,transcrib]'s notes3 ,! text ( ?is e-book has mo/ly be5 pres]v$ 9 its orig9al =m includ+ "s inconsi/5cy ( hyph5ation & use ( diacritics 7a]i=m_/ari=m74 ,?ree spell+ typos h be5 correct$ 7arrangm5t arrangem5t1 pully pulley1 dye die7 z h typos 9 equations on pages #dj & #dc4 ,"s miss+ punctuation has be5 correct$ sil5tly 7p]iods1 commas1 incorrect quotes74 ,footnotes h be5 position$ bel[ ! relevant p>agraphs4 ,9 ?is pla9 text v]sion1 italic text is d5ot$ by und]scores & bold text by 99a/]isks994 ,a c>et 77 indicates t ! foll[+ "* is sup]script$1 e4g4 ,d#b 7,d squ>$74 ,a ,,treatise ,,on ,,me*anics1 ,,by ,,capta9 ,,h5ry ,,kat]1 ,v4 ,,pres3 ,r4,s4 ----&---- ,,dionysius ,,l>dn]1 ,d4,c4,l4 ,f4,r4,s4 c4 c4 ,a ,,new ,,edition ,,revis$ ,,correct$4 #aheb4 ,illu/ration3 ,h4 ,corb\ld del4 ,e4 ,f9d] fc4 ,london3 ,,pr9t$ ,,= ,,longman1 ,,br[n1 ,,gre5 ,,longmans4 ,,pat]no/] ,,r[3 ,,adv]tisem5t4 ,?is ,treatise on ,me*anics1 :i* 0 orig9ally publi%$ 9 #ahcj1 is ! "w ( ,dr4 ,l>dn]1 ) ! exception ( ! tw5ty-fir/ *apt]1 :i* 0 writt5 by ! late ,capta9 ,kat]4 ,! pres5t edition has be5 revis$ & correct$ by ,dr4 ,l>dn]4 ,london1 ,janu>y1 #aheb4 ,,cont5ts4 ,,*ap4 ,i4 ,,prop]ties ,,( ,,matt]4 ,organs ( ,s5se4--,s5sations4--,prop]ties or ,qualities4--,obs]vation4 --,comp>ison & ,g5]alisation4--,p>ticul> & g5]al ,qualities4-- ,magnitude4--,size4--,volume4--,l9es4--, surfaces4--,edges4--,area4--,l5g?4 --,imp5etrability4--,app>5t ,p5etration4--,figure4--,diff]5t f ,volume4--,atoms4--,molecules4--,matt] sep>able4--,p>ticles4--,=ce4-- ,cohesion ( ,atoms4--,hypo!tical ,phrases unnecess>y4--,attraction4 #a ,,*ap4 ,,ii4 ,,prop]ties ,,( ,,matt]1 ,,cont9u$4 ,divisibility4--,unlimit$ ,divisibility4--,wolla/on's micrometric ,wire4 --,me?od ( mak+ x4--,?ickness ( a ,soap ,bubble4--,w+s ( ,insects4 --,gild+ ( ,wire = ,embroid]y4--,globules ( ! ,blood4-- ,animalcules4--,_! m9ute ,organisation4--,ultimate ,atoms4--,cry/als4-- ,porosity4--,volume4--,d5sity4--,quicksi lv] pass+ ?r\gh ,pores ( ,wood4--,filtration4--,porosity ( ,hydrophane4--,compressibility4-- ,ela/icity4--,dilatability4--,heat4--,co ntraction ( ,metal us$ to re/ore ! ,p]p5dicul> to ,walls ( a ,build+4--,imp5etrability ( ,air4--,compressibility ( x4--,ela/icity ( x4--,liquids n absolutely incompressible4--,exp]im5ts4--,ela/icity ( ,fluids4-- ,a]i=m ,fluids4--,dome/ic ,fire ,box4--,evolution ( ,heat by compress$ ,air4 #i ,,*ap4 ,,iii4 ,,in]tia4 ,in]tia4--,matt] ,incapable ( spontane\s ,*ange4--,imp$im5ts to ,motion4--,motion ( ! ,sol> ,sy/em4--,law ( ,nature4--,language us$ to express ,in]tia sometimes faulty4--,famili> ,examples ( ,in]tia4 #bg ,,*ap4 ,,iv4 ,,action ,,& ,,reaction4 ,in]tia 9 a s+le ,body4--,consequ5ces ( ,in]tia 9 two or m ,bodies4--,examples4--,effects ( ,impact4--,motion n e/imat$ by ,spe$ or ,velocity alone4--,examples4--,rule = e/imat+ ! ,quantity ( ,motion4--,action & ,reaction4--,examples (4--,velocity ( two ,bodies aft] ,impact4--,rule = f9d+ ! common ,velocity aft] ,impact4--,magnet & ,iron4--,fea!r & ,cannon ,ball imp++4 --,newton's ,laws ( ,motion4--,inutility (4--,famili> ,effects result+ f ,consequ5ces ( ,in]tia4 #cd ,,*ap4 ,v4 ,,composition ,,& ,,resolution ,,( ,,=ce4 ,motion & ,pressure4--,=ce4--,attraction4--,p>alle logram ( ,=ces4 --,resultant4--,compon5ts4--,composition ( ,=ce4--,resolution ( ,=ce4--,illu/rative ,exp]im5ts4--,composition ( ,pressures4-- ,!orems regulat+ ,pressures also regulate ,motion4--,examples4-- ,resolution ( ,motion4--,=ces 9 ,equilibrium4--,composition ( ,motion & ,pressure4--,illu/rations4--,boat 9 a ,curr5t4--,motions ( ,fi%es4 --,flight ( ,birds4--,sails ( a ,vessel4--,tack+4--,eque/rian ,feats4 --,absolute & relative ,motion4 #dh ,,*ap4 ,,vi4 ,,attraction4 ,impulse4--,me*anical ,/ate ( ,bodies4--,absolute ,re/4--,uni=m & rectil9e> ,motion4--,attractions4--,molecul> or atomic4--,int]/itial ,spaces 9 ,bodies4--,repulsion & ,attraction4--,cohesion4--,9 ,solids & ,fluids4--,manufacture ( ,%ot4--,capill>y ,attractions4--,%ort5+ ( ,rope by ,moi/ure4--,susp5sion ( ,liquids 9 capill>y ,tubes4-- ,capill>y ,siphon4--,aff9ity betwe5 ,quicksilv] & ,gold4--,examples ( ,aff9ity4--,sulphuric ,acid & ,wat]4--,oxyg5 & ,hydrog54--,oxyg5 & ,quicksilv]4--,magnetism4--,electricity & ,electro-,magnetism4-- ,gravitation4--,its ,law4--,examples (4--,dep5ds on ! ,mass4-- ,attraction betwe5 ! ,e>? & deta*$ ,bodies on its ,surface4-- ,weight4--,gravitation ( ! ,e>?4--,illu/rat$ by ,projectiles4-- ,plumb-,l9e4--,cav5di%'s ,exp]im5ts4 #fc ,,*ap4 ,,vii4 ,,t]re/rial ,,gravity4 ,ph5om5a ( fall+ ,bodies4--,gravity great] at ! ,poles ?an ,equator4--,heavy & light ,bodies fall ) equal ,spe$ to ! ,e>?4 --,exp]im5t4--,increas$ ,velocity ( fall+ ,bodies4--,pr9ciples ( uni=mly accel]at$ ,motion4--,relations betwe5 ! ,height1 ,"t1 & ,velocity4--,attwood's ,ma*9e4--,ret>d$ ,motion4 #hd ,,*ap4 ,,viii4 ,,( ,,! ,,motion ,,( ,,bodies ,,on ,,incl9$ ,,planes ,,& ,,curves4 ,=ce p]p5dicul> to a ,plane4--,oblique ,=ce4--,incl9$ ,plane4-- ,weight produces ,pressure & ,motion4--,motion uni=mly accel]at$4-- ,space mov$ ?r\gh 9 a giv5 ,"t4--,increas$ ,elevation produces increas$ ,=ce4--,p]p5dicul> & horizontal ,plane4--,f9al ,velocity4--,motion d[n a ,curve4--,dep5ds ^u ,velocity & ,curvature4 --,c5trifugal ,=ce4--,circle ( ,curvature4--,radius ( ,curvature4-- ,:irl+ ,table4--,exp]im5ts4--,sol> ,sy/em4--,examples ( c5trifugal ,=ce4 #he ,,*ap4 ,,ix4 ,,! ,,c5tre ,,( ,,gravity4 ,t]re/rial ,attraction ! comb9$ ,action ( p>allel ,=ces4-- ,s+le equival5t ,=ce4--,examples4--,me?od ( f9d+ ! ,c5tre ( ,gravity4--,l9e ( ,direction4--,globe4--,oblate ,sph]oid4--,prolate ,sph]oid4--,cube4--,/raight ,w&4--,flat ,plate4--,triangul> ,plate4-- ,c5tre ( ,gravity n always )9 ! ,body4--,a ,r+4--,exp]im5ts4 --,/able1 in/able1 & neutral ,equilibrium4--,motion & ,position ( ! ,arms & ,feet4--,effect ( ! ,knee-,jo9t4--,positions ( a ,danc]4 --,port] "u a ,load4--,motion ( a ,quadrup$4--,rope ,danc+4-- ,c5tre ( ,gravity ( two ,bodies sep>at$ f ea* o!r4-- ,ma!matical & exp]im5tal ,examples4--,! ,cons]vation ( ! ,motion ( ! ,c5tre ( ,gravity4--,sol> ,sy/em4--,c5tre ( ,gravity sometimes call$ ,c5tre ( ,in]tia4 #ajg ,,*ap4 ,x4 ,,! ,,me*anical ,,prop]ties ,,( ,,an ,,axis4 ,an ,axis4--,planets & common sp9n+ ,top4--,oscillation or ,vibration4 --,in/antane\s & cont9u$ ,=ces4--,p]cussion4--,cont9u$ ,=ce4 --,rotation4--,impress$ ,=ces4--,prop]ties ( a fix$ ,axis4--,movem5t ( ! ,=ce r\nd ! ,axis4--,lev]age ( ! ,=ce4--,impulse p]p5dicul> to1 b n cross+1 ! ,axis4--,radius ( ,gyration4-- ,c5tre ( ,gyration4--,mom5t ( ,in]tia4--,pr9cipal ,axes4--,c5tre ( ,p]cussion4 #abh ,,*ap4 ,,xi4 ,,( ,,! ,,p5dulum4 ,iso*ronism4--,exp]im5ts4--,simple ,p5dulum4--,examples illu/rative (4--,l5g? (4--,exp]im5ts ( ,kat]1 ,biot1 ,sab9e1 & o!rs4-- ,huyg5s' ,cycloidal ,p5dulum4 #ade ,,*ap4 ,,xii4 ,,( ,,simple ,,ma*9es4 ,/atics4--,dynamics4--,=ce4--,p[]4--,wei ght4--,lev]4--,cord4-- ,incl9$ ,plane4 #afj ,,*ap4 ,,xiii4 ,,( ,,! ,,lev]4 ,arms4--,fulcrum4--,?ree ,k9ds ( ,lev]s4--,cr[ ,b>4--,h&spike4--,o>4 --,nutcrack]s4--,turn+ ,la!4--,/eely>d4--,rectangul> ,lev]4-- ,hamm]4--,load betwe5 two ,be>]s4--,comb9ation ( ,lev]s4-- ,equival5t ,lev]4 #afg ,,*ap4 ,,xiv4 ,,( ,,:eel-,,"w4 ,:eel & ,axle4--,?ickness ( ! ,rope4--,ways ( apply+ ! ,p[]4 --,project+ ,p9s4--,w9dlass4--,w9*4--,axle4--,horizo ntal ,:eel4-- ,tread-,mill4--,cranes4--,wat]-,:eels4-- ,paddle-,:eel4--,ra*et-,:eel4-- ,rack4--,spr+ ( a ,wat*4--,fusee4--,/raps or ,cords4--,examples (4-- ,turn+ ,la!4--,revolv+ ,%afts4--,sp9n+ ,ma*9]y4--,saw-,mill4-- ,p9ion4--,leaves4--,crane4--,spur-,:eels 4--,cr[n-,:eels4--,bevell$ ,:eels4--,hunt+-,cog4--,*ronomet]s4--,ha ir-,spr+4--,balance-,:eel4 #agh ,,*ap4 ,,xv4 ,,( ,,! ,,pulley4 ,cord4--,%eave4--,fix$ ,pulley4--,fire ,escapes4--,s+le moveable ,pulley4--,sy/ems ( ,pulleys4--,smeaton's ,tackle4--,:ite's ,pulley4-- ,advantage (4--,runn]4--,spani% ,b>tons4 #aii ,,*ap4 ,,xvi4 ,,on ,,! ,,incl9$ ,,plane1 ,,w$ge1 ,,& ,,screw4 ,incl9$ ,plane4--,effect ( a ,weight on4--,p[] (4--,roads4--,p[] ,oblique to ! ,plane4--,plane sometimes moves "u ! ,weight4-- ,w$ge4--,sometimes =m$ ( two incl9$ ,planes4--,m p[]ful z its ,angle is acute4--,:]e us$4--,limits to ! ,angle4--,screw4 --,hunt]'s ,screw4--,examples4--,micromet] ,screw4 #bji ,,*ap4 ,,xvii4 ,,on ,,! ,,regulation ,,& ,,accumulation ,,( ,,=ce4 ,uni=mity ( ,op]ation4--,irregul>ity ( prime ,mov]4--,wat]-,mill4 --,w9d-,mill4--,/eam ,pressure4--,animal ,p[]4--,spr+4--,regulators4 --,/eam-,eng9e4--,gov]nor4--,self-act+ ,damp]4--,ta*omet]4-- ,accumulation ( ,p[]4--,examples4--,hamm]4--,flail4--,b[ -/r+4-- ,fire ,arms4--,air-,gun4--,/eam-,gun4--,in]t ,matt] a ,magaz9e = ,=ce4--,fly-,:eel4--,cond5s$ ,air4--,roll+ ,metal4--,co9+-,press4 #bbd ,,*ap4 ,,xviii4 ,,me*anical ,,contrivances ,,= ,,modify+ ,,motion4 ,division ( ,motion into rectil9e> & rotatory4--,cont9u$ & reciprocat+4--,examples4--,fl[+ ,wat]4--,w9d4--,animal ,motion4-- ,fall+ ( a ,body4--,syr+e-,pump4--,hamm]4--,/eam-,e ng9e4--,full+ ,mill4--,rose-,eng9e4--,app>atus ( ,zur$a4--,leupold's ,application ( x4--,hooke's univ]sal ,jo9t4--,circul> & alt]nate ,motion4-- ,examples4--,watt's ,me?ods ( connect+ ! ,motion ( ! ,pi/on ) t ( ! ,beam4--,p>allel ,motion4 #bde ,,*ap4 ,,xix4 ,,( ,,friction ,,& ,,! ,,rigidity ,,( ,,cordage4 ,friction & ,rigidity4--,laws ( ,friction4--,rigidity ( ,cordage4-- ,/r5g? ( ,mat]ials4--,resi/ance f ,friction4--,indep5d5t ( ! ,magnitude ( ,surfaces4--,examples4--,v9ce's ,exp]im5ts4--,effect ( ,velocity4--,means = dim9i%+ ,friction4--,friction ,:eels4-- ,angle ( ,repose4--,be/ ,angle ( ,draught4--,rail-,roads4--,/iffness ( ,ropes4 #bfj ,,*ap4 ,,xx4 ,,on ,,! ,,/r5g? ,,( ,,mat]ials4 ,difficulty ( det]m9+ ! ,laws :i* gov]n ! ,/r5g? ( ,mat]ials4--,=ces t5d+ to sep>ate ! ,p>ts ( a ,solid4--,laws by :i* ,solids resi/ ,compression4--,eul]'s !ory4--,transv]se ,/r5g? ( ,solids4--,/r5g? dim9i%$ by ! ,increase ( ,height4 --,lat]al or ,transv]se ,/ra94--,limits ( ,magnitude4--,relative ,/r5g? ( small ,animals great] ?an l>ge ones4 #bgb ,,*ap4 ,,xxi4 ,,on ,,balances ,,& ,,p5dulums4 ,weight4--,"t4--,! ,balance4--,fulcrum4--,c5tre ( ,gravity (4-- ,s5sibility (4--,positions ( ! ,fulcrum4--,beam v>i\sly con/ruct$4--,tr\ghton's ,balance4--,rob9son's ,balance4--,kat]'s ,balance4--,me?od ( adju/+ a ,balance4--,use ( x4--,precautions necess>y4--,( ,weights4--,adju/m5t (4--,dr4 ,black's ,balance4-- ,/eely>d4--,roman ,/at]a or ,/eely>d4--,conv5i5ce (4--,c4 ,paul's ,/eely>d4--,*9ese ,/eely>d4--,dani% ,balance4--,b5t ,lev] ,balance4 --,brady's ,balance4--,weigh+ ,ma*9e = ,turnpike ,roads4--,in/rum5ts = ,weigh+ by means ( a ,spr+4--,spr+ ,/eely>d4--,salt]'s ,spr+ ,balance4--,m>riott's ,dial ,weigh+ ,ma*9e4--,dynamomet]4-- ,comp5sation ,p5dulums4--,b>ton's ,gridiron ,p5dulum4--,table ( l9e> ,expansion4--,second ,table4--,h>rison's ,p5dulum4--,tr\ghton's ,p5dulum4--,b5z5b]g's ,p5dulum4--,w>d's ,comp5sation ,p5dulum4-- ,comp5sation ,tube ( ,juli5 le ,roy4--,dep>cieux's ,comp5sation4-- ,kat]'s ,p5dulum4--,re$'s ,p5dulum4--,ellicott's ,p5dulum4--,m]curial ,p5dulum4--,graham's ,p5dulum4--,comp5sation ,p5dulum ( ,wood & ,lead4--,smeaton's ,p5dulum4--,br[n's ,mode ( ,adju/m5t4 #bgh ,,! ,,elem5ts ,,( ,,me*anics4 ,,*ap4 ,i4 ,,prop]ties ,,( ,,matt]--,,magnitude--,,imp5etrability-- ,,figure--,,=ce4 7#a47 ,plac$ 9 ! mat]ial _w1 ,man is cont9ually expos$ to ! action ( an inf9ite v>iety ( objects by :i* he is surr\nd$4 ,! body1 to :i* ! ?9k+ & liv+ pr9ciples h be5 unit$1 is an app>atus exquisitely contriv$ to receive & to transmit impressions4 ,its v>i\s p>ts are organis$ ) obvi\s ref]5ce to ! sev]al ext]nal ag5ts by :i* x is to be effect$4 ,ea* organ is design$ to convey to ! m9d imm$iate notice ( "s peculi> action1 & is accord+ly endu$ ) a correspond+ susceptibility4 ,?is adaptation ( su* organs to ! p>ticul> influ5ces ( mat]ial ag5ts1 is r5d]$ /ill m conspicu\s :5 we consid] t1 h[ev] delicate its /ructure1 ea* organ is :olly ins5sible to e influ5ce except t to :i* x appe>s to be specially appropriat$4 ,! eye1 s int5sely susceptible ( impressions f light1 is n at all affect$ by ^? ( s\nd2 :ile ! f9e me*anism ( ! e>1 s s5sitively alive to e effect ( ! latt] class1 is altoge!r ins5sible to ! =m]4 ,! spl5d\r ( excessive light may occasion bl9dness1 & deafness may result f ! ro> ( a cannonade2 b nei!r ! sight nor ! he>+ c be injur$ by ! mo/ extreme action ( t pr9ciple :i* is design$ to affect ! o!r4 ,?us ! organs ( s5se are in/rum5ts by :i* ! m9d is enabl$ to det]m9e ! exi/5ce & ! qualities ( ext]nal ?+s4 ,! effects :i* ^! objects produce ^u ! m9d ?r\gh ! organs1 are call$ s5sations1 & ^! s5sations are ! imm$iate elem5ts ( all human k4 ,,matt] is ! g5]al "n :i* has be5 giv5 to t sub/ance1 :i*1 "u =ms inf9itely v>i\s1 affects ! s5ses4 ,metaphysicians h diff]$ 9 def9+ ?is pr9ciple4 ,"s h ev5 d\bt$ ( its exi/5ce4 ,b ^! discussions are beyond ! sph]e ( me*anical philosophy1 ! conclusions ( :i* are 9 n[ise affect$ by !m4 ,our inve/igations "h relate1 n to matt] z an ab/ract exi/5ce1 b to ^? qualities :i* we discov] 9 x by ! s5ses1 & ( ! exi/5ce ( :i* we are sure1 h[ev] ! "q z to matt] itself may be decid$4 ,:5 we speak ( 8bodies10 we mean ^? ?+s1 :atev] !y be1 :i* excite 9 our m9ds c]ta9 s5sations2 & ! p[]s to excite ^? s5sations are call$ 8prop]ties10 or 8qualities40 7#b47 ,to asc]ta9 by obs]vation ! prop]ties ( bodies1 is ! fir/ /ep t[>ds obta9+ a k ( nature4 ,h5ce man becomes a natural philosoph] ! mom5t he beg9s to feel & to p]ceive4 ,! fir/ /age ( life is a /ate ( con/ant & curi\s excitem5t4 ,obs]vation & att5tion1 ev] awake1 are engag$ ^u a succession ( objects new & wond]ful4 ,! l>ge repository ( ! memory is op5$1 & e h\r p\rs into x unb\nd$ /ores ( natural facts & appe>ances1 ! ri* mat]ials ( future k4 ,! ke5 appetite = discov]y implant$ 9 ! m9d = ! highe/ ends1 cont9ually /imulat$ by ! pres5ce ( :at is novel1 r5d]s torpid e o!r faculty1 & ! p[]s ( reflection & comp>ison are lo/ 9 ! incessant activity & unexhau/$ vig\r ( obs]vation4 ,aft] a season1 h[ev]1 ! m ord9>y classes ( ph5om5a cease to excite by _! novelty4 ,att5tion is drawn f ! discov]y ( :at is new1 to ! exam9ation ( :at is famili>4 ,f ! ext]nal _w ! m9d turns 9 ^u itself1 & ! fev]i% a/oni%m5t ( *ildhood gives place to ! m calm contemplation ( incipi5t maturity4 ,! va/ & het]og5e\s mass ( ph5om5a collect$ by pa/ exp]i5ce is br\ght "u review4 ,! great "w ( comp>ison beg9s4 ,memory produces h] /ores1 & reason arranges !m4 ,!n succe$ ^? fir/ attempts at g5]alisation :i* m>k ! dawn ( sci5ce 9 ! m9d4 ,to comp>e1 to classify1 to g5]alise1 seem to be in/9ctive prop5sities peculi> to man4 ,!y sep>ate him f inf]ior animals by a wide *asm4 ,x is to ^! p[]s t all ! high] m5tal attributes may be trac$1 & x is f _! "r application t all progress 9 sci5ce mu/ arise4 ,)\t ^! p[]s1 ! ph5om5a ( nature w\ld cont9ue a confus$ heap ( crude facts1 ) :i* ! memory might be load$1 b f :i* ! intellect w\ld d]ive no advantage4 ,comp>ison & g5]alisation are ! great dige/ive organs ( ! m9d1 by :i* only nutrition c be extract$ f ?is mass ( intellectual food1 & )\t :i*1 obs]vation ! mo/ ext5sive1 & att5tion ! mo/ unremitt+1 c be productive ( no real or useful advancem5t 9 k4 7#c47 ,^u review+ ^? prop]ties ( bodies :i* ! s5ses mo/ frequ5tly pres5t to u1 we obs]ve t v few ( !m are ess5tial to1 & insep>able f1 matt]4 ,! great] numb] may be call$ p>ticul> or peculi> qualities1 be+ f\nd 9 "s bodies b n 9 o!rs4 ,?us ! prop]ty ( attract+ iron is peculi> to ! load/one1 & n obs]vable 9 o!r sub/ances4 ,"o body excites ! s5sation ( gre51 ano!r ( r$1 & a ?ird is depriv$ ( all col\r4 ,a few *>act]i/ic & ess5tial qualities are1 h[ev]1 insep>able f matt] 9 :atev] /ate1 or "u :atev] =m x exi/4 ,su* prop]ties alone c be consid]$ z te/s ( mat]iality4 ,:]e _! pres5ce is nei!r manife/ to s5se1 nor demon/rable by reason1 !re matt] is n4 ,! pr9cipal ( ^! qualities are magnitude & imp5etrability4 7#d47 ,magnitude4--,e body occupies space1 t is1 x has magnitude4 ,?is is a prop]ty obs]vable by ! s5ses 9 all bodies :i* are n s m9ute z to elude !m1 & :i* ! und]/&+ c trace to ! smalle/ p>ticle ( matt]4 ,x is impossible1 by any /ret* ( imag9ation1 ev5 to conceive a portion ( matt] s m9ute z to h no magnitude4 ,! quantity ( space :i* a body occupies is sometimes call$ its magnitude4 ,9 colloquial phraseology1 ! ^w size is us$ to express ?is notion2 b ! mo/ correct t]m1 & t :i* we %all g5]ally adopt is volume4 ,?us we say1 ! volume ( ! e>? is s _m cubic miles1 ! volume ( ?is room is s _m cubic feet4 ,! ext]nal limits ( ! magnitude ( a body are l9es & surfaces1 l9es be+ ! limits :i* sep>ate ! sev]al surfaces ( ! same body4 ,! l9e> limits ( a body are also call$ edges4 ,?us ! l9e :i* sep>ates ! top ( a *e/ f "o ( its sides is call$ an edge4 ,! quantity ( a surface is call$ its area1 & ! quantity ( a l9e is call$ its l5g?4 ,?us we say1 ! area ( a field is s _m acres1 ! l5g? ( a rope is s _m y>ds4 ,! ^w 8magnitude0 is1 h[ev]1 (t5 us$ indiff]5tly = volume1 area1 & l5g?4 ,if ! objects ( inve/igation 7 ( a m complex & subtle "*1 z 9 metaphysics1 ?is un/eady application ( t]ms might be productive ( confusion1 & ev5 ( error2 b 9 ?is sci5ce ! mean+ ( ! t]m is evid5t1 f ! way 9 :i* x is appli$1 & no inconv5i5ce is f\nd to arise4 7#e47 ,imp5etrability4--,?is prop]ty w be mo/ cle>ly expla9$ by def9+ ! positive quality f :i* x takes its "n1 & ( :i* x m]ely signifies ! abs5ce4 ,a sub/ance w\ld be p5etrable if x 7 su* z to all[ ano!r to pass ?r\gh ! space :i* x occupies1 )\t di/urb+ its compon5t p>ts4 ,?us1 if a comet /rik+ ! e>? c\ld ent] x at "o side1 &1 pass+ ?r\gh x1 em]ge f ! o!r )\t sep>at+ or d]ang+ any bodies on or )9 ! e>?1 !n ! e>? w\ld be p5etrable by ! comet4 ,:5 bodies are said to be imp5etrable1 x is !re=e meant t "o _c pass ?r\gh ano!r )\t displac+ "s or all ( ! compon5t p>ts ( t o!r4 ,!re are _m in/ances ( app>5t p5etration2 b 9 all ^!1 ! p>ts ( ! body :i* seem to be p5etrat$ are displac$4 ,?us1 if ! po9t ( a ne$le be plung$ 9 a vessel ( wat]1 all ! wat] :i* previ\sly fill$ ! space into :i* ! ne$le ent]s w be displac$1 & ! level ( ! wat] w rise 9 ! vessel to ! same height z x w\ld by p\r+ 9 s mu* m wat] z w\ld fill ! space occupi$ by ! ne$le4 7#f47 ,figure4--,if ! h& be plac$ ^u a solid body1 we become s5sible ( its imp5etrability1 by ! ob/ruction :i* x opposes to ! entrance ( ! h& )9 its dim5sions4 ,we are also s5sible t ?is ob/ruction comm5ces at c]ta9 places2 t x has c]ta9 det]m9ate limits2 t ^! limitations are plac$ 9 c]ta9 directions relatively to ea* o!r4 ,! mutual relation :i* is f\nd to subsi/ betwe5 ^! b\nd>ies ( a body1 gives u ! notion ( its figure4 ,! figure & volume ( a body %\ld be c>efully di/+ui%$4 ,ea* is entirely indep5d5t ( ! o!r4 ,bodies hav+ v diff]5t volumes may h ! same figure2 & 9 l mann] bodies diff]+ 9 figure may h ! same volume4 ,! figure ( a body is :at 9 popul> language is call$ its %ape or =m4 ,! volume ( a body is t :i* is commonly call$ its size4 ,x w h5ce be easily und]/ood1 t "o body 7a globe1 = example7 may h t5 times ! volume ( ano!r 7globe71 & yet h ! same figure2 & t two bodies 7z a die & a globe7 may h figures altoge!r diff]5t1 & yet h equal volumes4 ,:at we h "h obs]v$ ( volumes w also be applicable to l5g?s & areas4 ,! arc ( a circle & a /raight l9e may h ! same l5g?1 al?\gh !y h diff]5t figures2 &1 on ! o!r h&1 two arcs ( diff]5t circles may h ! same figure1 b v unequal l5g?s4 ,! surface ( a ball is curv$1 t ( ! table plane2 & yet ! area ( ! surface ( ! ball may be equal to t ( ! table4 7#g47 ,atoms--,molecules4--,imp5etrability mu/ n be conf\nd$ ) insep>ability4 ,e body :i* has be5 br\ght "u human obs]vation is sep>able into p>ts2 & ^! p>ts1 h[ev] small1 are sep>able into o!rs1 /ill m m9ute4 ,to ?is process ( division no practical limit has ev] be5 f\nd4 ,nev]!less1 _m ( ! ph5om5a :i* ! rese>*es ( ^? :o h successfully exam9$ ! laws ( nature h develop$1 r5d] x highly probable t all bodies are compos$ ( elem5t>y p>ts :i* are indivisible & unalt]able4 ,! compon5t p>ts1 :i* may be call$ atoms1 are s m9ute1 z altoge!r to elude ! s5ses1 ev5 :5 aid$ by ! mo/ p[]ful sci5tific in/rum5ts4 ,! ^w molecule is (t5 us$ to signify compon5t p>ts ( a body s small z to escape s5sible obs]vation1 b n ultimate atoms1 ea* molecule be+ suppos$ to be =m$ ( sev]al atoms1 arrang$ accord+ to "s det]m9ate figure4 ,p>ticle is us$ also to express small compon5t p>ts1 b m g5]ally is appli$ to ^? :i* are n too m9ute to be discov]able by obs]vation4 7#h47 ,=ce4--,if ! p>ticles ( matt] 7 endu$ ) no prop]ty 9 relation to "o ano!r1 except _! mutual imp5etrability1 ! univ]se w\ld be l a mass ( s&1 )\t v>iety ( /ate or =m4 ,atoms1 :5 plac$ 9 juxtaposition1 w\ld nei!r coh]e1 z 9 solid bodies1 nor repel ea* o!r1 z 9 a]i=m sub/ances4 ,on ! contr>y1 we f9d t 9 "s cases ! atoms :i* compose bodies are n simply plac$ toge!r1 b a c]ta9 effect is manife/$ 9 _! /rong coh]5ce4 ,if !y 7 m]ely plac$ 9 juxtaposition1 _! sep>ation w\ld be effect$ z easily z any "o ( !m c\ld be remov$ f "o place to ano!r4 ,take a piece ( iron1 & attempt to sep>ate its p>ts3 ! ef=t w be /rongly resi/$1 & x w be a matt] ( mu* great] facility to move ! :ole mass4 ,x appe>s1 !re=e1 t 9 su* cases ! p>ts :i* are 9 juxtaposition coh]e & resi/ _! mutual sep>ation4 ,?is effect is d5om9at$ =ce2 & ! con/itu5t atoms are said to coh]e ) a great] or less degree ( =ce1 accord+ z !y oppose a great] or less resi/ance to _! mutual sep>ation4 ,! coh]5ce ( p>ticles 9 juxtaposition is an effect ( ! same class z ! mutual approa* ( p>ticles plac$ at a di/ance f ea* o!r4 ,x is n difficult to p]ceive t ! same influ5ce :i* causes ! bodies ,a & ,b to approa* ea* o!r1 :5 plac$ at "s di/ance asund]1 w1 :5 !y unite1 reta9 !m toge!r1 & oppose a resi/ance to _! sep>ation4 ,h5ce ?is effect ( ! mutual approximation ( bodies t[>ds ea* o!r is also call$ =ce4 ,=ce is g5]ally def9$ to be 8:atev] produces or opposes ! production ( motion 9 matt]40 ,9 ?is s5se1 x is a "n = ! unkn[n cause ( a kn[n effect4 ,x w\ld1 h[ev]1 be m philosophical to give ! "n1 n to ! cause1 ( :i* we are ignorant1 b to ! effect1 ( :i* we h s5sible evid5ce4 ,to obs]ve & to classify is ! :ole bus9ess ( ! natural philosoph]4 ,:5 causes are ref]r$ to1 x is impli$1 t effects ( ! same class arise f ! ag5cy ( ! same cause4 ,h[ev] probable ?is assumption may be1 x is altoge!r unnecess>y4 ,all ! objects ( sci5ce1 ! enl>gem5t ( m9d1 ! ext5sion & improvem5t ( k1 ! facility ( its acquisition1 are obta9$ by g5]alisation alone1 & no good c arise f ta9t+ our conclusions ) ! possible errors ( hypo!ses4 ,x may be "h1 once = all1 obs]v$1 t ! phraseology ( causation & hypo!ses has become s int]wov5 ) ! language ( sci5ce1 t x is impossible to avoid ! frequ5t use ( x4 ,?us1 we say1 8! magnet attracts iron20 ! expression attract intimat+ ! cause ( ! obs]v$ effect4 ,9 su* cases1 h[ev]1 we mu/ be und]/ood to mean ! effect itself1 f9d+ x less inconv5i5t to cont9ue ! use ( ! receiv$ phrases1 modify+ _! signification1 ?an to introduce new ones4 ,=ce1 :5 manife/$ by ! mutual approa* or cohesion ( bodies1 is also call$ attraction1 & x is v>i\sly d5om9at$1 accord+ to ! circum/ances "u :i* x is obs]v$ to act4 ,?us1 ! =ce :i* holds toge!r ! atoms ( solid bodies is call$ cohesive attraction4 ,! =ce :i* draws bodies to ! surface ( ! e>?1 :5 plac$ above x1 is call$ ! attraction ( gravitation4 ,! =ce :i* is exhibit$ by ! mutual approa*1 or adhesion1 ( ! load/one & iron1 is call$ magnetic attraction1 & s on4 ,:5 =ce is manife/$ by ! motion ( bodies f ea* o!r1 x is call$ repulsion4 ,?us1 if a piece ( glass1 hav+ be5 briskly rubb$ ) a silk h&k]*ief1 t\* successively two fea!rs1 ^! fea!rs1 if br\ght ne> ea* o!r1 w move asund]4 ,?is effect is call$ repulsion1 & ! fea!rs are said to repel ea* o!r4 7#i47 ,! influ5ce :i* =ces h ^u ! =m1 /ate1 arrangem5t1 & motions ( mat]ial sub/ances is ! pr9cipal object ( physical sci5ce4 ,9 its /rict s5se1 ,,me*anics is a t]m ( v ext5sive signification4 ,accord+ to ! m popul> usage1 h[ev]1 x has be5 g5]ally appli$ to t "p ( physical sci5ce :i* includes ! inve/igation ( ! ph5om5a ( motion & re/1 pressure & o!r effects develop$ by ! mutual action ( solid masses4 ,! consid]ation ( simil> ph5om5a1 exhibit$ 9 bodies ( ! liquid =m1 is consign$ to ,,hydro/atics1 & t ( a]i=m fluids to ,,pneumatics4 ,,*ap4 ,,ii4 ,,divisibility--,,porosity--,,d5sity--,, compressibility--,,ela/icity--,,dilatabi lity4 7#aj47 ,besides ! qualities ( magnitude & imp5etrability1 !re are sev]al o!r g5]al prop]ties ( bodies contemplat$ 9 me*anical philosophy1 & to :i* we %all h frequ5t occasion to ref]4 ,^? :i* we %all notice 9 ! pres5t *apt] are1 #a4 ,divisibility4 #b4 ,porosity--,d5sity4 #c4 ,compressibility--,ela/icity4 #d4 ,dilatability4 7#aa47 ,divisibility4--,obs]vation & exp]i5ce prove t all bodies ( s5sible magnitude1 ev5 ! mo/ solid1 consi/ ( p>ts :i* are sep>able4 ,to ! practical subdivision ( matt] !re seems to be no assignable limit4 ,num]\s examples ( ! division ( matt]1 to a degree almo/ exce$+ belief1 may be f\nd 9 exp]im5tal enquiries in/itut$ 9 physical sci5ce2 ! useful arts furni% _m in/ances n less /rik+2 b1 p]haps1 ! mo/ conspicu\s pro(s :i* c be produc$1 ( ! extreme m9ut5ess ( :i* ! p>ts ( matt] are susceptible1 arise f ! consid]ation ( c]ta9 p>ts ( ! organis$ _w4 7#ab47 ,! relative places ( />s 9 ! heav5s1 z se5 9 ! field ( view ( a telescope1 are m>k$ by f9e l9es ( wire plac$ be=e ! eye-glass1 & :i* cross ea* o!r at "r angles4 ,! />s appe>+ 9 ! telescope z m]e lucid po9ts )\t s5sible magnitude1 x is necess>y t ! wires :i* m>k _! places %\ld h a correspond+ t5uity4 ,b ^! wires be+ magnifi$ by ! eye-glass w\ld h an app>5t ?ickness1 :i* w\ld r5d] !m inapplicable to ?is purpose1 unless _! real dim5sions 7 ( a mo/ uncommon degree ( m9ut5ess4 ,to obta9 wire = ?is purpose1 ,dr4 ,wolla/on inv5t$ ! foll[+ process3--,a piece ( f9e plat9um wire1 a b1 is ext5d$ along ! axis ( a cyl9drical m\ld1 ,a ,b1 fig4 #a4 ,into ?is m\ld1 at ,a1 molt5 silv] is p\r$4 ,s9ce ! heat necess>y = ! fusion ( plat9um is mu* great] ?an t :i* reta9s silv] 9 ! liquid =m1 ! wire a b rema9s solid1 :ile ! m\ld ,a ,b is fill$ ) ! silv]4 ,:5 ! metal has become solid by be+ cool$1 & has be5 remov$ f ! m\ld1 a cyl9drical b> ( silv] is obta9$1 hav+ a plat9um wire 9 its axis4 ,?is b> is !n wire-drawn1 by =c+ x successively ?r\gh holes ,c1 ,d1 ,e1 ,f1 ,g1 ,h1 dim9i%+ 9 magnitude1 ! fir/ hole be+ a little less ?an ! wire at ! beg9n+ ( ! process4 ,by ^! means ! plat9um a b is wire-drawn at ! same "t & 9 ! same proportion ) ! silv]1 s t :atev] be ! orig9al proportion ( ! ?ickness ( ! wire a b to t ( ! m\ld ,a ,b1 ! same w be ! proportion ( ! plat9um wire to ! :ole at ! sev]al ?icknesses ,c1 ,d1 c4 ,if we suppose ! m\ld ,a ,b to be t5 times ! ?ickness ( ! wire a b1 !n ! silv] wire1 ?r\gh\t ! :ole process1 w be t5 times ! ?ickness ( ! plat9um wire :i* x includes )9 x4 ,! silv] wire may be drawn to a ?ickness n exce$+ ! #cjj? ( an in*4 ,! plat9um w ?us n exce$ ! #cjjj? ( an in*4 ,! wire is !n dipp$ 9 nitric acid1 :i* dissolves ! silv]1 b leaves ! plat9um solid4 ,by ?is me?od ,dr4 ,wolla/on succe$$ 9 obta9+ wire1 ! diamet] ( :i* did n exce$ ! #ahjjj? ( an in*4 ,a quantity ( ?is wire1 equal 9 bulk to a common die us$ 9 games ( *ance1 w\ld ext5d f ,p>is to ,rome4 7#ac47 ,newton succe$$ 9 det]m9+ ! ?ickness ( v ?9 lam9 ( transp>5t sub/ances by obs]v+ ! col\rs :i* !y reflect4 ,a soap bubble is a ?9 %ell ( wat]1 & is obs]v$ to reflect diff]5t col\rs f diff]5t p>ts ( its surface4 ,imm$iately be=e ! bubble bur/s1 a black spot may be obs]v$ ne> ! top4 ,at ?is "p ! ?ickness has be5 prov$ n to exce$ ! #b1ejj1jjj? ( an in*4 ,! transp>5t w+s ( c]ta9 insects are s att5uat$ 9 _! /ructure t #ej1jjj ( !m plac$ ov] ea* o!r w\ld n =m a pile a qu>t] ( an in* 9 height4 7#ad47 ,9 ! manufacture ( embroid]y x is necess>y to obta9 v f9e gilt silv] ?reads4 ,to accompli% ?is1 a cyl9drical b> ( silv]1 weigh+ #cfj ounces1 is cov]$ ) ab\t two ounces ( gold4 ,?is gilt b> is !n wire-drawn1 z 9 ! fir/ example1 until x is r$uc$ to a ?read s f9e t #cdjj feet ( x weigh less ?an an ounce4 ,! wire is !n flatt5$ by pass+ x betwe5 roll]s "u a sev]e pressure1 a process :i* increases its l5g?1 s t ab\t #djjj feet %all weigh "o ounce4 ,h5ce1 "o foot w weigh ! #djjj? "p ( an ounce4 ,! proportion ( ! gold to ! silv] 9 ! orig9al b> 0 t ( #b to #cfj1 or #a to #ahj4 ,s9ce ! same proportion is pres]v$ aft] ! b> has be5 wire-drawn1 x foll[s t ! quantity ( gold :i* cov]s "o foot ( ! f9e wire is ! #ahj? "p ( ! #djjj? ( an ounce2 t is ! #gbj1jjj? "p ( an ounce4 ,! quantity ( gold :i* cov]s "o in* ( ?is wire w be twelve times less ?an t :i* cov]s "o foot4 ,h5ce1 ?is quantity w be ! #h1fdj1jjj? "p ( an ounce4 ,if ?is in* be aga9 divid$ into #ajj equal p>ts1 e "p w be di/9ctly visible )\t ! aid ( microscopes4 ,! gold :i* cov]s ?is small b visible portion is ! #hfd1jjj1jjj? "p ( an ounce4 ,b we may proce$ ev5 fur!r2 ?is portion ( ! wire may be view$ by a microscope :i* magnifies #ejj times1 s t ! #ejj? "p ( x w ?us become visible4 ,9 ?is mann]1 !re=e1 an ounce ( gold may be divid$ into #dcb1jjj1jjj1jjj visible p>ts1 ea* ( :i* w possess all ! *>act]s & qualities f\nd 9 ! l>ge/ masses ( ! metal4 ,x w reta9 its solidity1 texture1 & col\r2 x w resi/ ! same ag5ts1 & ent] into comb9ation ) ! same sub/ances4 ,if ! gilt wire be dipp$ 9 nitric acid1 ! silv] )9 ! coat+ w be dissolv$1 b ! holl[ tube ( gold :i* surr\nd$ x w /ill coh]e & rema9 susp5d$4 7#ae47 ,! organis$ _w (f]s /ill m rem>kable examples ( ! inconceivable subtilty ( matt]4 ,! blood :i* fl[s 9 ! ve9s ( animals is n1 z x seems1 an uni=mly r$ liquid4 ,x consi/s ( flat discs ( a r$ col\r1 float+ 9 a transp>5t fluid call$ s]um4 ,9 diff]5t species ^! discs diff] bo? 9 figure & 9 magnitude4 ,9 man & all animals :i* suckle _! "y1 !y are p]fectly circul> or ne>ly s4 ,9 birds1 reptiles1 & fi%es1 !y are ( oval =m4 ,9 ! human species1 ! diamet] ( ^! discs is ab\t ! #cejj? ( an in*4 ,h5ce x foll[s1 t 9 a drop ( blood :i* w\ld rema9 susp5d$ f ! po9t ( a f9e ne$le1 !re mu/ be ab\t #c1jjj1jjj ( su* discs4 ,small z ^! discs are1 ! animal k+dom pres5ts be+s ^: :ole bodies are /ill m m9ute4 ,animalcules h be5 discov]$1 ^: magnitude is su*1 t a million ( !m d n exce$ ! bulk ( a gra9 ( s&2 & yet ea* ( ^! creatures is compos$ ( memb]s z curi\sly organis$ z ^? ( ! l>ge/ species2 !y h life & spontane\s motion1 & are endu$ ) s5se & in/9ct4 ,9 ! liquids 9 :i* !y live1 !y are obs]v$ to move ) a/oni%+ spe$ & activity2 nor are _! motions bl9d & =tuit\s1 b evid5tly gov]n$ by *oice1 & direct$ to an end4 ,!y use food & dr9k1 f :i* !y d]ive nutrition1 & are !re=e furni%$ ) a dige/ive app>atus4 ,!y h great muscul> p[]1 & are furni%$ ) limbs & muscles ( /r5g? & flexibility4 ,!y are susceptible ( ! same appetites1 & obnoxi\s to ! same passions1 ! gratification ( :i* is att5d$ ) ! same results z 9 our own species4 ,spallanzani obs]ves1 t c]ta9 animalcules dev\r o!rs s voraci\sly1 t !y fatt5 & become indol5t & sluggi% by ov]-fe$+4 ,aft] a meal ( ?is k9d1 if !y be conf9$ 9 di/ill$ wat]1 s z to be depriv$ ( all food1 _! condition becomes r$uc$2 !y rega9 _! _s & activity1 & amuse !mselves 9 ! pursuit ( ! m m9ute animals1 :i* are suppli$ to !m2 !y swall[ ^! )\t depriv+ !m ( life1 =1 by ! aid ( ! microscope1 ! "o has be5 obs]v$ mov+ )9 ! body ( ! o!r4 ,^! s+ul> appe>ances are n matt]s ( idle & curi\s obs]vation4 ,!y lead u to enquire :at p>ts are necess>y to produce su* results4 ,mu/ we n conclude t ^! creatures h he>t1 art]ies1 ve9s1 muscles1 s9ews1 t5dons1 n]ves1 circulat+ fluids1 & all ! concomitant app>atus ( a liv+ organis$ body8 ,& if s1 h[ inconceivably m9ute mu/ ^? p>ts be6 ,if a globule ( _! blood be>s ! same proportion to _! :ole bulk z a globule ( our blood be>s to our magnitude1 :at p[]s ( calculation c give an adequate notion ( its m9ut5ess8 7#af47 ,^! & _m o!r ph5om5a obs]v$ 9 ! imm$iate productions ( nature1 or develop$ by me*anical & *emical processes1 prove t ! mat]ials ( :i* bodies are =m$ are susceptible ( m9ut5ess :i* inf9itely exce$s ! p[]s ( s5sible obs]vation1 ev5 :5 ^? p[]s h be5 ext5d$ by all ! aids ( sci5ce4 ,%all we !n conclude t matt] is inf9itely divisible1 & t !re are no orig9al con/itu5t atoms ( det]m9ate magnitude & figure at :i* all subdivision mu/ cease8 ,su* an inf]5ce w\ld be unw>rant$1 ev5 _h we no o!r means ( judg+ ! "q1 except ^? ( direct obs]vation2 = x w\ld be impos+ t limit on ! works ( nature :i* %e has plac$ ^u our p[]s ( obs]v+ !m4 ,aid$ by reason1 h[ev]1 & a due consid]ation ( c]ta9 ph5om5a :i* come )9 our imm$iate p[]s ( obs]vation1 we are frequ5tly able to det]m9e o!r ph5om5a :i* are beyond ^? p[]s4 ,! diurnal motion ( ! e>? is n p]ceiv$ by u1 because all ?+s ar\nd u p>ticipate 9 x1 pres]ve _! relative position1 & appe> to be at re/4 ,b reason tells u t su* a motion mu/ produce ! alt]nations ( day & night1 & ! ris+ & sett+ ( all ! heav5ly bodies2 appe>ances :i* are pla9ly obs]vable1 & :i* betray ! cause f :i* !y arise4 ,aga91 we _c place ourselves at a di/ance f ! e>?1 & behold ! axis on :i* x revolves1 & obs]ve its peculi> obliquity to ! orbit 9 :i* ! e>? moves2 b we see & feel ! vicissitudes ( ! seasons1 an effect :i* is ! imm$iate consequ5ce ( t incl9ation1 & by :i* we are able to detect x4 7#ag47 ,s x is 9 ! pres5t case4 ,al?\gh we are unable by direct obs]vation to prove ! exi/5ce ( con/itu5t mat]ial atoms ( det]m9ate figure1 yet !re are _m obs]vable ph5om5a :i* r5d] _! exi/5ce 9 ! highe/ degree probable1 if n morally c]ta94 ,! mo/ rem>kable ( ?is class ( effects is obs]v$ 9 ! cry/allisation ( salts4 ,:5 salt is dissolv$ 9 a suffici5t quantity ( pure wat]1 x mixes ) ! wat] 9 su* a mann] z :olly to disappe> to ! sight & t\*1 ! mixture be+ "o uni=m transp>5t liquid l ! wat] itself1 be=e its union ) ! salt4 ,! pres5ce ( ! salt 9 ! wat] may1 h[ev]1 be asc]ta9$ by weigh+ ! mixture1 :i* w be f\nd to exce$ ! orig9al weight ( ! wat] by ! exact am\nt ( ! weight ( ! salt4 ,x is a well-kn[n fact1 t a c]ta9 degree ( heat w conv]t wat] into vap\r1 & t ! same degree ( heat does n produce ! same effect ^u salt4 ,! mixture ( salt & wat] be+ expos$ to ?is temp]ature1 ! wat] w gradually evaporate1 dis5gag+ itself f ! salt ) :i* x has be5 comb9$4 ,:5 s mu* ( ! wat] has evaporat$1 t :at rema9s is insuffici5t to keep 9 solution ! :ole ( ! salt1 a "p ( ! latt] ?us dis5gag$ f ! wat] w return to ! solid /ate4 ,! sal9e con/itu5t w n 9 ?is case collect 9 irregul> solid molecules2 b w exhibit itself 9 p>ticles ( regul> figure1 t]m9at$ by plane surfaces1 ! figure be+ always ! same = ! same species ( salt1 b diff]5t = diff]5t species4 ,^! p>ticles are call$ cry/als4 ,!re are sev]al circum/ances 9 ! =mation ( ^! cry/als :i* m]it att5tion4 ,if "o ( !m be deta*$ f ! o!rs1 & ! progress ( its =mation obs]v$1 x w be f\nd gradually to increase1 always pres]v+ its orig9al figure4 ,s9ce its increase mu/ be caus$ by ! cont9u$ accession ( sal9e molecules1 dis5gag$ by ! evaporation ( ! wat]1 x foll[s t ^! molecules mu/ be s =m$1 t by atta*+ !mselves successively to ! cry/al1 !y ma9ta9 ! regul>ity ( its b\nd+ planes1 & pres]ve _! mutual incl9ations unv>i$4 ,suppose a cry/al to be tak5 f ! liquid dur+ ! process ( cry/allisation1 & a piece brok5 f x s z to de/roy ! regul>ity ( its =m3 if ! cry/al ?us brok5 be re/or$ to ! liquid1 x w be obs]v$ gradually to resume its regul> =m1 ! atoms ( salt successively dismiss$ by ! vaporis+ wat] fill+ up ! irregul> cavities produc$ by ! fracture4 ,h5ce x foll[s1 t ! sal9e p>ticles :i* compose ! surface ( ! cry/al1 & ^? :i* =m ! int]ior ( its mass1 are simil>1 & ex]t simil> attractions on ! atoms dis5gag$ by ! wat]4 ,all ^! details ( ! process ( cry/allisation are v evid5t indications ( a det]m9ate figure 9 ! ultimate atoms ( ! sub/ances :i* are cry/allis$4 ,b besides ! sub/ances :i* are ?us r$uc$ by art to ! =m ( cry/als1 !re are l>g] classes :i* naturally exi/ 9 t /ate4 ,!re are c]ta9 planes1 call$ planes ( cleavage1 9 ! directions ( :i* natural cry/als are easily divid$4 ,^! planes1 9 sub/ances ( ! same k9d1 always h ! same relative position1 b diff] 9 diff]5t sub/ances4 ,! surfaces ( ! planes ( cleavage are q invisible be=e ! cry/al is divid$2 b :5 ! p>ts are sep>at$1 ^! surfaces exhibit a mo/ int5se poli%1 :i* no ef=t ( art c equal4 ,we may conceive cry/allis$ sub/ances to be regul> me*anical /ructures =m$ ( atoms ( a c]ta9 figure1 on :i* ! figure ( ! :ole /ructure mu/ dep5d4 ,! planes ( cleavage are p>allel to ! sides ( ! con/itu5t atoms2 & _! directions1 !re=e1 =m s _m conditions = ! det]m9ation ( _! figure4 ,! %ape ( ! atoms be+ ?us det]m9$1 x is n difficult to assign all ! v>i\s ways 9 :i* !y may be arrang$1 s z to produce figures :i* are accord+ly f\nd to correspond ) ! v>i\s =ms ( cry/als ( ! same sub/ance4 7#ah47 ,:5 ^! ph5om5a are duly consid]$ & comp>$1 little d\bt c rema9 t all sub/ances susceptible ( cry/allisation1 consi/ ( atoms ( det]m9ate figure4 ,?is is ! case ) all solid bodies :atev]1 :i* h come "u sci5tific obs]vation1 = !y h be5 sev]ally f\nd 9 or r$uc$ to a cry/allis$ =m4 ,liquids cry/allise 9 freez+1 & if ari=m fluids c\ld by any means be r$uc$ to ! solid =m1 !y w\ld probably also manife/ ! same effect4 ,h5ce x appe>s reasonable to presume1 t all bodies are compos$ ( atoms2 t ! diff]5t qualities ) :i* we f9d diff]5t sub/ances endu$1 dep5d on ! magnitude & figure ( ^! atoms2 t ^! atoms are inde/ructible & immutable by any natural process1 = we f9d ! qualities :i* dep5d on !m un*angeably ! same "u all ! influ5ces to :i* !y h be5 submitt$ s9ce _! creation2 t ^! atoms are s m9ute 9 _! magnitude1 t !y _c be obs]v$ by any means :i* human art has yet contriv$2 b /ill t magnitudes c be assign$ :i* !y d n exce$4 ,x is prop]1 h[ev]1 to obs]ve "h1 t ! v>i\s !orems ( me*anical sci5ce d n re/ ^u any hypo!sis conc]n+ ^! atoms z a basis4 ,^! !orems are n inf]r$ f ?is or any o!r supposition1 & !re=e _! tru? w\ld n be 9 anywise di/urb$1 ev5 ?\gh x %\ld be e/abli%$ t matt] is physically divisible 9 inf9itum4 ,! basis ( me*anical sci5ce is obs]v$ facts1 &1 s9ce ! reason+ is demon/rative1 ! conclusions h ! same degree ( c]ta9ty z ! facts f :i* !y are d$uc$4 7#ai47 ,porosity4--,! volume ( a body is ! quantity ( space includ$ )9 its ext]nal surfaces4 ,! mass ( a body1 is ! collection ( atoms or mat]ial p>ticles ( :i* x consi/s4 ,two atoms or p>ticles are said to be 9 contact1 :5 !y h approa*$ ea* o!r until arre/$ by _! mutual imp5etrability4 ,if ! compon5t p>ticles ( a body 7 9 contact1 ! volume w\ld be completely occupi$ by ! mass4 ,b ?is is n ! case4 ,we %all pres5tly prove1 t ! compon5t p>ticles ( no kn[n sub/ance are 9 absolute contact4 ,h5ce x foll[s t ! volume consi/s p>tly ( mat]ial p>ticles1 & p>tly ( int]/itial spaces1 :i* spaces are ei!r absolutely void & empty1 or fill$ by "s sub/ance ( a diff]5t k9d f ! body 9 "q4 ,^! int]/itial spaces are call$ pores4 ,9 bodies :i* are con/itut$ uni=mly ?r\gh\t _! entire dim5sions1 ! compon5t p>ticles & ! pores are uni=mly di/ribut$ ?r\gh ! volume2 t is1 a giv5 space 9 "o "p ( ! volume w conta9 ! same quantity ( matt] & ! same quantity ( pores z an equal space 9 ano!r "p4 7#bj47 ,! proportion ( ! quantity ( matt] to ! magnitude is call$ ! d5sity4 ,?us if ( two sub/ances1 "o conta9 9 a giv5 space twice z mu* matt] z ! o!r1 x is said to be 8twice z d5se40 ,! d5sity ( bodies is1 !re=e1 proportionate to ! clos5ess or proximity ( _! p>ticles2 & x is evid5t1 t ! great] ! d5sity1 ! less w be ! porosity4 ,! pores ( a body are frequ5tly fill$ ) ano!r body ( a m subtle nature4 ,if ! pores ( a body on ! surface ( ! e>?1 & expos$ to ! atmosph]e1 be great] ?an ! atoms ( air1 !n ! air may p]vade ! pores4 ,?is is f\nd to be ! case ) _m sorts ( wood :i* h an op5 gra94 ,if a piece ( su* wood1 or ( *alk1 or ( sug>1 be press$ to ! bottom ( a vessel ( wat]1 ! air :i* fills ! pores w be obs]v$ to escape 9 bubbles & to rise to ! surface1 ! wat] ent]+ ! pores1 & tak+ its place4 ,if a tall vessel or tube1 hav+ a wood5 bottom1 be fill$ ) quicksilv]1 ! liquid metal w be =c$ by its own weight ?r\gh ! pores ( ! wood1 & w be se5 escap+ 9 a silv] %[] f ! bottom4 7#ba47 ,! process ( filtration1 9 ! arts1 dep5ds on ! pres5ce ( pores ( su* a magnitude z to all[ a passage to ! liquid1 b to refuse x to ^? impurities f :i* x is to be dis5gag$4 ,v>i\s sub/ances are us$ z filtres2 b1 :atev] be us$1 ?is circum/ance %\ld always be rememb]$1 t no sub/ance c be sep>at$ f a liquid by filtration1 except "o ^: p>ticles are l>g] ?an ^? ( ! liquid4 ,9 g5]al1 filtres are us$ to sep>ate solid impurities f a liquid4 ,! mo/ ord9>y filtres are s(t /one1 pap]1 & *>coal4 7#bb47 ,all organis$ sub/ances 9 ! animal & vegetable k+doms are1 f _! v natures1 por\s 9 a high degree4 ,m9]als are por\s 9 v>i\s degrees4 ,among ! silici\s /ones is "o call$ hydrophane1 :i* manife/s its porosity 9 a v rem>kable mann]4 ,! /one1 9 its ord9>y /ate1 is semi-transp>5t4 ,if1 h[ev]1 x be plung$ 9 wat]1 :5 x is )drawn x is z transluc5t z glass4 ,! pores1 9 ?is case1 previ\sly fill$ ) air1 are p]vad$ by ! wat]1 betwe5 :i* & ! /one !re subsi/s a physical relation1 by :i* ! "o r5d]s ! o!r p]fectly transp>5t4 ,l>g] m9]al masses exhibit degrees ( porosity n less /rik+4 ,wat] p]colates ?r\gh ! sides & ro(s ( cav]ns & grottoes1 & be+ impregnat$ ) calc>e\s & o!r e>?s1 =ms /alactites1 or p5dant protub]ances1 :i* pres5t a curi\s appe>ance4 7#bc47 ,compressibility4--,t quality1 9 virtue ( :i* a body all[s its volume to be dim9i%$ )\t dim9i%+ its mass1 is call$ compressibility4 ,?is effect is produc$ by br++ ! con/itu5t p>ticles m close toge!r1 & !reby increas+ ! d5sity & dim9i%+ ! pores4 ,?is effect may be produc$ 9 sev]al ways2 b ! "n 8compressibility0 is only appli$ to x :5 x is caus$ by ! ag5cy ( me*anical =ce1 z by pressure or p]cussion4 ,all kn[n bodies1 :atev] be _! nature1 are capable ( hav+ _! dim5sions r$uc$ )\t dim9i%+ _! mass2 & ?is is "o ( ! mo/ conclusive pro(s t all bodies are por\s1 or t ! con/itu5t atoms are n 9 contact2 = ! space by :i* ! volume may be dim9i%$ mu/1 be=e ! dim9ution1 consi/ ( pores4 7#bd47 ,ela/icity4--,"s bodies1 :5 compress$ by me*anical ag5cy1 w resume _! =m] dim5sions ) a c]ta9 en]gy :5 reliev$ f ! op]ation ( ! =ce :i* has compress$ !m4 ,?is prop]ty is call$ ela/icity2 & x foll[s1 f ?is def9ition1 t all ela/ic bodies mu/ be compressible1 al?\gh ! conv]se is n true1 compressibility n necess>ily imply+ ela/icity4 7#be47 ,dilatability4--,?is quality is ! opposite ( compressibility4 ,x is ! capability obs]v$ 9 bodies to h _! volume enl>g$ )\t increas+ _! mass4 ,?is effect may be produc$ 9 sev]al ways4 ,9 ord9>y circum/ances1 a body may exi/ "u ! con/ant action ( a pressure by :i* its volume & d5sity are det]m9$4 ,x may happ51 t on ! occasional removal ( t pressure1 ! body w dilate by a quality inh]5t 9 its con/itution4 ,?is is ! case ) common air4 ,dilatation may also be ! effect ( heat1 z w pres5tly appe>4 ,! sev]al qualities ( bodies :i* we h notic$ 9 ?is *apt]1 :5 view$ 9 relation to ea* o!r1 pres5t _m circum/ances wor?y ( att5tion4 7#bf47 ,x is a physical law1 ( high g5]ality1 t an increase 9 ! temp]ature1 or degree ( heat by :i* a body is affect$1 is accompani$ by an increase ( volume2 & t a dim9ution ( temp]ature is accompani$ by a dim9ution ( volume4 ,! exceptions to ?is law w be notic$ & expla9$ 9 our treatise on ,,heat4 ,h5ce x appe>s t ! r$uction ( temp]ature is an effect :i*1 consid]$ me*anically1 is equival5t to compression or cond5sation1 s9ce x dim9i%es ! volume )\t alt]+ ! mass2 & s9ce ?is is an effect ( :i* all bodies :atev] are susceptible1 x foll[s t all bodies :atev] h pores4 7#bc47 ,! fact1 t ! elevation ( temp]ature produces an increase ( volume1 is manife/$ by num]\s exp]im5ts4 7#bg47 ,if a flaccid bladd] be ti$ at ! m\?1 s z to /op ! escape ( air1 & be !n held be=e a fire1 x w gradually swell1 & assume ! appe>ance ( be+ fully inflat$4 ,! small quantity ( air conta9$ 9 ! bladd] is1 9 ?is case1 s mu* dilat$ by ! heat1 t x occupies a consid]ably increas$ space1 & fills ! bladd]1 ( :i* x be=e only occupi$ a small "p4 ,:5 ! bladd] is remov$ f ! fire1 & all[$ to resume its =m] temp]ature1 ! air returns to its =m] dim5sions1 & ! bladd] becomes aga9 flaccid4 7#bh47 ,let ,a ,b1 fig4 #b4 be a glass tube1 ) a bulb at ! end ,a2 & let ! bulb ,a1 & a "p ( ! tube1 be fill$ ) any liquid1 col\r$ s z to be visible4 ,let ,c be ! level ( ! liquid 9 ! tube4 ,if ! bulb be n[ expos$ to heat1 by be+ plung$ 9 hot wat]1 ! level ( ! liquid ,c w rapidly rise t[>ds ,b4 ,?is effect is produc$ by ! dilatation ( ! liquid 9 ! bulb1 :i* fill+ a great] space1 a "p ( x is =c$ into ! tube4 ,?is exp]im5t may easily be made ) a common glass tube & a little port w9e4 ,!rmomet]s are con/ruct$ on ?is pr9ciple1 ! rise ( ! liquid 9 ! tube be+ us$ z an indication ( ! degree ( heat :i* causes x4 ,a p>ticul> acc\nt ( ^! useful in/rum5ts w be f\nd 9 our treatise on ,,heat4 7#bi47 ,! *ange ( dim5sion ( solids produc$ by *anges ( temp]ature be+ mu* less ?an t ( bodies 9 ! liquid or a]i=m /ate1 is n s easily obs]vable4 ,a rem>kable in/ance occurs 9 ! process ( %oe+ ! :eels ( c>riages4 ,! rim ( iron ) :i* ! :eel is to be b\nd1 is made 9 ! fir/ in/ance ( a diamet] some:at less ?an t ( ! :eel2 b be+ rais$ by ! application ( fire to a v high temp]ature1 its volume receives su* an increase1 t x w be suffici5t to embrace & surr\nd ! :eel4 ,:5 plac$ ^u ! :eel x is cool$1 & sudd5ly contract+ its dim5sions1 b9ds ! p>ts ( ! :eel firmly toge!r1 & becomes securely seat$ 9 its place ^u ! fellies4 7#cj47 ,x frequ5tly happ5s t ! /opp] ( a glass bottle or decant] becomes fix$ 9 its place s firmly1 t ! ex]tion ( =ce suffici5t to )draw x w\ld endang] ! vessel4 ,9 ?is case1 if a clo? wett$ ) hot-wat] be appli$ to ! neck ( ! bottle1 ! glass w exp&1 & ! neck w be enl>g$1 s z to all[ ! /opp] to be easily )drawn4 7#ca47 ,! contraction ( metal consequ5t ^u *ange ( temp]ature 0 appli$ "s "t ago 9 ,p>is to re/ore ! walls ( a tott]+ build+ to _! prop] position4 ,9 ! ,cons]vatoire des ,arts et ,mti]s1 ! walls ( a "p ( ! build+ 7 =c$ out ( ! p]p5dicul> by ! weight ( ! ro(1 s t ea* wall 0 lean+ outw>ds4 ,m4 ,mol>d conceiv$ ! notion ( apply+ ! irresi/ible =ce ) :i* metals contract 9 cool+1 to draw ! walls toge!r4 ,b>s ( iron 7 plac$ 9 p>allel directions across ! build+1 & at "r-angles to ! direction ( ! walls4 ,be+ pass$ ?r\gh ! walls1 nuts 7 screw$ on _! ends1 outside ! build+4 ,e alt]nate b> 0 !n heat$ by lamps1 & ! nuts screw$ close to ! walls4 ,! b>s 7 !n cool$1 & ! l5g?s be+ dim9i%$ by contraction1 ! nuts on _! extremities 7 drawn toge!r1 & ) !m ! walls 7 drawn ?r\gh an equal space4 ,! same process 0 repeat$ ) ! int]m$iate b>s1 & s on alt]nately until ! walls 7 br\ght into a p]p5dicul> position4 7#cb47 ,s9ce !re is a cont9ual *ange ( temp]ature 9 all bodies on ! surface ( ! globe1 x foll[s1 t !re is also a cont9ual *ange ( magnitude4 ,! sub/ances :i* surr\nd u are con/antly swell+ & contract+1 "u ! vicissitudes ( heat & cold4 ,!y gr[ small] 9 w9t]1 & dilate 9 summ]4 ,!y swell _! bulk on a w>m day1 & contract x on a cold "o4 ,^! curi\s ph5om5a are n notic$1 only because our ord9>y means ( obs]vation are n suffici5tly accurate to appreciate !m4 ,nev]!less1 9 "s famili> in/ances ! effect is v obvi\s4 ,9 w>m wea!r ! fle% swells1 ! vessels appe> fill$1 ! h& is plump1 & ! sk9 di/5d$4 ,9 cold wea!r1 :5 ! body has be5 expos$ to ! op5 air1 ! fle% appe>s to contract1 ! vessels %r9k1 & ! sk9 %rivels4 7#cc47 ,! ph5om5a att5d+ *ange ( temp]ature are conclusive pro(s ( ! univ]sal porosity ( mat]ial sub/ances1 b !y are n ! only pro(s4 ,_m sub/ances admit ( compression by ! m]e ag5cy ( me*anical =ce4 ,let a small piece ( cork be plac$ float+ on ! surface ( wat] 9 a bas9 or o!r vessel1 & an empty glass goblet be inv]t$ ov] ! cork1 s t its edge j meets ! wat]4 ,a portion ( air w !n be conf9$ 9 ! goblet1 & deta*$ f ! rema9d] ( ! atmosph]e4 ,if ! goblet be n[ press$ d[nw>ds1 s z to be entirely imm]s$1 x w be obs]v$1 t ! wat] w n fill x1 be+ exclud$ by ! imp5etrability ( ! air inclos$ 9 x4 ,?is exp]im5t1 !re=e1 is decisive ( ! fact1 t air1 "o ( ! mo/ subtle & att5uat$ sub/ances we "k (1 possesses ! quality ( imp5etrability4 ,x absolutely excludes any o!r body f ! space :i* x occupies at any giv5 mom5t4 ,b al?\gh ! wat] does n fill ! goblet1 yet if ! position ( ! cork :i* floats ^u its surface be notic$1 x w be f\nd t ! level ( ! wat] )9 has ris5 above its edge or rim4 ,9 fact1 ! wat] has p>tially fill$ ! goblet1 & ! air has be5 =c$ to contract its dim5sions4 ,?is effect is produc$ by ! pressure ( ! incumb5t wat] =c+ ! surface 9 ! goblet aga9/ ! air1 :i* yields until x is s f> compress$ t x acquires a =ce able to )/& ?is pressure4 ,?us x appe>s t air is capable ( be+ r$uc$ 9 its dim5sions by me*anical pressure1 indep5d5tly ( ! ag5cy ( heat4 ,x is compressible4 ,t ?is effect is ! consequ5ce ( ! pressure ( ! liquid w be easily made manife/ by %[+ t1 z ! pressure is increas$1 ! air is proportionally contract$ 9 its dim5sions2 & z x is dim9i%$1 ! dim5sions are on ! o!r h& enl>g$4 ,if ! dep? ( ! goblet 9 ! wat] be increas$1 ! cork w be se5 to rise 9 x1 %[+ t ! increas$ pressure1 at ! great] dep?1 causes ! air 9 ! goblet to be m cond5s$4 ,if1 on ! o!r h&1 ! goblet be rais$ t[>d ! surface1 ! cork w be obs]v$ to desc5d t[>d ! edge1 %[+ t z x is reliev$ f ! pressure ( ! liquid1 ! air gradually approa*es to its primitive dim5sions4 7#cd47 ,^! ph5om5a also prove1 t air has ! prop]ty ( ela/icity4 ,if x 7 simply compressible1 & n ela/ic1 x w\ld reta9 ! dim5sions to :i* x 0 r$uc$ by ! pressure ( ! liquid2 b ?is is n f\nd to be ! result4 ,z ! compress+ =ce is dim9i%$1 s 9 ! same proportion does ! air1 by its ela/ic virtue1 ex]t a =ce by :i* x resumes its =m] dim5sions4 ,t x is ! air alone :i* excludes ! wat] f ! goblet1 9 ! prec$+ exp]im5ts1 c easily be prov$4 ,:5 ! goblet is sunk deep 9 ! vessel ( wat]1 let x be incl9$ a little to "o side until its m\? is pres5t$ t[>ds ! side ( ! vessel2 let ?is incl9ation be s regulat$1 t ! surface ( ! wat] 9 ! goblet %all j rea* its edge4 ,^u a slight increase ( incl9ation1 air w be obs]v$ to escape f ! goblet1 & to rise 9 bubbles to ! surface ( ! wat]4 ,if ! goblet be !n re/or$ to its position1 x w be f\nd t ! cork w rise high] 9 x ?an be=e ! escape ( ! air4 ,! wat] 9 ?is case rises & fills ! space :i* ! air all[$ to escape has des]t$4 ,! same process may be repeat$ until all ! air has escap$1 & !n ! goblet w be completely fill$ by ! wat]4 7#ce47 ,liquids are compressible by me*anical =ce 9 s slight a degree1 t !y are consid]$ 9 all hydro/atical treatises z incompressible fluids4 ,!y are1 h[ev]1 n absolutely incompressible1 b yield slightly to v int5se pressure4 ,! "q ( ! compressibility ( liquids 0 rais$ at a remote p]iod 9 ! hi/ory ( sci5ce4 ,ne>ly two c5turies ago1 an exp]im5t 0 in/itut$ at ! ,academy del ,cim5to 9 ,flor5ce1 to asc]ta9 :e!r wat] be compressible4 ,) ?is view1 a holl[ ball ( gold 0 fill$ ) ! liquid1 & ! ap]ture exactly & firmly clos$4 ,! globe 0 !n submitt$ to a v sev]e pressure1 by :i* its figure 0 slightly *ang$4 ,n[ x is prov$ 9 geometry1 t a globe has ?is peculi> prop]ty1 t any *ange :atev] 9 its figure mu/ necess>ily dim9i% its volume or cont5ts4 ,h5ce x 0 inf]r$1 t if ! wat] did n issue ?r\gh ! pores ( ! gold1 or bur/ ! globe1 its compressibility w\ld be e/abli%$4 ,! result ( ! exp]im5t 01 t ! wat] did ooze ?r\gh ! pores1 & cov]$ ! surface ( ! globe1 pres5t+ ! appe>ance ( dew1 or ( /eam cool$ by ! metal4 ,b ?is exp]im5t 0 inconclusive4 ,x is q true1 t if ! wat] _h n escap$ ^u ! *ange ( figure ( ! globe1 ! compressibility ( ! liquid w\ld h be5 e/abli%$4 ,! escape ( ! wat] does n1 h[ev]1 prove its incompressibility4 ,to accompli% ?is1 x w\ld be necess>y fir/ to measure accurately ! volume ( wat] :i* transud$ by compression1 & next to measure ! dim9ution ( volume :i* ! vessel suff]$ by its *ange ( figure4 ,if ?is dim9ution 7 great] ?an ! volume ( wat] :i* escap$1 x w\ld foll[ t ! wat] rema9+ 9 ! globe _h be5 compress$1 not)/&+ ! escape ( ! rema9d]4 ,b ?is c\ld nev] be accompli%$ ) ! delicacy & exactitude necess>y 9 su* an exp]im5t2 &1 consequ5tly1 z f> z ! "q ( ! compressibility ( wat] 0 conc]n$1 no?+ 0 prov$4 ,x =ms1 h[ev]1 a v /rik+ illu/ration ( ! porosity ( s d5se a sub/ance z gold1 & proves t its pores are l>g] ?an ! elem5t>y p>ticles ( wat]1 s9ce ^! are capable ( pass+ ?r\gh !m4 7#cf47 ,x has s9ce be5 prov$1 t wat]1 & o!r liquids1 are compressible4 ,9 ! ye> #agfa1 ,canton communicat$ to ! ,royal ,society ! results ( "s exp]im5ts :i* prov$ ?is fact4 ,he provid$ a glass tube ) a bulb1 su* z t describ$ 9 7#bh71 & fill$ ! bulb & a "p ( ! tube ) wat] well purifi$ f air4 ,he !n plac$ ?is 9 an app>atus call$ a cond5s]1 by :i* he 0 enabl$ to submit ! surface ( ! liquid 9 ! tube to v int5se pressure ( cond5s$ air4 ,he f\nd t ! level ( ! liquid 9 ! tube fell 9 a p]ceptible degree ^u ! application ( ! pressure4 ,! same exp]im5t e/abli%$ ! fact1 t liquids are ela/ic2 = ^u remov+ ! pressure1 ! liquid rose to its orig9al level1 & !re=e resum$ its =m] dim5sions4 7#cg47 ,ela/icity does n always accompany compressibility4 ,if lead or iron be submitt$ to ! hamm]1 x may be h>d5$ & dim9i%$ 9 its volume2 b x w n resume its =m] volume aft] ea* /roke ( ! hamm]4 7#ch47 ,!re are "s bodies :i* ma9ta9 ! /ate ( d5sity 9 :i* !y are commonly f\nd by ! cont9ual ag5cy ( me*anical pressure2 & su* bodies are endu$ ) a quality1 9 virtue ( :i* !y w\ld enl>ge _! dim5sions )\t limit1 if ! pressure :i* conf9es !m 7 remov$4 ,su* bodies are call$ ela/ic fluids or gases1 & always exi/ 9 ! =m ( common air1 9 ^: me*anical prop]ties !y p>ticipate4 ,!y are h5ce (t5 call$ a]i=m fluids4 ,^? :o are provid$ ) an air-pump c easily e/abli% ?is prop]ty exp]im5tally4 ,take a flaccid bladd]1 su* z t already describ$ 9 7#bg471 & place x "u ! glass receiv] ( an air-pump3 by ?is in/rum5t we %all be able to remove ! air :i* surr\nds ! bladd] "u ! receiv]1 s z to relieve ! small quantity ( air :i* is inclos$ 9 ! bladd] f ! pressure ( ! ext]nal air3 :5 ?is is accompli%$1 ! bladd] w be obs]v$ to swell1 z if x 7 inflat$1 & w be p]fectly di/5d$4 ,! air conta9$ 9 x1 !re=e1 has a t5d5cy to dilate1 :i* takes effect :5 x ceases to be resi/$ by ! pressure ( surr\nd+ air4 7#ci47 ,x has be5 /at$ t ! increase or dim9ution ( temp]ature is accompani$ by an increase or dim9ution ( volume4 ,relat$ to ?is1 !re is ano!r ph5om5on too rem>kable to pass unnotic$1 al?\gh ?is is n ! prop] place to dwell ^u x3 x is ! conv]se ( ! =m]2 viz4 t an increase or dim9ution ( bulk is accompani$ by a dim9ution or increase ( temp]ature4 ,z ! application ( heat f "s =eign s\rce produces an increase ( dim5sions1 s if ! dim5sions be increas$ f any o!r cause1 a correspond+ portion ( ! heat :i* ! body _h be=e ! enl>gem5t1 w be absorb$ 9 ! process1 & ! temp]ature w be !reby dim9i%$4 ,9 ! same way1 s9ce ! ab/raction ( heat causes a dim9ution ( volume1 s if t dim9ution be caus$ by any o!r means1 ! body w give out ! heat :i* 9 ! o!r case 0 ab/ract$1 & w rise 9 its temp]ature4 ,num]\s & well-kn[n facts illu/rate ^! obs]vations4 ,a smi? by hamm]+ a piece ( b> iron1 & !reby compress+ x1 w r5d] x r$ hot4 ,:5 air is viol5tly compress$1 x becomes s hot z to ignite cotton & o!r sub/ances4 ,an +5i\s in/rum5t = produc+ a light = dome/ic uses has be5 con/ruct$1 consi/+ ( a small cyl9d]1 9 :i* a solid pi/on moves air-tight3 a little t9d]1 or dry sponge1 is atta*$ to ! bottom ( ! pi/on1 :i* is !n viol5tly =c$ into ! cyl9d]3 ! air betwe5 ! bottom ( ! cyl9d] & ! pi/on becomes int5sely compress$1 & evolves s mu* heat z to light ! t9d]4 ,9 all ! cases :]e friction or p]cussion produces heat or fire1 x is because !y are means ( compression4 ,! effects ( fl9ts1 ( pieces ( wood rubb$ toge!r1 ! w>m? produc$ by friction on ! fle%1 are all to be attribut$ to ! same cause4 ,,*ap4 ,,iii4 ,,in]tia4 7#dj47 ,! quality ( matt] :i* is ( all o!rs ! mo/ important 9 me*anical inve/igations1 is t :i* has be5 call$ ,in]tia4 ,matt] is incapable ( spontane\s *ange4 ,?is is "o ( ! e>lie/ & mo/ univ]sal results ( human obs]vation3 x is equival5t to /at+ t m]e matt] is depriv$ ( life2 = spontane\s action is ! only te/ ( ! pres5ce ( ! liv+ pr9ciple4 ,if we see a mass ( matt] und]go any *ange1 we nev] seek = ! cause ( t *ange 9 ! body itself2 we look = "s ext]nal cause produc+ x4 ,?is inability = volunt>y *ange ( /ate or qualities is a m g5]al pr9ciple ?an in]tia4 ,at any giv5 mom5t ( "t a body mu/ be 9 "o or o!r ( two /ates1 re/ or motion4 ,in]tia1 or inactivity1 signifies ! total abs5ce ( p[] to *ange ?is /ate4 ,a body endu$ ) in]tia _c ( itself1 & indep5d5t ( all ext]nal influ5ce1 comm5ce to move f a /ate ( re/2 nei!r c x :5 mov+ arre/ its progress & become quiesc5t4 7#da47 ,! same prop]ty by :i* a body is unable by any p[] ( its own to pass f a /ate ( re/ to "o ( motion1 or vice v]s1 also r5d]s x incapable ( increas+ or dim9i%+ any motion :i* x may h receiv$ f an ext]nal cause4 ,if a body be mov+ 9 a c]ta9 direction at ! rate ( t5 miles p] h\r1 x _c by any en]gy ( its own *ange its rate ( motion to elev5 or n9e miles an h\r4 ,?is is a direct consequ5ce ( t manife/ation ( in]tia :i* has j be5 expla9$4 ,= ! same p[] :i* w\ld cause a body mov+ at t5 miles an h\r to increase its rate to elev5 miles1 w\ld also cause ! same body at re/ to comm5ce mov+ at ! rate ( "o mile an h\r2 & ! same p[] :i* w\ld cause a body mov+ at ! rate ( t5 miles an h\r to move at ! rate ( n9e miles 9 ! h\r1 w\ld cause ! same body mov+ at ! rate ( "o mile an h\r to become quiesc5t4 ,x !re=e appe>s1 t to increase or dim9i% ! motion ( a body is an effect ( ! same k9d z to *ange ! /ate ( re/ into t ( motion1 or vice v]s4 7#db47 ,! effects & ph5om5a :i* h\rly fall "u our obs]vation af=d unnumb]$ examples ( ! inability ( lifeless matt] to put itself into motion1 or to increase any motion :i* may h be5 communicat$ to x4 ,b x does n happ5 t we h ! same direct & frequ5t evid5ce ( its inability to de/roy or dim9i% any motion :i* x may h receiv$4 ,& h5ce x arises1 t :ile no "o w d5y to matt] ! =m] effect ( in]tia1 few w at fir/ ackn[l$ge ! latt]4 ,inde$1 ev5 s late z ! "t ( ,,kepl]1 philosoph]s !mselves held x z a maxim1 t 8matt] is m incl9$ to re/ ?an to motion20 we ought n1 !re=e1 to be surpris$ if 9 ! pres5t day ^? :o h n be5 conv]sant ) physical sci5ce are sl[ to believe t a body once put 9 motion w\ld cont9ue = ev] to move ) ! same velocity1 if x 7 n /opp$ by "s ext]nal cause4 ,reason1 assi/$ by obs]vation1 w1 h[ev]1 soon dispel ?is illusion4 ,exp]i5ce %[s u 9 v>i\s ways1 t ! same causes :i* de/roy motion 9 "o direction are capable ( produc+ z mu* motion 9 ! opposite direction4 ,?us1 if a :eel1 sp9n+ on its axis ) a c]ta9 velocity1 be /opp$ by a h& seiz+ "o ( ! spokes1 ! ef=t :i* accompli%es ?is is exactly ! same z1 _h ! :eel be5 previ\sly at re/1 w\ld h put x 9 motion 9 ! opposite direction ) ! same velocity4 ,if a c>riage drawn by horses be 9 motion1 ! same ex]tion ( p[] 9 ! horses is necess>y to /op x1 z w\ld be necess>y to back x1 if x 7 at re/4 ,n[1 if ?is be admitt$ z a g5]al pr9ciple1 x mu/ be evid5t t a body :i* c de/roy or dim9i% its own motion mu/ also be capable ( putt+ itself into motion f a /ate ( re/1 or ( increas+ any motion :i* x has receiv$4 ,b ?is latt] is contr>y to all exp]i5ce1 & !re=e we are compell$ to admit t a body _c dim9i% or de/roy any motion :i* x has receiv$4 ,let u enquire :y we are m dispos$ to admit ! inability ( matt] to produce ?an to de/roy motion 9 itself4 ,we see mo/ ( ^? motions :i* take place ar\nd u on ! surface ( ! e>? subject to gradual decay1 & if n r5ew$ f "t to "t1 at l5g? cease4 ,a /one roll$ along ! gr\nd1 a :eel revolv+ on its axis1 ! heav+ ( ! deep aft] a /orm1 & all o!r motions produc$ 9 bodies by ext]nal causes1 decay1 :5 ! excit+ cause is susp5d$2 & if t cause d n r5ew its action1 !y ultimately cease4 ,b is !re no excit+ cause1 on ! o!r h&1 :i* ?us gradually deprives ^? bodies ( _! motion8--& if t cause 7 remov$1 or its int5sity dim9i%$1 w\ld n ! motion cont9ue1 or be m sl[ly ret>d$8 ,:5 a /one is roll$ along ! gr\nd1 ! inequalities ( its %ape z well z ^? ( ! gr\nd are imp$im5ts1 :i* ret>d & soon de/roy its motion4 ,r5d] ! /one r\nd1 & ! gr\nd level1 & ! motion w be consid]ably prolong$4 ,b /ill small asp]ities w rema9 on ! /one1 & on ! surface ov] :i* x rolls3 sub/itute = ! /one a ball ( highly-poli%$ /eel1 mov+ on a highly-poli%$ /eel plane1 truly level1 & ! motion w cont9ue )\t s5sible dim9ution = a v long p]iod2 b ev5 "h1 & 9 e in/ance ( motions produc$ by art1 m9ute asp]ities mu/ exi/ on ! surfaces :i* move 9 contact ) ea* o!r1 :i* mu/ resi/1 gradually dim9i%1 & ultimately de/roy ! motion4 ,indep5d5tly ( ! ob/ructions to ! cont9uation ( motion aris+ f friction1 !re is ano!r imp$im5t to :i* all motions on ! surface ( ! e>? are liable--! resi/ance ( ! air4 ,h[ mu* ?is may affect ! cont9uation ( motion appe>s by _m famili> effects4 ,on a calm day c>ry an op5 umbrella ) its concave side pres5t$ 9 ! direction 9 :i* y are mov+1 & a p[]ful resi/ance w be oppos$ to y\r progress1 :i* w increase ) e increase ( ! spe$ ) :i* y move4 7#dc47 ,we are n1 h[ev]1 )\t direct exp]i5ce to prove1 t motions :5 unresi/$ w = ev] cont9ue4 ,9 ! heav5s we f9d an app>atus1 :i* furni%es a sublime v]ification ( ?is pr9ciple4 ,!re1 remov$ f all casual ob/ructions & resi/ances1 ! va/ bodies ( ! univ]se roll on 9 _! appo9t$ pa?s ) un]r+ regul>ity1 pres]v+ )\t dim9ution all t motion :i* !y receiv$ at _! creation f ! h& :i* laun*$ !m into space4 ,?is alone1 unsupport$ by o!r reasons1 w\ld be suffici5t to e/abli% ! quality ( in]tia2 b view$ 9 connection ) ! o!r circum/ances previ\sly m5tion$1 no d\bt c rema9 t ?is is an univ]sal law ( nature4 7#dd47 ,x has be5 prov$1 t inability to *ange ! quantity ( motion is a consequ5ce ( in]tia4 ,! inability to *ange ! direction ( motion is ano!r consequ5ce ( ?is quality4 ,! same cause :i* increases or dim9i%es motion1 w\ld also give motion to a body at re/2 & !re=e we inf] t ! same inability :i* prev5ts a body f mov+ itself1 w also prev5t x f increas+ or dim9i%+ any motion :i* x has receiv$4 ,9 ! same mann] we c %[1 t any cause :i* *anges ! direction ( motion w\ld also give motion to a body at re/2 & !re=e if a body *ange ! direction ( its own motion1 ! same body might move itself f a /ate ( re/2 & !re=e ! p[] ( *ang+ ! direction ( any motion :i* x may h receiv$ is inconsi/5t ) ! quality ( in]tia4 7#de47 ,if a body1 mov+ f ,a1 fig4 #c4 to ,b1 receive at ,b a bl[ 9 ! direction ,c ,b ,e1 x w imm$iately *ange its direction to t ( ano!r l9e ,b ,d4 ,! cause :i* produces ?is *ange ( direction w\ld h put ! body 9 motion 9 ! direction ,b ,e1 _h x be5 quiesc5t at ,b :5 x su/a9$ ! bl[4 7#df47 ,aga91 suppose ,g ,h to be a h>d plane surface2 & let ! body be suppos$ to be p]fectly inela/ic4 ,:5 x /rikes ! surface at ,b1 x w comm5ce to move along x 9 ! direction ,b ,h4 ,?is *ange ( direction is produc$ by ! resi/ance ( ! surface4 ,if ! body1 in/ead ( meet+ ! surface 9 ! direction ,a ,b1 _h mov$ 9 ! direction ,e ,b1 p]p5dicul> to x1 all motion w\ld h be5 de/roy$1 & ! body r$uc$ to a /ate ( re/4 7#dg47 ,by ! =m] example x appe>s t ! deflect+ cause w\ld h put a quiesc5t body 9 motion1 & by ! latt] x w\ld h r$uc$ a mov+ body to a /ate ( re/4 ,h5ce ! ph5om5on ( a *ange ( direction is to be ref]r$ to ! same class z ! *ange f re/ to motion1 or f motion to re/4 ,! quality ( in]tia is1 !re=e1 inconsi/5t ) any *ange 9 ! direction ( motion :i* does n arise f an ext]nal cause4 7#dh47 ,f all t has be5 "h /at$1 we may inf] g5]ally1 t an inanimate p>cel ( matt] is incapable ( *ang+ its /ate ( re/ or motion2 t1 9 :atev] /ate x be1 9 t /ate x mu/ = ev] cont9ue1 unless di/urb$ by "s ext]nal cause2 t if x be 9 motion1 t motion mu/ always be uni=m1 or mu/ proce$ at ! same rate1 equal spaces be+ mov$ ov] 9 ! same "t3 any increase ( its rate mu/ betray "s impell+ cause2 any dim9ution mu/ proce$ f an imp$+ cause1 & nei!r ( ^! causes c exi/ 9 ! body itself2 t su* motion mu/ n only be con/antly at ! same uni=m rate1 b also mu/ be always 9 ! same direction1 any deflection f "o uni=m direction necess>ily aris+ f "s ext]nal influ5ce4 ,! language sometimes us$ to expla9 ! prop]ty ( in]tia 9 popul> works1 is em95tly calculat$ to mislead ! /ud5t4 ,! t]ms resi/ance & /ubbornness to move are faulty 9 ?is respect4 ,in]tia implies absolute passiv5ess1 a p]fect indiff]5ce to re/ or motion4 ,x implies z /rongly ! abs5ce ( all resi/ance to ! reception ( motion1 z x does ! abs5ce ( all p[] to move itself4 ,! t]m vis in]ti or =ce ( inactivity1 s frequ5tly us$ ev5 by au?ors pret5d+ to sci5tific accuracy1 is /ill m repreh5sible4 ,x is a contradiction 9 t]ms2 ! t]m inactivity imply+ ! abs5ce ( all =ce4 99 99 99 99 99 7#di47 ,be=e we close ?is *apt]1 x may be advantage\s to po9t out "s practical & famili> examples ( ! g5]al law ( in]tia4 ,! /ud5t mu/1 h[ev]1 recollect1 t ! great object ( sci5ce is g5]alisation1 & t 8 m9d is to be elevat$ to ! contemplation ( ! laws ( nature1 & to receive a habit ! v rev]se ( t :i* disposes u to enjoy ! desc5t f g5]als to p>ticul>s4 ,in/ances1 tak5 f ! occurr5ces ( ord9>y life1 may1 h[ev]1 be useful 9 v]ify+ ! g5]al law1 & 9 impress+ x ^u ! memory2 & = ?is reason1 we %all occasionally 9 ! pres5t treatise ref] to su* examples2 always1 h[ev]1 keep+ !m 9 subs]vi5ce to ! g5]al pr9ciples ( :i* !y are manife/ations1 & on :i* ! att5tion ( ! /ud5t %\ld nev] cease to be fix$4 7#ej47 ,if a c>riage1 a horse1 or a boat1 mov+ ) spe$1 be sudd5ly ret>d$ or /opp$1 by any cause :i* does n at ! same "t affect pass5g]s1 rid]s1 or any loose bodies :i* are c>ri$1 !y w be precipitat$ 9 ! direction ( ! motion2 because by reason ( _! in]tia1 !y p]sev]e 9 ! motion :i* !y %>$ 9 common ) t :i* transport$ !m1 & are n depriv$ ( t motion by ! same cause4 7#ea47 ,if a pass5g] leap f a c>riage 9 rapid motion1 he w fall 9 ! direction 9 :i* ! c>riage is mov+ at ! mom5t 8 feet meet ! gr\nd2 because 8 body1 on quitt+ ! vehicle1 reta9s1 by its in]tia1 ! motion :i* x _h 9 common ) x4 ,:5 he rea*es ! gr\nd1 ?is motion is de/roy$ by ! resi/ance ( ! gr\nd to ! feet1 b is reta9$ 9 ! upp] & heavi] "p ( ! body2 s t ! same effect is produc$ z if ! feet _h be5 tripp$4 7#eb47 ,:5 a c>riage is once put 9 motion ) a det]m9ate spe$ on a level road1 ! only =ce necess>y to su/a9 ! motion is t :i* is suffici5t to ov]come ! friction ( ! road2 b at />t+ a great] exp5diture ( =ce is necess>y1 inasmu* z n only ! friction is to be ov]come1 b ! =ce ) :i* ! vehicle is int5d$ to move mu/ be communicat$ to x4 ,h5ce we see t horses make a mu* great] ex]tion at />t+ ?an subsequ5tly1 :5 ! c>riage is 9 motion2 & we may also inf] ! inexp$i5cy ( attempt+ to />t at full spe$1 especially ) heavy c>riages4 7#ec47 ,c\rs+ owes all its int]e/ to ! in/9ctive consci\sness ( ! nature ( in]tia :i* seems to gov]n ! measures ( ! h>e4 ,! greyh\nd is a comp>atively heavy body mov+ at ! same or great] spe$ 9 pursuit4 ,! h>e d\bles1 t is1 sudd5ly *anges ! direction ( h] c\rse1 & turns back at an oblique angle ) ! direction 9 :i* %e _h be5 runn+4 ,! greyh\nd1 unable to resi/ ! t5d5cy ( its body to p]sev]e 9 ! rapid motion x _h acquir$1 is urg$ =w>d _m y>ds be=e x is able to *eck its spe$ & return to ! pursuit4 ,mean:ile ! h>e is ga9+ gr\nd 9 ! o!r direction1 s t ! animals are at a v consid]able di/ance asund] :5 ! pursuit is recomm5c$4 ,9 ?is way a h>e1 ?