d5cy to v>iation1 bo? individual & specific1 9 ! con/ant angle ( ! spiral2 "s elephants1 & "s species ( elephant1 und\bt$ly h a high] spiral angle ?an o!rs4 ,b 9 mo/ cases1 ! angle w\ld seem to be su* t a spiral configuration w\ld become v manife/ inde$ if only ! tusk pursu$ its /eady gr[?1 un*ang$ o!rwise 9 =m1 till x atta9$ ! dim5sions :i* we meet ) 9 ! mammo?4 ,9 a species su* z ,ma/odon angu/id5s1 or ,m4 arv]n5sis1 ! specific angle is l[ & ! tusk comp>atively /raight2 b ! ,am]ican ma/odons & ! exi/+ species ( elephant h tusks :i* d n diff] appreciably1 except 9 size1 f ! great spiral tusks ( ! mammo?1 ?\gh f _! comp>ative %ortness ! spiral is little develop$ & only appe>s to ! eye z a g5tle curve4 ,:]ev] ! too? is v long inde$1 z 9 ! mammo? or ! beav]1 ! effect ( "s slight & all b inevitable lat]al asymmetry 9 ! rate ( gr[? beg9s to %ew itself3 9 o!r words1 ! spiral is se5 to lie n absolutely 9 a plane1 b to be a curve ( d\ble curvature1 l a twi/$ horn4 ,we see ?is condition v well 9 ! huge can9e tusks ( ! ,babirussa2 x is a conspicu\s feature 9 ! mammo?1 & x is m or less p]ceptible 9 any l>ge tusk ( ! ord9>y elephants4 ,! =m ( a mol> too?1 :i* is ess5tially a bran*+ or budd+ sy/em1 & 9 :i* su* longitud9al gr[? z gives rise to a spiral curve is b little manife/1 con/itutes an entirely diff]5t problem ) :i* ,i %all n at pres5t attempt to deal4 #fce ,,*apt] ,,xiv ,,on ,,leaf-,,arrangem5t1 ,,or ,,phyllotaxis ,! beautiful configurations produc$ by ! ord]ly arrangem5t ( leaves or florets on a /em h long be5 an object ( admiration & curiosity4 ,leon>do da ,v9ci w\ld seem1 z ,sir ,!odore ,cook tells u1 to h be5 ! fir/ to record 8 ?\ghts ^u ?is subject2 b ! old ,greek & ,egyptian geomet]s are n likely to h left un/udi$ or unobs]v$ ! spiral traces ( ! leaves ^u a palm-/em1 or ! spiral curves ( ! petals ( a lotus or ! florets 9 a sunfl[]4 ,! spiral leaf-ord] has be5 reg>d$ by _m le>n$ botani/s z involv+ a fundam5tal law ( gr[?1 ( ! deepe/ & mo/ f>-rea*+ importance2 :ile o!rs1 su* z ,sa*s1 h look$ ^u ! :ole doctr9e ( 8phyllotaxis0 z 8a sort ( geometrical or ari?metical play+ ) ideas10 & 8! spiral !ory z a mode ( view gratuit\sly introduc$ into ! plant40 ,sa*s ev5 goes s f> z to decl>e ?is doctr9e 89 direct opposition to sci5tific inve/igation1 & bas$ ^u ! ideali/ic direction ( ! ,naturphilosophie10--! my/ical biology ( ,ok5 & 8 s*ool4 ,! ess5tial facts ( ! case are n difficult to und]/&2 b ! !ories built ^u !m are s v>i$1 s conflict+1 & sometimes s obscure1 t we mu/ n attempt to submit !m to detail$ analysis & criticism4 ,!re are two *ief ways by :i* we may approa* ! "q1 accord+ to :e!r we reg>d1 z ! m fundam5tal & typical1 "o or o!r ( ! two *ief modes 9 :i* ! ph5om5on pres5ts itself4 ,t is to say1 we may hold t ! ph5om5on is display$ 9 its ess5tial simplicity by ! corkscrew spirals1 or helices1 :i* m>k ! position ( ! leaves ^u a cyl9drical /em or on an #fcf elongat$ fir-cone2 or1 on ! o!r h&1 we may be m attract$ by1 & reg>d z ( great] importance1 ! log>i?mic spirals :i* we trace 9 ! curv+ r[s ( florets 9 ! discoidal infloresc5ce ( a sunfl[]4 ,:e!r "o way or ! o!r be ! bett]1 or ev5 :e!r "o be n positively correct & ! o!r radically wrong1 has be5 vehem5tly debat$4 ,9 my judgm5t !y are1 bo? ma!matically & biologically1 to be reg>d$ z insep>able & correlative ph5om5a4 ,! helical arrangem5t 7z 9 ! fir-cone7 0 c>efully /udi$ 9 ! middle ( ! eighte5? c5tury by ! celebrat$ ,bonnet1 ) ! help ( ,cal&r9i1 ! ma!matician4 ,memoirs publi%$ ab\t #ahce1 by ,s*imp] & ,braun1 greatly amplifi$ ,bonnet's inve/igations1 & introduc$ a nom5clature :i* /ill holds its own 9 botanical textbooks4 ,naumann & ! bro!rs ,bravais are among ^? :o cont9u$ ! inve/igation 9 ! ye>s imm$iately foll[+1 & ,h(mei/]1 9 #ahfh1 gave an admirable acc\nt & summ>y ( ! "w ( ^! & _m o!r writ]s#egc4 ,/>t+ f "s giv5 level & proce$+ upw>ds1 let u m>k ! position ( "s "o leaf 7,a7 ^u a cyl9drical /em4 ,ano!r1 & a y\ng] leaf 7,b7 w be f\nd /&+ at a c]ta9 di/ance ar\nd ! /em1 & a c]ta9 di/ance along ! /em1 #fcg f ! fir/4 ,! =m] di/ance may be express$ z a fractional 8div]g5ce0 7su* z two-fif?s ( ! circumf]5ce ( ! /em7 z ! botani/s describe x1 or by an 8angle ( azimu?0 7su* z #add7 z ! ma!matician w\ld be m likely to /ate x4 ,! position ( ,b relatively to ,a mu/ be det]m9$1 n only by ?is angle 1 9 ! horizontal plane1 b also by an angle 77 9 ! v]tical plane2 = ! height ( ,b above ! level ( ,a1 9 comp>ison ) ! diamet] ( ! cyl9d]1 w obvi\sly make a great diff]5ce 9 ! appe>ance ( ! :ole sy/em1 9 %ort ! position ( ea* leaf mu/ be express$ by ,f7 s9 74 ,b ?is matt] botanical /ud5ts h n conc]n$ !mselves )2 9 o!r words1 _! /udies h be5 limit$ 7or ma9ly limit$7 to ! relation ( ! leaves to "o ano!r 9 azimu?4 ,:atev] relation we h f\nd betwe5 ,a & ,b1 let precisely ! same relation subsi/ betwe5 ,b & ,c3 & s on4 ,let ! gr[? ( ! sy/em1 t is to say1 be cont9u\s & uni=m2 x is !n evid5t t we h ! elem5t>y conditions = ! developm5t ( a simple cyl9drical helix2 & ?is 8prim>y helix0 or 8g5etic spiral0 we c n[ trace1 w9d+ r\nd & r\nd ! /em1 ?r\gh ,a1 ,b1 ,c1 etc4 ,b if we c trace su* a helix ?r\gh ,a1 ,b1 ,c1 x foll[s f ! symmetry ( ! sy/em1 t we h only to jo9 ,a to "s o!r leaf to trace ano!r spiral helix1 su*1 = in/ance1 z ,a1 ,c1 ,e1 etc42 p>allel to :i* w run ano!r & simil> "o1 namely 9 ?is case ,b1 ,d1 ,f1 etc4 ,& ^! spirals w run 9 ! opposite direction to ! spiral ,,abc4 ,9 %ort1 ! exi/5ce ( "o helical arrangem5t ( po9ts implies & involves ! exi/5ce ( ano!r & !n ano!r helical patt]n1 j z1 9 ! patt]n ( a wall-pap]1 our eye travels f "o l9e> s]ies to ano!r4 ,a modification ( ! helical sy/em w be introduc$ :51 in/ead ( ! leaves appe>+1 or /&+1 9 s+ul> succession1 we get two or m appe>+ simultane\sly ^u ! same level4 ,if !re be two su*1 !n we %all h two g5]at+ spirals precisely equival5t to "o ano!r2 & we may call !m ,a1 ,b1 ,c1 etc41 & ,a1 ,b1 ,c1 & s on4 ,^! are ! cases :i* we call 8:orl$0 leaves1 or 9 ! simple/ case1 :]e #fch ! :orl consi/s ( two opposite leaves only1 we call !m decussate4 ,among ! ph5om5a ( phyllotaxis1 two po9ts 9 p>ticul> h be5 f\nd difficult ( explanation1 & h ar\s$ discussion4 ,^! are 7#a71 ! pres5ce ( ! log>i?mic spirals su* z we h already spok5 ( 9 ! sunfl[]2 & 7#b7 ! fact t1 z reg>ds ! numb] ( ! helical or spiral r[s1 c]ta9 num]ical co9cid5ces are apt to recur aga9 & aga91 to ! exclusion ( o!rs1 & s to become *>act]i/ic features ( ! ph5om5on4 ,! fir/ ( ^! appe>s to me to pres5t no difficulty4 ,x is a m]e matt] ( /rictly ma!matical 8de=mation40 ,! /em :i* we h begun to speak ( z a cyl9d] is n /rictly s1 inasmu* z x tap]s (f t[>ds its summit4 ,! curve :i* w9ds ev5ly ar\nd ?is /em is1 accord+ly1 n a true helix1 = t t]m is conf9$ to ! curve :i* w9ds ev5ly ar\nd ! cyl9d]3 x is a curve 9 space :i* 7l ! spiral curve we h /udi$ 9 our turb9ate %ells7 p>takes ( ! *>act]s ( a helix & ( a log>i?mic spiral1 & :i* is 9 fact a log>i?mic spiral ) its pole drawn out ( its orig9al plane by a =ce act+ 9 ! direction ( ! axis4 ,if we imag9e a tap]+ cyl9d]1 or cone1 project$1 by v]tical projection1 on a plane1 x becomes a circul> disc2 & a helix describ$ ab\t ! cone necess>ily becomes 9 ! disc a log>i?mic spiral describ$ ab\t a focus :i* corresponds to ! apex ( our cone4 ,9 l mann] we may project an id5tical spiral 9 space ^u su* surfaces z 7= in/ance7 a portion ( a sph]e or ( an ellipsoid2 & 9 all ^! cases we pres]ve ! spiral configuration1 :i* is ! m cle>ly br\ght into view ! m we r$uce ! v]tical compon5t by :i* x 0 accompani$4 ,! conv]se is1 ( c\rse1 equally true1 & equally obvi\s1 namely t any log>i?mic spiral trac$ ^u a circul> disc or sph]oidal surface w be trans=m$ into a correspond+ spiral helix :5 ! plane or sph]oidal disc is ext5d$ into an elongat$ cone approximat+ to a cyl9d]4 ,?is ma!matical conception is translat$1 9 botany1 into actual fact4 ,! fir-cone may be look$ ^u z a cyl9drical axis contract$ at bo? ends1 until #fci x becomes approximately an ellipsoidal solid ( revolution1 g5]at$ ab\t ! long axis ( ! ellipse2 & ! semi-ellipsoidal capitulum ( ! teasel1 ! m or less hemisph]ical "o ( ! ?i/le1 & ! flatt5$ b /ill convex "o ( ! sunfl[]1 are all beautiful & successive de=mations ( :at is typically a long1 conical1 & all b cyl9drical /em4 ,on ! o!r h&1 e /em z x gr[s out into its long cyl9drical %ape is b a de=mation ( ! little sph]oidal or ellipsoidal surface1 or cone1 :i* 0 its =]unn] 9 ! bud4 ,?is id5tity ( ! helical spirals ar\nd ! /em ) spirals project$ on a plane 0 cle>ly recognis$ by ,h(mei/]1 :o 0 accu/om$ to repres5t 8 diagrams ( leaf-arrangem5t ei!r 9 "o way or ! o!r1 ?\gh n 9 a /rictly geometrical projection#egd4 ,accord+ to ,mr ,a4 ,h4 ,*ur*#ege1 :o has dealt v c>efully & elaborately ) ! :ole "q ( phyllotaxis1 ! log>i?mic spirals su* z we see 9 ! disc ( ! sunfl[] h a f> great] importance & a f> deep] mean+ ?an ?is brief treatm5t ( m9e w\ld accord to !m3 & ,sir ,!odore ,cook1 9 8 book on ! ,curves ( ,life1 has adopt$ & has help$ to exp\nd & popul>ise ,mr ,*ur*'s inve/igations4 ,mr ,*ur*1 reg>d+ ! problem z "o ( 8uni=m gr[?10 easily arrives at ! conclusion t1 if ?is gr[? c be conceiv$ z tak+ place symmetrically ab\t a c5tral po9t or 8pole10 ! uni=m gr[? w\ld !n manife/ itself 9 log>i?mic spirals1 includ+ ( c\rse ! limit+ cases ( ! circle & /raight l9e4 ,) ?is /atem5t ,i h little fault to f9d2 x is 9 ess5ce id5tical ) mu* t ,i h said 9 a previ\s *apt]4 ,b o!r /atem5ts ( ,mr ,*ur*'s1 & _m !ories wov5 ab\t !m by ,sir ,t4 ,cook & himself1 ,i am less able to foll[4 ,mr ,*ur* tells u t ! ess5tial ph5om5on 9 ! sunfl[] disc is a s]ies ( or?ogonally int]sect+ log>i?mic spirals4 ,unless ,i :olly misappreh5d ,mr ,*ur*'s mean+1 ,i %\ld say t ?is is v f> f ess5tial4 ,! spirals #fdj int]sect isogonally1 b or?ogonal int]section w\ld be only "o p>ticul> case1 & 9 all probability a v infrequ5t "o1 9 ! int]section ( log>i?mic spirals develop$ ab\t a common pole4 ,aga9 on ! analogy ( ! hydrodynamic l9es ( =ce 9 c]ta9 vortex movem5ts1 & ( simil> l9es ( =ce 9 c]ta9 magnetic ph5om5a1 ,mr ,*ur* proce$s to argue t ! en]gies ( life foll[ l9es comp>able to ^? ( electric en]gy1 & t ! log>i?mic spirals ( ! sunfl[] are1 s to speak1 l9es ( equipot5tial#egf4 ,& ,sir ,t4 ,cook rem>ks t ?is 8!ory1 if correct1 w\ld be fundam5tal = all =ms ( gr[?1 ?\gh x w\ld be m easily obs]v$ 9 plant con/ruction ?an 9 animals40 ,! p>allel ,i am n able to foll[4 ,mr ,*ur* sees 9 phyllotaxis an organic my/]y1 a some?+ = :i* we are unable to sugge/ any precise cause3 a ph5om5on :i* is to be ref]r$1 someh[1 to waves ( gr[? emanat+ f a c5tre1 b on ! o!r h& n to be expla9$ by ! division ( an apical cell1 or any o!r hi/ological factor4 ,z ,sir ,t4 ,cook puts x1 8at ! gr[+ po9t ( a plant :]e ! new memb]s are be+ =m$1 !re is simply no?+ to see40 ,b x is impossible to deal satisfactorily1 9 brief space1 ei!r ) ,mr ,*ur*'s !ories1 or my own objections to !m#egg4 ,let x suffice to say t ,i1 = my "p1 see no subtle my/]y 9 ! matt]1 o!r ?an :at lies 9 ! /eady production ( simil> gr[+ p>ts1 simil>ly situat$1 at simil> successive int]vals ( "t4 ,if su* be ! case1 !n we are b\nd to h 9 #fda consequ5ce a s]ies ( symmetrical patt]ns1 ^: nature w dep5d ^u ! =m ( ! entire surface4 ,if ! surface be t ( a cyl9d] we %all h a sy/em1 or sy/ems1 ( spiral helices3 if x be a plane1 ) an inf9itely di/ant focus1 su* z we obta9 by 8unwrapp+0 our cyl9drical surface1 we %all h /raight l9es2 if x be a plane conta9+ ! focus )9 itself1 or if x be any o!r symmetrical surface conta9+ ! focus1 !n we %all h a sy/em ( log>i?mic spirals4 ,! appe>ance ( ^! spirals is sometimes spok5 ( z a 8subjective0 ph5om5on1 b ! description is inaccurate3 x is a purely ma!matical ph5om5on1 an insep>able second>y result ( o!r arrangem5ts :i* we1 = ! "t be+1 reg>d z prim>y4 ,:5 ! bricklay] builds a factory *imney1 he lays 8 bricks 9 a c]ta9 /eady1 ord]ly way1 ) no ?\ght ( ! spiral patt]ns to :i* ?is ord]ly sequ5ce inevitably leads1 & :i* spiral patt]ns are by no means 8subjective40 ,! design] ( a wall-pap] n only has no int5tion ( produc+ a patt]n ( criss-cross l9es1 b on ! contr>y he does 8 be/ to avoid !m2 nev]!less1 s long z 8 design is a symmetrical "o1 ! criss-cross int]sections inevitably come4 ,let u1 h[ev]1 leave ?is discussion1 & return to ! facts ( ! case4 ,our second "q1 :i* relates to ! num]ical co9cid5ces s famili> to all /ud5ts ( phyllotaxis1 is n to be set & answ]$ 9 a ^w4 ,let u1 = simplicity's sake1 avoid consid]ation ( simultane\s or :orl$ leaf orig9s1 & consid] only ! m frequ5t cases :]e a s+le 8g5etic spiral0 c be trac$ ?r\gh\t ! entire sy/em4 ,x is seldom t ?is prim>y1 g5etic spiral cat*es ! eye1 = ! leaves :i* imm$iately succe$ "o ano!r 9 ?is g5etic ord] are usually f> ap>t on ! circumf]5ce ( ! /em1 & x is only 9 close-pack$ arrangem5ts t ! eye readily appreh5ds ! cont9u\s s]ies4 ,accord+ly 9 su* a case z a fir-cone1 = in/ance1 x is c]ta9 ( ! second>y spirals or 8p>a/i*ies0 :i* cat* ! eye2 & among fir-cones1 we c easily c\nt ^!1 & we f9d !m to be #fdb on ! :ole v con/ant 9 numb]1 accord+ to ! species4 ,?us 9 _m cones1 su* z ^? ( ! ,norway spruce1 we c trace five r[s ( scales w9d+ /eeply up ! cone 9 "o direction1 & ?ree r[s w9d+ less /eeply ! o!r way2 9 c]ta9 o!r species1 su* z ! common l>*1 ! normal numb] is eight r[s 9 ! "o direction & five 9 ! o!r2 :ile 9 ! ,am]ican l>* we h aga9 ?ree 9 ! "o direction & five 9 ! o!r4 ,x n seldom happ5s t two arrangem5ts grade into "o ano!r on diff]5t p>ts ( "o & ! same cone4 ,among o!r cases 9 :i* su* spiral s]ies are readily visible we h1 = in/ance1 ! cr[d$ leaves ( ! /one-crops & mesembryan!mums1 & 7z we h said7 ! cr[d$ florets ( ! composites4 ,among ^! we may f9d pl5ty ( examples 9 :i* ! numb]s ( ! s]ial r[s are simil> to ^? ( ! fir-cones2 b 9 "s cases1 z 9 ! daisy & o!rs ( ! small] composites1 we %all be able to trace ?irte5 r[s 9 "o direction & tw5ty-"o 9 ! o!r1 or p]haps tw5ty-"o & ?irty-f\r2 :ile 9 a great big sunfl[] we may f9d 79 "o & ! same species7 ?irty-f\r & fifty-five1 fifty-five & eighty-n9e1 or ev5 z _m z eighty-n9e & "o hundr$ & =ty-f\r4 ,on ! o!r h&1 9 an ord9>y 8p5tam]\s0 fl[]1 su* z a ranunculus1 we may be able to trace1 9 ! arrangem5t ( its sepals1 petals & /am5s1 %ort] spiral s]ies1 ?ree 9 "o direction & two 9 ! o!r4 ,x w be at once obs]v$ t ^! arrangem5ts manife/ !mselves 9 connection ) v diff]5t ?+s1 9 ! ord]ly int]spac+ ( s+le leaves & ( entire florets1 & among all k9ds ( leaf-l /ructures1 foliage-leaves1 bracts1 cone-scales1 & ! v>i\s p>ts or memb]s ( ! fl[]4 ,aga9 we mu/ be c>eful to note t1 :ile ! above num]ical *>act]s are by mu* ! mo/ common1 s mu* s z to be deem$ 8normal10 _m o!r comb9ations are kn[n to occur4 ,! arrangem5t1 z we h se51 is apt to v>y :5 ! entire /ructure v>ies greatly 9 size1 z 9 ! disc ( ! sunfl[]4 ,x is also subject to less regul> v>iation )9 "o & ! same species1 z c always be discov]$ :5 we exam9e a suffici5tly l>ge sample ( fir-cones4 ,= in/ance1 out ( #eje #fdc cones ( ! ,norway spruce1 ,beal#egh f\nd #ib p] c5t4 9 :i* ! spirals 7 9 five & eight r[s2 9 #f p] c5t4 ! r[s 7 f\r & sev51 & 9 #d p] c5t4 !y 7 f\r & six4 ,9 ea* case !y 7 ne>ly equally divid$ z reg>ds direction2 = in/ance ( ! #dfg cones %ew+ ! five-eight arrangem5t1 ! five-s]ies ran 9 "r-h&$ spirals 9 #bbd cases1 & 9 left-h&$ spirals 9 #bdc4 ,omitt+ ! 8abnormal0 cases1 su* z we h se5 to occur 9 a small p]c5tage ( our cones ( ! spruce1 ! arrangem5ts :i* we h j m5tion$ may be set =? z foll[s1 7! fractional numb] us$ be+ simply an abbreviat$ symbol = ! numb] ( associat$ helices or p>a/i*ies :i* we c c\nt runn+ 9 ! opposite directions73 #b_/c1 #c_/e1 #e_/h1 #h_/ac1 #ac_/ba1 #ba_/cd1 #cd_/ee1 #ee_/hi1 #hi_/add4 ,n[ ^! numb]s =m a v int]e/+ s]ies1 :i* happ5s to h a numb] ( curi\s ma!matical prop]ties#egi4 ,we see1 = in/ance1 t ! d5om9ator ( ea* fraction is ! num]ator ( ! next2 & fur!r1 t ea* successive num]ator1 or d5om9ator1 is ! sum ( ! prec$+ two4 ,our imm$iate problem1 !n1 is to det]m9e1 if possible1 h[ ^! num]ical co9cid5ces come ab\t1 & :y ^! p>ticul> numb]s %\ld be s commonly met ) #fdd z to be consid]$ 8normal0 & *>act]i/ic features ( ! g5]al ph5om5on ( phyllotaxis4 ,! foll[+ acc\nt is bas$ on a %ort pap] by ,pr(essor ,p4 ,g4 ,tait#ehj4 ,illu/ration3 ,fig4 #cbe4 ,( ! two foll[+ diagrams1 ,fig4 #cbe repres5ts ! g5]al case1 & ,fig4 #cbf a p>ticul> "o1 = ! sake ( possibly great] simplicity4 ,bo? diagrams repres5t a portion ( a bran*1 or fir-cone1 reg>d$ z cyl9drical1 & unwrapp$ to =m a plane surface4 ,a1 a1 at ! two ends ( ! base-l9e1 repres5t ! same initial leaf or scale3 ,o is a leaf :i* c be rea*$ f ,a by m /eps 9 a "r-h& spiral 7develop$ into ! /raight l9e ,,ao71 & by n /eps f a 9 a left-h&$ spiral a,o4 ,n[ x is obvi\s 9 our fir-cone1 t we c include all ! scales ^u ! cone by tak+ s _m spirals 9 ! "o direction1 & aga9 include !m all by s _m 9 ! o!r4 ,accord+ly1 9 our diagrammatic con/ruction1 ! spirals ,,ao & a,o mu/1 & always c1 be s tak5 t m spirals p>allel to a,o1 & n spirals p>allel to ,,ao1 %all sep>ately include all ! leaves ^u ! /em or cone4 ,if m & n h a common factor1 l1 x c easily be %ewn t ! arrangem5t is composite1 & t !re are l fundam5tal1 or g5etic spirals1 & l leaves 7includ+ ,a7 :i* are situat$ exactly on ! l9e ,aa4 ,t is to say1 we h "h a :orl$ arrangem5t1 :i* we h agre$ to leave unconsid]$ 9 fav\r ( ! simpl] case4 ,we re/rict ourselves1 accord+ly1 to ! cases :]e !re is b "o g5etic spiral1 & :5 !re=e m & n are prime to "o ano!r4 ,our fundam5tal1 or g5etic1 spiral1 z we h se51 is t :i* passes f ,a 7or a7 to ! leaf :i* is situat$ ne>e/ to ! base-l9e ,aa4 ,! fundam5tal spiral w ?us be "r-h&$ 7,a1 ,p1 etc47 if ,p1 :i* is ne>] to ,a ?an to a1 be ?is leaf--left-h&$ if x be p4 ,t is to say1 we make x a conv5tion t we %all always1 = our fundam5tal spiral1 run #fde r\nd ! sy/em1 f "o leaf to ! next1 by ! %orte/ way4 ,illu/ration3 ,fig4 #cbf4 ,n[ x is obvi\s1 f ! symmetry ( ! figure 7z fur!r %ewn 9 ,fig4 #cbf71 t1 besides ! spirals runn+ along ,,ao & a,o1 we h a s]ies runn+ f ! /eps on a,o to ! /eps on ,,ao4 ,9 o!r words we c f9d a leaf 7,s7 ^u ,,ao1 :i*1 l ! leaf ,o1 is rea*$ directly by a spiral s]ies f ,a & f a1 su* t a,s includes n /eps1 & ,,z 7be+ "p ( ! old spiral l9e ,,ao7 n[ includes m n /eps4 ,&1 s9ce m & n are prime to "o ano!r 7= o!rwise ! sy/em w\ld h be5 a composite or :orl$ "o71 x is evid5t t we c cont9ue ?is process ( conv]g5ce until we come d[n to a #a1 #a arrangem5t1 t is to say to a leaf :i* is rea*$ by a s+le /ep1 9 opposite directions f ,a & f a1 :i* leaf is !re=e ! fir/ leaf1 next to ,a1 ( ! fundam5tal or g5]at+ spiral4 #fdf ,if our orig9al l9es along ,,ao & a,o conta91 = in/ance1 #ac & #h /eps respectively 7i4e4 m #ac1 n #h71 !n our next s]ies1 obs]vable 9 ! same cone1 w be #h & 7#ac #h7 or #e2 ! next #e & 7#h #e7 or #c2 ! next #c1 #b2 & ! next #b1 #a2 lead+ to ! ultimate condition ( #a1 #a4 ,^! are ! v s]ies :i* we h f\nd to be common1 or normal2 & s f> z our inve/igation has yet gone1 x has prov$ to u t1 if "o ( ^! exi/s1 x entails1 ipso facto1 ! pres5ce ( ! re/4 ,9 foll[+ d[n our s]ies1 accord+ to ! above con/ruction1 we h se5 t at e /ep we h *ang$ direction1 ! long] & ! %ort] sides ( our triangle *ang+ places e "t4 ,let u /op = a mom5t1 :5 we come to ! #a1 #b s]ies1 or ,,at1 a,t ( ,fig4 #cbf4 ,x is obvi\s t !re is no?+ to prev5t u mak+ a new #a1 #c s]ies if we please1 by cont9u+ ! g5]at+ spiral ?r\gh ?ree leaves1 & connect+ ! leaf s rea*$ directly ) our initial "o4 ,b 9 ! case repres5t$ 9 ,fig4 #cbf1 x is obvi\s t ^! two s]ies 7,a1 #a1 #b1 #c1 etc41 & a1 #c1 #f1 etc47 w be runn+ 9 ! same direction2 i4e4 !y w bo? be "r-h&$1 or bo? left-h&$ spirals4 ,! simple mean+ ( ?is is t ! ?ird leaf ( ! g5]at+ spiral 0 di/ant f our initial leaf by m ?an ! circumf]5ce ( ! cyl9drical /em2 9 o!r words1 t !re 7 m ?an two1 b less ?an ?ree leaves 9 a s+le turn ( ! fundam5tal spiral4 ,less ?an two !re c obvi\sly nev] be4 ,:5 !re are exactly two1 we h ! simple/ ( all possible arrangem5ts1 namely t 9 :i* ! leaves are plac$ alt]nately on opposite sides ( ! /em4 ,:5 !re are m ?an two1 b less ?an ?ree1 we h ! elem5t>y condition = ! production ( ! s]ies :i* we h be5 consid]+1 namely #a1 #b2 #b1 #c2 #c1 #e1 etc4 ,to put ! latt] "p ( ?is argum5t 9 m precise language1 let u say t3 ,if1 9 our desc5d+ s]ies1 we come to /eps #a & t1 :]e t is det]m9$ by ! condition t #a & t #a w\ld give spirals bo? "r-h&$1 or bo? left-h&$2 x foll[s t !re are less ?an t #a leaves 9 a s+le turn ( ! fundam5tal spiral4 ,&1 det]m9$ 9 ?is mann]1 x is f\nd 9 ! great majority ( cases1 9 fir-cones & a ho/ ( o!r examples ( phyllotaxis1 t t #b4 ,9 o!r words1 9 ! #fdg great majority ( cases1 we h :at corresponds to an arrangem5t next 9 ord] ( simplicity to ! simple/ case ( all3 next1 t is to say1 to ! arrangem5t :i* consi/s ( opposite & alt]nate leaves4 8,^! simple consid]ations10 z ,tait says1 8expla9 completely ! s-call$ my/]i\s appe>ance ( t]ms ( ! recurr+ s]ies #a1 #b1 #c1 #e1 #h1 #ac1 etc4#eha ,! o!r natural s]ies1 usually b mislead+ly repres5t$ by conv]g5ts to an inf9itely ext5d$ cont9u\s fraction1 are easily expla9$1 z above1 by tak+ t #c1 #d1 #e1 etc41 etc40 ,_m examples ( ^! latt] s]ies h be5 giv5 by ,dickson#ehb & o!r writ]s4 ,we h n[ le>n$1 among o!r elem5t>y facts1 t :]ev] any "o sy/em ( helical spirals is pres5t1 c]ta9 o!rs inv>iably & ( necessity accompany x1 & are def9itely relat$ to x4 ,9 any diagram1 su* z ,fig4 #cbf1 9 :i* we repres5t our leaf-arrangem5t by means ( uni=m & regul>ly int]spac$ dots1 we c draw "o s]ies ( spirals aft] ano!r1 & "o z easily z ano!r4 ,b 9 our fir-cone1 = in/ance1 "o p>ticul> s]ies1 or r two conjugate s]ies1 are always conspicu\s1 :ile ! o!rs are s\ght & f\nd ) comp>ative difficulty4 ,illu/ration3 ,fig4 #cbg4 ,! ph5om5on is illu/rat$ by ,fig4 #cbg1 a-d4 ,! gr\nd-plan ( all ^! diagrams is id5tically ! same4 ,! g5]at+ spiral 9 ea* case repres5ts a div]g5ce ( #c_/h1 or #ace ( azimu?2 & ! po9ts succe$ "o ano!r at ! same successional di/ances p>allel to ! axis4 ,! rectangul> outl9es1 :i* correspond to ! expos$ surface ( ! leaves or cone-scales1 are ( equal area1 & ( equal numb]4 ,nev]!less ! appe>ances pres5t$ by ^! diagrams are v diff]5t2 = 9 "o ! eye cat*es a #e_/h arrangem5t1 9 ano!r a #c_/e2 & s on1 d[n to an arrangem5t ( #a_/a4 ,! ma!matical side ( ?is v curi\s ph5om5on ,i h n attempt$ to inve/igate4 ,b x is q obvi\s t1 9 a sy/em )9 #fdh :i* v>i\s spirals are implicitly conta9$1 ! conspicu\sness ( "o set or ano!r does n dep5d ^u angul> div]g5ce4 ,x dep5ds on ! relative proportions 9 l5g? & bread? ( ! leaves !mselves2 or1 m /rictly speak+1 on ! ratio ( ! diagonals ( ! rhomboidal figure by :i* ea* leaf-area is circumscrib$4 ,:51 z 9 ! fir-cone1 ! scales by mutual compression con=m to ^! rhomboidal outl9es1 _! incl9$ edges at once guide ! eye 9 ! direction ( "s "o p>ticul> spiral2 & we %all n fail to notice t 9 su* cases ! usual #fdi result is to give u arrangem5ts correspond+ to ! middle diagrams 9 ,fig4 #cbg1 :i* are ! configurations 9 :i* ! quadrilat]al outl9es approa* mo/ ne>ly to a rectangul> =m1 & give u accord+ly ! lea/ possible ratio 7"u ! giv5 conditions7 ( sectional b\nd>y-wall to surface area4 ,! mann] 9 :i* "o sy/em ( spirals may be caus$ to slide1 s to speak1 into ano!r1 has be5 +5i\sly demon/rat$ by ,s*w5d5] on a me*anical model1 consi/+ ess5tially ( a framework :i* c be op5$ or clos$ to correspond ) "o aft] ano!r ( ! above s]ies ( diagrams#ehc4 ,! det]m9ation ( ! precise angle ( div]g5ce ( two consecutive leaves ( ! g5]at+ spiral does n ent] into ! above g5]al inve/igation 7?\gh ,tait gives1 9 ! same pap]1 a me?od by :i* x may be easily det]m9$72 & ! v fact t x does n s ent] %ews x to be ess5tially unimportant4 ,! det]m9ation ( s-call$ 8or?o/i*ies10 or precisely v]tical successions ( leaves1 is also unimportant4 ,we h no means1 o!r ?an obs]vation1 ( det]m9+ t "o leaf is v]tically above ano!r1 & spiral s]ies su* z we h be5 deal+ ) w appe>1 :e!r su* or?o/i*ies exi/1 :e!r !y be ne> or remote1 or :e!r ! angle ( div]g5ce be su* t no precise v]tical sup]position ev] occurs4 ,& la/ly1 ! fact t ! successional numb]s1 express$ z fractions1 #a_/b1 #b_/c1 #c_/e1 repres5t a conv]g5t s]ies1 ^: f9al t]m is equal to #jfahjc4441 ! sectio aurea or 8gold5 mean0 ( unity1 is se5 to be a ma!matical co9cid5ce1 devoid ( biological significance2 x is b a p>ticul> case ( ,lagrange's !orem t ! roots ( e num]ical equation ( ! second degree c be express$ by a p]iodic cont9u$ fraction4 ,! same numb] has a multitude ( curi\s ari?metical prop]ties4 ,x is ! f9al t]m ( all simil> s]ies to t ) :i* we h be5 deal+1 su* = in/ance z #a_/c1 #c_/d1 #d_/g1 etc41 or #a_/d1 #d_/e1 #e_/i1 etc4 ,x is a numb] belov$ ( ! circle-squ>]1 & ( all ^? :o seek to f9d1 & !n to p5etrate1 ! secrets ( ! ,great ,pyramid4 ,x is deep-set 9 ,py?agorean z well z 9 ,euclidean geometry4 ,x ent]s 7z ! *ord ( an angle ( #cf71 #fej into ! ?rice-isosceles triangle ( :i* we h spok5 on p4 #eaa2 x is a numb] :i* becomes 7by ! addition ( unity7 its own reciprocal2 its prop]ties nev] end4 ,to ,kepl] 7z ,nab] tells u7 x 0 a symbol ( ,creation1 or ,g5]ation4 ,its rec5t application to biology & art-criticism by ,sir ,!odore ,cook & o!rs is n new4 ,nab]'s book1 already quot$1 is full ( x4 ,zeis+1 9 #ahed1 f\nd 9 x ! key to all morphology1 & ! same writ]1 lat] on#ehd1 decl>$ x to dom9ate bo? ar*itecture & music4 ,b inde$1 to use ,sir ,?omas ,br[ne's words 7?\gh x 0 ( ano!r numb] t he spoke73 8,to enl>ge ?is contemplation into all ! my/]ies & secrets accommodable unto ?is numb]1 7 inexcusable ,py?agorisme40 ,if ?is numb] has any s]i\s claim at all to ent] into ! biological "q ( phyllotaxis1 ?is mu/ dep5d on ! fact1 fir/ emphasiz$ by ,*auncey ,wright#ehe1 t1 if ! successive leaves ( ! fundam5tal spiral be plac$ at ! p>ticul> azimu? :i* divides ! circle 9 ?is 8sectio aurea10 !n no two leaves w ev] be sup]pos$2 & ?us we are said to h 8! mo/ ?or\gh & rapid di/ribution ( ! leaves r\nd ! /em1 ea* new or high] leaf fall+ ov] ! angul> space betwe5 ! two old] ones :i* are ne>e/ 9 direction1 s z to divide x 9 ! same ratio 7,k71 9 :i* ! fir/ two or any two successive ones divide ! circumf]5ce4 ,n[ #e_/h & all successive fractions diff] inappreciably f ,k40 ,to ?is view !re are _m simple objections4 ,9 ! fir/ place1 ev5 #e_/h1 or #fbe1 is b a mod]ately close approximation to ! 8gold5 mean02 9 ! second place ! arrangem5ts by :i* a bett] approximation is got1 su* z #h_/ac1 #ac_/ba1 & ! v close approximations su* z #cd_/ee1 #ee_/hi1 #hi_/add1 etc41 are comp>atively r>e1 :ile ! mu* less close approximations ( #c_/e or #b_/c1 or ev5 #a_/b1 are extremely common4 ,aga91 ! g5]al type ( argum5t su* z t :i* ass]ts t ! plant is 8aim+ at0 some?+ :i* we may call an 8ideal angle0 is "o t _c comm5d itself to a pla9 /ud5t ( physical sci5ce3 nor is ! hypo!sis r5d]$ m acceptably :5 ,sir ,t4 ,cook qualifies x by tell+ u t 8all t a plant c d #fea is to v>y1 to make bl9d %ots at con/ructions1 or to #8mutate' z x is n[ t]m$2 & ! mo/ suitable ( ^! con/ructions w 9 ! long run be isolat$ by ! action ( ,natural ,selection40 ,f9ally1 & ?is is ! mo/ concrete objection ( all1 ! suppos$ isolation ( ! leaves1 or _! mo/ complete 8di/ribution to ! action ( ! surr\nd+ atmosph]e0 is manife/ly v little affect$ by any conditions :i* are conf9$ to ! angle ( azimu?4 ,if we c\ld imag9e a case 9 :i* all ! leaves ( ! /em1 or all ! scales ( a fir-cone1 7 cru%$ d[n to "o & ! same level1 into a simple r+ or :orl ( leaves1 !n inde$ !y w\ld h _! mo/ equable di/ribution "u ! condition ( ! 8ideal angle10 t is to say ( ! 8gold5 mean40 ,b if x be 7s to speak7 ,nature's object to set !m fur!r ap>t ?an !y actually are1 to give !m fre] exposure to ! air ?an !y actually h1 !n x is surely manife/ t ! simple way to d s is to elongate ! axis1 & to set ! leaves fur!r ap>t1 l5g?ways on ! /em4 ,?is has at once a f> m pot5t effect ?an any nice manipulation ( ! 8angle ( div]g5ce40 ,= x is obvi\s t 9 ,f7 s9 7 we h a great] range ( v>iation by alt]+ ?an by alt]+ 4 ,we come !n1 )\t m ado1 to ! conclusion t ! 8,fibonacci s]ies10 & its suppos$ usefulness1 & ! hypo!sis ( its introduction into plant-/ructure ?r\gh natural selection1 are all matt]s :i* des]ve no place 9 ! pla9 /udy ( botanical ph5om5a4 ,z ,sa*s %rewdly recognis$ ye>s ago1 all su* speculations z ^! h>k back to a s*ool ( my/ical idealism4 #feb ,,*apt] ,,xv ,,on ,,! ,,%apes ,,( ,,eggs1 ,,& ,,( ,,c]ta9 ,,o!r ,,holl[ ,,/ructures ,! eggs ( birds & all o!r h>d-%ell$ eggs1 su* z ^? ( ! tortoise & ! crocodile1 are simple solids ( revolution2 b !y diff] greatly 9 =m1 accord+ to ! configuration ( ! plane curve by ! revolution ( :i* ! egg is1 9 a ma!matical s5se1 g5]at$4 ,"s few eggs1 su* z ^? ( ! owl1 ! p5gu91 or ! tortoise1 are sph]ical or v ne>ly s2 a few m1 su* z ! grebe's1 ! cormorant's or ! pelican's1 are approximately ellipsoidal1 ) symmetrical or ne>ly symmetrical ends1 & some:at simil> are ! s-call$ 8cyl9drical0 eggs ( ! megapodes & ! s&-gr\se2 ! great majority1 l ! h5's egg1 are ovoid1 a little blunt] at "o end ?an ! o!r2 & "s1 by an exagg]ation ( ?is lack ( ant]o-po/]ior symmetry1 are blunt at "o end b *>act]i/ically po9t$ at ! o!r1 z is ! case ) ! eggs ( ! guillemot & puff91 ! s&pip]1 plov] & curlew4 ,x is an obvi\s b by no means negligible fact t ! egg1 :ile (t5 po9t$1 is nev] flatt5$ or discoidal2 x is a prolate1 b nev] an oblate1 sph]oid4 ,! c>eful /udy & collection ( birds' eggs w\ld seem to h begun ) ! ,c\nt de ,m>sigli#ehf1 ! same celebrat$ naturali/ :o fir/ /udi$ ! 8fl[]s0 ( ! coral1 & :o wrote ! ,hi/oire physique de la m]2 & ! specific =m1 z well z ! col\r & o!r attributes ( ! egg h be5 aga9 & aga9 discuss$1 & n lea/ by ! _m dilettanti naturali/s ( ! eighte5? c5tury :o soon foll[$ 9 ,m>sigli's foot/eps#ehg4 #fec ,we ne$ d no m ?an m5tion ,ari/otle's belief1 d\btless old 9 8 "t1 t ! m po9t$ egg produces ! male *ick51 & ! blunt] egg ! h52 ?\gh ?is !ory surviv$ into mod]n times#ehh & p]haps /ill l+]s on4 ,sev]al naturali/s1 su* z ,gn!r 7#aggb7 & ,bhle 7#ahah71 h tak5 ! tr\ble to disprove x by exp]im5t4 ,a m mod]n & m g5]ally accept$ explanation has be5 t ! =m ( ! egg is 9 direct relation to t ( ! bird :i* has to be hat*$ )9--a view t w\ld seem to h be5 fir/ set =? by ,naumann & ,bhle1 9 _! great treatise on eggs#ehi1 & adopt$ by ,des ,murs#eij & _m o!r well-kn[n writ]s4 ,9 a treatise by de ,lafresnaye#eia1 an elaborate comp>ison is made betwe5 ! skeleton & ! egg ( ! v>i\s birds1 to %ew1 = in/ance1 h[ ^? birds ) a deep-keel$ /]num laid r\nd$ eggs1 :i* alone c\ld accommodate ! =m ( ! "y4 ,accord+ to ?is view1 t 8,nature _h =ese5#eib0 ! =m adapt$ to & necess>y = ! gr[+ embryo1 x 0 easy to correlate ! owl ) its sph]ical egg1 ! div] ) its elliptical "o1 & 9 l mann] ! r\nd egg ( ! tortoise & ! elongat$ "o ( ! crocodile ) ! %ape ( ! creatures :i* _h aft]w>ds to be hat*$ !re94 ,a few writ]s1 su* z ,?i5emann#eic1 look$ at ! same facts ! o!r way1 & ass]t$ t ! =m ( ! egg 0 det]m9$ by t ( ! bird by :i* x 0 laid1 & 9 ^: body x _h be5 con=m$4 ,9 m rec5t times1 o!r !ories1 bas$ ^u ! pr9ciples ( ,natural ,selection1 h be5 curr5t & v g5]ally accept$1 to acc\nt = ^! div]sities ( =m4 ,! po9t$1 conical egg ( ! guillemot is g5]ally suppos$ to be an adaptation1 #fed advantage\s to ! species 9 ! circum/ances "u :i* ! egg is laid2 ! po9t$ egg is less apt ?an a sph]ical "o to roll (f ! n>r[ l$ge ( rock on :i* ?is bird is said to lay its solit>y egg1 & ! m po9t$ ! egg1 s mu* ! fitt] & likeli] is x to survive4 ,! fact t ! plov] or ! s&pip]1 bre$+ 9 v diff]5t situations1 lay eggs t are also conical1 elicits ano!r explanation1 to ! effect t "h ! conical =m p]mits ! _m l>ge eggs to be pack$ closely "u ! "m bird#eid4 ,:atev] tru? !re be 9 ^! app>5t adaptations to exi/+ circum/ances1 x is only by a v ha/y logic t we c accept !m z a v]a causa1 or adequate explanation ( ! facts2 & x is obvi\s t1 9 ! bird's egg1 we h an admirable case = ! direct inve/igation ( ! me*anical or physical significance ( its =m#eie4 ,( all ! _m naturali/s ( ! eighte5? & n9ete5? c5turies :o wrote on ! subject ( eggs1 "o alone 7s f> z ,i am aw>e7 ascrib$ ! =m ( ! egg to direct me*anical causes4 ,gn!r#eif1 9 #aggb1 decl>$ t ! m or less r\nd$ or po9t$ =m ( ! egg is a me*anical consequ5ce ( ! pressure ( ! oviduct at a "t :5 ! %ell is yet un=m$ or unsolidifi$2 & t accord+ly1 to expla9 ! r\nd egg ( ! owl or ! k+fi%]1 we h only to admit t ! oviduct ( ^! birds is some:at l>g] ?an t ( mo/ o!rs1 or less subject to viol5t contractions4 ,?is /atem5t conta9s1 9 ess5ce1 ! :ole /ory ( ! me*anical con=mation ( ! egg4 ,let u consid]1 v briefly1 ! conditions to :i* ! egg is subject 9 its passage d[n ! oviduct#eig4 7#a7 ,! 8egg10 z x ent]s ! oviduct1 consi/s ( ! yolk only1 enclos$ 9 its vitell9e membrane4 ,z x passes d[n ! fir/ portion ( ! oviduct1 ! :ite is gradually sup]add$1 #fee & becomes 9 turn surr\nd$ by ! 8%ell-membrane40 ,ab\t ?is latt] ! %ell is secret$1 rapidly & at a late p]iod2 ! egg hav+ mean:ile pass$ on into a wid] portion ( ! oviducal tube1 call$ 7by loose analogy1 z ,ow5 says7 ! 8ut]us40 ,"h ! egg assumes its p]man5t =m1 "h x becomes rigid1 & x is to ?is portion ( ! 8oviduct0 t our argum5t pr9cipally ref]s4 7#b7 ,bo? ! yolk & ! entire egg t5d to fill completely _! respective membranes1 &1 :e!r ?is be due to gr[? or imbibition on ! "p ( ! cont5ts or to contraction on ! "p ( ! surr\nd+ membranes1 ! result+ t5d5cy is = bo? yolk & egg to be1 9 ! fir/ in/ance1 sph]ical1 unless o!rwise di/ort$ by ext]nal pressure4 7#c7 ,! egg is subject to pressure )9 ! oviduct1 :i* is an ela/ic1 muscul> tube1 along ! walls ( :i* pass p]i/altic waves ( contraction4 ,^! muscul> contractions may be describ$ z ! contraction ( successive annuli ( muscle1 giv+ annul> 7or radial7 pressure to successive portions ( ! egg2 !y drive ! egg =w>d aga9/ ! frictional resi/ance ( ! tube1 :ile t5d+ at ! same "t to di/ort its =m4 ,:ile no?+ is kn[n1 s f> z ,i am aw>e1 ( ! muscul> physiology ( ! oviduct1 x is well kn[n 9 ! case ( ! inte/9e t ! pres5ce ( an ob/ruction leads to ! developm5t ( viol5t contractions 9 its re>1 :i* waves ( contraction die away1 & are sc>cely if at all propagat$ 9 advance ( ! ob/ruction4 7#d7 ,x is kn[n by obs]vation t a h5's egg is always laid blunt end =emo/4 7#e7 ,x c be %[n1 at lea/ z a v common rule1 t ^? eggs :i* are mo/ unsymmetrical1 or mo/ tap]$ (f po/]iorly1 are also eggs ( a l>ge size relatively to ! p>5t bird4 ,! guillemot is a notable case 9 po9t1 & s also are ! curlews1 s&pip]s1 phal]opes & t]ns4 ,we may accord+ly presume t ! m po9t$ eggs are ^? t are l>ge relatively to ! tube or oviduct ?r\gh :i* !y h to pass1 or1 9 o!r words1 are ^? :i* are subject to ! greate/ pressure :ile be+ =c$ along4 ,s g5]al is ?is relation t we may g /ill fur!r1 & presume ) great plausibility #fef 9 ! few exceptional cases 7( :i* ! apt]yx is ! mo/ conspicu\s7 :]e ! egg is relatively l>ge ?\gh n m>k$ly unsymmetrical1 t 9 ^! cases ! oviduct itself is 9 all probability l>ge 7z ,gn!r _h sugge/$7 9 proportion to ! size ( ! bird4 ,9 ! case ( ! common f[l we c trace a direct relation betwe5 ! size & %ape ( ! egg1 = ! fir/ eggs laid by a "y pullet are usually small]1 & at ! same "t are mu* m ne>ly sph]ical ?an ! lat] ones2 &1 moreov]1 "s bre$s ( f[ls lay proportionately small] eggs ?an o!rs1 & on ! :ole ! =m] eggs t5d to be r\nd] ?an ! latt]#eih4 ,we may n[ proce$ to inquire m p>ticul>ly h[ ! =m ( ! egg is controll$ by ! pressures to :i* x is subject$4 ,! egg1 j prior to ! =mation ( ! %ell1 is1 z we h se51 a fluid body1 t5d+ to a sph]ical %ape & enclos$ )9 a membrane4 ,our problem1 !n1 is3 ,giv5 a practically incompressible fluid1 conta9$ 9 a de=mable capsule1 :i* is ei!r 7a7 entirely inext5sible1 or 7b7 slightly ext5sible1 & :i* is plac$ 9 a long ela/ic tube ! walls ( :i* are radially contractile1 to det]m9e ! %ape "u pressure4 ,if ! capsule be sph]ical1 inext5sible1 & completely fill$ ) ! fluid1 absolutely no de=mation c take place4 ,! few eggs t are actually or approximately sph]ical1 su* z ^? ( ! tortoise or ! owl1 may ?us be alt]natively expla9$ z cases :]e little or no de=m+ pressure has be5 appli$ prior to ! solidification ( ! %ell1 or else z cases :]e ! capsule 0 s little capable ( ext5sion & s completely fill$ z to preclude ! possibility ( de=mation4 ,if ! capsule be n sph]ical1 b be inext5sible1 !n de=mation c take place "u ! ext]nal radial compression1 #feg only provid$ t ! pressure t5ds to make ! %ape m ne>ly sph]ical1 & !n only on ! fur!r supposition t ! capsule is also n entirely fill$ z ! de=mation proce$s4 ,9 o!r words1 an incompressible fluid conta9$ 9 an inext5sible envelope _c be de=m$ )\t puck]+ ( ! envelope tak+ place4 ,let u next assume1 z ! conditions by :i* ?is result may be avoid$1 7a7 t ! envelope is to "s ext5t ext5sible1 or 7b7 t ! :ole /ructure gr[s "u relatively fix$ conditions4 ,! two suppositions are practically id5tical ) "o ano!r 9 effect4 ,x is obvi\s t1 on ! presumption t ! envelope is only mod]ately ext5sible1 ! :ole /ructure c only be di/ort$ to a mod]ate degree away f ! sph]ical or sph]oidal =m4 ,at all po9ts ! %ape is det]m9$ by ! law ( ! di/ribution ( radial pressure )9 ! giv5 region ( ! tube1 surface friction help+ to ma9ta9 ! egg 9 position4 ,if ! egg be "u pressure f ! oviduct1 b )\t any m>k$ compon5t ei!r 9 a =w>d or backw>d direction1 ! egg w be compress$ 9 ! middle1 & w t5d m or less to ! =m ( a cyl9d] ) sph]ical ends4 ,! eggs ( ! grebe1 cormorant1 or crocodile may be suppos$ to receive _! %ape 9 su* circum/ances4 ,:5 ! egg is subject to ! p]i/altic contraction ( ! oviduct dur+ its =mation1 !n f ! nature & direction ( motion ( ! p]i/altic wave ! pressure w be greate/ some:]e beh9d ! middle ( ! egg2 9 o!r words1 ! tube is conv]t$ = ! "t be+ into a m conical =m1 & ! simple result foll[s t ! ant]ior end ( ! egg becomes ! broad] & ! po/]ior end ! n>r[]4 ,) a giv5 %ape & size ( body1 equilibrium 9 ! tube may be ma9ta9$ "u great] radial pressure t[>ds "o end ?an t[>ds ! o!r4 ,= example1 a cyl9d] hav+ conical ends1 ( semi-angles & respectively1 rema9s 9 equilibrium1 ap>t f friction1 if p cos#b p cos#b 1 s t at ! m tap]$ end :]e is small p is small4 ,!re=e ! :ole /ructure might assume su* a configuration1 or gr[ "u su* conditions1 f9ally becom+ rigid by solidification ( ! envelope4 #feh ,accord+ to ! prec$+ p>agraph1 we mu/ assume "s initial di/ribution ( pressure1 "s squeeze appli$ to ! po/]ior "p ( ! egg1 9 ord] to give x its tap]+ =m4 ,b1 t =m once acquir$1 ! egg may rema9 9 equilibrium bo? z reg>ds =m & position )9 ! tube1 ev5 aft] t excess ( pressure on ! po/]ior "p is reliev$4 ,moreov]1 ! above equation %ews t a normal pressure no great] & 7)9 c]ta9 limits7 actually less act+ ^u ! po/]ior "p ?an on ! ant]ior "p ( ! egg aft] ! %ell is =m$ w be suffici5t to communicate to x a =w>d motion4 ,?is is an important consid]ation1 = x %ews t ! ord9>y =m ( an egg1 & ev5 ! conical =m ( an extreme case su* z ! guillemot's1 is directly fav\rable to ! movem5t ( ! egg )9 ! oviduct1 blunt end =emo/4 ,! ma!matical /atem5t ( ! :ole case is z foll[s3 ,9 our egg1 consi/+ ( an ext5sible membrane fill$ ) an incompressible fluid & "u ext]nal pressure1 ! equation ( ! envelope is pn ,t7#a_/r #a_/r7 ,p1 :]e pn is ! normal compon5t ( ext]nal pressure at a po9t :]e r & r are ! radii ( curvature1 ,t is ! t5sion ( ! envelope1 & ,p ! int]nal fluid pressure4 ,?is is simply ! equation ( an ela/ic surface :]e ,t repres5ts ! coeffici5t ( ela/icity2 9 o!r words1 a flexible ela/ic %ell has ! same ma!matical prop]ties z our fluid1 membrane-cov]$ egg4 ,& ?is is ! id5tical equation :i* we h already _h s frequ5t occasion to employ 9 our discussion ( ! =ms ( cells2 save only t 9 ^! latt] we _h *iefly to /udy ! t5sion ,t 7i4e4 ! surface-t5sion ( ! semi-fluid cell7 & _h little or no?+ to d ) ! factor ( ext]nal pressure 7pn71 :i* 9 ! case ( ! egg becomes ( *ief importance4 ,! above equation is ! equation ( equilibrium1 s t x mu/ be assum$ ei!r t ! :ole body is at re/ or t its motion :ile "u pressure is n su* z to affect ! result4 ,tang5tial =ces1 :i* h be5 neglect$1 c\ld modify ! =m by alt]ation ( ,t4 ,9 our case we mu/1 & may v reasonably1 assume t any movem5t ( ! egg d[n ! oviduct dur+ ! p]iod :5 its =m is be+ impress$ ^u x is v sl[1 be+ possibly balanc$ by ! advance ( ! #fei p]i/altic wave :i* causes ! movem5t1 z well z by friction4 ,! quantity ,t is ! t5sion ( ! enclos+ capsule--! surr\nd+ membrane4 ,if ,t be con/ant or symmetrical ab\t ! axis ( ! body1 ! body is symmetrical4 ,b ! abnormal eggs t a h5 sometimes lays1 cyl9drical1 annulat$1 or q irregul>1 are due to local weak5+ ( ! membrane1 9 o!r words1 to asymmetry ( ,t4 ,n only asymmetry ( ,t1 b also asymmetry ( pn1 w r5d] ! body subject to de=mation1 & ?is factor1 ! unkn[n b regul>ly v>y+1 l>gely radial1 pressure appli$ by successive annuli ( ! oviduct1 is ! ess5tial cause ( ! =m1 & v>iations ( =m1 ( ! egg4 ,9 fact1 9 s f> z ! po/ulates correspond ne> en\gh to actualities1 ! above equation is ! equation ( all eggs 9 ! univ]se4 ,at lea/ ?is is s if we g5]alise x 9 ! =m pn ,t_/r ,t_/r ,p 9 recognition ( a possible diff]5ce betwe5 ! pr9cipal t5sions4 ,9 ! case ( ! sph]ical egg x is obvi\s t pn is ev]y:]e equal4 ,! simple/ case is :]e pn #j1 9 o!r words1 :]e ! egg is s small z practically to escape de=m+ pressure f ! tube4 ,b we may also conceive ! tube to be s ?9-wall$ & ext5sible z to press ) practically equal =ce ^u all p>ts ( ! conta9$ sph]e4 ,if :ile our egg be 9 process ( con=mation ! envelope be free at any "p f ext]nal pressure 7t is to say1 if pn #j71 !n x is obvi\s t t "p 7if ( circul> section7 w be a portion ( a sph]e4 ,?is is n unlikely to be ! case actually or approximately at "o or bo? poles ( ! egg1 & is evid5tly ! case ov] a consid]able portion ( ! ant]ior end ( ! plov]'s egg4 ,9 ! case ( ! conical egg ) sph]ical ends1 z is m or less ! case 9 ! plov]'s & ! guillemot's1 !n at ei!r end ( ! egg r & r are id5tical1 & !y are great] at ! blunt ant]ior end ?an at ! o!r4 ,if we may assume t pn vani%es at ! poles ( ! egg1 !n x is pla9 t ,t v>ies 9 ! neighb\rhood ( ^! poles1 &1 fur!r1 t ! t5sion ,t is greate/ at & ne> ! small end ( ! egg4 ,x is "h1 9 %ort1 t ! egg is mo/ likely to be irregul>ly di/ort$ or #ffj ev5 to bur/1 & x is "h t we mo/ commonly f9d irregul>ities ( %ape 9 abnormal eggs4 ,if "o portion ( ! envelope 7 to become practically /iff be=e p ceases to v>y1 t w\ld be tantam\nt to a sudd5 v>iation ( ,t1 & w\ld introduce asymmetry by ! imposition ( a b\nd>y condition 9 addition to ! above equation4 ,)9 ! egg lies ! yolk1 & ! yolk is inv>iably sph]ical or v ne>ly s1 :atev] be ! =m ( ! entire egg4 ,! reason is simple1 & lies 9 ! fact t ! yolk is itself enclos$ 9 ano!r membrane1 betwe5 :i* & ! out] membrane lies a fluid ! pres5ce ( :i* makes pn = ! inn] membrane practically con/ant4 ,! smallness ( friction is indicat$ by ! well-kn[n fact t ! 8g]m9al spot0 on ! surface ( ! yolk is always f\nd upp]mo/1 h[ev] we may place & :]ev] we may op5 ! egg2 t is to say1 ! yolk easily rotates )9 ! egg1 br++ its light] pole upp]mo/4 ,s1 ow+ to ?is lack ( friction 9 ! out] fluid1 or :ite1 :atev] %e> is produc$ )9 ! egg w n be easily transmitt$ to ! yolk1 &1 moreov]1 ow+ to ! same fluidity1 ! yolk w easily recov] its normal sph]icity aft] ! egg-%ell is =m$ & ! unequal pressure reliev$4 ,^!1 !n1 are ! g5]al pr9ciples involv$ 91 & illu/rat$ by1 ! configuration ( an egg2 & !y take u z f> z we c safely g )\t actual quantitative det]m9ations1 9 ea* p>ticul> case1 ( ! =ces conc]n$4 ,9 c]ta9 cases among ! inv]tebrates1 we aga9 f9d in/ances ( h>d-%ell$ eggs :i* h obvi\sly be5 m\ld$ by ! oviduct1 or s-call$ 8ootype10 9 :i* !y h la93 & n m]ely 9 su* a way z to %ew ! effects ( p]i/altic pressure ^u a uni=m ela/ic envelope1 b s z to impress ^u ! egg ! m or less irregul> =m ( ! cavity1 )9 :i* x _h be5 = a "t conta9$ & compress$4 ,aft] ?is fa%ion ,dr ,looss#eii ( ,cairo has #ffa expla9$ ! curi\s =m ( ! egg 9 ,bilh>zia 7,s*i/osoma7 haematobium1 a =midable p>asitic worm to :i* is due a disease wide-spread 9 ,africa & ,arabia1 & an especial sc\rge ( ! ,mecca pilgrims4 ,! egg 9 ?is worm is provid$ at "o end ) a little sp9e1 :i* n[ & !n is f\nd to be plac$ n t]m9ally b lat]ally or v5trally1 & :i* :5 s plac$ has be5 look$ ^u z ! m>k ( a suppos$ new species1 ,s4 ,mansoni4 ,z ,looss has n[ %ewn1 ! little sp9e mu/ be expla9$ z hav+ be5 m\ld$ )9 a little funnel-%ap$ expansion ( ! ut]us1 j :]e x communicates ) ! common duct lead+ f ! ov>y & yolk-gl&2 by ! accumulation ( eggs 9 ! ootype1 ! "o la/ =m$ is cr[d$ into a sideways position1 & !n1 :]e ! side-wall ( ! egg bulges 9 ! funnel-%ap$ orifice ( ! duct1 a little lat]al 8sp9e0 is =m$4 ,9 ano!r species1 ,s4 japonicum1 ! egg is describ$ z bulg+ into a s-call$ 8calotte10 or bubble-l convexity at ! end opposite to ! sp9e4 ,?is1 ,i ?9k1 may1 ) v little d\bt1 be ascrib$ to h>d5+ ( ! egg-%ell hav+ tak5 place j at ! p]iod :5 p>tial relief f pressure 0 be+ exp]i5c$ by ! egg 9 ! neighb\rhood ( ! dilat$ orifice ( ! oviduct4 ,?is case ( ,bilh>zia is n1 f our pres5t po9t ( view1 a v important "o1 b nev]!less x is int]e/+4 ,x ascribes to a me*anical cause a curi\s peculi>ity ( =m2 x %ews1 by ref]5ce to ?is me*anical pr9ciple1 t two conditions :i* 7 v diff]5t to ! sy/ematic naturali/'s eye1 7 really only two simple me*anical modifications ( ! same ?+2 & x de/roys ! *ief evid5ce = ! exi/5ce ( a suppos$ new species ( worm1 a cont9u$ belief 9 :i*1 among worms ( su* great pa?og5ic importance1 might lead to gravely errone\s pa?ological d$uctions4 ,on ! ,=m ( ,sea-ur*9s ,z a coroll>y to ! problem ( ! bird's egg1 we may consid] = a mom5t ! =ms assum$ by ! %ells ( ! sea-ur*9s4 ,^! latt] are commonly divid$ into two classes1 ! ,regul> & ! ,irregul> ,e*9ids4 ,! regul> sea-ur*9s1 save 9 #ffb slight details :i* d n affect our problem1 h a complete radial symmetry4 ,! axis ( ! animal's body is v]tical1 ) m\? bel[ & ! inte/9al outlet above2 & ar\nd ?is axis ! %ell is built z a symmetrical sy/em4 ,x foll[s t 9 horizontal section ! %ell is ev]y:]e circul>1 & we %all h only to consid] its =m z se5 9 v]tical section or projection4 ,! irregul> ur*9s 7v inaccurately s-call$7 h ! anal extremity ( ! body remov$ f its c5tral1 dorsal situation2 & x foll[s t !y h n[ a s+le plane ( symmetry1 ab\t :i* ! organism1 %ell & all1 is bilat]ally symmetrical4 ,we ne$ n conc]n ourselves 9 detail ) ! %apes ( _! %ells1 :i* may be v simply int]pret$1 by ! help ( radial co-ord9ates1 z de=mations ( ! circul> or 8regul>0 type4 ,! sea-ur*9 %ell consi/s ( a membrane1 /iff5$ into rigidity by calc>e\s deposits1 :i* con/itute a beautiful skeleton ( sep>ate1 neatly fitt+ 8ossicles40 ,! rigidity ( ! %ell is m app>5t ?an real1 = ! entire /ructure is1 9 a sluggi% way1 pla/ic2 inasmu* z ea* little ossicle is capable ( gr[?1 & ! entire %ell gr[s by increm5ts to ea* & all ( ^! multitud9\s elem5ts1 ^: individual gr[? involves a c]ta9 am\nt ( fre$om to move relatively to "o ano!r2 9 a few cases ! ossicles are s little develop$ t ! :ole %ell appe>s s(t & flexible4 ,! visc]a ( ! animal occupy b a small "p ( ! space )9 ! %ell1 ! cavity be+ ma9ly fill$ by a l>ge quantity ( wat]y fluid1 ^: d5sity mu/ be v ne> to t ( ! ext]nal sea-wat]4 ,ap>t f ! fact t ! sea-ur*9 cont9ues to gr[1 x is pla9 t we h "h ! same g5]al conditions z 9 ! egg-%ell1 & t ! =m ( ! sea-ur*9 is subject to a simil> equilibrium ( =ces4 ,b !re is ?is important diff]5ce1 t an ext]nal muscul> pressure 7su* z ! oviduct adm9i/]s dur+ ! consolidation ( egg-%ell71 is n[ lack+4 ,9 its place we h ! /eady cont9u\s influ5ce ( gravity1 & !re is yet ano!r =ce :i* 9 all probability we require to take into consid]ation4 ,:ile ! sea-ur*9 is alive1 an imm5se numb] ( delicate 8tube-feet10 ) suck]s at _! tips1 pass ?r\gh m9ute pores #ffc 9 ! %ell1 &1 l s _m long cables1 moor ! animal to ! gr\nd4 ,!y con/itute a symmetrical sy/em ( =ces1 ) "o resultant d[nw>ds1 9 ! direction ( gravity1 & ano!r outw>ds 9 a radial direction2 & if we look ^u ! %ell z orig9ally sph]ical1 bo? w t5d to depress ! sph]e into a flatt5$ cake4 ,we ne$ n consid] ! radial compon5t1 b may treat ! case z t ( a sph]ical %ell symmetrically depress$ "u ! influ5ce ( gravity4 ,?is is precisely ! condition :i* we h to deal ) 9 a drop ( liquid ly+ on a plate2 ! =m ( :i* is det]m9$ by its own uni=m surface-t5sion1 plus gravity1 act+ aga9/ ! uni=m int]nal hydro/atic pressure4 ,simple z ?is sy/em is1 ! full ma!matical inve/igation ( ! =m ( a drop is n easy1 & we c sc>cely hope t ! sy/ematic /udy ( ! ,e*9od]mata w ev] be conduct$ by me?ods bas$ on ,laplace's diff]5tial equation#fjj2 b we h no difficulty 9 see+ t ! v>i\s =ms repres5t$ 9 a s]ies ( sea-ur*9 %ells are no o!r ?an ^? :i* we may easily & p]fectly imitate 9 drops4 ,9 ! case ( ! drop ( wat] 7or ( any o!r p>ticul> liquid7 ! specific surface-t5sion is always con/ant1 & ! pressure v>ies inv]sely z ! radius ( curvature2 !re=e ! small] ! drop ! m ne>ly is x able to cons]ve ! sph]ical =m1 & ! l>g] ! drop ! m does x become flatt5$ "u gravity4 ,we c repres5t ! ph5om5on by us+ india-rubb] balls fill$ ) wat]1 ( diff]5t sizes2 ! little ones w rema9 v ne>ly sph]ical1 b ! l>g] w fall d[n 8( _! own weight10 into ! =m ( m & m flatt5$ cakes2 & we see ! same ?+ :5 we let drops ( heavy oil 7su* z ! or?otoluid5e spok5 ( on p4 #bai71 fall ?r\gh a tall column ( wat]1 ! little ones rema9+ r\nd1 & ! big ones gett+ m & m flatt5$ z !y s9k4 ,9 ! case ( ! sea-ur*91 ! same s]ies ( =ms may be assum$ to occur1 irrespective ( size1 ?r\gh v>iations 9 ,t1 ! specific t5sion1 or 8/r5g?10 ( ! envelop+ %ell4 ,accord+ly we may /udy1 entirely f ?is po9t ( view1 su* a s]ies z ! foll[+ 7,fig4 #cbh74 ,9 a v few cases1 su* z ! fossil ,palaee*9us1 we h an approximately sph]ical #ffd %ell1 t is to say a %ell s /rong t ! influ5ce ( gravity becomes negligible z a cause ( de=mation4 ,! ord9>y species ( ,e*9us beg9 to display a pron\nc$ depression1 & ?is rea*es its maximum 9 su* s(t-%ell$ flexible =ms z ,phormosoma4 ,on ! g5]al "q ,i took ! opportunity ( consult+ ,mr ,c4 ,r4 ,d>l+1 :o is an ackn[l$g$ exp]t 9 drops1 & he at once agre$ ) me t su* =ms z are repres5t$ 9 ,fig4 #cbh are no o!r ?an diagrammatic illu/rations ,illu/ration3 ,fig4 #cbh4 ,diagrammatic v]tical outl9es ( v>i\s ,sea-ur*9s3 ,a1 ,palaee*9us2 ,b1 ,e*9us acutus2 ,c1 ,cid>is2 ,d1 ,d ,coelopleurus2 ,e1 ,e ,g5icopatagus2 ,f1 ,phormosoma lucul5t]2 ,g1 ,p4 t5uis2 ,h1 ,a/h5osoma2 ,i1 ,ure*9us4 ( v>i\s k9ds ( drops1 8mo/ ( :i* c easily be reproduc$ 9 outl9e by ! aid ( liquids ( approximately equal d5sity to wat]1 al?