,illu/ration ,,pa? ,,( ,,biela',s ,,comet4 ,,lett]s ,,on ,,a/ronomy1 ,,9 ,,:i* ,,! ,,elem5ts ,,( ,,! ,,sci5ce ,,are ,,famili>ly ,,expla9$ ,,9 ,,connection ,,) ,,biographical ,,sket*es ,,( ,,! ,,mo/ ,,em95t ,,a/ronom]s4 ,,) ,,num]\s ,,engrav+s4 ,,by ,,d5ison ,,olm/$1 ,,ll4,d41 ,,pr(essor ,,( ,,natural ,,philosophy ,,& ,,a/ronomy ,,9 ,,yale ,,college ,revis$ ,edition4 ,,includ+ ,,! ,,late/ ,,discov]ies4 ,,new ,,york3 ,,h>p] ,,bro!rs1 ,,publi%]s1 #cbi #cca ,,pe>l ,,/reet1 ,,frankl9 ,,squ>e4 #ahee4 ,ent]$ accord+ to ,act ( ,congress1 9 ! ye> #ahdj1 by ,,m>%1 ,,cap51 ,,lyon1 ,,& ,,webb1 9 ! ,cl]k's ,(fice ( ! ,di/rict ,c\rt ( ,massa*usetts4 ,,adv]tisem5t ,,to ,,! ,,revis$ ,,edition4 ,,s9ce ! fir/ publication ( ^! ,lett]s1 9 #ahdj1 ! "w has pass$ ?r\gh num]\s editions1 & receiv$ _m tok5s ( public favor1 bo? z a class-book = s*ools & z a read+-book = ! family circle4 ,! valuable discov]ies made 9 ! sci5ce )9 a few ye>s h sugge/$ an additional ,lett]1 :i* is accord+ly annex$ to ! s]ies 9 ! pres5t revis$ =m1 giv+ a brief b compreh5sive notice ( all ! lead+ contributions ) :i* ,a/ronomy has ( late be5 enri*$4 ,! =m ( ,lett]s 0 *os5 on acc\nt ( ! great] fre$om x admits1 bo? ( matt] & ( /yle1 ?an a dress m purely sci5tific4 ,?us ! te*nical portion ( ! "w1 x 0 hop$1 might be reliev$1 & ! :ole r5d]$ attractive to ! y\?ful read] ( ei!r sex by int]sp]s+ sket*es ( ! ma/]-build]s :o1 9 successive ages1 h re>$ ! great temple ( ,a/ronomy1 compos+1 z !y d1 "s ( ! mo/ rem>kable & int]e/+ specim5s ( ! human race4 ,! "w 0 address$ to a female fri5d 7n[ no m71 :o 0 a di/+ui%$ ornam5t ( h] sex1 & ^: sup]ior intellect & ref9$ ta/e requir$ t ! "w %\ld be free f e ?+ sup]ficial 9 matt] or neglig5t 9 /yle2 & x 0 deem$ by ! writ] no ord9>y privilege t1 9 ! composition ( ! "w1 an image at once s exalt$ & s pure 0 cont9ually pres5t to 8 m5tal vision4 ,,yale ,,college1 ,janu>y1 #ahec4 ,,cont5ts4 ,,preface1 #c ,,lett] ,i4 ,introductory ,obs]vations1 #i ,,lett] ,,ii4 ,doctr9e ( ! ,sph]e1 #af ,,lett] ,,iii4 ,a/ronomical ,in/rum5ts4--,telescope1 #bi ,,lett] ,,iv4 ,telescope cont9u$1 #cf ,,lett] ,v4 ,obs]vatories1 #db ,,lett] ,,vi4 ,"t & ! ,cal5d>1 #ei ,,lett] ,,vii4 ,figure ( ! ,e>?1 #fi ,,lett] ,,viii4 ,diurnal ,revolution1 #ha ,,lett] ,,ix4 ,p>allax & ,refraction1 #hi ,,lett] ,x4 ,! ,sun1 #aja ,,lett] ,,xi4 ,annual ,revolution4--,seasons1 #aaa ,,lett] ,,xii4 ,laws ( ,motion1 #abf ,,lett] ,,xiii4 ,t]re/rial ,gravity1 #acd ,,lett] ,,xiv4 ,sir ,isaac ,newton4--,univ]sal ,gravitation4--,figure ( ! ,e>?'s ,orbit4--,precession ( ! ,equ9oxes1 #adc ,,lett] ,,xv4 ,! ,moon1 #aeg ,,lett] ,,xvi4 ,! ,moon4--,phases4--,h>ve/ ,moon4--,librations1 #agb ,,lett] ,,xvii4 ,moon's ,orbit4--,h] ,irregul>ities1 #ahj ,,lett] ,,xviii4 ,eclipses1 #aie ,,lett] ,,xix4 ,longitude4--,tides1 #bjh ,,lett] ,,xx4 ,planets4--,m]cury & ,v5us1 #bbe ,,lett] ,,xxi4 ,sup]ior ,planets3 ,m>s1 ,jupit]1 ,saturn1 & ,uranus1 #bdc ,,lett] ,,xxii4 ,cop]nicus4--,galileo1 #bed ,,lett] ,,xxiii4 ,saturn4--,uranus4--,a/]oids1 #bgd ,,lett] ,,xxiv4 ,! ,planet>y ,motions4--,kepl]'s ,laws4--,kepl]1 #bia ,,lett] ,,xxv4 ,comets1 #cab ,,lett] ,,xxvi4 ,comets1 #ccd ,,lett] ,,xxvii4 ,meteoric ,%[]s1 #cdf ,,lett] ,,xxviii4 ,fix$ ,/>s1 #cfe ,,lett] ,,xxix4 ,fix$ ,/>s1 #chc ,,lett] ,,xxx4 ,sy/em ( ! ,_w1 #cib ,,lett] ,,xxxi4 ,natural ,!ology1 #djf ,,lett] ,,xxxii4 ,rec5t ,discov]ies1 #dad ,index1 #dbc ,,lett]s ,,on ,,a/ronomy4 ,,lett] #a4 ,,introductory ,,obs]vations4 ,ye sacr$ ,muses1 ) ^: beauty fir$1 ,my s\l is ravi%$1 & my bra9 inspir$1 ,^: prie/ ,i am1 ^: holy fillets we>2 ,w\ld y y\r poet's fir/ petition he>1 ,give me ! ways ( w&]+ />s to "k1 ,! dep?s ( heav5 above1 & e>? bel[2 ,tea* me ! v>i\s labors ( ! moon1 ,& :5ce proce$ ?' eclipses ( ! sun2 ,:y fl[+ tides prevail ^u ! ma91 ,& 9 :at d>k recess !y %r9k aga92 ,:at %akes ! solid e>?1 :at cause delays ,! ,summ] nights1 & %ort5s ,w9t] days4 ,dryd5's ,virgil ,,to ,,mrs4 ,c---- ,m----4 ,,de> ,,madam1--,9 ! conv]sation we rec5tly held on ! /udy ( ,a/ronomy1 y express$ a /rong desire to become bett] acqua9t$ ) ?is noble sci5ce1 b said y _h always be5 repell$ by ! air ( sev]ity :i* x exhibits1 array$ z x is 9 s _m te*nical t]ms1 & su* ab/ruse ma!matical processes3 or1 if y _h tak5 up "s small] treatise1 ) ! hope ( avoid+ ^! p]plexities1 y _h always f\nd x s meag] & sup]ficial1 z to af=d y v little satisfaction4 ,y ask$1 if a "w might n be prep>$1 :i* w\ld convey to ! g5]al read] "s cle> & adequate k ( ! great discov]ies 9 a/ronomy1 & yet require = its p]usal no great] prep>ation1 ?an may be presum$ ( e well-educat$ ,engli% s*ol> ( ei!r sex4 ,y 7 pleas$ to add ! reque/1 t ,i w\ld write su* a "w1--a "w :i* %\ld comb9e1 ) a lum9\s exposition ( ! lead+ tru?s ( ! sci5ce1 "s acc\nt ( ! int]e/+ hi/orical facts ) :i* x is said ! records ( a/ronomical discov]y ab\nd4 ,hav+1 moreov]1 he>d mu* ( ! gr& discov]ies :i*1 )9 ! la/ fifty ye>s1 h be5 made among ! fix$ />s1 y express$ a /rong desire to le>n m respect+ ^! sublime rese>*es4 ,f9ally1 y desir$ to see ! argum5t = ! exi/5ce & natural attributes ( ! ,deity1 z furni%$ by a/ronomy1 m fully & cle>ly exhibit$1 ?an is done 9 any "w :i* y h hi!rto p]us$4 ,9 ! prep>ation ( ! propos$ treatise1 y urg$ me to supply1 ei!r 9 ! text or 9 notes1 e elem5t>y pr9ciple :i* w\ld be ess5tial to a p]fect und]/&+ ( ! "w2 = al?\gh1 :ile at s*ool1 y _h paid "s att5tion to geometry & natural philosophy1 yet s mu* "t _h s9ce elaps$1 t y\r memory requir$ to be refre%$ on ! mo/ simple pr9ciples ( ^! elem5t>y /udies1 & y pref]r$ t ,i %\ld consid] y z altoge!r unacqua9t$ ) !m4 ,al?