\gh mu* less fleet ?an a greyh\nd1 w (t5 escape x4 ,9 rac+1 ! horses %oot f> beyond ! w9n+-po/ be=e _! c\rse c be arre/$4 ,,*ap4 ,,iv4 ,,action ,,& ,,reaction4 7#ed47 ,! effects ( in]tia or inactivity1 consid]$ 9 ! la/ *apt]1 are su* z may be manife/$ by a s+le insulat$ body1 )\t ref]5ce to1 or connection )1 any o!r body :atev]4 ,!y might all be recognis$ if !re 7 b "o body exi/+ 9 ! univ]se4 ,!re are1 h[ev]1 o!r important results ( ?is law1 to ! developm5t ( :i* two bodies at lea/ are necess>y4 7#ee47 ,if a mass ,a1 fig4 #d41 mov+ t[>ds ,c1 imp+e ^u an equal mass1 :i* is quiesc5t at ,b1 ! two masses w move toge!r t[>ds ,c aft] ! impact4 ,b x w be obs]v$1 t _! spe$ aft] ! impact w be only half t ( ,a be=e x4 ,?us1 aft] ! impact1 ,a loses half its velocity2 & ,b1 :i* 0 be=e quiesc5t1 receives exactly ?is am\nt ( motion4 ,x appe>s1 !re=e1 9 ?is case1 t ,b receives exactly z mu* motion z ,a loses3 s t ! real quantity ( motion f ,b to ,c is ! same z ! quantity ( motion f ,a to ,b4 ,n[1 suppose t ,b consi/$ ( two masses1 ea* equal to ,a1 x w\ld be f\nd t 9 ?is case ! velocity ( ! triple mass aft] impact w\ld be "o-?ird ( ! velocity f ,a to ,b4 ,?us1 aft] impact1 ,a loses two-?irds ( its velocity &1 ,b consi/+ ( two masses ea* equal to ,a1 ea* ( ^! two receives "o-?ird ( ,a's motion2 s t ! :ole motion receiv$ by ,b is two-?irds ( ! motion ( ,a be=e impact4 ,by ! impact1 !re=e1 exactly z mu* motion is receiv$ by ,b z is lo/ by ,a4 ,a simil> result w be obta9$1 :atev] proportion may subsi/ betwe5 ! masses ,a & ,b4 ,suppose ,b to be t5 times ,a2 !n ! :ole motion ( ,a mu/1 aft] ! impact1 be di/ribut$ among ! p>ts ( ! unit$ masses ( ,a & ,b3 b ^! unit$ masses are1 9 ?is case1 elev5 times ! mass ( ,a4 ,n[1 z !y all move ) a common motion1 x foll[s t ,a's =m] motion mu/ be equally di/ribut$ among !m2 s t ea* "p %all h an elev5? "p ( x4 ,!re=e ! velocity aft] impact w be ! elev5? "p ( ! velocity ( ,a be=e x4 ,?us ,a loses by ! impact t5-elev5? p>ts ( its motion1 :i* are precisely :at ,b receives4 ,aga91 if ! masses ( ,a & ,b be #e & #g1 !n ! unit$ mass aft] impact w be #ab4 ,! motion ( ,a be=e impact w be equally di/ribut$ betwe5 ^! twelve p>ts1 s t ea* "p w h a twelf? ( x2 b five ( ^! p>ts belong to ! mass ,a1 & sev5 to ,b4 ,h5ce ,b w receive sev5-twelf?s1 :ile ,a reta9s five-twelf?s4 7#ef47 ,9 g5]al1 !re=e1 :5 a mass ,a 9 motion imp+es on a mass ,b at re/1 to f9d ! motion ( ! unit$ mass aft] impact1 8divide ! :ole motion ( ,a into z _m equal p>ts z !re are equal compon5t masses 9 ,a & ,b toge!r1 & !n ,b w receive by ! impact z _m p>ts ( ?is motion z x has equal compon5t masses40 ,?is is an imm$iate consequ5ce ( ! prop]ty ( in]tia1 expla9$ 9 ! la/ *apt]4 ,if we 7 to suppose t by _! mutual impact ,a 7 to give to ,b ei!r m or less motion ?an t :i* x 7,a7 loses1 x w\ld necess>ily foll[1 t ei!r ,a or ,b mu/ h a p[] ( produc+ or ( resi/+ motion1 :i* w\ld be inconsi/5t ) ! quality ( in]tia already def9$4 ,= if ,a give to ,b m motion ?an x loses1 all ! ov]plus or excess mu/ be excit$ 9 ,b by ! action ( ,a2 &1 !re=e1 ,a is n inactive1 b is capable ( excit+ motion :i* x does n possess4 ,on ! o!r h&1 ,b _c receive f ,a less motion ?an ,a loses1 because !n ,b mu/ be admitt$ to h ! p[] by its resi/ance ( de/roy+ all ! defici5cy2 a p[] ess5tially active1 & inconsi/5t ) ! quality ( in]tia4 7#eg47 ,if we contemplate ! effects ( impact1 :i* we h n[ describ$1 z facts asc]ta9$ by exp]im5t 7:i* !y may be71 we may take !m z fur!r v]ification ( ! univ]sality ( ! quality ( in]tia4 ,b1 on ! o!r h&1 we may view !m z ph5om5a :i* may c]ta9ly be pr$ict$ f ! previ\s k ( t quality2 & ?is is "o ( _m in/ances ( ! advantage :i* sci5ce possesses ov] k m]ely practical4 ,hav+ obta9$ by obs]vation or exp]i5ce a c]ta9 numb] ( simple facts1 & !nce d$uc$ ! g5]al qualities ( bodies1 we are enabl$1 by demon/rative reason+1 to discov] o!r facts :i* h nev] fall5 "u our obs]vation1 or1 if s1 may h nev] excit$ att5tion4 ,9 ?is way philosoph]s h discov]$ c]ta9 small motions & slight *anges :i* h tak5 place among ! heav5ly bodies1 & h direct$ ! att5tion ( a/ronomical obs]v]s to !m1 in/ruct+ !m ) ! greate/ precision z to ! exact mom5t ( "t & ! po9t ( ! firmam5t to :i* !y %\ld direct ! telescope1 9 ord] to witness ! pr$ict$ ev5t4 7#eh47 ,s9ce by ! quality ( in]tia a body c nei!r g5]ate nor de/roy motion1 x foll[s t :5 two bodies act ^u ea* o!r 9 any way :atev]1 ! total quantity ( motion 9 a giv5 direction1 aft] ! action takes place1 mu/ be ! same z be=e x1 = o!rwise "s motion w\ld be produc$ by ! action ( ! bodies1 :i* w\ld contradict ! pr9ciple t !y are in]t4 ,! ^w 8action0 is "h appli$1 p]haps improp]ly1 b accord+ to ! usage ( me*anical writ]s1 to express a c]ta9 ph5om5on or effect4 ,x is1 !re=e1 n to be und]/ood z imply+ any active pr9ciple 9 ! bodies to :i* x is attribut$4 7#ei47 ,9 ! cases ( collision ( :i* we h spok51 "o ( ! masses ,b 0 suppos$ to be quiesc5t be=e ! impact4 ,we %all n[ suppose x to be mov+ 9 ! same direction z ,a1 t is1 t[>ds ,c1 b ) a less velocity1 s t ,a %all ov]take x1 & imp+e ^u x4 ,aft] ! impact1 ! two masses w move t[>ds ,c ) a common velocity1 ! am\nt ( :i* we n[ propose to det]m9e4 ,if ! masses ,a & ,b be equal1 !n _! motions or velocities add$ toge!r mu/ be ! motion ( ! unit$ mass aft] impact1 s9ce no motion c ei!r be creat$ or de/roy$ by t ev5t4 ,b z ,a & ,b move ) a common motion1 ?is sum mu/ be equally di/ribut$ betwe5 !m1 & !re=e ea* w move ) a velocity equal to half ! sum ( _! velocities be=e ! impact4 ,?us1 if ,a h ! velocity #g1 & ,b h #e1 ! velocity ( ! unit$ mass aft] impact is #f1 be+ ! half ( #ab1 ! sum ( #g & #e4 ,if ,a & ,b be n equal1 suppose !m divid$ into equal compon5t p>ts1 & let ,a consi/ ( #h1 & ,b ( #f1 equal masses3 let ! velocity ( ,a be #ag1 s t ! motion ( ea* ( ! #h p>ts be+ #ag1 ! motion ( ! :ole w be #acf4 ,9 ! same mann]1 let ! velocity ( ,b be #aj1 ! motion ( ea* "p be+ #aj1 ! :ole motion ( ! #f p>ts w be #fj4 ,! sum ( ! two motions1 !re=e1 t[>ds ,c is #aif2 & s9ce none ( ?is c be lo/ by ! impact1 nor any motion add$ to x1 ?is mu/ also be ! :ole motion ( ! unit$ masses aft] impact4 ,be+ equally di/ribut$ among ! #ad compon5t p>ts ( :i* ^! unit$ masses consi/1 ea* "p w h a f\rte5? ( ! :ole motion4 ,h5ce1 #aif be+ divid$ by #ad1 we obta9 ! quoti5t #ad1 :i* is ! velocity ) :i* ! :ole moves4 7#fj47 ,9 g5]al1 !re=e1 :5 two masses mov+ 9 ! same direction imp+e "o ^u ! o!r1 & aft] impact move toge!r1 _! common velocity may be det]m9$ by ! foll[+ rule3 8,express ! masses & velocities by numb]s 9 ! usual way1 & multiply ! numb]s express+ ! masses by ! numb]s :i* express ! velocities2 ! two products ?us obta9$ be+ add$ toge!r1 & _! sum divid$ by ! sum ( ! numb]s express+ ! masses1 ! quoti5t w be ! numb] express+ ! requir$ velocity40 7#fa47 ,f ! prec$+ details1 x appe>s t motion is n adequately e/imat$ by spe$ or velocity4 ,= example1 a c]ta9 mass ,a1 mov+ at a det]m9ate rate1 has a c]ta9 quantity ( motion4 ,if ano!r equal mass ,b be add$ to ,a1 & a simil> velocity be giv5 to x1 z mu* m motion w evid5tly be call$ into exi/5ce4 ,9 o!r words1 ! two equal masses ,a & ,b unit$ h twice z mu* motion z ! s+le mass ,a _h :5 mov+ alone1 & ) ! same spe$4 ,! same reason+ w %[ t ?ree equal masses w ) ! same spe$ h ?ree times ! motion ( any "o ( !m4 ,9 g5]al1 !re=e1 ! velocity be+ ! same1 ! quantity ( motion w always be increas$ or dim9i%$ 9 ! same proportion z ! mass mov$ is increas$ or dim9i%$4 7#fb47 ,on ! o!r h&1 ! quantity ( motion does n dep5d on ! mass only1 b also on ! spe$4 ,if a c]ta9 det]m9ate mass move ) a c]ta9 det]m9ate spe$1 ano!r equal mass :i* moves ) twice ! spe$1 t is1 :i* moves ov] twice ! space 9 ! same "t1 w h twice ! quantity ( motion4 ,9 ?is mann]1 ! mass be+ ! same1 ! quantity ( motion w increase or dim9i% 9 ! same proportion z ! velocity4 7#fc47 ,! true e/imate1 !n1 ( ! quantity ( motion is f\nd by multiply+ toge!r ! numb]s :i* express ! mass & ! velocity4 ,?us1 9 ! example :i* has be5 la/ giv5 ( ! impact ( masses1 ! quantities ( motion be=e & aft] impact appe> to be z foll[3 ,be=e ,impact4 ,aft] ,impact4 ,mass ( ,a #h ,mass ( ,a #h ,velocity ( ,a #ag ,common velocity #ad ----------------- -------------- ,quantity ( #h #aga or #acf ,quantity ( #h #ad or #aab motion ( ,a motion ( ,a ----------------- -------------- ,mass ( ,b #f ,mass ( ,b #f ,velocity ( ,b #aj ,common velocity #ad ----------------- -------------- ,quantity ( #f #aj or #fj ,quantity ( #f #ad #hd motion ( ,b motion ( ,b ----------------- -------------- 99 ,! sign plac$ betwe5 two numb]s meant t !y are to be multipli$ toge!r4 ,by ?is calculation x appe>s t 9 ! impact ,a has lo/ a quantity ( motion express$ by #bd1 & t ,b has receiv$ exactly t am\nt4 ,! effect1 !re=e1 ( ! impact is a transf] ( motion f ,a to ,b2 b no new motion is produc$ 9 ! direction ,a ,c :i* did n exi/ be=e4 ,?is is obvi\sly consi/5t ) ! prop]ty ( in]tia1 & inde$ an inevitable result ( x4 ,^! results may be g5]alis$ & m cle>ly & concisely express$ by ! aid ( ! symbols ( ari?metic4 ,let a express ! velocity ( ,a4 ,let b express ! velocity ( ,b4 ,let x express ! velocity ( ! unit$ masses ( ,a & ,b aft] impact1 ea* ( ^! velocities be+ express$ 9 feet p] second1 & ! masses ( ,a & ,b be+ express$ by ! weight 9 p\nds4 ,we %all !n h ! mom5ta or mov+ =ces ( ,a & ,b be=e impact1 express$ by ,a a & ,b b1 & ! mov+ =ce ( ! unit$ mass aft] impact w be express$ by 7,a ,b7 x4 ,! mov+ =ce ( ,a aft] impact is ,a x1 & !re=e ! =ce x loses by ! collision w be 7,a a - ,a x74 ,! =ce ( ,b aft] impact w be ,b x1 & !re=e ! =ce x ga9s w be ,b x - ,b b4 ,b s9ce ! =ce lo/ by ,a mu/ be equal to ! =ce ga9$ by ,b1 we %all h ,a a - ,a x ,b x - ,b b f :i* x is easy to inf] 7,a ,b7 x ,a a ,b b & if x be requir$ to express ! velocity ( ! unit$ masses aft] impact1 we h x 7,a a ,b b7_/7,a ,b7 ,:5 x is said t ,a a & ,b b express ! mov+ =ces ( ,a & ,b1 x mu/ be und]/ood t ! unit ( mom5tum or mov+ =ce is 9 ! case "h suppos$1 ! =ce ) :i* a mass ( matt] weigh+ #a lb4 w\ld move if its velocity 7 #a foot p] second1 & accord+ly ! =ces ) :i* ,a & ,b move be=e impact are z _m times ?is z !re are units respectively 9 ! numb]s signifi$ by ! g5]al symbols ,a a & ,b b4 ,9 l mann]1 ! =ce ( ! unit$ masses aft] impact is z _m times great] ?an t ( #a lb4 mov+ ?r\gh #a foot p] second z !re are units 9 ! numb]s express$ by 7,a ,b7 x4 7#fd47 ,^! ph5om5a pres5t an example ( a law d$uc$ f ! prop]ty ( in]tia1 & g5]ally express$ ?us--8action & reaction are equal1 & 9 contr>y directions40 ,! /ud5t mu/1 h[ev]1 be cauti\s n to receive ^! t]ms 9 _! ord9>y acceptation4 ,aft] ! full explanation ( in]tia giv5 9 ! la/ *apt]1 x is1 p]haps1 sc>cely necess>y "h to repeat1 t 9 ! ph5om5a manife/$ by ! motion ( two bodies1 !re c be nei!r 8action0 nor 8reaction10 prop]ly s call$4 ,! bodies are absolutely incapable ei!r ( action or resi/ance4 ,! s5se 9 :i* ^! words mu/ be receiv$1 z us$ 9 ! law1 is m]ely an expression ( ! transf] ( a c]ta9 quantity ( motion f "o body to ano!r1 :i* is call$ an action 9 ! body :i* loses ! motion1 & a reaction 9 ! body :i* receives x4 ,! accession ( motion to ! latt] is said to proce$ f ! action ( ! =m]2 & ! loss ( ! same motion 9 ! =m] is ascrib$ to ! reaction ( ! latt]4 ,! :ole phraseology is1 h[ev]1 mo/ objectionable & unphilosophical1 & is calculat$ to create wrong notions4 7#fe47 ,! bodies imp++ 71 9 ! la/ case1 suppos$ to move 9 ! same direction4 ,we %all n[ consid] ! case 9 :i* !y move 9 opposite directions4 ,fir/1 let ! masses ,a & ,b be suppos$ to be equal1 & mov+ 9 opposite directions1 ) ! same velocity4 ,let ,c1 fig4 #e41 be ! po9t at :i* !y meet4 ,! equal motions 9 opposite directions w1 9 ?is case1 de/roy ea* o!r1 & bo? masses w be r$uc$ to a /ate ( re/4 ,?us1 ! mass ,a loses all its motion 9 ! direction ,a ,c1 :i* x may be suppos$ to transf] to ,b at ! mom5t ( impact4 ,b ,b hav+ previ\sly _h an equal quantity ( motion 9 ! direction ,b ,c1 w n[ h two equal motions impress$ ^u x1 9 directions imm$iately opposite2 & ^! motions neutralis+ ea* o!r1 ! mass becomes quiesc5t4 ,9 ?is case1 !re=e1 z 9 all ! =m] examples1 ea* body transf]s to ! o!r all ! motion :i* x loses1 consi/5tly ) ! pr9ciple ( 8action & reaction40 ,! masses ,a & ,b be+ /ill suppos$ equal1 let !m move t[>ds ,c ) diff]5t velocities4 ,let ,a move ) ! velocity #aj1 & ,b ) ! velocity #f4 ,( ! #aj p>ts ( motion ) :i* ,a is endu$1 #f be+ transf]r$ to ,b1 w de/roy ! equal velocity #f1 :i* ,b has 9 ! direction ,b ,c4 ,! bodies w !n move toge!r 9 ! direction ,c ,b1 ! f\r rema9+ p>ts ( ,a's motion be+ equally di/ribut$ betwe5 !m4 ,ea* body w1 !re=e1 h two p>ts ( ,a's orig9al motion1 & #b !re=e w be _! common velocity aft] impact4 ,9 ?is case1 ,a loses #h ( ! #aj p>ts ( its motion 9 ! direction ,a ,c4 ,on ! o!r h&1 ,b loses ! entire ( its #f p>ts ( motion 9 ! direction ,b ,c1 & receives #b p>ts 9 ! direction ,a ,c4 ,?is is equival5t to receiv+ #h p>ts ( ,a's motion 9 ! direction ,a ,c4 ,?us1 accord+ to ! law ( 8action & reaction10 ,b receives exactly :at ,a loses4 ,f9ally1 suppose t bo? ! masses & velocities ( ,a & ,b are unequal4 ,let ! mass ( ,a be #h1 & its velocity #i3 & let ! mass ( ,b be #f1 & its velocity #e4 ,! quantity ( motion ( ,a w be #gb1 & t ( ,b1 9 ! opposite direction1 w be #cj4 ,( ! #gb p>ts ( motion1 :i* ,a has 9 ! direction ,a ,c1 #cj be+ transf]r$ to ,b1 w de/roy all its #cj p>ts ( motion 9 ! direction ,b ,c1 & ! two masses w move 9 ! direction ,c ,b1 ) ! rema9+ #db p>ts ( motion1 :i* w be equally di/ribut$ among _! #ad compon5t masses4 ,ea* compon5t "p w1 !re=e1 receive #c p>ts ( motion2 & accord+ly #c w be ! common velocity ( ! unit$ mass aft] impact4 7#ff47 ,:5 two masses mov+ 9 opposite directions imp+e & move toge!r1 _! common velocity aft] impact may be f\nd by ! foll[+ rule3--8,multiply ! numb]s express+ ! masses by ^? :i* express ! velocities respectively1 & subtract ! less] product f ! great]2 divide ! rema9d] by ! sum ( ! numb]s express+ ! masses1 & ! quoti5t w be ! common velocity2 ! direction w be t ( ! mass :i* has ! great] quantity ( motion40 ,x may be %[n )\t difficulty1 t ! example :i* we h j giv5 obeys ! law ( 8action & reaction40 ,be=e impact4 ,aft] impact4 ,mass ( ,a #h ,mass ( ,a #h ,velocity ( ,a #i ,common velocity #c ------------ ----------- ,quantity ( motion #h #i or #gb ,quantity ( motion #h #c or #bd 9 direction ,a ,c 9 direction ,a ,c ------------ ----------- ,mass ( ,b #f ,mass ( ,b #f ,velocity ( ,b #e ,common velocity #c ------------ ----------- ,quantity ( motion #f #e or #cj ,quantity ( motion #f #c or #ah 9 direction ,b ,c 9 direction ,a ,c ------------ ----------- ,h5ce x appe>s t ! quantity ( motion 9 ! direction ,a ,c ( :i* ,a has be5 depriv$ by ! impact is #dh1 ! diff]5ce betwe5 #gb & #bd4 ,on ! o!r h&1 ,b loses by ! impact ! quantity #cj 9 ! direction ,b ,c1 :i* is equival5t to receiv+ #cj 9 ! direction ,a ,c4 ,b x also acquires a quantity #ah 9 ! direction ,a ,c1 :i*1 add$ to ! =m] #cj1 gives a total ( #dh receiv$ by ,b 9 ! direction ,a ,c4 ,?us ! same quantity ( motion :i* ,a loses 9 ! direction ,a ,c1 is receiv$ by ,b 9 ! same direction4 ,! law ( 8action & reaction0 is1 !re=e1 fulfill$4 ,?is result may 9 l mann] be g5]alis$4 ,reta9+ ! =m] symbols1 ! mov+ =ces ( ,a & ,b be=e impact w be ,a a & ,b b & _! =ces aft] impact w be ,a x & ,b x4 ,! =ce lo/ by ,a w !re=e be ,a a - ,a x4 ,! mass ,b w h lo/ all ! =ce ,b b :i* x _h 9 its =m] direction1 & w h receiv$ ! =ce ,b x 9 ! opposite direction4 ,!re=e ! actual =ce imp>t$ to ,b by ! collision w be ,b b ,b x4 ,b s9ce ! =ce lo/ by ,a mu/ be equal to t imp>t$ to ,b1 we %all h ,a a - ,a x ,b b ,b x & !re=e 7,a ,b7 x ,a a - ,b b & if ! common velocity aft] impact be requir$1 we h x 7,a a - ,b b7_/7,a ,b7 ,z a g5]al rule1 !re=e1 to f9d ! common velocity aft] impact4 ,multiply ! weights by ! previ\s velocities & take _! sum if ! bodies move 9 ! same direction1 & _! diff]5ce if !y move 9 opposite directions1 & divide ! "o or ! o!r by ! sum ( _! weights4 ,! greate/ w be ! velocity aft] impact4 7#fg47 ,! examples ( ! equality ( action & reaction 9 ! collision ( bodies may be exhibit$ exp]im5tally by a v simple app>atus4 ,let ,a1 fig4 #f41 & ,b be two balls ( s(t clay1 or any o!r sub/ance :i* is inela/ic1 or ne>ly s1 & let ^! be susp5d$ f ,c by equal /r+s1 s t !y may be 9 contact2 & let a graduat$ arc1 ( :i* ! c5tre is ,c1 be plac$ s t ! balls may oscillate ov] x4 ,"o ( ! balls be+ mov$ f its place ( re/ along ! arc1 & all[$ to desc5d ^u ! o!r ?r\gh a c]ta9 numb] ( degrees1 w /rike ! o!r ) a velocity correspond+ to t numb] ( degrees1 & bo? balls w !n move toge!r ) a velocity :i* may be e/imat$ by ! numb] ( degrees ( ! arc ?r\gh :i* !y rise4 7#fh47 ,9 all ^! cases 9 :i* we h expla9$ ! law ( 8action & reaction10 ! transf] ( motion f "o body to ! o!r has be5 made by impact or collision4 ,! ph5om5on has be5 select$ only because x is ! mo/ ord9>y way 9 :i* bodies are se5 to affect ea* o!r4 ,! law is1 h[ev]1 univ]sal1 & w be fulfill$ 9 :atev] mann] ! bodies may affect ea* o!r4 ,?us ,a may be connect$ ) ,b by a flexible /r+1 :i*1 at ! comm5cem5t ( ,a's motion1 is slack4 ,until ! /r+ becomes /ret*$1 t is1 until ,a's di/ance f ,b becomes equal to ! l5g? ( ! /r+1 ,a w cont9ue to h all ! motion fir/ impress$ ^u x4 ,b :5 ! /r+ is /ret*$1 a "p ( t motion is transf]r$ to ,b1 :i* is !n drawn aft] ,a2 & :atev] motion ,b 9 ?is way receives1 ,a mu/ lose4 ,all t has be5 obs]v$ ( ! effect ( motion transf]r$ by impact w be equally applicable 9 ?is case4 ,aga91 if ,b1 fig4 #d41 be a magnet mov+ 9 ! direction ,b ,c ) a c]ta9 quantity ( motion1 & :ile x is s mov+ a mass ( iron be plac$ at re/ at ,a1 ! attraction ( ! magnet w draw ! iron aft] x t[>ds ,c1 & w ?us communicate to ! iron a c]ta9 quantity ( motion 9 ! direction ( ,c4 ,all ! motion ?us communicat$ to ! iron ,a mu/ be lo/ by ! magnet ,b4 ,if ! magnet & ! iron 7 bo? plac$ quiesc5t at ,b & ,a1 ! attraction ( ! magnet w\ld cause ! iron to move f ,a t[>ds ,b2 b ! magnet 9 ?is case n hav+ any motion1 _c be lit]ally said to transf] a motion to ! iron4 ,at ! mom5t1 h[ev]1 :5 ! iron beg9s to move f ,a t[>ds ,b1 ! magnet w be obs]v$ to beg9 also to move f ,b t[>ds ,a2 & if ! velocities ( ! two bodies be express$ by numb]s1 & respectively multipli$ by ! numb]s express+ _! masses1 ! quantities ( motion ?us obta9$ w be f\nd to be exactly equal4 ,we h already expla9$ :y a quantity ( motion receiv$ 9 ! direction ,b ,a1 is equival5t to ! same quantity lo/ 9 ! direction ,a ,b4 ,h5ce x appe>s1 t ! magnet 9 receiv+ z mu* motion 9 ! direction ,b ,a1 z x gives 9 ! direction ,a ,b1 suff]s an effect :i* is equival5t to los+ z mu* motion direct$ t[>ds ,c z x has communicat$ to ! iron 9 ! same direction4 ,9 ! same mann]1 if ! body ,b _h any prop]ty 9 virtue ( :i* x might repel ,a1 x w\ld itself be repell$ ) ! same quantity ( motion4 ,9 a ^w1 :atev] be ! mann] 9 :i* ! bodies may affect ea* o!r1 :e!r by collision1 traction1 attraction1 or repulsion1 or by :atev] o!r "n ! ph5om5on may be designat$1 /ill x is an inevitable consequ5ce1 t any motion1 9 a giv5 direction1 :i* "o ( ! bodies may receive1 mu/ be accompani$ by a loss ( motion 9 ! same direction1 & to ! same am\nt1 by ! o!r body1 or ! acquisition ( z mu* motion 9 ! contr>y direction2 or1 f9ally1 by a loss 9 ! same direction1 & an acquisition ( motion 9 ! contr>y direction1 ! comb9$ am\nt ( :i* is equal to ! motion receiv$ by ! =m]4 7#fi47 ,f ! pr9ciple1 t ! =ce ( a body 9 motion dep5ds on ! mass & ! velocity1 x foll[s1 t any body1 h[ev] small1 may be made to move ) ! same =ce z any o!r body1 h[ev] great1 by giv+ to ! small] body a velocity :i* be>s to t ( ! great] ! same proportion z ! mass ( ! great] be>s to ! mass ( ! small]4 ,?us a fea!r1 t5 ?\s& ( :i* w\ld h ! same weight z a cannon-ball1 w\ld move ) ! same =ce if x _h t5 ?\s& times ! velocity2 & 9 su* a case1 ^! two bodies enc\nt]+ 9 opposite directions1 w\ld mutually de/roy ea* o!r's motion4 7#gj47 ,! consequ5ces ( ! prop]ty ( in]tia1 :i* h be5 expla9$ 9 ! pres5t & prec$+ *apt]s1 h be5 giv5 by ,newton1 9 8 ,,pr9cipia1 &1 aft] him1 9 mo/ ,engli% treatises on me*anics1 "u ! =m ( ?ree propositions1 :i* are call$ ! 8laws ( motion40 ,!y are z foll[3-- ,i4 8,e body mu/ p]sev]e 9 its /ate ( re/1 or ( uni=m motion 9 a /raight l9e1 unless x be compell$ to *ange t /ate by =ces impress$ ^u x40 ,,ii4 8,e *ange ( motion mu/ be proportional to ! impress$ =ce1 & mu/ be 9 ! direction ( t /raight l9e 9 :i* ! =ce is impress$40 ,,iii4 8,action mu/ always be equal & contr>y to reaction2 or ! actions ( two bodies ^u ea* o!r mu/ be equal1 & direct$ t[>ds contr>y sides40 ,:5 in]tia & =ce are def9$1 ! fir/ law becomes an id5tical proposition4 ,! second law _c be r5d]$ p]fectly intelligible until ! /ud5t has read ! *apt] on ! composition & resolution ( =ces1 =1 9 fact1 x is int5d$ z an expression ( ! :ole body ( results 9 t *apt]4 ,! ?ird law has be5 expla9$ 9 ! pres5t *apt]1 z f> z x c be r5d]$ intelligible 9 ! pres5t /age ( our progress4 ,we h notic$ ^! =mul>ies m f a respect = ! au?orities by :i* !y h be5 propos$ & adopt$1 ?an f any p]suasion ( _! utility4 ,_! full import _c be compreh5d$ until ne>ly ! :ole ( elem5t>y me*anics has be5 acquir$1 & !n all su* summ>ies become useless4 99 99 99 99 99 7#ga47 ,! consequ5ces d$uc$ f ! consid]ation ( ! quality ( in]tia 9 ?is *apt]1 w acc\nt = _m effects :i* fall "u our notice daily1 & ) :i* we h become s famili>1 t !y h almo/ ceas$ to excite curiosity4 ,"o ( ! facts ( :i* we h mo/ frequ5t practical illu/ration is1 t ! quantity ( motion or mov+ =ce1 z x is sometimes call$1 is e/imat$ by ! velocity ( ! motion1 & ! weight or mass ( ! ?+ mov$ conjo9tly4 ,if ! same =ce impel two balls1 "o ( "o p\nd weight1 & ! o!r ( two p\nds1 x foll[s1 s9ce ! balls c nei!r give =ce to !mselves1 nor resi/ t :i* is impress$ ^u !m1 t !y w move ) ! same =ce4 ,b ! light] ball w move ) twice ! spe$ ( ! heavi]4 ,! impress$ =ce :i* is manife/$ by giv+ velocity to a d\ble mass 9 ! "o1 is engag$ 9 giv+ a d\ble velocity to ! o!r4 ,if a cannon-ball 7 =ty times ! weight ( a musket-ball1 b ! musket-ball mov$ ) =ty times ! velocity ( ! cannon-ball1 bo? w\ld /rike any ob/acle ) ! same =ce1 & w\ld ov]come ! same resi/ance2 = ! "o w\ld acquire f its velocity z mu* =ce z ! o!r d]ives f its weight4 ,a v small velocity may be accompani$ by enorm\s =ce1 if ! mass :i* is mov$ ) t velocity be proportionally great4 ,a l>ge %ip1 float+ ne> ! pi] wall1 may approa* x ) s small a velocity z to be sc>cely p]ceptible1 & yet ! =ce w be s great z to cru% a small boat4 ,a gra9 ( %ot flung f ! h&1 & /rik+ ! p]son1 w occasion no pa91 & inde$ w sc>cely be felt1 :ile a block ( /one hav+ ! same velocity w\ld occasion dea?4 ,if a body 9 motion /rike a body at re/1 ! /rik+ body mu/ su/a9 z great a %ock f ! collision z if x _h be5 at re/1 & /ruck by ! o!r body ) ! same =ce4 ,= ! loss ( =ce :i* x su/a9s 9 ! "o direction1 is an effect ( ! same k9d z if1 be+ at re/1 x _h receiv$ z mu* =ce 9 ! opposite direction4 ,if a man1 walk+ rapidly or runn+1 enc\nt]s ano!r /&+ /ill1 he suff]s z mu* f ! collision z ! man aga9/ :om he /rikes4 ,if a lead5 bullet be dis*>g$ aga9/ a plank ( h>d wood1 x w be f\nd t ! r\nd %ape ( ! ball is de/roy$1 & t x has itself suff]$ a =ce by ! impact1 :i* is equival5t to ! effect :i* x produces ^u ! plank4 ,:5 two bodies mov+ 9 opposite directions meet1 ea* body su/a9s z great a %ock z if1 be+ at re/1 x _h be5 /ruck by ! o!r body ) ! unit$ =ces ( ! two4 ,?us1 if two equal balls1 mov+ at ! rate ( t5 feet 9 a second1 meet1 ea* w be /ruck ) ! same =ce z if1 be+ at re/1 ! o!r _h mov$ aga9/ x at ! rate ( tw5ty feet 9 a second4 ,9 ?is case "o "p ( ! %ock su/a9$ arises f ! loss ( =ce 9 "o direction1 & ano!r f ! reception ( =ce 9 ! opposite direction4 ,= ?is reason1 two p]sons walk+ 9 opposite directions receive f _! enc\nt] a m viol5t %ock ?an might be expect$4 ,if !y be ( ne>ly equal weight1 & "o be walk+ at ! rate ( ?ree & ! o!r f\r miles an h\r1 ea* su/a9s ! same %ock z if he _h be5 at re/1 & /ruck by ! o!r runn+ at ! rate ( sev5 miles an h\r4 ,?is pr9ciple acc\nts = ! de/ructive effects aris+ f %ips runn+ f\l ( ea* o!r at sea4 ,if two %ips ( #ejj tons burd5 enc\nt] ea* o!r1 sail+ at t5 knots an h\r1 ea* su/a9s ! %ock :i*1 be+ at re/1 x w\ld receive f a vessel ( #ajjj tons burd5 sail+ t5 knots an h\r4 ,x is a mi/ake to suppose1 t :5 a l>ge & small body enc\nt]1 ! small body suff]s a great] %ock ?an ! l>ge "o4 ,! %ock :i* !y su/a9 mu/ be ! same2 b ! l>ge body may be bett] able to be> x4 ,:5 ! fi/ ( a pugili/ /rikes ! body ( 8 antagoni/1 x su/a9s z great a %ock z x gives2 b ! fi/ be+ m fitt$ to endure ! bl[1 ! injury & pa9 are inflict$ on 8 oppon5t4 ,?is is n ! case1 h[ev]1 :5 fi/ meets fi/4 ,!n ! p>ts 9 collision are equally s5sitive & vuln]able1 & ! effect is aggravat$ by bo? hav+ approa*$ ea* o!r ) great =ce4 ,! effect ( ! bl[ is ! same z if "o fi/1 be+ held at re/1 7 /ruck by ! o!r ) ! comb9$ =ce ( bo?4 ,,*ap4 ,v4 ,,! ,,composition ,,& ,,resolution ,,( ,,=ce4 7#gb47 ,motion & pressure are t]ms too famili> to ne$ explanation4 ,x may be obs]v$1 g5]ally1 t def9itions 9 ! fir/ rudim5ts ( a sci5ce are seldom1 if ev]1 compreh5d$4 ,! =ce ( words is le>n$ by _! application2 & x is n until a def9ition becomes useless1 t we are taught ! mean+ ( ! t]ms 9 :i* x is express$4 ,moreov]1 we are p]haps ju/ifi$ 9 say+1 t 9 ! ma!matical sci5ces ! fundam5tal notions are ( s uncomp\nd$ a "*1 t def9itions1 :5 develop$ & enl>g$ ^u1 (t5 draw u into metaphysical subtleties & di/9ctions1 :i*1 :atev] be _! m]it or importance1 w\ld be "h altoge!r misplac$4 ,we %all1 !re=e1 at once take x = grant$1 t ! words motion & pressure express ph5om5a or effects :i* are ! subjects ( con/ant exp]i5ce & h\rly obs]vation2 & if ! sci5tific use ( ^! words be m precise ?an _! g5]al & popul> application1 t precision w soon be le>n$ by _! frequ5t use 9 ! pres5t treatise4 7#gc47 ,,=ce is ! "n giv5 9 me*anics to :atev] produces motion or pressure4 ,?is ^w is also (t5 us$ to express ! motion or pressure itself2 & :5 ! cause ( ! motion or pressure is n kn[n1 ?is is ! only correct use ( ! ^w4 ,?us1 :5 a piece ( iron moves t[>d a magnet1 x is usual to say t ! cause ( ! motion is 8! attraction ( ! magnet20 b 9 effect we are ignorant ( ! cause ( ?is ph5om5on2 & ! "n attraction w\ld be bett] appli$ to ! effect ( :i* we h exp]i5ce4 ,9 l mann] ! attraction & repulsion ( electrifi$ bodies %\ld be und]/ood1 n z names = unkn[n causes1 b z words express+ obs]v$ appe>ances or effects4 ,:5 a c]ta9 phraseology has1 h[ev]1 gott5 into g5]al use1 x is nei!r easy nor conv5i5t to sup]s$e x4 ,we %all1 !re=e1 be compell$1 9 speak+ ( motion & pressure1 to use ! language ( causation2 b mu/ advise ! /ud5t t x is effects & n causes :i* w be express$4 7#gd47 ,if two =ces act ^u ! same po9t ( a body 9 diff]5t directions1 a s+le =ce may be assign$1 :i*1 act+ on t po9t1 w produce ! same result z ! unit$ effects ( ! o!r two4 ,let ,p1 fig4 #g41 be ! po9t on :i* ! two =ces act1 & let _! directions be ,p ,a & ,p ,b4 ,f ! po9t ,p1 ^u ! l9e ,p ,a1 take a l5g? ,p a1 consi/+ ( z _m in*es z !re are ounces 9 ! =ce ,p ,a2 &1 9 l mann]1 take ,p b1 9 ! direction ,p ,b1 consi/+ ( z _m in*es z !re are ounces 9 ! =ce ,p ,b4 ,?r\gh a draw a l9e p>allel to ,p ,b1 & ?r\gh b draw a l9e p>allel to ,p ,a1 & suppose t ^! l9es meet at c4 ,!n draw ,p ,c4 ,a s+le =ce1 act+ 9 ! direction ,p ,c1 & consi/+ ( z _m ounces z ! l9e ,p c consi/s ( in*es1 w produce ^u ! po9t ,p ! same effect z ! two =ces ,p ,a & ,p ,b produce act+ toge!r4 7#ge47 ,! figure ,p a c b is call$ 9 ,,geometry a p>allelogram2 ! l9es ,p a1 ,p b1 are call$ its sides1 & ! l9e ,p c is call$ its diagonal4 ,?us ! me?od ( f9d+ an equival5t = two =ces1 :i* we h j expla9$1 is g5]ally call$ 8! p>allelogram ( =ces10 & is usually express$ ?us3 8,if two =ces be repres5t$ 9 quantity & direction by ! sides ( a p>allelogram1 an equival5t =ce w be repres5t$ 9 quantity & direction by its diagonal40 7#gf47 ,a s+le =ce1 :i* is ?us me*anically equival5t to two or m o!r =ces1 is call$ _! resultant1 & relatively to x !y are call$ its compon5ts4 ,9 any me*anical inve/igation1 :5 ! resultant is us$ = ! compon5ts1 :i* x always may be1 ! process is call$ 8! composition ( =ce40 ,x is1 h[ev]1 frequ5tly exp$i5t to sub/itute = a s+le =ce two or m =ces1 to :i* x is me*anically equival5t1 or ( :i* x is ! resultant4 ,?is process is call$ 8! resolution ( =ce40 7#gg47 ,to v]ify exp]im5tally ! !orem ( ! p>allelogram ( =ces is n difficult4 ,let two small :eels1 ,m ,n1 fig4 #h41 ) grooves 9 _! edges to receive a ?read1 be atta*$ to an upright bo>d1 or to a wall4 ,let a ?read be pass$ ov] !m1 hav+ weights ,a & ,b1 hook$ ^u loops at its extremities4 ,f any "p ,p ( ! ?read betwe5 ! :eels let a weight ,c be susp5d$3 x w draw ! ?read d[nw>ds1 s z to =m an angle ,m ,p ,n1 & ! app>atus w settle itself at re/ 9 "s det]m9ate position4 ,9 ?is /ate x is evid5t t s9ce ! weight ,c1 act+ 9 ! direction ,p ,c1 balances ! weights ,a & ,b1 act+ 9 ! directions ,p ,m & ,p ,n1 ^! two =ces mu/ be me*anically equival5t to a =ce equal to ! weight ,c1 & act+ directly upw>ds f ,p4 ,! weight ,c is !re=e ! quantity ( ! resultant ( ! =ces ,p ,m & ,p ,n2 & ! direction ( ! resultant is t ( a l9e drawn directly upw>ds f ,p4 ,to asc]ta9 h[ f> ?is is consi/5t ) ! !orem ( 8! p>allelogram ( =ces10 let a l9e ,p ,o be drawn ^u ! upright bo>d to :i* ! :eels are atta*$1 f ! po9t ,p upw>d1 9 ! direction ( ! ?read ,c ,p4 ,also1 let l9es be drawn ^u ! bo>d imm$iately "u ! ?reads ,p ,m & ,p ,n4 ,f ! po9t ,p1 on ! l9e ,p ,o1 take z _m in*es z !re are ounces 9 ! weight ,c4 ,let ! "p ( ,p ,o ?us measur$ be ,p c1 & f c draw c a p>allel to ,p ,n1 & c b p>allel to ,p ,m4 ,if ! sides ,p a & ,p b ( ! p>allelogram ?us =m$ be measur$1 x w be f\nd t ,p a w consi/ ( z _m in*es z !re are ounces 9 ! weight ,a1 & ,p b ( z _m in*es z !re are ounces 9 ! weight ,b4 ,9 ?is illu/ration1 ounces & in*es h be5 us$ z ! subdivisions ( weight & l5g?4 ,x is sc>cely necess>y to /ate1 t any o!r measures ( ^! quantities w\ld s]ve z well1 only obs]v+ t ! same d5om9ations mu/ be pres]v$ 9 all p>ts ( ! same inve/igation4 7#gh47 ,among ! philosophical app>atus ( ! ,univ]sity ( ,london1 is a v simple & conv5i5t in/rum5t :i* ,i con/ruct$ = ! exp]im5tal illu/ration ( ?is important !orem4 ,! :eels ,m ,n are atta*$ to ! tops ( two tall /&s1 ! heights ( :i* may be v>i$ at pleasure by an adju/+ screw4 ,a jo9t$ p>allelogram1 ,a ,b ,c ,d1 fig4 #i41 is =m$1 ^: sides are divid$ into in*es1 & ! jo9ts at ,a & ,b are moveable1 s z to v>y ! l5g?s ( ! sides at pleasure4 ,! jo9t ,c is fix$ at ! extremity ( a rul]1 also divid$ into in*es1 :ile ! opposite jo9t ,a is atta*$ to a brass loop1 :i* surr\nds ! diagonal rul] loosely1 s z to slide freely along x4 ,an adju/+ screw is provid$ 9 ?is loop s z to clamp x 9 any requir$ position4 ,9 mak+ ! exp]im5t1 ! sides ,a ,b & ,a ,d1 ,c ,b & ,c ,d are adju/$ by ! jo9ts ,b & ,a to ! same numb] ( in*es respectively z !re are ounces 9 ! weights ,a & ,b1 fig4 #h4 ,!n ! diagonal ,a ,c is adju/$ by ! loop & screw at ,a1 to z _m in*es z !re are ounces 9 ! weight ,c4 ,?is done1 ! po9t ,a is plac$ beh9d ,p1 fig4 #h41 & ! p>allelogram is held upright1 s t ! diagonal ,a ,c %all be 9 ! direction ( ! v]tical ?read ,p ,c4 ,! sides ,a ,b & ,a ,d w !n be f\nd to take ! direction ( ! ?reads ,p ,m & ,p ,n4 ,by *ang+ ! weights & ! l5g?s ( ! diagonal & sides ( ! p>allelogram1 ! exp]im5t may be easily v>i$ at pleasure4 7#gi47 ,9 ! examples ( ! composition ( =ces :i* we h "h giv51 ! effects ( ! =ces are ! production ( pressures1 or1 to speak m correctly1 ! !orem :i* we h illu/rat$1 is 8! composition ( pressures40 ,= ! po9t ,p is suppos$ to be at re/1 & to be drawn or press$ 9 ! directions ,p ,m & ,p ,n4 ,9 ! def9ition :i* has be5 giv5 ( ! ^w =ce1 x is decl>$ to include motions z well z pressures4 ,9 fact1 if motion be resi/$1 ! effect is conv]t$ into pressure4 ,! same cause act+ ^u a body1 w ei!r produce motion or pressure1 accord+ z ! body is free or re/ra9$4 ,if ! body be free1 motion ensues2 if re/ra9$1 pressure1 or bo? ^! effects toge!r4 ,x is !re=e consi/5t ) analogy to expect t ! same !orems :i* regulate pressures1 w also be applicable to motions2 & we f9d accord+ly a mo/ exact correspond5ce4 7#hj47 ,if a body h a motion 9 ! direction ,a ,b1 & at ! po9t ,p x receive ano!r motion1 su* z w\ld c>ry x 9 ! direction ,p ,c1 fig4 #aj41 7 x previ\sly quiesc5t at ,p1 x is requir$ to det]m9e ! direction :i* ! body w take1 & ! spe$ ) :i* x w move1 "u ^! circum/ances4 ,let ! velocity ) :i* ! body is mov+ f ,a to ,b be su*1 t x w\ld move ?r\gh a c]ta9 space1 suppose ,p ,n1 9 "o second ( "t1 & let ! velocity ( ! motion impress$ ^u x at ,p be su*1 t if x _h no previ\s motion x w\ld move f ,p to ,m 9 "o second4 ,f ! po9t ,m draw a l9e p>allel to ,p ,b1 & f ,n draw a l9e p>allel to ,p ,c1 & suppose ^! l9es to meet at "s po9t1 z ,o4 ,!n draw ! l9e ,p ,o4 ,9 consequ5ce ( ! two motions1 :i* are at ! same "t impress$ ^u ! body at ,p1 x w move 9 ! /raight l9e f ,p to ,o4 ,?us ! two motions1 :i* are express$ 9 quantity & direction by ! sides ( a p>allelogram1 w1 :5 giv5 to ! same body1 produce a s+le motion1 express$ 9 quantity & direction by its diagonal2 a !orem :i* is to motions exactly :at ! =m] 0 to pressures4 ,!re are v>i\s me?ods ( illu/rat+ exp]im5tally ! composition ( motion4 ,an ivory ball1 be+ plac$ ^u a p]fectly level squ>e table1 at "o ( ! corn]s1 & receiv+ two equal impulses1 9 ! directions ( ! sides ( ! table1 w move along ! diagonal4 ,app>atus = ?is exp]im5t diff] f ea* o!r only 9 ! way ( communicat+ ! impulses to ! ball4 7#ha47 ,z two motions simultane\sly communicat$ to a body are equival5t to a s+le motion 9 an int]m$iate direction1 s also a s+le motion may be me*anically replac$1 by two motions 9 directions express$ by ! sides ( any p>allelogram1 ^: diagonal repres5ts ! s+le motion4 ,?is process is 8! resolution ( motion10 & gives consid]able cle>ness & facility to _m me*anical inve/igations4 7#hb47 ,x is frequ5tly necess>y to express ! portion ( a giv5 =ce1 :i* acts 9 "s giv5 direction diff]5t f ! imm$iate direction ( ! =ce itself4 ,?us1 if a =ce act f ,a1 fig4 #aa41 9 ! direction ,a ,c1 we may require to e/imate :at "p ( t =ce acts 9 ! direction ,a ,b4 ,if ! =ce be a pressure1 take z _m in*es ,a ,p f ,a1 on ! l9e ,a ,c1 z !re are ounces 9 ! =ce1 & f ,p draw ,p ,m p]p5dicul> to ,a ,b2 !n ! "p ( ! =ce :i* acts along ,a ,b w be z _m ounces z !re are in*es 9 ,a ,m4 ,! =ce ,a ,b is me*anically equival5t to two =ces1 express$ by ! sides ,a ,m & ,a ,n ( ! p>allelogram2 b ,a ,n1 be+ p]p5dicul> to ,a ,b1 c h no effect on a body at ,a1 9 ! direction ( ,a ,b1 & !re=e ! effective "p ( ! =ce ,a ,p 9 ! direction ,a ,b is express$ by ,a ,m4 7#hc47 ,any numb] ( =ces act+ on ! same po9t ( a body may be replac$ by a s+le =ce1 :i* is me*anically equival5t to !m1 & :i* is1 !re=e1 _! resultant4 ,?is composition may be effect$ by ! successive application ( ! p>allelogram ( =ces4 ,let ! sev]al =ces be call$ ,a1 ,b1 ,c1 ,d1 ,e1 c4 ,draw ! p>allelogram ^: sides express ! =ces ,a & ,b1 & let its diagonal be ,a4 ,! =ce express$ by ,a w be equival5t to ,a & ,b4 ,!n draw ! p>allelogram ^: sides express ! =ces ,a & ,c1 & let its diagonal be ,b4 ,?is diagonal w express a =ce me*anically equival5t to ,a & ,c4 ,b ,a is me*anically equival5t to ,a & ,b1 & !re=e ,b is me*anically equival5t to ,a1 ,b1 & ,c4 ,next con/ruct a p>allelogram1 ^: sides express ! =ces ,b & ,d1 & let its diagonal be ,c4 ,! =ce express$ by ,c w be me*anically equival5t to ! =ces ,b & ,d2 b ! =ce ,b is equival5t to ,a1 ,b1 ,c1 & !re=e ,c is equival5t to ,a1 ,b1 ,c1 & ,d4 ,by cont9u+ ?is process x is evid5t1 t a s+le =ce may be f\nd1 :i* w be equival5t to1 & may be always sub/itut$ =1 any numb] ( =ces :i* act ^u ! same po9t4 ,if ! =ces :i* act ^u ! po9t neutralise ea* o!r1 s t no motion c ensue1 !y are said to be 9 equilibrium4 7#hd47 ,examples ( ! composition ( motion & pressure are cont9ually pres5t+ !mselves4 ,!y occur 9 almo/ e in/ance ( motion or =ce :i* falls "u our obs]vation4 ,! difficulty is to f9d an example :i*1 /rictly speak+1 is a simple motion4 ,:5 a boat is r[$ across a riv]1 9 :i* !re is a curr5t1 x w n move 9 ! direction 9 :i* x is impell$ by ! o>s4 ,nei!r w x take ! direction ( ! /ream1 b w proce$ exactly 9 t int]m$iate direction :i* is det]m9$ by ! composition ( =ce4 ,let ,a1 fig4 #ab41 be ! place ( ! boat at />t+2 & suppose t ! o>s are s work$ z to impel ! boat t[>ds ,b ) a =ce :i* w\ld c>ry x to ,b 9 "o h\r1 if !re 7 no curr5t 9 ! riv]4 ,b1 on ! o!r h&1 suppose ! rapidity ( ! curr5t is su*1 t )\t any ex]tion ( ! r[]s ! boat w\ld float d[n ! /ream 9 "o h\r to ,c4 ,f ,c draw ,c ,d p>allel to ,a ,b1 & draw ! /raight l9e ,a ,d diagonally4 ,! comb9$ effect ( ! o>s & ! curr5t w be1 t ! boat w be c>ri$ along ,a ,d1 & w arrive at ! opposite bank 9 "o h\r1 at ! po9t ,d4 ,if ! object be1 !re=e1 to rea* ! po9t ,b1 />t+ f ,a1 ! r[]s mu/ calculate1 z ne>ly z possible1 ! velocity ( ! curr5t4 ,!y mu/ imag9e a c]ta9 po9t ,e at su* a di/ance above ,b t ! boat w\ld be float$ by ! /ream f ,e to ,b 9 ! "t tak5 9 cross+ ! riv] 9 ! direction ,a ,e1 if !re 7 no curr5t4 ,if !y r[ t[>ds ! po9t ,e1 ! boat w arrive at ! po9t ,b1 mov+ 9 ! l9e ,a ,b4 ,9 ?is case ! boat is impell$ by two =ces1 t ( ! o>s 9 ! direction ,a ,e1 & t ( ! curr5t 9 ! direction ,a ,c4 ,! result w be1 accord+ to ! p>allelogram ( =ces1 a motion 9 ! diagonal ,a ,b4 ,! w9d & tide act+ ^u a vessel is a case ( a simil> k9d4 ,suppose t ! w9d is made to impel ! vessel 9 ! direction ( ! keel2 :ile ! tide may be act+ 9 any direction oblique to t ( ! keel4 ,! c\rse ( ! vessel is det]m9$ exactly 9 ! same mann] z t ( ! boat 9 ! la/ example4 ,! action ( ! o>s !mselves1 9 impell+ ! boat1 is an example ( ! composition ( =ce4 ,let ,a1 fig4 #ac41 be ! head1 & ,b ! /]n ( ! boat4 ,! boatman pres5ts 8 face t[>ds ,b1 & places ! o>s s t _! blades press aga9/ ! wat] 9 ! directions ,c ,e1 ,d ,f4 ,! resi/ance ( ! wat] produces =ces on ! side ( ! boat1 9 ! directions ,g ,l & ,h ,l1 :i*1 by ! composition ( =ce1 are equival5t to die diagonal =ce ,k ,l1 9 ! direction ( ! keel4 ,simil> obs]vations w apply to almo/ e body impell$ by in/rum5ts project+ f its sides1 & act+ aga9/ a fluid4 ,! motions ( fi%es1 ! act ( swimm+1 ! flight ( birds1 are all in/ances ( ! same k9d4 7#he47 ,! action ( w9d ^u ! sails ( a vessel1 & ! =ce !reby transmitt$ to ! keel1 modifi$ by ! rudd]1 is a problem :i* is solv$ by ! pr9ciples ( ! composition & resolution ( =ce2 b x is ( too complicat$ & difficult a nature to be introduc$ ) all its necess>y conditions & limitations 9 ?is place4 ,! "q may1 h[ev]1 be simplifi$1 if we consid] ! canvass ( ! sails to be /ret*$ s completely z to =m a plane surface4 ,let ,a ,b1 fig4 #ad41 be ! position ( ! sail1 & let ! w9d bl[ 9 ! direction ,c ,d4 ,if ! l9e ,c ,d be tak5 to express ! =ce ( ! w9d1 let ,d ,e ,c ,f be a p>allelogram1 ( :i* x is ! diagonal4 ,! =ce ,c ,d is equival5t to two =ces1 "o 9 ! direction ,f ,d ( ! plane ( ! canvass1 & ! o!r ,e ,d p]p5dicul> to ! sail4 ,! effect1 !re=e1 is ! same z if !re 7 two w9ds1 "o bl[+ 9 ! direction ( ,f ,d or ,b ,a1 t is aga9/ ! edge ( ! sail1 & ! o!r1 ,e ,d1 bl[+ full aga9/ its face4 ,x is evid5t t ! =m] w produce no effect :atev] ^u ! sail1 & t ! latt] w urge ! vessel 9 ! direction ,d ,g4 ,let u n[ consid] ?is =ce ,d ,g z act+ 9 ! diagonal ( ! p>allelogram ,d ,h ,g ,i4 ,x w be equival5t to two =ces1 ,d ,h & ,d ,i1 act+ along ! sides4 ,"o ( ^! =ces1 ,d ,h1 is 9 ! direction ( ! keel1 & ! o!r1 ,d ,i1 at "r angles to ! l5g? ( ! vessel1 s z to urge x sideways4 ,! =m ( ! vessel is evid5tly su* z to (f] a great resi/ance to ! latt] =ce1 & v little to ! =m]4 ,x consequ5tly proce$s ) consid]able velocity 9 ! direction ,d ,h ( its keel1 & makes way v sl[ly 9 ! sidew>d direction ,d ,i4 ,! latt] effect is call$ lee-way4 ,f ?is explanation x w be easily und]/ood1 h[ a w9d :i* is ne>ly oppos$ to ! c\rse ( a vessel may1 nev]!less1 be made to impel x by ! effect ( sails4 ,! angle ,b ,d ,v1 =m$ by ! sail & ! direction ( ! keel1 may be v oblique1 z may also be ! angle ,c ,d ,b =m$ by ! direction ( ! w9d & t ( ! sail4 ,!re=e ! angle ,c ,d ,v1 made up ( ^! two1 & :i* is t =m$ by ! direction ( ! w9d & t ( ! keel1 may be v oblique4 ,9 fig4 #ae4 ! w9d is ne>ly contr>y to ! direction ( ! keel1 & yet !re is an impell+ =ce express$ by ! l9e ,d ,h1 ! l9e ,c ,d express+1 z be=e1 ! :ole =ce ( ! w9d4 ,9 ?is example !re are two successive decompositions ( =ce4 ,fir/1 ! orig9al =ce ( ! w9d ,c ,d is resolv$ into two1 ,e ,d & ,f ,d2 & next ! elem5t ,e ,d1 or its equal ,d ,g1 is resolv$ into ,d ,i & ,d ,h2 s t ! orig9al =ce is resolv$ into ?ree1 viz4 ,f ,d1 ,d ,i1 ,d ,h1 :i*1 tak5 toge!r1 are me*anically equival5t to x4 ,! "p ,f ,d is entirely ineffectual2 x glides (f on ! surface ( ! canvass )\t produc+ any effect ^u ! vessel4 ,! "p ,d ,i produces lee-way1 & ! "p ,d ,h impels4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 7#hf47 ,if ! w9d1 h[ev]1 be directly contr>y to ! c\rse :i* x is requir$ t ! vessel %\ld take1 !re is no position :i* c be giv5 to ! sails :i* w impel ! vessel4 ,9 ?is case ! requir$ c\rse itself is resolv$ into two1 9 :i* ! vessel sails alt]nately1 a process :i* is call$ tack+4 ,?us1 suppose ! vessel is requir$ to move f ,a to ,e1 fig4 #af41 ! w9d sett+ f ,e to ,a4 ,! motion ,a ,b be+ resolv$ into two1 by be+ assum$ z ! diagonal ( a p>allelogram1 ! sides ,a a1 a ,b ( ! p>allelogram are successively sail$ ov]1 & ! vessel by ?is means arrives at ,b1 in/ead ( mov+ along ! diagonal ,a ,b4 ,9 ! same mann] %e moves along ,b b1 b ,c1 ,c c1 c ,d1 ,d d1 d ,e1 & arrives at ,e4 ,%e ?us sails cont9ually at a suffici5t angle ) ! w9d to obta9 an impell+ =ce1 yet at a suffici5tly small angle to make way 9 h] propos$ c\rse4 ,! consid]ation ( ! effect ( ! rudd]1 :i* we h omitt$ 9 ! prec$+ illu/ration1 af=ds ano!r in/ance ( ! resolution ( =ce4 ,we %all n1 h[ev]1 pursue ?is example fur!r4 7#hg47 ,a body fall+ f ! top ( ! ma/ :5 ! vessel is 9 full sail1 is an example ( ! composition ( motion4 ,x might be expect$1 t dur+ ! desc5t ( ! body1 ! vessel hav+ sail$ =w>d1 w\ld leave x beh9d1 & t1 !re=e1 x w\ld fall 9 ! wat] beh9d ! /]n1 or at lea/ on ! deck1 consid]ably beh9d ! ma/4 ,on ! o!r h&1 x is f\nd to fall at ! foot ( ! ma/1 exactly z x w\ld if ! vessel 7 n 9 motion4 ,to acc\nt = ?is1 let ,a ,b1 fig4 #ag41 be ! position ( ! ma/ :5 ! body at ! top is dis5gag$4 ,! ma/ is mov+ onw>ds ) ! vessel 9 ! direction ,a ,c1 s t 9 ! "t :i* ! body w\ld take to fall to ! deck1 ! top ( ! ma/ w\ld move f ,a to ,c4 ,b ! body be+ on ! ma/ at ! mom5t x is dis5gag$1 has ?is motion ,a ,c 9 common ) ! ma/2 & !re=e 9 its desc5t x is affect$ by two motions1 viz4 t ( ! vessel express$ by ,a ,c1 & its desc5d+ motion express$ by ,a ,b4 ,h5ce1 by ! composition ( motion1 x w be f\nd at ! opposite angle ,d ( ! p>allelogram1 at ! end ( ! fall4 ,dur+ ! fall1 h[ev]1 ! ma/ has mov$ ) ! vessel1 & has advanc$ to ,c ,d1 s t ! body falls at ! foot ( ! ma/4 7#hh47 ,an in/ance ( ! composition ( motion1 :i* is wor?y ( "s att5tion1 z x af=ds a pro( ( ! diurnal motion ( ! e>?1 is d]iv$ f obs]v+ ! desc5t ( a body f a v high t[]4 ,to r5d] ! explanation ( ?is m simple1 we %all suppose ! t[] to be on ! equator ( ! e>?4 ,let ,e ,p ,q1 fig4 #ah41 be a section ( ! e>? ?r\gh ! equator1 & let ,p ,t be ! t[]4 ,let u suppose t ! e>? moves on its axis 9 ! direction ,e ,p ,q4 ,! foot ,p ( ! t[] w1 !re=e1 9 "o day move ov] ! circle ,e ,p ,q1 :ile ! top ,t moves ov] ! great] circle ,t ,t ,r4 ,h5ce x is evid5t1 t ! top ( ! t[] moves ) great] spe$ ?an ! foot1 & !re=e 9 ! same "t moves ?r\gh a great] space4 ,n[ suppose a body plac$ at ! top2 x p>ticipates 9 ! motion :i* ! top ( ! t[] has 9 common ) ! e>?4 ,if x be dis5gag$1 x also receives ! desc5d+ motion ,t ,p4 ,let u suppose t ! body w\ld take five seconds to fall f ,t to ,p1 & t 9 ! same "t ! top ,t is mov$ by ! rotation ( ! e>? f ,t to ,t1 ! foot be+ mov$ f ,p to ,p4 ,! fall+ body is !re=e endu$ ) two motions1 "o express$ by ,t ,t1 & ! o!r by ,t ,p4 ,! comb9$ effect ( ^! w be f\nd 9 ! usual way by ! p>allelogram4 ,take ,t p equal to ,t ,t2 ! body w move f ,t to p 9 ! "t ( ! fall1 & w meet ! gr\nd at p4 ,b s9ce ,t ,t is great] ?an ,p ,p1 x foll[s t ! po9t p mu/ be at a di/ance f ,p equal to ! excess ( ,t ,t above ,p ,p4 ,h5ce ! body w n fall exactly at ! foot ( ! t[]1 b at a c]ta9 di/ance f x1 9 ! direction ( ! e>?'s motion1 t is1 ea/w>d4 ,?is is f\nd1 by exp]im5t1 to be actually ! case2 & ! di/ance f ! foot ( ! t[]1 at :i* ! body is obs]v$ to fall1 agrees ) t :i* is comput$ f ! motion ( ! e>?1 to z great a degree ( exactness z c\ld be expect$ f ! nature ( ! exp]im5t4 7#hi47 ,! prop]ties ( comp\nd$ motions cause "s ( ! eque/rian feats exhibit$ at public spectacles to be p]=m$ by a k9d ( ex]tion v diff]5t f t :i* ! spectators g5]ally attribute to ! p]=m]4 ,= example1 ! horseman /&+ on ! saddle leaps ov] a g>t] ext5d$ ov] ! horse at "r angles to 8 motion2 ! horse pass+ "u ! g>t]1 ! rid] lights ^u ! saddle at ! opposite side4 ,! ex]tion ( ! p]=m]1 9 ?is case1 is n t :i* he w\ld use 7 he to leap f ! gr\nd ov] a g>t] at ! same height4 ,9 ! latt] case1 he w\ld make an ex]tion to rise1 &1 at ! same "t1 to project 8 body =w>d4 ,9 ! case1 h[ev]1 ( ! horseman1 he m]ely makes t ex]tion :i* is necess>y to rise directly upw>ds to a suffici5t height to cle> ! g>t]4 ,! motion :i* he has 9 common ) ! horse1 comp\nd$ ) ! elevation acquir$ by 8 muscul> p[]1 accompli%es ! leap4 ,to expla9 ?is m fully1 let ,a ,b ,c1 fig4 #ai41 be ! direction 9 :i* ! horse moves1 ,a be+ ! po9t at :i* ! rid] quits ! saddle1 & ,c ! po9t at :i* he returns to x4 ,let ,d be ! highe/ po9t :i* is to be cle>$ 9 ! leap4 ,at ,a ! rid] makes a leap t[>ds ! po9t ,e1 & ?is mu/ be done at su* a di/ance f ,b1 t he w\ld rise f ,b to ,e 9 ! "t 9 :i* ! horse moves f ,a to ,b4 ,on dep>t+ f ,a1 ! rid] has1 !re=e1 two motions1 repres5t$ by ! l9es ,a ,e & ,a ,b1 by :i* he w move f ! po9t ,a to ! opposite angle ,d ( ! p>allelogram4 ,at ,d1 ! ex]tion ( ! leap be+ ov]come by ! weight ( 8 body1 he beg9s to return d[nw>d1 & w\ld fall f ,d to ,b 9 ! "t 9 :i* ! horse moves f ,b to ,c4 ,b at ,d he /ill reta9s ! motion :i* he _h 9 common ) ! horse2 & !re=e1 9 leav+ ! po9t ,d1 he has two motions1 express$ by ! l9es ,d ,f & ,d ,b4 ,! comp\nd$ effects ( ^! motions c>ry him f ,d to ,c4 ,/rictly speak+1 8 motion f ,a to ,d1 & f ,d to ,c1 is n 9 /raight l9es1 b 9 a curve4 ,x is n necess>y "h1 h[ev]1 to att5d to ?is circum/ance4 7#ij47 ,if a billi>d-ball /rike ! cu%ion ( ! table obliquely1 x w be reflect$ f x 9 a c]ta9 direction1 =m+ an angle ) ! direction 9 :i* x /ruck x4 ,?is af=ds an example ( ! resolution & composition ( motion4 ,we %all fir/ consid] ! effect :i* w\ld ensue if ! ball /ruck ! cu%ion p]p5dicul>ly4 ,let ,a ,b1 fig4 #bj41 be ! cu%ion1 & ,c ,d ! direction 9 :i* ! ball moves t[>ds x4 ,if ! ball & ! cu%ion 7 p]fectly inela/ic1 ! resi/ance ( ! cu%ion w\ld de/roy ! motion ( ! ball1 & x w\ld be r$uc$ to a /ate ( re/ at ,d4 ,if1 on ! o!r h&1 ! ball 7 p]fectly ela/ic1 x w\ld be reflect$ f ! cu%ion1 & w\ld receive z mu* motion f ,d to ,c aft] ! impact1 z x _h f ,c to ,d be=e x4 ,p]fect ela/icity1 h[ev]1 is a quality :i* is nev] f\nd 9 ^! bodies4 ,!y are always ela/ic1 b imp]fectly s4 ,consequ5tly ! ball aft] ! impact w be reflect$ f ,d t[>ds ,c1 b ) a less motion ?an t ) :i* x approa*$ f ,c to ,d4 ,n[ let u suppose t ! ball1 in/ead ( mov+ f ,c to ,d1 moves f ,e to ,d4 ,! =ce ) :i* x /rikes ,d be+ express$ by ,d ,e1 equal to ,e ,d1 may be resolv$ into two1 ,d ,f & ,d ,c4 ,! resi/ance ( ! cu%ion de/roys ,d ,c1 & ! ela/icity produces a contr>y =ce 9 ! direction ,d ,c1 b less ?an ,d ,c or ,d ,c1 because t ela/icity is imp]fect4 ,! l9e ,d ,c express+ ! =ce 9 ! direction ,c ,d1 let ,d ,g 7less ?an ,d ,c7 express ! reflective =ce 9 ! direction ,d ,c4 ,! o!r elem5t ,d ,f1 into :i* ! =ce ,d ,e is resolv$ by ! impact1 is n de/roy$ or modifi$ by ! cu%ion1 & !re=e1 on leav+ ! cu%ion at ,d1 ! ball is influ5c$ by two =ces1 ,d ,f 7:i* is equal to ,c ,e7 & ,d ,g4 ,consequ5tly x w move 9 ! diagonal ,d ,h4 7#ia47 ,! angle ,e ,d ,c is 9 ?is case call$ ! 8angle ( incid5ce10 & ,c ,d ,h is call$ 8! angle ( reflection40 ,x is evid5t1 f :at has be5 j inf]r$1 t ! ball1 be+ imp]fectly ela/ic1 ! angle ( incid5ce mu/ always be less ?an ! angle ( reflection1 & ) ! same obliquity ( incid5ce1 ! m imp]fect ! ela/icity is1 ! less w be ! angle ( reflection4 ,9 ! impact ( a p]fectly ela/ic body1 ! angle ( reflection w\ld be equal to ! angle ( incid5ce4 ,= !n ! l9e ,d ,g1 express+ ! reflective =ce1 w\ld be tak5 equal to ,c ,d1 & ! angle ,c ,d ,h w\ld be equal to ,c ,d ,e4 ,?is is f\nd by exp]im5t to be ! case :5 light is reflect$ f a poli%$ surface ( glass or metal4 ,motion is sometimes di/+ui%$ into absolute & relative4 ,:at 8relative motion0 means is easily expla9$4 ,if a man walk ^u ! deck ( a %ip f /em to /]n1 he has a relative motion :i* is measur$ by ! space ^u ! deck ov] :i* he walks 9 a giv5 "t4 ,b :ile he is ?us walk+ f /em to /]n1 ! %ip & its cont5ts1 includ+ himself1 are impell$ ?r\gh ! deep 9 ! opposite direction4 ,if x s happ5 t ! motion ( ! man1 f /em to /]n1 be exactly equal to ! motion ( ! %ip 9 ! contr>y way1 ! man w be1 relatively to ! surface ( ! sea & t ( ! e>?1 at re/4 ,?us1 relatively to ! %ip1 he is 9 motion1 :ile1 relatively to ! surface ( ! e>?1 he is at re/4 ,b /ill ?is is n absolute re/4 ,! surface itself is mov+ by ! diurnal rotation ( ! e>? ^u its axis1 z well z by ! annual motion 9 its orbit r\nd ! sun4 ,^! motions1 & o!rs to :i* ! e>? is subject1 mu/ be all comp\nd$ by ! !orem ( ! p>allelogram ( =ces be=e we c obta9 ! absolute /ate ( ! body ) respect to motion or re/4 ,,*ap4 ,,vi4 ,,attraction4 7#ib47 ,:atev] produces1 or t5ds to produce1 a *ange 9 ! /ate ( a p>ticle or mass ( matt] ) respect to motion or re/1 is a =ce4 ,re/1 or uni=m rectil9e> motion1 are !re=e ! only /ates 9 :i* any body c exi/ :i* is n subject to ! pres5t action ( "s =ce4 ,we are n1 h[ev]1 entitl$ to conclude1 t because a body is obs]v$ 9 "o or o!r ( ^! /ates1 x is !re=e un9flu5c$ by any =ces4 ,x may be "u ! imm$iate action ( =ces :i* neutralise ea* o!r3 ?us two =ces may be act+ ^u x :i* are equal1 & 9 opposite directions4 ,9 su* a case1 its /ate ( re/1 or ( uni=m rectil9e> motion1 w be undi/urb$4 ,! /ate ( uni=m rectil9e> motion decl>es m ) respect to ! body ?an ! /ate ( re/2 = ! =m] betrays ! action ( a =ce ^u ! body at "s antec$5t p]iod2 ?is action hav+ be5 susp5d$1 :ile its effect cont9ues to be obs]v$ 9 ! motion :i* x has produc$4 7#ic47 ,:5 ! /ate ( a body is *ang$ f re/ to uni=m rectil9e> motion1 ! action ( ! =ce is only mom5t>y1 9 :i* case x is call$ an impulse4 ,if a body 9 uni=m rectil9e> motion receive an impulse 9 ! direction 9 :i* x is mov+1 ! effect w be1 t x w cont9ue to move uni=mly 9 ! same direction1 b its velocity w be increas$ by ! am\nt ( spe$ :i* ! impulse w\ld h giv5 x _h x be5 previ\sly quiesc5t4 ,?us1 if ! previ\s motion be at ! rate ( t5 feet 9 a second1 & ! impulse be su* z w\ld move x f a /ate ( re/ at five feet 9 a second1 ! velocity1 aft] ! impulse1 w be fifte5 feet 9 a second4 ,b if ! impulse be receiv$ 9 a direction imm$iately oppos$ to ! previ\s motion1 !n x w dim9i% ! spe$ by t am\nt ( velocity :i* x w\ld give to ! body _h x be5 previ\sly at re/4 ,9 ! example already giv51 if ! impulse 7 oppos$ to ! previ\s motion1 ! velocity ( ! body aft] ! impulse w\ld be five feet 9 a second4 ,if ! impulse receiv$ 9 ! direction oppos$ to ! motion be su* z w\ld give to ! body at re/ a velocity equal to t ) :i* x is mov+1 !n ! effect w be1 t aft] ! impulse no motion w exi/2 & if ! impulse w\ld give x a /ill great] velocity1 ! body w be mov$ 9 ! opposite direction ) an uni=m velocity equal to ! excess ( t due to ! impulse ov] t :i* ! body previ\sly _h4 ,:5 a body 9 a /ate ( uni=m motion receives an impulse 9 a direction n co9cid+ ) t ( its motion1 x w move uni=mly aft] ! impulse 9 an int]m$iate direction1 :i* may be det]m9$ by ! pr9ciples e/abli%$ = ! composition ( motion 9 ! la/ *apt]4 ,?us x appe>s1 t :5ev] ! /ate ( a body is *ang$ ei!r f re/ to uni=m rectil9e> motion or vice v]sa1 or f "o /ate ( uni=m rectil9e> motion to ano!r1 diff]+ f t ei!r 9 velocity or direction1 or 9 bo?1 ! ph5om5on is produc$ by t peculi> modification ( =ce ^: action cont9ues b = a s+le in/ant1 & :i* has be5 call$ an impulse4 7#id47 ,9 mo/ cases1 h[ev]1 ! me*anical /ate ( a body is obs]v$ to be subject to a cont9ual *ange or t5d5cy to *ange4 ,we are surr\nd$ by innum]able examples ( ?is4 ,a body is plac$ on ! table4 ,a cont9ual pressure is excit$ on ! surface ( ! table4 ,?is pressure is only ! consequ5ce ( ! cont9ual t5d5cy ( ! body to move d[nw>ds4 ,if ! body 7 excit$ by a =ce ( ! nature ( an impulse1 ! effect ^u ! table w\ld be in/antane\s1 & w\ld imm$iately cease4 ,x w\ld1 9 fact1 be a bl[4 ,b ! cont9uation ( ! pressure proves ! cont9uation ( ! action ( ! =ce4 ,if ! table be remov$ f b5ea? ! body1 ! =ce :i* excites x be+ no long] resi/$1 w produce motion2 x is manife/$1 n z be=e1 by a t5d5cy to produce motion1 b by ! actual exhibition ( t ph5om5on4 ,n[ if ! excit+ =ce 7 an impulse1 ! body w\ld desc5d to ! gr\nd ) an uni=m velocity4 ,on ! o!r h&1 z w h]eaft] appe>1 e mom5t ( its fall increases its spe$1 & t spe$ is greate/ at ! in/ant x meets ! gr\nd4 ,a piece ( iron plac$ at a di/ance f a magnet approa*es x1 b n ) an uni=m velocity4 ,! =ce ( ! magnet cont9ues to act dur+ ! approa* ( ! iron1 & ea* mom5t gives x increas$ motion4 7#ie47 ,! =ces :i* are ?us 9 con/ant op]ation1 proce$ f secret ag5cies :i* ! human m9d has nev] be5 able to detect4 ,all ! analogies ( nature prove t !y are n ! imm$iate results ( ! div9e w1 b are second>y causes1 t is1 effects ( "s m remote pr9ciples4 ,to asc5d to ^! second>y causes1 & ?us z x 7 approa* "o /ep ne>] to ! ,creator1 is ! great bus9ess ( philosophy2 & ! mo/ c]ta9 means = accompli%+ ?is1 is dilig5tly to obs]ve1 to comp>e1 & to classify ! ph5om5a1 & to avoid assum+ ! exi/5ce ( any ?+ :i* has n ei!r be5 directly obs]v$1 or :i* _c be inf]r$ demon/ratively f natural ph5om5a4 ,philosophy %\ld foll[ nature1 & n lead h]4 ,:ile ! law ( in]tia1 e/abli%$ by obs]vation & reason1 decl>es ! inability ( matt]1 f any pr9ciple resid5t 9 x1 to *ange its /ate1 all ! ph5om5a ( ! univ]se prove t /ate to be 9 con/ant b regul> fluctuation4 ,!re is n 9 exi/5ce a s+le in/ance ( ! ph5om5on ( absolute re/1 or ( motion :i* is absolutely uni=m & rectil9e>4 ,9 bodies1 or ! p>ts ( bodies1 !re is no kn[n in/ance ( simple passive juxtaposition unaccompani$ by pressure or t5sion1 or "s o!r 8t5d5cy to motion40 ,innum]able secret p[]s are ev] at "w1 comp5sat+1 z x 71 = in]tia1 & supply+ ! mat]ial _w ) a sub/itute = ! pr9ciples ( action & w1 :i* give su* immeasurable sup]iority to ! "* ( life4 7#if47 ,! =ces :i* are ?us 9 cont9ual op]ation1 ^: exi/5ce is demon/rat$ by _! obs]v$ effects1 b ^: nature1 seat1 & mode ( op]ation are unkn[n to u1 are call$ by ! g5]al "n attractions4 ,^! =ces are classifi$ accord+ to ! analogies :i* prevail among _! effects1 9 ! same mann]1 & accord+ to ! same pr9ciples1 z organis$ be+s are gr\p$ 9 natural hi/ory4 ,9 t dep>tm5t ( natural sci5ce1 :5 individuals are di/ribut$ 9 classes1 ! object is m]ely to g5]alise1 & !reby promote ! enl>gem5t ( k2 b no?+ is or ought to be ?us assum$ respect+ ! ess5ce1 or real int]nal con/itution ( ! individuals4 ,accord+ to _! ext]nal & obs]vable *>act]s & qualities !y are class$2 & ?is classification %\ld nev] be adduc$ z an evid5ce ( any ?+ except t similitude ( qualities to :i* x ow$ its orig94 ,ph5om5a are to ! natural philosoph] :at organis$ be+s are to ! naturali/4 ,he gr\ps & classifies !m on ! same pr9ciples1 & ) a l object4 ,& z ! naturali/ gives to ea* species a "n applicable to ! individual be+s :i* exhibit correspond+ qualities1 s ! philosoph] gives to ea* =ce or attraction a "n correspond+ to ! ph5om5a ( :i* x is ! cause4 ,! naturali/ is ignorant ( ! real ess5ce or int]nal con/itution ( ! ?+ :i* he nom9ates1 & ( ! mann] 9 :i* x comes to possess or exhibit ^? qualities :i* =m ! basis ( 8 classification2 & ! natural philosoph] is equally ignorant ( ! nature1 seat1 & mode ( op]ation ( ! =ce :i* he assigns z ! cause ( an obs]v$ class ( effects4 ,^! obs]vations respect+ ! true import ( ! t]m 8attraction0 seem ! m necess>y to be premis$1 because ! g5]al phraseology ( physical sci5ce1 tak5 z language is commonly receiv$1 w seem to convey some?+ m4 ,! names ( ! sev]al attractions :i* we %all h to notice1 frequ5tly ref] ! seat ( ! cause to specific objects1 & seem to imply some?+ respect+ its mode ( op]ation4 ,?us1 :5 we say 8! magnet attracts a piece ( iron10 ! true philosophical import ( ! words is1 8t a piece ( iron plac$ 9 ! vic9ity ( ! magnet1 w move t[>ds x1 or plac$ 9 contact1 w adh]e to x1 s t "s =ce is necess>y to sep>ate !m40 ,9 ! ord9>y s5se1 h[ev]1 some?+ m ?an ?is simple fact is impli$4 ,x is ins9uat$ t ! magnet is ! seat ( ! =ce :i* gives motion to ! iron2 t 9 ! production ( ! ph5om5on1 ! magnet is an ag5t ex]t+ a c]ta9 influ5ce1 ( :i* ! iron is ! subject4 ,( all ?is1 h[ev]1 !re is no pro(2 on ! contr>y1 s9ce ! magnet mu/ move t[>ds ! iron ) j z mu* =ce z ! iron moves t[>ds ! magnet1 !re is z mu* reason to place ! seat ( ! =ce 9 ! iron1 & consid] x z an ag5t affect+ ! magnet4 ,b1 9 fact1 ! influ5ce :i* produces ?is ph5om5on may n be resid5t 9 ei!r ! "o body or ! o!r4 ,x may be imag9$ to be a prop]ty ( a m$ium 9 :i* bo? are plac$1 or to arise f "s ?ird body1 ! pres5ce ( :i* is n imm$iately obs]v$4 ,h[ev] attractive ^! & l speculations may be1 !y _c be all[$ a place 9 physical inve/igations1 nor %\ld consequ5ces drawn f su* hypo!ses be all[$ to ta9t our conclusions ) _! unc]ta9ty4 ,! /ud5t ought1 !re=e1 to be aw>e1 t :atev] may seem to be impli$ by ! language us$ 9 ?is sci5ce 9 relation to attractions1 no?+ is p]mitt$ to =m ! basis ( reason+ respect+ !m except _! effects2 & :atev] be ! common signification ( ! t]ms us$1 x is to ^! effects1 & to ^! alone1 !y %\ld be ref]r$4 7#ig47 ,attractions may be prim>ily di/ribut$ into two classes2 "o consi/+ ( ^? :i* exi/ betwe5 ! molecules or con/itu5t p>ts ( bodies1 & ! o!r betwe5 bodies !mselves4 ,! =m] are sometimes call$1 = di/9ction1 molecul> or atomic attractions4 ,)\t ! ag5cy ( molecul> =ces1 ! :ole face ( nature w\ld be depriv$ ( v>iety & beauty2 ! univ]se w\ld be a confus$ heap ( mat]ial atoms disp]s$ ?r\gh space1 )\t =m1 %ape1 coh]5ce1 or motion4 ,bodies w\ld nei!r h ! =ms ( solid1 liquid1 or air2 heat & light w\ld no long] produce _! wont$ effects2 organis$ be+s c\ld n exi/2 life itself1 z connect$ ) body1 w\ld be ext9ct4 ,atoms ( matt]1 :e!r di/ant or 9 juxtaposition1 w\ld h no t5d5cy to *ange _! places1 & all w\ld be et]nal /illness & re/4 ,if1 !n1 we are ask$ = a pro( ( ! exi/5ce ( molecul> =ces1 we may po9t to ! e>? & to ! heav5s2 we may "n e object :i* c be se5 or felt4 ,! :ole mat]ial _w is "o great result ( ! influ5ce ( ^! p[]ful ag5ts4 7#ih47 ,x has be5 prov$ 7#aa4 et seq47 t ! con/itu5t p>ticles ( bodies are ( inconceivable m9ut5ess1 & t !y are n 9 imm$iate contact 7#bc71 b sep>at$ f ea* o!r by int]/itial spaces1 :i*1 l ! atoms !mselves1 al?\gh too small to be directly obs]v$1 yet are inconte/ably prov$ to exi/1 by obs]vable ph5om5a1 f :i* _! exi/5ce demon/ratively foll[s4 ,! resi/ance :i* e body opposes to compression1 proves t a repulsive influ5ce prevails betwe5 ! p>ticles1 & t ?is repulsion is ! cause :i* keeps ! atoms sep>ate1 & ma9ta9s ! int]/itial spaces j m5tion$4 ,al?\gh ?is repulsion is f\nd to exi/ betwe5 ! molecules ( all sub/ances :atev]1 yet x has diff]5t degrees ( en]gy 9 diff]5t bodies4 ,?is is prov$ by ! fact1 t "s sub/ances admit ( easy compression1 :ile 9 o!rs1 ! ex]tion ( consid]able =ce is necess>y to produce ! smalle/ dim9ution 9 bulk4 ,! space ar\nd ea* atom ( a body1 ?r\gh :i* ?is repulsive influ5ce ext5ds1 is g5]ally limit$1 & imm$iately beyond x1 a =ce ( ! opposite k9d is manife/$1 viz4 attraction4 ,?us1 9 solid bodies1 ! p>ticles resi/ sep>ation z well z compression1 & ! application ( =ce is z necess>y to break ! body1 or divide x into sep>ate p>ts1 z to =ce its p>ticles into clos] aggregation4 ,x is by virtue ( ?is attraction t solid bodies ma9ta9 _! figure1 & t _! p>ts are n sep>at$ & scatt]$ l ^? ( fluids1 m]ely by _! own weight4 ,?is =ce is call$ ! attraction ( cohesion4 ,! cohesive =ce acts 9 diff]5t sub/ances ) diff]5t degrees ( en]gy3 9 "s its int5sity is v great2 b ! sph]e ( its influ5ce app>5tly v limit$4 ,?is is ! case ) all bodies :i* are h>d1 /rong1 & brittle1 :i* no =ce c ext5d or /ret* 9 any p]ceptible degree1 & :i* require a great =ce to break or te> !m asund]4 ,su*1 = example1 is ca/ iron1 c]ta9 /ones1 & v>i\s o!r sub/ances4 ,9 "s bodies ! cohesive =ce is weak1 b ! sph]e ( its action consid]able4 ,bodies :i* are easily ext5d$1 )\t be+ brok5 or torn asund]1 furni% examples ( ?is4 ,su* are ,indian-rubb]1 or ca\t*\c1 sev]al animal & vegetable products1 &1 9 g5]al1 all solids ( a s(t & viscid k9d4 ,betwe5 ^! extremes1 ! cohesive =ce may be obs]v$ 9 v>i\s degrees4 ,9 lead & o!r s(t metals1 its sph]e ( action is great]1 & its en]gy less1 ?an 9 ! =m] examples2 b its sph]e less1 & en]gy great]1 ?an 9 ! latt] ones4 ,x is f ! influ5ce ( ?is =ce1 & t ( ! repulsion1 ^: sph]e ( action is /ill clos] to ! compon5t atoms1 t all ! v>ieties ( texture :i* we d5om9ate h>d1 s(t1 t\gh1 brittle1 ductile1 pliant1 c4 arise4 ,aft] hav+ be5 brok51 or o!rwise sep>at$1 ! p>ts ( a solid may be aga9 unit$ by _! cohesion1 provid$ any consid]able numb] ( po9ts be br\ght into suffici5tly close contact4 ,:5 ?is is done by me*anical means1 h[ev]1 ! cohesion is n s /rong z be=e _! sep>ation1 & a comp>atively small =ce w be suffici5t aga9 to disunite !m4 ,two pieces ( lead fre%ly cut1 ) smoo? surfaces1 w adh]e :5 press$ toge!r1 & w require a consid]able =ce to sep>ate !m4 ,9 ! same mann] if a piece ( ,indian-rubb] be torn1 ! p>ts sep>at$ w aga9 coh]e1 by be+ br\ght toge!r ) a slight pressure4 ,! union ( ! p>ts 9 su* in/ances is easy1 because ! sph]e ?r\gh :i* ! influ5ce ( cohesion ext5ds is consid]able2 b ev5 9 bodies 9 :i* ?is influ5ce ext5ds ?r\gh a m limit$ space1 ! cohesion ( sep>ate pieces w be manife/$1 provid$ _! surfaces be highly poli%$1 s z to insure ! ne> approa* ( a great numb] ( _! p>ticles4 ,?us1 two poli%$ surfaces ( glass1 metal1 or /one1 w adh]e :5 br\ght into contact4 ,9 all ^! cases1 if ! bodies be disunit$ by me*anical =ce1 !y w sep>ate at exactly ! p>ts at :i* !y _h be5 unit$1 s t aft] _! sep>ation no "p ( ! "o w adh]e to ! o!r2 prov+ t ! =ce ( cohesion ( ! surfaces br\ght into contact is less ?an t :i* naturally held ! p>ticles ( ea* toge!r4 7#ii47 ,:5 a body is 9 ! liquid =m1 ! weight ( its p>ticles greatly pr$om9ates ov] _! mutual cohesion1 & consequ5tly if su* a body be unconf9$ x w be scatt]$ by its own weight2 if x be plac$ 9 any vessel1 x w settle itself1 by ! =ce ( its weight1 into ! l[e/ p>ts1 s t no space 9 ! vessel bel[ ! upp] surface ( ! liquid w be unoccupi$4 ,! p>ticles ( a solid body plac$ 9 ! vessel h exactly ! same t5d5cy1 by reason ( _! weight2 b ?is t5d5cy is resi/$ & prev5t$ f tak+ effect by _! /rong cohesion4 ,al?\gh ?is cohesion 9 solids is mu* great] ?an 9 liquids1 & productive ( m obvi\s effects1 yet ! pr9ciple is n altoge!r unobs]v$ 9 liquids4 ,wat] conv]t$ into vap\r by heat1 is divid$ into inconceivably m9ute p>ticles1 :i* asc5d 9 ! atmosph]e4 ,:5 x is !re depriv$ ( a "p ( t heat :i* gave x ! vapor\s =m1 ! p>ticles1 9 virtue ( _! cohesive =ce1 collect into r\nd drops1 9 :i* =m !y desc5d to ! e>?4 ,9 ! same mann]1 if a liquid be all[$ to fall gradually f ! lip ( a vessel1 x w n be dismiss$ 9 p>ticles indef9itely small1 z if its mass 7 incoh]5t1 l s& or p[d]1 b w fall 9 drops ( consid]able magnitude4 ,9 proportion z ! cohesive =ce is great]1 ^! drops affect a great] size4 ,?us1 oil & viscid liquids fall 9 l>ge drops2 e!r1 alcohol1 & o!rs 9 small ones4 ,two drops ( ra9 trickl+ d[n a w9d[ pane w coalesce :5 !y approa* ea* o!r2 & ! same ph5om5on is /ill m rem>kable1 if a few drops ( quicksilv] be scatt]$ on an horizontal plate ( glass4 ,x is ! cohesive pr9ciple :i* gives rotundity to gra9s ( %ot3 ! liquid metal is all[$ to fall l ra9 f a great elevation4 ,9 its desc5t ! drops become truly globul>1 & be=e !y rea* ! end ( _! fall !y are h>d5$ by cool+1 s t !y reta9 _! %ape4 ,x is also1 probably1 to ! cohesive attraction t we %\ld assign ! globul> =ms ( all ! great bodies ( ! univ]se2 ! sun1 planets1 satellites1 c41 :i* orig9ally may h be5 9 ! liquid /ate4 7#ajj47 ,molecul> attraction is also exhibit$ betwe5 ! p>ticles ( liquids & solids4 ,a drop ( wat] w n desc5d freely :5 x is 9 contact ) a p]p5dicul> glass plane3 x w adh]e to ! glass2 its desc5t w be ret>d$2 & if its weight be insuffici5t to ov]come ! adhesive =ce1 x w rema9 susp5d$4 ,if a plate ( glass be plac$ ^u ! surface ( wat] )\t be+ p]mitt$ to s9k1 x w require m =ce to raise x f ! wat] ?an is suffici5t m]ely to balance ! weight ( ! glass4 ,?is %[s ! adhesion ( ! wat] & glass1 & also ! cohesive =ce ) :i* ! p>ticles ( ! wat] resi/ sep>ation4 ,if a ne$le be dipp$ 9 c]ta9 liquids1 a drop w rema9 susp5d$ at its po9t :5 )drawn f !m3 &1 9 g5]al1 :5 a solid body has be5 imm]s$ 9 a liquid & )drawn1 x is wet2 t is1 "s ( ! liquid has adh]$ to its surfaces4 ,if no attraction exi/$ betwe5 ! solid & liquid1 ! solid w\ld be 9 ! same /ate aft] imm]sion z be=e4 ,?is is prov$ by liquids & solids betwe5 :i* no attraction exi/s4 ,if a piece ( glass be imm]s$ 9 m]cury1 x w be 9 ! same /ate :5 )drawn z be=e x 0 imm]s$4 ,no m]cury w adh]e to x2 x w n be wet4 ,:5 x ra9s1 ! p]son & ve/ure are affect$ only because ?is attraction exi/s betwe5 !m & wat]4 ,if x ra9$ m]cury1 none w\ld adh]e to !m4 7#aja47 ,:5 molecul> attraction is exhibit$ by liquids p]vad+ ! int]/ices ( por\s bodies1 asc5d+ 9 crevices or 9 ! bores ( small tubes1 x is call$ capill>y attraction4 ,in/ances ( ?is are innum]able4 ,liquids are ?us drawn into ! pores ( sponge1 sug>1 lamp-wick1 c4 ,! animal & vegetable k+dom furni% num]\s examples ( ?is class ( effects4 ,a weight be+ susp5d$ by a dry rope1 w be drawn upw>ds ?r\gh a consid]able height1 if ! rope be moi/5$ ) a wet sponge4 ,! attraction ( ! p>ticles compos+ ! rope = ! wat] is 9 ?is case s p[]ful1 t ! t5sion produc$ by sev]al hundr$ weight _c expel !m4 ,a glass tube1 ( small bore1 be+ dipp$ 9 wat] t+$ by mixture ) a little ink1 w reta9 a quantity ( ! liquid susp5d$ :5 )drawn4 ,! height ( ! liquid 9 ! tube w be se5 by look+ ?r\gh x4 ,x is f\nd t ! less ! bore ( ! tube is1 ! great] w be ! height ( ! column su/a9$4 ,a s]ies ( su* tubes fix$ 9 ! same frame1 ) _! l[] orifices at ! same level1 & ) bores gradually decreas+1 be+ dipp$ 9 ! liquid1 w exhibit columns gradually increas+4 ,a capill>y syphon is =m$ ( a hank ( cotton ?reads1 "o end ( :i* is imm]s$ 9 ! vessel conta9+ ! liquid1 & ! o!r is c>ri$ into ! vessel into :i* ! liquid is to be transf]r$4 ,! liquid may be ?us drawn f ! "o vessel into ! o!r4 ,! same effect may be produc$ by a glass syphon ) a small bore4 7#ajb47 ,x frequ5tly happ5s t a molecul> repulsion is exhibit$ betwe5 a solid & a liquid4 ,if a piece ( wood be imm]s$ 9 quicksilv]1 ! liquid w be depress$ at t "p ( ! surface :i* is ne> ! wood2 & 9 l mann]1 if x be conta9$ 9 a glass vessel1 x w be depress$ at ! edges4 ,9 a b>omet] tube1 ! surface ( ! m]cury is convex1 ow+ p>tly to ! repulsion betwe5 ! glass & m]cury4 ,all solids1 h[ev]1 d n repel m]cury4 ,if any gold5 tr9ket be dipp$ 9 t liquid1 or ev5 be expos$ = a mom5t to contact ) x1 ! gold w be in/antly int]m+l$ ) p>ticles ( quicksilv]1 ! metal *anges its col\r1 & becomes :ite l silv]1 & ! m]cury c only be extricat$ by a difficult process4 ,*a9s1 seals1 r+s1 c4 %\ld always be laid aside by ^? engag$ 9 exp]im5ts or o!r processes 9 :i* m]cury is us$4 7#ajc47 ,( all ! =ms "u :i* molecul> =ce is exhibit$1 t 9 :i* x takes ! "n ( aff9ity is att5d$ ) ! mo/ conspicu\s effects4 ,aff9ity is 9 *emi/ry :at in]tia is 9 me*anics1 ! basis ( ! sci5ce4 ,! pres5t treatise is n ! prop] place = any detail$ acc\nt ( ?is important class ( natural ph5om5a4 ,^? :o seek su* k are ref]r$ to our treatise on ,,*emi/ry4 ,s9ce1 h[ev]1 aff9ity sometimes influ5ces ! me*anical /ate ( bodies1 & affects _! me*anical prop]ties1 x w be necess>y "h to /ate s mu* respect+ x z to r5d] intelligible ^? ref]5ces :i* we may h occasion to make to su* effects4 ,:5 ! p>ticles ( diff]5t bodies are br\ght into close contact1 & m especially :51 be+ 9 a fluid /ate1 !y are mix$ toge!r1 _! union is frequ5tly obs]v$ to produce a comp\nd body1 diff]+ 9 its qualities f ei!r ( ! compon5t bodies4 ,?us ! bulk ( ! comp\nd is (t5 great] or less ?an ! unit$ volumes ( ! compon5t bodies4 ,! compon5t bodies may be ( ! ord9>y temp]ature ( ! atmosph]e1 & yet ! comp\nd may be ( a mu* high] or l[] temp]ature4 ,! compon5ts may be liquid1 & ! comp\nd solid4 ,! col\r ( ! comp\nd may be> no resemblance :atev] to t ( ! compon5ts4 ,! species ( molecul> action betwe5 ! compon5ts1 :i* produce ^! & simil>1 effects1 is call$ aff9ity4 7#ajd47 ,we %all limit ourselves "h to ! /atem5t ( a few examples ( ^! ph5om5a4 ,if a p9t ( wat] & a p9t ( sulphuric acid be mix$1 ! comp\nd w be consid]ably less ?an a qu>t4 ,! d5sity ( ! mixture is1 !re=e1 great] ?an t :i* w\ld result f ! m]e diffusion ( ! p>ticles ( ! "o fluid ?r\gh ^? ( ! o!r4 ,! p>ticles h assum$ a great] proximity1 & !re=e exhibit a mutual attraction4 ,9 ?is exp]im5t1 al?\gh ! liquids be=e be+ mix$ be ( ! temp]ature ( ! surr\nd+ air1 ! mixture w be s int5sely hot1 t ! vessel :i* conta9s x _c be t\*$ )\t pa94 ,if ! two a]i=m fluids1 call$ oxyg5 & hydrog51 be mix$ toge!r 9 a c]ta9 proportion1 ! comp\nd w be wat]4 ,9 ?is case1 ! compon5ts are diff]5t f ! comp\nd1 n m]ely 9 ! "o be+ air & ! o!r liquid1 b 9 o!r respects n less /rik+4 ,! comp\nd wat] ext+ui%es fire1 & yet ( ! compon5ts1 hydrog5 is "o ( ! mo/ inflammable sub/ances 9 nature1 & ! pres5ce ( oxyg5 is indisp5sably necess>y to su/a9 ! ph5om5on ( combu/ion4 ,oxyg5 gas1 unit$ ) quicksilv]1 produces a comp\nd ( a black col\r1 ! quicksilv] be+ :ite & ! gas col\rless4 ,:5 ^! sub/ances are comb9$ 9 ano!r proportion1 !y give a r$ comp\nd4 7#aje47 ,hav+ notic$ ! pr9cipal molecul> =ces1 we %all n[ proce$ to ! consid]ation ( ^? attractions :i* are exhibit$ betwe5 bodies exi/+ 9 masses4 ,! influ5ce ( molecul> attractions is limit$ to ins5sible di/ances4 ,on ! contr>y1 ! =ces :i* are n[ to be notic$ act at consid]able di/ances1 & to ! influ5ce ( "s !re is no limit1 ! effect1 h[ev]1 decreas+ z ! di/ance increases4 ,! effect ( ! load/one on iron is well kn[n1 & is "o ( ?is class ( =ces4 ,= a detail$ acc\nt ( ?is =ce1 & ! v>i\s ph5om5a ( :i* x is ! cause1 ! read] is ref]r$ to our treatise on ,,magnetism4 ,:5 glass1 wax1 amb]1 & o!r sub/ances are submitt$ to friction ) silk5 or wooll5 clo?1 !y are obs]v$ to attract fea!rs1 & o!r light bodies plac$ ne> !m4 ,a l effect is produc$ 9 sev]al o!r ways1 & is att5d$ ) o!r ph5om5a1 ! discussion ( :i* =ms a pr9cipal "p ( physical sci5ce4 ,! =ce ?us exhibit$ is call$ electricity4 ,= details respect+ x1 & = its connection ) magnetism1 ! read] is ref]r$ to our treatises on ,,electricity & ,,electro-,,magnetism4 7#ajf47 ,^! attractions exi/ ei!r betwe5 bodies ( p>ticul> k9ds1 or are develop$ by r$uc+ ! bodies :i* manife/ !m to a c]ta9 /ate by friction1 or "s o!r means4 ,!re is1 h[ev]1 an attraction1 :i* is manife/$ betwe5 bodies ( all species1 & "u all circum/ances :atev]2 an attraction1 ! int5sity ( :i* is :olly indep5d5t ( ! nature ( ! bodies1 & only dep5ds on _! masses & mutual di/ances4 ,?us1 if a mass ( metal & a mass ( clay be plac$ 9 ! va/ abyss ( space1 at a mile asund]1 !y w in/antly comm5ce to approa* ea* o!r ) c]ta9 velocities4 ,aga91 if a mass ( /one & ( wood respectively equal to ! =m]1 be plac$ at a l di/ance1 !y w also comm5ce to approa* ea* o!r ) ! same velocities z ! =m]4 ,?is univ]sal attraction1 :i* only dep5ds on ! quantity ( ! masses & _! mutual di/ances1 is call$ ! 8attraction ( gravitation40 ,we %all fir/ expla9 ! 8law0 ( ?is attraction1 & %all !n po9t out "s ( ! pr9cipal ph5om5a by :i* its exi/5ce & its laws are kn[n4 7#ajg47 ,! 8law ( gravitation0 sometimes f its univ]sality call$ ! 8law ( nature10 may be expla9$ z foll[s3 ,let u suppose two masses1 ,a & ,b1 plac$ beyond ! influ5ce or attraction ( any o!r bodies1 9 a /ate ( re/1 & at any propos$ di/ance f ea* o!r4 ,by _! mutual attraction !y w approa* ea* o!r1 b n ) ! same velocity4 ,! velocity ( ,a w be great] ?an t ( ,b1 9 ! same proportion z its mass is less ?an t ( ,b4 ,?us1 if ! mass ( ,b be twice t ( ,a1 :ile ,a approa*es ,b ?r\gh a space ( two feet1 ,b w approa* ,a ?r\gh a space ( "o foot4 ,h5ce x foll[s1 t ! =ce ) :i* ,a moves t[>ds ,b is equal to ! =ce ) :i* ,b moves t[>ds ,a 7#fh74 ,?is is only a consequ5ce ( ! prop]ty ( in]tia1 & is an example ( ! equality ( action & reaction1 z expla9$ 9 ,*apt] ,,iv4 ,! velocity ) :i* ,a & ,b approa* ea* o!r is e/imat$ by ! dim9ution ( _! di/ance1 ,a ,b1 by _! mutual approa* 9 a giv5 "t4 ,?us1 if 9 "o second ,a move t[>ds ,b ?r\gh a space ( two feet1 & 9 ! same "t ,b moves t[>ds ,a ?r\gh ! space ( "o foot1 !y w approa* ea* o!r ?r\gh a space ( ?ree feet 9 a second1 :i* w be _! relative velocity 7#ia74 ,if ! mass ( ,b be d\bl$1 x w attract ,a ) d\ble ! =m] =ce1 or1 :at is ! same1 w cause ,a to approa* ,b ) d\ble ! =m] velocity4 ,if ! mass ( ,b be trebl$1 x w attract ,a ) treble ! fir/ =ce1 &1 9 g5]al1 :ile ! di/ance ,a ,b rema9s ! same1 ! attractive =ce ( ,b ^u ,a w increase or dim9i% 9 exactly ! same proportion z ! mass ( ,b is increas$ or dim9i%$4 ,9 ! same mann]1 if ! mass ,a be d\bl$1 x w be attract$ by ,b ) a d\ble =ce1 because ,b ex]ts ! same degree ( attraction on e "p ( ! mass ,a1 & any addition :i* x may receive w n dim9i% or o!rwise affect ! influ5ce ( ,b on its =m] mass4 ,to express ?is 9 g5]al ari?metical symbols let a & b express ! space ?r\gh :i* ,a & ,b respectively w\ld be mov$ t[>ds ea* o!r by _! mutual attraction4 ,we w\ld !n h ,a a ,b b4 ,?us1 x is a g5]al law ( gravitation1 t s long z ! di/ance betwe5 two bodies rema9s ! same1 ea* w attract & be attract$ by ! o!r1 9 proportion to its mass2 & any increase or decrease ( ! mass w cause a correspond+ increase or decrease 9 ! am\nt ( ! attraction4 7#ajh47 ,we %all n[ expla9 ! law1 accord+ to :i* ! attraction is *ang$1 by *ang+ ! di/ance betwe5 ! bodies4 ,at ! di/ance ( "o mile ! body ,b attracts ,a ) a c]ta9 =ce4 ,at ! di/ance ( two miles1 ! masses n be+ *ang$1 ! attraction ( ,b ^u ,a w be "o-f\r? ( its am\nt at ! di/ance ( "o mile4 ,at ! di/ance ( ?ree miles1 x w be "o-n9? ( its orig9al am\nt2 at f\r miles1 x is r$uc$ to a sixte5?1 & s on4 ,! foll[+ table exhibits ! dim9ution ( ! attraction correspond+ to ! successive increase ( di/ance3 ---------------------------------------- ------ ,di/ance #a #b #c #d #e #f #g #h c4 ---------------------------------------- ------ ,attraction #a #a_/d #a_/ia_/afa_/bea_/cfa_/dia_/fd c4 ---------------------------------------- ------ ,9 ,,ari?metic1 t numb] :i* is f\nd by multiply+ any propos$ numb] by itself1 is call$ its squ>e4 ,?us #d1 t is1 #b multipli$ by #b1 is ! squ>e ( #b2 #i t is1 #c times #c1 is ! squ>e ( #c1 & s on4 ,on inspect+ ! above table1 x w be app>5t1 !re=e1 t ! attraction ( gravitation decreases 9 ! same proportion z ! squ>e ( ! di/ance f ! attract+ body increases1 ! mass ( bo? bodies 9 ?is case be+ suppos$ to rema9 ! same2 b if ! mass ( ei!r be increas$ or dim9i%$1 ! attraction w be increas$ or dim9i%$ 9 ! same proportion4 7#aji47 ,h5ce ! law ( gravitation may be ?us express$3 8,! mutual attraction ( two bodies increases 9 ! same proportion z _! masses are increas$1 & z ! squ>e ( _! di/ance is decreas$2 & x decreases 9 proportion z _! masses are decreas$1 & z ! squ>e ( _! di/ance is increas$40 ,?is law may be m cle>ly express$ by means ( g5]al symbols4 ,let f express ! =ce ) :i* a mass weigh+ #a lb4 w attract ano!r mass weigh+ #a lb41 at ! di/ance ( #a foot4 ,! =ce ) :i* !y w mutually attract1 :5 remov$ to ! di/ance express$ 9 feet by ,d1 w be f_/,d#b t is1 ! =ce f divid$ by ! squ>e ( ! numb] ,d4 ,if "o ( ! bodies1 in/ead ( weigh+ #a lb41 weigh ! numb] ( p\nds express$ by ,a1 _! mutual attraction w be increas$ ,a times1 & w !re=e be express$ by 7,a f7_/,d#b ,9 f9e1 if ! o!r be also ! numb] ( p\nds express$ by ,b1 _! mutual attraction w be 7,a ,b f7_/,d#b 7#aaj47 ,hav+ expla9$ ! law ( gravitation1 we %all n[ proce$ to %[ h[ ! exi/5ce ( ?is =ce is prov$1 & its law discov]$4 ,! e>? is kn[n to be a globul> mass ( matt]1 incomp>ably great] ?an any ( ! deta*$ bodies :i* are f\nd ^u its surface4 ,if "o ( ^! bodies susp5d$ at any propos$ height above ! surface ( ! e>? be dis5gag$1 x w be obs]v$ to desc5d p]p5dicul>ly to ! e>?1 t is1 9 ! direction ( ! e>?'s c5tre4 ,! =ce ) :i* x desc5ds w also be f\nd to be 9 proportion to ! mass1 )\t any reg>d to ! species ( ! body4 ,^! circum/ances are consi/5t ) ! acc\nt :i* we h giv5 ( gravitation4 ,b by t acc\nt we %\ld expect1 t z ! fall+ body is attract$ ) a c]ta9 =ce t[>ds ! e>?1 ! e>? itself %\ld be attract$ t[>ds x by ! same =ce2 & in/ead ( ! fall+ body mov+ t[>ds ! e>?1 :i* is ! ph5om5on obs]v$1 ! e>? & x %\ld move t[>ds ea* o!r1 & meet at "s int]m$iate po9t4 ,?is1 9 fact1 is ! case1 al?\gh x is impossible to r5d] ! motion ( ! e>? obs]vable1 = reasons :i* w easily be und]/ood4 ,s9ce all ! bodies ar\nd u p>ticipate 9 ?is motion1 x w\ld n be directly obs]vable1 ev5 ?\gh its quantity 7 suffici5tly great to be p]ceiv$ "u o!r circum/ances4 ,b sett+ aside ?is consid]ation1 ! space ?r\gh :i* ! e>? moves 9 su* a case is too m9ute to be ! subject ( s5sible obs]vation4 ,x has be5 /at$ 7#ajg71 t :5 two bodies attract ea* o!r1 ! space ?r\gh :i* ! great] approa*es ! less]1 be>s to t ?r\gh :i* ! less] approa*es ! great]1 ! same proportion z ! mass ( ! less] be>s to ! mass ( ! great]4 ,n[ ! mass ( ! e>? is m ?an #ajjj1jjj1jjj1jjj1jjj times ! mass ( any body :i* is obs]v$ to fall on its surface2 & !re=e if ev5 ! l>ge/ body :i* c come "u obs]vation 7 to fall ?r\gh an height ( #ejj feet1 ! correspond+ motion ( ! e>? w\ld be ?r\gh a space less ?an ! #ajjj1jjj1jjj1jjj1jjj? "p ( #ejj feet1 :i* is less ?an ! #ajj1jjj1jjj1jjj? "p ( an in*4 ,! attraction betwe5 ! e>? & deta*$ bodies on its surface is n only exhibit$ by ! desc5t ( ^! bodies :5 unsupport$1 b by _! pressure :5 support$4 ,?is pressure is :at is call$ weight4 ,! ph5om5a ( weight1 & ! desc5t ( heavy bodies1 w be fully inve/igat$ 9 ! next *apt]4 7#aaa47 ,x is n alone by ! direct fall ( bodies t ! gravitation ( ! e>? is manife/$4 ,! curvil9e> motion ( bodies project$ 9 directions diff]5t f ! p]p5dicul>1 is a comb9ation ( ! effects ( ! uni=m velocity :i* has be5 giv5 to ! projectile by ! impulse :i* x has receiv$1 & ! accel]at$ velocity :i* x receives f ! e>?'s attraction4 ,suppose a body plac$ at any po9t ,p1 fig4 #ba41 above ! surface ( ! e>?1 & let ,p ,c be ! direction ( ! e>?'s c5tre4 ,if ! body 7 all[$ to move )\t receiv+ any impulse1 x w\ld desc5d to ! e>? 9 ! direction ,p ,a1 ) an accel]at$ motion4 ,b suppose t at ! mom5t ( its dep>ture f ,p1 x receives an impulse 9 ! direction ,p ,b1 :i* w\ld c>ry x to ,b 9 ! "t ! body w\ld fall f ,p to ,a1 !n1 by ! composition ( motion1 ! body mu/ at ! end ( t "t be f\nd 9 ! l9e ,b ,d1 p>allel to ,p ,a4 ,if ! motion 9 ! direction ( ,p ,a 7 uni=m1 ! body ,p w\ld 9 ?is case move 9 ! /raight l9e f ,p to ,d4 ,b ?is is n ! case4 ,! velocity ( ! body 9 ! direction ,p ,a is at fir/ s small z to produce v little deflection ( its motion f ! l9e ,p ,b4 ,z ! velocity1 h[ev]1 increases1 ?is deflection increases1 s t x moves f ,p to ,d 9 a curve1 :i* is convex1 t[>ds ,p ,b4 ,! great] ! velocity ( ! projectile 9 ! direction ,p ,a1 ! great] sweep ! curve w take4 ,?us x w successively take ! =ms ,p ,d1 ,p ,e1 ,p ,f1 c41 & t velocity c be comput$1 :i* 7sett+ aside ! resi/ance ( ! air7 w\ld cause ! projectile to g completely r\nd ! e>?1 & return to ! po9t ,p f :i* x dep>t$4 ,9 ?is case1 ! body ,p w\ld cont9ue to revolve r\nd ! e>? l ! moon4 ,h5ce x is obvi\s1 t ! ph5om5on ( ! revolution ( ! moon r\nd ! e>?1 is no?+ m ?an ! comb9$ effects ( ! e>?'s attraction1 & ! impulse :i* x receiv$ :5 laun*$ into space by ! h& ( its ,creator4 7#aab47 ,?is is a great /ep 9 ! analysis ( ! ph5om5on ( gravitation4 ,we h ?us r$uc$ to ! same class two effects app>5tly v dissimil>1 ! rectil9e> desc5t ( a heavy body1 & ! ne>ly circul> revolution ( ! moon r\nd ! e>?4 ,h5ce we are conduct$ to a g5]alisation /ill m ext5sive4 ,z ! moon's revolution r\nd ! e>?1 9 an orbit ne>ly circul>1 is caus$ by ! comb9ation ( ! e>?'s attraction1 & an orig9al projectile impulse1 s also ! s+ul> ph5om5a ( ! planets' revolution r\nd ! sun 9 orbits ne>ly circul>1 mu/ be consid]$ an effect ( ! same class1 z well z ! revolution ( ! satellites ( ^? planets :i* are att5d$ by su* bodies4 ,al?