\gh "s ( !m are fugitive40 ,he f\nd a difficulty 9 ! case ( ! outl9e :i* repres5ts ,a/h5osoma1 b ! reason = ! anomaly is obvi\s2 ! flexible %ell has flatt5$ d[n until x has come 9 contact ) ! h>d skeleton ( ! jaws1 or 8,ari/otle's lant]n10 )91 & ! curvature ( ! outl9e is accord+ly di/urb$4 ,! elevat$1 conical %ells su* z ^? ( ,ure*9us & ,coelopleurus evid5tly call = "s fur!r explanation2 = !re is "h "s cause at "w #ffe to elevate1 r ?an to depress ! %ell4 ,mr ,d>l+ tells me t ^! =ms 8are ne>ly id5tical 9 %ape ) globules ,i h frequ5tly obta9$1 9 :i*1 on /&+1 bubbles ( gas rose to ! summit & press$ ! sk9 upw>ds1 )\t be+ able to escape40 ,! same condition may be at "w 9 ! sea-ur*92 b a simil> t5d5cy w\ld also be manife/$ by ! pres5ce 9 ! upp] "p ( ! %ell ( any accumulation ( sub/ance light] ?an wat]1 su* z is actually pres5t 9 ! masses ( fatty1 oily eggs4 ,on ! ,=m & ,bran*+ ( ,blood-vessels ,pass+ to :at may seem a v diff]5t subject1 we may inve/igate a numb] ( int]e/+ po9ts 9 connection ) ! =m & /ructure ( ! blood-vessels1 on ! same pr9ciple & by help ( ! same equations z ^? we h us$1 = in/ance1 9 /udy+ ! egg-%ell4 ,we "k t ! fluid pressure 7,p7 )9 ! vessel is balanc$ by 7#a7 ! t5sion 7,t7 ( ! wall1 divid$ by ! radius ( curvature1 & 7#b7 ! ext]nal pressure 7pn71 normal to ! wall3 accord+ to our =mula ,p pn ,t7#a_/r #a_/r74 ,if we neglect ! ext]nal pressure1 t is to say any support :i* may be giv5 to ! vessel by ! surr\nd+ tissues1 & if we deal only ) a cyl9drical ve9 or art]y1 ?is =mula becomes simplifi$ to ! =m ,p ,t_/,r4 ,t is to say1 "u con/ant pressure1 ! t5sion v>ies z ! radius4 ,b ! t5sion1 p] unit area ( ! vessel1 dep5ds ^u ! ?ickness ( ! wall1 t is to say on ! am\nt ( membran\s & especially ( muscul> tissue ( :i* x is compos$4 ,!re=e1 s long z ! pressure is con/ant1 ! ?ickness ( ! wall %\ld v>y z ! radius1 or z ! diamet]1 ( ! blood-vessel4 ,b x is n ! case t ! pressure is con/ant1 = x gradually falls (f1 by loss ?r\gh friction1 z we pass f ! l>ge art]ies to ! small2 & accord+ly we f9d t :ile1 = a "t1 ! cross-sections ( ! l>g] & small] vessels are symmetrical figures1 ) ! wall-?ickness proportional to ! size ( ! tube1 ?is proportion is gradually lo/1 & ! walls #fff ( ! small art]ies1 & /ill m ( ! capill>ies1 become exce$+ly ?91 & m s ?an 9 /rict proportion to ! n>r[+ ( ! tube4 ,9 ! case ( ! he>t we h1 )9 ea* ( its cavities1 a pressure :i*1 at any giv5 mom5t1 is con/ant ov] ! :ole wall-area1 b ! ?ickness ( ! wall v>ies v consid]ably4 ,= in/ance1 9 ! left v5tricle1 ! apex is by mu* ! ?9ne/ portion1 z x is also t ) ! greate/ curvature4 ,we may assume1 !re=e 7or at lea/ suspect71 t ! =mula1 t7#a_/r #a_/r7 ,c1 holds good2 t is to say1 t ! ?ickness 7t7 ( ! wall v>ies inv]sely z ! mean curvature4 ,?is may be te/$ exp]im5tally1 by dilat+ a he>t ) alcohol "u a kn[n pressure1 & !n measur+ ! ?ickness ( ! walls 9 v>i\s p>ts aft] ! :ole organ has become h>d5$4 ,by ?is means x is f\nd t1 = ea* ( ! cavities1 ! law holds good ) great accuracy#fja4 ,moreov]1 if we beg9 by dilat+ ! "r v5tricle & !n dilate ! left 9 l mann]1 until ! :ole he>t is equally & symmetrically dilat$1 we f9d 7#a7 t we h _h to use a pressure 9 ! left v5tricle f six to sev5 times z great z 9 ! "r v5tricle1 & 7#b7 t ! ?ickness ( ! walls is j 9 ! same proportion#fjb4 ,a great _m o!r problems ( a me*anical or hydrodynamical k9d arise 9 connection ) ! blood-vessels#fjc1 & :ile ^! are *iefly int]e/+ to ! physiologi/ !y h also _! int]e/ = ! morphologi/ 9 s f> z !y be> ^u /ructure & =m4 ,z an example ( su* me*anical problems #ffg we may take ! conditions :i* det]m9e or help to det]m9e ! mann] ( bran*+ ( an art]y1 or ! angle at :i* its bran*es are giv5 (f2 =1 z ,john ,hunt] said#fjd1 8,to keep up a circulation suffici5t = ! "p1 & no m1 ,nature has v>i$ ! angle ( ! orig9 ( ! art]ies accord+ly40 ,! g5]al pr9ciple is t ! =m & arrangem5t ( ! blood-vessels is su* t ! circulation proce$s ) a m9imum ( ef=t1 & ) a m9imum ( wall-surface1 ! latt] condition lead+ to a m9imum ( friction & be+ !re=e includ$ 9 ! fir/4 ,:at1 !n1 %\ld be ! angle ( bran*+1 su* t !re %all be ! lea/ possible loss ( en]gy 9 ! c\rse ( ! circulation8 ,9 ord] to solve ?is problem 9 any p>ticul> case we %\ld obvi\sly require to "k 7#a7 h[ ! loss ( en]gy dep5ds ^u ! di/ance travell$1 & 7#b7 h[ ! loss ( en]gy v>ies ) ! diamet] ( ! vessel4 ,! loss ( en]gy is evid5tly great] 9 a n>r[ tube ?an 9 a wide "o1 & great]1 obvi\sly1 9 a long j\rney ?an a %ort4 ,if ! ,illu/ration3 ,fig4 #cbi4 l>ge art]y1 ,,ab1 give (f a comp>atively n>r[ bran* lead+ to ,p 7su* z ,,cp1 or ,,dp71 ! r\te ,,acp is evid5tly %ort] ?an ,,adp1 b on ! o!r h&1 by ! latt] pa?1 ! blood has t>ri$ long] 9 ! wide vessel ,,ab1 & has _h a %ort] c\rse 9 ! n>r[ bran*4 ,! relative advantage ( ! two pa?s w dep5d on ! loss ( en]gy 9 ! portion ,,cd1 z comp>$ ) t 9 ! alt]native portion ,,cd1 ! latt] be+ %ort & n>r[1 ! =m] long & wide4 ,if we ask1 !n1 :i* factor is ! m important1 l5g? or wid?1 we may safely take x t ! "q is "o ( degree3 & t ! factor ( wid? w become mu* ! m important :]ev] ! art]y & its bran* are m>k$ly unequal 9 size4 ,9 o!r words1 x w\ld seem t = small bran*es a l>ge angle ( bifurcation1 & = l>ge bran*es a small "o1 is always ! bett]4 ,r\x has laid d[n c]ta9 rules 9 reg>d to ! bran*+ ( art]ies1 :i* correspond ) ! g5]al #ffh conclusions :i* we h j arriv$ at4 ,! mo/ important ( ^! are z foll[s3 7#a7 ,if an art]y bifurcate into two equal bran*es1 ^! bran*es come (f at equal angles to ! ma9 /em4 7#b7 ,if "o ( ! two bran*es be small] ?an ! o!r1 !n ! ma9 bran*1 or cont9uation ( ! orig9al art]y1 makes ) ! latt] a small] angle ?an does ! small] or 8lat]al0 bran*4 ,& 7#c7 all bran*es :i* are s small t !y sc>cely seem to weak5 or dim9i% ! ma9 /em come (f f x at a l>ge angle1 f ab\t #gj to #ij4 ,illu/ration3 ,fig4 #ccj4 ,we may foll[ ,hess 9 a fur!r inve/igation ( ?is ph5om5on4 ,let ,,ab be an art]y1 f :i* a bran* has to be giv5 (f s z to rea* ,p1 & let ,,acp1 ,,adp1 etc41 be alt]native c\rses :i* ! bran* may foll[3 ,,cd1 ,,de1 etc41 9 ! diagram1 be+ equal di/ances 7 l7 along ,,ab4 ,let u call ! angles ,,pcd1 ,,pce1 x#a1 x#b1 etc43 & ! di/ances ,,cd1 ,,de1 by :i* ea* bran* exce$s ! next 9 l5g?1 we %all call l#a1 l#b1 etc4 ,n[ x is evid5t t1 ( ! c\rses %ewn1 ,,acp is ! %orte/ :i* ! blood c take1 b x is also t by :i* its transit ?r\gh ! n>r[ bran* is ! longe/4 ,we may r$uce its transit ?r\gh ! n>r[ bran* m & m1 till we come to ,,cgp1 or r to a po9t :]e ! bran* comes (f at "r angles to ! ma9 /em2 b 9 s do+ we v consid]ably increase ! :ole di/ance travell$4 ,we may take x t !re w be "s int]m$iate po9t :i* w /rike ! balance ( advantage4 ,n[ x is easy to %ew t if1 9 ,fig4 #ccj1 ! r\te ,,adp & ,,aep 7two contigu\s r\tes7 be equally fav\rable1 !n any o!r r\te on ei!r side ( ^!1 su* z ,,acp or ,,afp1 mu/ be less fav\rable ?an ei!r4 ,let ,,adp & ,,aep1 !n1 be equally fav\rable2 t is to say1 let ! loss ( en]gy :i* ! blood suff]s 9 its passage along ^! two r\tes be equal4 #ffi ,!n1 if we make ! di/ance ,,de v small1 ! angles x#b & x#c are ne>ly equal1 & may be s treat$4 ,& aga91 if ,,de be v small1 !n ,,de,e becomes a "r angle1 & l#b 7or ,,de7 l cos x#b4 ,b if ,l be ! loss ( en]gy p] unit di/ance 9 ! wide tube ,,ab1 & ,l be ! correspond+ loss ( en]gy 9 ! n>r[ tube ,,dp1 etc41 !n l,l l#b ,l1 because1 z we h assum$1 ! loss ( en]gy on ! r\te ,,dp is equal to t on ! :ole r\te ,,dep4 ,!re=e l,l l,l cos x#b1 & cos x#b ,l_/,l4 ,t is to say1 ! mo/ fav\rable angle ( bran*+ w be su* t ! cos9e ( ! angle is equal to ! ratio ( ! loss ( en]gy :i* ! blood und]goes1 p] unit ( l5g?1 9 ! ma9 vessel1 z comp>$ ) t :i* x und]goes 9 ! bran*4 ,:ile ^! /atem5ts are s f> true1 & :ile !y und\bt$ly cov] a great numb] ( obs]v$ facts1 yet x is pla9 t1 z 9 all su* cases1 we mu/ reg>d !m n z a complete explanation1 b z factors 9 a complicat$ ph5om5on3 n =gett+ t 7z ! mo/ le>n$ ( all /ud5ts ( ! he>t & art]ies1 ,dr ,?omas ,"y1 said 9 8 ,croonian lecture#fje7 all su* que/ions z ^!1 & all matt]s connect$ ) ! muscul> & ela/ic p[]s ( ! blood-vessels1 8belong to ! mo/ ref9$ dep>tm5ts ( hydraulics40 ,"s o!r explanation mu/ be s\ght 9 ord] to acc\nt = a ph5om5on :i* p>ticul>ly impress$ ,john ,hunt]'s m9d1 namely ! gradually alt]+ angle at :i* ! successive int]co/al art]ies are giv5 (f f ! ?oracic aorta3 ! special int]e/ ( ?is case aris+ f ! regul>ity & symmetry ( ! s]ies1 = 8!re is n ano!r set ( art]ies 9 ! body ^: orig9s are s mu* ! same1 ^: (fices are s mu* ! same1 ^: di/ances f _! orig9 to ! place ( use1 & ^: uses 8 sizes#fjf are s mu* ! same40 #fgj ,,*apt] ,,xvi ,,on ,,=m ,,& ,,me*anical ,,effici5cy ,!re is a c]ta9 l>ge class ( morphological problems ( :i* we h n yet spok51 & ( :i* we %all be able to say b little4 ,nev]!less !y are s important1 s full ( deep !oretical significance1 & are s b\nd up ) ! g5]al "q ( =m & ( its det]m9ation z a result ( gr[?1 t an essay on gr[? & =m is b\nd to take acc\nt ( !m1 h[ev] imp]fectly & briefly4 ,! ph5om5a :i* ,i h 9 m9d are j ^? _m cases :]e adaptation1 9 ! /ricte/ s5se1 is obvi\sly pres5t1 9 ! cle>ly demon/rable =m ( me*anical fitness = ! ex]cise ( "s p>ticul> function or action :i* has become insep>able f ! life & well-be+ ( ! organism4 ,:5 we discuss c]ta9 s-call$ 8adaptations0 to outw>d circum/ance1 9 ! way ( =m1 col\r & s =?1 we are (t5 apt to use illu/rations conv9c+ en\gh to c]ta9 m9ds b unsatisfy+ to o!rs--9 o!r words1 incapable ( demon/ration4 ,) reg>d to col\ration1 = in/ance1 x is by col\rs 8cryptic10 8w>n+10 8signall+10 8mimetic10 & s on#fjg1 t we prosaically exp\nd1 & slavi%ly pr(ess to ju/ify1 ! va/ ,ari/otelian syn!sis t ,nature makes all ?+s ) a purpose & 8does no?+ 9 va940 ,only = a mom5t let u glance at "s few in/ances by :i* ! mod]n teleologi/ acc\nts = ?is or t manife/ation ( col\r1 & is l$ on & on to beliefs & doctr9es to :i* x becomes m & m difficult to subscribe4 #fga ,"s dang]\s & malignant animals are said 79 sob] e>ne/7 to we> a p]petual w>-pa9t1 9 ord] to 8rem9d _! enemies t !y _h bett] leave !m alone#fjh40 ,! wasp & ! hornet1 9 gallant black & gold1 are t]rible z an army ) bann]s2 & ! ,gila ,mon/] 7! poison-liz>d ( ! ,arizona des]t7 is spla%$ ) sc>let--its dread & black complexion /a9$ ) h]aldry m dismal4 ,b ! wasp-l liv]y ( ! noisy1 idle hov]-flies & drone-flies is b /age arm\r1 & 9 _! t9sel suits ! little c\nt]feit c[>dly knaves mimic ! fight+ crew4 ,! jewell$ spl5d\r ( ! peacock & ! humm+-bird1 & ! less effulg5t glory ( ! lyre-bird & ! ,argus pheasant1 are ascrib$ to ! unque/ion$ preval5ce ( vanity 9 ! "o sex & wantonness 9 ! o!r#fji4 ,! zebra is /rip$ t x may graze unnotic$ on ! pla91 ! tig] t x may lurk undiscov]$ 9 ! jungle2 ! b&$ ,*aetodont & ,pomac5trid fi%es are fur!r b$iz5$ to ! hues ( ! coral-reefs 9 :i* !y dwell#faj4 ,! tawny lion is yell[ z ! des]t s&2 b ! leop>d we>s its dappl$ hide to bl5d1 z x cr\*es on ! bran*1 ) ! sun-flecks peep+ ?r\gh ! leaves4 ,! pt>migan & ! sn[y owl1 ! arctic fox & ! pol> be>1 are :ite among ! sn[s2 b g he nor? or g he s\?1 ! rav5 7l ! jackdaw7 is boldly & impud5tly black4 ,! rabbit has 8 :ite scut1 & sundry antelopes _! piebald flanks1 t "o timor\s fugitive may hie aft] ano!r1 spy+ ! w>n+ signal4 ,! primeval t]ri] or collie-dog #fgb _h br[n spots ov] 8 eyes t he might seem awake :5 he 0 sleep+#faa3 s t an enemy might let ! sleep+ dog lie1 = ! s+ul> reason t he imag9$ him to be awake4 ,& a flock ( flam+os1 we>+ on rosy brea/ & crimson w+s a g>m5t ( invisibility1 fades away into ! sky at dawn or sunset l a cl\d inc>nad9e#fab4 ,to buttress ! !ory ( natural selection ! same in/ances ( 8adaptation0 7& _m m7 are us$1 :i* 9 an e>li] b n di/ant age te/ifi$ to ! wisdom ( ! ,creator & reveal$ to simple piety ! high purpose ( ,god4 ,9 ! words ( a c]ta9 le>n$ !ologian#fac1 8,! free use ( f9al causes to expla9 :at seems obscure 0 tempt+ly easy 4444 ,h5ce ! f9ali/ 0 (t5 ! man :o made a lib]al use ( ! ignava ratio1 or lazy argum5t3 :5 y fail$ to expla9 a ?+ by ! ord9>y process ( causality1 y c\ld 8expla90 x by ref]5ce to "s purpose ( nature or ( its ,creator4 ,?is me?od l5t itself ) dang]\s facility to ! well-meant endeav\rs ( ! old] !ologians to exp\nd & emphasise ! b5efic5ce ( ! div9e purpose40 ,mutatis mut&is1 ! passage c>ries its pla9 message to ! naturali/4 ,! fate ( su* argum5ts or illu/rations is always ! same4 ,!y attract & captivate = a:ile2 !y g to ! build+ ( a cre$1 :i* contempor>y or?odoxy def5ds "u its sev]e/ p5alties3 b ! "t comes :5 !y lose _! fasc9ation1 !y someh[ cease to satisfy & to conv9ce1 _! f\ndations are discov]$ to be insecure1 & 9 ! end no man tr\bles to controv]t !m4 ,b ( a v diff]5t ord] f all su* 8adaptations0 z ^!1 are ^? v p]fect adaptations ( =m :i*1 = in/ance1 fit a fi% = swimm+ or a bird = flight4 ,"h we are #fgc f> above ! region ( m]e hypo!sis1 = we h to deal ) que/ions ( me*anical effici5cy :]e /atical & dynamical consid]ations c be appli$ & e/abli%$ 9 detail4 ,! naval ar*itect le>ns a great "p ( 8 lesson f ! inve/igation ( ! /ream-l9es ( a fi%2 & ! ma!matical /udy ( ! /ream-l9es ( a bird1 & ( ! pr9ciples und]ly+ ! areas & curvatures ( its w+s & tail1 has help$ to lay ! v f\ndations ( ! mod]n sci5ce ( a]onautics4 ,:51 aft] attempt+ to compreh5d ! exquisite adaptation ( ! swall[ or ! albatross to ! navigation ( ! air1 we try to pass beyond ! empirical /udy & contemplation ( su* p]fection ( me*anical fitness1 & to ask h[ su* fitness came to be1 !n inde$ we may be excus$ if we /& wrapt 9 wond]m5t1 & if our m9ds be occupi$ & ev5 satisfi$ ) ! conception ( a f9al cause4 ,& yet all ! :ile1 ) no loss ( wond]m5t nor lack ( rev]5ce1 d we f9d ourselves con/ra9$ to believe t someh[ or o!r1 9 dynamical pr9ciples & natural law1 !re lie hidd5 ! /eps & /ages ( physical causation by :i* ! mat]ial /ructure 0 s %ap5 to its ends#fad4 ,b ! problems associat$ ) ^! ph5om5a are difficult at e /age1 ev5 long be=e we approa* to ! unsolv$ secrets ( causation2 & = my "p ,i readily confess t ,i lack ! requisite k = ev5 an elem5t>y discussion ( ! =m ( a fi% or ( a bird4 ,b 9 ! =m ( a bone we h a problem ( ! same k9d & ord]1 s f> simplifi$ & p>ticul>is$ t we may to "s ext5t deal ) x1 & may possibly ev5 f9d1 9 our p>tial compreh5sion ( x1 a p>tial clue to ! pr9ciples ( causation und]ly+ ?is :ole class ( problems4 ,be=e we speak ( ! =m ( a bone1 let u say a ^w ab\t1 ! me*anical prop]ties ( ! mat]ial ( :i* x is built#fae1 9 #fgd relation to ! /r5g? x has to manife/ or ! =ces x has to resi/3 und]/&+ always t we mean !reby ! prop]ties ( fre% or liv+ bone1 ) all its organic z well z inorganic con/itu5ts1 = dead1 dry bone is a v diff]5t ?+4 ,9 all ! /ructures rais$ by ! eng9e]1 9 beams1 pill>s & gird]s ( e k9d1 provision has to be made1 someh[ or o!r1 = /r5g? ( two k9ds1 /r5g? to resi/ compression or cru%+1 & /r5g? to resi/ t5sion or pull+ asund]4 ,! ev5ly load$ column is design$ ) a view to support+ a d[nw>d pressure1 ! wire-rope1 l ! t5don ( a muscle1 is adapt$ only to resi/ a t5sile /ress2 b 9 _m or mo/ cases ! two functions are v closely int]-relat$ & comb9$4 ,! case ( a load$ beam is a famili> "o2 ?\gh1 by ! way1 we are n[ told t x is by no means s simple z x looks1 & inde$ t 8! /resses & /ra9s 9 ?is log ( timb] are s complex t ! problem has n yet be5 solv$ 9 a mann] t reasonably accords ) ! kn[n /r5g? ( ! beam z f\nd by actual exp]im5t#faf40 ,h[ev]1 be t z x may1 we "k1 ,illu/ration3 ,fig4 #cca4 r\ghly1 t :5 ! beam is load$ 9 ! middle & support$ at bo? ends1 x t5ds to be b5t into an arc1 9 :i* condition its l[] fibres are be+ /ret*$1 or are und]go+ a t5sile /ress1 :ile its upp] fibres are und]go+ compression4 ,x foll[s t 9 "s int]m$iate lay] !re is a 8neutral zone10 :]e ! fibres ( ! wood are subject to no /ress ( ei!r k9d4 ,9 l mann]1 a v]tical pill> if unev5ly load$ 7z1 = in/ance1 ! %aft ( our ?igh-bone normally is7 w t5d to b5d1 & s to endure compression on its concave1 & t5sile /ress ^u its convex side4 ,9 _m cases x is ! bus9ess ( ! eng9e] to sep>ate out1 z f> z possible1 ! pressure-l9es f ! t5sion-l9es1 9 ord] to use sep>ate modes ( con/ruction1 or ev5 diff]5t mat]ials = ea*4 ,9 a #fge susp5sion-bridge1 = in/ance1 a great "p ( ! fabric is subject to t5sile /ra9 only1 & is built ?r\gh\t ( ropes or wires2 b ! massive pi]s at ei!r end ( ! bridge c>ry ! weight ( ! :ole /ructure & ( its load1 & endure all ! 8compression-/ra9s0 :i* are inh]5t 9 ! sy/em4 ,v mu* ! same is ! case 9 t wond]ful arrangem5t ( /ruts & ties :i* con/itute1 or complete1 ! skeleton ( an animal4 ,! 8skeleton10 z we see x 9 a ,museum1 is a poor & ev5 a mislead+ picture ( me*anical effici5cy#fag4 ,f ! eng9e]'s po9t ( view1 x is a diagram %[+ all ! compression-l9es1 b by no means all ( ! t5sion-l9es ( ! con/ruction2 x %ews all ! /ruts1 b few ( ! ties1 & p]haps we might ev5 say none ( ! pr9cipal ones2 x falls all to pieces unless we clamp x toge!r1 z be/ we c1 9 a m or less clumsy & immobilis$ way4 ,b 9 life1 t fabric ( /ruts is surr\nd$ & int]wov5 ) a complicat$ sy/em ( ties3 ligam5t & membrane1 muscle & t5don1 run betwe5 bone & bone2 & ! beauty & /r5g? ( ! me*anical con/ruction lie n 9 "o "p or 9 ano!r1 b 9 ! complete fabric :i* all ! p>ts1 s(t & h>d1 rigid & flexible1 t5sion-be>+ & pressure-be>+1 make up toge!r#fah4 ,h[ev] mu* we may f9d a t5d5cy1 :e!r 9 nature or art1 to sep>ate ^! two con/itu5t factors ( t5sion & compression1 we _c d s completely2 & accord+ly ! eng9e] seeks = a mat]ial :i* %all1 z ne>ly z possible1 (f] equal resi/ance to bo? k9ds ( /ra94 ,9 ! foll[+ table--,i borr[ x f ,sir ,donald ,mac,alister--we see approximately ! relative break+ 7or te>+7 limit & cru%+ limit 9 a few sub/ances4 #fgf ,av]age ,/r5g? ( ,mat]ials 79 kg4 p] sq4 mm474 ,t5sile ,cru%+ /r5g? /r5g? ,/eel #ajj #ade ,wr\ght ,iron #dj #bj ,ca/ ,iron #ab #gb ,wood #d #b ,bone #i-ab #ac-af ,at fir/ sight1 bone seems weak inde$2 b x has ! great & unusual advantage t x is v ne>ly z good = a tie z = a /rut1 ne>ly z /rong to )/& rupture1 or te>+ asund]1 z to resi/ cru%+4 ,we see t wr\ght-iron is only half z /rong to )/& ! =m] z ! latt]2 :ile 9 ca/-iron !re is a /ill great] discrepancy ! o!r way1 = x makes a good /rut b a v bad tie inde$4 ,ca/-/eel is n only actually /rong] ?an any ( ^!1 b x also possesses1 l bone1 ! two k9ds ( /r5g? 9 no v great relative disproportion4 ,:5 ! eng9e] con/ructs an iron or /eel gird]1 to take ! place ( ! primitive wood5 beam1 we "k t he takes advantage ( ! elem5t>y pr9ciple we h spok5 (1 & saves weight & economises mat]ial by leav+ out z f> z possible all ! middle portion1 all ! p>ts 9 ! neighb\rhood ( ! 8neutral zone02 & 9 s do+ he r$uces 8 gird] to an upp] & l[] 8flange10 connect$ toge!r by a 8web10 ! :ole resembl+1 9 cross-section1 an ,i or an 4 ,b x is obvi\s t1 if ! /ra9s 9 ! two flanges are to be equal z well z opposite1 & if ! mat]ial be su* z ca/-iron or wr\ght-iron1 "o or o!r flange mu/ be made mu* ?ick] ?an ! o!r 9 ord] t x may be equally /rong2 & if at times ! two flanges h1 z x 71 to *ange places1 or play ea* o!r's p>ts1 !n !re mu/ be introduc$ a m>g9 ( safety by mak+ bo? flanges ?ick en\gh to meet t k9d ( /ress 9 reg>d to :i* ! mat]ial happ5s to be weake/4 ,!re is great economy1 !n1 9 any mat]ial :i* is1 z ne>ly z possible1 equally /rong 9 bo? ways2 & s we see t1 f ! eng9e]'s or contractor's po9t ( view1 bone is a v good & suitable mat]ial = purposes ( con/ruction4 #fgg ,! ,i or ! ,h-gird] or rail is design$ to resi/ b5d+ 9 "o p>ticul> direction1 b if1 z 9 a tall pill>1 x be necess>y to resi/ b5d+ 9 all directions alike1 x is obvi\s t ! tubul> or cyl9drical con/ruction be/ meets ! case2 = x is pla9 t ?is holl[ tubul> pill> is b ! ,i-gird] turn$ r\nd e way1 9 a 8solid ( revolution10 s t on any two opposite sides compression & t5sion are equally met & resi/$1 & !re is n[ no ne$ = any sub/ance at all 9 ! way ( web or 8fill+0 )9 ! holl[ core ( ! tube4 ,& x is n only 9 ! support+ pill> t su* a con/ruction is useful2 x is appropriate 9 e case :]e /iffness is requir$1 :]e b5d+ has to be resi/$4 ,! long bone ( a bird's w+ has little or no weight to c>ry1 b x has to )/& p[]ful b5d+ mom5ts2 & 9 ! arm-bone ( a long-w+$ bird1 su* z an albatross1 we see ! tubul> con/ruction manife/$ 9 its p]fection1 ! bony sub/ance be+ r$uc$ to a ?91 p]fectly cyl9drical1 & almo/ empty %ell4 ,! quill ( ! bird's fea!r1 ! holl[ %aft ( a re$1 ! ?9 tube ( ! :eat-/raw be>+ its heavy burd5 9 ! e>1 are all illu/rations :i* ,galileo us$ 9 8 acc\nt ( ?is me*anical pr9ciple#fai4 ,two po9ts1 bo? ( consid]able importance1 pres5t !mselves "h1 & we may deal ) !m be=e we g fur!r4 ,9 ! fir/ place1 x is n difficult to see t1 9 our b5d+ beam1 ! /ra9 is greate/ at its middle2 if we press our walk+-/ick h>d aga9/ ! gr\nd1 x w t5d to snap midway4 ,h5ce1 if our cyl9drical column be expos$ to /rong b5d+ /resses1 x w be prud5t & economical to make its walls ?icke/ 9 ! middle & ?9n+ (f gradually t[>ds ! ends2 & if we look at a longitud9al section ( a ?igh-bone1 we %all see t ?is is j :at nature has done4 ,! ?ickness ( ! walls is no?+ less ?an a diagram1 or 8graph10 ( ! 8b5d+-mom5ts0 f "o po9t to ano!r along ! l5g? ( ! bone4 ,illu/ration3 ,fig4 #ccb4 ,! second po9t requires a little m explanation4 ,if we #fgh imag9e our load$ beam to be support$ at "o end only 7= in/ance1 by be+ built into a wall71 s z to =m :at is call$ a 8bracket0 or 8cantilev]10 !n we c see1 )\t mu* difficulty1 t ! l9es ( /ress 9 ! beam run some:at z 9 ! accompany+ diagram4 ,imm$iately "u ! load1 ! 8compression-l9es0 t5d to run v]tically d[nw>d2 b :]e ! bracket is fa/5$ to ! wall1 !re is pressure direct$ horizontally aga9/ ! wall 9 ! l[] "p ( ! surface ( atta*m5t2 & ! v]tical beg9n+ & ! horizontal end ( ^! pressure-l9es mu/ be cont9u$ into "o ano!r 9 ! =m ( "s ev5 ma!matical curve--:i*1 z x happ5s1 is "p ( a p>abola4 ,! t5sion-l9es are id5tical 9 =m ) ! compression-l9es1 ( :i* !y con/itute ! 8mirror-image02 & :]e ! two sy/ems int]cross1 !y d s at "r angles1 or 8or?ogonally0 to "o ano!r4 ,su* sy/ems ( /ress-l9es z ^! we %all deal ) aga92 b let u take note "h ( ! important1 ?\gh well-nigh obvi\s fact1 t :ile 9 ! beam !y bo? unite to c>ry ! load1 yet x is always possible to weak5 "o set ( l9es at ! exp5se ( ! o!r1 & 9 "s cases to d altoge!r away ) "o set or ! o!r4 ,= example1 :5 we replace our end-support$ beam by a curv$ bracket1 b5t upw>ds or d[nw>ds z ! case may be1 we h evid5tly cut away 9 ! "o case ! great] "p ( ! t5sion-l9es1 & 9 ! o!r ! great] "p ( ! compression-l9es4 ,& if in/ead ( bridg+ a /ream ) our beam ( wood we bridge x ) a rope1 x is evid5t t ?is new con/ruction conta9s all ! t5sion-l9es1 b none ( ! compression-l9es ( ! old4 ,! biological int]e/ connect$ ) ?is pr9ciple lies *iefly 9 ! me*anical con/ruction ( ! ru% or ! /raw1 or any o!r typically cyl9drical /em4 ,! mat]ial ( :i* ! /alk is con/ruct$ is v weak to )/& compression1 b p>ts ( x h a v great t5sile /r5g?4 ,s*w5d5]1 :o 0 bo? botani/ & eng9e]1 has elaborately inve/igat$ ! factor ( /r5g? 9 ! cyl9drical /em1 :i* ,galileo 0 ! fir/ to call att5tion to4 #fgi ,s*w5d5]#fbj %ew$ t ! /r5g? 0 conc5trat$ 9 ! little bundles ( 8ba/-tissue0 b t ^! ba/-fibres _h a t5sile /r5g? p] squ>e mm4 ( section1 up to ! limit ( ela/icity1 n less ?an t ( /eel-wire ( su* quality z 0 9 use 9 8 day4 ,= in/ance1 we see 9 ! foll[+ table ! load :i* v>i\s fibres1 & v>i\s wires1 7 f\nd capable ( su/a9+1 n up to ! break+-po9t1 b up to ! 8ela/ic limit10 or po9t beyond :i* complete recov]y to ! orig9al l5g? took place no long] aft] release ( ! load4 ,/ress1 or load 9 gms4 ,/ra91 or am\nt p] sq4 mm41 at ( /ret*+1 ,limit ( ,ela/icity p] mille ,secale c]eale #ae-bj #dd ,lilium auratum #ai #gf ,phormium t5ax #bj #acj ,papyrus antiquorum #bj #aeb ,mol9ia co]ulea #bb #aaj ,p9c5ectia recurvata #be #ade ,copp] wire #aba #aj ,brass wire #acc #ace ,iron wire #bai #aj ,/eel wire #bdf #ab ,9 o!r respects1 x is true1 ! plant-fibres 7 inf]ior to ! wires2 = ! =m] broke asund] v soon aft] ! limit ( ela/icity 0 pass$1 :ile ! iron-wire c\ld /&1 be=e snapp+1 ?ree times ! load :i* 0 measur$ by its limit ( ela/icity3 9 ! language ( a mod]n eng9e]1 ! ba/-fibres _h a l[ 8yield-po9t10 little above ! ela/ic limit4 ,b nev]!less1 )9 c]ta9 limits1 plant-fibre & wire 7 j z good & /rong "o z ! o!r4 ,& !n ,s*w5d5] proce$s to %ew1 9 _m beautiful diagrams1 ! v>i\s ways 9 :i* ^! /r&s ( /rong t5sile tissue are arrang$ 9 v>i\s cases3 sometimes1 9 ! simpl] cases1 =m+ num]\s small bundles arrang$ 9 a p]iph]al r+1 n q at ! p]iph]y1 = a c]ta9 am\nt ( space has to be left = liv+ & active tissue2 sometimes 9 a sp>s] r+ ( l>g] & #fhj /rong] bundles2 sometimes ) ^! bundles fur!r /r5g!n$ by radial balks or ridges2 sometimes ) all ! fibres set ,illu/ration3 ,fig4 #ccc4 close toge!r 9 a cont9u\s holl[ cyl9d]4 ,9 ! case figur$ 9 ,fig4 #ccc ,s*w5d5] calculat$ t ! resi/ance to b5d+ 0 at lea/ tw5ty-five times z great z x w\ld h be5 _h ! six ma9 bundles be5 br\ght close toge!r 9 a solid core4 ,9 _m cases ! c5tre ( ! /em is altoge!r empty2 9 all o!r cases x is fill$ ) s(t tissue1 suitable = ! asc5t ( sap or o!r functions1 b nev] su* z to conf] me*anical rigidity4 ,9 a tall conical /em1 su* z t ( a palm-tree1 we c see n only ^! pr9ciples 9 ! con/ruction ( ! cyl9drical trunk1 b we c obs]ve1 t[>ds ! apex1 ! bundles ( fibre curv+ ov] & int]cross+ or?ogonally ) "o ano!r1 exactly aft] ! fa%ion ( our /ress-l9es 9 ,fig4 #ccb2 b ( c\rse1 9 ?is case1 we are /ill deal+ ) t5sile memb]s1 ! opposite bundles tak+ on 9 turn1 z ! tree sways1 ! alt]nate function ( resi/+ t5sile /ra9#fba4 ,let u n[ come1 at la/1 to ! me*anical /ructure ( bone1 ( :i* we f9d a well-kn[n & classical illu/ration 9 ! v>i\s bones ( ! human leg4 ,9 ! case ( ! tibia1 ! bone is some:at wid5$ out above1 & its holl[ %aft is capp$ by an almo/ flatt5$ ro(1 on :i* ! weight ( ! body directly re/4 ,x is obvi\s t1 "u ^! circum/ances1 ! eng9e] w\ld f9d x necess>y to devise means = support+ ?is flat ro(1 & = di/ribut+ ! v]tical pressures :i* imp+e ^u x to ! cyl9drical walls ( ! %aft4 #fha ,illu/ration3 ,fig4 #ccd4 ,head ( ! human femur 9 section4 7,aft] ,s*f]1 f a photo by ,pr(4 ,a4 ,rob9son47 ,9 ! case ( ! bird's w+-bone1 ! holl[ ( ! bone is practically empty1 z we h already said1 be+ fill$ only ) air save = a ?9 lay] ( liv+ tissue imm$iately )9 ! cyl9d] ( bone2 b 9 our own bones1 & all weight-c>ry+ bones 9 g5]al1 ! holl[ space is fill$ ) m>r[1 blood-vessels & o!r tissues2 & among ^! liv+ tissues lies a f9e lattice-"w ( little int]lac$ 8trabeculae0 ( bone1 =m+ ! s-call$ 8cancell\s tissue40 ,! old] anatomi/s 7 cont5t to describe ?is cancell\s tissue z a sort ( 8spongy network10 or irregul> honeycomb1 until1 "s fifty ye>s ago1 a rem>kable discov]y 0 made reg>d+ x4 ,x 0 f\nd by ,h]mann ,mey] 7& aft]w>ds %ewn 9 great] detail by ,julius ,wolff & o!rs7 t ! trabeculae1 z se5 9 a longitud9al section ( a long bone1 7 arrang$ 9 a v def9ite & ord]ly way2 9 ! femur1 !y spread 9 beautiful curv+ #fhb l9es f ! head to ! tubul> %aft ( ! bone1 & ^! bundles ( l9es 7 cross$ by o!rs1 ) s nice a regul>ity ( arrangem5t t ea* int]cross+ 0 z ne>ly z possible an or?ogonal "o3 t is to say1 ! "o set ( fibres cross$ ! o!r ev]y:]e at "r angles4 ,a great eng9e]1 ,pr(essor ,culmann ( ,zri* 7to :om1 by ! way1 we owe ! :ole mod]n me?od ( 8graphic /atics071 happ5$ to see "s ( ,mey]'s draw+s & prep>ations1 & he recognis$ 9 a mom5t t 9 ! arrangem5t ( ! trabeculae we _h ,illu/ration3 ,fig4 #cce4 ,crane-head & femur4 7,aft] ,culmann & ,h4 ,mey]47 no?+ m nor less ?an a diagram ( ! l9es ( /ress1 or directions ( compression & t5sion1 9 ! load$ /ructure3 9 %ort1 t nature 0 /r5g!n+ ! bone 9 precisely ! mann] & direction 9 :i* /r5g? 0 ne$$4 ,9 ! accompany+ diagram ( a crane-head1 by ,culmann1 we recognise a slight modification 7caus$ entirely by ! curv$ %ape ( ! /ructure7 ( ! /ill simpl] l9es ( t5sion & compression :i* we h already se5 9 our end-support$ beam z repres5t$ 9 ,fig4 #ccb4 ,9 ! %aft ( ! crane1 ! concave #fhc or inn] side1 ov]hung by ! load$ head1 is ! 8compression-memb]02 ! out] side is ! 8t5sion-memb]02 & ! pressure-l9es1 />t+ f ! load$ surface1 ga!r !mselves toge!r1 always 9 ! direction ( ! resultant pressure1 till !y =m a close bundle runn+ d[n ! compress$ side ( ! %aft3 :ile ! t5sion-l9es1 runn+ upw>ds along ! opposite side ( ! %aft1 spread out ?r\gh ! head1 or?ogonally to1 & l9k+ toge!r1 ! sy/em ( compression-l9es4 ,! head ( ! femur 7,fig4 #cce7 is a little m complicat$ 9 =m & a little less symmetrical ?an ,culmann's diagrammatic crane1 f :i* x *iefly diff]s 9 ! fact t ! load is divid$ into two p>ts1 t namely :i* is borne by ! head ( ! bone1 & t small] portion :i* re/s ^u ! great tro*ant]2 b ?is m]ely am\nts to say+ t a not* has be5 cut out ( ! curv$ upp] surface ( ! /ructure1 & we h no difficulty 9 see+ t ! anatomical arrangem5t ( ! trabeculae foll[s precisely ! me*anical di/ribution ( compressive & t5sile /ress or1 9 o!r words1 accords p]fectly ) ! !oretical /ress-diagram ( ! crane4 ,! l9es ( /ress are bundl$ close toge!r along ! sides ( ! %aft1 & lo/ or conceal$ !re 9 ! sub/ance ( ! solid wall ( bone2 b 9 & ne> ! head ( ! bone1 a p]iph]al %ell ( bone does n suffice to conta9 !m1 & !y spread out ?r\gh ! c5tral mass 9 ! actual concrete =m ( bony trabeculae#fbb4 #fhd ,mutatis mut&is1 ! same ph5om5on may be trac$ 9 any o!r bone :i* c>ries weight & is liable to flexure2 & 9 ! os calcis & ! tibia1 & m or less 9 all ! bones ( ! l[] limb1 ! arrangem5t is f\nd to be v simple & cle>4 ,illu/ration3 ,fig4 #ccf4 ,diagram ( /ress-l9es 9 ! human foot4 7,f ,sir ,d4 ,mac,alister1 aft] ,h4 ,mey]47 ,?us1 9 ! os calcis1 ! weight re/+ on ! head ( ! bone has to be transmitt$ p>tly ?r\gh ! backw>d-project+ heel to ! gr\nd1 & p>tly =w>ds ?r\gh its articulation ) ! cuboid bone1 to ! ar* ( ! foot4 ,we ?us h1 v mu* z 9 a triangul> ro(-tree1 two compression-memb]s1 slop+ ap>t f "o ano!r2 & ^! h to be b\nd toge!r by a 8tie0 or t5sion-memb]1 correspond+ to ! ?ird1 horizontal memb] ( ! truss4 ,illu/ration3 ,fig4 #ccg4 ,trabecul> /ructure ( ! os calcis4 7,f ,mac,alister47 ,s f>1 deal+ :olly ) ! /resses & /ra9s due to t5sion & compression1 we h altoge!r omitt$ to speak ( a ?ird v important factor 9 ! eng9e]'s calculations1 namely :at is kn[n z 8%e>+ /ress40 ,a %e>+ =ce is "o :i* produces 8angul> di/ortion0 9 a figure1 or 7:at comes to ! same ?+7 :i* t5ds to cause its p>ticles to #fhe slide ov] "o ano!r4 ,a %e>+ /ress is a some:at complicat$ ?+1 & we mu/ try to illu/rate x 7h[ev] imp]fectly7 9 ! simple/ possible way4 ,if we build up a pill>1 = in/ance1 ( a pile ( flat horizontal slates1 or ( a pack ( c>ds1 a v]tical load plac$ ^u x w produce compression1 b w h no t5d5cy to cause "o c>d to slide1 or %e>1 ^u ano!r2 & 9 l mann]1 if we make up a cable ( p>allel wires &1 lett+ x hang v]tically1 load x ev5ly ) a weight1 aga9 ! t5sile /ress produc$ has no t5d5cy to cause "o wire to slip or %e> ^u ano!r4 ,b ! case w\ld h be5 v diff]5t if we _h built up our pill> ( c>ds or slates ly+ obliquely to ! l9es ( pressure1 = !n at once !re w\ld h be5 a t5d5cy = ! elem5ts ( ! pile to slip & slide asund]1 & to produce :at ! geologi/s call 8a fault0 9 ! /ructure4 ,some:at m g5]ally1 if ,,ab be a b>1 or pill>1 ( cross-section a "u a direct load ,p1 giv+ a /ress p] unit area p1 !n ! :ole pressure ,p pa4 ,let ,,cd be an oblique section1 incl9$ at an angle to ! cross-section2 ! pressure on ,,cd w evid5tly be pa cos 4 ,b at any po9t ,o 9 ,,cd1 ! pressure ,p may be resolv$ into ! =ce ,q act+ along ,,cd1 & ,n p]p5dicul> to x3 :]e ,n ,p cos 1 & ,q ,p s9 pa s9 4 ,! :ole =ce ,q ^u ,,cd q area ( ,,cd1 :i* is q a_/7cos 74 #fhf ,!re=e qa_/7cos 7 pa s9 1 !re=e q p s9 cos 1 p s9 #b4 ,!re=e :5 s9 #b #a1 t is1 :5 #de1 q is a maximum1 & p_/#b2 & :5 s9 #b #j1 t is :5 #j or #ij1 !n q vani%es altoge!r4 ,illu/ration3 ,fig4 #cch4 ,?is is z mu* z to say1 t a %e>+ /ress vani%es altoge!r along ! l9es ( maximum compression or t5sion2 x has a def9ite value 9 all o!r positions1 & a maximum value :5 x is incl9$ at #de to ei!r1 or half-way betwe5 ! two4 ,?is may be fur!r illu/rat$ 9 v>i\s simple ways4 ,:5 we submit a cubical block ( iron to compression 9 ! te/+ ma*9e1 x does n t5d to give way by crumbl+ all to pieces2 b z a rule x disrupts by %e>+1 & along "s plane approximately at #de to ! axis ( compression4 ,aga91 9 ! beam :i* we h already consid]$ "u a b5d+ mom5t1 we "k t if we sub/itute = x a pack ( c>ds1 !y w be /rongly %e>$ on "o ano!r2 & ! %e>+ /ress is greate/ 9 ! 8neutral zone10 :]e nei!r t5sion nor compression is manife/$3 t is to say 9 ! l9e :i* cuts at equal angles ( #de ! or?ogonally int]sect+ l9es ( pressure & t5sion4 ,9 %ort we see t1 :ile %e>+ /resses c by no means be got rid (1 ! dang] ( rupture or break+-d[n "u %e>+ /ress is completely got rid ( :5 we arrange ! mat]ials ( our con/ruction :olly along ! pressure-l9es & t5sion-l9es ( ! sy/em2 = along ^! l9es !re is no %e>4 ,to apply ^! pr9ciples to ! gr[? & developm5t ( our bone1 we h only to imag9e a little trabecula 7or gr\p ( trabeculae7 be+ secret$ & laid d[n =tuit\sly 9 any direction )9 ! sub/ance ( ! bone4 ,if x lie 9 ! direction ( "o ( ! pressure-l9es1 = in/ance1 x w be 9 a position ( comp>ative equilibrium1 or m9imal di/urbance2 b if x be incl9$ obliquely to ! pressure-l9es1 ! %e>+ =ce w at once t5d to act ^u x & move x away4 ,?is is nei!r m nor less ?an :at happ5s :5 we comb our #fhg hair1 or c>d a lock ( wool3 filam5ts ly+ 9 ! direction ( ! comb's pa? rema9 :]e !y 72 b ! o!rs1 "u ! influ5ce ( an oblique compon5t ( pressure1 are %e>$ out ( _! places till !y too come into co9cid5ce ) ! l9es ( =ce4 ,s /raws %[ h[ ! w9d bl[s--or r h[ x has be5 bl[+4 ,= e /raw t lies askew to ! w9d's pa? t5ds to be %e>$ into x2 b z soon z x has come to lie ! way ( ! w9d x t5ds to be di/urb$ no m1 save 7( c\rse7 by a viol5ce su* z to hurl x bodily away4 ,9 ! biological aspect ( ! case1 we mu/ always rememb] t our bone is n only a liv+1 b a highly pla/ic /ructure2 ! little trabeculae are con/antly be+ =m$ & de=m$1 demoli%$ & =m$ anew4 ,"h1 = once1 x is safe to say t 8h]$ity0 ne$ n & _c be invok$ to acc\nt = ! configuration & arrangem5t ( ! trabeculae3 = we c see !m1 at any "t ( life1 9 ! mak+1 "u ! direct action & control ( ! =ces to :i* ! sy/em is expos$4 ,if a bone be brok5 & s repair$ t its p>ts lie some:at out ( _! =m] place1 s t ! pressure-& t5sion-l9es h n[ a new di/ribution1 be=e _m weeks are ov] ! trabecul> sy/em w be f\nd to h be5 entirely remodell$1 s z to fall into l9e ) ! new sy/em ( =ces4 ,& z ,wolff po9t$ out1 ?is process ( recon/ruction ext5ds a long way (f f ! seat ( injury1 & s _c be look$ ^u z a m]e accid5t ( ! physiological process ( heal+ & repair2 = in/ance1 x may happ5 t1 aft] a fracture ( ! %aft ( a long bone1 ! trabecul> me%work is :olly alt]$ & recon/ruct$ )9 ! di/ant extremities ( ! bone4 ,moreov]1 9 cases ( transplantation ( bone1 = example :5 a diseas$ metac>pal is repair$ by means ( a portion tak5 f ! l[] end ( ! ulna1 ) a/oni%+ quickness ! pla/ic capabilities ( ! bony tissue are s manife/$ t nei!r 9 outw>d =m nor inw>d /ructure c ! old portion be di/+ui%$ f ! new4 ,h]e9 !n lies1 s f> z we c disc]n x1 a great "p at lea/ ( ! physical causation ( :at at fir/ sight /rikes u z a purely functional adaptation3 z a ph5om5on1 9 o!r words1 #fhh ^: physical cause is z obscure z its f9al cause or end is1 app>5tly1 manife/4 ,p>tly associat$ ) ! same ph5om5on1 & p>tly to be look$ ^u 7mean:ile at lea/7 z a fact ap>t1 is ! v important physiological tru? t a condition ( /ra91 ! result ( a /ress1 is a direct /imulus to gr[? itself4 ,?is inde$ is no less ?an "o ( ! c>d9al facts ( !oretical biology4 ,! soles ( our boots we> ?91 b ! soles ( our feet gr[ ?ick1 ! m we walk ^u !m3 = x w\ld seem t ! liv+ cells are 8/imulat$0 by pressure1 or by :at we call 8ex]cise10 to increase & multiply4 ,! surgeon kn[s1 :5 he b&ages a brok5 limb1 t 8 b&age is do+ some?+ m ?an m]ely keep+ ! p>ts toge!r3 & t ! ev51 con/ant pressure :i* he skilfully applies is a direct enc\ragem5t ( gr[? & an active ag5t 9 ! process ( repair4 ,9 ! classical exp]im5ts ( ,sdillot#fbc1 ! great] "p ( ! %aft ( ! tibia 0 excis$ 9 "s "y puppies1 leav+ ! :ole weight ( ! body to re/ ^u ! fibula4 ,! latt] bone is normally ab\t "o-fif? or six? ( ! diamet] ( ! tibia2 b "u ! new conditions1 & "u ! 8/imulus0 ( ! increas$ load1 x grew till x 0 z ?ick or ev5 ?ick] ?an ! normal bulk ( ! l>g] bone4 ,among plant tissues ?is ph5om5on is v app>5t1 & 9 a some:at rem>kable way2 = a /ra9 caus$ by a con/ant or increas+ weight 7su* z t 9 ! /alk ( a pe> :ile ! pe> is gr[+ & rip5+7 produces a v m>k$ increase ( /r5g? )\t any necess>y increase ( bulk1 b r by "s hi/ological1 or molecul>1 alt]ation ( ! tissues4 ,hegl]1 & also ,pfeff]1 h inve/igat$ ?is subject1 by load+ ! "y %oot ( a plant ne>ly to its break+ po9t1 & !n r$et]m9+ ! break+-/r5g? aft] a few days4 ,"s "y %oots ( ! sunfl[] 7 f\nd to break ) a /ra9 ( #afj gms42 b :5 load$ ) #aej gms41 & rete/$ aft] two days1 !y 7 able to support #bej gms42 & be+ aga9 load$ ) some?+ %ort ( ?is1 by next day !y su/a9$ #cjj gms41 & a few days lat] ev5 #djj gms4 #fhi ,su* exp]im5ts h be5 amply confirm$1 b s f> z ,i am aw>e1 we d n "k mu* m ab\t ! matt]3 we d n "k1 = in/ance1 h[ f> ! *ange is accompani$ by increase 9 numb] ( ! ba/-fibres1 ?r\gh trans=mation ( o!r tissues2 or h[ f> x is due to increase 9 size ( ^! fibres2 or :e!r x be n simply due to /r5g!n+ ( ! orig9al fibres by "s molecul> *ange4 ,b ,i %\ld be mu* incl9$ to suspect t ! latt] _h a good deal to d ) ! ph5om5on4 ,we "k n[adays t a railway axle1 or any o!r piece ( /eel1 is weak5$ by a con/ant succession ( frequ5tly int]rupt$ /ra9s2 x is said to be 8fatigu$10 & its /r5g? is re/or$ by a p]iod ( re/4 ,! conv]se effect ( cont9u$ /ra9 9 a uni=m direction may be illu/rat$ by a homely example4 ,! confection] takes a mass ( boil$ sug> or treacle 79 a p>ticul> molecul> condition det]m9$ by ! temp]ature to :i* x has be5 expos$71 & draws ! s(t /icky mass out into a rope2 & !n1 fold+ x up l5g?ways1 he repeats ! process aga9 & aga94 ,at fir/ ! rope is pull$ out ( ! ductile mass )\t difficulty2 b z ! "w goes on x gets h>d] to d1 until all ! man's =ce is us$ to /ret* ! rope4 ,"h we h ! ph5om5on ( increas+ /r5g?1 foll[+ me*anically on a re>rangem5t ( molecules1 z ! orig9al isotropic condition is transmut$ m & m into molecul> asymmetry or anisotropy2 & ! rope app>5tly 8adapts itself0 to ! increas$ /ra9 :i* x is call$ on to be>1 all aft] a fa%ion :i* at lea/ sugge/s a p>allel to ! increas+ /r5g? ( ! /ret*$ & weight$ fibre 9 ! plant4 ,= increase ( /r5g? by re>rangem5t ( ! p>ticles we h already a r\gh illu/ration 9 our lock ( wool or hank ( t[4 ,! piece ( t[ w c>ry b little weight :ile its fibres are tangl$ & awry3 b z soon z we h c>d$ x out1 & br\ght all its long fibres p>allel & side by side1 we may at once make ( x a /rong & useful cord4 ,9 "s su* ways z ^!1 !n1 x w\ld seem t we may co-ord9ate1 or hope to co-ord9ate1 ! ph5om5on ( gr[? ) c]ta9 ( ! beautiful /ructural ph5om5a :i* pres5t !mselves to our eyes z 8provisions10 or me*anical adaptations1 = ! display ( /r5g? :]e /r5g? is mo/ requir$4 #fij ,t is to say1 ! orig91 or causation1 ( ! ph5om5on w\ld seem to lie1 p>tly 9 ! t5d5cy ( gr[? to be accel]at$ "u /ra93 & p>tly 9 ! automatic effect ( %e>+ /ra91 by :i* x t5ds to displace p>ts :i* gr[ obliquely to ! direct l9es ( t5sion & ( pressure1 :ile leav+ ^? 9 place :i* happ5 to lie p>allel or p]p5dicul> to ^? l9es3 an automatic effect :i* we c probably trace z work+ on all scales ( magnitude1 & z acc\nt+ !re=e = ! re>rangem5t ( m9ute p>ticles 9 ! metal or ! fibre1 z well z = ! br++ into l9e ( ! fibres !mselves )9 ! plant1 or ( ! little trabeculae )9 ! bone4 ,b we may n[ attempt to pass f ! /udy ( ! individual bone to ! mu* wid] & n less beautiful problems ( me*anical con/ruction :i* are pres5t$ to u by ! skeleton z a :ole4 ,c]ta9 problems ( ?is class are by no means neglect$ by writ]s on anatomy1 & _m h be5 h&$ d[n f ,borelli1 & ev5 f old] writ]s4 ,= in/ance1 x is an old tradition ( anatomical tea*+ to po9t out 9 ! human body examples ( ! ?ree ord]s ( lev]s#fbd2 aga91 ! pr9ciple t ! limb-bones t5d to be %ort5$ 9 ord] to support ! weight ( a v heavy animal is well und]/ood by comp>ative anatomi/s1 9 accordance ) ,eul]'s law1 t ! weight :i* a column liable to flexure is capable ( support+ v>ies inv]sely z ! squ>e ( its l5g?2 & aga91 ! /atical equilibrium ( ! body1 9 relation = in/ance to ! erect po/ure ( man1 has long be5 a fav\rite !me ( ! philosophical anatomi/4 ,b ! g5]al me?od1 bas$ ^u t ( graphic /atics1 to :i* we h be5 introduc$ 9 our /udy ( a bone1 has n1 s f> z ,i "k1 be5 appli$ to ! g5]al fabric ( ! skeleton4 ,yet x is pla9 t ea* bone plays #fia a "p 9 relation to ! :ole body1 analog\s to t :i* a little trabecula1 or a little gr\p ( trabeculae1 plays )9 ! bone itself3 t is to say1 9 ! normal di/ribution ( =ces 9 ! body1 ! bones t5d to foll[ ! l9es ( /ress1 & especially ! pressure-l9es4 ,to demon/rate ?is 9 a compreh5sive way w\ld d\btless be difficult2 = we %\ld be deal+ ) a framework ( v great complexity1 & %\ld h to take acc\nt ( a great v>iety ( conditions#fbe4 ,?is framework is complicat$ z we see x 9 ! skeleton1 :]e 7z we h said7 x is only1 or *iefly1 ! /ruts ( ! :ole fabric :i* are repres5t$2 b to und]/& ! me*anical /ructure 9 detail1 we %\ld h to foll[ out ! /ill m complex arrangem5t ( ! ties1 z repres5t$ by ! muscles & ligam5ts1 & we %\ld also require mu* detail$ in=mation z to ! weights ( ! v>i\s p>ts & z to ! o!r =ces conc]n$4 ,)\t ^! latt] data we c only treat ! "q 9 a prelim9>y & imp]fect way4 ,b1 to take once aga9 a small & simplifi$ "p ( a big problem1 let u ?9k ( a quadrup$ 7= in/ance1 a horse7 9 a /&+ po/ure1 & see :e!r ! me?ods & t]m9ology ( ! eng9e] may n help u1 z !y did 9 reg>d to ! m9ute /ructure ( ! s+le bone4 ,/&+ f\r-squ>e ^u its =elegs & h9dlegs1 ) ! weight ( ! body susp5d$ betwe51 ! quadrup$ at once sugge/s to u ! analogy ( a bridge1 c>ri$ by its two pi]s4 ,& if x occurs to u1 z naturali/s1 t we nev] look at a /&+ quadrup$ )\t contemplat+ a bridge1 s1 conv]sely1 a simil> idea has occurr$ to ! eng9e]2 = ,pr(essor ,fidl]1 9 ?is ,treatise on ,bridge-,con/ruction1 deals ) ! *ief descriptive "p ( 8 subject "u ! head+ ( 8,! ,comp>ative ,anatomy ( ,bridges40 ,! designation is mo/ j1 = 9 /udy+ ! v>i\s types ( bridges we are /udy+ a s]ies ( well-plann$ skeletons#fbf2 & 7at ! co/ ( a little p$antry7 #fib we might g ev5 fur!r1 & /udy 7aft] ! fa%ion ( ! anatomi/7 ! 8o/eology0 & 8desmology0 ( ! /ructure1 t is to say ! bones :i* are repres5t$ by 8/ruts10 & ! ligam5ts1 etc41 :i* are repres5t$ by 8ties40 ,fur!rmore aft] ! me?ods ( ! comp>ative anatomi/1 we may classify ! families1 g5]a & species ( bridges accord+ to _! di/9ctive me*anical features1 :i* correspond to c]ta9 def9ite conditions & functions4 ,9 m ways ?an "o1 ! quadrup$al bridge is a rem>kable "o2 & p]haps its mo/ rem>kable peculi>ity is t x is a jo9t$ & flexible bridge1 rema9+ 9 equilibrium "u consid]able & sometimes great modifications ( its curvature1 su* z we see1 = in/ance1 :5 a cat humps or flatt5s h] back4 ,! fact t flexibility is an ess5tial feature 9 ! quadrup$al bridge1 :ile x is ! la/ ?+ :i* an eng9e] desires & ! fir/ :i* he seeks to provide aga9/1 w impose c]ta9 important limit+ conditions ^u ! design ( ! skeletal fabric2 b to ?is matt] we %all aft]w>ds return4 ,let u beg9 by consid]+ ! quadrup$ at re/1 :5 he /&s upright & motionless ^u 8 feet1 & :5 8 legs ex]cise no function save only to c>ry ! weight ( ! :ole body4 ,s f> z t function is conc]n$1 we might n[ p]haps comp>e ! horse's legs ) ! tall & sl5d] pi]s ( "s railway bridge2 b x is obvi\s t ^! jo9t$ legs are ill-adapt$ to receive ! horizontal ?ru/ ( any ar* t may be plac$ atop ( !m4 ,h5ce x foll[s t ! curv$ backbone ( ! horse1 :i* appe>s to cross l an ar* ! span betwe5 8 %\ld]s & 8 flanks1 _c be reg>d$ z an ar*1 9 ! #fic eng9e]'s s5se ( ! ^w4 ,x resembles an ar* 9 =m1 b n 9 function1 = x _c act z an ar* unless x be held back at ea* end 7z e ar* is held back7 by abutm5ts capable ( resi/+ ! horizontal ?ru/2 & ^! necess>y abutm5ts are n pres5t 9 ! /ructure4 ,b 9 v>i\s ways ! eng9e] c modify 8 sup]/ructure s z to supply ! place ( ^! ext]nal reactions1 :i* 9 ! simple ar* are obvi\sly indisp5sable4 ,?us1 = example1 we may beg9 by ins]t+ a /raight /eel tie1 ,,ab 7,fig4 #cci71 unit+ ! ends ( ! curv$ rib ,aa,b2 & ?is tie w supply ! place ( ! ext]nal reactions1 conv]t+ ! /ructure into a 8ti$ ar*10 su* z we may see 9 ! ro(s ( _m railway-/ations4 ,or we may g on to fill 9 ! space betwe5 ar* & tie by a 8web-sy/em10 conv]t+ x into :at ! eng9e] describes z a 8p>abolic b[/r+ gird]0 7,fig4 #cci;b74 ,9 ei!r case1 ! /ructure becomes an ,illu/ration3 ,fig4 #cci4 indep5d5t 8deta*$ gird]10 support$ at ea* end b n o!rwise fix$1 & consi/+ ess5tially ( an upp] compression-memb]1 ,aa,b1 & a l[] t5sion-memb]1 ,,ab4 ,b aga91 9 ! skeleton ( ! quadrup$1 ! necess>y tie1 ,,ab1 is n to be f\nd2 & x foll[s t ^! comp>atively simple types ( bridge d n correspond to1 nor d !y help u to und]/&1 ! type ( bridge :i* nature has design$ 9 ! skeleton ( ! quadrup$4 ,nev]!less if we try to look1 z an eng9e] w\ld look1 at ! actual design ( ! animal skeleton & ! actual di/ribution ( its load1 we f9d t1 ! "o is mo/ admirably adapt$ to ! o!r1 accord+ to ! /rict pr9ciples ( eng9e]+ con/ruction4 ,! /ructure is n an ar*1 nor a ti$ ar*1 nor a b[/r+ gird]3 b x is /rictly & beautifully #fid comp>able to ! ma9 gird] ( a d\ble-arm$ cantilev] bridge4 ,obvi\sly1 9 our quadrup$al bridge1 ! sup]/ructure does n t]m9ate 7z x did 9 our =m] diagram7 at ! two po9ts ( support1 b x ext5ds beyond !m at ea* end1 c>ry+ ! head at "o end & ! tail at ! o!r1 ^u a pair ( project+ arms or 8cantilev]s0 7,fig4 #cdf74 ,9 a typical cantilev] bridge1 su* z ! ,=? ,bridge 7,fig4 #cde71 a c]ta9 simplification is introduc$4 ,= ea* pi] c>ries1 9 ?is case1 its own d\ble-arm$ cantilev]1 l9k$ by a %ort connect+ gird] to ! next1 b s jo9t$ to x t no weight is transmitt$ f "o cantilev] to ano!r4 ,! bridge 9 %ort is cut into sep>ate sections1 practically indep5d5t ( "o ano!r2 at ! jo9ts a c]ta9 am\nt ( b5d+ is n preclud$1 b %e>+ /ra9 is evad$2 & ea* pi] c>ries only its own load4 ,by ?is arrangem5t ! eng9e] f9ds t design & con/ruction are alike simplifi$ & facilitat$4 ,9 ! case ( ! horse1 x is obvi\s t ! two pi]s ( ! bridge1 t is to say ! =e-legs & ! h9d-legs1 d n be> 7z !y d 9 ! ,=? ,bridge7 sep>ate & indep5d5t loads1 b ! :ole sy/em =ms a cont9u\s /ructure4 ,9 ?is case1 ! calculation ( ! loads w be a little m difficult & ! correspond+ design ( ! /ructure a little m complicat$4 ,we %all accord+ly simplify our problem v consid]ably if1 to beg9 )1 we look ^u ! quadrup$al skeleton z con/itut$ ( two sep>ate sy/ems1 t is to say ( two balanc$ cantilev]s1 "o support$ on ! =e-legs & ! o!r on ! h9d2 & we may deal aft]w>ds ) ! fact t ^! two cantilev]s are n indep5d5t1 b are b\nd up 9 "o common field ( =ce & plan ( con/ruction4 ,9 ! horse x is pla9 t ! two cantilev] sy/ems into :i* we may ?us analyse ! quadrup$al bridge are unequal 9 magnitude & importance4 ,! =e-"p ( ! animal is mu* bulki] ?an its h9d qu>t]s1 & ! fact t ! =e-legs c>ry1 z !y s evid5tly d1 a great] weight ?an ! h9d-legs has long be5 kn[n & is easily prov$2 we h only to walk a horse onto a weigh-bridge1 weigh fir/ 8 =e-legs & !n 8 h9d-legs1 to discov] t :at we may call 8 front half weighs #fie a good deal m ?an :at is c>ri$ on 8 h9d feet1 say ab\t ?ree-fif?s ( ! :ole weight ( ! animal4 ,! great 7or ant]ior7 cantilev] !n1 9 ! horse1 is con/itut$ by ! heavy head & /ill heavi] neck on "o side ( ! pi] :i* is repres5t$ by ! =e-legs1 & by ! dorsal v]tebrae c>ry+ a l>ge "p ( ! weight ( ! trunk ^u ! o!r side2 & ?is weight is s balanc$ ov] ! =e-legs t ! cantilev]1 :ile 8an*or$0 to ! o!r p>ts ( ! /ructure1 transmits b little ( its weight to ! h9d-legs1 & ! am\nt s transmitt$ w v>y ) ! position ( ! head & ) ! position ( any artificial load#fbg4 ,"u c]ta9 conditions1 z :5 ! head is ?ru/ well =w>d1 x is evid5t t ! h9d-legs w be actually reliev$ ( a portion ( ! comp>atively small load :i* is _! normal %>e4 ,our problem n[ is to discov]1 9 a r\gh & approximate way1 "s ( ! /ructural details :i* ! balanc$ load ^u ! d\ble cantilev] w impress ^u ! fabric4 ,work+ by ! me?ods ( graphic /atics1 ! eng9e]'s task is1 9 !ory1 "o ( great simplicity4 ,he beg9s by draw+ 9 outl9e ! /ructure :i* he desires to erect2 he calculates ! /resses & b5d+-mom5ts necessitat$ by ! dim5sions & load on ! /ructure2 he draws a new diagram repres5t+ ^! =ces1 & he designs & builds 8 fabric on ! l9es ( ?is /atical diagram4 ,he does1 9 %ort1 precisely :at we h se5 nature do+ 9 ! case ( ! bone4 ,= if we _h begun1 z x 71 by block+ out ! femur r\ghly1 & consid]+ its position & dim5sions1 its means ( support & ! load :i* x has to be>1 we c\ld h proce$$ at once to draw ! sy/em ( /ress-l9es :i* mu/ occupy ! field ( =ce3 & to precisely ^! /ress-l9es has nature kept 9 ! build+ ( ! bone1 d[n to ! m9ute arrangem5t ( its trabeculae4 ,! ess5tial function ( a bridge is to /ret* across a c]ta9 span1 & c>ry a c]ta9 def9ite load2 & ?is be+ s1 ! #fif *ief problem 9 ! design+ ( a bridge is to provide due resi/ance to ! 8b5d+-mom5ts0 :i* result f ! load4 ,^! b5d+-mom5ts w v>y f po9t to po9t along ! gird]1 & tak+ ! simple/ case ( a uni=m load support$ at bo? ends1 !y w be repres5t$ by po9ts on a p>abola4 ,if ! gird] be ( uni=m dep?1 t is to say if its two flanges1 ,illu/ration3 ,fig4 #cdj4 ,a1 ,span ( propos$ bridge4 ,b1 ,/ress diagram1 or diagram ( b5d+-mom5ts#fbh4 respectively "u t5sion & compression1 be p>allel to "o ano!r1 !n ! /ress ^u ^! flanges w v>y z ! b5d+-mom5ts1 & w accord+ly be v sev]e 9 ! middle & w dw9dle t[>ds ! ends4 ,b if we make ! dep? ( ! gird] ev]y:]e proportional to ! b5d+-mom5ts1 t is ,illu/ration3 ,fig4 #cda4 ,! bridge con/ruct$1 z a p>abolic gird]4 to say if we copy 9 ! gird] ! outl9es ( ! b5d+-mom5t diagram1 !n our design w automatically meet ! circum/ances ( ! case1 = ! horizontal /ress 9 ea* flange w n[ be uni=m ?r\gh\t ! l5g? ( ! gird]4 ,9 %ort1 9 #fig ,pr(essor ,fidl]'s words1 8,e diagram ( mom5ts repres5ts ! outl9e ( a fram$ /ructure :i* w c>ry ! giv5 load ) a uni=m horizontal /ress 9 ! pr9cipal memb]s40 ,illu/ration3 ,fig4 #cdb4 ,9 ! foll[+ diagrams 7,fig4 #cdb1 a1 b7 7:i* are tak5 f ! orig9al ones ( ,culmann71 we see at once t ! load$ beam or bracket 7a7 has a 8dang]-po9t0 close to its fix$ base1 t is to say at ! po9t remote/ f its load4 ,b 9 ! p>abolic bracket 7b7 !re is no dang]-po9t at all1 = ! dim5sions ( ! /ructure are made to increase p>i passu ) ! b5d+-mom5ts3 /ress & resi/ance v>y toge!r4 ,aga9 9 ,fig4 #cdj1 we h a simple span 7,a71 ) its /ress diagram 7,b72 & 9 ,fig4 #cda we h ! correspond+ p>abolic gird]1 ^: /resses are n[ uni=m ?r\gh\t4 ,9 fact we see t1 by a process ( conv]sion1 ! /ress diagram 9 ea* case becomes ! /ructural diagram 9 ! o!r#fbi4 ,n[ all ?is is b ! mod]n r5d]+ ( "o ( ,galileo's mo/ fam\s propositions4 ,9 ! ,dialogue :i* we h already quot$ m ?an once#fcj1 ,sagr$o says 8,x w\ld be a f9e ?+ if "o c\ld discov] ! prop] %ape to give a solid 9 ord] to make x equally resi/ant at e po9t1 9 :i* case a load plac$ at ! middle w\ld n produce fracture m easily ?an if plac$ at any o!r po9t40 ,& ,galileo 79 ! p]son ( ,salviati7 fir/ puts ! problem into its m g5]al =m2 & !n %ews u h[1 by giv+ a p>abolic outl9e to our beam1 we h its simple & compreh5sive solution4 ,9 ! case ( our cantilev] bridge1 we %ew ! primitive gird] #fih 9 ,fig4 #cdc1 ,a1 ) its b5d+-mom5t diagram 7,b72 & x is evid5t t1 if we turn ?is diagram upside d[n1 x w /ill be illu/rative1 j z be=e1 ( ! b5d+-mom5ts f po9t to po9t3 = z yet x is m]ely a diagram1 or graph1 ( relative magnitudes4 ,to ei!r ( ^! two /ress diagrams1 direct or inv]t$1 we may fit ! design ( ! con/ruction1 z 9 ,figs4 #cdc1 ,c & #cdd4 ,illu/ration3 ,fig4 #cdc4 ,illu/ration3 ,fig4 #cdd4 ,n[ 9 diff]5t animals ! am\nt & di/ribution ( ! load diff]s s greatly t we c expect no s+le diagram1 drawn f ! comp>ative anatomy ( bridges1 to apply equally well to all ! cases met ) 9 ! comp>ative anatomy ( quadrup$s2 b nev]!less we h already ga9$ an insight into ! g5]al pr9ciples ( 8/ructural design0 9 ! quadrup$al bridge4 ,9 our la/ diagram ! upp] memb] ( ! cantilev] is "u #fii t5sion2 x is repres5t$ 9 ! quadrup$ by ! ligam5tum nu*ae on ! "o side ( ! cantilev]1 & by ! suprasp9\s ligam5ts ( ! dorsal v]tebrae on ! o!r4 ,! compression memb] is simil>ly repres5t$1 on bo? sides ( ! cantilev]1 by ! v]tebral column1 or r by ! bodies ( ! v]tebrae2 :ile ! web1 or 8fill+10 ( ! gird]s1 t is to say ! upright or slop+ memb]s :i* ext5d f "o flange to ! o!r1 is repres5t$ on ! "o h& by ! sp9es ( ! v]tebrae1 & on ! o!r h&1 by ! oblique int]sp9\s ligam5ts & muscles4 ,! high sp9es ov] ! quadrup$'s )]s are no o!r ?an ! high /ruts :i* rise ov] ! support+ pi]s 9 ! p>abolic gird]1 & correspond to ! position ( ! maximal b5d+-mom5ts4 ,! fact t ^! tall v]tebrae ( ! )]s usually slope backw>ds1 sometimes /eeply1 9 a quadrup$1 is easily & obvi\sly expla9$#fca4 ,= ea* v]tebra t5ds to act z a 8h+$ lev]10 & its sp9e1 act$ on by ! t5sions transmitt$ by ! ligam5ts on ei!r side1 takes up its position z ! diagonal ( ! p>allelogram ( =ces to :i* x is expos$4 ,x happ5s t 9 ^! comp>atively simple types ( cantilev] bridge ! :ole ( ! p>abolic curvature is transf]r$ to "o or o!r ( ! pr9cipal memb]s1 ei!r ! t5sion-memb] or ! compression-memb] z ! case may be4 ,b x is ( c\rse equally p]missible to h bo? memb]s curv$1 9 opposite directions4 ,?is1 ?\gh n exactly ! case 9 ! ,=? ,bridge1 is approximately s2 = "h ! ma9 compression-memb] is curv$ or ar*$1 & ! ma9 t5sion-memb] slopes d[nw>ds on ei!r side f its maximal height above ! pi]s4 ,9 %ort1 ! ,=? ,bridge is a ne>] approa* ?an ei!r ( ! o!r cantilev] bridges :i* we h #gjj illu/rat$ to ! plan ( ! quadrup$al skeleton2 = ! ma9 compression-memb] almo/ exactly recalls ! =m ( ! v]tebral column1 :ile ! ma9 t5sion-memb]1 ?\gh n s closely simil> to ! suprasp9\s & nu*al ligam5ts1 corresponds to ! plan ( ^! 9 a some:at simplifi$ =m4 ,illu/ration3 ,fig4 #cde4 ,a two-arm$ cantilev] ( ! ,=? ,bridge4 ,?ick l9es1 compression-memb]s 7bones72 ?9 l9es1 t5sion-memb]s 7ligam5ts74 ,we may n[ pass )\t difficulty f ! two-arm$ cantilev] support$ on a s+le pi]1 z x is 9 ea* sep>ate section ( ! ,=? ,bridge1 or z we h imag9$ x to be 9 ! =equ>t]s ( a horse1 to ! condition :i* actually exi/s 9 t quadrup$1 :]e a two-arm$ cantilev] has its load di/ribut$ ov] two sep>ate pi]s4 ,?is is n precisely :at an eng9e] calls a 8cont9u\s0 gird]1 = t t]m is appli$ to a gird] :i*1 z a cont9u\s /ructure1 crosses two or m spans1 :ile "h !re is only "o4 ,b nev]!less1 ?is gird] ,illu/ration3 ,fig4 #cdf4 is effectively cont9u\s f ! head to ! tip ( ! tail2 & at ea* po9t ( support 7,a & ,b7 x is subject$ to ! negative b5d+-mom5t due to ! ov]hang+ load on ea* ( ! project+ cantilev] arms ,,ah & ,,bt4 ,! diagram ( b5d+-mom5ts w 7accord+ to ! ord9>y conv5tions7 lie bel[ #gja ! base l9e 7because ! mom5ts are negative71 & mu/ take "s su* =m z t %[n 9 ! diagram3 = ! gird] mu/ suff] its greate/ b5d+ /ress n at ! c5tre1 b at ! two po9ts ( support ,a & ,b1 :]e ! mom5ts are measur$ by ! v]tical ord9ates4 ,x is pla9 t ?is figure only diff]s f a repres5tation ( two indep5d5t two-arm$ cantilev]s 9 ! fact t !re is no po9t midway 9 ! span :]e ! b5d+-mom5t vani%es1 b only a region betwe5 ! two pi]s 9 :i* its magnitude t5ds to dim9i%4 ,illu/ration3 ,fig4 #cdg4 ,/ress-diagram ( horse's backbone4 ,! diagram effects a graphic summation ( ! positive & negative mom5ts1 b its =m may assume v>i\s modifications accord+ to ! me?od ( graphic summation :i* we may *oose to adopt2 & x is obvi\s also t ! =m ( ! diagram may assume _m modifications ( detail accord+ to ! actual di/ribution ( ! load4 ,9 all cases ! ess5tial po9ts to be obs]v$ are ^!3 fir/ly t ! gird] :i* is to resi/ ! b5d+-mom5ts induc$ by ! load mu/ possess its two pr9cipal memb]s--an upp] t5sion-memb] or tie1 repres5t$ by ligam5t1 & a l[] compression-memb] repres5t$ by bone3 ^! memb]s be+ unit$ by a web repres5t$ by ! v]tebral sp9es ) _! int]sp9\s ligam5ts1 & be+ plac$ "o above ! o!r 9 ! ord] nam$ because ! mom5ts are negative2 secondly we obs]ve t ! dep? ( ! web1 or di/ance ap>t ( ! pr9cipal memb]s1--t is to say ! height ( ! v]tebral sp9es1--mu/ be proportional to ! b5d+-mom5t at ea* po9t along ! l5g? ( ! gird]4 ,9 ! case ( an animal c>ry+ two-?irds ( 8 weight ^u 8 =e-legs & only "o-?ird ^u 8 h9d-legs1 ! b5d+-mom5t diagram w be unsymmetrical1 aft] ! fa%ion ( ,fig4 #cdg1 ! v]tical ord9ate at ,a be+ ?rice ! height ( t at ,b4 #gjb ,on ! o!r h& ! ,d9osaur1 ) 8 light head & enorm\s tail w\ld give u a mom5t-diagram ) ! opposite k9d ( asymmetry1 ! greate/ b5d+ /ress be+ n[ f\nd ov] ! haun*es1 at ,b 7,fig4 #cdh74 ,a glance at ! skeleton ( ,diplodocus ,c>negii w %ew u ! high v]tebral sp9es ov] ! lo9s1 9 precise correspond5ce ) ! requirem5ts ( ?is diagram3 j z 9 ! horse1 "u ! opposite conditions ( load1 ! highe/ v]tebral sp9es are ^? ( ! )]s1 t is to say ^? ( ! po/]ior c]vical & ant]ior dorsal v]tebrae4 ,illu/ration3 ,fig4 #cdh4 ,/ress-diagram ( backbone ( ,d9osaur4 ,we h n[ n only dealt ) ! g5]al resemblance1 bo? 9 /ructure & 9 function1 ( ! quadrup$al backbone ) its associat$ ligam5ts to a d\ble-arm$ cantilev] gird]1 b we h begun to see h[ ! *>act]s ( ! v]tebral sy/em mu/ diff] 9 diff]5t quadrup$s1 accord+ to ! conditions impos$ by ! v>y+ di/ribution ( ! load3 & 9 p>ticul> h[ ! height ( ! v]tebral sp9es :i* con/itute ! web w be 9 a def9ite relation1 z reg>ds magnitude & position1 to ! b5d+-mom5ts induc$ !reby4 ,we %\ld require mu* detail$ in=mation z to ! actual weights ( ! sev]al p>ts ( ! body be=e we c\ld foll[ out quantitatively ! me*anical effici5cy ( ea* type ( skeleton2 b 9 an approximate way :at we h already le>nt w enable u to trace _m int]e/+ correspond5ces betwe5 /ructure & function 9 ?is p>ticul> "p ( comp>ative anatomy4 ,we mu/1 h[ev]1 be c>eful to note t ! great cantilev] sy/em is n ( necessity con/itut$ by ! v]tical column & its ligam5ts alone1 b t ! pelvis1 firmly unit$ z x is to ! sacral v]tebrae1 & /ret*+ backw>ds f> beyond ! acetabulum1 becomes an intr9sic "p ( ! sy/em2 & help+ 7z x does7 to c>ry ! load ( ! abdom9al visc]a1 #gjc con/itutes a great portion ( ! po/]ior cantilev] arm1 or ev5 its *ief portion 9 cases :]e ! size & weight ( ! tail are insignificant1 z is ! case 9 ! majority ( t]re/rial mammals4 ,we may also note "h1 t j z a bridge is (t5 a 8comb9$0 or composite /ructure1 exhibit+ a comb9ation ( pr9ciples 9 its con/ruction1 s 9 ! quadrup$ we h1 z x 71 ano!r gird] support$ by ! same pi]s to c>ry ! visc]a2 & consi/+ ( an inv]t$ p>abolic gird]1 ^: compression-memb] is aga9 con/itut$ by ! backbone1 its t5sion-memb] by ! l9e ( ! /]num & ! abdom9al muscles1 :ile ! ribs & int]co/al muscles play ! "p ( ! web or fill+4 ,a v few in/ances mu/ suffice to illu/rate ! *ief v>iations 9 ! load1 & !re=e 9 ! b5d+-mom5t diagram1 & !re=e also 9 ! plan ( con/ruction1 ( v>i\s quadrup$s4 ,b let u beg9 by sett+ =?1 9 a few cases1 ! actual weights :i* are borne by ! =e-limbs & ! h9d-limbs1 9 our quadrup$al bridge#fcb4 ,on ,on ,=e- ,h9d- on on ,gross weight4 feet feet ,=e- ,h9d- ton cwts4 cwts4 cwts4 feet4 feet4 ,camel 7,bactrian7 -- #adbe #ibe #de #fgc #cbg ,llama -- #bge #age #hge #ffg #ccc ,elephant 7,indian7 #a #aege #bje #adge #ehb #dah ,horse -- #hbe #dge #ce #egf #dbd ,horse 7l>ge ,clydesdale7 -- #aee #he #gj #edh #deb ,x w be obs]v$ t 9 all ^! animals ! load ^u ! =e-feet prepond]ates consid]ably ov] t ^u ! h9d1 ! prepond]ance be+ r great] 9 ! elephant ?an 9 ! horse1 & m>k$ly great] 9 ! camel & ! llama ?an 9 ! o!r two4 ,b :ile ^! weights are helpful & sugge/ive1 x is obvi\s t !y d n g ne>ly f> en\gh to give u a full insight into ! con/ructional diagram to :i* ! animals are con=m$4 ,= su* a purpose we %\ld #gjd require to weigh ! total load1 n 9 two portions1 b 9 _m2 & we %\ld also h to take close acc\nt ( ! g5]al =m ( ! animal1 ( ! relation betwe5 t =m & ! di/ribution ( ! load1 & ( ! actual directions ( ea* bone & ligam5t by :i* ! =ces ( compression & t5sion 7 transmitt$4 ,all ?is lies beyond u = ! pres5t2 b nev]!less we may consid]1 v briefly1 ! pr9cipal cases involv$ 9 our enquiry1 ( :i* ! above animals =m only a p>tial & prelim9>y illu/ration4 ,illu/ration3 ,fig4 #cdi4 ,/ress-diagram ( ,titano!rium4 7#a7 ,:]ev] we h a heavily load$ ant]ior cantilev] arm1 t is to say :5ev] ! head & neck repres5t a consid]able fraction ( ! :ole weight ( ! body1 we t5d to h l>ge b5d+-mom5ts ov] ! =e-legs1 & correspond+ly high sp9es ov] ! v]tebrae ( ! )]s4 ,?is is ! case 9 ! great majority ( f\r-foot$1 t]re/rial animals1 ! *ief exceptions be+ f\nd 9 animals ) comp>atively small heads b l>ge & heavy tails1 su* z ! anteat]s or ! ,d9osaurian reptiles1 & also 7v naturally7 9 animals su* z ! crocodile1 :]e ! 8bridge0 c sc>cely be said to be develop$1 = ! long heavy body sags d[n to re/ ^u ! gr\nd4 ,! case is suffici5tly exemplifi$ by ! horse1 & /ill m notably by ! /ag1 ! ox1 or ! pig4 ,x is illu/rat$ 9 ! accompany+ diagram ( ! conditions 9 ! great ext9ct ,titano!rium4 7#b7 ,9 ! elephant & ! camel we h simil> conditions1 b slightly modifi$4 ,9 bo? cases1 & especially 9 ! latt]1 ! weight on ! =e-qu>t]s is relatively l>ge2 & 9 bo? cases ! b5d+-mom5ts are all ! l>g]1 by reason ( ! l5g? & =w>d ext5sion ( ! camel's neck1 & ! =w>d #gje position ( ! heavy tusks ( ! elephant4 ,9 bo? cases ! dorsal sp9es are l>ge1 b !y d n /rike u z exceptionally s2 b 9 bo? cases1 & especially 9 ! elephant1 !y slope backw>ds 9 a m>k$ degree4 ,ea* sp9e1 z already expla9$1 mu/ 9 all cases assume ! position ( ! diagonal 9 ! p>allelogram ( =ces def9$ by ! t5sions act+ on x at its extremity2 = x con/itutes a 8h+$ lev]10 by :i* ! b5d+-mom5ts on ei!r side are automatically balanc$2 & x is pla9 t ! m ! sp9e slopes backw>ds ! m x indicates a relatively l>ge /ra9 ?r[n ^u ! great ligam5t ( ! neck1 & a relief ( /ra9 ^u ! m directly act+1 b weak]1 ligam5ts ( ! back & lo9s4 ,9 bo? cases1 ! b5d+-mom5ts w\ld seem to be m ev5ly di/ribut$ ov] ! region ( ! back ?an1 = in/ance1 9 ! /ag1 ) its light h9d-qu>t]s & heavy load ( antl]s3 & 9 bo? cases ! high 8gird]0 is consid]ably prolong$1 by an ext5sion ( ! tall sp9es backw>ds 9 ! direction ( ! lo9s4 ,:5 we come to su* a case z ! mammo?1 ) its imm5sely heavy & imm5sely elongat$ tusks1 we p]ceive at once t ! b5d+-mom5ts ov] ! =e-legs are n[ v sev]e2 & we see also t ! dorsal sp9es 9 ?is region are mu* m conspicu\sly elevat$ ?an 9 ! ord9>y elephant4 7#c7 ,9 ! case ( ! giraffe we h1 )\t d\bt1 a v heavy load ^u ! =e-legs1 ?\gh no weigh+s are at h& to def9e ! ratio2 b z f> z possible ?is disproportionate load w\ld seem to be reliev$1 by help ( a d[nw>d z well z backw>d ?ru/1 ?r\gh ! slop+ back1 to ! unusually l[ h9d-qu>t]s4 ,! dorsal sp9es ( ! v]tebrae are v high & /rong1 & ! :ole gird]-sy/em v p]fectly =m$4 ,! elevat$1 r ?an protrud+ position ( ! head less5s ! ant]ior b5d+-mom5t z f> z possible2 b x leads to a /rong compressional /ress transmitt$ almo/ directly d[nw>ds ?r\gh ! neck3 9 correlation ) :i* we obs]ve t ! bodies ( ! c]vical v]tebrae are exceptionally l>ge & /rong & /eadily increase 9 size & /r5g? f ! head d[nw>ds4 7#d7 ,9 ! kang>oo1 ! =e-limbs are entirely reliev$ ( _! load1 & accord+ly ! tall sp9es ov] ! )]s1 :i* #gjf 7 s conspicu\s 9 all heavy-head$ quadrup$s1 h n[ completely vani%$4 ,! creature has become bip$al1 & body & tail =m ! extremities ( a s+le balanc$ cantilev]1 ^: maximal b5d+-mom5ts are m>k$ by /rong1 high lumb> & sacral v]tebrae1 & by iliac bones ( peculi> =m & exceptional /r5g?4 ,precisely ! same condition is illu/rat$ 9 ! ,iguanodon1 & bett] /ill by reason ( ! great bulk ( ! creature1 & ( ! heavy load :i* falls to be support$ by ! great cantilev] & by ! h9d-legs :i* =m its pi]s4 ,! long & heavy body & neck require a balance-weight 7z 9 ! kang>oo7 9 ! =m ( a long heavy tail4 ,& ! d\ble-arm$ cantilev]1 s con/itut$1 %ews a beautiful p>abolic curvature 9 ! grad$ heights ( ! :ole s]ies ( v]tebral sp9es1 :i* rise to a maximum ov] ! haun*es & die away sl[ly t[>ds ! neck & ! tip ( ! tail4 7#e7 ,9 ! case ( "s ( ! great ,am]ican fossil reptiles1 su* z ,diplodocus1 x has always be5 a m or less disput$ "q :e!r or n !y assum$1 l ,iguanodon1 an erect1 bip$al attitude4 ,9 all ( ^! we see an elongat$ pelvis1 &1 9 /ill m m>k$ degree1 we see elevat$ sp9\s processes ( ! v]tebrae ov] ! h9d-limbs2 9 all ( !m we h a long heavy tail1 & 9 mo/ ( !m we h a m>k$ r$uction 9 size & weight bo? ( ! =e-limb & ( ! head itself4 ,! great size ( ^! animals is n ( itself a pro( aga9/ ! erect attitude2 because x might well h be5 accompani$ by an aquatic or p>tially subm]g$ habitat1 & ! cru%+ /ress ( ! creature's huge bulk proportionately reliev$4 ,b we mu/ consid] ea* su* case 9 ! :ole light ( its own evid5ce2 & x is easy to see t1 j z ! quadrup$al mammal may c>ry ! great] "p b n all ( its weight ^u its =e-limbs1 s a heavy-tail$ reptile may c>ry ! great] "p ^u its h9d-limbs1 )\t ?is process go+ s f> z to relieve its =e-limbs ( all weight :atsoev]4 ,?is w\ld seem to be ! case 9 su* a =m z ,diplodocus1 & also 9 ,/egosaurus1 ^: re/oration by ,m>% is d\btless sub/antially correct#fcc4 ,! =e-limbs1 #gjg ?\gh comp>atively small1 are obvi\sly fa%ion$ = support1 b ! weight :i* !y h to c>ry is f> less ?an t :i* ! h9d-limbs be>4 ,! head is small & ! neck %ort1 :ile on ! o!r h& ! h9d-qu>t]s & ! tail are big & massive4 ,! backbone b5ds into a great1 d\ble-arm$ cantilev]1 culm9at+ ov] ! pelvis & ! h9d-limbs1 & "h furni%$ ) its highe/ & /ronge/ sp9es to sep>ate ! t5sion-memb] f ! compression-memb] ( ! gird]4 ,! =e-legs =m a second>y support+ pi] to ?is great cantilev]1 ! great] "p ( ^: weight is pois$ ^u ! h9d-limbs alone4 ,illu/ration3 ,fig4 #cej4 ,diagram ( ,/egosaurus4 7#f7 ,9 a bird1 su* z an o/ri* or a common f[l1 ! bip$al habit necessitates ! balanc+ ( ! load ^u a s+le d\ble-arm$ cantilev]-gird]1 j z 9 ! ,iguanodon & ! kang>oo1 b ! con/ruction is effect$ 9 a some:at diff]5t way4 ,! great heavy tail has entirely disappe>$2 b1 ?\gh f ! skeleton alone x w\ld seem t ne>ly all ! bulk ( ! animal lay 9 front ( ! h9d-limbs1 yet 9 ! liv+ bird we c easily p]ceive t ! great weight ( ! abdom9al organs lies susp5d$ beh9d ! socket = ! ?igh-bone1 & s hangs f ! po/]ior lev]-arm ( ! cantilev]1 balanc+ ! head & neck & ?orax ^: comb9$ weight hangs f #gjh ! ant]ior arm4 ,! great cantilev] gird] appe>s1 accord+ly1 balanc$ ov] ! h9d-legs4 ,x is n[ con/itut$ 9 "p by ! po/]ior dorsal or lumb> v]tebrae1 all traces ( special elevation hav+ disappe>$ f ! ant]ior dorsals2 b ! great] "p ( ! gird] is made up ( ! great iliac bones1 plac$ side by side1 & gripp+ firmly ! sacral v]tebrae1 (t5 almo/ to ! ext9ction ( ^! latt]4 ,9 ! =m ( ^! iliac bones1 ! ar*$ curvature ( _! upp] bord]1 9 _! elongation =e-&-aft to ov]hang bo? ways _! support+ pi]1 & 9 ! co9cid5ce ( _! greate/ height ) ! m$ian l9e ( support ov] ! c5tre ( gravity1 we recognise all ! *>act]i/ic prop]ties ( ! typical balanc$ cantilev]#fcd4 7#g7 ,we f9d a highly important coroll>y 9 ! case ( aquatic animals4 ,= "h ! effect ( gravity is neutralis$2 we h nei!r pi]s nor cantilev]s2 & we f9d accord+ly 9 all aquatic mammals ( :atsoev] gr\p--:ales1 seals or sea-c[s--t ! high ar*$ v]tebral sp9es ov] ! )]s1 or correspond+ /ructures ov] ! h9d-limbs1 h bo? entirely disappe>$4 ,j z ! cantilev] gird] t5d$ to become obsolete 9 ! aquatic mammal s does x t5d to weak5 & disappe> 9 ! aquatic bird4 ,!re is a v m>k$ contra/ betwe5 ! high-ar*$ /rongly-built pelvis 9 ! o/ri* or ! h51 & ! long1 ?91 comp>atively /raight & weakly bone :i* repres5ts x 9 a div]1 a grebe or a p5gu94 ,b 9 ! aquatic mammal1 su* z a :ale or a dolph9 7& n less s 9 ! aquatic bird71 /iffness mu/ be ensur$ 9 ord] to enable ! muscles to act aga9/ ! resi/ance ( ! wat] 9 ! act ( swimm+2 & accord+ly nature mu/ provide aga9/ b5d+-mom5ts irrespective ( gravity4 ,9 ! dolph91 at any rate z reg>ds its tail end1 ! conditions w be n v diff]5t f ^? ( a column or beam ) fix$ ends1 9 :i*1 "u deflexion1 !re w be two po9ts ( contr>y flexure1 z at ,c1 ,d1 9 ,fig4 #cea4 #gji ,illu/ration3 ,fig4 #cea4 ,"h1 betwe5 ,c & ,d we h a v>y+ b5d+-mom5t1 repres5t$ by a cont9u\s curve ) its maximal elevation midway betwe5 ! po9ts ( inflexion4 ,& correspond+ly1 9 our dolph91 we h a cont9u\s s]ies ( high dorsal sp9es1 ris+ to a maximum ab\t ! middle ( ! animal's body1 & fall+ to nil at "s di/ance f ! end ( ! tail4 ,x is _! bus9ess 7z usual7 to keep ! t5sion-memb]1 repres5t$ by ! /rong suprasp9\s ligam5ts1 wide ap>t f ! compression-memb]1 :i* is z usual repres5t$ by ! backbone itself4 ,b 9 our diagram we see t on ! fur!r side ( ,c & ,d we h a negative curve ( b5d+-mom5ts1 or b5d+-mom5ts 9 a contr>y direction4 ,)\t inquir+ h[ ^! /resses are precisely met t[>ds ! dolph9's head 7:]e ! coalesc$ c]vical v]tebrae sugge/ !mselves z a p>tial explanation71 we see at once t t[>ds ! tail !y are met by ! /rong s]ies ( *evron-bones1 :i* 9 ! caudal region1 :]e tall dorsal sp9es are no long] ne$$1 take _! place bel[ ! v]tebrae1 9 precise correspond5ce ) ! b5d+-mom5t diagram4 ,9 _m cases o!r ?an ^! aquatic ones1 :5 we h to deal ) animals ) long & heavy tails 7l ! ,iguanodon & ! kang>oo ( :i* we h already spok571 we are apt to meet ) simil>1 ?\gh usually %ort] *evron-bones2 & 9 all ^! cases we may see )\t difficulty t a negative b5d+-mom5t is !re to be resi/$4 ,9 ! dolph9 we may f9d a good illu/ration ( ! fact t n only is x necess>y to provide = rigidity 9 ! v]tical direction1 b also 9 ! horizontal1 :]e a t5d5cy to b5d+ mu/ be resi/$ on ei!r side4 ,?is function is effect$ 9 "p by ! ribs ) _! associat$ muscles1 b !y ext5d b a little way & _! efficacy = ?is purpose c be b small4 ,we h1 h[ev]1 beh9d ! region ( ! ribs & on ei!r side ( ! backbone a /rong s]ies ( elongat$ & flatt5$ transv]se processes1 =m+ a web = ! support ( a t5sion-memb] 9 ! usual =m ( ligam5t1 & s play+ a "p precisely analog\s to t p]=m$ by ! dorsal sp9es 9 ! same #gaj animal4 ,9 an ord9>y fi%1 su* z a cod or a haddock1 we see precisely ! same ?+3 ! backbone is /iff5$ by ! indisp5sable help ( its ?ree s]ies ( ligam5t-connect$ processes1 ! dorsal & ! two transv]se s]ies4 ,& "h we see 7z we see p>tly also among ! :ales71 t ^! ?ree s]ies ( processes1 or /ruts1 t5d to be arrang$ well-nigh at equal angles1 ( #abj1 ) "o ano!r1 giv+ ! greate/ & mo/ uni=m /r5g? ( :i* su* a sy/em is capable4 ,on ! o!r h&1 9 a flat fi%1 su* z a plaice1 :]e f ! natural mode ( progression x is necess>y t ! backbone %\ld be flexible 9 "o direction :ile /iff5$ 9 ano!r1 we f9d ! :ole outl9e ( ! fi% comp>able to t ( a d\ble b[/r+ gird]1 ! compression-memb] be+ 7z usual7 ! backbone1 ! t5sion-memb] on ei!r side be+ con/itut$ by ! int]sp9\s ligam5ts & muscles1 :ile ! web or fill+ is v beautifully repres5t$ by ! long & ev5ly grad$ sp9es1 :i* spr+ symmetrically f opposite sides ( ea* individual v]tebra4 ,! ma9 result at :i* we h n[ arriv$1 9 reg>d to ! con/ruction ( ! v]tebral column & its associat$ p>ts1 is t we may look ^u x z a c]ta9 type ( gird]1 ^: dep?1 z we _c help see+1 is ev]y:]e v ne>ly proportional to ! height ( ! correspond+ ord9ate 9 ! diagram ( mom5ts3 j z x is 9 ! gird] ( a cantilev] bridge z design$ by a mod]n eng9e]4 ,9 %ort1 aft] ! n9ete5? or tw5tie? c5tury eng9e] has done 8 be/ 9 fram+ ! design ( a big cantilev]1 he may f9d t "s ( 8 be/ ideas bad1 s to speak1 be5 anticipat$ ages ago 9 ! fabric ( ! great saurians & ! l>g] mammals4 ,b x is possible t ! mod]n eng9e] might be dispos$ to criticise ! skeleton gird] at two or ?ree po9ts2 & 9 p>ticul> he might ?9k ! gird]1 z we see x = in/ance 9 ,diplodocus or ,/egosaurus1 n deep en\gh = c>ry+ ! animal's enorm\s weight ( "s tw5ty tons4 ,if we adopt a mu* great] dep? 7or ratio ( dep? to l5g?7 z 9 ! mod]n cantilev]1 we %all greatly increase ! /r5g? ( ! /ructure2 b at ! same "t we %\ld greatly increase its rigidity1 & #gaa ?is is precisely :at1 9 ! circum/ances ( ! case1 x w\ld seem t nature is b\nd to avoid4 ,we ne$ n suppose t ! great saurian 0 by any means active & limb]2 b a c]ta9 am\nt ( activity & flexibility he 0 b\nd to h1 & 9 a ?\s& ways he w\ld f9d ! ne$ ( a backbone t %\ld be flexible z well z /rong4 ,n[ ?is op5s up a new aspect ( ! matt] & is ! beg9n+ ( a long1 long /ory1 = 9 e direction ?is d\ble requirem5t ( /r5g? & flexibility imposes new conditions ^u our design4 ,to repres5t all ! correlat$ quantities we %\ld h to con/ruct n only a diagram ( mom5ts b also a diagram ( ela/ic deflexion & its s-call$ 8curvature02 & ! eng9e] w\ld want to "k some?+ m ab\t ! mat]ial ( ! ligam5t\s t5sion-memb]--its modulus ( ela/icity 9 direct t5sion1 its ela/ic limit1 & its safe work+ /ress4 ,9 v>i\s ways our /ructural problem is beset by 8limit+ conditions40 ,n only mu/ rigidity be associat$ ) flexibility1 b also /ability mu/ be ensur$ 9 v>i\s positions & attitudes2 & ! prim>y function ( support or weight-c>ry+ mu/ be comb9$ ) ! provision ( po9ts d'appui = ! muscles conc]n$ 9 locomotion4 ,we _c hope to arrive at a num]ical or quantitative solution ( ?is complicate problem1 b we h f\nd x possible to trace x out 9 "p t[>ds a qualitative solution4 ,& speak+ broadly we may c]ta9ly say t 9 ea* case ! problem has be5 solv$ by nature h]self1 v mu* z %e solves ! difficult problems ( m9imal areas 9 a sy/em ( soap-bubbles2 s t ea* animal is fitt$ ) a backbone adapt$ to 8 own individual ne$s1 or 79 o!r words7 correspond+ exactly to ! mean resultant ( ! /resses to :i* z a me*anical sy/em x is expos$4 ,?r\gh\t ?is %ort discussion ( ! pr9ciples ( con/ruction1 limit$ to "o "p ( ! skeleton1 we see ! same g5]al pr9ciples at "w :i* we recognise 9 ! plan & con/ruction ( an individual bone4 ,t is to say1 we see a t5d5cy = mat]ial to be laid d[n j 9 ! l9es ( /ress1 & s z to evade !reby ! di/ortions & disruptions due to %e>4 ,9 ^! ph5om5a !re lies a def9ite law ( gr[?1 #gab :atev] its ultimate expression or explanation may come to be4 ,let u n press ei!r argum5t or hypo!sis too f>3 b be cont5t to see t skeletal =m1 z br\ght ab\t by gr[?1 is to a v l>ge ext5t det]m9$ by me*anical consid]ations1 & t5ds to manife/ itself z a diagram1 or reflect$ image1 ( me*anical /ress4 ,if we fail1 ow+ to ! imm5se complexity ( ! case1 to unravel all ! ma!matical pr9ciples involv$ 9 ! con/ruction ( ! skeleton1 we yet ga9 some?+1 & n a little1 by apply+ ?is me?od to ! famili> objects ( our anatomical /udy3 obvia conspicimus1 nubem pell5te ma!si#fce4 ,be=e we leave ?is subject ( me*anical adaptation1 let u dwell once m = a mom5t ^u ! consid]ations :i* arise f our conception ( a field ( =ce1 or field ( /ress1 9 :i* t5sion & compression 7= in/ance7 are inevitably comb9$1 & are met by ! mat]ials naturally fitt$ to resi/ !m4 ,x has be5 rem>k$ ov] & ov] aga9 h[ h>moni\sly ! :ole organism hangs toge!r1 & h[ ?r\gh\t its fabric "o "p is relat$ & fitt$ to ano!r 9 /rictly functional correlation4 ,b ?is conception1 ?\gh nev] d5i$1 is sometimes apt to be =gott5 9 ! c\rse ( t process ( m & m m9ute analysis by :i*1 = simplicity's sake1 we seek to unravel ! intricacies ( a complex organism4 ,we t5d1 z we analyse a ?+ into its p>ts or into its prop]ties1 to magnify ^!1 to exagg]ate _! app>5t indep5d5ce1 & to hide f ourselves 7at lea/ = a "t7 ! ess5tial integrity & individuality ( ! composite :ole4 ,we divide ! body into its organs1 ! skeleton into its bones1 z 9 v mu* ! same fa%ion we make a subjective analysis ( ! m9d1 accord+ to ! tea*+s ( psy*ology1 into compon5t factors3 b we "k v well t judgm5t & k1 c\rage or g5tl5ess1 love or fe>1 h no sep>ate exi/5ce1 b are someh[ m]e manife/ations1 or imag9>y co-effici5ts1 ( a mo/ complex integral4 ,& likewise1 z biologi/s1 we may g s f> z to say t ev5 ! bones !mselves are only 9 a limit$ & ev5 a deceptive s5se1 sep>ate & individual ?+s4 ,! skeleton beg9s z a cont9uum1 & a cont9uum x rema9s all life long4 ,! ?+s t l9k bone ) bone1 #gac c>tilage1 ligam5ts1 membranes1 are fa%ion$ out ( ! same primordial tissue1 & come into be+ p>i passu1 ) ! bones !mselves4 ,! entire fabric has its s(t p>ts & its h>d1 its rigid & its flexible p>ts2 b until we disrupt & dismemb] its bony1 gri/ly & fibr\s p>ts1 "o f ano!r1 x exi/s simply z a 8skeleton10 z "o integral & individual :ole4 ,a bridge 0 once ^u a "t a loose heap ( pill>s & rods & rivets ( /eel4 ,b ! id5tity ( ^! is lo/1 j z if !y 7 fus$ into a solid mass1 :5 once ! bridge is built2 _! sep>ate functions are only to be recognis$ & analys$ 9 s f> z we c analyse ! /resses1 ! t5sions & ! pressures1 :i* affect ?is "p ( ! /ructure or t2 & ^! =ces are n !mselves sep>ate entities1 b are ! resultants ( an analysis ( ! :ole field ( =ce4 ,moreov] :5 ! bridge is brok5 x is no long] a bridge1 & all its /r5g? is gone4 ,s is x precisely ) ! skeleton4 ,9 x is reflect$ a field ( =ce3 & keep+ pace1 z x 71 9 action & int]action ) ?is field ( =ce1 ! :ole skeleton & e "p !re(1 d[n to ! m9ute intr9sic /ructure ( ! bones !mselves1 is relat$ 9 =m & 9 position to ! l9es ( =ce1 to ! resi/ances x has to enc\nt]2 = by "o ( ! my/]ies ( biology1 resi/ance begets resi/ance1 & :]e pressure falls !re gr[? spr+s up 9 /r5g? to meet x4 ,&1 pursu+ ! same tra9 ( ?\ght1 we see t all ?is is true n ( ! skeleton alone b ( ! :ole fabric ( ! body4 ,muscle & bone1 = in/ance1 are insep>ably associat$ & connect$2 !y are m\ld$ "o ) ano!r2 !y come into be+ toge!r1 & act & react toge!r#fcf4 ,we may /udy !m ap>t1 b x is z a concession to our weakness & to ! n>r[ outlook ( our m9ds4 ,we see1 dimly p]haps1 b yet ) all ! assurance ( conviction1 t betwe5 muscle & bone !re c be no *ange 9 ! "o b x is correlat$ ) *anges 9 ! o!r2 t ?r\gh & ?r\gh !y are l9k$ 9 indissoluble association2 t !y are only sep>ate entities #gad 9 ?is limit$ & subord9ate s5se1 t !y are p>ts ( a :ole :i*1 :5 x loses its composite integrity1 ceases to exi/4 ,! biologi/1 z well z ! philosoph]1 le>ns to recognise t ! :ole is n m]ely ! sum ( its p>ts4 ,x is ?is1 & mu* m ?an ?is4 ,= x is n a bundle ( p>ts b an organisation ( p>ts1 ( p>ts 9 _! mutual arrangem5t1 fitt+ "o ) ano!r1 9 :at ,ari/otle calls 8a s+le & indivisible pr9ciple ( unity02 & ?is is no m]ely metaphysical conception1 b is 9 biology ! fundam5tal tru? :i* lies at ! basis ( ,ge(froy's 7or ,goe!'s7 law ( 8comp5sation10 or 8balancem5t ( gr[?40 ,nev]!less ,d>w9 f\nd no difficulty 9 believ+ t 8natural selection w t5d 9 ! long run to r$uce any "p ( ! organisation1 z soon z1 ?r\gh *ang$ habits1 x becomes sup]flu\s3 )\t by any means caus+ "s o!r "p to be l>gely develop$ 9 a correspond+ degree4 ,& conv]sely1 t natural selection may p]fectly well succe$ 9 l>gely develop+ an organ )\t requir+ z a necess>y comp5sation ! r$uction ( "s adjo9+ "p#fcg40 ,?is view has be5 develop$ into a doctr9e ( ! 8indep5d5ce ( s+le *>act]s0 7n to be confus$ ) ! g]m9al 8unit *>act]s0 ( ,m5delism71 especially by ! palaeontologi/s4 ,?us ,osborn ass]ts a 8pr9ciple ( h]$it>y correlation10 comb9$ ) a 8pr9ciple ( h]$it>y sep>ability :]eby ! body is a colony1 a mosaic1 ( s+le individual & sep>able *>act]s#fch40 ,i _c ?9k t !re is m ?an a small elem5t ( tru? 9 ?is doctr9e4 ,z ,kant said1 8die ,ursa*e d] ,art d] ,exi/5z bei j$em ,!ile e9es leb5d5 ,krp]s i/ im ,ganz5 en?alt540 ,&1 accord+ to ! tr5d or aspect ( our ?\ght1 we may look ^u ! co-ord9at$ p>ts1 n[ z relat$ & fitt$ to ! end or function ( ! :ole1 & n[ z relat$ to or result+ f ! physical causes inh]5t 9 ! entire sy/em ( =ces to :i* ! :ole has be5 expos$1 & "u ^: influ5ce x has come into be+#fci4 #gae ,x w\ld seem to me t ! me*anical pr9ciples & ph5om5a :i* we h dealt ) 9 ?is *apt] are ( no small importance to ! morphologi/1 all ! m :5 he is incl9$ to direct 8 /udy ( ! skeleton exclusively to ! problem ( phylog5y2 & especially :51 accord+ to ! me?ods ( mod]n comp>ative morphology1 he is apt to take ! skeleton to pieces1 & to draw f ! comp>ison ( a s]ies ( scapulae1 hum]i1 or individual v]tebrae1 conclusions z to ! desc5t & relation%ip ( ! animals to :i* !y belong4 ,x w\ld1 ,i d>e say1 be a gross exagg]ation to see 9 e bone no?+ m ?an a resultant ( imm$iate & direct physical or me*anical conditions2 = to d s w\ld be to d5y ! exi/5ce1 9 ?is connection1 ( a pr9ciple ( h]$ity4 ,& ?\gh ,i h tri$ ?r\gh\t ?is book to lay emphasis on ! direct action ( causes o!r ?an h]$ity1 9 %ort to circumscribe ! employm5t ( ! latt] z a work+ hypo!sis 9 morphology1 !re c /ill be no "q :atsoev] b t h]$ity is a va/ly important z well z a my/]i\s ?+2 x is "o ( ! great factors 9 biology1 h[ev] we may attempt to figure to ourselves1 or h[soev] we may fail ev5 to imag9e1 its und]ly+ physical explanation4 ,b ,i ma9ta9 t x is no less an exagg]ation if we t5d to neglect ^! direct physical & me*anical modes ( causation altoge!r1 & to see 9 ! *>act]s ( a bone m]ely ! results ( v>iation & ( h]$ity1 & to tru/1 9 consequ5ce1 to ^? *>act]s z a sure & c]ta9 & unque/ion$ guide to aff9ity & phylog5y4 ,comp>ative anatomy has its physiological side1 :i* fill$ m5's m9ds 9 ,john ,hunt]'s day1 & 9 ,ow5's day2 x has its #gaf classificatory & phylog5etic aspect1 :i* has all b fill$ m5's m9ds dur+ ! la/ c\ple ( g5]ations2 & we c lose sight ( nei!r aspect )\t risk ( error & misconception4 ,x is c]ta9 t ! "q ( phylog5y1 always difficult1 becomes especially s 9 cases :]e a great *ange ( physical or me*anical conditions has come ab\t1 & :]e accord+ly ! physical & physiological factors 9 connection ) *ange ( =m are b\nd to be l>ge4 ,to discuss ^! que/ions at l5g? w\ld be to ent] on a discussion ( ,lam>ck's philosophy ( biology1 & ( _m o!r ?+s besides4 ,b let u take "o s+le illu/ration4 ,! aff9ities ( ! :ales con/itute1 z w be readily admitt$1 a v h>d problem 9 phylog5etic classification4 ,we "k n[ t ! ext9ct ,zeuglodons are relat$ to ! old ,creodont c>nivores1 & !reby 7?\gh di/antly7 to ! seals2 & x is suppos$1 b x is by no means s c]ta91 t 9 turn !y are to be consid]$ z repres5t+1 or z alli$ to1 ! ance/ors ( ! mod]n too!d :ales#fdj4 ,! pro( ( any su* a cont5tion becomes1 to my m9d1 extraord9>ily difficult & complicat$2 & ! argum5ts commonly us$ 9 su* cases may be said 79 ,bacon's phrase7 to allure1 r ?an to extort ass5t4 ,?\gh ! ,zeuglodonts 7 aquatic animals1 we d n "k1 & we h no "r to suppose or to assume1 t !y swam aft] ! fa%ion ( a :ale 7any m ?an ! seal does71 t !y div$ l a :ale1 & leap$ l a :ale4 ,b ! fact t ! :ale does ^! ?+s1 & ! way 9 :i* he does !m1 is reflect$ 9 _m p>ts ( 8 skeleton--p]haps m or less 9 all3 s mu* s t ! l9es ( /ress :i* ^! actions impose are ! v plan & work+-diagram ( great "p ( 8 /ructure4 ,t ! ,zeuglodon has a scapula l t ( a :ale is to my m9d no necess>y argum5t t he is ak9 by blood-relation%ip to a :ale3 t 8 dorsal v]tebrae are v diff]5t f a :ale's is no conclusive argum5t t #gag su* blood-relation%ip is lack+4 ,! =m] fact goes a long way to prove t he us$ 8 flipp]s v mu* z a :ale does2 ! latt] goes /ill f>!r to prove t 8 g5]al movem5ts & equilibrium 9 ! wat] 7 totally diff]5t4 ,! :ale may be desc5d$ f ! ,c>nivora1 or might = t matt]1 z an old] s*ool ( naturali/s believ$1 be desc5d$ f ! ,ungulates2 b :e!r or no1 we ne$ n expect to f9d 9 him ! scapula1 ! pelvis or ! v]tebral column ( ! lion or ( ! c[1 = x w\ld be physically impossible t he c\ld live ! life he does ) any "o ( !m4 ,9 %ort1 :5 we hope to f9d ! miss+ l9ks betwe5 a :ale & 8 t]re/rial ance/ors1 x mu/ be n by means ( conclusions drawn f a scapula1 an axis1 or ev5 f a too?1 b by ! discov]y ( =ms s int]m$iate 9 _! g5]al /ructure z to indicate an organisation &1 ipso facto1 a mode ( life1 int]m$iate betwe5 ! t]re/rial & ! ,cetacean =m4 ,!re is no valid syllogism to ! effect t ,a has a flat curv$ scapula l a seal's1 & ,b has a flat1 curv$ scapula l a seal's3 & !re=e ,a & ,b are relat$ to ! seals & to ea* o!r2 x is m]ely a flagrant case ( an 8undi/ribut$ middle40 ,b !re is validity 9 an argum5t t ,b %ews 9 its g5]al /ructure1 ext5d+ ov] ?is bone & t bone1 resemblances bo? to ,a & to ! seals3 & t !re=e he may be presum$ to be relat$ to bo?1 9 8 h]$it>y habits ( life & 9 actual k9%ip by blood4 ,x is cognate to ?is argum5t t 7z e palaeontologi/ kn[s7 we f9d clues to aff9ity m easily1 t is to say ) less confusion & p]plexity1 9 c]ta9 /ructures ?an 9 o!rs4 ,! deep-seat$ rhy?ms ( gr[? :i*1 z ,i v5ture to ?9k1 are ! *ief basis ( morphological h]$ity1 br+ ab\t simil>ities ( =m1 :i* endure 9 ! abs5ce ( conflict+ =ces2 b a new sy/em ( =ces1 introduc$ by alt]$ environm5t & habits1 imp++ on ^? p>ticul> p>ts ( ! fabric :i* lie )9 ?is p>ticul> field ( =ce1 w assur$ly n be long ( manife/+ itself 9 notable & inevitable modifications ( =m4 ,& if ?is be really s1 x w fur!r imply t modifications ( =m w t5d to manife/ !mselves1 n s mu* 9 small & isolat$ ph5om5a1 9 ?is "p ( ! fabric or 9 t1 9 a scapula = in/ance or a hum]us3 b r 9 #gah "s sl[1 g5]al1 & m or less uni=m or grad$ modification1 spread ov] a numb] ( correlat$ p>ts1 & at times ext5d+ ov] ! :ole1 or ov] great portions1 ( ! body4 ,:e!r any su* g5]al t5d5cy to widespread & correlat$ trans=mation exi/s1 we %all attempt to discuss 9 ! foll[+ *apt]4 #gai ,,*apt] ,,xvii ,,on ,,! ,,!ory ,,( ,,trans=mations1 ,,or ,,! ,,comp>ison ,,( ,,relat$ ,,=ms#fda ,9 ! =ego+ *apt]s ( ?is book we h attempt$ to /udy ! int]-relations ( gr[? & =m1 & ! "p :i* c]ta9 ( ! physical =ces play 9 ?is complex int]action2 &1 z "p ( ! same enquiry1 we h tri$ 9 comp>atively simple cases to use ma!matical me?ods & ma!matical t]m9ology 9 ord] to describe & def9e ! =ms ( organisms4 ,we h le>n$ 9 s do+ t our own /udy ( organic =m1 :i* we call by ,goe!'s "n ( ,morphology1 is b a portion ( t wid] ,sci5ce ( ,=m :i* deals ) ! =ms assum$ by matt] "u all aspects & conditions1 &1 9 a /ill wid] s5se1 ) =ms :i* are !oretically imag9able4 ,! /udy ( =m may be descriptive m]ely1 or x may become analytical4 ,we beg9 by describ+ ! %ape ( an object 9 ! simple words ( common spee*3 we end by def9+ x 9 ! precise language ( ma!matics2 & ! "o me?od t5ds to foll[ ! o!r 9 /rict sci5tific ord] & hi/orical cont9uity4 ,?us1 = in/ance1 ! =m ( ! e>?1 ( a ra9drop or a ra9b[1 ! %ape ( ! hang+ *a91 or ! pa? ( a /one ?r[n up into ! air1 may all be describ$1 h[ev] inadequately1 9 common words2 b :5 we h le>n$ to compreh5d & to def9e ! sph]e1 ! cat5>y1 or ! p>abola1 we h made a wond]ful & p]haps a manifold advance4 ,! ma!matical def9ition ( a 8=m0 has a quality ( precision :i* 0 q lack+ 9 our e>li] /age ( m]e description2 x is express$ 9 few words1 or 9 /ill brief] symbols1 & ^! #gbj words or symbols are s pregnant ) mean+ t ?\ght itself is economis$2 we are br\ght by means ( x 9 t\* ) ,galileo's aphorism 7z old z ,plato1 z old z ,py?agoras1 z old p]haps z ! wisdom ( ! ,egyptians71 t 8! ,book ( ,nature is writt5 9 *>act]s ( ,geometry40 ,next1 we soon rea* ?r\gh ma!matical analysis to ma!matical syn!sis2 we discov] homologies or id5tities :i* 7 n obvi\s be=e1 & :i* our descriptions obscur$ r ?an reveal$3 z = in/ance1 :5 we le>n t1 h[ev] we hold our *a91 or h[ev] we fire our bullet1 ! cont\r ( ! "o or ! pa? ( ! o!r is always ma!matically homolog\s4 ,la/ly1 & ?is is ! greate/ ga9 ( all1 we pass quickly & easily f ! ma!matical conception ( =m 9 its /atical aspect to =m 9 its dynamical relations3 we pass f ! conception ( =m to an und]/&+ ( ! =ces :i* gave rise to x2 & 9 ! repres5tation ( =m & 9 ! comp>ison ( k9dr$ =ms1 we see 9 ! "o case a diagram ( =ces 9 equilibrium1 & 9 ! o!r case we disc]n ! magnitude & ! direction ( ! =ces :i* h suffic$ to conv]t ! "o =m into ! o!r4 ,"h1 s9ce a *ange ( mat]ial =m is only effect$ by ! movem5t ( matt]1 we h once aga9 ! support ( ! s*oolman's & ! philosoph]'s axiom1 8,ignorato motu1 ignoratur ,natura40 ,9 ! morphology ( liv+ ?+s ! use ( ma!matical me?ods & symbols has made sl[ progress2 & !re are v>i\s reasons = ?is failure to employ a me?od ^: advantages are s obvi\s 9 ! inve/igation ( o!r physical =ms4 ,to beg9 )1 !re w\ld seem to be a psy*ological reason ly+ 9 ! fact t ! /ud5t ( liv+ ?+s is by nature & tra9+ an obs]v] ( concrete objects & ph5om5a1 & ! habit ( m9d :i* he possesses & cultivates is ali5 to t ( ! !oretical ma!matician4 ,b ?is is by no means ! only reason2 = 9 ! k9dr$ subject ( m9]alogy1 = in/ance1 cry/als 7 /ill treat$ 9 ! days ( ,l9naeus z :olly )9 ! prov9ce ( ! naturali/1 & 7 describ$ by him aft] ! simple me?ods 9 use = animals & plants3 b z soon z ,hay %[$ ! application ( ma!matics to #gba ! description & classification ( cry/als1 8 me?ods 7 imm$iately adopt$ & a new sci5ce came into be+4 ,a l>ge "p ( ! neglect & suspicion ( ma!matical me?ods 9 organic morphology is due 7z we h p>tly se5 9 our op5+ *apt]7 to an +ra9$ & deep-seat$ belief t ev5 :5 we seem to disc]n a regul> ma!matical figure 9 an organism1 ! sph]e1 ! hexagon1 or ! spiral :i* we s recognise m]ely resembles1 b is nev] entirely expla9$ by1 its ma!matical analogue2 9 %ort1 t ! details 9 :i* ! figure diff]s f its ma!matical prototype are m important & m int]e/+ ?an ! features 9 :i* x agrees1 & ev5 t ! peculi> ae/hetic pleasure ) :i* we reg>d a liv+ ?+ is someh[ b\nd up ) ! dep>ture f ma!matical regul>ity :i* x manife/s z a peculi> attribute ( life4 ,?is view seems to me to involve a misappreh5sion4 ,!re is no su* ess5tial diff]5ce betwe5 ^! ph5om5a ( organic =m & ^? :i* are manife/$ 9 portions ( inanimate matt]#fdb4 ,no *a9 hangs 9 a p]fect cat5>y & no ra9drop is a p]fect sph]e3 & ?is = ! simple reason t =ces & resi/ances o!r ?an ! ma9 "o are inevitably at "w4 ,! same is true ( organic =m1 b x is = ! ma!matician to unravel ! conflict+ =ces :i* are at "w toge!r4 ,& ?is process ( inve/igation may lead u on /ep by /ep to new ph5om5a1 z x has done 9 physics1 :]e sometimes a k ( =m leads u to ! int]pretation ( =ces1 & at o!r times a k ( ! =ces at "w guides u t[>ds a bett] insight into =m4 ,i w\ld illu/rate ?is by ! case ( ! e>? itself4 ,aft] ! fundam5tal advance _h be5 made :i* taught u t ! _w 0 r\nd1 ,newton %[$ t ! =ces at "w ^u x mu/ lead to its be+ imp]fectly sph]ical1 & 9 ! c\rse ( "t its oblate sph]oidal %ape 0 actually v]ifi$4 ,b n[1 9 turn1 x has be5 %[n t its =m is /ill m complicat$1 & ! next /ep w be to seek = ! =ces t h de=m$ ! oblate sph]oid4 #gbb ,! organic =ms :i* we c def9e1 m or less precisely1 9 ma!matical t]ms1 & aft]w>ds proce$ to expla9 & to acc\nt = 9 t]ms ( =ce1 are ( _m k9ds1 z we h se52 b nev]!less !y are few 9 numb] comp>$ ) ,nature's all b inf9ite v>iety4 ,! reason = ?is is n f> to seek4 ,! liv+ organism repres5ts1 or occupies1 a field ( =ce :i* is nev] simple1 & :i* z a rule is ( imm5se complexity4 ,& j z 9 ! v simple/ ( actual cases we meet ) a dep>ture f su* symmetry z c\ld only exi/ "u conditions ( ideal simplicity1 s d we pass quickly to cases :]e ! int]f]5ce ( num]\s1 ?\gh /ill p]haps v simple1 causes leads to a resultant :i* lies f> beyond our p[]s ( analysis4 ,nor mu/ we =get t ! biologi/ is mu* m exact+ 9 8 requirem5ts1 z reg>ds =m1 ?an ! physici/2 = ! latt] is usually cont5t ) ei!r an ideal or a g5]al description ( =m1 :ile ! /ud5t ( liv+ ?+s mu/ ne$s be specific4 ,! physici/ or ma!matician c give u p]fectly satisfy+ expressions = ! =m ( a wave1 or ev5 ( a heap ( s&2 b we nev] ask him to def9e ! =m ( any p>ticul> wave ( ! sea1 nor ! actual =m ( any m\nta9-peak or hill#fdc4 #gbc ,= v>i\s reasons1 !n1 !re are a va/ multitude ( organic =ms :i* we are unable to acc\nt =1 or to def9e1 9 ma!matical t]ms2 & ?is is n seldom ! case ev5 9 =ms :i* are app>5tly ( great simplicity & regul>ity4 ,! curv$ outl9e ( a leaf1 = in/ance1 is su* a case2 its ovate1 lanceolate1 or cordate %ape is app>5tly v simple1 b ! difficulty ( f9d+ = x a ma!matical expression is v great inde$4 ,to def9e ! complicat$ outl9e ( a fi%1 = in/ance1 or ( a v]tebrate skull1 we nev] ev5 seek = a ma!matical =mula4 ,b 9 a v l>ge "p ( morphology1 our ess5tial task lies 9 ! comp>ison ( relat$ =ms r ?an 9 ! precise def9ition ( ea*2 & ! de=mation ( a complicat$ figure may be a ph5om5on easy ( compreh5sion1 ?\gh ! figure itself h to be left unanalys$ & undef9$4 ,?is process ( comp>ison1 ( recognis+ 9 "o =m a def9ite p]mutation or de=mation ( ano!r1 ap>t altoge!r f a precise & adequate und]/&+ ( ! orig9al 8type0 or /&>d ( comp>ison1 lies )9 ! imm$iate prov9ce ( ma!matics1 & f9ds its solution 9 ! elem5t>y use ( a c]ta9 me?od ( ! ma!matician4 ,?is me?od is ! ,me?od ( ,co-ord9ates1 on :i* is bas$ ! ,!ory ( ,trans=mations4 ,i imag9e t :5 ,desc>tes conceiv$ ! me?od ( co-ord9ates1 z a g5]alisation f ! proportional diagrams ( ! arti/ & ! ar*itect1 & long be=e ! imm5se possibilities ( ?is analysis c\ld be =ese51 he _h 9 m9d a v simple purpose2 x 0 p]haps no m ?an to f9d a way ( translat+ ! =m ( a curve into numb]s & into words4 ,?is is precisely :at we d1 by ! me?od ( co-ord9ates1 e "t we /udy a /ati/ical curve2 & conv]sely1 we translate numb]s into =m :5ev] we 8plot a curve0 to illu/rate a table ( mortality1 a rate ( gr[?1 or ! daily v>iation ( temp]ature or b>ometric pressure4 ,9 precisely ! same way x is possible to inscribe 9 a net ( rectangul> co-ord9ates ! outl9e1 = in/ance1 ( a fi%1 & s to translate #gbd x into a table ( numb]s1 f :i* aga9 we may at pleasure recon/ruct ! curve4 ,b x is ! next /ep 9 ! employm5t ( co-ord9ates :i* is ( special int]e/ & use to ! morphologi/2 & ?is /ep consi/s 9 ! alt]ation1 or 8trans=mation10 ( our sy/em ( co-ord9ates & 9 ! /udy ( ! correspond+ trans=mation ( ! curve or figure inscrib$ 9 ! co-ord9ate network4 ,let u inscribe 9 a sy/em ( ,c>tesian co-ord9ates ! outl9e ( an organism1 h[ev] complicat$1 or a "p !re(3 su* z a fi%1 a crab1 or a mammalian skull4 ,we may n[ treat ?is complicat$ figure1 9 g5]al t]ms1 z a function ( x1 y4 ,if we submit our rectangul> sy/em to 8de=mation10 on simple & recognis$ l9es1 alt]+1 = in/ance1 ! direction ( ! axes1 ! ratio ( x_/y1 or sub/itut+ = x & y "s m complicat$ expressions1 !n we %all obta9 a new sy/em ( co-ord9ates1 ^: de=mation f ! orig9al type ! inscrib$ figure w precisely foll[4 ,9 o!r words1 we obta9 a new figure1 :i* repres5ts ! old figure "u /ra91 & is a function ( ! new co-ord9ates 9 precisely ! same way z ! old figure 0 ( ! orig9al co-ord9ates x & y4 ,! problem is closely ak9 to t ( ! c>tograph] :o transf]s id5tical data to "o projection or ano!r2 & ^: object is to secure 7if x be possible7 a complete correspond5ce1 9 ea* small unit ( area1 betwe5 ! "o repres5tation & ! o!r4 ,! morphologi/ w n seek to draw 8 organic =ms 9 a new & artificial projection2 b1 9 ! conv]se aspect ( ! problem1 he w inquire :e!r two diff]5t b m or less obvi\sly relat$ =ms c be s analys$ & int]pret$ t ea* may be %[n to be a trans=m$ repres5tation ( ! o!r4 ,?is once demon/rat$1 x w be a comp>atively easy task 79 all probability7 to po/ulate ! direction & magnitude ( ! =ce capable ( effect+ ! requir$ trans=mation4 ,aga91 if su* a simple alt]ation ( ! sy/em ( =ces c be prov$ adequate to meet ! case1 we may f9d ourselves able to disp5se ) _m widely curr5t & m complicat$ hypo!ses ( biological causation4 ,= x is a maxim 9 physics t an effect ought n to be ascrib$ to #gbe ! jo9t op]ation ( _m causes if few are adequate to ! production ( x3 ,fru/ra fit p] plura1 quod fi]i pote/ p] pauciora4 ,x is evid5t t by ! comb9$ action ( appropriate =ces any mat]ial =m c be trans=m$ into any o!r3 j z out ( a 8%apeless0 mass ( clay ! pott] or ! sculptor models 8 arti/ic product2 or j z we attribute to ,nature h]self ! p[] to effect ! gradual & successive trans=mation ( ! simple/ into ! mo/ complex organism4 ,9 l mann] x is possible1 at lea/ !oretically1 to cause ! outl9e ( any clos$ curve to appe> z a projection ( any o!r :atsoev]4 ,b we ne$ n let ^! !oretical consid]ations det] u f our me?od ( comp>ison ( relat$ =ms4 ,we %all /rictly limit ourselves to cases :]e ! trans=mation necess>y to effect a comp>ison %all be ( a simple k9d1 & :]e ! trans=m$1 z well z ! orig9al1 co-ord9ates %all con/itute an h>moni\s & m or less symmetrical sy/em4 ,we %\ld fall into des]v$ & inevitable confusion if1 :e!r by ! ma!matical or any o!r me?od1 we attempt$ to comp>e organisms sep>at$ f> ap>t 9 ,nature & 9 zoological classification4 ,we are limit$1 n by ! nature ( our me?od1 b by ! :ole nature ( ! case1 to ! comp>ison ( organisms su* z are manife/ly relat$ to "o ano!r & belong to ! same zoological class4 ,our inquiry lies1 9 %ort1 j )9 ! limits :i* ,ari/otle himself laid d[n :51 9 def9+ a 8g5us10 he %[$ t 7ap>t f ^? sup]ficial *>act]s1 su* z col\r1 :i* he call$ 8accid5ts07 ! ess5tial diff]5ces betwe5 "o 8species0 & ano!r are m]ely diff]5ces ( proportion1 ( relative magnitude1 or 7z he phras$ x7 ( 8excess & defect40 8,save only = a diff]5ce 9 ! way ( excess or defect1 ! p>ts are id5tical 9 ! case ( su* animals z are ( "o & ! same g5us2 & by #8g5us' ,i mean1 = in/ance1 ,bird or ,fi%40 ,& aga93 8,)9 ! limits ( ! same g5us1 z a g5]al rule1 mo/ ( ! p>ts exhibit diff]5ces 444 9 ! way ( multitude or fewness1 magnitude or p>vitude1 9 %ort1 9 ! way ( excess or defect4 ,= #8! m' & #8! less' may be repres5t$ z #gbf #8excess' & #8defect#fdd4' 0 ,x is precisely ?is diff]5ce ( relative magnitudes1 ?is ,ari/otelian 8excess & defect0 9 ! case ( =m1 :i* our co-ord9ate me?od is especially adapt$ to analyse1 & to reveal & demon/rate z ! ma9 cause ( :at 7aga9 9 ! ,ari/otelian s5se7 we t]m 8specific0 diff]5ces4 ,! applicability ( our me?od to p>ticul> cases w dep5d ^u1 or be fur!r limit$ by1 c]ta9 practical consid]ations or qualifications4 ,( ^! ! *ief1 & inde$ ! ess5tial1 condition is1 t ! =m ( ! entire /ructure "u inve/igation %\ld be f\nd to v>y 9 a m or less uni=m mann]1 aft] ! fa%ion ( an approximately homog5e\s & isotropic body4 ,b an imp]fect isotropy1 provid$ always t "s 8pr9ciple ( cont9uity0 run ?r\gh its v>iations1 w n s]i\sly int]f]e ) our me?od2 x w only cause our trans=m$ co-ord9ates to be some:at less regul> & h>moni\s ?an are ^?1 = in/ance1 by :i* ! physici/ depicts ! motions ( a p]fect fluid or a !oretic field ( =ce 9 a uni=m m$ium4 ,aga91 x is ess5tial t our /ructure v>y 9 its entirety1 or at lea/ t 8indep5d5t v>iants0 %\ld be relatively few4 ,t indep5d5t v>iations occur1 t localis$ c5tres ( dim9i%$ or exagg]at$ gr[? w n[ & !n be f\nd1 is n only probable b manife/2 & !y may ev5 be s pron\nc$ z to appe> to con/itute new =mations altoge!r4 ,su* indep5d5t v>iants z ^! ,ari/otle himself cle>ly recognis$3 8,x happ5s fur!r t "s h p>ts t o!rs h n2 = in/ance1 "s birds h spurs & o!rs n1 "s h cre/s1 or combs1 & o!rs n2 b1 z a g5]al rule1 mo/ p>ts & ^? t g to make up ! bulk ( ! body are ei!r id5tical ) "o ano!r1 or diff] f "o ano!r 9 ! way ( contra/ & ( excess & defect4 ,= #8! m' & #8! less' may be repres5t$ z #8excess' or #8defect4' 0 ,if1 9 ! evolution ( a fi%1 = in/ance1 x be ! case t its sev]al & con/itu5t p>ts--head1 body1 & tail1 or ?is f9 & t f9--repres5t s _m indep5d5t v>iants1 !n our co-ord9ate sy/em w at once become too complex to be intelligible2 we %all be mak+ n "o comp>ison b sev]al #gbg sep>ate comp>isons1 & our g5]al me?od w be f\nd inapplicable4 ,n[ precisely ?is indep5d5t v>iability ( p>ts & organs--"h1 !re1 & ev]y:]e )9 ! organism--w\ld appe> to be implicit 9 our ord9>y accept$ notions reg>d+ v>iation2 &1 unless ,i am greatly mi/ak51 x is precisely on su* a conception ( ! easy1 frequ5t1 & normal indep5d5t v>iability ( p>ts t our conception ( ! process ( natural selection is fundam5tally bas$4 ,= ! morphologi/1 :5 comp>+ "o organism ) ano!r1 describes ! diff]5ces betwe5 !m po9t by po9t1 & 8"*0 by 8"*#fde40 ,if he is f "t to "t con/ra9$ to admit ! exi/5ce ( 8correlation0 betwe5 *>act]s 7z a hundr$ ye>s ago ,cuvi] fir/ %[$ ! way71 yet all ! :ile he recognises ?is fact ( correlation some:at vaguely1 z a ph5om5on due to causes :i*1 except 9 r>e in/ances1 he c h>dly hope to trace2 & he falls readily into ! habit ( ?9k+ & talk+ ( evolution z ?\gh x _h proce$$ on ! l9es ( 8 own descriptions1 po9t by po9t1 & "* by "*#fdf4 ,b if1 on ! o!r h&1 div]se & dissimil> fi%es c be ref]r$ z a :ole to id5tical functions ( v diff]5t co-ord9ate sy/ems1 ?is fact w ( itself con/itute a pro( t v>iation has proce$$ on def9ite & ord]ly l9es1 t a compreh5sive 8law ( gr[?0 has p]vad$ ! :ole /ructure 9 its integrity1 & t "s m or less simple & recognisable sy/em ( =ces has be5 at "w4 ,x w n only %[ h[ real & deep-seat$ is ! ph5om5on ( 8correlation10 9 reg>d to =m1 b x w also demon/rate ! fact t a correlation :i* _h seem$ too complex = analysis or #gbh compreh5sion is1 9 _m cases1 capable ( v simple graphic expression4 ,?is1 aft] _m trials1 ,i believe to be 9 g5]al ! case1 be>+ always 9 m9d t ! occurr5ce ( indep5d5t or localis$ v>iations mu/ (t5 be consid]$4 ,we are deal+ 9 ?is *apt] ) ! =ms ( relat$ organisms1 9 ord] to %ew t ! diff]5ces betwe5 !m are z a g5]al rule simple & symmetrical1 & j su* z might h be5 br\ght ab\t by a slight & simple *ange 9 ! sy/em ( =ces to :i* ! liv+ & gr[+ organism 0 expos$4 ,ma!matically speak+1 ! ph5om5on is id5tical ) "o met ) by ! geologi/1 :5 he f9ds a b$ ( fossils squeez$ flat or o!rwise symmetrically de=m$ by ! pressures to :i* !y1 & ! /rata :i* conta9 !m1 h be5 subject$4 ,9 ! fir/ /ep t[>ds fossilisation1 :5 ! body ( a fi% or %ellfi% is silt$ ov] & buri$1 we may take x t ! wet s& or mud ex]cises1 approximately1 a hydro/atic pressure--t is to say a pressure :i* is uni=m 9 all directions1 & by :i* ! =m ( ! buri$ object w n be appreciably *ang$4 ,z ! /rata consolidate & accumulate1 ! fossil organisms :i* !y conta9 w t5d to be flatt5$ by ! va/ sup]9cumb5t load1 j z ! /ratum :i* conta9s !m w also be compress$ & w h its molecul> arrangem5t m or less modifi$#fdg4 ,b ! de=mation due to direct v]tical pressure 9 a horizontal /ratum is n ne>ly s /rik+ z are ! de=mations produc$ by ! oblique or %e>+ /resses to :i* incl9$ & fold$ /rata h be5 expos$1 & by :i* _! v>i\s 8dislocations0 h be5 br\ght ab\t4 ,& especially 9 m\nta9 regions1 :]e ^! dislocations are especially num]\s & complicat$1 ! conta9$ fossils are apt to be s curi\sly & yet s symmetrically de=m$ 7usually by a simple %e>7 t !y may easily be int]pret$ z s _m di/9ct & sep>ate 8species#fdh40 ,a great numb] ( describ$ species1 & "h & !re a new g5us 7z ! g5us ,ellipsoli!s = an obliquely de=m$ ,goniatite or ,nautilus7 are said to re/ on no o!r f\ndation#fdi4 ,illu/ration3 ,fig4 #ceb4 ,illu/ration3 ,fig4 #cec4 ,illu/ration3 ,fig4 #ced4 ,illu/ration3 ,fig4 #cee4 ,if we beg9 by draw+ a net ( rectangul> equidi/ant co-ord9ates 7ab\t ! axes x & y71 we may alt] or de=m ?is #gbi network 9 v>i\s ways1 sev]al ( :i* are v simple inde$4 ,?us 7#a7 we may alt] ! dim5sions ( our sy/em1 ext5d+ x along "o or o!r axis1 & s conv]t+ ea* little squ>e into a correspond+ & directly proportionate oblong 7,fig4 #cec74 ,x foll[s t any figure :i* we may h inscrib$ 9 ! orig9al net1 & :i* we transf] to ! new1 w !reby be de=m$ 9 /rict proportion to ! de=mation ( ! entire configuration1 be+ /ill def9$ by correspond+ po9ts 9 ! network & be+ ?r\gh\t 9 con=mity ) ! orig9al figure4 ,= in/ance1 a circle inscrib$ 9 ! orig9al 8,c>tesian0 net w n[1 aft] ext5sion 9 ! y-direction1 be f\nd elongat$ #gcj into an ellipse4 ,9 elem5t>y ma!matical language1 = ! orig9al x & y we h sub/itut$ x#a & c y#a1 & ! equation to our orig9al circle1 x#b y#b a#b1 becomes t ( ! ellipse1 x#ab c#b y#ab a#b4 ,if ,i draw ! cannon-bone ( an ox 7,fig4 #ced1 ,a71 = in/ance1 )9 a sy/em ( rectangul> co-ord9ates1 & !n transf] ! same draw+1 po9t = po9t1 to a sy/em 9 :i* = ! x ( ! orig9al diagram we sub/itute x #bx_/#c1 we obta9 a draw+ 7,b7 :i* is a v close approximation to ! cannon-bone ( ! %eep4 ,9 o!r words1 ! ma9 7& p]haps ! only7 diff]5ce betwe5 ! two bones is simply t t ( ! %eep is elongat$1 along ! v]tical axis1 z comp>$ ) t ( ! ox 9 ! relation ( #c_/b4 ,& simil>ly1 ! long sl5d] cannon-bone ( ! giraffe 7,c7 is ref]able to ! same id5tical type1 subject to a r$uction ( bread?1 or increase ( l5g?1 correspond+ to x x_/#c4 7#b7 ,! second type is t :]e ext5sion is n equal or uni=m at all di/ances f ! orig93 b gr[s great] or less1 z1 = in/ance1 :5 we /ret* a tap]+ ela/ic b&4 ,9 su* cases1 z ,i h repres5t$ x 9 ,fig4 #cee1 ! ord9ate increases log>i?mically1 & = y we sub/itute y4 ,x is obvi\s t ?is log>i?mic ext5sion may involve bo? abscissae & ord9ates1 x becom+ x1 :ile y becomes y4 ,! circle 9 our orig9al figure is n[ de=m$ into "s su* %ape z t ( ,fig4 #cef4 ,?is me?od ( de=mation is a common "o1 & w (t5 be ( use to u 9 our comp>ison ( organic =ms4 7#c7 ,our ?ird type is ! 8simple %e>10 :]e ! rectangul> co-ord9ates become 8oblique10 _! axes be+ incl9$ to "o ano!r at a c]ta9 angle 4 ,our orig9al rectangle n[ becomes su* a figure z t ( ,fig4 #ceg4 ,! sy/em may n[ be describ$ 9 t]ms ( ! oblique axes ,x1 ,y2 or may be directly ref]r$ to new rectangul> co-ord9ates 1 by ! simple transposition x cot 1 y cosec 4 ,illu/ration3 ,fig4 #cef4 ,illu/ration3 ,fig4 #ceg4 ,illu/ration3 ,fig4 #ceh4 7#d7 ,yet ano!r important class ( de=mations may be repres5t$ by ! use ( radial co-ord9ates1 9 :i* "o set ( l9es are repres5t$ z radiat+ f a po9t or 8focus10 :ile ! o!r set are trans=m$ into circul> arcs cutt+ ! radii or?ogonally4 ,^! radial co-ord9ates are especially applicable #gca to cases :]e !re exi/s 7ei!r )9 or )\t ! figure7 "s "p :i* is suppos$ to suff] no de=mation2 a simple illu/ration is af=d$ by ! diagrams :i* illu/rate ! flexure ( a beam 7,fig4 #ceh74 ,9 biology ^! co-ord9ates w be especially applicable 9 cases :]e ! gr[+ /ructure includes a 8node10 or po9t :]e gr[? is abs5t or at a m9imum2 & ab\t :i* node ! rate ( gr[? may be assum$ to increase symmetrically4 ,precisely su* a case is furni%$ u 9 a leaf ( an ord9>y dicotyl$on4 ,! leaf ( a #gcb typical monocotyl$on--su* z a grass or a hyac9?1 = in/ance--gr[s cont9u\sly f its base1 & exhibits no node or 8po9t ( arre/40 ,its sides tap] (f gradually f its broad base to its sl5d] tip1 accord+ to "s law ( decrem5t specific to ! plant2 & any alt]ation 9 ! relative velocities ( longitud9al & transv]se gr[? w m]ely make ! leaf a little broad] or n>r[]1 & w effect no o!r conspicu\s alt]ation 9 its cont\r4 ,b if !re once come into exi/5ce a node1 or 8locus ( no gr[?10 ab\t :i* we may assume ! gr[?--:i* 9 ! hyac9? leaf 0 longitud9al & transv]se--to take place radially & transv]sely to ! radii1 !n we %all ,illu/ration3 ,fig4 #cei4 at once see1 9 ! fir/ place1 t ! slop+ & slightly curv$ sides ( ! hyac9? leaf suff] a trans=mation into :at we consid] a m typical & 8leaf-l0 %ape1 ! sides ( ! figure broad5+ out to a zone ( maximum bread? & !n draw+ inw>ds to ! po9t$ apex4 ,if we n[ alt] ! ratio betwe5 ! radial & tang5tial velocities ( gr[?--9 o!r words1 if we increase ! angles betwe5 correspond+ radii--we pass successively ?r\gh ! v>i\s configurations :i* ! botani/ describes z ! lanceolate1 ! ovate1 & f9ally ! cordate leaf4 ,^! successive *anges may to "s ext5t1 & 9 appropriate cases1 be trac$ z ! individual leaf gr[s #gcc to maturity2 b z a mu* m g5]al rule1 ! balance ( =ces1 ! ratio betwe5 radial & tang5tial velocities ( gr[?1 rema9s s nicely & con/antly balanc$ t ! leaf increases 9 size )\t conspicu\s modification ( =m4 ,x is r :at we may call a long-p]iod v>iation1 a t5d5cy = ! relative velocities to alt] f "o g5]ation to ano!r1 ^: result is br\ght into view by ?is me?od ( illu/ration4 ,illu/ration3 ,fig4 #cfj4 ,begonia da$alea4 ,!re are v>i\s coroll>ies to ?is me?od ( describ+ ! =m ( a leaf :i* may be "h allud$ to1 = we %all n return aga9 to ! subject ( radial co-ord9ates4 ,= in/ance1 ! s-call$ unsymmetrical leaf#fej ( a begonia1 9 :i* "o side ( ! leaf may be m]ely ovate :ile ! o!r has a cordate outl9e1 is se5 to be really a case ( unequal1 & n truly asymmetrical1 gr[? on ei!r side ( ! midrib4 ,!re is no?