\gh ! orbits 9 :i* ! comets move deviate v mu* f circles1 yet ?is does n h9d] ! application ( ! same pr9ciple to !m1 _! deviation f circles n dep5d+ on ! sun's attraction1 b only on ! direction & =ce ( ! orig9al impulse :i* put !m 9 motion4 7#aac47 ,we !re=e conclude t gravitation is ! pr9ciple :i*1 z x 71 animates ! univ]se4 ,all ! great *anges & revolutions ( ! bodies :i* compose our sy/em1 c be trac$ to or d]iv$ f ?is pr9ciple4 ,x /ill rema9s to %[ h[ t rem>kable law1 by :i* ?is =ce is decl>$ to increase or decrease 9 ! same proportion z ! squ>e ( ! di/ance f ! attract+ body is decreas$ or increas$1 may be v]ifi$ & e/abli%$4 ,x has be5 %[n1 t ! curvil9e> pa? ( a projectile dep5ds on1 & c be d]iv$1 by ma!matical reason+1 f ! consid]ation ( ! int5sity ( ! e>?'s attraction1 & ! =ce ( ! orig9al impulse1 or ! velocity ( projection4 ,9 ! same mann]1 by a rev]se process1 :5 we "k ! curve 9 :i* a projectile moves1 we c inf] ! am\nt ( ! attract+ =ce :i* gives ! curvature to its pa?4 ,9 ?is way1 f our k ( ! curvature ( ! moon's orbit1 & ! velocity ) :i* %e moves1 ! int5sity ( ! attraction :i* ! e>? ex]ts ^u h] c be exactly asc]ta9$4 ,^u comp>+ ?is ) ! =ce ( gravitation at ! e>?'s surface1 x is f\nd t ! latt] is z _m times great] ?an ! =m]1 z ! squ>e ( ! moon's di/ance is great] ?an ! squ>e ( ! di/ance ( a body on ! surface ( ! e>? f its c5tre4 7#aad47 ,if ?is 7 ! only fact :i* c\ld be br\ght to e/abli% ! law ( gravitation1 x might be ?\ght to be an accid5tal relation1 n necess>ily *>act]is+ ! attraction ( gravitation4 ,^u exam9+ ! orbits & velocities ( ! sev]al planets1 ! same result is1 h[ev]1 obta9$4 ,x is f\nd t ! =ces ) :i* !y are sev]ally attract$ by ! sun are great1 9 exactly ! same proportion z ! squ>es ( ! sev]al numb]s express+ _! di/ances are small4 ,! mutual gravitation ( bodies on ! surface ( ! e>? t[>ds ea* o!r is lo/ 9 ! pr$om9at+ =ce ex]t$ by ! e>? ^u all ( !m4 ,nev]!less1 9 "s cases1 ?is effect has n only be5 obs]v$1 b actually measur$4 ,a plumb-l9e1 "u ord9>y circum/ances1 hangs 9 a direction truly v]tical2 b if x be ne> a l>ge mass ( matt]1 z a m\nta91 x has be5 obs]v$ to be deflect$ f ! true v]tical1 t[>ds ! m\nta94 ,?is effect 0 obs]v$ by ,dr4 ,maskel9e ne> ! m\nta9 call$ ,skehalli51 9 ,scotl&1 & by ,fr5* a/ronom]s ne> ,*imboraco4 ,= p>ticul>s ( ^! obs]vations1 see our treatise on ,,geod,,sy4 ,cav5di% succe$$ 9 exhibit+ ! effects ( ! mutual gravitation ( metallic sph]es4 ,two globes ( lead ,a1 ,b1 ea* ab\t a foot 9 diamet]1 7 plac$ at a c]ta9 di/ance asund]4 ,a light rod1 to ! ends ( :i* 7 atta*$ small metallic balls ,c1 ,d1 0 susp5d$ at its c5tre ,e f a f9e wire1 & ! rod 0 plac$ z 9 fig4 #bb41 s t ! attractions ( ea* ( ! lead5 globes _h a t5d5cy to turn ! rod r\nd ! c5tre ,e 9 ! same direction4 ,a manife/ effect 0 produc$ ^u ! balls ,c1 ,d1 by ! gravitation ( ! sph]es4 ,9 ?is exp]im5t1 c>e mu/ be tak5 t no magnetic sub/ance is int]mix$ ) ! mat]ials ( ! balls4 ,hav+ s f> /at$ ! pr9ciples on :i* ! law ( gravitation is e/abli%$1 we %all dismiss ?is subject )\t fur!r details1 s9ce x m prop]ly belongs to ! subject ( ,,physical ,,a/ronomy2 to :i* we ref] ! read] = a complete demon/ration ( ! law1 & = ! detail$ developm5t ( its v>i\s & important consequ5ces4 ,,*ap4 ,,vii4 ,,t]re/rial ,,gravity4 7#aae47 ,,gravitation is ! g5]al "n giv5 to ?is attraction1 by :atev] masses ( matt] x may be manife/$4 ,z exhibit$ 9 ! effects produc$ by ! e>? ^u surr\nd+ bodies1 x is call$ 8t]re/rial gravity40 ,z ! attraction ( ! e>? is direct$ t[>ds its c5tre1 x might be expect$ t two plumb-l9es %\ld appe> n to be p>allel1 b s incl9$ to ea* o!r z to conv]ge to a po9t "u ! surface ( ! e>?4 ,?us1 if ,a ,b & ,c ,d1 fig4 #bc41 be two plumb-l9es1 ea* w be direct$ to ! c5tre ,o1 :]e1 if _! directions 7 cont9u$1 !y w\ld meet4 ,9 l mann]1 if two bodies 7 all[$ to fall f ,a & ,c1 !y w\ld desc5d 9 ! directions ,a ,b & ,c ,d1 :i* conv]ge to ,o4 ,obs]vation1 on ! contr>y1 %[s1 t plumb-l9es susp5d$ 9 places n f> di/ant f ea* o!r are truly p>allel2 & t bodies all[$ to fall desc5d 9 p>allel l9es4 ,?is app>5t p>allelism ( ! direction ( t]re/rial gravity is acc\nt$ = by ! enorm\s proportion :i* ! magnitude ( ! e>? be>s to ! di/ance betwe5 ! two plumb-l9es or ! two fall+ bodies :i* are comp>$4 ,if ! di/ance betwe5 ! places ,b1 ,d1 7 #abjj feet1 ! incl9ation ( ! l9es ,a ,b & ,c ,d w\ld n am\nt to a qu>t] ( a m9ute1 or ! #bdj? "p ( a degree4 ,b ! di/ance1 9 cases :]e ! p>allelism is assum$1 is nev] great] ?an1 & seldom s great z1 a few y>ds2 & h5ce ! incl9ation ( ! directions ,a ,b & ,c ,d is too small to be appreciat$ by any practical measure4 ,9 ! inve/igation ( ! ph5om5a ( fall+ bodies1 we %all1 !re=e1 assume1 t all ! p>ticles ( ! same body are attract$ 9 p>allel directions1 p]p5dicul> to an horizontal plane4 7#aaf47 ,s9ce ! int5sity ( t]re/rial gravity increases z ! squ>e ( ! di/ance decreases1 x might be expect$ t1 z a fall+ body approa*es ! e>?1 ! =ce :i* accel]ates x %\ld be cont9ually increas+1 &1 /rictly speak+1 x is s4 ,b any height ?r\gh :i* we obs]ve fall+ bodies to desc5d be>s s v small a proportion to ! :ole di/ance f ! c5tre1 t ! *ange ( int5sity ( ! =ce ( gravity is q beyond any practical means ( e/imat+ x4 ,! radius1 or ! di/ance f ! surface ( ! e>? to its c5tre1 is #djjj miles4 ,n[1 suppose a body desc5d$ ?r\gh ! height ( half a mile1 a di/ance v mu* beyond ^? us$ 9 exp]im5tal enquiries1 ! di/ances f ! c5tre1 at ! beg9n+ & end ( ! fall1 are !n 9 ! proportion ( #hjjj to #hjja1 & !re=e ! proportion ( ! =ce ( attraction at ! comm5cem5t to ! =ce at ! end1 be+ t ( ! squ>es ( ^! numb]s1 is #fd1jjj1jjj to #fd1jaf1jja1 :i*1 9 ! :ole desc5t1 is an increase ( ab\t "o "p 9 #djjj2 a quantity practically insignificant4 ,we %all1 !re=e1 9 expla9+ ! laws ( fall+ bodies1 assume t1 9 ! entire desc5t1 ! body is urg$ by a =ce ( uni=m int5sity4 ,al?\gh ! =ce :i* attracts all p>ts ( ! same body dur+ its desc5t 9 a giv5 place is ! same1 yet ! =ce ( gravity1 at diff]5t p>ts ( ! e>?'s surface1 has diff]5t int5sities4 ,! int5sity dim9i%es ) ! latitude1 s t x is great] t[>ds ! poles1 & less] t[>ds ! equator4 ,! causes ( ?is v>iation1 its law1 & ! exp]im5tal pro(s ( x1 w be expla9$1 :5 we %all treat ( c5trifugal =ce1 & ! motion ( p5dulums4 ,x is suffici5t m]ely to adv]t to x 9 ?is place4 7#aag47 ,s9ce ! e>?'s attraction acts sep>ately & equally on e p>ticle ( matt]1 )\t reg>d to ! nature or species ( ! body1 x foll[s t all bodies1 ( :atev] k9d1 or :atev] be _! masses1 mu/ be mov$ ) ! same velocity4 ,if two equal p>ticles ( matt] be plac$ at a c]ta9 di/ance above ! surface ( ! e>?1 !y w fall 9 p>allel l9es1 & ) exactly ! same spe$1 because ! e>? attracts !m equally4 ,9 ! same mann]1 a ?\s& p>ticles w\ld fall ) equal velocities4 ,n[1 ^! circum/ances w 9 no wise be *ang$ if ^? #ajjj p>ticles1 in/ead ( exi/+ sep>ately1 be aggregat$ into two solid masses1 "o consi/+ ( #iij p>ticles1 & ! o!r ( #aj4 ,we %all ?us h a heavy body & a light "o1 &1 accord+ to our reason+1 !y mu/ fall to ! e>? ) ! same spe$4 ,common exp]i5ce1 h[ev]1 is n always consi/5t ) ?is doctr9e4 ,:at are call$ light sub/ances1 z fea!rs1 gold-leaf1 pap]1 c41 are obs]v$ to fall sl[ly & irregul>ly1 :ile heavi] masses1 z solid pieces ( metal1 /ones1 c41 fall rapidly4 ,nay1 !re are n a few in/ances 9 :i* ! e>?1 in/ead ( attract+ bodies1 seems to repel !m1 z 9 ! case ( smoke1 vap\rs1 balloons1 & o!r sub/ances :i* actually asc5d4 ,we are to consid] t ! mass ( ! e>? is n ! only ag5t engag$ 9 ^! ph5om5a4 ,! e>? is surr\nd$ by an atmosph]e compos$ ( an ela/ic or a]i=m fluid4 ,?is atmosph]e has c]ta9 prop]ties1 :i* w be expla9$ 9 our treatise on ,,pneumatics1 & :i* are ! causes ( ! anomal\s circum/ances allud$ to4 ,light bodies rise 9 ! atmosph]e1 = ! same reason t a piece ( cork rises f ! bottom ( a vessel ( wat]2 & o!r light bodies fall m sl[ly ?an heavy ones1 = ! same reason t an egg 9 wat] falls to ! bottom m sl[ly ?an a lead5 bullet4 ,?is treatise is n ! place to give a direct explanation ( ^! ph5om5a4 ,x w be suffici5t = our pres5t purpose to %[1 t if !re 7 no atmosph]e1 all bodies1 heavy & light1 w\ld fall at ! same rate4 ,?is may easily be accompli%$ by ! aid ( an air-pump4 ,hav+ by t in/rum5t ab/ract$ ! air f a tall glass vessel1 we are enabl$1 by means ( a wire pass+ air-tight ?r\gh a hole 9 ! top1 to let fall sev]al bodies f ! top ( ! vessel to ! bottom4 ,^!1 :e!r !y be fea!rs1 pap]1 gold-leaf1 pieces ( money1 c4 all desc5d ) ! same spe$1 & /rike ! bottom at ! same mom5t4 7#aah47 ,e "o :o has se5 a heavy body fall f a height1 has witness$ ! fact1 t its velocity increases z x approa*es ! gr\nd4 ,b if ?is 7 n obs]vable by ! eye1 x w\ld be betray$ by ! effects4 ,x is well kn[n1 t ! =ce ) :i* a body /rikes ! gr\nd increases ) ! height f :5ce x has fall54 ,?is =ce1 h[ev]1 is proportional to ! velocity :i* x has at ! mom5t x meets ! gr\nd1 & !re=e ?is velocity increases ) ! height4 ,:5 ! obs]vations on attraction 9 ! la/ *apt] are well und]/ood1 x w be evid5t t ! velocity :i* a body has acquir$ 9 fall+ f any height1 is ! accumulat$ effects ( ! attraction ( t]re/rial gravity dur+ ! :ole "t ( ! fall4 ,ea* in/ant ( ! fall a new impulse is giv5 to ! body1 f :i* x receives additional velocity2 & its f9al velocity is compos$ ( ! aggregation ( all ! small increm5ts ( velocity :i* are ?us communicat$4 ,z we are at pres5t to suppose ! int5sity ( ! attraction inv>iable1 x w foll[ t ! velocity communicat$ to ! body 9 ea* in/ant ( "t w be ! same1 & !re=e t ! :ole quantity ( velocity produc$ or accumulat$ at ! end ( any "t is proportional to ! l5g? ( t "t4 ,?us1 if a c]ta9 velocity be produc$ 9 a body hav+ fall5 = "o second1 twice t velocity w be produc$ :5 x has fall5 = two seconds1 ?rice t velocity 9 ?ree seconds1 & s on4 ,su* is ! fundam5tal pr9ciple or *>act]i/ic ( uni=mly accel]at$ motion4 7#aai47 ,9 exam9+ ! circum/ances ( ! desc5t ( a body1 ! "t ( ! fall & ! velocity at ea* in/ant ( t "t are n ! only ?+s to be att5d$ to4 ,! spaces ?r\gh :i* x falls 9 giv5 int]vals ( "t1 c\nt$ ei!r f ! comm5cem5t ( its fall1 or f any propos$ epo* ( ! desc5t1 are equally important objects ( enquiry4 ,to e/imate ! space 9 ref]5ce to ! "t & ! f9al velocity1 we mu/ consid] t ?is space has be5 mov$ ?r\gh ) v>y+ spe$4 ,f a /ate ( re/ at ! beg9n+ ( ! fall1 ! spe$ gradually increases ) ! "t1 & ! f9al velocity is great] /ill ?an t :i* ! body _h at any prec$+ in/ant dur+ its desc5t4 ,we _c1 !re=e1 directly appreciate ! space mov$ ?r\gh 9 ?is case by ! "t & f9al velocity4 ,b z ! velocity increases uni=mly ) ! "t1 we %all obta9 ! av]age spe$1 by f9d+ t :i* ! body _h 9 ! middle ( ! int]val :i* elaps$ betwe5 ! beg9n+ & end ( ! fall1 & ?us ! space ?r\gh :i* ! body has actually fall5 is t ?r\gh :i* x w\ld move 9 ! same "t ) ?is av]age velocity uni=mly cont9u$4 ,b s9ce ! velocity :i* ! body receives 9 any "t1 c\nt$ f ! beg9n+ ( its desc5t1 is 9 ! proportion ( t "t1 x foll[s t ! velocity ( ! body aft] half ! :ole "t ( desc5t is half ! f9al velocity4 ,f :5ce x appe>s1 t ! height f :i* a body falls 9 any propos$ "t is equal to ! space ?r\gh :i* a body w\ld move 9 ! same "t ) half ! f9al velocity1 & x is !re=e equal to half ! space :i* w\ld be mov$ ?r\gh 9 ! same "t ) ! f9al velocity4 7#abj47 ,x foll[s f ?is reason+1 t betwe5 ! ?ree quantities1 ! height1 ! "t1 & ! f9al velocity1 :i* ent] into ! inve/igation ( ! ph5om5a ( fall+ bodies1 !re are two fix$ relations3 ,fir/1 ! "t1 c\nt$ f ! beg9n+ ( ! fall & ! f9al velocity1 are proportional ! "o to ! o!r2 s t z "o increases1 ! o!r increases 9 ! same proportion4 ,secondly1 ! height be+ equal to half ! space :i* w\ld be mov$ ?r\gh 9 ! "t ( ! fall1 ) ! f9al velocity1 mu/ h a fix$ proportion to ^! two quantities1 viz4 ! "t & ! f9al velocity1 or mu/ be proportional to ! product ( ! two numb]s :i* express !m4 ,b s9ce ! "t is always proportional to ! f9al velocity1 !y may be express$ by equal numb]s1 & ! product ( equal numb]s is ! squ>e ( ei!r ( !m4 ,h5ce1 ! product ( ! numb]s express+ ! "t & f9al velocity is equival5t to ! squ>e ( ! numb] express+ ! "t1 or to ! squ>e ( ! numb] express+ ! f9al velocity4 ,h5ce we inf]1 t ! height is always proportional to ! squ>e ( ! "t ( ! fall1 or to ! squ>e ( ! f9al velocity4 7#aba47 ,! use ( a few ma!matical *>act]s w r5d] ^! results m di/9ct1 ev5 to /ud5ts n conv]sant ) ma!matical sci5ce4 ,let ,s ! height f :i* ! body falls1 express$ 9 feet4 ,v ! velocity at ! end ( ! fall 9 feet p] second4 ,t ! numb] ( seconds 9 ! "t ( ! fall4 g ! numb] ( feet ?r\gh :i* a body w\ld fall 9 "o second4 ,x w !re=e foll[ t ! velocity acquir$ 9 "o second w be #b;g1 & ! velocity acquir$ 9 ,t seconds w !re=e be #b;g ,t2 s t ,v #b;g ,t #a ,s9ce ! space :i* a body falls ?r\gh 9 ,t seconds is f\nd by multiply+ ! space x falls ?r\gh 9 "o second by ,t#b1 we %all h ,s g ,t#b #b f :i*1 comb9$ ) #a we d$uce ,s ,v#b_/7d;g7 #c ,s 7#a_/b7,v ,t #d ,by ^! =mul>ies1 if ! height ?r\gh :i* a body falls freely 9 "o second be kn[n1 ! height ?r\gh :i* x w fall 9 any propos$ "t may be comput$4 ,= s9ce ! height is proportional to ! squ>e ( ! "t1 ! height ?r\gh :i* x w fall 9 two seconds w be f\r times t :i* x falls ?r\gh 9 "o second4 ,9 ?ree seconds x w fall ?r\gh n9e times t space2 9 f\r seconds1 sixte5 times2 9 five seconds1 tw5ty-five times1 & s on4 ,! foll[+1 !re=e1 is a g5]al rule to f9d ! height ?r\gh :i* a body w fall 9 any giv5 "t3 8,r$uce ! giv5 "t to seconds1 take ! squ>e ( ! numb] ( seconds 9 x1 & multiply ! height ?r\gh :i* a body falls 9 "o second by t numb]2 ! result w be ! height s\ght40 ,! foll[+ table exhibits ! heights & correspond+ times z f> z #aj seconds3 ---------------------------------------- ----- ,"t #a #b #c #d #e #f #g #h #i #aj ---------------------------------------- ----- ,height #a #d #i #af #be #cf #di #fd #ha #ajj ---------------------------------------- ----- ,ea* unit 9 ! numb]s ( ! fir/ r[ expresses a second ( "t1 & ea* unit 9 ^? ( ! second r[ expresses ! height ?r\gh :i* a body falls freely 9 a second4 7#abb47 ,if a body fall cont9ually = sev]al successive seconds1 ! spaces :i* x falls ?r\gh 9 ea* succe$+ second h a rem>kable relation among ea* o!r1 :i* may be easily d$uc$ f ! prec$+ table4 ,tak+ ! space mov$ ?r\gh 9 ! fir/ second /ill z our unit1 f\r times t space w be mov$ ?r\gh 9 ! fir/ two seconds4 ,subtract f ?is #a1 ! space mov$ ?r\gh 9 ! fir/ second1 & ! rema9d] #c is ! space ?r\gh :i* ! body falls 9 ! second second4 ,9 l mann] if #d1 ! height fall5 ?r\gh 9 ! fir/ two seconds1 be subtract$ f #i1 ! height fall5 ?r\gh 9 ! fir/ ?ree seconds1 ! rema9d] #e w be ! space fall5 ?r\gh 9 ! ?ird second4 ,to f9d ! space fall5 ?r\gh 9 ! f\r? second1 subtract #i1 ! space fall5 ?r\gh 9 ! fir/ ?ree seconds1 f #af1 ! space fall5 ?r\gh 9 ! fir/ f\r seconds1 & ! result is #g1 & s on4 ,x ?us appe>s t if ! space fall5 ?r\gh 9 ! fir/ second be call$ #a1 ! spaces describ$ 9 ! second1 ?ird1 f\r?1 fif?1 c4 seconds1 w be express$ by ! odd numb]s respectively1 #c1 #e1 #g1 #i1 c4 ,?is places 9 a /rik+ po9t ( view ! accel]at$ motion ( a fall+ body1 ! spaces mov$ ?r\gh 9 ea* succe$+ second be+ cont9ually increas$4 7#abc47 ,if velocity be e/imat$ by ! space ?r\gh :i* ! body w\ld move uni=mly 9 "o second1 !n ! f9al velocity ( a body fall+ = "o second w be #b2 = ) t f9al velocity ! body w\ld 9 "o second move ?r\gh twice ! height ?r\gh :i* x has fall54 7#abd47 ,s9ce ! f9al velocity increases 9 ! same proportion z ! "t1 x foll[s t aft] two seconds x is twice its am\nt aft] "o1 & aft] ?ree seconds ?rice t1 & s on4 ,?us1 ! foll[+ table exhibits ! f9al velocities correspond+ to ! times ( desc5t3 ---------------------------------------- ----------- ,"t #a #b #c #d #e #f #g #h #i #aj ---------------------------------------- ----------- ,f9al velocity #b #d #f #h #aj #ab #ad #af #ah #bj ---------------------------------------- ----------- ,! numb]s 9 ! second r[ express ! spaces ?r\gh :i* a body ) ! f9al velocity w\ld move 9 "o second1 ! unit be+1 z usual1 ! space ?r\gh :i* a body falls freely 9 "o second4 7#abe47 ,hav+ ?us develop$ !oretically ! laws :i* *>act]ise ! desc5t ( bodies1 fall+ freely by ! =ce ( gravity1 or by any o!r uni=m =ce ( ! same k9d1 x is necess>y t we %\ld %[ h[ ^! laws c be exhibit$ by actual exp]im5t4 ,!re are "s circum/ances att5d+ ! fall ( heavy bodies :i* w\ld r5d] x difficult1 if n impossible1 to illu/rate1 by ! direct obs]vation ( ?is ph5om5on1 ! prop]ties :i* h be5 expla9$ 9 ?is *apt]4 ,a body fall+ freely by ! =ce ( gravity1 z we %all h]eaft] prove1 desc5ds 9 "o second ( "t ?r\gh a height ( ab\t #af feet#a2 9 two seconds1 x w\ld1 !re=e1 fall ?r\gh f\r times t space1 or #fd feet2 9 ?ree seconds1 ?r\gh #i times ! height1 or #add feet2 & 9 f\r seconds1 ?r\gh #bef feet4 ,9 ord]1 !re=e1 to be enabl$ to obs]ve ! ph5om5a = only f\r seconds1 we %\ld comm& an height ( at lea/ #bef feet4 ,b fur!r2 ! velocity at ! end ( ! fir/ second w\ld be at ! rate ( #cb feet p] second2 at ! end ( ! second second1 x w\ld be #fd feet p] second2 & t[>ds ! end ( ! fall x w\ld be ab\t #abj feet p] second4 ,x is evid5t t ?is great degree ( rapidity w\ld be a s]i\s imp$im5t to accurate obs]vation1 ev5 ?\gh we %\ld be able to comm& ! requisite height4 ,x appe>s !re=e t ! numb] express$ by g 9 ! prec$+ =mul is #afjhc4 #a ,m exactly ?r\gh #af-a_/ab feet1 or #aic in*es4 ,x occurr$ to ,mr4 ,george ,attwood1 a ma!matician & natural philosoph] ( ! la/ c5tury1 t all ! ph5om5a ( fall+ bodies might be exp]im5tally exhibit$ & accurately obs]v$1 if a =ce ( ! same k9d z gravity1 viz4 an uni=mly accel]at+ =ce1 be us$1 b ( a mu* less int5sity2 s t :ile ! motion cont9ues to be gov]n$ by ! same laws1 its quantity may be s mu* dim9i%$1 t ! f9al velocity1 ev5 aft] a desc5t ( _m seconds1 %all be s mod]at$ z to admit ( mo/ delib]ate & exact obs]vation4 ,?is be+ once accompli%$1 no?+ m w\ld rema9 b to f9d ! height ?r\gh :i* a body w\ld fall 9 "o second1 or1 :at is ! same1 ! proportion ( ! =ce ( gravity to ! mitigat$ b uni=m accel]at+ =ce ?us sub/itut$ = x4 7#abf47 ,to realise ?is notion1 ,attwood con/ruct$ a :eel turn+ on its axle ) v little friction1 & hav+ a groove on its edge to receive a /r+4 ,ov] ?is :eel1 & 9 ! groove1 he plac$ a f9e silk5 cord1 to ! ends ( :i* 7 atta*$ equal cyl9drical weights4 ,?us plac$1 ! weights p]fectly balance ea* o!r1 & no motion ensues4 ,to "o ( ! weights he !n add$ a small quantity1 s z to give x a slight prepond]ance4 ,! load$ weight n[ began to desc5d1 draw+ up on ! o!r side ! unload$ weight4 ,! desc5t ( ! load$ weight1 "u ^! circum/ances1 is a motion exactly ( ! same k9d z ! desc5t ( a heavy body fall+ freely by ! =ce ( gravity2 t is1 x increases accord+ to ! same laws1 ?\gh at a v dim9i%$ rate4 ,to expla9 ?is1 suppose t ! load$ weight desc5ds f a /ate ( re/ ?r\gh "o in* 9 a second1 x w desc5d ?r\gh #d in*es 9 two seconds1 ?r\gh #i 9 ?ree1 ?r\gh #af 9 f\r1 & s on4 ,?us 9 #bj seconds1 x w\ld desc5d ?r\gh #djj in*es1 or #cc feet #d in*es1 a height :i*1 if x 7 necess>y1 c\ld easily be comm&$4 ,x might1 p]haps1 be ?\ght1 t s9ce ! weights susp5d$ at ! ends ( ! ?read are 9 equilibrium1 & !re=e h no t5d5cy ei!r to move or to resi/ motion1 ! additional weight plac$ ^u "o ( !m ought to desc5d z rapidly z x w\ld if x 7 all[$ to fall freely & unconnect$ ) !m4 ,x is v true t ?is weight w receive f ! attraction ( ! e>? ! same =ce :5 plac$ ^u "o ( ! susp5d$ weights1 z x w\ld if x 7 dis5gag$ f !m2 b 9 ! consequ5ces :i* ensue1 !re is ?is diff]5ce4 ,if x 7 unconnect$ ) ! susp5d$ weights1 ! :ole =ce impress$ ^u x w\ld be exp5d$ 9 accel]at+ its desc5t2 b be+ connect$ ) ! equal weights :i* su/a9 ea* o!r 9 equilibrium1 by ! silk5 cord pass+ ov] ! :eel1 ! =ce :i* is impress$ ^u ! add$ weight is exp5d$1 n z be=e1 9 giv+ velocity to ! add$ weight alone1 b to x toge!r ) ! two equal weights app5d$ to ! /r+1 "o ( :i* desc5ds ) ! add$ weight1 & ! o!r rises on ! opposite side ( ! :eel4 ,h5ce1 sett+ aside any effect :i* ! :eel itself produces1 ! velocity ( ! desc5t mu/ be less5$ j 9 proportion z ! mass among :i* ! impress$ =ce is to be di/ribut$ is increas$2 & !re=e ! rate ( ! fall be>s to t ( a body fall+ freely ! same proportion z ! add$ weight be>s to ! sum ( ! masses ( ! equal susp5d$ weights & ! add$ weight4 ,?us ! small] ! add$ weight is1 & ! great] ! equal susp5d$ weights are1 ! sl[] w ! rate ( desc5t be4 ,to r5d] ! circum/ances ( ! fall conv5i5tly obs]vable1 a v]tical %aft 7see fig4 #bd47 is usually provid$1 :i* is plac$ beh9d ! desc5d+ weight4 ,?is pill> is divid$ to in*es & halves1 & ( c\rse may be /ill m m9utely graduat$1 if necess>y4 ,a /age to receive ! fall+ weight is moveable on ?is pill>1 & capable ( be+ fix$ 9 any propos$ position by an adju/+ screw4 ,a p5dulum vibrat+ seconds1 ! beat ( :i* ought to be v audible1 is plac$ ne> ! obs]v]4 ,! load$ weight be+ ?us all[$ to desc5d = any propos$ "t1 or f any requir$ height1 all ! circum/ances ( ! desc5t may be accurately obs]v$1 & ! sev]al laws already expla9$ 9 ?is *apt] may be exp]im5tally v]ifi$4 7#abg47 ,! laws :i* gov]n ! desc5t ( bodies by gravity1 be+ rev]s$1 w be applicable to ! asc5t ( bodies project$ upw>ds4 ,if a body be project$ directly upw>ds ) any giv5 velocity1 x w rise to ! height f :i* x %\ld h fall5 to acquire t velocity4 ,! e>?'s attraction w1 9 ?is case1 gradually deprive ! body ( ! velocity :i* is communicat$ to x at ! mom5t at :i* x is project$4 ,consequ5tly1 ! ph5om5on w be t ( ret>d$ motion4 ,at ea* "p ( its asc5t x w h ! same velocity :i* x w\ld h if x desc5d$ to ! same place f ! highe/ po9t to :i* x rises4 ,h5ce x is cle>1 t all ! p>ticul>s relative to ! asc5t ( bodies may be imm$iately inf]r$ f ^? ( _! desc5t1 & !re=e ?is subject dem&s no fur!r notice4 ,to complete ! inve/igation ( ! ph5om5a ( fall+ bodies1 x w\ld n[ only rema9 to expla9 ! me?od ( asc]ta9+ ! exact height ?r\gh :i* a body w\ld desc5d 9 "o second1 if unresi/$ by ! atmosph]e1 or any o!r di/urb+ cause4 ,z ! solution ( ?is problem1 h[ev]1 requires ! aid ( pr9ciples n yet expla9$1 x mu/ = ! pres5t be po/pon$4 ,,*ap4 ,,viii4 ,,( ,,! ,,motion ,,( ,,bodies ,,on ,,incl9$ ,,planes ,,& ,,curves4 7#abh47 ,9 ! la/ *apt]1 we inve/igat$ ! ph5om5a ( bodies desc5d+ freely 9 ! v]tical direction1 & det]m9$ ! laws :i* gov]n1 n _! motion alone1 b t ( bodies urg$ by any uni=mly accel]at+ =ce :atev]4 ,we %all n[ consid] "s ( ! mo/ ord9>y cases 9 :i* ! free desc5t ( bodies is imp$$1 & ! effects ( _! gravitation modifi$4 7#abi47 ,if a body1 urg$ by any =ces :atev]1 be plac$ ^u a h>d unyield+ surface1 x w evid5tly rema9 at re/1 if ! resultant 7#gf7 ( all ! =ces :i* are appli$ to x be direct$ p]p5dicul>ly aga9/ ! surface4 ,9 ?is case1 ! effect produc$ is pressure1 b no motion ensues4 ,if only "o =ce act ^u ! body1 x w rema9 at re/1 provid$ ! direction ( t =ce be p]p5dicul> to ! surface4 ,b ! effect w be diff]5t1 if ! resultant ( ! =ces :i* are appli$ to ! body be oblique to ! surface4 ,9 t case ?is resultant1 :i*1 = simplicity1 may be tak5 z a s+le =ce1 may be consid]$ z me*anically equival5t to two =ces 7#gf71 "o 9 ! direction ( ! surface1 & ! o!r p]p5dicul> to x4 ,! latt] elem5t w be resi/$1 & w produce a pressure2 ! =m] w cause ! body to move4 ,?is w p]haps be m cle>ly appreh5d$ by ! aid ( a diagram4 ,let ,a ,b1 fig4 #be41 be ! surface1 & let ,p be a p>ticle ( matt] plac$ ^u x1 & urg$ by a =ce 9 ! direction ,p ,d1 p]p5dicul> to ,a ,b4 ,x is manife/1 t ?is =ce c only press ! p>ticle ,p aga9/ ,a ,b1 b _c give x any motion4 ,b let u suppose1 t ! =ce :i* urges ,p is 9 a direction ,p ,f1 oblique to ,a ,b4 ,tak+ ,p ,f z ! diagonal ( a p>allelogram1 ^: sides are ,p ,d & ,p ,c 7#gd71 ! =ce ,p ,f is me*anically equival5t to two =ces1 express$ by ! l9es ,p ,d & ,p ,c4 ,b ,p ,d1 be+ p]p5dicul> to ,a ,b1 produces pressure )\t motion1 & ,p ,c1 be+ 9 ! direction ( ,a ,b1 produces motion )\t pressure4 ,?us ! effect ( ! =ce ,p ,f is di/ribut$ betwe5 motion & pressure 9 a c]ta9 proportion1 :i* dep5ds on ! obliquity ( its direction to t ( ! surface4 ,! two extreme cases are1 #a4 ,:5 x is 9 ! direction ( ! surface2 x !n produces motion )\t pressure3 &1 #b4 ,:5 x is p]p5dicul> to ! surface2 x !n produces pressure )\t motion4 ,9 all int]m$iate directions1 h[ev]1 x w produce bo? ^! effects4 7#acj47 ,x w be v app>5t1 t ! m oblique ! direction ( ! =ce ,p ,f is to ,a ,b1 ! great] w be t "p ( x :i* produces motion1 & ! less w be t :i* produces pressure4 ,?is w be evid5t by inspect+ fig4 #bf4 ,9 ?is figure ! l9e ,p ,f1 :i* repres5ts ! =ce1 is equal to ,p ,f 9 fig4 #be4 ,b ,p ,d1 :i* expresses ! pressure1 is less 9 fig4 #bf4 ?an 9 fig4 #be41 :ile ,p ,c1 :i* expresses ! motion1 is great]4 ,s long1 !n1 z ! obliquity ( ! directions ( ! surface & ! =ce rema9 un*ang$1 s long w ! di/ribution ( ! =ce betwe5 motion & pressure rema9 ! same2 & !re=e1 if ! =ce itself rema9 ! same1 ! p>ts ( x :i* produce motion & pressure w be respectively equal4 7#aca47 ,^! g5]al pr9ciples be+ und]/ood1 no difficulty c arise 9 apply+ !m to ! motion ( bodies urg$ on incl9$ planes or curves by ! =ce ( gravity4 ,if a body be plac$ on an unyield+ horizontal plane1 x w rema9 at re/1 produc+ a pressure on ! plane equal to ! total am\nt ( its weight4 ,= 9 ?is case ! =ce :i* urges ! body1 be+ t ( t]re/rial gravity1 its direction is v]tical1 & !re=e p]p5dicul> to ! horizontal plane4 ,b if ! body ,p1 fig4 #be41 be plac$ ^u a plane ,a ,b1 oblique to ! direction ( ! =ce ( gravity1 !n1 accord+ to :at has be5 prov$ 7#abi71 ! weight ( ! body w be di/ribut$ into two p>ts1 ,p ,c & ,p ,d2 "o1 ,p ,d1 produc+ a pressure on ! plane ,a ,b1 & ! o!r1 ,p ,c1 produc+ motion d[n ! plane4 ,s9ce ! obliquity ( ! p]p5dicul> direction ,p ,f ( ! weight to t ( ! plane ,a ,b mu/ be ! same on :atev] "p ( ! plane ! weight may be plac$1 x foll[s 7#acj71 t ! proportion ,p ,c ( ! weight :i* urges ! body d[n ! plane mu/ be ! same ?r\gh\t its :ole desc5t4 7#acb47 ,h5ce x may easily be inf]r$1 t ! =ce d[n ! plane is uni=m2 = s9ce ! weight ( ! body ,p is always ! same1 & s9ce its proportion to t "p :i* urges x d[n ! plane is ! same1 x foll[s t ! quantity ( ?is "p _c v>y4 ,! motion ( a heavy body d[n an incl9$ plane is !re=e an uni=mly-accel]at$ motion1 & is *>act]is$ by all ! prop]ties ( uni=mly-accel]at$ motion1 expla9$ 9 ! la/ *apt]4 ,s9ce ,p ,f repres5ts ! =ce ( gravity1 t is1 ! =ce ) :i* ! body w\ld desc5d freely 9 ! v]tical direction1 & ,p ,c ! =ce ) :i* x moves d[n ! plane1 x foll[s t a body w\ld fall freely 9 ! v]tical direction f ,p to ,f 9 ! same "t z on ! plane x w\ld move f ,p to ,c4 ,9 ?is mann]1 !re=e1 :5 ! height ?r\gh :i* a body w\ld fall v]tically is kn[n1 ! space ?r\gh :i* x w\ld desc5d 9 ! same "t d[n any giv5 incl9$ plane may be imm$iately det]m9$4 ,= let ,a ,b1 fig4 #be41 be ! giv5 incl9$ plane1 & let ,p ,f be ! space ?r\gh :i* ! body w\ld fall 9 "o second4 ,f ,f draw ,f ,c p]p5dicul> to ! plane1 & ! space ,p ,c is t ?r\gh :i* ! body ,p w fall 9 "o second on ! plane4 7#acc47 ,z ! angle ,b ,a ,h1 :i* measures ! elevation ( ! plane1 is increas$1 ! obliquity ( ! v]tical direction ,p ,f ) ! plane is also increas$4 ,consequ5tly1 accord+ to :at has be5 prov$ 7#acj71 x foll[s1 t z ! elevation ( ! plane is increas$1 ! =ce :i* urges ! body d[n ! plane is also increas$1 & z ! elevation is dim9i%$1 ! =ce suff]s a correspond+ dim9ution4 ,! two extreme cases are1 #a4 ,:5 ! plane is rais$ until x becomes p]p5dicul>1 9 :i* case ! weight is p]mitt$ to fall freely1 )\t ex]t+ any pressure ^u ! plane2 &1 #b4 ,:5 ! plane is depress$ until x becomes horizontal1 9 :i* case ! :ole weight is support$1 & !re is no motion4 ,f ^! circum/ances x foll[s1 t by means ( an incl9$ plane we c obta9 an uni=mly-accel]at+ =ce ( any magnitude less ?an t ( gravity4 ,we h "h omitt$1 & %all = ! pres5t 9 e in/ance omit1 ! effects ( friction1 by :i* ! motion d[n ! plane is ret>d$4 ,hav+ fir/ inve/igat$ ! me*anical prop]ties ( bodies suppos$ to be free f friction1 we %all consid] friction sep>ately1 & %[ h[ ! pres5t results are modifi$ by x4 7#acd47 ,! accel]at+ =ces on diff]5t incl9$ planes may be comp>$ by ! pr9ciple expla9$ 9 7#aca74 ,let figs4 #be4 & #bf4 be two incl9$ planes1 & take ! l9es ,p ,f 9 ea* figure equal1 bo? express+ ! =ce ( gravity1 !n ,p ,c w be ! =ce :i* 9 ea* case urges ! body d[n ! plane4 ,z ! =ce d[n an incl9$ plane is less ?an t :i* urges a body fall+ freely 9 ! v]tical direction1 ! space ?r\gh :i* ! body mu/ fall to atta9 a c]ta9 f9al velocity mu/ be j s mu* great] z ! accel]at+ =ce is less4 ,on ?is pr9ciple we %all be able to det]m9e ! f9al velocity 9 desc5d+ ?r\gh any space on a plane1 comp>$ ) ! f9al velocity atta9$ 9 fall+ freely 9 ! v]tical direction4 ,suppose ! body ,p1 fig4 #bg41 plac$ at ! top ( ! plane1 & f ,h draw ! p]p5dicul> ,h ,c4 ,if ,b ,h repres5t ! =ce ( gravity1 ,b ,c w repres5t ! =ce d[n ! plane 7#aca74 ,9 ord] t ! body mov+ d[n ! plane %all h a f9al velocity equal to t ( "o :i* has fall5 freely f ,b to ,h1 x w be necess>y t x %\ld move f ,b d[n ! plane1 ?r\gh a space :i* be>s ! same proportion to ,b ,h z ,b ,h does to ,b ,c4 ,b s9ce ! triangle ,a ,b ,h is 9 all respects simil> to ,h ,b ,c1 only made ^u a l>g] scale1 ! l9e ,a ,b be>s ! same proportion to ,b ,h z ,b ,h be>s to ,b ,c4 ,h5ce1 9 fall+ on ! incl9$ plane f ,b to ,a1 ! f9al velocity is ! same z 9 fall+ freely f ,b to ,h4 ,x is evid5t t ! same w be true at :atev] level an horizontal l9e be drawn4 ,?us1 if ,i ,k be horizontal1 ! f9al velocity 9 fall+ on ! plane f ,b to ,i w be ! same z ! f9al velocity 9 fall+ freely f ,b to ,k4 7#ace47 ,! motion ( a heavy body d[n a curve diff]s 9 an important respect f ! motion d[n an incl9$ plane4 ,e "p ( ! plane be+ equally incl9$ to ! v]tical direction1 ! effect ( gravity 9 ! direction ( ! plane is uni=m2 &1 consequ5tly1 ! ph5om5a obey all ! e/abli%$ laws ( uni=mly-accel]at$ motion4 ,if1 h[ev]1 we suppose ! l9e ,b ,a1 on :i* ! body ,p desc5ds1 to be curv$ z 9 fig4 #bh41 ! obliquity ( its direction at diff]5t p>ts1 to ! direction ,p ,f ( gravity1 w evid5tly v>y4 ,9 ! pres5t in/ance1 ?is obliquity is great] t[>ds ,b & less t[>ds ,a1 & h5ce ! "p ( ! =ce ( gravity :i* gives motion to ! body is great] t[>ds ,b ?an t[>ds ,a 7#acj74 ,! =ce1 !re=e1 :i* urges ! body1 in/ead ( be+ uni=m z 9 ! incl9$ plane1 is "h gradually dim9i%$4 ,! rate ( ?is dim9ution dep5ds entirely on ! nature ( ! curve1 & c be d$uc$ f ! prop]ties ( ! curve by ma!matical reason+4 ,! details ( su* an inve/igation are n1 h[ev]1 ( a suffici5tly elem5t>y "* to all[ ( be+ introduc$ ) advantage into ?is treatise4 ,we mu/ !re=e limit ourselves to expla9 su* ( ! results z may be necess>y = ! developm5t ( ! o!r p>ts ( ! sci5ce4 7#acf47 ,:5 a heavy body is mov$ d[n an incl9$ plane by ! =ce ( gravity1 ! plane has be5 prov$ to su/a9 a pressure1 aris+ f a c]ta9 "p ( ! weight ,p ,d1 fig4 #be41 :i* acts p]p5dicul>ly to ! plane4 ,?is is also ! case 9 mov+ d[n a curve su* z ,b ,a1 fig4 #bh4 ,9 ?is case1 also1 ! :ole weight is di/ribut$ betwe5 t "p :i* is direct$ d[n ! curve1 & t :i*1 be+ p]p5dicul> to ! curve1 produces a pressure ^u x4 ,!re is1 h[ev]1 ano!r cause :i* produces pressure ^u ! curve1 & :i* has no op]ation 9 ! case ( ! incl9$ plane4 ,by ! prop]ty ( in]tia1 :5 a body is put 9 motion 9 any direction1 x mu/ p]sev]e 9 t direction1 unless x be deflect$ f x by an effici5t =ce4 ,9 ! motion d[n an incl9$ plane ! direction is nev] *ang$1 & !re=e by its in]tia ! fall+ body reta9s all ! motion impress$ ^u x cont9ually 9 ! same direction2 b :5 x desc5ds ^u a curve1 its direction is con/antly v>y+1 & ! resi/ance ( ! curve be+ ! deflect+ cause1 ! curve mu/ su/a9 a pressure equal to t =ce1 :i* w\ld ?us be capable ( cont9ually deflect+ ! body f ! rectil9e> pa? 9 :i* x w\ld move 9 virtue ( its in]tia4 ,?is pressure entirely dep5ds on ! curvature ( ! pa? 9 :i* ! body is con/ra9$ to move1 & on its in]tia1 & is !re=e altoge!r indep5d5t ( ! weight1 & w\ld1 9 fact1 exi/ if ! weight 7 )\t effect4 7#acg47 ,?is pressure has be5 d5om9at$ c5trifugal =ce1 because x ev9ces a t5d5cy ( ! mov+ body to fly f ! c5tre ( ! curve 9 :i* x is mov$4 ,its quantity dep5ds conjo9tly on ! velocity ( ! motion & ! curvature ( ! pa? ?r\gh :i* ! body is mov$4 ,z circles may be describ$ ) e degree ( curvature1 accord+ to ! l5g? ( ! radius1 or ! di/ance f _! circumf]5ce to _! c5tre1 x foll[s t1 :atev] be ! curve 9 :i* ! body moves1 a circle c always be assign$ :i* has ! same curvature z is f\nd at any propos$ po9t ( ! giv5 curve4 ,su* a circle is call$ 8! circle ( curvature0 at t po9t ( ! curve2 & z all curves1 except ! circle1 v>y _! degrees ( curvature at diff]5t po9ts1 x foll[s t diff]5t p>ts ( ! same curve w h diff]5t circles ( curvature4 ,x is evid5t t ! great] ! radius ( a circle is1 ! less is its curvature3 ?us ! circle ) ! radius ,a ,b1 fig4 #bi41 is m curv$ ?an t ^: radius is ,c ,d1 & t 9 ! exact proportion ( ! radius ,c ,d to ! radius ,a ,b4 ,! radius ( ! circle ( curvature = any "p ( a curve is call$ 8! radius ( curvature0 ( t "p4 7#ach47 ,! c5trifugal pressure increases z ! radius ( curvature increases2 b x also has a dep5d5ce on ! velocity ) :i* ! mov+ body sw+s r\nd ! c5tre ( ! circle ( curvature4 ,?is velocity is e/imat$ ei!r by ! actual space ?r\gh :i* ! body moves1 or by ! angul> velocity ( a l9e drawn f ! c5tre ( ! circle to ! mov+ body4 ,t body c>ries "o end ( ?is l9e ) x1 :ile ! o!r rema9s fix$ at ! c5tre4 ,z ?is angul> sw+ r\nd ! c5tre increases1 ! c5trifugal pressure increases4 ,to e/imate ! rate at :i* ?is pressure 9 g5]al v>ies1 x is necess>y to multiply ! squ>e ( ! numb] express+ ! angul> velocity by t :i* expresses ! radius ( curvature1 & ! =ce increases 9 ! same proportion z ! product ?us obta9$4 7#aci47 ,we h obs]v$ t ! same causes :i* produce pressure on a body re/ra9$1 w produce motion if ! body be free4 ,accord+ly1 if a body be mov$ by any effici5t cause 9 a curve1 x w1 by reason ( ! c5trifugal =ce1 fly (f1 & ! mov+ =ce ) :i* x w ?us retreat f ! c5tre r\nd :i* x is :irl$ w be a measure ( ! c5trifugal =ce4 ,^u ?is pr9ciple an app>atus call$ a :irl+ table has be5 con/ruct$1 = ! purpose ( exhibit+ exp]im5tal illu/rations ( ! laws ( c5trifugal =ce4 ,by ?is ma*9e we are enabl$ to place any propos$ weights at any giv5 di/ances f c5tres r\nd :i* !y are :irl$1 ei!r ) ! same angul> velocity1 or ) velocities hav+ a c]ta9 proportion4 ,?reads atta*$ to ! :irl+ weights are c>ri$ to ! c5tres r\nd :i* !y respectively revolve1 & !re1 pass+ ov] pulleys1 are connect$ ) weights :i* may be v>i$ at pleasure4 ,:5 ! :irl+ weights fly f _! respective c5tres1 by reason ( ! c5trifugal =ce1 !y draw up ! weights atta*$ to ! o!r ends ( ! ?reads1 & ! am\nt ( ! c5trifugal =ce is e/imat$ by ! weight :i* x is capable ( rais+4 ,) ?is in/rum5t ! foll[+ exp]im5ts may be exhibit$3-- ,exp4 #a4 ,equal weights :irl$ ) ! same velocity at equal di/ances f ! c5tre raise ! same weight1 & !re=e h ! same c5trifugal =ce4 ,exp4 #b4 ,equal weights :irl$ ) ! same angul> velocity at di/ances f ! c5tre 9 ! proportion ( "o to two1 w raise weights 9 ! same proportion4 ,!re=e ! c5trifugal =ces are 9 t proportion4 ,exp4 #c4 ,equal weights :irl$ at equal di/ances ) angul> velocities :i* are z "o to two1 w raise weights z "o to f\r1 t is1 z ! squ>es ( ! angul> velocities4 ,!re=e ! c5trifugal =ces are 9 t proportion4 ,exp4 #d4 ,equal weights :irl$ at di/ances :i* are z two to ?ree1 ) angul> velocities :i* are z "o to two1 w raise weights :i* are z two to twelve2 t is1 z ! products ( ! di/ances two & ?ree1 & ! squ>es "o & f\r1 ( ! angul> velocities4 ,h5ce1 ! c5trifugal =ces are 9 ?is proportion4 ,! c5trifugal =ce mu/ also increase z ! mass ( ! body mov$ increases2 =1 l attraction1 ea* p>ticle ( ! mov+ body is sep>ately & equally affect$ by x4 ,h5ce a d\ble mass1 mov+ at ! same di/ance1 & ) ! same velocity1 w h a d\ble =ce4 ,! foll[+ exp]im5t v]ifies ?is3-- ,exp4 #e4 ,if weights1 :i* are z "o to two1 be :irl$ at equal di/ances ) ! same velocity1 !y w raise weights :i* are z "o to two4 ,! law :i* gov]ns c5trifugal =ce may !n be express$ 9 g5]al symbols briefly ?us3-- ,let c ! c5trifugal =ce ) :i* a weight ( "o lb4 revolv+ 9 a circle 9 "o second1 ! radius ( :i* is "o foot1 w\ld act on a /r+ connect+ x ) ! c5tre4 ,! =ce ) :i* x w\ld act on a /r+1 ! l5g? ( :i* is ,r feet1 w\ld be c ,r2 & if in/ead ( revolv+ 9 "o second x revolv$ 9 ,t seconds1 ! =ce w\ld be 7c ,r7_/,t#b2 & if ! revolv+ mass 7 ,w lbs4 ! =ce w\ld be ,c 7c ,w ,r7_/,t#b4 ,?is =mula includes ! entire !ory ( c5trifugal =ce4 ,b x c be %[n t ! numb] express$ by c is #abbf1 & consequ5tly ,c 7#abbf ,w ,r7_/,t#b4 ,x is (t5 m conv5i5t to use ! numb] ( revolutions made 9 a giv5 "t ?an ! "t ( "o revolution4 ,let ,n !n express ! numb] ( revolutions1 or fraction ( a revolution1 made 9 "o second1 & we %all h ,t #a_/,n4 ,!re=e ,c #abbf ,w ,r ,n#b4 7#adj47 ,! consid]ation ( c5trifugal =ce proves1 t if a body be obs]v$ to move 9 a curvil9e> pa?1 "s effici5t cause mu/ exi/ :i* prev5ts x f fly+ (f1 & :i* compels x to revolve r\nd ! c5tre4 ,if ! body be connect$ ) ! c5tre by a ?read1 cord1 or rod1 !n ! effect ( ! c5trifugal =ce is to give t5sion to ! ?read1 cord1 or rod4 ,if an unyield+ curv$ surface be plac$ on ! convex side ( ! pa?1 !n ! =ce w produce pressure on ?is surface4 ,b if a body is obs]v$ to move 9 a curve )\t any visible mat]ial connection ) its c5tre1 & )\t any ob/ruction on ! convex side ( its pa? to resi/ its retreat1 z is ! case ) ! motions ( ! planets r\nd ! sun1 & ! satellites r\nd ! planets1 x is usual to assign ! cause to ! attraction ( ! body :i* occupies ! c5tre3 9 ! pres5t in/ance ! sun is t body1 & x is cu/om>y to say t ! attraction ( ! sun1 neutralis+ ! effects ( ! c5trifugal =ce ( ! planets1 reta9s !m 9 _! orbits4 ,we h else:]e animadv]t$ on ! inaccurate & unphilosophical /yle ( ?is phraseology1 9 :i* t]ms are admitt$ :i* intimate n only an unkn[n cause1 b assign its seat1 & intimate some?+ ( its nature4 ,all t we are entitl$ to decl>e 9 ?is case is1 t a motion is cont9ually impress$ ^u ! planet2 t ?is motion is direct$ t[>ds ! sun2 t x c\nt]acts ! c5trifugal =ce2 b f :5ce ?is motion proce$s1 :e!r x be a virtue resid5t 9 ! sun1 or a prop]ty ( ! m$ium or space 9 :i* bo? sun & planets are plac$1 or :atev] o!r influ5ce may be its proximate cause1 we are altoge!r ignorant4 99 99 99 99 99 7#ada47 ,num]\s examples ( ! effects ( c5trifugal =ce may be produc$4 ,if a /one or o!r weight be plac$ 9 a sl+1 :i* is :irl$ r\nd by ! h& 9 a direction p]p5dicul> to ! gr\nd1 ! /one w n fall out ( ! sl+1 ev5 :5 x is at ! top ( its circuit1 &1 consequ5tly1 has no support b5ea? x4 ,! c5trifugal =ce1 9 ?is case1 act+ f ! h&1 :i* is ! c5tre ( rotation1 is great] ?an ! weight ( ! body1 & !re=e prev5ts its fall4 ,9 l mann]1 a glass ( wat] may be :irl$ s rapidly t ev5 :5 ! m\? ( ! glass is pres5t$ d[nw>ds1 ! wat] w /ill be reta9$ 9 x by ! c5trifugal =ce4 ,if a bucket ( wat] be susp5d$ by a numb] ( ?reads1 & ^! ?reads be twi/$ by turn+ r\nd ! bucket _m times 9 ! same direction1 on all[+ ! cords to untwi/1 ! bucket w be :irl$ rapidly r\nd1 & ! wat] w be obs]v$ to rise on its sides & s9k at its c5tre1 ow+ to ! c5trifugal =ce ) :i* x is driv5 f ! c5tre4 ,?is effect might be c>ri$ s f>1 t all ! wat] w\ld fl[ ov] & leave ! bucket ne>ly empty4 7#adb47 ,a c>riage1 or horseman1 or p$e/rian1 pass+ a corn] moves 9 a curve1 & suff]s a c5trifugal =ce1 :i* increases ) ! velocity1 & :i* impresses on ! body a =ce direct$ f ! corn]4 ,an animal causes its weight to resi/ ?is =ce1 by volunt>ily incl9+ its body t[>ds ! corn]4 ,9 ?is case1 let ,a ,b1 fig4 #cj41 be ! body2 ,c ,d is ! direction ( ! weight p]p5dicul> to ! gr\nd1 & ,c ,f is ! direction ( ! c5trifugal =ce p>allel to ! gr\nd & f ! corn]4 ,! body ,a ,b is incl9$ to ! corn]1 s t ! diagonal =ce 7#gd71 :i* is me*anically equival5t to ! weight & c5trifugal =ce1 %all be 9 ! direction ,c ,a1 & %all !re=e produce ! pressure ( ! feet ^u ! gr\nd4 ,z ! velocity is increas$1 ! c5trifugal =ce is also increas$1 & !re=e a great] incl9ation ( ! body is necess>y to resi/ x4 ,we accord+ly f9d t ! m rapidly a corn] is turn$1 ! m ! animal incl9es 8 body t[>ds x4 ,a c>riage1 h[ev]1 n hav+ volunt>y motion1 _c make ?is comp5sation = ! di/urb+ =ce :i* is call$ into exi/5ce by ! gradual *ange ( direction ( ! motion2 consequ5tly x w1 "u c]ta9 circum/ances1 be ov]turn$1 fall+ ( c\rse outw>ds1 or f ! corn]4 ,if ,a ,b be ! c>riage1 & ,c1 fig4 #ca41 ! place at :i* ! weight is pr9cipally collect$1 ?is po9t ,c w be "u ! influ5ce ( two =ces3 ! weight1 :i* may be repres5t$ by ! p]p5dicul> ,c ,d1 & ! c5trifugal =ce1 :i* w be repres5t$ by a l9e ,c ,f1 :i* %all h ! same proportion to ,c ,d z ! c5trifugal =ce has to ! weight4 ,n[ ! comb9$ effect ( ^! two =ces w be ! same z ! effect ( a s+le =ce1 repres5t$ by ,c ,g4 ,?us1 ! pressure ( ! c>riage on ! road is br\ght ne>] to ! out] :eel ,b4 ,if ! c5trifugal =ce be> ! same proportion to ! weight z ,c ,f 7or ,d ,b71 fig4 #cb41 be>s to ,c ,d1 ! :ole pressure is ?r[n ^u ! :eel ,b4 ,if ! c5trifugal =ce be> to ! weight a great] proportion ?an ,d ,b has to ,c ,d1 !n ! l9e ,c ,f1 :i* repres5ts x1 fig4 #cc41 w be great] ?an ,d ,b4 ,! diagonal ,c ,g1 :i* repres5ts ! comb9$ effects ( ! weight & c5trifugal =ce1 w 9 ?is case pass outside ! :eel ,b1 & !re=e ?is resultant w be unresi/$4 ,to p]ceive h[ f> x w t5d to ov]turn ! c>riage1 let ! =ce ,c ,g be resolv$ into two1 "o 9 ! direction ( ,c ,b1 & ! o!r ,c ,k1 p]p5dicul> to ,c ,b4 ,! =m] ,c ,b w be resi/$ by ! road1 b ! latt] ,c ,k w t5d to lift ! c>riage ov] ! ext]nal :eel4 ,if ! velocity & ! curvature ( ! c\rse be cont9u$ = a suffici5t "t to enable ?is =ce ,c ,k to elevate ! weight1 s t ! l9e ( direction %all fall on ,b1 ! c>riage w be ov]?r[n4 ,x is evid5t f :at has be5 n[ /at$1 t ! *ances ( ov]?r[ "u ^! circum/ances dep5d on ! proportion ( ,b ,d to ,c ,d1 or :at is to ! same purpose1 ( ! di/ance betwe5 ! :eels to ! height ( ! pr9cipal seat ( ! load4 ,x w be %[n 9 ! next *apt]1 t !re is a c]ta9 po9t1 call$ ! c5tre ( gravity1 at :i* ! entire weight ( ! vehicle & its load may be conceiv$ to be conc5trat$4 ,?is is ! po9t :i* 9 ! pres5t inve/igation we h m>k$ ,c4 ,! security ( ! c>riage1 !re=e1 dep5ds on ! greatness ( ! di/ance betwe5 ! :eels & ! smallness ( ! elevation ( ! c5tre ( gravity above ! road2 = ei!r or bo? ( ^! circum/ances w increase ! proportion ( ,b ,d to ,c ,d4 7#adc47 ,9 ! eque/rian feat exhibit$ 9 ! r+ at ! amphi!atre1 :5 ! horse moves r\nd ) ! p]=m] /&+ on ! saddle1 bo? ! horse & rid] incl9e cont9ually t[>ds ! c5tre ( ! r+1 & ! incl9ation increases ) ! velocity ( ! motion3 by ?is incl9ation _! weights c\nt]act ! effect ( ! c5trifugal =ce1 exactly z 9 ! case already m5tion$ 7#adb47 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 7#add47 ,if a body be all[$ to fall by its weight d[n a convex surface1 su* z ,a ,b1 fig4 #cd41 x w\ld cont9ue ^u ! surface until x arrive at ,b b = ! effect ( ! c5trifugal =ce3 ?is1 giv+ x a motion f ! c5tre ( ! curve1 w cause x to quit ! curve at a c]ta9 po9t ,c1 :i* c be easily f\nd by ma!matical computation4 7#ade47 ,! mo/ rem>kable & important manife/ation ( c5trifugal =ce is obs]v$ 9 ! effects produc$ by ! rotation ( ! e>? ^u its axis4 ,let ! circle 9 fig4 #ce4 repres5t a section ( ! e>?1 ,a ,b be+ ! axis on :i* x revolves4 ,?is rotation causes ! matt] :i* composes ! mass ( ! e>? to revolve 9 circles r\nd ! diff]5t po9ts ( ! axis z c5tres at ! v>i\s di/ances at :i* ! compon5t p>ts ( ?is mass are plac$4 ,z !y all revolve ) ! same angul> velocity1 !y w be affect$ by c5trifugal =ces1 :i* w be great] or less 9 proportion z _! di/ances f ! c5tre are great] or less4 ,consequ5tly ! p>ts ( ! e>? :i* are situat$ ab\t ! equator1 ,d1 w be m /rongly affect$ by c5trifugal =ce ?an ^? ab\t ! poles1 ,a ,b4 ,! effect ( ?is diff]5ce has be5 t ! compon5t matt] ab\t ! equator has actually be5 driv5 f>!r f ! c5tre ?an t ab\t ! poles1 s t ! figure ( ! e>? has swell$ out at ! sides1 & appe>s proportionally depress$ at ! top & bottom1 resembl+ ! %ape ( an orange4 ,an exagg]at$ repres5tation ( ?is figure is giv5 9 fig4 #cf42 ! real diff]5ce betwe5 ! di/ances ( ! poles & equator f ! c5tre be+ too small to be p]ceptible 9 a diagram4 ,! exact proportion ( ,c ,a to ,c ,d has nev] yet be5 c]ta9ly asc]ta9$4 ,"s obs]vations make ,c ,d exce$ ,c ,a by #a_/bgg1 & o!rs by only #a_/ccc4 ,! latt]1 h[ev]1 seems ! m probable4 ,x may be consid]$ to be includ$ betwe5 ^! limits4 ,! same cause op]ates m p[]fully 9 o!r planets :i* revolve m rapidly on _! axes4 ,jupit] & ,saturn h =ms :i* are consid]ably m elliptical4 7#adf47 ,! c5trifugal =ce ( ! e>?'s rotation also affects deta*$ bodies on its surface4 ,if su* bodies 7 n held ^u ! surface by ! e>?'s attraction1 !y w\ld be imm$iately flung (f by ! :irl+ motion 9 :i* !y p>ticipate4 ,! c5trifugal =ce1 h[ev]1 really dim9i%es ! effects ( ! e>?'s attraction on ^? bodies1 or1 :at is ! same1 dim9i%es _! weights4 ,if ! e>? did n revolve on its axis1 ! weight ( bodies 9 all places equally di/ant f ! c5tre w\ld be ! same2 b ?is is n s :5 ! bodies1 z !y d1 move r\nd ) ! e>?4 ,!y acquire f ! c5trifugal =ce a t5d5cy to fly f ! axis1 :i* increases ) _! di/ance f t axis1 & is !re=e great] ! ne>] !y are to ! equator1 & less z !y approa* ! pole4 ,b !re is ano!r reason :y ! c5trifugal =ce is m effici5t1 9 ! opposition :i* x gives to gravity ne> ! equator ?an ne> ! poles4 ,?is =ce does n act f ! c5tre ( ! e>?1 b is direct$ f ! e>?'s axis4 ,x is1 !re=e1 n directly oppos$ to gravity1 except on ! equator itself4 ,on leav+ ! equator1 & proce$+ t[>ds ! poles1 x is less & less oppos$ to gravity1 z w be pla9 on inspect+ fig4 #ce41 :]e ! l9es ,p ,c all repres5t ! direction ( gravity1 & ! l9es ,p ,f repres5t ! direction ( ! c5trifugal =ce4 ,s9ce1 !n1 z we proce$ f ! equator t[>ds ! poles1 n only ! am\nt ( ! c5trifugal =ce is cont9ually dim9i%$1 b also x acts less & less 9 opposition to gravity1 x foll[s t ! weights ( bodies are mo/ dim9i%$ by x at ! equator1 & less s t[>ds ! poles4 ,s9ce bodies are commonly weigh$ by balanc+ !m aga9/ o!r bodies ( kn[n weight1 x may be ask$1 h[ ! ph5om5a we h be5 j describ+ c be asc]ta9$ z a matt] ( fact8 = :atev] be ! body aga9/ :i* x may be balanc$1 t body mu/ suff] j z mu* dim9ution ( weight z e o!r1 & consequ5tly1 all be+ dim9i%$ 9 ! same proportion1 ! balance w be pres]v$ ?\gh ! weights be *ang$4 ,to r5d] ?is effect obs]vable1 x w be necess>y to comp>e ! effects ( gravity ) "s ph5om5on :i* is n affect$ by ! c5trifugal =ce ( ! e>?'s rotation1 & :i* w be ! same at e "p ( ! e>?4 ,! means ( accompli%+ ?is w be expla9$ 9 a subsequ5t *apt]4 ,,*ap4 ,,ix4 ,,! ,,c5tre ,,( ,,gravity4 7#adg47 ,by ! e>?'s attraction1 all ! p>ticles :i* compose ! mass ( a body are solicit$ by equal =ces 9 p>allel directions d[nw>ds4 ,if ^! compon5t p>ticles 7 plac$ 9 m]e juxtaposition1 )\t any me*anical connection1 ! =ce impress$ on any "o ( !m c\ld 9 n[ise affect ! o!rs1 & ! mass w\ld1 9 su* a case1 be contemplat$ z an aggregation ( small p>ticles ( matt]1 ea* urg$ by an indep5d5t =ce4 ,b ! bodies :i* are ! subjects ( inve/igation 9 me*anical sci5ce are n f\nd 9 ?is /ate4 ,solid bodies are coh]5t masses1 ! p>ticles ( :i* are firmly b\nd toge!r1 s t any =ce :i* affects "o1 be+ modifi$ accord+ to circum/ances1 w be transmitt$ ?r\gh ! :ole body4 ,liquids accommodate !mselves to ! %ape ( ! surfaces on :i* !y re/1 & =ces affect+ any "o "p are transmitt$ to o!rs1 9 a mann] dep5d+ on ! peculi> prop]ties ( ?is class ( bodies4 ,z all bodies1 :i* are subjects ( me*anical enquiry1 on ! surface ( ! e>?1 mu/ be cont9ually influ5c$ by t]re/rial gravity1 x is desirable to obta9 "s easy & summ>y me?od ( e/imat+ ! effect ( ?is =ce4 ,to consid] x1 z is unavoidable 9 ! fir/ in/ance1 ! comb9$ action ( an inf9ite numb] ( equal & p>allel =ces solicit+ ! elem5t>y molecules d[nw>ds1 w\ld be att5d$ ) manife/ inconv5i5ce4 ,an inf9ite numb] ( =ces1 & an inf9ite subdivision ( ! mass1 w\ld =m p>ts ( e me*anical problem4 ,to ov]come ?is difficulty1 & to obta9 all ! ease & simplicity :i* c be desir$ 9 elem5t>y inve/igations1 x is only necess>y to det]m9e "s =ce1 ^: s+le effect %all be equival5t to ! comb9$ effects ( ! gravitation ( all ! molecules ( ! body4 ,if ?is c be accompli%$1 t s+le =ce might be introduc$ into all problems to repres5t ! :ole effect ( ! e>?'s attraction1 & no reg>d ne$ be _h to any p>ticles ( ! body1 except t on :i* ?is =ce acts4 7#adh47 ,to discov] su* a =ce1 if x exi/1 we %all fir/ enquire :at prop]ties mu/ necess>ily *>act]ise x4 ,let ,a ,b1 fig4 #cg41 be a solid body plac$ ne> ! surface ( ! e>?4 ,its p>ticles are all solicit$ d[nw>ds1 9 ! directions repres5t$ by ! arr[s4 ,n[1 if !re be any s+le =ce equival5t to ^! comb9$ effects1 two prop]ties may be at once assign$ to x3 #a4 ,x mu/ be pres5t$ d[nw>ds1 9 ! common direction ( ^? =ces to :i* x is me*anically equival5t2 &1 #b4 x mu/ be equal 9 int5sity to _! sum1 or1 :at is ! same1 to ! =ce ) :i* ! :ole mass w\ld desc5d4 ,we %all !n suppose x to h ?is int5sity1 & to h ! direction ( ! arr[ ,d ,e4 ,n[1 if ! s+le =ce1 9 ! direction ,d ,e1 be equival5t to all ! sep>ate attractions :i* affect ! p>ticles1 we may suppose all ^! attractions remov$1 & ! body ,a ,b influ5c$ only by a s+le attraction1 act+ 9 ! direction ,d ,e4 ,?is be+ admitt$1 x foll[s t if ! body be plac$ ^u a prop1 imm$iately "u ! direction ( ! l9e ,d ,e1 or be susp5d$ f a fix$ po9t imm$iately above its direction1 x w rema9 motionless4 ,= ! :ole attract+ =ce 9 ! direction ,d ,e w1 9 ! "o case1 press ! body on ! prop1 &1 9 ! o!r case1 w give t5sion to ! cord1 rod1 or :atev] o!r means ( susp5sion be us$4 7#adi47 ,b suppose ! body 7 susp5d$ f "s po9t ,p1 n 9 ! direction ( ! l9e ,d ,e4 ,let ,p ,c be ! direction ( ! ?read by :i* ! body is susp5d$4 ,its :ole weight1 accord+ to ! supposition :i* we h adopt$1 mu/ !n act 9 ! direction ,c ,e4 ,tak+ ,c ,f to repres5t ! weight2 x may be consid]$ z me*anically equival5t to two =ces 7#gd71 ,c ,i & ,c ,h4 ,( ^! ,c ,h1 act+ directly f ! po9t ,p1 m]ely produces pressure ^u x1 & gives t5sion to ! cord ,p ,c2 b ,c ,i1 act+ at "r angles to ,c ,p1 produces motion r\nd ,p z a c5tre1 & 9 ! direction ,c ,i1 t[>ds a v]tical l9e ,p ,g1 drawn ?r\gh ! po9t ,p4 ,if ! body ,a ,b _h be5 on ! o!r side ( ! l9e ,p ,g1 x w\ld h mov$ 9 l mann] t[>ds x1 & !re=e 9 ! direction contr>y to its pres5t motion4 ,h5ce we mu/ inf]1 t :5 ! body is susp5d$ f a fix$ po9t1 x _c rema9 at re/1 if t fix$ po9t be n plac$ 9 ! direction ( ! l9e ,d ,e2 &1 on ! o!r h&1 t if ! fix$ po9t be 9 ! direction ( t l9e1 x _c move4 ,a practical te/ is ?us sugge/$1 by :i* ! l9e ,d ,e may be at once discov]$4 ,let a ?read be atta*$ to any po9t ( ! body1 & let x be susp5d$ by ?is ?read f a hook or o!r fix$ po9t4 ,! direction ( ! ?read1 :5 ! body becomes quiesc5t1 w be t ( a s+le =ce equival5t to ! gravitation ( all ! compon5t p>ts ( ! mass4 7#aej47 ,an enquiry is "h sugge/$3 does ! direction ( ! equival5t =ce ?us det]m9$ dep5d on ! position ( ! body ) respect to ! surface ( ! e>?1 & h[ is ! direction ( ! equival5t =ce affect$ by a *ange 9 t position8 ,?is "q may be at once solv$ if ! body be susp5d$ by diff]5t po9ts1 & ! directions :i* ! susp5d+ ?read takes 9 ea* case relatively to ! figure & dim5sions ( ! body exam9$4 ,! body be+ susp5d$ 9 ?is mann] f any po9t1 let a small hole be bor$ ?r\gh x1 9 ! exact direction ( ! ?read1 s t if ! ?read 7 cont9u$ bel[ ! po9t :]e x is atta*$ to ! body1 x w\ld pass ?r\gh ?is hole4 ,! body be+ successively susp5d$ by sev]al diff]5t po9ts on its surface1 let z _m small holes be bor$ ?r\gh x 9 ! same mann]4 ,if ! body be !n cut ?r\gh1 s z to discov] ! directions :i* ! sev]al holes h tak51 !y w be all f\nd to cross ea* o!r at "o po9t )9 ! body2 or ! same fact may be discov]$ ?us3 a ?9 wire1 :i* ne>ly fills ! holes be+ pass$ ?r\gh any "o ( !m1 x w be f\nd to int]cept ! passage ( a simil> wire ?r\gh any o!r4 ,?is s+ul> fact tea*es u1 :at inde$ c be prov$ by ma!matical reason+ )\t exp]im5t1 t !re is "o po9t 9 e body ?r\gh :i* ! s+le =ce1 :i* is equival5t to ! gravitation ( all its p>ticles1 mu/ pass1 9 :atev] position ! body be plac$4 ,?is po9t is call$ ! c5tre ( gravity4 7#aea47 ,9 :atev] situation a body may be plac$1 ! c5tre ( gravity w h a t5d5cy to desc5d 9 ! direction ( a l9e p]p5dicul> to ! horizon1 & :i* is call$ ! l9e ( direction ( ! weight4 ,if ! body be altoge!r free & unre/rict$ by any resi/ance or imp$im5t1 ! c5tre ( gravity w actually desc5d 9 ?is direction1 & all ! o!r po9ts ( ! body w move ) ! same velocity 9 p>allel directions1 s t dur+ its fall ! position ( ! p>ts ( ! body1 ) respect to ! gr\nd1 w be unalt]$4 ,b if ! body1 z is mo/ usual1 be subject to "s resi/ance or re/ra9t1 x w ei!r rema9 unmov$1 its weight be+ exp5d$ 9 excit+ pressure on ! re/ra9+ po9ts or surfaces1 or x w move 9 a direction & ) a velocity dep5d+ on ! circum/ances :i* re/ra9 x4 ,9 ord] to det]m9e ^! effects1 to pr$ict ! pressure produc$ by ! weight if ! body be quiesc5t1 or ! mix$ effects ( motion & pressure1 if x be n s1 x is necess>y 9 all cases to be able to assign ! place ( ! c5tre ( gravity4 ,:5 ! magnitude & figure ( ! body1 & ! d5sity ( ! matt] :i* occupies its dim5sions1 are kn[n1 ! place ( ! c5tre ( gravity c be det]m9$ ) ! greate/ precision by ma!matical calculation4 ,! process by :i* ?is is accompli%$1 h[ev]1 is n ( a suffici5tly elem5t>y nature to be prop]ly introduc$ into ?is treatise4 ,to r5d] x intelligible w\ld require ! aid ( "s ( ! mo/ advanc$ analytical pr9ciples2 & ev5 to express ! position ( ! po9t 9 "q1 except 9 v p>ticul> in/ances1 w\ld be impossible1 )\t ! aid ( peculi> symbols4 7#aeb47 ,!re are c]ta9 p>ticul> =ms ( body 9 :i*1 :5 !y are uni=mly d5se1 ! place ( ! c5tre ( gravity c be easily assign$1 & prov$ by reason+1 :i* is g5]ally intelligible2 b 9 all cases :atev]1 ?is po9t may be easily det]m9$ by exp]im5t4 7#aec47 ,if a body uni=mly d5se h su* a %ape t a po9t may be f\nd on ei!r side ( :i* 9 all directions ar\nd x ! mat]ials ( ! body are simil>ly di/ribut$1 t po9t w obvi\sly be ! c5tre ( gravity4 ,= if x be support$1 ! gravitation ( ! p>ticles on "o side draw+ !m d[nw>ds1 is resi/$ by an effect ( exactly ! same k9d & ( equal am\nt on ! opposite side1 & s ! body rema9s balanc$ on ! po9t4 ,! mo/ rem>kable body ( ?is k9d is a globe1 ! c5tre ( :i* is evid5tly its c5tre ( gravity4 ,a figure1 su* z fig4 #ch41 call$ an oblate sph]oid1 has its c5tre ( gravity at its c5tre1 ,c4 ,su* is ! figure ( ! e>?4 ,! same may be obs]v$ ( ! elliptical solid1 fig4 #ci41 :i* is call$ a prolate sph]oid4 ,a cube1 & "s o!r regul> solids1 b\nd$ by plane surfaces1 h a po9t )9 !m1 su* z above describ$1 & :i* is1 !re=e1 _! c5tre ( gravity4 ,su* are fig4 #dj4 ,a /raight w& ( uni=m ?ickness has its c5tre ( gravity at ! c5tre ( its l5g?2 & a cyl9drical body has its c5tre ( gravity 9 its c5tre1 at ! middle ( its l5g? or axis4 ,su* is ! po9t ,c1 fig4 #da4 ,a flat plate ( any uni=m sub/ance1 & :i* has 9 e "p an equal ?ickness1 has its c5tre ( gravity at ! middle ( its ?ickness1 & "u a po9t ( its surface1 :i* is to be det]m9$ by its %ape4 ,if x be circul> or elliptical1 ?is po9t is its c5tre4 ,if x h any regul> =m1 b\nd$ by /raight edges1 x is t po9t :i* is equally di/ant f its sev]al angles1 z ,c 9 fig4 #db4 7#aed47 ,!re are "s cases 9 :i*1 al?\gh ! place ( ! c5tre ( gravity is n s obvi\s z 9 ! examples j giv51 /ill x may be discov]$ )\t any ma!matical process1 :i* is n easily und]/ood4 ,suppose ,a ,b ,c1 fig4 #dc41 to be a flat triangul> plate ( uni=m ?ickness & d5sity4 ,let x be imag9$ to be divid$ into n>r[ b>s1 by l9es p>allel to ! side ,a ,c1 z repres5t$ 9 ! figure4 ,draw ,b ,d f ! angle ,b to ! middle po9t ,d ( ! side ,a ,c4 ,x is n difficult to p]ceive1 t ,b ,d w divide equally all ! b>s into :i* ! triangle is conceiv$ to be divid$4 ,n[ if ! flat triangul> plate ,a ,b ,c be plac$ 9 a horizontal position on a /raight edge co9cid+ ) ! l9e ,b ,d1 x w be balanc$3 = ! b>s p>allel to ,a ,c w be sev]ally balanc$ by ! edge imm$iately "u _! middle po9t2 s9ce t middle po9t is ! c5tre ( gravity ( ea* b>4 ,s9ce1 !n1 ! triangle is balanc$ on ! edge1 ! c5tre ( gravity mu/ be some:]e imm$iately ov] x1 & mu/1 !re=e1 be )9 ! plate at "s po9t "u ! l9e ,b ,d4 ,! same reason+ w prove t ! c5tre ( gravity ( ! plate is "u ! l9e ,a ,e1 drawn f ! angle ,a to ! middle po9t ,e ( ! side ,b ,c4 ,to p]ceive ?is1 x is only necess>y to consid] ! triangle divid$ into b>s p>allel to ,b ,c1 & !nce to %[ t x w be balanc$ on an edge plac$ "u ,a ,e4 ,s9ce !n ! c5tre ( gravity ( ! plate is "u ! l9e ,b ,d1 & also "u ,a ,e1 x mu/ be "u ! po9t ,g1 at :i* ^! l9es cross ea* o!r2 & x is accord+ly at a dep? b5ea? ,g1 equal to half ! ?ickness ( ! plate4 ,?is may be exp]im5tally v]ifi$ by tak+ a piece ( t9 or c>d1 & cutt+ x into a triangul> =m4 ,! po9t ,g be+ f\nd by draw+ ,b ,d & ,a ,e1 :i* divide two sides equally1 x w be balanc$ if plac$ ^u ! po9t ( a p9 at ,g4 ,! c5tre ( gravity ( a triangle be+ ?us det]m9$1 we %all be able to f9d ! position ( ! c5tre ( gravity ( any plate ( uni=m ?ickness & d5sity :i* is b\nd$ by /raight edges1 z w be %[n h]eaft]4 7#agc47 7#aee47 ,! c5tre ( gravity is n always includ$ )9 ! volume ( ! body1 t is1 x is n enclos$ by its surfaces4 ,num]\s examples ( ?is c be produc$4 ,if a piece ( wire be b5t into any =m1 ! c5tre ( gravity w r>ely be 9 ! wire4 ,suppose x be br\ght to ! =m ( a r+4 ,9 t case1 ! c5tre ( gravity ( ! wire w be ! c5tre ( ! circle1 a po9t n =m+ any "p ( ! wire itself3 nev]!less ?is po9t may be prov$ to h ! *>act]i/ic prop]ty ( ! c5tre ( gravity2 = if ! r+ be susp5d$ by any po9t1 ! c5tre ( ! r+ mu/ always settle itself "u ! po9t ( susp5sion4 ,if ?is c5tre c\ld be suppos$ to be connect$ ) ! r+ by v f9e ?reads1 ^: weight w\ld be insignificant1 & :i* might be unit$ by a knot or o!rwise at ! c5tre1 ! r+ w\ld be balanc$ ^u a po9t plac$ "u ! knot4 ,9 l mann]1 if ! wire be =m$ into an ellipse1 or any o!r curve simil>ly arrang$ r\nd a c5tre po9t1 t po9t w be its c5tre ( gravity4 7#aef47 ,to f9d ! c5tre ( gravity exp]im5tally1 ! me?od describ$ 9 7#adi1 #aej7 may be us$4 ,9 ?is case two po9ts ( susp5sion w be suffici5t to det]m9e x2 = ! directions ( ! susp5d+ cord be+ cont9u$ ?r\gh ! body1 w cross ea* o!r at ! c5tre ( gravity4 ,^! directions may also be f\nd by plac+ ! body on a %>p po9t1 & adju/+ x s z to be balanc$ ^u x4 ,9 ?is case a l9e drawn ?r\gh ! body directly upw>ds f ! po9t w pass ?r\gh ! c5tre ( gravity1 & !re=e two su* l9es mu/ cross at t po9t4 7#aeg47 ,if ! body h two flat p>allel surfaces l %eet metal1 /iff pap]1 c>d1 bo>d1 c41 ! c5tre ( gravity may be f\nd by balanc+ ! body 9 two positions on an horizontal /raight edge4 ,! po9t :]e ! l9es m>k$ by ! edge cross ea* o!r w be imm$iately "u ! c5tre ( gravity4 ,?is may be v]ifi$ by %[+ t ! body w be balanc$ on a po9t ?us plac$1 or t if x be susp5d$1 ! po9t ?us det]m9$ w always come "u ! po9t ( susp5sion4 ,! position ( ! c5tre ( gravity ( su* bodies may also be f\nd by plac+ ! body on an horizontal table hav+ a /raight edge4 ,! body be+ mov$ beyond ! edge until x is 9 t position 9 :i* ! slighte/ di/urbance w cause x to fall1 ! c5tre ( gravity w !n be imm$iately ov] ! edge4 ,?is be+ done 9 two positions1 ! c5tre ( gravity w be det]m9$ z be=e4 7#aeh47 ,x has be5 already /at$1 t :5 ! body is p]fectly free1 ! c5tre ( gravity mu/ necess>ily move d[nw>ds1 9 a direction p]p5dicul> to an horizontal plane4 ,:5 ! body is n free1 ! circum/ances :i* re/ra9 x g5]ally p]mit ! c5tre ( gravity to move 9 c]ta9 directions1 b ob/ruct its motion 9 o!rs4 ,?us if a body be susp5d$ f a fix$ po9t by a flexible cord1 ! c5tre ( gravity is free to move 9 e direction except ^? :i* w\ld c>ry x f>!r f ! po9t ( susp5sion ?an ! l5g? ( ! cord4 ,h5ce if we conceive a globe or sph]e to surr\nd ! po9t ( susp5sion on e side to a di/ance equal to t ( ! c5tre ( gravity f ! po9t ( susp5sion1 :5 ! cord is fully /ret*$1 ! c5tre ( gravity w be at lib]ty to move 9 e direction )9 ?is sph]e4 ,!re are an inf9ite v>iety ( circum/ances "u :i* ! motion ( a body may be re/ra9$1 & 9 :i* a mo/ important & useful class ( me*anical problems orig9ate4 ,be=e we notice o!rs1 we %all1 h[ev]1 exam9e t :i* has j be5 describ$ m p>ticul>ly4 ,let ,p1 fig4 #dd41 be ! po9t ( susp5sion1 & ,c ! c5tre ( gravity1 & suppose ! body s plac$ t ,c %all be )9 ! sph]e already describ$4 ,! cord w !re=e be slack5$1 & 9 ?is /ate ! body w be free4 ,! c5tre ( gravity w !re=e desc5d 9 ! p]p5dicul> direction until ! cord becomes fully ext5d$2 ! t5sion w !n prev5t its fur!r motion 9 ! p]p5dicul> direction4 ,! d[nw>d =ce mu/ n[ be consid]$ z ! diagonal ( a p>allelogram1 & equival5t to two =ces ,c ,d & ,c ,e1 9 ! directions ( ! sides1 z already expla9$ 9 7#adi74 ,! =ce ,c ,d w br+ ! c5tre ( gravity into ! direction ,p ,f1 p]p5dicul>ly "u ! po9t ( susp5sion4 ,s9ce ! =ce ( gravity acts cont9ually on ,c 9 its approa* to ,p ,f1 x w move t[>ds t l9e ) accel]at$ spe$1 & :5 x has arriv$ !re x w h acquir$ a =ce to :i* no ob/ruction is imm$iately oppos$1 & consequ5tly by its in]tia x reta9s ?is =ce1 & moves beyond ,p ,f on ! o!r side4 ,b :5 ! po9t ,c gets into ! l9e ,p ,f1 x is 9 ! l[e/ possible position2 = x is at ! l[e/ po9t ( ! sph]e :i* limits its motion4 ,:5 x passes to ! o!r side ( ,p ,f1 x mu/ !re=e beg9 to asc5d1 & ! =ce ( gravity1 :i*1 9 ! =m] case1 accel]at$ its desc5t1 w n[ = ! same reason1 & ) equal en]gy1 oppose its asc5t4 ,?is w be easily und]/ood4 ,let ,c be any po9t :i* x may h atta9$ 9 asc5d+2 ,c ,g1 ! =ce ( gravity1 is n[ equival5t to ,c ,d & ,c ,e4 ,! latt] z be=e produces t5sion2 b ! =m] ,c ,d is 9 a direction imm$iately oppos$ to ! motion1 & !re=e ret>ds x4 ,?is ret>dation w cont9ue until all ! motion acquir$ by ! body 9 its desc5t f ! fir/ position has be5 de/roy$1 & !n x w beg9 to return to ,p ,f1 & s x w cont9ue to vibrate f ! "o side to ! o!r until ! friction on ! po9t ,p1 & ! resi/ance ( ! air1 gradually deprive x ( its motion1 & br+ x to a /ate ( re/ 9 ! direction ,p ,f4 ,b = ! effects ( friction & atmosph]ic resi/ance1 ! body w\ld cont9ue = ev] to oscillate equally f side to side ( ! l9e ,p ,f4 7#aei47 ,! ph5om5on j develop$ is only an example ( an ext5sive class4 ,:5ev] ! circum/ances :i* re/ra9 ! body are ( su* a nature t ! c5tre ( gravity is prev5t$ f desc5d+ bel[ a c]ta9 level1 b n1 on ! o!r h&1 re/ra9$ f ris+ above x1 ! body w rema9 at re/ if ! c5tre ( gravity be plac$ at ! l[e/ limit ( its level2 any di/urbance w cause x to oscillate ar\nd ?is /ate1 & x _c return to a /ate ( re/ until friction or "s o!r cause h depriv$ x ( ! motion communicat$ by ! di/urb+ =ce4 7#afj47 ,"u ! circum/ances :i* we h j describ$1 ! body c\ld n ma9ta9 itself 9 a /ate ( re/ 9 any position except t 9 :i* ! c5tre ( gravity is1 at ! l[e/ po9t ( ! space 9 :i* x is free to move4 ,?is1 h[ev]1 is n always ! case4 ,suppose x 7 susp5d$ by an inflexible rod in/ead ( a flexible /r+2 ! c5tre ( gravity w\ld !n n only be prev5t$ f rec$+ f ! po9t ( susp5sion1 b also f approa*+ x2 9 fact1 x w\ld be always kept at ! same di/ance f x4 ,?us1 in/ead ( be+ capable ( mov+ any:]e )9 ! sph]e1 x is n[ capable ( mov+ on its surface only4 ,! reason+ us$ 9 ! la/ case may also be appli$ "h1 to prove t :5 ! c5tre ( gravity is on ei!r side ( ! p]p5dicul> ,p ,f1 x w fall t[>ds ,p ,f & oscillate1 & t if x be plac$ 9 ! l9e ,p ,f1 x w rema9 9 equilibrium4 ,b 9 ?is case !re is ano!r position1 9 :i* ! c5tre ( gravity may be plac$ s z to produce equilibrium4 ,if x be plac$ at ! highe/ po9t ( ! sph]e 9 :i* x moves1 ! :ole =ce act+ on x w !n be direct$ on ! po9t ( susp5sion1 p]p5dicul>ly d[nw>ds1 & w be entirely exp5d$ 9 produc+ pressure on t po9t2 consequ5tly1 ! body w 9 ?is case be 9 equilibrium4 ,b ?is /ate ( equilibrium is ( a "* v diff]5t f t 9 :i* ! c5tre ( gravity 0 at ! l[e/ "p ( ! sph]e4 ,9 ! pres5t case any displacem5t1 h[ev] slight1 ( ! c5tre ( gravity1 w c>ry x to a l[] level1 & ! =ce ( gravity w !n prev5t its return to its =m] /ate1 & w impel x d[nw>ds until x atta9 ! l[e/ po9t ( ! sph]e1 & r\nd t po9t x w oscillate4 7#afa47 ,! two /ates ( equilibrium :i* h be5 j notic$1 are call$ /able & in/able equilibrium4 ,! "* ( ! =m] is1 t any di/urbance ( ! /ate produces oscillation ab\t x2 b any di/urbance ( ! latt] /ate produces a total ov]?r[1 & f9ally causes oscillation ar\nd ! /ate ( /able equilibrium4 ,let ,a ,b1 fig4 #de41 be an elliptical bo>d re/+ on its edge on an horizontal plane4 ,9 ! position "h repres5t$1 ! extremity ,p ( ! less] axis be+ ! po9t ( support1 ! bo>d is 9 /able equilibrium2 = any motion on ei!r side mu/ cause ! c5tre ( gravity ,c to asc5d 9 ! directions ,c ,o1 & oscillation w ensue4 ,if1 h[ev]1 x re/ ^u ! small] end1 z 9 fig4 #df41 ! position w\ld /ill be a /ate ( equilibrium1 because ! c5tre ( gravity is directly above ! po9t ( support2 b x w\ld be in/able equilibrium1 because ! slighte/ displacem5t ( ! c5tre ( gravity w\ld cause x to desc5d4 ,?us an egg or a lemon may be balanc$ on ! end1 b ! lea/ di/urbance w ov]?r[ x4 ,on ! contr>y1 x w easily re/ on ! side1 & any di/urbance w produce oscillation4 7#afb47 ,:5 ! circum/ances "u :i* ! body is plac$ all[ ! c5tre ( gravity to move only 9 an horizontal l9e1 ! body is 9 a /ate :i* may be call$ neutral equilibrium4 ,! slighte/ =ce w move ! c5tre ( gravity1 b w nei!r produce oscillation nor ov]?r[ ! body1 z 9 ! la/ two cases4 ,an example ( ?is /ate is furni%$ by a cyl9d] plac$ ^u an horizontal plane4 ,z ! cyl9d] is roll$ ^u ! plane1 ! c5tre ( gravity ,c1 fig4 #dg41 moves 9 a l9e p>allel to ! plane ,a ,b1 & di/ant f x by ! radius ( ! cyl9d]4 ,! body w ?us re/ indiff]5tly 9 any position1 because ! l9e ( direction always falls ^u a po9t ,p at :i* ! body re/s ^u ! plane4 ,if ! plane 7 incl9$1 z 9 fig4 #dh41 a body might be s %ap$1 t :ile x w\ld roll ! c5tre ( gravity w\ld move horizontally4 ,9 ?is case ! body w\ld re/ indiff]5tly on any "p ( ! plane1 z if x 7 horizontal1 provid$ ! friction be suffici5t to prev5t ! body f slid+ d[n ! plane4 ,if ! c5tre ( gravity ( a cyl9d] happ5 n to co9cide ) its c5tre by reason ( ! want ( uni=mity 9 ! mat]ials ( :i* x is compos$1 x w n be 9 a /ate ( neutral equilibrium on an horizontal plane1 z 9 fig4 #dg4 ,9 ?is case let ,g1 fig4 #di41 be ! c5tre ( gravity4 ,9 ! position "h repres5t$1 :]e ! c5tre ( gravity is imm$iately bel[ ! c5tre ,c1 ! /ate w be /able equilibrium1 because a motion on ei!r side w\ld cause ! c5tre ( gravity to asc5d2 b 9 fig4 #ej41 :]e ,g is imm$iately above ,c1 ! /ate is in/able equilibrium1 because a motion on ei!r side w\ld cause ,g to desc5d1 & ! body w\ld turn into ! position fig4 #di4 7#afc47 ,a cyl9d] ( ?is k9d w1 "u c]ta9 circum/ances1 roll up an incl9$ plane4 ,let ,a ,b1 fig4 #ea41 be ! incl9$ plane1 & let ! cyl9d] be s plac$ t ! l9e ( direction f ,g %all be above ! po9t ,p at :i* ! cyl9d] re/s ^u ! plane4 ,! :ole weight ( ! body act+ 9 ! direction ,g ,d w obvi\sly cause ! cyl9d] to roll t[>ds ,a1 provid$ ! friction be suffici5t to prev5t slid+2 b al?\gh ! cyl9d] 9 ?is case asc5ds1 ! c5tre ( gravity ,g really desc5ds4 ,:5 ,g is s plac$ t ! l9e ( direction ,g ,d %all fall on ! po9t ,p1 ! cyl9d] w be 9 equilibrium1 because its weight acts ^u ! po9t on :i* x re/s4 ,!re are two cases repres5t$ 9 fig4 #eb4 & fig4 #ec41 9 :i* ,g takes ?is position4 ,fig4 #eb4 repres5ts ! /ate ( /able1 & fig4 #ec4 ( in/able equilibrium4 7#afd47 ,:5 a body is plac$ ^u a base1 its /ability dep5ds ^u ! position ( ! l9e ( direction & ! height ( ! c5tre ( gravity above ! base4 ,if ! l9e ( direction fall )9 ! base1 ! body w /& firm2 if x fall on ! edge ( ! base1 x w be 9 a /ate 9 :i* ! slighte/ =ce w ov]?r[ x on t side at :i* ! l9e ( direction falls2 & if ! l9e ( direction fall )\t ! base1 ! body mu/ turn ov] t edge :i* is ne>e/ to ! l9e ( direction4 ,9 fig4 #ed4 & fig4 #ee41 ! l9e ( direction ,g ,p falls )9 ! base1 & x is obvi\s t ! body w /& firm2 = any attempt to turn x ov] ei!r edge w\ld cause ! c5tre ( gravity to asc5d4 ,b 9 fig4 #ef4 ! l9e ( direction falls ^u ! edge1 & if ! body be turn$ ov]1 ! c5tre ( gravity imm$iately comm5ces to desc5d4 ,until x be turn$ ov]1 h[ev]1 ! c5tre ( gravity is support$ by ! edge4 ,9 fig4 #eg4 ! l9e ( direction falls outside ! base1 ! c5tre ( gravity has a t5d5cy to desc5d f ,g t[>ds ,a1 & ! body w accord+ly fall 9 t direction4 7#afe47 ,:5 ! l9e ( direction falls )9 ! base1 bodies w always /& firm1 b n ) ! same degree ( /ability4 ,9 g5]al1 ! /ability dep5ds on ! height ?r\gh :i* ! c5tre ( gravity mu/ be elevat$ be=e ! body c be ov]?r[n4 ,! great] ?is height is1 ! great] 9 ! same proportion w be ! /ability4 ,let ,b ,a ,c1 fig4 #eh41 be a pyramid1 ! c5tre ( gravity be+ at ,g4 ,to turn ?is ov] ! edge ,b1 ! c5tre ( gravity2 mu/ be c>ri$ ov] ! ar* ,g ,e1 & mu/ !re=e be rais$ ?r\gh ! height ,h ,e4 ,if1 h[ev]1 ! pyramid 7 tall] relatively to its base1 z 9 fig4 #ei41 ! height ,h ,e w\ld be proportionally less2 & if ! base 7 v small 9 ref]5ce to ! height1 z 9 fig4 #fj41 ! height ,h ,e w\ld be v small1 & a slight =ce w\ld ?r[ x ov] ! edge ,b4 ,x is obvi\s t ! same obs]vations may be appli$ to all figures :atev]1 ! conclusions j d$uc$ dep5d+ only on ! di/ance ( ! l9e ( direction f ! edge ( ! base1 & ! height ( ! c5tre ( gravity above x4 7#aff47 ,h5ce we may p]ceive ! pr9ciple on :i* ! /ability ( load$ c>riages dep5ds4 ,:5 ! load is plac$ at a consid]able elevation above ! :eels1 ! c5tre ( gravity is elevat$1 & ! c>riage becomes proportionally insecure4 ,9 coa*es = ! conveyance ( pass5g]s1 ! luggage is !re=e sometimes plac$ bel[ ! body ( ! coa*2 light p>cels ( l>ge bulk may be plac$ on ! top ) impunity4 ,:5 ! c5tre ( gravity ( a c>riage is mu* elevat$1 !re is consid]able dang] ( ov]?r[1 if a corn] be turn$ %>ply & ) a rapid pace2 = ! c5trifugal =ce !n act+ on ! c5tre ( gravity w easily raise x ?r\gh ! small height :i* is necess>y to turn ! c>riage ov] ! ext]nal :eels 7#adb74 7#afg47 ,! same waggon w h great] /ability :5 load$ ) a heavy sub/ance :i* occupies a small space1 su* z metal1 ?an :5 x c>ries ! same weight ( a light] sub/ance1 su* z hay2 because ! c5tre ( gravity 9 ! latt] case w be mu* m elevat$4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,if a l>ge table be plac$ ^u a s+le leg 9 its c5tre1 x w be impracticable to make x /& firm2 b if ! pill> on :i* x re/s t]m9ate 9 a tripod1 x w h ! same /ability z if x _h ?ree legs atta*$ to ! po9ts directly ov] ! places :]e ! feet ( ! tripod re/4 7#afh47 ,:5 a solid body is support$ by m po9ts ?an "o1 x is n necess>y = its /ability t ! l9e ( direction %\ld fall on "o ( ^? po9ts4 ,if !re be only two po9ts ( support1 ! l9e ( direction mu/ fall betwe5 !m4 ,! body is 9 ?is case support$ z effectually z if x re/$ on an edge co9cid+ ) a /raight l9e drawn f "o po9t ( support to ! o!r4 ,if !re be ?ree po9ts ( support1 :i* are n rang$ 9 ! same /raight l9e1 ! body w be support$ 9 ! same mann] z x w\ld be by a base co9cid+ ) ! triangle =m$ by /raight l9es jo9+ ! ?ree po9ts ( support4 ,9 ! same mann]1 :atev] be ! numb] ( po9ts on :i* ! body may re/1 its virtual base w be f\nd by suppos+ /raight l9es drawn1 jo9+ ! sev]al po9ts successively4 ,:5 ! l9e ( direction falls )9 ?is base1 ! body w always /& firm1 & o!rwise n4 ,! degree ( /ability is det]m9$ 9 ! same mann] z if ! base 7 a cont9u$ surface4 7#afi47 ,necessity & exp]i5ce tea* an animal to adapt its po/ures & motions to ! position ( ! c5tre ( gravity ( 8 body4 ,:5 a man /&s1 ! l9e ( direction ( 8 weight mu/ fall )9 ! base =m$ by 8 feet4 ,if ,a ,b1 ,c ,d1 fig4 #fa41 be ! feet1 ?is base is ! space ,a ,b ,d ,c4 ,x is evid5t1 t ! m 8 toes are turn$ outw>ds1 ! m contract$ ! base w be 9 ! direction ,e ,f1 & ! m liable he w be to fall backw>ds or =w>ds4 ,also1 ! clos] 8 feet are toge!r1 ! m contract$ ! base w be 9 ! direction ,g ,h1 & ! m liable he w be to fall t[>ds ei!r side4 ,:5 a man walks1 ! legs are alt]nately lift$ f ! gr\nd1 & ! c5tre ( gravity is ei!r unsupport$ or ?r[n f ! "o side to ! o!r4 ,! body is also ?r[n a little =w>d1 9 ord] t ! t5d5cy ( ! c5tre ( gravity to fall 9 ! direction ( ! toes may assi/ ! muscul> action 9 propell+ ! body4 ,?is =w>d incl9ation ( ! body increases ) ! spe$ ( ! motion4 ,b = ! flexibility ( ! knee-jo9t ! lab\r ( walk+ w\ld be mu* great] ?an x is2 = ! c5tre ( gravity w\ld be m elevat$ by ea* /ep4 ,! l9e ( motion ( ! c5tre ( gravity 9 walk+ is repres5t$ by fig4 #fb41 & deviates b little f a regul> horizontal l9e1 s t ! elevation ( ! c5tre ( gravity is subject to v slight v>iation4 ,b if !re 7 no knee-jo9t1 z :5 a man has wood5 legs1 ! c5tre ( gravity w\ld move z 9 fig4 #fc41 s t at ea* /ep ! weight ( ! body w\ld be lift$ ?r\gh a consid]able height1 & !re=e ! lab\r ( walk+ w\ld be mu* increas$4 ,if a man /& on "o leg1 ! l9e ( direction ( 8 weight mu/ fall )9 ! space on :i* 8 foot treads4 ,! smallness ( ?is space1 comp>$ ) ! height ( ! c5tre ( gravity1 acc\nts = ! difficulty ( ?is feat4 ,! position ( ! c5tre ( gravity ( ! body *anges ) ! po/ure & position ( ! limbs4 ,if ! arm be ext5d$ f "o side1 ! c5tre ( gravity is br\ght ne>] to t side ?an x 0 :5 ! arm hung p]p5dicul>ly4 ,:5 danc]s1 /&+ on "o leg1 ext5d ! o!r at "r angles to x1 !y mu/ incl9e ! body 9 ! direction opposite to t 9 :i* ! leg is ext5d$1 9 ord] to br+ ! c5tre ( gravity ov] ! foot :i* supports !m4 ,:5 a port] c>ries a load1 8 position mu/ be regulat$ by ! c5tre ( gravity ( 8 body & ! load tak5 toge!r4 ,if he bore ! load on 8 back1 ! l9e ( direction w\ld pass beyond 8 heels1 & he w\ld fall backw>ds4 ,to br+ ! c5tre ( gravity ov] 8 feet he accord+ly leans =w>d1 fig4 #fd4 ,if a nurse c>ry a *ild 9 h] arms1 %e leans back = a l reason4 ,:5 a load is c>ri$ on ! head1 ! be>] /&s upright1 t ! c5tre ( gravity may be ov] 8 feet4 ,9 asc5d+ a hill1 we appe> to incl9e =w>d2 & 9 desc5d+1 to lean backw>d1 b 9 tru?1 we are /&+ upright ) respect to a level plane4 ,?is is necess>y to keep ! l9e ( direction betwe5 ! feet1 z is evid5t f fig4 #fe4 ,a p]son sitt+ on a *air :i* has no back _c rise f x )\t ei!r /oop+ =w>d to br+ ! c5tre ( gravity ov] ! feet1 or draw+ back ! feet to br+ !m "u ! c5tre ( gravity4 ,a quadrup$ nev] raises bo? feet on ! same side simultane\sly1 = ! c5tre ( gravity w\ld !n be unsupport$4 ,let ,a ,b ,c ,d1 fig4 #ff41 be ! feet4 ,! base on :i* x /&s is ,a ,b ,c ,d1 & ! c5tre ( gravity is ne>ly ov] ! po9t ,o1 :]e ! diagonals cross ea* o!r4 ,! legs ,a & ,c be+ rais$ toge!r1 ! c5tre ( gravity is support$ by ! legs ,b & ,d1 s9ce x falls betwe5 !m2 & :5 ,b & ,d are rais$ x is1 9 l mann]1 support$ by ! feet ,a & ,c4 ,! c5tre ( gravity1 h[ev]1 is (t5 unsupport$ = a mom5t2 = ! leg ,b is rais$ f ! gr\nd be=e ,a comes to x1 z is pla9 f obs]v+ ! track ( a horse's feet1 ! m>k ( ,a be+ ^u or be=e t ( ,b4 ,9 ! m rapid paces ( all animals ! c5tre ( gravity is at int]vals unsupport$4 ,! feats ( rope-danc]s are exp]im5ts on ! managem5t ( ! c5tre ( gravity4 ,! evolutions ( ! p]=m] are f\nd to be facilitat$ by hold+ 9 8 h& a heavy pole4 ,8 security 9 ?is case dep5ds1 n on ! c5tre ( gravity ( 8 body1 b on t ( 8 body & ! pole tak5 toge!r4 ,?is po9t is ne> ! c5tre ( ! pole1 s t1 9 fact1 he may be said to hold 9 8 h&s ! po9t on ! position ( :i* ! facility ( 8 feats dep5ds4 ,)\t ! aid ( ! pole ! c5tre ( gravity w\ld be )9 ! trunk ( ! body1 & its position c\ld n be adapt$ to circum/ances ) ! same ease & rapidity4 7#agj47 ,! c5tre ( gravity ( a mass ( fluid is t po9t :i* w\ld h ! prop]ties :i* h be5 prov$ to belong to ! c5tre ( gravity ( a solid1 if ! fluid 7 solidifi$ )\t *ang+ 9 any respect ! quantity or arrangem5t ( its p>ts4 ,?is po9t also possesses o!r prop]ties1 9 ref]5ce to fluids1 :i* w be inve/igat$ 9 ,,hydro/atics & ,,pneumatics4 7#aga47 ,! c5tre ( gravity ( two bodies sep>at$ f "o ano!r1 is t po9t :i* w\ld possess ! prop]ties ascrib$ to ! c5tre ( gravity1 if ! two bodies 7 unit$ by an inflexible l9e1 ! weight ( :i* might be neglect$4 ,to f9d ?is po9t ma!matically is a v simple problem4 ,let ,a & ,b1 fig4 #fg41 be ! two bodies1 & a & b _! c5tres ( gravity4 ,draw ! "r l9e a b1 & divide x at ,c1 9 su* a mann] t a ,c %all h ! same proportion to b ,c z ! mass ( ! body ,b has to ! mass ( ! body ,a4 ,?is may easily be v]ifi$ exp]im5tally4 ,let ,a & ,b be two bodies1 ^: weight is consid]able1 9 comp>ison ) t ( ! rod a b1 :i* jo9s !m4 ,let a f9e silk5 /r+1 ) its ends atta*$ to !m1 be hung ^u a p92 & on ! same p9 let a plumb-l9e be susp5d$4 ,9 :atev] position ! bodies may be hung1 x w be obs]v$ t ! plumb-l9e w cross ! rod a b at ! same po9t1 & t po9t w divide ! l9e a b into p>ts a ,c & b ,c1 :i* are 9 ! proportion ( ! mass ( ,b to ! mass ( ,a4 7#agb47 ,! c5tre ( gravity ( ?ree sep>ate bodies is def9$ 9 ! same mann] z t ( two1 & may be f\nd by fir/ det]m9+ ! c5tre ( gravity ( two2 & !n suppos+ _! masses conc5trat$ at t po9t1 s z to =m "o body1 & f9d+ ! c5tre ( gravity ( t & ! ?ird4 ,9 ! same mann] ! c5tre ( gravity ( any numb] ( bodies may be det]m9$4 7#agc47 ,if a plate ( uni=m ?ickness be b\nd$ by /raight edges1 its c5tre ( gravity may be f\nd by divid+ x into triangles by diagonal l9es1 z 9 fig4 #fh41 & hav+ det]m9$ by 7#aed7 ! c5tres ( gravity ( ! sev]al triangles1 ! c5tre ( gravity ( ! :ole plate w be _! common c5tre ( gravity1 f\nd z above4 7#agd47 ,al?