+ m my/]i\s 9 its con=mation ?an1 = in/ance1 9 t ( a =k$ twig 9 :i* "o limb ( ! =k has gr[n long] ?an ! o!r4 ,! case ( ! begonia leaf is ( suffici5t int]e/ to des]ve illu/ration1 & 9 ,fig4 #cfj ,i h outl9$ a leaf ( ! l>ge ,begonia da$alea4 ,on ! small] left-h& side ( ! leaf ,i h tak5 at r&om ?ree po9ts1 a1 b1 c1 & h measur$ ! angles1 ,a,oa1 etc41 :i* ! radii f ! hilus ( ! leaf to ^! po9ts make ) ! m$ian axis4 ,on ! o!r side ( ! leaf ,i h m>k$ ! po9ts a1 b1 c1 su* t ! radii drawn to ?is m>g9 ( ! leaf are equal to ! =m]1 ,oa to ,oa1 etc4 ,n[ if ! two sides ( ! leaf are #gcd ma!matically simil> to "o ano!r1 x is obvi\s t ! respective angles %\ld be 9 cont9u$ proportion1 i4e4 z ,a,oa is to ,a,oa1 s %\ld ,a,ob be to ,a,ob4 ,?is proves to be v ne>ly ! case4 ,= ,i h measur$ ! ?ree angles on "o side1 & "o on ! o!r1 & h !n comp>$1 z foll[s1 ! calculat$ ) ! obs]v$ values ( ! o!r two3 ,a,oa ,a,ob ,a,oc ,a,oa ,a,ob ,a,oc ,obs]v$ values #ab #bh4e #hh -- -- #aeg ,calculat$ values -- -- -- #ba4e #ea4a -- ,obs]v$ values -- -- -- #bj #eb -- ,! agreem5t is v close1 & :at discrepancy !re is may be amply acc\nt$ =1 fir/ly1 by ! slight irregul>ity ( ! s9u\s m>g9 ( ! leaf2 & secondly1 by ! fact t ! true axis or midrib ( ! leaf is n /raight b slightly curv$1 & !re=e t x is curvil9e> & n rectil9e> triangles :i* we ought to h measur$4 ,:5 we und]/& ^! few po9ts reg>d+ ! p]iph]al curvature ( ! leaf1 x is easy to see t its pr9cipal ve9s approximate closely to a beautiful sy/em ( isogonal co-ord9ates4 ,x is also obvi\s t we c easily pass1 by a process ( %e>+1 f ^? cases :]e ! pr9cipal ve9s />t f ! base ( ! leaf to ^?1 z 9 mo/ dicotyl$ons1 :]e !y arise successively f ! midrib4 ,x may sometimes happ5 t ! node1 or 8po9t ( arre/10 is at ! upp] in/ead ( ! l[] end ( ! leaf-blade2 & occasionally !re may be a node at bo? ends4 ,9 ! =m] case1 z we h x 9 ! daisy1 ! =m ( ! leaf w be1 z x 71 inv]t$1 ! broad1 m or less he>t-%ap$1 outl9e appe>+ at ! upp] end1 :ile bel[ ! leaf tap]s gradually d[nw>ds to an ill-def9$ base4 ,9 ! latt] case1 z 9 ,dionaea1 we obta9 a leaf equally exp&$1 & simil>ly ovate or cordate1 at bo? ends4 ,we may notice1 la/ly1 t ! %ape ( a solid fruit1 su* z an apple or a *]ry1 is a solid ( revolution1 develop$ f simil> curves & to be expla9$ on ! same pr9ciple4 ,9 ! *]ry we h a 8po9t ( arre/0 at ! base ( ! b]ry1 :]e x jo9s its p$uncle1 & ab\t ?is po9t ! fruit 79 imag9>y section7 swells out into a cordate outl9e2 :ile 9 ! #gce apple we h two su* well-m>k$ po9ts ( arre/1 above & bel[1 & ab\t bo? ( !m ! same con=mation t5ds to arise4 ,! bean & ! human kidney owe _! 8r5i=m0 %ape to precisely ! same ph5om5on1 namely1 to ! exi/5ce ( a node or 8hilus10 ab\t :i* ! =ces ( gr[? are radially & symmetrically arrang$4 ,mo/ ( ! trans=mations :i* we h hi!rto consid]$ 7o!r ?an t ( ! simple %e>7 are p>ticul> cases ( a g5]al trans=mation1 obta9able by ! me?od ( conjugate functions & equival5t to ! projection ( ! orig9al figure on a new plane4 ,appropriate trans=mations1 on ^! g5]al l9es1 provide = ! cases ( a coaxial sy/em :]e ! ,c>tesian co-ord9ates are replac$ by coaxial circles1 or a confocal sy/em 9 :i* !y are replac$ by confocal ellipses & hyp]bolas4 ,illu/ration3 ,fig4 #cfa4 ,yet ano!r curi\s & important trans=mation1 belong+ to ! same class1 is t by :i* a sy/em ( /raight l9es becomes trans=m$ into a con=mal sy/em ( log>i?mic spirals3 ! /raight l9e ,y ,,ax c correspond+ to ! log>i?mic spiral ,a log r c 7,fig4 #cfa74 ,?is beautiful & simple trans=mation lets u at once conv]t1 = in/ance1 ! /raight conical %ell ( ! ,pt]opod or ! ,or?oc]as into ! log>i?mic spiral ( ! ,nautiloid2 x involves a ma!matical symbolism :i* is b a slight ext5sion ( t :i* we h employ$ 9 our elem5t>y treatm5t ( ! log>i?mic spiral4 ,^! v>i\s sy/ems ( coord9ates1 :i* we h n[ briefly consid]$1 are sometimes call$ 8iso!rmal co-ord9ates10 f ! fact t1 :5 employ$ 9 ?is p>ticul> bran* ( physics1 !y p]fectly repres5t ! ph5om5a ( ! conduction ( heat1 ! cont\r l9es ( equal temp]ature appe>+1 "u appropriate conditions1 z ! or?ogonal l9es ( ! co-ord9ate sy/em4 ,& x foll[s t #gcf ! 8law ( gr[?0 :i* our biological analysis by means ( or?ogonal co-ord9ate sy/ems presupposes1 or at lea/ =e%ad[s1 is "o accord+ to :i* ! organism gr[s or develops along /ream l9es1 :i* may be def9$ by a suitable ma!matical trans=mation4 ,:5 ! sy/em becomes no long] or?ogonal1 z 9 _m ( ! foll[+ illu/rations--= in/ance1 t ( ,or?agoriscus 7,fig4 #chb71--!n ! trans=mation is no long] )9 ! rea* ( comp>atively simple ma!matical analysis4 ,su* dep>ture f ! typical symmetry ( a 8/ream-l9e0 sy/em is1 9 ! fir/ in/ance1 suffici5tly acc\nt$ = by ! simple fact t ! develop+ organism is v f> f be+ homog5e\s & isotropic1 or1 9 o!r words1 does n behave l a p]fect fluid4 ,b ?\gh "u su* circum/ances our co-ord9ate sy/ems may be no long] capable ( /rict ma!matical analysis1 !y w /ill indicate graphically ! relation ( ! new co-ord9ate sy/em to ! old1 & conv]sely w furni% u ) "s guidance z to ! 8law ( gr[?10 or play ( =ces1 by :i* ! trans=mation has be5 effect$4 ,be=e we pass f ?is brief discussion ( trans=mations 9 g5]al1 let u glance at "o or two cases 9 :i* ! =ces appli$ are m or less intelligible1 b ! result+ trans=mations are1 f ! ma!matical po9t ( view1 exce$+ly complicat$4 ,! 8m>bl$ pap]s0 ( ! bookb9d] are a beautiful illu/ration ( visible 8/ream l9es40 ,on a di%ful ( a sort ( semi-liquid gum ! workman du/s a few simple l9es or pat*es ( col\r+ matt]2 & !n1 by pass+ a comb ?r\gh ! liquid1 he draws ! col\r-b&s into ! /reaks1 waves1 & spirals :i* con/itute ! m>bl$ patt]n1 & :i* he !n transf]s to %eets ( pap] laid d[n ^u ! gum4 ,by "s su* sy/em ( %e>s1 by ! effect ( unequal traction or unequal gr[? 9 v>i\s directions & sup]pos$ on an orig9ally simple patt]n1 we may acc\nt = ! n dissimil> m>bl$ patt]ns :i* we recognise1 = in/ance1 on a l>ge s]p5t's sk94 ,b x mu/ be rem>k$1 9 ! case ( ! m>bl$ pap]1 t ?\gh ! me?od ( application ( ! =ces is simple1 yet 9 ! aggregate ! sy/em ( =ces set up by ! _m #gcg tee? ( ! comb is exce$+ly complex1 & its complexity is reveal$ 9 ! complicat$ 8diagram ( =ces0 :i* con/itutes ! patt]n4 ,to take ano!r & /ill m in/ructive illu/ration4 ,to turn "o circle 7or sph]e7 into two circles w\ld be1 f ! po9t ( view ( ! ma!matician1 an extraord9>ily difficult trans=mation2 b1 physically speak+1 its a*ievem5t may be extremely simple4 ,! little r\nd g\rd gr[s naturally1 by its symmetrical =ces ( expansive gr[?1 into a big1 r\nd1 or some:at oval pumpk9 or melon4 ,b ! ,moori% husb&man ties a rag r\nd its middle1 & ! same =ces ( gr[?1 unalt]$ save = ! pres5ce ( ?is trammel1 n[ exp& ! globul> /ructure into two sup]pos$ & connect$ globes4 ,& aga91 by v>y+ ! position ( ! encircl+ b&1 or by apply+ sev]al su* ligatures in/ead ( "o1 a great v>iety ( artificial =ms ( 8g\rd0 may be1 & actually are1 produc$4 ,x is cle>1 ,i ?9k1 t we may acc\nt = _m ord9>y biological processes ( developm5t or trans=mation ( =m by ! exi/5ce ( trammels or l9es ( con/ra9t1 :i* limit & det]m9e ! action ( ! expansive =ces ( gr[? t w\ld o!rwise be uni=m & symmetrical4 ,?is case has a close p>allel 9 ! op]ations ( ! glassbl[]1 to :i* we h already1 m ?an once1 ref]r$ 9 pass+#fea4 ,! glassbl[] />ts 8 op]ations ) a tube1 :i* he fir/ closes at "o end s z to =m a holl[ vesicle1 )9 :i* 8 bla/ ( air ex]cises a uni=m pressure on all sides2 b ! sph]ical con=mation :i* ?is uni=m expansive =ce w\ld naturally t5d to produce is modifi$ into all k9ds ( =ms by ! trammels or resi/ances set up z ! workman lets "o "p or ano!r ( 8 bubble be unequally heat$ or cool$4 ,x 0 ,oliv] ,w5dell ,holmes :o fir/ %ew$ ?is curi\s p>allel betwe5 ! op]ations ( ! glassbl[] & ^? ( ,nature1 :5 %e />ts1 z %e s (t5 does1 ) a simple tube#feb4 ,! alim5t>y canal1 #gch ! art]ial sy/em includ+ ! he>t1 ! c5tral n]v\s sy/em ( ! v]tebrate1 includ+ ! bra9 itself1 all beg9 z simple tubul> /ructures4 ,& ) !m ,nature does j :at ! glassbl[] does1 &1 we might ev5 say1 no m ?an he4 ,= %e c exp& ! tube "h & n>r[ x !re2 ?ick5 its walls or ?9 !m2 bl[ (f a lat]al (f%oot or caecal div]ticulum2 b5d ! tube1 or twi/ & coil x2 & infold or crimp its walls z1 s to speak1 %e pleases4 ,su* a =m z t ( ! human /oma* is easily expla9$ :5 x is reg>d$ f ?is po9t ( view2 x is simply an ill-bl[n bubble1 a bubble t has be5 r5d]$ lopsid$ by a trammel or re/ra9t along "o side1 su* z to prev5t its symmetrical expansion--su* a trammel z is produc$ if ! glassbl[] lets "o side ( 8 bubble get cold1 & su* z is actually pres5t 9 ! /oma* itself 9 ! =m ( a muscul> b&4 ,we may n[ proce$ to consid] & illu/rate a few p]mutations or trans=mations ( organic =m1 out ( ! va/ multitude :i* are equally op5 to ?is me?od ( inquiry4 ,illu/ration3 ,fig4 #cfb4 ,we h already comp>$ 9 a prelim9>y fa%ion ! metac>pal or cannon-bone ( ! ox1 ! %eep1 & ! giraffe 7,fig4 #ced72 & we h se5 t ! ess5tial diff]5ce 9 =m betwe5 ^! ?ree bones is a matt] ( relative l5g? & bread?1 su* t1 if we r$uce ! figures to an id5tical /&>d ( l5g? 7or id5tical values ( y71 ! bread? 7or value ( x7 w be approximately two-?irds t ( ! ox 9 ! case ( ! %eep & "o-?ird t ( ! ox 9 ! case ( ! giraffe4 ,we may easily1 = ! sake ( clos] comp>ison1 det]m9e ^! ratios m accurately1 = in/ance1 if x be our purpose to comp>e ! diff]5t racial v>ieties )9 ! limits ( a s+le species4 ,& 9 su* cases1 by ! way1 z :5 we comp>e ) "o ano!r v>i\s bre$s or races ( cattle or ( horses1 ! ratios #gci ( l5g? & bread? 9 ?is p>ticul> bone are extremely significant#fec4 ,if1 in/ead ( limit+ ourselves to ! cannon-bone1 we inscribe ! entire foot ( our sev]al ,ungulates 9 a co-ord9ate sy/em1 ! same ratios ( x t s]v$ u = ! cannon-bones /ill give u a fir/ approximation to ! requir$ comp>ison2 b ev5 9 ! case ( su* closely alli$ =ms z ! ox & ! %eep !re is evid5tly some?+ want+ 9 ! comp>ison4 ,! reason is t ! relative elongation ( ! sev]al p>ts1 or individual bones1 has n proce$$ equally or proportionately 9 all cases2 9 o!r words1 t ! equations = x w n suffice )\t "s simultane\s modification ( ! values ( y 7,fig4 #cfb74 ,9 su* a case x may be f\nd possible to satisfy ! v>y+ values ( y by "s log>i?mic or o!r =mula2 b1 ev5 if t be possible1 x w probably be some:at difficult ( discov]y or v]ification 9 su* a case z ! pres5t1 ow+ to ! fact t we h too few well-m>k$ po9ts ( correspond5ce betwe5 ! "o object & ! o!r1 & t especially along ! %aft ( su* long bones z ! cannon-bone ( ! ox1 ! de]1 ! llama1 or ! giraffe !re is a complete lack ( easily recognisable correspond+ po9ts4 ,9 su* a case a brief tabul> /atem5t ( app>5tly correspond+ values ( y1 or ( ^? obvi\sly correspond+ values :i* co9cide ) ! b\nd>ies ( ! sev]al bones ( ! foot1 w1 z 9 ! foll[+ example1 enable u to disp5se ) a fre% equation4 a b c d y 7,ox7 #j #ah #bg #db #ajj y 7,%eep7 #j #aj #ai #cf #ajj y 7,giraffe7 #j #e #aj #bd #ajj ,?is summ>y ( values ( y1 c\pl$ ) ! equations = ! #gdj value ( x1 w enable u1 f any draw+ ( ! ox's foot1 to con/ruct a figure ( t ( ! %eep or ( ! giraffe ) rem>kable accuracy4 ,illu/ration3 ,fig4 #cfc4 ,t und]ly+ ! v>y+ am\nts ( ext5sion to :i* ! p>ts or segm5ts ( ! limb h be5 subject !re is a law1 or pr9ciple ( cont9uity1 may be disc]n$ f su* a diagram z ! above 7,fig4 #cfc71 :]e ! values ( y 9 ! case ( ! ox are plott$ z a /raight l9e1 & ! correspond+ values = ! %eep 7extract$ f ! above table7 are se5 to =m a m or less regul> & ev5 curve4 ,?is simple graphic result implies ! exi/5ce ( a comp>atively simple equation betwe5 y & y4 ,illu/ration3 ,fig4 #cfd4 7,aft] ,alb]t ,dr]47 ,an elem5t>y application ( ! pr9ciple ( co-ord9ates to ! /udy ( proportion1 z we h "h us$ x to illu/rate ! v>y+ proportions ( a bone1 0 9 common use 9 ! sixte5? & sev5te5? c5turies by arti/s 9 _! /udy ( ! human =m4 ,! me?od is probably mu* m anci5t1 & may ev5 be classical#fed2 x is fully describ$ & put 9 practice by ,alb]t ,dr] 9 8 ,geometry1 & especially 9 8 ,treatise on ,proportion#fee4 ,9 ?is latt] "w1 ! mann] 9 :i* ! #gda human figure1 features1 & facial expression are all trans=m$ & modifi$ by slight v>iations 9 ! relative magnitude ( ! p>ts is admirably & copi\sly illu/rat$ 7,fig4 #cfd74 ,illu/ration3 ,fig4 #cfe4 ,9 a tapir's foot !re is a /rik+ diff]5ce1 & yet at ! same "t !re is an obvi\s und]ly+ resemblance1 betwe5 ! middle toe & ei!r ( its unsymmetrical lat]al neighb\rs4 ,let u take ! m$ian t]m9al phalanx & inscribe its outl9e 9 a net ( rectangul> equidi/ant co-ord9ates 7,fig4 #cfe1 a74 ,let u !n make a simil> network ab\t axes :i* are no long] at "r angles1 b incl9$ to "o ano!r at an angle ( ab\t #ej 7b74 ,if into ?is new network we fill 91 po9t = po9t1 an outl9e precisely correspond+ to our orig9al draw+ ( ! middle toe1 we %all f9d t we h already repres5t$ ! ma9 features ( ! adjac5t lat]al "o4 ,we %all1 h[ev]1 p]ceive t our new diagram looks a little too bulky on "o side1 ! inn] side1 ( ! lat]al toe4 ,if n[ we sub/itute = our equidi/ant ord9ates1 ord9ates :i* get gradually clos] & clos] toge!r z we pass t[>ds ! m$ian side ( ! toe1 !n we %all obta9 a diagram :i* diff]s 9 no ess5tial respect f an actual outl9e copy ( ! lat]al toe 7c74 ,9 %ort1 ! diff]5ce betwe5 ! outl9e ( ! middle toe ( ! tapir & ! next lat]al toe may be almo/ completely express$ by say+ t if ! "o be repres5t$ by rectangul> equidi/ant co-ord9ates1 ! o!r w be repres5t$ by oblique co-ord9ates1 ^: axes make an angle ( #ej1 & 9 :i* ! abscissal int]spaces decrease 9 a c]ta9 log>i?mic ratio4 ,we treat$ our orig9al complex curve or projection ( ! tapir's toe z a function ( ! =m ,f 7x1 y7 #j4 ,! figure ( ! tapir's lat]al #gdb toe is a precisely id5tical function ( ! =m ,f 7ex1 y#a7 #j1 :]e x#a1 y#a are oblique co-ord9ate axes incl9$ to "o ano!r at an angle ( #ej4 ,illu/ration3 ,fig4 #cff4 7,aft] ,alb]t ,dr]47 ,dr] 0 acqua9t$ ) ^! oblique co-ord9ates also1 & ,i h copi$ two illu/rative figures f 8 book#fef4 ,illu/ration3 ,fig4 #cfg4 ,oi?ona nana4 ,illu/ration3 ,fig4 #cfh4 ,sapphir9a4 ,9 ,fig4 #cfg ,i h sket*$ ! common ,copepod ,oi?ona nana1 #gdc & h inscrib$ x 9 a rectangul> net1 ) abscissae ?ree-fif?s ! l5g? ( ! ord9ates4 ,side by side 7,fig4 #cfh7 is drawn a v diff]5t ,copepod1 ( ! g5us ,sapphir9a2 & ab\t x is drawn a network su* t ea* co-ord9ate passes 7z ne>ly z possible7 ?r\gh po9ts correspond+ to ^? ( ! =m] figure4 ,x w be se5 t two diff]5ces are app>5t4 7#a7 ,! values ( y 9 ,fig4 #cfh are l>ge 9 ! upp] "p ( ! figure1 & dim9i% rapidly t[>ds its base4 7#b7 ,! values ( x are v l>ge 9 ! neighb\rhood ( ! orig91 b dim9i% rapidly z we pass t[>ds ei!r side1 away f ! m$ian v]tical axis2 & x is probable t !y d s accord+ to a def9ite1 b some:at complicat$1 ratio4 ,if1 in/ead ( seek+ = an actual equation1 we simply tabulate our values ( x & y 9 ! second figure z comp>$ ) ! fir/ 7j z we did 9 comp>+ ! feet ( ! ,ungulates71 we get ! dim5sions ( a net 9 :i*1 by simply project+ ! figure ( ,oi?ona1 we obta9 t ( ,sapphir9a )\t fur!r tr\ble1 e4g43 x 7,oi?ona7 #j #c #f #i #ab #ae -- x 7,sapphir9a7 #j #h #aj #ab #ac #ad -- y 7,oi?ona7 #j #e #aj #ae #bj #be #cj y 7,sapphir9a7 #j #b #g #c #bc #cb #dj ,9 ?is mann]1 ) a s+le model or type to copy f1 we may record 9 v brief space ! data requisite = ! production ( approximate outl9es ( a great numb] ( =ms4 ,= in/ance ! diff]5ce1 at fir/ sight imm5se1 betwe5 ! att5uat$ body ( a ,caprella & ! ?ick-set body ( a ,cyamus is obvi\sly little1 & is probably no?+1 m ?an a diff]5ce ( relative magnitudes1 capable ( tabulation by numb]s & ( complete expression by means ( rectil9e> co-ord9ates4 ,! ,cru/acea af=d innum]able in/ances ( m complex de=mations4 ,?us we may comp>e v>i\s high] ,cru/acea ) "o ano!r1 ev5 9 ! case ( su* dissimil> =ms z a lob/] & a crab4 ,x is obvi\s t ! :ole body ( ! =m] is elongat$ z comp>$ ) ! latt]1 & t ! crab is relatively broad 9 ! region ( ! c>apace1 :ile x tap]s (f rapidly t[>ds its att5uat$ & abbreviat$ tail4 ,9 a g5]al way1 ! elongat$ rectangul> sy/em ( co-ord9ates #gdd 9 :i* we may inscribe ! outl9e ( ! lob/] becomes a %ort5$ triangle 9 ! case ( ! crab4 ,9 a little m detail we may comp>e ! outl9e ( ! c>apace 9 v>i\s crabs "o ) ano!r3 & ! comp>ison w be f\nd easy & significant1 ev51 9 _m cases1 d[n to m9ute details1 su* z ! numb] & situation ( ! m>g9al sp9es1 ?\gh ^! are 9 o!r cases subject to indep5d5t v>iability4 ,illu/ration3 ,fig4 #cfi4 ,c>apaces ( v>i\s crabs4 #a1 ,g]yon2 #b1 ,cory/es2 #c1 ,scyrama?ia2 #d1 ,p>alomis2 #e1 ,lupa2 #f1 ,*or9us4 ,if we *oose1 to beg9 )1 su* a crab z ,g]yon 7,fig4 #cfi1 #a71 & inscribe x 9 our equidi/ant rectangul> co-ord9ates1 we %all see t we pass easily to =ms m elongat$ 9 a transv]se #gde direction1 su* z ,matuta or ,lupa 7#e71 & conv]sely1 by transv]se compression1 to su* a =m z ,cory/es 7#b74 ,9 c]ta9 o!r cases ! c>apace con=ms to a triangul> diagram1 m or less curvil9e>1 z 9 ,fig4 #d1 :i* repres5ts ! g5us ,p>alomis4 ,"h we c easily see t ! po/]ior bord] is transv]sely elongat$ z comp>$ ) t ( ,g]yon1 :ile at ! same "t ! ant]ior "p is longitud9ally ext5d$ z comp>$ ) ! po/]ior4 ,a sy/em ( slightly curv$ & conv]g+ ord9ates1 ) or?ogonal & log>i?mically int]spac$ abscissal l9es1 z %[n 9 ! figure1 appe>s to satisfy ! conditions4 ,9 an int]e/+ s]ies ( cases1 su* z ! g5us ,*or9us1 or ,scyrama?ia1 & 9 ! spid]-crabs g5]ally1 we appe> to h j ! conv]se ( ?is4 ,:ile ! c>apace ( ^! crabs pres5ts a some:at triangul> =m1 :i* seems at fir/ sight m or less simil> to ^? j describ$1 we soon see t ! actual po/]ior bord] is n[ n>r[ in/ead ( broad1 ! broade/ "p ( ! c>apace correspond+ precisely1 n to t :i* is broade/ 9 ,p>alomis1 b to t :i* 0 broade/ 9 ,g]yon2 :ile ! mo/ /rik+ diff]5ce f ! latt] lies 9 an ant]o-po/]ior l5g!n+ ( ! =ep>t ( ! c>apace1 culm9at+ 9 a great elongation ( ! frontal region1 ) its two sp9es or 8horns40 ,! curv$ ord9ates "h conv]ge po/]iorly & div]ge widely 9 front 7,figs4 #c & #f71 :ile ! decrem5tal int]spac+ ( ! abscissae is v m>k$ inde$4 ,we put our me?od to a sev]] te/ :5 we attempt to sket* an entire & complicat$ animal ?an :5 we simply comp>e correspond+ p>ts su* z ! c>apaces ( v>i\s ,malaco/raca1 or relat$ bones z 9 ! case ( ! tapir's toes4 ,nev]!less1 up to a c]ta9 po9t1 ! me?od /&s ! te/ v well4 ,9 o!r words1 "o p>ticul> mode & direction ( v>iation is (t5 7or ev5 usually7 s prom95t & s p>am\nt ?r\gh\t ! entire organism1 t "o compreh5sive sy/em ( co-ord9ates suffices to give a fair picture ( ! actual ph5om5on4 ,to take ano!r illu/ration f ! ,cru/acea1 ,i h drawn r\ghly 9 ,fig4 #cgj1 #a a little amphipod ( ! family ,phoxocephalidae 7,h>p9ia sp474 ,de=m+ ! co-ord9ates ( ! figure into ! #gdf curv$ or?ogonal sy/em 9 ,fig4 #b1 we at once obta9 a v fair repres5tation ( an alli$ g5us1 belong+ to a diff]5t family ( amphipods1 namely ,/egocephalus4 ,z we proce$ fur!r f our type our co-ord9ates w require great] de=mation1 & ! resultant figure w usually be some:at less accurate4 ,9 ,fig4 #c ,i %[ a network1 to :i*1 if we transf] our diagram ( ,h>p9ia or ( ,/egocephalus1 we %all obta9 a tol]able repres5tation ( ! ab]rant g5us ,hyp]ia1 ) its n>r[ abdom51 its r$uc$ pleural lappets1 its great eyes1 & its inflat$ head4 ,illu/ration3 ,fig #cgj4 #a4 ,h>p9ia plumosa ,kr4 #b4 ,/egocephalus inflatus ,kr4 #c4 ,hyp]ia galba4 ,! hydroid zoophytes con/itute a 8polymorphic0 gr\p1 )9 :i* a va/ numb] ( species h already be5 di/+ui%$2 & ! lab\rs ( ! sy/ematic naturali/ are con/antly add+ to ! numb]4 ,! specific di/9ctions are = ! mo/ "p bas$1 n ^u *>act]s directly pres5t$ #gdg by ! liv+ animal1 b ^u ! =m1 size & arrangem5t ( ! little cups1 or 8calycles10 secret$ & inhabit$ by ! little individual polypes :i* compose ! comp\nd organism4 ,! v>iations1 :i* are app>5tly inf9ite1 ( ^! con=mations are easily se5 to be a "q ( relative magnitudes1 & are capable ( complete expression1 sometimes by v simple1 sometimes by some:at m complex1 co-ord9ate networks4 ,illu/ration3 ,fig4 #cga4 a1 ,campanul>ia macroscyphus1 ,allm42 b1 ,gono?yraea hyal9a1 ,h9cks2 c1 ,clytia ,john/oni1 ,ald]4 ,= in/ance1 ! v>y+ %apes ( ! simple w9eglass-%ap$ cups ( ! ,campanul>idae are at once suffici5tly repres5t$ & comp>$ by means ( simple ,c>tesian co-ord9ates 7,fig4 #cga74 ,9 ! two alli$ families ( ,plumul>iidae & ,aglaoph5iidae ! calycles are set unilat]ally ^u a jo9t$ /em1 & small cup-l /ructures 7hold+ rudim5t>y polypes7 are associat$ ) ! l>ge calycles 9 def9ite numb] & position4 ,^! small calyculi are v>iable 9 numb]1 b 9 ! great majority ( cases !y accompany ! l>ge calycle 9 gr\ps ( ?ree--two /&+ by its upp] bord]1 & "o1 :i* is especially v>iable 9 =m & magnitude1 ly+ at its base4 ,! /em is liable to flexure &1 9 a high degree1 to ext5sion or compression2 & ^! v>iations ext5d1 (t5 on an exagg]at$ scale1 to ! relat$ calycles4 ,z a result we f9d t we c draw v>i\s sy/ems ( curv$ or s9u\s co-ord9ates1 :i* express1 all b completely1 ! configuration ( ! v>i\s #gdh hydroids :i* we inscribe !re9 7,fig4 #cgb74 ,! comp>ative smoo?ness or d5ticulation ( ! m>g9 ( ! calycle1 & ! numb] ( its d5ticles1 con/itutes an indep5d5t v>iation1 & requires sep>ate description2 we h already se5 7p4 #bcf7 t ?is d5ticulation is 9 all probability due to a p>ticul> physical cause4 ,illu/ration3 ,fig4 #cgb4 a1 ,cladoc>pus cr5atus1 ,f42 b1 ,aglaoph5ia pluma1 ,l42 c1 ,a4 rhyn*oc>pa1 ,a42 d1 ,a cornuta1 ,k42 e1 ,a4 ramulosa1 ,k4 ,illu/ration3 ,fig4 #cgc4 ,argyropelecus ,olf]si4 ,illu/ration3 ,fig4 #cgd4 ,/]noptyx diaphana4 ,among ! fi%es we discov] a great v>iety ( de=mations1 "s ( !m ( a v simple k9d1 :ile o!rs are m /rik+ & m unexpect$4 ,a comp>atively simple case1 involv+ a simple %e>1 is illu/rat$ by ,figs4 #cgc & #cgd4 ,fig4 #cgc repres5ts1 )9 ,c>tesian co-ord9ates1 a c]ta9 little oceanic fi% kn[n z ,argyropelecus ,olf]si4 ,fig4 #dgd repres5ts precisely ! same outl9e1 transf]r$ to a sy/em ( oblique co-ord9ates ^: #gdi axes are incl9$ at an angle ( #gj2 b ?is is n[ 7z f> z c be se5 on ! scale ( ! draw+7 a v good figure ( an alli$ fi%1 assign$ to a diff]5t g5us1 "u ! "n ( ,/]noptyx diaphana4 ,! de=mation illu/rat$ by ?is case ( ,argyropelecus is precisely analog\s to ! simple/ & commone/ k9d ( de=mation to :i* fossils are subject 7z we h se5 on p4 #eec7 z ! result ( %e>+-/resses 9 ! solid rock4 ,illu/ration3 ,fig4 #cge4 ,sc>us sp4 ,illu/ration3 ,fig4 #cgf4 ,pomacan?us4 ,fig4 #cge is an outl9e diagram ( a typical ,sc>oid fi%4 ,let u de=m its rectil9e> co-ord9ates into a sy/em ( 7approximately7 coaxial circles1 z 9 ,fig4 #cgf1 & !n fill+ into ! new sy/em1 space by space & po9t by po9t1 our =m] diagram ( ,sc>us1 we obta9 a v good outl9e ( an alli$ fi%1 belong+ to a neighb\r+ family1 ( ! g5us ,pomacan?us4 ,?is case is all ! m int]e/+1 because ^u ! body ( our ,pomacan?us !re are /rik+ col\r b&s1 :i* correspond 9 direction v closely to ! l9es ( our new curv$ ord9ates4 ,9 l mann]1 ! /ill m biz>re outl9es ( o!r fi%es ( ! same family ( ,*aetodonts w be f\nd to correspond to v slight modifications ( simil> co-ord9ates2 9 o!r words1 to small v>iations 9 ! values ( ! con/ants ( ! coaxial curves4 ,9 ,figs4 #cgg-chj ,i h repres5t$ ano!r s]ies ( ,acan?opt]ygian fi%es1 n v di/antly relat$ to ! =ego+4 ,if we />t ?is s]ies ) ! figure ( ,polyprion1 9 ,fig4 #cgg1 we see t ! outl9es ( ,pseudopriacan?us 7,fig4 #cgh7 & ( ,seba/es or ,scorpa5a 7,fig4 #cgi7 are easily d]iv$ by sub/itut+ a sy/em ( triangul>1 or radial1 co-ord9ates = ! rectangul> ones 9 #gej :i* we _h inscrib$ ,polyprion4 ,! v curi\s fi% ,antigonia capros1 an oceanic relative ( our own 8bo>-fi%10 con=ms closely to ! peculi> de=mation repres5t$ 9 ,fig4 #chj4 ,illu/ration3 ,fig4 #cgg4 ,polyprion4 ,illu/ration3 ,fig4 #cgh4 ,pseudopriacan?us altus4 ,illu/ration3 ,fig4 #cgi4 ,scorpa5a sp4 ,illu/ration3 ,fig4 #chj4 ,antigonia capros4 ,illu/ration3 ,fig4 #cha4 ,diodon4 ,illu/ration3 ,fig4 #chb4 ,or?agoriscus4 ,fig4 #cha is a common1 typical ,diodon or porcup9e-fi%1 & 9 ,fig4 #chb ,i h de=m$ its v]tical co-ord9ates into a sy/em ( conc5tric circles1 & its horizontal co-ord9ates into a sy/em ( curves :i*1 approximately & provisionally1 are made to resemble a sy/em ( hyp]bolas#feg4 ,! old outl9e1 transf]r$ #gea 9 its integrity to ! new network1 appe>s z a manife/ repres5tation ( ! closely alli$1 b v diff]5t look+1 sunfi%1 ,or?agoriscus mola4 ,?is is a p>ticul>ly in/ructive case ( de=mation or trans=mation4 ,x is true t1 9 a ma!matical s5se1 x is n a p]fectly satisfactory or p]fectly regul> de=mation1 = ! sy/em is no long] isogonal2 b nev]!less1 x is symmetrical to ! eye1 & obvi\sly approa*es to an isogonal sy/em "u c]ta9 conditions ( friction or con/ra9t4 ,& z su* x acc\nts1 by "o s+le integral trans=mation1 = all ! app>5tly sep>ate & di/9ct ext]nal diff]5ces betwe5 ! two fi%es4 ,x leaves ! p>ts ne> to ! orig9 ( ! sy/em1 ! :ole region ( ! head1 ! op]cul> orifice & ! pectoral f91 practically un*ang$ #geb 9 =m1 size & position2 & x %ews a great] & great] app>5t modification ( size & =m z we pass f ! orig9 t[>ds ! p]iph]y ( ! sy/em4 ,9 a ^w1 x is suffici5t to acc\nt = ! new & /rik+ cont\r 9 all its ess5tial details1 ( r\nd$ body1 exagg]at$ dorsal & v5tral f9s1 & truncat$ tail4 ,9 l mann]1 & us+ precisely ! same co-ord9ate networks1 x appe>s to me possible to %ew ! relations1 almo/ bone = bone1 ( ! skeletons ( ! two fi%es2 9 o!r words1 to recon/ruct ! skeleton ( ! "o f our k ( ! skeleton ( ! o!r1 "u ! guidance ( ! same correspond5ce z is indicat$ 9 _! ext]nal configuration4 ,! family ( ! crocodiles has _h a special int]e/ = ! evolutioni/ ev] s9ce ,huxley po9t$ out t1 9 a degree only second to ! horse & its ance/ors1 x furni%es u ) a close & almo/ unbrok5 s]ies ( transitional =ms1 runn+ d[n 9 cont9u\s succession f "o geological =mation to ano!r4 ,i %\ld be incl9$ to transpose ?is g5]al /atem5t into o!r t]ms1 & to say t ! ,crocodilia con/itute a case 9 :i*1 ) unusually little complication f ! pres5ce ( indep5d5t v>iants1 ! tr5d ( "o p>ticul> mode ( trans=mation is visibly manife/$4 ,if we exclude mean:ile f our comp>ison a few ( ! olde/ ( ! crocodiles1 su* z ,belodon1 :i* diff] m fundam5tally f ! re/1 we %all f9d a long s]ies ( g5]a 9 :i* we c ref] n only ! *ang+ cont\rs ( ! skull1 b ev5 ! %ape & size ( ! _m con/itu5t bones & _! int]v5+ spaces or 8vacuities10 to "o & ! same simple sy/em ( trans=m$ co-ord9ates4 ,! mann] 9 :i* ! skulls ( v>i\s ,crocodilians diff] f "o ano!r may be suffici5tly illu/rat$ by ?ree or f\r examples4 ,illu/ration3 ,fig4 #chc4 ,a1 ,crocodilus porosus4 ,b1 ,c4 am]icanus4 ,c1 ,notosu*us t]re/ris4 ,let u take "o ( ! typical mod]n crocodiles z our /&>d ( =m1 e4g4 ,c4 porosus1 & inscribe x1 z 9 ,fig4 #chc1 a1 9 ! usual ,c>tesian co-ord9ates4 ,by de=m+ ! rectangul> network into a triangul> sy/em1 ) ! apex ( ! triangle a little way 9 front ( ! sn\t1 z 9 b1 we pass to su* a =m z ,c4 am]icanus4 ,by an exagg]ation ( ! same process we at once get an approximation to ! =m ( "o ( ! %>p-sn\t$1 #gec or longiro/r9e1 crocodiles1 su* z ! g5us ,tomi/oma2 &1 9 ! species figur$1 ! oblique position ( ! orbits1 ! ar*$ cont\r ( ! occipital bord]1 & c]ta9 o!r *>act]s sugge/ a c]ta9 am\nt ( curvature1 su* z ,i h repres5t$ 9 ! diagram 7,fig4 #chc1 b71 on ! "p ( ! horizontal co-ord9ates4 ,9 ! /ill m elongat$ skull ( su* a =m z ! ,indian ,gavial1 ! :ole skull has und]gone a great longitud9al ext5sion1 or1 9 o!r words1 ! ratio ( x_/y is greatly dim9i%$2 & ?is ext5sion is n uni=m1 b is at a maximum 9 ! region ( ! nasal & maxill>y bones4 ,?is especially elongat$ region is at ! same "t n>r[$ 9 an exceptional degree1 & its excessive n>r[+ is repres5t$ by a curvature1 convex t[>ds ! m$ian axis1 on ! "p ( ! v]tical ord9ates4 ,let u take z a la/ illu/ration "o ( ! ,mesozoic crocodiles1 ! little ,notosu*us1 f ! ,cretace\s =mation4 ,?is little crocodile is v diff]5t f our type 9 ! proportions ( its skull4 ,! region ( ! sn\t1 9 front ( & includ+ ! frontal bones1 is greatly %ort5$2 f con/itut+ fully two-?irds ( ! :ole l5g? ( ! skull 9 ,crocodilus1 x n[ con/itutes less ?an half1 or1 say1 ?ree-sev5?s ( ! :ole2 & ! :ole skull1 & especially its po/]ior "p1 is curi\sly compact1 broad1 & squat4 ,! orbit is unusually l>ge4 ,if 9 ! diagram ( ?is skull we select a numb] ( po9ts obvi\sly correspond+ #ged to po9ts :]e our rectangul> co-ord9ates int]sect p>ticul> bones or o!r recognisable features 9 our typical crocodile1 we %all easily discov] t ! l9es jo9+ ^! po9ts 9 ,notosu*us fall into su* a co-ord9ate network z t :i* is repres5t$ 9 ,fig4 #chc1 c4 ,to all int5ts & purposes1 !n1 ?is n v complex sy/em1 repres5t+ "o h>moni\s 8de=mation10 acc\nts = all ! diff]5ces betwe5 ! two figures1 & is suffici5t to enable "o at any "t to recon/ruct a detail$ draw+1 bone = bone1 ( ! skull ( ,notosu*us f ! model furni%$ by ! common crocodile4 ,illu/ration3 ,fig4 #chd4 ,pelvis ( 7,a7 ,/egosaurus2 7,b7 ,camptosaurus4 ,! _m div]se =ms ( ,d9osaurian reptiles1 all ( :i* manife/ a /rong family lik5ess und]ly+ mu* sup]ficial div]sity1 furni% u ) pl5tiful mat]ial = comp>ison by ! me?od ( trans=mations4 ,z an in/ance1 ,i h figur$ ! pelvic bones ( ,/egosaurus & ( ,camptosaurus 7,fig4 #chd1 a1 b7 to %[ t1 :5 ! =m] is tak5 z our ,c>tesian type1 a slight curvature & an approximately log>i?mic ext5sion ( ! x-axis br+s u easily to ! configuration ( ! o!r4 ,9 ! orig9al specim5 ( ,camptosaurus describ$ by ,m>%#feh1 ! ant]ior portion ( ! iliac bone is miss+2 & 9 ,m>%'s re/oration ?is "p ( ! bone is drawn z ?\gh x came some:at abruptly to a %>p po9t4 ,9 my figure ,i #gee h complet$ ?is miss+ "p ( ! bone 9 h>mony ) ! g5]al co-ord9ate network :i* is sugge/$ by our comp>ison ( ! two entire pelves2 & ,i v5ture to ?9k t ! result is m natural 9 appe>ance1 & m likely to be correct ?an 0 ,m>%'s conjectural re/oration4 ,x w\ld seem1 9 fact1 t !re is an obvi\s field = ! employm5t ( ! me?od ( co-ord9ates 9 ?is task ( reproduc+ miss+ portions ( a /ructure to ! prop] scale & 9 h>mony ) relat$ types4 ,to ?is subject we %all pres5tly return4 ,illu/ration3 ,fig4 #che4 ,%\ld]-girdle ( ,cryptocleidus4 a1 "y2 b1 adult4 ,illu/ration3 ,fig4 #chf4 ,%\ld]-girdle ( ,i*?yosaurus4 ,9 ,fig4 #che1 a1 b1 ,i h drawn ! %\ld]-girdle ( ,cryptocleidus1 a ,plesiosaurian reptile1 half-gr[n 9 ! "o case & full-gr[n 9 ! o!r4 ,! *ange ( =m dur+ gr[? 9 ?is region ( ! body is v consid]able1 & its nature is well br\ght out by ! two co-ord9ate sy/ems4 ,9 ,fig4 #chf ,i h drawn ! %\ld]-girdle ( an ,i*?yosaur1 ref]r+ x to ,cryptocleidus z a /&>d ( comp>ison4 ,! int]clavicle1 :i* is pres5t 9 ,i*?yosaurus1 is m9ute & hidd5 9 ,cryptocleidus2 b ! num]\s o!r diff]5ces betwe5 ! two #gef =ms1 *ief among :i* is ! great elongation 9 ,i*?yosaurus ( ! two clavicles1 are all se5 by our diagrams to be "p & p>cel ( "o g5]al & sy/ematic de=mation4 ,illu/ration3 ,fig4 #chg4 a1 ,skull ( ,dimorphodon4 b1 ,skull ( ,pt]anodon4 ,be=e we leave ! gr\p ( reptiles we may glance at ! v /rangely modifi$ skull ( ,pt]anodon1 "o ( ! ext9ct fly+ reptiles1 or ,pt]osauria4 ,9 ?is v curi\s skull ! region ( ! jaws1 or beak1 is greatly elongat$ & po9t$2 ! occipital bone is drawn out into an enorm\s backw>dly-direct$ cre/2 ! po/]ior "p ( ! l[] jaw is simil>ly produc$ backw>ds2 ! orbit is small2 & ! quadrate bone is /rongly incl9$ d[nw>ds & =w>ds4 ,! :ole skull has a configuration :i* /&s1 app>5tly1 9 ! /ronge/ possible contra/ to t ( a m normal ,orni?osaurian su* z ,dimorphodon4 ,b if we inscribe ! latt] 9 ,c>tesian coord9ates 7,fig4 #chg1 a71 & ref] our ,pt]anodon to a sy/em ( oblique co-ord9ates 7b71 9 :i* ! two co-ord9ate sy/ems ( p>allel l9es become ea* a p5cil ( div]g+ rays1 we make manife/ a correspond5ce :i* ext5ds uni=mly ?r\gh\t all p>ts ( ^! v diff]5t-look+ skulls4 ,illu/ration3 ,fig4 #chh4 ,pelvis ( ,ar*aeopt]yx4 ,illu/ration3 ,fig4 #chi4 ,pelvis ( ,apatornis4 ,we h dealt s f>1 & = ! mo/ "p we %all cont9ue to deal1 ) our co-ord9ate me?od z a means ( comp>+ "o kn[n /ructure ) ano!r4 ,b x is obvi\s1 z ,i h said1 #geg t x may also be employ$ = draw+ hypo!tical /ructures1 on ! assumption t !y h v>i$ f a kn[n =m 9 "s def9ite way4 ,& ?is process may be especially useful1 & w be mo/ obvi\sly legitimate1 :5 we apply x to ! p>ticul> case ( repres5t+ int]m$iate /ages betwe5 two =ms :i* are actually kn[n to exi/1 9 o!r words1 ( recon/ruct+ ! transitional /ages ?r\gh :i* ! c\rse ( evolution mu/ h successively travell$ if x has br\ght ab\t ! *ange f "s ance/ral type to its presum$ desc5dant4 ,"s little "t ago ,i s5t to my fri5d1 ,mr ,g]h>d ,heilmann ( ,cop5hag51 a few ( my own r\gh co-ord9ate diagrams1 includ+ "s 9 :i* ! pelves ( c]ta9 anci5t & primitive birds 7 comp>$ "o ) ano!r4 ,mr ,heilmann1 :o is bo? a skill$ draughtsman & an able morphologi/1 return$ me a set ( diagrams :i* are a va/ improvem5t on my own1 #geh & :i* are reproduc$ 9 ,figs4 #chh-cic4 ,"h we h1 z extreme cases1 ! pelvis ( ,ar*aeopt]yx1 ! mo/ anci5t ( kn[n birds1 & t ( ,apatornis1 "o ( ! fossil 8too!d0 ,illu/ration3 ,fig4 #cij4 ,! co-ord9ate sy/ems ( ,figs4 #chh & #chi1 ) ?ree int]m$iate sy/ems int]polat$4 ,illu/ration3 ,fig4 #cia4 ,! fir/ int]m$iate co-ord9ate network1 ) its correspond+ inscrib$ pelvis4 birds f ! ,nor? ,am]ican ,cretace\s =mations--a bird %ew+ "s resemblance to ! mod]n t]ns4 ,! pelvis ( ,ar*aeopt]yx is tak5 z our type1 & ref]r$ accord+ly to #gei ,c>tesian co-ord9ates 7,fig4 #chh72 :ile ! correspond+ coord9ates ( ! v diff]5t pelvis ( ,apatornis are repres5t$ 9 ,fig4 #chi4 ,9 ,fig4 #cij ! outl9es ( ^! two co-ord9ate sy/ems are sup]pos$ ^u "o ano!r1 & ^? ( ?ree int]m$iate & equidi/ant co-ord9ate sy/ems are int]polat$ betwe5 !m4 ,f ea* ( ^! latt] sy/ems1 s det]m9$ by direct int]polation1 a complete co-ord9ate diagram is drawn1 & ! correspond+ outl9e ( a pelvis is f\nd f ea* ( ^! sy/ems ( co-ord9ates1 z 9 ,figs4 #cia1 #cib4 ,f9ally1 9 ,fig4 #cic ! complete s]ies is repres5t$1 beg9n+ ) ! kn[n pelvis ( ,ar*aeopt]yx1 & lead+ up by our ?ree int]m$iate hypo!tical types to ! kn[n pelvis ( ,apatornis4 ,illu/ration3 ,fig4 #cib4 ,! second & ?ird int]m$iate co-ord9ate networks1 ) _! correspond+ inscrib$ pelves4 ,among mammalian skulls ,i w take two illu/rations only1 "o drawn f a comp>ison ( ! human skull ) t ( ! high] apes1 & ano!r f ! gr\p ( ,p]issodactyle #gfj ,ungulates1 ! gr\p :i* includes ! rh9oc]os1 ! tapir1 & ! horse4 ,illu/ration3 ,fig4 #cic4 ,! pelves ( ,ar*aeopt]yx & ( ,apatornis1 ) ?ree transitional types int]polat$ betwe5 !m4 ,let u beg9 by *oos+ z our type ! skull ( ,hyra*yus agr>ius1 ,cope1 f ! ,middle ,eoc5e ( ,nor? ,am]ica1 z figur$ by ,osborn 9 8 ,monograph ( ! ,ext9ct ,rh9oc]oses#fei 7,fig4 #cid74 ,illu/ration3 ,fig4 #cid4 ,skull ( ,hyra*yus agr>ius4 7,aft] ,osborn47 ,illu/ration3 ,fig4 #cie4 ,skull ( ,ac]a!rium tridactylum4 7,aft] ,osborn47 ,! _m o!r =ms ( primitive rh9oc]os describ$ 9 ! monograph diff] f ,hyra*yus 9 v>i\s details--9 ! *>act]s ( ! tee?1 sometimes 9 ! numb] ( ! toes1 & s =?2 & !y also diff] v consid]ably 9 ! g5]al #gfa appe>ance ( ! skull4 ,b ^! diff]5ces 9 ! con=mation ( ! skull1 conspicu\s z !y are at fir/ sight1 w be f\nd easy to br+ "u ! conception ( a simple & homog5e\s trans=mation1 su* z w\ld result f ! application ( "s n v complicat$ /ress4 ,= in/ance1 ! correspond+ co-ord9ates ( ,ac]a!rium tridactylum1 z %[n 9 ,fig4 #cie1 indicate t ! ess5tial diff]5ce betwe5 ?is skull & ! =m] "o may be summ$ up by say+ t ! long axis ( ! skull ( ,ac]a!rium has und]gone a slight d\ble curvature1 :ile ! upp] p>ts ( ! skull h at ! same "t be5 #gfb subject to a v]tical expansion1 or to gr[? 9 some:at great] proportion ?an ! l[] p>ts4 ,precisely ! same *anges1 on a some:at great] scale1 give u ! skull ( an exi/+ rh9oc]os4 ,illu/ration3 ,fig4 #cif4 ,occipital view ( ! skulls ( v>i\s ext9ct rh9oc]oses 7,ac]a!rium spp474 7,aft] ,osborn47 ,among ! species ( ,ac]a!rium1 ! po/]ior1 or occipital1 view ( ! skull pres5ts specific diff]5ces :i* are p]haps m conspicu\s ?an ^? furni%$ by ! side view2 & ^! diff]5ces are v /rik+ly br\ght out by ! s]ies ( con=mal trans=mations :i* ,i h repres5t$ 9 ,fig4 #cif4 ,9 ?is case x w p]haps be notic$ t ! correspond5ce is n always q accurate 9 small details4 ,x c\ld easily h be5 made mu* m accurate by giv+ a slightly s9u\s curvature to c]ta9 ( ! co-ord9ates4 ,b z !y /&1 ! correspond5ce indicat$ is v close1 & ! simplicity ( ! figures illu/rates all ! bett] ! g5]al "* ( ! trans=mation4 ,by simil> & n m viol5t *anges we pass easily to su* alli$ =ms z ! ,titano!res 7,fig4 #cig72 & ! well-kn[n s]ies ( species ( ,titano!rium1 by :i* ,pr(essor ,osborn has #gfc illu/rat$ ! evolution ( ?is g5us1 con/itutes a simple & suitable case = ! application ( our me?od4 ,b our me?od enables u to pass ov] great] gaps ?an ^!1 & to disc]n ! g5]al1 & to a v l>ge ext5t ev5 ! detail$1 resemblances betwe5 ! skull ( ! rh9oc]os & ^? ( ! tapir or ! horse4 ,f ! ,c>tesian co-ord9ates 9 :i* we h begun by inscrib+ ! skull ( a primitive rh9oc]os1 we pass to ! tapir's skull 7,fig4 #cih71 fir/ly1 by conv]t+ ! rectangul> into a triangul> network1 by :i* we repres5t ! depression ( ! ant]ior & ! progressively increas+ elevation ( ! po/]ior "p ( ! skull2 & secondly1 by giv+ to ! v]tical ord9ates a curvature su* z to br+ ab\t a c]ta9 longitud9al compression1 or cond5sation1 9 ! =ep>t ( ! skull1 especially 9 ! nasal & orbital regions4 ,illu/ration3 ,fig4 #cig4 ,titano!rium robu/um4 ,illu/ration3 ,fig4 #cih4 ,tapir's skull4 ,! con=mation ( ! horse's skull dep>ts f t ( our primitive ,p]issodactyle 7t is to say our e>ly type ( rh9oc]os1 ,hyra*yus7 9 a direction t is ne>ly ! opposite ( t tak5 by ,titano!rium & by ! rec5t species ( rh9oc]os4 ,= we p]ceive1 by ,fig4 #cii1 t ! horizontal co-ord9ates1 :i* 9 ^! latt] cases became trans=m$ into curves ) ! concavity upw>ds1 are curv$1 9 ! case ( ! horse1 9 ! opposite direction4 ,& ! v]tical ord9ates1 :i* are also curv$1 some:at 9 ! same fa%ion z 9 ! tapir1 are v ne>ly equidi/ant1 in/ead ( be+1 z 9 t animal1 cr[d$ toge!r ant]iorly4 ,ord9ates & abscissae =m an oblique #gfd sy/em1 z is %[n 9 ! figure4 ,9 ?is case ,i h attempt$ to produce ! network beyond ! region :i* is actually requir$ to include ! diagram ( ! horse's skull1 9 ord] to %[ bett] ! =m ( ! g5]al trans=mation1 ) a "p only ( :i* we h actually to deal4 ,illu/ration3 ,fig4 #cii4 ,horse's skull4 ,illu/ration3 ,fig4 #djj4 ,rabbit's skull4 ,x is at fir/ sight n a little surpris+ to f9d t we c pass1 by a cognate & ev5 simpl] trans=mation1 f our ,p]issodactyle skulls to t ( ! rabbit2 b ! fact t we c easily d s is a simple illu/ration ( ! und\bt$ aff9ity :i* exi/s betwe5 ! ,rod5tia1 especially ! family ( ! ,leporidae1 & ! m primitive ,ungulates4 ,= my "p1 ,i w\ld g fur!r2 = ,i ?9k !re is /rong reason to believe t ! ,p]issodactyles are m closely relat$ to ! ,leporidae ?an ! =m] are to ! o!r ,ungulates1 or ?an ! ,leporidae are to ! re/ ( ! ,rod5tia4 ,be t z x may1 x is obvi\s f ,fig4 #djj t ! rabbit's skull con=ms to a sy/em ( #gfe co-ord9ates correspond+ to ! ,c>tesian co-ord9ates 9 :i* we h inscrib$ ! skull ( ,hyra*yus1 ) ! diff]5ce1 fir/ly1 t ! horizontal ord9ates ( ! latt] are trans=m$ into equidi/ant curv$ l9es1 approximately arcs ( circles1 ) _! concavity direct$ d[nw>ds2 & secondly1 t ! v]tical ord9ates are trans=m$ into a p5cil ( rays approximately or?ogonal to ! circul> arcs4 ,9 %ort1 ! configuration ( ! rabbit's skull is d]iv$ f t ( our primitive rh9oc]os by ! unexpect$ly simple process ( submitt+ ! latt] to a ,illu/ration3 ,fig4 #dja4 ,a1 outl9e diagram ( ! ,c>tesian co-ord9ates ( ! skull ( ,hyraco!rium or ,eohippus1 z %ewn 9 ,fig4 #djb1 ,a4 ,h1 outl9e ( ! correspond+ projection ( ! horse's skull4 ,b-,g1 int]m$iate1 or int]polat$1 outl9es4 /rong & uni=m flexure 9 ! d[nw>d direction 7cf4 ,fig4 #ceh1 p4 #gca74 ,9 ! case ( ! rabbit ! configuration ( ! individual bones does n con=m q s well to ! g5]al trans=mation z x does :5 we are comp>+ ! sev]al ,p]issodactyles "o ) ano!r2 & ! *ief dep>tures f con=mity w be f\nd 9 ! size ( ! orbit & 9 ! outl9e ( ! imm$iately surr\nd+ bones4 ,! simple fact is t ! relatively enorm\s eye ( ! rabbit con/itutes an indep5d5t v>iation1 :i* _c be br\ght into ! g5]al & fundam5tal trans=mation1 b mu/ be dealt ) #gfh sep>ately4 ,! enl>gem5t ( ! eye1 l ! modification 9 =m & numb] ( ! tee?1 is a sep>ate ph5om5on1 :i* supplem5ts b 9 no way contradicts our g5]al comp>ison ( ! skulls tak5 9 _! entirety4 ,illu/ration3 two pr9t$ pages ,fig4 #djb4 ,a1 skull ( ,hyraco!rium1 f ! ,eoc5e1 aft] ,w4 ,b4 ,scott2 ,h1 skull ( horse1 repres5t$ z a co-ord9ate trans=mation ( t ( ,hyraco!rium1 & to ! same scale ( magnitude2 ,b-,g1 v>i\s artificial or imag9>y types1 recon/ruct$ z int]m$iate /ages betwe5 ,a & ,h2 ,m1 skull ( ,mesohippus1 f ! ,oligoc5e1 aft] ,scott1 = comp>ison ) ,c2 ,p1 skull ( ,protohippus1 f ! ,mioc5e1 aft] ,cope1 = comp>ison ) ,e2 ,pp1 l[] jaw ( ,protohippus placidus 7aft] ,mat!w & ,gidley71 = comp>ison ) ,f2 ,mi1 ,miohippus 7aft] ,osborn71 ,pa1 ,p>ahippus 7aft] ,pet]son71 %ew+ resemblance1 b less p]fect agreem5t1 ) ,c & ,d4 ,be=e we leave ! ,p]issodactyla & _! allies1 let u look a little m closely into ! case ( ! horse & its imm$iate relations or ance/ors1 do+ s ) ! help ( a set ( diagrams :i* ,i aga9 owe to ,mr ,g]>d ,heilmann#ffj4 ,"h we />t afre%1 ) ! skull 7,fig4 #djb1 ,a7 ( ,hyraco!rium 7or ,eohippus71 inscrib$ 9 a simple ,c>tesian network4 ,at ! o!r end ( ! s]ies 7,h7 is a skull ( ,equus1 9 its own correspond+ network2 & ! int]m$iate /ages 7,b-,g7 are all drawn by direct & simple int]polation1 z 9 ,mr ,heilmann's =m] s]ies ( draw+s ( ,ar*aeopt]yx & ,apatornis4 ,9 ?is pres5t case1 ! relative magnitudes are %ewn1 z well z ! =ms1 ( ! sev]al skulls4 ,alongside ( ^! recon/ruct$ diagrams1 are set figures ( c]ta9 ext9ct 8horses0 7,equidae or ,palaeo!riidae71 & 9 two cases1 viz4 ,mesohippus & ,protohippus 7,m1 ,p71 x w be se5 t ! actual fossil skull co9cides 9 ! mo/ p]fect fa%ion ) "o ( ! hypo!tical =ms or /ages :i* our me?od %ews to be implicitly involv$ 9 ! transition f ,hyraco!rium to ,equus4 ,9 a ?ird case1 t ( ,p>ahippus 7,pa71 ! correspond5ce 7z ,mr ,heilmann po9ts out7 is by no means exact4 ,! outl9e ( ?is skull comes ne>e/ to t ( ! hypo!tical transition /age ,d1 b ! 8fit0 is n[ a bad "o2 = ! skull ( ,p>ahippus is evid5tly a long]1 /raight] & n>r[] skull1 & diff]s 9 o!r m9or *>act]s besides4 ,9 %ort1 ?\gh "s writ]s h plac$ ,p>ahippus 9 ! direct l9e ( desc5t betwe5 ,equus & ,eohippus1 we see at once t !re is no place = x !re1 & t x mu/1 accord+ly1 repres5t a some:at div]g5t bran* or (f%oot ( ! ,equidae#ffa4 ,x may be notic$1 especially 9 ! case ( ,protohippus #gfi 7,p71 t ! configuration ( ! angle ( ! jaw does n tally q s accurately ) t ( our hypo!tical diagrams z d o!r p>ts ( ! skull4 ,z a matt] ( fact1 ?is region is some:at v>iable1 9 diff]5t species ( a g5us1 & ev5 9 diff]5t individuals ( ! same species2 9 ! small figure 7,pp7 ( ,protohippus placidus ! correspond5ce is m exact4 ,illu/ration3 ,fig4 #djc4 ,human scapulae 7aft] ,dwight74 ,a1 ,caucasian2 ,b1 ,negro2 ,c1 ,nor? ,am]ican ,indian 7f ,k5tucky ,m\nta9s74 ,9 consid]+ ?is s]ies ( figures we _c b be /ruck1 n only ) ! regul>ity ( ! succession ( 8trans=mations10 b also ) ! slight & inconsid]able diff]5ces :i* sep>ate ! kn[n & record$ /ages1 & ev5 ! two extremes ( ! :ole s]ies4 ,^! diff]5ces are no great] 7save 9 reg>d to actual magnitude7 ?an ^? betwe5 "o human skull & ano!r1 at lea/ if we take into acc\nt ! old] or remot] races2 & !y are aga9 no great]1 b if any?+ less1 ?an ! range ( v>iation1 racial & individual1 9 c]ta9 o!r human bones1 = in/ance ! scapula#ffb4 ,! v>iability ( ?is latt] bone is great1 b x is nei!r #ggj surpris+ nor peculi>2 = x is l9k$ ) all ! consid]ations ( me*anical effici5cy & functional modification :i* we dealt ) 9 our la/ *apt]4 ,! scapula occupies1 z x 71 a focus 9 a v important field ( =ce2 & ! l9es ( =ce conv]g+ on x w be v greatly modifi$ by ! v>y+ developm5t ( ! muscles ov] a l>ge area ( ! body & ( ! uses to :i* !y are habitually put4 ,illu/ration3 ,fig4 #djd4 ,human skull4 ,illu/ration3 ,fig4 #dje4 ,co-ord9ates ( *impanzee's skull1 z a projection ( ! ,c>tesian co-ord9ates ( ,fig4 #djd4 ,let u n[ inscribe 9 our ,c>tesian co-ord9ates ! outl9e ( a human skull 7,fig4 #djd71 = ! purpose ( comp>+ x ) ! skulls ( "s ( ! high] apes4 ,we "k be=eh& t ! ma9 diff]5ces betwe5 ! human & ! simian types dep5d ^u ! enl>gem5t or expansion ( ! bra9 & bra9case 9 man1 & ! relative dim9ution or enfeeblem5t ( 8 jaws4 ,toge!r ) ^! *anges1 ! 8facial angle0 increases f an oblique angle to ne>ly a "r angle 9 man1 #gga & ! configuration ( e con/itu5t bone ( ! face & skull und]goes an alt]ation4 ,we d n "k to beg9 )1 & we are n %ewn by ! ord9>y me?ods ( comp>ison1 h[ f> ^! v>i\s *anges =m "p ( "o h>moni\s & congru5t trans=mation1 or :e!r we are to look1 = in/ance1 ^u ! *anges und]gone by ! frontal1 ! occipital1 ! maxill>y1 & ! m&ibul> regions z a cong]ies ( sep>ate modifications or indep5d5t v>iants4 ,b z soon z we h m>k$ out a numb] ( po9ts 9 ! gorilla's or *impanzee's skull1 correspond+ ) ^? :i* our co-ord9ate network int]sect$ 9 ! human skull1 we f9d t ^! correspond+ po9ts may be at once l9k$ up by smoo?ly curv$ l9es ( int]section1 :i* =m a new sy/em ( co-ord9ates & con/itute a simple 8projection0 ( our human skull4 ,! network repres5t$ 9 ,fig4 #dje con/itutes su* a projection ( ! human skull on :at we may call1 figuratively speak+1 ! 8plane0 ( ! *impanzee2 & ! full diagram 9 ,fig4 #djf demon/rates ! correspond5ce4 ,9 ,fig4 #djg ,i h %ewn ! simil> de=mation 9 ! case ( a baboon1 & x is obvi\s t ! trans=mation is ( precisely ! same ord]1 & diff]s only 9 an increas$ int5sity or degree ( de=mation4 ,illu/ration3 ,fig4 #djf4 ,skull ( *impanzee4 ,illu/ration3 ,fig4 #djg4 ,skull ( baboon4 ,9 bo? dim5sions1 z we pass f above d[nw>ds & f beh9d =w>ds1 ! correspond+ areas ( ! network are se5 to increase 9 a gradual & approximately log>i?mic ord] 9 ! l[] z comp>$ ) ! high] type ( skull2 &1 9 %ort1 x becomes at once manife/ t ! modifications ( jaws1 bra9case1 & ! regions betwe5 are all portions ( "o cont9u\s & integral process4 ,x is ( c\rse easy to draw ! #ggb inv]se diagrams1 by :i* ! ,c>tesian co-ord9ates ( ! ape are trans=m$ into curvil9e> & non-equidi/ant co-ord9ates 9 man4 ,f ?is comp>ison ( ! gorilla's or *impanzee's ) ! human skull we realise t an inh]5t weakness und]lies ! an?ropologi/'s me?od ( comp>+ skulls by ref]5ce to a small numb] ( axes4 ,! mo/ important ( ^! are ! 8facial0 & 8basicranial0 axes1 :i* include betwe5 !m ! 8facial angle40 ,b x is1 9 ! fir/ place1 evid5t t ^! axes are m]ely ! pr9cipal axes ( a sy/em ( co-ord9ates1 & t _! re/rict$ & isolat$ use neglects all t c be le>n$ f ! fill+ 9 ( ! re/ ( ! co-ord9ate network4 ,&1 9 ! second place1 ! 8facial axis10 = in/ance1 z ord9>ily us$ 9 ! an?ropological comp>ison ( "o human skull ) ano!r1 or ( ! human skull ) ! gorilla's1 is 9 all cases treat$ z a /raight l9e2 b our inve/igation has %ewn t rectil9e> axes only meet ! case 9 ! simple/ & mo/ closely relat$ trans=mations2 & t1 = in/ance1 9 ! an?ropoid skull no rectil9e> axis is homolog\s ) a rectil9e> axis 9 a man's skull1 b :at is a /raight l9e 9 ! "o has become a c]ta9 def9ite curve 9 ! o!r4 ,mr ,heilmann tells me t he has tri$1 b )\t success1 to obta9 a transitional s]ies betwe5 ! human skull & "s prehuman1 an?ropoid type1 :i* s]ies 7z 9 ! case ( ! ,equidae7 %\ld be f\nd to conta9 o!r kn[n types 9 direct l9e> sequ5ce4 ,x appe>s impossible1 h[ev]1 to obta9 su* a s]ies1 or to pass by successive & cont9u\s gradations ?r\gh su* =ms z ,mesopi!cus1 ,pi!can?ropus1 ,homo ne&]?al5sis1 & ! l[] or high] races ( mod]n man4 ,! failure is n ! fault ( our me?od4 ,x m]ely indicates t no "o /raight l9e ( desc5t1 or ( consecutive trans=mation1 exi/s2 b on ! contr>y1 t among human & an?ropoid types1 rec5t & ext9ct1 we h to d ) a complex problem ( div]g5t1 r ?an ( cont9u\s1 v>iation4 ,& 9 l mann]1 easy z x is to correlate ! baboon's & *impanzee's skulls sev]ally ) t ( man1 & easy z x is to see t ! *impanzee's skull is mu* ne>] to ! human type ?an is ! baboon's1 x is also n difficult to p]ceive t ! s]ies is n1 #ggc /rictly speak+1 cont9u\s1 & t nei!r ( our two apes lies precisely on ! same direct l9e or sequ5ce ( de=mation by :i* we may hypo!tically connect ! o!r ) man4 ,illu/ration3 ,fig4 #djh4 ,skull ( dog1 comp>$ ) ! human skull ( ,fig4 #djd4 ,z a f9al illu/ration ,i h drawn ! outl9e ( a dog's skull 7,fig4 #djh71 & inscrib$ x 9 a network comp>able ) ! ,c>tesian network ( ! human skull 9 ,fig4 #djd4 ,"h we attempt to bridge ov] a wid] gulf ?an we h cross$ 9 any ( our =m] comp>isons4 ,b1 nev]!less1 x is obvi\s t our me?od /ill holds good1 9 spite ( ! fact t !re are v>i\s specific diff]5ces1 su* z ! op5 or clos$ orbit1 etc41 :i* h to be sep>ately describ$ & acc\nt$ =4 ,we see t ! *ief ess5tial diff]5ces 9 plan betwe5 ! dog's skull & ! man's lie 9 ! fact t1 relatively speak+1 ! =m] tap]s away 9 front1 a triangul> tak+ ! place ( a rectangul> con=mation2 secondly1 t1 co9cid5t ) ! tap]+ (f1 !re is a progressive elongation1 or pull+ out1 ( ! :ole =ep>t ( ! skull2 & la/ly1 z a m9or diff]5ce1 t ! /raight v]tical ord9ates ( ! human skull become curv$1 ) _! convexity direct$ =w>ds1 9 ! dog4 ,:ile ! net result is t 9 ! dog1 j z 9 ! *impanzee1 ! bra9-pan is small] & ! jaws are l>g] ?an 9 man1 x is n[ conspicu\sly evid5t t ! co-ord9ate network ( ! ape is by no means int]m$iate betwe5 ^? :i* fit ! o!r two4 ,! mode ( de=mation is on diff]5t l9es2 &1 :ile x may be correct to say t ! *impanzee & ! baboon are m brute-l1 x w\ld be by no means accurate to ass]t t !y are m dog-l1 ?an man4 #ggd ,9 ?is brief acc\nt ( co-ord9ate trans=mations & ( _! morphological utility ,i h dealt ) plane co-ord9ates only1 & h made no m5tion ( ! less elem5t>y subject ( co-ord9ates 9 ?ree-dim5sional space4 ,9 !ory !re is no difficulty :atsoev] 9 su* an ext5sion ( our me?od2 x is j z easy to ref] ! =m ( our fi% or ( our skull to ! rectangul> co-ord9ates x1 y1 z1 or to ! pol> co-ord9ates 1 1 1 z x is to ref] _! plane projections to ! two axes to :i* our inve/igation has be5 conf9$4 ,& t x w\ld be advantage\s to d s goes )\t say+2 = x is ! %ape ( ! solid object1 n t ( ! m]e draw+ ( ! object1 t we want to und]/&2 & already we h f\nd "s ( our easy problems 9 solid geometry lead+ u 7z 9 ! case ( ! =m ( ! bivalve & ev5 ( ! univalve %ell7 quickly 9 ! direction ( co-ord9ate analysis & ! !ory ( con=mal trans=mations4 ,b ?is ext5d$ !me ,i h n attempt$ to pursue1 & x mu/ be left to o!r times1 & to o!r h&s4 ,nev]!less1 let u glance = a mom5t at ! sort ( simple cases1 ! simple/ possible cases1 ) :i* su* an inve/igation might beg92 & we h f\nd our plane co-ord9ate sy/ems s easily & effectively applicable to c]ta9 fi%es t we may seek among !m = our fir/ & t5tative introduction to ! ?ree-dim5sional field4 ,x is obvi\s en\gh t ! same me?od ( description & analysis :i* we h appli$ to "o plane1 we may apply to ano!r3 draw+ by obs]vation1 & by a process ( trial & error1 our v>i\s cross-sections & ! co-ord9ate sy/ems :i* seem be/ to correspond4 ,b ! new & important problem :i* n[ em]ges is to correlate ! de=mation or trans=mation :i* we discov] 9 "o plane ) t :i* we h obs]v$ 9 ano!r3 & at l5g?1 p]haps1 aft] grasp+ ! g5]al pr9ciples ( su* correlation1 to =eca/ approximately :at is likely to take place 9 ! o!r two planes ( ref]5ce :5 we are acqua9t$ ) "o1 t is to say1 to det]m9e ! values along "o axis 9 t]ms ( ! o!r two4 ,let u imag9e a common 8r\nd0 fi%1 & a common 8flat0 fi%1 su* z a haddock & a plaice4 ,^! two fi%es are n z nicely adapt$ = comp>ison by means ( plane co-ord9ates z #gge "s :i* we h /udi$1 ow+ to ! pres5ce ( ess5tially unimportant1 b yet conspicu\s diff]5ces 9 ! position ( ! eyes1 or 9 ! numb] ( ! f9s1--t is to say 9 ! mann] 9 :i* ! cont9u\s dorsal f9 ( ! plaice appe>s 9 ! haddock to be cut or scollop$ into a numb] ( sep>ate f9s4 ,b speak+ broadly1 & ap>t f su* m9or diff]5ces z ^!1 x is manife/ t ! *ief factor 9 ! case 7s f> z we at pres5t see7 is simply ! broad5+ out ( ! plaice's body1 z comp>$ ) ! haddock's1 9 ! dorso-v5tral direction1 t is to say1 along ! y axis2 9 o!r words1 ! ratio x_/y is mu* less1 7& inde$ little m ?an half z great71 9 ! haddock ?an 9 ! plaice4 ,b we also recognise at once t :ile ! plaice 7z comp>$ ) ! haddock7 is exp&$ 9 "o direction1 x is also flatt5$1 or ?9n$ out1 9 ! o!r3 y increases1 b z dim9i%es1 relatively to x4 ,& fur!rmore1 we soon see t ?is is a common or ev5 a g5]al ph5om5on4 ,! high1 exp&$ body 9 our ,antigonia or 9 our sun-fi% is at ! same "t flatt5$ or compress$ f side to side1 9 comp>ison ) ! relat$ fi%es :i* we h *os5 z /&>ds ( ref]5ce or comp>ison2 & conv]sely1 su* a fi% z ! skate1 :ile x is exp&$ f side to side 9 comp>ison ) a %>k or dogfi%1 is at ! same "t flatt5$ or depress$ 9 its v]tical section4 ,we proce$ !n1 to enquire :e!r !re be any simple relation ( magnitude disc]nible betwe5 ^! tw9 factors ( expansion & compression2 & ! v fact t ! two dim5sions t5d to v>y inv]sely already assures u t1 9 ! g5]al process ( de=mation1 ! volume is less affect$ ?an are ! l9e> dim5sions4 ,"s ye>s ago1 :5 ,i 0 /udy+ ! l5g?-weight co-effici5t 9 fi%es 7( :i* we h already spok5 9 ,*ap4 ,,iii1 p4 #ih71 t is to say ! coeffici5t k 9 ! =mula ,w k ,l#c1 or k ,w_/,l#c1 ,i 0 n a little surpris$ to f9d t k 0 all b id5tical 9 two su* diff]5t look+ fi%es z our haddock & our plaice3 ?us indicat+ t ^! two fi%es1 little z !y resemble "o ano!r ext]nally 7?\gh !y belong to two closely relat$ families71 h approximately ! same volume :5 !y are equal 9 l5g?2 or1 9 o!r words1 t ! ext5t to :i* ! plaice's body has become exp&$ or broad5$ is j ab\t #ggf comp5sat$ = by ! ext5t to :i* x has also got flatt5$ or ?9n$4 ,9 %ort1 if we c\ld p]mit ourselves to conceive ( a haddock be+ directly trans=m$ into a plaice1 a v l>ge "p ( ! *ange w\ld be simply acc\nt$ = by suppos+ ! =m] fi% to be 8roll$ out10 z a bak] rolls a piece ( d\gh4 ,?is is1 z x 71 an extreme case ( ! balancem5t des organes1 or 8comp5sation ( p>ts40 ,simple ,c>tesian co-ord9ates w n suffice v well to comp>e ! haddock ) ! plaice1 = ! de=mation und]gone by ! =m] 9 comp>ison ) ! latt] is m on ! l9es ( t by :i* we h comp>$ our ,antigonia ) our ,polyprion2 t is to say1 ! expansion is great] t[>ds ! middle ( ! fi%'s l5g?1 & dw9dles away t[>ds ei!r end4 ,b aga9 simplify+ our illu/ration to ! utmo/1 & be+ cont5t ) a r\gh comp>ison1 we may ass]t t1 :5 haddock & plaice are br\ght to ! same /&>d ( l5g?1 we c inscribe !m bo? 7approximately7 9 rectangul> co-ord9ate networks1 su* t ,y 9 ! plaice is ab\t twice z great z y 9 ! haddock4 ,b if ! volumes ( ! two fi%es be equal1 ?is is z mu* z to say t xyz 9 ! "o case 7or r ! summation ( all ^! values7 is equal to ,,xyz 9 ! o!r2 & !re=e 7s9ce ,x x1 & ,y #by71 x foll[s t ,z z_/#b4 ,:5 we h drawn our v]tical transv]se section ( ! haddock 7or project$ t fi% 9 ! yz plane71 we h reason accord+ly to anticipate t we c draw a simil> projection 7or section7 ( ! plaice by simply d\bl+ ! y's & halv+ ! z's3 &1 v approximately1 ?is turns out to be ! case4 ,! plaice is 79 r\nd numb]s7 j ab\t twice z broad & also j ab\t half z ?ick z ! haddock2 & !re=e ! ratio ( bread? to ?ickness 7or y to z7 is j ab\t f\r times z great 9 ! "o case z 9 ! o!r4 ,x is true t ?is simple1 or simplifi$1 illu/ration c>ries u b a v little way1 & only half prep>es u = mu* great] complications4 ,= in/ance1 we h no "r or reason to presume t ! equality ( weights1 or volumes1 is a common1 mu* less a g5]al rule4 ,& aga91 9 all cases ( m complex de=mation1 su* z t by :i* we h comp>$ ,diodon ) ! sunfi%1 we mu/ be prep>$ = v mu* m #ggg recondite me?ods ( comp>ison & analysis1 lead+ d\btless to v mu* m complicat$ results4 ,9 ?is la/ case1 ( ,diodon & ! sunfi%1 we h se5 t ! v]tical expansion ( ! latt] z comp>$ ) ! =m] fi%1 increases rapidly z we g backw>ds t[>ds ! tail2 b we c by no means say t ! lat]al compression increases 9 l proportion4 ,if any?+1 x w\ld seem t ! said expansion & compression t5d to v>y inv]sely2 = ! ,diodon is v ?ick 9 front & greatly ?9n$ away beh9d1 :ile ! flatt5$ sunfi% is m ne>ly ( ! same ?ickness all ! way along4 ,int]e/+ z ! :ole subject is we mu/ mean:ile leave x alone2 recognis+1 h[ev]1 t if ! difficulties ( description & repres5tation c\ld be ov]come1 x is by means ( su* co-ord9ates 9 space t we %\ld at la/ obta9 an adequate & satisfy+ picture ( ! processes ( de=mation & ( ! directions ( gr[?#ffc4 #ggh ,,epilogue4 ,9 ! beg9n+ ( ?is book ,i said t its scope & treatm5t 7 ( s prefatory a k9d t ( o!r preface x _h no ne$2 & n[1 = ! same reason1 ) no =mal & elaborate conclusion d ,i br+ x to a close4 ,! fact t ,i set little /ore by c]ta9 po/ulates 7(t5 deem$ to be fundam5tal7 ( our pres5t-day biology ! read] w h discov]$ & ,i h n endeav\r$ to conceal4 ,b x is n = ! sake ( polemical argum5t t ,i h writt51 & ! doctr9es :i* ,i d n subscribe to ,i h only spok5 ( by ! way4 ,my task is f9i%$ if ,i h be5 able to %ew t a c]ta9 ma!matical aspect ( morphology1 to :i* z yet ! morphologi/ gives little he$1 is int]wov5 ) 8 problems1 complem5t>y to 8 descriptive task1 & helpful1 nay ess5tial1 to 8 prop] /udy & compreh5sion ( ,=m4 ,hic artem remumque repono4 ,& :ile ,i h s\ght to %ew ! naturali/ h[ a few ma!matical concepts & dynamical pr9ciples may help & guide him1 ,i h tri$ to %ew ! ma!matician a field = 8 lab\r1--a field :i* few h ent]$ & no man has explor$4 ,"h may be f\nd homely problems1 su* z (t5 tax ! highe/ skill ( ! ma!matician1 & rew>d 8 +5uity all ! m = _! trivial associations & outw>d semblance ( simplicity4 ,t ,i am no skill$ ma!matician ,i h _h little ne$ to confess1 b some?+ ( ! use & beauty ( ma!matics ,i ?9k ,i am able to und]/&4 ,i "k t 9 ! /udy ( mat]ial ?+s1 numb]1 ord] & position are ! ?reefold clue to exact k2 t ^! ?ree1 9 ! ma!matician's h&s1 furni% ! 8fir/ outl9es = a sket* ( ! ,univ]se02 t by squ>e & circle we are help$1 l ,emile ,v]ha]5's c>p5t]1 to conceive 8,les lois indubitables et fcondes ,qui sont la rgle et la cl>t du monde40 ,= ! h>mony ( ! _w is made manife/ 9 ,=m & ,numb]1 & ! he>t & s\l & all ! poetry ( ,natural #ggi ,philosophy are embodi$ 9 ! concept ( ma!matical beauty4 ,a great] ?an ,v]ha]5 _h ?is 9 m9d :5 he told ( 8! gold5 compasses1 prep>$ ,9 ,god's et]nal /ore40 ,a great] ?an ,milton _h magnifi$ ! !me & glorifi$ ,him 8:o sitte? ^u ! circle ( ! e>?10 say+3 ,he measure? ! wat]s 9 ! holl[ ( 8 h&1 he mete? out ! heav5s ) 8 span1 he compreh5de? ! du/ ( ! e>? 9 a measure4 ,moreov] ! p]fection ( ma!matical beauty is su* 7z ,maclaur9 le>n$ ( ! bee71 t :atsoev] is mo/ beautiful & regul> is also f\nd to be mo/ useful & excell5t4 ,! liv+ & ! dead1 ?+s animate & inanimate1 we dwell]s 9 ! _w & ?is _w :]e9 we dwell1-- 1--are b\nd alike by physical & ma!matical law4 8,cont]m9\s ) space & coeval ) "t is ! k+dom ( ,ma!matics2 )9 ?is range h] dom9ion is supreme2 o!rwise ?an accord+ to h] ord] no?+ c exi/1 & no?+ takes place 9 contradiction to h] laws40 ,s said1 "s =ty ye>s ago1 a c]ta9 ma!matician2 & ,philolaus ! ,py?agorean _h said mu* ! same4 ,b ) no less love & insight has ! sci5ce ( ,=m & ,numb] be5 apprais$ 9 our own day & g5]ation by a v great ,naturali/ inde$3--by t old man eloqu5t1 t wise /ud5t & pupil ( ! ant & ! bee1 :o di$ b ye/]day1 & :o 9 8 all b saecul> life ta/$ ( ! fir/fruits ( immortality2 :o curi\sly conjo9$ ! wisdom ( antiquity ) ! le>n+ ( to-day2 ^: ,prov5al v]se seems set to ,dorian music2 9 ^: pla9e/ words is a s\nd z ( bees' indu/ri\s murmur2 & :o1 be+ ( ! same blood & m>r[ ) ,plato & ,py?agoras1 saw 9 ,numb] 8la clef de la vote10 & f\nd 9 x 8le comm5t et le p\rquoi des *oses40 ,,notes3 #a ,^! say+s ( ,kant & ( ,du ,bois1 & o!rs l to !m1 h be5 ! text ( _m disc\rses3 see1 = in/ance1 ,/allo's ,concepts1 p4 #ba1 #ahhb2 ,hb]1 ,biol4 ,c5tralbl4 ,,xix1 p4 #bhd1 #ahij1 etc4 ,cf4 also ,jellett1 ,rep4 ,brit4 ,ass4 #ahgd1 p4 #a4 #b 8,quum enim mundi univ]si fabrica sit p]fectissima1 atque a ,creatore sapi5tissimo absoluta1 nihil omn9o 9 mundo cont+it 9 quo non maximi m9imive ratio quaepiam eluceat2 quamobrem dubium prorsus e/ nullum qu9 omnes mundi effectus ex causis f9alibus1 ope me?odi maximorum et m9imorum1 aeque felicit] det]m9>i queant atque ex ipsis causis effici5tibus40 ,me?odus inv5i5di1 etc4 #agdd 7cit4 ,ma*1 ,sci5ce ( ,me*anics1 #aijb1 p4 #dee74 #c ,cf4 ,opp4 7ed4 ,erdmann71 p4 #ajf1 8,bi5 lo9 d'exclure les causes f9ales4441 c'e/ de l qu'il faut t\t dduire en ,physique40 #d ,cf4 p4 #afb4 8,la =ce vitale dirige des phnomnes qu'elle ne produit pas3 les ag5ts physiques produis5t des phnomnes qu'ils ne dirig5t pas40 #e ,x is n[ & !n conc$$ ) reluctance4 ,?us ,enriques1 a le>n$ & philosophic naturali/1 writ+ 8della economia di so/anza nelle osse cave0 7,ar*4 f4 ,entw4 ,me*4 ,,xx1 #aijf71 says 8una c]ta impronta di teleologismo qu e l rima/a1 mio malgrado1 9 que/o scritto40 #f ,cf4 ,clel&1 ,on ,t]m9al ,=ms ( ,life1 ,j4 ,anat4 & ,phys4 ,,xviii1 #ahhd4 #g ,conkl91 ,embryology ( ,crepidula1 ,j\rn4 ( ,morphol4 ,,xiii1 p4 #bjc1 #ahig2 ,lillie1 ,f4 ,r41 ,adaptation 9 ,cleavage1 ,woods ,holl ,biol4 ,lectures1 pp4 #dc-fg1 #ahii4 #h ,i am incl9$ to trace back ,dries*'s tea*+ ( ,entele*y to no less a p]son ?an ,melan*?on4 ,:5 ,bacon 7de ,augm4 ,,iv1 #c7 /ates ) disapproval t ! s\l 8has be5 reg>d$ r z a function ?an z a sub/ance10 ,r4 ,l4 ,ellis po9ts out t he is ref]r+ to ,melan*?on's exposition ( ! ,ari/otelian doctr9e4 ,= ,melan*?on1 ^: view ( ! p]ipatetic philosophy _h long great influ5ce 9 ! ,prote/ant ,univ]sities1 affirm$ t1 accord+ to ! true view ( ,ari/otle's op9ion1 ! s\l is n a sub/ance1 b an 1 or function4 ,he def9$ x z qua$am ci5s actiones--a description all b id5tical ) t ( ,claude ,b]n>d's 8=ce vitale40 #i ,ray ,lanke/]1 ,encycl4 ,brit4 7#i? ed471 art4 8,zoology10 p4 #hjf1 #ahhh4 #aj ,alfr$ ,russel ,wallace1 especially 9 8 lat] ye>s1 reli$ ^u a direct b some:at crude teleology4 ,cf4 8 ,_w ( ,life1 a ,manife/ation ( ,creative ,p[]1 ,directive ,m9d & ,ultimate ,purpose1 #aiaj4 #aa ,janet1 ,les ,causes ,f9ales1 #ahgf1 p4 #cej4 #ab ,! phrase is ,leibniz's1 9 8 ,?odice4 #ac ,cf4 7int4 al47 ,bosanquet1 ,! ,mean+ ( ,teleology1 ,proc4 ,brit4 ,acad4 #aije-f1 pp4 #bce-bde4 ,cf4 also ,leibniz 7,disc\rs de ,mtaphysique2 ,lettres 9dites1 ed4 de ,c>eil1 #aheg1 p4 #ced2 cit4 ,janet1 p4 #fdc71 8,l'un et l'autre e/ bon1 l'un et l'autre peut tre utile 444 et les auteurs qui suiv5t ces r\tes diffr5tes ne devrai5t po9t se maltrait]3 et seq40 #ad ,! read] w und]/& t ,i speak1 n ( ! 8sev]e & dilig5t inquiry0 ( v>iation or ( 8=tuity10 b m]ely ( ! easy assumption t ^! ph5om5a are a suffici5t basis on :i* to re/1 ) ! all-p[]ful help ( natural selection1 a !ory ( def9ite & progressive evolution4 #ae ,revue ,philosophique4 ,,xxxiii1 #ahib4 #af ,?is g5]al pr9ciple 0 cle>ly grasp$ by ,dr ,george ,ra9ey 7a le>n$ physician ( ,/ ,b>?olomew's7 _m ye>s ago1 & express$ 9 su* words z ! foll[+3 8444444x is illogical to suppose t 9 ! case ( vital organisms a di/9ct =ce exi/s to produce results p]fectly )9 ! rea* ( physical ag5cies1 especially z 9 _m in/ances no end c\ld be atta9$ 7 t ! case1 b t ( oppos+ "o =ce by ano!r capable ( effect+ exactly ! same purpose40 7,on ,artificial ,calculi1 ,q4,j4,m4,s4 7,trans4 ,microsc4 ,soc471 ,,vi1 p4 #di1 #aheh47 ,cf4 also ,helmholtz1 infra cit41 p4 #i4 #ag ,:]eby he incurr$ ! reproa* ( ,socrates1 9 ! ,pha$o4 #ah ,9 a fam\s lecture 7,cons]vation ( ,=ces appli$ to ,organic ,nature1 ,proc4 ,roy4 ,in/it41 ,april #ab1 #ahfa71 ,helmholtz laid x d[n1 z 8! fundam5tal pr9ciple ( physiology10 t 8,!re may be o!r ag5ts act+ 9 ! liv+ body ?an ^? ag5ts :i* act 9 ! inorganic _w2 b ^? =ces1 z f> z !y cause *emical & me*anical influ5ce 9 ! body1 mu/ be q ( ! same "* z inorganic =ces3 9 ?is at lea/1 t _! effects mu/ be rul$ by necessity1 & mu/ always be ! same :5 act+ 9 ! same conditions2 & s !re _c exi/ any arbitr>y *oice 9 ! direction ( _! actions40 ,x w\ld foll[ f ?is1 t1 l ! o!r 8physical0 =ces1 !y mu/ be subject to ma!matical analysis & d$uction4 ,cf4 also ,dr ,t4 ,"y's ,croonian ,lecture ,on ! ,he>t & ,art]ies1 ,phil4 ,trans4 #ahji1 p4 #a2 ,coll4 ,works1 ,i1 #eaa4 #ai ,ektropismus1 od] die physikalis*e ,!orie des ,leb5s1 ,leipzig1 #aiaj4 #bj ,wilde ,lecture1 ,nature1 ,m>* #ab1 #aijh2 ibid4 ,sept4 #f1 #aijj1 p4 #dhe2 ,ae!r & ,matt]1 p4 #bhh4 ,cf4 also ,"l ,kelv91 ,=tnightly ,review1 #ahib1 p4 #cac4 #ba ,joly1 ,! ,abundance ( ,life1 ,proc4 ,roy4 ,dubl9 ,soc4 ,,vii1 #ahij2 & 9 ,sci5tific ,essays1 etc4 #aiae1 p4 #fj et seq4 #bb ,papillon1 ,hi/oire de la philosophie mod]ne1 ,i1 p4 #cjj4 #bc ,) ! special & important prop]ties ( colloidal matt] we are1 = ! "t be+1 n conc]n$4 #bd ,cf4 ,hans ,przibram1 ,anw5dung elem5t>] ,ma!matik auf ,biologis*e ,probleme 79 ,r\x's ,vortrge1 ,heft ,,iii71 ,leipzig1 #aijh1 p4 #aj4 #be ,! subject is treat$ f an eng9e]+ po9t ( view by ,pr(4 ,james ,?omson1 ,comp>isons ( ,simil> ,/ructures z to ,ela/icity1 ,/r5g?1 & ,/ability1 ,trans4 ,in/4 ,eng9e]s1 ,scotl&1 #ahgf 7,collect$ ,pap]s1 #aiab1 pp4 #cfa-cgb71 & by ,pr(4 ,a4 ,b>r1 ibid4 #ahii2 see also ,rayleigh1 ,nature1 ,april #bb1 #aiae4 #bf ,cf4 ,sp5c]1 ,! ,=m ( ! ,e>?1 etc41 ,phil4 ,mag4 ,,xxx1 pp4 #aid-f1 #ahdg2 also ,pr9ciples ( ,biology1 pt4 ,,ii1 *4 ,i1 #ahfd 7p4 #abc1 etc474 #bg ,george ,l\is ,lesage 7#agbd-ahjc71 well kn[n z ! au?or ( "o ( ! few attempts to expla9 gravitation4 7,cf4 ,l]ay1 ,con/itution de la ,matire1 #ahfi2 ,kelv91 ,proc4 ,r4 ,s4 ,e4 ,,vii1 p4 #egg1 #ahgb1 etc42 ,cl]k ,maxwell1 ,phil4 ,trans4 vol4 #aeg1 p4 #ej1 #ahfg2 art4 8,atom10 ,encycl4 ,brit4 #ahge1 p4 #df47 #bh ,cf4 ,pi]re ,prvo/1 ,notices de la vie et des crits de ,lesage1 #ahje2 quot$ by ,janet1 ,causes ,f9ales1 app4 ,,iii4 #bi ,discorsi e ,dimo/razioni matemati*e1 intorno due nuove sci5ze1 att55ti alla ,mecanica1 ed ai ,movim5ti ,locali3 appresso gli ,elzevirii1 ,,mdcxxxviii4 ,op]e1 ed4 ,fav>o1 ,,viii1 p4 #afi seq4 ,transl4 by ,h5ry ,crew & ,a4 de ,salvio1 #aiad1 p4 #acj1 etc4 ,see ,nature1 ,june #ag1 #aiae4 #cj ,s ,w]n] rem>k$ t ,mi*ael ,angelo & ,bramanti c\ld n h built ( gypsum at ,p>is on ! scale !y built ( trav]t9 9 ,rome4 #ca ,sir ,g4 ,gre5hill1 ,det]m9ation ( ! greate/ height to :i* a ,tree ( giv5 proportions c gr[1 ,cambr4 ,phil4 ,soc4 ,pr4 ,,iv1 p4 #fe1 #ahha1 & ,*ree1 ibid4 ,,vii1 #ahib4 ,cf4 ,poynt+ & ,?omson's ,prop]ties ( ,matt]1 #aijg1 p #ii4 #cb ,9 l mann] ! :eat-/raw b5ds ov] "u ! weight ( ! load$ e>1 & ! tip ( ! cat's tail b5ds ov] :5 held upright1--n because !y 8possess flexibility10 b because !y out/rip ! dim5sions )9 :i* /able equilibrium is possible 9 a v]tical position4 ,! kitt5's tail1 on ! o!r h&1 /&s up spiky & /raight4 #cc ,mod]n ,pa9t]s4 #cd ,! /em ( ! giant bamboo may atta9 a height ( #fj metres1 :ile n m ?an ab\t #dj cm4 9 diamet] ne> its base1 :i* dim5sions are n v f> %ort ( ! !oretical limits 7,a4 ,j4 ,ew>t1 ,phil4 ,trans4 vol4 #aih1 p4 #ga1 #aijf74 #ce ,trans4 ,zool4 ,soc4 ,,iv1 #ahej1 p4 #bg4 #cf ,x w\ld seem to be a common if n a g5]al rule t m>9e organisms1 zoophytes1 molluscs1 etc41 t5d to be l>g] ?an ! correspond+ & closely relat$ =ms liv+ 9 fre% wat]4 ,:ile ! ph5om5on may h v>i\s causes1 x has be5 attribut$ 7among o!rs7 to ! simple fact t ! =ces ( gr[? are less antagonis$ by gravity 9 ! d5s] m$ium 7cf4 ,h\ssay1 ,la ,=me et la ,vie1 #aijj1 p4 #hae74 ,! effect ( gravity on outw>d =m is illu/rat$1 = in/ance1 by ! contra/ betwe5 ! uni=mly upw>d bran*+ ( a sea-we$ & ! droop+ curves ( a %rub or tree4 #cg ,! analogy is n a v /rict "o4 ,we are n tak+ acc\nt1 = in/ance1 ( a proportionate increase 9 ?ickness ( ! boil]-plates4 #ch ,let ,l be ! l5g?1 ,s ! 7wett$7 surface1 ,t ! tonnage1 ,d ! displacem5t 7or volume7 ( a %ip2 & let x cross ! ,atlantic at a spe$ ,v4 ,!n1 9 comp>+ two %ips1 simil>ly con/ruct$ b ( diff]5t magnitudes1 we "k t ,l ,v#b1 ,s ,l#b ,v#d1 ,d ,t ,l#c ,v#f2 also ,r 7resi/ance7 ,s ,v#b ,v#f2 ,h 7horse-p[]7 ,r ,v ,v#g2 & ! coal 7,c7 necess>y = ! voyage ,h_/,v ,v#f4 ,t is to say1 9 ord9>y eng9e]+ language1 to increase ! spe$ across ! ,atlantic by #a p] c5t4 ! %ip's l5g? mu/ be increas$ #b p] c5t41 h] tonnage or displacem5t #f p] c5t41 h] coal-consumpt also #f p] c5t41 h] horse-p[]1 & !re=e h] boil]-capacity1 #g p] c5t4 ,h] bunk]s1 accord+ly1 keep pace ) ! enl>gem5t ( ! %ip1 b h] boil]s t5d to increase out ( proportion to ! space available4 #ci ,?is is ! result arriv$ at by ,helmholtz1 ,ueb] e9 ,!orem geometris* hnli*e ,bewegung5 flssig] ,krp] betreff5d1 neb/ ,anw5dung auf das ,problem ,luftballons zu l5k51 ,monatsb]4 ,akad4 ,b]l91 #ahgc1 pp4 #eja-ad4 ,x 0 criticis$ & *all5g$ 7some:at ra%ly7 by ,k4 ,mll5h(1 ,die ,grsse d] ,flugfl*51 etc41 ,pflg]'s ,ar*iv1 ,,xxxv1 p4 #djg1 ,,xxxvi1 p4 #edh1 #ahhe4 #dj ,cf4 also ,*abri]1 ,vol des ,insectes1 ,mm4 ,mus4 ,hi/4 ,nat4 ,p>is1 ,,vi-,,viii1 #ahbj-bb4 #da ,a]ial ,flight1 vol4 ,,ii 7,a]odonetics71 #aijh1 p4 #aej4 #db ,by ,lan*e/]1 op4 cit4 p4 #aca4 #dc ,cf4 ,l'empire de l'air2 orni?ologie applique l'aviation4 #ahha4 #dd ,de ,motu ,animalium1 ,i1 prop4 cciv1 ed4 #afhe1 p4 #bdc4 #de ,h>l1 ,on ,atmosph]ic ,pressure 9 pa/ ,geological ,ages1 ,bull4 ,geol4 ,soc4 ,fr4 ,,xi1 pp4 #aah-aba2 or ,cosmos1 p4 #cj1 ,july #h1 #aiaa4 #df ,introduction to ,entomology1 #ahbf1 ,,ii1 p4 #aij4 ,k4 & ,s41 l _m less le>n$ au?ors1 are fond ( popul> illu/rations ( ! 8wond]s ( ,nature10 to ! neglect ( dynamical pr9ciples4 ,!y sugge/1 = in/ance1 t if ! :ite ant 7 z big z a man1 its tunnels w\ld be 8magnific5t cyl9d]s ( m ?an ?ree hundr$ feet 9 diamet]02 & t if a c]ta9 noisy ,brazilian insect 7 z big z a man1 its voice w\ld be he>d all ! _w ov]3 8s t ,/5tor becomes a mute :5 comp>$ ) ^! insects60 ,x is an easy consequ5ce ( an?ropomorphism1 & h5ce a common *>act]i/ic ( fairy-tales1 to neglect ! pr9ciple ( dynamical1 :ile dwell+ on ! aspect ( geometrical1 simil>ity4 #dg ,i4e4 ! available en]gy ( muscle1 9 ft4-lbs4 p] lb4 ( muscle1 is ! same = all animals3 a po/ulate :i* requires consid]able qualification :5 we are comp>+ v diff]5t k9ds ( muscle1 su* z ! insect's & ! mammal's4 #dh ,prop4 clxxvii4 ,animalia m9ora et m9us pond]osa majores saltus efficiunt respectu sui corporis1 si caet]a fu]9t p>ia4 #di ,see also 7int4 al471 ,john ,b]n\lli1 de ,motu ,musculorum1 ,basil41 #afid2 ,*abry1 ,mcanisme du ,saut1 ,j4 de l',anat4 et de la ,physiol4 ,,xix1 #ahhc2 ,sur la longueur des membres des animaux sauteurs1 ibid4 ,,xxi1 p4 #cef1 #ahhe2 ,le ,hello1 ,de l'action des organes locomoteurs1 etc41 ibid4 ,,xxix1 p4 #fe-ic1 #ahic1 etc4 #ej ,re*]*es sur la =ce absolue des muscles des ,inv]tbrs1 ,bull4 ,acad4 ,e4 de ,belgique 7#c71 ,,vi1 ,,vii1 #ahhc-hd2 see also ibid4 7#b71 ,,xx1 #ahfe1 ,,xxii1 #ahff2 ,ann4 ,mag4 ,n4 ,h4 ,,xvii1 p4 #aci1 #ahff1 ,,xix1 p4 #ie1 #ahfg4 ,! subject 0 also well treat$ by ,/raus-,drckheim1 9 8 ,considrations gnrales sur l'anatomie comp>e des animaux articuls1 #ahbh4 #ea ,! fact t ! limb t5ds to sw+ 9 p5dulum-"t 0 fir/ obs]v$ by ! bro!rs ,web] 7,me*anik d] m5s*l4 ,gehw]kzeuge1 ,gtt+51 #ahcf74 ,"s lat] writ]s h criticis$ ! /atem5t 7e4g4 ,fis*]1 ,die ,k9ematik des ,be9s*w+5s etc41 ,abh4 ma?4 phys4 ,kl4 k4 ,s*s4 ,ges4 ,,xxv-,,xxviii1 #ahii-aijc71 b = all t1 ) prop] qualifications1 x rema9s sub/antially true4 #eb ,quot$ 9 ,mr ,john ,bi%op's int]e/+ article 9 ,todd's ,cyclopa$ia1 ,,iii1 p4 #ddc4 #ec ,!re is probably also ano!r factor involv$ "h3 = 9 b5d+1 & !re=e %ort5+1 ! leg we br+ its c5tre ( gravity ne>] to ! pivot1 t is to say1 to ! jo9t1 & s ! muscle t5ds to move x ! m quickly4 #ed ,proc4 ,psy*ical ,soc4 ,,xii1 pp4 #cch-cee1 #ahig4 #ee ,= v>i\s calculations ( ! increase ( surface due to hi/ological & anatomical subdivision1 see ,e4 ,babak1 ,ueb] die ,ob]fl*55twickelung bei ,organism51 ,biol4 ,c5tralbl4 ,,xxx1 pp4 #bbe-bci1 #beg-bfg1 #aiaj4 ,9 connection ) ! physical !ory ( surface-en]gy1 ,wolfgang ,o/wald has introduc$ ! conception ( specific surface1 t is to say ! ratio ( surface to volume1 or ,s_/,v4 ,9 a cube1 ,v l#c1 & ,s #fl#b2 !re=e ,s_/,v #f_/l4 ,!re=e if ! side l measure #f cm41 ! ratio ,s_/,v #a1 & su* a cube may be tak5 z our /&>d1 or unit ( specific surface4 ,a human blood-corpuscle has1 accord+ly1 a specific surface ( some:]e ab\t #ad1jjj or #ae1jjj4 ,x is f\nd 9 physical *emi/ry t surface en]gy becomes an important factor :5 ! specific surface rea*es a value ( #aj1jjj or !reby4 #ef ,?\gh ! entire egg is n increas+ 9 mass1 ?is is n to say t its liv+ protoplasm is n increas+ all ! :ile at ! exp5se ( ! res]ve mat]ial4 #eg ,cf4 ,tait1 ,proc4 ,r4,s4,e4 ,v1 #ahff1 & ,,vi1 #ahfh4 #eh ,physiolog4 ,notiz5 7#i71 p4 #dbe1 #ahie4 ,cf4 ,/rasbrg]1 ,ueb] die ,wirkungssphre d] ,k]ne und die ,zellgrsse1 ,hi/olog4 ,beitr4 7#e71 pp4 #ie-abi1 #ahic2 ,j4 ,j4 ,g]assim[1 ,ueb] die ,grsse des ,zellk]nes1 ,beih4 ,bot4 ,c5tralbl4 ,,xviii1 #aije2 also ,g4 ,levi & ,t4 ,t]ni1 ,le v>iazioni dell' indice plasmatico-nucle>e durante l'int]c9esi1 ,ar*4 ,ital4 di ,anat4 ,x1 p4 #ede1 #aiaa4 #ei ,ar*4 f4 ,entw4 ,me*4 ,,iv1 #ahih1 pp4 #ge1 #bdg4 #fj ,conkl91 ,e4 ,g41 ,cell-size & nucle>-size1 ,j4 ,exp4 ,zool4 ,,xii4 pp4 #a-ih1 #aiab4 #fa ,?us ! fibres ( ! cry/all9e l5s are ( ! same size 9 l>ge & small dogs2 ,rabl1 ,z4 f4 w4 ,z4 ,,lxvii1 #ahii4 ,cf4 7int4 al47 ,pe>son1 ,on ! ,size ( ! ,blood-corpuscles 9 ,rana1 ,biometrika1 ,,vi1 p4 #djc1 #aiji4 ,dr ,?omas ,"y caught sight ( ! ph5om5on1 e>ly 9 la/ c5tury3 8,! solid p>ticles ( ! blood d n by any means v>y 9 magnitude 9 ! same ratio ) ! bulk ( ! animal10 ,natural ,philosophy1 ed4 #ahde1 p4 #dff2 & ,leeuw5hoek & ,/eph5 ,hales 7 aw>e ( x a hundr$ ye>s be=e4 ,b 9 ?is case1 ?\gh ! blood-corpuscles %[ no relation ( magnitude to ! size ( ! animal1 !y d seem to h "s relation to its activity4 ,at lea/ ! corpuscles 9 ! sluggi% ,amphibia are mu* ! l>ge/ kn[n to u1 :ile ! smalle/ are f\nd among ! de] & o!r agile & spe$y mammals4 7,cf4 ,gulliv]1 ,p4,z4,s4 #ahge1 p4 #dgd1 etc47 ,?is app>5t correlation may h its be>+ on mod]n views ( ! surface-cond5sation or adsorption ( oxyg5 9 ! blood-corpuscles1 a process :i* w\ld be greatly facilitat$ & int5sifi$ by ! increase ( surface due to _! m9ut5ess4 #fb ,cf4 ,p4 ,enriques1 ,la =ma come funzione della gr&ezza3 ,ric]*e sui gangli n]vosi degli ,inv]tebrati1 ,ar*4 f4 ,entw4 ,me*4 ,,xxv1 p4 #fee1 #aijg-h4 #fc ,:ile ! diff]5ce 9 cell-volume is va/ly less ?an t betwe5 ! volumes1 & v mu* less also ?an t betwe5 ! surfaces1 ( ! respective animals1 yet !re is a c]ta9 diff]5ce2 & ?is x has be5 attempt$ to correlate ) ! ne$ = ea* cell 9 ! _m-cell$ ganglion ( ! l>g] animal to possess a m complex 8ex*ange-sy/em0 ( bran*es1 = int]communication ) its m num]\s neighb\rs4 ,ano!r explanation is bas$ on ! fact t1 :ile su* cells z cont9ue to divide ?r\gh\t life t5d to uni=mity ( size 9 all mammals1 ^? :i* d n d s1 & 9 p>ticul> ! ganglion cells1 cont9ue to gr[1 & _! size becomes1 !re=e1 a function ( ! duration ( life4 ,cf4 ,g4 ,levi1 ,/udii sulla gr&ezza delle cellule1 ,ar*4 ,ital4 di ,anat4 e di ,embryolog4 ,v1 p4 #bia1 #aijf4 #fd ,bov]i4 ,zell5-/udi51 ,v4 ,ueb] die ,abhngigkeit d] ,k]ngrsse und ,zell5zahl d] ,seeigell>v5 von d] ,*romosom5zahl d] ,ausgangszell54 ,j5a1 #aije4 #fe ,rec5t important rese>*es sugge/ t su* ultra-m9ute 8filt]-pass]s0 are ! true cause ( c]ta9 acute maladies commonly ascrib$ to ! pres5ce ( mu* l>g] organisms2 cf4 ,hort1 ,lak9 & ,b5ians1 ,! true infective ,ag5t 9 ,c]ebrosp9al ,fev]1 etc41 ,j4 ,roy4 ,army ,m$4 ,corps1 ,feb4 #aiaj4 #ff ,zur ,erk5ntniss d] ,kolloide1 #aije1 p4 #abb2 :]e !re w be f\nd an int]e/+ discussion ( v>i\s molecul> & o!r m9ute magnitudes4 #fg ,encyclopa$ia ,britannica1 #i? edit41 vol4 ,,iii1 p4 #db1 #ahge4 #fh ,sur la limite de petitesse des organismes1 ,bull4 ,soc4 ,r4 des ,sc4 md4 et nat4 de ,bruxelles1 ,jan4 #aijc2 ,rec4 d'uvres 7,physiol4 gnrale71 p4 #cbe4 #fi ,cf4 ,a4 ,fis*]1 ,vorlesung5 b] ,bakt]i51 #ahig1 p4 #ej4 #gj ,f4 ,h(mei/]1 quot$ 9 ,cohnheim's ,*emie d] ,eiweisskrp]1 #aijj1 p4 #ah4 #ga ,mc,kendrick arriv$ at a /ill l[] e/imate1 ( ab\t #abej proteid molecules 9 ! m9ute/ organisms4 ,brit4 ,ass4 ,rep4 #aija1 p4 #hjh4 #gb ,cf4 ,p]r91 ,les ,atomes1 #aiad1 p4 #gd4 #gc ,cf4 ,tait1 ,on ,compression ( ,air 9 small ,bubbles1 ,proc4 ,r4 ,s4 ,e4 ,v1 #ahfe4 #gd ,phil4 ,mag4 ,,xlviii1 #ahii2 ,collect$ ,pap]s1 ,,iv1 p4 #dcj4 #ge ,c>p5t]1 ,! ,microscope1 edit4 #ahfb1 p4 #ahe4 #gf ,! mod]n lit]ature on ! ,br[nian ,movem5t is v l>ge1 ow+ to ! value :i* ! ph5om5on is %ewn to h 9 det]m9+ ! size ( ! atom4 ,= a full]1 b /ill elem5t>y acc\nt1 see ,j4 ,cox1 ,beyond ! ,atom1 #aiac1 pp4 #aah-abh2 & see1 fur!r1 ,p]r91 ,les ,atomes1 pp4 #aai-ahi4 #gg ,cf4 ,r4 ,gans1 ,wie fall5 ,/be und ,s*eib5 9 e9] reib5d5 ,flssigkeit8 ,mn*5] ,b]i*t1 #aiaa1 p4 #aia2 ,k4 ,przibram1 ,ueb] die ,br[n's*e ,bewegung ni*t kugelfrmig] ,teil*51 ,wi5] ,b]4 #aiab1 p4 #bcci4 #gh ,ueb] die ungeordnete ,bewegung ni$]] ,?i]e1 ,pflg]'s ,ar*iv1 ,,cliii1 p4 #dja1 #aiac4 #gi ,sometimes we f9d "o & ! same diagram suffice1 :e!r ! int]vals ( "t be great or small2 & we !n invoke 8,wolff's ,law10 & ass]t t ! life-hi/ory ( ! individual repeats1 or recapitulates1 ! hi/ory ( ! race4 #hj ,our subject is "o ( ,bacon's 8,in/ances ( ! ,c\rse10 or /udies :]e9 we 8measure ,nature by p]iods ( ,"t40 ,9 ,bacon's ,catalogue ( ,p>ticul> ,hi/ories1 "o ( ! odd hundr$ hi/ories or inve/igations :i* he =e%ad[$ is precisely t :i* we are engag$ on1 viz4 a 8,hi/ory ( ! ,gr[? & ,increase ( ! ,body1 9 ! :ole & 9 its p>ts40 #ha ,cf4 ,ari/otle1 ,phys4 vi1 #e1 #bce a #aa1 1 4 ,bacon emphasis$1 9 l mann]1 ! fact t 8all motion or natural action is p]=m$ 9 "t3 "s m quickly1 "s m sl[ly1 b all 9 p]iods det]m9$ & fix$ 9 ! nature ( ?+s4 ,ev5 ^? actions :i* seem to be p]=m$ sudd5ly1 & 7z we say7 9 ! tw9kl+ ( an eye1 are f\nd to admit ( degree 9 respect ( duration40 ,nov4 ,org4 ,,xlvi4 #hb ,cf4 7e4g47 ,elem4 ,physiol4 ed4 #agff1 ,,viii1 p4 #aad1 8,ducimur autem ad evolutionem potissimum1 qu&o a p]fecto animale retrorsum progr$imur1 et increm5torum atque mutationum s]iem relegimus4 ,ita inv5iemus p]fectum illud animal fuisse imp]fectius1 alt]ius figurae et fabricae1 et d5ique rude et in=me3 et tam5 idem semp] animal sub iis div]sis phasibus fuisse1 quae absque ullo saltu p]petuos p>vosque p] gradus coha]eant40 #hc ,beitrge zur ,entwickelungsges*i*te des ,hhn*5s im ,ei1 p4 #dj1 #ahag4 ,r\x ascribes ! same views also to ,von ,ba] & to ,r4 ,h4 ,lotze 7,allg4 ,physiologie1 p4 #cec1 #ahea74 #hd ,r\x1 ,die ,entwickelungsme*anik1 p4 #ii1 #aije4 #he ,op4 cit4 p4 #cjb1 8,magnum hoc naturae in/rum5tum1 etiam 9 corpore animato evolv5do pot5t] op]atur2 etc40 #hf ,ibid4 p4 #cjf4 8,subtiliora i/a1 et aliquantum hypo!si mi/a1 tam5 magnum mihi vid5tur speciem v]i hab]e40 #hg ,cf4 ,81 ,on ! ,pr9ciples ( ,animal ,morphology1 ,proc4 ,r4 ,s4 ,e4 ,,xv1 #ahhh1 p4 #bid3 8,my own attempts to introduce "s elem5t>y me*anical or physiological conceptions into embryology h n g5]ally be5 agre$ to by morphologi/s4 ,to "o x seem$ ridicul\s to speak ( ! ela/icity ( ! g]m9al lay]s2 ano!r ?\ght t1 by su* consid]ations1 we #8put ! c>t be=e ! horse'3 & "o m rec5t au?or /ates1 t we h bett] ?+s to d 9 embryology ?an to discuss t5sions ( g]m9al lay]s & simil> que/ions1 s9ce all explanations mu/ ( necessity be ( a phylog5etic nature4 ,?is opposition to ! application ( ! fundam5tal pr9ciples ( sci5ce to embryological que/ions w\ld sc>cely be intelligible _h x n a dogmatic backgr\nd4 ,no o!r explanation ( liv+ =ms is all[$ ?an h]$ity1 & any :i* is f\nd$ on ano!r basis mu/ be reject$ 4444444 ,to ?9k t h]$ity w build organic be+s )\t me*anical means is a piece ( unsci5tific my/icism40 #hh ,h]twig1 ,o41 ,zeit und ,/reitfrag5 d] ,biologie1 ,,ii4 #ahig4 #hi ,cf4 ,r\x1 ,gesammelte ,abh&lung51 ,,ii1 p4 #ca1 #ahie4 #ij ,treatise on ,comp>ative ,embryology1 ,i1 p4 #d1 #ahha4 #ia ,cf4 ,fick1 ,anal4 ,anzeig]1 ,,xxv1 p4 #aij1 #aijd4 #ib #a/ ed4 p4 #ddd2 #f? ed4 p4 #cij4 ,! /ud5t %\ld n fail to consult ! passage 9 "q2 = !re is always a risk ( misund]/&+ or mis9t]pretation :5 "o attempts to epitomise ,d>w9's c>efully cond5s$ argum5ts4 #ic 8,9 omni r]um naturalium hi/oria utile e/ m5suras def9iri et num]os10 ,hall]1 ,elem4 ,physiol4 ,,ii1 p4 #beh1 #agfj4 ,cf4 ,hales1 ,vegetable ,/aticks1 ,introduction4 #id ,brussels1 #ahga4 ,cf4 ! same au?or's ,physique sociale1 #ahce1 & ,lettres sur la ?orie des probabilits1 #ahdf4 ,see also1 = ! g5]al subject1 ,boyd1 ,r41 ,tables ( weights ( ! ,human ,body1 etc4 ,phil4 ,trans4 vol4 ,,cli1 #ahfa2 ,rob]ts1 ,c41 ,manual ( ,an?ropometry1 #ahgh2 ,daffn]1 ,f41 ,das ,wa*/hum des ,m5s*5 7#bnd ed471 #aijb1 etc4 #ie ,dr ,johnson 0 n f> wrong 9 say+ t 8life decl9es f ?irty-five02 ?\gh ! ,autocrat ( ! ,breakfa/-table1 l ,cic]o1 decl>es t 8! furnace is 9 full bla/ = t5 ye>s long]40 #if ,joly1 ,! ,abundance ( ,life1 #aiae 7#ahij71 p4 #hf4 #ig 8,l\ pes1 m/re de t\t ,le poids1 matre de t\t1 m/re snso v]g\gno1 ,que te tirasso en bas de sa brutalo p\gno10 ,j4 ,h4 ,fabre1 ,oubreto pr\v5alo1 p4 #fa4 #ih ,! cont9uity ( ! ph5om5on ( gr[?1 & ! natural passage f ! phase ( increase to t ( decrease or decay1 are admirably discuss$ by ,enriques1 9 8,la morte10 ,riv4 di ,sci5za1 #aijg1 & 9 8,wa*/hum und se9e analytis*e ,d>/ellung10 ,biol4 ,c5tralbl4 ,june1 #aiji4 ,hall] 7,elem4 ,,vii1 p4 #fh7 recognis$ decrem5tum z a phase ( gr[?1 n less important 7!oretically7 ?an increm5tum3 8tri/is1 s$ copiosa1 haec e/ mat]ies40 #ii ,cf4 7int4 al471 ,fri$5?al1 ,h41 ,das ,wa*/um des ,krp]gewi*tes 444 9 v]s*i$55 ,leb5slt]n1 ,zeit4 f4 allg4 ,physiol4 ,,ix1 pp4 #dhg-ead1 #aiji4 #ajj ,z ,hall] obs]v$ x to d 9 ! *ick 7,elem4 ,,viii1 p4 #bid73 8,hoc it]um increm5tum miro ord9e ita di/ribuitur1 ut 9 pr9cipio incubationis maximum e/3 inde p]petuo m9uatur40 #aja ,!re is a fam\s passage 9 ,lucretius 7v4 #hhc7 :]e he comp>es ! c\rse ( life1 or rate ( gr[?1 9 ! horse & 8 boyi% ma/]3 ,pr9cipio circum tribus actis impig] annis ,floret equus1 pu] hautquaquam1 etc4 #ajb ,m9ot1 ,c4 ,s41 ,s5esc5ce & ,rejuv5ation1 ,j\rn4 ( ,physiol4 ,,xii1 pp4 #ig-aec1 #ahia2 ,! ,problem ( ,age1 ,gr[? & ,dea?1 ,pop4 ,sci5ce ,mon?ly 7,june-,dec471 #aijg4 #ajc ,quot$ 9 ,vi]ordt's ,anatomis*e 444 ,dat5 und ,tabell51 #aijf4 p4 #ac4 #ajd ,uns]e ,krp]=m1 ,leipzig1 #ahgd4 #aje ,no su* po9t ( inflection appe>s 9 ! curve ( weight accord+ to ,c4 ,m4 ,jackson's data 7,on ! ,pr5atal ,gr[? ( ! ,human ,body1 etc41 ,am]4 ,j\rn4 ( ,anat4 ,,ix1 #ajji1 pp4 #abf1 #aef71 nor 9 ^? quot$ by him f ,ahlfeld1 ,fehl+ & o!rs4 ,b x is pla9 t ! v rapid increase ( ! mon?ly weights1 approximately 9 ! ratio ( ! cubes ( ! correspond+ l5g?s1 w\ld t5d to conceal any su* brea* ( cont9uity1 unless x happ5$ to be v m>k$ inde$4 ,moreov] 9 ! case ( ,jackson's data 7& probably also 9 ! o!rs7 ! actual age ( ! embryos 0 n det]m9$1 b 0 e/imat$ f _! l5g?s4 ,! foll[+ is ,jackson's e/imate ( av]age weights at int]vals ( a lun> mon?3 ,mon?s #j #a #b #c #d #e #f #g #h #i #aj ,wt 9 gms4 #j #jd #c #cf #abj #ccj #fjj #ajjj #aejj #bbjj #cbjj #ajf ,g4 ,kraus 7aft] ,walli*-,m>tius71 ,ann4 du ,j>d9 bot4 de ,buit5zorg1 ,,xii1 #a1 #ahid1 p4 #baj4 ,cf4 ,w4 ,o/wald1 ,zeitli*e ,eig5s*aft51 etc4 p4 #ef4 #ajg ,cf4 ,*odat1 ,r41 et ,monni]1 ,a41 ,sur la c\rbe de croissance des vgtaux1 ,bull4 ,h]b4 ,boissi] 7#b71 ,v1 pp4 #fae1 #faf1 #aije4 #ajh ,cf4 ,fr4 ,boas1 ,gr[? ( ,toronto ,*ildr51 ,rep4 ( ,u4,s4 ,comm4 ( ,education1 #ahif-g1 pp4 #aeda-aeii1 #ahih2 ,boas & ,cl>k ,wissl]1 ,/ati/ics ( ,gr[?1 ,education ,rep4 #aijd1 pp4 #be-acb1 #aijf2 ,h4 ,p4 ,b[dit*1 ,rep4 ,mass4 ,/ate ,bo>d ( ,heal?1 #ahgg2 ,k4 ,pe>son1 ,on ! ,magnitude ( c]ta9 coeffici5ts ( ,correlation 9 ,man1 ,pr4 ,r4 ,s4 ,,lxvi1 #aijj4 #aji l4c4 p4 #db1 & o!r pap]s !re quot$4 #aaj ,see1 = an admirable rsum ( facts1 ,wolfgang ,o/wald1 ,ueb] die ,zeitli*e ,eig5s*aft5 d] ,entwickelungsvorgnge 7#ga pp471 ,leipzig1 #aijh 7,r\x's ,vortrge1 ,heft ,v73 to :i* "w ,i am mu* indebt$4 ,a long li/ ( obs]vations on ! gr[?-rate ( v>i\s animals is also giv5 by ,h4 ,przibram1 ,exp4 ,zoologie1 #aiac1 pt4 ,,iv 7,vitalitt71 pp4 #he-hg4 #aaa ,cf4 ,/ ,l\p1 ,vitesse de croissance *ez les ,s\ris1 ,bull4 ,soc4 ,zool4 ,fr4 ,,xviii1 #bdb1 #ahic2 ,rob]tson1 ,ar*4 f4 ,entwickelungsme*4 ,,xxv1 p4 #ehg1 #aijh2 ,donaldson4 ,boas ,memorial ,volume1 ,new ,york1 #aijf4 #aab ,luciani e ,lo ,monaco1 ,ar*4 ,ital4 de ,biologie1 ,,xxvii1 p4 #cdj1 #ahig4 #aac ,s*ap]1 ,ar*4 f4 ,entwickelungsme*4 ,,xiv1 p4 #cef1 #aijb4 ,cf4 ,b>fur?1 ,v]su*e b] die ,v]w&lung d] ,fros*l>v51 ,ar*4 f4 mikr4 ,anat4 ,,xxix1 #ahhg4 #aad ,joh4 ,s*midt1 ,contributions to ! ,life-hi/ory ( ! ,eel1 ,rapports du ,conseil ,int]n4 p\r l'exploration de la ,m]1 vol4 ,v1 pp4 #acg-bgd1 ,cop5hague1 #aijf4 #aae ,t ! metamorphoses ( an insect are b phases 9 a process ( gr[?1 0 fir/ly cle>ly recognis$ by ,swamm]dam1 ,biblia ,naturae1 #agcg1 pp4 #f1 #egi etc4 #aaf ,f ,bose1 ,j4 ,c41 ,plant ,response1 ,london1 #aijf1 p4 #dag4 #aag ,?is ph5om5on1 ( increm5tum inequale1 z oppos$ to increm5tum 9 univ]sum1 0 mo/ c>efully /udi$ by ,hall]3 8,increm5tum inequale multis modis fit1 ut aliae p>tes corporis aliis cel]ius increscant4 ,diximus hep> m9us fi]i1 majorem pulmonem1 m9imum ?ymum1 etc40 7,elem4 ,,viii 7#b71 p4 #cd74 #aah ,see 7int] alia7 ,fis*el1 ,a41 ,v>iabilitt und ,wa*/hum des embryonal5 ,krp]s1 ,morphol4 ,jahrb4 ,,xxiv1 pp4 #cfi-djd1 #ahif4 ,oppel1 ,v]glei*ung des ,entwickelungsgrades d] ,organe zu v]s*i$55 ,entwickelungszeit5 bei ,wirbel?i]51 ,j5a1 #ahia4 ,faucon1 ,a41 ,peses et ,m5surations ftales diffr5ts ges de la grossesse4 7,?se47 ,p>is1 #ahig4 ,loisel1 ,g41 ,croissance comp>e en poids et en longueur des ftus mle et femelle dans l'espce huma9e1 ,c4 ,r4 ,soc4 de ,biologie1 ,p>is1 #aijc4 ,jackson1 ,c4 ,m41 ,pre-natal gr[? ( ! human body & ! relative gr[? ( ! v>i\s organs & p>ts1 ,am4 ,j4 ( ,anat4 ,,ix1 #aiji2 ,po/-natal gr[? & v>iability ( ! body & ( ! v>i\s organs 9 ! alb9o rat1 ibid4 ,,xv1 #aiac4 #aai l4c4 p4 #aedb4 #abj ,v>iation & ,correlation 9 ,bra9-weight1 ,biometrika1 ,,iv1 pp4 #ac-ajd1 #aije4 #aba ,die ,suge?i]e1 p4 #aag4 #abb ,am]4 ,j4 ( ,anatomy1 ,,viii1 pp4 #cai-cec1 #aijh4 ,donaldson 7,j\rn4 ,comp4 ,neur4 & ,psy*ol4 ,,xviii1 pp4 #cde-cib1 #aijh7 also gives a log>i?mic =mula = bra9-weight 7y7 z comp>$ ) body-weight 7x71 :i* 9 ! case ( ! :ite rat is y #eed #efi log7x #hg71 & ! agreem5t is v close4 ,b ! =mula is admitt$ly empirical & z ,raymond ,pe>l says 7,am]4 ,nat4 #aiji1 p4 #cjc71 8no ult]ior biological significance is to be atta*$ to x40 #abc ,biometrika1 ,,iv1 pp4 #ac-ajd1 #aijd4 #abd ,donaldson1 ,h4 ,h41 ,a ,comp>ison ( ! ,:ite ,rat ) ,man 9 respect to ! ,gr[? ( ! entire ,body1 ,boas ,memorial ,vol41 ,new ,york1 #aijf1 pp4 #e-bf4 #abe ,besides _m pap]s quot$ by ,dubois on ! gr[? & weight ( ! bra91 & num]\s pap]s 9 ,biometrika1 see also ! foll[+3 ,zieh51 ,?41 ,das ,gehirn3 ,massv]hltnisse1 9 ,b>deleb5's ,h&b4 d] ,anat4 des ,m5s*51 ,,iv1 pp4 #cec-chf1 #ahii4 ,spitzka1 ,e4 ,a41 ,bra9-weight ( ,animals ) special ref]5ce to ! ,weight ( ! ,bra9 9 ! ,macaque ,monkey1 ,j4 ,comp4 ,neurol4 ,,xiii1 pp4 #i-ag1 #aijc4 ,w>neke1 ,p41 ,mitteilung neu] ,gehirn und ,krp]gewi*tsbe/immung5 bei ,sug]n1 neb/ ,zusamm5/ellung d] gesammt5 bi%] beoba*tet5 absolut5 und relativ5 ,gehirngewi*te bei d5 v]s*i$55 ,species1 ,j4 f4 ,psy*ol4 u4 ,neurol4 ,,xiii1 pp4 #cee-djc1 #aiji4 ,donaldson1 ,h4 ,h41 ,on ! regul> seasonal ,*anges 9 ! relative ,weight ( ! ,c5tral ,n]v\s ,sy/em ( ! ,leop>d ,frog1 ,j\rn4 ( ,morph4 ,,xxii1 pp4 #ffc-fid1 #aiaa4 #abf ,cf4 ,j5k9son1 ,gr[?1 ,v>iability & ,correlation 9 ,"y ,tr\t1 ,biometrika1 ,,viii1 pp4 #ddd-dee1 #aiab4 #abg ,cf4 *ap4 xvii1 p4 #gci4 #abh 8 444,i m>k$ 9 ! same mann] z ! ,v9e1 "y ,honeysuckle %oots1 etc44442 & ,i f\nd 9 !m all a gradual scale ( unequal ext5sions1 ^? p>ts ext5d+ mo/ :i* 7 t5d]e/10 ,vegetable ,/aticks1 ,exp4 cxxiii4 #abi ,f ,sa*s1 ,textbook ( ,botany1 #ahhb1 p4 #hbj4 #acj ,v>iation & ,diff]5tiation 9 ,c]atophyllum1 ,c>negie ,in/4 ,publications1 ,no4 #eh1 ,wa%+ton1 #aijg4 #aca ,cf4 ,lmmel1 ,ueb] p]iodis*e ,v>iation5 9 ,organism51 ,biol4 ,c5tralbl4 ,,xxii1 pp4 #cfh-cgf1 #aijc4 #acb ,h]e9 lies ! easy answ] to a cont5tion frequ5tly rais$ by ,b]gson1 & to :i* he ascribes great importance1 t 8a m]e v>iation ( size is "o ?+1 & a *ange ( =m is ano!r40 ,?us he consid]s 8a *ange 9 ! =m ( leaves0 to con/itute 8a pr(\nd morphological diff]5ce40 ,creative ,evolution1 p4 #ga4 #acc ,i d n say t ! assumption t ^! two gr\ps ( e>wigs 7 ( diff]5t ages is altoge!r an easy "o2 = ( c\rse1 ev5 9 an insect ^: metamorphosis is s simple z ! e>wig's1 consi/+ only 9 ! acquisition ( w+s or w+-cases1 we usually take x = grant$ t gr[? proce$s no m aft] ! f9al /age1 or 8adult =m0 is atta9$1 & fur!r t ?is adult =m is atta9$ at an approximately con/ant age1 & con/ant magnitude4 ,b ev5 if we are n p]mitt$ to ?9k t ! e>wig may h gr[n1 or m\lt$1 aft] once ! elytra 7 produc$1 x seems to me f> f impossible1 & f> f unlikely1 t prior to ! appe>ance ( ! elytra "o m /age ( gr[?1 or "o m m\lt took place 9 "s cases ?an 9 o!rs3 = ! numb] ( m\lts is kn[n to be v>iable 9 _m species ( ,or?opt]a4 ,un=tunately ,bateson tells u no?+ ab\t ! sizes or total l5g?s ( 8 e>wigs2 b 8 figures sugge/ t x 0 bigg] e>wigs t _h ! long] tails2 & t ! rate ( gr[? ( ! tails _h _h a c]ta9 def9ite ratio to t ( ! bodies1 b n necess>ily a simple ratio ( equality4 #acd ,jackson1 ,c4 ,m41 ,j4 ( ,exp4 ,zool4 ,,xix1 #aiae1 p4 #ii2 cf4 also ,hans ,aron1 ,unt]s4 b] die ,bee9flssung d] ,wa*/um dur* die ,ernhrung1 ,b]l4 kl94 ,wo*5bl4 ,,li1 pp4 #igb-igg1 #aiac1 etc4 #ace ,! temp]ature limitations ( life1 & to "s ext5t ( gr[?1 are summ>is$ = a l>ge numb] ( species by ,dav5port1 ,exp]4 ,morphology1 cc4 viii1 xviii1 & by ,hans ,przibram1 ,exp4 ,zoologie1 ,,iv1 c4 v4 #acf ,raumur3 ,l'art de faire clore et lev] en t\te saison des oiseaux dome/iques1 foit p> le moy5 de la *aleur du fumi]1 ,p>is1 #agdi4 #acg ,cf4 7int4 al47 de ,vries1 ,h41 ,matriaux p\r la connaissance de l'influ5ce de la temprature sur les plantes1 ,ar*4 ,nerl4 ,v1 #che-dja1 #ahgj4 ,kpp51 ,wrme und ,pflanz5wa*/um1 ,bull4 ,soc4 ,imp4 ,nat4 ,mosc\4 ,,xliii1 pp4 #da-aaj1 #ahgj4 #ach ,blackman1 ,f4 ,f41 ,ann4 ( ,botany1 ,,xix1 p4 #bha1 #aije4 #aci ,= v>i\s in/ances ( a 8temp]ature coeffici5t0 9 physiological processes1 see ,kanitz1 ,zeits*r4 f4 ,elektro*emie1 #aijg1 p4 #gjg2 ,biol4 ,c5tralbl4 ,,xxvii1 p4 #aa1 #aijg2 ,h]tzog1 ,r4 ,o41 ,temp]ature9fluss auf die ,entwicklungsges*w9digkeit d] ,organism51 ,zeits*r4 f4 ,elektro*emie1 ,,xi1 p #hbj1 #aije2 ,krogh1 ,quantitative ,relation betwe5 ,temp]ature & ,/&>d ,metabolism1 ,int4 ,zeits*r4 f4 physik4-*em4 ,biologie1 ,i1 p4 #dia1 #aiad2 ,ptt]1 ,a41 ,ueb] ,temp]aturkoeffici5t51 ,zeits*r4 f4 allgem4 ,physiol4 ,,xvi1 p4 #egd1 #aiad4 ,also ,coh51 ,physical ,*emi/ry = ,physicians & ,biologi/s 7,engli% edition71 #aijc2 ,pike1 ,f4 ,h41 & ,scott4 ,e4 ,l41 ,! ,regulation ( ! ,physico-*emical ,condition ( ! ,organism1 ,am]ican ,naturali/1 ,jan4 #aiae1 & v>i\s pap]s quot$ !re94 #adj ,cf4 ,err]a1 ,l41 ,l',optimum1 #ahif 7,rec4 d',oeuvres1 ,physiol4 gnrale1 pp4 #cch-cfh1 #aiaj72 ,sa*s1 ,physiologie d4 ,pflanz51 #ahhb1 p4 #bcc2 ,pfeff]1 ,pflanz5physiologie1 ii1 p4 #gh1 #aijd2 & cf4 ,jo/1 ,ueb] die ,reactionsges*w9digkeit im ,organismus1 ,biol4 ,c5tralbl4 ,,xxvi1 pp4 #bbe-bdd1 #aijf4 #ada ,aft] ,kpp51 ,bull4 ,soc4 ,nat4 ,mosc\1 ,,xliii1 pp4 #da-aaj1 #ahga4 #adb ,botany1 p4 #chg4 #adc ,leit*1 ,i41 ,"s ,exp]im5ts on ! ,influ5ce ( ,temp]ature on ! ,rate ( ,gr[? 9 ,pisum sativum1 ,ann4 ( ,botany1 ,,xxx1 pp4 #be-df1 #aiaf4 7,cf4 especially ,table ,,iii1 p4 #de47 #add ,blackman1 ,f4 ,f41 ,presid5tial ,address 9 ,botany1 ,brit4 ,ass4 ,dubl91 #aijh4 #ade ,rec4 de l',in/4 ,bot4 de ,bruxelles1 ,,vi1 #aijf4 #adf ,h]twig1 ,o41 ,e9fluss d] ,temp]atur auf die ,entwicklung von ,rana fusca und ,r4 escul5ta1 ,ar*4 f4 mikrosk4 ,anat4 ,,li1 p4 #cai1 #ahih4 ,cf4 also ,bialaszewicz1 ,k41 ,beitrge z4 ,k5ntniss d4 ,wa*/humsvorgnge bei ,amphibi5embryon51 ,bull4 ,acad4 ,sci4 de ,cracovie1 p4 #ghc1 #aijh2 ,ab/r4 9 ,ar*4 f4 ,entwicklungsme*4 ,,xxviii1 p4 #afj1 #aiji4 #adg ,d] ,grad d] ,bes*leunigung ti]is*] ,entwickelung dur* erhhte ,temp]atur1 ,a4 f4 ,entw4 ,me*4 ,,xx4 p4 #acj1 #aije4 ,m rec5tly1 ,bialaszewicz has det]m9$ ! coeffici5t = ! rate ( segm5tation 9 ,rana z be+ #bd p] #aj ,c4 #adh ,das ,wa*/um des ,m5s*51 p4 #cbi1 #aijb4 #adi ,! diurnal p]iodicity is beautifully %ewn 9 ! case ( ! ,hop by ,joh4 ,s*midt 7,c4 ,r4 du ,laboratoire de ,c>lsb]g1 ,x1 pp4 #bce-bdh1 ,cop5hague1 #aiac74 #aej ,trans4 ,botan4 ,soc4 ,ed9burgh1 ,,xviii1 #ahia1 p4 #def4 #aea ,i _h n receiv$1 :5 ?is 0 writt51 ,mr ,d\glass's pap]1 ,on a me?od ( e/imat+ ,ra9fall by ! ,gr[? ( ,trees1 ,bull4 ,am]4 ,geograph4 ,soc4 ,,xlvi1 pp4 #cba-cce1 #aiad4 ,mr ,d\glass does n fail to notice ! long p]iod "h describ$2 b he lays m /ress on ! occurr5ce ( %ort] cycles 7( #aa1 #ba & #cc ye>s71 well kn[n to meteorologi/s4 ,mr ,d\glass is incl9$ 7& ,i ?9k rightly7 to correlate ! v>iations 9 gr[? directly ) fluctuations 9 ra9fall1 t is to say ) alt]nate p]iods ( moi/ure & aridity2 b he po9ts out t ! temp]ature curves 7& also ! sunspot curves7 are m>k$ly simil>4 #aeb ,x may well be t ! effect is n due to light aft] all2 b to increas$ absorption ( heat by ! soil1 z a result ( ! long h\rs ( exposure to ! sun4 #aec ,on gr[? 9 relation to light1 see ,dav5port1 ,exp4 ,morphology1 ,,ii1 *4 xvii4 ,9 "s cases 7z 9 ! roots ( ,peas71 exposure to light seems to h no effect on gr[?2 9 o!r cases1 z 9 diatoms 7accord+ to ,:ipple's exp]im5ts1 quot$ by ,dav5port1 ,,ii1 p4 #dbc71 ! effect ( light on gr[? or multiplication is well-m>k$1 measurable1 & app>5tly capable ( expression by a log>i?mic =mula4 ,! discrepancy w\ld seem to arise f ! fact t1 :ile light-en]gy always t5ds to be absorb$ by ! *lorophyll ( ! plant1 conv]t$ into *emical en]gy1 & /or$ 9 ! %ape ( />* or o!r res]ve mat]ials1 ! actual rate ( gr[? dep5ds on ! rate at :i* ^! res]ves are drawn on3 & ?is is ano!r matt]1 9 :i* light-en]gy is no long] directly conc]n$4 #aed ,cf4 = in/ance1 ,ngeli's classical acc\nt ( ! effect ( *ange ( habitat on ,alp9e & o!r plants3 ,sitzungsb]4 ,bai]4 ,akad4 ,wiss4 #ahfe1 pp4 #bbh-bhd4 #aee ,cf4 ,blackman1 ,f4 ,f41 ,presid5tial ,address 9 ,botany1 ,brit4 ,ass4 ,dubl91 #aijh4 ,! fact 0 fir/ enunciat$ by ,baudrimont & ,/ ,ange1 ,re*]*es sur le dveloppem5t du ftus1 ,mm4 ,acad4 ,sci4 ,,xi1 p4 #dfi1 #ahea4 #aef ,cf4 ,loeb1 ,unt]su*ung5 zur physiol4 ,morphologie d] ,?i]e1 #ahib2 also ,exp]im5ts on ,cleavage1 ,j4 ( ,morph4 ,,vii1 p4 #bec1 #ahib2 ,zusamm5/ellung d] ,ergebnisse e9ig] ,arbeit5 b] die ,dynamik des ?i]is*5 ,wa*/hum1 ,ar*4 f4 ,entw4 ,me*4 ,,xv1 #aijb-c1 p4 #ffi2 ,dav5port1 ,on ! ,rle ( ,wat] 9 ,gr[?1 ,bo/on ,soc4 ,n4 ,h4 #ahig2 ,ida ,h4 ,hyde1 ,am4 ,j4 ( ,physiol4 ,,xii1 #aije1 p4 #bda1 etc4 #aeg ,pflg]'s ,ar*iv1 ,,lv1 #ahic4 #aeh ,beitrge zur ,k5ntniss d] ,wa*/umsvorgnge bei ,amphibi5embryon51 ,bull4 ,acad4 ,sci4 de ,cracovie1 #aijh1 p4 #ghc2 cf4 ,ar*4 f4 ,entw4 ,me*4 ,,xxviii1 p4 #afj1 #aiji2 ,,xxxiv1 p4 #dhi1 #aiab4 #aei ,fehl+1 ,h41 ,ar*4 fr ,gynaekologie1 ,,xi1 #ahgg2 cf4 ,morgan1 ,exp]im5tal ,zoology1 p4 #bdj1 #aijg4 #afj ,hb]1 ,r41 ,b$eutung d] ,!orie d] ,lsung5 fr ,physiologie und ,m$iz91 ,biol4 ,c5tralbl4 ,,xix1 #ahii2 cf4 pp4 #bgb-bgd4 #afa ,s*mankewits* has made o!r int]e/+ obs]vations on *ange ( size & =m1 aft] "s g5]ations1 9 relation to *ange ( d5sity2 e4g4 9 ! flagellate infusorian ,anisonema ac9us1 ,bts*li 7,z4 f4 w4 ,z4 ,,xxix1 p4 #dbi1 #ahgg74 #afb ,^! 8,fezzan-worms10 :5 fir/ describ$1 7 suppos$ to be 8insects' eggs02 cf4 ,humboldt1 ,p]sonal ,n>rative1 ,,vi1 i1 #h1 note2 ,kirby & ,sp5ce1 ,lett] ,x4 #afc ,cf4 ,introd4 l'tude de la mdec9e exprim5tale1 #ahhe1 p4 #aaj4 #afd ,cf4 ,abonyi1 ,z4 f4 w4 ,z4 ,,cxiv1 p4 #acd1 #aiae4 ,b ,frdricq has %ewn t ! am\nt ( ,na,cl 9 ! blood ( ,cru/acea 7,c>c9us mo5as7 v>ies1 & all b corresponds1 ) ! d5sity ( ! wat] 9 :i* ! creature has be5 kept 7,ar*4 de ,zool4 ,exp4 et ,gn4 7#b71 ,,iii1 p4 xxxv1 #ahhe72 & o!r results ( ,frdricq's1 & v>i\s data giv5 or quot$ by ,bottazzi 7,osmotis*] ,druck und elektris*e ,leitungsfhigkeit d] ,flssigkeit5 d] ,organism51 9 ,a%]-,spiro's ,ergebn4 d4 ,physiologie1 ,,vii1 pp4 #afj-djb1 #aijh7 sugge/ t ! case ( ! br9e-%rimps mu/ be look$ ^u z an extreme or exceptional "o4 #afe ,cf4 ,s*mankewits*1 ,z4 f4 w4 ,zool4 ,,xxv1 #ahge1 ,,xxix1 #ahgg1 etc42 transl4 9 app5dix to ,pack>d's ,monogr4 ( ,n4 ,am]ican ,phyllopoda1 #ahhc1 pp4 #dff-ead2 ,daday de ,des1 ,ann4 ,sci4 ,nat4 7,zool471 7#i71 ,,xi1 #aiaj2 ,samt] und ,heymons1 ,abh4 d4 ,k4 pr4 ,akad4 ,wiss4 #aijb2 ,bateson1 ,mat4 = ! ,/udy ( ,v>iation1 #ahid1 pp4 #if-aja2 ,anik91 ,mit?4 ,kais4 ,univ4 ,tomsk1 ,,xiv3 ,zool4 ,c5tralbl4 ,,vi1 pp4 #gef-gfj1 #aijh2 ,abonyi1 ,z4 f4 w4 ,z4 ,,cxiv1 pp4 #if-afh1 #aiae 7) copi\s bibliography71 etc4 #aff ,accord+ to ! empirical canon ( physiology1 t 7z ,frdricq expresses x7 8,l'tre vivant e/ ag5c de telle manire que *aque influ5ce p]turbatrice provoque d'elle-mme la mise en activit de l'app>eil comp5sateur qui doit neutralis] et rp>] le dommage40 #afg ,su* ph5om5a come precisely "u ! head ( :at ,bacon call$ ,in/ances ( ,magic3 8,by :i* ,i mean ^? :]e9 ! mat]ial or effici5t cause is scanty & small z comp>$ ) ! "w or effect produc$2 s t ev5 :5 !y are common1 !y seem l miracles1 "s at fir/ sight1 o!rs ev5 aft] att5tive consid]ation4 ,^! magical effects are br\ght ab\t 9 ?ree ways 444 ( :i* "o is by excitation or invitation 9 ano!r body1 z 9 ! magnet :i* excites numb]less ne$les )\t los+ any ( its virtue1 or 9 yea/ & su*-l40 ,nov4 ,org41 cap4 li4 #afh ,monni]1 ,a41 ,les matires m9rales1 et la loi d'accroissem5t des ,vgtaux1 ,publ4 de l',in/4 de ,bot4 de l',univ4 de ,g5ve 7#g71 ,,iii1 #aije4 ,cf4 ,rob]tson1 ,on ! ,normal ,rate ( ,gr[? ( an ,individual1 & its ,bio*emical ,significance1 ,ar*4 f4 ,entw4 ,me*4 ,,xxv1 pp4 #eha-fad1 ,,xxvi1 pp4 #ajh-aah1 #aijh2 ,wolfgang ,o/wald1 ,die zeitli*5 ,eig5s*aft5 d] ,entwickelungsvorgnge1 #aijh2 ,hatai1 ,s41 ,int]pretation ( ,gr[?-curves f a ,dynamical ,/&po9t1 ,anat4 ,record1 ,v1 p4 #cgc1 #aiaa4 #afi ,bio*em4 ,zeits*r4 ,,ii1 #aijf1 p4 #cd4 #agj ,ev5 a cry/al may be said1 9 a s5se1 to display 8autocatalysis03 = ! bigg] its surface becomes1 ! m rapidly does ! mass g on increas+4 #aga ,cf4 ,loeb1 ,! ,/imulation ( ,gr[?1 ,sci5ce1 ,may #ad1 #aiae4 #agb ,b4 coli-communis1 accord+ to ,bu*n]1 t5ds to d\ble 9 #bb m9utes2 9 #bd h\rs1 !re=e1 a s+le individual w\ld be multipli$ by some?+ l #ajbh2 ,sitzungsb]4 ,mn*54 ,ges4 ,morphol4 u4 ,physiol4 ,,iii1 pp4 #fe-ga1 #ahhh4 ,cf4 ,m>%all ,w>d1 ,biology ( ,bacillus ramosus1 etc4 ,pr4 ,r4 ,s4 ,,lviii1 #bfe-dfh1 #ahie4 ,! comp>atively l>ge infusorian ,/yloni*ia1 accord+ to ,maupas1 w\ld multiply 9 a mon? by #ajdc4 #agc ,cf4 ,enriques1 ,wa*/hum und se9e analytisehe ,d>/ellung1 ,biol4 ,c5tralbl4 #aiji1 p4 #ccg4 #agd ,cf4 7int4 al47 ,mellor1 ,*emical ,/atics & ,dynamics1 #aijd1 p4 #bia4 #age ,cf4 ,rob]tson1 l4c4 #agf ,see1 = a brief resum ( ?is subject1 ,morgan's ,exp]im5tal ,zoology1 *ap4 xvi4 #agg ,am]4 ,j4 ( ,physiol41 ,x1 #aijd4 #agh ,c4,r4 ,,cxxi1 ,,cxxii1 #ahie-if4 #agi ,cf4 ,loeb1 ,sci5ce1 ,may #ad1 #aiae4 #ahj ,cf4 ,baumann u4 ,roos1 ,vorkomm5 von ,iod im ,?i]krp]1 ,zeits*r4 fr ,physiol4 ,*em4 ,,xxi1 ,,xxii1 #ahie1 #f4 #aha ,le ,no-,vitalisme1 ,rev4 ,sci5tifique1 ,m>s #aiaa1 p4 #bb 7( repr9t74 #ahb ,la vie et la mort1 p4 #dc1 #aijb4 #ahc ,cf4 ,d5dy1 ,evolution>y ,biology1 #aiab1 p4 #djh2 ,brit4 ,ass4 ,report 7,portsm\?71 #aiaa1 p4 #bgh4 #ahd ,lucret4 v1 #hgg4 8,lucretius n[h]e seems to recognise ! possibility ( improvem5t or *ange ( species by #8natural selection'2 ! animals rema9 z !y 7 at ! fir/1 except t ! weak] & m useless k9ds h be5 cru%$ out4 ,h5ce he /&s 9 m>k$ contra/ ) mod]n evolutioni/s40 ,kelsey's note1 ad loc4 #ahe ,ev5 aft] we h s n>r[$ ! scope & sph]e ( natural selection1 x is /ill h>d to und]/&2 = ! causes ( ext9ction are (t5 wellnigh z h>d to compreh5d z are ^? ( ! orig9 ( species4 ,if we ass]t 7z has be5 lightly done7 t ,smilodon p]i%$ ow+ to its gigantic tusks1 t ,teleosaurus 0 h&icapp$ by its exagg]at$ sn\t1 or ,/egosaurus weigh$ d[n by its intol]able load ( arm\r1 we may be rem9d$ ( o!r k9dr$ =ms to %[ t simil> conditions did n necess>ily lead to ext]m9ation1 or t rapid ext9ction ensu$ ap>t f any su* visible or app>5t disadvantages4 ,cf4 ,lucas1 ,f4 ,a41 ,on ,mom5tum 9 ,v>iation1 ,am]4 ,nat4 xli1 p4 #df1 #aijg4 #ahf ,see ,pr(essor ,t4 ,h4 ,morgan's ,reg5]ation 7#caf pp471 #aija = a full acc\nt & copi\s bibliography4 ,! e>ly exp]im5ts on reg5]ation1 by ,vallisn]i1 ,raumur1 ,bonnet1 ,trembley1 ,ba/]1 & o!rs1 are epitomis$ by ,hall]1 ,elem4 ,physiologiae1 ,,viii1 p4 #aef seq4 #ahg ,j\rn4 ,exp]im4 ,zool4 ,,vii1 p4 #cig1 #aiji4 #ahh ,op4 cit4 p4 #djf1 ,exp4 ,,iv4 #ahi ,! exp]im5ts ( ,loeb on ! gr[? ( ,tubul>ia 9 v>i\s sal9e solutions1 ref]r$ to on p4 #abe1 might z well or bett] h be5 ref]r$ to "u ! head+ ( reg5]ation1 z !y 7 p]=m$ on cut pieces ( ! zoophyte4 7,cf4 ,morgan1 op4 cit4 p4 #ce47 #aij ,p[]s ( ! ,creator1 ,i1 p4 #g1 #ahea4 ,see also ,r>e & ,rem>kable ,animals1 ,,ii1 pp4 #ag-ai1 #ij1 #ahdg4 #aia ,lillie1 ,f4 ,r41 ,! smalle/ ,p>ts ( ,/5tor capable ( ,reg5]ation1 ,j\rn4 ( ,morphology1 ,,xii1 p4 #bci1 #ahig4 #aib ,bov]i1 ,entwicklungsfhigkeit k]nlos] ,seeigelei]1 etc41 ,ar*4 f4 ,entw4 ,me*4 ,,ii1 #ahie4 ,see also ,morgan1 ,/udies ( ! p>tial l>vae ( ,spha]e*9us1 ibid4 #ahie2 ,j4 ,loeb1 ,on ! ,limits ( ,divisibility ( ,liv+ ,matt]1 ,biol4 ,lectures1 #ahid1 etc4 #aic ,cf4 ,przibram1 ,h41 ,s*e]5umkehr bei dekapod5 ,cru/ace51 ,ar*4 f4 ,entw4 ,me*4 ,,xix1 #aha-bdg1 #aije2 ,,xxv1 #bff-cdd1 #aijg4 ,emmel1 ibid4 ,,xxii1 #edb1 #aijf2 ,reg5]ation ( lo/ p>ts 9 ,lob/]1 ,rep4 ,comm4 ,inl& ,fi%]ies1 ,rhode ,isl&1 ,,xxxv1 ,,xxxvi1 #aije-f2 ,sci5ce 7n4s471 ,,xxvi1 #hc-hg1 #aijg4 ,zel5y1 ,comp5satory ,regulation1 ,j4 ,exp4 ,zool4 ,,ii1 #a-ajb1 #cdg-cfi1 #aije2 etc4 #aid ,lob/]s are occasionally f\nd ) two symmetrical claws3 :i* are !n usually s]rat$1 sometimes 7b v r>ely7 bo? blunt-too!d4 ,cf4 ,calman1 ,p4,z4,s4 #aijf1 pp4 #fcc1 #fcd1 & reff4 #aie ,wilson1 ,e4 ,b41 ,rev]sal ( ,symmetry 9 ,alpheus het]o*elis1 ,biol4 ,bull4 ,,iv1 p4 #aig1 #aijc4 #aif ,j4 ,exp4 ,zool4 ,,vii1 p4 #deg1 #aiji4 #aig ,biologica1 ,,iii1 p4 #afa1 ,june4 #aiac4 #aih ,anatomical & ,pa?ological ,obs]vations1 p4 #c1 #ahde2 ,anatomical ,memoirs1 ,,ii1 p4 #cib1 #ahfh4 #aii ,gi>d1 ,a41 ,l'uf et les dbuts de l'volution1 ,bull4 ,sci4 du ,nord de la ,fr4 ,,viii1 pp4 #beb-beh1 #ahgf4 #bjj ,entwickelungsvorgnge d] ,eizelle1 #ahgf2 ,inve/igations on ,microscopic ,foams & ,protoplasm1 p4 #a1 #ahid4 #bja ,j\rn4 ( ,morphology1 ,i1 p4 #bbi1 #ahhg4 #bjb ,:ile x has be5 v common to look ^u ! ph5om5a ( mitosis z suffici5tly expla9$ by ! results t[>ds :i* !y seem to lead1 we may f9d "h & !re a /rong prote/ aga9/ ?is mode ( int]pretation4 ,! foll[+ is a case 9 po9t3 8,on a t5t d'tablir dans la mitose dite primitive plusieurs catgories1 plusieurs types de mitose4 ,on a *oisi le plus s\v5t comme base de ces sy/mes des concepts ab/raits et tlologiques3 rp>tition plus ou mo9s exacte de la *romat9e entre les deux noyaux-fils suivant qu'il y a ou non des *romosomes 7,dange>d71 di/ribution p>ticulire et signification duali/e des sub/ances nuclaires 7sub/ance k9tique et sub/ance gnrative ou hrditaire1 ,h>tmann et ses lves71 etc4 ,p\r moi t\s ces essais sont rejet] catgoriquem5t cause de leur c>actre f9ali/e2 de plus1 ils sont con/ruits sur des concepts non dmontrs1 et qui p>fois reprs5t5t des gnralisations absolum5t errones40 ,a4 ,alexeieff1 ,ar*iv fr ,proti/5kunde1 ,,xix1 p4 #cdd1 #aiac4 #bjc ,?is is ! old philosophic axiom writ l>ge3 ,ignorato motu1 ignoratur natura2 :i* aga9 is b an adaptation ( ,ari/otle's phrase1 1 z equival5t to ! 8,effici5t ,cause40 ,fitz,gerald holds t 8all explanation consi/s 9 a description ( und]ly+ motions02 ,sci5tific ,writ+s1 #aijb1 p4 #che4 #bjd ,z :5 ,ngeli conclud$ t ! organism is1 9 a c]ta9 s5se1 8vorgebildet02 ,beitr4 zur wiss4 ,botanik1 ,,ii1 #ahfj4 ,cf4 ,e4 ,b4 ,wilson1 ,! ,cell1 etc41 p4 #cjb4 #bje 8,la matire arrange p> une sagesse div9e doit tre ess5tiellem5t organise p>t\t 444 il y a ma*9e dans les p>ties de la ma*9e ,naturelle l'inf9i40 ,sur le pr9cipe de la ,vie1 p4 #dca 7,erdmann74 ,?is is ! v conv]se ( ! doctr9e ( ! ,atomi/s1 :o c\ld n conceive a condition 8ubi dimidiae p>tis p>s semp] habebit ,dimidiam p>tem1 nec res praef9iet ulla40 #bjf ,cf4 an int]e/+ passage f ! ,elem5ts 7,i1 p4 #dde1 ,moleswor?'s edit471 quot$ by ,ow51 ,hunt]ian ,lectures on ! ,inv]tebrates1 #bnd ed4 pp4 #dj1 #da1 #ahee4 #bjg 8,wir mss5 de%alb d5 leb5d5 ,zell51 abgeseh5 von d] ,molekul>/ructur d] organis*5 ,v]b9dung5 wel*e sie en?lt1 no* e9e &]e und 9 &]] ,weise complicirte ,/ructur zus*reib51 und diese es i/ wel*e wir mit dem ,nam5 ,organisation bezei*n510 ,brcke1 ,die ,elem5t>organism51 ,wi5] ,sitzungsb]4 ,,xliv1 #ahfa1 p4 #chf2 quot$ by ,wilson1 ,! ,cell1 etc4 p4 #bhi4 ,cf4 also ,h>dy1 ,j\rn4 ( ,physiol4 ,,xxiv1 #ahii1 p4 #aei4 #bjh ,precisely z 9 ! ,lucretian concursus1 motus1 ordo1 positura1 figurae1 :]eby bodies mutato ord9e mutant naturam4 #bji ,otto ,w>burg1 ,beitrge zur ,physiologie d] ,zelle1 insbesond]e b] die ,oxidationsges*w9digkeit 9 ,zell52 9 ,a%]-,spiro's ,ergebnisse d] ,physiologie1 ,,xiv1 pp4 #bec-ccg1 #aiad 7see p4 #cae74 7,cf4 ,bayliss1 ,g5]al ,physiology1 #aiae1 p4 #eij74 #baj ,h>dy1 ,w4 ,b41 ,on "s ,problems ( ,liv+ ,matt] 7,gu?rie ,lecture71 ,tr4 ,physical ,soc4 ,london1 xxviii1 p4 #ii-aah1 #aiaf4 #baa ,z a matt] ( fact bo? phrases occur1 side by side1 9 ,graham's classical pap] on 8,liquid ,diffusion appli$ to ,analysis10 ,phil4 ,trans4 ,,cli1 p4 #ahd1 #ahfa2 ,*em4 & ,phys4 ,rese>*es 7ed4 ,angus ,smi?71 #ahgf1 p4 #eed4 #bab ,l4 ,rhumbl]1 ,me*anis*e ,erklrung d] ,aehnli*keit zwis*5 ,magnetis*5 ,kraftl9i5sy/em5 und ,zell!ilungsfigur51 ,ar*4 f4 ,entw4 ,me*4 ,,xv1 p4 #dhb1 #aijc4 #bac ,gall>do1 ,a41 ,essai d'int]pretation des figures c>yoc9tiques1 ,anales del ,museo de ,bu5os-,aires 7#b71 ,,ii1 #ahif2 ,la division de la cellule1 ph5omne bipolaire de c>actre electro-colloidal1 ,ar*4 f4 ,entw4 ,me*4 ,,xxviii1 #aiji1 etc4 #bad ,ar*4 f4 ,entw4 ,me*4 ,,iii1 ,,iv1 #ahif-ig4 #bae ,on v>i\s !ories ( ! me*anism ( mitosis1 see 7e4g47 ,wilson1 ,! ,cell 9 ,developm5t1 etc41 pp4 #ajj-aad2 ,meves1 ,zell!ilung1 9 ,m]kel u4 ,bonnet's ,ergebnisse d] ,anatomie1 etc41 ,,vii1 ,,viii1 #ahig-h2 ,ida ,h4 ,hyde1 ,am]4 ,j\rn4 ( ,physiol4 ,,xii1 pp4 #bda-bge1 #aije2 & especially ,pr5ant1 ,a41 ,!ories et int]prtations physiques de la mitose1 ,j4 de l',anat4 et ,physiol4 ,,xlvi1 pp4 #eaa-egh1 #aiaj4 #baf ,h>tog1 ,m41 ,une =ce n\velle3 le mitok9tisme1 ,c4,r4 #aa ,juli1 #aiaj2 ,mitok9etism 9 ! ,mitotic ,sp9dle & 9 ! ,polya/]s1 ,ar*4 f4 ,entw4 ,me*4 ,,xxvii1 pp4 #ada-ade1 #aiji2 cf4 ibid4 ,,xl1 pp4 #cc-fd1 #aiad4 ,cf4 also ,h>tog's pap]s 9 ,proc4 ,r4 ,s4 7,b71 ,,lxxvi1 #aije2 ,sci5ce ,progress 7n4 s471 ,i1 #aijg2 ,riv4 di ,sci5za1 ,,ii1 #aijh2 ,c4 ,r4 ,assoc4 fr4 p\r l',avancem4 des ,sc4 #aiad1 etc4 #bag ,! configurations1 z obta9$ by ! usual exp]im5tal me?ods1 7 ( c\rse kn[n long be=e ,f>aday's day1 & con/itut$ ! 