\gh ! c5tre ( gravity takes its "n f ! famili> prop]ties :i* x has 9 ref]5ce to deta*$ bodies ( inconsid]able magnitude1 plac$ on or ne> ! surface ( ! e>?1 yet x possesses prop]ties ( a mu* m g5]al & n less important nature4 ,"o ( ! mo/ rem>kable ( ^! is1 t ! c5tre ( gravity ( any numb] ( sep>ate bodies is nev] affect$ by ! mutual attraction1 impact1 or o!r influ5ce :i* ! bodies may transmit f "o to ano!r4 ,?is is a necess>y consequ5ce ( ! equality ( action & reaction expla9$ 9 ,*apt] ,,iv4 ,= if ,a & ,b1 fig4 #fg41 attract ea* o!r1 & *ange _! places to ,a & ,b1 ! space a a w h to b b ! same proportion z ,b has to ,a1 & !re=e by :at has j be5 prov$ 7#aga7 ! same proportion z a ,c has to b ,c4 ,x foll[s1 t ! rema9d]s a ,c & b ,c w be 9 ! proportion ( ,b to ,a1 & t ,c w cont9ue to be ! c5tre ( gravity ( ! bodies aft] !y h approa*$ by _! mutual attraction4 ,suppose1 = example1 t ,a & ,b 7 #ablbs4 & #hlbs4 respectively1 & t a b 7 #dj feet4 ,! po9t ,c mu/ 7#aga7 divide a b into two p>ts1 9 ! proportion ( #h to #ab1 or ( #b to #c4 ,h5ce x is obvi\s t a ,c w be #af feet1 & b ,c #bd feet4 ,n[1 suppose t ,a & ,b attract ea* o!r1 & t ,a approa*es ,b ?r\gh two feet4 ,!n ,b mu/ approa* ,a ?r\gh ?ree feet4 ,_! di/ances f ,c w n[ be #ad feet & #ba feet1 :i*1 be+ 9 ! proportion ( ,b to ,a1 ! po9t ,c w /ill be _! c5tre ( gravity4 ,h5ce x foll[s1 t if a sy/em ( bodies1 plac$ at re/1 be p]mitt$ to obey _! mutual attractions1 al?\gh ! bodies w !reby be sev]ally mov$1 yet _! common c5tre ( gravity mu/ rema9 quiesc5t4 7#age47 ,:5 "o ( two bodies is mov+ 9 a /raight l9e1 ! o!r be+ at re/1 _! common c5tre ( gravity mu/ move 9 a p>allel /raight l9e4 ,let ,a & ,b1 fig4 #fi41 be ! c5tres ( gravity ( ! bodies1 & let ,a move f ,a to a1 ,b rema9+ at re/4 ,draw ! l9es ,a ,b & a ,b4 ,9 e position :i* ! body ,b assumes dur+ its motion1 ! c5tre ( gravity ,c divides ! l9e jo9+ !m into p>ts ,a ,c1 ,b ,c1 :i* are 9 ! proportion ( ! mass ,b to ! mass ,a4 ,n[1 suppose any numb] ( l9es drawn f ,b to ! l9e ,a a2 a p>allel ,c c to ,a a ?r\gh ,c divides all ^! l9es 9 ! same proportion2 & !re=e1 :ile ! body ,a moves f ,a to a1 ! common c5tre ( gravity moves f ,c to c4 ,if bo? ! bodies ,a & ,b mov$ uni=mly 9 /raight l9es1 ! c5tre ( gravity w\ld h a motion comp\nd$ 7#gd7 ( ! two motions ) :i* x w\ld be affect$1 if ea* mov$ :ile ! o!r rema9$ at re/4 ,9 ! same mann]1 if !re 7 ?ree bodies1 ea* mov+ uni=mly 9 a /raight l9e1 _! common c5tre ( gravity w\ld h a motion comp\nd$ ( t motion :i* x w\ld h if "o rema9$ at re/ :ile ! o!r two mov$1 & t :i* ! motion ( ! fir/ w\ld give x if ! la/ two rema9$ at re/2 & 9 ! same mann] x may be prov$1 t :5 any numb] ( bodies move ea* 9 a /raight l9e1 _! common c5tre ( gravity w h a motion comp\nd$ ( ! motions :i* x receives f ! bodies sev]ally4 ,x may happ5 t ! sev]al motions :i* ! c5tre ( gravity receives f ! bodies ( ! sy/em w neutralise ea* o!r2 & ?is does1 9 fact1 take place = su* motions z are ! consequ5ces ( ! mutual action ( ! bodies ^u "o ano!r4 7#agf47 ,if a sy/em ( bodies be n "u ! imm$iate influ5ce ( any =ces1 & _! mutual attraction be conceiv$ to be susp5d$1 !y mu/ sev]ally be ei!r at re/ or 9 uni=m rectil9e> motion 9 virtue ( _! in]tia4 ,h5ce1 _! common c5tre ( gravity mu/ also be ei!r at re/ or 9 uni=m rectil9e> motion4 ,n[1 if we suppose _! mutual attractions to take effect1 ! /ate ( _! common c5tre ( gravity w n be *ang$1 b ! bodies w sev]ally receive motions comp\nd$ ( _! previ\s uni=m rectil9e> motions & ^? :i* result f _! mutual attractions4 ,! comb9$ effects w cause ea* body to revolve 9 an orbit r\nd ! common c5tre ( gravity1 or w precipitate x t[>ds t po9t4 ,b /ill t po9t w ma9ta9 its =m] /ate undi/urb$4 ,?is con/itutes "o ( ! g5]al laws ( me*anical sci5ce1 & is ( great importance 9 physical a/ronomy4 ,x is kn[n by ! title 8! cons]vation ( ! motion ( ! c5tre ( gravity40 7#agg47 ,! sol> sy/em is an in/ance ( ! class ( ph5om5a to :i* we h j ref]r$4 ,all ! motions ( ! bodies :i* compose x c be trac$ to c]ta9 uni=m rectil9e> motions1 receiv$ f "s =m] impulse1 or f a =ce ^: action has be5 susp5d$1 & ^? motions :i* necess>ily result f ! pr9ciple ( gravitation4 ,b we %all n "h insi/ fur!r on ?is subject1 :i* m prop]ly belongs to ano!r dep>tm5t ( ! sci5ce4 7#agh47 ,if a solid body suff] an impact 9 ! direction ( a l9e pass+ ?r\gh its c5tre ( gravity1 all ! p>ticles ( ! body w be driv5 =w>d ) ! same velocity 9 l9es p>allel to ! direction ( ! impact1 & ! :ole =ce ( ! motion w be equal to t ( ! impact4 ,! common velocity ( ! p>ts ( ! body w 9 ?is case be det]m9$ by ! pr9ciples expla9$ 9 ,*apt] ,,iv4 ,! impell+ =ce be+ equally di/ribut$ among all ! p>ts1 ! velocity w be f\nd by divid+ ! num]ical value ( t =ce by ! numb] express+ ! mass4 ,if any numb] ( impacts be giv5 simultane\sly to diff]5t po9ts ( a body1 a c]ta9 complex motion w g5]ally ensue4 ,! mass w h a relative motion r\nd ! c5tre ( gravity z if x 7 fix$1 :ile t po9t w move =w>d uni=mly 9 a /raight l9e1 c>ry+ ! body ) x4 ,! relative motion ( ! mass r\nd ! c5tre ( gravity may be f\nd by consid]+ ! c5tre ( gravity z a fix$ po9t1 r\nd :i* ! mass is free to move1 & !n det]m9+ ! motion :i* ! appli$ =ces w\ld produce4 ,?is motion be+ suppos$ to cont9ue un9t]rupt$1 let all ! =ces be imag9$ to be appli$ 9 _! prop] directions & quantities to ! c5tre ( gravity4 ,by ! pr9ciples = ! composition ( =ce !y w be me*anically equival5t to a s+le =ce ?r\gh t po9t4 ,9 ! direction ( ?is s+le =ce ! c5tre ( gravity w move & h ! same velocity z if ! :ole mass 7 !re conc5trat$ & receiv$ ! impell+ =ces4 7#agi47 ,^! g5]al prop]ties1 :i* are entirely indep5d5t ( gravity1 r5d] ! 8c5tre ( gravity0 an inadequate title = ?is important po9t4 ,"s physical writ]s h1 consequ5tly1 call$ x ! 8c5tre ( in]tia40 ,! 8c5tre ( gravity10 h[ev]1 is ! "n by :i* x is /ill g5]ally designat$4 ,,*ap4 ,x4 ,,! ,,me*anical ,,prop]ties ,,( ,,an ,,axis4 7#ahj47 ,:5 a body has a motion ( rotation1 ! l9e r\nd :i* x revolves is call$ an axis4 ,e po9t ( ! body mu/ 9 ?is case move 9 a circle1 ^: c5tre lies 9 ! axis1 & ^: radius is ! di/ance ( ! po9t f ! axis4 ,sometimes :ile ! body revolves1 ! axis itself is moveable1 & n unfrequ5tly 9 a /ate ( actual motion4 ,! motions ( ! e>? & planets1 or t ( a common sp9n+-top1 are examples ( ?is4 ,! cases1 h[ev]1 :i* w be consid]$ 9 ! pres5t *apt]1 are *iefly ^? 9 :i* ! axis is immovable1 or at lea/ :]e its motion has no relation to ! ph5om5a "u inve/igation4 ,in/ances ( ?is are s frequ5t & obvi\s1 t x seems sc>cely necess>y to p>ticul>ise !m4 ,:eel-"w ( e description1 ! mov+ p>ts ( wat*es & clocks1 turn+ la!s1 mill-"w1 doors & lids on h+es1 are all obvi\s examples4 ,9 tools or o!r in/rum5ts :i* "w on jo9ts or pivots1 su* z scissors1 %e>s1 p9c]s1 al?\gh ! jo9t or pivot be n absolutely fix$1 x is to be consid]$ s 9 ref]5ce to ! me*anical effect4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,9 "s cases1 z 9 mo/ ( ! :eels ( wat*es & clocks1 fly-:eels & *ucks ( ! turn+ la!1 & ! arms ( w9d-mills1 ! body turns cont9ually 9 ! same direction1 & ea* ( its po9ts trav]ses a complete circle dur+ e revolution ( ! body r\nd its axis4 ,9 o!r in/ances ! motion is alt]nate or reciprocat+1 its direction be+ at int]vals rev]s$4 ,su* is ! case 9 p5dulums ( clocks1 balance-:eels ( *ronomet]s1 ! tr$dle ( ! la!1 doors & lids on h+es1 scissors1 %e>s1 p9c]s1 c4 ,:5 ! alt]nation is con/ant & regul>1 x is call$ oscillation or vibration1 z 9 p5dulums & balance-:eels4 7#aha47 ,to expla9 ! prop]ties ( an axis ( rotation x w be necess>y to consid] ! diff]5t k9ds ( =ces to ! action ( :i* a body moveable on su* an axis may be submitt$1 to %[ h[ ?is action dep5ds on _! sev]al quantities & directions1 to di/+ui% ! cases 9 :i* ! =ces neutralise ea* o!r & mutually equilibrate f ^? 9 :i* motion ensues1 to det]m9e ! effect :i* ! axis suff]s1 &1 9 ! cases :]e motion is produc$1 to e/imate ! effects ( ^? c5trifugal =ces 7#acg47 :i* are creat$ by ! mass ( ! body :irl+ r\nd ! axis4 ,=ces 9 g5]al h be5 di/+ui%$ by ! duration ( _! action into in/antane\s & cont9u$ =ces4 ,! effect ( an in/antane\s =ce is produc$ 9 an inf9itely %ort "t4 ,if ! body :i* su/a9s su* an action be previ\sly quiesc5t & free1 x w move ) a uni=m velocity 9 ! direction ( ! impress$ =ce4 7#ic47 ,if1 on ! o!r h&1 ! body be n free1 b s re/ra9$ t ! impulse _c put x 9 motion1 !n ! fix$ po9ts or l9es :i* resi/ ! motion su/a9 a correspond+ %ock at ! mom5t ( ! impulse4 ,?is effect1 :i* is call$ p]cussion1 is1 l ! =ce :i* causes x1 in/antane\s4 ,a cont9u$ =ce produces a cont9u$ effect4 ,if ! body be free & previ\sly quiesc5t1 ?is effect is a cont9ual increase ( velocity4 ,if ! body be s re/ra9$ t ! appli$ =ce _c put x 9 motion1 ! effect is a cont9u$ pressure on ! po9ts or l9es :i* su/a9 x4 7#id47 ,x may happ51 h[ev]1 t al?\gh ! body be n absolutely free to move 9 ob$i5ce to ! =ce appli$ to x1 yet /ill x may n be altoge!r s re/ra9$ z to resi/ ! effect ( t =ce & rema9 at re/4 ,if ! po9t at :i* a =ce is appli$ be free to move 9 a c]ta9 direction n co9cid+ ) t ( ! appli$ =ce1 t =ce w be resolv$ into two elem5ts2 "o ( :i* is 9 ! direction 9 :i* ! po9t is free to move1 & ! o!r at "r angles to t direction4 ,! po9t w move 9 ob$i5ce to ! =m] elem5t1 & ! latt] w produce p]cussion or pressure on ! po9ts or l9es :i* re/ra9 ! body4 ,9 fact1 9 su* cases ! resi/ance (f]$ by ! circum/ances :i* conf9e ! motion ( ! body modifies ! motion :i* x receives1 & z e *ange ( motion mu/ be ! consequ5ce ( a =ce appli$ 7#dd471 ! fix$ po9ts or l9es :i* (f] ! resi/ance mu/ suff] a correspond+ effect4 ,x may happ5 t ! =ces impress$ on ! body1 :e!r !y be cont9u$ or in/antane\s1 are su* z1 7 x free1 w\ld communicate to x a motion :i* ! circum/ances :i* re/ra9 x d n =bid x to receive4 ,9 su* a case ! fix$ po9ts or l9es :i* re/ra9 ! body su/a9 no =ce1 & ! ph5om5a w be ! same 9 all respects z if ^! po9ts or l9es 7 n fix$4 ,x w be easy to apply ^! g5]al reflections to ! case 9 :i* a solid body is moveable on a fix$ axis4 ,su* a body is susceptible ( no motion except "o ( rotation on t axis4 ,if x be submitt$ to ! action ( in/antane\s =ces1 "o or o!r ( ! foll[+ effects mu/ ensue4 #a4 ,! axis may resi/ ! =ces1 & prev5t any motion4 #b4 ,! axis may modify ! effect ( ! =ces su/a9+ a correspond+ p]cussion1 & ! body receiv+ a motion ( rotation4 #c4 ,! =ces appli$ may be su* z w\ld cause ! body to sp9 r\nd ! axis ev5 7 x n fix$1 9 :i* case ! body w receive a motion ( rotation1 b ! axis w suff] no p]cussion4 ,:at has be5 j obs]v$ ( ! effect ( in/antane\s =ces is likewise applicable to cont9u$ ones4 #a4 ,! axis may entirely resi/ ! effect ( su* =ces1 9 :i* case x w suff] a pressure :i* may be e/imat$ by ! rules = ! composition ( =ce4 #b4 ,x may modify ! effect ( ! appli$ =ces1 9 :i* case x mu/ also su/a9 a pressure1 & ! body mu/ receive a motion ( rotation :i* is subject to con/ant v>iation1 ow+ to ! incessant action ( ! =ces4 #c4 ,! =ces may be su* z w\ld communicate to ! body ! same rotatory motion if ! axis 7 n fix$4 ,9 ?is case ! =ces w produce no pressure on ! axis4 ,! impress$ =ces are n ! only causes :i* affect ! axis ( a body dur+ ! ph5om5on ( rotation4 ,?is species ( motion calls into action o!r =ces dep5d+ on ! in]tia ( ! mass1 :i* produce effects ^u ! axis1 & :i* play a prom95t "p 9 ! !ory ( rotation4 ,:ile ! body revolves on its axis1 ! compon5t p>ticles ( its mass move 9 circles1 ! c5tres ( :i* are plac$ 9 ! axis4 ,! radius ( ! circle 9 :i* ea* p>ticle moves is ! l9e drawn f t p>ticle p]p5dicul> to ! axis4 ,x has be5 already prov$ t a p>ticle ( matt]1 mov+ r\nd a c5tre1 is att5d$ ) a c5trifugal =ce proportionate to ! radius ( ! circle 9 :i* x moves & to ! squ>e ( its angul> velocity4 ,:5 a solid body revolves on its axis1 all its p>ts are :irl$ r\nd toge!r1 ea* p]=m+ a complete revolution 9 ! same "t4 ,! angul> velocity is consequ5tly ! same = all1 & ! diff]5ce ( ! c5trifugal =ces ( diff]5t p>ticles mu/ entirely dep5d ^u _! di/ances f ! axis4 ,! t5d5cy ( ea* p>ticle to fly f ! axis1 aris+ f ! c5trifugal =ce1 is resi/$ by ! cohesion ( ! p>ts ( ! mass1 & 9 g5]al ?is t5d5cy is exp5d$ 9 excit+ a pressure or /ra9 ^u ! axis4 ,x ought to be recollect$1 h[ev]1 t ?is pressure or /ra9 is altoge!r diff]5t f t already m5tion$1 & produc$ by ! =ces :i* give motion to ! body4 ,! latt] dep5ds entirely ^u ! quantity & directions ( ! appli$ =ces 9 relation to ! axis3 ! =m] dep5ds on ! figure & d5sity ( ! body1 & ! velocity ( its motion4 ,^! v complex effects r5d] a simple & elem5t>y exposition ( ! me*anical prop]ties ( a fix$ axis a matt] ( consid]able difficulty4 ,inde$1 ! complete ma!matical developm5t ( ?is !ory long elud$ ! skill ( ! mo/ acute geomet]s1 & x 0 only at a comp>atively late p]iod t x yield$ to ! se>*+ analysis ( mod]n sci5ce4 7#ahb47 ,to comm5ce ) ! mo/ simple case1 we %all consid] ! body z submitt$ to ! action ( a s+le =ce4 ,! effect ( ?is =ce w v>y accord+ to ! relation ( its direction to t ( ! axis4 ,!re are two ways 9 :i* a body may be conceiv$ to be moveable ar\nd an axis4 #a4 ,by hav+ pivots at two po9ts :i* re/ 9 sockets1 s t :5 ! body is mov$ x mu/ revolve r\nd ! "r l9e jo9+ ! pivots z an axis4 #b4 ,a ?9 cyl9drical rod may pass ?r\gh ! body1 on :i* x may turn 9 ! same mann] z a :eel ^u its axle4 ,if ! =ce be appli$ to ! body 9 ! direction ( ! axis1 x is evid5t t no motion c ensue1 & ! effect produc$ w be a pressure on t pivot t[>ds :i* ! =ce is direct$4 ,if 9 ?is case ! body revolv$ on a cyl9drical rod1 ! t5d5cy ( ! =ce w\ld be to make x slide along ! rod )\t revolv+ r\nd x4 ,let u next suppose ! =ce to be appli$ n 9 ! direction ( ! axis itself1 b p>allel to x4 ,let ,a ,b1 fig4 #gj41 be ! axis1 & let ,c ,d be ! direction ( ! =ce appli$4 ,! pivots be+ suppos$ to be at ,a & ,b1 draw ,a ,g & ,b ,f p]p5dicul> to ,a ,b4 ,! =ce ,c ,d w be equival5t to ?ree =ces1 "o act+ f ,b t[>ds ,a1 equal 9 quantity to ! =ce ,c ,d4 ,?is =ce w evid5tly produce a correspond+ pressure on ! pivot ,a4 ,! o!r two =ces w act 9 ! directions ,a ,g & ,b ,f1 & w h respectively to ! =ce ,c ,d ! same proportion z ,a ,e has to ,a ,b4 ,su* w be ! me*anical effect ( a =ce ,c ,d p>allel to ! axis4 ,& z ^! effects are all direct$ on ! pivots1 no motion c ensue4 ,if ! body revolve on a cyl9drical rod1 ! =ces ,a ,g & ,b ,f w\ld produce a /ra9 ^u ! axis1 :ile ! ?ird =ce 9 ! direction ,b ,a w\ld h a t5d5cy to make ! body slide along x4 7#ahc47 ,if ! =ce appli$ to ! body be direct$ ^u ! axis1 & at "r angles to x1 no motion c be produc$4 ,9 ?is case1 if ! body be support$ by pivots at ,a & ,b1 ! =ce ,k ,l1 p]p5dicul> to ! l9e ,a ,b1 w be di/ribut$ betwe5 ! pivots1 produc+ a pressure on ea* proportional to its di/ance f ! o!r4 ,! pressure on ,a hav+ to ! pressure on ,b ! same proportion z ,l ,b has to ,l ,a4 ,if ! =ce ,k ,h be direct$ obliquely to ! axis1 x w be equival5t to two =ces 7#gf471 "o ,k ,l p]p5dicul> to ! axis1 & ! o!r ,k ,m p>allel to x4 ,! effect ( ea* ( ^! may be inve/igat$ z 9 ! prec$+ cases4 ,9 all ^! obs]vations ! body has be5 suppos$ to be submitt$ to ! action ( "o =ce only4 ,if sev]al =ces act ^u x1 ! direction ( ea* ( !m cross+ ! axis ei!r p]p5dicul>ly or obliquely1 or tak+ ! direction ( ! axis or any p>allel direction1 _! effects may be simil>ly inve/igat$4 ,9 ! same mann] we may det]m9e ! effects ( any numb] ( =ces ^: comb9$ results are me*anically equival5t to =ces :i* ei!r int]sect ! axis or are p>allel to x4 7#ahd47 ,if any =ce be appli$ ^: direction lies 9 a plane oblique to ! axis1 x c always be resolv$ into two elem5ts 7#gf471 "o ( :i* is p>allel to ! axis1 & ! o!r 9 a plane p]p5dicul> to x4 ,! effect ( ! =m] has be5 already det]m9$1 & !re=e we %all at pres5t conf9e our att5tion to ! latt]4 ,suppose ! axis to be p]p5dicul> to ! pap]1 & to pass ?r\gh ! po9t ,g1 fig4 #ga4 & let ,a ,b ,c be a section ( ! body4 ,x w be conv5i5t to consid] ! section v]tical & ! axis horizontal1 omitt+1 h[ev]1 any notice ( ! effect ( ! weight ( ! body4 ,let a weight ,w be susp5d$ by a cord ,q ,w f any po9t ,q4 ,?is weight w evid5tly h a t5d5cy to turn ! body r\nd 9 ! direction ,a ,b ,c4 ,let ano!r cord be atta*$ to any o!r po9t ,p1 &1 be+ c>ri$ ov] a :eel ,r1 let a di% ,s be atta*$ to x1 & let f9e s& be p\r$ into ?is di% until ! t5d5cy ( ,s to turn ! body r\nd ! axis 9 ! direction ( ,c ,b ,a balances ! opposite t5d5cy ( ,w4 ,let ! weights ( ,w & ,s be !n exactly asc]ta9$1 & also let ! di/ances ,g ,i & ,g ,h ( ! cords f ! axis be exactly measur$4 ,x w be f\nd t1 if ! numb] ( ounces 9 ! weight ,s be multipli$ by ! numb] ( in*es 9 ,g ,h1 & also ! numb] ( ounces 9 ,w by ! numb] ( in*es 9 ,g ,i1 equal products w be obta9$4 ,?is exp]im5t may be v>i$ by v>y+ ! position ( ! :eel ,r1 & !reby *ang+ ! direction ( ! /r+ ,p ,r1 9 :i* cases x w be always f\nd necess>y to v>y ! weight ( ,s 9 su* a mann]1 t :5 ! numb] ( ounces 9 x is multipli$ by ! numb] ( in*es 9 ! di/ance ( ! /r+ f ! axis1 ! product obta9$ %all be equal to t ( ! weight ,w by ! di/ance ,g ,i4 ,we h "h us$ ounces & in*es z ! measures ( weight & di/ance2 b x is obvi\s t any o!r measures w\ld be equally applicable4 ,f :at has be5 j /at$ x foll[s1 t ! en]gy ( ! weight ( ,s to move ! body on its axis1 does n dep5d alone ^u ! actual am\nt ( t weight1 b also ^u ! di/ance ( ! /r+ f ! axis4 ,if1 :ile ! position ( ! /r+ rema9s unalt]$1 ! weight ( ,s be increas$ or dim9i%$1 ! resi/+ weight ,w mu/ be increas$ or dim9i%$ 9 ! same proportion4 ,b if1 :ile ! weight ( ,s rema9s unalt]$1 ! di/ance ( ! /r+ ,p ,r f ! axis ,g be increas$ or dim9i%$1 x w be f\nd necess>y to increase or dim9i% ! resi/+ weight ,w 9 exactly ! same proportion4 ,x !re=e appe>s t ! increase or dim9ution ( ! di/ance ( ! direction ( a =ce f ! axis has ! same effect ^u its p[] to give rotation z a simil> increase or dim9ution ( ! =ce itself4 ,! p[] ( a =ce to produce rotation is1 !re=e1 accurately e/imat$1 n by ! =ce alone1 b by ! product f\nd by multiply+ ! =ce by ! di/ance ( its direction f ! axis4 ,x is frequ5tly necess>y 9 me*anical sci5ce to ref] to ?is p[] ( a =ce1 &1 accord+ly1 ! product j m5tion$ has receiv$ a p>ticul> d5om9ation4 ,x is call$ ! mom5t ( ! =ce r\nd ! axis4 7#ahe47 ,! di/ance ( ! direction ( a =ce f ! axis is sometimes call$ ! lev]age ( ! =ce4 ,! mom5t ( a =ce is !re=e f\nd by multiply+ ! =ce by its lev]age1 & ! en]gy ( a giv5 =ce to turn a body r\nd an axis is proportional to ! lev]age ( t =ce4 ,f all t has be5 obs]v$ x may easily be inf]r$ t1 if sev]al =ces affect a body moveable on an axis1 hav+ t5d5cies to turn x 9 diff]5t directions1 !y w mutually neutralise ea* o!r & produce equilibrium1 if ! sum ( ! mom5ts ( ^? =ces :i* t5d to turn ! body 9 "o direction be equal to ! sum ( ! mom5ts ( ^? :i* t5d to turn x 9 ! opposite direction4 ,?us1 if ! =ces ,a1 ,b1 ,c1 444 t5d to turn ! body f "r to left1 & ! di/ances ( _! directions f ! axis be a1 b1 c1 444 & ! =ces ,a1 ,b1 ,c1 444 t5d to move x f left to "r1 & ! di/ances ( _! directions f ! axis be a1 b1 c1 4442 !n ^! =ces w produce equilibrium1 if ! products f\nd by multiply+ ! ounces 9 ,a1 ,b1 ,c1 444 respectively by ! in*es 9 a1 b1 c1 444 :5 add$ toge!r be equal to ! products f\nd by multiply+ ! ounces 9 ,a1 ,b1 ,c1 444 by ! in*es 9 a1 b1 c1 444 respectively :5 add$ toge!r4 ,b if ei!r ( ^! sets ( products :5 add$ toge!r exce$ ! o!r1 ! correspond+ set ( =ces w prevail1 & ! body w revolve on its axis4 7#ahf47 ,:5 a body receives an impulse 9 a direction p]p5dicul> to ! axis1 b n cross+ x1 a uni=m rotatory motion is produc$4 ,! velocity ( ?is motion dep5ds on ! =ce ( ! impulse1 ! di/ance ( ! direction ( ! impulse f ! axis1 & ! mann] 9 :i* ! mass ( ! body is di/ribut$ r\nd ! axis4 ,x is to be consid]$ t ! :ole =ce ( ! impulse is %>$ among/ ! v>i\s p>ts ( ! mass1 & is transmitt$ to !m f ! po9t :]e ! impulse is appli$ by reason ( ! cohesion & t5acity ( ! p>ts1 & ! impossibility ( "o "p yield+ to a =ce )\t c>ry+ all ! o!r p>ts ) x4 ,! =ce appli$ acts ^u ^? p>ticles ne>] to ! axis ?an its own direction "u advantage\s circum/ances2 =1 accord+ to :at has be5 already expla9$1 _! p[] to resi/ ! effect ( ! appli$ =ce is small 9 ! same proportion ) _! di/ance4 ,on ! o!r h&1 ! appli$ =ce acts ^u p>ticles ( ! mass1 at a great] di/ance ?an its own direction1 "u circum/ances proportionably disadvantage\s2 = _! resi/ance to ! appli$ =ce is great 9 proportion to _! di/ances f ! axis4 ,let ,c ,d1 fig4 #gb41 be a section ( ! body made by a plane pass+ ?r\gh ! axis ,a ,b4 ,suppose ! impulse to be appli$ at ,p1 p]p5dicul> to ?is plane1 & at ! di/ance ,p ,o f ! axis4 ,! effect ( ! impulse be+ di/ribut$ ?r\gh ! mass w cause ! body to revolve on ,a ,b1 ) a uni=m velocity4 ,!re is a c]ta9 po9t ,g1 at :i*1 if ! :ole mass 7 conc5trat$1 x w\ld receive f ! impulse ! same velocity r\nd ! axis4 ,! di/ance ,o ,g is call$ ! radius ( gyration ( ! axis ,a ,b1 & ! po9t ,g is call$ ! c5tre ( gyration relatively to t axis4 ,! effect ( ! impulse ^u ! mass conc5trat$ at ,g is great 9 exactly ! same proportion z ,o ,g is small4 ,?is easily foll[s f ! prop]ty ( mom5ts :i* has be5 already expla9$2 f :5ce x may be inf]r$1 t ! great] ! radius ( gyration is1 ! less w be ! velocity :i* ! body w receive f a giv5 impulse4 7#ahg47 ,s9ce ! radius ( gyration dep5ds on ! mann] 9 :i* ! mass is arrang$ r\nd ! axis1 x foll[s t = diff]5t axes 9 ! same body !re w be diff]5t radii ( gyration4 ,( all axes tak5 9 ! same body p>allel to ea* o!r1 t :i* passes ?r\gh ! c5tre ( gravity has ! lea/ radius ( gyration4 ,if ! radius ( gyration ( any axis pass+ ?r\gh ! c5tre ( gravity be giv51 t ( any p>allel axis c be f\nd2 = ! squ>e ( ! radius ( gyration ( any axis is equal to ! squ>e ( ! di/ance ( t axis f ! c5tre ( gravity add$ to ! squ>e ( ! radius ( gyration ( ! p>allel axis ?r\gh ! c5tre ( gravity4 7#ahh47 ,! product ( ! num]ical expressions = ! mass ( ! body & ! squ>e ( ! radius ( gyration is a quantity mu* us$ 9 me*anical sci5ce1 & has be5 call$ ! mom5t ( in]tia4 ,! mom5ts ( in]tia1 !re=e1 = diff]5t axes 9 ! same body are proportional to ! squ>es ( ! correspond+ radii ( gyration2 & consequ5tly increase z ! di/ances ( ! axes f ! c5tre ( gravity increase4 7#ahg47 7#ahi47 ,f :at has be5 expla9$ 9 7#ahg471 x foll[s1 t ! mom5t ( in]tia ( any axis may be comput$ by common ari?metic1 if ! mom5t ( in]tia ( a p>allel axis ?r\gh ! c5tre ( gravity be previ\sly kn[n4 ,to det]m9e ?is la/1 h[ev]1 w\ld require analytical processes altoge!r unsuitable to ! nature & objects ( ! pres5t treatise4 ,! velocity ( rotation :i* a body receives f a giv5 impulse is great 9 exactly ! same proportion z ! mom5t ( in]tia is small4 ,?us ! mom5t ( in]tia may be consid]$ 9 rotatory motion analog\s to ! mass ( ! body 9 rectil9e> motion4 ,f :at has be5 expla9$ 9 7#ahg47 x foll[s t a giv5 impulse at a giv5 di/ance f ! axis w communicate ! greate/ angul> velocity :5 ! axis passes ?r\gh ! c5tre ( gravity1 & t ! velocity :i* x w communicate r\nd o!r axes w be dim9i%$ 9 ! same proportion z ! squ>es ( _! di/ances f ! c5tre ( gravity add$ to ! squ>e ( ! radius ( gyration = a p>allel axis ?r\gh ! c5tre ( gravity are augm5t$4 7#aij47 ,if any po9t :atev] be assum$ 9 a body1 & "r l9es be conceiv$ to div]ge 9 all directions f t po9t1 !re are g5]ally two ( ^! l9es1 :i* be+ tak5 z axes ( rotation1 "o has a great] & ! o!r a less mom5t ( in]tia ?an any ( ! o!rs4 ,x is a rem>kable circum/ance1 t1 :atev] be ! nature ( ! body1 :atev] be its %ape1 & :atev] be ! position ( ! po9t assum$1 ^! two axes ( greate/ & lea/ mom5t w always be at "r angles to ea* o!r4 ,^! axes & a ?ird ?r\gh ! same po9t1 & at "r angles to bo? ( !m1 are call$ ! pr9cipal axes ( t po9t f :i* !y div]ge4 ,to =m a di/9ct notion ( _! relative position1 let ! axis ( greate/ mom5t be imag9$ to lie horizontally f nor? to s\?1 & ! axis ( lea/ mom5t f ea/ to we/2 !n ! ?ird pr9cipal axis w be pres5t$ p]p5dicul>ly upw>ds & d[nw>ds4 ,! fir/ two be+ call$ ! pr9cipal axes ( greate/ & lea/ mom5t1 ! ?ird may be call$ ! int]m$iate pr9cipal axis4 7#aia47 ,al?\gh ! mom5ts ( ! ?ree pr9cipal axes be 9 g5]al unequal1 yet bodies may be f\nd hav+ c]ta9 axes = :i* ^! mom5ts may be equal4 ,9 "s cases ! mom5t ( ! int]m$iate axis is equal to t ( ! pr9cipal axis ( greate/ mom5t3 9 o!rs x is equal to t ( ! pr9cipal axis ( lea/ mom5t1 & 9 o!rs ! mom5ts ( all ! ?ree pr9cipal axes are equal to ea* o!r4 ,if ! mom5ts ( any two ( ?ree pr9cipal axes be equal1 ! mom5ts ( all axes ?r\gh ! same po9t & 9 _! plane w also be equal2 & if ! mom5ts ( ! ?ree pr9cipal axes ?r\gh a po9t be equal1 ! mom5ts ( all axes :atev]1 ?r\gh ! same po9t1 w be equal4 7#aib47 ,if ! mom5ts ( ! pr9cipal axes ?r\gh ! c5tre ( gravity be kn[n1 ! mom5ts = all o!r axes ?r\gh t po9t may be easily comput$4 ,to effect ?is x is only necess>y to multiply ! mom5ts ( ! pr9cipal axes by ! squ>es ( ! co-s9es ( ! angles =m$ by !m respectively ) ! axis ^: mom5t is s\ght4 ,! products be+ add$ toge!r w give ! requir$ mom5t4 7#aic47 ,by comb9+ ?is result ) t ( 7#ahi471 x w be evid5t t ! mom5t ( all axes :atev] may be det]m9$1 if ^? ( ! pr9cipal axes ?r\gh ! c5tre ( gravity be kn[n4 7#aid47 ,x is obvi\s t ! pr9cipal axis ( lea/ mom5t ?r\gh ! c5tre ( gravity has a less mom5t ( in]tia ?an any o!r axis :atev]4 ,= x has1 by its def9ition 7#aij47 a less mom5t ( in]tia ?an any o!r axis ?r\gh ! c5tre ( gravity1 & e o!r axis ?r\gh ! c5tre ( gravity has a less mom5t ( in]tia ?an a p>allel axis ?r\gh any o!r po9t 7#ahg47 & 7#ahi47 7#aie47 ,if two ( ! pr9cipal axes ?r\gh ! c5tre ( gravity h equal mom5ts ( in]tia1 all axes 9 any plane p>allel to ! plane ( ^! axes1 & pass+ ?r\gh ! po9t :]e a p]p5dicul> f ! c5tre ( gravity meets t plane1 mu/ h equal mom5ts ( in]tia4 ,= by 7#aia47 all axes 9 ! plane ( ^? two h equal mom5ts1 & by 7#ahi47 ! axes 9 ! p>allel plane h mom5ts :i* exce$ ^! by ! same quantity1 be+ equally di/ant f !m4 7#ahg47 ,h5ce x is obvi\s t if ! ?ree pr9cipal axes ?r\gh ! c5tre ( gravity h equal mom5ts1 all axes situat$ 9 any giv5 plane1 & pass+ ?r\gh ! po9t :]e ! p]p5dicul> f ! c5tre ( gravity meets t plane1 w h equal mom5ts1 be+ equally di/ant f p>allel axes ?r\gh ! c5tre ( gravity4 7#aif47 ,if ! ?ree pr9cipal axes ?r\gh ! c5tre ( gravity h unequal mom5ts1 !re is no po9t :atev] = :i* all axes w h equal mom5ts2 b if ! pr9cipal axis ( lea/ mom5t & ! int]m$iate pr9cipal axis ?r\gh ! c5tre ( gravity h equal mom5ts1 !n !re w be two po9ts on ! pr9cipal axis ( greate/ mom5t1 equally di/ant at opposite sides ( ! c5tre ( gravity1 at :i* all axes w h equal mom5ts4 ,if ! ?ree pr9cipal axes ?r\gh ! c5tre ( gravity h equal mom5ts1 no o!r po9t ( ! body c h pr9cipal axes ( equal mom5t4 7#aig47 ,:5 a body revolves on a fix$ axis1 ! p>ts ( its mass are :irl$ 9 circles r\nd ! axis2 & s9ce !y move ) a common angul> velocity1 !y w h c5trifugal =ces proportional to _! di/ances f ! axis4 ,if ! compon5t p>ts ( ! mass 7 n unit$ toge!r by cohesive =ces ( en]gies great] ?an ^! c5trifugal =ces1 !y w\ld be sep>at$1 & w\ld fly (f f ! axis2 b _! cohesion prev5ts ?is1 & causes ! effects ( ! diff]5t c5trifugal =ces1 :i* affect ! diff]5t p>ts ( ! mass1 to be transmitt$ s z to modify ea* o!r1 & f9ally to produce "o or m =ces me*anically equival5t to ! :ole1 & :i* are ex]t$ ^u ! axis & resi/$ by x4 ,we propose n[ to expla9 ^! effects1 z f> z x is possible to r5d] !m intelligible )\t ! aid ( ma!matical language4 ,x is obvi\s t any numb] ( equal p>ts ( ! mass1 :i* are uni=mly arrang$ 9 a circle r\nd ! axis1 h equal c5trifugal =ces act+ f ! c5tre ( ! circle 9 e direction4 ,^! mutually neutralise ea* o!r1 & !re=e ex]t no =ce on ! axis4 ,! same may be said ( all p>ts ( ! mass :i* are regul>ly & equally di/ribut$ on e side ( ! axis4 ,also if equal masses be plac$ at equal di/ances on opposite sides ( ! axis1 _! c5trifugal =ces w de/roy ea* o!r4 ,h5ce x appe>s t ! pressure :i* ! axis ( rotation su/a9s f ! c5trifugal =ces ( ! revolv+ mass1 arises f ! unequal di/ribution ( ! matt] ar\nd x4 ,f ?is reason+ x w be easily p]ceiv$ t 9 ! foll[+ examples ! axis ( rotation w su/a9 no pressure4 ,a globe revolv+ on any ( its diamet]s1 ! d5sity be+ ! same at equal di/ances f ! c5tre4 ,a sph]oid or a cyl9d] revolv+ on its axis1 ! d5sity be+ equal at equal di/ances f ! axis4 ,a cube revolv+ on an axis :i* passes ?r\gh ! c5tre ( two opposite bases1 be+ ( uni=m d5sity4 ,a circul> plate ( uni=m ?ickness & d5sity revolv+ on "o ( its diamet]s z an axis4 7#aih47 ,9 all ^! examples x w be obs]v$ t ! axis ( rotation passes ?r\gh ! c5tre ( gravity4 ,! g5]al !orem1 ( :i* !y are only p>ticul> in/ances1 is1 8if a body revolve on a pr9cipal axis1 pass+ ?r\gh ! c5tre ( gravity1 ! axis w su/a9 no pressure f ! c5trifugal =ce ( ! revolv+ mass40 ,?is is a prop]ty 9 :i* ! pr9cipal axes ?r\gh ! c5tre ( gravity are unique4 ,!re is no o!r axis on :i* a body c\ld revolve )\t pressure4 ,if two ( ! pr9cipal axes ?r\gh ! c5tre ( gravity h equal mom5ts1 e axis 9 _! plane has ! same mom5t1 & is to be consid]$ equally z a pr9cipal axis4 ,9 ?is case ! body w\ld revolve on any ( ^! axes )\t pressure4 ,a homog5e\s sph]oid furni%es an example ( ?is4 ,if any ( ! diamet]s ( ! e>?'s equator 7 a fix$ axis1 ! e>? w\ld revolve on x )\t produc+ pressure4 ,if ! ?ree pr9cipal axes ?r\gh ! c5tre ( gravity h equal mom5ts1 all axes ?r\gh ! c5tre ( gravity are to be consid]$ z pr9cipal axes4 ,9 ?is case ! body w\ld revolve )\t pressure on any axis ?r\gh ! c5tre ( gravity4 ,a globe1 9 :i* ! d5sity ( ! mass at equal di/ances f ! c5tre is ! same1 is an example ( ?is4 ,su* a body w\ld revolve )\t pressure on any axis ?r\gh its c5tre4 7#aii47 ,s9ce no pressure is excit$ on ! axis 9 ^! cases1 ! /ate ( ! body w n be *ang$1 if dur+ its rotation ! axis cease to be fix$4 ,! body w not)/&+ cont9ue to revolve r\nd ! axis1 & ! axis w ma9ta9 its position4 ,?us a sp9n+-top ( homog5e\s mat]ial & symmetrical =m w revolve /eadily 9 ! same position1 until ! friction ( its po9t ) ! surface on :i* x re/s deprives x ( motion4 ,?is is a ph5om5on :i* c only be exhibit$ :5 ! axis ( rotation is a pr9cipal axis ?r\gh ! c5tre ( gravity4 7#bjj47 ,if ! body revolve r\nd any axis ?r\gh ! c5tre ( gravity1 :i* is n a pr9cipal axis1 ! c5trifugal pressure is repres5t$ by two =ces1 :i* are equal & p>allel1 b :i* act 9 opposite directions on diff]5t po9ts ( ! axis4 ,! effect ( ^! =ces is to produce a /ra9 ^u ! axis1 & give ! body a t5d5cy to move r\nd ano!r axis at "r angles to ! =m]4 7#bja47 ,if ! fix$ axis on :i* a body revolves be a pr9cipal axis ?r\gh any po9t diff]5t f ! c5tre ( gravity1 !n a pressure w be produc$ by ! c5trifugal =ce ( ! revolv+ mass1 & ?is pressure w act at "r angles to ! axis on ! po9t to :i* x is a pr9cipal axis1 & 9 ! plane ?r\gh t axis & ! c5tre ( gravity4 ,! am\nt ( ! pressure w be proportional to ! mass ( ! body1 ! di/ance ( ! c5tre ( gravity f ! axis1 & ! squ>e ( ! velocity ( rotation4 7#bjb47 ,s9ce ! :ole pressure is 9 ?is case excit$ on a s+le po9t1 ! /ability ( ! axis w n be di/urb$1 provid$ t po9t alone be fix$4 ,s t ev5 ?\gh ! axis %\ld be free to turn on t po9t1 no motion w ensue z long z no ext]nal =ces act ^u ! body4 7#bjc47 ,if ! axis ( rotation be n a pr9cipal axis1 ! c5trifugal =ces w produce an effect :i* _c be repres5t$ by a s+le =ce4 ,! effect may be und]/ood by conceiv+ two =ces to act on diff]5t po9ts ( ! axis at "r angles to x & to ea* o!r4 ,! quantities ( ^! pressures & _! directions dep5d on ! figure & d5sity ( ! mass & ! position ( ! axis1 9 a mann] :i* _c be expla9$ )\t ! aid ( ma!matical language & pr9ciples4 7#bjd47 ,! effects ^u ! axis :i* h be5 n[ expla9$ are ^? :i* arise f ! motion ( rotation1 f :atev] cause t motion may h aris54 ,! =ces :i* produce t motion1 h[ev]1 are att5d$ ) effects on ! axis :i* /ill rema9 to be notic$4 ,:5 ^! =ces1 :e!r !y be ( ! nature ( in/antane\s actions or cont9u$ =ces1 are entirely resi/$ by ! axis1 _! directions mu/ sev]ally be 9 a plane pass+ ?r\gh ! axis1 or !y mu/1 by ! pr9ciples ( ! composition ( =ce 7#gd47 et seq41 be me*anically equival5t to =ces 9 t plane4 ,9 e o!r case ! impress$ =ces mu/ produce motion1 &1 except 9 c]ta9 cases1 mu/ also produce effects ^u ! axis4 ,by ! rules = ! composition ( =ce x is possible 9 all cases to resolve ! impress$ =ces into o!rs :i* are ei!r 9 planes ?r\gh ! axis1 or 9 planes p]p5dicul> to x1 or1 f9ally1 "s 9 planes ?r\gh x1 & o!rs 9 planes p]p5dicul> to x4 ,! effect ( ^? :i* are 9 planes ?r\gh ! axis has be5 already expla9$2 & we %all n[ conf9e our att5tion to ^? impell+ =ces :i* act at "r angles to ! axis1 & :i* produce motion4 ,x w be suffici5t to consid] ! effect ( a s+le =ce at "r angles to ! axis2 = :atev] be ! numb] ( =ces :i* act ei!r simultane\sly or successively1 ! effect ( ! :ole w be decid$ by comb9+ _! sep>ate effects4 ,! effect :i* a s+le =ce produces dep5ds on two circum/ances1 #a4 ,! position ( ! axis ) respect to ! figure & mass ( ! body1 & #b4 ,! quantity & direction ( ! =ce itself4 ,9 g5]al ! %ock :i* ! axis su/a9s f ! impact may be repres5t$ by two impacts appli$ to x at diff]5t po9ts1 "o p>allel to ! impress$ =ce1 & ! o!r p]p5dicul> to x1 b bo? p]p5dicul> to ! axis4 ,!re are c]ta9 circum/ances1 h[ev]1 "u :i* ?is effect w be modifi$4 ,if ! impulse :i* ! body receives be 9 a direction p]p5dicul> to a plane ?r\gh ! axis & ! c5tre ( gravity1 & at a di/ance f ! axis :i* be>s to ! radius ( gyration 7#ahf47 ! same proportion z t l9e be>s to ! di/ance ( ! c5tre ( gravity f ! axis1 !re are c]ta9 cases 9 :i* ! impulse w produce no p]cussion4 ,to *>act]ise ^! cases g5]ally w\ld require analytical =mul :i* _c conv5i5tly be translat$ into ord9>y language4 ,t po9t ( ! plane1 h[ev]1 :]e ! direction ( ! impress$ =ce meets x1 :5 no p]cussion on ! axis is produc$1 is call$ ! c5tre ( p]cussion4 ,if ! axis ( rotation be a pr9cipal axis1 ! c5tre ( p]cussion mu/ be 9 ! "r l9e drawn ?r\gh ! c5tre ( gravity1 int]sect+ ! axis at "r angles1 & at ! di/ance f ! axis already expla9$4 ,if ! axis ( rotation be p>allel to a pr9cipal axis ?r\gh ! c5tre ( gravity1 ! c5tre ( p]cussion w be det]m9$ 9 ! same mann]4 7#bje47 ,!re are _m positions :i* ! axis may h 9 :i* !re w be no c5tre ( p]cussion2 t is1 !re w be no direction 9 :i* an impulse c\ld be appli$ )\t produc+ a %ock ^u ! axis4 ,"o ( ^! positions is :5 x is a pr9cipal axis ?r\gh ! c5tre ( gravity4 ,?is is ! only case ( rotation r\nd an axis 9 :i* no effect arises f ! c5trifugal =ce2 & !re=e x foll[s t ! only case 9 :i* ! axis su/a9s no effect f ! motion produc$1 is "o 9 :i* x mu/ necess>ily suff] an effect f t :i* produces ! motion4 ,if ! body be act$ ^u by cont9u$ =ces1 _! effect is at ea* in/ant det]m9$ by ! g5]al pr9ciples = ! composition ( =ce4 ,,*ap4 ,,xi4 ,,on ,,! ,,p5dulum4 7#bjf47 ,:5 a body is plac$ on a horizontal axis :i* does n pass ?r\gh its c5tre ( gravity1 x w rema9 9 p]man5t equilibrium only :5 ! c5tre ( gravity is imm$iately bel[ ! axis4 ,if ?is po9t be plac$ 9 any o!r situation1 ! body w oscillate f side to side1 until ! atmosph]ical resi/ance & ! friction ( ! axis de/roy its motion4 7#aei1 #afj47 ,su* a body is call$ a p5dulum4 ,! sw++ motion :i* x receives is call$ oscillation or vibration4 7#bjg47 ,! use ( ! p5dulum1 n only = philosophical purposes1 b 9 ! ord9>y economy ( life1 r5d]s x a subject ( consid]able importance4 ,x furni%es ! mo/ exact means ( measur+ "t1 & ( det]m9+ ) precision v>i\s natural ph5om5a4 ,by its means ! v>iation ( ! =ce ( gravity 9 diff]5t latitudes is discov]$1 & ! law ( t v>iation exp]im5tally exhibit$4 ,9 ! pres5t *apt]1 we propose to expla9 ! g5]al pr9ciples :i* regulate ! oscillation ( p5dulums4 ,m9ute details conc]n+ _! con/ruction w be giv5 9 ! tw5ty-fir/ *apt] ( ?is volume4 7#bjh47 ,a simple p5dulum is compos$ ( a heavy molecule atta*$ to ! end ( a flexible ?read1 & susp5d$ by a fix$ po9t ,o1 fig4 #gc4 ,:5 ! p5dulum is plac$ 9 ! position ,o ,c1 ! molecule be+ v]tically bel[ ! po9t ( susp5sion1 x w rema9 9 equilibrium2 b if x be drawn into ! position ,o ,a & !re lib]at$1 x w desc5d t[>ds ,c1 mov+ ?r\gh ! arc ,a ,c ) accel]at$ motion4 ,hav+ arriv$ at ,c & acquir$ a c]ta9 velocity1 x w1 by reason ( its in]tia1 cont9ue to move 9 ! same direction4 ,x w !re=e comm5ce to asc5d ! arc ,c ,a ) ! velocity s acquir$4 ,dur+ its asc5t1 ! weight ( ! molecule ret>ds its motion 9 exactly ! same mann] z x _h accel]at$ x 9 desc5d+ f ,a to ,c2 & :5 ! molecule has asc5d$ ?r\gh ! arc ,c ,a equal to ,c ,a1 its entire velocity w be de/roy$1 & x w cease to move 9 t direction4 ,x w ?us be plac$ at ,a 9 ! same mann] z 9 ! fir/ in/ance x _h be5 plac$ at ,a1 & consequ5tly x w desc5d f ,a to ,c ) accel]at$ motion1 9 ! same mann] z x fir/ mov$ f ,a to ,c4 ,x w !n asc5d f ,c to ,a1 & s on1 cont9ually4 ,9 ?is case ! ?read1 by :i* ! molecule is susp5d$1 is suppos$ to be p]fectly flexible1 inext5sible1 & ( inconsid]able weight4 ,! po9t ( susp5sion is suppos$ to be )\t friction1 & ! atmosph]e to (f] no resi/ance to ! motion4 ,x is evid5t f :at has be5 /at$1 t ! times ( mov+ f ,a to ,a & f ,a to ,a are equal1 & w cont9ue to be equal s long z ! p5dulum cont9ues to vibrate4 ,if ! numb] ( vibrations p]=m$ by ! p5dulum 7 regi/]$1 & ! "t ( ea* vibration kn[n1 ?is in/rum5t w\ld become a *ronomet]4 ,! rate at :i* ! motion ( ! p5dulum is accel]at$ 9 its desc5t t[>ds its l[e/ position is n uni=m1 because ! =ce :i* impels x is cont9ually decreas+1 & altoge!r disappe>s at ! po9t ,c4 ,! impell+ =ce arises f ! effect ( gravity on ! susp5d$ molecule1 & ?is effect is always produc$ 9 ! v]tical direction ,a ,v4 ,! great] ! angle ,o ,a ,v is1 ! less effici5t ! =ce ( gravity w be 9 accel]at+ ! molecule3 ?is angle evid5tly increases z ! molecule approa*es ,c1 :i* w appe> by inspect+ fig4 #gc4 ,at ,c1 ! =ce ( gravity act+ 9 ! direction ,c ,b is totally exp5d$ 9 giv+ t5sion to ! ?read1 & is ineffici5t 9 mov+ ! molecule4 ,x foll[s1 !re=e1 t ! impell+ =ce is greate/ at ,a1 & cont9ually dim9i%es f ,a to ,c1 :]e x altoge!r vani%es4 ,! same obs]vations w be applicable to ! ret>d+ =ce f ,c to ,a1 & to ! accel]at+ =ce f ,a to ,c1 & s on4 ,:5 ! l5g? ( ! ?read & ! int5sity ( ! =ce ( gravity are giv51 ! "t ( vibration dep5ds on ! l5g? ( ! arc ,a ,c1 or on ! magnitude ( ! angle ,a ,o ,c4 ,if1 h[ev]1 ?is angle d n exce$ a c]ta9 limit ( magnitude1 ! "t ( vibration w be subject to no s5sible v>iation1 h[ev] t angle may v>y4 ,?us ! "t ( oscillation w be ! same1 :e!r ! angle ,a ,o ,c be #b1 or #a #cj1 or #a1 or any less] magnitude4 ,?is prop]ty ( a p5dulum is express$ by ! ^w iso*ronism4 ,! /rict demon/ration ( ?is prop]ty dep5ds on ma!matical pr9ciples1 ! details ( :i* w\ld n be suitable to ! pres5t treatise4 ,x is n difficult1 h[ev]1 to expla9 g5]ally h[ x happ5s t ! same p5dulum w sw+ ?r\gh great] & small] arcs ( vibration 9 ! same "t4 ,if x sw+ f ,a1 ! =ce ( gravity at ! comm5cem5t ( its motion impels x ) an effect dep5d+ on ! obliquity ( ! l9es ,o ,a & ,a ,v4 ,if x comm5ce its motion f a1 ! impell+ effect f ! =ce ( gravity w be consid]ably less ?an at ,a2 consequ5tly1 ! p5dulum beg9s to move at a sl[] rate1 :5 x sw+s f a ?an :5 x moves f ,a3 ! great] magnitude ( ! sw+ is !re=e comp5sat$ by ! increas$ velocity1 s t ! great] & ! small] arcs ( vibration are mov$ ?r\gh 9 ! same "t4 7#bji47 ,to e/abli% ?is prop]ty exp]im5tally1 x is only necess>y to susp5d a small ball ( metal1 or o!r heavy sub/ance1 by a flexible ?read1 & to put x 9 a /ate ( vibration1 ! entire arc ( vibration n exce$+ #d or #e1 ! friction on ! po9t ( susp5sion & o!r causes w gradually dim9i% ! arc ( vibration1 s t aft] ! lapse ( "s h\rs x w be s small1 t ! motion w sc>cely be disc]n$ )\t microscopic aid4 ,if ! vibration ( ?is p5dulum be obs]v$ 9 ref]5ce to a correct timekeep]1 at ! comm5cem5t1 at ! middle1 & t[>ds ! end ( its motion1 ! rate w be f\nd to suff] no s5sible *ange4 ,?is rem>kable law ( iso*ronism 0 "o ( ! e>lie/ discov]ies ( ,galileo4 ,x is said1 t :5 v "y1 he obs]v$ a *&eli] susp5d$ f ! ro( ( a *ur* 9 ,pisa sw++ ) a p5dul\s motion1 & 0 /ruck ) ! uni=mity ( ! rate ev5 :5 ! ext5t ( ! sw+ 0 subject to evid5t v>iation4 7#baj47 ,x has be5 /at$ 9 7#aag47 t ! attraction ( gravity affects all bodies equally1 & moves !m ) ! same velocity1 :atev] be ! nature or quantity ( ! mat]ials ( :i* !y are compos$4 ,s9ce x is ! =ce ( gravity :i* moves ! p5dulum1 we %\ld !re=e expect t ! circum/ances ( t motion %\ld n be affect$ ei!r by ! quantity or quality ( ! p5dul\s body4 ,& we f9d ?is1 9 fact1 to be ! case2 = if small pieces ( diff]5t heavy sub/ances su* z lead1 brass1 ivory1 c41 be susp5d$ by f9e ?reads ( equal l5g?1 !y w vibrate 9 ! same "t1 provid$ _! weights be> a consid]able proportion to ! atmosph]ical resi/ance1 or t !y be susp5d$ 9 vacuo4 7#baa47 ,s9ce ! "t ( vibration ( a p5dulum1 :i* oscillates 9 small arcs1 dep5ds nei!r on ! magnitude ( ! arc ( vibration nor on ! quality or weight ( ! p5dul\s body1 x w be necess>y to expla9 ! circum/ances on :i* ! v>iation ( ?is "t dep5ds4 ,! fir/ & mo/ /rik+ ( ^! circum/ances is ! l5g? ( ! susp5d+ ?read4 ,! rude/ exp]im5ts w demon/rate ! fact1 t e increase 9 ! l5g? ( ?is ?read w produce a correspond+ increase 9 ! "t ( vibration2 b accord+ to :at law does ?is increase proce$8 ,if ! l5g? ( ! ?read be d\bl$ or trebl$1 w ! "t ( vibration also be increas$ 9 a d\ble or treble proportion8 ,?is problem is capable ( exact ma!matical solution1 & ! result %[s t ! "t ( vibration increases n 9 ! proportion ( ! increas$ l5g? ( ! ?read1 b z ! squ>e root ( t l5g?2 t is to say1 if ! l5g? ( ! ?read be increas$ 9 a f\r-fold proportion1 ! "t ( vibration w be augm5t$ 9 a two-fold proportion4 ,if ! ?read be increas$ to n9e times its l5g?1 ! "t ( vibration w be trebl$1 & s on4 ,?is relation is exactly ! same z t :i* 0 prov$ to subsi/ betwe5 ! spaces ?r\gh :i* a body falls freely1 & ! times ( fall4 ,9 ! table1 page #hi1 if ! figures repres5t+ ! height be und]/ood to express ! l5g? ( diff]5t p5dulums1 ! figures imm$iately above !m w express ! correspond+ times ( vibration4 ,?is law ( ! proportion ( ! l5g?s ( p5dulums to ! squ>es ( ! "t ( vibration may be exp]im5tally e/abli%$ 9 ! foll[+ mann]3-- ,let ,a1 ,b1 ,c1 fig4 #gd41 be ?ree small pieces ( metal ea* atta*$ by ?reads to two po9ts ( susp5sion1 & let !m be plac$ 9 ! same v]tical l9e "u ! po9t ,o2 suppose !m s adju/$ t ! di/ances ,o ,a1 ,o ,b1 & ,o ,c %all be 9 ! proportion ( ! numb]s #a1 #d1 & #i4 ,let !m be remov$ f ! v]tical 9 a direction at "r angles to ! plane ( ! pap]1 s t ! ?reads %all be 9 ! same plane1 & !re=e ! ?ree p5dulums w h ! same angle ( vibration4 ,be+ n[ lib]at$1 ! p5dulum ,a w imm$iately ga9 ^u ,b1 & ,b ^u ,c1 s t ,a w h complet$ "o vibration be=e ,b or ,c4 ,at ! end ( ! second vibration ( ,a1 ! p5dulum ,b w h arriv$ at ! end ( its fir/ vibration1 s t ! susp5d+ ?reads ( ,a & ,b w !n be sep>at$ by ! :ole angle ( vibration2 at ! end ( ! f\r? vibration ( ,a ! susp5d+ ?reads ( ,a & ,b w return to _! fir/ position1 ,b hav+ complet$ two vibrations2 ?us ! proportion ( ! times ( vibration ( ,b & ,a w be #b to #a1 ! proportion ( _! l5g?s be+ #d to #a4 ,at ! end ( ! ?ird vibration ( ,a1 ,c w h complet$ "o vibration1 & ! susp5d+ /r+s w co9cide 9 ! position di/ant by ! :ole angle ( vibration f _! fir/ position4 ,s t ?ree vibrations ( ,a are p]=m$ 9 ! same "t z "o ( ,c3 ! proportion ( ! "t ( vibration ( ,c & ,a are1 !re=e1 #c to #a1 ! proportion ( _! l5g?s be+ #i to #a1 con=mably to ! law already expla9$4 7#bab47 ,9 all ! prec$+ obs]vations we h assum$ t ! mat]ial ( ! p5dul\s body is ( inconsid]able magnitude1 its :ole weight be+ conceiv$ to be collect$ 9 a physical po9t4 ,?is is g5]ally call$ a simple p5dulum2 b s9ce ! conditions ( a susp5d+ ?read )\t weight1 & a heavy molecule )\t magnitude1 _c h practical exi/5ce1 ! simple p5dulum mu/ be consid]$ z imag9>y1 & m]ely us$ to e/abli% hypo!tical !orems1 :i*1 ?\gh inapplicable 9 practice1 are nev]!less ! means ( inve/igat+ ! laws :i* gov]n ! real ph5om5a ( p5dul\s bodies4 ,a p5dul\s body be+ ( det]m9ate magnitude1 its sev]al p>ts w be situat$ at diff]5t di/ances f ! axis ( susp5sion4 ,if ea* compon5t "p ( su* a body 7 sep>ately connect$ ) ! axis ( susp5sion by a f9e ?read1 x w\ld1 be+ unconnect$ ) ! o!r p>ticles1 be an indep5d5t simple p5dulum1 & w\ld oscillate accord+ to ! laws already expla9$4 ,x !re=e foll[s t ^? p>ticles ( ! body :i* are ne>e/ to ! axis ( susp5sion w\ld1 if lib]at$ f _! connection ) ! o!rs1 vibrate m rapidly ?an ^? :i* are m remote4 ,! connection1 h[ev]1 :i* ! p>ticles ( ! body h1 by reason ( _! solidity1 compels !m all to vibrate 9 ! same "t4 ,consequ5tly1 ^? p>ticles :i* are ne>] ! axis are ret>d$ by ! sl[] motion ( ^? :i* are m remote2 :ile ! m remote p>ticles1 on ! o!r h&1 are urg$ =w>d by ! great] t5d5cy ( ! ne>] p>ticles to rapid vibration4 ,?is w be m readily compreh5d$1 if we conceive two p>ticles ( matt] ,a & ,b1 fig4 #ge41 to be connect$ ) ! same axis ,o by an inflexible wire ,o ,c1 ! weight ( :i* may be neglect$4 ,if ,b 7 remov$1 ,a w\ld vibrate 9 a c]ta9 "t dep5d+ ^u ! di/ance ,o ,a4 ,if ,a 7 remov$1 & ,b plac$ ^u ! wire at a di/ance ,b ,o equal to f\r times ,a ,o1 ,b w\ld vibrate 9 twice ! =m] "t4 ,n[ if bo? be plac$ on ! wire at ! di/ances j m5tion$1 ! t5d5cy ( ,a to vibrate m rapidly w be transmitt$ to ,b by means ( ! wire1 & w urge ,b =w>d m quickly ?an if ,a 7 n pres5t3 on ! o!r h&1 ! t5d5cy ( ,b to vibrate m sl[ly w be transmitt$ by ! wire to ,a1 & w cause x to move m sl[ly ?an if ,b 7 n pres5t4 ,! inflexible quality ( ! connect+ wire w 9 ?is case compel ,a & ,b to vibrate simultane\sly1 ! "t ( vibration be+ great] ?an t ( ,a1 & less ?an t ( ,b1 if ea* vibrat$ unconnect$ ) ! o!r4 ,if1 in/ead ( suppos+ two p>ticles ( matt] plac$ on ! wire1 a great] numb] 7 suppos$ to be plac$ at v>i\s di/ances f ,o1 x is evid5t ! same reason+ w\ld be applicable4 ,!y w\ld mutually affect ea* o!r's motion2 ^? plac$ ne>e/ to po9t ,o accel]at+ ! motion ( ^? m remote1 & be+ !mselves ret>d$ by ! latt]4 ,among ^! p>ticles "o w\ld be f\nd 9 :i* all ^! effects w\ld be mutually neutralis$1 all ! p>ticles ne>] ,o be+ ret>d$ 9 ref]5ce to t motion :i* !y w\ld h if unconnect$ ) ! re/1 & ^? m remote be+ 9 ! same respect accel]at$4 ,! po9t at :i* su* a p>ticle is plac$ is call$ ! c5tre ( oscillation4 ,:at has be5 "h obs]v$ ( ! effects ( p>ticles ( matt] plac$ ^u rigid wire w be equally applicable to ! p>ticles ( a solid body4 ,^? :i* are ne>] to ! axis are urg$ =w>d by ^? :i* are m remote1 & are 9 _! turn ret>d$ by !m2 & z ) ! p>ticles plac$ ^u ! wire1 !re is a c]ta9 p>ticle ( ! body at :i* ! effects are mutually neutralis$1 & :i* vibrates 9 ! same "t z x w\ld if x 7 unconnect$ ) ! o!r p>ts ( ! body1 & simply connect$ by a f9e ?read to ! axis4 ,by ?is c5tre ( oscillation ! calculations respect+ ! vibration ( a solid body are r5d]$ z simple z ^? ( a molecule ( inconsid]able magnitude4 ,all ! prop]ties :i* h be5 expla9$ z belong+ to a simple p5dulum may ?us be transf]r$ to a vibrat+ body ( any magnitude & figure1 by consid]+ x z equival5t to a s+le p>ticle ( matt] vibrat+ at its c5tre ( oscillation4 7#bac47 ,x foll[s f ?is reason+1 t ! virtual l5g? ( a p5dulum is to be e/imat$ by ! di/ance ( its c5tre ( oscillation f ! axis ( susp5sion1 & !re=e t ! times ( vibration ( diff]5t p5dulums are 9 ! same proportion z ! squ>e roots ( ! di/ances ( _! c5tres ( oscillation f _! axes4 ,! inve/igation ( ! position ( ! c5tre ( oscillation is1 9 mo/ cases1 a subject ( intricate ma!matical calculation4 ,x dep5ds on ! magnitude & figure ( ! p5dul\s body1 ! mann] 9 :i* ! mass is di/ribut$ ?r\gh its volume1 or ! d5sity ( its sev]al p>ts1 & ! position ( ! axis on :i* x sw+s4 ,! place ( ! c5tre ( oscillation may be det]m9$ :5 ! position ( ! c5tre ( gravity & ! c5tre ( gyration are kn[n2 = ! di/ance ( ! c5tre ( oscillation f ! axis w always be obta9$ by divid+ ! squ>e ( ! radius ( gyration 7#ahf47 by ! di/ance ( ! c5tre ( gravity f ! axis4 ,?us if #f be ! radius ( gyration1 & #i ! di/ance ( gravity f ! axis1 #cf divid$ by #i1 :i* is #d1 w be ! di/ance ( ! c5tre ( oscillation f ! axis4 ,h5ce x may be inf]r$ g5]ally1 t ! great] ! proportion :i* ! radius ( gyration be>s to ! di/ance ( ! c5tre ( gravity f ! axis1 ! great] w be ! di/ance ( ! c5tre ( oscillation4 ,x foll[s f ?is reason+1 t ! l5g? ( a p5dulum is n limit$ by ! dim5sions ( its volume4 ,if ! axis be s plac$ t ! c5tre ( gravity is ne> x1 & ! c5tre ( gyration comp>atively remov$ f x1 ! c5tre ( oscillation may be plac$ f> beyond ! limits ( ! p5dul\s body4 ,suppose ! c5tre ( gravity is at a di/ance ( "o in* f ! axis1 & ! c5tre ( gyration #ab in*es1 ! c5tre ( oscillation w !n be at ! di/ance ( #add in*es1 or #ab feet4 ,su* a p5dulum may n 9 its greate/ dim5sions exce$ "o foot1 & yet its "t ( vibration w\ld be equal to t ( a simple p5dulum ^: l5g? is #ab feet4 ,by ^! means p5dulums ( small dim5sions may be made to vibrate z sl[ly z may be desir$4 ,! in/rum5ts call$ metronomes1 us$ = m>k+ ! "t ( musical p]=mances1 are con/ruct$ on ?is pr9ciple4 7#bad47 ,! c5tre ( oscillation is di/+ui%$ by a v rem>kable prop]ty 9 relation to ! axis ( susp5sion4 ,if ,a1 fig4 #gf41 be ! po9t ( susp5sion1 & ,o ! correspond+ c5tre ( oscillation1 ! "t ( vibration ( ! p5dulum w n be *ang$ if x be rais$ f its support1 inv]t$1 & susp5d$ f ! po9t ,o4 ,x foll[s1 !re=e1 t if ,o be tak5 z ! po9t ( susp5sion1 ,a w be ! correspond+ c5tre ( oscillation4 ,^! two po9ts are1 !re=e1 conv]tible4 ,?is prop]ty may be v]ifi$ exp]im5tally 9 ! foll[+ mann]4 ,a p5dulum be+ put into a /ate ( vibration1 let a small heavy body be susp5d$ by a f9e ?read1 ! l5g? ( :i* is s adju/$ t x vibrates simultane\sly ) ! p5dulum4 ,let ! di/ance f ! po9t ( susp5sion to ! c5tre ( ! vibrat+ body be measur$1 & take ?is di/ance on ! p5dulum f ! axis ( susp5sion d[nw>ds2 ! place ( ! c5tre ( oscillation w ?us be obta9$1 s9ce ! di/ance s measur$ f ! axis is ! l5g? ( ! equival5t simple p5dulum4 ,if ! p5dulum be n[ rais$ f its support1 inv]t$1 & susp5d$ f ! c5tre ( oscillation ?us obta9$1 x w be f\nd to vibrate simultane\sly ) ! body susp5d$ by ! ?read4 7#bae47 ,?is prop]ty ( ! int]*angeable nature ( ! c5tres ( oscillation & susp5sion has be51 at a late p]iod1 adopt$ by ,capta9 ,kat]1 z an accurate means ( det]m9+ ! l5g? ( a p5dulum4 ,hav+ asc]ta9$ ) great accuracy two po9ts ( susp5sion at :i* ! same body w vibrate 9 ! same "t1 ! di/ance betwe5 ^! po9ts be+ accurately measur$1 is ! l5g? ( ! equival5t simple p5dulum4 ,see ,*apt] ,,xxi4 7#baf47 ,! mann] 9 :i* ! "t ( vibration ( a p5dulum dep5ds on its l5g? be+ expla9$1 we are next to consid] h[ ?is "t is affect$ by ! attraction ( gravity4 ,x is obvi\s t1 s9ce ! p5dulum is mov$ by ?is attraction1 ! rapidity ( its motion w be increas$1 if ! impell+ =ce receive any augm5tation2 b x /ill is to be decid$1 9 :at exact proportion ! "t ( oscillation w be dim9i%$ by any propos$ increase 9 ! int5sity ( ! e>?'s attraction4 ,x c be demon/rat$ ma!matically1 t ! "t ( "o vibration ( a p5dulum has ! same proportion to ! "t ( fall+ freely 9 ! p]p5dicul> direction1 ?r\gh a height equal to half ! l5g? ( ! p5dulum1 z ! circumf]5ce ( a circle has to its diamet]4 ,s9ce1 !re=e1 ! times ( vibration ( p5dulums are 9 a fix$ proportion to ! times ( fall+ freely ?r\gh spaces equal to ! halves ( _! l5g?s1 x foll[s t ^! times h ! same relation to ! =ce ( attraction z ! times ( fall+ freely ?r\gh _! l5g?s h to t =ce4 ,if ! int5sity ( ! =ce ( gravity 7 increas$ 9 a f\r-fold proportion1 ! "t ( fall+ ?r\gh a giv5 height w\ld be dim9i%$ 9 a two-fold proportion2 if ! int5sity 7 increas$ to a n9e-fold proportion1 ! "t ( fall+ ?r\gh a giv5 space w\ld be dim9i%$ 9 a ?ree-fold proportion1 & s on2 ! rate ( dim9ution ( ! "t be+ always z ! squ>e root ( ! increas$ =ce4 ,by :at has be5 j /at$ ?is law w also be applicable to ! vibration ( p5dulums4 ,any increase 9 ! int5sity ( ! =ce ( gravity w\ld cause a giv5 p5dulum to vibrate m rapidly1 & ! increas$ rapidity ( ! vibration w\ld be 9 ! same proportion z ! squ>e root ( ! increas$ int5sity ( ! =ce ( gravity4 7#bag47 ,! laws :i* regulate ! times ( vibration ( p5dulums 9 relation to "o ano!r be+ well und]/ood1 ! :ole !ory ( ^! in/rum5ts w be complet$1 :5 ! me?od ( asc]ta9+ ! actual "t ( vibration ( any p5dulum1 9 ref]5ce to its l5g?1 has be5 expla9$4 ,9 su* an inve/igation1 ! two elem5ts to be det]m9$ are1 #a4 ! exact "t ( a s+le vibration1 &1 #b4 ! exact di/ance ( ! c5tre ( oscillation f ! po9t ( susp5sion4 ,! =m] is asc]ta9$ by putt+ a p5dulum 9 motion 9 ! pres5ce ( a good *ronomet]1 & obs]v+ precisely ! numb] ( oscillations :i* are made 9 any propos$ numb] ( h\rs4 ,! entire "t dur+ :i* ! p5dulum sw+s1 be+ divid$ by ! numb] ( oscillations made dur+ t "t1 ! exact "t ( "o oscillation w be obta9$4 ,! di/ance ( ! c5tre ( oscillation f ! po9t ( susp5sion may be r5d]$ a matt] ( easy calculation1 by giv+ a c]ta9 uni=m figure & mat]ial to ! p5dul\s body4 7#bah47 ,! "t ( vibration ( "o p5dulum ( kn[n l5g? be+ ?us obta9$1 we %all be enabl$ imm$iately to solve ei!r ( ! foll[+ problems4 8,to f9d ! l5g? ( a p5dulum :i* %all vibrate 9 a giv5 "t40 8,to f9d ! "t ( vibration ( a p5dulum ( a giv5 l5g?40 ,! =m] is solv$ z foll[s3 ! "t ( vibration ( ! kn[n p5dulum is to ! "t ( vibration ( ! requir$ p5dulum1 z ! squ>e root ( ! l5g? ( ! kn[n p5dulum is to ! squ>e root ( ! l5g? ( ! requir$ p5dulum4 ,?is l5g? is !re=e f\nd by ! ord9>y rules ( ari?metic4 ,! latt] may be solv$ z foll[s3 ! l5g? ( ! kn[n p5dulum is to ! l5g? ( ! propos$ p5dulum1 z ! squ>e ( ! "t ( vibration ( ! kn[n p5dulum is to ! squ>e ( ! "t ( vibration ( ! propos$ p5dulum4 ,! latt] "t may !re=e be f\nd by ari?metic4 7#bai47 ,s9ce ! rate ( a p5dulum has a kn[n relation to ! int5sity ( ! e>?'s attraction1 we are enabl$1 by ?is in/rum5t1 n only to detect c]ta9 v>iations 9 t attraction 9 v>i\s p>ts ( ! e>?1 b also to discov] ! actual am\nt ( ! attraction at any giv5 place4 ,! actual am\nt ( ! e>?'s attraction at any giv5 place is e/imat$ by ! height ?r\gh :i* a body w\ld fall freely at t place 9 any giv5 "t1 z 9 "o second4 ,to det]m9e ?is1 let ! l5g? ( a p5dulum :i* w\ld vibrate 9 "o second at t place be f\nd4 ,z ! circumf]5ce ( a circle is to its diamet]#b 7a kn[n proportion71 s w "o second be to ! "t ( fall+ ?r\gh a height equal to half ! l5g? ( ?is p5dulum4 ,?is "t is !re=e a matt] ( ari?metical calculation4 ,x has be5 prov$ 9 7#abj471 t ! heights1 ?r\gh :i* a body falls freely1 are 9 ! same proportion z ! squ>es ( ! times2 f :5ce x foll[s1 t ! squ>e ( ! "t ( fall+ ?r\gh a height equal to half ! l5g? ( ! p5dulum is to "o second z half ! l5g? ( t p5dulum is to ! height ?r\gh :i* a body w\ld fall 9 "o second4 ,?is height1 !re=e1 may be imm$iately comput$1 & ?us ! actual am\nt ( ! =ce ( gravity at any giv5 place may be asc]ta9$4 #b ,?is ratio is t ( #ca1daf to #aj1jjj v ne>ly4 7#bbj47 ,to comp>e ! =ce ( gravity 9 diff]5t p>ts ( ! e>?1 x is only necess>y to sw+ ! same p5dulum 9 ! places "u consid]ation1 & to obs]ve ! rapidity ( its vibrations4 ,! proportion ( ! =ce ( gravity 9 ! sev]al places w be t ( ! squ>es ( ! velocity ( ! vibration4 ,obs]vations to ?is effect h be5 made at sev]al places1 by ,biot1 ,kat]1 ,sab9e1 & o!rs4 ,! e>? be+ a mass ( matt] ( a =m ne>ly sph]ical1 revolv+ ) consid]able velocity on an axis1 its compon5t p>ts are affect$ by a c5trifugal =ce2 9 virtue ( :i*1 !y h a t5d5cy to fly (f 9 a direction p]p5dicul> to ! axis4 ,?is t5d5cy increases 9 ! same proportion z ! di/ance ( any "p f ! axis increases1 & consequ5tly ^? p>ts ( ! e>? :i* are ne> ! equator1 are m /rongly affect$ by ?is influ5ce ?an ^? ne> ! pole4 ,x has be5 already expla9$ 7#ade47 t ! figure ( ! e>? is affect$ by ?is cause1 & t x has acquir$ a sph]oidal =m4 ,! c5trifugal =ce1 act+ 9 opposition to ! e>?'s attraction1 dim9i%es its effects2 & consequ5tly1 :]e ?is =ce is m effici5t1 a p5dulum w vibrate m sl[ly4 ,by ^! means ! rate ( vibration ( a p5dulum becomes an indication ( ! am\nt ( ! c5trifugal =ce4 ,b ?is latt] v>ies 9 proportion to ! di/ance ( ! place f ! e>?'s axis2 & ?us ! rate ( a p5dulum indicates ! relation ( ! di/ances ( diff]5t p>ts ( ! e>?'s surface f its axis4 ,! figure ( ! e>? may be ?us asc]ta9$1 & t :i* !ory assigns to x1 x may be practically prov$ to h4 ,?is1 h[ev]1 is n ! only me?od by :i* ! figure ( ! e>? may be det]m9$4 ,! m]idians be+ sections ( ! e>? ?r\gh its axis1 if _! figure 7 exactly det]m9$1 t ( ! e>? w\ld be kn[n4 ,measurem5ts ( arcs ( m]idians on a l>ge scale h be5 execut$1 & are /ill be+ made 9 v>i\s p>ts ( ! e>?1 ) a view to det]m9e ! curvature ( a m]idian at diff]5t latitudes4 ,?is me?od is indep5d5t ( e hypo!sis conc]n+ ! d5sity & int]nal /ructure ( ! e>?1 & is consid]$ by "s to be susceptible ( m accuracy ?an t :i* dep5ds on ! obs]vations ( p5dulums4 7#bba47 ,x has be5 /at$ t1 :5 ! arc ( vibration ( a p5dulum is n v small1 a v>iation 9 its l5g? w produce a s5sible effect on ! "t ( vibration4 ,to con/ruct a p5dulum su* t ! "t ( vibration may be indep5d5t ( ! ext5t ( ! sw+1 0 a fav\rite speculation ( geomet]s4 ,?is problem 0 solv$ by ,huyg5s1 :o %[$ t ! curve call$ a cycloid1 previ\sly discov]$ & describ$ by ,galileo1 possess$ ! iso*ronal prop]ty2 t is1 t a body mov+ 9 x by ! =ce ( gravity1 w\ld vibrate 9 ! same "t1 :atev] be ! l5g? ( ! arc describ$4 ,let ,o ,a1 fig4 #gg41 be a horizontal l9e1 & let ,o ,b be a circle plac$ bel[ ?is l9e1 & 9 contact ) x4 ,if ?is circle be roll$ ^u ! l9e f ,o t[>ds ,a1 a po9t ^u its circumf]5ce1 :i* at ! beg9n+ ( ! motion is plac$ at ,o1 w dur+ ! motion trace ! curve ,o ,c ,a4 ,?is curve is call$ a cycloid4 ,if ! circle be suppos$ to roll 9 ! opposite direction t[>ds ,a1 ! same po9t w trace ano!r cycloid ,o ,c ,a4 ,! po9ts ,c & ,c be+ ! l[e/ po9ts ( ! curves1 if ! p]p5dicul>s ,c ,d & ,c ,d be drawn1 !y w respectively be equal to ! diamet] ( ! circle4 ,by a kn[n prop]ty ( ?is curve1 ! arcs ,o ,c & ,o ,c are equal to twice ! diamet] ( ! circle4 ,f ! po9t ,o suppose a flexible ?read to be susp5d$1 ^: l5g? is twice ! diamet] ( ! circle1 & :i* su/a9s a p5dul\s body ,p at its extremity4 ,if ! curves ,o ,c & ,o ,c1 f ! plane ( ! pap]1 be rais$ s z to =m surfaces to :i* ! ?read may be appli$1 ! extremity ,p w ext5d to ! po9ts ,c & ,c1 :5 ! entire ?read has be5 appli$ to ei!r ( ! curves4 ,z ! ?read is deflect$ on ei!r side ( its v]tical position1 x is appli$ to a great] or less] portion ( ei!r curve1 accord+ to ! quantity ( its deflection f ! v]tical4 ,if x be deflect$ on ea* side until ! po9t ,p rea*es ! po9ts ,c & ,c1 ! extremity w\ld trace a cycloid ,c ,p ,c precisely equal & simil> to ^? already m5tion$4 ,avail+ himself ( ?is prop]ty ( ! curve1 ,huyg5s con/ruct$ 8 cycloidal p5dulum4 ,! "t ( vibration 0 subject to no v>iation1 h[ev] ! arc ( vibration might *ange1 provid$ only t ! l5g? ( ! /r+ ,o ,p cont9u$ ! same4 ,if small arcs ( ! cycloid be tak5 on ei!r side ( ! po9t ,p1 !y w n s5sibly diff] f arcs ( a circle describ$ ) ! c5tre ,o & ! radius ,o ,p2 =1 9 slight deflections f ! v]tical position1 ! effect ( ! curves ,o ,c & ,o ,c on ! ?read ,o ,p is altoge!r inconsid]able4 ,x is = ?is reason t :5 ! arcs ( vibration ( a circul> p5dulum are small1 !y p>take ( ! prop]ty ( iso*ronism peculi> to ^? ( a cycloid4 ,b :5 ! deflection ( ,p f ! v]tical is great1 ! effect ( ! curves ,o ,c & ,o ,c on ! ?read produces a consid]able deviation ( ! po9t ,p f ! arc ( ! circle ^: c5tre is ,o & ^: radius is ,o ,p1 & consequ5tly ! prop]ty ( iso*ronism w no long] be obs]v$ 9 ! circul> p5dulum4 ,,*ap4 ,,xii4 ,,( ,,simple ,,ma*9es4 7#bbb47 ,a ,,ma*9e is an in/rum5t by :i* =ce or motion may be transmitt$ & modifi$ z to its quantity & direction4 ,!re are two ways 9 :i* a ma*9e may be appli$1 & :i* give rise to a division ( me*anical sci5ce into p>ts d5om9at$ ,,/atics & ,,dynamics2 ! "o includ+ ! !ory ( equilibrium1 & ! o!r ! !ory ( motion4 ,:5 a ma*9e is consid]$ /atically1 x is view$ z an in/rum5t by :i* =ces ( det]m9ate quantities & direction are made to balance o!r =ces ( o!r quantities & o!r directions4 ,if x be view$ dynamically1 x is consid]$ z a means by :i* c]ta9 motions ( det]m9ate quantity & direction may be made to produce o!r motions 9 o!r directions & quantities4 ,x w n be conv5i5t1 h[ev]1 9 ! pres5t treatise1 to foll[ ?is division ( ! subject4 ,we %all1 on ! o!r h&1 z hi!rto1 consid] ! ph5om5a ( equilibrium & motion toge!r4 ,! effects ( ma*9]y are too frequ5tly describ$ 9 su* a mann] z to inve/ !m ) ! appe>ance ( p>adox1 & to excite a/oni%m5t at :at appe>s to contradict ! results ( ! mo/ common exp]i5ce4 ,x w be our object "h to take a diff]5t c\rse1 & to attempt to %[ t ^? effects :i* h be5 held up z matt]s ( a/oni%m5t are ! necess>y1 natural1 & obvi\s results ( causes adapt$ to produce !m 9 a mann] analog\s to ! objects ( mo/ famili> exp]i5ce4 7#bbc47 ,9 ! application ( a ma*9e !re are ?ree ?+s to be consid]$4 #a4 ,! =ce or resi/ance :i* is requir$ to be su/a9$1 oppos$1 or ov]come4 #b4 ,! =ce :i* is us$ to su/a91 support1 or ov]come t resi/ance4 #c4 ,! ma*9e itself by :i* ! effect ( ?is latt] =ce is transmitt$ to ! =m]4 ,( :atev] nature be ! =ce or ! resi/ance :i* is to be su/a9$ or ov]come1 x is te*nically call$ ! weight1 s9ce1 :atev] x be1 a weight ( equival5t effect may always be f\nd4 ,! =ce :i* is employ$ to su/a9 or ov]come x is te*nically call$ ! p[]4 7#bbd47 ,9 express+ ! effect ( ma*9]y x is usual to say t ! p[] su/a9s ! weight2 b ?is1 9 fact1 is n ! case1 & h5ce arises t appe>ance ( p>adox :i* has already be5 allud$ to4 ,if1 = example1 x is said t a p[] ( "o ounce su/a9s ! weight ( "o ton1 a/oni%m5t is n unnaturally excit$1 because ! fact1 z ?us /at$1 if ! t]ms be lit]ally int]pret$1 is physically impossible4 ,no p[] less ?an a ton c1 9 ! ord9>y acceptation ( ! ^w1 support ! weight ( a ton4 ,x w1 h[ev]1 be ask$ h[ x happ5s t a ma*9e appe>s to d ?is8 h[ x happ5s t by hold+ a silk5 ?read1 :i* an ounce weight w\ld snap1 _m hundr$ weight may be su/a9$8 ,to expla9 ?is x w only be necess>y to consid] ! effect ( a ma*9e1 :5 ! p[] & weight are 9 equilibrium4 7#bbe47 ,9 e ma*9e !re are "s fix$ po9ts or props2 & ! arrangem5t ( ! p>ts is always su*1 t ! pressure1 excit$ by ! p[] or weight1 or bo?1 is di/ribut$ among ^! props4 ,if ! weight am\nt to tw5ty hundr$1 x is possible s to di/ribute x1 t any proportion1 h[ev] great1 ( x may be ?r[n on ! fix$ po9ts or props ( ! ma*9e2 ! rema9+ "p only c prop]ly be said to be support$ by ! p[]1 & ?is "p c nev] be great] ?an ! p[]4 ,consid]+ ! effect 9 ?is way1 x appe>s t ! p[] supports j s mu* ( ! weight & no m z is equal to its own =ce1 & t all ! rema9+ "p ( ! weight is su/a9$ by ! ma*9e4 ,! =ce ( ^! obs]vations w be m app>5t :5 ! nature & prop]ties ( ! me*anic p[]s & o!r ma*9es h be5 expla9$4 7#bbf47 ,:5 a ma*9e is consid]$ dynamically1 its effects are expla9$ on diff]5t pr9ciples4 ,x is true t1 9 ?is case1 a v small p[] may elevate a v great weight2 b nev]!less1 9 s do+1 :atev] be ! ma*9e us$1 ! total exp5diture ( p[]1 9 rais+ ! weight ?r\gh any height1 is nev] less ?an t :i* w\ld be exp5d$ if ! p[] 7 imm$iately appli$ to ! weight )\t ! int]v5tion ( any ma*9e4 ,?is circum/ance arises f an univ]sal prop]ty ( ma*9es by :i* ! velocity ( ! weight is always less ?an t ( ! p[]1 9 exactly ! same proportion z ! p[] itself is less ?an ! weight2 s t :5 a c]ta9 p[] is appli$ to elevate a weight1 ! rate at :i* ! elevation is effect$ is always sl[ 9 ! same proportion z ! weight is great4 ,f a due consid]ation ( ?is rem>kable law1 x w easily be und]/ood1 t a ma*9e c nev] dim9i% ! total exp5diture ( p[] necess>y to raise any weight or to ov]come any resi/ance4 ,9 su* cases1 all t a ma*9e ev] does or ev] c d1 is to enable ! p[] to be exp5d$ at a sl[ rate1 & 9 a m advantage\s direction ?an if x 7 imm$iately appli$ to ! weight or ! resi/ance4 ,let u suppose t ,p is a p[] am\nt+ to an ounce1 & t ,w is a weight am\nt+ to #ej ounces1 & t ,p elevates ,w by means ( a ma*9e4 ,9 virtue ( ! prop]ty already /at$1 x foll[s1 t :ile ,p moves ?r\gh #ej feet1 ,w w be mov$ ?r\gh #a foot2 b 9 mov+ ,p ?r\gh #ej feet1 #ej di/9ct ef=ts are made1 by ea* ( :i* #a ounce is mov$ ?r\gh #a foot1 & by :i* collectively #ej di/9ct ounces might be successively rais$ ?r\gh #a foot4 ,b ! weight ,w is #ej ounces1 & has be5 rais$ ?r\gh #a foot2 f :5ce x appe>s1 t ! exp5diture ( p[] is equal to t :i* w\ld be necess>y to raise ! weight )\t ! int]v5tion ( any ma*9e4 ,?is important pr9ciple may be pres5t$ "u ano!r aspect1 :i* w p]haps r5d] x m app>5t4 ,suppose ! weight ,w 7 actually divid$ into #ej equal p>ts1 or suppose x 7 a vessel ( liquid weigh+ #ej ounces1 & conta9+ #ej equal measures2 if ^! #ej measures 7 successively lift$ ?r\gh a height ( #a foot2 ! ef=ts necess>y to accompli% ?is w\ld be ! same z ^? us$ to move ! p[] ,p ?r\gh #ej feet1 & x is obvi\s1 t ! total exp5diture ( =ce w\ld be ! same z t :i* w\ld be necess>y to lift ! entire cont5ts ( ! vessel ?r\gh #a foot4 ,:5 ! nature & prop]ties ( ! me*anic p[]s & o!r ma*9es h be5 expla9$1 ! =ce ( ^! obs]vations w be m di/9ctly p]ceiv$4 ,! effects ( props & fix$ po9ts 9 su/a9+ a "p ( ! weight1 & sometimes ! :ole1 bo? ( ! weight & p[]1 w !n be manife/1 & e ma*9e w furni% a v]ification ( ! rem>kable proportion betwe5 ! velocities ( ! weight & p[]1 :i* has enabl$ u to expla9 :at might o!rwise be p>adoxical & difficult ( compreh5sion4 7#bbg47 ,! mo/ simple species ( ma*9es are ^? :i* are commonly d5om9at$ ! ,,me*anic ,,p[]s4 ,^! h be5 diff]5tly enum]at$ by diff]5t writ]s4 ,if1 h[ev]1 ! object be to arrange 9 di/9ct classes1 & 9 ! smalle/ possible numb] ( !m1 ^? ma*9es :i* are alike 9 pr9ciple1 ! me*anic p[]s may be r$uc$ to ?ree4 #a4 ,! lev]4 #b4 ,! cord4 #c4 ,! incl9$ plane4 ,to "o or o!r ( ^! classes all simple ma*9es :atev] may be r$uc$1 & all complex ma*9es may be resolv$ into simple elem5ts :i* come "u !m4 7#bbh47 ,! fir/ class includes e ma*9e :i* is compos$ ( a solid body revolv+ on a fix$ axis1 al?\gh ! "n lev] has be5 commonly conf9$ to cases :]e ! ma*9e affects c]ta9 p>ticul> =ms4 ,?is is by f> ! mo/ useful class ( ma*9es1 & w require 9 subsequ5t *apt]s v detail$ developm5t4 ,! g5]al pr9ciple1 ^u :i* equilibrium is e/abli%$ betwe5 ! p[] & weight 9 ma*9es ( ?is class has be5 already expla9$ 9 7#ahc47 ,! p[] & weight are always suppos$ to be appli$ 9 directions at "r angles to ! axis4 ,if l9es be drawn f ! axis p]p5dicul> to ! directions ( p[] & weight1 equilibrium w subsi/1 provid$ ! p[] multipli$ by ! p]p5dicul> di/ance ( its direction f ! axis1 be equal to ! weight multipli$ by ! p]p5dicul> di/ance ( its direction f ! axis4 ,?is is a pr9ciple to :i* we %all h occasion to ref] 9 expla9+ ! v>i\s ma*9es ( ?is class4 7#bbi47 ,if ! mom5t ( ! p[] 7#ahd47 be great] ?an t ( ! weight1 ! effect ( ! p[] w prevail ov] t ( ! weight1 & elevate x2 b if1 on ! o!r h&1 ! mom5t ( ! p[] be less ?an t ( ! weight1 ! p[] w be insuffici5t to support ! weight1 & w all[ x to fall4 7#bcj47 ,! second class ( simple ma*9es includes all ^? cases 9 :i* =ce is transmitt$ by means ( flexible ?reads1 ropes1 or *a9s4 ,! pr9ciple1 by :i* ! effects ( ^! ma*9es are e/imat$1 is1 t ! t5sion ?r\gh\t ! :ole l5g? ( ! same cord1 provid$ x be p]fectly flexible1 & free f ! effects ( friction1 mu/ be ! same4 ,?us1 if a =ce act+ at "o end be balanc$ by a =ce act+ at ! o!r end1 h[ev] ! cord may be b5t1 or :atev] c\rse x may be compell$ to take1 by any causes :i* may affect x betwe5 its ends1 ^! =ces mu/ be equal1 provid$ ! cord be free to move ov] any ob/acles :i* may deflect x4 ,)9 ?is class ( ma*9es are includ$ all ! v>i\s =ms ( pulleys4 7#bca47 ,! ?ird class ( simple ma*9es includes all ^? cases 9 :i* ! weight or resi/ance is support$ or mov$ on a h>d surface incl9$ to ! v]tical direction4 ,! effects ( su* ma*9es are e/imat$ by resolv+ ! :ole weight ( ! body into two elem5ts by ! p>allelogram ( =ces4 ,"o ( ^! elem5ts is p]p5dicul> to ! surface1 & support$ by its resi/ance2 ! o!r is p>allel to ! surface1 & support$ by ! p[]4 ,! proportion1 !re=e1 ( ! p[] to ! weight w always dep5d on ! obliquity ( ! surface to ! direction ( ! weight4 ,?is w be easily und]/ood by ref]r+ to :at has be5 already expla9$ 9 ,*apt] ,,viii4 ,"u ?is class ( ma*9es come ! incl9$ plane1 commonly s call$1 ! w$ge1 ! screw1 & v>i\s o!rs4 7#bcb47 ,9 ord] to simplify ! developm5t ( ! elem5t>y !ory ( ma*9es1 x is exp$i5t to omit ! consid]ation ( _m circum/ances1 ( :i*1 h[ev]1 a /rict acc\nt mu/ be tak5 be=e any practically useful application ( t !ory c be attempt$4 ,a ma*9e1 z we mu/ = ! pres5t contemplate x1 is a ?+ :i* c h no real or practical exi/5ce4 ,its v>i\s p>ts are consid]$ to be free f friction3 all surfaces :i* move 9 contact are suppos$ to be inf9itely smoo? & poli%$4 ,! solid p>ts are conceiv$ to be absolutely inflexible4 ,! weight & in]tia ( ! ma*9e itself are :olly neglect$1 & we reason ^u x z if x 7 dive/$ ( ^! qualities4 ,cords & ropes are suppos$ to h no /iffness1 to be inf9itely flexible4 ,! ma*9e1 :5 x moves1 is suppos$ to suff] no resi/ance f ! atmosph]e1 & to be 9 all respects circum/anc$ z if x 7 9 vacuo4 ,x is sc>cely necess>y to /ate1 t1 all ^! suppositions be+ false1 none ( ! consequ5ces d$uc$ f !m c be true4 ,nev]!less1 z x is ! bus9ess ( art to br+ ma*9es z ne> to ?is /ate ( ideal p]fection z possible1 ! conclusions :i* are ?us obta9$1 ?\gh false 9 a /rict s5se1 yet deviate f ! tru? 9 b a small degree4 ,l ! fir/ outl9e ( a picture1 !y resemble 9 _! g5]al features t tru? to :i*1 aft] _m subsequ5t corrections1 !y mu/ f9ally approximate4 ,aft] a fir/ approximation has be5 made on ! sev]al false suppositions :i* h be5 m5tion$1 v>i\s effects1 :i* h be5 previ\sly neglect$1 are successively tak5 into acc\nt4 ,r\ghness1 rigidity1 imp]fect flexibility1 ! resi/ance ( air & o!r fluids1 ! effects ( ! weight & in]tia ( ! ma*9e1 are sev]ally exam9$1 & _! laws & prop]ties detect$4 ,! modifications & corrections1 ?us sugge/$ z necess>y to be introduc$ into our =m] conclusions1 are appli$1 & a second approximation1 b /ill only an approximation1 to tru? is made4 ,=1 9 inve/igat+ ! laws :i* regulate ! sev]al effects j m5tion$1 we are compell$ to proce$ ^u a new gr\p ( false suppositions4 ,to det]m9e ! laws :i* regulate ! friction ( surfaces1 x is necess>y to assume t e "p ( ! surfaces ( contact are uni=mly r\gh2 t ! solid p>ts :i* are imp]fectly rigid1 & ! cords :i* are imp]fectly flexible1 are con/itut$ ?r\gh\t _! entire dim5sions ( a uni=m mat]ial2 s t ! imp]fection does n prevail m 9 "o "p ?an ano!r4 ,?us1 all irregul>ity is left out ( acc\nt1 & a g5]al av]age ( ! effects tak54 ,x is obvi\s1 !re=e1 t by ^! means we h /ill fail$ 9 obta9+ a result exactly con=mable to ! real /ate ( ?+s2 b x is equally obvi\s1 t we h obta9$ "o mu* m con=mable to t /ate ?an _h be5 previ\sly accompli%$1 & suffici5tly ne> x = mo/ practical purposes4 ,?is app>5t imp]fection 9 our in/rum5ts & p[]s ( inve/igation is n peculi> to me*anics3 x p]vades all dep>tm5ts ( natural sci5ce4 ,9 a/ronomy1 ! motions ( ! cele/ial bodies1 & _! v>i\s *anges & appe>ances z develop$ by !ory1 assi/$ by obs]vation & exp]i5ce1 are only approximations to ! real motions & appe>ances :i* take place 9 nature4 ,x is true t ^! approximations are susceptible ( almo/ unlimit$ accuracy2 b /ill !y are1 & ev] w cont9ue to be1 only approximations4 ,optics & all o!r bran*es ( natural sci5ce are liable to ! same obs]vations4 ,,*ap4 ,,xiii4 ,,( ,,! ,,lev]4 7#bcc47 ,an inflexible1 /raight b>1 turn+ on an axis1 is commonly call$ a lev]4 ,! arms ( ! lev] are ^? p>ts ( ! b> :i* ext5d on ea* side ( ! axis4 ,! axis is call$ ! fulcrum or prop4 7#bcd47 ,lev]s are commonly divid$ into ?ree k9ds1 accord+ to ! relative positions ( ! p[]1 ! weight1 & ! fulcrum4 ,9 a lev] ( ! fir/ k9d1 z 9 fig4 #gh41 ! fulcrum is betwe5 ! p[] & weight4 ,9 a lev] ( ! second k9d1 z 9 fig4 #gi41 ! weight is betwe5 ! fulcrum & p[]4 ,9 a lev] ( ! ?ird k9d1 z 9 fig4 #hj41 ! p[] is betwe5 ! fulcrum & weight4 7#bce47 ,9 all ^! cases1 ! p[] w su/a9 ! weight 9 equilibrium1 provid$ its mom5t be equal to t ( ! weight4 7#ahd47 ,b ! mom5t ( ! p[] is1 9 ?is case1 equal to ! product obta9$ by multiply+ ! p[] by its di/ance f ! fulcrum2 & ! mom5t ( ! weight by multiply+ ! weight by its di/ance f ! fulcrum4 ,?us1 if ! numb] ( ounces 9 ,p1 be+ multipli$ by ! numb] ( in*es 9 ,p ,f1 be equal to ! numb] ( ounces 9 ,w1 multipli$ by ! numb] ( in*es 9 ,w ,f1 equilibrium w be e/abli%$4 ,x is evid5t f ?is1 t z ! di/ance ( ! p[] f ! fulcrum increases 9 comp>ison to ! di/ance ( ! weight f ! fulcrum1 9 ! same degree exactly w ! proportion ( ! p[] to ! weight dim9i%4 ,9 o!r words1 ! proportion ( ! p[] to ! weight w be always ! same z t ( _! di/ances f ! fulcrum tak5 9 a rev]se ord]4 ,9 cases :]e a small p[] is requir$ to su/a9 or elevate a great weight1 x w !re=e be necess>y ei!r to remove ! p[] to a great di/ance f ! fulcrum1 or to br+ ! weight v ne> x4 7#bcf47 ,num]\s examples ( lev]s ( ! fir/ k9d may be giv54 ,a cr[-b>1 appli$ to elevate a /one or o!r weight1 is an in/ance4 ,! fulcrum is ano!r /one plac$ ne> t :i* is to be rais$1 & ! p[] is ! h& plac$ at ! o!r end ( ! b>4 ,a h&spike is a simil> example4 ,a pok] appli$ to raise fuel is a lev] ( ! fir/ k9d1 ! fulcrum be+ ! b> ( ! grate4 ,scissors1 %e>s1 nipp]s1 p9c]s1 & o!r simil> in/rum5ts are compos$ ( two lev]s ( ! fir/ k9d2 ! fulcrum be+ ! jo9t or pivot1 & ! weight ! resi/ance ( ! sub/ance to be cut or seiz$2 ! p[] be+ ! f+]s appli$ at ! o!r end ( ! lev]s4 ,! brake ( a pump is a lev] ( ! fir/ k9d2 ! pump-rods & pi/on be+ ! weight to be rais$4 7#bcg47 ,examples ( lev]s ( ! second k9d1 ?\gh n s frequ5t z ^? j m5tion$1 are n uncommon4 ,an o> is a lev] ( ! second k9d4 ,! reaction ( ! wat] aga9/ ! blade is ! fulcrum4 ,! boat is ! weight1 & ! h& ( ! boatman ! p[]4 ,! rudd] ( a %ip or boat is an example ( ?is k9d ( lev]1 & expla9$ 9 a simil> way4 ,! *ipp+ knife is a lev] ( ! second k9d4 ,! end atta*$ to ! b5* is ! fulcrum1 & ! weight ! resi/ance ( ! sub/ance to be cut1 plac$ b5ea? x4 ,a door mov$ ^u its h+es is ano!r example4 ,nut-crack]s are two lev]s ( ! second k9d2 ! h+e :i* unites !m be+ ! fulcrum1 ! resi/ance ( ! %ell plac$ betwe5 !m be+ ! weight1 & ! h& appli$ to ! extremity be+ ! p[]4 ,a :eelb>r[ is a lev] ( ! second k9d2 ! fulcrum be+ ! po9t at :i* ! :eel presses on ! gr\nd1 & ! weight be+ t ( ! b>r[ & its load1 collect$ at _! c5tre ( gravity4 ,! same obs]vation may be appli$ to all two-:eel$ c>riages1 :i* are p>tly su/a9$ by ! animal :i* draws !m4 7#bch47 ,9 a lev] ( ! ?ird k9d1 ! weight1 be+ m di/ant f ! fulcrum ?an ! p[]1 mu/ be proportionably less ?an x4 ,9 ?is in/rum5t1 !re=e1 ! p[] acts ^u ! weight to a me*anical disadvantage1 inasmu* z a great] p[] is necess>y to support or move ! weight ?an w\ld be requir$ if ! p[] 7 imm$iately appli$ to ! weight1 )\t ! int]v5tion ( a ma*9e4 ,we %all1 h[ev]1 h]eaft] %[ t ! advantage :i* is lo/ 9 =ce is ga9$ 9 despat*1 & t 9 proportion z ! weight is less ?an ! p[] :i* moves x1 s w ! spe$ ( its motion be great] ?an t ( ! p[]4 ,h5ce a lev] ( ! ?ird k9d is only us$ 9 cases :]e ! ex]tion ( great p[] is a consid]ation subord9ate to ^? ( rapidity & despat*4 ,! mo/ /rik+ example ( lev]s ( ! ?ird k9d is f\nd 9 ! animal economy4 ,! limbs ( animals are g5]ally lev]s ( ?is description4 ,! socket ( ! bone is ! fulcrum2 a /rong muscle atta*$ to ! bone ne> ! socket is ! p[]2 & ! weight ( ! limb1 toge!r ) :atev] resi/ance is oppos$ to its motion1 is ! weight4 ,a slight contraction ( ! muscle 9 ?is case gives a consid]able motion to ! limb3 ?is effect is p>ticul>ly conspicu\s 9 ! motion ( ! arms & legs 9 ! human body2 a v inconsid]able contraction ( ! muscles at ! %\ld]s & hips giv+ ! sweep to ! limbs f :i* ! body d]ives s mu* activity4 ,! tr$dle ( ! turn+ la! is a lev] ( ! ?ird k9d4 ,! h+e :i* atta*es x to ! floor is ! fulcrum1 ! foot appli$ to x ne> ! h+e is ! p[]1 & ! crank ^u ! axis ( ! fly-:eel1 ) :i* its extremity is connect$1 is ! weight4 ,tongs are lev]s ( ?is k9d1 z also ! %e>s us$ 9 %e>+ %eep4 ,9 ^! cases ! p[] is ! h& plac$ imm$iately bel[ ! fulcrum or po9t :]e ! two lev]s are connect$4 7#bci47 ,:5 ! p[] is said to support ! weight by means ( a lev] or any o!r ma*9e1 x is only meant t ! p[] keeps ! ma*9e 9 equilibrium1 & !reby enables x to su/a9 ! weight4 ,x is necess>y to att5d to ?is di/9ction1 to remove ! difficulty :i* may arise f ! p>adox ( a small p[] su/a9+ a great weight4 ,9 a lev] ( ! fir/ k9d1 ! fulcrum ,f1 fig4 #gh41 or axis1 su/a9s ! unit$ =ces ( ! p[] & weight4 ,9 a lev] ( ! second k9d1 if ! p[] be suppos$ to act ov] a :eel ,r1 fig4 #gi41 ! fulcrum ,f su/a9s a pressure equal to ! diff]5ce betwe5 ! p[] & weight1 & ! axis ( ! :eel ,r su/a9s a pressure equal to twice ! p[]2 s t ! total pressures on ,f & ,r are equival5t to ! unit$ =ces ( ! p[] & weight4 ,9 a lev] ( ! ?ird k9d simil> obs]vations are applicable4 ,! :eel ,r1 fig4 #hj41 su/a9s a pressure equal to twice ! p[]1 & ! fulcrum ,f su/a9s a pressure equal to ! diff]5ce betwe5 ! p[] & weight4 ,^! facts may be exp]im5tally e/abli%$ by atta*+ a /r+ to ! lev] imm$iately ov] ! fulcrum1 & susp5d+ ! lev] by t /r+ f ! arm ( a balance4 ,! c\nt]pois+ weight1 :5 ! fulcrum is remov$1 w1 9 ! fir/ case1 be equal to ! sum ( ! weight & p[]1 & 9 ! la/ two cases equal to _! diff]5ce4 7#bdj47 ,we h hi!rto omitt$ ! consid]ation ( ! effect ( ! weight ( ! lev] itself4 ,if ! c5tre ( gravity ( ! lev] be 9 ! v]tical l9e ?r\gh ! axis1 ! weight ( ! in/rum5t w h no o!r effect ?an to increase ! pressure on ! axis by its own am\nt4 ,b if ! c5tre ( gravity be on ! same side ( ! axis ) ! weight1 z at ,g1 x w oppose ! effect ( ! p[]1 a c]ta9 "p ( :i* mu/ !re=e be all[$ to support x4 ,to asc]ta9 :at "p ( ! p[] is ?us exp5d$1 x is to be consid]$ t ! mom5t ( ! weight ( ! lev] collect$ at ,g1 is f\nd by multiply+ t weight by ! di/ance ,g ,f4 ,! mom5t ( t "p ( ! p[] :i* supports ?is mu/ be equal to x2 !re=e1 x is only necess>y to f9d h[ mu* ( ! p[] multipli$ by ,p ,f w be equal to ! weight ( ! lev] multipli$ by ,g ,f4 ,?is is a "q 9 common ari?metic4 ,if ! c5tre ( gravity ( ! lev] be at a diff]5t side ( ! axis f ! weight1 z at ,g1 ! weight ( ! in/rum5t w co-op]ate ) ! p[] 9 su/a9+ ! weight ,w4 ,to det]m9e :at portion ( ! weight ,w is ?us su/a9$ by ! weight ( ! lev]1 x is only necess>y to f9d h[ mu* ( ,w1 multipli$ by ! di/ance ,w ,f1 is equal to ! weight ( ! lev] multipli$ by ,g ,f4 ,9 ^! cases ! pressure on ! fulcrum1 z already e/imat$1 w always be increas$ by ! weight ( ! lev]4 7#bda47 ,! s5se 9 :i* a small p[] is said to su/a9 a great weight1 & ! mann] ( accompli%+ ?is1 be+ expla9$1 we %all n[ consid] h[ ! p[] is appli$ 9 mov+ ! weight4 ,let ,p ,w1 fig4 #ha41 be ! places ( ! p[] & weight1 & ,f t ( ! fulcrum1 & let ! p[] be depress$ to ,p :ile ! weight is rais$ to ,w4 ,! space ,p ,p evid5tly be>s ! same proportion to ,w ,w1 z ! arm ,p ,f to ,w ,f4 ,?us if ,p ,f be t5 times ,w ,f1 ,p ,p w be t5 times ,w ,w4 ,a p[] ( "o p\nd at ,p be+ mov$ f ,p to ,p1 w c>ry a weight ( t5 p\nds f ,w to ,w4 ,b 9 ?is case x ought n to be said1 t a less] weight moves a great]1 = x is n difficult to %[1 t ! total exp5diture ( =ce 9 ! motion ( "o p\nd f ,p to ,p is exactly ! same z 9 ! motion ( t5 p\nds f ,w to ,w4 ,if ! space ,p ,p be t5 in*es1 ! space ,w ,w w be "o in*4 ,a weight ( "o p\nd is !re=e mov$ ?r\gh t5 successive in*es1 & 9 ea* in* ! =ce exp5d$ is t :i* w\ld be suffici5t to move "o p\nd ?r\gh "o in*4 ,! total exp5diture ( =ce f ,p to ,p is t5 times ! =ce necess>y to move "o p\nd ?r\gh "o in*1 or :at is ! same1 x is t :i* w\ld be necess>y to move t5 p\nds ?r\gh "o in*4 ,b ?is is exactly :at is accompli%$ by ! opposite end ,w ( ! lev]2 = ! weight ,w is t5 p\nds1 & ! space ,w ,w is "o in*4 ,if ! weight ,w ( t5 p\nds c\ld be conv5i5tly divid$ into t5 equal p>ts ( "o p\nd ea*1 ea* "p might be sep>ately rais$ ?r\gh "o in*1 )\t ! int]v5tion ( ! lev] or any o!r ma*9e4 ,9 ?is case1 ! same quantity ( p[] w\ld be exp5d$1 & exp5d$ 9 ! same mann] z 9 ! case j m5tion$4 ,x is evid5t1 !re=e1 t :5 a ma*9e is appli$ to raise a weight or to ov]come resi/ance1 z mu* =ce mu/ be really us$ z if ! p[] 7 imm$iately appli$ to ! weight or resi/ance4 ,all t is accompli%$ by ! ma*9e is to enable ! p[] to d t by a succession ( di/9ct ef=ts :i* %\ld be o!rwise p]=m$ by a s+le ef=t4 ,^! obs]vations w be f\nd to be applicable to all ma*9es :atev]4 7#bdb47 ,weigh+ ma*9es ( almo/ e k9d1 :e!r us$ = comm]cial or philosophical purposes1 are v>ieties ( ! lev]4 ,! common balance1 :i*1 ( all weigh+ ma*9es1 is ! mo/ p]fect & be/ adapt$ = ord9>y use1 :e!r 9 comm]ce or exp]im5tal philosophy1 is a lev] ) equal arms4 ,9 ! /eel-y>d "o weight s]ves z a c\nt]poise & measure ( o!rs ( diff]5t am\nt1 by receiv+ a lev]age v>iable accord+ to ! v>y+ am\nt ( ! weight aga9/ :i* x acts4 ,a detail$ acc\nt ( su* in/rum5ts w be f\nd 9 ,*apt] ,,xxi4 7#bdc47 ,we h hi!rto consid]$ ! p[] & weight z act+ on ! lev]1 9 directions p]p5dicul> to its l5g? & p>allel to ea* o!r4 ,?is does n always happ54 ,let ,a ,b1 fig4 #hc41 be a lev] ^: fulcrum is ,f1 & let ,a ,r be ! direction ( ! p[]1 & ,b ,s ! direction ( ! weight4 ,if ! l9es ,r ,a & ,s ,b be cont9u$1 & p]p5dicul>s ,f ,c & ,f ,d drawn f ! fulcrum to ^? l9es1 ! mom5t ( ! p[] w be f\nd by multiply+ ! p[] by ! l9e ,f ,c1 & ! mom5t ( ! weight by multiply+ ! weight by ,f ,d4 ,if ^! mom5ts be equal1 ! p[] w su/a9 ! weight 9 equilibrium4 7#ahe74 ,x is evid5t1 t ! same reason+ w be applicable :5 ! arms ( ! lev] are n 9 ! same direction4 ,^! arms may be ( any figure or %ape1 & may be plac$ relatively to ea* o!r 9 any position4 7#bdd47 ,9 ! rectangul> lev] ! arms are p]p5dicul> to ea* o!r1 & ! fulcrum ,f1 fig4 #hd41 is at ! "r angle4 ,! mom5t ( ! p[]1 9 ?is case1 is ,p multipli$ by ,a ,f1 & t ( ! weight ,w multipli$ by ,b ,f4 ,:5 ! in/rum5t is 9 equilibrium ^! mom5ts mu/ be equal4 ,:5 ! hamm] is us$ = draw+ a nail1 x is a lev] ( ?is k9d3 ! claw ( ! hamm] is ! %ort] arm2 ! resi/ance ( ! nail is ! weight2 & ! h& appli$ to ! h&le ! p[]4 7#bde47 ,:5 a beam re/s on two props ,a ,b1 fig4 #he41 & supports1 at "s int]m$iate place ,c1 a weight ,w1 ?is weight is di/ribut$ betwe5 ! props 9 a mann] :i* may be det]m9$ by ! pr9ciples already expla9$4 ,if ! pressure on ! prop ,b be consid]$ z a p[] su/a9+ ! weight ,w1 by means ( ! lev] ( ! second k9d ,b ,a1 !n ?is p[] multipli$ by ,b ,a mu/ be equal to ! weight multipli$ by ,c ,a4 ,h5ce ! pressure on ,b w be ! same fraction ( ! weight z ! "p ,a ,c is ( ,a ,b4 ,9 ! same mann] x may be prov$1 t ! pressure on ,a is ! same fraction ( ! weight z ,b ,c is ( ,b ,a4 ,?us1 if ,a ,c be "o ?ird1 & !re=e ,b ,c two ?irds ( ,b ,a1 ! pressure on ,b w be "o ?ird ( ! weight1 & ! pressure on ,a two ?irds ( ! weight4 ,x foll[s f ?is reason+1 t if ! weight be 9 ! middle1 equally di/ant f ,b & ,a1 ea* prop w su/a9 half ! weight4 ,! effect ( ! weight ( ! beam itself may be det]m9$ by consid]+ x to be collect$ at its c5tre ( gravity4 ,if ?is po9t1 !re=e1 be equally di/ant f ! props1 ! weight ( ! beam w be equally di/ribut$ betwe5 !m4 ,accord+ to ^! pr9ciples1 ! mann] 9 :i* a load borne on poles betwe5 two be>]s is di/ribut$ betwe5 !m may be asc]ta9$4 ,z ! ef=ts ( ! be>]s & ! direction ( ! weight are always p>allel2 ! position ( ! poles relatively to ! horizon makes no diff]5ce 9 ! di/ribution ( ! weights betwe5 ! be>]s4 ,:e!r !y asc5d or desc5d1 or move on a level plane1 ! weight w be simil>ly %>$ betwe5 !m4 ,if ! beam ext5d beyond ! prop1 z 9 fig4 #hf41 & ! weight be susp5d$ at a po9t n plac$ betwe5 !m1 ! props mu/ be appli$ at diff]5t sides ( ! beam4 ,! pressures :i* !y su/a9 may be calculat$ 9 ! same mann] z 9 ! =m] case4 ,! pressure ( ! prop ,b may be consid]$ z a p[] su/a9+ ! weight ,w by means ( ! lev] ,b ,c4 ,h5ce1 ! pressure ( ,b1 multipli$ by ,b ,a1 mu/ be equal to ! weight ,w multipli$ by ,a ,c4 ,!re=e1 ! pressure on ,b be>s ! same proportion to ! weight z ,a ,c does to ,a ,b4 ,9 ! same mann]1 consid]+ ,b z a fulcrum1 & ! pressure ( ! prop ,a z ! p[]1 x may be prov$ t ! pressure ( ,a be>s ! same proportion to ! weight z ! l9e ,b ,c does to ,a ,b4 ,x !re=e appe>s1 t ! pressure on ! prop ,a is great] ?an ! weight4 7#bdf47 ,:5 great p[] is requir$1 & x is inconv5i5t to con/ruct a long lev]1 a comb9ation ( lev]s may be us$4 ,9 fig4 #hg4 su* a sy/em ( lev]s is repres5t$1 consi/+ ( ?ree lev]s ( ! fir/ k9d4 ,! mann] 9 :i* ! effect ( ! p[] is transmitt$ to ! weight may be inve/igat$ by consid]+ ! effect ( ea* lev] successively4 ,! p[] at ,p produces an upw>d =ce at ,p1 :i* be>s to ,p ! same proportion z ,p ,f to ,p ,f4 ,!re=e1 ! effect at ,p is z _m times ! p[] z ! l9e ,p ,f is ( ,p ,f4 ,?us1 if ,p ,f be t5 times ,p ,f1 ! upw>d =ce at ,p is t5 times ! p[]4 ,! arm ,p ,f ( ! second lev] is press$ upw>ds by a =ce equal to t5 times ! p[] at ,p4 ,9 ! same mann] ?is may be %[n to produce an effect at ,p z _m times great] ?an ,p z ,p ,f is great] ?an ,p ,f4 ,?us1 if ,p ,f be twelve times ,p ,f1 ! effect at ,p w be twelve times t ( ,p4 ,b ?is la/ 0 t5 times ! p[]1 & !re=e ! ,p w be "o hundr$ & tw5ty times ! p[]4 ,9 ! same mann] x may be %[n t ! weight is z _m times great] ?an ! effect at ,p z ,p ,f is great] ?an ,w ,f4 ,if ,p ,f be five times ,w ,f1 ! weight w be five times ! effect at ,p4 ,b ?is effect is "o hundr$ & tw5ty times ! p[]1 & !re=e ! weight w\ld be six hundr$ times ! p[]4 ,9 ! same mann] ! effect ( any comp\nd sy/em ( lev]s may be asc]ta9$ by tak+ ! proportion ( ! weight to ! p[] 9 ea* lev] sep>ately1 & multiply+ ^! numb]s toge!r4 ,9 ! example giv51 ^! proportions are #aj1 #ab1 & #e1 :i* multipli$ toge!r give #fjj4 ,9 fig4 #hg4 ! lev]s compos+ ! sy/em are ( ! fir/ k9d2 b ! pr9ciples ( ! calculation w n be alt]$ if !y be ( ! second or ?ird k9d1 or "s ( "o k9d & "s ( ano!r4 7#bdg47 ,t numb] :i* expresses ! proportion ( ! weight to ! equilibrat+ p[] 9 any ma*9e1 we %all call ! p[] ( ! ma*9e4 ,?us1 if1 9 a lev]1 a p[] ( "o p\nd support a weight ( t5 p\nds1 ! p[] ( ! ma*9e is t54 ,if a p[] ( #blbs4 support a weight ( #aalbs41 ! p[] ( ! ma*9e is #e-a_/b1 #b be+ conta9$ 9 #aa #e-a_/b times4 7#bdh47 ,z ! di/ances ( ! p[] & weight f ! fulcrum ( a lev] may be v>i$ at pleasure1 & any assign$ proportion giv5 to !m1 a lev] may always be conceiv$ hav+ a p[] equal to t ( any giv5 ma*9e4 ,su* a lev] may be call$1 9 relation to t ma*9e1 ! equival5t lev]4 ,z e complex ma*9e consi/s ( a numb] ( simple ma*9es act+ "o ^u ano!r1 & z ea* simple ma*9e may be repres5t$ by an equival5t lev]1 ! complex ma*9e w be repres5t$ by a comp\nd sy/em ( equival5t lev]s4 ,f :at has be5 prov$ 9 7#bdf471 x !re=e foll[s t ! p[] ( a complex ma*9e may be calculat$ by multiply+ toge!r ! p[]s ( ! sev]al simple ma*9es ( :i* x is compos$4 ,,*ap4 ,,xiv4 ,,( ,,:eel-,,"w4 7#bdi47 ,:5 a lev] is appli$ to raise a weight1 or ov]come a resi/ance1 ! space ?r\gh :i* x acts at any "o "t is small1 & ! "w mu/ be accompli%$ by a succession ( %ort & int]mitt+ ef=ts4 ,9 fig4 #ha41 aft] ! weight has be5 rais$ f ,w to ,w1 ! lev] mu/ aga9 return to its fir/ position1 to repeat ! action4 ,dur+ ?is return ! motion ( ! weight is susp5d$1 & x w fall d[nw>ds unless "s provision be made to su/a9 x4 ,! common lev] is1 !re=e1 only us$ 9 cases :]e weights are requir$ to be rais$ ?r\gh small spaces1 & "u ^! circum/ances its great simplicity /rongly recomm5ds x4 ,b :]e a cont9u\s motion is to be produc$1 z 9 rais+ ore f ! m9e1 or 9 weigh+ ! an*or ( a vessel1 "s contrivance mu/ be adopt$ to remove ! int]mitt+ action ( ! lev]1 & r5d] x cont9ual4 ,! v>i\s =ms giv5 to ! lev]1 ) a view to accompli% ?is1 are g5]ally d5om9at$ ! :eel & axle4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,9 fig4 #hh41 ,a ,b is a horizontal axle1 :i* re/s 9 pivots at its extremities1 or is support$ 9 gudgeons1 & capable ( revolv+4 ,r\nd ?is axis a rope is coil$1 :i* su/a9s ! weight ,w4 ,on ! same axis a :eel ,c is fix$1 r\nd :i* a rope is coil$ 9 a contr>y direction1 to :i* is app5d$ ! p[] ,p4 ,! mom5t ( ! p[] is f\nd by multiply+ x by ! radius ( a :eel1 & ! mom5t ( ! weight1 by multiply+ x by ! radius ( its axle4 ,if ^! mom5ts be equal 7#ahe471 ! ma*9e w be 9 equilibrium4 ,:5ce x appe>s t ! p[] ( ! ma*9e 7#bdg47 is express$ by ! proportion :i* ! radius ( ! :eel be>s to ! radius ( ! axle2 or1 :at is ! same1 ( ! diamet] ( ! :eel to ! diamet] ( ! axle4 ,?is pr9ciple is applicable to ! :eel & axle 9 e v>iety ( =m "u :i* x c be pres5t$4 7#bej47 ,x is evid5t t z ! p[] desc5ds cont9ually1 & ! rope is uncoil$ f ! :eel1 ! weight w be rais$ cont9ually1 ! rope by :i* x is susp5d$ be+ at ! same "t coil$ ^u ! axle4 ,:5 ! ma*9e is 9 equilibrium1 ! =ces ( bo? ! weight & p[] are su/a9$ by ! axle1 & di/ribut$ betwe5 its props1 9 ! mann] expla9$ 9 7#bde47 ,:5 ! ma*9e is appli$ to raise a weight1 ! velocity ) :i* ! p[] moves is z _m times great] ?an t ) :i* ! weight rises1 z ! weight itself is great] ?an ! p[]4 ,?is is a pr9ciple :i* has already be5 notic$1 & :i* is common to all ma*9es :atsoev]4 ,x may h5ce be prov$1 t 9 ! elevation ( ! weight a quantity ( p[] is exp5d$ equal to t :i* w\ld be necess>y to elevate ! weight if ! p[] 7 imm$iately appli$ to x1 )\t ! int]v5tion ( any ma*9e4 ,?is has be5 expla9$ 9 ! case ( ! lev] 9 7#bda471 & may be expla9$ 9 ! pres5t in/ance 9 ne>ly ! same words4 ,9 "o revolution ( ! ma*9e ! l5g? ( rope uncoil$ f ! :eel is equal to ! circumf]5ce ( ! :eel1 & ?r\gh ?is space ! p[] mu/ !re=e move4 ,at ! same "t ! l5g? ( rope coil$ ^u ! axle is equal to ! circumf]5ce ( ! axle1 & ?r\gh ?is space ! weight mu/ be rais$4 ,! spaces1 !re=e1 ?r\gh :i* ! p[] & weight move 9 ! same "t1 are 9 ! proportion ( ! circumf]5ces ( ! :eel & axle2 b ^! circumf]5ces are 9 ! same proportion z _! diamet]s4 ,!re=e ! velocity ( ! p[] w be> to ! velocity ( ! weight ! same proportion z ! diamet] ( ! :eel be>s to ! diamet] ( ! axle1 or1 :at is ! same1 z ! weight be>s to ! p[] 7#bdi74 7#bea47 ,we h "h omitt$ ! consid]ation ( ! ?ickness ( ! rope4 ,:5 ?is is consid]$1 ! =ce mu/ be conceiv$ z act+ 9 ! direction ( ! c5tre ( ! rope1 & !re=e ! ?ickness ( ! rope :i* supports ! p[] ought to be add$ to ! diamet] ( ! :eel1 & ! ?ickness ( ! rope :i* supports ! weight to ! diamet] ( ! axle4 ,x is ! m necess>y to att5d to ?is circum/ance1 z ! /r5g? ( ! rope necess>y to support ! weight causes its ?ickness to be> a consid]able proportion to ! diamet] ( ! axle2 :ile ! rope :i* su/a9s ! p[] n requir+ ! same /r5g?1 & be+ appli$ to a l>g] circle1 be>s a v inconsid]able proportion to its diamet]4 7#beb47 ,9 num]\s =ms ( ! :eel & axle1 ! weight or resi/ance is appli$ by a rope coil$ ^u ! axle2 b ! mann] 9 :i* ! p[] is appli$ is v v>i\s1 & n (t5 by means ( a rope4 ,! circumf]5ce ( a :eel sometimes c>ries project+ p9s1 z repres5t$ 9 fig4 #hh41 to :i* ! h& is appli$ to turn ! ma*9e4 ,an in/ance ( ?is occurs 9 ! :eel us$ 9 ! /e]age ( a vessel4 ,9 ! common w9dlass1 ! p[] is appli$ by means ( a w9*1 :i* is a rectangul> lev]1 z repres5t$ 9 fig4 #hi4 ,! arm ,b ,c ( ! w9* repres5ts ! radius ( ! :eel1 & ! p[] is appli$ to ,c ,d at "r angles to ,b ,c4 ,9 "s cases no :eel is atta*$ to ! axle2 b x is pi]c$ ) holes direct$ t[>ds its c5tre1 9 :i* long lev]s are incessantly ins]t$1 & a cont9u\s action produc$ by sev]al m5 work+ at ! same "t2 s t :ile "s are transf]r+ ! lev]s f hole to hole1 o!rs are work+ ! w9dlass4 ,! axle is sometimes plac$ 9 a v]tical position1 ! :eel or lev]s be+ mov$ horizontally4 ,! cap/an is an example ( ?is3 a v]tical axis is fix$ 9 ! deck ( ! %ip2 ! circumf]5ce is pi]c$ ) holes pres5t$ t[>ds its c5tre4 ,^! holes receive long lev]s1 z repres5t$ 9 fig4 #ij4 ,! m5 :o "w ! cap/an walk cont9ually r\nd ! axle1 press+ =w>d ! lev]s ne> _! extremities4 ,9 "s cases ! :eel is turn$ by ! weight ( animals plac$ at its circumf]5ce1 :o move =w>d z fa/ z ! :eel desc5ds1 s z to ma9ta9 _! position cont9ually at ! extremity ( ! horizontal diamet]4 ,! treadmill1 fig4 #ia41 & c]ta9 cranes1 su* z fig4 #ib41 are examples ( ?is4 ,9 wat]-:eels1 ! p[] is ! weight ( wat] conta9$ 9 buckets at ! circumf]5ce1 z 9 fig4 #ic41 :i* is call$ an ov]-%ot :eel3 & sometimes by ! impulse ( wat] aga9/ float-bo>ds at ! circumf]5ce1 z 9 ! "u-%ot :eel1 fig4 #id4 ,bo? ^! pr9ciples act 9 ! brea/-:eel1 fig4 #ie4 ,9 ! paddle-:eel ( a /eam-boat1 ! p[] is ! resi/ance :i* ! wat] (f]s to ! motion ( ! paddle-bo>ds4 ,9 w9dmills1 ! p[] is ! =ce ( ! w9d act+ on v>i\s p>ts ( ! arms1 & may be consid]$ z diff]5t p[]s simultane\sly act+ on diff]5t :eels hav+ ! same axle4 7#bec47 ,9 mo/ cases 9 :i* ! :eel & axle is us$1 ! action ( ! p[] is liable to occasional susp5sion or int]mission1 9 :i* case "s contrivance is necess>y to prev5t ! recoil ( ! weight4 ,a rat*et :eel ,r1 fig4 #hh41 is provid$ = ?is purpose1 :i* is a contrivance :i* p]mits ! :eel to turn 9 "o direction2 b a cat* :i* falls betwe5 ! tee? ( a fix$ :eel prev5ts its motion 9 ! o!r direction4 ,! effect ( ! p[] or weight is sometimes transmitt$ to ! :eel or axle by means ( a /raight b>1 on ! edge ( :i* tee? are rais$1 :i* engage !mselves 9 correspond+ tee? on ! :eel or axle4 ,su* a b> is call$ a rack2 & an in/ance ( its use may be obs]v$ 9 ! mann] ( work+ ! pi/ons ( an air-pump4 7#bed47 ,! p[] ( ! :eel & axle be+ express$ by ! numb] ( times ! diamet] ( ! axle is conta9$ 9 t ( ! :eel1 !re are obvi\sly only two ways by :i* ?is p[] may be increas$2 viz4 ei!r by increas+ ! diamet] ( ! :eel1 or dim9i%+ t ( ! axle4 ,9 cases :]e great p[] is requir$1 ea* ( ^! me?ods is att5d$ ) practical inconv5i5ce & difficulty4 ,if ! diamet] ( ! :eel be consid]ably enl>g$1 ! ma*9e w become unwieldy1 & ! p[] w "w ?r\gh an unmanageable space4 ,if1 on ! o!r h&1 ! p[] ( ! ma*9e be increas$ by r$uc+ ! ?ickness ( ! axle1 ! /r5g? ( ! axle w become insuffici5t = ! support ( t weight1 ! magnitude ( :i* _h r5d]$ ! increase ( ! p[] ( ! ma*9e necess>y4 ,to comb9e ! requisite /r5g? ) mod]ate dim5sions & great me*anical p[] is1 !re=e1 impracticable 9 ! ord9>y =m ( ! :eel & axle4 ,?is has1 h[ev]1 be5 accompli%$ by giv+ diff]5t ?icknesses to diff]5t p>ts ( ! axle1 & c>ry+ a rope1 :i* is coil$ on ! ?9n] "p1 ?r\gh a :eel atta*$ to ! weight1 & coil+ x 9 ! opposite direction on ! ?ick] "p1 z 9 fig4 #if4 ,to inve/igate ! proportion ( ! p[] to ! weight 9 ?is case1 let fig4 #ig4 repres5t a section ( ! app>atus at "r angles to ! axis4 ,! weight is equally susp5d$ by ! two p>ts ( ! rope1 ,s & ,s1 & !re=e ea* "p is /ret*$ by a =ce equal to half ! weight4 ,! mom5t ( ! =ce1 :i* /ret*es ! rope ,s1 is half ! weight multipli$ by ! radius ( ! ?9n] "p ( ! axle4 ,?is =ce be+ at ! same side ( ! c5tre ) ! p[]1 co-op]ates ) x 9 support+ ! =ce :i* /ret*es ,s1 & :i* acts at ! o!r side ( ! c5tre4 ,by ! pr9ciple e/abli%$ 9 7#ahe471 ! mom5ts ( ,p & ,s mu/ be equal to t ( ,s2 & !re=e if ,p be multipli$ by ! radius ( ! :eel1 & add$ to half ! weight multipli$ by ! radius ( ! ?9n] "p ( ! axle1 we mu/ obta9 a sum equal to half ! weight multipli$ by ! radius ( ! ?ick] "p ( ! axle4 ,h5ce x is easy to p]ceive1 t ! p[] multipli$ by ! radius ( ! :eel is equal to half ! weight multipli$ by ! diff]5ce ( ! radii ( ! ?ick] & ?9n] p>ts ( ! axle2 or1 :at is ! same1 ! p[] multipli$ by ! diamet] ( ! :eel1 is equal to ! weight multipli$ by half ! diff]5ce ( ! diamet]s ( ! ?9n] & ?ick] p>ts ( ! axle4 ,a :eel & axle con/ruct$ 9 ?is mann] is equival5t to an ord9>y "o1 9 :i* ! :eel has ! same diamet]1 & ^: axle has a diamet] equal to half ! diff]5ce ( ! diamet]s ( ! ?ick] & ?9n] p>ts4 ,! p[] ( ! ma*9e is express$ by ! proportion :i* ! diamet] ( ! :eel be>s to half ! diff]5ce ( ^! diamet]s2 & !re=e ?is p[]1 :5 ! diamet] ( ! :eel is giv51 does n1 z 9 ! ord9>y :eel & axle1 dep5d on ! smallness ( ! axle1 b on ! smallness ( ! diff]5ce ( ! ?9n] & ?ick] p>ts ( x4 ,! axle may1 !re=e1 be con/ruct$ ( su* a ?ickness z to give x all ! requisite /r5g?1 & yet ! diff]5ce ( ! diamet]s ( its diff]5t p>ts may be s small z to give x all ! requisite p[]4 7#bee47 ,x (t5 happ5s t a v>y+ weight is to be rais$1 or resi/ance ov]come by a uni=m p[]4 ,if1 9 su* a case1 ! weight be rais$ by a rope coil$ ^u a uni=m axle1 ! action ( ! p[] w\ld n be uni=m1 b w\ld v>y ) ! weight4 ,x is1 h[ev]1 9 mo/ cases desirable or necess>y t ! weight or resi/ance1 ev5 ?\gh x v>y1 %all be mov$ uni=mly4 ,?is w be accompli%$ if by any means ! lev]age ( ! weight is made to increase 9 ! same proportion z ! weight dim9i%es1 & to dim9i% 9 ! same proportion z ! weight increases3 = 9 t case ! mom5t ( ! weight w nev] v>y1 :atev] x ga9s by ! increase ( weight be+ lo/ by ! dim9i%$ lev]age1 & :atev] x loses by ! dim9i%$ weight be+ ga9$ by ! increas$ lev]age4 ,an axle1 ! surface ( :i* is curv$ 9 su* a mann]1 t ! ?ickness on :i* ! rope is coil$ cont9ually increas$ or dim9i%es 9 ! same proportion z ! weight or resi/ance dim9i%es or increases1 w produce ?is effect4 ,x is obvi\s t all t has be5 said respect+ a v>iable weight or resi/ance1 is also applicable to a v>iable p[]1 :i*1 !re=e1 may1 by ! same means1 be made to produce a uni=m effect4 ,an in/ance ( ?is occurs 9 a wat*1 :i* is mov$ by a spiral spr+4 ,:5 ! wat* has be5 w\nd up1 ?is spr+ acts ) its greate/ int5sity1 & z ! wat* goes d[n1 ! ela/ic =ce ( ! spr+ gradually loses its en]gy4 ,?is spr+ is connect$ by a *a9 ) an axle ( v>y+ ?ickness1 call$ a fusee4 ,:5 ! spr+ is at its greate/ int5sity1 ! *a9 acts ^u ! ?9ne/ "p ( ! fusee1 & z x is uncoil$ x acts ^u a "p ( ! fusee :i* is cont9ually increas+ 9 ?ickness1 ! spr+ at ! same "t los+ its ela/ic p[] 9 exactly ! same proportion4 ,a repres5tation ( ! fusee1 & ! cyl9drical box :i* conta9s ! spr+1 is giv5 9 fig4 #ih41 & ( ! spr+ itself 9 fig4 #ii4 7#bef47 ,:5 great p[] is requir$1 :eels & axles may be comb9$ 9 a mann] analog\s to a comp\nd sy/em ( lev]s1 expla9$ 9 7#bdf47 ,9 ?is case ! p[] acts on ! circumf]5ce ( ! fir/ :eel1 & its effect is transmitt$ to ! circumf]5ce ( ! fir/ axle4 ,t circumf]5ce is plac$ 9 connection ) ! circumf]5ce ( ! second :eel1 & ! effect is !reby transmitt$ to ! circumf]5ce ( ! second axle1 & s on4 ,x is obvi\s f :at 0 prov$ 9 7#bdh471 t ! p[] ( su* a comb9ation ( :eels & axles w be f\nd by multiply+ toge!r ! p[]s ( ! sev]al :eels ( :i* x is compos$4 ,x is sometimes conv5i5t to compute ?is p[] by numb]s express+ ! proportions ( ! circumf]5ces or diamet]s ( ! sev]al :eels1 to ! circumf]5ces or diamet]s ( ! sev]al axles respectively4 ,?is computation is made by fir/ multiply+ ! numb]s toge!r :i* express ! circumf]5ces or diamet]s ( ! :eels1 & !n multiply+ toge!r ! numb]s :i* express ! circumf]5ces or diamet]s ( ! sev]al axles4 ,! proportion ( ! two products w express ! p[] ( ! ma*9e4 ,?us1 if ! circumf]5ces or diamet]s be z ! numb]s #aj1 #ad1 & #ae1 _! product w be #bajj2 & if ! circumf]5ces or diamet]s ( ! axles be express$ by ! numb]s #c1 #d1 & #e1 _! product w be #fj1 & ! p[] ( ! ma*9e w be express$ by ! proportion ( #bajj & #fj1 or #ce to #a4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 7#beg47 ,! mann] 9 :i* ! circumf]5ces ( ! axles act ^u ! circumf]5ces ( ! :eels 9 comp\nd :eel-"w is v>i\s4 ,sometimes a /rap or cord is appli$ to a groove 9 ! circumf]5ce ( ! axle1 & c>ri$ r\nd a simil> groove 9 ! circumf]5ce ( ! succe$+ :eel4 ,! friction ( ?is cord or /rap ) ! groove is suffici5t to prev5t its slid+ & to communicate ! =ce f ! axle to ! :eel1 or vice v]sa4 ,?is me?od ( connect+ :eel-"w is repres5t$ 9 fig4 #ajj4 ,num]\s examples ( :eels & axles driv5 by /raps or cords occur 9 ma*9]y appli$ to almo/ e dep>tm5t ( ! arts & manufactures4 ,9 ! turn+ la!1 ! :eel work$ by ! tr$dle is connect$ ) ! m&rel by a catgut cord pass+ ?r\gh grooves 9 ! :eel & axle4 ,9 all great factories1 revolv+ %afts are c>ri$ along ! ap>tm5ts1 on :i*1 at c]ta9 int]vals1 /raps are atta*$ pass+ r\nd _! circumf]5ces & c>ri$ r\nd ! :eels :i* give motion to ! sev]al ma*9es4 ,if ! :eels1 connect$ by /raps or cords1 are requir$ to revolve 9 ! same direction1 ^! cords are arrang$ z 9 fig4 #ajj42 b if !y are requir$ to revolve 9 contr>y directions1 !y are appli$ z 9 fig4 #aja4 ,"o ( ! *ief advantages ( ! me?od ( transmitt+ motion betwe5 :eels & axles by /raps or cords1 is t ! :eel & axle may be plac$ at any di/ance f ea* o!r :i* may be f\nd conv5i5t1 & may be made to turn ei!r 9 ! same or contr>y directions4 7#beh47 ,:5 ! circumf]5ce ( ! :eel acts imm$iately on ! circumf]5ce ( ! succe$+ axle1 "s means mu/ necess>ily be adopt$ to prev5t ! :eel f mov+ 9 contact ) ! axle )\t compell+ ! latt] to turn4 ,if ! surfaces ( bo? 7 p]fectly smoo?1 s t all friction 7 remov$1 x is obvi\s t ei!r w\ld slide ov] ! surface ( ! o!r1 )\t communicat+ motion to x4 ,b1 on ! o!r h&1 if !re 7 any asp]ities1 h[ev] small1 ^u ^! surfaces1 !y w\ld become mutually ins]t$ among ea* o!r1 & nei!r ! :eel nor axle c\ld move )\t caus+ ! asp]ities ) :i* its edge is /udd$ to enc\nt] ^? asp]ities :i* project f ! surface ( ! o!r2 & ?us1 until ^! projections %\ld be brok5 (f1 bo? :eel & axle mu/ be mov$ at ! same "t4 ,x is on ?is acc\nt t if ! surfaces ( ! :eels & axles are by any means r5d]$ r\gh1 & press$ toge!r ) suffici5t =ce1 ! motion ( ei!r w turn ! o!r1 provid$ ! load or resi/ance be n great] ?an ! =ce necess>y to break (f ^! small projections :i* produce ! friction4 ,9 cases :]e great p[] is n requir$1 motion is communicat$ 9 ?is way ?r\gh a tra9 ( :eel-"w1 by r5d]+ ! surface ( ! :eel & axle r\gh1 ei!r by fac+ !m ) buff lea!r1 or ) wood cut across ! gra94 ,?is me?od is sometimes us$ 9 sp9n+ ma*9]y1 :]e "o l>ge buff$ :eel1 plac$ 9 a horizontal position1 revolves 9 contact ) sev]al small buff$ roll]s1 ea* roll] communicat+ motion to a sp9dle4 ,! position ( ! :eel ,w1 & ! roll]s ,r ,r1 c41 are repres5t$ 9 fig4 #ajb4 ,ea* roll] c be ?r[n out ( contact ) ! :eel1 & re/or$ to x at pleasure4 ,! communication ( motion betwe5 :eels & axles by friction has ! advantage ( great smoo?ness & ev5ness1 & ( proce$+ ) little noise2 b ?is me?od c only be us$ 9 cases :]e ! resi/ance is n v consid]able1 & !re=e is seldom adopt$ 9 works on a l>ge scale4 ,dr4 ,gregory m5tions an in/ance ( a saw mill at ,s\?ampton1 :]e ! :eels act ^u ea* o!r by ! contact ( ! end gra9 ( wood4 ,! ma*9]y makes v little noise1 & we>s v well1 hav+ be5 us$ n less ?an #bj ye>s4 7#bei47 ,! mo/ usual me?od ( transmitt+ motion ?r\gh a tra9 ( :eel-"w is by ! =mation ( tee? ^u _! circumf]5ces1 s t ^! ind5tures ( ea* :eel fall betwe5 ! correspond+ ones ( t 9 :i* x works1 & ensure ! action s long z ! /ra9 is n s great z to fracture ! too?4 ,9 ! =mation ( tee? v m9ute att5tion mu/ be giv5 to _! figure1 9 ord] t ! motion may be communicat$ f :eel to :eel ) smoo?ness & uni=mity4 ,?is c only be accompli%$ by %ap+ ! tee? accord+ to curves ( a peculi> k9d1 :i* ma!maticians h inv5t$1 & assign$ rules = draw+4 ,! ill consequ5ces ( neglect+ ?is w be v app>5t1 by consid]+ ! nature ( ! action :i* w\ld be produc$ if ! tee? 7 =m$ ( squ>e project+ p9s1 z 9 fig4 #ajc4 ,:5 ! too? ,a comes into contact ) ,b1 x acts obliquely ^u x1 &1 z x moves1 ! corn] ( ,b slides ^u ! plane surface ( ,a 9 su* a mann] z to produce mu* friction1 & to gr9d away ! side ( ,a & ! end ( ,b4 ,z !y approa* ! position ,c ,d1 !y su/a9 a jolt ! mom5t _! surfaces come into full contact2 & aft] pass+ ! position ( ,c ,d1 ! same scrap+ & gr9d+ effect is produc$ 9 ! opposite direction1 until by ! revolution ( ! :eels ! tee? become dis5gag$4 ,^! effects are avoid$ by giv+ to ! tee? ! curv$ =ms repres5t$ 9 fig4 #ajd4 ,by su* means ! surfaces ( ! tee? roll ^u ea* o!r ) v inconsid]able friction1 & ! direction 9 :i* ! pressure is excit$ is always t ( a l9e ,m ,n1 t\*+ ! two :eels1 & at "r angles to ! radii4 ,?us ! pressure be+ always ! same1 & act+ ) ! same lev]age1 produces a uni=m effect4 7#bfj47 ,:5 :eels "w toge!r1 _! tee? mu/ necess>ily be ( ! same size1 & !re=e ! proportion ( _! circumf]5ces may always be e/imat$ by ! numb] ( tee? :i* !y c>ry4 ,h5ce x foll[s1 t 9 comput+ ! p[] ( comp\nd :eel-"w1 ! numb] ( tee? may always be us$ to express ! circumf]5ces respectively1 or ! diamet]s :i* are proportional to ^! circumf]5ces4 ,:5 tee? are rais$ ^u an axle1 x is g5]ally call$ a p9ion1 & 9 t case ! tee? are call$ leaves4 ,! rule = comput+ ! tra9 ( :eel-"w giv5 9 7#bef47 w be express$ z foll[s3 :5 ! :eel & axle c>ry tee?1 multiply toge!r ! numb] ( tee? 9 ea* ( ! :eels1 & next ! numb] ( leaves 9 ea* ( ! p9ions2 ! proportion ( ! two products w express ! p[] ( ! ma*9e4 ,if "s ( ! :eels & axles c>ry tee?1 & o!rs n1 ?is computation may be made by us+ = ^? circumf]5ces :i* d n be> tee? ! numb] ( tee? :i* w\ld fill !m4 ,fig4 #aje4 repres5ts a tra9 ( ?ree :eels & p9ions4 ,! :eel ,f :i* be>s ! p[]1 & ! axle :i* be>s ! weight1 h no tee?2 b x is easy to f9d ! numb] ( tee? :i* !y w\ld c>ry4 7#bfa47 ,x is evid5t t ea* p9ion revolves mu* m frequ5tly 9 a giv5 "t ?an ! :eel :i* x drives4 ,?us1 if ! p9ion ,c be furni%$ ) t5 tee?1 & ! :eel ,e1 :i* x drives1 h sixty tee?1 ! p9ion ,c mu/ turn six times1 9 ord] to turn ! :eel ,e once r\nd4 ,! velocities ( revolution ( e :eel & p9ion :i* "w 9 "o ano!r w !re=e h ! same proportion z _! numb] ( tee? tak5 9 a rev]se ord]1 & by ?is means ! relative velocity ( :eels & p9ions may be det]m9$ accord+ to any propos$ rate4 ,:eel-"w1 l all o!r ma*9]y1 is us$ to transmit & modify =ce 9 e dep>tm5t ( ! arts & manufactures2 b x is also us$ 9 cases :]e motion alone1 & n =ce1 is ! object to be atta9$4 ,! mo/ rem>kable example ( ?is occurs 9 wat* & clock-"w1 :]e ! object is m]ely to produce uni=m motions ( rotation1 hav+ c]ta9 proportions1 & )\t any reg>d to ! elevation ( weights1 or ! ov]com+ ( resi/ances4 7#bfb47 ,a crane is an example ( comb9ation ( :eel-"w us$ = ! purpose ( rais+ or l[]+ great weights4 ,fig4 #ajf4 repres5ts a ma*9e ( ?is k9d4 ,a ,b is a /rong v]tical beam1 re/+ on a pivot1 & secur$ 9 its position by beams 9 ! floor4 ,x is capable1 h[ev]1 ( turn+ on its axis1 be+ conf9$ betwe5 roll]s atta*$ to ! beams & fix$ 9 ! floor4 ,c ,d is a project+ arm call$ a gib1 =m$ ( beams :i* are mortis$ into ,a ,b4 ,! :eel-"w is m\nt$ 9 two ca/-iron crosses1 bolt$ on ea* side ( ! beams1 "o ( :i* appe>s at ,e ,f ,g ,h4 ,! w9* at :i* ! p[] is appli$ is at ,i4 ,?is c>ries a p9ion imm$iately beh9d ,h4 ,?is p9ion works 9 a :eel ,k1 :i* c>ries ano!r p9ion ^u its axle4 ,?is la/ p9ion works 9 a l>g] :eel ,l1 :i* c>ries ^u its axis a b>rel ,m1 on :i* a *a9 or rope is coil$4 ,! *a9 passes ov] a pulley ,d at ! top ( ! gib4 ,at ! end ( ! *a9 a hook ,o is atta*$1 to support ! weight ,w4 ,dur+ ! elevation ( ! weight x is conv5i5t t its recoil %\ld be h9d]$ 9 case ( any occasional susp5sion ( ! p[]4 ,?is is accompli%$ by a rat*et :eel atta*$ to ! b>rel ,m1 z expla9$ 9 7#bec472 b :5 ! weight ,w is to be l[]$1 ! cat* mu/ be remov$ f ?is rat*et :eel4 ,9 ?is case ! too rapid desc5t ( ! weight is 9 "s cases *eck$ by pressure excit$ on "s "p ( ! :eel-"w1 s z to produce suffici5t friction to ret>d ! desc5t 9 any requir$ degree1 or ev5 to susp5d x1 if necess>y4 ,! v]tical beam at ,b re/+ on a pivot1 & be+ fix$ betwe5 roll]s1 all[s ! gib to be turn$ r\nd 9 any direction2 s t a weight rais$ f "o side ( ! crane may be c>ri$ r\nd1 & deposit$ on ano!r side1 at any di/ance )9 ! range ( ! gib4 ,?us1 if a crane be plac$ ^u a :>f ne> a vessel1 weights may be rais$1 & :5 elevat$1 ! gib may be turn$ r\nd s z to let !m desc5d into ! hold4 ,! p[] ( ?is ma*9e may be comput$ ^u ! pr9ciples already expla9$4 ,! magnitude ( ! circle1 9 :i* ! p[] at ,i moves1 may be det]m9$ by ! radius ( ! w9*1 & !re=e ! numb] ( tee? :i* a :eel ( t size w\ld c>ry may be f\nd4 ,9 l mann] we may det]m9e ! numb] ( leaves 9 a p9ion ^: magnitude w\ld be equal to ! b>rel ,m4 ,let ! fir/ numb] be multipli$ by ! numb] ( tee? 9 ! :eel ,k1 & t product by ! numb] ( tee? 9 ! :eel ,l4 ,next let ! numb] ( leaves 9 ! p9ion ,h be multipli$ by ! numb] ( leaves 9 ! p9ion atta*$ to ! axle ( ! :eel ,k1 & let t product be multipli$ by ! numb] ( leaves 9 a p9ion1 ^: diamet] is equal to t ( ! b>rel ,m4 ,^! two products w express ! p[] ( ! ma*9e4 7#bfc47 ,too!d :eels are ( ?ree k9ds1 di/+ui%$ by ! position :i* ! tee? be> ) respect to ! axis ( ! :eel4 ,:5 !y are rais$ ^u ! edge ( ! :eel z 9 fig4 #aje41 !y are call$ spur :eels1 or spur ge>4 ,:5 !y are rais$ p>allel to ! axis1 z 9 fig4 #ajg41 x is call$ a cr[n :eel4 ,:5 ! tee? are rais$ on a surface incl9$ to ! plane ( ! :eel1 z 9 fig4 #ajh41 !y are call$ bevell$ :eels4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,if a motion r\nd "o axis is to be communicat$ to ano!r axis p>allel to x1 spur ge> is g5]ally us$4 ,?us1 9 fig4 #aje41 ! ?ree axes are p>allel to ea* o!r4 ,if a motion r\nd "o axis is to be communicat$ to ano!r at "r angles to x1 a cr[n :eel1 work+ 9 a spur p9ion1 z 9 fig4 #ajg41 w s]ve4 ,or ! same object may be obta9$ by two bevell$ :eels1 z 9 fig4 #ajh4 ,if a motion r\nd "o axis is requir$ to be communicat$ to ano!r incl9$ to x at any propos$ angle1 two bevell$ :eels c always be us$4 ,9 fig4 #aji4 let ,a ,b & ,a ,c be ! two axles2 two bevell$ :eels1 su* z ,d ,e & ,e ,f1 on ^! axles w transmit ! motion or rotation f "o to ! o!r1 & ! relative velocity may1 z usual1 be regulat$ by ! proportional magnitude ( ! :eels4 7#bfd47 ,9 ord] to equalise ! we> ( ! tee? ( a :eel & p9ion1 :i* "w 9 "o ano!r1 x is necess>y t e leaf ( ! p9ion %\ld "w 9 succession ?r\gh e too? ( ! :eel1 & n cont9ually act ^u ! same set ( tee?4 ,if ! tee? c\ld be accurately %ap$ accord+ to ma!matical pr9ciples1 & ! mat]ials ( :i* !y are =m$ be p]fectly uni=m1 ?is precaution w\ld be less necess>y2 b z slight inequalities1 bo? ( mat]ial & =m1 mu/ necess>ily exi/1 ! effects ( ^! %\ld be z f> z possible equalis$1 by di/ribut+ !m ?r\gh e "p ( ! :eel4 ,= ?is purpose x is usual1 especially 9 mill-"w1 :]e consid]able =ce is us$1 s to regulate ! proportion ( ! numb] ( tee? 9 ! :eel & p9ion1 t ! same leaf ( ! p9ion %all n be engag$ twice ) any "o too? ( ! :eel1 until aft] ! action ( a numb] ( tee?1 express$ by ! product ( ! numb] ( tee? 9 ! :eel & p9ion4 ,let u suppose t ! p9ion conta9s t5 leaves1 :i* we %all d5om9ate by ! numb]s #a1 #b1 #c1 c41 & t ! :eel conta9s #fj tee? simil>ly d5om9at$4 ,at ! comm5cem5t ( ! motion suppose ! leaf #a ( ! p9ion engages ! too? #a ( ! :eel2 !n aft] "o revolution ! leaf #a ( ! p9ion w engage ! too? #aa ( ! :eel1 & aft] two revolutions ! leaf #a ( ! p9ion w engage ! too? #ba ( ! :eel2 & 9 l mann]1 aft] #c1 #d1 & #e revolutions ( ! p9ion1 ! leaf #a w engage successively ! tee? #ca1 #da1 & #ea ( ! :eel4 ,aft] ! six? revolution1 ! leaf #a ( ! p9ion w aga9 engage ! too? #a ( ! :eel4 ,?us x is evid5t1 t 9 ! case "h suppos$ ! leaf #a ( ! p9ion w cont9ually be engag$ ) ! tee? #a1 #aa1 #ba1 #ca1 #da1 & #ea ( ! :eel1 & no o!rs4 ,! l may be said ( e leaf ( ! p9ion4 ,?us ! leaf #b ( ! p9ion w be successively engag$ ) ! tee? #b1 #ab1 #bb1 #cb1 #db1 & #eb ( ! :eel1 & no o!rs4 ,any accid5tal inequalities ( ^! tee? w !re=e cont9ually act ^u ea* o!r1 until ! circumf]5ce ( ! :eel be divid$ into p>ts ( t5 tee? ea*1 unequally worn4 ,?is effect w\ld be avoid$ by giv+ ei!r ! :eel or p9ion "o too? m or "o too? less4 ,?us1 suppose ! :eel1 in/ead ( hav+ sixty tee?1 _h sixty-"o1 !n aft] six revolutions ( ! p9ion ! leaf #a ( ! p9ion w\ld be engag$ ) ! too? #fa ( ! :eel2 & aft] "o revolution ( ! :eel1 ! leaf #b ( ! p9ion w\ld be engag$ ) ! too? #a ( ! :eel4 ,?us1 dur+ ! fir/ revolution ( ! :eel ! leaf #a ( ! p9ion w\ld be successively engag$ ) ! tee? #a1 #aa1 #ba1 #ca1 #da1 #ea1 & #fa ( ! :eel3 at ! comm5cem5t ( ! second revolution ( ! :eel ! leaf #b ( ! p9ion w\ld be engag$ ) ! too? #a ( ! :eel2 & dur+ ! second revolution ( ! :eel ! leaf #a ( ! p9ion w\ld be successively engag$ ) ! tee? #aj1 #bj1 #cj1 #dj1 #ej1 & #fj ( ! :eel4 ,9 ! same mann] x may be %[n1 t 9 ! ?ird revolution ( ! :eel ! leaf #a ( ! p9ion w\ld be successively engag$ ) ! tee? #i1 #ai1 #bi1 #ci1 #di1 & #ei ( ! :eel3 dur+ ! f\r? revolution ( ! :eel ! leaf #a ( ! p9ion w\ld be successively engag$ ) ! tee? #h1 #ah1 #bh1 #ch1 #dh1 & #eh ( ! :eel4 ,by cont9u+ ?is reason+ x w appe>1 t dur+ ! t5? revolution ( ! :eel ! leaf #a ( ! p9ion w be engag$ successively ) ! tee? #b1 #ab1 #bb1 #cb1 #db1 & #eb ( ! :eel4 ,at ! comm5cem5t ( ! elev5? revolution ( ! :eel ! leaf #a ( ! p9ion w be engag$ ) ! too? #a ( ! :eel1 z at ! beg9n+ ( ! motion4 ,x is evid5t1 !re=e1 t dur+ ! fir/ t5 revolutions ( ! :eel ea* leaf ( ! p9ion has be5 successively engag$ ) e too? ( ! :eel1 & t dur+ ^! t5 revolutions ! p9ion has revolv$ sixty-"o times4 ,?us ! leaves ( ! p9ion h act$ six hundr$ & t5 times ^u ! tee? ( ! :eel1 be=e two tee? c h act$ twice ^u ea* o!r4 ,! odd too? :i* produces ?is effect is call$ by millwrights ! hunt+ cog4 7#bfe47 ,! mo/ famili> case 9 :i* :eel-"w is us$ to produce & regulate motion m]ely1 )\t any ref]5ce to weights to be rais$ or resi/ances to be ov]come1 is t ( *ronomet]s4 ,9 wat* & clock "w ! object is to cause a :eel to revolve ) a uni=m velocity1 & at a c]ta9 rate4 ,! motion ( ?is :eel is indicat$ by an index or h& plac$ ^u its axis1 & c>ri$ r\nd ) x4 ,9 proportion to ! l5g? ( ! h& ! circle ov] :i* its extremity plays is enl>g$1 & its motion becomes m p]ceptible4 ,?is circle is divid$1 s t v small fractions ( a revolution ( ! h& may be accurately obs]v$4 ,9 mo/ *ronomet]s x is requir$ to give motion to two h&s1 & sometimes to ?ree4 ,^! motions proce$ at diff]5t rates1 accord+ to ! subdivisions ( "t g5]ally adopt$4 ,"o :eel revolves 9 a m9ute1 be>+ a h& :i* plays r\nd a circle divid$ into sixty equal p>ts2 ! motion ( ! h& ov] ea* "p indicat+ "o second1 & a complete revolution ( ! h& be+ p]=m$ 9 "o m9ute4 ,ano!r :eel revolves once1 :ile ! =m] revolves sixty times2 consequ5tly ! h& c>ri$ by ?is :eel revolves once 9 sixty m9utes1 or "o h\r4 ,! circle on :i* x plays is1 l ! =m]1 divid$ into sixty equal p>ts1 & ! motion ( ! h& ov] ea* division is p]=m$ 9 "o m9ute4 ,?is is g5]ally call$ ! m9ute h&1 & ! =m] ! second h&4 ,a ?ird :eel revolves once1 :ile t :i* c>ries ! m9ute h& revolves twelve times2 consequ5tly ?is la/ :eel1 :i* c>ries ! h\r h&1 revolves at a rate twelve times less ?an t ( ! m9ute h&1 & !re=e sev5 hundr$ & tw5ty times less ?an ! second h&4 ,we %all n[ endeav\r to expla9 ! mann] 9 :i* ^! motions are produc$ & regulat$4 ,let ,a1 ,b1 ,c1 ,d1 ,e1 fig4 #aaj41 repres5t a tra9 ( :eels1 & a1 b1 c1 d repres5t _! p9ions1 e be+ a cyl9d] on ! axis ( ! :eel ,e1 r\nd :i* a rope is coil$1 su/a9+ a weight ,w4 ,let ! effect ( ?is weight transmitt$ ?r\gh ! tra9 ( :eels be oppos$ by a p[] ,p act+ ^u ! :eel ,a1 & let ?is p[] be suppos$ to be ( su* a nature z to cause ! weight ,w to desc5d ) a uni=m velocity1 & at any propos$ rate4 ,! :eel ,e c>ries on its circumf]5ce eighty-f\r tee?4 ,! :eel ,d c>ries eighty tee?2 ! :eel ,c is also furni%$ ) eighty tee?1 & ! :eel ,b ) sev5ty-five4 ,! p9ions d & c are ea* furni%$ ) twelve leaves1 & ! p9ions b & a ) t54 ,if ! p[] at ,p be s regulat$ z to all[ ! :eel ,a to revolve once 9 a m9ute1 ) a uni=m velocity1 a h& atta*$ to ! axis ( ?is :eel w s]ve z ! second h&4 ,! p9ion a c>ry+ t5 tee? mu/ revolve sev5 times & a half to produce "o revolution ( ,b1 consequ5tly fifte5 revolutions ( ! :eel ,a w produce two revolutions ( ! :eel ,b2 ! :eel ,b1 !re=e1 revolves twice 9 fifte5 m9utes4 ,! p9ion b mu/ revolve eight times to produce "o revolution ( ! :eel ,c1 & !re=e ! :eel ,c mu/ revolve once 9 f\r qu>t]s ( an h\r1 or 9 "o h\r4 ,if a h& be atta*$ to ! axis ( ?is :eel1 x w h ! motion necess>y = ! m9ute h&4 ,! p9ion c mu/ revolve six times & two ?irds to produce "o revolution ( ! :eel ,d1 & !re=e ?is :eel mu/ revolve once 9 six h\rs & two ?irds4 ,! p9ion d revolves sev5 times = "o revolution ( ! :eel ,e1 & !re=e ! :eel ,e w revolve once 9 =ty-six h\rs & two ?irds4 ,on ! axis ( ! :eel ,c a second p9ion may be plac$1 furni%$ ) sev5 leaves1 :i* may lead a :eel ( eighty-f\r tee?1 s t ?is :eel %all turn once dur+ twelve turns ( ! :eel ,c4 ,if a h& be fix$ ^u ! axis1 ?is h& w revolve once = twelve revolutions ( ! m9ute h& fix$ ^u ! axis ( ! :eel ,c2 t is1 x w revolve once 9 twelve h\rs4 ,if x play ^u a dial divid$ into twelve equal p>ts1 x w move ov] ea* "p 9 an h\r1 & w s]ve ! purpose ( ! h\r h& ( ! *ronomet]4 ,we h "h suppos$ t ! second h&1 ! m9ute h&1 & ! h\r h& move on sep>ate dials4 ,?is1 h[ev]1 is n necess>y4 ,! axis ( ! h\r h& is commonly a tube1 inclos+ )9 x t ( ! m9ute h&1 s t ! same dial s]ves = bo?4 ,! second h&1 h[ev]1 is g5]ally furni%$ ) a sep>ate dial4 7#bff47 ,we %all n[ expla9 ! mann] 9 :i* a p[] is appli$ to ! :eel ,a1 s z to regulate & equalise ! effect ( ! weight ,w4 ,suppose ! :eel ,a furni%$ ) ?irty tee?1 z 9 fig4 #aaa42 if no?+ *eck ! motion1 ! weight ,w w\ld desc5d ) an accel]at$ velocity1 & w\ld communicate an accel]at$ motion to ! :eel ,a4 ,?is effect1 h[ev]1 is int]rupt$ by ! foll[+ contrivance3--,l ,m is a p5dulum vibrat+ on ! c5tre ,l1 & s regulat$ t ! "t ( its oscillation is "o second4 ,! pallets ,i & ,k are connect$ ) ! p5dulum1 s z to oscillate ) x4 ,9 ! position ( ! p5dulum repres5t$ 9 ! figure1 ! pallet ,i /ops ! motion ( ! :eel ,a1 & entirely susp5ds ! action ( ! weight ,w1 fig4 #aaj41 s t = a mom5t ! entire ma*9e is motionless4 ,! weight ,m1 h[ev]1 falls by its gravity t[>ds ! l[e/ position1 & dis5gages ! pallet ,i f ! too? ( ! :eel4 ,! weight ,w beg9s !n to take effect1 & ! :eel ,a turns f ,a t[>ds ,b4 ,mean:ile ! p5dulum ,m oscillates to ! o!r side1 & ! pallet ,k falls "u a too? ( ! :eel ,a1 & *ecks = a mom5t its fur!r motion4 ,on ! return+ vibration ! pallet ,k becomes aga9 dis5gag$1 & all[s ! too? ( ! :eel to escape1 & by ! influ5ce ( ! weight ,w ano!r too? passes be=e ! motion ( ! :eel ,a is aga9 *eck$ by ! int]position ( ! pallet ,i4 ,f ?is explanation x w appe> t1 9 two vibrations ( ! p5dulum1 "o too? ( ! :eel ,a passes ! pallet ,i1 & !re=e1 if ! :eel ,a be furni%$ ) #cj tee?1 x w be all[$ to make "o revolution dur+ #fj vibrations ( ! p5dulum4 ,if1 !re=e1 ! p5dulum be regulat$ s z to vibrate seconds1 ?is :eel w revolve once 9 a m9ute4 ,f ! action ( ! pallets 9 *eck+ ! motion ( ! :eel ,a1 & all[+ its tee? alt]nately to escape1 ?is has be5 call$ ! escapem5t :eel2 & ! :eel & pallets toge!r are g5]ally call$ ! escapem5t1 or 'scapem5t4 ,we h already expla9$1 t by reason ( ! friction on ! po9ts ( support1 & o!r causes1 ! sw+ ( ! p5dulum w\ld gradually dim9i%1 & its vibration at l5g? cease4 ,?is1 h[ev]1 is prev5t$ by ! action ( ! tee? ( ! scapem5t :eel ^u ! pallets1 :i* is j suffici5t to communicate t quantity ( =ce to ! p5dulum :i* is necess>y to c\nt]act ! ret>d+ effects1 & to ma9ta9 its motion4 ,x ?us appe>s1 t al?\gh ! effect ( ! gravity ( ! weight ,w 9 giv+ motion to ! ma*9e is at int]vals susp5d$1 yet ?is "p ( ! =ce is n lo/1 be+1 dur+ ^! int]vals1 employ$ 9 giv+ to ! p5dulum all t motion :i* x w\ld lose by ! resi/ances to :i* x is inevitably expos$4 ,9 /ation>y clocks1 & 9 o!r cases 9 :i* ! bulk ( ! ma*9e is n an objection1 a desc5d+ weight is us$ z ! mov+ p[]4 ,b 9 wat*es & portable *ronomet]s1 ?is w\ld be att5d$ ) evid5t inconv5i5ce4 ,9 su* cases1 a spiral spr+1 call$ ! ma9spr+1 is ! mov+ p[]4 ,! mann] 9 :i* ?is spr+ communicates rotation to an axis1 & ! +5i\s me?od ( equalis+ ! effect ( its v>iable ela/icity by giv+ to x a lev]age1 :i* increases z ! ela/ic =ce dim9i%es1 h be5 already expla9$4 7#bee47 ,a simil> objection lies aga9/ ! use ( a p5dulum 9 portable *ronomet]s4 ,a spiral spr+ ( a simil> k9d1 b inf9itely m delicate1 call$ a hair spr+1 is sub/itut$ 9 its place4 ,?is spr+ is connect$ ) a nicely-balanc$ :eel1 call$ ! balance :eel1 :i* plays 9 pivots4 ,:5 ?is :eel is turn$ to a c]ta9 ext5t 9 "o direction1 ! hair spr+ is coil$ up1 & its ela/icity causes ! :eel to recoil1 & return to a position 9 :i* ! en]gy ( ! spr+ acts 9 ! opposite direction4 ,! balance :eel !n returns1 & cont9ually vibrates 9 ! same mann]4 ,! axis ( ?is :eel is furni%$ ) pallets simil> to ^? ( ! p5dulum1 :i* are alt]nately engag$ ) ! tee? ( a cr[n :eel1 :i* takes ! place ( ! scapem5t :eel already describ$4 ,a g5]al view ( ! "w ( a common wat* is repres5t$ 9 fig4 #aaa4 bis4 ,a is ! balance :eel be>+ pallets p p ^u its axis2 ,c is ! cr[n :eel1 ^: tee? are suff]$ to escape alt]nately by ^? pallets 9 ! mann] already describ$ 9 ! scapem5t ( a clock4 ,on ! axis ( ! cr[n :eel is plac$ a p9ion d1 :i* drives ano!r cr[n :eel ,k4 ,on ! axis ( ?is is plac$ ! p9ion c1 :i* plays 9 ! tee? ( ! ?ird :eel ,l4 ,! p9ion b on ! axis ( ,l is engag$ ) ! :eel ,m1 call$ ! c5tre :eel4 ,! axle ( ?is :eel is c>ri$ up ?r\gh ! c5tre ( ! dial4 ,a p9ion a is plac$ ^u x1 :i* works 9 ! great :eel ,n4 ,on ?is :eel ! ma9spr+ imm$iately acts4 ,o ,p is ! ma9spr+ /ripp$ ( its b>rel4 ,! axis ( ! :eel ,m pass+ ?r\gh ! c5tre ( ! dial is squ>$ at ! end to receive ! m9ute h&4 ,a second p9ion ,q is plac$ ^u ?is axle :i* drives a :eel ,t4 ,on ! axle ( ?is :eel a p9ion g is plac$1 :i* drives ! h\r :eel ,v4 ,?is :eel is plac$ ^u a tubul> axis1 :i* incloses )9 x ! axis ( ! :eel ,m4 ,?is tubul> axis pass+ ?r\gh ! c5tre ( ! dial1 c>ries ! h\r h&4 ,! :eels ,a1 ,b1 ,c1 ,d1 ,e1 fig4 #aaj41 correspond to ! :eels ,c1 ,k1 ,l1 ,m1 ,n1 fig4 #aab42 & ! p9ions a1 b1 c1 d1 e1 fig4 #aji41 correspond to ! p9ions d1 c1 b1 a1 fig4 #aaa4 ,f :at has already be5 expla9$ ( ^! :eels1 x w be obvi\s t ! :eel ,m1 fig4 #aaa41 revolves once 9 an h\r1 caus+ ! m9ute h& to move r\nd ! dial once 9 t "t4 ,?is :eel at ! same "t turns ! p9ion ,q :i* leads ! :eel ,t4 ,?is :eel aga9 turns ! p9ion g :i* leads ! h\r :eel ,v4 ,! leaves & tee? ( ^! p9ions & :eels are proportion$1 z already expla9$1 s t ! :eel ,v revolves once dur+ twelve revolutions ( ! :eel ,m4 ,! h\r h&1 !re=e1 :i* is c>ri$ by ! tubul> axle ( ! :eel ,v1 moves once r\nd ! dial 9 twelve h\rs4 ,our object "h has n be5 to give a detail$ acc\nt ( wat* & clock "w1 a subject = :i* we mu/ ref] ! read] to ! prop] dep>tm5t ( ?is "w4 ,su* a g5]al acc\nt has only be5 attempt$ z may expla9 h[ too? & p9ion "w may be appli$ to regulate motion4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,,*ap4 ,,xv4 ,,( ,,! ,,pulley4 7#bfg47 ,! next class ( simple ma*9es1 :i* pres5t !mselves to our att5tion1 is t :i* we h call$ ! cord4 ,if a rope 7 p]fectly flexible1 & 7 capable ( be+ b5t ov] a %>p edge1 & ( mov+ ^u x )\t friction1 we %\ld be enabl$ by its means to make a =ce 9 any "o direction ov]come resi/ance1 or communicate motion 9 any o!r direction4 ,?us if ,p1 fig4 #aab41 be su* an edge1 a p]fectly flexible rope pass+ ov] x w\ld be capable ( transmitt+ a =ce ,s ,f to a resi/ance ,q ,r1 s z to support or ov]come ,r1 or by a motion 9 ! direction ( ,s ,f to produce ano!r motion 9 ! direction ,r ,q4 ,b z no mat]ials ( :i* ropes c be con/ruct$ c give !m p]fect flexibility1 & z 9 proportion to ! /r5g? by :i* !y are enabl$ to transmit =ce _! rigidity increases1 x is necess>y1 9 practice1 to adopt means to remove or mitigate ^? effects :i* att5d imp]fect flexibility1 & :i* w\ld o!rwise r5d] cords practically inapplicable z ma*9es4 ,:5 a cord is us$ to transmit a =ce f "o direction to ano!r1 its /iffness r5d]s "s =ce necess>y 9 b5d+ x ov] ! angle ,p1 :i* ! two directions =m2 & if ! angle be %>p1 ! ex]tion ( su* a =ce may be att5d$ ) ! rupture ( ! cord4 ,if1 in/ead ( b5d+ ! rope at "o po9t ov] a s+le angle1 ! *ange ( direction 7 produc$ by successively deflect+ x ov] sev]al angles1 ea* ( :i* w\ld be less %>p ?an a s+le "o c\ld be1 ! =ce requisite = ! deflection1 z well z ! liability ( ruptur+ ! cord1 w\ld be consid]ably dim9i%$4 ,b ?is end w be /ill m p]fectly atta9$ if ! deflection ( ! cord be produc$ by b5d+ x ov] ! surface ( a curve4 ,if a rope 7 appli$ only to su/a91 & n to move a weight1 ?is w\ld be suffici5t to remove ! inconv5i5ces aris+ f its rigidity4 ,b :5 motion is to be produc$1 ! rope1 9 pass+ ov] ! curv$ surface1 w\ld be subject to excessive friction1 & consequ5tly to rapid we>4 ,?is inconv5i5ce is remov$ by caus+ ! surface on :i* ! rope runs to move ) x1 s t no m friction is produc$ ?an w\ld arise f ! curv$ surface roll+ ^u ! rope4 7#bfh47 ,all ^! ends are atta9$ by ! common pulley1 :i* consi/s ( a :eel call$ a %eave1 fix$ 9 a block & turn+ on a pivot4 ,a groove is =m$ 9 ! edge ( ! :eel 9 :i* ! rope runs1 ! :eel revolv+ ) x4 ,su* an app>atus is repres5t$ 9 fig4 #aac4 ,we %all1 = ! pres5t1 omit ! consid]ation ( t "p ( ! effects ( ! /iffness & friction ( ! ma*9e :i* is n remov$ by ! contrivance j expla9$1 & %all consid] ! rope z p]fectly flexible & mov+ )\t friction4 ,f ! def9ition ( a flexible cord1 x foll[s1 t its t5sion1 or ! =ce by :i* x is /ret*$ ?r\gh\t its entire l5g?1 mu/ be uni=m4 ,f ?is pr9ciple1 & ?is alone1 all ! me*anical prop]ties ( pulleys may be d]iv$4 ,al?\gh1 z already expla9$1 ! :ole me*anical efficacy ( ?is ma*9e dep5ds on ! qualities ( ! cord1 & n on ^? ( ! block & %eave1 :i* are only introduc$ to remove ! accid5tal effects ( /iffness & friction2 yet x has be5 usual to give ! "n pulley to ! block & %eave1 & a comb9ation ( blocks1 %eaves1 & ropes is call$ a tackle4 7#bfi47 ,:5 ! rope passes ov] a s+le :eel1 :i* is fix$ 9 its position1 z 9 fig4 #aac41 ! ma*9e is call$ a fix$ pulley4 ,s9ce ! t5sion ( ! cord is uni=m ?r\gh\t its l5g?1 x foll[s1 t 9 ?is ma*9e ! p[] & weight are equal4 ,= ! weight /ret*es t "p ( ! cord :i* is betwe5 ! weight & pulley1 & ! p[] /ret*es t "p betwe5 ! p[] & ! pulley4 ,& s9ce ! t5sion ?r\gh\t ! :ole l5g? is ! same1 ! weight mu/ be equal to ! p[]4 ,h5ce x appe>s t no me*anical advantage is ga9$ by ?is ma*9e4 ,nev]!less1 !re is sc>cely any eng9e1 simple or complex1 att5d$ ) m conv5i5ce4 ,9 ! application ( p[]1 :e!r ( m5 or animals1 or aris+ f natural =ces1 !re are always "s directions 9 :i* x may be ex]t$ to mu* great] conv5i5ce & advantage ?an o!rs1 & 9 _m cases ! ex]tion ( ^! p[]s is limit$ to a s+le direction4 ,a ma*9e1 !re=e1 :i* enables u to give ! mo/ advantage\s direction to ! mov+ p[]1 :atev] be ! direction ( ! resi/ance oppos$ to x1 contributes z mu* practical conv5i5ce z "o :i* enables a small p[] to balance or ov]come a great weight4 ,9 direct+ ! p[] aga9/ ! resi/ance1 x is (t5 necess>y to use two fix$ pulleys4 ,?us1 9 elevat+ a weight ,a1 fig4 #aad41 to ! summit ( a build+1 by ! /r5g? ( a horse mov+ bel[1 two fix$ pulleys ,b & ,c may be us$4 ,! rope is c>ri$ f ,a ov] ! pulley ,b2 &1 pass+ d[nw>ds1 is br\ght "u ,c1 & f9ally drawn by ! animal on ! horizontal plane4 ,9 ! same mann] sails are spread1 & flags hoi/$ on ! y>ds & ma/s ( a %ip1 by sailors pull+ a rope on ! deck4 ,by means ( ! fix$ pulley a man may raise himself to a consid]able height1 or desc5d to any propos$ dep?4 ,if he be plac$ 9 a *air or bucket atta*$ to "o end ( a rope :i* is c>ri$ ov] a fix$ pulley1 by lay+ hold ( ?is rope on ! o!r side1 z repres5t$ 9 fig4 #aae41 he may1 at w1 desc5d to a dep? equal to half ( ! entire l5g? ( ! rope1 by cont9ually yield+ rope on ! "o side1 & depress+ ! bucket or *air by 8 weight on ! o!r4 ,fire-escapes h be5 con/ruct$ on ?is pr9ciple1 ! fix$ pulley be+ atta*$ to "s "p ( ! build+4 7#bgj47 ,a s+le moveable pulley is repres5t$ 9 fig4 #aaf4 ,a cord is c>ri$ f a fix$ po9t ,f1 & pass+ ?r\gh a block ,b1 atta*$ to a weight ,w1 passes ov] a fix$ pulley ,c1 ! p[] be+ appli$ at ,p4 ,we %all fir/ suppose ! p>ts ( ! cord on ea* side ! :eel ,b to be p>allel2 9 ?is case1 ! :ole weight ,w be+ su/a9$ by ! p>ts ( ! cords ,b ,c & ,b ,f1 & ^! p>ts be+ equally /ret*$ 7#bfh471 ea* mu/ su/a9 half ! weight1 :i* is !re=e ! t5sion ( ! cord4 ,?is t5sion is resi/$ by ! p[] at ,p1 :i* mu/1 !re=e1 be equal to half ! weight4 ,9 ?is ma*9e1 !re=e1 ! weight is twice ! p[]4 7#bga47 ,if ! p>ts ( ! cord ,b ,c & ,b ,f be n p>allel1 z 9 fig4 #aag41 a great] p[] ?an half ! weight is !re=e necess>y to su/a9 x4 ,to det]m9e ! p[] necess>y to support a giv5 weight1 9 ?is case take ! l9e ,b ,a 9 ! v]tical direction1 consi/+ ( z _m in*es z ! weight consi/s ( ounces2 f ,a draw ,a ,d p>allel to ,b ,c1 & ,a ,e p>allel to ,b ,f2 ! =ce ( ! weight repres5t$ by ,a ,b w be equival5t to two =ces repres5t$ by ,b ,d & ,b ,e4 7#gd47 ,! numb] ( in*es 9 ^! l9es respectively w repres5t ! numb] ( ounces :i* are equival5t to ! t5sions ( ! p>ts ,b ,f & ,b ,c ( ! cord4 ,b z ^! t5sions are equal1 ,b ,d & ,b ,e mu/ be equal1 & ea* w express ! am\nt ( ! p[] ,p1 :i* /ret*es ! cord at ,p ,c4 ,x is evid5t t ! f\r l9es1 ,a ,e1 ,e ,b1 ,b ,d1 & ,d ,a1 are equal4 ,& z ea* ( !m repres5ts ! p[]1 ! weight :i* is repres5t$ by ,a ,b mu/ be less ?an twice ! p[] :i* is repres5t$ by ,a ,e & ,e ,b tak5 toge!r4 ,x foll[s1 !re=e1 t z p>ts ( ! ropes :i* support ! weight dep>t f p>allelism ! ma*9e becomes less & less efficaci\s2 & !re are c]ta9 obliquities at :i* ! equilibrat+ p[] w\ld be mu* great] ?an ! weight4 7#bgb47 ,! me*anical p[] ( pulleys admits ( be+ almo/ indef9itely increas$ by comb9ation4 ,sy/ems ( pulleys may be divid$ into two classes2 ^? 9 :i* a s+le rope is us$1 & ^? :i* consi/ ( sev]al di/9ct ropes4 ,fig4 #aah4 & #aai4 repres5t two sy/ems ( pulleys1 ea* hav+ a s+le rope4 ,! weight is 9 ea* case atta*$ to a moveable block1 ,b1 9 :i* are fix$ two or m :eels2 ,a is a fix$ block1 & ! rope is successively pass$ ov] ! :eels above & bel[1 &1 aft] pass+ ov] ! la/ :eel above1 is atta*$ to ! p[]4 ,! t5sion ( t "p ( ! cord to :i* ! p[] is atta*$ is produc$ by ! p[]1 & !re=e equival5t to x1 & ! same t5sion mu/ ext5d ?r\gh\t its :ole l5g?4 ,! weight is su/a9$ by all ^? p>ts ( ! cord :i* pass f ! l[] block1 & z ! =ce :i* /ret*es !m all is ! same1 viz4 t ( ! p[]1 ! effect ( ! weight mu/ be equally di/ribut$ among !m1 _! directions be+ suppos$ to be p>allel4 ,x w be evid5t1 f ?is reason+1 t ! weight w be z _m times great] ?an ! p[] z ! numb] ( cords :i* support ! l[] block4 ,?us1 if !re be six cords1 ea* cord w support a six? "p ( ! weight1 t is1 ! weight w be six times ! t5sion ( ! cord1 or six times ! p[]4 ,9 fig4 #aah4 ! cord is repres5t$ z be+ f9ally atta*$ to a hook on ! upp] block4 ,b x may be c>ri$ ov] an additional :eel fix$ 9 t block1 & f9ally atta*$ to a hook 9 ! l[] block1 z 9 fig4 #aai41 by :i* "o w be add$ to ! p[] ( ! ma*9e1 ! numb] ( cords at ! l[] block be+ increas$ by "o4 ,9 ! sy/em repres5t$ 9 fig4 #aah4 ! :eels are plac$ 9 ! blocks "o above ! o!r2 9 fig4 #aai4 !y are plac$ side by side4 ,9 all sy/ems ( pulleys ( ?is class1 ! weight ( ! l[] block is to be consid]$ z a "p ( ! weight to be rais$1 & 9 e/imat+ ! p[] ( ! ma*9e1 ?is %\ld always be att5d$ to4 7#bgc47 ,:5 ! p[] ( ! ma*9e1 & !re=e ! numb] ( :eels1 is consid]able1 "s difficulty arises 9 ! arrangem5t ( ! :eels & cords4 ,! celebrat$ ,smeaton contriv$ a tackle1 :i* takes its "n f him1 9 :i* !re are t5 :eels 9 ea* block3 five l>ge :eels plac$ side by side1 & five small] ones simil>ly plac$ above !m 9 ! l[] block1 & bel[ !m 9 ! upp]4 ,fig4 #abj4 repres5ts ,smeaton's blocks )\t ! rope4 ,! :eels are m>k$ ) ! numb]s #a1 #b1 #c1 c41 9 ! ord] 9 :i* ! rope is to be pass$ ov] !m4 ,z 9 ?is pulley #bj di/9ct p>ts ( ! rope support ! l[] block1 ! weight1 includ+ ! l[] block1 w be #bj times ! equilibrat+ p[]4 7#bgd47 ,9 all ^! sy/ems ( pulleys1 e :eel has a sep>ate axle1 & !re is a di/9ct :eel = e turn ( ! rope at ea* block4 ,ea* :eel is att5d$ ) friction on its axle1 & also ) friction betwe5 ! %eave & block4 ,! ma*9e is by ?is means robb$ ( a great "p ( its efficacy1 s9ce1 to ov]come ! friction alone1 a consid]able p[] is 9 mo/ cases necess>y4 ,an +5i\s contrivance has be5 sugge/$1 by :i* all ! advantage ( a l>ge numb] ( :eels may be obta9$ )\t ! multipli$ friction ( di/9ct %eaves & axles4 ,to compreh5d ! excell5ce ( ?is contrivance1 x w be necess>y to consid] ! rate at :i* ! rope passes ov] ! sev]al :eels ( su* a sy/em1 z fig4 #aah4 ,if "o foot ( ! rope ,g ,f pass ov] ! pulley ,f1 two feet mu/ pass ov] ! pulley ,e1 because ! di/ance betwe5 ,f & ,e be+ %ort5$ "o foot1 ! total l5g? ( ! rope ,g ,f ,e mu/ be %ort5$ two feet4 ,^! two feet ( rope mu/ pass 9 ! direction ,e ,d1 & ! :eel ,d1 ris+ "o foot1 ?ree feet ( rope mu/ consequ5tly pass ov] x4 ,^! ?ree feet ( rope pass+ 9 ! direction ,d ,c1 & ! rope ,d ,c be+ also %ort5$ "o foot by ! asc5t ( ! l[] block1 f\r feet ( rope mu/ pass ov] ! :eel ,c4 ,9 ! same way x may be %[n t five feet mu/ pass ov] ,b1 & six feet ov] ,a4 ,?us1 :atev] be ! numb] ( :eels 9 ! upp] & l[] blocks1 ! p>ts ( ! rope :i* pass 9 ! same "t ov] ! :eels 9 ! l[] block are 9 ! proportion ( ! odd numb]s #a1 #c1 #e1 c42 & ^? :i* pass ov] ! :eels 9 ! upp] block 9 ! same "t1 are z ! ev5 numb]s #b1 #d1 #f1 c4 ,if ! :eels 7 all ( equal size1 z 9 fig4 #aai41 !y w\ld revolve ) velocities proportional to ! rate at :i* ! rope passes ov] !m4 ,s t1 :ile ! fir/ :eel bel[ revolves once1 ! fir/ :eel above w revolve twice2 ! second :eel bel[ ?ree times2 ! second :eel above1 f\r times1 & s on4 ,if1 h[ev]1 ! :eels diff]$ 9 size 9 proportion to ! quantity ( rope :i* mu/ pass ov] !m1 !y w\ld evid5tly revolve 9 ! same "t4 ,?us1 if ! fir/ :eel above 7 twice ! size ( ! fir/ :eel bel[1 "o revolution w\ld ?r[ (f twice ! quantity ( rope4 ,aga91 if ! second :eel bel[ 7 ?rice ! size ( ! fir/ :eel bel[1 x w\ld ?r[ (f 9 "o revolution ?rice ! quantity ( rope1 & s on4 ,:eels ?us proportion$1 revolv+ 9 exactly ! same "t1 might be all plac$ on "o axle1 & w\ld p>take ( "o common motion1 or1 :at is to ! same effect1 sev]al grooves might be cut ^u ! face ( "o solid :eel1 ) diamet]s 9 ! proportion ( ! odd numb]s #a1 #c1 & #e1 c41 = ! l[] pulley1 & correspond+ grooves on ! face ( ano!r solid :eel repres5t$ by ! ev5 numb]s #b1 #d1 #f1 c41 = ! upp] pulley4 ,! rope be+ pass$ successively ov] ! grooves ( su* :eels1 w\ld be ?r[n (f exactly 9 ! same mann] z if e groove 7 ^u a sep>ate :eel1 & e :eel revolv$ indep5d5tly ( ! o!rs4 ,su* is ,:ite's pulley1 repres5t$ 9 fig4 #aba4 ,! advantage ( ?is ma*9e1 :5 accurately con/ruct$1 is v consid]able4 ,! friction1 ev5 :5 great resi/ances are to be oppos$1 is v trifl+2 b1 on ! o!r h&1 x has correspond+ disadvantages :i* greatly circumscribe its practical utility4 ,9 ! workman%ip ( ! grooves great difficulty is f\nd 9 giv+ !m ! exact proportions4 ,9 do+ :i*1 ! ?ickness ( ! rope mu/ be accurately all[$ =2 & consequ5tly x foll[s1 t ! same pulley c nev] act except ) a rope ( a p>ticul> diamet]4 ,a v slight deviation f ! true proportion ( ! grooves w cause ! rope to be unequally /ret*$1 & w ?r[ on "s p>ts ( x an undue proportion ( ! weight1 :ile o!r p>ts become ne>ly1 & sometimes altoge!r slack4 ,besides ^! defects1 ! rope is s liable to d]angem5t by be+ ?r[n out ( ! grooves1 t ! pulley c sc>cely be consid]$ portable4 ,= ^! & o!r reasons1 ?is ma*9e1 +5i\s z x unque/ionably is1 has nev] be5 ext5sively us$4 7#bge47 ,9 ! sev]al sy/ems ( pulleys j expla9$1 ! hook to :i* ! fix$ block is atta*$ supports ! entire ( bo? ! p[] & weight4 ,:5 ! ma*9e is 9 equilibrium1 ! p[] only supports s mu* ( ! weight z is equal to ! t5sion ( ! cord1 all ! rema9d] ( ! weight be+ ?r[n on ! fix$ po9t1 accord+ to :at 0 obs]v$ 9 7#bbe47 ,if ! p[] be mov$ s z to raise ! weight1 x w move ) a velocity z _m times great] ?an t ( ! weight z ! weight itself is great] ?an ! p[]4 ,?us 9 fig4 #aah4 if ! weight atta*$ to ! l[] block asc5d "o foot1 six feet ( l9e w pass ov] ! pulley ,a1 accord+ to :at has be5 already prov$4 ,?us1 ! p[] w desc5d ?r\gh six feet1 :ile ! weight rises "o foot4 ,b1 9 ?is case1 ! weight is six times ! p[]4 ,all ! obs]vations 9 7#bbf47 w !re=e be applicable to ! cases ( great weights rais$ by small p[]s by means ( ! sy/em ( pulleys j describ$4 7#bgf47 ,:5 two or m ropes are us$1 pulleys may be comb9$ 9 v>i\s ways s z to produce any degree ( me*anical effect4 ,if to any ( ! sy/ems already describ$ a s+le moveable pulley be add$1 ! p[] ( ! ma*9e w\ld be d\bl$4 ,9 ?is case1 ! second rope is atta*$ to ! hook ( ! l[] block1 z 9 fig4 #abb41 & be+ c>ri$ ?r\gh a moveable pulley atta*$ to ! weight1 x is f9ally br\ght up to a fix$ po9t4 ,! t5sion ( ! second cord is equal to half ! weight 7#bgj472 & !re=e ! p[] ,p1 by means ( ! fir/ cord1 w h only half ! t5sion :i* x w\ld h if ! weight 7 atta*$ to ! l[] block4 ,a moveable pulley ?us appli$ is call$ a runn]4 ,illu/ration3 ,c4 ,v>ley1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 7#bgg47 ,two sy/ems ( pulleys1 call$ ,spani% b>tons1 hav+ ea* two ropes1 are repres5t$ 9 fig4 #abc4 ,! t5sion ( ! rope ,p ,a ,b ,c 9 ! fir/ sy/em is equal to ! p[]2 & !re=e ! p>ts ,b ,a & ,b ,c support a portion ( ! weight equal to twice ! p[]4 ,! rope ,e ,a supports ! t5sions ( ,a ,p & ,a ,b2 & !re=e ! t5sion ( ,a ,e ,d is twice ! p[]4 ,?us1 ! unit$ t5sions ( ! ropes :i* support ! pulley ,b is f\r times ! p[]1 :i* is !re=e ! am\nt ( ! weight4 ,9 ! second sy/em1 ! rope ,p ,a ,d is /ret*$ by ! p[]4 ,! rope ,a ,e ,b ,c acts aga9/ ! unit$ t5sions ,a ,p & ,a ,d2 & !re=e ! t5sion ( ,a ,e or ,e ,b is twice ! p[]4 ,?us1 ! weight acts aga9/ ?ree t5sions2 two ( :i* are equal to twice ! p[]1 & ! rema9+ "o is equal to ! p[]4 ,! weight is !re=e equal to five times ! p[]4 ,a s+le rope may be s arrang$ ) "o moveable pulley z to support a weight equal to ?ree times ! p[]4 ,9 fig4 #abd4 ?is arrangem5t is repres5t$1 :]e ! numb]s suffici5tly indicate ! t5sion ( ! rope1 & ! proportion ( ! weight & p[]4 ,9 fig4 #abe4 ano!r me?od ( produc+ ! same effect ) two ropes is repres5t$4 7#bgh47 ,if sev]al s+le moveable pulleys be made successively to act ^u ea* o!r1 ! effect is d\bl$ by e additional pulley3 su* a sy/em z ?is is repres5t$ 9 fig4 #abf4 ,! t5sion ( ! fir/ rope is equal to ! p[]2 ! second rope acts aga9/ twice ! t5sion ( ! fir/1 & !re=e x is /ret*$ ) a =ce equal to twice ! p[]3 ! ?ird rope acts aga9/ twice ?is t5sion1 & !re=e x is /ret*$ ) a =ce equal to f\r times ! p[]1 & s on4 ,9 ! sy/em repres5t$ 9 fig4 #abf4 !re are ?ree ropes1 & ! weight is eight times ! p[]4 ,ano!r rope w\ld r5d] x sixte5 times ! p[]1 & s on4 ,9 ?is sy/em1 x is obvi\s t ! ropes w require to h diff]5t degrees ( /r5g?1 s9ce ! t5sion to :i* !y are subject increases 9 a d\ble proportion f ! p[] to ! weight4 7#bgi47 ,if ea* ( ! ropes1 in/ead ( be+ atta*$ to fix$ po9ts at ! top1 are c>ri$ ov] fix$ pulleys1 & atta*$ to ! sev]al moveable pulleys respectively1 z 9 fig4 #abg41 ! p[] ( ! ma*9e w be greatly increas$2 = 9 t case ! =ces :i* /ret* ! successive ropes increase 9 a treble in/ead ( a d\ble proportion1 z w be evid5t by att5d+ to ! numb]s :i* express ! t5sions 9 ! figure4 ,"o rope w\ld r5d] ! weight ?ree times ! p[]1 two ropes n9e times1 ?ree ropes tw5ty-sev5 times1 & s on4 ,an arrangem5t ( pulleys is repres5t$ 9 fig4 #abh41 by :i* ea* rope1 in/ead ( be+ f9ally atta*$ to a fix$ po9t1 z 9 fig4 #abf41 is atta*$ to ! weight4 ,! weight is 9 ?is case support$ by ?ree ropes2 "o /ret*$ ) a =ce equal to ! p[]2 ano!r ) a =ce equal to twice ! p[]2 & a ?ird ) a =ce equal to f\r times ! p[]4 ,! weight is !re=e1 9 ?is case1 sev5 times ! p[]4 7#bhj47 ,if ! ropes1 in/ead ( be+ atta*$ to ! weight1 pass ?r\gh :eels1 z 9 fig4 #abi41 & are f9ally atta*$ to ! pulleys above1 ! p[] ( ! ma*9e w be consid]ably increas$4 ,9 ! sy/em "h repres5t$ ! weight is tw5ty-six times ! p[]4 7#bha47 ,9 consid]+ ^! sev]al comb9ations ( pulleys1 we h omitt$ to e/imate ! effects produc$ by ! weights ( ! %eaves & blocks4 ,)\t ent]+ into ! details ( ?is computation1 x may be obs]v$ g5]ally1 t 9 ! sy/ems repres5t$ 9 figs4 #abf41 #abg4 ! weight ( ! :eel & blocks acts aga9/ ! p[]2 b t 9 figs4 #abh4 & #abi4 !y assi/ ! p[]s 9 support+ ! weight4 ,9 ! sy/ems repres5t$ 9 fig4 #abc4 ! weight ( ! pulleys1 to a c]ta9 ext5t1 neutralise ea* o!r4 7#bhb47 ,x w 9 all cases be f\nd1 t t quantity by :i* ! weight exce$s ! p[] is support$ by fix$ po9ts2 & !re=e1 al?\gh x be commonly /at$ t a small p[] supports a great weight1 yet 9 ! pulley1 z 9 all o!r ma*9es1 ! p[] supports no m ( ! weight ?an is exactly equal to its own am\nt4 ,x w n be necess>y to e/abli% ?is 9 ea* ( ! examples :i* h be5 giv53 hav+ expla9$ x 9 "o in/ance1 ! /ud5t w f9d no difficulty 9 apply+ ! same reason+ to o!rs4 ,9 fig4 #abf41 ! fix$ pulley su/a9s a =ce equal to twice ! p[]1 & by x ! p[] giv+ t5sion to ! fir/ rope su/a9s a "p ( ! weight equal to itself4 ,! fir/ hook su/a9s a portion ( ! weight equal to ! t5sion ( ! fir/ /r+1 or to ! p[]4 ,! second hook su/a9s a =ce equal to twice ! p[]2 & ! ?ird hook su/a9s a =ce equal to f\r times ! p[]4 ,! ?ree hooks !re=e su/a9 a portion ( ! weight equal to sev5 times ! p[]2 & ! weight itself be+ eight times ! p[]1 x is evid5t t ! "p ( ! weight :i* rema9s to be support$ by ! p[] is equal to ! p[] itself4 7#bhc47 ,:5 a weight is rais$ by any ( ! sy/ems ( pulleys :i* h be5 la/ describ$1 ! proportion betwe5 ! velocity ( ! weight & ! velocity ( ! p[]1 s frequ5tly notic$ 9 o!r ma*9es1 w always be obs]v$4 ,9 ! sy/em ( pulleys repres5t$ 9 fig4 #abf4 ! weight be+ eight times ! p[]1 ! velocity ( ! p[] w be eight times t ( ! weight4 ,if ! p[] be mov$ ?r\gh eight feet1 t "p ( ! rope betwe5 ! fix$ pulley & ! fir/ moveable pulley w be %ort5$ by eight feet4 ,& s9ce ! two p>ts :i* lie above ! fir/ moveable pulley mu/ be equally %ort5$1 ea* w be dim9i%$ by f\r feet2 !re=e ! fir/ pulley w rise ?r\gh f\r feet :ile ! p[] moves ?r\gh eight feet4 ,9 ! same way x may be %[n1 t :ile ! fir/ pulley moves ?r\gh f\r feet1 ! second moves ?r\gh two2 & :ile ! second moves ?r\gh two1 ! ?ird1 to :i* ! weight is atta*$1 is rais$ ?r\gh "o foot4 ,:ile ! p[]1 !re=e1 is c>ri$ ?r\gh eight feet1 ! weight is mov$ ?r\gh "o foot4 ,by reason+ simil> to ?is1 x may be %[n t ! space ?r\gh :i* ! p[] is mov$ 9 e case is z _m times great] ?an ! height ?r\gh :i* ! weight is rais$1 z ! weight is great] ?an ! p[]4 7#bhd47 ,f its portable =m1 *eapness ( con/ruction1 & ! facility ) :i* x may be appli$ 9 almo/ e situation1 ! pulley is "o ( ! mo/ useful ( ! simple ma*9es4 ,! me*anical advantage1 h[ev]1 :i* x appe>s 9 !ory to possess is consid]ably dim9i%$ 9 practice1 ow+ to ! /iffness ( ! cordage1 & ! friction ( ! :eels & blocks4 ,by ?is means x is comput$ t 9 mo/ cases s great a proportion z two ?irds ( ! p[] is lo/4 ,! pulley is mu* us$ 9 build+1 :]e weights are to be elevat$ to great heights4 ,b its mo/ ext5sive application is f\nd 9 ! rigg+ ( %ips1 :]e almo/ e motion is accompli%$ by its means4 7#bhe47 ,9 all ! examples ( pulleys1 we h suppos$ ! p>ts ( ! rope su/a9+ ! weight & ea* ( ! moveable pulleys to be p>allel to ea* o!r4 ,if !y be subject to consid]able obliquity1 ! relative t5sions ( ! diff]5t ropes mu/ be e/imat$ accord+ to ! pr9ciple appli$ 9 7#bga47 ,,*ap4 ,,xvi4 ,,on ,,! ,,incl9$ ,,plane1 ,,w$ge1 ,,& ,,screw4 7#bhf47 ,! incl9$ plane is ! mo/ simple ( all ma*9es4 ,x is a h>d plane surface =m+ "s angle ) a horizontal plane1 t angle n be+ a "r angle4 ,:5 a weight is plac$ on su* a plane1 a two-fold effect is produc$4 ,a "p ( ! effect ( ! weight is resi/$ by ! plane1 & produces a pressure ^u x2 & ! rema9d] urges ! weight d[n ! plane1 & w\ld produce a pressure aga9/ any surface resi/+ its motion plac$ 9 a direction p]p5dicul> to ! plane 7#aca47 ,let ,a ,b1 fig4 #acj41 be su* a plane1 ,b ,c its horizontal base1 ,a ,c its height1 & ,a ,b ,c its angle ( elevation4 ,let ,w be a weight plac$ ^u x4 ,?is weight acts 9 ! v]tical direction ,w ,d1 & is equival5t to two =ces1 ,w ,f p]p5dicul> to ! plane1 & ,w ,e direct$ d[n ! plane 7#gd47 ,if a plane be plac$ at "r angles to ! incl9$ plane bel[ ,w1 x w resi/ ! desc5t ( ! weight1 & su/a9 a pressure express$ by ,w ,e4 ,?us1 ! weight ,w re/+ 9 ! corn]1 in/ead ( produc+ "o pressure 9 ! direction ,w ,d1 w produce two pressures1 "o express$ by ,w ,f ^u ! incl9$ plane1 & ! o!r express$ by ,w ,e ^u ! resi/+ plane4 ,^! pressures respectively h ! same proportion to ! entire weight z ,w ,f & ,w ,e h to ,w ,d1 or z ,d ,e & ,w ,e h to ,w ,d1 because ,d ,e is equal to ,w ,f4 ,n[ ! triangle ,w ,e ,d is 9 all respects simil> to ! triangle ,a ,b ,c1 ! "o diff]+ f ! o!r only 9 ! scale on :i* x is con/ruct$4 ,!re=e1 ! ?ree l9es ,a ,c1 ,c ,b1 & ,b ,a1 are 9 ! same proportion to ea* o!r z ! l9es ,w ,e1 ,e ,d1 & ,w ,d4 ,h5ce1 ,a ,b has to ,a ,c ! same proportion z ! :ole weight has to ! pressure direct$ t[>d ,b1 & ,a ,b has to ,b ,c ! same proportion z ! :ole weight has to ! pressure on ! incl9$ plane4 ,we h "h suppos$ ! weight to be su/a9$ ^u ! incl9$ plane by a h>d plane fix$ at "r angles to x4 ,b ! p[] necess>y to su/a9 ! weight w be ! same 9 :atev] way x is appli$1 provid$ x act 9 ! direction ( ! plane4 ,?us1 a cord may be atta*$ to ! weight1 & /ret*$ t[>ds ,a1 or ! h&s ( m5 may be appli$ to ! weight bel[ x1 s z to resi/ its desc5t t[>ds ,b4 ,b 9 :atev] way x be appli$1 ! am\nt ( ! p[] w be det]m9$ 9 ! same mann]4 ,suppose ! weight to consi/ ( z _m p\nds z !re are in*es 9 ,a ,b1 !n ! p[] requisite to su/a9 x ^u ! plane w consi/ ( z _m p\nds z !re are in*es 9 ,a ,c1 & ! pressure on ! plane w am\nt to z _m p\nds z !re are in*es 9 ,b ,c4 ,f :at has be5 /at$ x may easily be inf]r$ t ! less ! elevation ( ! plane is1 ! less w be ! p[] requisite to su/a9 a giv5 weight ^u x1 & ! great] w be ! pressure ^u x4 ,suppose ! incl9$ plane ,a ,b to turn ^u a h+e at ,b1 & to be depress$ s t its angle ( elevation %all be dim9i%$1 x is evid5t t z ?is angle decreases ! height ( ! plane decreases1 & its base increases4 ,?us1 :5 x takes ! position ,b ,a1 ! height ,a ,c is less ?an ! =m] height ,a ,c1 :ile ! base ,b ,c is great] ?an ! =m] base ,b ,c4 ,! p[] requisite to support ! weight ^u ! plane 9 ! position ,b ,a is repres5t$ by ,a ,c1 & is z mu* less ?an ! p[] requisite to su/a9 x ^u ! plane ,a ,b1 z ! height ,a ,c is less ?an ! height ,a ,c4 ,on ! o!r h&1 ! pressure ^u ! plane 9 ! position ,b ,a is z mu* great] ?an ! pressure ^u ! plane ,b ,a1 z ! base ,b ,c is great] ?an ! base ,b ,c4 7#bhg47 ,! p[] ( an incl9$ plane1 consid]$ z a ma*9e1 is !re=e e/imat$ by ! proportion :i* its l5g? be>s to its height4 ,?is p[] is always increas$ by dim9i%+ ! elevation ( ! plane4 ,roads :i* are n level may be reg>d$ z incl9$ planes1 & loads drawn ^u !m 9 c>riages1 consid]$ 9 ref]5ce to ! p[]s :i* impel !m1 are subject to all ! conditions :i* h be5 e/abli%$ = incl9$ planes4 ,! incl9ation ( ! road is e/imat$ by ! height correspond+ to "s propos$ l5g?4 ,?us x is said to rise "o foot 9 fifte51 "o foot 9 tw5ty1 c41 mean+ t if fifte5 or tw5ty feet ( ! road be tak5 z ! l5g? ( an incl9$ plane1 su* z ,a ,b1 ! correspond+ height w be "o foot4 ,or ! same may be express$ ?us3 t if fifte5 or tw5ty feet be measur$ ^u ! road1 ! diff]5ce ( ! levels ( ! two extremities ( ! di/ance measur$ is "o foot4 ,accord+ to ?is me?od ( e/imat+ ! incl9ation ( roads1 ! p[] requisite to su/a9 a load ^u !m 7sett+ aside ! effect ( friction71 is always proportional to t elevation4 ,?us1 if a road rise "o foot 9 tw5ty1 a p[] ( "o ton w be suffici5t to su/a9 tw5ty tons1 & s on4 ,on a horizontal plane ! only resi/ance :i* ! p[] has to ov]come is ! friction ( ! load ) ! plane1 & ! consid]ation ( ?is be+ = ! pres5t omitt$1 a weight once put 9 motion w\ld cont9ue mov+ = ev]1 )\t any fur!r action ( ! p[]4 ,b if ! plane be incl9$1 ! p[] w be exp5d$ 9 rais+ ! weight ?r\gh ! p]p5dicul> height ( ! plane4 ,?us1 9 a road :i* rises "o foot 9 t51 ! p[] is exp5d$ 9 rais+ ! weight ?r\gh "o p]p5dicul> foot = e t5 feet ( ! road ov] :i* x is mov$4 ,z ! exp5diture ( p[] dep5ds ^u ! rate at :i* ! weight is rais$ p]p5dicul>ly1 x is evid5t t ! great] ! incl9ation ( ! road is1 ! sl[] ! motion mu/ be ) ! same =ce4 ,if ! en]gy ( ! p[] be su* z to raise ! weight at ! rate ( "o foot p] m9ute1 ! weight may be mov$ 9 ea* m9ute ?r\gh t l5g? ( ! road :i* corresponds to a rise ( "o foot4 ,?us1 if two roads rise "o at ! rate ( a foot 9 fifte5 feet1 & ! o!r at ! rate ( "o foot 9 tw5ty feet1 ! same exp5diture ( p[] w move ! weight ?r\gh fifte5 feet ( ! "o1 & tw5ty feet ( ! o!r at ! same rate4 ,f su* consid]ations z ^!1 x w readily appe> t x may (t5 be m exp$i5t to c>ry a road ?r\gh a circuit\s r\te ?an to cont9ue x 9 ! mo/ direct c\rse2 = ?