8conv]g5t & div]g5t magnetic curves0 ( eighte5? c5tury ma!maticians4 ,z ,leslie said1 9 #ahba1 !y 7 8reg>d$ ) wond] by a c]ta9 class ( dream+ philosoph]s1 :o did n hesitate to consid] !m z ! actual traces ( an invisible fluid1 p]petually circulat+ betwe5 ! poles ( ! magnet40 ,f>aday's great advance 0 to int]pret !m z indications ( /ress 9 a m$ium1--( t5sion or attraction along ! l9es1 & ( repulsion transv]se to ! l9es1 ( ! diagram4 #bah ,cf4 also ! curi\s ph5om5on 9 a divid+ egg describ$ z 8sp9n+0 by ,mrs ,g4 ,f4 ,&rews1 ,j4 ( ,morph4 ,,xii1 pp4 #cfg-chi1 #ahig4 #bai ,:itman1 ,j4 ( ,morph4 ,,ii1 p4 #dj1 #ahhi4 #bbj 8,s\v5t il n'y a qu'une sp>ation physique entre le cytoplasme et le suc nuclaire1 comme entre deux liquides immiscibles1 etc420 ,alexeieff1 ,sur la mitose dite 8primitive10 ,ar*4 f4 ,proti/5k4 ,,xxix1 p4 #ceg1 #aiac4 #bba ,! appe>ance ( 8vacuolation0 is a result ( endosmosis or ! diffusion ( a less d5se fluid into ! d5s] plasma ( ! cell4 ,caet]is p>ibus1 x is less app>5t 9 m>9e organisms ?an 9 ^? ( fre%wat]1 & 9 _m or mo/ m>9e ,ciliates & ev5 ,rhizopods a contractile vacuole has n be5 obs]v$ 7,bts*li1 9 ,bronn's ,protozoa1 p4 #adad72 x is also abs5t1 & probably = ! same reason1 9 p>asitic ,protozoa1 su* z ! ,greg>9es & ! ,entamoebae4 ,rossba* %ew$ t ! contractile vacuole ( ord9>y fre%wat] ,ciliates 0 v greatly dim9i%$ 9 a #e p] c5t4 solution ( ,na,cl1 & all b disappe>$ 9 a #a p] c5t4 solution ( sug> 7,arb4 z4 z4 ,in/4 ,wrzburg1 #ahgb1 cf4 ,mass>t1 ,ar*4 de ,biol4 ,,lx1 p4 #eae1 #ahhi74 ,act9ophrys sol1 :5 gradually acclimatis$ to sea-wat]1 loses its vacuoles1 & vice v]sa 7,grub]1 ,biol4 ,c5tralbl4 ,,ix1 p4 #bb1 #ahhi72 & ! same is true ( ,amoeba 7,zuelz]1 ,ar*4 f4 ,entw4 ,me*4 #aiaj1 p4 #fcb74 ,! gradual enl>gem5t ( ! contractile vacuole is precisely analog\s to ! *ange ( size ( a bubble until ! gases on ei!r side ( ! film are equally diffus$1 z describ$ long ago by ,drap] 7,phil4 ,mag4 7n4 s471 ,,xi1 p4 #eei1 #ahcg74 ,rhumbl] has %ewn t contractile or pulsat+ vacuoles may be well imitat$ 9 *lor(orm-drops1 susp5d$ 9 wat] 9 :i* v>i\s sub/ances are dissolv$ 7,ar*4 f4 ,entw4 ,me*4 ,,vii1 #ahih1 p4 #ajc74 ,! pressure )9 ! contractile vacuole1 always great] ?an )\t1 dim9i%es ) its size1 be+ inv]sely proportional to its radius2 & :5 x lies ne> ! surface ( ! cell1 z 9 a ,heliozoon1 x bur/s z soon z x rea*es a ?9ness :i* its viscosity or molecul> cohesion no long] p]mits x to ma9ta94 #bbb ,cf4 p4 #ffj4 #bbc ,! elongat$ or curv$ 8macronucleus0 ( an ,infusorian is to be look$ ^u z a s+le mass ( *romat91 r ?an z an aggregation ( p>ticles 9 a fluid drop1 z 9 ! case describ$4 ,x has a %ape ( its own1 9 :i* ord9>y surface-t5sion plays a v subord9ate "p4 #bbd ,?orie physico-*imique de la ,vie1 p4 #gc1 #aiaj2 ,me*anism ( ,life1 p4 #ef1 #aiaa4 #bbe ,:5ce ! "n 8mitosis0 7,greek 1 a ?read71 appli$ fir/ by ,flemm+ to ! :ole ph5om5on4 ,kollmann 7,biol4 ,c5tralbl4 ,,ii1 p4 #ajg1 #ahhb7 call$ x divisio p] fila1 or divisio laqueis implicata4 ,_m ( ! e>li] /ud5ts1 su* z ,van ,b5$5 7,re*4 sur la maturation de l'uf1 ,ar*4 de ,biol4 ,,iv1 #ahhc71 & ,h]mann 7,zur ,lehre v4 d4 ,ent/ehung d4 k>yok9etis*5 ,sp9del1 ,ar*4 f4 mikrosk4 ,anat4 ,,xxxvii1 #ahia7 ?\ght !y recognis$ actual muscul> ?reads1 draw+ ! nucle> mat]ial asund] t[>ds ! respective foci or poles2 & "s su* view 0 long ma9ta9$ by o!r writ]s1 ,bov]i1 ,heid5ha91 ,flemm+1 ,r4 ,h]twig1 & _m m4 ,9 fact1 ! exi/5ce ( contractile ?reads1 or ! ascription to ! sp9dle r ?an to ! poles or c5trosomes ( ! active =ces conc]n$ 9 nucle> division1 =m$ ! ma9 t5et ( all ^? :o decl9$ to g beyond ! 8contractile prop]ties ( protoplasm0 = an explanation ( ! ph5om5on4 7,cf4 also ,j4 ,w4 ,j5k9son1 ,q4 ,j4 ,m4 ,s4 ,,xlviii1 p4 #dga1 #aijd47 #bbf ,cf4 ,bts*li1 ,o41 ,ueb] die kn/li*e ,na*ahmung d] k>yok9etis*5 ,figur1 ,v]h4 ,m$4 ,nat4 ,v]4 ,heidelb]g1 ,v1 pp4 #bh-da 7#ahib71 #ahig4 #bbg ,arrh5ius1 9 describ+ a typical colloid precipitate1 does s 9 t]ms t are v closely applicable to ! ord9>y microscopic appe>ance ( ! protoplasm ( ! cell4 ,! precipitate consi/s1 he says1 8en un rseau d'une sub/ance solide cont5ant peu d'eau1 dans les mailles duquel e/ inclus un fluide cont5ant un peu de colloide dans beauc\p d'eau 444 ,evidemm5t cette /ructure se =me cause de la petite diffr5ce de poids spcifique des deux phases1 et de la consi/ance gluante des p>ticules sp>es1 qui s'atta*5t en =me de rseau40 ,rev4 ,sci5tifique1 ,feb4 #aiaa4 #bbh ,f4 ,s*w>tz1 9 ,cohn's ,beitr4 z4 ,biologie d] ,pflanz51 ,v1 p4 #a1 #ahhg4 #bbi ,fis*]1 ,anat4 ,anzeig]1 ,,ix1 p4 #fgh1 #ahid1 ,x1 p4 #gfi1 #ahie4 #bcj ,see1 9 p>ticul>1 ,w4 ,b4 ,h>dy1 ,on ! /ructure ( ,cell ,protoplasm1 ,j\rn4 ( ,physiol4 ,,xxiv1 pp4 #aeh-bjg1 #ahhi2 also ,hb]1 ,physikalis*e ,*emie d] ,zelle und d] ,gewebe1 #aijb4 ,cf4 7int4 al47 ,flemm+1 ,zellsub/anz1 ,k]n und ,zell!ilung #ahhb1 p4 #ea1 etc4 #bca ,my description & diagrams 7,figs #db-ea7 are bas$ on ^? ( ,pr(essor ,e4 ,b4 ,wilson4 #bcb ,if ! ^w p]meability be deem$ too directly sugge/ive ( ! ph5om5a ( magnetism we may replace x by ! m g5]al t]m ( specific inductive capacity4 ,?is w\ld cov] ! p>ticul> case1 :i* is by no means an improbable "o1 ( our ph5om5a be+ due to a 8surface *>ge0 borne by ! nucleus itself & also by ! *romosomes3 ?is surface *>ge be+ 9 turn ! result ( a diff]5ce 9 inductive capacity betwe5 ! body or p>ticle & its surr\nd+ m$ium4 7,cf4 footnote1 p4 #ahg47 #bcc ,on ! effect ( electrical influ5ces 9 alt]+ ! surface-t5sions ( ! colloid p>ticles1 see ,br$ig1 ,anorganis*e ,f]m5te1 pp4 #ae1 #af1 #aija4 #bcd ,! ,cell1 etc4 p4 #ff4 #bce ,lillie1 ,r4 ,s41 ,am]4 ,j4 ( ,physiol4 ,,viii1 p4 #bhb1 #aijc4 #bcf ,we h n tak5 acc\nt 9 ! above p>agraphs ( ! obvi\s fact t ! suppos$ symmetrical field ( =ce is di/ort$ by ! pres5ce 9 x ( ! m or less p]meable bodies2 nor is x necess>y = u to d s1 = to t di/ort$ field ! above argum5t cont9ues to apply1 ^w = ^w4 #bcg ,m4 ,fo/]1 ,lectures on ! ,hi/ory ( ,physiology1 #aija1 p4 #fb4 #bch ,op4 cit4 pp4 #aaj & #ia4 #bci ,lamb1 ,a4 ,b41 ,a new ,explanation ( ! ,me*anism ( ,mitosis1 ,j\rn4 ,exp4 ,zool4 ,v1 pp4 #bg-cc1 #aijh4 #bdj ,am]4 ,j4 ( ,physiol4 ,,viii1 pp4 #bgc-bhc1 #aijc 7vide supra1 p4 #aha72 cf4 ibid4 ,,xv1 pp4 #df-hd1 #aije4 ,cf4 also ,biological ,bullet91 ,,iv1 p4 #age4 #aijc4 #bda ,9 l mann] ,h>dy has %ewn t colloid p>ticles migrate ) ! negative /ream if ! reaction ( ! surr\nd+ fluid be alkal9e1 & vice v]sa4 ,! :ole subject is mu* wid] ?an ^! brief allusions sugge/1 & is ess5tially "p ( ,qu9cke's !ory ( ,electrical ,diffusion or ,endosmosis3 accord+ to :i* ! p>ticles & ! fluid 9 :i* !y float 7or ! fluid & ! capill>y walls ?r\gh :i* x fl[s7 ea* c>ry a *>ge1 !re be+ a discont9uity ( pot5tial at ! surface ( contact1 & h5ce a field ( =ce lead+ to p[]ful tang5tial or %e>+ /resses1 communicat+ to ! p>ticles a velocity :i* v>ies ) ! d5sity p] unit area ( ! surface *>ge4 ,see ,w4 ,b4 ,h>dy's pap] on ,coagulation by ,electricity1 ,j\rn4 ( ,physiol4 ,,xxiv1 p4 #bhh-cjd1 #ahii1 also ,h>dy & ,h4 ,w4 ,h>vey1 ,surface ,electric ,*>ges ( ,liv+ ,cells1 ,proc4 ,r4 ,s4 ,,lxxxiv 7,b71 pp4 #bag-bbf1 #aiaa1 & pap]s quot$ !re94 ,cf4 also ,e4 ,n4 ,h>vey's obs]vations on ! convection ( unicellul> organisms 9 an electric field 7,/udies on ! ,p]meability ( ,cells1 ,j\rn4 ( ,exp]4 ,zool4 ,x1 pp4 #ejh-eef1 #aiaa74 #bdb ,on ,diff]5ces 9 ,electrical ,pot5tial 9 ,develop+ ,eggs1 ,am]4 ,j\rn4 ( ,physiol4 ,,xii1 pp4 #bda-bge1 #aije4 ,?is pap] conta9s an excell5t summ>y ( v>i\s physical !ories ( ! segm5tation ( ! cell4 #bdc ,gray has rec5tly demon/rat$ a tempor>y increase ( electrical conductivity 9 sea-ur*9 eggs dur+ ! process ( f]tilisation 7,! ,electrical ,conductivity ( f]tilis$ & unf]tilis$ ,eggs1 ,j\rn4 ,m>4 ,biol4 ,assoc4 ,x1 pp4 #ej-ei1 #aiac74 #bdd ,s*ewiak(f1 ,ueb] die k>yok9etis*e ,k]n!ilung d] ,euglypha alveolata1 ,morph4 ,jahrb4 ,,xiii1 pp4 #aic-beh1 #ahhh 7see p4 #baf74 #bde ,coe1 ,w4 ,r41 ,maturation & ,f]tilization ( ! ,egg ( ,c]ebratulus1 ,zool4 ,jahrb*] 7,anat4 ,ab?471 ,,xii1 pp4 #dbe-dgf1 #ahii4 #bdf ,?us1 = example1 ,f>m] & ,digby 7,on ,dim5sions ( ,*romosomes consid]$ 9 relation to ,phylog5y1 ,phil4 ,trans4 7,b71 ,,ccv1 pp4 #a-bc1 #aiad7 h be5 at pa9s to %ew1 9 confutation ( ,meek 7ibid4 ,,cciii1 pp4 #a-gd1 #aiab71 t ! wid? ( ! *romosomes _c be correlat$ ) ! ord] ( phylog5y4 #bdg ,cf4 also ,ar*4 f4 ,entw4 ,me*4 ,x1 p4 #eb1 #aijj4 #bdh ,cf4 ,loeb1 ,am4 ,j4 ( ,physiol4 ,,vi1 p4 #cb1 #aijb2 ,erlang]1 ,biol4 ,c5tralbl4 ,,xvii1 pp4 #aeb1 #cci1 #ahig2 ,conkl91 ,biol4 ,lectures1 ,woods ,holl1 p4 #fi1 etc4 #ahih-i4 #bdi ,rob]tson1 ,t4 ,b41 ,note on ! ,*emical ,me*anics ( ,cell ,division1 ,ar*4 f4 ,entw4 ,me*4 ,,xxvii1 p4 #bi1 #aiji1 ,,xxxv1 p4 #fib4 #aiac4 ,cf4 ,r4 ,s4 ,lillie1 ,j4 ,exp4 ,zool4 ,,xxi1 pp4 #cfi-djb1 #aiaf4 #bej ,cf4 ,d',arsonval1 ,ar*4 de ,physiol4 p4 #dfj1 #ahhi2 ,ida ,h4 ,hyde1 op4 cit4 p4 #bdb4 #bea ,cf4 ,plateau's rem>ks 7,/atique des liquides1 ,,ii1 p4 #aed7 on ! t5d5cy t[>ds equilibrium1 r ?an actual equilibrium1 9 _m ( 8 sy/ems ( soap-films4 #beb ,b "u artificial conditions1 8polysp]my0 may take place1 e4g4 "u ! action ( dilute poisons1 or ( an abnormally high temp]ature1 ^! be+ all1 d\btless1 conditions "u :i* ! surface-t5sion is dim9i%$4 #bec ,fol1 ,h41 ,re*]*es sur la fcondation1 #ahgi4 ,r\x1 ,w41 ,beitrge zur ,entwickelungsme*anik des ,embryo1 ,ar*4 f4 ,mikr4 ,anat4 ,,xix1 #ahhg4 ,:itman1 ,c4 ,o41 ,ok9esis1 ,j\rn4 ( ,morph4 ,i1 #ahhg4 #bed ,wilson4 ,! ,cell1 p4 #gg4 #bee ,eight & twelve are by mu* ! commone/ numb]s1 six & sixte5 com+ next 9 ord]4 ,if we may judge by ! li/ giv5 by ,e4 ,b4 ,wilson 7,! ,cell1 p4 #bjf71 ov] #hj ( ! obs]v$ cases lie betwe5 #f & #af1 & ne>ly #fj betwe5 #h & #ab4 #bef ,!ory ( ,cells1 p4 #aia4 #beg ,! ,cell 9 ,developm5t1 etc4 p4 #ei2 cf4 pp4 #chh1 #dac4 #beh ,e4g4 ,brcke1 ,elem5t>organism51 p4 #chg3 8,wir mss5 9 d] ,zelle e95 kle95 ,?i]leib seh51 und drf5 die ,analogi51 wel*e zwis*5 ihr und d5 kle9/5 ,?i]=m5 exi/ir51 niemals aus d5 ,aug5 lass540 #bei ,:itman1 ,c4 ,o41 ,! ,inadequacy ( ! ,cell-!ory1 ,j\rn4 ( ,morphol4 ,,viii1 pp4 #fci-feh1 #ahic2 ,s$gwick1 ,a41 ,on ! ,inadequacy ( ! ,cellul> ,!ory ( ,developm5t1 ,q4,j4,m4,s4 ,,xxxvii1 pp4 #hg-aja1 #ahie1 ,,xxxviii1 pp4 #cca-ccg1 #ahif4 ,cf4 ,b\rne1 ,g4 ,c41 ,a ,criticism ( ! ,cell-!ory2 be+ an answ] to ,mr ,s$gwick's article1 etc41 ibid4 ,,xxxviii1 pp4 #acg-agd1 #ahif4 #bfj ,cf4 ,h]twig1 ,o41 ,die ,zelle und die ,gewebe1 #ahic1 p4 #a2 8,die ,zell51 9 wel*e d] ,anatom die pflanzli*5 und ?i]is*5 ,organism5 z]legt1 s9d die ,trg] d] ,leb5sfunktion52 sie s9d1 wie ,vir*[ si* ausg$rckt hat1 die #8,leb5se9heit54' ,von diesem ,gesi*tspunkt aus betra*tet1 ers*e9t d] ,gesammtleb5sprocess e9es zusamm5gesetzt5 ,organismus ni*ts ,&]es zu se9 als das h*/ v]wickelte ,resultat d] e9zeln5 ,leb5sprocesse se9] zahlrei*51 v]s*i$5 functionir5d5 ,zell540 #bfa ,j\rn4 ( ,morph4 ,,viii1 p4 #fec1 #ahic4 #bfb ,neue ,grundlegung5 zur ,k5ntniss d] ,zelle1 ,morph4 ,jahrb4 ,,viii1 pp4 #bgb1 #cac1 #ccc1 #ahhc4 #bfc ,j\rn4 ( ,morph4 ,,ii1 p4 #di1 #ahhi4 #bfd ,phil4 ,trans4 ,,cli1 p4 #ahc1 #ahfa2 ,rese>*es1 ed4 ,angus ,smi?1 #ahgg1 p4 #eec4 #bfe ,cf4 ,kelv91 ,on ! ,molecul> ,tactics ( a ,cry/al1 ,! ,boyle ,lecture1 ,ox=d1 #ahic1 ,baltimore ,lectures1 #aijd1 pp4 #fab-fdb4 ,"h ,kelv9 0 ma9ly foll[+ ,bravais's 7& ,frank5heim's7 !ory ( 8space-lattices10 b he _h be5 l>gely anticipat$ by ! cry/allograph]s4 ,= an acc\nt ( ! developm5t ( ! subject 9 mod]n cry/allography1 by ,sohncke1 von ,f$or[1 ,s*nfliess1 ,b>l[ & o!rs1 see ,tutton's ,cry/allography1 *ap4 ix1 pp4 #aah-acd1 #aiaa4 #bff ,9 a homog5e\s cry/all9e arrangem5t1 symmetry compels a locus ( "o prop]ty to be a plane or set ( planes2 ! locus 9 ?is case be+ t ( lea/ surface pot5tial en]gy4 #bfg ,?is is :at ,graham call$ ! wat] ( gelat9ation1 on ! analogy ( wat] ( cry/allisation2 ,*em4 & ,phys4 ,rese>*es1 p4 #eig4 #bfh ,"h1 9 a non-cry/all9e or r&om arrangem5t ( p>ticles1 symmetry ensures t ! pot5tial en]gy %all be ! same p] unit area ( all surfaces2 & x foll[s f geometrical consid]ations t ! total surface en]gy w be lea/ if ! surface be sph]ical4 #bfi ,lehmann1 ,o41 ,flssige ,kry/alle1 s[ie ,pla/icitt von ,kry/all5 im allgeme951 etc41 #bfd pp4 #ci pll41 ,leipsig1 #aijd4 ,= a semi-popul>1 illu/rat$ acc\nt1 see ,tutton's ,cry/als 7,int4 ,sci4 ,s]ies71 #aiaa4 #bgj ,z ,graham said ( an alli$ ph5om5on 7! s-call$ blood-cry/als ( ,funke71 x 8illu/rates ! maxim t 9 nature !re are no abrupt transitions1 & t di/9ctions ( class are nev] absolute40 #bga ,cf4 ,przibram1 ,h41 ,kri/all-analogi5 zur ,entwickelungsme*anik d] ,organism51 ,ar*4 f4 ,entw4 ,me*4 ,,xxii1 p4 #bjg1 #aijf 7) copi\s bibliography72 ,lehmann1 ,s*e9b> leb5de ,kri/alle und ,myel9=m51 ibid4 ,,xxvi1 p4 #dhc1 #aijh4 #bgb ,! idea ( a 8surface-t5sion0 9 liquids 0 fir/ enunciat$ by ,segn]1 ,de figuris sup]fici]um fluid>um1 9 ,comm5t4 ,soc4 ,roy4 ,gtt+51 #agea1 p4 #cja4 ,hooke1 9 ! ,micrographia 7#affe1 ,obs4 ,,viii1 etc471 _h call$ att5tion to ! globul> or sph]ical =m ( ! little morsels ( /eel /ruck (f by a fl9t1 & _h %ewn h[ to make a p[d] ( su* sph]ical gra9s1 by heat+ f9e fil+s to melt+ po9t4 8,?is ,pha5om5on0 he said 8proce$s f a propriety :i* belongs to all k9ds ( fluid ,bodies m or less1 & is caus$ by ! ,incongruity ( ! ,ambi5t & includ$ ,fluid1 :i* s acts & modulates ea* o!r1 t !y acquire1 z ne] z is possible1 a sph]ical or globul> =m44440 #bgc ,sci5ce ( ,me*anics1 #aijb1 p4 #cie2 see also ,ma*'s article ,ueb] die physikalis*e ,b$eutung d] ,gesetze d] ,symmetrie1 ,lotos1 ,,xxi1 pp4 #aci-adg1 #ahga4 #bgd ,simil>ly1 ,sir ,david ,brew/] & o!rs made p[]ful l5ses by simply dropp+ small drops ( ,canada balsam1 ca/or oil1 or o!r /rongly refractive liquids1 on to a glass plate3 ,on ,new ,philosophical ,in/rum5ts 7,description ( a new ,fluid ,microscope71 ,ed9burgh1 #ahac1 p4 #dac4 #bge ,beitrge z4 ,physiologie d4 ,protoplasma1 ,pflg]'s ,ar*iv1 ,,ii1 p4 #cjg1 #ahfi4 #bgf ,pogg5d4 ,annal51 ,,xciv1 pp4 #ddg-dei1 #ahee4 ,cf4 ,/re?ill ,wright1 ,phil4 ,mag4 ,feb4 #ahfj4 #bgg ,haycraft & ,c>li] po9t$ out 7,proc4 ,r4,s4,e4 ,,xv1 pp4 #bbj-bbd1 #ahhh7 t ! amoeboid movem5ts ( a :ite blood-corpuscle are only manife/$ :5 ! corpuscle is 9 contact ) "s solid sub/ance3 :ile float+ freely 9 ! plasma or s]um ( ! blood1 ^! corpuscles are sph]ical1 t is to say !y are at re/ & 9 equilibrium4 ,! same fact has rec5tly be5 record$ anew by ,l$+ham 7,on ,phagocytosis f an adsorptive po9t ( view1 ,j\rn4 ( ,hygi5e1 ,,xii1 p4 #cbd1 #aiab74 ,on ! emission ( pseudopodia z br\ght ab\t by *anges 9 surface t5sion1 see also 7int4 al47 ,j5s51 ,ueb] d5 ,geotropismus ni$]] ,organism51 ,pflg]'s ,ar*iv1 ,,liii1 #ahic4 ,j5s5 rem>ks t 9 ,orbitolites1 ! pseudopodia issu+ ?r\gh ! pores ( ! %ell fir/ float freely1 !n z !y gr[ long] b5d ov] till !y t\* ! gr\nd1 :]eupon !y beg9 to display amoeboid & /ream+ motions4 ,v]worn indicates 7,allg4 ,physiol4 #ahie1 p4 #dbi71 & ,dav5port says 7,exp]im4 ,morphology1 ,,ii1 p4 #cgf7 t 8?is p]si/5t cl++ to ! sub/ratum is a #8?igmotropic' reaction1 & "o :i* belongs cle>ly to ! category ( #8response4' 0 7,cf4 ,ptt]1 ,?igmotaxis bei ,proti/51 ,a4 f4 ,physiol4 #aijj1 ,suppl4 p4 #bdg47 ,b x is n cle> to my m9d t to acc\nt = ?is simple ph5om5on we ne$ invoke o!r factors ?an gravity & surface-action4 #bgh ,cf4 ,pauli1 ,allgeme9e physikalis*e ,*emie d4 ,zell5 u4 ,gewebe1 9 ,a%]-,spiro's ,ergebnisse d] ,physiologie1 #aiab2 ,przibram1 ,vitalitt1 #aiac1 p4 #f4 #bgi ,! surface-t5sion !ory ( protoplasmic movem5t has be5 d5i$ by _m4 ,cf4 7e4g471 ,j5n+s1 ,h4 ,s41 ,contributions to ! ,/udy ( ! ,behavi\r ( ! ,l[] ,organisms1 ,c>negie ,in/4 #aijd1 pp4 #acj-bcj2 ,dell+]1 ,o4 ,p41 ,locomotion ( ,amoebae1 etc4 ,j\rn4 ,exp4 ,zool4 ,,iii1 pp4 #ccg-ceg1 #aijf2 also v>i\s pap]s by ,max ,heid5ha91 9 ,anatom4 ,hefte 7,m]kel und ,bonnet71 etc4 #bhj ,^! v>i\s movem5ts ( a liquid surface1 & o!r /ill m /rik+ movem5ts su* z ^? ( a piece ( camphor float+ on wat]1 7 at "o "t ascrib$ by c]ta9 physici/s to a peculi> =ce1 sui g5]is1 ! =ce pipolique ( ,dutro*et3 until van d] ,m5sbrugghe %ew$ t diff]5ces ( surface t5sion 7 en\gh to acc\nt = ?is :ole s]ies ( ph5om5a 7,sur la t5sion sup]ficielle des liquides considre au po9t de vue de c]ta9s m\vem5ts obs]vs leur surface1 ,mm4 ,c\r4 ,acad4 de ,belgique1 ,,xxxiv1 #ahfi2 cf4 ,plateau1 p4 #bhc74 #bha ,cf4 infra1 p4 #cjf4 #bhb ,cf4 p4 #cb4 #bhc ,or1 m /rictly speak+1 unless its ?ickness be less ?an twice ! range ( ! molecul> =ces4 #bhd ,x foll[s t ! t5sion1 dep5d+ only on ! surface-conditions1 is indep5d5t ( ! ?ickness ( ! film4 #bhe ,?is simple b imm5sely important =mula is due to ,laplace 7,mcanique ,cle/e1 ,bk4 x4 suppl4 ,?orie de l'action capillaire1 #ahjf74 #bhf ,sur la surface de rvolution dont la c\rbure moy5ne e/ con/ante1 ,j\rn4 de ,m4 ,li\ville1 ,,vi1 p4 #cji1 #ahda4 #bhg ,see ,liquid ,drops & ,globules1 #aiad1 p4 #aa4 ,rob]t ,boyle us$ turp5t9e 9 mu* ! same way4 ,= o!r me?ods see ,plateau1 op4 cit4 p4 #aed4 #bhh ,felix ,plateau recomm5ds ! use ( a weight$ ?read1 or plumb-l9e1 drawn up out ( a j> ( wat] or oil2 ,phil4 ,mag4 ,,xxxiv1 p4 #bdf1 #ahfg4 #bhi ,cf4 ,boys1 ,c4 ,v41 ,on ,qu>tz ,fibres1 ,nature1 ,july #aa1 #ahhi2 ,w>burton1 ,c41 ,! ,sp9n+ ,app>atus ( ,geometric ,spid]s1 ,q4,j4,m4,s4 ,,xxxi1 pp4 #bi-ci1 #ahij4 #bij ,j4 ,blackwall1 ,spid]s ( ,great ,brita9 7,ray ,society71 #ahei1 p4 #aj2 ,trans4 ,l9n4 ,soc4 ,,xvi1 p4 #dgg1 #ahcc4 #bia ,! int]m$iate sph]ules appe>1 ) great regul>ity & beauty1 :5ev] a liquid jet breaks up into drops2 see ! in/antane\s photographs 9 ,poynt+ & ,?omson's ,prop]ties ( ,matt]1 pp4 #aea1 #aeb1 7ed4 #aijg74 #bib ,khne1 ,unt]su*ung5 b] das ,protoplasma1 #ahfd1 p4 #ge1 etc4 #bic ,a ,/udy ( ,spla%es1 #aijh1 p4 #ch1 etc42 ,segm5tation ( a ,liquid ,annulus1 ,proc4 ,roy4 ,soc4 ,,xxx1 pp4 #di-fj1 #ahhj4 #bid ,cf4 ibid4 pp4 #ag1 #gg4 ,! same ph5om5on is beautifully & cont9u\sly evid5t :5 a /rong jet ( wat] f a tap imp+es on a curv$ surface & !n %oots (f x4 #bie ,see a ,/udy ( ,spla%es1 p4 #ed4 #bif ,a case :i* we h n specially consid]$1 b :i* may be f\nd to des]ve consid]ation 9 biology1 is t ( a cell or drop susp5d$ 9 a liquid ( v>y+ d5sity1 = in/ance 9 ! upp] lay]s ( a fluid 7e4g4 sea-wat]7 at ^: surface cond5sation is go+ on1 s z to produce a /eady d5sity-gradi5t4 ,9 ?is case ! normally sph]ical drop w be flatt5$ into an oval =m1 ) its maximum surface-curvature ly+ at ! level :]e ! d5sities ( ! drop & ! surr\nd+ liquid are j equal4 ,! sectional outl9e ( ! drop has be5 %ewn to be n a true oval or ellipse1 b a some:at complicat$ qu>tic curve4 7,rice1 ,phil4 ,mag4 ,jan4 #aiae47 #big ,inde$ any non-isotropic /iffness1 ev5 ?\gh ,t rema9$ uni=m1 w\ld simulate1 & be indi/+ui%able f1 a condition ( non-/iffness & non-isotropic ,t4 #bih ,a non-symmetry ( ,t & ,t might also be capable ( explanation z a result ( 8liquid cry/allisation40 ,?is hypo!sis is ref]r$ to1 9 connection ) ! blood-corpuscles1 on p4 #bgb4 #bii ,! case ( ! sn[-cry/als is a p>ticul>ly int]e/+ "o2 = _! 8di/ribution0 is 9 "s ways analog\s to :at we f9d1 = in/ance1 among our microscopic skeletons ( ,radiol>ians4 ,t is to say1 we may "o day meet ) myriads ( "s "o p>ticul> =m or species only1 & ano!r day ) myriads ( ano!r2 :ile at ano!r "t & place we may f9d species int]m+l$ 9 inexhau/ible v>iety4 7,cf4 e4g4 ,j4 ,glai%]1 ,ill4 ,london ,news1 ,feb4 #ag1 #ahee2 ,q4,j4,m4,s4 ,,iii1 pp4 #agi-ahe1 #ahee74 #cjj ,cf4 ,b]gson1 ,creative ,evolution1 p4 #ajg3 8,c]ta9 ,=am9if]a h n v>i$ s9ce ! ,silurian epo*4 ,unmov$ witnesses ( ! innum]able revolutions t h upheav$ our planet1 ! ,l+ulae are today :at !y 7 at ! remote/ times ( ! palaeozoic era40 #cja ,ray ,lanke/]1 ,a4,m4,n4,h4 7#d71 ,,xi1 p4 #cba1 #ahgc4 #cjb ,leidy1 ,p>asites ( ! ,t]mites1 ,j4 ,nat4 ,sci41 ,philadelphia1 ,,viii1 pp4 #dbe-ddg1 #ahgd-ha2 cf4 ,saville ,k5t's ,infusoria1 ,,ii1 p4 #eea4 #cjc ,op4 cit4 p4 #gi4 #cjd ,brady1 ,*all5g] ,monograph1 pl4 ,,xx1 p4 #bcc4 #cje ,t ! ,=am9if]a n only c b d hang f ! surface ( ! wat] is confirm$ by ! foll[+ apt quotation :i* ,i owe to ,mr ,e4 ,h]on-,all53 8,qu& on place1 comme il a t dit1 le dpt prov5ant du lavage des fucus dans un flacon que l'on remplit de n\velle eau1 on voit au b\t d'une heure environ les animaux ,gromia duj>d9ii se mettre en m\vem5t et comm5c] grimp]4 ,six heures aprs ils tapiss5t l'extrieur du flacon1 de sorte que les plus levs sont tr5te-six ou qu>ante-deux millimetres du fond2 le l5dema9 beauc\p d'entre eux1 aprs avoir atte9t le niveau du liquide1 ont cont9u ramp] sa surface1 en se laissant p5dre au-dess\s comme c]ta9s mollusques ga/ropodes40 7,duj>d91 ,f41 ,obs]vations n\velles sur les prt5dus cphalopodes microscopiques1 ,ann4 des ,sci4 ,nat4 7#b71 ,,iii1 p4 #cab1 #ahce47 #cjf ,cf4 ,boas1 ,spolia ,atlantica1 #ahhf1 pl4 #f4 #cjg ,?is cellul> patt]n w\ld seem to be relat$ to ! 8cohesion figures0 describ$ by ,toml9son 9 v>i\s surface-films 7,phil4 ,mag4 #ahfa to #ahgj72 to ! 8tesselat$ /ructure0 9 liquids describ$ by ,pr(essor ,james ,?omson 9 #ahhb 7,collect$ ,pap]s1 p4 #acf72 & to ! t\rbillons cellulaires ( ,pr(4 ,h4 ,bn>d 7,ann4 de ,*imie 7#g71 ,,xxiii1 pp4 #fb-add1 #aija1 7#h71 ,,xxiv1 pp4 #efc-eff1 #aiaa71 ,rev4 gnr4 des ,sci4 ,,xi1 p4 #abfh1 #aijj2 cf4 also ,e4 ,h4 ,web]4 7,pogg5d4 ,ann4 ,,xciv1 p4 #deb1 #ahee1 etc474 ,! ph5om5on is ( great int]e/ & v>i\s appe>ances h be5 ref]r$ to x1 9 biology1 geology1 metallurgy & ev5 a/ronomy3 = ! floccul5t cl\ds 9 ! sol> photosph]e %ew an analog\s configuration4 7,see lett]s by ,k]r ,grant1 ,l>mor1 ,wag] & o!rs1 9 ,nature1 ,april #af to ,june #aa1 #aiad47 ,9 _m in/ances1 m>k$ by /rict symmetry or regul>ity1 x is v possible t ! int]f]5ce ( waves or ripples may play its "p 9 ! ph5om5on4 ,b 9 ! majority ( cases1 x is fairly c]ta9 t localis$ c5tres ( action1 or ( dim9i%$ t5sion1 are pres5t1 su* z might be provid$ by du/-p>ticles 9 ! case ( ,d>l+'s exp]im5t 7cf4 infra1 p4 #eij74 #cjh ,ueb] physikalis*5 ,eig5s*aft5 dnn]1 fe/] ,lamell51 ,s4,b4 ,b]l94 ,akad4 #ahhh1 pp4 #ghi1 #gij4 #cji ,c]ta9 palaeontologi/s 7e4g4 ,haeusl] & ,sp&el7 h ma9ta9$ t 9 ea* family or g5us ! pla9 smoo?-%ell$ =ms are ! primitive & anci5t ones1 & t ! ribb$ & o!rwise ornam5t$ %ells make _! appe>ance at lat] dates 9 ! c\rse ( a def9ite evolution 7cf4 ,rhumbl]1 ,=am9if]5 d] ,plankton-,exp$ition1 #aiaa1 i1 p4 #ba74 ,if ?is 7 true x w\ld be ( fundam5tal importance3 b ?is book ( m9e w\ld n des]ve to be writt54 #caj ,a ,/udy ( ,spla%es1 p4 #aaf4 #caa ,see ,silliman's ,j\rnal1 ,,ii1 p4 #agi1 #ahbj2 & cf4 ,plateau1 op4 cit4 ,,ii1 pp4 #acd1 #dfa4 #cab ,! pres5ce or abs5ce ( ! contractile vacuole or vacuoles is "o ( ! *ief di/9ctions1 9 sy/ematic zoology1 betwe5 ! ,heliozoa & ! ,radiol>ia4 ,z we h se5 on p4 #afe 7footnote71 x is probably no m ?an a physical consequ5ce ( ! diff]5t conditions ( exi/5ce 9 fre% wat] & 9 salt4 #cac ,cf4 ,d(le91 ,lehrbu* d] ,protozo5kunde1 #aiaa1 p4 #dbb4 #cad ,cf4 ,m9*91 ,introduction to ! ,/udy ( ! ,protozoa1 #aiad p4 #bic1 ,fig4 #abg4 #cae ,cf4 ,c4 ,a4 ,k(oid & ,olive ,swezy1 ,on ,tri*omonad ,flagellates1 etc4 ,pr4 ,am]4 ,acad4 ( ,arts & ,sci4 ,,li1 pp4 #bhi-cgh1 #aiae4 #caf ,d4 ,l4 ,mack9non1 ,h]petomonads f ! ,alim5t>y ,tract ( c]ta9 ,dungflies1 ,p>asitology1 ,,iii1 p4 #bfh1 #aiaj4 #cag ,proc4 ,roy4 ,soc4 ,,xii1 pp4 #bea-beg1 #ahfb-c4 #cah ,cf4 7int4 al47 ,lehmann1 ,ueb] s*e9b> leb5de ,kri/alle und ,myel9=m51 ,ar*4 f4 ,entw4 ,me*4 ,,xxvi1 p4 #dhc1 #aijh2 ,ann4 d4 ,physik1 ,,xliv1 p4 #ifi1 #aiad4 #cai ,cf4 ,b4 ,moore & ,h4 ,c4 ,roaf1 ,on ! ,osmotic ,equilibrium ( ! ,r$ ,blood ,corpuscle1 ,bio*em4 ,j\rnal1 ,,iii1 p4 #ee1 #aijh4 #cbj ,= an attempt to expla9 ! =m ( a blood-corpuscle by surface-t5sion alone1 see ,rice1 ,phil4 ,mag4 ,nov4 #aiad2 b cf4 ,%ort]1 ibid4 ,jan4 #aiae4 #cba ,koltz(f1 ,n4 ,k41 ,/udi5 b] die ,ge/alt d] ,zelle1 ,ar*4 f4 mikrosk4 ,anat4 ,,lxvii1 pp4 #cfd-ega1 #aije2 ,biol4 ,c5tralbl4 ,,xxiii1 pp4 #fhj-fif1 #aijc1 ,,xxvi1 pp4 #hed-hfc1 #aijf2 ,ar*4 f4 ,zell=s*ung1 ,,ii1 pp4 #a-fe1 #aijh1 ,,vii1 pp4 #cdd-dbc1 #aiaa2 ,anat4 ,anzeig]1 ,,xli1 pp4 #ahc-bjf1 #aiab4 #cbb ,cf4 supra1 p4 #abi4 #cbc ,z ,be! po9ts out 7,zellge/alt1 ,plateaus*e ,flssigkeit/igur und ,neur(ibrille1 ,anat4 ,anz4 ,,xl4 p4 #bji1 #aiaa71 ! spiral fibres ( :i* ,koltz(f speaks mu/ lie 9 ! surface1 & n )9 ! sub/ance1 ( ! cell ^: con=mation is affect$ by !m4 #cbd ,see = a fur!r b /ill elem5t>y acc\nt1 ,mi*aelis1 ,dynamics ( ,surfaces1 #aiad1 p4 #bb seq42 ,macallum1 ,ob]fl*5spannung und ,leb5s]s*e9ung51 9 ,a%]-,spiro's ,ergebnisse d] ,physiologie1 ,,xi1 pp4 #eih-feh1 #aiaa2 see also ,w4 ,w4 ,taylor's ,*emi/ry ( ,colloids1 #aiae1 p4 #bba seq41 ,wolfgang ,o/wald1 ,grundriss d] ,kolloid*emie1 #aiji1 & o!r text-books ( physical *emi/ry2 & ,bayliss's ,pr9ciples ( ,g5]al ,physiology1 pp4 #ed-gc1 #aiae4 #cbe ,! fir/ in/ance ( :at we n[ call an adsorptive ph5om5on 0 obs]v$ 9 soap-bubbles4 ,leid5fro/1 9 #agef1 0 aw>e t ! out] lay] ( ! bubble 0 cov]$ by an 8oily0 lay]4 ,a hundr$ ye>s lat] ,dupr %ew$ t 9 a soap-solution ! soap t5ds to conc5trate at ! surface1 s t ! surface-t5sion ( a v weak solution is v little diff]5t f t ( a /rong "o 7,?orie mcanique de la *aleur1 #ahfi1 p4 #cgf2 cf4 ,plateau1 ,,ii1 p4 #ajj74 #cbf ,?is id5tical ph5om5on 0 ! basis ( ,qu9cke's !ory ( amoeboid movem5t 7,ueb] p]iodis*e ,ausbreitung von ,flssigkeitsob]fl*51 etc41 ,,sb4 ,b]l94 ,akad4 #ahhh1 pp4 #gia-hjf2 cf4 ,pflg]'s ,ar*iv1 #ahgi1 p4 #acf74 #cbg ,j4 ,will>d ,gibbs1 ,equilibrium ( ,het]og5e\s ,sub/ances1 ,tr4 ,conn4 ,acad4 ,,iii1 pp4 #chj-djj1 #ahgf1 also 9 ,collect$ ,pap]s1 ,i1 pp4 #ahe-bah1 ,london1 #aijf2 ,j4 ,j4 ,?omson1 ,applications ( ,dynamics to ,physics & ,*emi/ry1 #ahhh 7,surface t5sion ( solutions71 p4 #aij4 ,see also 7int4 al47 ! v>i\s pap]s by ,c4 ,m4 ,lewis1 ,phil4 ,mag4 7#f71 ,,xv1 p4 #dii1 #aijh1 ,,xvii1 p4 #dff1 #aiji1 ,zeits*r4 f4 physik4 ,*emie1 ,,lxx1 p4 #abi1 #aiaj2 ,miln]1 ,phil4 ,mag4 7#f71 ,,xiii1 p4 #if1 #aijg1 etc4 #cbh ,g4 ,f4 ,fitz,gerald1 ,on ! ,!ory ( ,muscul> ,contraction1 ,brit4 ,ass4 ,rep4 #ahgh2 also 9 ,sci5tific ,writ+s1 ed4 ,l>mor1 #aijb1 pp4 #cd1 #ge4 ,a4 d',arsonval1 ,relations entre l'lectricit animale et la t5sion sup]ficielle1 ,c4 ,r4 ,,cvi1 p4 #agdj4 #ahhh2 cf4 ,a4 ,imb]t1 ,le mcanisme de la contraction musculaire1 dduit de la considration des =ces de t5sion sup]ficielle1 ,ar*4 de ,phys4 7#e71 ,,ix1 pp4 #bhi-cja1 #ahig4 #cbi ,ueb] die ,natur d] ,b9dung d] ,gase im ,blut und 9 se95 ,be/&!il51 ,kolloid4 ,zeits*r4 ,,ii1 pp4 #bfd-bgb1 #bid-cja1 #aijh2 cf4 ,loewy1 ,dissociationsspannung des ,oxyhaemoglob9 im ,blut1 ,ar*4 f4 ,anat4 und ,physiol4 #aijd1 p4 #bca4 #ccj ,we may trace ! fir/ /eps 9 ! /udy ( ?is ph5om5on to ,mels5s1 :o f\nd t ?9 films ( :ite ( egg become firm & insoluble 7,sur les modifications apportes l'album9e 444 p> l'action purem5t mcanique1 ,c4 ,r4 ,acad4 ,sci4 ,,xxxiii1 p4 #bdg1 #ahea72 & ,h>t+ made simil> obs]vations ab\t ! same "t4 ,ramsd5 has inve/igat$ ! same subject1 & also ! m g5]al ph5om5on ( ! =mation ( album9oid & fatty membranes by adsorption3 cf4 ,koaguli]ung d] ,eiweisskrp] auf me*anis*] ,wege1 ,ar*4 f4 ,anat4 u4 ,phys4 7,phys4 ,ab?47 #ahid1 p4 #eag2 ,abs*eidung fe/] ,krp] 9 ,ob]fl*5s*i*t5 ,z4 f4 phys4 ,*em4 ,,xlvii1 p4 #cda1 #aijb2 ,proc4 ,r4 ,s4 ,,lxxii1 p4 #aef1 #aijd4 ,= a g5]al review ( ! :ole subject see ,h4 ,zangg]1 ,ueb] ,membran5 und ,membranfunktion51 9 ,a%]-,spiro's ,ergebnisse d] ,physiologie1 ,,vii1 pp4 #ii-afj1 #aijh4 #cca ,cf4 ,taylor1 ,*emi/ry ( ,colloids1 p4 #beb4 #ccb ,/rasbrg]1 ,ueb] ,cytoplasma/ruktur51 etc4 ,jahrb4 f4 wiss4 ,bot4 ,,xxx1 #ahig2 ,r4 ,a4 ,h>p]1 ,k]n!ilung und freie ,zellbildung im ,ascus1 ibid42 cf4 ,wilson1 ,! ,cell 9 ,developm5t1 etc4 pp4 #ec-ee4 #ccc ,cf4 ,a4 ,gurwits*1 ,morphologie und ,biologie d] ,zelle1 #aijd1 pp4 #afi-ahe2 ,meves1 ,die ,*ondriosom5 als ,trg] erbli*] ,anlag51 ,ar*4 f4 mikrosk4 ,anat4 #aijh1 p4 #gb2 ,j4 ,o4 ,w4 ,b>ratt1 ,*anges 9 ,*ondriosomes1 etc4 ,q4,j4,m4,s4 ,,lviii1 pp4 #eec-eff1 #aiac1 etc42 ,a4 ,ma!ws1 ,*anges 9 ,/ructure ( ! ,pancreas ,cell1 etc41 ,j4 ( ,morph4 ,,xv 7,suppl471 pp4 #aga-bbb1 #ahii4 #ccd ,! "q :e!r *romosomes1 *ondriosomes or *romidia be ! true vehicles or transmitt]s ( 8h]$ity0 is n )\t its analogy to ! old] problem ( :e!r ! p9eal gl& or ! pituit>y body 7 ! actual seat & domicile ( ! s\l4 #cce ,cf4 ,c4 ,c4 ,dobell1 ,*romidia & ! ,b9ucle>ity ,hypo!ses2 a review & a criticism1 ,q4,j4,m4,s4 ,,liii1 #bgi-cbf1 #aiji2 ,pr5ant1 ,a41 ,les ,mito*ondries et l',erga/oplasme1 ,j\rn4 de l',anat4 et de la ,physiol4 ,,xlvi1 pp4 #bag-bhe1 #aiaj 7bo? ) copi\s bibliography74 #ccf ,traube 9 p>ticul> has ma9ta9$ t 9 diff]5ces ( surface-t5sion we h ! orig9 ( ! active =ce productive ( osmotic curr5ts1 & t h]e9 we f9d an explanation1 or an approa* to an explanation1 ( _m ph5om5a :i* 7 =m]ly deem$ peculi>ly 8vital0 9 _! "*4 8,die ,diff]5z d] ,ob]fl*5spannung5 od] d] ,ob]fl*5druck e9e ,kraft d>/ellt1 wel*e als treib5de ,kraft d] ,osmose1 an die ,/elle des ni*t mit dem ,ob]fl*5druck id5tis*5 osmotis*5 ,druckes1 zu setz5 i/1 etc40 7,ob]fl*5druck und se9e ,b$eutung im ,organismus1 ,pflg]'s ,ar*iv1 ,,cv1 p4 #eei1 #aijd47 ,cf4 also ,h>dy 7,pr4 ,phys4 ,soc4 ,,xxviii1 p4 #aaf1 #aiaf71 8,if ! surface film ( a colloid membrane sep>at+ two masses ( fluid 7 to *ange 9 su* a way z to l[] ! pot5tial ( ! wat] 9 x1 wat] w\ld ent] ! region f bo? sides at once4 ,b if ! *ange ( /ate 7 to be propagat$ z a wave ( *ange1 />t+ at "o face & dy+ out at ! o!r face1 wat] w\ld be c>ri$ along f "o side ( ! membrane to ! o!r4 ,a succession ( su* waves w\ld ma9ta9 a fl[ ( fluid40 #ccg ,on ! ,di/ribution ( ,potassium 9 animal & vegetable ,cells2 ,j\rn4 ( ,physiol4 ,,xxxii1 p4 #ie1 #aije4 #cch ,! read] w recognise t !re is a fundam5tal diff]5ce1 & contra/1 betwe5 su* exp]im5ts z ^! ( ,pr(essor ,macallum's & ! ord9>y /a9+ processes ( ! hi/ologi/4 ,! latt] are 7z a g5]al rule7 purely empirical1 :ile ! =m] endeav\r to reveal ! true micro*emi/ry ( ! cell4 8,on peut dire que la micro*imie n'e/ encore qu' la priode d'essai1 et que l'av5ir de l'hi/ologie et spcialem5t de la cytologie e/ t\t enti] dans la micro*imie0 7,pr5ant1 ,a41 ,m?odes et rsultats de la ,micro*imie1 ,j\rn4 de l',anat4 et de la ,physiol4 ,,xlvi1 pp4 #cdc-djd1 #aiaj74 #cci ,cf4 ,macallum1 ,presid5tial ,address1 ,section ,i1 ,brit4 ,ass4 ,rep4 7,%effield71 #aiaj1 p4 #gdd4 #cdj ,9 accordance ) a simple coroll>y to ! ,gibbs-,?omson law4 #cda ,x c easily be prov$ 7by equat+ ! increase ( en]gy /or$ 9 an increas$ surface to ! "w done 9 increas+ t surface71 t ! t5sion measur$ p] unit bread?1 ,tab1 is equal to ! en]gy p] unit area1 ,eab4 #cdb ,! pres5ce ( ?is little liquid 8b\rrelet10 drawn f ! mat]ial ( :i* ! p>tition-walls !mselves are compos$1 is obvi\sly t5d+ to a r$uction ( ! int]nal surface-area4 ,& x may be t x is z well1 or bett]1 acc\nt$ = on ?is gr\nd ?an on ,plateau's assumption t x repres5ts a 8surface ( cont9uity40 #cdc ,a simil> 8b\rrelet0 is admirably se5 at ! l9e ( junction betwe5 a float+ bubble & ! liquid on :i* x floats2 9 :i* case x con/itutes a 8masse annulaire10 ^: ma!matical prop]ties & relation to ! =m ( ! ne>ly hemisph]ical bubble1 h be5 inve/igat$ by van d] ,m5sbrugghe 7cf4 ,plateau1 op4 cit41 p4 #chf74 ,! =m ( ! sup]ficial vacuoles 9 ,act9ophrys or ,act9ospha]ium involves an id5tical problem4 #cdd ,9 an actual calculation we mu/ ( c\rse always take acc\nt ( ! t5sions on bo? sides ( ea* film or membrane4 #cde ,h(mei/]1 ,pr+%eim's ,jahrb4 ,,iii1 p4 #bgb1 #ahfc2 ,hdb4 d4 physiol4 ,bot4 ,i1 #ahfg1 p4 #abi4 #cdf ,sa*s1 ,ueb] die ,anordnung d] ,zell5 9 jng/5 ,pflanz5!il51 ,v]h4 phys4 m$4 ,ges4 ,wrzburg1 ,,xi1 pp4 #bai-bdb1 #ahgg2 ,ueb] ,zell5anordnung und ,wa*/hum1 ibid4 ,,xii1 #ahgh2 ,ueb] die dur* ,wa*/hum b$+te ,v]s*iebung kle9/] ,!il*5 9 trajectoris*5 ,curv51 ,monatsb]4 k4 ,akad4 ,wiss4 ,b]l91 #ahhj2 ,physiology ( ,plants1 *ap4 xxvii1 pp4 #dca-dei1 ,ox=d1 #ahhg4 #cdg ,s*w5d5]1 ,ueb] d5 ,bau und das ,wa*/hum des ,fle*t5?allus1 ,naturf4 ,ges4 ,zri*1 ,febr4 #ahfj1 pp4 #bgb-bif4 #cdh ,re9ke1 ,lehrbu* d] ,botanik1 #ahhj1 p4 #eai4 #cdi ,cf4 ,leitgeb1 ,unt]s4 b] die ,leb]moose1 ,,ii1 p4 #d1 ,graz1 #ahha4 #cej ,raub]1 ,neue ,grundlegung5 zur ,k5ntniss d] ,zelle1 ,morph4 ,jahrb4 ,,viii1 pp4 #bgi1 #ccd1 #ahhb4 #cea ,c4 ,r4 ,acad4 ,sc4 ,,xxxiii1 p4 #bdg1 #ahea2 ,ann4 de *imie et de phys4 7#c71 ,,xxxiii1 p4 #agj1 #ahea2 ,bull4 ,r4 ,acad4 ,belg4 ,,xxiv1 p4 #eca1 #aheg4 #ceb ,klebs1 ,biolog4 ,c5tralbl4 ,,vii1 pp4 #aic-bja1 #ahhg4 #cec ,l4 ,err]a1 ,sur une condition fondam5tale d'quilibre des cellules vivantes1 ,c4 ,r41 ,,ciii1 p4 #hbb1 #ahhf2 ,bull4 ,soc4 ,belge de ,microscopie1 ,,xiii1 ,oct4 #ahhf2 ,recueil d'uvres 7,physiologie gnrale71 #aiaj1 pp4 #bja-bje4 #ced ,l4 ,*abry1 ,embryologie des ,ascidi5s1 ,j4 ,anat4 et ,physiol4 ,,xxiii1 p4 #bff1 #ahhg4 #cee ,rob]t1 ,embryologie des ,troques1 ,ar*4 de ,zool4 exp4 et gn4 7#c71 ,x1 #ahib4 #cef 8,dass d] ,fur*ungsmodus etwas fr das ,zuknftige unwes5tli*es i/10 ,z4 f4 w4 ,z4 ,,lv1 #ahic1 p4 #cg4 ,) ?is /atem5t comp>e1 or contra/1 t ( ,conkl91 quot$ on p4 #d2 cf4 also pp4 #aeg1 #cdh 7footnotes74 #ceg de ,wildeman1 ,etudes sur l'atta*e des cloisons cellulaires1 ,mm4 ,c\ronn4 de l',acad4 ,r4 de ,belgique1 ,,liii1 #hd pp41 #ahic-d4 #ceh ,x 0 s t]m$ by ,conkl9 9 #ahig1 9 8 pap] on ,crepidula 7,j4 ( ,morph4 ,,xiii1 #ahig74 ,x is ! ,qu]fur*e ( ,rabl 7,morph4 ,jahrb4 ,v1 #ahgi72 ! ,pol>fur*e ( ,o4 ,h]twig 7,j54 ,zeits*r4 ,,xiv1 #ahhj72 ! ,bre*ungsl9ie ( ,raub] 7,neue ,grundlage zur ,k4 d] ,zelle1 ,m4 ,jb4 ,,viii1 #ahhb74 ,x is c>efully discuss$ by ,rob]t1 ,dv4 des ,troques1 ,ar*4 de ,zool4 ,exp4 et ,gn4 7#c71 ,x1 #ahib1 p4 #cjg seq4 #cei ,?us ,wilson 7,j4 ( ,morph4 ,,viii1 #ahie7 decl>$ t 9 ,amphioxus ! pol> furr[ 0 occasionally abs5t1 & ,dries* took occasion to criticise & to ?r[ d\bt ^u ! /atem5t 7,ar*4 f4 ,entw4 ,me*4 ,i1 #ahie1 p4 #dah74 #cfj ,precisely ! same rem>k 0 made long ago by ,dries*3 8,das s (t sehematis* gezei*nete ,vi]zell5/adium mit zwei si* 9 zwei ,punkt5 s*eid5de ,m$ian5 kann man wohl getro/ aus d] ,reihe des ,exi/i]5d5 /rei*510 ,entw4 me*4 ,/udi51 ,z4 f4 w4 ,z4 ,,liii1 p4 #aff1 #ahib4 ,cf4 also 8 ,ma?4 me*anis*e ,b$eutung morphologis*] ,probleme d] ,biologie1 ,j5a1 #ei pp4 #ahia4 #cfa ,comp>e1 h[ev]1 p4 #bii4 #cfb ,ricreatione dell' oc*io e della m5te1 nell' ,oss]vatione delle ,*iocciole1 ,roma1 #afha4 #cfc ,cf4 "s ( ,j4 ,h4 ,v9c5t's photographs ( ripples1 9 ,phil4 ,mag4 #ahig-ahii2 or ^? ( ,f4 ,r4 ,watson1 9 ,phys4 ,review1 #ahig1 #aija1 #aiaf4 ,! appe>ance w dep5d on ! rate ( ! wave1 & 9 turn on ! surface-t5sion2 ) a l[ t5sion "o w\ld probably see only a mov+ 8jabble40 ,fitz,gerald ?\ght diatom-patt]ns might be due to electromagnetic vibrations 7,works1 p4 #ejc1 #aijb74 #cfd ,cu%man1 ,j4 ,a4 & ,h5d]son1 ,w4 ,p41 ,am]4 ,nat4 ,,xl1 pp4 #gig-hjb1 #aijf4 #cfe ,?is does n m]ely neglect ! brok5 ones b all ^: c5tres lie betwe5 ?is circle & a hexagon inscrib$ 9 x4 #cff ,= m detail$ calculations see a pap] by 8,h4,m40 8 ,h4 ,munro1 9 ,q4 ,j4 ,m4 ,s4 ,,vi1 p4 #hc1 #aheh4 #cfg ,cf4 ,h>tog1 ,! ,dual ,=ce ( ! ,divid+ ,cell1 ,sci5ce ,progress 7n4s471 ,i1 ,oct4 #aijg1 & o!r pap]s4 ,also ,baltz]1 ,ueb] mehrpolige ,mitos5 bei ,seeigelei]n1 ,inaug4 ,diss4 #aijh4 #cfh ,obs]vations sur les ,abeilles1 ,mm4 ,acad4 ,sc4 ,p>is1 #agab1 p4 #bii4 #cfi ,z expla9$ by ,leslie ,ellis1 9 8 essay 8,on ! ,=m ( ,bees' ,cells10 9 ,ma!matical & o!r ,writ+s1 #ahec1 p4 #cec2 cf4 ,o4 ,t]quem1 ,n\v4 ,ann4 ,ma?4 #ahef1 p4 #agh4 #cgj ,phil4 ,trans4 ,,xlii1 #agdc1 pp4 #efe-ega4 #cga ,mm4 de l',acad4 de ,b]l91 #agha4 #cgb ,cf4 ,gregory1 ,examples1 p4 #ajf1 ,wood's ,homes )\t ,h&s1 #ahfe1 p4 #dbh1 ,ma*1 ,sci5ce ( ,me*anics1 #aijb1 p4 #dec1 etc41 etc4 #cgc ,orig9 ( ,species1 *4 ,,viii 7#f? ed41 p4 #bba74 ,! cells ( v>i\s bees1 humble-bees & social wasps h be5 describ$ & ma!matically inve/igat$ by ,k4 ,mll5h(f1 ,pflg]'s ,ar*iv ,,xxxii1 p4 #ehi1 #ahhc2 b 8 _m int]e/+ results are too complex to epitomise4 ,= figures ( v>i\s ne/s & combs see 7e4g47 von ,bttel-,reep51 ,biol4 ,c5tralbl4 ,,xxxiii1 pp4 #d1 #hi1 #abi1 #ahc1 #aijc4 #cgd ,d>w9 _h a some:at simil> idea1 ?\gh he all[$ m play to ! bee's in/9ct or consci\s int5tion4 ,?us1 :5 he notic$ c]ta9 half-complet$ cell-walls to be concave on "o side & convex on ! o!r1 b to become p]fectly flat :5 re/or$ = a %ort "t to ! hive1 he says3 8,x 0 absolutely impossible1 f ! extreme ?9ness ( ! little plate1 t !y c\ld h effect$ ?is by gnaw+ away ! convex side2 & ,i suspect t ! bees 9 su* cases /& on opposite sides & pu% & b5d ! ductile & w>m wax 7:i* z ,i h tri$ is easily done7 into its prop] int]m$iate plane1 & ?us flatt5 x40 #cge ,s9ce writ+ ! above1 ,i see t ,mll5h(f gives ! same explanation1 & decl>es t ! wax5 wall is actually a ,flssigkeit%ut*51 or liquid film4 #cgf ,bonnet criticis$ ,buffon's explanation1 on ! gr\nd t 8 description 0 incomplete2 = ,buffon took no acc\nt ( ! ,m>aldi pyramids4 #cgg ,buffon1 ,hi/oire ,naturelle1 ,,iv1 p4 #ii4 ,among _m o!r pap]s on ! ,bee's cell1 see ,b>clay1 ,mem4 ,w]n]ian ,soc4 ,,ii1 p4 #bei 7#ahab71 #ahah2 ,%>pe1 ,phil4 ,mag4 ,,iv1 #ahbh1 pp4 #ai-ba2 ,l4 ,lalanne1 ,ann4 ,sci4 ,nat4 7#b7 ,zool4 ,,xiii1 pp4 #ceh-cgd1 #ahdj2 ,haughton1 ,ann4 ,mag4 ,nat4 ,hi/4 7#c71 ,,xi1 pp4 #dae-dbi1 #ahfc2 ,a4 ,r4 ,wallace1 ibid4 ,,xii1 p4 #cjc1 #ahfc2 ,jeffries ,wyman4 ,pr4 ,am]4 ,acad4 ( ,arts & ,sc4 ,,vii1 pp4 #fh-hc1 #ahfh2 ,*auncey ,wright1 ibid4 ,,iv1 p4 #dcb1 #ahfj4 #cgh ,sir ,w4 ,?omson1 ,on ! ,division ( ,space ) ,m9imum ,p>titional ,area1 ,phil4 ,mag4 7#e71 ,,xxiv1 pp4 #ejc-ead1 ,dec4 #ahhg2 cf4 ,baltimore ,lectures1 #aijd1 p4 #fae4 #cgi ,also discov]$ indep5d5tly by ,sir ,david ,brew/]1 ,trans4 ,r4,s4,e4 ,,xxiv1 p4 #eje1 #ahfg1 ,,xxv1 p4 #aae1 #ahfi4 #chj ,von ,f$or[ _h already describ$ 79 ,russian7 ! same figure1 "u ! "n ( cubo-octah$ron1 or hepta-p>alleloh$ron1 limit$ h[ev] to ! case :]e all ! faces are plane4 ,?is figure1 toge!r ) ! cube1 ! hexagonal prism1 ! rhombic dodecah$ron & ! 8elongat$ dodecah$ron10 con/itut$ ! five plane-fac$1 p>allel-sid$ figures by :i* space is capable ( be+ completely fill$ & symmetrically p>tition$2 ! s]ies s =m+ ! f\ndation ( ,von ,f$or['s !ory ( cry/all9e /ructure4 ,! elongat$ dodecah$ron is1 ess5tially1 ! figure ( ! bee's cell4 #cha ,f4 ,r4 ,lillie1 ,embryology ( ! ,unionidae1 ,j\rn4 ( ,morphology1 ,x1 p4 #ab1 #ahie4 #chb ,e4 ,b4 ,wilson1 ,! ,cell-l9eage ( ,n]eis1 ,j\rn4 ( ,morphology1 ,,vi1 p4 #deb1 #ahib4 #chc ,x is highly probable1 & we may reasonably assume1 t ! two little triangles d n actually meet at an apical po9t1 b m]ge into "o ano!r by a twi/1 or m9ute surface ( complex curvature1 s z n to contrav5e ! normal conditions ( equilibrium4 #chd ,pr(essor ,p$die has giv5 me ?is int]e/+ & important result1 b ! ma!matical reason+ is too l5g?y to be set =? "h4 #che ,cf4 ,rhumbl]1 ,ar*4 f4 ,entw4 ,me*4 ,,xiv1 p4 #dja1 #aijb2 ,as%eton1 ibid4 ,,xxxi1 pp4 #df-gh1 #aiaj4 #chf ,m4 ,rob]t 7l4 c4 p4 #cje7 has compil$ a long li/ ( cases among ! molluscs & ! worms1 :]e ! initial segm5tation ( ! egg proce$s by equal or unequal division4 ,! two cases are ab\t equally num]\s4 ,b l _m o!r writ]s1 he w\ld ascribe ?is equality or inequality r to a provision = ! future ?an to a direct effect ( imm$iate physical causation3 8,il semble assez probable1 comme on l'a dit s\v5t1 que la plus gr&e taille d'un bla/omre e/ lie l'importance et au dveloppem5t prcoce des p>ties du corps qui doiv5t en natre3 il y aurait l une sorte de reflet des /ades po/rieures du dveloppem5t sur les premires phnomnes1 ce que ,m4 ,ray ,lanke/] appelle precoci\s segregation4 ,il faut av\] p\rtant qu'on e/ p>fois assez emb>rass p\r assign] une cause p>eilles diffr5ces40 #chg ,! pr9ciple is well illu/rat$ 9 an exp]im5t ( ,sir ,david ,brew/]'s 7,trans4 ,r4,s4,e4 ,,xxv1 p4 #aaa1 #ahfi74 ,a soap-film is drawn ov] ! rim ( a w9e-glass1 & !n cov]$ by a wat*-glass4 ,! film is incl9$ or %ak5 till x becomes atta*$ to ! glass cov]+1 & x !n imm$iately *anges place1 leav+ its transv]se position to take up t ( a sph]ical segm5t ext5d+ f "o side ( ! w9e-glass to its cov]1 & s enclos+ ! same volume ( air z =m]ly b ) a great economy ( surface1 precisely z 9 ! case ( our sph]ical p>tition cutt+ (f "o corn] ( a cube4 #chh ,cf4 ,wildeman1 ,atta*e des ,cloisons1 etc41 pls4 #a1 #b4 #chi ,nova ,acta ,k4 ,leop4 ,akad4 ,,xi1 #a1 pl4 ,,iv4 #cij ,cf4 ,protoplasmame*anik1 p4 #bbi3 8,ins(]n lieg5 also die ,v]hltnisse hi] wes5tli* &]s als bei d] ,z]!ilung hohl] ,krp]=m5 dur* flssige ,lamell54 ,w5n die ,membran bei d] ,zell!ilung die von dem ,pr9zip d] kle9/5 ,fl*5 ge=d]te ,lage und ,krmmung annimmt1 s w]d5 wir d5 ,grund dafr 9 &r] ,weise abzuleit5 hab540 #cia ,!re is1 ,i ?9k1 "s ambiguity or disagreem5t among botani/s z to ! use ( ?is latt] t]m3 ! s5se 9 :i* ,i am us+ x1 viz4 = any p>tition :i* meets ! out] or p]iph]al wall at "r angles 7! /rictly radial p>tition be+ = ! pres5t exclud$71 is1 h[ev]1 cle>4 #cib ,cit4 ,plateau1 ,/atique des ,liquides1 i1 p4 #ceh4 #cic ,ev5 9 a ,protozoon 7,eugl5a viridis71 :5 kept alive "u artificial compression1 ,ryd] f\nd a process ( cell-division to occur :i* he comp>es to ! segm5t+ bla/od]m ( a fi%'s egg1 & :i* corresponds 9 its ess5tial features ) t "h describ$4 ,contrib4 ,zool4 ,lab4 ,univ4 ,p5nsylvania1 ,i1 pp4 #cg-ej1 #ahic4 #cid ,?is1 l _m simil> figures1 is manife/ly drawn "u ! influ5ce ( ,sa*s's !oretical views1 or assumptions1 reg>d+ or?ogonal trajectories1 coaxial circles1 confocal ellipses1 etc4 #cie ,su* preconceptions z ,raub] ent]ta9$ 7 all 9 a direction likely to lead him away f su* ph5om5a z he has fai?fully depict$4 ,raub] _h no idea :atsoev] ( ! pr9ciples by :i* we are guid$ 9 ?is discussion1 nor does he introduce at all ! analogy ( surface-t5sion1 or any o!r purely physical concept4 ,b he 0 deeply "u ! influ5ce ( ,sa*s's rule ( rectangul> int]section2 & he 0 accord+ly dispos$ to look ^u ! configuration repres5t$ above 9 ,fig4 #afh1 #f1 z ! mo/ typical or mo/ primitive4 #cif ,cf4 ,raub]1 ,neue ,grundlage z4 ,k4 d] ,zelle1 ,morph4 ,jahrb4 ,,viii1 #ahhc1 pp4 #bgc1 #bgd3 8,i* betone no*1 dass unt] me95 ,figur5 diej5ige g> ni*t en?alt5 i/1 wel*e zum ,typus d] ,batra*i]fur*ung gehrig am mei/5 bekannt i/ 4444 ,es hab5 s ausgezei*nete ,beoba*t] sie als vorh&5 bes*rieb51 dass es mir ni*t e9fall5 kann1 sie b]haupt ni*t anzu]k5n540 #cig ,r\x's exp]im5ts 7 p]=m$ ) drops ( p>aff9 susp5d$ 9 dilute alcohol1 to :i* a little calcium acetate 0 add$ to =m a soapy pellicle ov] ! drops & prev5t !m f reunit+ ) "o ano!r4 #cih ,cf4 7e4g47 ,cl]k ,maxwell1 ,on ,reciprocal ,figures1 etc41 ,trans4 ,r4 ,s4 ,e4 ,,xxvi1 p4 #i1 #ahgj4 #cii ,see ,greville1 ,k4 ,r41 ,monograph ( ! ,g5us ,a/]olampra1 ,q4,j4,m4,s4 ,,viii1 7,trans471 pp4 #ajb-abd1 #ahfj2 cf4 ,,ibid4 7n4s471 ,,ii1 pp4 #da-ee1 #ahfb4 #djj ,! same is true ( ! insect's w+2 b 9 ?is case ,i d n haz>d a conjectural explanation4 #dja ,ann4 ,mag4 ,n4 ,h4 7#b71 ,,iii1 p4 #abf1 #ahdi4 #djb ,phil4 ,trans4 ,,clvii1 pp4 #fdc-fef1 #ahfg4 #djc ,sa*s1 ,pflanz5physiologie 7,vorlesung ,,xxiv71 #ahhb2 cf4 ,raub]1 ,neue ,grundlage zur ,k5ntniss d] ,zelle1 ,morphol4 ,jahrb4 ,,viii1 p4 #cjc seq41 #ahhc2 ,e4 ,b4 ,wilson1 ,cell-l9eage ( ,n]eis1 ,j\rn4 ( ,morphology1 ,,vi1 p4 #ddh1 #ahib1 etc4 #djd ,9 ! foll[+ acc\nt ,i foll[ closely on ! l9es laid d[n by ,b]?old2 ,protoplasmame*anik1 cap4 vii4 ,_m botanical ph5om5a id5tical & simil> to ^? "h dealt )1 are elaborately discuss$ by ,sa*s 9 8 ,physiology ( ,plants 7*ap4 xxvii1 pp4 #dca-dei1 ,ox=d1 #ahhg72 & 9 8 e>li] pap]s1 ,ueb] die ,anordnung d] ,zell5 9 jng/5 ,pflanz5!il51 & ,ueb] ,zell5anordnung und ,wa*/hum 7,arb4 d4 botan4 ,in/4 ,wrzburg1 #ahgh1 #ahgi74 ,b ,sa*s's treatm5t diff]s entirely f t :i* ,i adopt & advocate "h3 8 explanations be+ bas$ on 8 8law0 ( rectangul> succession1 & involv+ complicat$ sy/ems ( confocal conics1 ) _! or?ogonally int]sect+ ellipses & hyp]bolas4 #dje ,cf4 p4 #cfi4 #djf ,!re is mu* in=mation reg>d+ ! *emical composition & m9]alogical /ructure ( %ells & o!r organic products 9 ,h4 ,c4 ,sorby's ,presid5tial ,address to ! ,geological ,society 7,proc4 ,geol4 ,soc4 #ahgi1 pp4 #ef-ic72 b ,sorby fail$ to recognise t association ) 8organic0 matt]1 or ) colloid matt] :e!r liv+ or dead1 introduc$ a new s]ies ( purely physical ph5om5a4 #djg ,vesque1 ,ann4 des ,sc4 ,nat4 7,bot47 7#e71 ,,xix1 p4 #caj1 #ahgd4 #djh ,cf4 ,kllik]1 ,icones ,hi/iologicae1 #ahfd1 pp4 #aai1 etc4 #dji ,9 an int]e/+ pap] by ,irv9e & ,sims ,woodhead on ! 8,secretion ( ,c>bonate ( ,lime by ,animals0 7,proc4 ,r4 ,s4 ,e4 ,,xvi1 #ahhi1 p4 #cea7 x is ass]t$ t 8lime salts1 ( :atev] =m1 are deposit$ only 9 vitally inactive tissue40 #daj ,! tube ( ,t]$o %ews no trace ( organic matt]1 b consi/s ( irregul> prismatic cry/als3 ! :ole /ructure 8be+ id5tical ) t ( small ve9s ( calcite1 su* z are se5 9 ?9 sections ( rocks0 7,sorby1 ,proc4 ,geol4 ,soc4 #ahgi1 p4 #eh74 ,?is1 !n1 w\ld seem to be a some:at exceptional case ( a %ell laid d[n completely outside ( ! animal's ext]nal lay] ( organic or colloid sub/ance4 #daa ,c4 ,r4 ,soc4 ,biol4 ,p>is 7#i71 ,i1 pp4 #ag-bj1 #ahhi2 ,c4 ,r4 ,ac4 ,sc4 ,,cviii1 pp4 #aif-h1 #ahhi4 #dab ,cf4 ,h]on-,all51 ,phil4 ,trans4 7,b71 vol4 ,,ccvi1 p4 #bfb1 #aiae4 #dac ,see ,l$uc1 ,me*anism ( ,life 7#aiaa71 *4 ,x1 = copi\s ref]5ces to o!r works on ! artificial production ( 8organic0 =ms4 #dad ,lectures on ! ,molecul> ,asymmetry ( ,natural ,organic ,comp\nds1 ,*emical ,soc4 ( ,p>is1 #ahfj1 & also 9 ,o/wald's ,klassik] d4 ex4 ,wiss4 ,no4 #bh1 & 9 ,alembic ,club ,repr9ts1 ,no4 #ad1 ,ed9burgh1 #ahig2 cf4 ,ri*>dson1 ,g4 ,m41 ,f\ndations ( ,/]eo*emi/ry1 ,n4 ,y4 #aija4 #dae ,japp1 ,/]eometry & ,vitalism1 ,brit4 ,ass4 ,rep4 7,bri/ol71 p4 #hac1 #ahih2 cf4 also a volum9\s discussion 9 ,nature1 #ahih-i4 #daf ,!y repres5t ! g5]al !orem ( :i* p>ticul> cases are f\nd1 = in/ance1 9 ! asymmetry ( ! f]m5ts 7or enzymes7 :i* act ^u asymmetrical bodies1 ! "o fitt+ ! o!r1 accord+ to ,emil ,fis*]'s well-kn[n phrase1 z lock & key4 ,cf4 8 ,b$eutung d] ,/]eo*emie fr die ,physiologie1 ,z4 f4 physiol4 ,*emie1 ,v1 p4 #fj1 #ahii1 & v>i\s pap]s 9 ! ,b]4 d4 d4 *em4 ,ges4 f #ahid4 #dag ,9 accordance ) ,emil ,fis*]'s conception ( 8asymmetric syn!sis10 x is n[ held to be m likely t ! process is syn!tic ?an analytic3 m likely1 t is to say1 t ! plant builds up f ! fir/ "o asymmetric body to ! exclusion ( ! o!r1 ?an t x 8selects0 or 8picks out0 7z ,japp suppos$7 ! "r-h&$ or ! left-h&$ molecules f an orig9al1 optically inactive1 mixture ( ! two2 cf4 ,a4 ,mc,kenzie1 ,/udies 9 ,asymmetric ,syn!sis1 ,j\rn4 ,*em4 ,soc4 7,trans471 ,,lxxxv1 p4 #abdi1 #aijd4 #dah ,see = a full] discussion1 ,hans ,przibram1 ,vitalitt1 #aiac1 ,kap4 iv1 ,/(fwe*sel 7,assimilation und ,katalyse74 #dai ,cf4 ,cotton1 ,ann4 de ,*im4 et de ,phys4 7#g71 ,,viii1 pp4 #cdg-dcb 7cf4 p4 #cgc71 #ahif4 #dbj ,byk1 ,a41 ,zur ,frage d] ,spaltb>keit von ,razemv]b9dung5 dur* ,zirkul>pol>isi]tes ,li*t1 e9 ,beitrag zur primr5 ,ent/ehung optis*-activ] ,sub/anz51 ,zeits*4 f4 physikal4 ,*emie1 ,,xlix1 p4 #fda1 #aijd4 ,x mu/ be admitt$ t fur!r positive evid5ce on ^! l9es is /ill awant+4 #dba ,cf4 7int4 al47 ,emil ,fis*]1 ,unt]su*ung5 b] ,am9osur51 ,prote9e1 etc4 ,b]l91 #aijf4 #dbb ,japp1 l4 c4 p4 #hbh4 #dbc ,ra9ey1 ,g41 ,on ! ,elem5t>y ,=mation ( ! ,skeletons ( ,animals1 & o!r ,h>d ,/ructures =m$ 9 connection ) ,liv+ ,tissue1 ,brit4 ,=4 ,m$4 ,*4 ,rev4 ,,xx1 pp4 #dea-dgf1 #aheg2 publi%$ sep>ately ) additions1 #hvo4 ,london1 #aheh4 ,= o!r pap]s by ,ra9ey on k9dr$ subjects see ,q4 ,j4 ,m4 ,s4 ,,vi 7,tr4 ,microsc4 ,soc471 pp4 #da-ej1 #aheh1 ,,vii1 pp4 #bab-bbe1 #ahei1 ,,viii1 pp4 #a-aj1 #ahfj1 ,i 7n4 s471 pp4 #bc-cb1 #ahfa4 ,cf4 also ,ord1 ,w4 ,m41 ,on ,molecul> ,coalesc5ce1 & on ! influ5ce ex]cis$ by ,colloids ^u ! ,=ms ( ,inorganic ,matt]1 ,q4 ,j4 ,m4 ,s4 ,,xii1 pp4 #bai-bci1 #ahgb2 & also ! e>ly b /ill int]e/+ obs]vations ( ,mr ,*>les ,hat*ett1 ,*emical ,exp]im5ts on ,zoophytes2 ) "s obs]vations on ! compon5t p>ts ( ,membrane1 ,phil4 ,trans4 #ahjj4 pp4 #cbg-djb4 #dbd ,cf4 ,qu9cke1 ,ueb] unsi*tb>e ,flssigkeitss*i*t51 ,ann4 d] ,physik1 #aijb4 #dbe ,see = in/ance o!r excell5t illu/rations 9 ,c>p5t]'s article 8,%ell10 9 ,todd's ,cyclopdia1 vol4 ,,iv4 pp4 #eej-ega1 #ahdg-di4 ,accord+ to ,c>p5t]1 ! %ells ( ! mollusca 7& also ( ! cru/acea7 are 8ess5tially compos$ ( cells1 consolidat$ by a deposit ( c>bonate ( lime 9 _! int]ior40 ,t is to say1 ,c>p5t] suppos$ t ! sph]ulites1 or calcosph]ites ( ,h>t+1 71 to beg9 )1 j s _m liv+ protoplasmic cells4 ,soon aft]w>ds h[ev]1 ,huxley po9t$ out t ! mode ( =mation1 :ile at fir/ sight 8irresi/ibly sugge/+ a cellul> /ructure1 444 is 9 reality no?+ ( ! k9d10 b 8is simply ! result ( ! concretion>y mann] 9 :i* ! calc>e\s matt] is deposit$02 ibid4 art4 8,tegum5t>y ,organs10 vol4 ,v1 p4 #dhg1 #ahei4 ,quekett 7,lectures on ,hi/ology1 vol4 ,,ii1 p4 #cic1 #ahed1 & ,q4 ,j4 ,m4 ,s4 ,,xi1 pp4 #ie-ajd1 #ahfc7 support$ ,c>p5t]2 b ,williamson 7,hi/ological ,features 9 ! ,%ells ( ! ,cru/acea1 ,q4 ,j4 ,m4 ,s4 ,,viii1 pp4 #ce-dg1 #ahfj7 amply confirm$ ,huxley's view1 :i* 9 ! end ,c>p5t] himself adopt$ 7,! ,microscope1 #ahfb1 p4 #fjd74 ,a l controv]sy arose lat] 9 reg>d to corals4 ,mrs ,gordon 7,m4 ,m4 ,ogilvie7 ass]t$ t ! coral 0 built up 8( successive lay]s ( calcifi$ cells1 :i* hang toge!r at fir/ by _! cell-walls1 & ultimately1 z cry/all9e *anges cont9ue1 =m ! individual lam9ae ( ! skeletal /ructures0 7,phil4 ,trans4 ,,clxxxvii1 p4 #ajb1 #ahif73 :]eas v4 ,ko* _h figur$ ! coral z =m$ out ( a mass ( 8,kalkconcrem5te0 or 8cry/all9e sph]oids10 laid d[n outside ! ectod]m1 & precisely simil> bo? 9 _! e>ly r\nd$ & lat] polygonal /ages 7?\gh von ,ko* 0 n aw>e ( ! fact7 to ! calcosph]ites ( ,h>t+ 7,entw4 d4 ,kalkskelettes von ,a/]oides1 ,mit?4 ,zool4 ,/4 ,neapel1 ,,iii1 pp4 #bhd-bij1 pl4 ,,xx1 #ahhb74 ,la/ly ,du]d5 %ew$ t ext]nal to1 & app>5tly secret$ by ! ectod]m lies a homog5e\s organic matrix or membrane1 89 :i* ! m9ute calc>e\s cry/als =m+ ! skeleton are laid d[n0 7,! ,coral ,sid]a/raea radians1 etc41 ,c>negie ,in/4 ,wa%+ton1 #aijd1 p4 #cd74 ,cf4 also ,m4 ,m4 ,ogilvie-,gordon1 ,q4 ,j4 ,m4 ,s4 ,,xlix1 p4 #bjc1 #aije1 etc4 #dbf ,cf4 ,clap>de1 ,z4 f4 w4 ,z4 ,,xix1 p4 #fjd1 #ahfi4 #dbg ,spicules extremely l ^? ( ! ,alcyon>ia occur also 9 a few sponges2 cf4 7e4g471 ,vaughan ,j5n+s1 ,j\rn4 ,l9n4 ,soc4 ,,xxiii1 p4 #eca1 pl4 #ac1 fig4 #h1 #ahia4 #dbh ,mem4 ,man*e/] ,lit4 & ,phil4 ,soc4 ,,lx1 p4 #aa1 #aiaf4 #dbi ,mumm]y1 ,j4 ,h41 ,on ,calcification 9 ,enamel & ,d5t9e1 ,phil4 ,trans4 ,,ccv 7,b71 pp4 #ie-aaa1 #aiad4 #dcj ,! artificial concretion repres5t$ 9 ,fig4 #bjb is id5tical 9 appe>ance ) ! concretions f\nd 9 ! kidney ( ,nautilus1 z figur$ by ,willey 7,zoological ,results1 p4 lxxvi1 ,fig4 #b1 #aijb74 #dca ,cf4 ,taylor's ,*emi/ry ( ,colloids1 p4 #ah1 etc41 #aiae4 #dcb ,?is rule1 undream$ ( by ,err]a1 supports & ju/ifies ! c>d9al assumption 7( :i* we h _h s mu* to say 9 discuss+ ! =ms ( cells & tissues7 t ! incipi5t cell-wall behaves z1 & inde$ actually is1 a liquid film 7cf4 p4 #cjf74 #dcc ,cf4 p4 #bed4 #dcd ,cf4 ,h>t+1 op4 cit41 pp4 #bb1 #ej3 8,j'avais cru d'abord que ces c\*es conc5triques tai5t produites p> l'alt]nance de la *aleur ou de la lumire1 p5dant le j\r et la nuit4 ,mais l'expri5ce1 expressm5t in/itue p\r exam9] cette "q1 y a rpondu ngativem5t40 #dce ,liesegang1 ,r4 ,e41 ,ueb] die ,s*i*tung5 bei ,diffusion51 ,leipzig1 #aijg1 & o!r e>li] pap]s4 #dcf ,cf4 ,taylor's ,*emi/ry ( ,colloids1 pp4 #adf-adh1 #aiae4 #dcg ,cf4 ,s4 ,c4 ,brad=d1 ,! ,liesegang ,ph5om5on & ,concretion>y ,/ructure 9 ,rocks1 ,nature1 ,,xcvii1 p4 #hj1 #aiaf2 cf4 ,sci4 ,progress1 ,x1 p4 #cfi1 #aiaf4 #dch ,cf4 ,f>aday1 ,on ,ice ( ,irregul> ,fusibility1 ,phil4 ,trans41 #aheh1 p4 #bbh2 ,rese>*es 9 ,*emi/ry1 etc41 #ahei1 p4 #cgd2 ,tyndall1 ,=ms ( ,wat]1 p4 #agh1 #ahgb2 ,toml9son1 ,c41 ,on "s effects ( small ,quantities ( ,=eign ,matt] on ,cry/allisation1 ,phil4 ,mag4 7#e7 ,,xxxi1 p4 #cic1 #ahia1 & o!r pap]s4 #dci ,a ,/udy 9 ,cry/allisation1 ,j4 ( ,soc4 ( ,*em4 ,indu/ry1 ,,xxv1 p4 #adc1 #aijf4 #ddj ,ueb] ,zon5bildung 9 kolloidal5 ,m$i51 ,j5a1 #aiac4 #dda ,v]h4 d4 d4 ,zool4 ,gesells*4 p4 #agi1 #aiab4 #ddb ,desc5t ( ,man1 ,,ii1 pp4 #acb-aec1 #ahga4 #ddc ,z a matt] ( fact1 ! ph5om5a associat$ ) ! developm5t ( an 8ocellus0 are or may be ( great complexity1 inasmu* z !y involve n only a grad$ di/ribution ( pigm5t1 b also1 9 8optical0 coloration1 a symmetrical di/ribution ( /ructure or =m4 ,! subject !re=e des]ves v c>eful discussion1 su* z ,bateson gives to x 7,v>iation1 *ap4 xii74 ,?is1 by ! way1 is "o ( ! v r>e cases 9 :i* ,bateson appe>s incl9$ to sugge/ a purely physical explanation ( an organic ph5om5on3 8,! sugge/ion is /rong t ! :ole s]ies ( r+s 79 ,morpho7 may h be5 =m$ by "s "o c5tral di/urbance1 some:at z a s]ies ( conc5tric waves may be =m$ by ! spla% ( a /one ?r[n into a pool1 etc40 #ddd ,cf4 also ,sir ,d4 ,brew/]1 ,on optical prop]ties ( ,"m ( ,pe>l1 ,phil4 ,trans4 #ahad1 p4 #cig4 #dde ,bi$]mann1 ,w41 ,ueb] die ,b$eutung von ,kri/allisationsprozess5 d] ,skelette wirbellos] ,?i]e1 nam5tli* d] ,mollusk5s*al51 ,z4 f4 allg4 ,physiol4 ,i1 p4 #aed1 #aijb2 ,ueb] ,bau und ,ent/ehung d] ,mollusk5s*ale1 ,j54 ,zeits*r4 ,,xxxvi1 pp4 #a-afd1 #aijb4 ,cf4 also ,/e9mann1 ,ueb] ,s*ale und ,kalk/e9bildung51 ,b]4 ,naturf4 ,ges4 ,freiburg i4 ,br ,,iv1 #ahhi2 ,liesegang1 ,naturw4 ,wo*5s*r4 p4 #fda1 #aiaj4 #ddf ,cf4 ,bts*li1 ,ueb] die ,h]/ellung kn/li*] ,/rkekrn] od] von ,sphrokry/all5 d] ,/rke1 ,v]h4 nat4 m$4 ,v]4 ,heidelb]g1 ,v1 pp4 #deg-dgb1 #ahif4 #ddg ,unt]su*ung5 b] die ,/rkekrn]1 ,j5a1 #aije4 #ddh ,cf4 ,w+e1 ,m$del4 fra ,komm4 = ,havund]sgelse 7,fisk]i71 ,,iv1 p4 #bj1 ,cop5hag51 #aiae4 #ddi ,! anhydrite is sulphate ( lime 7,ca,s,o#d72 ! polyhalite is a triple sulphate ( lime1 magnesia & pota% 7#b ,ca,s,o#d4 ,mg,s,o#d4 ,k#b,,s#d #b ,h#b,o74 #dej ,cf4 van't ,h(f1 ,physical ,*emi/ry 9 ! ,s]vice ( ! ,sci5ces1 p4 #ii seq4 ,*icago1 #aijc4 #dea ,sphrocry/alle von ,kalkoxalat bei ,kakte51 ,b]4 d4 d4 ,bot4 ,gesells*4 p4 #agh1 #ahhe4 #deb ,pauli1 ,w4 u4 ,samec1 ,m41 ,ueb] ,lsli*keitsbee9flssung von ,elektrolyt5 dur* ,eiweisskrp]1 ,bio*em4 ,zeits*r4 ,,xvii1 p4 #bce1 #aiaj4 ,"s ( ^! results 7 kn[n mu* e>li]2 cf4 ,fokk] 9 ,pflg]'s ,ar*iv1 ,,vii1 p4 #bgd1 #ahgc2 also ,irv9e & ,sims ,woodhead1 op4 cit4 p4 #cdg4 #dec ,:i*1 9 #ajjj p>ts ( a%1 conta9s ab\t #hdj p>ts ( phosphate & #gf p>ts ( calcium c>bonate4 #ded ,cf4 ,drey]1 ,fr41 ,die ,pr9cipi5 d] ,g]/bildung bei ,rhizopod51 ,spongi5 und ,e*9od]m51 ,j54 ,zeits*r4 ,,xxvi1 pp4 #bjd-dfh1 #ahib4 #dee ,9 an anomal\s & v rem>kable ,au/ralian sponge1 j describ$ by ,pr(essor ,d5dy 7,nature1 ,may #ah1 #aiaf1 p4 #bec7 "u ! "n ( ,colloscl]ophora1 ! spicules are 8gelat9\s10 consi/+ ( a gel ( colloid silica ) a high p]c5tage ( wat]4 ,x is n /at$ :e!r an organic colloid is pres5t toge!r ) ! silica4 ,^! gelat9\s spicules arise z exudations on ! out] surface ( cells1 & come to lie 9 int]cellul> spaces or vesicles4 #def ,li/]1 9 ,willey's ,zoological ,results1 pt ,,iv1 p4 #dei1 #aijj4 #deg ,! peculi> spicules ( ,a/roscl]a are n[ said to consi/ ( sph]ules1 or calcosph]ites1 ( aragonite1 spores ( a c]ta9 r$ seawe$ =m+ ! nuclei1 or />t+-po9ts1 ( ! concretions 7,r4 ,kirkpatrick1 ,proc4 ,r4 ,s4 ,,lxxxiv 7,b71 p4 #egi1 #aiaa74 #deh ,see = in/ance ! plates 9 ,?el's ,monograph ( ! ,*all5g] ,holo?uroidea2 also ,sollas's ,tetract9ellida1 p4 lxi4 #dei ,= v num]\s illu/rations ( ! triradiate & quadriradiate spicules ( ! calc>e\s sponges1 see 7int4 al471 pap]s by ,d5dy 7,q4 ,j4 ,m4 ,s4 ,,xxxv1 #ahic71 ,m9*9 7,p4 ,z4 ,s4 #aijd71 ,j5k9 7,p4 ,z4 ,s4 #aijh71 etc4 #dfj ,cf4 aga9 ,bn>d's ,t\rbillons cellulaires1 ,ann4 de ,*imie1 #aija1 p4 #hd4 #dfa ,lg]1 ,/olc & o!rs1 9 ,d(le9's ,lehrbu* d4 ,protozo5kunde1 #aiaa1 p4 #iab4 #dfb ,see1 = in/ance1 ! figures ( ! segm5t+ egg ( ,synapta 7aft] ,sel5ka71 9 ,kors*elt & ,heid]'s ,v]glei*5de ,entwicklungsges*i*te 7,allgem4 ,?41 #cte ,lief471 p4 #ai1 #aiji4 ,on ! spiral type ( segm5tation z a second>y d]ivative1 due to me*anical causes1 ( ! 8radial0 type ( segm5tation1 see ,e4 ,b4 ,wilson1 ,cell-l9eage ( ,n]eis1 ,j\rn4 ( ,morphology1 ,,vi1 p4 #dej1 #ahib4 #dfc ,kors*elt & ,heid]1 p4 #af4 #dfd ,*all4 ,rep4 ,hexact9ellida1 pls4 xvi1 liii1 lxxvi1 lxxxviii4 #dfe 8,hi]bei nahm d] kohl5saure ,kalk e9e halb-kry/all9is*e ,bes*aff5heit an1 und ge/altete si* unt] ,aufnahme von ,kry/allwass] und 9 ,v]b9dung mit e9] g]+5 ,quantitt von organis*] ,sub/anz zu j55 individuell51 fe/5 ,krp]n1 wel*e dur* die natrli*e ,z*tung als ,spicula zur ,skeletbildung b5tzt1 und spt]h9 dur* die ,we*selwirkung von ,anpassung und ,v]]bung im ,kampfe ums ,dase9 auf das ,vielfltig/e umgebildet und diff]5zi]t wurd540 ,die ,kalks*wmme1 ,i1 p4 #cgg1 #ahgb2 cf4 also pp4 #dhb1 #dhc4 #dff ,op4 cit4 p4 #dhc4 8,die geordnete1 (t s sehr regelmssige und zi]li*e ,zusamm5setzung des ,skeletsy/ems i/ zum grs/5 ,!ile unmittelb>es ,product d] ,wass]/rmung2 die *>act]i/is*e ,lag]ung d] ,spicula i/ von d] con/ant5 ,ri*tung des ,wass]/roms h]vorgebra*t2 zum kle9/5 ,!ile i/ sie die ,folge von ,anpassung5 an unt]geordnete uss]e ,exi/5zb$+ung540 #dfg ,mat]ials = a ,monograph ( ! ,ascones1 ,q4 ,j4 ,m4 ,s4 ,,xl4 pp4 #dfi-ehg1 #ahih4 #dfh ,haeckel1 9 8 ,*all5g] ,monograph1 p4 clxxxviii 7#ahhg7 e/imat$ ! numb] ( kn[n =ms at #dcad species1 includ$ 9 #gci g5]a4 ,( ^!1 #cejh species 7 describ$ = ! fir/ "t 9 t "w4 #dfi ,cf4 ,gamble1 ,radiol>ia 7,lanke/]'s ,treatise on ,zoology71 vol4 ,i1 p4 #aca1 #aiji4 ,cf4 also pap]s by ,v4 ,hck]1 9 ,j54 ,zeits*r4 ,,xxxix1 p4 #eha1 #aije1 ,z4 f4 wiss4 ,zool4 ,,lxxxiii1 p4 #ccf1 #aije1 ,ar*4 f4 ,proti/5kunde1 ,,ix1 p4 #aci1 #aijg1 etc4 #dgj ,bts*li1 ,ueb] die *emis*e ,natur d] ,skeletsub/anz d] ,acan?>ia1 ,zool4 ,anz4 ,,xxx1 p4 #ghd1 #aijf4 #dga ,= figures ( ^! cry/als see ,br&t1 ,f4 u4 ,fl4 d4 ,golfes von ,neapel1 ,,xiii1 ,radiol>ia1 #ahhe1 pl4 v4 ,cf4 ,j4 ,mll]1 ,ueb] die ,?alassicoll51 etc4 ,abh4 ,k4 ,akad4 ,wiss4 ,b]l91 #aheh4 #dgb ,cele/9e1 or cele/ite1 is ,sr,s,o#d ) "s ,ba,o replac+ ,sr,o4 #dgc ,) ! colloid *emi/s1 we may adopt 7z ,rhumbl] has done7 ! t]ms spumoid or emulsoid to d5ote an agglom]ation ( fluid-fill$ vesicles1 re/rict+ ! "n fro? to su* vesicles :5 fill$ ) air or "s o!r gas4 #dgd ,cf4 ,koltz(f1 ,zur ,frage d] ,zellge/alt1 ,anat4 ,anzeig]1 ,,xli1 p4 #aij1 #aiab4 #dge ,mm4 de l',acad4 des ,sci41 ,/4 ,pt]sb\rg1 ,,xii1 ,nr4 #aj1 #aijb4 #dgf ,! mann] 9 :i* ! m9ute spicules ( ,raphidiophrys arrange !mselves r\nd ! bases ( ! pseudopodial rays is a simil> ph5om5on4 #dgg ,rhumbl]1 ,physikalis*e ,analyse von ,leb5s]s*e9ung5 d] ,zelle1 ,ar*4 f4 ,entw4 ,me*4 ,,vii1 p4 #ajc1 #ahih4 #dgh ,! :ole ph5om5on is describ$ by biologi/s z a 8surpris+ exhibition ( con/ructive & selective activity10 & is ascrib$1 9 v>y+ phraseology1 to intellig5ce1 skill1 purpose1 psy*ical activity1 or 8microscopic m5tality03 t is to say1 to ,gal5's 1 or 8arti/ic creativ5ess0 7cf4 ,brock's ,gal51 #aiaf1 p4 xxix74 ,cf4 ,c>p5t]1 ,m5tal ,physiology1 #ahgd1 p4 #da2 ,norman1 ,ar*itectural a*ievem5ts ( ,little ,masons1 etc41 ,ann4 ,mag4 ,nat4 ,hi/4 7#e71 ,i1 p4 #bhd1 #ahgh2 ,h]on-,all51 ,contributions 444 to ! ,/udy ( ! ,=am9if]a1 ,phil4 ,trans4 7,b71 ,,ccvi1 pp4 #bbg-bgi1 #aiae2 ,!ory & ,ph5om5a ( ,purpose & ,intellig5ce exhibit$ by ! ,protozoa1 z illu/rat$ by selection & behavi\r 9 ! ,=am9if]a1 ,j\rn4 ,r4 ,microscop4 ,soc4 pp4 #edg-eeg1 #aiae2 ibid41 pp4 #acg-adj1 #aiaf4 ,pr(4 ,j4 ,a4 ,?omson 7,new ,/atesman1 ,oct4 #bc1 #aiae7 describes a c]ta9 little =am9if]1 ^: protoplasmic body is ov]laid by a cru/ ( sponge-spicules1 z 8a psy*o-physical individuality ^: exp]im5ts 9 self-expression include a ma/]ly treatm5t ( sponge-spicules1 & illu/rate t organic skill :i* came be=e ! dawn ( ,art40 ,sir ,ray ,lanke/] f9ds x 8n difficult to conceive ( ! exi/5ce ( a me*anism 9 ! protoplasm ( ! ,protozoa :i* selects & rejects build+-mat]ial1 & det]m9es ! %apes ( ! /ructures built1 comp>able to t me*anism :i* is assum$ to exi/ 9 ! n]v\s sy/em ( insects & o!r animals :i* #8automatically' g ?r\gh wond]fully elaborate s]ies ( complicat$ actions40 ,& he agrees ) 8,d>w9 & o!rs :o h attribut$ ! build+ up ( ^! inh]it$ me*anisms to ! age-long action ( ,natural ,selection1 & ! survival ( ^? individuals possess+ qualities or #8tricks' ( life-sav+ value10 ,j4 ,r4 ,microsc4 ,soc4 ,april1 #aiaf1 p4 #acf4 #dgi ,rhumbl]1 ,das ,protoplasma als physikalis*es ,sy/em1 ,j5a1 p4 #eia1 #aiad2 also 9 ,ar*4 f4 ,entwickelungsme*4 ,,vii1 pp4 #bgi-cce1 #ahih4 #dhj ,v]worn1 ,psy*o-physiologis*e ,proti/5-,/udi51 ,j5a1 #ahhi 7#bai pp474 #dha ,leidy1 ,j41 ,fre%-wat] ,rhizopods ( ,n4 ,am]ica1 #ahgi1 p4 #bfb1 pl4 xli1 figs4 #aa1 #ab4 #dhb ,c>noy1 ,biologie ,cellulaire1 p4 #bdd1 fig4 #ajh2 cf4 ,drey]1 op4 cit4 #ahib1 fig4 #ahe4 #dhc ,9 all ^! latt] cases we recognise a relation to1 or ext5sion (1 ! pr9ciple ( ,plateau's b\rrelet1 or van d] ,m5sbrugghe's masse annulaire1 ( :i* we h already spok5 7p4 #big74 #dhd ,ap>t f ! fact t ! apex ( ea* pyramid is int]rupt$1 or truncat$1 by ! pres5ce ( ! little c5tral cell1 x is also possible t ! solid angles are n precisely equival5t to ^? ( ,m>aldi's pyramids1 ow+ to ! fact t !re is a c]ta9 am\nt ( di/ortion1 or axial asymmetry1 9 ! ,nassell>ian sy/em4 ,9 o!r words 7to judge f ,haeckel's figures71 ! tetrah$ral symmetry 9 ,nassell>ia is n absolutely regul>1 b has a ma9 axis ab\t :i* ?ree ( ! trih$ral pyramids are symmetrical1 ! f\r? hav+ its solid angle some:at dim9i%$4 #dhe ,cf4 ,f>aday's beautiful exp]im5ts1 ,on ! ,mov+ ,gr\ps ( ,p>ticles f\nd on ,vibrat+ ,ela/ic ,surfaces1 etc41 ,phil4 ,trans4 #ahca1 p4 #bii2 ,rese>*es 9 ,*em4 & ,phys4 #ahei1 pp4 #cad-ceh4 #dhf ,we ne$ n g s f> z to suppose t ! ext]nal lay] ( cells :olly lack$ ! p[] ( secret+ a skeleton4 ,9 _m ( ! ,nassell>iae figur$ by ,haeckel 7= !re are _m v>iant =ms or species besides t repres5t$ "h71 ! skeleton ( ! p>tition-walls is v slightly & scantily develop$4 ,9 su* a case1 if we imag9e its few & scanty /r&s to be brok5 away1 ! c5tral tetrah$ral figure w\ld be set free1 & w\ld h all ! appe>ance ( a complete & indep5d5t /ructure4 #dhg ,! 8b\rrelet0 is n only1 z ,plateau expresses x1 a 8surface ( cont9uity10 b we also recognise t x t5ds 7s f> z mat]ial is available = its production7 to fur!r less5 ! free surface-area4 ,on its relation to vap\r-pressure & to ! /ability ( foam1 see ,fitz,gerald's int]e/+ note 9 ,nature1 ,feb4 #a1 #ahid 7,works1 p4 #cji74 #dhh ,( ! _m ?\s& figures 9 ! hundr$ & =ty plates ( ?is beautifully illu/rat$ book1 !re is sc>cely "o :i* does n depict1 n[ pat5tly1 n[ 9 pregnant sugge/ion1 "s subtle & elegant geometrical configuration4 #dhi ,!y 7 kn[n 7( c\rse7 long be=e ,plato3 4 #dij ,if ! equation ( any plane face ( a cry/al be writt5 9 ! =m h x k y l z #a1 !n h1 k1 l are ! indices ( :i* we are speak+4 ,!y are ! reciprocals ( ! p>amet]s1 or reciprocals ( ! di/ances f ! orig9 at :i* ! plane meets ! sev]al axes4 ,9 ! case ( ! regul> or p5tagonal dodecah$ron ^! indices are #b1 #a #e1 #j4 ,kepl] describ$ z foll[s1 briefly b adequately1 ! common *>act]i/ics ( ! dodecah$ron & icosah$ron3 8,duo sunt corpora regul>ia1 dodeca$ron et icosa$ron1 quorum illud qu9quangulis figuratur expresse1 hoc triangulis quidem s$ 9 qu9quanguli =mam coaptatis4 ,utriusque horum corporum ipsiusque adeo qu9quanguli /ructura p]fici non pote/ s9e proportione illa1 quam hodi]ni geometrae div9am appellant0 7,de nive sexangula 7#afaa71 ,op]a1 ed4 ,fris*1 ,,vii1 p4 #gbc74 ,"h ,kepl] 0 deal+1 some:at aft] ! mann] ( ,sir ,?omas ,br[ne1 ) ! my/]ies ( ! qu9cunx1 & also ( ! hexagon2 & 0 seek+ = an explanation ( ! my/]i\s or ev5 my/ical beauty ( ! #e-petall$ or #c-petall$ fl[]1--pul*ritud9is aut proprietatis figurae1 quae animam h>um plant>um *>act]isavit4 #dia ,cf4 ,tutton1 ,cry/allography1 p4 #icb1 #aiaa4 #dib ,h[ev]1 we c (t5 recognise1 9 a small art]y = in/ance1 t ! s-call$ 8circul>0 fibres t5d to take a slightly oblique1 or spiral1 c\rse4 #dic ,! spiral fibres1 or a l>ge portion ( !m1 con/itute :at ,se>le call$ 8! rope ( ! he>t0 7,todd's ,cyclopa$ia1 ,,ii1 p4 #fba1 #ahcf74 ,! 8twi/$ s9ews ( ! he>t0 7 kn[n to e>ly anatomi/s1 & h be5 frequ5tly & elaborately /udi$3 = in/ance1 by ,g]dy 7,bull4 ,fac4 ,m$4 ,p>is1 #ahbj1 pp4 #dj-adh71 & by ,pettigrew 7,phil4 ,trans4 #ahfd71 & ( late by ,j4 ,b4 ,macallum 7,johns ,hopk9s ,hospital ,report1 ,,ix1 #aijj7 & by ,frankl9 ,p4 ,mall 7,am]4 ,j4 ( ,anat4 ,,xi1 #aiaa74 #did ,cf4 ,bts*li1 8,protozoa10 9 ,bronn's ,?i]rei*1 ,,ii1 p4 #hdh1 ,,iii1 p4 #aghe1 etc41 #ahhc-hg2 ,j5n+s1 ,am]4 ,nat4 ,,xxxv1 p4 #cfi1 #aija2 ,ptt]1 ,?igmotaxie bei ,proti/51 ,ar*4 f4 ,anat4 u4 ,phys4 7,phys4 ,ab?4 ,suppl471 pp4 #bdc-cjb1 #aijj4 #die ,a great numb] ( spiral =ms1 bo? organic & artificial1 are describ$ & beautifully illu/rat$ 9 ,sir ,t4 ,a4 ,cook's ,curves ( ,life1 #aiad1 & ,spirals 9 ,nature & ,art1 #aijc4 #dif ,cf4 ,v9es1 ,! ,hi/ory ( ! ,scorpioid ,cyme1 ,j\rn4 ( ,botany 7n4s471 ,x1 pp4 #c-i1 #ahha4 #dig ,leslie's ,geometry ( ,curv$ ,l9es1 p4 #dag1 #ahba4 ,?is is practically id5tical ) ,ar*im$es' own def9ition 7ed4 ,torelli1 p4 #bai72 cf4 ,cantor1 ,ges*i*te d] ,ma!matik1 ,i1 p4 #bfb1 #ahhj4 #dih ,see an int]e/+ pap] by ,:itwor?1 ,w4 ,a41 8,! ,equiangul> ,spiral1 its *ief prop]ties prov$ geometrically10 9 ! ,mess5g] ( ,ma!matics 7#a71 ,i1 p4 #e1 #ahfb4 #dii ,i am well aw>e t ! debt ( ,greek sci5ce to ,egypt & ! ,ea/ is vigor\sly d5i$ by _m s*ol>s1 "s ( :om g s f> z to believe t ! ,egyptians nev] _h any sci5ce1 save only "s 8r\gh rules ( ?umb = measur+ fields & pyramids0 7,burnet's ,greek ,philosophy1 #aiad1 p4 #e74 #ejj ,euclid 7,,ii1 def4 #b74 #eja ,cf4 ,treutle91 ,z4 f4 ,ma?4 u4 ,phys4 7,hi/4 litt4 ,ab?471 ,,xxviii1 p4 #bji1 #ahhc4 #ejb ,?is is ! s-call$ ,dreifa*glei*s*5kelige ,dreieck2 cf4 ,nab]1 op4 infra cit4 ,! ratio #a 3 #jfah is aga9 n h>d to f9d 9 ?is con/ruction4 #ejc ,see1 on ! ma!matical hi/ory ( ! ,gnomon1 ,hea?'s ,euclid1 ,i1 passim1 #aijh2 ,zeu!n1 ,!orme de ,py?agore1 ,g5ve1 #aijd2 also a curi\s & int]e/+ book1 ,das ,!orem des ,py?agoras1 by ,dr4 ,h4 ,a4 ,nab]1 ,ha>lem1 #aijh4 #ejd ,= _m beautiful geometrical con/ructions bas$ on ! molluscan %ell1 see ,colman1 ,s4 & ,coan1 ,c4 ,a41 ,nature's ,h>monic ,unity 7*4 ix1 ,con*ology71 ,new ,york1 #aiab4 #eje ,! ,rev4 ,h4 ,moseley1 ,on ! ,geometrical ,=ms ( ,turb9at$ & ,discoid ,%ells1 ,phil4 ,trans4 pp4 #cea-cgj4 #ahch4 #ejf ,x w be obs]v$ t "h ,moseley1 speak+ z a ma!matician & consid]+ ! l9e> spiral1 speaks ( :orls :5 he means ! l9e> b\nd>ies1 or l9es trac$ by ! revolv+ radius vector2 :ile ! con*ologi/ usually applies ! t]m :orl to ! :ole space betwe5 ! two b\nd>ies4 ,z con*ologi/s1 !re=e1 we call ! bread? ( a :orl :at ,moseley look$ ^u z ! di/ance betwe5 two consecutive :orls4 ,b ?is latt] nom5clature ,moseley himself (t5 uses4 #ejg ,9 ! case ( ,turbo1 & all o!r 8turb9ate0 %ells1 we are deal+ n ) a plane log>i?mic spiral1 z 9 ,nautilus1 b ) a 8gau*e0 spiral1 su* t ! radius vector no long] revolves 9 a plane p]p5dicul> to ! axis ( ! sy/em1 b is incl9$ to t axis at "s con/ant angle 774 ,! figure /ill pres]ves its cont9u$ simil>ity1 & may ) /rict accuracy be call$ a log>i?mic spiral 9 space4 ,x is evid5t t its envelope w be a "r circul> cone2 & inde$ x is commonly spok5 ( z a log>i?mic spiral wrapp$ ^u a cone1 its pole co9cid+ ) ! apex ( ! cone4 ,x foll[s t ! di/ances ( successive :orls ( ! spiral measur$ on ! same /raight l9e pass+ ?r\gh ! apex ( ! cone1 are 9 geometrical progression1 & conv]sely j z 9 ! =m] case4 ,b ! ratio betwe5 any two consecutive int]spaces 7i4e4 ,r#c ,r#b_/,r#b ,r#a7 is n[ equal to #b s9 cot 1 be+ ! semi-angle ( ! envelop+ cone4 7,cf4 ,moseley1 ,phil4 ,mag4 ,,xxi1 p4 #cjj1 #ahdb47 #ejh ,z ! successive increm5ts evid5tly con/itute simil> figures1 simil>ly relat$ to ! pole 7,p71 x foll[s t _! l9e> dim5sions are to "o ano!r z ! radii vectores drawn to simil> po9ts 9 !m3 = in/ance z ,p ,p#a1 ,p ,p#b1 :i* 79 ,fig4 #bfd1 #a7 are radii vectores drawn to ! po9ts :]e !y meet ! common b\nd>y4 #eji ,! equation to ! surface ( a turb9ate %ell is discuss$ by ,moseley 7,phil4 ,trans4 tom4 cit4 p4 #cgj71 bo? 9 t]ms ( pol> coord9ates & ( ! rectangul> coord9ates x1 y1 z4 ,a m elegant repres5tation c be giv5 9 vector notation1 by ! me?od ( quat]nions4 #eaj ,j4 ,c4 ,m4 ,re9ecke1 ,m>is protogaei ,nautilos1 etc41 ,coburg1 #ahah4 ,leopold von ,bu*1 ,ueb] die ,ammonit5 9 d5 lt]5 ,gebirgss*i*t51 ,abh4 ,b]l94 ,akad41 ,phys4 ,kl4 pp4 #ace-aeh1 #ahcj2 ,ann4 ,sc4 ,nat4 ,,xxviii1 pp4 #e-dc1 #ahcc2 cf4 ,elie de ,beaumont1 ,sur l'enr\lem5t des ,ammonites1 ,soc4 ,philom41 ,pr4 v]b4 pp4 #de-dh1 #ahda4 #eaa ,biblia ,naturae sive ,hi/oria ,insectorum1 ,leydae1 #agcg1 p4 #aeb4 #eab ,alcide ,d',orbigny1 ,bull4 de la soc4 gol4 ,fr4 ,,xiii1 p4 #bjj1 #ahdb2 ,c\rs lm4 de ,palontologie1 ,,ii1 p4 #e1 #ahea4 ,a some:at simil> in/rum5t 0 describ$ by ,b\be4 9 ,bull4 soc4 gol4 ,i1 p4 #bcb1 #ahca4 ,naumann's ,con*yliomet] 7,pogg5d4 ,ann4 ,,liv1 p4 #edd1 #ahde7 0 an application ( ! screw-micromet]2 x 0 provid$ also ) a rotat+ /age1 = angul> measurem5t4 ,x 0 adapt$ = ! ,/udy ( a discoid or ammonitoid %ell1 :ile ,d',orbigny's in/rum5t 0 meant = ! /udy ( a turb9ate %ell4 #eac ,x is obvi\s t ! ratios ( opposite :orls1 or ( radii #ahj ap>t1 are repres5t$ by ! squ>e roots ( ^! values2 & ! ratios ( :orls or radii #ij ap>t1 by ! squ>e roots ( ^! aga94 #ead ,= ! correction to be appli$ 9 ! case ( ! helicoid1 or 8turb9ate0 %ells1 see p4 #eeg4 #eae ,on ! ,measurem5t ( ! ,curves =m$ by ,cephalopods & o!r ,mollusks4 ,phil4 ,mag4 7#e71 ,,vi1 pp4 #bda-bfc1 #ahgh4 #eaf ,= an example ( ?is me?od1 see ,blake1 l4c4 p4 #bea4 #eag ,naumann1 ,c4 ,f41 ,ueb] die ,spiral5 von ,con*yli51 ,abh4 k4 s*s4 ,ges4 pp4 #aec-aif1 #ahdf2 ,ueb] die cycloc5tris*e ,con*ospirale u4 b] das ,w9dungsgesetz von ,planorbis corneus1 ibid4 ,i1 pp4 #aga-aie1 #ahdi2 ,spirale von ,nautilus u4 ,ammonites galeatus1 ,b]4 k4 s*s4 ,ges4 ,,ii1 p4 #bf1 #ahdh2 ,spirale von ,amm4 ,ramsau]i1 ibid4 ,,xvi1 p4 #ba1 #ahfd2 see also ,pogg5dorff's ,annal51 ,l1 p4 #bbc1 #ahdj2 ,,li1 p4 #bde1 #ahda2 ,,liv1 p4 #eda1 #ahde1 etc4 #eah ,s&b]g]1 ,g41 ,spiral5 des ,ammonites ,amal!us1 ,a4 ,gaytani1 und ,goniatites intumesc5s1 ,zeits*r4 d4 d4 ,geol4 ,gesells*4 ,x1 pp4 #ddf-ddi1 #aheh4 #eai ,grabau1 ,a4 ,h41 ,ueb] die ,naumanns*e ,con*ospirale1 etc4 ,inauguraldiss4 ,leipzig1 #ahgb2 ,die ,spiral5 von ,con*yli51 etc4 ,programm1 ,nr4 #ejb1 ,leipzig1 #ahhb4 #ebj ,x has be5 po9t$ out to me t x does n foll[ at once & obvi\sly t1 because ! int]space ,,ab is a mean proportional betwe5 ! bread?s ( ! adjac5t :orls1 !re=e ! :ole di/ance ,,ob is a mean proportional betwe5 ,,oa & ,,oc4 ,?is is a coroll>y :i* requires to be prov$2 b ! pro( is easy4 #eba ,a beautiful con/ruction3 /up5dum ,naturae artificium1 ,l9naeus4 #ebb ,engli% edition1 p4 #ecg1 #aijj4 ,! *apt] is revis$ by ,pr(4 ,alpheus ,hyatt1 to :om ! nom5clature is l>gely due4 ,= a m copi\s t]m9ology1 see ,hyatt1 ,phylog5y ( an ,acquir$ ,*>act]i/ic1 p4 #dbb seq41 #ahid4 #ebc ,?is latt] conclusion is adopt$ by ,willey1 ,zoological ,results1 p4 #gdg1 #aijb4 #ebd ,see ,moseley1 op4 cit4 pp4 #cfa seq4 #ebe ,9 ,nautilus1 ! 8hood0 has some:at diff]5t dim5sions 9 ! two sexes1 & ^! diff]5ces are impress$ ^u ! %ell1 t is to say ^u its 8g5]at+ curve40 ,! latt] con/itutes a some:at broad] ellipse 9 ! male ?an 9 ! female4 ,b ?is diff]5ce is n to be detect$ 9 ! "y2 9 o!r words1 ! =m ( ! g5]at+ curve p]ceptibly alt]s ) advanc+ age4 ,some:at simil> diff]5ces 9 ! %ells ( ,ammonites 7 long ago suspect$1 by ,d',orbigny1 to be due to sexual diff]5ces4 7,cf4 ,willey1 ,natural ,sci5ce1 ,,vi1 p4 #daa1 #ahie2 ,zoological ,results1 p4 #gdb1 #aijb47 #ebf ,macali/]1 ,alex41 ,obs]vations on ! ,mode ( ,gr[? ( ,discoid & ,turb9at$ ,%ells1 ,p4 ,r4 ,s4 ,,xviii1 pp4 #ebi-ecb1 #ahgj4 #ebg ,see figures 9 ,arnold ,lang's ,comp>ative ,anatomy 7,engli% translation71 ,,ii1 p4 #afa1 #aijb4 #ebh ,kapp]s1 ,c4 ,u4 ,a41 ,die ,bildung kn/li*] ,mollusk5s*al51 ,zeits*r4 f4 allg4 ,physiol4 ,,vii1 p4 #aff1 #aijh4 #ebi ,we ne$ n assume a close relation%ip1 nor inde$ any m ?an su* a "o z p]mits u to comp>e ! %ell ( a ,nautilus ) t ( a ,ga/ropod4 #ecj ,cf4 ,ow51 8,^! %ells ,nautilus & ,ammonites are revolutely spiral or coil$ ov] ! back ( ! animal1 n involute l ,spirula03 ,palaeontology1 #ahfa1 p4 #ig2 cf4 ,mem4 on ! ,pe>ly ,nautilus1 #ahcb2 also ,p4,z4,s4 #ahgh1 p4 #iee4 #eca ,! case ( ,t]ebratula or ( ,gryphaea w\ld be closely analog\s1 if ! small] valve 7 less closely connect$ & co-articulat$ ) ! l>g]4 #ecb 8,x has be5 sugge/$1 & ,i ?9k 9 "s qu>t]s adopt$ z a dogma1 t ! =mation ( successive septa 9 ,nautilus is correlat$ ) ! recurr5ce ( reproductive p]iods4 ,?is is n ! case1 s9ce1 accord+ to my obs]vations1 propagation only takes place aft] ! la/ septum is =m$20 ,willey1 ,zoological ,results1 p4 #gdf1 #aijb4 #ecc ,cf4 ,woodw>d1 ,h5ry1 ,on ! ,/ructure ( ,cam]at$ ,%ells1 ,pop4 ,sci4 ,rev4 ,,xi1 pp4 #aac-abj1 #ahgb4 #ecd ,see ,willey1 ,contributions to ! ,natural ,hi/ory ( ! ,pe>ly ,nautilus1 ,zoological ,results1 etc4 p4 #gdi1 #aijb4 ,cf4 also ,ba!r1 ,%ell-gr[? 9 ,cephalopoda1 ,ann4 ,mag4 ,n4 ,h4 7#f71 ,i1 pp #bih-caj1 #ahhh2 ibid4 pp4 #dba-dbg1 & o!r pap]s by ,blake1 ,rief/ahl1 etc4 quot$ !re94 #ece ,x 0 ?is t l$ ,james ,b]n\lli1 9 imitation ( ,ar*im$es1 to h ! log>i?mic spiral grav5 on 8 tomb1 ) ! pi\s motto1 ,eadem mutata resurgam4 ,on ,goodsir's grave ! same symbol is re9scrib$4 #ecf ,! 8lobes0 & 8saddles0 :i* arise 9 ?is mann]1 & on ^: arrangem5t ! mod]n classification ( ! nautiloid & ammonitoid %ells l>gely dep5ds1 7 fir/ recognis$ & nam$ by ,leopold von ,bu*1 ,ann4 ,sci4 ,nat4 ,,xxvii1 ,,xxviii1 #ahbi4 #ecg ,blake has rem>k$ ^u ! fact 7op4 cit4 p4 #bdh7 t 9 "s ,cyrtoc]ata we may h a curv$ %ell 9 :i* ! ornam5ts approximately run at a con/ant angul> di/ance f ! pole1 :ile ! septa approximate to a radial direction2 & t 8?us "o law ( gr[? is illu/rat$ by ! inside1 & ano!r by ! outside40 ,9 ?is !re is no?+ at :i* we ne$ wond]4 ,x is m]ely a case :]e ! g5]at+ curve is set v obliquely to ! axis ( ! %ell2 b :]e ! septa1 :i* h no necess>y relation to ! m\? ( ! %ell1 take _! places1 z usual1 at a c]ta9 def9ite angle to ! walls ( ! tube4 ,?is relation ( ! septa to ! walls ( ! tube arises aft] ! tube itself is fully =m$1 & ! obliquity ( gr[? ( ! op5 end ( ! tube has no relation to ! matt]4 #ech ,cf4 pp4 #bee1 #dfc1 etc4 #eci ,9 a few cases1 accord+ to ,aw]9zew & ,rhumbl]1 :]e ! *amb]s are add$ on 9 conc5tric s]ies1 z 9 ,orbitolites1 we h ! cry/all9e /ructure arrang$ radially 9 ! radial walls b tang5tially 9 ! conc5tric ones3 :]eby we t5d to obta91 on a m9ute scale1 a sy/em ( or?ogonal trajectories1 comp>able to t :i* we %all pres5tly /udy 9 connection ) ! /ructure ( bone4 ,cf4 ,s4 ,aw]9zew1 ,kalks*ale d] ,rhizopod51 ,z4 f4 w4 ,z4 ,,lxxiv1 pp4 #dgh-dij1 #aijc4 #edj ,rhumbl]1 ,l41 ,die ,doppels*al5 von ,orbitolites und &]] ,=am9if]51 etc41 ,ar*4 f4 ,proti/5kunde1 ,i1 pp4 #aic-bif1 #aijb2 & o!r pap]s4 ,also ,die ,=am9if]5 d] ,planktonexp$ition1 ,i1 #aiaa1 pp4 #ej-ef4 #eda ,bn>d1 ,h1 ,les t\rbillons cellulaires1 ,ann4 de ,*imie 7#h71 ,,xxiv1 #aija4 ,cf4 also ! patt]n ( cilia on an ,infusorian1 z figur$ by ,bts*li 9 ,bronn's ,protozoa1 ,,iii1 p4 #abha1 #ahhg4 #edb ,a simil> hexagonal patt]n is obta9$ by ! mutual repulsion ( float+ magnets 9 ,mr ,r4 ,w4 ,wood's exp]im5ts1 ,phil4 ,mag4 ,,xlvi1 pp4 #afb-afd1 #ahih4 #edc ,cf4 ,d',orbigny1 ,alc41 ,tableau m?odique de la classe des ,cphalopodes1 ,ann4 des ,sci4 ,nat4 7#a71 ,,vii1 pp4 #bde-cae1 #ahbf2 ,duj>d94 ,flix1 ,obs]vations n\velles sur les prt5dus ,cphalopodes microscopiques1 ibid4 7#b71 ,,iii1 pp4 #ajh1 #aji1 #cab-cae1 #ahce2 ,re*]*es sur les organismes infrieurs1 ibid4 ,,iv1 pp4 #cdc-cgg1 #ahce1 etc4 #edd ,x is obvi\s t ! actual outl9e ( a =am9if]al1 j z ( a molluscan %ell1 may dep>t widely f a log>i?mic spiral4 ,:5 we say "h1 = %ort1 t ! %ell is a log>i?mic spiral1 we m]ely mean t x is ess5tially relat$ to "o3 t x c be inscrib$ 9 su* a spiral1 or t correspond+ po9ts 7su*1 = in/ance1 z ! c5tres ( gravity ( successive *amb]s1 or ! extremities ( successive septa7 wall always be f\nd to lie ^u su* a spiral4 #ede von ,mll]1 ,v41 ,die spiral-gewund55 ,=am9if]a des russis*5 ,kohl5kalks1 ,mm4 de l',acad4 ,imp4 ,sci41 ,/ ,pt]sb\rg 7#g71 ,,xxv1 #ahgh4 #edf ,z von ,mll] is c>eful to expla91 ,naumann's =mula = ! 8cycloc5tric con*ospiral0 is appropriate to ?is & o!r spiral ,=am9if]a1 s9ce we h 9 all ^! cases a c5tral or initial *amb]1 approximately sph]ical1 ab\t :i* ! log>i?mic spiral is coil$ 7cf4 ,fig4 #cji74 ,9 species :]e ! c5tral *amb] is especially l>ge1 ,naumann's =mula is all ! m advantage\s4 ,b x is pla9 t x is only requir$ :5 we are deal+ ) diamet]s1 or ) radii2 s long z we are m]ely comp>+ ! bread?s ( successive :orls1 ! two =mulae come to ! same ?+4 #edg ,van ,it]son1 ,g41 ,ma!m4 u4 mikrosk4-anat4 ,/udi5 b] ,blatt/ellung51 neb/ ,betra*tung5 b] d5 ,s*al5bau d] ,miliol951 #cca pp41 ,j5a1 #aijg4 #edh ,hans ,przibram ass]ts t ! l9e> ratio ( successive *amb]s t5ds 9 _m ,=am9if]a to approximate to #abf1 :i* #b2 9 o!r words1 t ! volumes ( successive *amb]s t5d to d\ble4 ,?is ,przibram w\ld br+ into relation ) ano!r law1 viz4 t insects & o!r ar?ropods t5d to m\lt1 or to metamorphose1 j :5 !y d\ble _! weights1 or increase _! l9e> dim5sions 9 ! ratio ( #a 3 #b4 7,die ,kamm]progression d] ,=am9if]5 als ,p>allele zur ,hutungsprogression d] ,mantid51 ,ar*4 f4 ,entw4 ,me*4 ,,xxxiv p4 #fhj1 #ahac47 ,nei!r rule seems to me to be well gr\nd$4 #edi ,cf4 ,s*acko1 ,g41 ,ueb] ,globig]9a-,e9s*luss bei ,orbul9a1 ,wiegmann's ,ar*iv1 ,,xlix1 p4 #dbh1 #ahhc2 ,brady1 ,*all4 ,rep41 p4 #fjg1 #ahhd4 #eej ,cf4 ,brady1 ,h4 ,b41 ,*all5g] ,rep41 ,=am9if]a1 #ahhd1 p4 #bjc1 pl4 ,,xiii4 #eea ,brady1 op4 cit41 p4 #bjf2 ,bats*1 "o ( ! e>lie/ writ]s on ,=am9if]a1 _h already notic$ t ?is :ole s]ies ( e>-%ap$ & crozi]-%ap$ %ells 0 fill$ 9 by gradational =ms2 ,con*yli5 des ,sees&es1 #agia1 p4 #d1 pl4 ,,vi1 fig4 #ae;a-f4 ,see also1 9 p>ticul>1 ,drey]1 ,p5]oplis2 e9e ,/udie zur biologis*5 ,morphologie und zur ,speciesfrage1 ,leipzig1 #ahih2 also ,eim] und ,fick]t1 ,artbildung und ,v]w&s*aft bei d5 ,=am9if]51 ,tb+] zool4 ,arbeit51 ,,iii1 p4 #ce1 #ahii4 #eeb ,d(le91 ,protozo5kunde1 #aiaa1 p4 #bfc2 8,0 diese ,art v]anls/ 9 dies] ,weise geleg5tli* zu v>r51 i/ vorlufig no* ganz r?selhaft40 #eec ,9 ! case ( ,globig]9a1 "s f\rte5 species 7out ( a v mu* l>g] numb] ( describ$ =ms7 7 all[$ by ,brady 79 #ahhd7 to be di/9ct2 & ?is li/ has be51 ,i believe1 r add$ to ?an dim9i%$4 ,b ^! s-call$ species dep5d = ! mo/ "p on slight diff]5ces ( degree1 diff]5ces 9 ! angle ( ! spiral1 9 ! ratio ( magnitude ( ! segm5ts1 or 9 _! area ( contact "o ) ano!r4 ,moreov] ) ! exception ( "o or two 8dw>f0 =ms1 said to be limit$ to ,arctic & ,ant>ctic wat]s1 !re is no pr9ciple ( geographical di/ribution to be disc]n$ among/ !m4 ,a species f\nd fossil 9 ,new ,brita9 turns up 9 ! ,nor? ,atlantic3 a species describ$ f ! ,we/ ,indies is r$iscov]$ at ! ice-b>ri] ( ! ,ant>ctic4 #eed ,drey]1 ,f41 ,pr9cipi5 d] ,g]/bildung bei ,rhizopod51 etc41 ,j54 ,zeits*r4 ,,xxvi1 pp4 #bjd-dfh1 #ahib4 #eee ,a difficulty arises 9 ! case ( =ms 7l ,p5]oplis7 :]e ! "y %ell appe>s to be m complex ?an ! old1 ! fir/ =m$ portion be+ closely coil$ :ile ! lat] additions become /raight & simple3 8die bi=m5 ,art5 v]halt5 si*1 kurz gesagt4 g]ade umgekehrt als man na* dem biog5etis*5 ,grundgesetz erw>t5 sollte10 ,rhumbl]1 op4 cit41 p4 #cc etc4 #eef 8,das ,fe/igkeitspr9zip als ,mov5s d] ,weit]5twicklung i/ zu int]essant und fr die ,auf/ellung me9es ,sy/ems zu wi*tig um die ,frage un]rt]t zu lass51 w>um diese ,bevorzgung d] ,fe/igkeit /attgefund5 hat4 ,me9] ,ansi*t na* lautet die ,antwort auf diese ,frage e9fa*1 weil die ,=am9if]5 mei/5s unt] ,v]hltniss5 leb51 die ihre ,s*al5 9 hohem ,grade d] ,gefahr des ,z]bre*5s aussetz52 es muss also e9e =twahr5de ,auslese des ,fe/]5 /attf9d510 ,rhumbl]1 op4 cit41 p4 #bb4 #eeg 8,die ,=am9if]5 kiesige od] grobs&ige ,gebiete des ,me]esbod5s ni*t lieb51 u4s4w403 :]e ! la/ two words h no p>ticul> mean+1 save only t 7z ,m4 ,aurelius says7 8( ?+s t use to be1 we say commonly t !y love to be40 #eeh ,9 reg>d to ! ,=am9if]a1 8die ,palaeontologie ls/ uns leid] an ,anfang d] ,/ammesges*i*te fa/ gnzli* im ,/i*e10 ,rhumbl]1 op4 cit41 p4 #ad4 #eei ,! evolutioni/ !ory1 z ,b]gson puts x1 8consi/s above all 9 e/abli%+ relations ( ideal k9%ip1 & 9 ma9ta9+ t :]ev] !re is ?is relation (1 s to speak1 logical affiliation betwe5 =ms1 !re is also a relation ( *ronological succession betwe5 ! species 9 :i* ^! =ms are mat]ialis$03 ,creative ,evolution1 #aiaa1 p4 #bf4 ,cf4 supra1 p4 #bea4 #efj ,9 ! case ( ! ram's horn1 ! assumption t ! r+s are annual is probably ju/ifi$4 ,9 cattle !y are mu* less conspicu\s1 b are sometimes well-m>k$ 9 ! c[2 & 9 ,sw$5 !y are !n call$ 8calf-r+s10 f a belief t !y record ! numb] ( (fspr+4 ,t is to say1 ! gr[? ( ! horn is suppos$ to be ret>d$ dur+ ge/ation1 & to be accel]at$ aft] p>turition1 :5 sup]flu\s n\ri%m5t seeks a new outlet4 7,cf4 ,lnnb]g1 ,p4,z4,s41 p4 #fhi1 #aijj47 #efa ,cf4 ,sir ,v4 ,brooke1 ,on ! ,l>ge ,%eep ( ! ,?ian ,%an1 ,p4,z4,s41 p4 #eaa1 #ahge4 #efb ,cf4 ,lnnb]g1 ,e41 ,on ! ,/ructure ( ! ,musk ,ox1 ,p4,z4,s41 pp4 #fhf-gah1 #aijj4 #efc ,/ ,v5ant1 ,de la torsion des prismes1 avec des considrations sur leur flexion1 etc41 ,mm4 des ,savants trang]s1 ,p>is1 ,,xiv1 pp4 #bcc-efj1 #ahef4 #efd ,?is is n difficult to d1 ) consid]able accuracy1 if ! clay be kept well wett$1 or semi-fluid1 & ! smoo?+ be done ) a l>ge wet bru%4 #efe ,! curves are well %ewn 9 mo/ ( ,sir ,v4 ,brooke's figures ( ! v>i\s species ( ,argali1 9 ! pap] quot$ on p4 #fad4 #eff ,climb+ ,plants1 #ahfe 7#bnd edit4 #ahge72 ,p[] ( ,movem5t 9 ,plants1 #ahhj4 #efg ,palm1 ,ueb] das ,w9d5 d] ,pflanz51 #ahbg2 von ,mohl1 ,bau und ,w9d5 d] ,rank51 etc41 #ahbg2 ,dutro*et1 ,m\vem5ts rvolutifs spontans1 ,c4,r4 #ahdc1 etc4 #efh ,cf4 7e4g47 ,lepes*k91 ,zur ,k5ntnis des ,me*anismus d] ,v>iationsbewegung51 ,b]4 d4 d4 ,bot4 ,gesells*4 ,,xxvi ,a1 pp4 #gbd-gce1 #aijh2 also ,a4 ,trndle1 ,d] ,e9fluss des ,li*tes auf die ,p]meabilitt des ,plasmahaut1 ,jahrb4 wiss4 ,bot4 ,,xlviii1 pp4 #aga-bhb1 #aiaj4 #efi ,= an elaborate /udy ( antl]s1 see ,rrig1 ,a41 ,ar*4 f4 ,entw4 ,me*4 ,x1 pp4 #ebe-fdd1 #aijj1 ,,xi1 pp4 #fe-adh1 #bbe-cji1 #aija2 ,h(fmann1 ,c41 ,zur ,morphologie d] rez5t5 ,hirs*51 #ge pp41 #bc pls41 #aija3 also ,sir ,victor ,brooke1 ,on ! ,classification ( ! ,c]vidae1 ,p4,z4,s41 pp4 #hhc-ibh1 #ahgh4 ,= a discussion ( ! developm5t ( horns & antl]s1 see ,gad[1 ,h41 ,p4,z4,s41 pp4 #bjf-bbb1 #aijb1 & works quot$ !re94 #egj ,cf4 ,rhumbl]1 ,l41 ,ueb] die ,abhngigkeit des ,geweihwa*/ums d] ,hirs*e1 speziell des ,edelhirs*es1 vom ,v]lauf d] ,blutgefsse im ,kolb5geweih1 ,zeits*r4 f4 ,=/4 und ,jagdwes51 #aiaa1 pp4 #bie-cad4 #ega ,! fact t 9 "o v small de]1 ! little ,s\? ,am]ican ,coassus1 ! antl] is r$uc$ to a simple %ort spike1 does n preclude ! g5]al di/9ction :i* ,i h drawn4 ,9 ,coassus we h ! beg9n+s ( an antl]1 :i* has n yet manife/$ its t5d5cy to exp&2 & 9 ! _m alli$ species ( ! ,am]ican g5us ,c>iacus1 we f9d ! expansion manife/$ 9 v>i\s simple modes ( ramification or bifurcation4 7,cf4 ,sir ,v4 ,brooke1 ,classification ( ! ,c]vidae1 p4 #hig47 #egb ,cf4 also ! imm5se range ( v>iation 9 elks' horns1 z describ$ by ,lnnb]g1 ,p4,z4,s4 ,,ii1 pp4 #ceb-cfj1 #aijb4 #egc ,besides pap]s ref]r$ to bel[1 & _m o!rs quot$ 9 ,sa*'s ,botany & else:]e1 ! foll[+ are important3 ,braun1 ,alex41 ,v]gl4 ,unt]su*ung b] die ,ordnung d] ,s*upp5 an d5 ,tann5zapf51 etc41 ,v]h4 ,c>4 ,leop4 ,akad4 ,,xv1 pp4 #aii-dja1 #ahca2 ,dr ,c4 ,s*imp]'s ,vortrge b] die ,mgli*keit e9es wiss5s*aftli*5 ,v]/ndnisses d] ,blatt/ellung1 etc41 ,flora1 ,,xviii1 pp4 #ade-aia1 #gcg-gef1 #ahce2 ,s*imp]1 ,c4 ,f41 ,geometris*e ,anordnung d] um e9e ,axe p]iph]is*e ,blattgebilde1 ,v]h&l4 ,s*weiz4 ,ges41 pp4 #aac-aag1 #ahcf2 ,bravais1 ,l4 & ,a41 ,essai sur la disposition des feuilles curvisries1 ,ann4 ,sci4 ,nat4 7#b71 ,,vii1 pp4 #db-aaj1 #ahcg2 ,sur la disposition symmtrique des infloresc5ces1 ibid41 pp4 #aic-bba1 #bia-cdh1 ,,viii1 pp4 #aa-db1 #ahch2 ,sur la disposition gnrale des feuilles rectisries1 ibid4 ,,xii1 pp4 #e-da1 #fe-gg1 #ahci2 ,zeis+1 ,normalv]hltniss d] *emis*5 und morphologis*5 ,proportion51 ,leipzig1 #ahef2 ,naumann1 ,c4 ,f41 ,ueb] d5 ,qu9cunx als ,gesetz d] ,blatt/ellung bei ,sigill>ia1 etc41 ,neues ,jahrb4 f4 ,m9]4 #ahdb1 pp4 #daj-dag2 ,le/ib\dois1 ,t41 ,phyllotaxie anatomique1 ,p>is1 #ahdh2 ,h5sl[1 ,g41 ,phyllotaxis1 ,london1 #ahga2 ,wiesn]1 ,bem]kung5 b] rationale und irrationale ,div]g5z51 ,flora1 ,,lviii1 pp4 #aac-aae1 #aci-adc1 #ahge2 ,airy1 ,h41 ,on ,leaf ,arrangem5t1 ,proc4 ,r4 ,s4 ,,xxi1 p4 #agf1 #ahgc2 ,s*w5d5]1 ,s41 ,me*anis*e ,!orie d] ,blatt/ellung51 ,leipzig1 #ahgh2 ,delp9o1 ,f41 ,causa meccanica della filotassi qu9cunciale1 ,g5ova1 #ahhj2 de ,c&olle1 ,c41 tude de ,phyllotaxie1 ,g5ve1 #ahha4 #egd ,allgeme9e ,morphologie d] ,gew*se1 p4 #ddb1 etc4 #ahfh4 #ege ,relation ( ,phyllotaxis to ,me*anical ,laws1 ,ox=d1 #aija-aijc2 cf4 ,ann4 ( ,botany1 ,,xv1 p4 #dha1 #aija4 #egf 8,! proposition is t ! g5etic spiral is a log>i?mic spiral1 homolog\s ) ! l9e ( curr5t-fl[ 9 a spiral vortex2 & t 9 su* a sy/em ! action ( or?ogonal =ces w be mapp$ out by o!r or?ogonally int]sect+ log>i?mic spirals--! #8p>a/i*ies' 02 ,*ur*1 op4 cit4 ,i1 p4 #db4 #egg ,mr ,*ur*'s :ole !ory1 if x be n bas$ ^u1 is int]wov5 )1 ,sa*s's !ory ( ! or?ogonal int]section ( cell-walls1 & ! elaborate !ories ( ! symmetry ( a gr[+ po9t or apical cell :i* are connect$ !re)4 ,accord+ to ,mr ,*ur*1 8! law ( ! or?ogonal int]section ( cell-walls at a gr[+ apex may be tak5 z g5]ally accept$0 7p4 #cb72 b ,i h tak5 a v diff]5t view ( ,sa*s's law1 9 ! eigh? *apt] ( ! pres5t book4 ,) reg>d to 8 own & ,sa*s's hypo!ses1 ,mr ,*ur* makes ! foll[+ curi\s rem>k 7p4 #db73 8,nor are ! hypo!ses "h put =w>d m imag9ative ?an t ( ! p>aboloid apex ( ,sa*s :i* rema9s incapable ( pro(1 or 8 con/ruction = ! apical cell ( ,pt]is :i* does n satisfy ! evid5ce ( 8 own draw+s40 #egh ,am]4 ,naturali/1 ,,vii1 p4 #ddi1 #ahgc4 #egi ,?is celebrat$ s]ies1 :i* appe>s 9 ! cont9u$ fraction 7#a_/a7 7#a_/7a 77 etc4 & is closely connect$ ) ! ,sectio aurea or ,gold5 ,mean1 is commonly call$ ! ,fibonacci s]ies1 aft] a v le>n$ twelf? c5tury ari?metician 7kn[n also z ,leon>do ( ,pisa71 :o has "s claims to be consid]$ ! introduc] ( ,arabic num]als into *ri/ian ,europe4 ,x is call$ ,lami's s]ies by "s1 aft] ,fa!r ,b]n>d ,lami1 a contempor>y ( ,newton's1 & "o ( ! co-discov]]s ( ! p>allelogram ( =ces4 ,x 0 well-kn[n to ,kepl]1 :o1 9 8 pap] ,de nive sexangula 7cf4 supra1 p4 #dhj71 discuss$ x 9 connection ) ! =m ( ! dodecah$ron & icosah$ron1 & ) ! t]n>y or qu9>y symmetry ( ! fl[]4 7,cf4 ,ludwig1 ,f41 ,kepl] b] das ,vorkomm5 d] ,fibonaccireihe im ,pflanz5rei*1 ,bot4 ,c5tralbl4 ,,lxviii1 p4 #g1 #ahif74 ,pr(essor ,william ,allman1 ,pr(essor ( ,botany 9 ,dubl9 7fa!r ( ! hi/orian ( ,greek geometry71 speculat+ on ! same facts1 put =w>d ! curi\s sugge/ion t ! cellul> tissue ( ! dicotyl$ons1 or exog5s1 w\ld be f\nd to consi/ ( dodecah$ra4 & t ( ! monocotyl$ons or endog5s ( icosah$ra 7,on ! ma!matical connexion betwe5 ! p>ts ( ,vegetables3 ab/ract ( a ,memoir read be=e ! ,royal ,society 9 ! ye> #ahaa 7privately pr9t$1 n4d474 ,cf4 ,de ,c&olle1 ,organognie vgtale1 ,i1 p4 #ecd74 #ehj ,proc4 ,roy4 ,soc4 ,ed94 ,,vii1 p4 #cia1 #ahgb4 #eha ,! necess>y exi/5ce ( ^! recurr+ spirals is also prov$1 9 a some:at diff]5t way1 by ,leslie ,ellis1 ,on ! ,!ory ( ,vegetable ,spirals1 9 ,ma!matical & o!r ,writ+s1 #ahec1 pp4 #ceh-cgb4 #ehb ,proc4 ,roy4 ,soc4 ,ed94 ,,vii1 p4 #cig1 #ahgb2 ,trans4 ,roy4 ,soc4 ,ed94 ,,xxvi1 p4 #eje1 #ahgj-ga4 #ehc ,a common =m ( pail-%ap$ wa/e-pap] basket1 ) wide rhomboidal me%es ( cane1 is well-nigh z good a model z is requir$4 #ehd ,deuts*e ,vi]teljahrss*rift1 p4 #bfa1 #ahfh4 #ehe ,memoirs ( ,am]4 ,acad4 ,,ix1 p4 #chi4 #ehf ,de avibus circa aquas ,danubii vagantibus et de ips>um ,nidis 7,vol4 ,v ( ! ,danubius ,pannonico-mysicus71 ,hagae ,com41 #agbf4 #ehg ,sir ,?omas ,br[ne _h a collection ( eggs at ,norwi*1 accord+ to ,evelyn1 9 #afga4 #ehh ,cf4 ,lapi]re1 9 ,buffon's ,hi/oire ,naturelle1 ed4 ,sonn9i1 #ahjj4 #ehi ,ei] d] ,vgel ,deuts*l&s1 #ahah-bh 7cit4 des ,murs1 p4 #cf74 #eij ,trait d',oologie1 #ahfj4 #eia ,lafresnaye1 ,f4 de1 ,comp>aison des ufs des ,oiseaux avec leurs squelettes1 comme seul mov5 de reconnatre la cause de leurs diffr5tes =mes1 ,rev4 ,zool41 #ahde1 pp4 #ahj-ahg1 #bci-bdd4 #eib ,cf4 ,des ,murs1 p4 #fg3 8,elle devait encore p5s] au mom5t o ce g]me aurait beso9 de l'espace ncessaire son accroissem5t1 ce mom5t o 444 il devra remplir exactem5t l'int]valle circonscrit p> sa fragile prison1 etc40 #eic ,?i5emann1 ,f4 ,a4 ,l41 ,sy/4 ,d>/ellung d] ,=tpflanzung d] ,vgel ,europas4 ,leipzig1 #ahbe-ch4 #eid ,cf4 ,newton's ,diction>y ( ,birds1 #ahic1 p4 #aia2 ,szielasko1 ,ge/alt d] ,vogelei]1 ,j4 f4 ,orni?4 ,,liii1 pp4 #bgc-big1 #aije4 #eie ,jacob ,/e9] sugge/$ a ,c>tesian oval1 r mr c1 z a g5]al =mula = all eggs 7cf4 ,fe*n]1 ,b]4 s*s4 ,ges41 #ahdi1 p4 #eg72 b ?is =mula 7:i* fails 9 su* a case z ! guillemot71 is purely empirical1 & has no me*anical f\ndation4 #eif ,gn!r1 ,f4 ,c41 ,sammlung von ,ne/]n und ,ey]n v]s*i$5] ,vgel1 ,nrnb4 #aggb4 ,cf4 also ,raymond ,pe>l1 ,morphog5etic ,activity ( ! ,oviduct1 ,j4 ,exp4 ,zool4 ,,vi1 pp4 #cci-cei1 #aiji4 #eig ,! foll[+ acc\nt is 9 "p repr9t$ f ,nature1 ,june #d1 #aijh4 #eih ,9 s f> z our explanation involves a %ap+ or m\ld+ ( ! egg by ! ut]us or 8oviduct0 7an ag5cy supplem5t$ by ! prop] t5sions ( ! egg71 x is curi\s to note t ?is is v mu* ! same z t old view ( ,telesius reg>d+ ! =mation ( ! embryo 7,de r]um natura1 ,,vi1 cc4 #d & #aj71 :i* he _h inh]it$ f ,gal51 & ( :i* ,bacon speaks 7,nov4 ,org4 cap4 #ej2 cf4 ,ellis's note74 ,bacon expressly rem>ks t 8,telesius %\ld h be5 able to %ew ! l =mation 9 ! %ells ( eggs40 ,?is old !ory ( embryonic modell+ survives only 9 our usage ( ! t]m 8matrix0 = a 8m\ld40 #eii ,j\rnal ( ,tropical ,m$ic9e1 #ae? ,june1 #aiaa4 ,i leave ?is p>agraph z x 0 writt51 ?\gh x is n[ once m ass]t$ t ! t]m9al & lat]al-sp9$ eggs belong to sep>ate & di/9ct species ( ,bilh>zia 7,leip]1 ,brit4 ,m$4 ,j\rn41 #ah? ,m>*1 #aiaf1 p4 #daa74 #fjj ,cf4 ,ba%=? & ,adams1 ,!oretical ,=ms ( ,drops1 etc41 ,cambridge1 #ahhc4 #fja ,woods1 ,r4 ,h41 ,on a ,physical ,!orem appli$ to t5se ,membranes1 ,j\rn4 ( ,anat4 & ,phys4 ,,xxvi1 pp4 #cfb-cga1 #ahib4 ,a simil> inve/igation ( ! t5sions 9 ! ut]9e wall1 & ( ! v>y+ ?ickness ( its muscles1 0 attempt$ by ,haughton 9 8 ,animal ,me*anics1 pp4 #aea-aeh1 #ahgc4 #fjb ,?is corresponds ) a det]m9ation ( ! normal pressures 79 sy/ole7 by ,krohl1 z be+ 9 ! ratio ( #a 3 #fh4 #fjc ,cf4 ,s*walbe1 ,g41 ,ueb] ,we*selbeziehung5 und ihr ,e9fluss auf die ,ge/altung des ,art]i5sy/em1 ,j54 ,zeits*r4 ,,xii1 p4 #bfg1 #ahgh1 ,r\x1 ,ueb] die ,v]zweigung5 d] ,blutgefss5 des ,m5s*51 ibid4 ,,xii1 p4 #bje1 #ahgh2 ,ueb] die ,b$eutung d] ,abl5kung des ,art]i5/mm5 bei d] ,a/aufgabe1 ibid4 ,,xiii1 p4 #cja1 #ahgi2 ,hess1 ,walt]1 ,e9e me*anis* b$+te ,gesetzmssigkeit im ,bau des ,blutgefsssy/ems1 ,a4 f4 ,entw4 ,me*4 ,,xvi1 p4 #fcb1 #aijc2 ,?oma1 ,r41 ,ueb] die ,hi/og5ese und ,hi/ome*anik des ,blutgefsssy/ems1 #ahic4 #fjd ,essays1 etc41 edit$ by ,ow51 ,i1 p4 #acd1 #ahfa4 #fje ,on ! ,functions ( ! ,he>t & ,art]ies1 ,phil4 ,trans4 #ahji1 pp4 #a-ca1 cf4 #ahjh1 pp4 #afd-ahf2 ,collect$ ,works1 ,i1 pp4 #eaa-ecd1 #ahee4 ,! same lesson is convey$ by all su* "w z t ( ,volkmann1 ,e4 ,h4 ,web] & ,poiseuille4 ,cf4 ,/eph5 ,hales' ,/atical ,essays1 ,,ii1 ,introduction3 8,especially consid]+ t !y i4e4 animal ,bodies are 9 a mann] fram$ ( "o cont9u$ ,maze ( innum]able ,canals1 9 :i* ,fluids are incessantly circulat+1 "s ) great ,=ce & ,rapidity1 o!rs ) v diff]5t ,degrees ( rebat$ ,velocity3 ,h5ce1 etc40 #fjf 8,sizes0 is ,ow5's editorial em5dation1 :i* seems amply ju/ifi$4 #fjg ,= a m elaborate classification1 into col\rs cryptic1 procryptic1 anticryptic1 apatetic1 epigamic1 sematic1 episematic1 aposematic1 etc41 see ,p\lton's ,col\rs ( ,animals 7,int4 ,sci5tific ,s]ies1 ,,lxviii71 #ahij2 cf4 also ,meldola1 ,r41 ,v>iable ,protective ,col\r+ 9 ,insects1 ,p4,z4,s4 #ahgc1 pp4 #aec-afb1 etc4 #fjh ,d5dy1 ,evolution>y ,biology1 p4 #ccf1 #aiab4 #fji ,delight 9 beauty is "o ( ! pleasures ( ! imag9ation2 !re is no limit to its indulg5ce1 & no end to ! results :i* we may ascribe to its ex]cise4 ,b z = ! p>ticul> 8/&>d ( beauty0 :i* ! bird 7= in/ance7 admires & selects 7z ,d>w9 says 9 ! ,orig91 p4 #gj1 edit4 #ahhd71 we are v mu* 9 ! d>k1 & we run ! risk ( argu+ 9 a circle3 = wellnigh all we c safely say is :at ,addison says 79 ! #dab? ,spectator7--t ea* diff]5t species 8is mo/ affect$ ) ! beauties ( its own k9d 4444 ,h9c m]ula 9 nigro se oblectat nigra m>ito2 444 h9c noctua tetram ,canitiem al>um et glaucos miratur ocellos40 #faj ,cf4 ,bridge1 ,t4 ,w41 ,cambridge ,natural ,hi/ory 7,fi%es71 ,,vii1 p4 #agc1 #aijd2 also ,fris*1 ,k4 v41 ,ueb] f>bige ,anpassung bei ,fis*e1 ,zool4 ,jahrb4 7,abt4 ,allg4 ,zool471 ,,xxxii1 pp4 #aga-bcj1 #aiad4 #faa ,nature1 ,l1 p4 #egb2 ,,li1 pp4 #cc1 #eg1 #ecc1 #ahid-ie4 #fab ,!y are 8wond]fully fitt$ = #8vani%m5t' aga9/ ! flu%$1 ri*-col\r$ skies ( e>ly morn+ & ev5+ 4444 _! *ief fe$+-times02 & 8look l a real sunset or dawn1 repeat$ on ! opposite side ( ! heav5s1--ei!r ea/ or we/ z ! case may be03 ,?ay]1 ,conceal+-coloration 9 ! ,animal ,k+dom1 ,new ,york1 #aiji1 pp4 #aed-aee4 ,?is hypo!sis1 l ! re/1 is n free f difficulty4 ,twilight is apt to be %ort 9 ! homes ( ! flam+o3 & moreov]1 ,mr ,abel ,*apman1 :o wat*$ !m on ! ,guadalquivir1 tells u t !y fe$ by day4 #fac ,pr9cipal ,gall[ay1 ,philosophy ( ,religion1 p4 #cdd1 #aiad4 #fad ,cf4 ,pr(essor ,fl9t1 9 8 ,preface to ,affleck's translation ( ,janet's ,causes f9ales3 8,we are1 no d\bt1 /ill a long way f a me*anical !ory ( organic gr[?1 b x may be said to be ! quaesitum ( mod]n sci5ce1 & no "o c say t x is a *ima]a40 #fae ,cf4 ,sir ,donald ,mac,alister1 ,h[ a ,bone is ,built1 ,engl4 ,ill4 ,mag4 #ahhd4 #faf ,pr(essor ,claxton ,fidl]1 ,on ,bridge ,con/ruction1 p4 #bb 7#d? ed471 #aiji2 cf4 7int4 al47 ,love's ,ela/icity1 p4 #bj 7,hi/orical ,introduction71 #bnd ed41 #aijf4 #fag ,9 prep>+ or 8mac]at+0 a skeleton1 ! naturali/ n[adays c>ries on ! process till no?+ is left b ! :it5$ bones4 ,b ! old anatomi/s1 ^: object 0 n ! /udy ( 8comp>ative0 morphology b ! wid] !me ( comp>ative physiology1 7 wont to mac]ate by easy /ages2 & 9 _m ( _! mo/ in/ructive prep>ations1 ! ligam5ts 7 int5tionally left 9 connection ) ! bones1 & z "p ( ! 8skeleton40 #fah ,9 a few anatomical diagrams1 = in/ance 9 "s ( ! draw+s 9 ,s*maltz's ,atlas d] ,anatomie des ,pf]des1 we may see ! sy/em ( 8ties0 diagrammatically ins]t$ 9 ! figure ( ! skeleton4 ,cf4 ,gregory1 ,on ! pr9ciples ( ,quadrup$al ,locomotion1 ,ann4 ,n4 ,y4 ,acad4 ( ,sci5ces1 ,,xxii1 p4 #bhi1 #aiab4 #fai ,galileo1 ,dialogues conc]n+ ,two ,new ,sci5ces 7#afch71 ,crew & ,salvio's translation1 ,new ,york1 #aiad1 p4 #aej2 ,op]e1 ed4 ,fav>o1 ,,viii1 p4 #ahf4 ,cf4 ,borelli1 ,de ,motu ,animalium1 ,i1 prop4 ,,clxxx1 #afhe4 ,cf4 also ,camp]1 ,p41 ,la /ructure des os dans les oiseaux1 ,opp4 ,,iii1 p4 #dei1 ed4 #ahjc2 ,raub]1 ,a41 ,galileo b] ,kno*5=m51 ,morphol4 ,jahrb4 ,,vii1 pp4 #cbg1 #cbh1 #ahha2 ,paolo ,enriques1 ,della economia di so/anza nelle osse cave1 ,ar*4 f4 ,ent4 ,me*4 ,,xx1 pp4 #dbg-dfe1 #aijf4 #fbj ,das me*anis*e ,pr9zip4 im anatomis*5 ,bau d] ,monocotyl51 ,leipzig1 #ahgd4 #fba ,= fur!r botanical illu/rations1 see 7int4 al47 ,hegl]1 ,e9fluss d] ,zugkraft5 auf die ,fe/igkeit und die ,ausbildung me*anis*] ,gewebe 9 ,pflanz51 ,,sb4 s*s4 ,ges4 d4 ,wiss4 p4 #fch1 #ahia2 ,kny1 ,l41 ,e9fluss von ,zug und ,druck auf die ,ri*tung d] ,s*eidew&e 9 si* teil5d5 ,pflanz5zell51 ,b]4 d4 bot4 ,gesells*4 ,,xiv1 #ahif2 ,sa*s1 ,me*anomorphose und ,phylog5ie1 ,flora1 ,,lxxviii1 #ahid2 cf4 also ,pflg]1 ,e9wirkung d] ,s*w]kraft1 etc41 b] die ,ri*tung d] ,zell!ilung1 ,ar*iv1 ,,xxxiv1 #ahhd4 #fbb ,among o!r works on ! me*anical con/ruction ( bone see3 ,b\rg]y1 ,trait de l'anatomie 7,i4 ,o/ologie71 #ahcb 7) admirable illu/rations ( trabecul> /ructure72 ,fick1 ,l41 ,die ,ursa*5 d] ,kno*5=m51 ,gtt+51 #aheg2 ,mey]1 ,h41 ,die ,ar*itektur d] ,spongiosa1 ,ar*iv f4 ,anat4 und ,physiol4 ,,xlvii1 pp4 #fae-fbh1 #ahfg2 ,/atik u4 ,me*anik des m5s*li*5 ,kno*5g]/es1 ,leipzig1 #ahgc2 ,wolff1 ,j41 ,die inn]e ,ar*itektur d] ,kno*51 ,ar*4 f4 ,anat1 und ,phys4 ,l1 #ahgj2 ,das ,gesetz d] ,trans=mation bei ,kno*51 #ahib2 von ,ebn]1 ,v41 ,d] fe9]e ,bau d] ,kno*5sub/anz1 ,wi5] ,b]i*t1 ,,lxxii1 #ahge2 ,raub]1 ,anton1 ,ela/izitt und ,fe/igkeit d] ,kno*51 ,leipzig1 #ahgf2 ,o4 ,mes]]1 ,ela/1 u4 ,fe/igk4 d4 m5s*li*5 ,kno*51 ,/uttg>t1 #ahhj2 ,mac,alister1 ,sir ,donald1 ,h[ a ,bone is ,built1 ,engli% ,illu/r4 ,mag4 pp4 #fdj-fdi1 #ahhd2 ,rasum[sky1 ,ar*itektonik des ,fussskelets1 ,int4 ,monatss*r4 f4 ,anat4 p4 #aig1 #ahhi2 ,zs*okke1 ,weit]e ,unt]s4 b] das ,v]hltniss d] ,kno*5bildung zur ,/atik und ,me*anik des ,v]tebrat5skelets1 ,zri*1 #ahib2 ,r\x1 ,w41 ,ges4 ,abh&lung5 b] ,entwicklungsme*anik d] ,organism51 ,bd4 ,i1 ,funktionelle ,anpassung1 ,leipzig1 #ahie2 ,triepel1 ,h41 ,die ,/ossfe/igkeit d] ,kno*51 ,ar*4 f4 ,anat4 u4 ,phys4 #aijj2 ,gebh>dt1 ,funktionell wi*tige ,anordnungsweis5 d] fe9]5 und grb]5 ,bauelem5te des ,wirbel?i]kno*5s1 etc41 ,ar*4 f4 ,entw4 ,me*4 #aijj-aiaj2 ,kir*n]4 ,a41 ,ar*itektur d] ,metat>sali51 ,a4 f4 ,e4 ,m4 ,,xxiv1 #aijg2 ,triepel1 ,h]m41 ,die trajectorielle ,/ructur5 79 ,e9f4 9 die ,physikalis*e ,anatomie1 #aijh72 ,dixon1 ,a4 ,f41 ,ar*itecture ( ! ,cancell\s ,tissue =m+ ! ,upp] ,end ( ! ,femur1 ,j\rn4 ( ,anat4 & ,phys4 7#c7 ,,xliv1 pp4 #bbc-bcj1 #aiaj4 #fbc ,sdillot1 ,de l'influ5ce des fonctions sur la /ructure et la =me des organes2 ,c4 ,r4 ,,lix1 p4 #eci1 #ahfd2 cf4 ,,lx1 p4 #ig1 #ahfe1 ,,lxviii4 p4 #addd4 #ahfi4 #fbd ,e4g4 7#a7 ! head1 nodd+ backw>ds & =w>ds on a fulcrum1 repres5t$ by ! atlas v]tebra1 ly+ betwe5 ! weight & ! p[]2 7#b7 ! foot1 rais+ on tip-toe ! weight ( ! body aga9/ ! fulcrum ( ! gr\nd1 :]e ! weight is betwe5 ! fulcrum & ! p[]1 ! latt] be+ repres5t$ by ! t5do ,a*illis2 7#c7 ! arm1 lift+ a weight 9 ! h&1 ) ! p[] 7i4e4 ! biceps muscle7 betwe5 ! fulcrum & ! weight4 7,! second case1 by ! way1 has be5 mu* disput$2 cf4 ,haycraft 9 ,s*f]'s ,textbook ( ,physiology1 p4 #bea1 #aijj47 #fbe ,our problem is analog\s to ,dr ,?omas ,"y's problem ( ! be/ disposition ( ! timb]s 9 a wood5 %ip 7,phil4 ,trans4 #ahad1 p4 #cjc74 ,he 0 n long ( f9d+ t ! =ces :i* may act ^u ! fabric are v num]\s & v v>iable1 & t ! be/ mode ( resi/+ !m1 or be/ /ructural arrangem5t = ultimate /r5g?1 becomes an imm5sely complicat$ problem4 #fbf ,9 l mann]1 ,cl]k ,maxwell c\ld n help employ+ ! t]m 8skeleton0 9 def9+ ! ma!matical conception ( a 8frame10 con/itut$ by po9ts & _! int]connect+ l9es3 9 /udy+ ! equilibrium ( :i*1 we consid] its diff]5t po9ts z mutually act+ on ea* o!r ) =ces ^: directions are ^? ( ! l9es jo9+ ea* pair ( po9ts4 ,h5ce 7says ,maxwell71 89 ord] to exhibit ! me*anical action ( ! frame 9 ! mo/ elem5t>y mann]1 we may draw x z a skeleton1 9 :i* ! diff]5t po9ts are jo9$ by /raight l9es1 & we may indicate by numb]s atta*$ to ^! l9es ! t5sions or compressions 9 ! correspond+ pieces ( ! frame0 7,trans4 ,r4 ,s4 ,e4 ,,xxvi1 p4 #a1 #ahgj74 ,x foll[s t ! diagram s con/ruct$ repres5ts a 8diagram ( =ces10 9 ?is limit$ s5se t x is geometrical z reg>ds ! position & direction ( ! =ces1 b ari?metical z reg>ds _! magnitude4 ,x is to j su* a diagram t ! animal's skeleton t5ds to approximate4 #fbg ,:5 ! jockey cr\*es ov] ! neck ( 8 race-horse1 & :5 ,tod ,sloan introduc$ ! 8,am]ican seat10 ! object 9 bo? cases is to relieve ! h9d-legs ( weight1 & s leave !m free = ! "w ( propulsion4 ,nev]!less1 we mu/ n exagg]ate ! %>e tak5 by ! h9d-limbs 9 ?is latt] duty2 cf4 ,/illman1 ,! ,horse 9 ,motion1 p4 #fi1 #ahhb4 #fbh ,?is & ! foll[+ diagrams are borr[$ & adapt$ f ,pr(essor ,fidl]'s ,bridge ,con/ruction4 #fbi ,! me?od ( con/ruct+ reciprocal diagrams1 9 :i* "o %\ld repres5t ! outl9es ( a frame1 & ! o!r ! sy/em ( =ces necess>y to keep x 9 equilibrium1 0 fir/ indicat$ 9 ,culmann's ,graphis*e ,/atik2 x 0 greatly develop$ soon aft]w>ds by ,macquorn ,rank9e 7,phil4 ,mag4 ,feb4 #ahfd1 & ,appli$ ,me*anics1 passim71 to :om is ma9ly due ! g5]al application ( ! pr9ciple to eng9e]+ practice4 #fcj ,dialogues conc]n+ ,two ,new ,sci5ces 7#afch73 ,crew & ,salvio's translation1 p4 #adj seq4 #fca ,! =m & direction ( ! v]tebral sp9es h be5 frequ5tly & elaborately describ$2 cf4 7e4g47 ,gottlieb1 ,h41 ,die ,anticl9ie d] ,wirbelsule d] ,suge?i]e1 ,morphol4 ,jahrb4 ,,lxix1 pp4 #agi-bbj1 #aiae1 & _m works quot$ !re94 ,accord+ to ,morita1 ,ueb] die ,ursa*5 d] ,ri*tung und ,ge/alt d] ?oracal5 ,dorn=tstze d] ,suge?i]wirbelsule 7ibi cit4 p4 #bja71 v>i\s *anges take place 9 ! direction or incl9ation ( ^! processes 9 rabbits1 aft] section ( ! int]sp9\s ligam5ts & muscles4 ,^! *anges seem to be v mu* :at we %\ld expect1 on simple me*anical gr\nds4 ,see also ,fis*]1 ,o41 ,!oretis*e ,grundlag5 fr e9e ,me*anik d] leb5d5 ,krp]1 ,leipzig1 pp4 #c1 #cgb1 #aijf4 #fcb ,i owe ! fir/ f\r ( ^! det]m9ations to ! k9dness ( ,dr ,*alm]s ,mit*ell1 :o _h !m made = me at ! ,zoological ,society's ,g>d5s2 :ile ! great ,clydesdale c>?orse 0 weigh$ = me by a fri5d 9 ,dundee4 #fcc ,?is pose ( ,diplodocus1 & ( o!r ,sauropod\s reptiles1 has be5 mu* discuss$4 ,cf4 7int4 al47 ,abel1 ,o41 ,abh4 k4 k4 zool4 bot4 ,ges4 ,wi51 ,v4 #aiji-aj 7#fj pp472 ,torni]1 ,,sb4 ,ges4 ,naturf4 ,fr4 ,b]l91 pp4 #aic-bji1 #aiji2 ,hay1 ,o4 ,p41 ,am]4 ,nat4 ,oct4 #aijh2 ,tr4 ,wa%4 ,acad4 ,sci4 ,,xlii1 pp4 #a-be1 #aiaj2 ,holl&1 ,am]4 ,nat4 ,may1 #aiaj1 pp4 #bei-bhc2 ,mat!w1 ibid4 pp4 #edg-efj2 ,gilmore1 ,c4 ,w4 7,re/oration ( ,/egosaurus74 ,pr4 ,u4,s4 ,nat4 ,museum1 #aiae4 #fcd ,! =m ( ! cantilev] is mu* less typical 9 ! small fly+ birds1 :]e ! /r5g? ( ! pelvic region is insur$ 9 ano!r way1 ) :i* we ne$ n "h /op to deal4 #fce ,! motto 0 ,macquorn ,rank9e's4 #fcf ,john ,hunt] 0 seldom wrong2 b ,i _c believe t he 0 "r :5 he said 7,sci5tific ,works1 ed4 ,ow51 ,i1 p4 #cga71 8,! bones1 9 a me*anical view1 appe> to be ! fir/ t are to be consid]$4 ,we c /udy _! %ape1 connexions1 numb]1 uses1 etc41 )\t consid]+ any o!r "p ( ! body40 #fcg ,orig9 ( ,species1 #f? ed4 p4 #aah4 #fch ,am]4 ,naturali/1 ,april1 #aiae1 p4 #aih1 etc4 ,cf4 infra1 p4 #gbg4 #fci ,dries* sees 9 8,entele*y0 t some?+ :i* diff]5tiates ! :ole f ! sum ( its p>ts 9 ! case ( ! organism3 8,! organism1 we "k1 is a sy/em ! s+le con/itu5ts ( :i* are inorganic 9 !mselves2 only ! :ole con/itut$ by !m 9 _! typical ord] or arrangem5t owes its specificity to #8,entele*y' 0 7,gif=d ,lectures1 p4 #bbi1 #aijh73 & ,i ?9k x c\ld be %ewn t _m o!r philosoph]s h said precisely ! same ?+4 ,s f> z ! argum5t goes1 ,i fail to see h[ ?is ,entele*y is %ewn to be peculi>ly or specifically relat$ to ! liv+ organism4 ,! conception t ! :ole is always some?+ v diff]5t f its p>ts is a v anci5t doctr9e4 ,! read] w p]haps rememb] h[1 9 ano!r ve91 ! !me is treat$ by ,m>t9us ,scribl]us3 8,9 e ,jack !re is a meat-roa/+ ,quality1 :i* nei!r resides 9 ! fly1 nor 9 ! weight1 nor 9 any p>ticul> :eel ( ! ,jack1 b is ! result ( ! :ole composition2 etc41 etc40 #fdj 8,!re c be no d\bt t ,fraas is correct 9 reg>d+ ?is type 7,procetus7 z an annectant =m betwe5 ! ,zeuglodonts & ! ,creodonta1 b1 al?\gh ! orig9 ( ! ,zeuglodonts is ?us made cle>1 x /ill seems to be by no means s c]ta9 z t au?or believes1 t !y may n !mselves be ! ance/ral =ms ( ! ,odontoceti02 ,&rews1 ,t]ti>y ,v]tebrata ( ! ,fayum1 #aijf1 p4 #bce4 #fda ,repr9t$1 ) "s *anges & additions1 f a pap] 9 ! ,trans4 ,roy4 ,soc4 ,ed94 ,l1 pp4 #heg-ie1 #aiae4 #fdb ,m4 ,b]gson repudiates1 ) peculi> confid5ce1 ! application ( ma!matics to biology4 ,cf4 ,creative ,evolution1 p4 #ba1 8,calculation t\*es1 at mo/1 c]ta9 ph5om5a ( organic de/ruction4 ,organic creation1 on ! contr>y1 ! evolution>y ph5om5a :i* prop]ly con/itute life1 we _c 9 any way subject to a ma!matical treatm5t40 #fdc ,9 ?is !re lies a c]ta9 ju/ification = a say+ ( ,m9ot's1 ( ! great] "p ( :i*1 nev]!less1 ,i am he>tily incl9$ to disapprove4 8,we biologi/s10 he says1 8_c deplore too frequ5tly or too emphatically ! great ma!matical delusion by :i* m5 (t5 ( great if limit$ ability h be5 misl$ into becom+ advocates ( an errone\s conception ( accuracy4 ,! delusion is t no sci5ce is accurate until its results c be express$ ma!matically4 ,! error comes f ! assumption t ma!matics c express complex relations4 ,un=tunately ma!matics h a v limit$ scope1 & are bas$ ^u a few extremely rudim5t>y exp]i5ces1 :i* we make z v little *ildr5 & ( :i* no adult has any recollection4 ,! fact t f ?is basis m5 ( g5ius h evolv$ wond]ful me?ods ( deal+ ) num]ical relations %\ld n bl9d u to ano!r fact1 namely1 t ! obs]vational basis ( ma!matics is1 psy*ologically speak+1 v m9ute comp>$ ) ! obs]vational basis ( ev5 a s+le m9or bran* ( biology 4444 ,:ile !re=e "h & !re ! ma!matical me?ods may aid u1 we ne$ a k9d & degree ( accuracy ( :i* ma!matics is absolutely incapable 4444 ,) human m9ds con/itut$ z !y actually are1 we _c anticipate t !re w ev] be a ma!matical expression = any organ or ev5 a s+le cell1 al?