\gh ! measur$ l5g? ( road may be consid]ably great] ?an 9 ! =m] case1 yet m may be ga9$ 9 spe$ ) ! same exp5diture ( p[] ?an is lo/ by ! increase ( di/ance4 ,by att5d+ to ^! circum/ances1 mod]n road-mak]s h greatly facilitat$ & exp$it$ ! int]c\rse betwe5 di/ant places4 7#bhh47 ,if ! p[] act obliquely to ! plane1 x w h a tw(old effect2 a "p be+ exp5d$ 9 support+ or draw+ ! weight1 & a "p 9 dim9i%+ or increas+ ! pressure ^u ! plane4 ,let ,w ,p1 fig4 #acj41 be ! p[]4 ,?is w be equival5t to two =ces1 ,w ,f1 p]p5dicul> to ! plane1 & ,w ,e 9 ! direction ( ! plane4 7#gd47 ,9 ord] t ! p[] %\ld su/a9 ! weight1 x is necess>y t t "p ,w ,e ( ! p[] :i* acts 9 ! direction ( ! plane %\ld be equal to t "p ,w ,e1 fig4 #acj41 ( ! weight :i* acts d[n ! plane4 ,! o!r "p ,w ,f ( ! p[] act+ p]p5dicul> to ! plane is imm$iately oppos$ to t "p ,w ,f ( ! weight :i* produces pressure4 ,! pressure ^u ! plane w !re=e be dim9i%$ by ! am\nt ( ,w ,f4 ,! am\nt ( ! p[] :i* w equilibrate ) ! weight may1 9 ?is case1 be f\nd z foll[s4 ,take ,w ,e equal to ,w ,e1 & draw ,e ,p p]p5dicul> to ! plane1 & meet+ ! direction ( ! p[]4 ,! proportion ( ! p[] to ! weight w be t ( ,w ,p to ,w ,d4 ,& ! proportion ( ! pressure to ! weight w be t ( ! diff]5ce betwe5 ,w ,f & ,w ,f to ,w ,d4 ,if ! am\nt ( ! p[] h a less proportion to ! weight ?an ,w ,p has to ,w ,d1 x w n support ! body on ! plane1 b w all[ x to desc5d4 ,& if x h a great] proportion1 x w draw ! weight up ! plane t[>ds ,a4 7#bhi47 ,x sometimes happ5s t a weight ^u "o incl9$ plane is rais$ or support$ by ano!r weight ^u ano!r incl9$ plane4 ,?us1 if ,a ,b & ,a ,b1 fig4 #aca41 be two incl9$ planes =m+ an angle at ,a1 & ,w ,w be two weights plac$ ^u ^! planes1 & connect$ by a cord pass+ ov] a pulley at ,a1 ! "o weight w ei!r su/a9 ! o!r1 or "o w desc5d1 draw+ ! o!r up4 ,to det]m9e ! circum/ances "u :i* ^! effects w ensue1 draw ! l9es ,w ,d & ,w ,d 9 ! v]tical direction1 & take ^u !m z _m in*es z !re are ounces 9 ! weights respectively4 ,w ,d & ,w ,d be+ ! l5g?s ?us tak51 & !re=e repres5t+ ! weights1 ! l9es ,w ,e & ,w ,e w repres5t ! effects ( ^! weights respectively d[n ! planes4 ,if ,w ,e & ,w ,e be equal1 ! weights w su/a9 ea* o!r )\t motion4 ,b if ,w ,e be great] ?an ,w ,e1 ! weight ,w w desc5d1 draw+ ! weight ,w up4 ,& if ,w ,e be great] ?an ,w ,e1 ! weight ,w w desc5d1 draw+ ! weight ,w up4 ,9 e case ! l9es ,w ,f & ,w ,f w repres5t ! pressures ^u ! planes respectively4 ,x is n necess>y1 = ! effect j describ$1 t ! incl9$ planes %\ld1 z repres5t$ 9 ! figure1 =m an angle ) ea* o!r4 ,!y may be p>allel1 or 9 any o!r position1 ! rope be+ c>ri$ ov] a suffici5t numb] ( :eels plac$ s z to give x ! necess>y deflection4 ,?is me?od ( mov+ loads is frequ5tly appli$ 9 great public works :]e rail-roads are us$4 ,load$ waggons desc5d "o incl9$ plane1 :ile o!r waggons1 ei!r empty or s load$ z to p]mit ! desc5t ( ^? ) :i* !y are connect$1 are drawn up ! o!r4 7#bij47 ,9 ! application ( ! incl9$ plane :i* we h hi!rto notic$1 ! ma*9e itself is suppos$ to be fix$ 9 its position1 :ile ! weight or load is mov$ ^u x4 ,b x frequ5tly happ5s t resi/ances are to be ov]come :i* d n admit ( be+ ?us mov$4 ,9 su* cases1 in/ead ( mov+ ! load ^u ! planes1 ! plane is to be mov$ "u or aga9/ ! load4 ,let ,d ,e1 fig4 #acb41 be a heavy beam secur$ 9 a v]tical position betwe5 guides ,f ,g & ,h ,i1 s t x is free to move upw>ds & d[nw>ds1 b n lat]ally4 ,let ,a ,b ,c be an incl9$ plane1 ! extremity ( :i* is plac$ b5ea? ! end ( ! beam4 ,a =ce appli$ to ! back ( ?is plane ,a ,c1 9 ! direction ,c ,b1 w urge ! plane "u ! beam s z to raise ! beam to ! position repres5t$ 9 fig4 #acc4 ,?us1 :ile ! incl9$ plane is mov$ ?r\gh ! di/ance ,c ,b1 ! beam is rais$ ?r\gh ! height ,c ,a4 7#bia47 ,:5 ! incl9$ plane is appli$ 9 ?is mann]1 x is call$ a w$ge4 ,& if ! p[] appli$ to ! back 7 a cont9u$ pressure1 its proportion to ! weight w\ld be t ( ,a ,c to ,c ,b4 ,x foll[s1 !re=e1 t ! m acute ! angle ,b is1 ! m p[]ful w be ! w$ge4 ,9 "s cases1 ! w$ge is =m$ ( two incl9$ planes1 plac$ base to base1 z repres5t$ 9 fig4 #acd4 ,! !oretical e/imation ( ! p[] ( ?is ma*9e is n applicable 9 practice ) any degree ( accuracy4 ,?is is 9 "p ow+ to ! enorm\s proportion :i* ! friction 9 mo/ cases be>s to ! !oretical value ( ! p[]1 b /ill m to ! nature ( ! p[] g5]ally us$4 ,! =ce ( a bl[ is ( a nature s :olly diff]5t f cont9u$ =ces1 su* z ! pressure ( weights1 or ! resi/ance (f]$ by ! cohesion ( bodies1 t x admits ( no num]ical comp>ison ) !m4 ,h5ce we _c prop]ly /ate ! proportion :i* ! =ce ( a bl[ be>s to ! am\nt ( a weight or resi/ance4 ,! w$ge is almo/ inv>iably urg$ by p]cussion2 :ile ! resi/ances :i* x has to ov]come are z con/antly =ces ( ! o!r k9d4 ,al?\gh1 h[ev]1 no exact num]ical comp>ison c be made1 yet x may be /at$ 9 a g5]al way t ! w$ge is m & m p[]ful z its angle is m acute4 ,illu/ration3 ,c4 ,v>ley1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,9 ! arts & manufactures1 w$ges are us$ :]e enorm\s =ce is to be ex]t$ ?r\gh a v small space4 ,?us x is resort$ to = splitt+ masses ( timb] or /one4 ,%ips are rais$ 9 docks by w$ges driv5 "u _! keels4 ,! w$ge is ! pr9cipal ag5t 9 ! oil-mill4 ,! se$s f :i* ! oil is to be extract$ are introduc$ into hair bags1 & plac$ betwe5 planes ( h>d wood4 ,w$ges ins]t$ betwe5 ! bags are driv5 by all[+ heavy beams to fall on !m4 ,! pressure ?us excit$ is s int5se1 t ! se$s 9 ! bags are =m$ into a mass ne>ly z solid z wood4 ,in/ances h occurr$ 9 :i* ! w$ge has be5 us$ to re/ore a tott]+ edifice to its p]p5dicul> position4 ,all cutt+ & pi]c+ in/rum5ts1 su* z knives1 razors1 scissors1 *isels1 c41 nails1 p9s1 ne$les1 awls1 c4 are w$ges4 ,! angle ( ! w$ge1 9 ^! cases1 is m or less acute1 accord+ to ! purpose to :i* x is to be appli$4 ,9 det]m9+ ?is1 two ?+s are to be consid]$--! me*anical p[]1 :i* is increas$ by dim9i%+ ! angle ( ! w$ge2 & ! /r5g? ( ! tool1 :i* is always dim9i%$ by ! same cause4 ,!re is1 !re=e1 a practical limit to ! increase ( ! p[]1 & t degree ( %>pness only is to be giv5 to ! tool :i* is consi/5t ) ! /r5g? requisite = ! purpose to :i* x is to be appli$4 ,9 tools int5d$ = cutt+ wood1 ! angle is g5]ally ab\t #cj4 ,= iron x is f #ej to #fj2 & = brass1 f #hj to #ij4 ,tools :i* act by pressure may be made m acute ?an ^? :i* are driv5 by a bl[2 & 9 g5]al ! s(t] & m yield+ ! sub/ance to be divid$ is1 & ! less ! p[] requir$ to act ^u x1 ! m acute ! w$ge may be con/ruct$4 ,9 _m cases ! utility ( ! w$ge dep5ds on t :i* is entirely omitt$ 9 its !ory1 viz4 ! friction :i* arises betwe5 its surface & ! sub/ance :i* x divides4 ,?is is ! case :5 p9s1 bolts1 or nails are us$ = b9d+ ! p>ts ( /ructures toge!r2 9 :i* case1 7 x n = ! friction1 !y w\ld recoil f _! places1 & fail to produce ! desir$ effect4 ,ev5 :5 ! w$ge is us$ z a me*anical eng9e1 ! pres5ce ( friction is absolutely indisp5sable to its practical utility4 ,! p[]1 z has already be5 /at$1 g5]ally acts by successive bl[s1 & is !re=e subject to con/ant int]mission1 & b = ! friction ! w$ge w\ld recoil betwe5 ! int]vals ( ! bl[s ) z mu* =ce z x _h be5 driv5 =w>d4 ,?us ! object ( ! lab\r w\ld be cont9ually fru/rat$4 ,! friction 9 ?is case is ( ! same use z a rat*et :eel1 b is mu* m necess>y1 z ! p[] appli$ to ! w$ge is m liable to int]mission ?an 9 ! cases :]e rat*et :eels are g5]ally us$4 7#bib47 ,:5 a road directly asc5ds ! side ( a hill1 x is to be consid]$ z an incl9$ plane2 b x w n lose its me*anical "*1 if1 in/ead ( directly asc5d+ t[>ds ! top ( ! hill1 x w9ds successively r\nd x1 & gradually asc5ds s z aft] sev]al revolutions to rea* ! top4 ,9 ! same mann] a pa? may be conceiv$ to surr\nd a pill> by :i* ! asc5t may be facilitat$ ^u ! pr9ciple ( ! incl9$ plane4 ,w9d+ /airs con/ruct$ 9 ! int]ior ( great columns p>take ( ?is "*2 = al?\gh ! asc5t be produc$ by successive /eps1 yet if a floor c\ld be made suffici5tly r\gh to prev5t ! feet f slipp+1 ! asc5t w\ld be accompli%$ ) equal facility4 ,9 su* a case ! w9d+ pa? w\ld be equival5t to an incl9$ plane1 b5t into su* a =m z to accommodate x to ! peculi> circum/ances 9 :i* x w\ld be requir$ to be us$4 ,x w n be difficult to trace ! resemblance betwe5 su* an adaptation ( ! incl9$ plane & ! appe>ances pres5t$ by ! ?read ( a screw3 & x may h5ce be easily und]/ood t a screw is no?+ m ?an an incl9$ plane con/ruct$ ^u ! surface ( a cyl9d]4 ,?is w1 p]haps1 be m app>5t by ! foll[+ contrivance3 ,let ,a ,b1 fig4 #ace41 be a common r\nd rul]1 & let ,c ,d ,e be a piece ( :ite pap] cut 9 ! =m ( an incl9$ plane1 ^: height ,c ,d is equal to ! l5g? ( ! rul] ,a ,b1 & let ! edge ,c ,e ( ! pap] be m>k$ ) a broad black l9e3 let ! edge ,c ,d be appli$ to ! rul] ,a ,b1 & be+ atta*$ !reto1 let ! pap] be roll$ r\nd ! rul]2 ! rul] w !n pres5t ! appe>ance ( a screw1 fig4 #acf4 ! ?read ( ! screw be+ m>k$ by ! black l9e ,c ,e1 w9d+ cont9ually r\nd ! rul]4 ,let ,d ,f1 fig4 #ace41 be equal to ! circumf]5ce ( ! rul]1 & draw ,f ,g p>allel to ,d ,c1 & ,g ,h p>allel to ,d ,e1 ! "p ,c ,g ,f ,d ( ! pap] w exactly surr\nd ! rul] once3 ! "p ,c ,g w =m "o convolution ( ! ?read1 & may be consid]$ z ! l5g? ( "o incl9$ plane surr\nd+ ! cyl9d]1 ,c ,h be+ ! correspond+ height1 & ,g ,h ! base4 ,! p[] ( ! screw does n1 z 9 ! ord9>y cases ( ! incl9$ plane1 act p>allel to ! plane or ?read1 b at "r angles to ! l5g? ( ! cyl9d] ,a ,b1 or1 :at is to ! same effect1 p>allel to ! base ,h ,g2 !re=e ! proportion ( ! p[] to ! weight w be1 accord+ to pr9ciples already expla9$1 ! same z t ( ,c ,h to ! space ?r\gh :i* ! p[] moves p>allel to ,h ,g 9 "o revolution ( ! screw4 ,h ,c is evid5tly ! di/ance betwe5 ! successive positions ( ! ?read z x w9ds r\nd ! cyl9d]2 & x appe>s f :at has be5 j /at$1 t ! less ?is di/ance is1 or1 9 o!r words1 ! f9] ! ?read is1 ! m p[]ful ! ma*9e w be4 7#bic47 ,9 ! application ( ! screw ! weight or resi/ance is n1 z 9 ! incl9$ plane & w$ge1 plac$ ^u ! surface ( ! plane or ?read4 ,! p[] is usually transmitt$ by caus+ ! screw to move 9 a concave cyl9d]1 on ! int]ior surface ( :i* a spiral cavity is cut1 correspond+ exactly to ! ?read ( ! screw1 & 9 :i* ! ?read w move by turn+ r\nd ! screw cont9ually 9 ! same direction4 ,?is holl[ cyl9d] is usually call$ ! nut or concave screw4 ,! screw surr\nd$ by its spiral ?read is repres5t$ 9 fig4 #acg42 & a section ( ! same play+ 9 ! nut is repres5t$ 9 fig4 #ach4 ,!re are sev]al ways 9 :i* ! effect ( ! p[] may be convey$ to ! resi/ance by ?is app>atus4 ,fir/1 let u suppose t ! nut ,a ,b is fix$4 ,if ! screw be cont9ually turn$ on its axis1 by a lev] ,e ,f ins]t$ 9 "o end ( x1 x w be mov$ 9 ! direction ,c ,d1 advanc+ e revolution ?r\gh a space equal to ! di/ance betwe5 two contigu\s ?reads4 ,by turn+ ! lev] 9 an opposite direction1 ! screw w be mov$ 9 ! direction ,d ,c4 ,if ! screw be fix$1 s z to be incapable ei!r ( mov+ longitud9ally or revolv+ on its axis1 ! nut ,a ,b may be turn$ ^u ! screw by a lev]1 & w move on ! screw t[>ds ,c or t[>ds ,d1 accord+ to ! direction 9 :i* ! lev] is turn$4 ,9 ! =m] case we h suppos$ ! nut to be absolutely immoveable1 & 9 ! latt] case ! screw to be absolutely immoveable4 ,x may happ51 h[ev]1 t ! nut1 ?\gh capable ( revolv+1 is incapable ( mov+ longitud9ally2 & t ! screw1 ?\gh incapable ( revolv+1 is capable ( mov+ longitud9ally4 ,9 t case1 by turn+ ! nut ,a ,b ^u ! screw by ! lev]1 ! screw w be urg$ 9 ! direction ,c ,d or ,d ,c1 accord+ to ! way 9 :i* ! nut is turn$4 ,! app>atus may1 on ! contr>y1 be s arrang$1 t ! nut1 ?\gh incapable ( revolv+1 is capable ( mov+ longitud9ally2 & ! screw1 ?\gh capable ( revolv+1 is incapable ( mov+ longitud9ally4 ,9 ?is case1 by turn+ ! screw 9 ! "o direction or 9 ! o!r1 ! nut ,a ,b w be urg$ 9 ! direction ,c ,d or ,d ,c4 ,all ^! v>i\s arrangem5ts may be obs]v$ 9 diff]5t applications to ! ma*9e4 7#bid47 ,a screw may be cut ^u a cyl9d] by plac+ ! cyl9d] 9 a turn+ la!1 & giv+ x a rotatory motion ^u its axis4 ,! cutt+ po9t is !n pres5t$ to ! cyl9d]1 & mov$ 9 ! direction ( its l5g?1 at su* a rate z to be c>ri$ ?r\gh ! di/ance betwe5 ! int5d$ ?read1 :ile ! cyl9d] revolves once4 ,! relative motions ( ! cutt+ po9t & ! cyl9d] be+ pres]v$ ) p]fect uni=mity1 ! ?read w be cut f "o end to ! o!r4 ,! %ape ( ! ?reads may be ei!r squ>e1 z 9 fig4 #acg41 or triangul>1 z 9 fig4 #aci4 7#bie47 ,! screw is g5]ally us$ 9 cases :]e sev]e pressure is to be excit$ ?r\gh small spaces2 x is !re=e ! ag5t 9 mo/ presses4 ,9 fig4 #adj41 ! nut is fix$1 & by turn+ ! lev]1 :i* passes ?r\gh ! head ( ! screw1 a pressure is excit$ ^u any sub/ance plac$ ^u ! plate imm$iately "u ! end ( ! screw4 ,9 fig4 #ada41 ! screw is incapable ( revolv+1 b is capable ( advanc+ 9 ! direction ( its l5g?4 ,on ! o!r h&1 ! nut is capable ( revolv+1 b does n advance 9 ! direction ( ! screw4 ,:5 ! nut is turn$ by means ( ! screw ins]t$ 9 x1 ! screw advances 9 ! direction ( its l5g?1 & urges ! bo>d :i* is atta*$ to x upw>ds1 s z to press any sub/ance plac$ betwe5 x & ! fix$ bo>d above4 ,9 cases :]e liquids or juices are to be express$ f solid bodies1 ! screw is ! ag5t g5]ally employ$4 ,x is also us$ 9 co9+1 :]e ! impression ( a die is to be made ^u a piece ( metal1 & 9 ! same way 9 produc+ ! impression ( a seal ^u wax or o!r sub/ance adapt$ to receive x4 ,:5 s(t & light mat]ials1 su* z cotton1 are to be r$uc$ to a conv5i5t bulk = transportation1 ! screw is us$ to compress !m1 & !y are ?us r$uc$ into h>d d5se masses4 ,9 pr9t+1 ! pap] is urg$ by a sev]e & sudd5 pressure ^u ! types1 by means ( a screw4 7#bif47 ,z ! me*anical p[] ( ! screw dep5ds ^u ! relative magnitude ( ! circumf]5ce ?r\gh :i* ! p[] revolves1 & ! di/ance betwe5 ! ?reads1 x is evid5t1 t1 to increase ! efficacy ( ! ma*9e1 we mu/ ei!r increase ! l5g? ( ! lev] by :i* ! p[] acts1 or dim9i% ! magnitude ( ! ?read4 ,al?\gh !re is no limit 9 !ory to ! increase ( ! me*anical efficacy by ^! means1 yet practical inconv5i5ce arises :i* effectually prev5ts t increase be+ c>ri$ beyond a c]ta9 ext5t4 ,if ! lev] by :i* ! p[] acts be increas$1 ! same difficulty arises z 0 already expla9$ 9 ! :eel & axle 7#bed472 ! space ?r\gh :i* ! p[] %\ld act w\ld be s unwieldy1 t its application w\ld become impracticable4 ,if1 on ! o!r h&1 ! p[] ( ! ma*9e be increas$ by dim9i%+ ! size ( ! ?read1 ! /r5g? ( ! ?read w be s dim9i%$1 t a slight resi/ance w te> x f ! cyl9d]4 ,! cases 9 :i* x is necess>y to increase ! p[] ( ! ma*9e1 be+ ^? 9 :i* ! greate/ resi/ances are to be ov]come1 ! object w evid5tly be defeat$1 if ! means *os5 to increase t p[] deprive ! ma*9e ( ! /r5g? :i* is necess>y to su/a9 ! =ce to :i* x is to be submitt$4 7#big47 ,^! inconv5i5ces are remov$ by a contrivance ( ,mr4 ,hunt]1 :i*1 :ile x gives to ! ma*9e all ! requisite /r5g? & compactness1 all[s x to h an almo/ unlimit$ degree ( me*anical efficacy4 ,?is contrivance consi/s 9 ! use ( two screws1 ! ?reads ( :i* may h any /r5g? & magnitude1 b :i* h a v small diff]5ce ( bread?4 ,:ile ! work+ po9t is urg$ =w>d by t :i* has ! great] ?read1 x is drawn back by t :i* has ! less2 s t dur+ ea* revolution ( ! screw1 in/ead ( be+ advanc$ ?r\gh a space equal to ! magnitude ( ei!r ( ! ?reads1 x moves ?r\gh a space equal to _! diff]5ce4 ,! me*anical p[] ( su* a ma*9e w be ! same z t ( a s+le screw hav+ a ?read1 ^: magnitude is equal to ! diff]5ce ( ! magnitudes ( ! two ?reads j m5tion$4 ,?us1 )\t inconv5i5tly increas+ ! sweep ( ! p[]1 on ! "o h&1 or1 on ! o!r1 dim9i%+ ! ?read until ! necess>y /r5g? is lo/1 ! ma*9e w acquire an efficacy limit$ by no?+ b ! smallness ( ! diff]5ce betwe5 ! two ?reads4 ,?is pr9ciple 0 fir/ appli$ 9 ! mann] repres5t$ 9 fig4 #adb4 ,a is ! great] ?read1 play+ 9 ! fix$ nut2 ,b is ! less] ?read1 cut ^u a small] cyl9d]1 & play+ 9 a concave screw1 cut )9 ! great] cyl9d]4 ,dur+ e revolution ( ! screw1 ! cyl9d] ,a desc5ds ?r\gh a space equal to ! di/ance betwe5 its ?reads4 ,at ! same "t ! small] cyl9d] ,b asc5ds ?r\gh a space equal to ! di/ance betwe5 ! ?reads cut ^u x3 ! effect is1 t ! bo>d ,d desc5ds ?r\gh a space equal to ! diff]5ce betwe5 ! ?reads ^u ,a & ! ?reads ^u ,b1 & ! ma*9e has a p[] proportionate to ! smallness ( ?is diff]5ce4 ,?us1 suppose ! screw ,a has tw5ty ?reads 9 an in*1 :ile ! screw ,b has tw5ty-"o2 dur+ "o revolution1 ! screw ,a w desc5d ?r\gh a space equal to ! #bj? "p ( an in*4 ,if1 dur+ ?is motion1 ! screw ,b did n turn )9 ,a1 ! bo>d ,d w\ld be advanc$ ?r\gh ! #bj? ( an in*2 b because ! holl[ screw )9 ,a turns ^u ,b1 ! screw ,b w1 relatively to ,a1 be rais$ 9 "o revolution ?r\gh a space equal to ! #ba/ "p ( an in*4 ,?us1 :ile ! bo>d ,d is depress$ ?r\gh ! #bj? ( an in* by ! screw ,a1 x is rais$ ?r\gh ! #ba/ ( an in* by ! screw ,b4 ,x is1 !re=e1 on ! :ole1 depress$ ?r\gh a space equal to ! excess ( ! #bj? ( an in* above ! #ba/ ( an in*1 t is1 ?r\gh ! #dbj? ( an in*4 ,! p[] ( ?is ma*9e w1 !re=e1 be express$ by ! numb] ( times ! #dbj? ( an in* is conta9$ 9 ! circumf]5ce ?r\gh :i* ! p[] moves4 7#bih47 ,9 ! practical application ( ?is pr9ciple at pres5t ! arrangem5t is some:at diff]5t4 ,! two ?reads are usually cut on diff]5t p>ts ( ! same cyl9d]4 ,if nuts be suppos$ to be plac$ ^u ^!1 :i* are capable ( mov+ 9 ! direction ( ! l5g?1 b n ( revolv+1 x is evid5t t by turn+ ! screw once r\nd1 ea* nut w be advanc$ ?r\gh a space equal to ! bread? ( ! respective ?reads4 ,by ?is means ! two nuts w ei!r approa* ea* o!r1 or mutually rec$e1 accord+ to ! direction 9 :i* ! screw is turn$1 ?r\gh a space equal to ! diff]5ce ( ! bread? ( ! ?reads1 & !y w ex]t a =ce ei!r 9 compress+ or ext5d+ any sub/ance plac$ betwe5 !m1 proportionate to ! smallness ( t diff]5ce4 7#bii47 ,a too!d :eel is sometimes us$ in/ead ( a nut1 s t ! same quality by :i* ! revolution ( ! screw urges ! nut =w>d is appli$ to make ! :eel revolve4 ,! screw is 9 ?is case call$ an endless screw1 because its action ^u ! :eel may be cont9u$ )\t limit4 ,?is application ( ! screw is repres5t$ 9 fig4 #adc4 ,p is ! w9* to :i* ! p[] is appli$2 & its effect at ! circumf]5ce ( ! :eel is e/imat$ 9 ! same mann] z ! effect ( ! screw ^u ! nut4 ,?is effect is to be consid]$ z a p[] act+ ^u ! circumf]5ce ( ! :eel2 & its proportion to ! weight or resi/ance is to be calculat$ 9 ! same mann] z ! proportion ( ! p[] to ! weight 9 ! :eel & axle4 7#cjj47 ,we h hi!rto consid]$ ! screw z an eng9e us$ to ov]come great resi/ances4 ,x is also em95tly useful 9 sev]al dep>tm5ts ( exp]im5tal sci5ce1 = ! measurem5t ( v m9ute motions & spaces1 ! magnitude ( :i* c\ld sc>cely be asc]ta9$ by any o!r means4 ,! v sl[ motion :i* may be imp>t$ to ! end ( a screw1 by a v consid]able motion 9 ! p[]1 r5d]s x peculi>ly well adapt$ = ?is purpose4 ,to expla9 ! mann] 9 :i* x is appli$--suppose a screw to be s cut z to h fifty ?reads 9 an in*1 ea* revolution ( ! screw w advance its po9t ?r\gh ! fiftie? "p ( an in*4 ,n[1 suppose ! head ( ! screw to be a circle1 ^: diamet] is an in*1 ! circumf]5ce ( ! head w be some?+ m ?an ?ree in*es3 ?is may be easily divid$ into a hundr$ equal p>ts di/9ctly visible4 ,if a fix$ index be pres5t$ to ?is graduat$ circumf]5ce1 ! hundr$? "p ( a revolution ( ! screw may be obs]v$1 by not+ ! passage ( "o division ( ! head "u ! index4 ,s9ce "o entire revolution ( ! head moves ! po9t ?r\gh ! fiftie? ( an in*1 "o division w correspond to ! five ?\s&? ( an in*4 ,9 ord] to obs]ve ! motion ( ! po9t ( ! screw 9 ?is case1 a f9e wire is atta*$ to x1 :i* is c>ri$ across ! field ( view ( a p[]ful microscope1 by :i* ! motion is s magnifi$ z to be di/9ctly p]ceptible4 ,a screw us$ = su* purposes is call$ a micromet] screw4 ,su* an app>atus is usually atta*$ to ! limbs ( graduat$ in/rum5ts1 = ! purposes ( a/ronomical & o!r obs]vation4 ,)\t ! aid ( ?is app>atus1 no obs]vation c\ld be tak5 ) great] accuracy ?an ! am\nt ( ! smalle/ division ^u ! limb4 ,?us1 if an in/rum5t = measur+ angles 7 divid$ into small arcs ( "o m9ute1 & an angle 7 obs]v$ :i* br\ght ! index ( ! in/rum5t to "s po9t betwe5 two divisions1 we c\ld only conclude t ! obs]v$ angle mu/ consi/ ( a c]ta9 numb] ( degrees & m9utes1 toge!r ) an additional numb] ( seconds1 :i* w\ld be unkn[n1 inasmu* z !re w\ld be no means ( asc]ta9+ ! fraction ( a m9ute betwe5 ! index & ! adjac5t division ( ! in/rum5t4 ,b if a screw be provid$1 ! po9t ( :i* moves ?r\gh a space equal to "o division ( ! in/rum5t1 ) sixty revolutions ( ! head1 & t ! head itself be divid$ into "o hundr$ equal p>ts1 ea* complete revolution ( ! screw w correspond to ! sixtie? "p ( a m9ute1 or to "o second1 & ea* division on ! head ( ! screw w correspond to ! hundr$? "p ( a second4 ,! index be+ atta*$ to ?is screw1 let ! head be turn$ until ! index be mov$ f its obs]v$ position to ! adjac5t division ( ! limb4 ,! numb] ( complete revolutions ( ! screw necess>y to accompli% ?is w be ! numb] ( seconds2 & ! numb] ( p>ts ( a revolution ov] ! complete numb] ( revolutions w be ! hundr$? p>ts ( a second necess>y to be add$ to ! degrees & m9utes prim>ily obs]v$4 ,x is n1 h[ev]1 only to su* in/rum5ts t ! micromet] screw is applicable2 any spaces :atev] may be measur$ by x4 ,an in/ance ( its me*anical application may be m5tion$ 9 a /eel-y>d1 an in/rum5t = asc]ta9+ ! am\nt ( weights by a giv5 weight1 slid+ on a long graduat$ arm ( a lev]4 ,! di/ance f ! fulcrum1 at :i* ?is weight c\nt]poises ! weight to be asc]ta9$1 s]ves z a measure to ! am\nt ( t weight4 ,:5 ! slid+ weight happ5s to be plac$ betwe5 two divisions ( ! arm1 a micromet] screw is us$ to asc]ta9 ! fraction ( ! division4 ,hunt]'s screw1 already describ$1 seems to be well adapt$ to micrometrical purposes2 s9ce ! motion ( ! po9t may be r5d]$ indef9itely sl[1 )\t requir+ an exquisitely f9e ?read1 su* z 9 ! s+le screw w\ld be necess>y4 ,,*ap4 ,,xvii4 ,,on ,,! ,,regulation ,,& ,,accumulation ,,( ,,=ce4 7#cja47 ,x is frequ5tly indisp5sable1 & always desirable1 t ! op]ation ( a ma*9e %\ld be regul> & uni=m4 ,sudd5 *anges 9 its velocity1 & desultory v>iations 9 ! effective en]gy ( its p[]1 are (t5 injuri\s or de/ructive to ! app>atus itself1 & :5 appli$ to manufactures nev] fail to produce unev5ness 9 ! "w4 ,to inv5t me?ods = insur+ ! regul> motion ( ma*9]y1 by remov+ ^? causes ( inequality :i* may be avoid$1 & by comp5sat+ o!rs1 has !re=e be5 a problem to :i* mu* att5tion & +5uity h be5 direct$4 ,?is is *iefly accompli%$ by controll+1 &1 z x 71 measur+ out ! p[] accord+ to ! exig5cies ( ! ma*9e1 & caus+ its effective en]gy to be always comm5surate ) ! resi/ance :i* x has to ov]come4 ,illu/ration3 ,c4 ,v>ley1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,irregul>ity 9 ! motion ( ma*9]y may proce$ f "o or m ( ! foll[+ causes3--#a4 irregul>ity 9 ! prime mov]2 #b4 occasional v>iation 9 ! am\nt ( ! load or resi/ance2 &1 #c4 because1 9 ! v>i\s positions :i* ! p>ts ( ! ma*9e assume dur+ its motion1 ! p[] may n be transmitt$ ) equal effect to ! work+ po9t4 ,! en]gy ( ! prime mov] is seldom if ev] regul>4 ,! =ce ( wat] v>ies ) ! copi\sness ( ! /ream4 ,! p[] :i* impels ! w9dmill is prov]bially caprici\s4 ,! pressure ( /eam v>ies ) ! int5sity ( ! furnace4 ,animal p[]1 ! result ( w1 temp]1 & heal? is difficult ( control4 ,human lab\r is mo/ ( all unmanageable2 h5ce no ma*9e works s irregul>ly z "o :i* is manipulat$4 ,9 "s cases ! mov+ =ce is subject1 by ! v conditions ( its exi/5ce1 to con/ant v>iation1 z 9 ! example ( a spr+1 :i* gradually loses its en]gy z x recoils4 7#bee47 ,9 _m in/ances ! prime mov] is liable to regul> int]mission1 & is actually susp5d$ = c]ta9 int]vals ( "t4 ,?is is ! case 9 ! s+le act+ /eam-eng9e1 :]e ! pressure ( ! /eam urges ! desc5t ( ! pi/on1 b is susp5d$ dur+ its asc5t4 ,! load or resi/ance to :i* ! ma*9e is appli$ is n less fluctuat+4 ,9 mills !re are a multiplicity ( p>ts :i* are sev]ally liable to be occasionally dis5gag$1 & to h _! op]ation susp5d$4 ,9 l>ge factories = sp9n+1 weav+1 pr9t+1 c4 a great numb] ( sep>ate sp9n+ ma*9es1 looms1 presses1 or o!r eng9es1 are usually work$ by "o common mov]1 su* z a wat]-:eel or /eam-eng9e4 ,9 ^! cases ! numb] ( ma*9es employ$ f "t to "t necess>ily v>ies ) ! fluctuat+ dem& = ! articles produc$1 & f o!r causes4 ,"u su* circum/ances ! velocity ) :i* e "p ( ! ma*9]y is mov$ w\ld suff] correspond+ *anges1 increas+ its rapidity ) e augm5tation ( ! mov+ p[] or dim9ution ( ! resi/ance1 or be+ ret>d$ 9 its spe$ by ! contr>y circum/ances4 ,b ev5 :5 ! prime mov] & ! resi/ance are bo? regul>1 or r5d]$ s by prop] contrivances1 /ill x w r>ely happ5 t ! ma*9e by :i* ! en]gy ( ! "o is transmitt$ to ! o!r conveys ?is ) unimpair$ effect 9 all ! phases ( its op]ation4 ,to give a g5]al notion ( ?is cause ( inequality to ^? :o h n be5 famili> ) ma*9]y w\ld n be easy1 )\t hav+ rec\rse to an example4 ,= ! pres5t we %all m]ely /ate1 t ! sev]al mov+ p>ts ( e ma*9e assume 9 succession a v>iety ( positions2 t at regul> p]iods !y return to _! fir/ position1 & aga9 und]go ! same succession ( *anges4 ,9 ! diff]5t positions ?r\gh :i* !y are c>ri$ 9 e p]iod ( motion1 ! efficacy ( ! ma*9e to transmit ! p[] to ! resi/ance is diff]5t1 & ?us ! effective en]gy ( ! ma*9e 9 act+ ^u ! resi/ance w\ld be subject to cont9ual fluctuation4 ,?is w be m cle>ly und]/ood :5 we come to expla9 ! me?ods ( c\nt]act+ ! defect or equalis+ ! action ( ! p[] ^u ! resi/ance4 ,su* are ! *ief causes ( ! inequalities incid5tal to ! motion ( ma*9]y1 & we n[ propose to describe a few ( ! _m +5i\s contrivances :i* ! skill ( eng9e]s has produc$ to remove ! consequ5t inconv5i5ces4 7#cjb47 ,sett+ aside1 = ! pres5t1 ! la/ cause ( inequality1 & consid]+ ! ma*9]y1 :atev] x be1 to transmit ! p[] to ! resi/ance )\t irregul> int]ruption1 x is evid5t t e contrivance1 hav+ = its object to r5d] ! velocity uni=m1 c only accompli% ?is by caus+ ! v>iations ( ! p[] & resi/ance to be proportionate to ea* o!r4 ,?is may be done ei!r by increas+ or dim9i%+ ! p[] z ! resi/ance increases or dim9i%es2 or by increas+ or dim9i%+ ! resi/ance z ! p[] increases or dim9i%es4 ,accord+ to ! facilities or conv5i5ce pres5t$ by ! peculi> circum/ances ( ! case ei!r ( ^! me?ods is adopt$4 ,! contrivances = effect+ ?is are call$ regulators4 ,mo/ regulators act ^u t "p ( ! ma*9e :i* comm&s ! supply ( ! p[] by means ( lev]s1 or "s o!r me*anical contrivance1 s z to *eck ! quantity ( ! mov+ pr9ciple convey$ to ! ma*9e :5 ! velocity has a t5d5cy to increase2 &1 on ! o!r h&1 to increase t supply ^u any undue abatem5t ( its spe$4 ,9 a wat]-mill ?is is done by act+ ^u ! %uttle2 9 a w9d-mill1 by an adju/m5t ( ! sail-clo?2 & 9 a /eam-eng9e1 by op5+ or clos+1 9 a great] or less degree1 ! valve by :i* ! cyl9d] is suppli$ ) /eam4 7#cjc47 ,( all ! contrivances = regulat+ ma*9]y1 t :i* is be/ kn[n & mo/ commonly us$ is ! gov]nor4 ,?is regulator1 :i* _h be5 long 9 use 9 mill-"w & o!r ma*9]y1 has ( late ye>s attract$ m g5]al notice by its beautiful adaptation 9 ! /eam-eng9es ( ,watt4 ,x consi/s ( heavy balls ,b ,b1 fig4 #add41 atta*$ to ! extremities ( rods ,b ,f4 ,^! rods play ^u a jo9t at ,e1 pass+ ?r\gh a mortise 9 ! v]tical /em ,d ,d4 ,at ,f !y are unit$ by jo9ts to ! %ort rods ,f ,h1 :i* are aga9 connect$ by jo9ts at ,h to a r+ :i* slides ^u ! v]tical %aft ,d ,d4 ,f ?is description x w be app>5t t :5 ! balls ,b are drawn f ! axis1 _! upp] arms ,e ,f are caus$ to increase _! div]g5ce 9 ! same mann] z ! blades ( a scissors are op5$ by sep>at+ ! h&les4 ,^!1 act+ ^u ! r+ by means ( ! %ort l9ks ,f ,h1 draw x d[n ! v]tical axis f ,d t[>ds ,e4 ,a contr>y effect is produc$ :5 ! balls ,b are br\ght clos] to ! axis1 & ! div]g5ce ( ! rods ,b ,e dim9i%$4 ,a horizontal :eel ,w is atta*$ to ! v]tical axis ,d ,d1 hav+ a groove to receive a rope or /rap ^u its rim4 ,?is /rap passes r\nd ! :eel or axis by :i* motion is transmitt$ to ! ma*9]y to be regulat$1 s t ! sp9dle or %aft ,d ,d w always be made to revolve ) a spe$ proportionate to t ( ! ma*9]y4 ,z ! %aft ,d ,d revolves1 ! balls ,b are c>ri$ r\nd x ) a circul> motion1 & consequ5tly acquire a c5trifugal =ce :i* causes !m to rec$e f ! axle1 & !re=e to depress ! r+ ,h4 ,on ! edge or rim ( ?is r+ is =m$ a groove1 :i* is embrac$ by ! prongs ( a =k ,i1 at ! extremity ( "o arm ( a lev] ^: fulcrum is at ,g4 ,! extremity ,k ( ! o!r arm is connect$ by "s means ) ! "p ( ! ma*9e :i* supplies ! p[]4 ,9 ! pres5t in/ance we %all suppose x a /eam-eng9e1 9 :i* case ! rod ,k ,i communicates ) a flat circul> valve ,v1 plac$ 9 ! pr9cipal /eam-pipe1 & s arrang$ t1 :5 ,k is elevat$ z f> z by _! div]g5ce ! balls ,b h p[] ov] x1 ! passage ( ! pipe w be clos$ by ! valve ,v1 & ! passage ( /eam entirely /opp$2 &1 on ! o!r h&1 :5 ! balls subside to _! l[e/ position1 ! valve w be pres5t$ ) its edge 9 ! direction ( ! tube1 s z to int]cept no "p ( ! /eam4 ,! prop]ty :i* r5d]s ?is in/rum5t s admirably adapt$ to ! purpose to :i* x is appli$ is1 t :5 ! div]g5ce ( ! balls is n v consid]able1 !y mu/ always revolve ) ! same velocity1 :e!r !y move at a great] or less] di/ance f ! v]tical axis4 ,if any circum/ance increases t velocity1 ! balls in/antly rec$e f ! axis1 & clos+ ! valve ,v1 *eck ! supply ( /eam1 & !reby dim9i%+ ! spe$ ( ! motion1 re/ore ! ma*9e to its =m] rate4 ,if1 on ! contr>y1 t fix$ velocity be dim9i%$1 ! c5trifugal =ce be+ no long] suffici5t to support ! balls1 !y desc5d t[>ds ! axle1 op5 ! valve ,v1 &1 increas+ ! supply ( /eam1 re/ore ! prop] velocity ( ! ma*9e4 ,:5 ! gov]nor is appli$ to a wat]-:eel x is made to act ^u ! %uttle ?r\gh :i* ! wat] fl[s1 & controls its quantity z effectually1 & ^u ! same pr9ciple1 z has j be5 expla9$ 9 ref]5ce to ! /eam-eng9e4 ,:5 appli$ to a w9dmill x regulates ! sail-clo? s z to dim9i% ! efficacy ( ! p[] ^u ! arms z ! =ce ( ! w9d increases1 or vice v]s4 ,9 cases :]e ! resi/ance admits ( easy & conv5i5t *ange1 ! gov]nor may act s z to accommodate x to ! v>y+ en]gy ( ! p[]4 ,?is is (t5 done 9 corn-mills1 :]e x acts ^u ! %uttle :i* metes out ! corn to ! mill/ones4 ,:5 ! p[] :i* drives ! mill increases1 a proportionally increas$ fe$ ( corn is giv5 to ! /ones1 s t ! resi/ance be+ v>i$ 9 ! ratio ( ! p[]1 ! same velocity w be ma9ta9$4 7#cjd47 ,9 "s cases ! c5trifugal =ce ( ! revolv+ balls is n suffici5tly great to control ! p[] or ! resi/ance1 & regulators ( a diff]5t k9d mu/ be resort$ to4 ,! foll[+ contrivance is call$ ! wat]-regulator3-- ,a common pump is work$ by ! ma*9e1 ^: motion is to be regulat$1 & wat] is ?us rais$ & dis*>g$ into a ci/]n4 ,x is all[$ to fl[ f ?is ci/]n ?r\gh a pipe ( a giv5 magnitude4 ,:5 ! wat] is pump$ up ) ! same velocity z x is dis*>g$ by ?is pipe1 x is evid5t t ! level ( ! wat] 9 ! ci/]n w be /ation>y1 s9ce x receives f ! pump ! exact quantity :i* x dis*>ges f ! pipe4 ,b if ! pump ?r[ 9 m wat] 9 a giv5 "t ?an is dis*>g$ by ! pipe1 ! ci/]n w beg9 to be fill$1 & ! level ( ! wat] w rise4 ,if1 on ! o!r h&1 ! supply f ! pump be less ?an ! dis*>ge f ! pipe1 ! level ( ! wat] 9 ! ci/]n w subside4 ,s9ce ! rate at :i* wat] is suppli$ f ! pump w always be proportional to ! velocity ( ! ma*9e1 x foll[s t e fluctuation 9 ?is velocity w be indicat$ by ! ris+ or subsid+ ( ! level ( ! wat] 9 ! ci/]n1 & t level nev] c rema9 /ation>y1 except at t exact velocity :i* supplies ! quantity ( wat] dis*>g$ by ! pipe4 ,?is pipe may be con/ruct$ s z by an adju/m5t to dis*>ge ! wat] at any requir$ rate2 & ?us ! ci/]n may be adapt$ to indicate a con/ant velocity ( any propos$ am\nt4 ,if ! ci/]n 7 con/antly wat*$ by an att5dant1 ! velocity ( ! ma*9e might be abat$ by regulat+ ! p[] :5 ! level ( ! wat] is obs]v$ to rise1 or increas$ :5 x falls2 b ?is is mu* m effectually & regul>ly p]=m$ by caus+ ! surface ( ! wat] itself to p]=m ! duty4 ,a float or l>ge holl[ metal ball is plac$ ^u ! surface ( ! wat] 9 ! ci/]n4 ,?is ball is connect$ ) a lev] act+ ^u "s "p ( ! ma*9]y1 :i* controls ! p[] or regulates ! am\nt ( resi/ance1 z already expla9$ 9 ! case ( ! gov]nor4 ,:5 ! level ( ! wat] rises1 ! buoyancy ( ! ball causes x to rise also ) a =ce equal to ! diff]5ce betwe5 its own weight & ! weight ( z mu* wat] z x displaces4 ,by enl>g+ ! float+ ball1 a =ce may be obta9$ suffici5tly great to move ^? p>ts ( ! ma*9]y :i* act ^u ! p[] or resi/ance1 & ?us ei!r to dim9i% ! supply ( ! mov+ pr9ciple or to increase ! am\nt ( ! resi/ance1 & !reby ret>d ! motion & r$uce ! velocity to its prop] limit4 ,:5 ! level ( ! wat] 9 ! ci/]n falls1 ! float+ ball be+ no long] support$ on ! liquid surface1 desc5ds ) ! =ce ( its own weight1 & produc+ an effect ^u ! p[] or resi/ance contr>y to ! =m]1 increases ! effective en]gy ( ! "o1 or dim9i%es t ( ! o!r1 until ! velocity prop] to ! ma*9e be re/or$4 ,! s5sibility ( ^! regulators is increas$ by mak+ ! surface ( wat] 9 ! ci/]n z small z possible2 = !n a small *ange 9 ! rate at :i* ! wat] is suppli$ by ! pump w produce a consid]able *ange 9 ! level ( ! wat] 9 ! ci/]n4 ,in/ead ( us+ a float1 ! ci/]n itself may be susp5d$ f ! lev] :i* controls ! supply ( ! p[]1 & 9 ?is case a slid+ weight may be plac$ on ! o!r arm1 s t x w balance ! ci/]n :5 x conta9s t quantity ( wat] :i* corresponds to ! fix$ level already expla9$4 ,if ! quantity ( wat] 9 ! ci/]n be increas$ by an undue velocity ( ! ma*9e1 ! weight ( ! ci/]n w prepond]ate1 draw d[n ! arm ( ! lev]1 & *eck ! supply ( ! p[]4 ,if1 on ! o!r h&1 ! supply ( wat] be too small1 ! ci/]n w no long] balance ! c\nt]poise1 ! arm by :i* x is susp5d$ w be rais$1 & ! en]gy ( ! p[] w be increas$4 7#cje47 ,9 ! /eam-eng9e ! self-regulat+ pr9ciple is c>ri$ to an a/oni%+ pit* ( p]fection4 ,! ma*9e itself raises 9 due quantity ! cold wat] necess>y to cond5se ! /eam4 ,x pumps (f ! hot wat] produc$ by ! /eam1 :i* has be5 cool$1 & lodges x 9 a res]voir = ! supply ( ! boil]4 ,x c>ries f ?is res]voir exactly t quantity ( wat] :i* is necess>y to supply ! wants ( ! boil]1 & lodges x !re9 accord+ z x is requir$4 ,x brea!s ! boil] ( r$undant /eam1 & pres]ves t :i* rema9s fit1 bo? 9 quantity & quality1 = ! use ( ! eng9e4 ,x bl[s its own fire1 ma9ta9+ its int5sity1 & increas+ or dim9i%+ x accord+ to ! quantity ( /eam :i* x is necess>y to raise2 s t :5 mu* "w is expect$ f ! eng9e1 ! fire is proportionally brisk & vivid4 ,x breaks & prep>es its own fuel1 & scatt]s x ^u ! b>s at prop] times & 9 due quantity4 ,x op5s & closes its sev]al valves at ! prop] mom5ts1 works its own pumps1 turns its own :eels1 & is only n alive4 ,among s _m beautiful examples ( ! self-regulat+ pr9ciple1 x is difficult to select4 ,we %all1 h[ev]1 m5tion "o or two1 & = o!rs ref] ! read] to our treatise on ?is subject4#c #c ,l>dn] on ! ,/eam-,eng9e1 ,/eam-,navigation1 ,roads1 & ,railways4 #h? edition4 #ahea4 ,x is necess>y 9 ?is ma*9e t ! wat] 9 ! boil] be ma9ta9$ con/antly at ! same level1 &1 !re=e1 t z mu* be suppli$1 f "t to "t1 z is consum$ by evaporation4 ,a pump :i* is wr\ght by ! eng9e itself supplies a ci/]n ,c1 fig4 #ade41 ) hot wat]4 ,at ! bottom ( ?is ci/]n is a valve ,v op5+ into a tube :i* desc5ds into ! boil]4 ,?is valve is connect$ by a wire ) ! arm ( a lev] on ! fulcrum ,d1 ! o!r arm ,e ( :i* is also connect$ by a wire ) a /one float ,f1 :i* is p>tially imm]s$ 9 ! wat] ( ! boil]1 & is balanc$ by a slid+ weight ,a4 ,! weight ,a only c\nt]poises ! /one float ,f by ! aid ( its buoyance 9 ! wat]2 = if ! wat] be remov$1 ! /one ,f w prepond]ate1 & raise ! weight ,a4 ,:5 ! wat] 9 ! boil] is at its prop] level1 ! l5g? ( ! wire connect+ ! valve ,v ) ! lev] is s adju/$ t ?is valve %all be clos$1 ! wire at ! same "t be+ fully ext5d$4 ,:51 by evaporation1 ! wat] 9 ! boil] beg9s to be dim9i%$1 ! level falls1 & ! /one weight ,f1 be+ no long] support$1 ov]comes ! c\nt]poise ,a1 raises ! arm ( ! lev]1 &1 pull+ ! wire1 op5s ! valve ,v4 ,! wat] 9 ! ci/]n ,c !n fl[s ?r\gh ! tube into ! boil]1 & cont9ues to fl[ until ! level be s rais$ t ! /one weight ,f is aga9 elevat$1 ! valve ,v clos$1 & ! fur!r supply ( wat] f ! ci/]n ,c susp5d$4 ,9 ord] to r5d] ! op]ation ( ?is app>atus easily intelligible1 we h "h suppos$ an imp]fection :i* does n exi/4 ,accord+ to :at has j be5 /at$1 ! level ( ! wat] 9 ! boil] desc5ds f its prop] height1 & subsequ5tly returns to x4 ,b1 9 fact1 ?is does n happ54 ,! float ,f & valve ,v adju/ !mselves1 s t a con/ant supply ( wat] passes ?r\gh ! valve1 :i* proce$s exactly at ! same rate z t at :i* ! wat] 9 ! boil] is consum$4 7#cjf47 ,9 ! same ma*9e !re occurs a s+ul>ly happy example ( self-adju/m5t1 9 ! me?od by :i* ! /r5g? ( ! fire is regulat$4 ,! gov]nor regulates ! supply ( /eam to ! eng9e1 & proportions x to ! "w to be done4 ,) ?is "w1 !re=e1 ! dem&s ^u ! boil] increase or dim9i%1 & ) ^! dem&s ! production ( /eam 9 ! boil] ought to v>y4 ,9 fact1 ! rate at :i* /eam is g5]at$ 9 ! boil]1 ought to be equal to t at :i* x is consum$ 9 ! eng9e1 o!rwise "o ( two effects mu/ ensue3 ei!r ! boil] w fail to supply ! eng9e ) /eam1 or /eam w accumulate 9 ! boil]1 be+ produc$ 9 undue quantity1 &1 escap+ at ! safety valve1 w ?us be wa/$4 ,x is1 !re=e1 necess>y to control ! ag5t :i* g5]ates ! /eam1 namely1 ! fire1 & to v>y its int5sity f "t to "t1 proportion+ x to ! dem&s ( ! eng9e4 ,to accompli% ?is1 ! foll[+ contrivance has be5 adopt$3--,let ,t1 fig4 #adf41 be a tube ins]t$ 9 ! top ( ! boil]1 & desc5d+ ne>ly to ! bottom4 ,! pressure ( ! /eam conf9$ 9 ! boil]1 act+ ^u ! surface ( ! wat]1 =ces x to a c]ta9 height 9 ! tube ,t4 ,a weight ,f1 half imm]s$ 9 ! wat] 9 ! tube1 is susp5d$ by a *a91 :i* passes ov] ! :eels ,p ,p1 & is balanc$ by a metal plate ,d1 9 ! same mann] z ! /one float1 fig4 #ade41 is balanc$ by ! weight ,a4 ,! plate ,d passes ?r\gh ! m\? ( ! flue ,e z x issues f9ally f ! boil]2 s t :5 ! plate ,d falls x /ops ! flue1 susp5d+ !reby ! draught ( air ?r\gh ! furnace1 mitigat+ ! int5sity ( ! fire1 & *eck+ ! production ( /eam4 ,if1 on ! contr>y1 ! plate ,d be drawn up1 ! draught is increas$1 ! fire is r5d]$ m active1 & ! production ( /eam 9 ! boil] is /imulat$4 ,n[1 suppose t ! boil] produces /eam fa/] ?an ! eng9e consumes x1 ei!r because ! load on ! eng9e has be5 dim9i%$1 &1 !re=e1 its consumption ( /eam r$uc$1 or because ! fire has become too int5se2 ! consequ5ce is1 t ! /eam1 beg9n+ to accumulate 9 ! boil]1 w press ^u ! surface ( ! wat] ) increas$ =ce1 & ! wat] w be rais$ 9 ! tube ,t4 ,! weight ,f w1 !re=e1 be lift$1 & ! plate ,d w desc5d1 dim9i%1 or /op ! draught1 mitigate ! fire1 & ret>d ! production ( /eam1 & w cont9ue to d s until ! rate at :i* /eam is produc$ %all be comm5surate to ! wants ( ! eng9e4 ,if1 on ! o!r h&1 ! production ( /eam be inadequate to ! exig5cy ( ! ma*9e1 ei!r because ( an increas$ load1 or ( ! insuffici5t =ce ( ! fire1 ! /eam 9 ! boil] w lose its ela/icity1 & ! surface ( ! wat] n su/a9+ its wont$ pressure1 ! wat] 9 ! tube ,t w fall2 consequ5tly ! weight ,f w desc5d1 & ! plate ,d w be rais$4 ,! flue be+ ?us op5$1 ! draught w be increas$1 & ! fire r5d]$ m int5se4 ,?us ! production ( /eam becomes m rapid1 & is r5d]$ suffici5tly abundant = ! purposes ( ! eng9e4 ,?is app>atus is call$ ! self-act+ damp]4 7#cjg47 ,:5 a p]fectly uni=m rate ( motion has n be5 atta9$1 x is (t5 necess>y to indicate small v>iations ( velocity4 ,! foll[+ contrivance1 call$ a ta*omet]#d1 has be5 inv5t$ to accompli% ?is4 ,a cup1 fig4 #adg41 is fill$ to ! level ,c ,d ) quicksilv]1 & is atta*$ to a sp9dle1 :i* is :irl$ by ! ma*9e 9 ! same mann] z ! gov]nor already describ$4 ,x is well kn[n t ! c5trifugal =ce produc$ by ?is :irl+ motion w cause ! m]cury to rec$e f ! c5tre & rise ^u ! sides ( ! cup1 s t its surface w assume ! concave appe>ance repres5t$ 9 fig4 #adh4 ,9 ?is case ! c5tre ( ! surface w obvi\sly h fall5 bel[ its orig9al level1 fig4 #adg41 & ! edges w h ris5 above t level4 ,z ?is effect is produc$ by ! velocity ( ! ma*9e1 s x is proportionate to t velocity1 & subject to correspond+ v>iations4 ,any me?od ( r5d]+ visible small *anges 9 ! c5tral level ( ! surface ( ! quicksilv] w indicate m9ute v>iations 9 ! velocity ( ! ma*9e4 #d ,f ! ,greek words ta*os spe$1 & metron measure4 ,a glass tube ,a1 op5 at bo? ends1 & exp&+ at "o extremity into a bell ,b1 is imm]s$ ) its wid] end 9 ! m]cury1 ! surface ( :i* w /& at ! same level 9 ! bell ,b1 & 9 ! cup ,c ,d4 ,! tube is s susp5d$ z to be unconnect$ ) ! cup4 ,?is tube is !n fill$ to a c]ta9 height ,a1 ) spirits t+$ ) "s col\r+ matt]1 to r5d] x easily obs]vable4 ,:5 ! cup is :irl$ by ! ma*9e to :i* x is atta*$1 ! level ( ! quicksilv] 9 ! bell falls1 leav+ m space = ! spirits1 :i*1 !re=e1 desc5ds 9 ! tube4 ,z ! motion is cont9u$1 e *ange ( velocity causes a correspond+ *ange 9 ! level ( ! m]cury1 &1 !re=e1 also 9 ! level ,a ( ! spirits4 ,x w be obs]v$1 t1 9 consequ5ce ( ! capacity ( ! bell ,b be+ mu* great] ?an t ( ! tube ,a1 a v small *ange 9 ! level ( ! quicksilv] 9 ! bell w produce a consid]able *ange 9 ! height ( ! spirits 9 ! tube4 ,?us ?is +5i\s in/rum5t becomes a v delicate indicator ( v>iations 9 ! motion ( ma*9]y4 7#cjh47 ,! gov]nor1 & o!r me?ods ( regulat+ ! motion ( ma*9]y :i* h be5 j describ$1 are adapt$ pr9cipally to cases 9 :i* ! proportion ( ! resi/ance to ! load is subject to c]ta9 fluctuations or gradual *anges1 or at lea/ to cases 9 :i* ! resi/ance is n at any "t entirely )drawn1 nor ! en]gy ( ! p[] actually susp5d$4 ,circum/ances1 h[ev]1 frequ5tly occur 9 :i*1 :ile ! p[] rema9s 9 full activity1 ! resi/ance is at int]vals sudd5ly remov$ & z sudd5ly aga9 returns4 ,on ! o!r h&1 cases also pres5t !mselves1 9 :i*1 :ile ! resi/ance is cont9u$1 ! impell+ p[] is subject to int]mission at regul> p]iods4 ,9 ! =m] case1 ! ma*9e w\ld be driv5 ) a ru9\s rapidity dur+ ^? p]iods at :i* x is reliev$ f its load1 & on ! return ( ! load e "p w\ld suff] a viol5t /ra91 f its endeav\r to reta9 ! velocity :i* x _h acquir$1 & ! spe$y de/ruction ( ! eng9e c\ld n fail to ensue4 ,9 ! latt] case1 ! motion w\ld be greatly ret>d$ or entirely susp5d$ dur+ ^? p]iods at :i* ! mov+ p[] is depriv$ ( its activity1 &1 consequ5tly1 ! motion :i* x w\ld communicate w\ld be s irregul> z to be useless = ! purposes ( manufactures4 ,x is also frequ5tly desirable1 by means ( a weak b cont9u$ p[]1 to produce a sev]e b in/antane\s effect4 ,?us a bl[ may be requir$ to be giv5 by ! muscul> action ( a man's arm ) a =ce to :i*1 unaid$ by me*anical contrivance1 its /r5g? w\ld be entirely inadequate4 ,9 all ^! cases1 x is evid5t t ! object to be atta9$ is1 an effectual me?od ( accumulat+ ! en]gy ( ! p[] s z to make x available aft] ! action by :i* x has be5 produc$ has ceas$4 ,?us1 9 ! case 9 :i* ! load is at p]iodical int]vals )drawn f ! ma*9e1 if ! =ce ( ! p[] c\ld be imp>t$ to some?+ by :i* x w\ld be pres]v$1 s z to be br\ght aga9/ ! load :5 x aga9 return$1 ! inconv5i5ce w\ld be remov$4 ,9 l mann]1 9 ! case :]e ! p[] itself is subject to int]mission1 if a "p ( ! =ce :i* x ex]ts 9 its int]vals ( action c\ld be accumulat$ & pres]v$1 x might be br\ght to be> ^u ! ma*9e dur+ its p]iods ( susp5sion4 ,by ! same means ( accumulat+ =ce1 ! /r5g? ( an infant1 by repeat$ ef=ts1 might produce effects :i* w\ld be va9ly attempt$ by ! s+le & mom5t>y action ( ! /ronge/ man4 7#cji47 ,! prop]ty ( in]tia1 expla9$ & illu/rat$ 9 ! ?ird & f\r? *apt]s ( ?is volume furni%es an easy & effectual me?od ( accompli%+ ?is4 ,a mass ( matt] reta9s1 by virtue ( its in]tia1 ! :ole ( any =ce :i* may h be5 giv5 to x1 except t "p ( :i* friction & ! atmosph]ic resi/ance deprives x4 ,by contrivances :i* are well kn[n & pres5t no difficulty1 ! "p ( ! mov+ =ce ?us lo/ may be r5d]$ comp>atively small1 & ! mov+ mass may be reg>d$ z reta9+ ne>ly ! :ole ( ! =ce impress$ ^u x4 ,to r5d] ?is me?od ( accumulat+ =ce fully intelligible1 let u fir/ imag9e a poli%$ level plane on :i* a heavy globe ( metal1 also poli%$1 is plac$4 ,x is evid5t t ! globe w rema9 at re/ on any "p ( ! plane )\t a t5d5cy to move 9 any direction4 ,z ! friction is ne>ly remov$ by ! poli% ( ! surfaces1 ! globe w be easily mov$ by ! lea/ =ce appli$ to x4 ,suppose a slight impulse giv5 to x1 :i* w cause x to move at ! rate ( "o foot 9 a second4 ,sett+ aside ! effects ( friction1 x w cont9ue to move at ?is rate = any l5g? ( "t4 ,! same impulse repeat$ w increase its spe$ to two feet p] second4 ,a ?ird impulse to ?ree feet1 & s on4 ,?us #aj1jjj repetitions ( ! impulse w cause x to move at ! rate ( #aj1jjj feet p] second4 ,if ! body to :i* ^! impulses 7 communicat$ 7 a cannon ball1 x might1 by a con/ant repetition ( ! impell+ =ce1 be at l5g? made to move ) z mu* =ce z if x 7 project$ f ! mo/ p[]ful piece ( ordnance4 ,! =ce ) :i* ! ball 9 su* a case w\ld /rike a build+ might be suffici5t to r$uce x to ru9s1 & yet su* =ce w\ld be no?+ m ?an ! accumulation ( a numb] ( weak ef=ts n beyond ! p[] ( a *ild to ex]t1 :i* are /or$ up1 & pres]v$1 z x 71 by ! mov+ mass1 & !reby br\ght to be>1 at ! same mom5t1 ^u ! po9t to :i* ! =ce is direct$4 ,x is ! sum ( a numb] ( actions ex]t$ successively1 &1 dur+ a long int]val1 br\ght into op]ation at "o & ! same mom5t4 ,b ! case :i* is "h suppos$ _c actually occur2 because we h n usually any practical means ( mov+ a body = any consid]able "t 9 ! same direction )\t mu* friction1 & )\t enc\nt]+ num]\s ob/acles :i* w\ld imp$e its progress4 ,x is n1 h[ev]1 ess5tial to ! effect :i* is to be produc$1 t ! motion %\ld be 9 a /raight l9e4 ,if a lead5 weight be atta*$ to ! end ( a light rod or cord1 & be :irl$ by ! =ce ( ! arm 9 a circle1 x w gradually acquire increas$ spe$ & =ce1 & at l5g? may receive an impetus :i* w\ld cause x to p5etrate a piece ( bo>d z effectually z if x 7 dis*>g$ f a musket4 ,! =ce ( a hamm] or sl$ge dep5ds p>tly on its weight1 b mu* m on ! pr9ciple j expla9$4 ,7 x all[$ m]ely to fall by ! =ce ( its weight ^u ! head ( a nail1 or ^u a b> ( heat$ iron :i* is to be flatt5$1 an inconsid]able effect w\ld be produc$4 ,b :5 x is wield$ by ! arm ( a man1 x receives at e mom5t ( its motion increas$ =ce1 :i* is f9ally exp5d$ 9 a s+le in/ant on ! head ( ! nail1 or on ! b> ( iron4 ,! effects ( flails 9 ?re%+1 ( clubs1 :ips1 canes1 & in/rum5ts = /rik+1 axes1 hat*ets1 cleav]s1 & all in/rum5ts :i* cut by a bl[1 dep5d on ! same pr9ciple1 & are simil>ly expla9$4 ,! b[-/r+ :i* impels ! arr[ does n produce its effect at once4 ,x cont9ues to act ^u ! %aft until x resumes its /raight position1 & !n ! arr[ takes flight ) ! =ce accumulat$ dur+ ! cont9uance ( ! action ( ! /r+1 f ! mom5t x 0 dis5gag$ f ! f+] ( ! b[-man4 ,fire-arms !mselves act ^u a simil> pr9ciple1 z also ! air-gun & /eam-gun4 ,9 ^! in/rum5ts ! ball is plac$ 9 a tube1 & sudd5ly expos$ to ! pressure ( a highly ela/ic fluid1 ei!r produc$ by explosion z 9 fire-arms1 by previ\s cond5sation z 9 ! air-gun1 or by ! evaporation ( highly heat$ liquids z 9 ! /eam-gun4 ,b 9 e case ?is pressure cont9ues to act ^u x until x leaves ! m\? ( ! tube1 & !n x dep>ts ) ! :ole =ce communicat$ to x dur+ its passage along ! tube4 7#caj47 ,f all ^! consid]ations x w easily be p]ceiv$ t a mass ( in]t matt] may be reg>d$ z a magaz9e 9 :i* =ce may be deposit$ & accumulat$1 to be us$ 9 any way :i* may be necess>y4 ,= _m reasons1 :i* w be suffici5tly obvi\s1 ! =m commonly giv5 to ! mass ( matt] us$ = ?is purpose 9 ma*9]y is t ( a :eel1 9 ! rim ( :i* x is pr9cipally collect$4 ,conceive a massive r+ ( metal1 fig4 #adi41 connect$ ) a c5tral box or nave by light spokes1 & turn+ on an axis ) little friction4 ,su* an app>atus is call$ a fly-:eel4 ,if any =ce be appli$ to x1 ) t =ce 7mak+ "s slight d$uction = friction7 x w move1 & w cont9ue to move until "s ob/acle be oppos$ to its motion1 :i* w receive f x a "p ( ! =ce x has acquir$4 ,! uses ( ?is app>atus w be easily und]/ood by examples ( its application4 ,suppose t a heavy /amp] or hamm] is to be rais$ to a c]ta9 height1 & !nce to be all[$ to fall1 & t ! p[] us$ = ?is purpose is a wat]-:eel4 ,:ile ! /amp] asc5ds1 ! p[] ( ! :eel is ne>ly balanc$ by its weight1 & ! motion ( ! ma*9e is sl[4 ,b ! mom5t ! /amp] is dis5gag$ & all[$ to fall1 ! p[] ( ! :eel1 hav+ no resi/ance1 nor any object on :i* to exp5d itself1 sudd5ly accel]ates ! ma*9e1 :i* moves ) a spe$ proportion$ to ! am\nt ( ! p[]1 until x aga9 engages ! /amp]1 :5 its velocity is z sudd5ly *eck$4 ,e "p suff]s a /ra91 & ! ma*9e moves aga9 sl[ly until x dis*>ges its load1 :5 x is aga9 accel]at$1 & s on4 ,9 ?is case1 besides ! c]ta9ty ( injury & we>1 & ! probability ( fracture f ! sudd5 & frequ5t *anges ( velocity1 ne>ly ! :ole =ce ex]t$ by ! p[] 9 ! int]vals betwe5 ! comm5cem5t ( ea* desc5t ( ! /amp] & ! next asc5t is lo/4 ,^! defects are remov$ by a fly-:eel4 ,:5 ! /amp] is dis*>g$1 ! en]gy ( ! p[] is exp5d$ 9 mov+ ! :eel1 :i*1 by reason ( its great mass1 w n receive an undue velocity4 ,9 ! int]val betwe5 ! desc5t & asc5t ( ! /amp]1 ! =ce ( ! p[] is lodg$ 9 ! heavy rim ( ! fly-:eel4 ,:5 ! /amp] is aga9 tak5 up by ! ma*9e1 ?is =ce is br\ght to be> ^u x1 comb9$ ) ! imm$iate p[] ( ! wat]-:eel1 & ! /amp] is elevat$ ) ne>ly ! same velocity z t ) :i* ! ma*9e mov$ 9 ! int]val ( its desc5t4 7#caa47 ,9 _m cases1 :5 ! mov+ p[] is n subject to v>iation1 ! efficacy ( ! ma*9e to transmit x to ! work+ po9t is subject to cont9ual *ange4 ,! sev]al p>ts ( e ma*9e h c]ta9 p]iods ( motion1 9 :i* !y pass ?r\gh a v>iety ( positions1 to :i* !y cont9ually return aft] /at$ int]vals4 ,9 ^! diff]5t positions ! effect ( ! p[] transmitt$ to ! work+ po9t is diff]5t2 & cases ev5 occur 9 :i* ?is effect is altoge!r annihilat$1 & ! ma*9e is br\ght into a pr$icam5t 9 :i* ! p[] loses all influ5ce ov] ! weight4 ,9 su* cases ! aid ( a fly-:eel is effectual & indisp5sable4 ,9 ^? phases ( ! ma*9e1 :i* are mo/ fav\rable to ! transmission ( =ce1 ! fly-:eel %>es ! effect ( ! p[] ) ! load1 & reta9+ ! =ce ?us receiv$ directs x ^u ! load at ! mom5ts :5 ! transmission ( p[] by ! ma*9e is ei!r feeble or altoge!r susp5d$4 ,^! g5]al obs]vations w1 p]haps1 be m cle>ly appreh5d$ by an example ( an application ( ! fly-:eel1 9 a case su* z ^? n[ allud$ to4 ,let ,a ,b ,c ,d ,e ,f1 fig4 #aej41 be a crank1 :i* is a d\ble w9* 77#beb47 & fig4 #hi471 by :i* an axle1 ,a ,b ,e ,f1 is to be turn$4 ,atta*$ to ! middle ( ,c ,d by a jo9t is a rod1 :i* is connect$ ) a beam1 work$ ) an alt]nate motion on a c5tre1 l ! brake ( a pump1 & driv5 by any con/ant p[]1 su* z a /eam-eng9e4 ,! b> ,c ,d is to be c>ri$ ) a circul> motion r\nd ! axis ,a ,e4 ,let ! ma*9e1 view$ 9 ! direction ,a ,b ,e ,f ( ! axis1 be conceiv$ to be repres5t$ 9 fig4 #aea41 :]e ,a repres5ts ! c5tre r\nd :i* ! motion is to be produc$1 & ,g ! po9t :]e ! connect+ rod ,g ,h is atta*$ to ! arm ( ! crank4 ,! circle ?r\gh :i* ,g is to be urg$ by ! rod is repres5t$ by ! dott$ l9e4 ,9 ! position repres5t$ 9 fig4 #aea41 ! rod act+ 9 ! direction ,h ,g has its full p[] to turn ! crank ,g ,a r\nd ! c5tre ,a4 ,z ! crank comes into ! position repres5t$ 9 fig4 #aeb41 ?is p[] is dim9i%$1 & :5 ! po9t ,g comes imm$iately bel[ ,a1 z 9 fig4 #aec41 ! =ce 9 ! direction ,h ,g has no effect 9 turn+ ! crank r\nd ,a1 b1 on ! contr>y1 is entirely exp5d$ 9 pull+ ! crank 9 ! direction ,a ,g1 &1 !re=e1 only acts ^u ! pivots or gudgeons :i* support ! axle4 ,at ?is crisis ( ! motion1 !re=e1 ! :ole effective en]gy ( ! p[] is annihilat$4 ,aft] ! crank has pass$ to ! position repres5t$ 9 fig4 #aed41 ! direction ( ! =ce :i* acts ^u ! connect+ rod is *ang$1 & n[ ! crank is drawn upw>d 9 ! direction ,g ,h4 ,9 ?is position ! mov+ =ce has "s efficacy to produce rotation r\nd ,a1 :i* efficacy cont9ually increases until ! crank atta9s ! position %[n 9 fig4 #aee41 :5 its p[] is greate/4 ,pass+ f ?is position its efficacy is cont9ually dim9i%$1 until ! po9t ,g comes imm$iately above ! axis ,a1 fig4 #aef4 ,"h aga9 ! p[] loses all its efficacy to turn ! axle4 ,! =ce 9 ! direction ,g ,h or ,h ,g c obvi\sly produce no o!r effect ?an a /ra9 ^u ! pivots or gudgeons4 ,9 ! critical situations repres5t$ 9 fig4 #aec41 & fig4 #aef41 ! ma*9e w\ld be incapable ( mov+1 7 ! imm$iate =ce ( ! p[] ! only impell+ pr9ciple4 ,b hav+ be5 previ\sly 9 motion by virtue ( ! in]tia ( its v>i\s p>ts1 x has a t5d5cy to cont9ue 9 motion2 & if ! resi/ance ( ! load & ! effects ( friction be n too great1 ?is disposition to pres]ve its /ate ( motion w extricate ! ma*9e f ! dilemma 9 :i* x is involv$ 9 ! cases j m5tion$1 by ! peculi> arrangem5t ( its p>ts4 ,9 _m cases1 h[ev]1 ! =ce ?us acquir$ dur+ ! phases ( ! ma*9e1 9 :i* ! p[] is active1 is insuffici5t to c>ry x ?r\gh ! dead po9ts 7fig4 #aec4 & fig4 #aef472 & 9 all cases ! motion w\ld be v unequal1 be+ cont9ually ret>d$ z x approa*$ ^! po9ts1 & cont9ually accel]at$ aft] x pass$ !m4 ,a fly-:eel atta*$ to ! axis ,a1 or to "s o!r "p ( ! ma*9]y1 w effectually remove ?is defect4 ,:5 ! crank assumes ! positions 9 fig4 #aea4 & fig4 #aee41 ! p[] is 9 full play ^u x1 & a %>e ( ! effect is imp>t$ to ! massive rim ( ! fly-:eel4 ,:5 ! crank gets into ! pr$icam5t exhibit$ 9 fig4 #aec4 & fig4 #aef41 ! mom5tum :i* ! fly-:eel receiv$ :5 ! crank act$ ) mo/ advantage1 imm$iately extricates ! ma*9e1 &1 c>ry+ ! crank beyond ! dead po9t1 br+s ! p[] aga9 to be> ^u x4 ,! a/oni%+ effects ( a fly-:eel1 z an accumulator ( =ce1 h l$ "s into ! error ( suppos+ t su* an app>atus increases ! actual p[] ( a ma*9e4 ,x is hop$1 h[ev]1 t aft] :at has be5 expla9$ respect+ ! in]tia ( matt] & ! true effects ( ma*9es1 ! read] w n be liable to a simil> mi/ake4 ,on ! contr>y1 z a fly _c act )\t friction1 & z ! am\nt ( ! friction1 l t ( in]tia1 is 9 proportion to ! weight1 a portion ( ! actual mov+ =ce mu/ unavoidably be lo/ by ! use ( a fly4 ,9 cases1 h[ev]1 :]e a fly is prop]ly appli$ ?is loss ( p[] is inconsid]able1 comp>$ ) ! advantage\s di/ribution ( :at rema9s4 ,illu/ration3 ,c4 ,v>ley1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,z an accumulator ( =ce1 a fly c nev] h m =ce ?an has be5 appli$ to put x 9 motion4 ,9 ?is respect x is analog\s to an ela/ic spr+1 or ! =ce ( cond5s$ air1 or any o!r p[] :i* d]ives its exi/5ce f causes purely me*anical4 ,9 b5d+ a spr+ a gradual exp5diture ( p[] is necess>y4 ,on ! recoil ?is p[] is ex]t$ 9 a mu* %ort] "t ?an t consum$ 9 its production1 b its total am\nt is n alt]$4 ,air is cond5s$ by a succession ( manual ef=ts1 "o ( :i* alone w\ld be incapable ( project+ a lead5 ball ) any consid]able =ce1 & all ( :i* c\ld n be imm$iately appli$ to ! ball at ! same in/ant4 ,b ! res]voir ( cond5s$ air is a magaz9e 9 :i* a great numb] ( su* ef=ts are /or$ up1 s z to be br\ght at once into action4 ,if a ball be expos$ to _! effect1 x may be project$ ) a de/ructive =ce4 ,9 mills = roll+ metal ! fly-:eel is us$ 9 ?is way4 ,! wat]-:eel or o!r mov+ p[] is all[$ = "s "t to act ^u ! fly-:eel alone1 no load be+ plac$ ^u ! ma*9e4 ,a =ce is ?us ga9$ :i* is suffici5t to roll a l>ge piece ( metal1 to :i* )\t su* means ! mill w\ld be q inadequate4 ,9 ! same mann] a =ce may be ga9$ by ! arm ( a man act+ on a fly = a few seconds1 suffici5t to impress an image on a piece ( metal by an in/antane\s /roke4 ,! fly is1 !re=e1 ! pr9cipal ag5t 9 co9+ presses4 7#cab47 ,! p[] ( a fly is (t5 transmitt$ to ! work+ po9t by means ( a screw4 ,at ! extremities ( ! cross arm ,a ,b1 fig4 #aeg41 :i* works ! screw1 two heavy balls ( metal are plac$4 ,:5 ! arm ,a ,b is :irl$ r\nd1 ^? masses ( metal acquire a mom5tum1 by :i* ! screw1 be+ driv5 d[nw>d1 urges ! die ) an imm5se =ce aga9/ ! sub/ance de/9$ to receive ! impression4 ,"s eng9es us$ 9 co9+ h flies ) arms f\r feet long1 be>+ "o hundr$ weight at ea* ( _! extremities4 ,by turn+ su* an arm at ! rate ( "o entire circumf]5ce 9 a second1 ! die w be driv5 aga9/ ! metal ) ! same =ce z t ) :i* #gejj p\nds weight w\ld fall f ! height ( #af feet2 an enorm\s p[]1 if ! simplicity & compactness ( ! ma*9e be consid]$4 ,! place to be assign$ to a fly-:eel relatively to ! o!r p>ts ( ! ma*9]y is det]m9$ by ! purpose = :i* x is us$4 ,if x be int5d$ to equalise ! action1 x %\ld be ne> ! work+ po9t4 ,?us1 9 a /eam-eng9e1 x is plac$ on ! crank :i* turns ! axle by :i* ! p[] ( ! eng9e is transmitt$ to ! object x is f9ally design$ to affect4 ,on ! contr>y1 9 h&mills1 su* z ^? commonly us$ = gr9d+ c(fee1 c41 x is plac$ ^u ! axis ( ! w9* by :i* ! ma*9e is work$4 ,! op5 "w ( f5d]s1 fire-grates1 & simil> ornam5tal articles con/ruct$ 9 metal1 is produc$ by ! action ( a fly1 9 ! mann] already describ$4 ,! cutt+ tool1 %ap$ accord+ to ! patt]n to be execut$1 is atta*$ to ! end ( ! screw2 & ! metal be+ held 9 a prop] position b5ea? x1 ! fly is made to urge ! tool d[nw>ds ) su* =ce z to /amp out pieces ( ! requir$ figure4 ,:5 ! patt]n is complicat$1 & x is necess>y to pres]ve ) exactness ! relative situation ( its diff]5t p>ts1 a numb] ( pun*es are impell$ toge!r1 s z to /rike ! entire piece ( metal at ! same in/ant1 & 9 ?is mann] ! mo/ elaborate op5 "w is execut$ by a s+le /roke4 ,,*ap4 ,,xviii4 ,,me*anical ,,contrivances ,,= ,,modify+ ,,motion4 7#cac47 ,! classes ( simple ma*9es d5om9at$ me*anic p[]s1 h relation *iefly to ! peculi> pr9ciple :i* det]m9es ! action ( ! p[] on ! weight or resi/ance4 ,9 expla9+ ?is arrangem5t v>i\s o!r reflections h be5 incid5tally mix$ up ) our inve/igations2 yet /ill mu* rema9s to be unfold$ be=e ! /ud5t c =m a j notion ( ^? means by :i* ! complex ma*9]y us$ 9 ! arts & manufactures s effectually atta9s ! ends1 to ! accompli%m5t ( :i* x is direct$4 ,by a p[] ( a giv5 en]gy to oppose a resi/ance ( a diff]5t en]gy1 or by a mov+ pr9ciple hav+ a giv5 velocity to g5]ate ano!r velocity ( a diff]5t am\nt1 is only "o ( ! _m objects to be effect$ by a ma*9e4 ,9 ! arts & manufactures ! k9d ( motion produc$ is g5]ally ( great] importance ?an its rate4 ,! latt] may affect ! quantity ( "w done 9 a giv5 "t1 b ! =m] is ess5tial to ! p]=mance ( ! "w 9 any quantity :atev]4 ,9 ! practical application ( ma*9es1 ! object to be atta9$ is g5]ally to communicate to ! work+ po9t "s peculi> sort ( motion suitable to ! uses = :i* ! ma*9e is int5d$2 b x r>ely happ5s t ! mov+ p[] has ?is sort ( motion4 ,h5ce1 ! ma*9e mu/ be s contriv$ t1 :ile t "p on :i* ?is p[] acts is capable ( mov+ 9 ob$i5ce to x1 its connection ) ! o!r p>ts %all be su* t ! work+ po9t may receive t motion :i* is necess>y = ! purposes to :i* ! ma*9e is appli$4 ,to give a p]fect solution ( ?is problem x w\ld be necess>y to expla91 fir/1 all ! v>ieties ( mov+ p[]s :i* are at our disposal2 secondly1 all ! v>iety ( motions :i* x may be necess>y to produce2 &1 ?irdly1 to %[ all ! me?ods by :i* ea* v>iety ( prime mov] may be made to produce ! sev]al species ( motion 9 ! work+ po9t4 ,x is obvi\s t su* an enum]ation w\ld be impracticable1 & ev5 an approximation to x w\ld be unsuitable to ! pres5t treatise4 ,nev]!less1 s mu* +5uity has be5 display$ 9 _m ( ! contrivances = modify+ motion1 & an acqua9tance ) "s ( !m is s ess5tial to a cle> compreh5sion ( ! nature & op]ation ( complex ma*9es1 t x w\ld be improp] to omit "s acc\nt ( ^? at lea/ :i* mo/ frequ5tly occur 9 ma*9]y1 or :i* are mo/ conspicu\s = elegance & simplicity4 ,! v>ieties ( motion :i* mo/ commonly pres5t !mselves 9 ! practical application ( me*anics may be divid$ into rectil9e> & rotatory4 ,9 rectil9e> motion ! sev]al p>ts ( ! mov+ body proce$ 9 p>allel /raight l9es ) ! same spe$4 ,9 rotatory motion ! sev]al po9ts revolve r\nd an axis1 ea* p]=m+ a complete circle1 or simil> p>ts ( a circle1 9 ! same "t4 ,ea* ( ^! may aga9 be resolv$ into cont9u$ & reciprocat+4 ,9 a cont9u$ motion1 :e!r rectil9e> or rotatory1 ! p>ts move con/antly 9 ! same direction1 :e!r t be 9 p>allel /raight l9es1 or 9 rotation on an axis4 ,9 reciprocat+ motion ! sev]al p>ts move alt]nately 9 opposite directions1 trac+ ! same spaces f end to end cont9ually4 ,?us1 !re are f\r pr9cipal species ( motion :i* m frequ5tly ?an any o!rs act ^u1 or are requir$ to be transmitt$ by1 ma*9es3-- #a4 ,cont9u$ rectil9e> motion4 #b4 ,reciprocat+ rectil9e> motion4 #c4 ,cont9u$ circul> motion4 #d4 ,reciprocat+ circul> motion4 ,^! w be m cle>ly und]/ood by examples ( ea* k9d4 ,cont9u$ rectil9e> motion is obs]v$ 9 ! fl[+ ( a riv]1 9 a fall ( wat]1 9 ! bl[+ ( ! w9d1 9 ! motion ( an animal ^u a /raight road1 9 ! p]p5dicul> fall ( a heavy body1 9 ! motion ( a body d[n an incl9$ plane4 ,reciprocat+ rectil9e> motion is se5 9 ! pi/on ( a common syr+e1 9 ! rod ( a common pump1 9 ! hamm] ( a pavi]1 ! pi/on ( a /eam-eng9e1 ! /amp]s ( a full+ mill4 ,cont9u$ circul> motion is exhibit$ 9 all k9ds ( :eel-"w1 & is s common1 t to p>ticul>ise x is ne$less4 ,reciprocat+ circul> motion is se5 9 ! p5dulum ( a clock1 & 9 ! balance-:eel ( a wat*4 ,we %all n[ expla9 "s ( ! contrivances by :i* a p[] hav+ "o ( ^! motions may be made to communicate ei!r ! same species ( motion *ang$ 9 its velocity or direction1 or any ( ! o!r ?ree k9ds ( motion4 7#cad47 ,by a cont9u$ rectil9e> motion ano!r cont9u$ rectil9e> motion 9 a diff]5t direction may be produc$1 by "o or m fix$ pulleys4 ,a cord pass$ ov] ^!1 "o end ( x be+ mov$ by ! p[]1 w transmit ! same motion un*ang$ to ! o!r end4 ,if ! directions ( ! two motions cross ea* o!r1 "o fix$ pulley w be suffici5t2 see fig4 #aac41 :]e ! h& takes ! direction ( ! "o motion1 & ! weight t ( ! o!r4 ,9 ?is case ! pulley mu/ be plac$ 9 ! angle at :i* ! directions ( ! two motions cross ea* o!r4 ,if ?is angle be di/ant f ! places at :i* ! objects 9 motion are situate1 an inconv5i5t l5g? ( rope may be necess>y4 ,9 ?is case ! same may be effect$ by ! use ( two pulleys1 z 9 fig4 #aeh4 ,if ! directions ( ! two motions be p>allel1 two pulleys mu/ be us$ z 9 fig4 #aeh41 :]e ,p ,a is "o motion1 & ,b ,w ! o!r4 ,9 ^! cases ! axles ( ! two :eels are p>allel4 ,x may s happ5 t ! directions ( ! two motions nei!r cross ea* o!r nor are p>allel4 ,?is w\ld happ51 = example1 if ! direction ( "o 7 ^u ! pap] 9 ! l9e ,p ,a1 :ile ! o!r 7 p]p5dicul> to ! pap] f ! po9t ,o4 ,9 ?is case two pulleys %\ld be us$1 ! axle ( "o ,o be+ p]p5dicul> to ! pap]1 :ile ! axle ( ! o!r ,o %\ld be on ! pap]4 ,?is w be evid5t by a little reflection4 ,9 g5]al1 ! axle ( ea* pulley mu/ be p]p5dicul> to ! two directions 9 :i* ! rope passes f its groove2 & by due att5tion to ?is condition x w be p]ceiv$1 t a cont9u$ rectil9e> motion may be transf]r$ f any "o direction to any o!r direction1 by means ( a cord & two pulleys1 )\t *ang+ its velocity4 ,if x be necess>y to *ange ! velocity1 any ( ! sy/ems ( pulleys describ$ 9 *ap4 ,,xv4 may be us$ 9 addition to ! fix$ pulleys4 ,by ! :eel & axle any "o cont9u$ rectil9e> motion may be made to produce ano!r 9 any o!r direction1 & ) any o!r velocity4 ,x has be5 already expla9$ 7#bej47 t ! proportion ( ! velocity ( ! p[] to t ( ! weight is z ! diamet] ( ! :eel to ! diamet] ( ! axle4 ,! ?ickness ( ! axle be+ !re=e regulat$ 9 relation to ! size ( ! :eel1 s t _! diamet]s %all h t proportion :i* subsi/s betwe5 ! propos$ velocities1 "o condition ( ! problem w be fulfill$4 ,! rope coil$ ^u ! axle may be c>ri$1 by means ( "o or m fix$ pulleys1 into ! direction ( "o ( ! propos$ motions1 :ile t :i* surr\nds ! :eel is c>ri$ into ! direction ( ! o!r by simil> means4 7#cae47 ,by ! :eel & axle a cont9u$ rectil9e> motion may be made to produce a cont9u$ rotatory motion1 or vice v]s4 ,if ! p[] be appli$ by a rope coil$ ^u ! :eel1 ! cont9u$ motion ( ! p[] 9 a /raight l9e w cause ! ma*9e to h a rotatory motion4 ,aga91 if ! weight be appli$ by a rope coil$ ^u ! axle1 a p[] hav+ a rotatory motion appli$ to ! :eel w cause ! cont9u$ asc5t ( ! weight 9 a /raight l9e4 ,cont9u$ rectil9e> & rotatory motions may be made to produce ea* o!r1 by caus+ a too!d :eel to "w 9 a /raight b>1 call$ a rack1 c>ry+ tee? ^u its edge4 ,su* an app>atus is repres5t$ 9 fig4 #aei4 ,9 "s cases ! tee? ( ! :eel "w 9 ! l9ks ( a *a94 ,! :eel is !n call$ a rag-:eel1 fig4 #afj4 ,/raps1 b&s1 or ropes1 may communicate rotation to a :eel1 by _! friction 9 a groove ^u its edge4 ,a cont9u$ rectil9e> motion is produc$ by a cont9u$ circul> motion 9 ! case ( a screw4 ,! lev] :i* turns ! screw has a cont9u$ circul> motion1 :ile ! screw itself advances ) a cont9u$ rectil9e> motion4 ,! cont9u$ rectil9e> motion ( a /ream ( wat] act+ ^u a :eel produces cont9u$ circul> motion 9 ! :eel1 fig4 #ic1 #id1 #ie4 ,9 l mann] ! cont9u$ rectil9e> motion ( ! w9d produces a cont9u$ circul> motion 9 ! arms ( a w9dmill4 ,cranes = rais+ & l[]+ heavy weights conv]t a circul> motion ( ! p[] into a cont9u$ rectil9e> motion ( ! weight4 7#caf47 ,cont9u$ circul> motion may produce reciprocat+ rectil9e> motion1 by a great v>iety ( +5i\s contrivances4 ,reciprocat+ rectil9e> motion is us$ :5 heavy /amp]s are to be rais$ to a c]ta9 height1 & all[$ to fall ^u "s object plac$ b5ea? !m4 ,?is may be accompli%$ by a :eel be>+ on its edge curv$ tee?1 call$ wip]s4 ,! /amp] is furni%$ ) a project+ arm or peg1 b5ea? :i* ! wip]s are successively br\ght by ! revolution ( ! :eel4 ,z ! :eel revolves ! wip] raises ! /amp]1 until its extremity passes ! extremity ( ! project+ arm ( ! /amp]1 :5 ! latt] imm$iately falls by its own weight4 ,x is !n tak5 up by ! next wip]1 & s ! process is cont9u$4 ,a simil> effect is produc$ if ! :eel be p>tially furni%$ ) tee?1 & ! /amp] c>ry a rack 9 :i* ^! tee? "w4 ,su* an app>atus is repres5t$ 9 fig4 #afa4 ,x is sometimes necess>y t ! reciprocat+ rectil9e> motion %all be p]=m$ at a c]ta9 v>y+ rate 9 bo? directions4 ,?is may be accompli%$ by ! ma*9e repres5t$ 9 fig4 #afb4 ,a :eel ^u ! axle ,c turns uni=mly 9 ! direction ,a ,b ,d ,e4 ,a rod mn moves 9 guides1 :i* only p]mit x to asc5d & desc5d p]p5dicul>ly4 ,its extremity m re/s ^u a pa? or groove rais$ f ! face ( ! :eel1 & %ap$ into su* a curve t z ! :eel revolves ! rod mn %all be mov$ alt]nately 9 opposite directions ?r\gh ! guides1 ) ! requir$ velocity4 ,! mann] 9 :i* ! velocity v>ies w dep5d on ! =m giv5 to ! groove or *annel rais$ ^u ! face ( ! :eel1 & ?is may be %ap$ s z to give any v>iation to ! motion ( ! rod mn :i* may be requir$ = ! purpose to :i* x is to be appli$4 ,! rose-eng9e 9 ! turn+-la! is con/ruct$ on ?is pr9ciple4 ,x is also us$ 9 sp9n+ ma*9]y4 ,x is (t5 necess>y t ! rod to :i* reciprocat+ motion is communicat$ %all be urg$ by ! same =ce 9 bo? directions4 ,a :eel p>tially furni%$ ) tee?1 act+ on two racks plac$ on diff]5t sides ( x1 & bo? connect$ ) ! b> or rod to :i* ! reciprocat+ motion is to be communicat$1 w accompli% ?is4 ,su* an app>atus is repres5t$ 9 fig4 #afc41 & ne$s no fur!r explanation4 ,ano!r contrivance = ! same purpose is %[n 9 fig4 #afd41 :]e ,a is a :eel turn$ by a w9* ,h1 & connect$ ) a rod or beam mov+ 9 guides by ! jo9t ab4 ,z ! :eel ,a is turn$ by ! w9* ,h ! beam is mov$ betwe5 ! guides alt]nately 9 opposite directions1 ! ext5t ( its range be+ gov]n$ by ! l5g? ( ! diamet] ( ! :eel4 ,su* an app>atus is us$ = gr9d+ & poli%+ plane surfaces1 & also occurs 9 silk ma*9]y4 ,an app>atus appli$ by ,m4 ,zur$a 9 a ma*9e = prick+ holes 9 lea!r is repres5t$ 9 fig4 #afe4 ,! :eel ,a ,b has its circumf]5ce =m$ into tee?1 ! %ape ( :i* may be v>i$ accord+ to ! circum/ances "u :i* x is to be appli$4 ,"o extremity ( ! rod ab re/s ^u ! tee? ( ! :eel ^u :i* x is press$ by a spr+ at ! o!r extremity4 ,:5 ! :eel revolves1 x communicates to ?is rod a reciprocat+ rectil9e> motion4 ,leupold has appli$ ?is me*anism to move ! pi/ons ( pumps4#e ,^u ! v]tical axis ( a horizontal hydraulic :eel is fix$ ano!r horizontal :eel1 :i* is furni%$ ) sev5 tee? 9 ! mann] ( a cr[n :eel 7#bfc474 ,^! tee? are %ap$ l incl9$ planes1 ! int]vals betwe5 !m be+ equal to ! l5g? ( ! planes4 ,project+ arms atta*$ to ! pi/on rods re/ ^u ! cr[n ( ?is :eel2 &1 z x revolves1 ! incl9$ surfaces ( ! tee?1 be+ =c$ "u ! arm1 raise ! rod ^u ! pr9ciple ( ! w$ge4 ,to dim9i% ! ob/ruction aris+ f friction1 ! project+ arms ( ! pi/on rods are provid$ ) roll]s1 :i* run ^u ! tee? ( ! :eel4 ,9 "o revolution ( ! :eel ea* pi/on makes z _m asc5ts & desc5ts z !re are tee?4 #e ,!atrum ,ma*9>um1 tom4 ii4 pl4 #cf4 fig4 #c4 7#cag47 ,:eel-"w furni%es num]\s examples ( cont9u$ circul> motion r\nd "o axis1 produc+ cont9u$ circul> motion r\nd ano!r4 ,if ! axles be 9 p>allel directions1 & n too di/ant1 rotation may be transmitt$ f "o to ! o!r by two spur-:eels 7#bfc472 & ! relative velocities may be det]m9$ by giv+ a correspond+ proportion to ! diamet] ( ! :eels4 ,if a rot>y motion is to be communicat$ f "o axis to ano!r p>allel to x1 & at any consid]able di/ance1 x _c 9 practice be accompli%$ by :eels alone1 = _! diamet]s w\ld be too l>ge4 ,9 ?is case a /rap or *a9 is c>ri$ r\nd ! circumf]5ces ( bo? :eels4 ,if !y are int5d$ to turn 9 ! same direction1 ! /rap is arrang$ z 9 fig4 #ajj42 b if 9 contr>y directions x is cross$1 z 9 fig4 #aja4 ,9 ?is case1 z ) too!d :eels1 ! relative velocities are det]m9$ by ! proportion ( ! diamet]s ( ! :eels4 ,if ! axles be di/ant & n p>allel1 ! cord1 by :i* ! motion is transmitt$1 mu/ be pass$ ov] groov$ :eels1 or fix$ pulleys1 prop]ly plac$ betwe5 ! two axles4 ,x may happ5 t ! /ra9 ^u ! :eel1 to :i* ! motion is to be transmitt$1 is too great to all[ ( a /rap or cord be+ us$4 ,9 ?is case1 a %aft ext5d+ f ! "o axis to ano!r1 & c>ry+ two bevell$ :eels 7#bfc471 w accompli% ! object4 ,"o ( ^! bevell$ :eels is plac$ ^u ! %aft ne> to1 & 9 connection )1 ! :eel f :i* ! motion is to be tak51 & ! o!r at a "p ( x ne> to1 & 9 connection )1 t :eel to :i* ! motion is to be convey$1 fig4 #aff4 ,! me?ods ( transmitt+ rotation f "o axis to ano!r p]p5dicul> to x1 by cr[n & by bevell$ :eels1 h be5 expla9$ 9 7#bfc474 ,! endless screw 7#bii47 is a ma*9e by :i* a rotatory motion r\nd "o axis may communicate a rotatory motion r\nd ano!r p]p5dicul> to x4 ,! p[] revolves r\nd an axis co9cid+ ) ! l5g? ( ! screw1 & ! axis ( ! :eel driv5 by ! screw is at "r angles to ?is4 ,! axis to :i* rotation is to be giv51 or f :i* x is to be tak51 is sometimes v>iable 9 its position4 ,9 su* cases1 an +5i\s contrivance1 call$ a univ]sal jo9t1 inv5t$ by ! celebrat$ ,dr4 ,hooke1 may be us$4 ,! two %afts or axles ,a ,b1 fig4 #afg41 betwe5 :i* ! motion is to be communicat$1 t]m9ate 9 semicircles1 ! diamet]s ( :i*1 ,c ,d & ,e ,f1 are fix$ 9 ! =m ( a cross1 _! extremities mov+ freely 9 bu%es plac$ 9 ! extremities ( ! semicircles4 ,?us1 :ile ! c5tral cross rema9s unmov$1 ! %aft ,a & its semicircul> end may revolve r\nd ,c ,d z an axis2 & ! %aft ,b & its semicircul> end may revolve r\nd ,e ,f z an axis4 ,if ! %aft ,a be made to revolve )\t *ang+ its direction1 ! po9ts ,c ,d w move 9 a circle ^: c5tre is at ! middle ( ! cross4 ,! motion ?us giv5 to ! cross w cause ! po9ts ,e ,f to move 9 ano!r circle r\nd ! same c5tre1 & h5ce ! %aft ,b w be made to revolve4 ,illu/ration3 ,c4 ,v>ley1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,?is in/rum5t w n transmit ! motion if ! angle "u ! directions ( ! %afts be less ?an #adj4 ,9 ?is case a d\ble jo9t1 z repres5t$ 9 fig4 #afh41 w answ] ! purpose4 ,?is consi/s ( f\r semicircles unit$ by two crosses1 & its pr9ciple & op]ation is ! same z 9 ! la/ case4 ,univ]sal jo9ts are ( great use 9 adju/+ ! position ( l>ge telescopes1 :]e1 :ile ! obs]v] cont9ues to look ?r\gh ! tube1 x is necess>y to turn endless screws or :eels ^: axes are n 9 an accessible position4 ,! cross is n indisp5sably necess>y 9 ! univ]sal jo9t4 ,a hoop1 ) f\r p9s project+ f x at f\r po9ts equally di/ant f ea* o!r1 or divid+ ! circle ( ! hoop into f\r equal arcs1 w answ] ! purpose4 ,^! p9s play 9 ! bu%es ( ! semicircles 9 ! same mann] z ^? ( ! cross4 ,! univ]sal jo9t is mu* us$ 9 cotton-mills1 :]e %afts are c>ri$ to a consid]able di/ance f ! prime mov]1 & great advantage is ga9$ by divid+ !m into conv5i5t l5g?s1 connect$ by a jo9t ( ?is k9d4 7#cah47 ,9 ! practical application ( ma*9]y1 x is (t5 necess>y to connect a "p hav+ a cont9u$ circul> motion ) ano!r :i* has a reciprocat+ or alt]nate motion1 s t ei!r may move ! o!r4 ,!re are _m contrivances by :i* ?is may be effect$4 ,"o ( ! mo/ rem>kable examples ( x is pres5t$ 9 ! scapem5ts ( wat*es & clocks4 ,9 ?is case1 h[ev]1 x c sc>cely be said ) /rict propriety t x is ! rotation ( ! scapem5t-:eel 7#bff47 :i* communicates ! vibration to ! balance-:eel or p5dulum4 ,t vibration is produc$ 9 ! "o case by ! peculi> nature ( ! spiral spr+ fix$ ^u ! axis ( ! balance-:eel1 & 9 ! o!r case by ! gravity ( ! p5dulum4 ,! =ce ( ! scapem5t-:eel only ma9ta9s ! vibration1 & prev5ts its decay by friction & atmosph]ic resi/ance4 ,nev]!less1 betwe5 ! two p>ts ?us mov+ !re exi/s a me*anical connection1 :i* is g5]ally br\ght )9 ! class ( contrivances n[ "u consid]ation4 ,a beam vibrat+ on an axis1 & driv5 by ! pi/on ( a /eam-eng9e1 or any o!r p[]1 may communicate rot>y motion to an axis by a connector & a crank4 ,?is app>atus has be5 already describ$ 9 7#caa474 ,e /eam-eng9e :i* works by a beam af=ds an example ( ?is4 ,! work+ beam is g5]ally plac$ ov] ! eng9e1 ! pi/on rod be+ atta*$ to "o end ( x1 :ile ! connect+ rod unites ! o!r end ) ! crank4 ,9 boat-eng9es1 h[ev]1 ?is position w\ld be inconv5i5t1 requir+ m room ?an c\ld easily be sp>$4 ,! pi/on rod1 9 ^! cases1 is1 !re=e1 connect$ ) ! end ( ! beam by long rods1 & ! beam is plac$ beside & bel[ ! eng9e4 ,! use ( a fly-:eel "h w\ld also be objectionable4 ,! effect ( ! dead po9ts expla9$ 9 7#caa47 is avoid$ )\t ! aid ( a fly1 by plac+ two cranks ^u ! revolv+ axle1 & work+ !m by two pi/ons4 ,! cranks are s plac$ t :5 ei!r is at its dead po9t1 ! o!r is 9 its mo/ fav\rable position4 ,a :eel ,a1 fig4 #afi41 arm$ ) wip]s1 act+ ^u a sl$ge-hamm] ,b1 fix$ ^u a c5tre or axle ,c1 w1 by a cont9u$ rotatory motion1 give ! hamm] ! reciprocat+ motion necess>y = ! purposes to :i* x is appli$4 ,! mann] 9 :i* ?is acts mu/ be evid5t on inspect+ ! figure4 ,! tr$dle ( ! la! furni%es an obvi\s example ( a vibrat+ circul> motion produc+ a cont9u$ circul> "o4 ,! tr$dle acts ^u a crank1 :i* gives motion to ! pr9cipal :eel1 9 ! same mann] z already describ$ 9 ref]5ce to ! work+ beam & crank 9 ! /eam-eng9e4 ,by ! foll[+ +5i\s me*anism an alt]nate or vibrat+ =ce may be made to communicate a circul> motion cont9ually 9 ! same direction4 ,let ,a ,b1 fig4 #agj41 be an axis receiv+ an alt]nate motion f "s =ce appli$ to x1 su* z a sw++ weight4 ,two rat*et :eels 7#bec47 m & n are fix$ on ?is axle1 _! tee? be+ incl9$ 9 opposite directions4 ,two too!d :eels ,c & ,d are likewise plac$ ^u x1 b s arrang$ t !y turn ^u ! axle ) a little friction4 ,^! :eels c>ry two cat*es p1 q1 :i* fall into ! tee? ( ! rat*et :eels m1 n1 b fall on opposite sides con=mably to ! incl9ation ( ! tee? already m5tion$4 ,! effect ( ^! cat*es is1 t if ! axis be made to revolve 9 "o direction1 "o ( ! two too!d :eels is always compell$ 7by ! cat* aga9/ :i* ! motion is direct$7 to revolve ) x1 :ile ! o!r is p]mitt$ to rema9 /ation>y 9 ob$i5ce to any =ce suffici5tly great to ov]come its friction ) ! axle on :i* x is plac$4 ,! :eels ,c & ,d are bo? engag$ by bevell$ tee? 7#bfc47 ) ! :eel ,e4 ,accord+ to ?is arrangem5t1 9 :i*ev] direction ! axis ,a ,b is made to revolve1 ! :eel ,e w cont9ually turn 9 ! same direction1 &1 !re=e1 if ! axle ,a ,b be made to turn alt]nately 9 ! "o direction & ! o!r1 ! :eel ,e w n *ange ! direction ( its motion4 ,let u suppose t ! axle ,a ,b is turn$ aga9/ ! cat* p4 ,! :eel ,c w !n be made to turn ) ! axle4 ,?is w drive ! :eel ,e 9 ! same direction4 ,! tee? on ! opposite side ( ! :eel ,e be+ engag$ ) ^? ( ! :eel ,d1 ! latt] w be turn$ ^u ! axle1 ! friction1 :i* alone resi/s its motion 9 t direction1 be+ ov]come4 ,let ! motion ( ! axle ,a ,b be n[ rev]s$4 ,s9ce ! tee? ( ! rat*et :eel n are mov$ aga9/ ! cat* q1 ! :eel ,d w be compell$ to revolve ) ! axle4 ,! :eel ,e w be driv5 9 ! same direction z be=e1 & ! :eel ,c w be mov$ on ! axle ,a ,b1 & 9 a contr>y direction to ! motion ( ! axle1 ! friction be+ ov]come by ! =ce ( ! :eel ,e4 ,?us1 :ile ! axle ,a ,b is turn$ alt]nately 9 ! "o direction & ! o!r1 ! :eel ,e is con/antly mov$ 9 ! same direction4 ,x is evid5t t ! direction 9 :i* ! :eel ,e moves may be rev]s$ by *ang+ ! position ( ! rat*et :eels & cat*es4 7#cai47 ,x is (t5 necess>y to communicate an alt]nate circul> motion1 l t ( a p5dulum1 by means ( an alt]nate motion 9 a /raight l9e4 ,a rem>kable in/ance ( ?is occurs 9 ! /eam eng9e4 ,! mov+ =ce 9 ?is ma*9e is ! pressure ( /eam1 :i* impels a pi/on f end to end alt]nately 9 a cyl9d]4 ,! =ce ( ?is pi/on is communicat$ to ! work+ beam by a /rong rod1 :i* passes ?r\gh a coll> 9 "o end ( ! pi/on4 ,s9ce x is necess>y t ! /eam includ$ 9 ! cyl9d] %\ld n escape betwe5 ! pi/on rod & ! coll> ?r\gh :i* x moves1 & yet1 t x %\ld move z freely & be subject to z little resi/ance z possible1 ! rod is turn$ s z to be truly cyl9drical1 & is well poli%$4 ,x is evid5t t1 "u ^! circum/ances1 x mu/ n be subject to any lat]al or cross /ra91 :i* w\ld b5d x t[>ds "o side or ! o!r ( ! cyl9d]4 ,b ! end ( ! beam to :i* x communicates motion1 if connect$ imm$iately ) ! rod by a jo9t1 w\ld draw x alt]nately to ! "o side & ! o!r1 s9ce x moves 9 ! arc ( a circle1 ! c5tre ( :i* is at ! c5tre ( ! beam4 ,x is necess>y1 !re=e1 to contrive "s me?od ( connect+ ! rod & ! end ( ! beam1 s t :ile ! "o %all asc5d & desc5d 9 a /raight l9e1 ! o!r may move 9 ! circul> arc4 ,! me?od :i* fir/ sugge/s itself to accompli% ?is is1 to con/ruct an ar*-head ^u ! end ( ! beam1 z 9 fig4 #aga4 ,let ,c be ! c5tre on :i* ! beam works1 & let ,b ,d be an ar* atta*$ to ! end ( ! beam1 be+ a "p ( a circle hav+ ,c = its c5tre4 ,to ! highe/ po9t ,b ( ! ar* a *a9 is atta*$1 :i* is c>ri$ ^u ! face ( ! ar* ,b ,a1 & ! o!r end ( :i* is atta*$ to ! pi/on rod4 ,"u ^! circum/ances x is evid5t1 t :5 ! =ce ( ! /eam impels ! pi/on d[nw>ds1 ! *a9 ,p ,a ,b w draw ! end ( ! beam d[n1 & w1 !re=e1 elevate ! o!r end4 ,:5 ! /eam-eng9e is us$ = c]ta9 purposes1 su* z pump+1 ?is arrangem5t is suffici5t4 ,! pi/on 9 t case is n =c$ upw>ds by ! pressure ( /eam4 ,dur+ its asc5t x is n subject to ! action ( any =ce ( /eam1 & ! o!r end ( ! beam falls by ! weight ( ! pump-rods draw+ ! pi/on1 at ! opposite end ,a1 to ! top ( ! cyl9d]4 ,?us ! ma*9e is 9 fact passive dur+ ! asc5t ( ! pi/on1 & ex]ts its p[] only dur+ ! desc5t4 ,if ! ma*9e1 h[ev]1 be appli$ to purposes 9 :i* a con/ant action ( ! mov+ =ce is necess>y1 z is always ! case 9 manufactures1 ! =ce ( ! pi/on mu/ drive ! beam 9 its asc5t z well z 9 its desc5t4 ,! arrangem5t j describ$ _c effect ?is2 = al?\gh a *a9 is capable ( transmitt+ any =ce1 by :i* its extremities are drawn 9 opposite directions1 yet x is1 f its flexibility1 incapable ( communicat+ a =ce :i* drives "o extremity ( x t[>ds ! o!r4 ,9 ! "o case ! pi/on fir/ pulls d[n ! beam1 & !n ! beam pulls up ! pi/on4 ,! *a91 because x is inext5sible1 is p]fectly capable ( bo? ^! actions2 & be+ flexible1 x applies itself to ! ar*-head ( ! beam1 s z to ma9ta9 ! direction ( its =ce ^u ! pi/on cont9ually 9 ! same /raight l9e4 ,b :5 ! pi/on acts ^u ! beam 9 bo? ways1 9 pull+ x d[n & pu%+ x up1 ! *a9 becomes ineffici5t1 be+ f its flexibility incapable ( ! latt] action4 ,! problem might be solv$ by ext5d+ ! l5g? ( ! pi/on rod1 s t its extremity %all be above ! beam1 & us+ two *a9s2 "o connect+ ! highe/ po9t ( ! rod ) ! l[e/ po9t ( ! ar*-head1 & ! o!r connect+ ! highe/ po9t ( ! ar*-head ) a po9t on ! rod bel[ ! po9t :i* meets ! ar*-head :5 ! pi/on is at ! top ( ! cyl9d]1 fig4 #agb4 ,! connection requir$ may also be made by arm+ ! ar*-head ) tee?1 fig4 #agc41 & caus+ ! pi/on rod to t]m9ate 9 a rack4 ,9 cases :]e1 z 9 ! /eam-eng9e1 smoo?ness ( motion is ess5tial1 ?is me?od is objectionable2 & "u any circum/ances su* an app>atus is liable to rapid we>4 ,! me?od contriv$ by ,watt1 = connect+ ! motion ( ! pi/on ) t ( ! beam1 is "o ( ! mo/ +5i\s & elegant solutions ev] propos$ = a me*anical problem4 ,he conceiv$ ! motion ( two /raight rods ,a ,b1 ,c ,d1 fig4 #agd41 mov+ on c5tres or pivots ,a & ,c1 s t ! extremities ,b & ,d w\ld move 9 ! arcs ( circles hav+ _! c5tres at ,a & ,c4 ,! extremities ,b & ,d ( ^! rods he conceiv$ to be connect$ ) a ?ird rod ,b ,d unit$ ) !m by pivots on :i* x c\ld turn freely4 ,to ! sy/em ( rods ?us connect$ let an alt]nate motion on ! c5tres ,a & ,c be communicat$3 ! po9ts ,b & ,d w move upw>ds & d[nw>ds 9 ! arcs express$ by ! dott$ l9es1 b ! middle po9t ,p ( ! connect+ rod ,b ,d w move upw>ds & d[nw>ds )\t any s5sible deviation f a /raight l9e4 ,to prove ?is demon/ratively w\ld require "s ab/ruse ma!matical inve/igation4 ,x may1 h[ev]1 be r5d]$ 9 "s degree app>5t by reason+ ( a loos] & m popul> nature4 ,z ! po9t ,b is rais$ to ,e1 x is also drawn aside t[>ds ! "r4 ,at ! same "t ! o!r extremity ,d ( ! rod ,b ,d is rais$ to ,e1 & is drawn aside t[>ds ! left4 ,! ends ( ! rod ,b ,d be+ ?us at ! same "t drawn equally t[>ds opposite sides1 its middle po9t ,p w suff] no lat]al d]angem5t1 & w move directly upw>ds4 ,on ! o!r h&1 if ,b be mov$ d[nw>ds to ,f1 x w be drawn lat]ally to ! "r1 :ile ,d be+ mov$ to ,f w be drawn to ! left4 ,h5ce1 z be=e1 ! middle po9t ,p su/a9s no lat]al d]angem5t1 b m]ely desc5ds4 ,?us1 z ! extremities ,b & ,d move upw>ds & d[nw>ds 9 circles1 ! middle po9t ,p moves upw>ds & d[nw>ds 9 a /raight l9e4#f #f ,9 a /rictly ma!matical s5se1 ! pa? ( ! po9t ,p is a curve1 & n a /raight l9e2 b 9 ! play giv5 to x 9 its application to ! /eam-eng9e1 x moves ?r\gh a "p only ( its entire locus1 & ?is "p ext5d+ equally on ea* side ( a po9t ( inflection1 ! radius ( curvature is inf9ite1 s t 9 practice ! deviation f a /raight l9e1 :5 prop] proportions are obs]v$ 9 ! rods1 is imp]ceptible4 ,! application ( ?is geometrical pr9ciple 9 ! /eam-eng9e ev9ces mu* +5uity4 ,! same arm ( ! beam usually works two pi/ons1 t ( ! cyl9d] & t ( ! air-pump4 ,! app>atus is repres5t$ on ! arm ( ! beam 9 fig4 #age4 ,! beam moves alt]nately upw>ds & d[nw>ds on its axis ,a4 ,e po9t ( x1 !re=e1 describes a "p ( a circle ( :i* ,a is ! c5tre4 ,let ,b be ! po9t :i* divides ! arm ,a ,g into two equal p>ts ,a ,b & ,b ,g2 & let ,c ,d be a /raight rod1 equal 9 l5g? to ,g ,b1 & fix$ on a c5tre or pivot ,c on :i* x is at lib]ty to play4 ,! end ,d ( ?is rod is connect$ by a /raight b> ) ! po9t ,b1 by pivots on :i* ! rod ,b ,d turns freely4 ,if ! beam be n[ suppos$ to rise & fall alt]nately1 ! po9ts ,b & ,d w move upw>ds & d[nw>ds 9 circul> arcs1 &1 z already expla9$ ) respect to ! po9ts ,b ,d1 fig4 #agd41 ! middle po9t ,p ( ! connect+ rod ,b ,d w move upw>ds & d[nw>ds )\t lat]al deflection4 ,to ?is po9t "o ( ! pi/on rods :i* are to be work$ is atta*$4 ,to compreh5d ! me?od ( work+ ! o!r pi/on1 conceive a rod ,g ,p1 equal 9 l5g? to ,b ,d1 to be atta*$ to ! end ,g ( ! beam by a pivot on :i* x moves freely2 & let its extremity ,p be connect$ ) ,d by ano!r rod ,p ,d1 equal 9 l5g? to ,g ,b1 & play+ on po9ts at ,p & ,d4 ,! pi/on rod ( ! cyl9d] is atta*$ to ! po9t ,p1 & ?is po9t has a motion precisely simil> to t ( ,p1 )\t any lat]al d]angem5t1 b ) a range 9 ! p]p5dicul> direction twice z great4 ,?is w be app>5t by conceiv+ a /raight l9e drawn f ! c5tre ,a ( ! beam to ,p1 :i* w also pass ?r\gh ,p4 ,s9ce ,g ,p is always p>allel to ,b ,p1 x is evid5t t ! triangle ,p ,g ,a is always simil> to ,p ,b ,a1 & has its sides & angles simil>ly plac$1 b ^? sides are ea* twice ! magnitude ( ! correspond+ sides ( ! o!r triangle4 ,h5ce ! po9t ,p mu/ be subject to ! same *anges ( position z ! po9t ,p1 ) ?is diff]5ce only1 t 9 ! same "t x moves ov] a space ( twice ! magnitude4 ,9 fact1 ! l9e trac$ by ,p is ! same z t trac$ by ,p1 b on a scale twice z l>ge4 ,?is contrivance is usually call$ ! p>allel motion1 b ! same "n is g5]ally appli$ to all contrivances by :i* a circul> motion is made to produce a rectil9e> "o4 ,,*ap4 ,,xix4 ,,( ,,friction ,,& ,,! ,,rigidity ,,( ,,cordage4 7#cbj47 ,) a view to ! simplification ( ! elem5t>y !ory ( ma*9es1 ! consid]ation ( sev]al me*anical effects ( great practical importance has be5 po/pon$1 & ! att5tion ( ! /ud5t has be5 direct$ exclusively to ! way 9 :i* ! mov+ p[] is modifi$ 9 be+ transmitt$ to ! resi/ance indep5d5tly ( su* effects4 ,a ma*9e has be5 reg>d$ z an in/rum5t by :i* a mov+ pr9ciple1 inapplicable 9 its exi/+ /ate to ! purpose = :i* x is requir$1 may be *ang$ ei!r 9 its velocity or direction1 or 9 "s o!r "*1 s z to be adapt$ to t purpose4 ,b 9 accompli%+ ?is1 ! sev]al p>ts ( ! ma*9e h be5 consid]$ z possess+ 9 a p]fect degree qualities :i* !y enjoy only 9 an imp]fect degree2 & accord+ly ! conclusions to :i* by su* reason+ we are conduct$ are infect$ ) errors1 ! am\nt ( :i* w dep5d on ! degree 9 :i* ! ma*9]y falls %ort ( p]fection 9 ^? qualities :i* !oretically are imput$ to x4 ,illu/ration3 ,c4 ,v>ley1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,( ! sev]al p>ts ( a ma*9e1 "s are design$ to move1 :ile o!rs are fix$2 & ( ^? :i* move1 "s h motions diff]+ 9 quantity & direction f ^? ( o!rs4 ,! sev]al p>ts1 :e!r fix$ or movable1 are subject to v>i\s /ra9s & pressures1 :i* !y are int5d$ to resi/4 ,^! =ces n only v>y accord+ to ! load :i* ! ma*9e has to ov]come1 b also accord+ to ! peculi> =m & /ructure ( ! ma*9e itself4 ,dur+ ! op]ation ! surfaces ( ! movable p>ts move 9 imm$iate contact ) ! surfaces ei!r ( fix$ p>ts or ( p>ts hav+ o!r motions4 ,if ^! surfaces 7 endu$ ) p]fect smoo?ness or poli%1 & ! sev]al p>ts subject to /ra9s possess$ p]fect inflexibility & inf9ite /r5g?1 !n ! effects ( ma*9]y might be practically inve/igat$ by ! pr9ciples already expla9$4 ,b ! mat]ials ( :i* e ma*9e is =m$ are endu$ ) limit$ /r5g?1 & !re=e ! load :i* is plac$ ^u x mu/ be re/rict$ accord+ly1 else x w be liable to be di/ort$ by ! flexure1 or ev5 to be de/roy$ by ! fracture ( ^? p>ts :i* are submitt$ to an undue /ra94 ,! surfaces ( ! movable p>ts1 & ^? surfaces ) :i* !y move 9 contact1 _c 9 practice be r5d]$ s smoo? b t su* r\ghness & inequality w rema9 z s5sibly to imp$e ! motion4 ,to ov]come su* an imp$im5t requires no inconsid]able "p ( ! mov+ p[]4 ,?is "p is1 !re=e1 int]cept$ be=e its arrival at ! work+ po9t1 & ! resi/ance to be f9ally ov]come is depriv$ ( x4 ,! prop]ty ?us dep5d+ on ! imp]fect smoo?ness ( surfaces1 & imp$+ ! motion ( bodies ^: surfaces are 9 imm$iate contact1 is call$ friction4 ,be=e we c =m a j e/imate ( ! effects ( ma*9]y1 x is necess>y to det]m9e ! =ce lo/ by ?is imp$im5t1 & ! laws :i* "u diff]5t circum/ances regulate t loss4 ,:5 cordage is engag$ 9 ! =mation ( any "p ( a ma*9e1 x has hi!rto be5 consid]$ z possess+ p]fect flexibility4 ,?is is n ! case 9 practice2 & ! want ( p]fect flexibility1 :i* is call$ rigidity1 r5d]s a c]ta9 quantity ( =ce necess>y to b5d a cord or rope ov] ! surface ( an axle or ! groove ( a :eel4 ,dur+ ! motion ( ! rope a diff]5t "p ( x mu/ ?us be cont9ually b5t1 & ! =ce :i* is exp5d$ 9 produc+ ! necess>y flexure mu/ be d]iv$ f ! mov+ p[]1 & is ?us int]cept$ on its way to ! work+ po9t4 ,9 calculat+ ! effects ( cordage1 due reg>d mu/ be _h to ?is wa/e ( p[]2 & !re=e x is necess>y to enquire into ! laws :i* gov]n ! flexure ( imp]fectly flexible ropes1 & ! way 9 :i* ^! affect ! ma*9es 9 :i* ropes are commonly us$4 ,to complete1 !re=e1 ! elem5t>y !ory ( ma*9]y1 we propose 9 ! pres5t & foll[+ *apt] to expla9 ! pr9cipal laws :i* det]m9e ! effects ( friction1 ! rigidity ( cordage1 & ! /r5g? ( mat]ials4 7#cba47 ,if a horizontal plane surface 7 p]fectly smoo?1 & free f ! smalle/ inequalities1 & a body hav+ a flat surface also p]fectly smoo? 7 plac$ ^u x1 any =ce appli$ to ! latt] w\ld put x 9 motion1 & t motion w\ld cont9ue undim9i%$ z long z ! body w\ld rema9 ^u ! smoo? horizontal surface4 ,b if ?is surface1 in/ead ( be+ e :]e p]fectly ev51 _h 9 p>ticul> places small project+ em95ces1 a c]ta9 quantity ( =ce w\ld be necess>y to c>ry ! mov+ body ov] ^!1 & a proportional dim9ution 9 its rate ( motion w\ld ensue4 ,?us1 if su* em95ces 7 ( frequ5t occurr5ce1 ea* w\ld deprive ! body ( a "p ( its spe$1 s t betwe5 t & ! next x w\ld move ) a less velocity ?an x _h betwe5 ! same & ! prec$+ "o4 ,?is decrease be+ cont9u$ by a suffici5t numb] ( su* em95ces enc\nt]+ ! body 9 succession1 ! velocity w\ld at la/ be s mu* dim9i%$ t ! body w\ld n h suffici5t =ce to c>ry x ov] ! next em95ce1 & its motion w\ld ?us altoge!r cease4 ,n[1 in/ead ( ! em95ces be+ at a consid]able di/ance asund]1 suppose !m to be contigu\s1 & to be spread 9 e direction ov] ! horizontal plane1 & also suppose correspond+ em95ces to be ^u ! surface ( ! mov+ body2 ^! projections incessantly enc\nt]+ "o ano!r w cont9ually ob/ruct ! motion ( ! body1 & w gradually dim9i% its velocity1 until x be r$uc$ to a /ate ( re/4 ,su* is ! cause ( friction4 ,! am\nt ( ?is resi/+ =ce increases ) ! magnitude ( ^! asp]ities1 or ) ! r\ghness ( ! surfaces2 b x does n solely dep5d on ?is4 ,! surfaces rema9+ ! same1 a little reflection on ! me?od ( illu/ration j adopt$1 w %[ t ! am\nt ( friction ought also to dep5d ^u ! =ce ) :i* ! surfaces mov+ "o ^u ! o!r are press$ toge!r4 ,x is evid5t1 t z ! weight ( ! body suppos$ to move ^u ! horizontal plane is increas$1 a proportionally great] =ce w be necess>y to c>ry x ov] ! ob/acles :i* x enc\nt]s1 & !re=e x w ! m spe$ily be depriv$ ( its velocity & r$uc$ to a /ate ( re/4 7#cbb47 ,?us we might pr$ict ) probability1 t :i* accurate exp]im5tal enquiry proves to be true1 t ! resi/ance f friction dep5ds conjo9tly on ! r\ghness ( ! surfaces & ! =ce ( ! pressure4 ,:5 ! surfaces are ! same1 a d\ble pressure w produce a d\ble am\nt ( friction1 a treble pressure a treble am\nt ( friction1 & s on4 ,exp]im5t also1 h[ev]1 gives a result :i*1 at lea/ at fir/ view1 might n h be5 anticipat$ f ! mode ( illu/ration we h adopt$4 ,x is f\nd t ! resi/ance aris+ f friction does n at all dep5d on ! magnitude ( ! surface ( contact2 b provid$ ! nature ( ! surfaces & ! am\nt ( pressure rema9 ! same1 ?is resi/ance w be equal1 :e!r ! surfaces :i* move "o ^u ! o!r be great or small4 ,?us1 if ! mov+ body be a flat block ( wood1 ! face ( :i* is equal to a squ>e foot 9 magnitude1 & ! edge ( :i* does n exce$ a squ>e in*1 x w be subject to ! same am\nt ( friction1 :e!r x move ^u its broad face or ^u its n>r[ edge4 ,if we consid] ! effect ( ! pressure 9 ea* case1 we %all be able to p]ceive :y ?is mu/ be ! case4 ,let u suppose ! weight ( ! block to be #add ounces4 ,:5 x re/s ^u its face1 a pressure to ?is am\nt acts ^u a surface ( #add squ>e in*es1 s t a pressure ( "o ounce acts ^u ea* squ>e in*4 ,! total resi/ance aris+ f friction w1 !re=e1 be #add times t resi/ance :i* w\ld be produc$ by a surface ( "o squ>e in* "u a pressure ( "o ounce4 ,n[1 suppose ! block plac$ ^u its edge1 !re is !n a pressure ( #add ounces ^u a surface equal to "o squ>e in*4 ,b x has be5 already %[n1 t :5 ! surface is ! same1 ! friction mu/ increase 9 proportion to ! pressure4 ,h5ce we inf] t ! friction produc$ 9 ! pres5t case is #add times ! friction :i* w\ld be produc$ by a pressure ( "o ounce act+ on "o squ>e in* ( surface1 :i* is ! same resi/ance z t :i* ! body 0 prov$ to be subject to :5 re/+ on its face4 ,^! two laws1 t friction is indep5d5t ( ! magnitude ( ! surface1 & is proportional to ! pressure :5 ! quality ( ! surfaces is ! same1 are useful 9 practice1 & g5]ally true4 ,9 v extreme cases !y are1 h[ev]1 9 error4 ,:5 ! pressure is v int5se1 9 proportion to ! surface1 ! friction is some:at less ?an x w\ld be by ^! laws2 & :5 x is v small 9 proportion to ! surface1 x is some:at great]4 7#cbc47 ,!re are two me?ods ( e/abli%+ by exp]im5t ! laws ( friction1 :i* h be5 j expla9$4 ,fir/4 ,! surfaces betwe5 :i* ! friction is to be det]m9$ be+ r5d]$ p]fectly flat1 let "o be fix$ 9 ! horizontal position on a table ,t ,t1 fig4 #agf42 & let ! o!r be atta*$ to ! bottom ( a box ,b ,c1 adapt$ to receive weights1 s z to v>y ! pressure4 ,let a silk5 cord ,s ,p1 atta*$ to ! box1 be c>ri$ p>allel to ! table ov] a :eel at ,p1 & let a di% ,d be susp5d$ f x4 ,if no friction exi/$ betwe5 ! surfaces1 ! smalle/ weight app5d$ to ! cord w\ld draw ! box t[>ds ,p ) a cont9ually increas+ spe$4 ,b ! friction :i* always exi/s int]rupts ?is effect1 & a small weight may act ^u ! /r+ )\t mov+ ! box at all4 ,let weights be put 9 ! di% ,d1 until a suffici5t =ce is obta9$ to ov]come ! friction )\t giv+ ! box an accel]at$ motion4 ,su* a weight is equival5t to ! am\nt ( ! friction4 ,! am\nt ( ! weight ( ! box be+ previ\sly asc]ta9$1 let ?is weight be n[ d\bl$ by plac+ additional weights 9 ! box4 ,! pressure w ?us be d\bl$1 & x w be f\nd t ! weight ( ! di% ,d & its load1 :i* be=e 0 able to ov]come ! friction1 is n[ altoge!r inadequate to x4 ,let additional weights be plac$ 9 ! di% until ! friction be c\nt]act$ z be=e1 & x w be obs]v$1 t ! :ole weight necess>y to produce ?is effect is exactly twice ! weight :i* produc$ x 9 ! =m] case4 ,?us x appe>s t a d\ble am\nt ( pressure produces a d\ble am\nt ( friction2 & 9 a simil> way x may be prov$1 t any propos$ increase or decrease ( ! pressure w be att5d$ ) a proportionate v>iation 9 ! am\nt ( ! friction4 ,second4 ,let "o ( ! surfaces be atta*$ to a flat plane ,a ,b1 fig4 #agg41 :i* c be plac$ at any incl9ation ) an horizontal plane ,b ,c1 ! o!r surface be+1 z be=e1 atta*$ to ! box adapt$ to receive weights4 ,! box be+ plac$ ^u ! plane1 let ! latt] be slightly elevat$4 ,! t5d5cy ( ! box to desc5d ^u ,a ,b1 w be> ! same proportion to its entire weight z ! p]p5dicul> ,a ,e be>s to ! l5g? ( ! plane ,a ,b 7#bhf474 ,?us if ! l5g? ,a ,b be #cf in*es1 & ! height ,a ,e be ?ree in*es1 t is a twelf? "p ( ! l5g?1 !n ! t5d5cy ( ! weight to move d[n ! plane is equal to a twelf? "p ( its :ole am\nt4 ,if ! weight 7 twelve ounces1 & ! surfaces p]fectly smoo?1 a =ce ( "o ounce act+ up ! plane w\ld be necess>y to prev5t ! desc5t ( ! weight4 ,9 ?is case also ! pressure on ! plane w be repres5t$ by ! l5g? ( ! base ,b ,e 7#bhf471 t is1 x w be> ! same proportion to ! :ole weight z ,b ,e be>s to ,b ,a4 ,! relative am\nts ( ! weight1 ! t5d5cy to desc5d1 & ! pressure1 w always be exhibit$ by ! relative l5g?s ( ,a ,b1 ,a ,e1 & ,b ,e4 ,?is be+ premis$1 let ! elevation ( ! plane ,a ,b be gradually increas$ until ! t5d5cy ( ! weight to desc5d j ov]comes ! friction1 b n s mu* z to all[ ! box to desc5d ) accel]at$ spe$4 ,! proportion ( ! :ole weight1 :i* !n acts d[n ! plane1 w be f\nd by measur+ ! height ,a ,e1 & ! pressure w be det]m9$ by measur+ ! base ,b ,e4 ,n[ let ! weight 9 ! box be increas$1 & x w be f\nd t ! same elevation is necess>y to ov]come ! friction2 nor w ?is elevation suff] any *ange1 h[ev] ! pressure or ! magnitude ( ! surfaces :i* move 9 contact may be v>i$4 ,s9ce1 !re=e1 9 all ^! cases1 ! height ,a ,e & ! base ,b ,e rema9 ! same1 x foll[s t ! proportion betwe5 ! friction & pressure is undi/urb$4 7#cbd47 ,! law t friction is proportional to ! pressure1 has be5 que/ion$ by ! late pr(essor ,v9ce ( ,cambridge1 :o d$uc$ f a s]ies ( exp]im5ts1 t al?\gh ! friction increases ) ! pressure1 yet t x increases 9 a some:at less ratio2 & f ?is x w\ld foll[1 t ! v>iation ( ! surface ( contact mu/ produce "s effect ^u ! am\nt ( friction4 ,! law1 z we h expla9$ x1 h[ev]1 is suffici5tly ne> ! tru? = mo/ practical purposes4 7#cbe47 ,!re are sev]al circum/ances reg>d+ ! quality ( ! surfaces :i* produce important effects on ! quantity ( friction1 & :i* ought to be notic$ "h4 ,?is resi/ance is diff]5t 9 ! surfaces ( diff]5t sub/ances4 ,:5 ! surfaces are ^? ( wood newly plan$1 x am\nts to ab\t half ! pressure1 b is diff]5t 9 diff]5t k9ds ( wood4 ,! friction ( metallic surfaces is ab\t "o f\r? ( ! pressure4 ,9 g5]al ! friction betwe5 ! surfaces ( bodies ( diff]5t k9ds is less ?an betwe5 ^? ( ! same k9d4 ,?us1 betwe5 wood & metal ! friction is ab\t "o fif? ( ! pressure4 ,x is evid5t t ! smoo!r ! surfaces are ! less w be ! friction4 ,on ?is acc\nt1 ! friction ( surfaces1 :5 fir/ br\ght into contact1 is (t5 great] ?an aft] _! attrition has be5 cont9u$ = a c]ta9 "t1 because t process has a t5d5cy to remove & rub (f ^? m9ute asp]ities & projections on :i* ! friction dep5ds4 ,b ?is has a limit1 & aft] a c]ta9 quantity ( attrition ! friction ceases to decrease4 ,newly plan$ surfaces ( wood h at fir/ a degree ( friction :i* is equal to half ! entire pressure1 b aft] !y are worn by attrition x is r$uc$ to a ?ird4 ,if ! surfaces 9 contact be plac$ ) _! gra9s 9 ! same direction1 ! friction w be great] ?an if ! gra9s cross ea* o!r4 ,sme>+ ! surfaces ) unctu\s matt] dim9i%es ! friction1 probably by fill+ ! cavities betwe5 ! m9ute projections :i* produce ! friction4 ,:5 ! surfaces are fir/ plac$ 9 contact1 ! friction is less ?an :5 !y are suff]$ to re/ s = "s "t2 ?is is prov$ by obs]v+ ! =ce :i* 9 ea* case is necess>y to move ! "o ^u ! o!r1 t =ce be+ less if appli$ at ! fir/ mom5t ( contact ?an :5 ! contact has cont9u$4 ,?is1 h[ev]1 has a limit4 ,!re is a c]ta9 "t1 diff]5t 9 diff]5t sub/ances1 )9 :i* ?is resi/ance atta9s its greate/ am\nt4 ,9 surfaces ( wood ?is takes place 9 ab\t two m9utes2 9 metals ! "t is imp]ceptibly %ort2 & :5 a surface ( wood is plac$ ^u a surface ( metal1 x cont9ues to increase = sev]al days4 ,! limit is l>g] :5 ! surfaces are great1 & belong to sub/ances ( diff]5t k9ds4 ,! velocity ) :i* ! surfaces move ^u "o ano!r produces b little effect ^u ! friction4 7#cbf47 ,!re are sev]al ways 9 :i* bodies may move "o ^u ! o!r1 9 :i* friction w produce diff]5t effects4 ,! pr9cipal ( ^! are1 fir/1 ! case :]e "o body slides ov] ano!r2 ! second1 :]e a body hav+ a r\nd =m rolls ^u ano!r2 &1 ?irdly1 :]e an axis revolves )9 a holl[ cyl9d]1 or ! holl[ cyl9d] revolves ^u ! axis4 ,) ! same am\nt ( pressure & a l quality ( surface1 ! quantity ( friction is greate/ 9 ! fir/ case & lea/ 9 ! second4 ,! friction 9 ! second case also dep5ds on ! diamet] ( ! body :i* rolls1 & is small 9 proportion z t diamet] is great4 ,?us a c>riage ) l>ge :eels is less imp$$ by ! friction ( ! road ?an "o ) small :eels4 ,9 ! ?ird case1 ! lev]age ( ! :eel aids ! p[] 9 ov]com+ ! friction4 ,let fig4 #agh4 repres5t a section ( ! :eel & axle2 let ,c be ! c5tre ( ! axle1 & let ,b ,e be ! holl[ cyl9d] 9 ! nave ( ! :eel 9 :i* ! axle is ins]t$4 ,if ,b be ! "p on :i* ! axle presses1 & ! :eel turn 9 ! direction ,n ,d ,m1 ! friction w act at ,b 9 ! direction ,b ,f1 & ) ! lev]age ,b ,c4 ,! p[] acts aga9/ ?is at ,d 9 ! direction ,d ,a1 & ) ! lev]age ,d ,c4 ,x is !re=e evid5t1 t z ,d ,c is great] ?an ,b ,c1 9 ! same proportion does ! p[] act ) me*anical advantage on ! friction4 7#cbg47 ,contrivances = dim9i%+ ! effects ( friction dep5d on ! prop]ties j expla9$1 ! motion ( roll+ be+ z mu* z possible sub/itut$ = t ( slid+2 & :]e ! motion ( roll+ _c be appli$1 t ( a :eel ^u its axle is us$4 ,9 "s cases bo? ^! motions are comb9$4 ,if a heavy load be drawn ^u a plane 9 ! mann] ( a sl$ge1 ! motion w be t ( slid+1 ! species :i* is att5d$ ) ! greate/ quantity ( friction2 b if ! load be plac$ ^u cyl9drical roll]s1 ! nature ( ! motion is *ang$1 & becomes t 9 :i* !re is ! lea/ quantity ( friction4 ,?us l>ge blocks ( /one1 or heavy beams ( timb]1 :i* w\ld require an enorm\s p[] to move !m on a level road1 are easily advanc$ :5 roll]s are put "u !m4 ,:5 v heavy weights are to be mov$ ?r\gh small spaces1 ?is me?od is us$ ) advantage2 b :5 loads ore to be transport$ to consid]able di/ances1 ! process is inconv5i5t & sl[1 ow+ to ! necessity ( cont9ually replac+ ! roll]s 9 front ( ! load z !y are left beh9d by its progressive advancem5t4 ,! :eels ( c>riages may be reg>d$ z roll]s :i* are cont9ually c>ri$ =w>d ) ! load4 ,9 addition to ! friction ( ! roll+ motion on ! road1 !y h1 x is true1 ! friction ( ! axle 9 ! nave2 b1 on ! o!r h&1 !y are free f ! friction ( ! roll]s ) ! "u surface ( ! load1 or ! c>riage 9 :i* ! load is transport$4 ,! advantages ( :eel c>riages 9 dim9i%+ ! effects ( friction is sometimes attribut$ to ! sl[ness ) :i* t axle moves )9 ! box1 comp>$ ) ! rate at :i* ! :eel moves ov] ! road2 b ?is is errone\s4 ,! quantity ( friction does n 9 any case v>y consid]ably ) ! velocity ( ! motion1 b lea/ ( all does x 9 t p>ticul> k9d ( motion "h consid]$4 ,9 c]ta9 cases1 :]e x is ( great importance to remove ! effects ( friction1 a contrivance call$ friction-:eels1 or friction-roll]s1 is us$4 ,! axle ( a friction-:eel1 in/ead ( revolv+ )9 a holl[ cyl9d]1 :i* is fix$1 re/s ^u ! edges ( :eels :i* revolve ) x2 ! species ( motion ?us becomes t 9 :i* ! friction is ( lea/ am\nt4 ,let ,a ,b & ,d ,c1 fig4 #agi41 be two :eels revolv+ on pivots ,p ,q ) z little friction z possible1 & s plac$ t ! axle ,o ( a ?ird :eel ,e ,f may re/ betwe5 _! edges4 ,z ! :eel ,e ,f revolves1 ! axle ,o1 in/ead ( gr9d+ its surface on ! surface on :i* x presses1 c>ries t surface ) x1 caus+ ! :eels ,a ,b1 ,c ,d1 to revolve4 ,9 :eel c>riages1 ! r\ghness ( ! road is m easily ov]come by l>ge :eels ?an by small ones4 ,! cause ( ?is arises p>tly f ! l>ge :eels n be+ s liable to s9k into holes z small ones1 b m because1 9 surm\nt+ ob/acles1 ! load is elevat$ less abruptly4 ,?is w be easily und]/ood by obs]v+ ! curves 9 fig4 #ahj41 :i* repres5t ! elevation ( ! axle 9 ea* case4 7#cbh47 ,if a c>riage 7 capable ( mov+ on a road )\t friction1 ! mo/ advantage\s direction 9 :i* a =ce c\ld be appli$ to draw x w\ld be p>allel to ! road4 ,:5 ! motion is imp$$ by friction1 x is bett]1 h[ev]1 t ! l9e ( draught %\ld be incl9$ to ! road1 s t ! draw+ =ce may be exp5d$ p>tly 9 less5+ ! pressure on ! road1 & p>tly 9 advanc+ ! load4 ,let ,w1 fig4 #aha41 be a load :i* is to be mov$ ^u ! plane surface ,a ,b4 ,if ! draw+ =ce be appli$ 9 ! direction ,c ,d1 p>allel to ! plane ,a ,b1 x w h to ov]come ! friction produc$ by ! pressure ( ! :ole weight ( ! load ^u ! plane2 b if x be incl9$ upw>ds 9 ! direction ,c ,e1 x w be equival5t to two =ces express$ 7#gd47 by ,c ,g & ,c ,f4 ,! "p ,c ,g has ! effect ( light5+ ! pressure ( ! c>riage ^u ! road1 & !re=e ( dim9i%+ ! friction 9 ! same proportion4 ,! "p ,c ,f draws ! load along ! plane4 ,s9ce ,c ,f is less ?an ,c ,e or ,c ,d ! :ole mov+ =ce1 x is evid5t t a "p ( ! =ce ( draught is lo/ by ?is obliquity2 b1 on ! o!r h&1 a "p ( ! oppos+ resi/ance is also remov$4 ,if ! latt] exce$ ! =m]1 an advantage w be ga9$ by ! obliquity2 b if ! =m] exce$ ! latt]1 =ce w be lo/4 ,by ma!matical reason+1 f\nd$ on ^! consid]ations1 x is prov$ t ! be/ angle ( draught is exactly t obliquity :i* %\ld be giv5 to ! road 9 ord] to enable ! c>riage to move ( itself4 ,?is obliquity is sometimes call$ ! angle ( repose1 & is t angle :i* det]m9es ! proportion ( ! friction to ! pressure 9 ! second me?od1 expla9$ 9 7#cbc474 ,! m r\gh ! road is1 ! great] w ?is angle be2 & !re=e x foll[s1 t on bad roads ! obliquity ( ! traces to ! road %\ld be great] ?an on good ones4 ,on a smoo? ,macadamis$ way1 a v slight declivity w\ld cause a c>riage to roll by its own weight3 h5ce1 9 ?is case1 ! traces %\ld be ne>ly p>allel to ! road4 ,9 rail roads1 = l reasons1 ! l9e ( draught %\ld be p>allel to ! road1 or ne>ly s4 7#cbi47 ,:5 ropes or cords =m a "p ( ma*9]y1 ! effects ( _! imp]fect flexibility are 9 a c]ta9 degree c\nt]act$ by b5d+ !m ov] ! grooves ( :eels4 ,b al?\gh ?is s f> dim9i%es ^! effects z to r5d] ropes practically useful1 yet /ill1 9 calculat+ ! p[]s ( ma*9]y1 x is necess>y to take into acc\nt "s consequ5ces ( ! rigidity ( cordage :i* ev5 by ^! means are n remov$4 ,to expla9 ! way 9 :i* ! /iffness ( a rope modifies ! op]ation ( a ma*9e1 we %all suppose x b5t ov] a :eel & /ret*$ by weights ,a ,b1 fig4 #ahb41 at its extremities4 ,! weights ,a & ,b be+ equal1 & act+ at ,c & ,d 9 opposite ways1 balance ! :eel4 ,if ! weight ,a receive an addition1 x w ov]come ! resi/ance ( ,b1 & turn ! :eel 9 ! direction ,d ,e ,c4 ,n[1 = ! pres5t1 let u suppose t ! rope is p]fectly inflexible2 ! :eel & weights w be turn$ into ! position repres5t$ 9 fig4 #ahc4 ,! lev]age by :i* ,a acts w be dim9i%$1 & w become ,o ,f1 hav+ be5 be=e ,o ,c2 & ! lev]age by :i* ,b acts w be increas$ to ,o ,g1 hav+ be5 be=e ,o ,d4 ,b ! rope n be+ inflexible w yield p>tially to ! effects ( ! weights ,a & ,b1 & ! p>ts ,a ,c & ,b ,d w be b5t into ! =ms repres5t$ 9 fig4 #ahd4 ,! =m ( ! curvature :i* ! rope on ea* side ( ! :eel receives is /ill su* t ! desc5d+ weight ,a works ) a dim9i%$ lev]age ,f ,o1 :ile ! asc5d+ weight resi/s x ) an increas$ lev]age ,g ,o4 ,?us s mu* ( ! mov+ p[] is lo/1 by ! /iffness ( ! rope1 z is necess>y to comp5sate ?is disadvantage\s *ange 9 ! p[] ( ! ma*9e4 ,,*ap4 ,,xx4 ,,on ,,! ,,/r5g? ,,( ,,mat]ials4 7#ccj47 ,exp]im5tal enquiries into ! laws :i* regulate ! /r5g? ( solid bodies1 or _! p[] to resi/ =ces v>i\sly appli$ to te> or break !m1 are ob/ruct$ by practical difficulties1 ! nature & ext5t ( :i* are s disc\rag+ t few h v5tur$ to enc\nt] !m at all1 & /ill few] h _h ! /ead9ess to p]sev]e until any result %[+ a g5]al law has be5 obta9$4 ,^! difficulties arise1 p>tly f ! great =ces :i* mu/ be appli$1 b m f ! peculi> nature ( ! objects ( ^? exp]im5ts4 ,! end to :i* su* an enquiry mu/ be direct$ is ! developm5t ( a g5]al law2 t is1 su* a rule z w\ld be rigidly obs]v$ if ! mat]ials1 ! /r5g? ( :i* is ! object ( enquiry1 7 p]fectly uni=m 9 _! texture1 & subject to no casual inequalities4 ,9 proportion z ^! inequalities are frequ5t1 exp]im5ts mu/ be multipli$1 t a long av]age may embrace cases v>y+ 9 bo? extremes1 s z to elim9ate ea* o!r's effects 9 ! f9al result4 ,! mat]ials ( :i* /ructures & works ( art are compos$ are liable to s _m & s consid]able inequalities ( texture1 t any rule :i* c be d$uc$1 ev5 by ! mo/ ext5sive s]ies ( exp]im5ts1 mu/ be reg>d$ z a mean result1 f :i* individual examples w be f\nd to v>y 9 s great a degree1 t m ?an usual caution mu/ be obs]v$ 9 its practical application4 ,! details ( ?is subject belong to eng9e]+1 m prop]ly ?an to ! elem5ts ( me*anics4 ,nev]!less1 a g5]al view ( ! mo/ important pr9ciples :i* h be5 e/abli%$ respect+ ! /r5g? ( mat]ials w n be misplac$ 9 ?is treatise4 ,a piece ( solid matt] may be submitt$ to ! action ( a =ce t5d+ to sep>ate its p>ts 9 sev]al ways2 ! pr9cipal ( :i* are1-- #a4 ,to a direct pull1--z :5 a rope or wire is /ret*$ by a weight4 ,:5 a tie-beam resi/s ! sep>ation ( ! sides ( a /ructure1 c4 #b4 ,to a direct pressure or ?ru/1--z :5 a weight re/s ^u a pill>4 #c4 ,to a transv]se /ra91--z :5 weights on ! ends ( a lev] press x on ! fulcrum4 7#cca47 ,if a solid be submitt$ to a =ce :i* draws x 9 ! direction ( its l5g?1 hav+ a t5d5cy to pull its ends 9 opposite directions1 its /r5g? or p[] to resi/ su* a =ce is proportional to ! magnitude ( its transv]se section4 ,?us1 suppose a squ>e rod ( metal ,a ,b1 fig4 #ahe41 ( ! bread? & ?ickness ( "o in*1 be pull$ by a =ce 9 ! direction ,a ,b1 & t a c]ta9 =ce is f\nd suffici5t to te> x2 a rod ( ! same metal ( twice ! bread? & ! same ?ickness w require d\ble ! =ce to break x2 "o ( treble ! bread? & ! same ?ickness w require treble ! =ce to break x1 & s on4 ,! reason ( ?is is evid5t4 ,a rod ( d\ble or treble ! ?ickness1 9 ?is case1 is equival5t to two or ?ree equal & simil> rods :i* equally & sep>ately resi/ ! draw+ =ce1 & !re=e possess a degree ( /r5g? proportionate to _! numb]4 ,x w easily be p]ceiv$1 t :atev] be ! section1 ! same reason+ w be applicable1 & ! p[] ( resi/ance w1 9 g5]al1 be proportional to its magnitude or area4 ,if ! mat]ial 7 p]fectly uni=m ?r\gh\t its dim5sions1 ! resi/ance to a direct pull w\ld n be affect$ by ! l5g? ( ! rod4 ,9 practice1 h[ev]1 ! increase ( l5g? is f\nd to less5 ! /r5g?4 ,?is is to be attribut$ to ! increas$ *ance ( inequality4 7#ccb47 ,no satisfactory results h be5 obta9$ ei!r by !ory or exp]im5t respect+ ! laws by :i* solids resi/ compression4 ,! p[] ( a p]p5dicul> pill> to support a weight plac$ ^u x evid5tly dep5ds on its ?ickness1 or ! magnitude ( its base1 & on its height4 ,x is c]ta9 t :5 ! height is ! same1 ! /r5g? increases ) e increase ( ! base1 b x seems d\btful :e!r ! /r5g? be exactly proportional to ! base4 ,t is1 if two columns ( ! same mat]ial h equal heights1 & ! base ( "o be d\ble ! base ( ! o!r1 ! /r5g? ( "o w be great]1 b x is n c]ta9 :e!r x w exactly d\ble t ( ! o!r4 ,accord+ to ! !ory ( ,eul]1 :i* is 9 a c]ta9 degree v]ifi$ by ! exp]im5ts ( ,muss*5brock1 ! /r5g? w be increas$ 9 a great] proportion ?an ! base1 s t1 if ! base be d\bl$1 ! /r5g? w be m ?an d\bl$4 ,:5 ! base is ! same1 ! /r5g? is dim9i%$ by increas+ ! height1 & ?is decrease ( /r5g? is proportionally great] ?an ! increase ( height4 ,accord+ to ,eul]'s !ory1 ! decrease ( /r5g? is proportional to ! squ>e ( ! height2 t is1 :5 ! height is increas$ 9 a two-fold proportion1 ! /r5g? is dim9i%$ 9 a f\r-fold proportion4 7#ccc47 ,! /ra9 to :i* solids =m+ ! p>ts ( /ructures ( e k9d are mo/ commonly expos$ is ! lat]al or transv]se /ra91 or t :i* acts at "r angles to _! l5g?s4 ,if any /ra9 act obliquely to ! direction ( _! l5g? x may be resolv$ into two =ces 7#gf471 "o 9 ! direction ( ! l5g?1 & ! o!r at "r angles to ! l5g?4 ,t "p :i* acts 9 ! direction ( ! l5g? w produce ei!r compression or a direct pull1 & its effect mu/ be inve/igat$ accord+ly4 ,al?\gh ! results ( !ory1 z well z ^? ( exp]im5tal inve/igations1 pres5t great discordances respect+ ! transv]se /r5g? ( solids1 yet !re are "s p>ticul>s1 9 :i* !y1 = ! mo/ "p1 agree2 to ?is x is our object "h to conf9e our obs]vations1 decl9+ all details relat+ to disput$ po9ts4 ,let ,a ,b ,c ,d1 fig4 #ahf41 be a beam1 support$ at its ends ,a & ,b4 ,its /r5g? to support a weight at ,e press+ d[nw>ds at "r angles to its l5g? is evid5tly proportional to its bread?1 ! o!r ?+s be+ ! same4 ,= a beam ( d\ble or treble bread?1 & ( ! same ?ickness1 is equival5t to two or ?ree equal & simil> beams plac$ side by side4 ,s9ce ea* ( ^! w\ld possess ! same /r5g?1 ! :ole tak5 toge!r w\ld possess d\ble or treble ! /r5g? ( any "o ( !m4 ,:5 ! bread? & l5g? are ! same ! /r5g? obvi\sly increases ) ! dep?1 b n 9 ! same proportion4 ,! increase ( /r5g? is f\nd to be mu* great] 9 proportion ?an ! increase ( dep?4 ,by ! !ory ( ,galileo1 a d\ble or treble ?ickness ought to increase ! /r5g? 9 a f\r-fold or n9e-fold proportion1 & exp]im5ts 9 mo/ cases d n mat]ially v>y f ?is rule4 ,if :ile ! bread? & dep? rema9 ! same1 ! l5g? ( ! beam1 or r1 ! di/ance betwe5 ! po9ts ( support1 v>y1 ! /r5g? w v>y accord+ly1 decreas+ 9 ! same proportion z ! l5g? increases4 ,f ^! obs]vations x appe>s1 t ! transv]se /r5g? ( a beam dep5ds m on its ?ickness ?an its bread?4 ,h5ce we f9d t a broad ?9 bo>d is mu* /rong] :5 its edge is pres5t$ upw>ds4 ,on ?is pr9ciple ! joi/s or raft]s ( floors & ro(s are con/ruct$4 ,if two beams be 9 all respects simil>1 _! /r5g?s w be 9 ! proportion ( ! squ>es ( _! l5g?s4 ,let ! l5g?1 bread?1 & dep? ( ! "o be respectively d\ble ! l5g?1 bread?1 & dep? ( ! o!r4 ,by ! d\ble bread? ! beam d\bles its /r5g?1 b by d\bl+ ! l5g? half ?is /r5g? is lo/4 ,?us ! increase ( l5g? & bread? c\nt]act ea* o!r's effects1 & z f> z !y are conc]n$ ! /r5g? ( ! beam is n *ang$4 ,b by d\bl+ ! ?ickness ! /r5g? is increas$ 9 a f\r-fold proportion1 t is1 z ! squ>e ( ! l5g?4 ,9 ! same mann] x may be %[n1 t :5 all ! dim5sions are trebl$1 ! /r5g? is increas$ 9 a n9e-fold proportion1 & s on4 7#ccd47 ,9 all /ructures ! mat]ials h to support _! own weight1 & !re=e _! available /r5g? is to be e/imat$ by ! excess ( _! absolute /r5g? above t degree ( /r5g? :i* is j suffici5t to support _! own weight4 ,?is consid]ation leads to "s conclusions1 ( :i* num]\s & /rik+ illu/rations are pres5t$ 9 ! works ( nature & art4 ,we h se5 t ! absolute /r5g? ) :i* a lat]al /ra9 is resi/$ is 9 ! proportion ( ! squ>e ( ! l9e> dim5sions ( simil> p>ts ( a /ructure1 & !re=e ! am\nt ( ?is /r5g? increases rapidly ) e increase ( ! dim5sions ( a body4 ,b at ! same "t ! weight ( ! body increases 9 a /ill m rapid proportion4 ,?us1 if ! sev]al dim5sions be d\bl$1 ! /r5g? w be increas$ 9 a f\r-fold b ! weight 9 an eight-fold proportion4 ,if ! dim5sions be trebl$1 ! /r5g? w be multipli$ n9e times1 b ! weight tw5ty-sev5 times4 ,aga91 if ! dim5sions be multipli$ f\r times1 ! /r5g? w be multipli$ sixte5 times1 & ! weight sixty-f\r times1 & s on4 ,h5ce x is obvi\s1 t al?\gh ! /r5g? ( a body ( small dim5sions may greatly exce$ its weight1 &1 !re=e1 x may be able to support a load _m times its own weight2 yet by a great increase 9 ! dim5sions ! weight increas+ 9 a mu* great] degree ! available /r5g? may be mu* dim9i%$1 & su* a magnitude may be assign$1 t ! weight ( ! body mu/ exce$ its /r5g?1 & x n only w\ld be unable to support any load1 b w\ld actually fall to pieces by its own weight4 ,! /r5g? ( a /ructure ( any k9d is n1 !re=e1 to be det]m9$ by t ( its model1 :i* w always be mu* /rong] 9 proportion to its size4 ,all works natural & artificial h limits ( magnitude :i*1 :ile _! mat]ials rema9 ! same1 !y _c surpass4 ,9 con=mity ) :at has j be5 expla9$1 x has be5 obs]v$1 t small animals are /rong] 9 proportion ?an l>ge ones2 t ! "y plant has m available /r5g? 9 proportion ?an ! l>ge =e/ tree2 t *ildr5 are less liable to injury f accid5t ?an m51 c4 ,b al?\gh to a c]ta9 ext5t ^! obs]vations are j1 yet x ought n to be =gott51 t ! me*anical conclusions :i* !y are br\ght to illu/rate are f\nd$ on ! supposition1 t ! small] & great] bodies :i* are comp>$ are compos$ ( precisely simil> mat]ials4 ,?is is n ! case 9 any ( ! examples "h adduc$4 ,,*ap4 ,,xxi4 ,,on ,,balances ,,& ,,p5dulums4 7#cce47 ,! prec$+ *apt]s h be5 conf9$ almo/ :olly to ! consid]ation ( ! laws ( me*anics1 )\t ent]+ into a p>ticul> description ( ! ma*9]y & in/rum5ts dep5dant ^u ^? laws4 ,su* descriptions w\ld h int]f]$ too mu* ) ! regul> progress ( ! subject1 & x !re=e appe>$ pref]able to devote a *apt] exclusively to ?is portion ( ! "w4 ,p]haps !re are no ideas :i* man receives ?r\gh ! m$ium ( s5se :i* may n be ref]r$ ultimately to matt] & motion4 ,9 proportion1 !re=e1 z he becomes acqua9t$ ) ! prop]ties ( ! "o & ! laws ( ! o!r1 8 k is ext5d$1 8 com=ts are multipli$2 he is enabl$ to b5d ! p[]s ( nature to 8 w1 & to con/ruct ma*9]y :i* effects ) ease t :i* ! unit$ lab\r ( ?\s&s w\ld 9 va9 be ex]t$ to accompli%4 ,( ! prop]ties ( matt]1 "o ( ! mo/ important is its weight1 & ! elem5t :i* m+les insep>ably ) ! laws ( motion is "t4 ,9 ! pres5t *apt] x is our int5tion to describe su* in/rum5ts z are usually employ$ = det]m9+ ! weight ( bodies4 ,to attempt a description ( ! v>i\s ma*9es :i* are us$ = ! measurem5t ( "t1 w\ld lead u into too wide a field = ! pres5t occasion1 & we %all1 !re=e1 conf9e ourselves to an acc\nt ( ! me?ods :i* h be5 practis$ to p]fect1 to p]fect t in/rum5t :i* af=ds ! mo/ correct means ( measur+ "t1 ! p5dulum4 ,! in/rum5t by :i* we are enabl$ to det]m9e1 ) great] accuracy ?an by any o!r means1 ! relative weight ( a body1 comp>$ ) ! weight ( ano!r body assum$ z a /&>d1 is ! balance4 ,illu/ration3 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,( ! ,balance4 ,! balance may be describ$ z consi/+ ( an inflexible rod or lev]1 call$ ! beam1 furni%$ ) ?ree axes2 "o1 ! fulcrum or c5tre ( motion situat$ 9 ! middle1 ^u :i* ! beam turns1 & ! o!r two ne> ! extremities1 & at equal di/ances f ! middle4 ,^! la/ are call$ ! po9ts ( support1 & s]ve to su/a9 ! pans or scales4 ,! po9ts ( support & ! fulcrum are 9 ! same "r l9e1 & ! c5tre ( gravity ( ! :ole %\ld be a little bel[ ! fulcrum :5 ! position ( ! beam is horizontal4 ,! arms ( ! lev] be+ equal1 x foll[s t if equal weights be put into ! scales no effect w be produc$ on ! position ( ! balance1 & ! beam w rema9 horizontal4 ,if a small addition be made to ! weight 9 "o ( ! scales1 ! horizontality ( ! beam w be di/urb$2 & aft] oscillat+ = "s "t1 x w1 on atta9+ a /ate ( re/1 =m an angle ) ! horizon1 ! ext5t ( :i* is a measure ( ! delicacy or s5sibility ( ! balance4 ,z ! s5sibility ( a balance is ( ! utmo/ importance 9 nice sci5tific enquiries1 we %all ent] some:at at l>ge into a consid]ation ( ! circum/ances by :i* ?is prop]ty is influ5c$4 ,9 fig4 #ahg4 let ,a ,b repres5t ! beam drawn f ! horizontal position by a v small weight plac$ 9 ! scale susp5d$ f ! po9t ( support ,b2 !n ! =ce t5d+ to draw ! beam f ! horizontal position may be express$ by ,p ,b1 multipli$ by su* v small weight act+ ^u ! po9t ,b4 ,let ! c5tre ( gravity ( ! :ole be at ,g2 !n ! =ce act+ aga9/ ! =m] w be ,g ,p multipli$ into ! weight ( ! beam & scales1 & :5 ^! =ces are equal1 ! beam w re/ 9 an incl9$ position4 ,h5ce we may p]ceive t z ! c5tre ( gravity is ne>] to or fur!r f ! fulcrum ,s1 7e ?+ else rema9+ ! same7 ! s5sibility ( ! balance w be increas$ or dim9i%$4 ,=1 suppose ! c5tre ( gravity 7 remov$ to g1 !n to produce an oppos+ =ce equal to t act+ ^u ! extremity ( ! beam1 ! di/ance g p f ! p]p5dicul> l9e mu/ be increas$ until x becomes ne>ly equal to ,g ,p2 b = ?is purpose ! end ( ! beam ,b mu/ desc5d1 :i* w increase ! angle ,h ,s ,b4 ,z all weights plac$ 9 ! scales are ref]r$ to ! l9e jo9+ ! po9ts ( support1 & z ?is l9e is above ! c5tre ( gravity ( ! beam :5 n load$1 su* weights w raise ! c5tre ( gravity2 b x w be se5 t ! s5sibility ( ! balance1 z f> z x dep5ds ^u ?is cause1 w rema9 unalt]$4 ,=1 call+ ! di/ance ,s ,g unity1 ! di/ance ( ! c5tre ( gravity f ! po9t ,s 7to :i* ! weight :i* has be5 add$ is ref]r$7 w be express$ by ! reciprocal ( ! weight ( ! beam s increas$2 t is1 if ! weight ( ! beam be d\bl$ by weights plac$ 9 ! scales1 ,s g w be "o half ( ,s ,g2 & if ! weight ( ! beam be 9 l mann] trebl$1 ,s g w be "o ?ird ( ,s ,g1 & s on4 ,& z ,g ,p v>ies z ,s ,g1 g p w be inv]sely proportionate to ! increas$ weight ( ! beam1 & consequ5tly1 ! product obta9$ by multiply+ g p by ! weight ( ! beam & its load w be a con/ant quantity1 & ! s5sibility ( ! balance1 z be=e /at$1 w suff] no alt]ation4 ,we w n[ suppose t ! fulcrum ,s1 fig4 #ahh41 is situat$ bel[ ! l9e jo9+ ! po9ts ( support1 & t ! c5tre ( gravity ( ! beam :5 n load$ is at ,g4 ,also t :5 a v small weight is plac$ 9 ! scale susp5d$ f ! po9t ,b1 ! beam is drawn f its horizontal position1 ! deviation be+ a measure ( ! s5sibility ( ! balance4 ,!n1 z be=e /at$1 ,g ,p multipli$ by ! weight ( ! beam w be equal to ,p ,b multipli$ by ! v small additional weight act+ on ! po9t ,b4 ,n[ if we place equal weights 9 bo? scales1 su* additional weights w be ref]r$ to ! po9t ,w1 & ! result+ di/ance ( ! c5tre ( gravity f ! po9t ,w1 call+ ,w ,g unity1 w be express$ z be=e by ! reciprocal ( ! increas$ weight ( ! load$ beam4 ,b ,g ,p w decrease 9 a great] proportion ?an ,w ,g3 ?us1 suppos+ ! weight ( ! beam to be d\bl$1 ,w g w\ld be "o half ( ,w ,g2 b g p1 z w be evid5t on an inspection ( ! figure1 w be less ?an half ( ,g ,p2 & ! same small weight :i* 0 be=e appli$ to ! po9t ,b1 if n[ add$1 w\ld depress ! po9t ,b1 until ! di/ance g p became su* z t1 :5 multipli$ by ! weight ( ! :ole1 ! product w\ld be z be=e equal to ,p ,b1 multipli$ by ! be=e m5tion$ v small add$ weight4 ,! s5sibility ( ! balance1 !re=e1 9 ?is case w\ld be increas$4 ,if ! beam be suffici5tly load$1 ! c5tre ( gravity w at l5g? be rais$ to ! fulcrum ,s1 & ! beam w re/ indiff]5tly 9 any position4 ,if m weight be !n add$1 ! c5tre ( gravity w be rais$ above ! fulcrum1 & ! beam w turn ov]4 ,la/ly1 if ! fulcrum ,s1 fig4 #ahi41 is above ! l9e jo9+ ! two po9ts ( support1 z any additional weights plac$ 9 ! scales w be ref]r$ to ! po9t ,w1 9 ! l9e jo9+ ,a & ,b1 if ! weight ( ! beam be d\bl$ by su* add$ weights1 & ! c5tre ( gravity be consequ5tly rais$ to g1 ,w g w become equal to half ( ,w ,g4 ,b g p1 be+ great] ?an "o half ( ,g ,p1 ! end ( ! beam ,b w rise until g p becomes su* z to be equal1 :5 multipli$ by ! :ole increas$ weight ( ! beam1 to ,p ,b1 multipli$ by ! small weight1 :i* we suppose to h be5 plac$ z 9 ! prec$+ examples1 9 ! scale4 ,f :at has be5 said x w be se5 t !re are ?ree positions ( ! fulcrum :i* influ5ce ! s5sibility ( ! balance3 fir/1 :5 ! fulcrum & ! po9ts ( support are 9 a "r l9e1 :5 ! s5sibility ( ! balance w rema9 ! same1 ?\gh ! weight ) :i* ! beam is load$ %\ld be v>i$3 secondly1 :5 ! fulcrum is bel[ ! l9e jo9+ ! two po9ts ( support1 9 :i* case ! s5sibility ( ! balance w be increas$ by additional weights1 until at l5g? ! c5tre ( gravity is rais$ above ! fulcrum1 :5 ! beam w turn ov]2 &1 ?irdly1 :5 ! fulcrum is above ! l9e jo9+ ! two po9ts ( support1 9 :i* case ! s5sibility ( ! balance w be dim9i%$ z ! weight ) :i* ! beam is load$ is increas$4 ,! s5sibility ( a balance1 z "h def9$1 is ! angul> deviation ( ! beam occasion$ by plac+ an additional con/ant small weight 9 "o ( ! scales2 b x is frequ5tly express$ by ! proportion :i* su* small additional weight be>s to ! weight ( ! beam & its load1 & sometimes to ! weight ! value ( :i* is to be det]m9$4 ,?is proportion1 h[ev]1 w evid5tly v>y ) diff]5t weights1 except 9 ! case :]e ! c5tre ( gravity ( ! beam is 9 ! l9e jo9+ ! po9ts support+ ! scales1 ! fulcrum be+ above ?is l9e1 & x is !re=e necess>y1 9 e o!r case1 :5 speak+ ( ! s5sibility ( ! balance1 to designate ! weight ) :i* x is load$3 ?us1 if a balance has a troy p\nd 9 ea* scale1 & ! horizontality ( ! beam v>ies a c]ta9 small quantity1 j p]ceptible on ! addition ( "o hundr$? ( a gra91 we say t ! balance is s5sible to #a_/aaebjjj "p ( its load ) a p\nd 9 ea* scale1 or t x w det]m9e ! weight ( a troy p\nd )9 #a_/egfjjj "p ( ! :ole4 ,! ne>] ! c5tre ( gravity ( a balance is to its fulcrum ! sl[] w be ! oscillations ( ! beam4 ,! numb] ( oscillations1 !re=e1 made by ! beam 9 a giv5 "t 7a m9ute = example71 af=ds ! mo/ accurate me?od ( judg+ ( ! s5sibility ( ! balance1 :i* w be ! great] z ! oscillations are few]4 ,balances ( ! mo/ p]fect k9d1 & ( su* only x is our pres5t object to treat1 are usually furni%$ ) adju/m5ts1 by means ( :i* ! l5g? ( ! arms1 or ! di/ances ( ! fulcrum f ! po9ts ( support1 may be equalis$1 & ! fulcrum & ! two po9ts ( support be plac$ 9 a "r l9e2 b ^! adju/m5ts1 z w h]eaft] be se51 are n absolutely necess>y4 ,! beam is v>i\sly con/ruct$1 accord+ to ! purposes to :i* ! balance is to be appli$4 ,sometimes x is made ( a rod ( solid /eel2 sometimes ( two holl[ cones jo9$ at _! bases2 &1 9 "s balances1 ! beam is a frame 9 ! =m ( a rhombus3 ! pr9cipal object 9 all1 h[ev]1 is to comb9e /r5g? & inflexibility ) lightness4 ,a balance ( ! be/ k9d1 made by ,tr\ghton1 is s contriv$ z to be conta9$1 :5 n 9 use1 9 a draw] bel[ ! case2 & :5 9 use1 x is protect$ f any di/urbance f curr5ts ( air1 by be+ enclos$ 9 ! case above ! draw]1 ! back & front ( :i* are ( plate glass4 ,!re are doors 9 ! sides1 ?r\gh :i* ! scale-pans are load$1 & !re is a door at ! top ?r\gh :i* ! beam may be tak5 out4 ,a /rong brass pill>1 9 ! c5tre ( ! box1 supports a squ>e piece1 on ! front & back ( :i* rise two ar*es1 ne>ly semicircul>1 on :i* are fix$ two horizontal planes ( agate1 int5d$ to support ! fulcrum4 ,)9 ! pill> is a cyl9drical tube1 :i* slides up & d[n by means ( a h&le on ! outside ( ! case4 ,to ! top ( ?is int]ior tube is fix$ an ar*1 ! t]m9ations ( :i* pass b5ea? & outside ( ! two ar*es be=e describ$4 ,^! t]m9ations are =m$ into ,y s1 de/9$ to receive ! ends ( ! fulcrum1 :i* are made cyl9drical = ?is purpose1 :5 ! int]ior tube is elevat$ 9 ord] to relieve ! axis :5 ! balance is n 9 use4 ,on depress+ ! int]ior tube1 ! ,y s quit ! axis1 & leave x 9 its prop] position on ! agate planes4 ,! beam is ab\t eighte5 in*es long1 & is =m$ ( two holl[ cones ( brass1 jo9$ at _! bases4 ,! ?ickness ( ! brass does n exce$ #jjb ( an in*1 b by means ( circul> r+s driv5 into ! cones at int]vals !y are r5d]$ almo/ inflexible4 ,across ! middle ( ! beam passes a cyl9d] ( /eel1 ! l[] side ( :i* is =m$ into an edge1 hav+ an angle ( ab\t ?irty degrees1 :i*1 be+ h>d5$ & well poli%$1 con/itutes ! fulcrum1 & re/s ^u ! agate planes = ! l5g? ( ab\t #jje ( an in*4 ,ea* po9t ( susp5sion is =m$ ( an axis hav+ two %>p concave edges1 ^u :i* re/ at "r angles two o!r %>p concave edges =m$ 9 ! spur-%ap$ piece to :i* ! /r+s c>ry+ ! scale-pan are atta*$4 ,! two po9ts are adju/able1 ! "o horizontally1 = ! purpose ( equalis+ ! arms ( ! beam1 & ! o!r v]tically1 = br++ ! po9ts ( susp5sion & ! fulcrum into a "r l9e4 ,su* is ! =m ( ,tr\ghton's balance3 we %all n[ give ! description ( a balance z con/ruct$ by ,mr4 ,rob9son ( ,devon%ire ,/reet1 ,portl& ,place3-- ,! beam ( ?is balance is only t5 in*es long4 ,x is a frame ( bell-metal 9 ! =m ( a rhombus4 ,! fulcrum is an equilat]al triangul> prism ( /eel "o in* 9 l5g?2 b ! edge on :i* ! beam vibrates is =m$ to an angle ( #abj1 9 ord] to prev5t any injury f ! weight ) :i* x may be load$4 ,! *ief peculi>ity 9 ?is balance consi/s 9 ! knife-edge :i* =ms ! fulcrum be>+ ^u an agate plane ?r\gh\t its :ole l5g?1 :]eas we h se5 9 ! balance be=e describ$ t ! :ole weight is support$ by portions only ( ! knife-edge1 am\nt+ toge!r to "o t5? ( an in*4 ,! supports = ! scales are knife-edges ea* six t5?s ( an in* long4 ,^! are ea* furni%$ ) two press+ screws1 by means ( :i* !y may be made p>allel to ! c5tral knife-edge4 ,ea* end ( ! beam is sprung obliquely upw>ds & t[>ds ! middle1 s z to =m a spr+ ?r\gh :i* a pu%+ screw passes1 :i* s]ves to v>y ! di/ance ( ! po9t ( support f ! fulcrum1 &1 at ! same "t1 by its oblique action to raise or depress x1 s z to furni% a means ( br++ ! po9ts ( support & ! fulcrum into a "r l9e4 ,a piece ( wire1 f\r in*es long1 on :i* a screw is cut1 proce$s f ! middle ( ! beam d[nw>ds4 ,?is is po9t$ to s]ve z an index1 & a small brass ball moves on ! screw1 by *ang+ ! situation ( :i* ! place ( ! c5tre ( gravity may be v>i$ at pleasure4 ,! fulcrum1 z be=e rem>k$1 re/s ^u an agate plane ?r\gh\t its :ole l5g?1 & ! scale-pans are atta*$ to planes ( agate :i* re/ ^u ! knife-edges =m+ ! po9ts ( support4 ,?is me?od ( support+ ! scale-pans1 we h reason to believe1 is due to ,mr4 ,cav5di%4 ,^u ! l[] half ( ! pill> to :i* ! agate plane is fix$1 a tube slides up & d[n by means ( a lev] :i* passes to ! outside ( ! case4 ,f ! top ( ?is tube arms proce$ obliquely t[>ds ! ends ( ! balance1 s]v+ to support a horizontal piece1 c>ry+ at ea* extremity two sets ( ,y s1 "o a little above ! o!r4 ,! upp] ,y s are de/9$ to receive ! agate planes to :i* ! scale-pans are atta*$1 & ?us to relieve ! knife-edges f _! pressure2 ! l[] to receive ! knife-edges :i*1 =m ! po9ts ( support1 consequ5tly ^! latt] ,y s1 :5 9 action1 su/a9 ! :ole beam4 ,:5 ! lev] is fre$ f a not* 9 :i* x is lodg$1 a spr+ is all[$ to act ^u ! tube we h m5tion$1 & to elevate x4 ,! upp] ,y s fir/ meet ! agate planes c>ry+ ! scale-pans & free !m f ! knife-edges4 ,! l[] ,y s !n come into action & raise ! :ole beam1 elevat+ ! c5tral knife-edge above ! agate plane4 ,?is is ! usual /ate ( ! balance :5 n 9 use3 :5 x is to be br\ght into action1 ! rev]se ( :at we h describ$ takes place4 ,on press+ d[n ! lev]1 ! c5tral knife-edge fir/ meets ! agate plane1 & aft]w>ds ! two agate planes c>ry+ ! scale-pans are deposit$ ^u _! support+ knife-edges4 ,a balance ( ?is con/ruction 0 employ$ by ! writ] ( ?is article 9 adju/+ ! national /&>d p\nd4 ,) a p\nd troy 9 ea* scale1 ! addition ( "o hundr$? ( a gra9 caus$ ! index to v>y "o division1 equal to "o t5? ( an in*1 & ,mr4 ,rob9son adju/s ^! balances s t ) "o ?\s& gra9s 9 ea* scale1 ! index v>ies p]ceptibly on ! addition ( "o ?\s&? ( a gra91 or ( "o-million? "p ( ! weight to be det]m9$4 ,x may n be un9t]e/+ to subjo91 f ! ,philosophical ,transactions = #ahbf1 ! description ( a balance p]haps ! mo/ s5sible t has yet be5 made1 con/ruct$ = v]ify+ ! national /&>d bu%el4 ,! au?or says1-- 8,! weight ( ! bu%el measure1 toge!r ) ! #hj lbs4 ( wat] x %\ld conta91 0 ab\t #bej lbs42 & z ,i c\ld f9d no balance capable ( det]m9+ s l>ge a weight ) suffici5t accuracy1 ,i 0 "u ! necessity ( con/ruct+ "o = ?is express purpose4 8,i fir/ tri$ ca/ iron2 b ?\gh ! beam 0 made z light z 0 consi/5t ) ! requisite degree ( /r5g?1 ! in]tia ( su* a mass appe>$ to be s consid]able1 t mu* "t mu/ h be5 lo/ be=e ! balance w\ld h answ]$ to ! small diff]5ces ,i wi%$ to asc]ta94 ,lightness 0 a prop]ty ess5tially necess>y1 & bulk 0 v desirable1 9 ord] to preclude su* errors z might arise f ! beam be+ p>tially affect$ by sudd5 alt]ations ( temp]ature4 ,i !re=e det]m9$ to employ wood1 a mat]ial 9 :i* ! requisites ,i s\ght 7 comb9$4 ,! beam 0 made ( a plank ( mahogany1 ab\t #g,o in*es long1 #bb in*es wide1 & #b-a_/d ?ick1 tap]+ f ! middle to ! extremities4 ,an op5+ 0 cut 9 ! c5tre1 & /rong blocks screw$ to ea* side ( ! plank1 to =m a be>+ = ! back ( a knife-edge :i* pass$ ?r\gh ! c5tre4 ,blocks 7 also screw$ to ea* side at ! extremities ( ! beam on :i* re/$ ! backs ( ! knife-edges = support+ ! pans4 ,! op5+ 9 ! c5tre 0 made suffici5tly l>ge to admit ! support h]eaft] to be describ$1 ^u :i* ! knife-edge re/$4 8,9 all beams :i* ,i h se51 ) ! exception ( ^? made by ,mr4 ,rob9son1 ! :ole weight is su/a9$ by %ort portions at ! extremities ( ! knife-edge2 & ! weight be+ ?us ?r[n ^u a few po9ts1 ! knife-edge becomes m liable to *ange its figure & to suff] injury4 8,to rem$y ?is defect1 ! c5tral knife-edge ( ! beam ,i am describ+ 0 made #f in*es1 & ! two o!rs #e in*es long4 ,!y 7 triangul> prisms ) equal sides ( ?ree f\r?s ( an in*1 v c>efully f9i%$1 & ! edges ultimately =m$ to an angle ( #abj4 8,ea* knife-edge 0 screw$ to a ?ick plate ( brass1 ! surfaces 9 contact hav+ be5 previ\sly gr\nd toge!r2 & ^! plates 7 screw$ to ! beam1 ! knife-edges be+ plac$ 9 ! same plane1 & z ne>ly equidi/ant & p>allel to ea* o!r z c\ld be done by con/ruction4 8,! support ^u :i* ! c5tral knife-edge re/$ ?r\gh\t its :ole l5g? 0 =m$ ( a plate ( poli%$ h>d /eel1 screw$ to a block ( ca/ iron4 ,?is block 0 pass$ ?r\gh ! op5+ be=e m5tion$ 9 ! c5tre ( ! beam1 & prop]ly atta*$ to a frame ( ca/ iron4 8,! /irrups to :i* ! scales 7 hook$ re/$ ^u plates ( poli%$ /eel to :i* !y 7 atta*$1 & ! "u surfaces ( :i* 7 =m$ by c>eful gr9d+ into cyl9drical segm5ts4 ,^! 7 9 contact ) ! knife-edges _! :ole l5g?1 & 7 kn[n to be 9 _! prop] position by ! correspond5ce ( _! extremities ) ^? ( ! knife-edges4 ,a well imag9$ contrivance 0 appli$ by ,mr4 ,bate = rais+ ! beam :5 load$1 9 ord] to prev5t unnecess>y we> ( ! knife-edge1 & = ! purpose ( adju/+ ! place ( ! c5tre ( gravity1 :5 ! beam 0 load$ ) ! weight requir$ to be det]m9$1 a screw c>ry+ a movable ball project$ v]tically f ! middle ( die beam4 8,! p]=mance ( ?is balance fully equall$ my expectations4 ,) two hundr$ & fifty p\nds 9 ea* scale1 ! addition ( a s+le gra9 occasion$ an imm$iate v>iation 9 ! index ( "o tw5tie? ( an in*1 ! radius be+ fifty in*es40 ,f ! prec$+ acc\nt x appe>s t ?is balance is s5sible to #a_/agejjjj "p ( ! weight :i* 0 to be det]m9$4 ,we %all n[ describe ! me?od to be pursu$ 9 adju/+ a balance4 #a4 ,to br+ ! po9ts ( susp5sion & ! fulcrum into a "r l9e4 ,make ! vibrations ( ! balance v sl[ by mov+ ! weight :i* influ5ces ! c5tre ( gravity1 & br+ ! beam into a horizontal position1 by means ( small bits ( pap] ?r[n into ! scales4 ,!n load ! scales ) ne>ly ! greate/ weight ! beam is fitt$ to c>ry4 ,if ! vibrations are p]=m$ 9 ! same "t z be=e1 no fur!r adju/m5t is necess>y2 b if ! beam vibrates quick]1 or if x ov]sets1 cause x to vibrate 9 ! same "t z at fir/1 by mov+ ! adju/+ weight1 & note ! di/ance ?r\gh :i* ! weight has pass$4 ,move ! weight !n 9 ! contr>y direction ?r\gh d\ble ?is di/ance1 & !n produce ! =m] sl[ motion by means ( ! screw act+ v]tically on ! po9t ( support4 ,repeat ?is op]ation until ! adju/m5t is p]fect4 #b4 ,to make ! arms ( ! beam ( an equal l5g?4 ,put weights 9 ! scales z be=e2 br+ ! beam z ne>ly z possible to a horizontal position1 & note ! division at :i* ! index /&s2 unhook ! scales1 & transf] !m ) _! weights to ! o!r ends ( ! beam1 :51 if ! index po9ts to ! same division1 ! arms are ( an equal l5g?2 b if n1 br+ ! index to ! division :i* _h be5 not$1 by plac+ small weights 9 "o or ! o!r scale4 ,take away half ^! weights1 & br+ ! index aga9 to ! obs]v$ division by ! adju/+ screw1 :i* acts horizontally on ! po9t ( support4 ,if ! scale-pans are kn[n to be ( ! same weight1 x w n be necess>y to *ange ! scales1 b m]ely to transf] ! weights f "o scale-pan to ! o!r4 ,( ! ,use ( ! ,balance4 ,?\gh we h describ$ ! me?od ( adju/+ ! balance1 ^! adju/m5ts1 z we h be=e rem>k$1 may be disp5s$ )4 ,inde$1 9 all delicate sci5tific op]ations1 x is advisable nev] to rely ^u adju/m5ts1 :i*1 aft] e c>e has be5 employ$ 9 effect+ !m1 c only be consid]$ z approximations to ! tru?4 ,we %all1 !re=e1 n[ describe ! be/ me?od ( asc]ta9+ ! weight ( a body1 & :i* does n dep5d on ! accuracy ( ^! adju/m5ts4 ,hav+ levell$ ! case :i* conta9s ! balance1 & ?r[n ! beam out ( action1 place a weight 9 ea* scale-pan ne>ly equal to ! weight :i* is to be det]m9$4 ,l[] ! beam v g5tly till x is 9 action1 & by means ( ! adju/m5t = rais+ or l[]+ ! c5tre ( gravity1 cause ! beam to vibrate v sl[ly4 ,remove ^! weights1 & place ! sub/ance1 ! weight ( :i* is to be det]m9$ 9 "o ( ! scale-pans2 c>efully c\nt]poise x by means ( any conv5i5t sub/ances put into ! o!r scale-pan1 & obs]ve ! division at :i* ! index /&s2 remove ! body1 ! weight ( :i* is to be asc]ta9$1 & sub/itute /&>d weights = x s z to br+ ! index to ! same division z be=e4 ,^! weights w be equal to ! weight ( ! body4 ,if x be requir$ to comp>e two weights toge!r :i* are int5d$ to be equal1 & to asc]ta9 _! diff]5ce1 if any1 ! me?od ( proce$+ w be ne>ly ! same4 ,! /&>d weight is to be c>efully c\nt]pois$1 & ! division at :i* ! index /&s1 not$4 ,& n[ x w be conv5i5t to add 9 ei!r ( ! scales "s small weight1 su* z "o or two hundr$?s ( a gra91 & m>k ! numb] ( divisions pass$ ov] 9 consequ5ce by ! index1 by :i* ! value ( "o division ( ! scale w be kn[n4 ,?is %\ld be repeat$ a few times1 & ! mean tak5 = great] c]ta9ty4 ,hav+ not$ ! division at :i* ! index re/s1 ! /&>d weight is to be remov$1 & ! weight :i* is to be comp>$ ) x sub/itut$ = x4 ,! index is !n aga9 to be not$1 & ! diff]5ce betwe5 ?is & ! =m] indication w give ! diff]5ce betwe5 ! weights 9 p>ts ( a gra94 ,if ! balance is adju/$ s z to be v s5sible1 x w be long be=e x comes to a /ate ( re/4 ,x may1 !re=e1 sometimes be advisable to take ! mean ( ! ext5t ( ! vibrations ( ! index z ! po9t :]e x w\ld re/1 & ?is may be repeat$ sev]al times = great] accuracy4 ,x mu/1 h[ev]1 be rememb]$1 t x is n safe to d ?is :5 ! ext5t ( ! vibrations is beyond "o or two divisions ( ! scale2 b ) ?is limitation x is1 p]haps1 z good a me?od z c be pursu$4 ,_m precautions are necess>y to ensure a satisfactory result4 ,! weights %\ld nev] be t\*$ by ! h&2 = n only w\ld ?is oxydate ! weight1 b by rais+ its temp]ature x w\ld appe> light]1 :5 plac$ 9 ! scale-pan1 ?an x %\ld d1 9 consequ5ce ( ! asc5t ( ! heat$ air4 ,= ! l>g] weights a wood5 =k or tongs1 accord+ to ! =m ( ! weight1 %\ld be employ$2 & = ! small]1 a pair ( =ceps made ( copp] w be f\nd ! mo/ conv5i5t4 ,?is metal possess+ suffici5t ela/icity to op5 ! =ceps on _! be+ releas$ f pressure1 & yet n oppos+ a resi/ance suffici5t to int]f]e ) t delicacy ( t\* :i* is desirable 9 su* op]ations4 ,( ,weights4 ,x mu/ be obvi\s1 t ! excell5ce ( ! balance w\ld be ( little use1 unless ! weights employ$ 7 equally to be dep5d$ ^u4 ,! weights may ei!r be accurately adju/$1 or ! diff]5ce betwe5 ea* weight & ! /&>d may be det]m9$1 &1 consequ5tly1 its true value asc]ta9$4 ,x has be5 already %[n h[ ! latt] may be effect$1 9 ! in/ructions :i* h be5 giv5 = comp>+ two weights toge!r2 & we %all n[ %[ ! readie/ mode ( adju/+ weights to an exact equality ) a giv5 /&>d4 ,! mat]ial ( ! weight may be ei!r brass or plat9a1 & its =m may be cyl9drical3 ! diamet] be+ ne>ly twice ! height4 ,a small sph]ical knob is screw$ into ! c5tre1 a space be+ left "u ! screw to receive ! portions ( f9e wire us$ 9 ! adju/m5t4 ,x w be conv5i5t to =m a cavity 9 ! bottom ( ea* weight to receive ! knob ( ! weight ^u :i* x may be plac$4 ,ea* weight is n[ to be comp>$ ) ! /&>d1 & %\ld x be too heavy1 x is to be r$uc$ till x becomes 9 a v small degree too light1 :5 ! am\nt ( ! defici5cy is to be c>efully det]m9$4 ,"s v f9e silv] wire is n[ to be tak51 & ! weight ( ?ree or f\r feet ( x asc]ta9$4 ,f ?is x w be kn[n :at l5g? ( ! wire is equal to ! error ( ! weight to be adju/$2 & ?is l5g? be+ cut (f is to be enclos$ "u ! screw4 ,to gu>d aga9/ any possible error1 x w be advisable be=e ! screw is firmly fix$ 9 its place1 aga9 to comp>e ! weight ) ! /&>d4 ,! mo/ approv$ me?od ( mak+ weights express+ ! decimal p>ts ( a gra91 is to det]m9e1 z be=e1 ) great c>e1 ! weight ( a c]ta9 l5g? ( f9e wire1 & !n to cut (f su* portions z are equal to ! weights requir$4 ,be=e we conclude ?is article we %all give a description1 f ! ,annals ( ,philosophy = #ahbe1 ( 8a v s5sible balance10 us$ by ! late ,dr4 ,black3-- 8,a ?9 piece ( fir wood1 n ?ick] ?an a %ill+1 & a foot long1 ?ree t5?s ( an in* broad 9 ! middle1 & "o t5? & a half at ea* end1 is divid$ by transv]se l9es into tw5ty p>ts2 t is1 t5 p>ts on ea* side ( ! middle4 ,^! are ! pr9cipal divisions1 & ea* ( !m is subdivid$ into halves & qu>t]s4 ,across ! middle is fix$ "o ( ! smalle/ ne$les ,i c\ld procure1 to s]ve z an axis1 & x is fix$ 9 its place by means ( a little seal+ wax4 ,! num]ation ( ! divisions is f ! middle to ea* end ( ! beam4 ,! fulcrum is a bit ( plate brass1 ! middle ( :i* lies flat on my table :5 ,i use ! balance1 & ! two ends are b5t up to a "r angle s z to /& upright4 ,^! two ends are gr\nd at ! same "t on a flat hone1 t ! extreme surfaces ( !m may be 9 ! same plane2 & _! di/ance is su* t ! ne$le1 :5 laid across !m1 re/s on !m at a small di/ance f ! sides ( ! beam4 ,!y rise above ! surface ( ! table only "o t5? & a half or two t5?s ( an in*1 s t ! beam is v limit$ 9 its play4 ,see fig4 #aij4 8,! weights ,i use are "o globule ( gold1 :i* weighs "o gra91 & two or ?ree o!rs :i* weigh "o t5? ( a gra9 ea*2 & also a numb] ( small r+s ( f9e brass wire1 made 9 ! mann] fir/ m5tion$ by ,mr4 ,lewis1 by app5d+ a weight to ! wire1 & coil+ x ) ! t5sion ( t weight r\nd a ?ick] brass wire 9 a close spiral1 aft] :i*1 ! extremity ( ! spiral be+ ti$ h>d ) wax$ ?read1 ,i put ! cov]$ wire into a vice1 & apply+ a %>p knife1 :i* is /ruck ) a hamm]1 ,i cut ?r\gh a great numb] ( ! coils at "o /roke1 & f9d !m z exactly equal to "o ano!r z c be desir$4 ,^? ,i use happ5 to be ! #a_/cj "p ( a gra9 ea*1 or #cjj ( !m weigh t5 gra9s2 b ,i h o!rs mu* light]4 8,y w p]ceive t by means ( ^! weights plac$ on diff]5t p>ts ( ! beam1 ,i c le>n ! weight ( any little mass f "o gra91 or a little m1 to ! #a_/abjj ( a gra94 ,= if ! ?+ to be weigh$ weighs "o gra91 x w1 :5 plac$ on "o extremity ( ! beam1 c\nt]poise ! l>ge gold weight at ! o!r extremity4 ,if x weighs half a gra9 x w c\nt]poise ! heavy gold weight plac$ at #e4 ,if x weigh #f_/aj ( a gra91 y mu/ place ! heavy gold weight at #e1 & "o ( ! light] ones at ! extremity to c\nt]poise x1 & if x weighs only "o or two1 or ?ree or f\r hundr$?s ( a gra91 x w be c\nt]pois$ by "o ( ! small gold weights plac$ at ! fir/ or second1 or ?ird or f\r? division4 ,if1 on ! contr>y1 x weighs "o gra9 & a fraction1 x w be c\nt]pois$ by ! heavy gold weight at ! extremity1 & "o or m ( ! light] ones plac$ 9 "s o!r "p ( ! beam4 8,?is beam has s]v$ me hi!rto = e purpose2 b _h ,i occasion = a m delicate "o1 ,i c\ld make x easily by tak+ a mu* ?9n] & light] slip ( wood1 & gr9d+ ! ne$le to give x an edge4 ,x w\ld also be easy to make x c>ry small scales ( pap] = p>ticul> purposes40 ,! writ] ( ?is article has us$ a balance ( ?is k9d1 & f9ds t x is s5sible to #a_/ajjj ( a gra9 :5 load$ ) t5 gra9s4 ,x is necess>y1 h[ev]1 :]e accuracy is requir$1 to employ a scale-pan4 ,?is may be made ( ?9 c>d pap]1 %ap$ z 9 fig4 #aia4 ,a ?read is to be pass$ ?r\gh ! two ends1 by tight5+ :i* !y may be br\ght ne> ea* o!r4 ,! mo/ conv5i5t weights = ?is beam appe> to be two ( "o gra9 ea*1 & "o ( "o t5? ( a gra94 ,!y %\ld be made ( /raight wire2 & if ! beam be not*$ at ! divisions1 !y may be lodg$ 9 ^! not*es v conv5i5tly4 ,t5 divisions on ea* side ( ! middle w be suffici5t4 ,! weight ( ! scale-pan mu/ fir/ be c>efully asc]ta9$1 9 ord] t x may be d$uct$ f ! weight1 aft]w>ds det]m9$1 ( ! scale-pan & ! sub/ance x may conta94 ,if ! scale-pan be plac$ at ! t5? division ( ! beam1 x is evid5t t by means ( ! two gra9 weights1 a great] weight _c be det]m9$ ?an "o gra9 & n9e t5?s2 b if ! scale-pan be plac$ at any o!r division ( ! beam1 ! result+ app>5t weight mu/ be increas$ by multiply+ x by t51 & divid+ by ! numb] ( ! division at :i* ! scale-pan is plac$2 & 9 ?is mann] x is evid5t t if ! scale-pan be plac$ at ! division numb]$ #a1 a weight am\nt+ to n9ete5 gra9s may be det]m9$4 ,we h be5 tempt$ to describe ?is little app>atus1 because x is extremely simple 9 its con/ruction1 may be easily made1 & may be v usefully employ$ on _m occasions :]e extreme accuracy is n necess>y4 ,description ( ! ,/eely>d4 ,! /eely>d is a lev]1 hav+ unequal arms2 & 9 its mo/ simple =m x is s arrang$1 t "o weight alone s]ves to det]m9e a great v>iety ( o!rs1 by slid+ x along ! long] arm ( ! lev]1 & ?us v>y+ its di/ance f ! fulcrum4 ,x has be5 demon/rat$1 *apt] xiii41 t 9 ! lev] ! proportion ( ! p[] to ! weight w be always ! same z t ( _! di/ances f ! fulcrum1 tak5 9 a rev]se ord]2 consequ5tly1 :5 a con/ant weight is us$1 & an equilibrium e/abli%$ by slid+ ?is weight on ! long] arm ( ! lev]1 ! relative weight ( ! sub/ance weigh$1 to ! con/ant weight1 w be 9 ! same proportion z ! di/ance ( ! con/ant weight f ! fulcrum is to ! l5g? ( ! %ort] arm4 ,?us1 suppose ! l5g? ( ! %ort] arm1 or ! di/ance ( ! fulcrum f ! po9t f :i* ! weight to be det]m9$ is susp5d$1 to be "o in*2 let ! long] arm ( ! lev] be divid$ into p>ts ( "o in* ea*1 beg9n+ at ! fulcrum4 ,n[ let ! con/ant weight be equal to "o p\nd1 & let ! /eely>d be s con/ruct$ t ! %ort] arm %all be suffici5tly heavy to c\nt]poise ! long] :5 ! b> is unload$4 ,!n suppose a sub/ance1 ! weight ( :i* is five p\nds1 to be susp5d$ f ! %ort] arm4 ,x w be f\nd t :5 ! con/ant weight is plac$ at ! di/ance ( five in*es f ! fulcrum1 ! weights w be 9 equilibrium1 & ! b> consequ5tly horizontal4 ,9 ?is /eely>d1 !re=e1 ! di/ance ( ea* in* f ! fulcrum indicates a weight ( "o p\nd4 ,an in/rum5t ( ?is =m 0 us$ by ! ,romans1 & x is usually describ$ z ! ,roman /at]a or /eely>d4 ,a repres5tation ( x is giv5 at fig4 #aib4 ,! /eely>d is 9 v g5]al use = ! co>s] purposes ( comm]ce1 b con/ruct$ diff]5tly f t :i* we h describ$4 ,! beam ) ! scales or hooks is seldom 9 equilibrium ^u ! po9t ,f1 :5 ! weight ,p is remov$2 b ! long] arm usually prepond]ates1 & ! comm5cem5t ( ! graduations1 !re=e1 is n at ,f1 b at "s po9t betwe5 ,b & ,f4 ,! common /eely>d1 :i* we h repres5t$ at fig4 #aic41 is usually furni%$ ) two po9ts1 f ei!r ( :i* ! sub/ance1 ! weight ( :i* is to be det]m9$1 may be susp5d$4 ,! value ( ! divisions is 9 ?is case increas$ 9 proportion z ! l5g? ( ! %ort] arm is decreas$4 ,?us1 9 ! /eely>d :i* we h describ$1 if !re be a second po9t ( susp5sion at ! di/ance ( half an in* f ! fulcrum1 ea* division ( ! long] arm w indicate two p\nds in/ead ( "o1 & ^! divisions are usually m>k$ ^u ! opposite edge ( ! /eely>d1 :i* is made to turn ov]4 ,?is in/rum5t is v conv5i5t1 because x requires b "o weight2 & ! pressure on ! fulcrum is less ?an 9 ! balance1 :5 ! sub/ance to be weigh$ is heavi] ?an ! con/ant weight4 ,b1 on ! contr>y1 :5 ! con/ant weight exce$s ! sub/ance to be weigh$1 ! pressure on ! fulcrum is great] 9 ! /eely>d ?an 9 ! balance1 & ! balance is1 !re=e1 pref]able 9 det]m9+ small weights4 ,!re is also an advantage 9 ! balance1 because ! subdivision ( weights c be effect$ ) a great] degree ( precision ?an ! subdivision ( ! arm ( ! /eely>d4 ,c4 ,paul's ,/eely>d4 ,a /eely>d has be5 con/ruct$ by ,mr4 ,c4 ,paul1 inspector ( weights & measures at ,g5eva1 :i* is mu* to be pref]r$ to t 9 common use4 ,mr4 ,c4 ,paul /ates1 t /eely>ds h two advantages ov] balances3 #a4 ,t _! axis ( susp5sion is n load$ ) any o!r weight ?an t ( ! m]*&ise1 ! con/ant weight ( ! app>atus itself except$2 :ile ! axis ( ! balance1 besides ! weight ( ! in/rum5t1 su/a9s a weight d\ble to t ( ! m]*&ise4 #b4 ,! use ( ! balance requires a consid]able assortm5t ( weights1 :i* causes a proportional increase 9 ! price ( ! app>atus1 indep5d5tly ( ! *ances ( error :i* x multiplies1 & ( ! "t employ$ 9 produc+ an equilibrium4 #a4 ,9 ,c4 ,paul's /eely>d ! c5tres ( ! movem5t ( susp5sion1 or ! two con/ant c5tres1 are plac$ on ! exact l9e ( ! divisions ( ! beam2 an elevation almo/ imp]ceptible 9 ! axis ( ! beam1 de/9$ to comp5sate = ! v slight flexion ( ! b>1 alone except$4 #b4 ,! app>atus1 by ! con/ruction ( ! beam1 is balanc$ bel[ its c5tre ( motion1 s t :5 no weight is susp5d$ ! beam naturally rema9s horizontal1 & resumes t position :5 remov$ f x1 z also :5 ! /eely>d is load$1 & ! weight is at ! division :i* ought to %[ h[ mu* ! m]*&ise weighs4 ,! horizontal situation 9 ?is /eely>d1 z well z 9 ! o!rs1 is kn[n by means ( ! tongue :i* rises v]tically above ! axis ( susp5sion4 #c4 ,x may be discov]$1 t ! /eely>d is d]ang$ if1 :5 n load$1 ! beam does n rema9 horizontal4 #d4 ,! advantage ( a great & a small side 7:i* 9 ! o!r augm5ts ! ext5t ( _! p[] ( weigh+7 is suppli$ by a v simple process1 :i* accompli%es ! same end ) "s additional advantages4 ,?is process is to employ on ! same division diff]5t weights4 ,! numb]s ( ! divisions on ! b>1 po9t out ! degree ( heav9ess express$ by ! correspond+ weights4 ,= example1 :5 ! l>ge weight ( ! l>ge /eely>d weighs #af lbs41 ea* division x passes ov] on ! b> is equival5t to a p\nd2 ! small weight1 weigh+ sixte5 times less ?an ! l>ge "o1 w repres5t on ea* ( ^! divisions ! sixte5? "p ( a p\nd1 or "o ounce2 & ! opposite face ( ! b> is m>k$ by p\nds at ea* sixte5? division4 ,9 ?is con/ruction1 !re=e1 we h ! advantage ( be+ able1 by employ+ bo? weights at once1 to asc]ta91 = example1 almo/ )9 an ounce1 ! weight ( #ejj p\nds ( m]*&ise4 ,x w be suffici5t to add :at is indicat$ by ! small weight 9 ounces1 to t ( ! l>ge "o 9 p\nds1 aft] an equilibrium has be5 obta9$ by ! position ( ! two weights1 viz4 ! l>ge "o plac$ at ! next p\nd bel[ its real weight1 & ! small "o at ! division :i* det]m9es ! numb] ( ounces to be add$4 #e4 ,z ! beam is graduat$ only on "o edge1 x may h ! =m ( a ?9 b>1 :i* r5d]s x mu* less susceptible ( be+ b5t by ! action ( ! weight1 & af=ds room = mak+ ! figures m visible on bo? ! faces4 #f4 ,9 ^! /eely>ds ! disposition ( ! axes is n only su* t ! beam repres5ts a ma!matical lev] )\t weight1 b 9 ! pr9ciple ( its division1 ! int]val betwe5 e two divisions is a det]m9$ & aliquot "p ( ! di/ance betwe5 ! two fix$ po9ts ( susp5sion2 & ea* ( ! two weights employ$ has = its absolute weight ! unity ( ! weight x repres5ts1 multipli$ by ! numb] ( ! divisions conta9$ 9 ! int]val betwe5 ! two c5tres ( motion4 ,?us1 suppos+ ! arms ( ! /eely>d divid$ 9 su* a mann] t t5 divisions are exactly conta9$ 9 ! di/ance betwe5 ! two con/ant c5tres ( motion1 a weight to express ! p\nds on ea* division ( ! beam mu/ really weigh t5 p\nds2 t to po9t out ! ounces on ! same divisions mu/ weigh t5 ounces1 c4 ,s t ! same /eely>d may be adapt$ to any sy/em ( measures :atev]1 & 9 p>ticul> to ! decimal sy/em1 by v>y+ ! absolute heav9ess ( ! weights1 & _! relation ) ea* o!r4 ,b to trace out1 9 a few words1 ! advantages ( ! /eely>ds con/ruct$ by ,c4 ,paul = comm]cial purposes1 we %all only obs]ve1-- #a4 ,t ! buy] & sell] are c]ta9 ( ! correctness ( ! in/rum5t1 if ! beam rema9s horizontal :5 x is unload$ & 9 its usual position4 #b4 ,t ^! /eely>ds h "o susp5sion less ?an ! old ones1 & are s mu* m simple4 #c4 ,t by ^! means we obta91 ) ! greate/ facility1 by employ+ two weights1 ! exact weight ( m]*&ise1 ) all ! approximation t c be desir$1 & ev5 ) a great] precision ?an t giv5 by common balances4 ,!re are few ( ^! :i*1 :5 load$ ) #ejj p\nds at ea* end1 give decid$ indication ( an ounce v>iation2 & ! /eely>ds ( ,c4 ,paul possess t advantage1 & co/ "o half less ?an balances ( equal dom9ion4 #d4 ,9 ! la/ place1 we may v]ify at pleasure ! ju/ness ( ! weights1 by ! transposition :i* _! ratio to ea* o!r w p]mit2 = example1 by obs]v+ :e!r1 :5 ! weight ( "o p\nd is br\ght back "o division1 & ! weight ( "o ounce c>ri$ =w>d sixte5 divisions1 ! equilibrium /ill rema9s4 ,x is on ?is simple & advantage\s pr9ciple t ,c4 ,paul has con/ruct$ 8 univ]sal /eely>d4 ,x s]ves = weigh+ 9 ! usual mann]1 & accord+ to any sy/em ( weights1 all pond]able bodies to ! precision ( half a gra9 9 ! weight ( a hundr$ ounces2 t is to say1 ( a t5-?