\gh =mulae w cont9ue to be useful = deal+ n[ & !n ) isolat$ details4440 7op4 cit41 p4 #ai1 #aiaa74 ,x 7 easy to discuss & criticise ^! sweep+ ass]tions1 :i* p]haps _h _! orig9 & p>5tage 9 an obit] dictum ( ,huxley's1 to ! effect t 8,ma!matics is t /udy :i* kn[s no?+ ( obs]vation1 no?+ ( exp]im5t1 no?+ ( induction1 no?+ ( causation0 7cit4 ,cajori1 ,hi/ ( ,elem4 ,ma!matics1 p4 #bhc74 ,b ,gauss call$ ma!matics 8a sci5ce ( ! eye02 & ,sylve/] assures u t 8mo/1 if n all1 ( ! great ideas ( mod]n ma!matics h _h _! orig9 9 obs]vation0 7,brit4 ,ass4 ,address1 #ahfi1 & ,laws ( ,v]se1 p4 #abj1 #ahgj74 #fdd ,hi/oria ,animalium ,i1 #a4 #fde ,cf4 supra1 p4 #gad4 #fdf ,cf4 ,osborn1 ,h4 ,f41 ,on ! ,orig9 ( ,s+le ,*>act]s1 z obs]v$ 9 fossil & liv+ ,animals & ,plants1 ,am]4 ,nat4 ,,xlix1 pp4 #aic-bci1 #aiae 7& o!r pap]s72 ibid4 p4 #aid1 8,ea* individual is compos$ ( a va/ numb] ( some:at simil> new or old *>act]s1 ea* "* has its indep5d5t & sep>ate hi/ory1 ea* "* is 9 a c]ta9 /age ( evolution1 ea* "* is correlat$ ) ! o!r *>act]s ( ! individual 4444 ,! real problem has always be5 t ( ! orig9 & developm5t ( *>act]s4 ,s9ce ! ,orig9 ( ,species appe>$1 ! t]ms v>iation & v>iability h always ref]r$ to s+le *>act]s2 if a species is said to be v>iable1 we mean t a consid]able numb] ( ! s+le *>act]s or gr\ps ( *>act]s ( :i* x is compos$ are v>iable10 etc4 #fdg ,cf4 ,sorby1 ,qu>t4 ,j\rn4 ,geol4 ,soc4 7,proc471 #ahgi1 p4 #hh4 #fdh ,cf4 ,d',orbigny1 ,alc41 ,c\rs lm4 de ,palontologie1 etc41 ,i1 pp4 #add-adh1 #ahdi2 see also ,%>pe1 ,daniel1 ,on ,slaty ,cleavage1 ,q4,j4,g4,s4 ,,iii1 p4 #gd1 #ahdg4 #fdi ,?us ,ammonites erugatus1 :5 compress$1 has be5 describ$ z ,a4 planorbis3 cf4 ,blake1 ,j4 ,f41 ,phil4 ,mag4 7#e71 ,,vi1 p4 #bfj1 #ahgh4 ,wett/e9 has %ewn t sev]al species ( ! fi%-g5us ,lepidopus h be5 bas$ on specim5s artificially de=m$ 9 v>i\s ways3 ,ueb] die ,fis*fauna des ,t]tir5 ,gl>n]s*ief]s1 ,abh4 ,s*w4 ,palaeont4 ,gesells*4 ,,xiii1 #ahhf 7see especially pp4 #bc-ch1 pl4 ,i74 ,! :ole subject1 int]e/+ z x is1 has be5 little /udi$3 bo? ,blake & ,wett/e9 deal ) x ma!matically4 #fej ,cf4 ,sir ,?omas ,br[ne1 9 ,! ,g>d5 ( ,cyrus3 8,b :y (ttimes "o side ( ! leaf is unequall unto ! o!r1 z 9 ,hazell & ,oaks1 :y on ei!r side ! ma/] ve9 ! less] & d]ivative *annels /& n directly opposite1 nor at equall angles1 respectively unto ! adv]se side1 b ^? ( "o side d (t5 exce$ ! o!r1 z ! ,wallnut & _m m1 des]ves ano!r enquiry40 #fea ,:]e g\rds are common1 ! glass-bl[] is /ill apt to take !m = a prototype1 z ! prehi/oric pott] also did4 ,= in/ance1 a tall1 annulat$ ,flor5ce oil-flask is an exact b no long] a consci\s imitation ( a g\rd :i* has be5 conv]t$ into a bottle 9 ! mann] describ$4 #feb ,cf4 ,elsie ,v5n]1 *ap4 ii4 #fec ,?is significance is p>ticul>ly rem>kable 9 connection ) ! developm5t ( spe$1 = ! metac>pal region is ! seat ( v important lev]age 9 ! propulsion ( ! body4 ,9 ! ,museum ( ! ,royal ,college ( ,surgeons 9 ,ed9burgh1 !re /& side by side ! skeleton ( an imm5se c>?orse 7celebrat$ = hav+ drawn all ! /ones ( ! ,bell ,rock ,ligh?\se to ! %ore71 & a beautiful skeleton ( a racehorse1 :i* 7?\gh ! fact is disput$7 !re is good reason to believe is ! actual skeleton ( ,eclipse4 ,:5 ,i 0 a boy my gr&fa!r us$ to po9t out to me t ! cannon-bone ( ! little rac] is n only relatively1 b actually1 long] ?an t ( ! great ,clydesdale4 #fed ,cf4 ,vitruvius1 ,,iii1 #a4 #fee ,les quatres livres d',alb]t ,dr] de la proportion des p>ties et p\rtraicts des corps huma9s1 ,arnheim1 #afac1 folio 7& e>li] editions74 ,cf4 also ,lavat]1 ,essays on ,physiognomy1 ,,iii1 p4 #bga1 #agii4 #fef ,x 0 ^! v draw+s ( ,dr]'s t gave to ,pet] ,camp] 8 notion ( ! 8facial angle40 ,camp]'s me?od ( comp>ison 0 ! v same z ours1 save t he only drew ! axes1 )\t fill+ 9 ! network1 ( 8 coord9ate sy/em2 he saw cle>ly ! ess5tial fact1 t ! skull v>ies z a :ole1 & t ! 8facial angle0 is ! index to a g5]al de=mation4 8,! great object 0 to %ew t natural diff]5ces might be r$uc$ to rules1 ( :i* ! direction ( ! facial l9e =ms ! norma or canon2 & t ^! directions & incl9ations are always accompani$ by correspond5t =m1 size & position ( ! o!r p>ts ( ! cranium10 etc42 f ,dr ,t4 ,cogan's preface to ,camp]'s "w ,on ! ,connexion betwe5 ! ,sci5ce ( ,anatomy & ! ,arts ( ,draw+1 ,pa9t+ & ,sculpture 7#agfh871 quot$ 9 ,dr ,r4 ,hamilton's ,memoir ( ,camp]1 9 ,lives ( ,em95t ,naturali/s 7,nat4 ,libr471 ,ed94 #ahdj4 #feg ,! co-ord9ate sy/em ( ,fig4 #chb is some:at diff]5t f t :i* ,i drew & publi%$ 9 my =m] pap]4 ,x is n unlikely t fur!r inve/igation w fur!r simplify ! comp>ison1 & %ew x to involve a /ill m symmetrical sy/em4 #feh ,d9osaurs ( ,nor? ,am]ica1 pl4 ,,lxxxi1 etc4 #ahif4 #fei ,mem4 ,am]4 ,mus4 ( ,nat4 ,hi/4 ,i1 ,,iii1 #ahih4 #ffj ,^! & also o!r coord9ate diagrams w be f\nd 9 ,mr ,g4 ,heilmann's book ,fugl5es ,af/amn+1 #cih pp41 ,cop5hag51 #aiaf2 see especially pp4 #cfh-chj4 #ffa ,cf4 ,w4 ,b4 ,scott 7,am]4 ,j\rn4 ( ,sci5ce1 ,,xlviii1 pp4 #cce-cgd1 #ahid71 8,we f9d t any mammalian s]ies at all complete1 su* z t ( ! horses1 is rem>kably cont9u\s1 & t ! progress ( discov]y is /eadily fill+ up :at few gaps rema94 ,s closely d successive /ages foll[ ^u "o ano!r t x is sometimes extremely difficult to arrange !m all 9 ord]1 & to di/+ui% cle>ly ^? memb]s :i* belong 9 ! ma9 l9e ( desc5t1 & ^? :i* repres5t incipi5t bran*es4 ,"s phylog5ies actually suff] f an emb>rassm5t ( ri*es40 #ffb ,cf4 ,dwight1 ,t41 ,! ,range ( ,v>iation ( ! ,human ,scapula1 ,am]4 ,nat4 ,,xxi1 pp4 #fbg-fch1 #ahhg4 ,cf4 also ,turn]1 ,*all5g] ,rep4 ,,xlvii1 on ,human ,skeletons1 p4 #hf1 #ahhf3 8,i ga!r bo? f my own measurem5ts1 & ^? ( o!r obs]v]s1 t ! range ( v>iation 9 ! relative l5g? & bread? ( ! scapula is v consid]able 9 ! same race1 s t x ne$s a l>ge numb] ( bones to enable "o to obta9 an accurate idea ( ! mean ( ! race40 #ffc ,!re is a pap] on ! ma!matical /udy ( organic =ms & organic processes by ! le>n$ & celebrat$ ,gu/av ,!odor ,fe*n]1 :i* ,i h only lately read1 b :i* w\ld h be5 ( no little use & help to our argum5t _h ,i kn[n x be=e4 7,ueb] die ma!matis*e ,beh&lung organis*] ,ge/alt5 und ,processe1 ,b]i*te d4 k4 s*s4 ,gesells*41 ,ma?4-phys4 ,cl41 ,leipzig1 #ahdi1 pp4 #ej-fd47 ,fe*n]'s treatm5t is m purely ma!matical & less physical 9 its scope & be>+ ?an ours1 & 8 pap] is b a %ort "o2 b ! conclusions to :i* he is l$ diff] little f our own4 ,let me quote a s+le s5t5ce :i*1 toge!r ) its context1 runs precisely on ! l9es ( ! discussion ) :i* ?is *apt] ( ours began4 8,s i/ also die ma!matis*e ,be/immb>keit im ,gebiete des ,organis*5 ganz eb5 s gut vorh&5 als 9 dem des ,unorganis*51 und 9 letzt]em eb5 sol*5 od] quival5t5 ,bes*rnkung5 unt]worf5 als 9 er/]em2 und nur s(]n die unorganis*5 ,=m5 und das unorganis*e ,ges*eh5 si* e9] e9fa*]5 ,gesetzli*keit mehr nh]n als die organis*51 kann die ,approximation im unorganis*5 ,gebiet lei*t] und weit] getrieb5 w]d5 als im organis*54 ,dies wre d] ganze1 sona* re9 relative1 ,unt]s*i$40 ,"h 9 a nut%ell1 9 words writt5 "s sev5ty ye>s ago1 is ! gi/ ( ! :ole matt]4 ,an int]e/+ little book ( ,s*iap>elli's 7:i* ,i ought to h kn[n long ago7--,=me organi*e naturali e =me geometri*e pure1 ,milano1 ,hoepli1 #ahih--;has likewise come into my h&s too late = discussion4 #ghj ,,index4 ,abbe's diffraction plates1 #cbc ,abel1 ,o41 #gjf ,abonyi1 ,a41 #abg ,acan?>ia1 spicules (1 #deh ,acan?ometridae1 #dfb ,accel]ation1 #fd ,ac]a!rium1 #gfa ,a*lya1 #bdd ,acromegaly1 #ace ,act9omma1 #dfi ,act9omyxidia1 #deb ,act9ophrys1 #afe1 #aig1 #bfd1 #bih ,act9ospha]ium1 #aig1 #bff1 #bih1 #dfh ,adams1 ,j4 ,c41 #ffc ,adaptation1 #fgj ,addison1 ,joseph1 #fga ,adiantum1 #djh ,adsorption1 #aib1 #bjh1 #bda1 #bgg1 #ceg2 ori5tirte1 #ddj1 #eij2 pseudo1 #bhb ,agglut9ation1 #bja ,aglaoph5ia1 #gdh ,airy1 ,h41 #fcf ,album9 molecule1 #da ,alcyon>ia1 #chg1 #dac1 #dbd1 #dei ,alexeieff1 ,a41 #aeg1 #afe ,allmann1 ,w41 #fdc ,alpheus1 claws (1 #aej ,alp9e plants1 #abd ,altmann's granules1 #bhe ,alveol> me%work1 #agj ,ammonites1 #ebf1 #ecj1 #ecg1 #eci1 #eej1 #eeb1 #egf1 #ehc1 #ehd1 #gbh ,amoeba1 #ab1 #afe1 #bji1 #bab1 #bde1 #bee1 #bhh1 #dfc1 #fje ,amphidiscs1 #ddj ,amphioxus1 #caa ,ampull>ia1 #efj ,anaba5a1 #cjj ,anaxagoras1 #h ,ancyloc]as1 #eej ,&rews1 ,g4 ,f41 #afd2 ,c4 ,w41 #gaf ,anhydrite1 #dcc ,anik91 ,w4 ,p41 #acj ,anisonema1 #abf ,anisotropy1 #bda1 #ceg ,anomia1 #efe1 #efg ,antelopes1 horns (1 #fad1 #fga ,an!ridia1 #cjc1 #djc1 #dje1 #dji ,an?oc]os1 spore (1 #cig ,an?ogorgia1 spicules (1 #dac ,an?ropometry1 #ea ,anticl9e1 #cfj ,antigonia1 #gej1 #gge ,antl]s1 #fbh ,apatornis1 #geg ,apocynum1 poll5 (1 #cif ,apty*us1 #egf ,ara*noidiscus1 #chg ,ara*nophyllum1 #cbe ,arcella1 #cbc ,arce/es1 #eci1 #edj ,ar*aeopt]yx1 #geg ,ar*im$es1 #ehj2 spiral (1 #ejc1 #ebd1 #eeb ,argali1 horns (1 #fag ,argiope1 #efa ,argonauta1 #edf1 #efa ,argus pheasant1 #dca1 #fca ,argyropelecus1 #gdh ,ari/otle1 #c1 #d1 #e1 #h1 #ae1 #ach1 #adi1 #aeh1 #eji1 #fec1 #gad1 #gbe1 #gbf ,arizona trees1 #aba ,arrh5ius1 ,sv41 #bh1 #dh1 #aga ,artemia1 #abg ,artemis1 #efa ,asc>is megalocephala1 #ahj1 #aie ,as*emonella1 #bee ,as%eton1 ,r41 #cdd ,a/]9a1 #cdb ,a/]oides1 #dbc ,a/]olampra1 #chf ,a/]s1 #afg1 #agd ,a/h5osoma1 #ffd ,a/rorhiza1 #bee1 #dfc1 #ehg1 #fjg ,a/roscl]a1 #dcf ,asymmetric sub/ances1 #daf ,asymmetry1 #bda ,atrypa1 #efi ,au]ba*1 ,f41 #i ,aulacan?a1 #dfj ,aula/rum1 #dga ,aulonia1 #dfh ,auricul> height1 #ic ,autocatalysis1 #aca ,auximones1 #ace ,aw]9zew1 ,s41 #ehi ,babak1 ,e41 #cb ,babirussa1 tee? (1 #fcd ,baboon1 skull (1 #gga ,bacillus1 #ci2 ,b4 ramosus1 #acc ,bacon1 ,"l1 #d1 #e1 #ea1 #ec1 #aca1 #fef1 #gaf ,bact]ia1 #bde1 #bej ,ba]1 ,k4 ,e41 von1 #c1 #ee1 #eg1 #aee ,balancem5t1 #gad1 #ggf ,balf\r1 ,f4 ,m41 #eg1 #cdh ,baltz]1 ,fr41 #cbg ,bamboo1 gr[? (1 #gg ,b>clay1 ,j41 #ccd ,b>fur?1 ,d41 #he ,b>l[1 ,w41 #bjb ,b>ratt1 ,j4 ,o4 ,w41 #bhe ,b>?ol9us1 ,e41 #cbi ,ba%=?1 ,fr41 #ffc ,ba/-fibres1 /r5g? (1 #fgi ,ba/]1 ,job1 #ach ,bateson1 ,w41 #ajd1 #dca ,ba!r1 ,f4 ,a41 #egh ,bats*1 ,a4 ,j4 ,g4 ,k41 #fjf ,baudrimont1 ,a41 & ,/ ,ange1 #abd ,baumann & ,roos1 #acf ,bayliss1 ,w4 ,m41 #ace1 #bgg ,beads or globules1 #bcd ,beak1 %ape (1 #fcb ,beal1 ,w4 ,j41 #fdc ,beam1 load$1 #fgd ,bee's cell1 #cbg1 #ggi ,begonia1 #dab1 #gcc ,beisa antelope1 horns (1 #faf1 #fba ,bell]ophon1 #eej ,bn>d1 ,h41 #bei1 #cai1 #ddh1 #eij ,b5d+ mom5ts1 #ai1 #fgg1 #fif ,b5$51 ,ed4 van1 #aec1 #agj1 #aih ,b]gson1 ,h41 #g1 #ajc1 #bea1 #faa1 #gba ,b]n>d1 ,claude1 #b1 #ac1 #abg ,b]n\lli1 ,james1 #ehj2 ,john1 #cj1 #ed ,b]?old1 ,g41 #h1 #bcd1 #bih1 #cjf1 #cbb1 #cdf1 #cea1 #ceg1 #ceh1 #cgb1 #cii ,be!1 ,a41 #bgf ,bialaszewicz1 ,k41 #aad1 #abe ,bi$]mann1 ,w41 #dca ,bilh>zia1 egg (1 #fef ,b9ucle>ity1 #bhf ,biocry/allisation1 #ded ,biog5etis*es ,grundgesetz1 #fjh ,biometrics1 #gh ,bird1 flight (1 #bd2 =m (1 #fgc ,bisection ( solids1 #ceb1 etc4 ,bi%op1 ,john #ca ,bivalve %ells1 #efa ,bj]knes1 ,v4 #ahf ,blackman1 ,f4 ,f4 #ajh1 #aaj1 #aad1 #abd1 #aca1 #acb ,blackwall1 ,j4 #bcd ,blake1 ,j4 ,f4 #ecf1 #edg1 #eec1 #egh1 #ehc1 #gbh ,bla/osph]e1 #ef1 #cdd ,blood-corpuscles1 =m (1 #bgj2 size (1 #cf ,blood-vessels1 #ffe ,boas1 ,fr41 #gi ,bodo1 #bcj1 #bfi ,bo]haave1 ,h]mann1 #chj ,bonanni1 ,f41 #cah ,bone1 #dbe1 #dce2 repair (1 #fhg2 /ructure (1 #fgc1 #fhj ,bonnet1 ,*41 #ajh1 #ach1 #ccd1 #fce ,borelli1 ,j4 ,a41 #h1 #bg1 #bi1 #cah1 #fgg1 #fij ,bosanquet1 ,b41 #e ,boscovi*1 ,fa!r ,r4 ,j41 ,s4,j41 #h ,bose1 ,j4 ,c41 #hg ,bo/ryx1 #ejb ,bottazzi1 ,f41 #abg ,bottomley1 ,j4 ,t41 #ace ,b\be1 ,n41 #ebi ,b\rg]y1 ,j4 ,m41 #fhc ,b\rne1 ,g4 ,c41 #aii ,b\rrelet1 ,plateau's1 #big1 #cci1 #ddf1 #dgj1 #dgg ,bov]i1 ,?41 #ch1 #adg1 #agj1 #aih ,b[dit*1 ,h4 ,p41 #fa1 #gi ,b[]1 ,f4 ,o41 #djf ,b[man1 ,j4 ,h41 #dbh ,boyd1 ,r41 #fa ,boys1 ,c4 ,v41 #bcc ,bra*iopods1 #efa1 #efh1 #egg ,brad=d1 ,s4 ,c41 #dbh ,brady1 ,h4 ,b41 #bee1 #fjf ,bra91 gr[? (1 #hi2 weight (1 #ij ,bran*ipus1 #abh1 #cdb ,br&t1 ,k41 #dei1 #dhb ,brau]1 ,a41 #ahj ,braun1 ,a41 #fcf ,bravais1 ,l4 & ,a41 #bjb1 #ejb1 #fcf ,br$ig1 ,g41 #agh ,brew/]1 ,sir ,d41 #bji1 #ccg1 #cej1 #dca ,bridge1 ,t4 ,w41 #fga ,bridge con/ruction1 #ah1 #fia ,br9e %rimps1 #abg ,brooke1 ,sir ,v41 #fad1 #fbd1 #fbh1 #fca ,br[ne1 ,sir ,t41 #cbd1 #cbi1 #dhj1 #fej1 #feb1 #gcc ,br[nian movem5t1 #de1 #bgi1 #dba ,brcke1 ,c41 #afj1 #aii ,bucc9um1 #ebj1 #ebg ,bu*1 ,leopold von1 #ebh1 #ehc ,bu*n]1 ,hans1 #acc ,budd+1 #bac1 #cii ,buffon1 on ! bee's cell1 #ccc ,bhle1 ,c4 ,a41 #fec ,bulimus1 #edi1 #eef ,burnet1 ,j41 #eji ,bts*li1 ,o41 #afe1 #agj1 #aga1 #bjd1 #dcb1 #dcd1 #deh1 #dib ,bttel-,reep51 ,h4 von1 #ccb ,byk1 ,a41 #dai ,cactus1 spha]ocry/als1 9 #dcd ,cadets1 gr[? ( ,g]man1 #aai ,cal&r9i1 ,g4 ,l41 #fcf ,calcosph]ites1 #dba1 #dcd ,callimitra1 #dgb ,calli?amnion1 spore (1 #cif ,calman1 ,t4 ,w41 #adi ,calyptraea1 #eef ,camel1 #gjc1 #gjd ,campanul>ia1 #bcg1 #bfb1 #gdg ,campbell1 ,d4 ,h41 #cjb1 #cig1 #djb ,camp]1 ,p41 #gdb ,camptosaurus1 #ged ,cannon bone1 #gcj ,cantilev]1 #fgh1 #fid ,cantor1 ,moritz1 #ejc ,caprella1 #gdc ,capr9ella1 #efg1 #egg ,c>apace ( crabs1 #gdd ,c>dium1 #efa ,c>iacus1 #fbi ,c>li]1 ,e4 ,w41 #baa ,c>noy1 ,j4 ,b41 #dfh ,c>p5t]1 ,w4 ,b41 #de1 #dbb1 #dfe ,c>yok9esis1 #ad1 #aeg1 etc4 ,cass9i1 ,d41 #cbi ,cassis1 #eei ,catabolic products1 #dce ,catalytic action1 #acj ,cat5oid1 #bah1 #bbc1 #bbg1 #beb ,causation1 #f ,cavol9ia1 #egc ,cayley1 ,a41 #che ,cele/ite1 #dei ,cell-!ory1 #aig1 #aii ,cells1 =ms (1 #bja2 sizes (1 #ce ,cellul> pa?ology1 #bjj2 tissue1 artificial1 #cbj ,c5ospha]a1 #dgj ,c5tres ( =ce1 #aef1 #aif ,c5trosome1 #afg1 #afh1 #agc ,cephalopods1 #edh1 etc42 eggs (1 #cgh ,c]atophyllum1 gr[? (1 #ig ,c]atorh9us1 #fab ,c]ebratulus1 egg (1 #ahi ,c]ian?us1 #abe ,c]i?ium1 #ecj1 #eeg1 #eei ,*abri]1 ,j41 #be ,*abry1 ,l41 #cj1 #cjf1 #dae ,*aetodont fi%es1 #fga1 #gdi ,*aetopt]us1 egg (1 #aie ,*amois1 horns (1 #fae ,*apman1 ,abel1 #fgb ,*>a1 #cjc ,*>act]s1 biological1 #aif1 #gbg ,*evron bones1 #gji ,*ick1 hat*+ (1 #ajh ,*ilomonas1 #aad ,*ladni figures1 #chf1 #dge ,*lorophyll1 #bia ,*oan(lagellates1 #bec ,*odat1 ,r41 #gh1 #acb ,*ole/]91 #bgb ,*ondriosomes1 #bhe ,*or9us1 #gdd ,*ree1 ,c41 #ai ,*romat91 #aec ,*romidia1 #bhf ,*romosomes1 #aeg1 #agc1 #agi1 #aha1 #aij1 #aie ,*ur*1 ,a4 ,h41 #fci ,cic]o1 #fb ,cic9nus1 #ejb ,cid>is1 #ffd ,circogonia1 #dgi ,cladoc>pus1 #gdh ,clap>de1 ,e4 ,r1 #dbc ,cla?rul9a1 #dgj ,clausilia1 #ebj1 #edi ,claws1 #adi1 #fcb ,clel&1 ,john1 #d ,cleodora1 #egj-ege ,climate & gr[?1 #aba ,clio1 #egj ,close pack+1 #dec ,clytia1 #gdg ,coan1 ,c4 ,a41 #ead ,coassus1 #fbi ,cod1 otoli?s (1 #dcb2 skeleton (1 #gaj ,codonella1 #bdh ,codosiga1 #bec ,coe1 ,w4 ,r41 #ahi ,coeffici5t ( gr[?1 #aec2 ( temp]ature1 #aji ,coelopleurus1 #ffd ,cogan1 ,dr ,t41 #gdb ,coh51 ,a41 #aaj ,cohesion figures1 #bei ,coll>-cells1 #bec ,colloids1 #afb1 #agh1 #bja1 #bgi1 #dab1 #dba1 etc4 ,colloscl]ophora1 #dcf ,collospha]a1 #dei ,colman1 ,s41 #ead ,comos]is1 #cbg ,comp5sation1 law (1 #gad1 #ggf ,con*ospiral1 #eca1 #eci1 #eid ,con*yliomet]1 #ebi ,concretions1 #daj1 etc4 ,conjugate curves1 #efa1 #fac ,conkl91 ,e4 ,g41 #cf1 #aia1 #caj1 #cdj1 #cgg ,cono/ats1 #dbg ,cont9u\s gird]1 #gjj ,contractile vacuole1 #afe1 #bfd ,conus1 #eeg1 #eei1 #efj ,cook1 ,sir ,t4 ,a41 #dic1 #fce1 #fci1 #fej ,co-ord9ates1 #gbc ,corals1 #cbe1 #chh1 #dbc ,cornev91 ,*41 #ajb ,cornuspira1 #eid ,correlation1 #gh1 #gbg ,cory/es1 #gdd ,cotton1 ,a41 #dah ,cox1 ,j41 #df ,crane-head1 #fhb ,crayfi%1 sp]m-cells (1 #bgc ,creodonta1 #gaf ,crepidula1 #cf1 #caj1 #cdj ,creseis1 #egj ,cri/ell>ia1 #eae1 #fjj ,crocodile1 #gjd1 #geb ,crocus1 gr[? (1 #hh ,crookes1 ,sir ,w41 #cb ,cryptocleidus1 #gee ,cry/als1 #bjb1 #bej1 #dbi1 #ddd1 #dhj1 #fja ,ct5ophora1 #cia ,cube1 p>tition (1 #cdf ,cucumis1 gr[? (1 #aji ,culmann1 ,pr(essor ,c41 #fhb1 #fig ,cultellus1 #efd ,curlew1 eggs (1 #feb ,cu%man1 ,j4 ,a41 #cbc ,cuvi]1 #gbg ,cuvi]9a1 #beh1 #egj ,cyamus1 #gdc ,cya?ophyllum1 #cbe1 #cia ,cyclamm9a1 #eie1 #eif1 #fjb ,cyclas1 #efa ,cyclo/oma1 #eed ,cyl9d]1 #bah1 #bbg1 #cgg ,cymba1 #eei ,cyme1 #ejb ,cypraea1 #edg1 #eed1 #efj1 #efa ,cyrt9a1 #efi ,cyrtoc]ata1 #ehc ,cy/oli?s1 #dab ,daday de ,dees1 ,e4 v41 #acj ,daffn]1 ,fr41 #fa1 #aah ,dalyell1 ,sir ,john ,g41 #adf ,danilewsky1 ,b41 #ace ,d>l+1 ,c4 ,r41 #bai1 #beg1 #ffd ,d',arsonval1 ,a41 #aib1 #bha ,d>w91 ,c41 #d1 #dd1 #eg1 #ccb1 #dca1 #dfe1 #edi1 #fbd1 #fga1 #gad ,da/re1 ,a41 #acf ,dav5port1 ,c4 ,b41 #ajg1 #abc1 #abe1 #abf1 #baa ,de ,c&olle1 ,a41 #ajh1 #fdc2 ,a4 ,p41 #bj2 ,c41 #fcf ,decapod ,cru/acea1 sp]m-cells (1 #bgc ,de]1 antl]s (1 #fbh ,de=mation1 #fch1 #gbh1 etc4 ,degree1 diff]5ces (1 #ehf1 #gbe ,delage1 ,yves1 #aec ,delaunay1 ,c4 ,e41 #bah ,delisle1 #ca ,dell+]1 ,o4 ,p41 #bab ,delph9ula1 #eeg ,delp9o1 ,f41 #fcf ,democritus1 #dd ,d5dy1 ,a41 #acg1 #dcf1 #ddj1 #fga ,d5talium1 #ece1 #ecg1 #edf1 #eee1 #eef1 #efa ,d5t9e1 #dbe ,desc>tes1 ,r41 #ahe1 #gbc ,des ,murs1 ,o41 #fec ,devaux1 ,h41 #dc ,de ,vries1 ,h41 #ajh ,diatoms1 #bad1 #chf1 #dbf ,dic]as1 #efg ,dickson1 ,alex41 #fdg ,dictyota1 #cjc1 #cef1 #dgd ,diet & gr[?1 #acd ,difflugia1 #dfc1 #dff ,diffusion figures1 #bei1 #dcj ,dimorphism ( e>wigs1 #aje ,dimorphodon1 #gef ,d95ympha1 #beb ,d9obryon1 #bdh ,d9osaurs1 #gjb1 #gjd1 #ged ,diodon1 #gea1 #ggg ,dionaea1 #gcd ,diplodocus1 #gjb1 #gjf1 #gaj ,disc1 segm5tation ( a1 #cfg ,discorb9a1 #fjb ,di/igma1 #bdf ,di/ribution1 geographical1 #deg1 #fjf ,ditrupa1 #ehf ,dixon1 ,a4 ,f41 #fhd ,dobell1 ,c4 ,c41 #bhf ,dodecah$ron1 #ccf1 #dgh1 etc4 ,d(le91 ,f4 ,j41 #df1 #bfg1 #fjf ,dog's skull1 #ggc ,dolium1 #ebf1 #ebh1 #ecj1 #eeg1 #eei1 #efj ,dolph91 skeleton (1 #gji ,donaldson1 ,h4 ,h41 #hb1 #ic ,dorataspis1 #dha ,d',orbigny1 ,alc41 #ebi1 #eee1 #eia1 #gbh ,d\glass1 ,a4 ,e41 #aba ,drap]1 ,j4 ,w41 #afe1 #bfd ,drey]1 ,f4 ,r41 #dce1 #ddg1 #dee1 #dfh1 #fjf1 #fjh ,dries*1 ,h41 #d1 #ce1 #aeg1 #cjf1 #caj1 #cab1 #cgg1 #cgh1 #gad ,dromia1 #bge ,drops1 #dd1 #beg1 #ehg ,du ,bois-,reymond1 ,emil1 #a1 #ib ,du]d51 ,j4 ,e41 #dbc ,duf\r1 ,l\is1 #bai ,duj>d91 ,f41 #beg1 #eia ,dunan1 #g ,duncan1 ,p4 ,m>t91 #chh ,dupr1 ,a?anase1 #bgi ,durb91 ,m>ion ,l41 #ach ,dr]1 ,a41 #ee1 #gdj1 #gdb ,dutro*et1 ,r4 ,j4 ,h41 #bab1 #fbd ,dwight1 ,t41 #gfi ,dynamical simil>ity1 #ag ,e>?worm1 calcosph]es 91 #dbc ,e>wigs1 dimorphism 91 #ajd ,ebn]1 ,v4 von1 #ddd1 #fhc ,e*9od]ms1 l>val1 #cib2 spicules (1 #ddi ,e*9us1 #cgg1 #cgh1 #ffd ,eclipse1 skeleton (1 #gci ,ectos>c1 #bha ,eel1 gr[? (1 #he ,effici5cy1 me*anical1 #fgj ,effici5t cause1 #f1 #aeh1 #bdh ,eggs ( birds1 #feb ,eiffel t[]1 #bj ,eight cells1 gr\p+ (1 #cha1 etc4 ,eim]1 ,?41 #fjf ,e9/e9 =mula1 #dg ,ela/ic curve1 #bai1 #bfe1 #bga ,elat]s1 #dhi ,electrical convection1 #ahg2 /imulation ( gr[?1 #aec ,elephant1 #ba1 #fcc1 #gjc1 #gjd ,elk1 antl]s (1 #fbi1 #fcb ,ellipsoli!s1 #gbh ,ellis1 ,r4 ,leslie1 #d1 #cbi1 #fdg2 ,m4 ,m41 #adg1 #fef ,elodea1 #cbb ,em>g9ula1 #eef ,emmel1 ,v4 ,e41 #adi ,emp$ocles1 #h ,emp]or ,mo?1 #dca ,ency/m5t1 #bac1 #bhc ,engelmann1 ,t4 ,w41 #baj1 #bhe ,enriques1 ,p41 #d1 #cf1 #fd1 #acc1 #acd1 #fgg ,entele*y1 #d1 #gad ,entosol5ia1 #ddi ,enzymes1 #ace ,epeira1 #bcc ,epicurus1 #dg ,epid]mis1 #cad1 #cgj ,epilobium1 poll5 (1 #cif ,epipolic =ce1 #bab ,equatorial plate1 #agd ,equiangul> spiral1 #ej1 #eje ,equilibrium1 figures (1 #bbg ,equipot5tial l9es1 #fdj ,equisetum1 spores (1 #bij1 #dhi ,err]a1 ,leo1 #h1 #dj1 #aaj1 #aaa1 #bac1 #cjf1 #cdf1 #cdh1 #dbf ,ery?rotri*ia1 #ceh1 #cgb1 #cij ,e?mospha]a1 #dgj ,eua/rum1 #bad ,eu*>is1 #cia ,euclid1 #eji ,eugl5a1 #cgf ,euglypha1 #ahi ,eul]1 ,l41 #c1 #bjh1 #che1 #dhd1 #fij ,eulima1 #eei ,eunicea1 spicules (1 #dbd ,euomphalus1 #eeg1 #eei ,evelyn1 ,john1 #feb ,evolution1 #edi1 #faj1 etc4 ,ew>t1 ,a4 ,j41 #bj ,fabre1 ,j4 ,h41 #fd1 #ggi ,facial angle1 #gdb1 #ggj1 #ggb ,f>aday1 ,m41 #afc1 #afg1 #dbh1 #dge ,f>m]1 ,j4 ,b4 & ,digby1 #aij ,fatigue1 molecul>1 #fhi ,faucon1 ,a41 #hh ,favosites1 #cbe ,fe*n]1 ,g4 ,t41 #fed1 #ggg ,f$or[1 ,e4 ,s4 von1 #cch ,fehl+1 ,h41 #gf1 #abf ,f]ns1 spores (1 #cif ,f]tilisation1 #aic ,fezzan-worms1 #abg ,fibonacci1 #fdc ,fibrill5konus1 #bhe ,fick1 ,r41 #eg1 #fhc ,fick]t1 ,c41 #fjf ,fidl]1 ,pr(4 ,t4 ,claxton1 #fia1 #fgd1 #fif ,films1 liquid1 #bae1 #bag1 #dbf ,filt]-pass]s1 #ci ,f9al cause1 #c1 #bdh1 #gad ,fir-cone1 #fce1 #fdg ,fis*el1 ,alfr$1 #hh ,fis*]1 ,alfr$1 #dj1 #agb2 ,emil1 #dag1 #dah2 ,otto1 #cj1 #fii ,fi%es1 =ms (1 #gdh ,fission1 multiplication by1 #aea ,fissurella1 #eef ,fitz,gerald1 ,g4 ,f41 #aeh1 #bha1 #cbc1 #ddj1 #dgg ,flagellum1 #bdf1 #bfg1 #bia ,flemm+1 ,w41 #agj1 #agb1 #ahj ,flight1 #bd ,fl9t1 ,pr(essor1 #fgc ,fluid cry/als1 #bjd1 #bgb1 #dhe ,flut$ patt]n1 #bfj ,fly's cornea1 #cbd ,fol1 ,h]mann1 #afh1 #aid ,follicul9a1 #bdi ,=am9if]a1 #bad1 #bee1 #dae1 #die1 #eae ,=? ,bridge1 #fid1 #fii1 #gjj ,fossula1 #cij ,fo/]1 ,m41 #ahe ,fraas1 ,e41 #gaf ,frank5heim1 ,m4 ,l41 #bjb ,frazee1 ,o4 ,e41 #aec ,frdricq1 ,l41 #abg1 #acj ,free cell =mation1 #cif ,fri$5?al1 ,h41 #fd ,fris*1 ,k4 von1 #fga ,frog1 egg (1 #caj1 #cfc1 #cgh1 #chb2 gr[? (1 #ic1 #abf ,fro? or foam1 #aga1 #bje1 #cje1 #cad1 #cbb1 #cdc ,fr\de1 ,w41 #bb ,fucus1 #cee ,fundulus1 #abe ,fusul9a1 #eic1 #eid ,fusus1 #ebg1 #eeg ,gad[1 ,h4 ,f41 #fbh ,gala!a1 #bgc ,gal51 #c1 #dfe1 #fef ,galileo1 #h1 #ai1 #bh1 #efb1 #fgg1 #gbj ,gall>do1 ,a41 #afc ,gall[ay1 ,pr9cipal1 #fgb ,gamble1 ,f4 ,a41 #deh ,ganglion-cells1 size (1 #cg ,gans1 ,r41 #df ,g>d5 ( ,cyrus1 #cbd1 #cbi ,ga/rula1 #cdd ,gauss1 ,k4 ,f41 #bjg1 #bgh1 #gbc ,gebh>dt1 ,w41 #dcj1 #fhc ,gelat9ation1 wat] (1 #bjc ,g5]at+ curves & spirals1 #ebf1 #efa1 #fae1 #fcg1 #fda ,geodetics1 #ddj1 #dhh ,ge(froy ,/ ,hilaire1 ,et4 de1 #gad ,geotropism1 #baa ,g]assim[1 ,j4 ,j41 #ce ,g]dy1 ,p4 ,n41 #dia ,g]yon1 #gdd ,ge/altungskraft1 #dhe ,gi>d1 ,a41 #aef ,gilmore1 ,c4 ,w41 #gjg ,giraffe1 #gje1 #gcj1 #gch ,gir>dia1 #cba1 #djh ,glai%]1 ,j41 #bej ,glassbl[+1 #bch1 #gcg ,gley1 ,e41 #ace1 #acf ,globig]9a1 #bad1 #bcd1 #ddj1 #die1 #ehi1 #fjb1 #fjd1 #fjf ,gnomon1 #eji1 #eae1 #eia ,goat1 horns (1 #fac ,goat mo?1 w+s (1 #dcj ,goebel1 ,k41 #cba1 #cig1 #djh ,goe!1 #bj1 #ch1 #aii1 #gad1 #gai ,gold5 ,mean1 #eaa1 #fdc1 #fdi ,golds*midt1 ,r41 #bhf ,goniatites1 #eej1 #gbh ,gono?yraea1 #gdg ,goodsir1 ,john1 #aef1 #aif1 #ehj ,gottlieb1 ,h41 #fii ,g\rd1 =m (1 #gcg ,grabau1 ,a4 ,h41 #eca1 #eci1 #eej ,graham1 ,?omas1 #afb1 #bja1 #bjc ,grant1 ,k]r1 #bei ,grantia1 #dde ,graphic /atics1 #fhb ,gravitation1 #ab1 #cb ,gray1 ,j41 #ahh ,gre5hill1 ,sir ,a4 ,g41 #ai ,gregory1 ,d4 ,f41 #ccj1 #fge ,greville1 ,r4 ,k41 #chf ,gromia1 #bcd1 #beg ,grub]1 ,a41 #afe ,gryphaea1 #edf1 #egf1 #egg ,gu>d-cells1 #cid ,gud]nats*1 ,j4 ,f41 #acf ,guillemot1 egg (1 #feb ,gulliv]1 ,g41 #cf ,gn!r1 ,f4 ,c41 #fcc1 #fed ,gurwits*1 ,a41 #bhe ,hck]1 ,v41 #deh ,haddock1 #ggd ,haeckel1 ,e41 #aii1 #dde1 #ded1 #dee1 #deg1 #dfg1 #dhj1 #dha ,hair1 pigm5tation (1 #dcj ,hales1 ,/eph51 #cf1 #ei1 #ie1 #ffi ,haliotis1 #ead1 #ebg1 #edf1 #edg1 #eed1 #eee1 #eeg1 #efa ,hall1 ,c4 ,e41 #aai ,hall]1 ,a4 von1 #b1 #ed1 #ef1 #ei1 #fd1 #fh ,h>de/y1 ,irv+1 #cg ,h>dy1 ,w4 ,b41 #afj1 #afb1 #agb1 #ahg1 #bhg ,h>l1 ,n41 #bh ,h>mozones1 #ace ,h>pa1 #ebf1 #ebh1 #eei ,h>p]1 ,r4 ,a41 #bhc ,h>p9ia1 #gdf ,h>t+1 ,p41 #bhb1 #dbj1 #dbf1 #dcd ,h>tog1 ,m41 #afc1 #cbg ,h>vey1 ,e4 ,n4 & ,h4 ,w41 #ahg ,hatai1 ,s41 #acb1 #ace ,hat*ett1 ,c41 #dbj ,hats*ek1 ,b41 #ahj ,haughton1 ,rev4 ,s41 #ccd1 #fff ,hay1 ,r4 ,j41 #gbj ,hay1 ,o4 ,p41 #gjg ,haycraft1 ,j4 ,b41 #baa1 #fij ,head1 l5g? (1 #ic ,he>t1 gr[? (1 #hi2 muscles (1 #dij ,hea?1 ,sir ,t41 #eaa ,hegel1 ,g4 ,w4 ,f41 #d ,hegl]1 #fhj1 #fhh ,heid5ha91 ,m41 #agj1 #bab ,heilmann1 ,g]h>d1 #geg1 #gfh1 #ggb ,helicoid1 #bcj2 cyme1 #ejb1 #fje ,helicomet]1 #ebi ,helico/yla1 #eeg ,heliolites1 #cbf ,heliozoa1 #bfd1 #dfj ,helix1 #ebh1 #eeg ,helmholtz1 ,h4 von1 #b1 #i1 #be ,h5d]son1 ,w4 ,p41 #cbc ,h5sl[1 ,g41 #fcf ,h]$ity1 #aeh1 #bhf1 #gae ,h]mann1 ,f41 #agj ,h]o ( ,alex&ria1 #eji ,h]on-,all51 ,e41 #beg1 #dae1 #dfe ,h]petomonas1 #bfh ,h]twig1 ,o41 #ef1 #aad1 #aec1 #aii1 #caj2 ,r41 #agj1 #bhe ,h]tzog1 ,r4 ,o41 #aji ,hess1 ,w41 #fff1 #ffh ,het]onym\s horns1 #fai ,het]ophyllia1 #chh ,hexact9ellids1 #dbi1 #deb1 #dec ,hexagonal symmetry1 #cai1 #cbc1 #dga1 #eac ,hickson1 ,s4 ,j41 #dbd ,hippopus1 #efa ,81 ,w41 #ee1 #ef1 #gd1 #ge ,hobbes1 ,?omas1 #aei ,hb]1 ,r41 #a1 #abf1 #acj1 #agb ,hodograph1 #eaf ,h(fmann1 ,c41 #fbh ,h(mei/]1 ,f41 #da2 ,w41 #hg1 #baj1 #bcd1 #cjd1 #cjf1 #fcf1 #fci ,holl&1 ,w4 ,j41 #gjg ,holmes1 ,o4 ,w41 #fb1 #gcg ,holo?uroid spicules1 #ddj1 #dea ,homonym\s horns1 #fai ,homoplasy1 #bea ,hooke1 ,rob]t1 #bje ,hop1 gr[? (1 #aah2 /em (1 #fbg ,horace1 #dd ,hormones1 #ace ,horns1 #fab ,horse1 #fid1 #gja1 #gjc1 #gfd ,h\ssay1 ,f41 #ba ,hub]1 ,p41 #ccb ,huia bird1 #fcc ,humboldt1 ,a4 von1 #abg ,hume1 ,david1 #f ,hunt]1 ,john1 #ffg1 #ffi1 #gac1 #gae ,huxley1 ,t4 ,h41 #dbc1 #gbb1 #geb ,hyac9?1 #cbb1 #cid ,hyalaea1 #ega-egg ,hyalonema1 #ddb ,hyatt1 ,a41 #edh ,hyde1 ,ida ,h41 #abe1 #afc1 #ahd1 #ahh ,hydra1 #beb2 egg (1 #afd ,hydract9ia1 #cdb ,hydraulics1 #ffi ,hydro*>is1 #bcd ,hyp]ia1 #gdf ,hyra*yus1 #gfj1 #gfe ,hyraco!rium1 #gff1 #gfh ,ibex1 #fag ,ice1 /ructure (1 #dbh ,i*?yosaurus1 #gee ,icosah$ron1 #dgh ,iguanodon1 #gjf1 #gjh ,ina*us1 sp]m-cells (1 #bgc ,infusoria1 #bdf1 #dhi ,intussusception1 #bjb ,inul91 #dcb ,invag9ation1 #ef1 #cdd ,iod9e1 #acf ,irv9e1 ,rob]t1 #dad1 #dcd ,isoc>dia1 #efa1 #egg ,isop]imetrical problems1 #bjh1 #cdf ,isotonic solutions1 #acj1 #bgd ,it]son1 ,g4 van1 #eie ,jackson1 ,c4 ,m41 #ge1 #hh1 #ajf ,jam91 ,j4 ,c41 #dah ,janet1 ,paul1 #e1 #ah1 #fgc ,japp1 ,f4 ,r41 #dag ,jellett1 ,j4 ,h41 #a ,j5k91 ,c4 ,f41 #ddd ,j5k9son1 ,j4 ,w41 #id1 #aad1 #agj ,j5n+s1 ,h4 ,s41 #bab1 #dib2 ,vaughan1 #dbd ,j5s51 ,p41 #baa ,johnson1 ,dr ,s41 #fb ,joly1 ,john1 #i1 #fc ,jo/1 ,l41 #aaj1 #aaa ,juncus1 pi? (1 #cce ,jung]mannia1 #djd ,kang>oo1 #gje1 #gjf1 #gji ,kanitz1 ,al41 #aji ,kant1 ,immanuel1 #a1 #c1 #gad ,kapp]s1 ,c4 ,u4 ,a41 #eff ,kellicott1 ,w4 ,e41 #ia ,kelv91 ,"l1 #i1 #di1 #ahh1 #bjb1 #ccf1 #dec ,kepl]1 #cbh1 #dhj1 #dhf1 #fdc1 #fej ,ki5itz-,g]l(f1 ,f41 #djd1 #djh ,kirby & ,sp5ce1 #bh1 #cj1 #abg ,kir*n]1 ,a41 #fhc ,kirkpatrick1 ,r41 #dcg ,klebs1 ,g41 #cjf ,kny1 ,l41 #fhj ,ko*1 ,g4 von1 #dbc ,ko5ig1 ,samuel1 #ccj ,k(oid1 ,c4 ,a41 #bfh ,kllik]1 ,a4 von1 #dac ,kollmann1 ,m41 #agj ,koltz(f1 ,n4 ,k41 #bgc1 #dfb ,kon9ck9a1 #egj ,koodoo1 horns (1 #fbd ,kpp51 ,wladimir1 #aaa ,korotneff1 ,a41 #cgg ,kraus1 ,g41 #gg ,krogh1 ,a41 #aji ,krohl1 #fff ,khne1 ,w41 #bce ,k/]1 ,e41 #dcj ,lafresnaye1 ,f4 de1 #fec ,lag5a1 #bea1 #bef1 #bfj1 #ehg ,lagrange1 ,j4 ,l41 #fdi ,lalanne1 ,l41 #ccd ,lam>ck1 ,j4 ,b4 de1 #edi1 #gaf ,lamb1 ,a4 ,b41 #ahf ,lamell>ia1 #eed ,lamellibran*s1 #efa ,lami1 ,b41 #bif1 #fdc ,lam9>ia1 #cae ,lammel1 ,r41 #ajj ,lan*e/]1 ,f4 ,w41 #bf ,lang1 ,arnold1 #efa ,lanke/]1 ,sir ,e4 ,ray1 #d1 #bea1 #cdh1 #dfe ,laplace1 ,p4 ,s4 de1 #a1 #bjg1 #bag ,l>mor1 ,sir ,j41 #i1 #bei ,lavat]1 ,j4 ,c41 #gdj ,law1 ,borelli's1 #bi2 ,br&t's1 #dhb2 ( ,con/ant ,angle1 #eii2 ,err]a's1 #bac1 #cjf2 ,fr\de's1 #bb2 ,lam>le's1 #cji2 ( ,mass1 #acj2 ,maup]tuis's1 #bjh2 ,mll]'s1 #dha2 ( ,optimum1 #aaj2 van't ,h(f's1 #aji2 ,will>d-,gibbs'1 #bhj2 ,wolff's1 #c1 #ea1 #aee ,leap+1 #bi ,leaves1 arrangem5t (1 #fce2 =m (1 #gca ,l$+ham1 ,j4 ,c4 ,g41 #baa ,l$uc1 ,/phane1 #afb1 #afg1 #ahe1 #bai1 #bei1 #dae1 #dbh1 #dca1 #eij ,leeuw5hoek1 ,a4 van1 #cf1 #bji ,leg]1 ,l41 #deb ,le ,hello1 ,p41 #cj ,lehmann1 ,o41 #bjc1 #bgb1 #ddj1 #dhe1 #eij ,leibniz1 ,g4 ,w4 von1 #c1 #e1 #aei1 #che ,leid5fro/1 ,j4 ,g41 #bgi ,leidy1 ,j41 #beb1 #dfh ,leip]1 ,r4 ,t41 #ffj ,leit*1 ,i41 #aab ,leitgeb1 ,h41 #cje ,l5g?-weight coeffici5t1 #ih-ajc1 #gge ,leon>do da ,v9ci1 #bg1 #fce2 ( ,pisa1 #fdc ,lepes*k91 #fbe ,leptocephalus1 #hg ,l]ay1 ,ad41 #ah ,lesage1 ,g4 ,l41 #ah ,leslie1 ,sir ,john1 #afc1 #ejc ,le/ib\dois1 ,t41 #fcf ,leucocytes1 #baa ,lev]s1 ,ord]s (1 #fij ,levi1 ,g41 #ce1 #cg ,lewis1 ,c4 ,m41 #bhj ,lhuili]1 ,s4 ,a4 ,j41 #ccj ,liesegang's r+s1 #dbg1 #dge ,light1 pressure (1 #dh ,lillie1 ,f4 ,r41 #d1 #adg1 #cda2 ,r4 ,s41 #ahj1 #ahg1 #aib ,lima1 #efe ,limac9a1 #ega ,l9es ( =ce1 #afc2 ( gr[?1 #efb ,l+ula1 #bea1 #efg ,l9naeus1 #bh1 #bej1 #edg1 #gbj ,lion1 bra9 (1 #ia ,liquid ve9s1 #bfe ,li/]1 ,m>t91 #cah2 ,j4 ,j41 #dcf ,li/+1 ,j4 ,b41 #che ,li?o/rotion1 #cbe ,littor9a1 #ebd ,lituites1 #edf1 #eej ,llama1 #gjc ,lob/]s' claws1 #adi ,locke1 ,john1 #f ,loeb1 ,j41 #abe1 #acb1 #ace1 #acf1 #adg1 #aeg1 #aia1 #aic ,loewy1 ,a41 #bha ,log>i?mic spiral1 #dic1 etc4 ,loisel1 ,g41 #hh ,loligo1 %ell (1 #ege ,lo ,monaco1 #hc ,lnnb]g1 ,e41 #fad1 #fcb ,looss1 ,a41 #ffj ,lotze1 ,r4 ,h41 #ee ,love1 ,a4 ,e4 ,h41 #fgd ,lucas1 ,f4 ,a41 #ach ,luciani1 ,l41 #hc ,lucretius1 #dg1 #ga1 #acg1 #afj ,ludwig1 ,c>l1 #b2 ,f41 #fdc2 ,h4 ,j41 #cdb ,lupa1 #gdd ,lup9us1 gr[? (1 #aji1 #aab ,macali/]1 ,a41 #eeg ,mac,alister1 ,sir ,d41 #fgc1 #fhc ,macallum1 ,a4 ,b41 #bgg1 #bhg1 #ceg1 #cie2 ,j4 ,b41 #dib ,mc,coy1 ,f41 #chh ,ma*1 ,ern/1 #bji1 #ccj ,ma*a]odus1 tee? (1 #fcc ,mc,kendrick1 ,j4 ,g41 #db ,mc,kenzie1 ,a41 #dah ,mack9non1 ,d4 ,l41 #bfh ,maclaur91 ,col91 #ccj1 #ggi ,macroscaphites1 #eej ,mactra1 #efb ,magnitude1 #af ,maill>d1 ,l41 #afc ,maize1 gr[? (1 #aji1 #aaa1 #bih ,mall1 ,f4 ,p41 #dib ,maltaux1 ,mlle1 #aad ,mammo?1 #fcd1 #gje ,man1 gr[? (1 #fa2 skull (1 #ggj ,m>aldi1 ,j4 ,p41 #cbi1 #dgc ,m>bl$ pap]s1 #gcf ,m>cus ,aurelius1 #fji ,m>khor1 horns (1 #fai ,m>%1 ,o4 ,c41 #gjf1 #ged ,m>sigli1 ,comte ,l4 ,f4 de1 #feb ,mass>t1 ,j41 #aad ,ma/odon1 #fcd ,ma!matics1 #gai1 #ggh1 etc4 ,ma!ws1 ,a41 #bhe ,matrix1 #fef ,matt] & en]gy1 #aa ,mat!w1 ,w4 ,d41 #gjg ,matuta1 #gdd ,maupas1 ,m41 #acc ,maup]tuis1 #c1 #e1 #bjh ,maxwell1 ,j4 ,cl]k1 #i1 #ah1 #dj1 #dd1 #afj1 #bjg1 #che1 #fia ,me*anical effici5cy1 #fgj ,me*anism1 #e1 #afa1 #ahe1 etc4 ,meek1 ,c4 ,f4 ,u41 #aij ,melan*?on1 #d ,melanopsis1 #eeg ,meldola1 ,r41 #fgj ,melipona1 #ccb ,mellor1 ,j4 ,w41 #acd ,melo1 #ebe ,melobesia1 #dab ,mels5s1 ,l4 ,h4 ,f41 #bhb ,membrane-=mation1 #bha ,m5sbrugghe1 ,g4 van d]1 #bab1 #bih1 #dgj ,mes]]1 ,o41 #fhc ,mesoc>pus1 #bhi ,mesohippus1 #gff ,metamorphosis1 #hb ,meves1 ,f41 #afc1 #bhe ,mey]1 ,ar?ur1 #dcb2 ,g4 ,h41 #h1 #fhb1 #fhc ,micellae1 #aeg ,mi*aelis1 ,l41 #bgg ,micro*emi/ry1 #bhh ,micrococci1 #ci1 #bde1 #bej ,micromonas1 #ch ,miliolidae1 #eie1 #fjd ,miln]1 ,r4 ,s41 #bhj ,milton1 ,john1 #ggi ,mimicry1 #fga ,m9*91 ,e4 ,a41 #bfg1 #ddd1 #ddi1 #dee ,m9imal areas1 #bjh1 #bae1 #bbe1 #bic1 #cjf1 #ccf1 #cdi ,m9ot1 ,c4 ,s41 #cg1 #gb1 #gbb ,miohippus1 #gfg ,mit*ell1 ,p4 ,*alm]s1 #gjc ,mitosis1 #agj ,mitra1 #eeg1 #eei ,mbius1 ,k41 #ddi ,modiola1 #efb ,mohl1 ,h4 von1 #fbd ,mol> & molecul> =ces1 #ec ,mole-cricket1 *romosomes (1 #aha ,molecul> asymmetry1 #daf ,molecules1 #da ,mll]1 ,v4 von1 #eic ,monni]1 ,a41 #gh1 #acb ,monticulipora1 #cbf ,moore1 ,b41 #bgb ,morey1 ,s41 #bfd ,morgan1 ,t4 ,h41 #abf1 #acd1 #ach1 #adg ,morita1 #fii ,morphodynamique1 #aef ,morphologie syn?tique1 #dbj ,morphology1 #gai1 etc4 ,morse1 ,max1 #acf ,moseley1 ,h41 #h1 #eah1 #eba1 #ech1 #eec1 #eee1 #eib ,moss1 embryo (1 #cgd2 gemma (1 #djc2 rhizoids (1 #cef ,m\ill>d1 ,l4 ,p41 #bg ,m\se1 gr[? (1 #hb ,mucor1 sporangium (1 #cjc ,mll5h(1 ,k4 von1 #be1 #ccb ,mll]1 ,fritz1 #c2 ,johannes1 #dei1 #dha ,mumm]y1 ,j4 ,h41 #dbe ,munro1 ,h41 #cbc ,musk-ox1 horns (1 #fae ,mya1 #dbb1 #efa ,myonemes1 #efb ,nab]1 ,h4 ,a41 #eaa1 #fej ,ngeli1 ,c41 #abd1 #aei1 #baj ,nassell>ia1 #dgb ,natica1 #eed1 #eeg1 #eei ,natural selection1 #d1 #eh1 #acg1 #def1 #ehf1 #fji1 #fea1 #fec ,naumann1 ,c4 ,f41 #ebi1 #eca1 #eci1 #eej1 #egg1 #eid1 #fcf2 ,j4 ,f41 #fec ,nautilus1 #cee1 #did1 #eja1 #eae1 #eah1 #ecb1 #ece1 #edf1 #eeb1 #eeg1 #ege1 #egg1 #ehj1 #eib1 #fcc2 hood (1 #eed2 kidney (1 #dbe2 ,n4 umbilicatus1 #edb1 #edg1 #eed ,neb5k]n1 #bhe ,neottia1 poll5 (1 #cif ,n]eis1 egg (1 #cdb1 #cgh1 #dec ,n]ita1 #ebb1 #eee ,neumayr1 ,m41 #fjh ,neutral zone1 #fgd1 #fgf1 #fhf ,newton1 #a1 #f1 #aeh1 #fdc1 #gba ,ni*olson1 ,h4 ,a41 #cbe1 #cbg ,noctiluca1 #bdf ,nodoid1 #bah1 #bbc ,nodos>ia1 #bfb1 #ece1 #fjd ,norman1 ,a4 ,m41 #dfe ,norris1 ,ri*>d1 #bgb ,no/oc1 #cjj1 #cac ,notosu*us1 #gec ,nucle> sp9dle1 #agj2 /ructure1 #aff ,nummulites1 #ejd1 #eeb1 #eia ,nussbaum1 ,m41 #aih ,oekotrau/es1 #eej ,ogilvie-,gordon1 ,m4 ,m41 #dbc ,oil-globules1 ,plateau's1 #bai ,oi?ona1 #gdb ,ok51 ,l41 #d1 #fce ,oliva1 #eed ,ootype1 #ffj ,op]cul9a1 #eid ,op]culum ( ga/ropods1 #eba ,oppel1 ,a41 #hh ,optimum temp]ature1 #aaj ,orbitolites1 #fje ,orbul9a1 #ei1 #bbe1 #beg1 #ehg1 #eih1 #fjd1 #fjg ,organs1 gr[? (1 #hh ,or?agoriscus1 #gea1 #gge1 #ggg ,or?is1 #efa1 #efg ,or?oc]as1 #eae1 #edh1 #eea1 #eef1 #egi1 #gce ,or?og5esis1 #edi ,or?ogonal trajectories1 #cje1 #cgg1 #djj1 #fdj1 #fgh ,or?o/i*ies1 #fdi ,or?otoluid5e1 #bai ,oryx1 horns (1 #faf ,osborn1 ,h4 ,f41 #gad1 #gbg1 #gfj ,oscillatoria1 #cjj ,osmosis1 #abd1 #bhg1 etc4 ,osmunda1 #cif1 #djf ,o/rea1 #efb ,o/ri*1 #be1 #gjg1 #gjh ,o/wald1 ,wilhelm1 #dd1 #aca1 #dbf2 ,wolfgang1 #cb1 #gg1 #hb1 #acb1 #bgg1 #bha ,otoli?s1 #dbe1 #dcb ,ovis ,ammon1 #fad ,ow51 ,sir ,r41 #bj1 #ege1 #fed1 #ffi1 #gae ,ox1 cannon-bone (1 #gcj1 #gch2 gr[? (1 #ajb ,oxalate1 calcium1 #dab1 #dcd ,palaee*9us1 #ffc ,palm1 #fbd ,p&]1 ,c4 ,h41 #ee ,pang5esis1 #dd1 #aeg ,papillon1 ,f]n&1 #aj ,pappus ( ,alex&ria1 #cbh ,p>abolic gird]1 #fic1 #fif ,p>ahippus1 #gfg ,p>alomis1 #gdd ,p>aphyses ( mosses1 #cea ,p>a/i*ies1 #fdj1 #fda ,passiflora1 poll5 (1 #cif ,pa/eur1 ,l41 #daf ,patella1 #efa ,pauli1 ,w41 #baa1 #dcd ,pe>l1 ,raymond1 #ij1 #ig1 #fed ,pe>ls1 #dbe1 #dca ,pe>son1 ,k>l1 #cf1 #gh ,peas1 gr[? (1 #aab ,pect51 #efb ,p$die1 ,w41 #ahb1 #bgb1 #cdd1 #ddh ,pellia1 spore (1 #cjb ,pels5e]1 ,p41 #egj ,p5dulum1 #cj ,p5]oplis1 #fjf ,p]c5tage-curves1 ,m9ot's1 #gb ,p]icl9e1 #cfj ,p]iploca1 poll5 (1 #cif ,p]i/ome1 #bci ,p]meability1 magnetic1 #agg1 #ahb ,p]r91 ,j41 #dc1 #df ,pet]1 ,k>l1 #aag ,pettigrew1 ,j4 ,b41 #dij ,pfeff]1 ,w41 #aaa1 #bgc1 #fhh ,pflg]1 ,e41 #fhj ,phagocytosis1 #baa ,phascum1 #djh ,phase ( curve1 #fh1 #ha1 etc4 ,phasianella1 #eeg1 #eei ,phatnaspis1 #dhb ,phillipsa/raea1 #cbg ,philolaus1 #ggi ,pholas1 #efa ,phormosoma1 #ffd ,phractaspis1 #dhd ,phyllotaxis1 #fce ,phylog5y1 #aif1 #bea1 #edh1 #gaf ,pike1 ,f4 ,h41 #aaj ,pileopsis1 #eee ,p9acoc]as1 #ehd ,pi!can?ropus1 #ggb ,pi? ( ru%1 #cce ,plaice1 #ih1 #aje1 #aag1 #dcb1 #gaj1 #ggd ,planorbis1 #eci1 #edg1 #eed1 #eeg1 #eei ,plateau1 ,f41 #cj1 #bcb2 ,j4 ,a4 ,f41 #aib1 #bab1 #bah1 #bci1 #bge1 #big1 #cgd1 #dgg ,plato1 #b1 #dgh1 #gbj2 ,platonic bodies1 #dgh ,plesiosaurs1 #gee ,pleuroc>pus1 #bhi ,pleuropus1 #egc ,pleurotom>ia1 #eeg ,plumul>iidae1 #gdg ,pluteus l>va1 #cib1 #dae ,podocoryne1 #cdb ,po9c>1 ,h41 #acd ,poiseuille1 ,j4 ,l4 ,m41 #ffi ,pol> bodies1 #agi2 furr[1 #caj1 #cdj ,pol>is$ light1 #dah ,pol>ity1 morphological1 #aff1 #afh1 #bdf1 #bie1 #bhd ,poll51 #cif1 #cii ,polyhalite1 #dcc ,polyprion1 #gdi1 #ggf ,polysp]my1 #aic ,polytri*um1 #cee ,pomacan?us1 #gdi ,pop(f1 ,m41 #bhf ,potamides1 #eed ,potassium1 9 liv+ cells1 #bhh ,pot5tial en]gy1 #bjh1 #bid1 #fja1 etc4 ,pott]'s :eel1 #bch ,potts1 ,r41 #abf ,p\*et1 ,g41 #dae ,p\lton1 ,e4 ,b41 #fgj ,poynt+1 ,j4 ,h41 #bce ,precoci\s segregation1 #cdh ,pre=mation1 #ed1 #aei ,pr5ant1 ,a41 #afc1 #ajd1 #ahi1 #bhf1 #bhi ,prvo/1 ,pi]re1 #ah ,pr+%eim1 ,n41 #cgg ,probabilities1 !ory (1 #fa ,productus1 #efg ,protective col\ration1 #fga ,protococcus1 #ei1 #cjj1 #daj ,protocon*1 #eca ,protohippus1 #gfg ,protoplasm1 /ructure (1 #agb ,przibram1 ,hans1 #af1 #hb1 #ajg1 #adi1 #bjd1 #baa1 #dah1 #eie2 ,k>l1 #df ,psammobia1 #efd ,pseuopriacau?us1 #gdi ,pt]anodon1 #gef ,pt]is1 an!ridia (1 #dji ,pt]opods (1 #beh1 #egj ,pulv9ul9a1 #ead1 #eie1 #fjj1 #fjb ,pupa1 #ecj1 #edi1 #eef ,ptt]1 ,a41 #aaj1 #baa1 #dib ,pyrosoma1 egg (1 #cgg ,py?agoras1 #b1 #eji1 #fea1 #gbj1 #ggi ,quadrant1 bisection (1 #cei ,quekett1 ,j4 ,t41 #dbc ,quetelet1 ,a41 #fa1 #gh1 #ic ,qu9cke1 ,g4 ,h41 #ahg1 #aia1 #bgi1 #dba ,rabbit1 skull (1 #gfd ,rabl1 ,k41 #cf1 #caj ,radial co-ord9ates1 #gcj ,radiol>ia1 #beb1 #bfd1 #deg1 #dfg1 #ehh1 #fjg ,ra9ey1 ,george1 #g1 #dbj1 #dca1 #dcd ,ra9fall & gr[?1 #aba ,ram1 horns (1 #fac-fbd ,ramsd51 ,w41 #bhb ,ramul9a1 #bee ,rank9e1 ,w4 ,j4 ,macquorn1 #fig1 #gab ,ransom's waves1 #afd ,raphides1 #dab1 #dbi1 #dcd ,raphidiophrys1 #dfj1 #dfc ,rasum[sky1 #fhc ,rat1 gr[? (1 #ajf ,ra?1 ,o4 vom1 #aha ,raub]1 ,a41 #bjj1 #cje1 #caj1 #chj1 #chb1 #cih1 #fgg1 #fhc ,ray1 ,john1 #c ,rayleigh1 ,"l1 #dc1 #dd ,raumur1 ,r4 ,a4 de1 #h1 #ajh1 #cbi ,reciprocal diagrams1 #fig ,rees1 ,r4 van1 #cgd ,reg5]ation1 #ach ,reid1 ,e4 ,waym\?1 #bgb ,re9ecke1 ,j4 ,c4 ,m41 #ebh ,re9ke1 ,j41 #cjc1 #cje1 #cee1 #cef ,r5i=m %ape1 #gce ,reticul>ia1 #efi ,reticulat$ patt]ns1 #beh ,rticulum plasmatique1 #dfh ,rhabdamm9a1 #ehi ,rheophax1 #bfc ,rh9oc]os1 #fab1 #gfj ,rhumbl]1 ,l41 #afb1 #afe1 #bfj1 #cbb1 #cdd1 #dfe1 #dff1 #ehi1 #eij1 #eie1 #eii1 #fjh1 #fbh ,rhyn*onella1 #efa ,riccia1 #cgb1 #djc1 #dje ,rice1 ,j41 #bdb1 #bgc ,ri*>dson1 ,g4 ,m41 #daf ,rief/ahl1 ,e41 #egh ,riemann1 ,b41 #che ,ripples1 #cc1 #bfa1 #cbc ,rivul>ia1 #cjj ,roaf1 ,h4 ,c41 #bgb ,rob]t1 ,a41 #cjf1 #cci1 #cdh1 #cgg ,rob]ts1 ,c41 #fa ,rob]tson1 ,t4 ,b41 #hb1 #acb1 #aia1 #aib ,rob9son1 ,a41 #fha ,rrig1 ,a41 #fbh ,rose1 ,gu/av1 #dba ,rossba*1 ,m4 ,j41 #afe ,rotalia1 #bad1 #ece1 #fjb ,rotif]a1 cells (1 #ch ,r\lettes1 #bah ,r\x1 ,w41 #h1 #ee1 #eg1 #aeg1 #aid1 #cgh1 #chc1 #fff1 #fhc ,rul$ surfaces1 #bcj1 #bgj1 #ehb ,rusk91 ,john1 #bj ,russ[1 ----1 #gc1 #ge ,ryd]1 ,j4 ,a41 #cgf ,sa*s1 ,j41 #ce1 #ch1 #ie1 #ajh1 #aaj1 #aaa1 #bjj1 #cfj1 #cih1 #cii1 #fbd1 #fce1 #fdj1 #fea1 #fhj ,sa*s's rule1 #big1 #cjj1 #cje1 #cdg1 #cgf ,saddles1 ( ammonites1 #ehc ,sagr9a1 #bfc ,/ ,v5ant1 ,b>r de1 #fba1 #fbg ,salam&]1 sp]m-cells (1 #agi ,salp+oeca1 #bdh ,salt1 cry/als (1 #dbi ,salv9ia1 #cgg ,samec1 ,m41 #dcd ,samt]1 ,m4 & ,heymons1 #acj ,s&b]g]1 ,g41 #eci ,sapphir9a1 #gdb ,saville ,k5t1 ,w41 #bdf1 #bdg1 #bdh ,scal>ia1 #ebf1 #edg1 #eed1 #eeg1 #eei ,scale1 effect (1 #ag1 #dch ,scaphites1 #eej ,scapula1 human1 #gfi ,sc>us1 #gdi ,s*acko1 ,g41 #fjd ,s*ap]1 ,a4 ,a41 #hc ,s*aud9n1 ,f41 #df1 #bhf ,s*e]5umkehr1 #adi ,s*ewiak(f1 ,w41 #ahi1 #dfb ,s*imp]1 ,c4 ,f41 #ejb1 #fcf ,s*maltz1 ,a41 #fge ,s*mankewits*1 ,w41 #acj ,s*midt1 ,johann1 #he1 #hg1 #aah ,s*nflies1 ,a41 #bjb ,s*ultze1 ,f4 ,e41 #deb1 #ded ,s*walbe1 ,g41 #fff ,s*wann1 ,!odor1 #aii1 #chj1 #eia ,s*w>tz1 ,fr41 #agb ,s*w5d5]1 ,s41 #baj1 #cje1 #fcf1 #fgh ,scorpa5a1 #gdi ,scorpioid cyme1 #ejb ,scott1 ,e4 ,l41 #aaj2 ,w4 ,b41 #gfh ,scyroma?ia1 #gdd ,se>le1 ,h41 #dia ,sea ur*9s1 #ffa2 egg (1 #agc2 gr[? (1 #aag1 #adg ,seba/es1 #gdi ,sectio aurea1 #eaa1 #fdc1 #fdi ,s$gwick1 ,a41 #aig1 #aii ,sdillot1 ,*>les ,e41 #fhh ,segm5tation ( egg1 #eg1 #caj1 #cdd1 #chb1 etc42 spiral d41 #cga1 #dec ,segn]1 ,j4 ,a4 von1 #bje ,selag9ella1 #djd ,semi-p]meable membranes1 #bgb ,sepia1 #ege1 #egg ,septa1 #egg1 #eib ,s]pula1 #fjc ,sexual *>act]s1 #ace ,%>pe1 ,d41 #gbh ,%e>+ /ress1 #fhd1 #gcj1 etc4 ,%eep1 #fac1 #gcj1 #gch ,%ell1 =mation (1 #dbb ,sig>etus1 #eed ,silkworm1 gr[? (1 #hc ,similitude1 pr9ciple (1 #ag ,sims ,woodhead1 ,g41 #dad1 #dcd ,siphonogorgia1 #dac ,skeleton1 #ai1 #dch1 #fge1 #fia1 etc4 ,sn[ cry/als1 #bej1 #dhj1 #faa ,soap-bubbles1 #dc1 #bai1 #bii1 #cjg1 etc4 ,socrates1 #h ,sohncke1 ,l4 ,a41 #bjb ,solanum1 #fbe ,sol>ium1 #edg1 #eed1 #eeg1 #eei ,solecurtus1 #efd ,sol51 #efe ,sollas1 ,w4 ,j41 #ddj1 #dej1 #dee ,solubility ( salts1 #dcd ,sorby1 ,h4 ,c41 #dab1 #dad1 #gbh ,spallanzani1 ,l41 #ach ,span ( arms1 #fc1 #ic ,spang5b]g1 ,fr41 #cdb ,specific *>act]s1 #bdf1 #chj2 inductive capacity1 #agg2 surface1 #cb1 #bae ,sp5c]1 ,h]b]t1 #ah1 #bb ,sp]matozoon1 pa? (1 #aic ,sp]m-cells ( ,cru/acea1 #bgc ,sphacel>ia1 #cea ,spha]e*9us1 #aag1 #adg ,sphagnum1 #djb1 #djg ,sph]e1 #bah1 #bbe ,sph]ocry/als1 #dcd ,sph]ulites1 #dbb ,spicules1 #bhb1 #daa1 etc4 ,spid]'s web1 #bca ,sp9dle1 nucle>1 #afi1 #agd ,sp9n+ ( protoplasm1 #afd ,spiral1 geodetic1 #dhh2 log>i?mic1 #dic1 etc42 segm5tation1 #cga1 #dec ,spireme1 #agc1 #ahj ,spirif]1 #efa1 #efh ,spirillum1 #df1 #bec ,spiro*aetes1 #df1 #bcj1 #bff ,spirographis1 #ehf ,spirogyra1 #ab1 #bba1 #bbg1 #bdb1 #bdd1 #bge1 #bhg1 #bhi ,spirorbis1 #ehf1 #fjc ,spirula1 #ebh1 #edg1 #eed1 #ege1 #egg ,spitzka1 ,e4 ,a41 #ib ,spla%es1 #bce1 #bcf1 #bed1 #bfj ,sponge-spicules1 #dcf1 #ddj ,spontane\s g5]ation1 #dbj ,sporangium1 #djf ,spottiswoode1 ,w41 #ggi ,spray1 #bcf ,/allo1 ,j4 ,b41 #a ,/&>d deviation1 #gh ,/>*1 #dcb ,/>l+1 ,e4 ,h41 #ace ,/assfurt salt1 #dcc ,/egocephalus1 #gdf ,/egosaurus1 #gjf1 #gjg1 #gaj1 #ged ,/e9]1 ,jacob1 #fed ,/e9mann1 ,g41 #dca ,/ellate cells1 #cce ,/5tor1 #adg ,/]eometry1 #dag ,/]noptyx1 #gdh ,/illmann1 ,j4 ,d4 ,b41 #fie ,/ ,l\p1 ,r41 #hb ,/okes1 ,sir ,g4 ,g41 #dd ,/olc1 ,ant41 #deb ,/oma*1 muscles (1 #dij ,/omata1 #cic ,/omatella1 #eed ,/rasbrg]1 ,e41 #ce1 #bhc1 #dji ,/raus-,drckheim1 ,h4 ,e41 #cj ,/ream-l9es1 #bej1 #fgc1 #gcf ,/r5g? ( mat]ials1 #fgf1 #fgi ,/reptoplasma1 #cia ,/rophom5a1 #efg ,/ud]1 ,t41 #dac ,/yloni*ia1 #acc ,succ9ea1 #eef ,sunfl[]1 #did1 #fce1 #fci1 #fhh ,surface en]gy1 #cb1 #cd1 #aia1 #bjg1 #bgh1 #bic1 #dfj1 #eii ,survival ( species1 #bea ,sutures ( cephalopods1 #ehc ,swamm]dam1 ,j41 #h1 #hg1 #chj1 #ebh1 #ehe ,swezy1 ,olive1 #bfh ,sylve/]1 ,j4 ,j41 #gbc ,symmetry1 mean+ (1 #bji ,synapta1 egg (1 #dec ,syncytium1 #bjj ,synhelia1 #cbg ,szielasko1 ,a41 #fed ,tadpole1 gr[? (1 #hc1 #aad1 #ach1 #aec ,tait1 ,p4 ,g41 #ce1 #dc1 #bjg1 #fdd ,taonia1 #cee1 #cef ,tapetum1 #djg ,tapir1 #gda1 #gfc ,taylor1 ,w4 ,w41 #bgg1 #bhb1 #dbf1 #dbh ,tee?1 #dbd1 #fab1 #fcb ,telescopium1 #eeg ,telesius1 ,b]n>d9us1 #fef ,tell9a1 #efb ,temp]ature coeffici5t1 #aji ,t]ebra1 #ebi1 #eeg1 #eei ,t]ebratula1 #efh1 #egd1 #egf ,t]$o1 #dad ,t]ni1 ,t41 #ce ,t]quem1 ,o41 #cbi ,tes*1 ,j4 ,j41 #egc ,tetract9ellida1 #ddc1 #dej ,tetrah$ral symmetry1 #cae1 #cif1 #dgf ,tetrakaidecah$ron1 #ccg ,tetraspores1 #cif ,textul>ia1 #fjd ,?amna/raea1 #cbg ,?ay]1 ,j4 ,e41 #fgb ,!cidium1 #egj ,!cosmilia1 #cbe ,?el1 ,h41 #dea ,?i5emann1 ,f4 ,a4 ,l41 #fec ,?i/le1 capitulum (1 #fci ,?oma1 ,r41 #fff ,?omson1 ,james1 #ah1 #bei2 ,j4 ,a41 #dfe2 ,j4 ,j41 #bce1 #bhj2 ,wyville1 #dff ,?uramm9a1 #bef ,?yroid gl&1 #acf ,"t-elem5t1 #ea1 #dif1 etc42 "t-en]gy diagram1 #fc ,t9t9nus1 #bdh ,tissues1 =ms (1 #bic ,titano!rium1 #gjd1 #gfb ,tomi/oma1 #gec ,toml9son1 ,c41 #bei1 #dbh ,torni]1 ,g41 #gjg ,torsion1 #fba1 #fbd ,tra*elophyllum1 #bdi ,trans=mations1 !ory (1 #efb1 #gai ,traube1 ,m41 #bhg ,trees1 gr[? (1 #aai2 height (1 #ai ,trembley1 ,abraham1 #ach1 #adf ,treutle91 ,p41 #eaj ,trianea1 hairs (1 #bcd ,triangle1 prop]ties (1 #ejh2 ( =ces1 #bie ,tria/]s1 #cbg ,tri*od9a1 #beb ,tri*oma/ix1 #bfg ,triepel1 ,h41 #fhc1 #fhd ,trilocul9a1 #eie ,triton1 #eed ,tro*us1 #cgg1 #eeg1 #efj2 embryology (1 #cdj ,trndle1 ,a41 #fbe ,trophon1 #ebf ,tr\t1 gr[? (1 #id ,trypanosomes1 #bde1 #bff1 #bfi ,tubul>ia1 #abe1 #abf1 #adf ,turb9ate %ells1 #ecd ,turbo1 #eah1 #eee ,turgor1 #abe ,turn]1 ,sir ,w41 #gfi ,turritella1 #dhi1 #ebd1 #ebg1 #eee1 #eeg1 #eei ,tusks1 #eae1 #fab ,tutton1 ,a4 ,e4 ,h41 #bjb ,tw9+ plants1 #fbd ,tyndall1 ,john1 #dbh ,umbilicus ( %ell1 #edg ,und]fe$+1 effect (1 #ajf ,undulatory membrane1 #bff ,unduloid1 #bah1 #bbb1 #bbi1 #bdf1 #bef ,unio1 #cda ,univalve %ells1 #eec ,ure*9us1 #ffd ,vag9icola1 #bdh ,vallisn]i1 ,ant41 #ach ,van ,it]son1 ,g41 #eie ,van ,rees1 ,r41 #cgd ,van't ,h(f1 ,j4 ,h41 #a1 #aaj1 #dcc ,v>iability1 #gh1 #ajc ,v5ation ( w+s1 #che ,v]ha]51 ,emile1 #ggh ,v]worn1 ,m41 #aih1 #baa1 #dfg1 #fje ,vesque1 ,j41 #dab ,vi]ordt1 ,k41 #gc ,villi1 #cb ,v9c5t1 ,j4 ,h41 #cbc ,v9es1 ,s4 ,h41 #ejb ,vir*[1 ,r41 #bjj1 #bhf ,vital ph5om5a1 #ad1 #dag1 etc4 ,vitruvius1 #gdj ,volkmann1 ,a4 ,w41 #ffi ,voltaire1 #d1 #adf ,vorticella1 #bcg1 #bdf1 #bia ,wag]1 ,h4 ,w4 ,t41 #bei ,walk+1 #cj ,wallace1 ,a4 ,r41 #e1 #dcb1 #edi ,walli*-,m>tius1 #gg ,w>burg1 ,o41 #afa ,w>burton1 ,c41 #bcc ,w>d1 ,h4 ,m>%all1 #acc ,w>necke1 ,p41 #ic ,watase1 ,s41 #cgh ,wat]1 9 gr[?1 #abe ,watson1 ,f4 ,r41 #cbc ,web]1 ,e4 ,h41 #baj1 #bei1 #ffi2 ,e4 ,h4 & ,w4 ,e41 #cj2 ,max1 #ia ,weight1 curve (1 #fd1 etc4 ,weismann1 ,a41 #aeh ,w]n]1 ,a4 ,g41 #ai ,wett/e91 ,r4 von1 #gbh ,:ale1 aff9ities1 #gaf2 size1 #ba2 /ructure1 #gjh ,:ipple1 ,i4 ,l41 #abc ,:itman1 ,c4 ,o41 #aeg1 #afd1 #aic1 #aid1 #aii1 #bjj ,:itwor?1 ,w4 ,a41 #ejf1 #eab ,wi5]1 ,a4 ,f41 #de ,wildeman1 ,e4 de1 #cjg1 #cee ,willey1 ,a41 #dbe1 #edh1 #eee1 #egh ,williamson1 ,w4 ,c41 #dbc1 #fji ,willughby1 ,fr41 #cah ,wilson1 ,e4 ,b41 #aej1 #afc1 #agc1 #aie1 #aii1 #caa1 #cda1 #cdb1 #cih1 #dec ,w+e1 ,o41 #dcc ,w9t] eggs1 #bhc ,wissl]1 ,cl>k1 #gi ,wissn]1 ,j41 #fcf ,whl]1 ,fr41 #daf1 #dbj ,wolff1 ,j41 #fhc2 ,j4 ,c4 ,f41 #c1 #ea1 #aee ,wood1 ,r4 ,w41 #eij ,woods1 ,r4 ,h41 #fff ,woodw>d1 ,h41 #egh2 ,s4 ,p41 #eed1 #efg ,wor?+ton1 ,a4 ,m41 #bce1 #bed ,wreszne[ski1 ,a41 #bdi ,wright1 ,*auncey1 #cce ,wright1 ,t4 ,/re?ill1 #baj ,wyman1 ,jeffrey1 #cce ,yea/ cell1 #bac1 #bdb ,yield-po9t1 #fgi ,yolk ( egg1 #afe1 #ffj ,"y1 ,?omas1 #i1 #cf1 #ffi1 #fia ,zangg]1 ,h41 #bhb ,zeis+1 ,a41 #fcf1 #fej ,zel5y1 ,c41 #adi ,zeuglodon1 #gaf ,zeu!n1 ,h4 ,g41 #eaa ,zieh51 ,*41 #ib ,zittel1 ,k4 ,a4 von1 #cbe1 #cbg1 #edh1 #ehd ,zoogloea1 #bhb ,zs*okke1 ,f41 #fhc ,zsigmondy1 #ci ,zuelz]1 ,m41 #afe ,,cambridge3 ,,pr9t$ ,,by ,j4 ,b4 ,,peace1 ,m4,a41 ,,at ,,! ,,univ]sity ,,press #hji ,,selection ,,f ,,! ,,g5]al ,,catalogue ,,( ,,books ,,publi%$ ,,by ,,! ,,cambridge ,,univ]sity ,,press ,,gr[? ,,9 ,,l5g?3 ,,embryological ,,essays4 ,by ,,ri*>d ,,as%eton1 ,m4,a41 ,sc4,d41 ,f4,r4,s4 ,) #db illu/rations4 ,demy #hvo4 #bs #f;d net4 ,,exp]im5tal ,,zoology4 ,by ,,hans ,,przibram1 ,ph4,d4 ,"p ,i4 ,embryog5y1 an acc\nt ( ! laws gov]n+ ! developm5t ( ! animal egg z asc]ta9$ by exp]im5t4 ,) #af plates4 ,royal #hvo4 #gs #f;d net4 ,,zoology4 ,,an ,,elem5t>y ,,text-,,book4 ,by ,a4 ,e4 ,,%ipley1 ,sc4,d41 ,f4,r4,s41 & ,e4 ,w4 ,,macbride1 ,d4,sc41 ,f4,r4,s4 ,?ird edition1 enl>g$ & re-writt54 ,) #cfj illu/rations4 ,demy #hvo4 #abs #f;d net4 ,cambridge ,zoological ,s]ies4 ,,! ,,natural ,,hi/ory ,,( ,,"s ,,common ,,animals4 ,by ,,oswald ,h4 ,,latt]1 ,m4,a4 ,) #ed illu/rations4 ,cr[n #hvo4 #es net4 ,cambridge ,biological ,s]ies4 ,,! ,,orig9 ,,& ,,influ5ce ,,( ,,! ,,?or\ghbr$ ,,horse4 ,by ,w4 ,,ridgeway1 ,sc4,d41 ,litt4,d41 ,f4,b4,a41 ,disney ,pr(essor ( ,ar*ology & ,fell[ ( ,gonville & ,caius ,college4 ,) #adc illu/rations4 ,demy #hvo4 #abs #f;d net4 ,cambridge ,biological ,s]ies4 ,,! ,,v]tebrate ,,skeleton4 ,by ,s4 ,h4 ,,reynolds1 ,m4,a41 ,pr(essor ( ,geology 9 ! ,univ]sity ( ,bri/ol4 ,second edition4 ,demy #hvo4 #aes net4 ,cambridge ,zoological ,s]ies4 ,,outl9es ,,( ,,v]tebrate ,,pal,,ontology ,,= ,,/ud5ts ,,( ,,zoology4 ,by ,,ar?ur ,,smi? ,,woodw>d1 ,m4,a41 ,f4,r4,s4 ,) #bbh illu/rations4 ,demy #hvo4 #ads net4 ,cambridge ,biological ,s]ies4 ,,pal,,ontology--,,inv]tebrate4 ,by ,,h5ry ,,woods1 ,m4,a41 ,f4,g4,s4 ,f\r? edition4 ,) #aea illu/rations4 ,cr[n #hvo4 #fs net4 ,cambridge ,biological ,s]ies4 ,,morphology ,,& ,,an?ropology4 ,a ,h&book = ,/ud5ts4 ,by ,w4 ,l4 ,h4 ,,duckwor?1 ,m4,a41 ,m4,d41 ,sc4,d4 ,second edition4 ,volume ,i4 ,) #bjh illu/rations4 ,demy #hvo4 #ajs #f;d net4 ,,/udies ,,f ,,! ,,morphological ,,laboratory4 ,edit$ by ,,adam ,,s$gwick1 ,m4,a41 ,f4,r4,s4 ,royal #hvo4 ,vol4 ,,ii1 ,"p ,i4 #ajs net4 ,vol4 ,,ii1 ,"p ,,ii4 #gs #f;d net4 ,vol4 ,,iii1 ,p>ts ,i & ,,ii4 #gs #f;d net ea*4 ,vol4 ,,iv1 ,"p ,i4 #abs #f;d net4 ,vol4 ,,iv1 ,"p ,,ii4 #ajs net4 ,vol4 ,,iv1 ,"p ,,iii4 #es net4 ,vol4 ,v1 ,"p ,i4 #gs #f;d net4 ,vol4 ,v1 ,"p ,,ii4 #es net4 ,vol4 ,,vi4 #aes net4 ,,! ,,det]m9ation ,,( ,,sex4 ,by ,l4 ,,donca/]1 ,sc4,d41 ,fell[ ( ,k+'s ,college1 ,cambridge4 ,) #bc plates4 ,demy #hvo4 #gs #f;d net4 ,,conditions ,,( ,,life ,,9 ,,! ,,sea4 ,a %ort acc\nt ( ,quantitative ,m>9e ,biological ,rese>*4 ,by ,,james ,,john/one1 ,fi%]ies ,laboratory1 ,univ]sity ( ,liv]pool4 ,) *>t & #ca illu/rations4 ,demy #hvo4 #is net4 ,,m5del',s ,,pr9ciples ,,( ,,h]$ity4 ,by ,w4 ,,bateson1 ,m4,a41 ,f4,r4,s41 ,v4,m4,h41 ,director ( ! ,john ,innes ,horticultural ,in/itution4 ,?ird impression ) additions4 ,) #c portraits1 #f col\r$ plates1 & #ch figures4 ,royal #hvo4 #abs net4 ,,! ,,elem5ts ,,( ,,botany4 ,by ,sir ,,francis ,,d>w91 ,sc4,d41 ,m4,b41 ,f4,r4,s41 ,fell[ ( ,*ri/'s ,college4 ,second edition4 ,) #id illu/rations4 ,cr[n #hvo4 #ds #f;d net4 ,cambridge ,biological ,s]ies4 ,,practical ,,physiology ,,( ,,plants4 ,by ,sir ,,francis ,,d>w91 ,sc4,d41 ,f4,r4,s41 & ,e4 ,,hamilton ,,acton1 ,m4,a4 ,?ird edition4 ,) #de illu/rations4 ,cr[n #hvo4 #ds #f;d net4 ,cambridge ,biological ,s]ies4 ,,botany4 ,a ,text-,book = ,s5ior ,/ud5ts4 ,by ,d4 ,,?oday1 ,m4,a41 ,lectur] 9 ,physiological ,botany & ,assi/ant ,director ( ! ,botanical ,laboratories 9 ! ,univ]sity ( ,man*e/]4 ,) #bje figures4 ,l>ge cr[n #hvo4 #es #f;d net4 ,,alg4 ,volume ,i1 ,myxophyce1 ,p]id9ie1 ,bacill>ie1 ,*lorophyce1 toge!r ) a brief summ>y ( ! ,occurr5ce & ,di/ribution ( ,fre%wat] ,alg4 ,by ,g4 ,s4 ,,we/1 ,m4,a41 ,d4,sc41 ,a4,r4,c4,s41 ,f4,l4,s41 ,mason ,pr(essor ( ,botany 9 ! ,univ]sity ( ,birm+ham4 ,) #bga illu/rations4 ,l>ge royal #hvo4 #bes net4 ,cambridge ,botanical ,h&books4 ,,! ,,philosophy ,,( ,,biology4 ,by ,,james ,,john/one1 ,d4,sc4 ,demy #hvo4 #is net4 ,,cambridge ,,manuals ,,( ,,sci5ce ,,& ,,lit]ature4 ,g5]al ,editors3 ,p4 ,,giles1 ,litt4,d41 & ,a4 ,c4 ,,sew>d1 ,m4,a41 ,f4,r4,s4 ,royal #afmo4 ,clo?1 #as #c;d net ea*4 ,lea!r1 #bs #f;d net ea*4 ,,! ,,com+ ,,( ,,evolution4 ,by ,,john ,w4 ,,judd1 ,c4,b41 ,,ll4,d41 ,f4,r4,s4 ,) #d plates4 ,,h]$ity ,,9 ,,! ,,light ,,( ,,rec5t ,,rese>*4 ,by ,l4 ,,donca/]1 ,sc4,d4 ,) #ab figures4 ,,prehi/oric ,,man4 ,by ,w4 ,l4 ,h4 ,,duckwor?1 ,m4,a41 ,m4,d41 ,sc4,d4 ,) #b tables & #bh figures4 ,,primitive ,,animals4 ,by ,g4 ,,smi?1 ,m4,a4 ,) #bf figures4 ,,! ,,life-,,/ory ,,( ,,insects4 ,by ,pr(4 ,g4 ,h4 ,,c>p5t]4 ,) #bd illu/rations4 ,,e>?worms ,,& ,,_! ,,allies4 ,by ,,frank ,e4 ,,b$d>d1 ,m4,a4 7,oxon471 ,f4,r4,s41 ,f4,r4,s4,e4 ,) #ac figures4 ,,spid]s4 ,by ,,cecil ,,w>burton1 ,m4,a4 ,) #ac figures4 ,,bees ,,& ,,wasps4 ,by ,o4 ,h4 ,,latt]1 ,m4,a41 ,f4,e4,s4 ,) #ba illu/rations4 ,,! ,,flea4 ,by ,h4 ,,russell4 ,) #i illu/rations4 ,,life ,,9 ,,! ,,sea4 ,by ,,james ,,john/one1 ,b4,sc4 ,) frontispiece1 #d figures & #e tailpieces4 ,,plant-,,animals4 ,by ,f4 ,w4 ,,keeble1 ,sc4,d4 ,) #bc figures4 ,,plant-,,life ,,on ,,l& ,,consid]$ ,,9 ,,"s ,,( ,,its ,,biological ,,aspects4 ,by ,f4 ,o4 ,,b[]1 ,sc4,d41 ,f4,r4,s4 ,) #bg figures4 ,,l9ks ,,) ,,! ,,pa/ ,,9 ,,! ,,plant ,,_w4 ,by ,a4 ,c4 ,,sew>d1 ,m4,a41 ,f4,r4,s4 ,) frontispiece & #bj figures4 ,cambridge ,univ]sity ,press ,fett] ,lane1 ,london3 ,c4 ,f4 ,clay1 ,manag] ,,transcrib]',s ,,note ,orig9al spell+ & gramm> h be5 g5]ally reta9$1 ) "s exceptions not$ bel[4 ,orig9al pr9t$ page numb]s are %[n l ?is3 #eb4 ,orig9al small caps are n[ upp]case4 ,italics look l ?is4 ,footnotes h be5 r5umb]$ #a-ffc & relocat$ to ! end ( ! book1 ahead ( ! ,index4 ,! transcrib] produc$ ! cov] image & h]eby assigns x to ! public doma94 ,orig9al page images are available f ar*ive4org--se>* = 8ongr[?=m#aiag?om04 ,"s tables & illu/rations h be5 mov$ f _! orig9al locations )9 p>agraphs ( text to ne>by locations betwe5 p>agraphs4 ,?is includes1 = example1 ! full-page table pr9t$ on page #fg1 :i* page numb] is remov$ f ^! ebook editions4 ,"s o!r tables & illu/rations h be5 left :]e !y orig9ally lay1 9 ! middle ( p>agraphs ( text4 ,"s1 b n all ditto m>ks 1 includ+ 8d401 h be5 elim9at$4 ,enl>g$ curly brackets turn$ horizontal1 us$ z graphic devices 9 ! pr9t$ book to comb9e in=mation 9 two or m columns ( a table1 h be5 elim9at$4 ,enl>g$ curly brackets 1 us$ z graphic devices to sugge/ comb9ation ( in=mation ov] two or m l9es ( text1 h be5 elim9at$4 ,= example1 on page #ge1 9 ! la/ column ( ! table1 two l5g?s1 #dij & #ejj1 7 pr9t$1 ! latt] "u ! =m]1 ) a l>ge "r curly bracket comb9+ !m4 ,! transcrib] has *ang$ t con/ruction to 8#dij-ejj01 tak+ ! orig9al to mean a range4 ,page #ajf4 ,*ang$ 8x we c\ld believe0 to 8if we c\ld believe04 ,page #ajg4 ,*ang$ 87m470 to 87mm4701 9 column #c ( ! table4 ,page #aag4 ,bo? 8,q#aj0 & 8,q#aj0 appe> on ! page z orig9ally pr9t$4 ,page #bgbn4 ,*ang$ 8,proc4 ,r y4 ,soc4 ,,xii0 to 8,proc4 ,roy4 ,soc4 ,,xii04 ,page #cfh4 ,p]haps1 ! orig9al 8,! area ( ! enl>g$ sector1 p,,oa0 %\ld read 8,! area ( ! enl>g$ sector1 ,p,,oa04 ,page #dbhn4 ,*ang$ 8,ph5onemon0 to 8,ph5om5on04 ,page #dfcn4 ,*ang$ 8,raphidophrys0 to 8,raphidiophrys04 ,page #edc4 ,! ,unicode "* u#b;a#h;c great]-?an above d\ble-l9e equal above less-?an is pretty r>e1 & may n display prop]ly 9 mo/ fonts4 ,an image is us$ in/ead ( ! ,unicode 9 all b ! simple text edition4 ,page #fgf4 ,! ,unicode "* u#bccf ,,apl functional symbol i-beam is also unusual4 ,an image is sub/itut$ 9 all b ! simple text edition4 ,page #gdh4 ,*ang$ 8,fig4 #dgd0 to 8,fig4 #cgd04 ,page #gfh4 ,*ang$ 89 ! case ( ,pro ohippus0 to 89 ! case ( ,protohippus04 ,!re 7 ?ree footnotes on ?is page1 b only two footnote an*ors4 ,! second footnote1 miss+ an an*or1 said 8 ,cf4 ,zittel1 ,grundzge d4 ,palaeontologie1 p4 #dfc1 #aiaa40