\s&? "p4 ,x is employ$1 besides1 = asc]ta9+ ! specific gravity ( solids1 ( liquids1 & ( air1 by processes extremely simple1 & :i* d n require _m subdivisions 9 ! weights4 ,we ?9k ! description above giv5 w be suffici5tly intelligible )\t a repres5tation ( ?is in/rum5t4 ,an acc\nt ( its application to ! det]m9ation ( specific gravities w be f\nd 9 vol4 iii4 ( ! ,philosophical ,magaz9e4 ,! ,*9ese ,/eely>d4 ,?is in/rum5t is us$ 9 ,*9a & ! ,ea/ ,indies = weigh+ gems1 preci\s metals1 c4 ,! beam is a small rod ( ivory1 ab\t a foot 9 l5g?4 ,^u ?is are ?ree l9es ( divisions1 m>k$ by f9e silv] /uds1 all beg9n+ f ! end ( ! beam1 :5ce ! fir/ is ext5d$ #h in*es1 ! second #f-a_/b1 & ! ?ird #h-a_/b4 ,! fir/ is ,european weight1 & ! o!r two ,*9ese4 ,at ! o!r end ( ! beam hangs a r\nd scale1 & at ?ree sev]al di/ances f ?is end are holes1 ?r\gh :i* pass s _m f9e /r+s1 s]v+ z diff]5t po9ts ( susp5sion4 ,! fir/ di/ance makes #a-c_/e in*es1 ! second #c-a_/e1 or d\ble ! =m]1 & ! ?ird #d-d_/e1 or triple ! same4 ,! in/rum5t1 :5 us$1 is held by "o ( ! /r+s1 & a seal$ weight ( ab\t #a-a_/d oz4 troy1 is slid ^u ! beam until an equilibrium is produc$2 ! weight ( ! body is !n indicat$ by ! graduat$ scale above m5tion$4 ,! ,dani% ,balance4 ,! ,dani% balance is a /raight b> or lev]1 hav+ a heavy weight fix$ to "o end1 & a hook or scale-pan to receive ! sub/ance1 ! weight ( :i* is to be det]m9$1 susp5d$ f ! o!r end4 ,! fulcrum is moveable1 & is made to slide ^u ! b>1 till ! beam re/s 9 a horizontal position1 :5 ! place ( ! fulcrum indicates ! weight requir$4 ,9 ord] to con/ruct a balance ( ?is k9d1 let ! di/ance ( ! c5tre ( gravity f t po9t to :i* ! sub/ance to be weigh$ is susp5d$ be f\nd by exp]im5t1 :5 ! beam is unload$4 ,multiply ?is di/ance by ! weight ( ! :ole app>atus1 & divide ! product by ! weight ( ! app>atus increas$ by ! weight ( ! body4 ,?is w give ! di/ance f ! po9t ( susp5sion1 at :i* ! fulcrum be+ plac$1 ! :ole w be 9 equilibrio3 = example1 suppos+ ! di/ance ( ! c5tre ( gravity f ! po9t ( susp5sion to be #aj in*es1 & ! weight ( ! :ole app>atus to be t5 p\nds2 suppose1 also1 x 7 requir$ to m>k ! divisions :i* %\ld indicate weights ( "o1 two1 or ?ree p\nds1 c4 ,fir/1 = ! place ( ! division indicat+ "o p\nd we h 7#aj #aj7_/7aj #a7 #ajj_/7aj #a7 #i-a_/aa in*es1 ! place ( ! division m>k+ "o p\nd4 ,= two p\nds we h #ajj_/7aj #b7 #h-a_/c in*es1 ! place ( ! division indicat+ two p\nds2 & = ?ree p\nds #ajj_/7aj #c7 #g-i_/ac in*es = ! place ( ! division indicat+ ?ree p\nds1 & s on4 ,?is balance is subject to ! inconv5i5ce ( ! divisions becom+ mu* %ort] z ! weight increases4 ,! di/ance betwe5 ! divisions indicat+ "o & two p\nds be+1 9 ! example we h giv51 ab\t sev5 t5?s ( an in*1 :il/ t betwe5 #bj & #ba p\nds is only "o t5? ( an in*2 consequ5tly a v small error 9 ! place ( ! divisions indicat+ ! l>g] weights w\ld occasion v inaccurate results4 ,! ,dani% balance is repres5t$ at fig4 #aid4 ,! ,b5t ,lev] ,balance4 ,?is in/rum5t is repres5t$ at fig4 #aie4 ,! weight at ,c1 is fix$ at ! end ( ! b5t lev] ,a ,b ,c1 :i* is support$ by its axis ,b on ! pill> ,i ,h4 ,a scale-pan ,e1 is susp5d$ f ! o!r end ( ! lev] at ,a4 ,?r\gh ! c5tre ( motion ,b draw ! horizontal l9e ,k ,b ,g1 ^u :i*1 f ,a & ,c let fall ! p]p5dicul>s ,a ,k & ,c ,d4 ,!n if ,b ,k & ,b ,d are reciprocally proportional to ! weights at ,a & ,c1 !y w be 9 equilibrio1 b if n1 ! weight ,c w move upw>ds or d[nw>ds along ! arc ,f ,g till t ratio is obta9$4 ,if ! lev] be s b5t t :5 ,a co9cides ) ! l9e ,g ,k1 ,c co9cides ) ! v]tical ,b ,h1 !n z ,c moves f ,f to ,g1 its mom5tum w increase :ile t ( ! weight 9 ! scale-pan ,e w decrease4 ,h5ce ! weight 9 ,e1 correspond+ to diff]5t positions ( ! balance1 may be express$ on ! graduat$ arc ,f ,g4 ,brady's ,balance1 or ,weigh+ ,app>atus4 ,?is p>takes ( ! prop]ties bo? ( ! b5t lev] balance & ( ! /eely>d4 ,x is repres5t$1 at fig4 #aif4 ,a ,b ,c is a frame ( ca/ iron hav+ a great "p ( its weight t[>ds ,a4 ,f is a fulcrum1 & ,e a moveable susp5d]1 hav+ a scale & hook at its l[] extremity4 ,e ,k ,g are ?ree di/9ct places1 to :i* ! susp5d] ,e may be appli$1 & to :i* belong respectively ! ?ree graduat$ scales ( division express+ weights1 f ,c1 c d1 & a b4 ,:5 ! scale & susp5d] are appli$ at ,g1 ! app>atus is 9 equilibrio1 ) ! edge ,a ,b horizontal1 & ! susp5d] cuts ! z]o on ! scale a b4 ,n[1 any sub/ance1 ! weight ( :i* is to be asc]ta9$1 be+ put into ! scale1 ! :ole app>atus turns ab\t ,f1 & ! "p t[>ds ,b desc5ds till ! equilibrium is aga9 e/abli%$1 :5 ! weight ( ! body is read (f f ! scale a b1 :i* regi/]s to ounces & ext5ds to two p\nds4 ,if ! weight ( ! body exce$ two p\nds1 & be less ?an elev5 p\nds1 ! susp5d] is plac$ at ,k2 & :5 ! scale is empty1 ! numb] #b is f\nd to ! "r ( ! index ( ! susp5d]4 ,if n[ weights exce$+ two p\nds be plac$ 9 ! scale1 ! :ole aga9 turns ab\t ,f1 & ! weight ( ! body is %[n on ! graduat$ arc c d1 :i* ext5ds to elev5 p\nds1 & regi/]s to e two ounces4 ,if ! weight ( ! body exce$ elev5 p\nds1 ! susp5d] is hung on at ,e1 & ! weights are asc]ta9$ 9 ! same mann] on ! scale f ,c to ?irty p\nds1 ! subdivisions be+ on ?is scale qu>t]s ( p\nds4 ,! same pr9ciples w\ld obvi\sly apply to weights great] or less ?an ! above4 ,to prev5t mi/ake1 ! ?ree po9ts ( support ,g1 ,k1 ,e1 are numb]$ #a1 #b1 #c2 & ! correspond+ arcs are respectively numb]$ 9 ! same mann]4 ,:5 ! hook is us$ in/ead ( ! scale1 ! latt] is turn$ upw>ds1 !re be+ a jo9t at m = t purpose4 ,! ,weigh+ ,ma*9e = ,turnpike ,roads4 ,?is ma*9e is = ! purpose ( asc]ta9+ ! weight ( heavy bodies1 su* z :eel c>riages4 ,x consi/s ( a wood5 plat=m plac$ ov] a pit made 9 ! l9e ( ! road1 & :i* conta9s ! ma*9]y4 ,! pit is wall$ )9side1 & ! plat=m is fitt$ to ! walls ( ! pit1 b )\t t\*+ !m1 & x is !re=e at lib]ty to move freely up & d[n4 ,! plat=m is support$ by lev]s plac$ b5ea? x1 & is exactly level ) ! surface ( ! road1 s t a c>riage is easily drawn on x1 ! :eels be+ ^u ! plat=m :il/ ! horses are ^u ! solid gr\nd beyond x4 ,! con/ruction ( ?is ma*9e w be readily und]/ood by ref]5ce to fig4 #aig41 9 :i* ! plat=m is suppos$ to be transp>5t s z to all[ ( ! lev]s be+ se5 bel[ x4 ,a1 ,b1 ,c1 ,d1 repres5t f\r lev]s t5d+ t[>ds ! c5tre ( ! plat=m1 & ea* moveable on its fulcrum at ,a1 ,b1 ,c1 ,d2 ! fulcrum ( ea* re/s ^u a piece securely fix$ 9 ! corn] ( ! pit4 ,! plat=m is support$ ^u ! cross p9s a1 b1 c1 d1 by means ( pieces ( iron :i* project f x ne> its corn]s1 & :i* are repres5t$ 9 ! plate by ! %ort d>k l9es cross+ ! p9s a1 b1 c1 d4 ,! f\r lev]s are connect$ "u ! c5tre ( ! plat=m1 b n s z to prev5t _! free motion1 & are support$ by a long lev] at ! po9t ,f1 ! fulcrum ( :i* re/s ^u a piece ( masonry at ,e3 ! end ( ?is la/ lev] passes bel[ ! surface ( ! road into ! turnpike h\se1 & is !re atta*$ to "o arm ( a balance1 or1 z 9 ,salmon's pat5t weigh+ ma*9e1 to a /rap pass+ r\nd a cyl9d] :i* w9ds up a small weight r\nd a spiral1 & indicates1 by means ( an index1 ! weight plac$ ^u ! plat=m4 ,illu/ration3 ,captn4 ,kat]1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,suppose ! di/ance f ,a to ,f to be t5 times z great z t f ,a to a1 !n a =ce ( "o p\nd appli$ b5ea? ,f w\ld balance t5 p\nds appli$ at a1 or ^u ! plat=m4 ,aga93 let ! di/ance f ,e to ,g be also t5 times great] ?an ! di/ance f ! fulcrum ,e to ,f2 !n a =ce ( "o p\nd appli$ to raise up ! end ( ! lev] ,g w\ld c\nt]poise a weight ( t5 p\nds plac$ ^u ,f4 ,n[1 z we ga9 t5 times ! p[] by ! fir/ lev]s1 & t5 times m by ! lev] ,e ,g1 x foll[s1 t a =ce ( "o p\nd t5d+ to elevate ,g1 w\ld balance #ajj lbs4 plac$ on ! plat=m2 s t if ! end ( ! lev] ,g be atta*$ to "o arm ( a balance1 a weight ( #aj lbs4 plac$ 9 a scale susp5d$ f ! o!r arm1 w express ! value ( #ajjj lbs4 plac$ ^u ! plat=m4 ,! lev]s are c\nt]pois$1 :5 ! plat=m is n load$1 by a weight ,h appli$ to ! end ( ! la/ lev]1 cont9u$ beyond ! fulcrum = t purpose4 ,( ,in/rum5ts = weigh+ by means ( a ,spr+4 ,! spr+ is well adapt$ to ! con/ruction ( a weigh+ ma*9e1 f ! prop]ty x possesses ( yield+ 9 proportion to ! =ce impress$1 & consequ5tly giv+ a scale ( equal p>ts = equal additions ( weight4 ,x is liable1 h[ev]1 to suff] injury1 unless ! /eel ( :i* x is compos$ be v well temp]$1 f a want ( p]fect ela/icity1 &1 consequ5tly1 f n return+ to its orig9al place aft] x has be5 =cibly compress$4 ,?is1 h[ev]1 mu/ be consid]$ to arise1 9 a great measure1 f imp]fection ( workman%ip1 or ( ! mat]ial employ$1 or f its hav+ be5 subject$ to too great a =ce4 ,! ,spr+ ,/eely>d4 ,! little in/rum5t kn[n by ?is "n is 9 v g5]al use1 & is p>ticul>ly conv5i5t :]e great accuracy is n necess>y1 z a spr+ :i* w asc]ta9 weights f "o p\nd to fifty1 is conta9$ 9 a cyl9d] only #d in*es long & #c_/d in* diamet]4 ,?is in/rum5t is repres5t$ at fig4 #aih4 ,x consi/s ( a tube ( iron1 ( ! dim5sions j /at$1 clos$ at ! bottom1 to :i* is atta*$ an iron hook = support+ ! sub/ance to be weigh$2 a rod ( iron a b1 f\r t5?s ( an in* wide & "o t5? ?ick1 is firmly fix$ 9 ! circul> plate c d1 :i* slides smoo?ly 9 ! iron tube4 ,a /rong /eel spr+ is also fa/5$ to ?is plate1 & pass$ r\nd ! rod a b )\t t\*+ x1 & )\t com+ 9 contact ) ! int]ior ( ! cyl9drical tube4 ,! tube is clos$ at ! top by a circul> piece ( iron ?r\gh :i* ! piece a b passes4 ,^u ! face ( a b ! weight is express$ by divisions1 ea* ( :i* indicates "o p\nd1 & five ( su* divisions 9 ! in/rum5t n[ be=e u occupy two t5?s ( an in*4 ,! divisions1 not)/&+1 are ( suffici5t size to enable !m to be subdivid$ by ! eye4 ,to use ?is in/rum5t1 ! sub/ance to be weigh$ is susp5d$ by ! hook1 ! in/rum5t be+ held by a r+ pass+ ?r\gh ! rod at ! o!r end4 ,! spr+ !n suff]s a compression proportionate to ! weight1 & ! numb] ( p\nds is indicat$ by ! division on ! rod :i* is cut by ! top ( ! cyl9drical tube4 ,salt]'s improv$ ,spr+ ,balance4 ,a v neat =m ( ! in/rum5t la/ describ$ has be5 rec5tly br\ght be=e ! public by ,mr4 ,salt]1 "u ! "n ( ! ,improv$ ,spr+ ,balance4 ,x is repres5t$ at fig4 #aii4 ,! spr+ is conta9$ 9 ! upp] half ( a cyl9d] beh9d ! brass plate =m+ ! face ( ! in/rum5t2 & ! rod is fix$ to ! l[] extremity ( ! spr+1 :i* is consequ5tly ext5d$1 in/ead ( be+ compress$1 by ! application ( ! weight4 ,! divisions1 ea* indicat+ half a p\nd1 are engrav$ ^u ! face ( ! brass plate1 & are po9t$ out by an index atta*$ to ! rod4 ,m>riott's ,pat5t ,dial ,weigh+ ,ma*9e4 ,! ext]ior ( ?is in/rum5t is repres5t$ at fig4 #bjj41 & ! int]ior at fig4 #bja4 ,a ,b ,c is a %all[ brass box1 hav+ a solid piece z repres5t$ at ,a1 to :i* ! spr+ ,d ,e ,f is firmly fix$ by a nut at ,d4 ,! o!r end ( ! spr+ at ,f is p9n$ to ! brass piece ,g ,h1 to ! "p ( :i* at ,g is also fix$ ! iron rack$ plate ,i4 ,a screw ,l s]ves z a /op to keep ?is rack 9 its place4 ,! tee? ( ! rack fit into ^? ( ! p9ion ,m1 ! axis ( :i* passes ?r\gh ! c5tre ( ! dial-plate1 & c>ries an index :i* po9ts out ! weight4 ,! brass piece ,g ,h is m]ely a plate :]e x passes ov] ! spr+1 & ! tail piece ,h1 to :i* ! weight is susp5d$1 passes ?r\gh an op5+ 9 ! side ( ! box4 ,( ! ,dynamomet]4 ,?is is an important in/rum5t 9 me*anics1 calculat$ to measure ! muscul> /r5g? ex]t$ by m5 & animals4 ,x consi/s ess5tially ( a spr+ /eely>d1 su* z t we fir/ describ$4 ,?is is sometimes employ$ alone1 & sometimes 9 comb9ation ) v>i\s lev]s1 :i* all[ ( ! spr+ be+ made m delicate1 & consequ5tly increase ! ext5t ( ! divisions indicat+ ! weight4 ,! fir/ in/rum5t ( ?is k9d appe>s to h be5 inv5t$ by ,mr4 ,graham1 b x 0 too bulky & inconv5i5t = use4 ,m4 le ,roy made "o ( a m simple con/ruction4 ,x consi/$ ( a metal tube1 ab\t a foot long1 plac$ v]tically ^u a /&1 & conta9+ 9 ! inside a spiral spr+1 hav+ above x a graduat$ rod t]m9at+ 9 a globe4 ,?is rod ent]$ ! tube m or less 9 proportion to ! =ce appli$ to ! globe1 & ! divisions indicat$ ! quantity ( ?is =ce4 ,!re=e1 :5 a man press$ ^u ! globe ) all 8 /r5g?1 ! divisions ^u ! rod %[$ ! numb] ( p\nds weight to :i* x 0 equal4 ,an in/rum5t ( ?is k9d = det]m9+ ! =ce ( a bl[ /ruck by a man ) 8 fi/ 0 lately exhibit$ at ! ,national ,repository4 ,x 0 fix$ to a wall1 f :i* x project$ horizontally4 ,9 place ( ! globe !re 0 a cu%ion to receive ! bl[1 & z ! sudd5ness ) :i* ! spr+ return$ r5d]$ x impossible to read ! division ^u ! rod1 ano!r rod simil>ly divid$ 0 =c$ 9 by ! plate =m+ ! basis ( ! cu%ion1 & rema9$ /ation>y :5 ! spr+ return$4 ,! common spr+ /eely>d1 h[ev]1 :i* we fir/ describ$1 is 9 pr9ciple ! same z ,m4 le ,roy's dynamomet]1 & is mu* m conv5i5tly con/ruct$ = ! purpose we are consid]+4 ,! r+ at "o end may be fix$ to an immovable object1 & ! hook at ! o!r atta*$ to a man1 or to an animal1 & ! ext5t to :i* ! graduat$ rod is drawn out ( ! cyl9d] %[s at once ! =ce :i* is appli$4 ,?\gh ?is is p]haps ! be/1 & c]ta9ly ! mo/ simple dynamomet]1 o!rs h be5 contriv$1 :i* are1 h[ev]1 b modifications ( ! spr+ /eely>d4 ,"o ( ^! is repres5t$ at fig4 #bjb4 ,! spiral spr+ acts 9 ! mann] be=e describ$1 b its divisions are increas$ 9 size1 & !re=e r5d]$ m p]ceptible by means ( a rack fix$ to ! plate1 act+ aga9/ ! spiral spr+1 ! tee? ( :i* move a p9ion ^u :i* ! arm ,i is fix$1 po9t+ to ! graduat$ arc ,k4 ,ano!r dynamomet] has be5 inv5t$ by ,mr4 ,salmon2 x is repres5t$ at fig4 #bjc4 & is a comb9ation ( lev]s ) ! spr+4 ,by means ( ^! lev]s a mu* m delicate spr+1 & :i* is !re=e m s5sible1 may be employ$ ?an 9 ! dynamomet] la/ describ$4 ,! mann] 9 :i* ^! lev]s & spr+ act w be readily und]/ood by an inspection ( ! figure4 ,l ! weigh+ ma*9e = c>riages1 ! fulcrum ( ea* lev] is at "o end1 & ! =ce is dim9i%$ 9 pass+ to ! spr+1 9 ! ratio ( ! l5g? ( its arms4 ,! spr+ moves a p9ion by means ( a rack1 ^u :i* p9ion a h& is plac$1 indicat+ by divisions ^u a circul> dial-plate1 ! am\nt ( ! =ce employ$4 ,! spr+ us$ 9 ?is ma*9e is calculat$ to weigh only ab\t #ej lbs4 in/ead ( ab\t #e cwt41 z 9 ! la/ describ$2 b by means ( ! lev]s :i* int]v5e betwe5 x & ! =ce appli$1 x w s]ve to e/imate a =ce equal to #f cwt41 & might obvi\sly be made to g to a mu* great] ext5t1 by v>y+ ! ratio ( ! l5g? ( ! arms ( ! lev]s4 ,,on ,,comp5sation ,,p5dulums4 7#ccf47 ,x is said ( ,galileo t1 :5 v "y1 he obs]v$ a lamp susp5d$ f ! ro( ( a *ur* at ,pisa1 sw++ backw>ds & =w>ds ) a p5dul\s motion4 ,?is1 if x _h be5 rem>k$ at all by an un$ucat$ m9d1 w\ld1 mo/ probably1 h be5 pass$ by z a common occurr5ce1 unwor?y ( ! slighte/ notice2 b to ! m9d imbu$ ) sci5ce no incid5t is insignificant2 & a circum/ance app>5tly ! mo/ trivial1 :5 subject$ to ! giant =ce ( exp&$ intellect1 may become ( imm5se importance to ! improvem5t & to ! well-be+ ( man4 ,! fall ( an apple1 x is said1 sugge/$ to ,newton ! !ory ( gravitation1 & 8 p[]ful m9d spe$ily ext5d$ to all creation t great law :i* br+s an apple to ! gr\nd4 ,! sw++ ( a lamp 9 a *ur* at ,pisa1 view$ by ! pi]c+ intellect ( ,galileo1 gave rise to an in/rum5t :i* af=ds ! mo/ p]fect measure ( "t1 :i* s]ves to det]m9e ! figure ( ! e>?1 & :i* is insep>ably connect$ ) all ! ref9em5ts ( mod]n a/ronomy4 ,! prop]ties ( ! p5dulum1 & ! mann] 9 :i* x s]ves to measure "t1 h be5 fully expla9$ 9 *apt] xi42 & if a sub/ance c\ld be f\nd n susceptible ( any *ange 9 its dim5sions f a *ange ( temp]ature1 no?+ m w\ld be necess>y1 z ! c5tre ( oscillation w\ld always rema9 at ! same di/ance f ! po9t ( susp5sion4 ,z e kn[n sub/ance1 h[ev]1 exp&s ) heat1 & contracts ) cold1 ! l5g? ( ! p5dulum w v>y ) e alt]ation ( temp]ature1 & ?us ! "t ( its vibration w suff] a correspond+ *ange4 ,! effect ( a diff]5ce ( temp]ature ( #be1 or t :i* usually occurs betwe5 w9t] & summ]1 w\ld occasion a clock furni%$ ) a p5dulum hav+ an iron rod to ga9 or lose six seconds 9 tw5ty-f\r h\rs4 ,x became1 !n1 highly important to discov] "s means ( c\nt]act+ ?is v>iation to :i* ! l5g? ( ! p5dulum 0 liable1 or1 9 o!r words1 to devise a me?od by :i* ! c5tre ( oscillation %\ld1 "u e *ange ( temp]ature1 rema9 at ! same di/ance f ! po9t ( susp5sion3 happily1 ! diff]5ce 9 ! rate ( expansion ( diff]5t metals pres5t$ a ready means ( effect+ ?is4 ,graham1 9 ! ye> #agae1 made sev]al exp]im5ts to asc]ta9 ! relative expansions ( v>i\s metals1 ) a view ( avail+ himself ( ! diff]5ce ( ! expansions ( two or m ( !m :5 oppos$ to ea* o!r1 to con/ruct a comp5sat+ p5dulum4 ,b ! diff]5ce he f\nd 0 s small1 t he gave up all hope ( be+ able to accompli% 8 object 9 t way4 ,kn[+1 h[ev]1 t m]cury 0 mu* m affect$ by a giv5 *ange ( temp]ature ?an any o!r sub/ance1 he saw t if ! m]cury c\ld be made to asc5d :ile ! rod ( ! p5dulum became long]1 & vice v]s1 ! c5tre ( oscillation might always be kept at ! same di/ance f ! po9t ( susp5sion4 ,?is idea happily gave bir? to ! m]curial p5dulum1 :i* is n[ 9 v g5]al use4 ,illu/ration3 ,captn4 ,kat]1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,9 ! mean "t1 ,graham's sugge/ion excit$ ! +5uity ( ,h>rison1 orig9ally a c>p5t] at ,b>ton 9 ,l9coln%ire1 :o1 9 #agbf1 produc$ a p5dulum =m$ ( p>allel brass & /eel rods1 kn[n by ! "n ( ! gridiron p5dulum4 ,9 ! m]curial p5dulum1 ! bob or weight is ! mat]ial af=d+ ! comp5sation2 b 9 ! gridiron p5dulum ! object is atta9$ by ! great] expansion ( ! brass rods1 :i* raise ! bob upw>ds t[>ds ! po9t ( susp5sion z mu* z ! /eel rods elongate d[nw>ds4 ,9 ! pres5t article1 we %all describe su* comp5sation p5dulums z appe> to u likely to answ] be/ 9 practice2 & we tru/ we %all be able to simplify ! subject s z to r5d] a k ( ma!matics 9 ! con/ruction ( ?is important in/rum5t unnecess>y4 ,! foll[+ table conta9s ! l9e> expansion ( v>i\s sub/ances 9 p>ts ( _! l5g?1 occasion$ by a *ange ( temp]ature am\nt+ to "o degree4 ,we h tak5 ! lib]ty ( extract+ x f a v valuable pap] by ,f4 ,bailey1 ,esq41 on ! m]curial comp5sation p5dulum1 publi%$ 9 ! ,memoirs ( ! ,a/ronomical ,society ( ,london = #ahbd4 ,,table ,i4 ,l9e> ,expansion ( v>i\s ,sub/ances = ,"o ,degree ( ,fahr5heit's ,!rmomet]4 ---------------------------------------- ------------------ ,sub/ances4 ,expansions4 ,au?ors4 ---------------------------------------- ------------------ ,:ite ,deal1 #jjjjjbbfhe ,capta9 ,kat]4 #jjjjjbhddd ,dr4 ,/ruve4 ,engli% ,fl9t ,glass1 #jjjjjdghhg ,dulong & ,petit4 ,iron 7ca/71 #jjjjjfagjj ,g5]al ,roy4 #jjjjjfeffh ,dulong & ,petit4 ,iron 7wire71 #jjjjjfhfac ,lavoisi] & ,l4 ,iron 7b>71 #jjjjjfihdd ,hassl>4 ,/eel 7rod71 #jjjjjfceif ,g5]al ,roy4 ,commission]s ( ,brass1 #jjjjajddjj ,weights & ,measures --mean ( sev]al exp]im5ts4 ,lead1 #jjjjaeibei ,smeaton4 ,z9c1 #jjjjafcdbf ,ditto4 ,z9c 7hamm]$71 #jjjjagbfhe ,ditto4 ,m]cury 9 bulk1 #jjjajjaj ,dulong & ,petit4 ---------------------------------------- ------------------ ,f ?is table x is easy to det]m9e ! l5g? ( a rod ( any sub/ance ! expansion ( :i* %all be equal to t ( a rod ( giv5 l5g? ( any o!r sub/ance4 ,! l5g?s ( su* rods w be inv]sely proportionate to _! expansions4 ,if1 !re=e1 we divide ! less] expansion by ! great] 7suppos+ ! rod ! l5g? ( :i* is giv5 to be made ( ! less] expansible mat]ial71 & multiply ! giv5 l5g? by ?is quoti5t1 we %all h ! requir$ l5g? ( a rod1 ! expansion ( :i* w be equal to t ( ! rod giv54 ,= example3--,! expansion ( a rod ( /eel be+1 f ! above table1 #jjjjjfceif1 & t ( brass1 #jjjjajddjj2 if x 7 requir$ to det]m9e ! l5g? ( a rod ( brass :i* %\ld exp& z mu* z a rod ( /eel ( #ci in*es 9 l5g?1 we h #jjjjjfceif_/jjjjajddjj #fjia1 :i*1 multipli$ by #ci1 gives #bcge in*es = ! l5g? ( brass requir$4 ,we %all "h1 9 ord] to facilitate calculation1 give ! ratio ( ! l5g?s ( su* sub/ances z may be employ$ 9 ! con/ruction ( comp5sation p5dulums4 ,,table ,,ii4 ---------------------------------------- ----------- ,/eel rod & brass comp5sation1 z #a3 #fjia ,iron wire rod & lead comp5sation1 #dcjh ,/eel rod & lead comp5sation1 #ciic ,iron wire rod & z9c comp5sation1 #cigc ,/eel rod & z9c comp5sation1 #cfhb ,glass rod & lead comp5sation1 #cjjg ,glass rod & z9c comp5sation1 #bggc ,deal rod & lead comp5sation1 #adbg ,deal rod & z9c comp5sation1 #acac ,/eel rod & m]cury 9 a /eel cyl9d]1 #jgbh ,/eel rod & m]cury 9 a glass cyl9d]1 #jgjc ,glass rod & m]cury 9 a glass cyl9d]1 #jebi ---------------------------------------- ----------- ,x is evid5t t 9 ?is table ! decimals express ! l5g? ( a rod ( ! comp5sat+ mat]ial1 ! expansion ( :i* is equal to t ( a p5dulum rod ^: l5g? is unity4 ,z we are n aw>e ( ! exi/5ce ( any "w :i* conta9s in/ructions t might enable an arti/ or an amateur to make a comp5sation p5dulum1 we %all endeav\r to give su* detail$ in=mation z may free ! subject f e difficulty4 ,! p5dulum ( a clock is g5]ally susp5d$ by a spr+1 fix$ to its upp] extremity1 & pass+ ?r\gh a slit made 9 a piece :i* is call$ ! cock ( ! p5dulum4 ,! po9t ( susp5sion is1 !re=e1 t "p ( ! spr+ :i* meets ! l[] surface ( ! cock4 ,n[ ! di/ance ( ! c5tre ( oscillation ( ! p5dulum f ?is po9t may be v>i$ 9 two ways2 ! "o by draw+ up ! spr+ ?r\gh ?is slit1 & ! o!r by rais+ ! bob ( ! p5dulum4 ,ei!r ( ^! me?ods may be practis$ 9 ! comp5sation p5dulum1 b ! =m] is subject to objections f :i* ! latt] is exempt4 ,suppose x 7 requir$ to comp5sate a p5dulum ( #ci in*es 9 l5g?1 ( /eel1 by means ( ! expansion ( a brass rod4 ,"h1 ref]r+ to fig4 #bjd41 we h ,s ,c #ci in*es 7:i* is to rema9 con/ant7 ( /eel2 ! p5dulum spr+1 pass+ ?r\gh ! cock at ,s1 is atta*$ to ano!r rod ( /eel1 :i* is fix$ to ! cross piece ,r ,a at ,a4 ,! o!r end ( ! cross piece at ,r is fa/5$ to a brass rod1 ! l[] extremity ( :i* is fix$ to ! cock ( ! p5dulum at ,b4 ,n[ ! brass rod ,b ,r mu/ exp& upw>ds1 z mu* z ! /eel rod ,a ,c exp&s d[nw>ds2 & ! l5g? ( ! brass mu/ be su* z to effect ?is1 leav+ #ci in*es ( ! /eel rod bel[ ! cock ( ! p5dulum4 ,let u fir/ try #hj in*es ( /eel4 ,multiply+ ?is by #fjia1 we h #dhgc in*es = ! l5g? ( brass1 :i* comp5sates #hj in*es ( /eel4 ,b z #dhgc in*es ( ! /eel1 equal 9 l5g? to ! brass1 w\ld 9 ?is case be above ! cock ( ! p5dulum1 x w\ld leave only #cabg in*es bel[ x1 in/ead ( #ci in*es4 ,let u n[ try #ajj in*es ( /eel4 ,?is1 multipli$ z be=e by #fjia1 gives #fjia in*es1 accord+ to ! expansions :i* we h us$1 = ! l5g? ( ! brass rod1 & leaves #ciji in*es bel[ ! cock ( ! p5dulum1 :i* is suffici5tly ne> = our pres5t purpose4 ,f :at has be5 said we may p]ceive t ! total l5g? ( ! mat]ial ( :i* ! p5dulum rod is compos$ mu/ be always equal to ! l5g? ( ! p5dulum add$ to ! l5g? ( ! comp5sation4 ,9 ?is in/ance we h effect$ our object1 by draw+ ! p5dulum-spr+ ?r\gh ! slit2 b we w n[ %[ h[ ! same ?+ may be done by mov+ ! bob ( ! p5dulum4 ,at fig4 #bje41 let ,s ,c1 z be=e1 be equal to #ci in*es4 ,let ! /eel rod ,s ,d turn (f at "r angles at ,d1 & let a rod ( brass ,b ,r1 ( #fa in*es 9 l5g?1 asc5d p]p5dicul>ly f ?is cross piece to ,r4 ,to ! upp] "p ( ! brass rod fix ano!r cross piece ,r ,a1 & f ! extremity ,a let a /eel rod desc5d to ,e1 b5d+ x z 9 ! figure till x rea*es ,c4 ,n[ ! total l5g? ( ! pieces ( /eel exp&+ d[nw>ds is equal to ,s ,d1 ,d ,f1 & ,f ,c 7am\nt+ toge!r to #ci in*es71 to :i* mu/ be add$ a l5g? ( /eel equal to t ( ! brass rod ,b ,r1 7#fa in*es71 mak+ toge!r #ajj in*es ( /eel z be=e1 ! expansion ( :i* d[nw>ds is comp5sat$ by t ( ! brass rod1 ( #fa in*es 9 l5g?1 exp&+ upw>ds4 ,?is =m1 h[ev]1 is evid5tly inconv5i5t1 f ! great l5g? ( brass & /eel :i* is c>ri$ above ! cock ( ! p5dulum2 b x is ! same ?+ :e!r ! brass & /eel be ea* 9 "o piece1 or divid$ into sev]al1 provid$ ! pieces ( /eel be all s arrang$ z to exp& d[nw>ds1 & ^? ( brass upw>ds4 ,?us1 at fig4 #bjf41 ! portions ( /eel exp&+ d[nw>ds are toge!r equal1 z be=e1 to #ajj in*es1 & ! two brass pieces exp&+ upw>ds are toge!r equal to #fa in*es4 ,s t1 9 fact1 ! two la/ =ms ( comp5sation :i* we h describ$ diff] 9 no respect f ea* o!r 9 pr9ciple1 b only 9 ! arrangem5t ( ! mat]ials4 ,! la/ is ! half ( ! gridiron p5dulum1 ! rema9+ b>s be+ m]ely duplicates ( ^? we h describ$1 & s]v+ no o!r purpose b to =m a secure frame-"w4 ,h>rison's ,gridiron ,p5dulum4 ,aft] :at has be5 said1 little m is necess>y ?an to give a repres5tation ( ?is p5dulum4 ,?is is done at fig4 #bjg41 9 :i* ! d>k] l9es repres5t ! /eel rods1 & ! light] ^? ( brass4 ,! c5tral rod is fix$ at its l[] extremity to ! middle ( ! ?ird cross piece f ! bottom1 & passes freely ?r\gh holes 9 ! cross pieces :i* are above1 :il/ ! o!r rods are secur$ ne> _! extremities to ! cross pieces by p9s pass+ ?r\gh !m4 ,9 ord] to r5d] ! :ole m secure1 ! b>s pass freely ?r\gh holes made 9 two o!r cross pieces1 ! extremities ( :i* are fix$ to ! ext]ior /eel wires4 ,z diff]5t k9ds ( ! same metal v>y 9 _! rate ( expansion1 ! p5dulum :5 f9i%$ may be f\nd ^u trial to be n duly comp5sat$4 ,9 ?is case "o or m ( ! cross pieces is %ift$ high] or l[] ^u ! b>s1 & secur$ by p9s pass$ ?r\gh fre% holes4 ,tr\ghton's ,tubul> ,p5dulum4 ,?is is an admirable modification ( ,h>rison's gridiron p5dulum4 ,x is repres5t$ at fig4 #bjh41 :]e x may be se5 t x has ! appe>ance ( a simple p5dulum1 z ! :ole comp5sation is conceal$ )9 a tube six t5?s ( an in* 9 diamet]4 ,a /eel wire1 ab\t "o t5? ( an in* 9 diamet]1 is fix$ 9 ! usual mann] to ! spr+ by :i* ! p5dulum is susp5d$4 ,?is wire passes to ! bottom ( an int]ior brass tube1 9 ! c5tre ( :i* x is firmly screw$4 ,! top ( ?is tube is clos$1 ! /eel rod pass+ freely ?r\gh a hole 9 ! c5tre4 ,into ! top ( ?is int]ior tube two /eel wires1 ( "o t5? ( an in* 9 diamet]1 are screw$ into holes made 9 t diamet]1 :i* is at "r angles to ! motion ( ! p5dulum4 ,^! wires pass d[n ! tube )\t t\*+ ei!r x or ! c5tral rod1 ?r\gh holes made 9 ! piece :i* closes ! bottom ( ! int]ior tube4 ,! l[] extremities ( ^! wires1 :i* project a little beyond ! inn] tube1 are securely fix$ 9 a piece :i* closes ! bottom ( an ext]ior brass tube1 :i* is ( su* a diamet] z j to all[ ! int]ior tube to pass freely ?r\gh x1 & ( a suffici5t l5g? to ext5d a little above x4 ,! top ( ! ext]ior tube is clos$ l t ( ! int]ior1 hav+ also a hole 9 its c5tre1 to all[ ! fir/ /eel rod to pass freely ?r\gh x4 ,into ! top ( ! ext]ior tube1 9 t diamet] :i* co9cides ) ! motion ( ! p5dulum1 a second pair ( /eel wires ( ! same diamet] z ! =m] are screw$1 _! di/ance f ! c5tral rod be+ equal to ! di/ance ( ea* f ! fir/ pair4 ,!y consequ5tly pass d[n )9 ! int]ior tube1 & ?r\gh holes made 9 ! pieces clos+ ! l[] ends ( bo? ! int]ior & ext]ior tubes4 ,! l[] ends ( ^! wires are fa/5$ to a %ort cyl9drical piece ( brass ( ! same diamet] z ! ext]ior tube1 to :i* ! bob is susp5d$ by its c5tre4 ,illu/ration3 ,captn4 ,kat]1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,fig4 #bji4 is a full siz$ section ( ! rod2 ! ?ree conc5tric circles repres5t ! two tubes1 & ! rectangul> position ( ! two pair ( wires r\nd ! middle "o is %[n by ! five small circles4 ,fig4 #baj4 is ! "p :i* closes ! upp] end ( ! int]ior tube4 ,! two small circles are ! two wires :i* proce$ f x1 & ! ?ree l>ge circles %[ ! holes ?r\gh :i* ! middle wire & ! o!r pair ( wires pass4 ,fig4 #baa4 is ! bottom ( ! int]ior tube4 ,! small circle 9 ! c5tre is :]e ! c5tral rod is fa/5$ to x1 ! o!rs ! holes = ! o!r f\r wires to pass ?r\gh4 ,fig4 #bab4 is ! "p :i* closes ! top ( ! ext]nal tube4 ,9 ! l>ge circle 9 ! c5tre a small brass tube is fix$1 :i* s]ves z a cov]+ = ! upp] "p ( ! middle wire1 & ! two small circles are to receive ! wires ( ! la/ expansion4 ,fig4 #bac4 repres5ts ! bottom ( ! ext]ior tube1 9 :i* ! small circles %[ ! places :]e ! wires ( ! second expansion are fa/5$1 & ! l>g] ones ! holes = ! o!r pair ( wires to pass ?r\gh4 ,fig4 #bad4 is a cyl9drical piece ( brass1 %[+ ! mann] 9 :i* ! l[] ends ( ! wires ( ! la/ expansion are fa/5$ to x1 & ! hole 9 ! middle is t by :i* x is p9n$ to ! c5tre ( ! bob4 ,! upp] ends ( ! two pair ( wires are1 z we h obs]v$1 fa/5$ by screw+ !m into ! pieces :i* /op up ! ends ( ! tubes1 b at ! l[] ends !y are all fix$ z repres5t$ 9 fig4 #bad4 ,! pieces repres5t$ by figs4 #bac4 & #bad4 h ea* a jo9t$ motion1 by means ( :i* ! fell[ wires ( ea* pair w\ld be equally /ret*$1 al?\gh !y 7 n exactly ( ! same l5g?4 ,! action ( ?is p5dulum is evid5tly ! same z t ( ! gridiron p5dulum1 z we h ?ree l5g?s ( /eel exp&+ d[nw>ds1 & two ( brass exp&+ upw>ds4 ,! weight ( ! p5dulum has a t5d5cy to /raight5 ! /eel rods1 & ! tubul> =m ( ! brass comp5sation effectually precludes ! fe> ( its b5d+2 an advantage n possess$ by ! gridiron p5dulum1 9 :i* brass rods are employ$4 ,mr4 ,tr\ghton1 to ! acc\nt he has giv5 ( ?is p5dulum 9 ,ni*olson's ,j\rnal1 = ,decemb]1 #ahjd1 has add$ ! l5g?s ( ! diff]5t p>ts ( :i* x 0 compos$1 & ! expansions ( brass & /eel f :i* ^! l5g?s 7 comput$4 ,! l5g? ( ! int]ior tube 0 #cai in*es1 & t ( ! ext]ior "o #cbh in*es1 to :i* mu/ be add$ #jd1 ! quantity by :i* 9 ?is p5dulum ! c5tre ( oscillation is high] ?an ! c5tre ( ! bob4 ,^! are all ( brass4 ,! p>ts :i* are ( /eel are1--! middle wire1 :i*1 includ+ #jf1 ! l5g? ( ! susp5sion spr+1 is #cic in*es4 ,! fir/ pair ( wires #cbe in*es2 & ! second pair1 #ccb in*es4 ,! expansions us$ 71 = brass #jjjjafff1 & = /eel #jjjjjffa1 9 p>ts ( _! l5g? = "o degree ( temp]ature4 ,b5z5b]g's ,p5dulum4 ,?is p5dulum is m5tion$ 9 ,ni*olson's ,j\rnal = ,april1 #ahjd1 & is tak5 f ,voigt's ,magaz9 fr d5 ,neue/5 ,zu/&e d] ,naturkunde1 vol4 iv4 p4 #ghg4 ,! comp5sation appe>s to h be5 effect$ by a s+le rod ( lead 9 ! c5tre1 ( ab\t half an in* ?ick2 ! desc5d+ rods 7 made ( ! be/ ?ick iron wire4 ,z ?is p5dulum des]ves att5tion f ! ease ) :i* x may be made1 & z o!rs :i* h s9ce be5 produc$ resemble x 9 pr9ciple1 we h giv5 a repres5tation ( x at fig4 #bae41 :]e ,a ,b ,c ,d are two rods ( iron wire rivet$ into ! cross pieces ,a ,c ,b ,d4 ,e ,f is a rod ( lead p9n$ to ! middle ( ! piece ,b ,d1 & also at its upp] extremity to ! cross piece ,g ,h1 into :i* ! second pair ( iron wires are fix$1 :i* pass d[nw>ds freely ?r\gh holes made 9 ! cross piece ,b ,d4 ,! l[] extremities ( ^! la/ iron wires are fa/5$ into ! piece ,k ,l1 :i* c>ries ! bob ( ! p5dulum4 ,to det]m9e ! l5g? ( lead necess>y = ! comp5sation1 we mu/ recollect1 z be=e1 t ! di/ance f ! po9t ( susp5sion to ! c5tre ( ! bob 7speak+ always ( a p5dulum int5d$ to vibrate seconds7 mu/ be #ci in*es4 ,let u suppose ! total l5g? ( ! iron wire to be #fj in*es2 !n1 f ! table :i* we h giv51 we h #dcjh = ! l5g? ( a rod ( lead1 ! expansion ( :i* is equival5t to t ( an iron rod ^: l5g? is unity4 ,multiply+ #fj in*es by #dcjh1 we h #behd in*es ( lead1 :i* w\ld comp5sate #fj in*es ( iron2 b ?is1 tak5 f #fj in*es1 leaves only #cdaf in/ead ( #ci in*es4 ,try+ aga91 9 l mann]1 #fhe in*es ( iron1 we f9d #bie in*es ( lead = ! l5g?1 af=d+ an equival5t comp5sation1 & :i*1 tak5 f #fhe in*es1 leaves #ci in*es4 ,! l5g? ( ! rod ( lead !n requir$ z a comp5sation 9 ?is p5dulum is ab\t #bi-a_/b in*es4 ,! writ] ( ?is article w\ld sugge/ ano!r =m = ?is p5dulum1 :i* has ! advantage ( great] simplicity ( con/ruction4 ,s ,a1 fig4 #baf41 is a rod ( iron wire1 to :i* ! p5dulum spr+ is atta*$4 ,^u ?is passes a cyl9drical tube ( lead1 #bi-a_/b in*es long1 :i* is ei!r p9n$ at its l[] extremity to ! end ( ! iron rod ,s ,a1 or re/s ^u a nut firmly screw$ ^u ! extremity ( ?is rod4 ,a tube ( %eet iron passes ov] ! tube ( lead1 & is furni%$ at top ) a flan*e1 by :i* x is support$ ^u ! lead5 tube2 or x may be fa/5$ to ! top ( ?is tube 9 any mann] t may be ?\ght conv5i5t4 ,! bob ( ! p5dulum may be ei!r pass$ ^u ! iron tube 7cont9u$ to a suffici5t l5g?7 & secur$ by a p9 pass+ ?r\gh ! c5tre ( ! bob1 or ! iron tube may be t]m9at$ by an iron wire s]v+ ! same purpose4 ,"h we h evid5tly ! same expansions upw>ds & d[nw>ds z 9 ! gridiron =m1 giv5 to ?is p5dulum by ,mr4 ,b5z5b]g1 jo9$ to ! compactness ( ,tr\ghton's tubul> p5dulum4 ,w>d's ,comp5sation ,p5dulum4 ,9 ! ye> #ahjf1 ,mr4 ,h5ry ,w>d1 ( ,bl&=d 9 ,dorset%ire1 receiv$ ! silv] m$al ( ! ,society ( ,arts = ! comp5sation p5dulum :i* we are ab\t to describe4 ,fig4 #bag4 is a side view ( ! p5dulum rod :5 toge!r4 ,h ,h & ,i ,i are two flat rods ( iron ab\t an eigh? ( an in* ?ick4 ,k ,k is a b> ( z9c plac$ betwe5 !m1 & is ne>ly a qu>t] ( an in* ?ick4 ,! corn]s ( ! iron b>s are bevell$ (f1 :i* gives !m a mu* light] appe>ance4 ,^! b>s are kept toge!r by means ( ?ree screws1 ,o ,o ,o1 :i* pass ?r\gh oblong holes 9 ! b>s ,h ,h & ,k ,k1 & screw into ! rod ,i ,i4 ,! b> ,h ,h is fa/5$ to ! b> ( z9c ,k ,k1 by ! screw m1 :i* is call$ ! adju/+ screw4 ,?is screw is tapp$ into ,h ,h1 & passes j ?r\gh ,k ,k2 b t "p ( ! screw :i* passes ,k ,k has its ?reads turn$ (f4 ,! iron b> ,i ,i has a %\ld] at its upp] end1 & re/s on ! top ( ! z9c b> ,k ,k & is :olly support$ by x4 ,!re are sev]al holes = ! screw m1 9 ord] to adju/ ! comp5sation4 ,! action ( ?is p5dulum is simil> to t la/ describ$1 ! z9c exp&+ upw>ds z mu* z ! iron rods exp& d[nw>ds1 & consequ5tly ! in/ance f ! po9t ( susp5sion to ! c5tre ( oscillation rema9s ! same4 ,illu/ration3 ,captn4 ,kat]1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,mr4 ,w>d /ates t ! expansion ( ! z9c he us$ 7hamm]$ z9c7 0 great] ?an t giv5 9 ! tables4 ,he f\nd t ! true l5g? ( ! z9c b> %\ld be ab\t #bc in*es2 our computation w\ld make x ne>ly #bf4 ,! ,comp5sation ,tube ( ,juli5 le ,roy4 ,we m5tion ?is m]ely to /ate t x is simil> 9 pr9cipal to ! app>atus repres5t$ at fig4 #bjd41 ) m]ely ?is diff]5ce1 t1 in/ead ( ! /eel rod be+ fix$ to a cross piece proce$+ f ! brass b> ,b ,r1 x is atta*$ to a cap fix$ ^u a brass tube 7?r\gh :i* x passes7 ( ! same l5g? z t ( ! brass rod ,b ,r4 ,cass9i spoke well ( ?is p5dulum1 & x 0 us$ 9 ! obs]vatory ( ,cluny ab\t ! ye> #agdh4 ,dep>cieux's ,comp5sation4 ,?is 0 contriv$ 9 ! same ye> z t inv5t$ by ,juli5 le ,roy4 ,x is repres5t$ at fig4 #bah41 :]e ,a ,b ,d ,f is a /eel b>1 ! ends ( :i* are to be fix$ to ! l[] sides ( pieces =m+ a "p ( ! cock ( ! p5dulum4 ,g ,e ,i ,h is ( brass1 & /&s ) its extremities re/+ on ! horizontal "p ,b ,d ( ! /eel frame4 ,! upp] "p ,e ,i ( ! brass frame passes above ! cock ( ! p5dulum1 & admits ! tapp$ wire ,k1 to :i* ! p5dulum spr+ is fix$ ?r\gh a squ>$ hole 9 ! middle4 ,a nut ^u ?is tapp$ wire gives ! adju/m5t = "t4 ,! spr+ passes ?r\gh ! slit 9 ! cock 9 ! usual mann]4 ,x may be easily p]ceiv$ t ?is p5dulum is 9 pr9ciple ! same z t ( ,le ,roy2 ! expansion ( ! total l5g? ( /eel ,a ,b ,s ,c d[nw>ds be+ comp5sat$ by ! equival5t expansion ( ! brass b> ,g ,e upw>ds4 ,x is1 h[ev]1 pref]able to ,le ,roy's1 because ! comp5sation is conta9$ 9 ! clock case4 ,dep>cieux _h previ\sly publi%$1 9 ! ye> #agci1 an improvem5t ( an imp]fectly comp5sat+ p5dulum1 propos$ 9 ! ye> #agcc by ,regnauld1 a clockmak] ( ,*alons4 ,9 ?is p5dulum ,dep>cieux employ$ a lev] ) unequal arms to increase ! effect ( ! expansion ( ! brass rod1 :i* 0 too %ort4 ,we may "h rem>k1 t all fix$ comp5sations are liable to ! same objection1 namely1 t ( n mov+ ) ! p5dulum1 & !re=e n tak+ precisely ! same temp]ature4 ,capta9 ,kat]'s ,comp5sation ,p5dulum4 ,9 ,ni*olson's ,j\rnal1 = ,july1 #ahjh1 is ! description ( a comp5sation p5dulum by ! writ] ( ?is article4 ,9 ?is p5dulum ! rod is ( :ite deal1 ?ree qu>t]s ( an in* wide1 & a qu>t] ( an in* ?ick4 ,x 0 plac$ 9 an ov51 & suff]$ to rema9 !re = a long "t until x became a little *>r$4 ,! ends 7 !n soak$ 9 melt$ seal+-wax2 & ! rod1 be+ clean$1 0 coat$ sev]al times ) copal v>ni%4 ,to ! l[] extremity ( ! rod a cap ( brass 0 firmly fix$1 f :i* a /rong /eel screw proce$$ = ! purpose ( regulat+ ! p5dulum = "t 9 ! usual mann]4 ,a squ>e tube ( z9c 0 ca/1 sev5 in*es long & ?ree qu>t]s ( an in* squ>e2 ! int]nal dim5sions be+ f\r t5?s ( an in*4 ,! l[] "p ( ! p5dulum rod 0 cut away on ! two sides1 s z to slide ) p]fect fre$om )9 ! tube ( z9c4 ,to ! bottom ( ?is z9c tube a piece ( brass a qu>t] ( an in* ?ick 0 sold]$1 9 :i* a circul> hole 0 made ne>ly f\r t5?s ( an in* 9 diamet]1 hav+ a screw on ! inside4 ,a cyl9d] ( z9c1 furni%$ ) a correspond+ screw on its surface1 fitt$ into ?is ap]ture1 & a ?9 plate ( brass screw$ ^u ! cyl9d]1 s]v$ z a clamp to prev5t any %ake aft] ! l5g? ( z9c necess>y = comp5sation %\ld h be5 det]m9$4 ,a hole 0 made ?r\gh ! axis ( ! cyl9d]1 ?r\gh :i* pass$ ! /eel screw t]m9at+ ! p5dulum rod4 ,an op5+ 0 made ?r\gh ! bob ( ! p5dulum1 ext5d+ to its c5tre1 to admit ! squ>e tube ( z9c :i* 0 fix$ at its upp] extremity to ! c5tre ( ! bob4 ,! p5dulum rod pass$ ?r\gh ! bob 9 ! usual mann]1 & ! :ole 0 support$ by a nut on ! /eel screw at ! extremity4 ,9 ?is =m ! comp5sation acts imm$iately ^u ! c5tre ( ! bob1 elevat+ x along ! rod z mu* z ! rod elongates d[nw>ds3 ! me?od ( calculat+ ! l5g? ( ! requir$ comp5sation is precisely ! same z t we h be=e giv54 ,assum+ ! l5g? ( ! deal rod to be #dc in*es1 & multiply+ ?is by #acac f ,table ,,ii41 we h #efd in*es = ! l5g? ( ! z9c necess>y to c\nt]act ! expansion ( ! deal4 ,! l5g? ( ! /eel screw betwe5 ! t]m9ation ( ! p5dulum rod & ! nut 0 two in*es1 & t ( ! susp5sion spr+ "o in*4 ,n[1 #c in*es ( /eel multipli$ by #cfhb w\ld give #aaj in*es = ! l5g? ( z9c :i* w\ld comp5sate ! /eel1 &1 add+ ?is to #efd in*es1 we h #fgd in*es = ! :ole l5g? ( z9c requir$4 ,9 ?is p5dulum1 ! l5g? ( ! comp5sat+ "p may be v>i$ by means ( ! z9c cyl9d] furni%$ ) a screw = t purpose4 ,! bob ( ?is p5dulum & its comp5sation are repres5t$ at fig4 #bai4 ,x has be5 object$ to ! use ( wood5 p5dulum rods1 t x is difficult1 if n impossible1 to secure !m f ! action ( moi/ure1 :i* w\ld at once be fatal to _! correct p]=mance4 ,! p5dulum n[ be=e u has1 h[ev]1 be5 go+ ) b little int]mission s9ce x 0 fir/ con/ruct$3 x is atta*$ to a sid]eal clock1 n ( a sup]ior description1 & expos$ to v consid]able v>iations ( moi/ure & dryness2 yet ! *ange 9 its rate has be5 s v trifl+ z to au?orize ! belief t moi/ure has little or no effect ^u a wood5 rod prep>$ 9 ! mann] we h describ$4 ,its rate1 "u diff]5t temp]atures1 %[s t x is ov]-comp5sat$2 ! l5g? ( ! z9c rema9+1 z /at$ 9 ,ni*olson's ,j\rnal #gdb in*es1 in/ead ( :i* x appe>s1 by our pres5t comp5sation1 t x %\ld be #fgh in*es4 ,reid's ,comp5sation ,p5dulum4 ,mr4 ,adam ,reid ( ,woolwi* pres5t$ to ! ,society ( ,arts1 9 #ahji1 a comp5sation p5dulum1 = :i* he 0 rew>d$ ) fifte5 gu9eas4 ,?is p5dulum is ! same 9 pr9ciple ) t la/ describ$2 ! rod1 h[ev]1 is ( /eel in/ead ( wood1 & ! comp5sation possesses no means ( adju/m5t4 ,?is p5dulum is repres5t$ at fig4 #bbj41 :]e ,s ,b is ! /eel rod1 a little ?ick] :]e x ent]s ! bob ,c1 & ( a loz5ge %ape to prev5t ! bob turn+1 b above & bel[ x is cyl9drical4 ,a tube ( z9c ,d passes to ! c5tre ( ! bob f bel[1 & ! bob is support$ ^u x by a piece :i* crosses its c5tre1 & :i* meets ! upp] end ( ! tube4 ,! rod be+ pass$ ?r\gh ! bob & z9c tube1 a nut is appli$ ^u a screw at ! l[] extremity ( ! rod 9 ! usual mann]4 ,if ! comp5sation %\ld be too mu*1 ! z9c tube is to be %ort5$ until x is correct4 ,! l5g? ( ! z9c tube w be ! same 9 ?is p5dulum z 9 t ( ,mr4 ,w>d--ab\t #bc in*es1 if 8 exp]im5ts are to be reli$ ^u4 ,! objection to ?is p5dulum appe>s to be its great l5g?1 :i* am\nts to #fb in*es4 ,we conceive x w\ld be pref]able to place ! z9c above ! bob1 z 9 ! modification :i* we h sugge/$ ( ,b5z5b]g's p5dulum4 ,ellicott's ,p5dulum4 ,x appe>s t ! idea ( comb9+ ! expansions ( diff]5t metals ) a lev]1 s z to =m a comp5sation p5dulum1 orig9at$ ) ,mr4 ,graham2 = ,mr4 ,%ort1 9 ! ,philosophical ,transactions = #ageb1 /ates t he 0 in=m$ by ,mr4 ,%elton1 t ,mr4 ,graham1 9 ! ye> #agcg1 made a p5dulum1 consi/+ ( ?ree b>s1 "o ( /eel betwe5 two ( brass2 & t ! /eel b> act$ ^u a lev] s z to raise ! p5dulum :5 l5g!n$ by heat1 & to let x d[n :5 %ort5$ by cold4 ,illu/ration3 ,captn4 ,kat]1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,?is p5dulum1 h[ev]1 0 f\nd ^u trial to move by j]ks1 & 0 !re=e laid aside by ! inv5tor to make way = ! m]curial p5dulum4 ,mr4 ,%ort also says t ,mr4 ,fo!r+ham1 a quak] ( ,l9coln%ire1 caus$ a p5dulum to be made1 9 ! ye> #agch or #agci1 consi/+ ( two b>s1 "o ( brass & ! o!r ( /eel1 fa/5$ toge!r by screws ) lev]s to raise or let d[n ! bob1 & t ^! lev]s 7 plac$ above ! bob4 ,mr4 ,john ,ellicott ( ,london _h made v1 accurate exp]im5ts on ! relative expansions ( sev5 diff]5t metals1 :i*1 h[ev]1 w be f\nd to diff] m or less f ! results ( ! exp]im5ts ( o!rs4 ,x is n1 h[ev]1 f ?is to be conclud$ t ,ellicott's det]m9ations 7 errone\s2 = ! expansion ( a metal w suff] consid]able *ange ev5 by ! processes to :i* x is necess>ily subject$ 9 ! con/ruction ( a p5dulum4 ,x is !re=e desirable1 :5ev] a comp5sation p5dulum is to be made1 t ! expansions ( ! mat]ials employ$ %\ld be det]m9$ aft] ! processes ( drill+1 fil+1 & hamm]+ h be5 gone ?r\gh4 ,x _h be5 object$ to ,h>rison's gridiron p5dulum1 t ! adju/m5ts ( ! rods 0 inconv5i5t1 & t ! expansion ( ! bob support$ at its l[] edge w\ld1 unless tak5 into ! acc\nt1 vitiate ! comp5sation4 ,^! consid]ations1 x is suppos$1 gave rise to ,ellicott's p5dulum1 :i* is ne>ly simil> to ^? we h j m5tion$4 ,ellicott's p5dulum is ?us con/ruct$3--,a b> ( brass & a b> ( iron are firmly fix$ toge!r at _! upp] ends1 ! b> ( brass ly+ ^u ! b> ( iron1 :i* is ! rod ( ! p5dulum4 ,^! b>s are held ne> ea* o!r by screws pass+ ?r\gh oblong holes 9 ! brass1 & tapp$ into ! iron1 & ?us ! brass is all[$ to exp& or contract freely ^u ! iron ) any *ange ( temp]ature4 ,! brass b> passes to ! c5tre ( ! bob ( ! p5dulum1 a little above & bel[ :i* ! iron is left broad] = ! purpose ( atta*+ ! lev]s to x1 & ! iron is made ( a suffici5t l5g? to pass q ?r\gh ! bob ( ! p5dulum4 ,! pivots ( two /rong /eel lev]s turn 9 two holes drill$ 9 ! broad "p ( ! iron b>4 ,! %ort arms ( ^! lev]s are 9 contact ) ! l[] extremity ( ! brass b>1 & _! long] arms support ! bob ( ! p5dulum by meet+ ! heads ( two screws :i* pass horizontally f ea* side ( ! bob t[>ds its c5tre4 ,by advanc+ ^! screws t[>ds ! c5tre ( ! bob1 ! long] arms ( ! lev] are %ort5$1 & ?us ! comp5sation may be readily adju/$4 ,at ! l[] end ( ! iron rod1 "u ! bob1 a /rong d\ble spr+ is fix$1 to support ! great] "p ( ! weight ( ! bob by its pressure upw>ds aga9/ two po9ts at equal di/ances f ! p5dulum rod4 ,mr4 ,ellicott gave a description ( ?is p5dulum to ! ,royal ,society 9 #ageb1 b he says ! ?\ght 0 execut$ 9 #agch4 ,z ?is p5dulum is v seldom met )1 we ?9k x unnecess>y to give a repres5tation ( x4 ,comp5sation by means ( a ,comp\nd ,b> ( ,/eel & ,brass4 ,sev]al comp5sations = p5dulums h be5 propos$1 by means ( a comp\nd b> =m$ ( /eel & brass sold]$ toge!r4 ,9 a b> ( ?is description1 ! brass exp&+ m ?an ! /eel1 ! b> becomes curv$ by a *ange ( temp]ature1 ! brass side becom+ convex & ! /eel concave ) heat4 ,n[1 if a b> ( ?is description h its ends re/+ on supports on ea* side ! cock ( ! p5dulum1 ! b> pass+ above ! cock ) ! brass upp]mo/1 if ! p5dulum spr+ be atta*$ to ! middle ( ! b>1 & x pass 9 ! usual mann] ?r\gh ! slit ( ! cock1 x is evid5t t1 by an increase ( temp]ature1 ! b> w become curv$ upw>ds1 & ! p5dulum spr+ be drawn upw>ds ?r\gh ! slit1 & ?us ! elongation ( ! p5dulum d[nw>ds w be comp5sat$4 ,! comp5sation may be adju/$ by v>y+ ! di/ance ( ! po9ts ( support f ! middle ( ! b>4 ,su* 0 "o ( ! modes ( comp5sation propos$ by ,ni*olson4 ,o!rs ( ! same description 7t is1 ) comp\nd b>s7 h be5 br\ght be=e ! public by ,mr4 ,?omas ,d\ghty & ,mr4 ,david ,rit*ie2 b z !y are suppos$ to be liable to _m practical objections1 we d n ?9k x requisite to describe !m m p>ticul>ly4 ,!re is1 h[ev]1 a mode ( comp5sation by means ( a comp\nd b>1 describ$ by ,m4 ,biot 9 ! fir/ volume ( 8 ,trait de ,physique1 :i* appe>s to possess consid]able m]it1 ( :i* he m5tions hav+ fir/ witness$ ! successful employm5t by ! inv5tor1 a clockmak] nam$ ,m>t94 ,at fig4 #bba41 ,s ,c1 is ! rod ( ! p5dulum1 made1 9 ! usual mann]1 ( iron or /eel2 ?is rod passes ?r\gh ! middle ( a comp\nd b> ( brass & /eel 7! brass be+ und]mo/71 :i* %\ld be furni%$ ) a %ort tube & screws1 by means ( :i*1 or by pass+ a p9 ?r\gh ! tube & rod1 x may be securely fix$ at any "p ( ! p5dulum rod4 ,two small equal weights ,w ,w slide along ! comp\nd b>1 &1 :5 _! prop] position has be5 det]m9$1 may be securely clamp$4 ,! mann] 9 :i* ?is comp5sation acts is ?us3--,suppose ! temp]ature to increase1 ! brass exp&+ m ?an ! /eel1 ! b> becomes curv$1 & its extremities c>ry+ ! weights ,w & ,w are elevat$1 & ?us ! place ( ! c5tre ( oscillation is made to approa* ! po9t ( susp5sion z mu*1 :5 ! comp5sation is prop]ly adju/$1 z x _h rec$$ f x by ! elongation ( ! p5dulum rod4 ,!re are ?ree me?ods ( adju/+ ?is comp5sation3 ! fir/1 by increas+ or dim9i%+ ! weights ,w & ,w2 ! second1 by v>y+ ! di/ance ( ! weights ,w & ,w f ! middle ( ! b>2 & ! ?ird1 by v>y+ ! di/ance ( ! b> f ! bob ( ! p5dulum1 tak+ c>e n to pass ! middle ( ! rod4 ,! effect ( ! comp5sation is great] z ! weights ,w & ,w are great] or m di/ant f ! c5tre ( ! b>1 & also z ! b> is ne>] to ! bob ( ! p5dulum4 ,m4 ,biot says t he & ,m4 ,mat?ieu employ$ a p5dulum ( ?is k9d = a long "t 9 mak+ a/ronomical obs]vations 9 :i* !y 7 desir\s ( atta9+ an extreme degree ( precision1 & t !y f\nd its rate to be always p]fectly regul>4 ,9 all ! p5dulums :i* we h describ$1 ! bob is suppos$ to be fix$ to ! rod by a p9 pass+ ?r\gh its c5tre1 & ! adju/m5t = "t is to be made by means ( a small weight slid+ ^u ! rod4 ,( ! ,m]curial ,p5dulum4 ,we h be5 guid$1 9 our arrangem5t ( ! p5dulums :i* we h describ$1 by ! simil>ity 9 ! mode ( comp5sation employ$2 & we h n[ to treat ( t me?od ( comp5sation :i* is effect$ by ! expansion ( ! mat]ial ( :i* ! bob itself ( ! p5dulum is compos$4 ,on ?is subject1 z we h be=e obs]v$1 an admirable pap]1 f ! p5 ( ,mr4 ,francis ,baily1 may be f\nd 9 ! ,memoirs ( ! ,a/ronomical ,society ( ,london1 :i* leaves no?+ to be desir$ by ! ma!matical read]4 ,b z our object is to simplify1 & to r5d] our subjects z popul> z may be1 we mu/ endeav\r to sub/itute = ! p]fect accuracy :i* ,mr4 ,baily's pap] pres5ts1 su* rules z may be f\nd n only readily intelligible1 b practically applicable1 )9 ! limits ( ^? inevitable errors :i* arise f a want ( k ( ! exact expansion ( ! mat]ials employ$4 ,at fig4 #bbb41 let ,s ,b repres5t ! rod ( a p5dulum1 & ,f ,c ,b a metallic tube or cyl9d]1 support$ by a nut at ! extremity ( ! p5dulum rod1 9 ! usual mann]1 & hav+ a great] expansibility ?an t ( ! rod4 ,n[ ,c1 ! c5tre ( gravity1 suppos+ ! rod to be )\t weight1 w be 9 ! middle ( ! cyl9d]2 & if ,c ,b1 or half ! cyl9d]1 be ( su* a l5g? z to exp& upw>ds z mu* z ! p5dulum rod ,s ,b exp&s d[nw>ds1 x is evid5t t ! c5tre ( gravity ,c w rema91 "u any *ange ( temp]ature1 at ! same di/ance f ! po9t ( susp5sion ,s4 ,m4 ,biot imag9$ t1 9 effect+ ?is1 a comp5sation suffici5tly accurate w\ld be obta9$2 b ,mr4 ,baily has %[n t ?is is by no means ! fact4 ,let u suppose ! place ( ! c5tre ( oscillation to be at ,o1 ab\t ?ree or f\r t5?s ( an in*1 9 a p5dulum ( ! usual con/ruction1 bel[ ! c5tre ( gravity4 ,n[1 ! object ( ! comp5sation is to pres]ve ! di/ance f ,s to ,o inv>iable1 & n ! di/ance f ,s to ,c4 ,! di/ance ( ! c5tre ( oscillation v>ies ) ! l5g? ( ! cyl9d] ,f ,b1 & h5ce suff]s an alt]ation 9 its di/ance f ! po9t ( susp5sion by ! elongation ( ! cyl9d]1 al?\gh ! di/ance ( ! c5tre ( gravity ,c f ! po9t ( susp5sion rema9s unalt]$4 ,we %all endeav\r to r5d] ?is p]fectly famili>4 ,suppose a metallic cyl9d]1 #f in*es long1 to be susp5d$ by a ?read #cf in*es long1 ?us =m+ a p5dulum 9 :i* ! di/ance ( ! c5tre ( gravity f ! po9t ( susp5sion is #ci in*es3 ! c5tre ( oscillation 9 su* a p5dulum w be ne>ly "o t5? ( an in* bel[ ! c5tre ( gravity4 ,n[ let u imag9e cyl9drical portions ( equal l5g?s to be add$ to ea* end ( ! cyl9d]1 until x rea*es ! po9t ( susp5sion2 we %all !n h a cyl9d] ( #gh in*es 9 l5g?1 ! c5tre ( gravity ( :i* w /ill be at ! di/ance ( #ci in*es f ! po9t ( susp5sion4 ,b x is well kn[n t ! c5tre ( oscillation ( su* a cyl9d] is at ! di/ance ( ab\t two ?irds ( its l5g? f ! po9t ( susp5sion4 ,! c5tre ( oscillation1 !re=e1 has be5 remov$1 by ! elongation ( ! cyl9d]1 ab\t #ac in*es bel[ ! c5tre ( gravity1 :il/ ! c5tre ( gravity has rema9$ /ation>y4 ,n[ ! same ?+ z t :i* we h j describ$ takes place1 ?\gh 9 a v m9or degree1 ) our =m] cyl9d]1 employ$ z a comp5sat+ bob to a p5dulum4 ,! rod exp&s d[nw>ds1 ! c5tre ( gravity rema9s at ! same di/ance f ! po9t ( susp5sion1 & ! cyl9d] elongates bo? above & bel[ ?is po9t2 ! consequ5ce ( :i* is1 t ?\gh ! c5tre ( gravity has rema9$ /ation>y1 ! di/ance ( ! c5tre ( oscillation f ! po9t ( susp5sion has increas$4 ,x is1 !re=e1 evid5t t ! l5g? ( ! comp5sation mu/ be su* z to c>ry ! c5tre ( gravity a little ne>] to ! po9t ( susp5sion ?an x 0 be=e ! expansion took place2 by :i* means ! c5tre ( oscillation w be re/or$ to its =m] di/ance f ! po9t ( susp5sion4 ,let u suppose ! expansions to h tak5 place1 & t ! c5tre ( gravity1 rema9+ at ! same di/ance f ! po9t ( susp5sion1 ! c5tre ( oscillation is remov$ to a great] di/ance1 z we h be=e expla9$4 ,x is well kn[n t ! product obta9$ by multiply+ ! di/ance f ! po9t ( susp5sion to ! c5tre ( gravity1 by ! di/ance f ! c5tre ( gravity to ! c5tre ( oscillation1 is a con/ant quantity2 if1 !re=e1 ! di/ance f ! c5tre ( gravity to ! po9t ( susp5sion be less5$1 ! di/ance f ! c5tre ( gravity to ! c5tre ( oscillation w be proportionally1 ?\gh n equally1 increas$1 & ! c5tre ( oscillation w1 !re=e1 be elevat$4 ,we see1 !n1 if we elevate ! c5tre ( gravity precisely ! requisite quantity1 by employ+ a suffici5t l5g? ( ! comp5sat+ mat]ial1 t al?\gh ! di/ance f ! c5tre ( gravity to ! po9t ( susp5sion is less5$1 yet ! di/ance f ! po9t ( susp5sion to ! c5tre ( oscillation w suff] no *ange4 ,! foll[+ rule = f9d+ ! l5g? ( ! comp5sat+ mat]ial 9 a p5dulum ( ! k9d we h be5 consid]+ w be f\nd suffici5tly accurate = all practical purposes3-- ,f9d 9 ! mann] be=e direct$ ! l5g? ( ! comp5sat+ mat]ial1 ! expansion ( :i* w be equal to t ( ! rod ( ! p5dulum4 ,d\ble ?is l5g?1 & increase ! product by its "o-t5? "p1 :i* w give ! total l5g? requir$4 ,we %all give examples ( ?is z we proce$4 ,graham's ,m]curial ,p5dulum4 ,x 0 9 ! ye> #agba t ,graham fir/ put up a p5dulum ( ?is description1 & subject$ x to ! te/ ( exp]im5t2 b x appe>s to h be5 aft]w>ds set aside to make way = ,h>rison's gridiron p5dulum1 or = o!rs ( a simil> description4 ,= "s ye>s pa/1 h[ev]1 its m]its h be5 m g5]ally kn[n1 & x is n surpris+ t x %\ld be consid]$ z pref]able to o!rs1 bo? f ! simplicity ( its con/ruction1 & ! p]fect ease ) :i* ! comp5sation may be adju/$4 ,we h already allud$ to ,mr4 ,baily's v able pap] on ?is p5dulum1 & we %all take ! lib]ty ( extract+ f x ! foll[+ description3-- ,at fig4 #bbc4 is a draw+ ( ! m]curial p5dulum1 z con/ruct$ 9 ! mann] propos$ by ,mr4 ,baily4 8,! rod ,s ,f is made ( /eel1 & p]fectly /raight2 its =m may be ei!r cyl9drical1 ( ab\t a qu>t] ( an in* 9 diamet]1 or a flat b>1 ?ree eigh?s ( an in* wide1 & "o eigh? ( an in* ?ick3 its l5g? f ,s to ,f1 t is1 f ! bottom ( ! spr+ to ! bottom ( ! rod at ,f1 %\ld be #cd in*es4 ,! l[] "p ( ?is rod1 :i* passes ?r\gh ! top ( ! /irrup1 & ab\t half an in* above & bel[ ! same1 mu/ be =m$ into a co>se & deep screw1 ab\t two t5?s ( an in* 9 diamet]1 & hav+ ab\t ?irty turns 9 an in*4 ,a /eel nut ) a mill$ head mu/ be plac$ at ! end ( ! rod1 9 ord] to support ! /irrup2 & a simil> nut mu/ also be plac$ on ! rod above ! head ( ! /irrup1 9 ord] to screw firmly d[n on ! same1 & ?us secure x 9 its position1 aft] x has be5 adju/$ ne>ly to ! requir$ rate4 ,^! nuts are repres5t$ at ,b & ,c4 ,a small slit is cut 9 ! rod1 :]e x passes ?r\gh ! head ( ! /irrup1 ?r\gh :i* a /eel p9 ,e is screw$1 9 ord] to keep ! /irrup f turn+ r\nd on ! rod4 ,! /irrup itself is also made ( /eel1 & ! side pieces %\ld be ( ! same =m z ! rod1 9 ord] t !y may readily acquire ! same temp]ature4 ,! top ( ! /irrup consi/s ( a flat piece ( /eel1 %ap$ z 9 ! draw+1 some:at m ?an ?ree eigh?s ( an in* ?ick4 ,?r\gh ! middle ( ! top 7:i* at ?is "p is ab\t "o in* deep7 a hole mu/ be drill$ suffici5tly l>ge to enable ! screw ( ! rod to pass freely1 b )\t %ak+4 ,! inside height ( ! /irrup f ,a to ,d may be #h-a_/b in*es1 & ! inside wid? betwe5 ! b>s ab\t ?ree in*es4 ,! bottom piece %\ld be ab\t ?ree eigh?s ( an in* ?ick1 & holl[$ out ne>ly a qu>t] ( an in* deep1 s z to admit ! glass cyl9d] freely4 ,?is glass cyl9d] %\ld h a brass or iron cov] ,g1 :i* %\ld fit ! m\? ( x freely1 ) a %\ld] project+ on ea* side1 by means ( :i* x %\ld be screw$ to ! side b>s ( ! /irrup1 & ?us be secur$ always 9 ! same position4 ,?is cap %\ld n press on ! glass cyl9d]1 s z to prev5t its expansion4 ,! measures above giv5 may require a slight modification1 accord+ to ! weight ( ! m]cury employ$1 & ! magnitude ( ! cyl9d]3 ! f9al adju/m5t1 h[ev]1 may be safely left to ! arti/4 ,"s p]sons h recomm5d$ t a circul> piece ( ?ick plate glass %\ld float on ! m]cury1 9 ord] to pres]ve its surface uni=mly level4#g ,! "p at ! bottom m>k$ ,h is a piece ( brass fa/5$ ) screws to ! front ( ! bottom ( ! /irrup1 ?r\gh a small hole1 9 :i* a /eel wire or common ne$le is pass$1 9 ord] to indicate 7on a scale affix$ to ! case ( ! clock7 ! arc ( vibration4 ,?is wire %\ld m]ely re/ 9 ! hole1 :]eby x may be easily remov$ :5 x is requir$ to deta* ! p5dulum f ! clock1 9 ord] t ! /irrup might !n /& securely on its base4 ,"o ( ! screw holes %\ld be r l>g] ?an ! body ( ! screw1 9 ord] to admit ( a small adju/m5t1 9 case ! /eel wire %\ld n /& exactly p]p5dicul> to ! axis ( motion4 ,! scale %\ld be divid$ into degrees1 & n in*es1 obs]v+ t ) a radius ( #dd in*es 7! e/imat$ di/ance f ! b5d ( ! spr+ to ! end ( ! /eel wire7 ! l5g? ( ea* degree on ! scale mu/ be #jgfh in*40 #g ,! v>iation produc$ 9 ! height ( ! column ( m]cury 7suppos$ to be #f-a_/b in*es high7 by an alt]ation ( #af 9 ! temp]ature w be only #a_/ajj ( an in*1 or 9 o!r words1 #a_/ajj ( an in* w be ! total v>iation f its mean /ate1 by an alt]ation ( #cb 9 ! temp]ature4 ,x is !re=e probable t1 9 mo/ cases ( mod]ate alt]ation 9 ! temp]ature1 ! c5tre only ( ! column ( m]cury is subject to elevation & depression1 :il/ ! ext]ior p>ts rema9 atta*$ to ! sides ( ! glass vessel4 ,x 0 ) a view to obviate ?is inconv5i5ce t ,h5ry ,br[ne1 ,esq4 ( ,portl& ,place 7,i believe7 fir/ sugge/$ ! piece ( float+ glass4 ,9 ord] to det]m9e ! l5g? ( ! m]curial column necess>y to =m ! comp5sation = ?is p5dulum1 we mu/ proce$ 9 ! foll[+ mann]3-- ,let u suppose ! l5g? ( ! /eel rod & /irrup toge!r to be #db in*es4 ,! absolute expansion ( ! m]cury is #jjjajjaj2 b x is n ! absolute expansion1 b ! v]tical expansion 9 a glass cyl9d]1 :i* is requir$1 & ?is w evid5tly be influ5c$ by ! expansion ( ! base ( ?is cyl9d]4 ,x is easily demon/rable t1 if we multiply ! l9e> expansion ( any sub/ance 7always suppos$ to be a v small "p ( its l5g?7 by #c1 we may 9 all cases take ! result = ! cubical or absolute expansion ( su* sub/ance4 ,9 l mann]1 if we multiply ! l9e> expansion by #b1 we %all h ! sup]ficial expansion4 ,if we want ! app>5t expansion ( m]cury1 ! absolute or cubical expansion ( ! glass vessel mu/ be d$uct$ f ! absolute expansion ( ! m]cury1 :i* w leave its excess or app>5t expansion4 ,9 l mann]1 d$uct+ ! sup]ficial expansion ( glass f ! absolute expansion ( m]cury1 we %all h its relative v]tical expansion4 ,n[1 tak+ ! rate ( expansion ( glass to be #jjjjjdgi1 & multiply+ x by #b1 ! relative v]tical expansion ( ! m]cury 9 ! glass cyl9d] w be #jjjajjaj - #jjjjjieh #jjjjijeb4 ,! expansion ( a /eel rod1 accord+ to our table1 is #jjjjjfceif2 :i*1 divid$ by #jjjjijeb1 gives #jgjc = ! l5g? ( a column ( m]cury1 ! expansion ( :i* is equal to t ( a /eel rod ^: l5g? is unity4 ,we h n[ to multiply #db in*es by #jgjc1 :i* gives #bie in*es2 & ?is1 d$uct$ f #db1 leaves #cia in*es2 s t ! l5g? ( rod we h *os5 is suffici5tly ne> ! tru?4 ,n[1 d\ble #bie in*es1 & add "o t5? ( its product1 & we %all h #fdi in*es = ! l5g? ( ! m]curial column =m+ ! requisite comp5sation4 ,mr4 ,baily's m accurate calculation gives #fca in*es4 ,a m]curial comp5sation p5dulum may be =m$1 hav+ a cyl9d] ( /eel or iron1 ) its top con/ruct$ 9 ! same mann] z ! top ( ! /irrup1 s z to receive ! screw ( ! rod4 ,to f9d ! l5g? ( ! m]curial column necess>y 9 a p5dulum ( ?is description 7t is1 ) a cyl9d] made ( /eel71 we mu/ d\ble ! l9e> expansion ( /eel1 & take x f ! absolute expansion ( m]cury to obta9 ! relative v]tical expansion ( ! m]cury4 ,?is w be #jjjajjaj - #jjjjabgb #jjjjhgch2 &1 proce$+ z be=e1 we h #jjjjjfceif_/jjjjhgch #jgbgi4 ,let ! l5g? ( ! /eel rod be1 z be=e1 #db in*es4 ,multiply+ ?is by #jgbgi1 we h #cjeg1 :i* be+ d\bl$1 & "o t5? ( ! product add$1 we obta9 #fgb in*es = ! l5g? ( ! comp5sat+ m]curial column2 :i* ,mr4 ,baily /ates to be #fei4 ,a m]curial comp5sation p5dulum hav+ a rod ( glass has be5 employ$ by ! writ] ( ?is article1 :o has _h reason to ?9k well ( its p]=mance4 ,its *eapness & simplicity mu* recomm5d x4 ,x is m]ely a cyl9d] ( glass ( ab\t #g in*es 9 dep?1 & #b-a_/b in*es diamet]1 t]m9at$ by a long neck1 :i* =ms ! rod ( ! p5dulum1 ! :ole bl[n 9 "o piece4 ,a cap ( brass is clamp$ by means ( screws to ! top ( ! rod1 & to ?is ! p5dulum spr+ is p9n$4 ,we h unque/ionable au?ority = say+1 t ! m]curial p5dulum ( ! usual con/ruction1 t is1 ) a /eel rod & glass cyl9d]1 is n affect$ by a *ange ( temp]ature simultane\sly 9 all its p>ts4 ,n[1 ! p5dulum ( :i* we are treat+ be+ =m$ ?r\gh\t ( ! same mat]ial 9 a s+le piece1 & 9 e "p ( ! same ?ickness1 x is presum$ x _c exp& 9 a l9e> direction1 until ! temp]ature has p5etrat$ to ! :ole int]ior surface ( ! glass1 :5 x is rapidly diffus$ ?r\gh ! mass ( m]cury4 ,m4 ,biot m5tions t a p5dulum ( ?is k9d 0 =m]ly us$ 9 ,france1 & expresses 8 surprise t x 0 no long] employ$1 z he _h he>d x v highly spok5 (4 ,! writ] ( ?is article has also us$ a p5dulum ) a glass rod1 :i* diff]s f t we h j m5tion$1 9 hav+ ! l[] end ( ! rod firmly fix$ 9 a socket atta*$ to ! c5tre ( a circul> iron plate1 on ! circumf]5ce ( :i* a screw is cut1 :i* fits into a coll> ( iron1 support+ ! cyl9d] 7to :i* x is cem5t$7 by means ( a circul> lip4 ,?is arrangem5t1 ?\gh p]haps less p]fect ?an t we h j describ$1 ! p5dulum n be+ 9 "o piece1 has ! advantage ( all[+ a circul> plate ( glass to be plac$ ^u ! surface ( ! m]cury1 z practis$ by ,mr4 ,br[ne4 ,to det]m9e ! l5g? ( a column ( m]cury = a glass p5dulum1 let u suppose ! glass1 includ+ ! cyl9d]1 to be #da in*es 9 l5g?4 ,multiply+ ?is by #jebi1 ! numb] tak5 f ,table ,,ii4 = a glass rod & m]cury 9 a glass cyl9d]1 we h #bag in*es = ! uncorrect$ l5g? ( m]cury1 :i* comp5sates #da in*es ( glass4 ,suppose ! /eel spr+ to be "o in* & a half long3 multiply+ ?is by #jgjc1 ! appropriate decimal tak5 f ,table ,,ii41 we h #ja1 ! l5g? ( m]cury due to ! /eel1 mak+ ) ! =m] #bbg in*es1 :i*1 be+ d\bl$1 & ! product increas$ by its "o-t5? "p1 we obta9 five in*es = ! l5g? ( ! requir$ column ( m]cury4 ,comp5sation ,p5dulum ( ,wood & ,lead1 on ! ,pr9ciple ( ! ,m]curial ,p5dulum4 ,if by any contrivance wood c\ld be r5d]$ imp]vi\s to moi/ure1 x w\ld af=d "o ( ! mo/ conv5i5t sub/ances kn[n = a comp5sation p5dulum4 ,x does n appe> t suffici5t exp]im5ts h be5 made ^u ?is subject to decide ! "q4 ,mr4 ,br[ne ( ,portl& ,place1 :o has devot$ mu* ( 8 "t & att5tion to ! mo/ delicate enquiries ( ?is k9d1 has1 we believe1 f\nd t if a teak rod is well gild$1 x w n aft]w>ds be affect$ by moi/ure4 ,at all ev5ts1 x makes a f> sup]ior p5dulum1 :5 ?us prep>$1 to :at x does :5 su* prep>ation is omitt$4 ,mr4 ,baily1 9 ! pap] we h be=e allud$ to1 proposes an economical p5dulum to be con/ruct$ by means ( a lead5 cyl9d] & a deal rod4 ,he pref]s lead to z9c1 on acc\nt ( its inf]ior price1 & ! ease ) :i* x may be =m$ into ! requir$ %ape2 & z !re is no consid]able diff]5ce 9 _! rates ( expansion1 x is equally applicable to ! purpose4 ,let ! l5g? ( ! deal rod be tak5 at #df in*es4 ,!n1 to f9d ! l5g? ( ! cyl9d] ( lead to comp5sate ?is1 we h1 9 ,table ,,ii41 #adbg = su* a p5dulum2 :i*1 be+ multipli$ by #df1 ! product d\bl$1 & "o t5? ( ! result add$ to x1 gives #addd in*es = ! l5g? ( ! lead5 cyl9d]4 ,mr4 ,baily's comp5sation gives #adc in*es4 ,illu/ration3 ,captn4 ,kat]1 del4 ,h4 ,adl>d1 sc4 ,london1 ,pubd4 by ,longman ,co4 ,! rod is recomm5d$ to be made ( ab\t ?ree eigh?s ( an in* 9 diamet]3 ! lead5 cyl9d] is to be ca/ ) a hole ?r\gh its c5tre1 :i* w admit ) p]fect fre$om ! cyl9drical end ( ! rod4 ,! cyl9d] is support$ ^u a nut1 :i* screws on ! end ( ! rod 9 ! usual mann]4 ,?is p5dulum is repres5t$ at fig4 #bbd4 ,mr4 ,baily proposes t ! p5dulum %\ld be adju/$ ne>ly to ! giv5 rate by means ( ! screw at ! bottom1 & t ! f9al adju/m5t be made by means ( a slid] mov+ along ! rod4 ,inde$1 ?is is a means ( adju/m5t :i* we w\ld recomm5d to be employ$ 9 e p5dulum4 ,smeaton's ,p5dulum4 ,we %all conclude our acc\nt ( comp5sation p5dulums ) a description ( t inv5t$ by ,mr4 ,smeaton4 ,! comp5sation = temp]ature 9 ?is p5dulum is effect$ by comb9+ ! two modes1 :i* h be5 s fully describ$ 9 ! prec$+ "p ( ?is article4 ,! p5dulum rod is ( solid glass1 & is furni%$ ) a /eel screw & nut at ! bottom 9 ! usual mann]4 ,^u ! glass rod a holl[ cyl9d] ( z9c1 ab\t ! eigh? ( an in* ?ick1 & ab\t #ab in*es long1 passes freely1 & re/s ^u ! nut at ! bottom ( ! p5dulum rod4 ,ov] ! z9c cyl9d] passes a tube made ( %eet-iron4 ,! edge ( ?is tube at ! top is turn$ inw>ds1 & is not*$ s z to all[ ( ?is be+ effect$4 ,a flan*e is ?us =m$1 by :i* ! iron tube is support$1 ^u ! z9c cyl9d]4 ,! l[] edge ( ! iron tube is turn$ outw>ds1 s z to =m a base de/9$ to support a lead5 cyl9d]1 :i* we are ab\t to describe4 ,a cyl9d] ( lead1 r m ?an #ab in*es long1 is ca/ ) a hole ?r\gh its axis1 ( su* a diamet] z to all[ ( its slid+ freely1 b )\t %ake1 ^u ! iron tube ov] :i* x passes1 & by ! l[] extremity ( :i* x is support$4 ,n[ ! z9c1 re/+ ^u ! nut & exp&+ upw>ds1 w raise ! :ole ( ! rema9+ "p ( ! comp5sation4 ,?is expansion upw>ds w be slightly c\nt]act$ by ! less] expansion d[nw>ds ( ! iron tube1 :i* c>ries ) x ! lead5 cyl9d]4 ,! cyl9d] ( lead n[ acts ^u ! pr9ciple ( ! m]curial p5dulum1 &1 exp&+ upw>ds1 contributes t :i* 0 want+ to re/ore ! c5tre ( oscillation to its prop] di/ance f ! po9t ( susp5sion4 ,?is p5dulum1 we h be5 in=m$1 does well 9 practice1 & we are n aw>e t any description ( x has be5 be=e publi%$4 ,! me?od ( calculat+ ! l5g? ( ! tubes requir$ to =m ! comp5sation is v simple2 no?+ m is necess>y ?an to f9d ! l5g? ( z9c1 ! expansion ( :i* is equal to t ( ! p5dulum rod4 ,let ! p5dulum rod be compos$ ( #dc in*es ( glass1 ! spr+ be+ an in* & a half long1 & ! screw betwe5 ! end ( ! glass rod & ! nut half an in*1 mak+ 9 ! :ole two in*es ( /eel & #dc in*es ( glass4 ,n[ to f9d ! l5g? ( z9c t w comp5sate ! glass1 we h1 f ,table ,,ii41 = glass & z9c #bggc1 :i*1 multipli$ by #dc1 gives #aaib in*es4 ,9 l mann] we obta9 z a comp5sation = two in*es ( /eel #jgd ( z9c1 :i*1 add$ to #aaib1 gives #abff in*es = ! total l5g? ( ! z9c cyl9d]4 ,n[ if ! iron tube & ! lead cyl9d] be ea* made ( ! same l5g? z ! z9c1 & arrang$ z we h describ$1 ! comp5sation w be p]fect4 ,to prove ?is1 f9d1 by means ( ! expansions giv5 9 ,table ,i41 ! actual expansion ( ea* ( ! sub/ances employ$ 9 ! p5dulum1 & we %all h ! foll[+ results3-- ,! expansion ( #abff in*es ( z9c exp&+ upw>ds is #jjjbahf ,d$uct t ( #abff in*es ( iron exp&+ d[nw>ds #jjjjhfi -------- ,rema9+ effect ( expansion upw>ds1 ref]r$ to ! l[] extremity ( ! iron tube #jjjacag ,n[1 = ! lead4--,on ! pr9ciple ( ! m]curial comp5sation1 subtract "o t5? "p ( ! l5g? ( ! cyl9d]1 & take half ! rema9d]1 & we %all h six in*es ( lead1 ! expansion ( :i* upw>ds is #jjjjiee -------- ,total expansion ( ! comp5sation upw>ds #jjjbbgb -------- ,to f9d ! expansion ( ! rod1 we h ! expansion ( #dc in*es ( glass #jjjbjei ,( two in*es ( /eel #jjjjabg -------- ,total expansion ( ! p5dulum rod #jjjbahf ,agree+ ne> en\gh ) t ( ! comp5sation be=e f\nd4 ,z we conceive we h be5 suffici5tly explicit 9 our description ( ?is p5dulum1 9 ! con/ruction ( :i* no difficulty pres5ts itself1 we ?9k an engrav$ repres5tation ( x w\ld be sup]flu\s4 ,we h hi!rto treat$ only ( comp5sations = temp]ature2 b !re is ano!r k9d ( error1 :i* has be5 sometimes insi/$ ^u1 aris+ f a v>iation 9 ! d5sity ( ! atmosph]e4 ,if ! d5sity ( ! atmosph]e be increas$1 ! p5dulum w exp]i5ce a great] resi/ance1 ! arc ( vibration w 9 consequ5ce be dim9i%$1 & ! p5dulum w vibrate fa/]4 ,?is1 h[ev]1 is 9 "s measure c\nt]act$ by ! increas$ buoyancy ( ! atmosph]e1 :i*1 act+ 9 opposition to gravity1 occasions ! p5dulum to vibrate sl[]4 ,if ! "o effect exactly equall$ ! o!r1 x is evid5t no error w\ld arise2 & 9 a pap] by ,mr4 ,davies ,gilb]t1 ,presid5t ( ! ,royal ,society ( ,london1 publi%$ 9 ! ,qu>t]ly ,j\rnal = #ahbf1 he has prov$ t1 by a happy *ance1 ! arc 9 :i* p5dulums ( clocks are usually made to vibrate is ! arc at :i* ?is comp5sation ( error takes place4 ,?is arc1 = a p5dulum hav+ a brass bob1 is #a #ef #cj on ea* side ( ! p]p5dicul>2 & = a m]curial p5dulum1 #a #ca #dd1 or ab\t "o degree & a half4 ,x is well kn[n t1 if a p5dulum vibrates 9 a circul> arc1 ! times ( vibration w v>y ne>ly z ! squ>es ( ! arcs2 b if ! p5dulum c\ld be made to vibrate 9 a cycloid1 ! "t ( its vibration 9 arcs ( diff]5t ext5t w\ld !n rema9 ! same4 ,huyg5s & o!rs1 !re=e1 endeav\r$ to effect ?is by plac+ ! spr+ ( ! p5dulum betwe5 *eeks ( a cycloidal =m4 ,:5 escapem5ts are employ$ :i* d n insure an unv>y+ impulse to ! p5dulum1 ! =ce may be unequally transmitt$ ?r\gh ! tra9 ( ! clock 9 consequ5ce ( unavoidable imp]fections ( workman%ip1 & ! arc ( vibration may suff] "s increase or dim9ution f ?is cause4 ,to discov] a rem$y = ?is is c]ta9ly desirable4 ,! writ] ( ?is article "s ye>s ago imag9$ a mode1 :i* he believes has also be5 sugge/$ by o!rs1 by :i* he conceiv$ a p5dulum might be made to describe an arc approa*+ 9 =m to t ( a cycloid4 ,! p5dulum spr+ 0 ( a triangul> =m1 & ! po9t or v]tex 0 p9n$ into ! top ( ! p5dulum rod1 ! base ( ! triangle =m+ ! axis ( susp5sion4 ,n[ x is evid5t t :5 ! p5dulum is 9 motion1 ! spr+ w resi/ b5d+ at ! axis ( susp5sion1 ) a =ce 9 "s sort proportionate to ! base ( ! triangle4 ,suppose ! p5dulum to h arriv$ at ! ext5t ( its vibrations2 ! spr+ w pres5t a curv$ appe>ance2 & if ! di/ance f ! po9t ( susp5sion to ! c5tre ( oscillation be !n measur$1 x w evid5tly1 9 consequ5ce ( ! curvature ( ! spr+1 be %ort] ?an ! di/ance f ! po9t ( susp5sion to ! c5tre ( oscillation1 measur$ :5 ! p5dulum is 9 a p]p5dicul> position1 & consequ5tly :5 ! spr+ is p]fectly /raight4 ,! base ( ! triangle may be dim9i%$1 or ! spr+ be made ?9n]2 ei!r ( :i* w less5 its effect4 ,we _c say h[ ?is plan might answ] ^u fur!r trial1 z suffici5t exp]im5ts 7 n made at ! "t to au?orize a decisive conclusion4 ,we h ?us complet$ our acc\nt ( comp5sation p5dulums2 b be=e we conclude1 x may n be unacceptable if we (f] a few rem>ks on "s po9ts :i* may be f\nd ( practical utility4 ,! cock ( ! p5dulum %\ld be firmly fix$ ei!r to ! wall or to ! case ( ! clock1 & n to ! clock itself1 z is sometimes done1 & :i* has occasion$ mu* irregul>ity 9 its rate1 f ! motion communicat$ to ! po9t ( susp5sion4 ,we pref] a bracket or %elf ( ca/ iron or brass1 ^u :i* ! clock may be fix$1 & ! cock c>ry+ ! p5dulum atta*$ to its p]p5dicul> back4 ,?is bracket may ei!r be screw$ to ! back ( ! clock-case1 or1 :i* is ! bett] mode1 securely fix$ to ! wall2 & if ! latt] be adopt$1 ! :ole may be def5d$ f ! atmosph]e1 or f du/1 by ! clock-case1 :i* ?us has no connection ei!r ) ! clock or ) ! p5dulum4 ,! po9t ( susp5sion %\ld be di/9ctly def9$ & immovable4 ,?is may be readily effect$1 aft] ! p5dulum %all h tak5 ! direction ( gravity1 by means ( a /rong screw ent]+ ! cock 7:i* %\ld be v /\t7 on "o side1 & press+ a flat piece ( brass into firm contact ) ! spr+4 ,! impulse %\ld be giv5 9 t plane ( ! rod :i* co9cides ) ! plane ( vibration pass+ ?r\gh ! axis ( ! rod4 ,if ! impulse be giv5 at any po9t ei!r be=e or beh9d ?is plane1 ! probable result w be a tremul\s un/eady motion ( ! p5dulum4 ,a few r\gh trials1 & mov+ ! weight1 w br+ ! p5dulum ne> its int5d$ "t ( vibration1 :i* %\ld be left a little too sl[2 :5 ! bob %\ld be firmly fix$ to ! rod1 if ! =m ( ! p5dulum w admit ( x1 by a p9 or screw pass+ ?r\gh its c5tre4 ,! m delicate adju/m5t may be complet$ by %ift+ ! place ( ! slid] ) :i* ! p5dulum is suppos$ to be furni%$ on ! rod4 ,mr4 ,br[ne 7( :om we h be=e spok57 practises ! foll[+ v delicate mode ( adju/m5t = rate1 :i* w be f\nd extremely conv5i5t1 z x is n necess>y to /op ! p5dulum 9 ord] to make ! requir$ alt]ation4 ,hav+ asc]ta9$1 by exp]im5t1 ! effect produc$ on ! rate ( ! clock1 by plac+ a weight ^u ! bob equal to a giv5 numb] ( gra9s1 he prep>es c]ta9 small] weights ( %eet-lead1 :i* are turn$ up at ! corn]s1 t !y may be conv5i5tly laid hold ( by a pair ( =ceps1 & ! effect ( ^! small weights on ! rate ( ! clock w be1 ( c\rse1 kn[n by proportion4 ,! rate be+ suppos$ to be 9 defect1 ! weights necess>y to correct ?is may be deposit$1 )\t difficulty1 ^u ! bob ( ! p5dulum1 or ^u "s conv5i5t plane surface1 plac$ 9 ord] to receive !m3 & %\ld x be necess>y to remove any "o ( ! weights1 ?is may readily be done by employ+ a delicate pair ( =ceps1 )\t produc+ ! slighte/ di/urbance 9 ! motion ( ! p5dulum4 ,,index4 ,a4 ,action & reaction1 #cd4 ,a]i=m fluids1 #bf4 ,animalcules1 #ab4 ,atmosph]e1 imp5etrability (1 #bb4 ,compressibility & ela/icity (1 #bc4 ,atoms1 #f4 ,coh]5ce (1 #g4 ,attraction1 magnetic1 ( gravitation1 #h1 #ej1 #fd4 ,molecul> or atomic1 #fi4 ,cohesion1 #gj4 ,attwood1 ma*9e (1 #ib4 ,axes1 pr9cipal1 #ach4 ,axis1 me*anical prop]ties (1 #abh4 ,b4 ,balance1 #bgi4 ,( ,bates1 #bhh4 ,use (1 #bhi4 ,dani%1 #bii4 ,b5t-lev] ( ,brady1 #cja4 ,bodies1 #b4 ,l9es1 surfaces1 edges1 area1 l5g? (1 #d4 ,figure1 volume1 %ape (1 #e4 ,porosity (1 #ag4 ,compressibility (1 #ah4 ,ela/icity1 dilatibility (1 #ai4 ,in]tia (1 #bg4 ,rule = det]m9+ velocity (2 motion ( two bodies aft] impact1 #ch4 ,c4 ,capill>y attraction1 #gc4 ,cap/an1 #agi4 ,cause & effect1 #g4 ,circle ( curvature1 #ii4 ,cog1 hunt+1 #aia4 ,compon5ts1 #ea4 ,cord1 #afc4 ,cordage1 friction & rigidity (1 #bfj4 ,crank1 #bda4 ,cry/allisation1 #ad4 ,cycloid1 #aeh4 ,d4 ,damp]1 self-act+1 #bcd4 ,dep>cieux's comp5sation p5dulum1 #cai4 ,diagonal1 #ea4 ,dynamics1 #afj4 ,dynamomet]1 #cje4 ,e4 ,electricity1 #gf4 ,electro-magnetism1 #gf4 ,equilibrium1 neutral1 in/able1 & /able1 #aah4 ,f4 ,figure1 #e4 ,fly-:eel1 #bci4 ,=ce1 #f4 ,composition & resolution (1 #di4 ,c5trifugal1 #ih4 ,mom5t (2 lev]age (1 #ace4 ,regulation & accumulation (1 #bbd4 ,friction1 effects (1 #if4 ,laws (1 #bfd4 ,g4 ,gov]nor1 #bbg4 ,gravitation1 attraction (1 #gg4 ,t]re/rial1 #hd4 ,gravity1 c5tre (1 #ajg4 ,gyration1 radius (1 c5tre (1 #acg4 ,h4 ,hooke's univ]sal jo9t1 #beb4 ,hydrophane1 porosity (1 #ah4 ,i4 ,impact1 #ci4 ,impulse1 #fe4 ,incl9$ plane1 #afc-bji4 ,incl9$ roads1 #baa4 ,in]tia1 #bg4 ,laws (1 #cb4 ,mom5t (1 #acg4 ,j4 ,juli5 le ,roy1 comp5sation tube (1 #cai4 ,l4 ,lev]1 #afc4 ,fulcrum (2 ?ree k9ds (1 #afg4 ,equival5t1 #agf4 ,l9e ( direction1 #aaj4 ,liquids1 compressibility (1 #bd4 ,load/one1 #fh4 ,m4 ,ma*9es1 simple1 #afj4 ,p[] (1 #age4 ,regulation (1 #bbe4 ,magnet1 #fh4 ,magnetic attraction1 #h4 ,magnetism1 #gf4 ,magnitude1 #d4 ,m>riott's pat5t weigh+ ma*9e1 #cje4 ,mat]ials1 /r5g? (1 #bgb4 ,matt]1 prop]ties (1 #b4 ,imp5etrability (1 #d4 ,atoms (2 molecules (1 #f4 ,divisibility (1 #i4 ,examples ( ! subtilty (1 #ab4 ,limit to ! divisibility (1 #ac4 ,porosity (2 d5sity (1 #ag4 ,compressibility (1 #ah4 ,ela/icity & dilatability (1 #ai4 ,imp5etrability (1 #bb4 ,in]tia (1 #bg4 ,me*anical sci5ce1 f\ndation (1 #af4 ,metronomes1 pr9ciples (1 #aec4 ,molecules1 #f4 ,motion1 laws (1 #df4 ,uni=mly accel]at$1 #hg4 ,table illu/rative (1 #ij4 ,ret>d$2 ( bodies on incl9$ planes & curves1 #id4 ,rot>y & progressive1 #abg4 ,me*anical contrivances = ! modification (1 #bde4 ,cont9u$ rectil9e>2 reciprocatory rectil9e>2 cont9u$ circul>2 reciprocat+ circul>1 #bdf4 ,n4 ,newton1 me?od (1 = det]m9+ ! ?ickness ( transp>5t sub/ances1 #aj4 ,laws ( motion (1 #df4 ,o4 ,oscillation1 #abi4 ,( ! p5dulum1 #ade4 ,c5tre (1 #aeb4 ,p4 ,p>allelogram1 #ea4 ,p>ticle1 #f4 ,p5dulum1 oscillation or vibration (1 #ade4 ,iso*ronism (1 #adg4 ,c5tre ( oscillation (1 #aeb4 ,( ,tr\ghton1 #bhd4 ,comp5sation1 #cjg4 ,( ,h>rison1 #cac4 ,tubul>1 ( ,tr\ghton1 #cad4 ,( ,b5z5b]g1 #caf4 ,w>d's comp5sation1 #cah4 ,capta9 ,kat]'s comp5sation1 #cbj4 ,reid's2 ,ellicott's comp5sation1 #cbb4 ,/eel & brass comp5sation1 #cbd4 ,m]curial1 #cbf4 ,graham's m]curial1 #cbi4 ,wood & lead1 #ccd4 ,smeaton's1 #cce4 ,p]cussion1 #acj4 ,c5tre (1 #add4 ,planes ( cleavage1 #ae4 ,porosity1 #ag4 ,p[]1 #afa4 ,prop]ties1 #b4 ,projectiles1 curvil9e> pa? (1 #hb4 ,pulley1 #afd4 ,tackle2 fix$1 #aih4 ,s+le moveable1 #bjj4 ,call$ a runn]2 ,spani% b>tons1 #bje4 ,r4 ,rail-roads1 #bac4 ,regulat+ damp]1 #bcc4 ,regulators1 #bbg4 ,repulsion1 #h4 ,molecul>1 #gd4 ,resultant1 #ea4 ,rose-eng9e1 #bej4 ,s4 ,salt]s1 spr+ balance (1 #cje4 ,screw1 #bji4 ,concave1 #bag4 ,micromet]1 #bbc4 ,%ape1 #e4 ,siphon1 capill>y1 #gc4 ,spr+1 #cjd4 ,/atics1 #afj4 ,/eely>d1 #bid4 ,c4 ,paul's1 #bif4 ,*9ese1 #bii4 ,t4 ,table1 :irl+1 #ii4 ,ta*omet]1 #bcd4 ,tread-mill1 #agi4 ,v4 ,velocity1 angul>1 #ii4 ,vibration1 #abi4 ,( ! p5dulum1 #ade4 ,c5tre (1 #aeb4 ,volume1 #e-ag4 ,w4 ,wat*1 ma9spr+ (2 balance :eel (1 #aie4 ,wat] regulator1 #bbi4 ,w$ge1 #bji4 ,use (1 #bae4 ,weight1 #afa-bia4 ,weigh+ ma*9es1 #bgh4 ,= turnpike roads1 #cjb4 ,by means ( a spr+1 #cjc4 ,:eels1 spur1 cr[n1 bevell$1 #ahi4 ,escapem5t1 #aid4 ,:eel & axle1 #agg4 ,:eel-"w1 #agf4 ,w9*1 #agi4 ,w9dlass1 #agh4 ,wolla/on's wire1 #aj4 ,z4 ,zur$a1 app>atus (2 ,leupold's application (1 #bea4 ,,end ,,( ,,me*anics4 ,,london3 ,,spottiswoodes & ,,%aw ,new-/reet-,squ>e4