\gh1 to satisfy a m9d1 s cultivat$ & inquisitive z y\rs1 may require a great] v>iety ( p[]s & atta9m5ts ?an ,i possess1 yet1 z y 7 pleas$ to urge me to ! trial1 ,i h resolv$ to make ! attempt1 & w see h[ f> ,i may be able to lead y into ! int]ior ( ?is beautiful temple1 )\t oblig+ y to =ce y\r way ?r\gh ! j>gon ( ! s*ools4 ,a/ronomy1 h[ev]1 is a v difficult or a comp>atively easy /udy1 accord+ to ! view we take ( x4 ,! inve/igation ( ! great laws :i* gov]n ! motions ( ! heav5ly bodies has comm&$ ! highe/ ef=ts ( ! human m9d2 b pr(\nd tru?s1 :i* x requir$ ! mightie/ ef=ts ( ! intellect to disclose1 are (t51 :5 once discov]$1 simple 9 _! complexion1 & may be express$ 9 v simple t]ms4 ,?us1 ! creation ( t elem5t1 on ^: my/]i\s ag5cy dep5d all ! =ms ( beauty & lovel9ess1 is enunciat$ 9 ^! few monosyllables1 ,& ,god said1 let !re be light1 & !re 0 light2 & ! doctr9e ( univ]sal gravitation1 :i* is ! key t unlocks ! my/]ies ( ! univ]se1 is simply ?is1--t e portion ( matt] 9 ! univ]se t5ds t[>ds e o!r4 ,! ?ree great laws ( motion1 also1 are1 :5 /at$1 s pla91 t !y seem h>dly to ass]t any ?+ b :at we knew be=e4 ,t all bodies1 if at re/1 w cont9ue s1 z is decl>$ by ! fir/ law ( motion1 until "s =ce moves !m2 or1 if 9 motion1 w cont9ue s1 until "s =ce /ops !m1 appe>s s mu* a matt] ( c\rse1 t we c at fir/ h>dly see any good reason :y x %\ld be dignifi$ ) ! title ( ! fir/ great law ( motion2 & yet x conta9s a tru? :i* x requir$ pr(\nd sagacity to discov] & exp\nd4 ,x is1 !re=e1 a pleas+ consid]ation to ^? :o h n ei!r ! leisure ( ! ability to foll[ ! a/ronom] ?r\gh ! intricate & labori\s processes1 :i* conduct$ him to 8 great discov]ies1 t !y may fully avail !mselves ( ! results ( ?is va/ toil1 & easily und]/& tru?s :i* x requir$ ages ( ! sev]e/ labor to unfold4 ,! descriptive p>ts ( a/ronomy1 or :at may be call$ ! natural hi/ory ( ! heav5s1 is /ill m easily und]/ood ?an ! laws ( ! cele/ial motions4 ,! revelations ( ! telescope1 & ! wond]s x has disclos$ 9 ! sun1 9 ! moon1 9 ! planets1 & especially 9 ! fix$ />s1 are facts n difficult to be und]/ood1 al?\gh !y may affect ! m9d ) a/oni%m5t4 ,! great practical purpose ( a/ronomy to ! _w is1 enabl+ u safely to navigate ! ocean4 ,!re are inde$ _m o!r b5efits :i* x conf]s on man2 b ?is is ! mo/ important4 ,if1 h[ev]1 y ask1 :at advantages ! /udy ( a/ronomy promises1 z a bran* ( education1 ,i answ]1 t few subjects promise to ! m9d s mu* pr(it & ent]ta9m5t4 ,x is agre$ by writ]s on ! human m9d1 t ! intellectual p[]s are enl>g$ & /r5g!n$ by ! habitual contemplation ( great objects1 :ile !y are contract$ & weak5$ by be+ con/antly employ$ ^u little or trifl+ subjects4 ,! =m] elevate1 ! latt] depress1 ! m9d1 to _! own level4 ,n[1 e ?+ 9 a/ronomy is great4 ,! magnitudes1 di/ances1 & motions1 ( ! heav5ly bodies2 ! amplitude ( ! firmam5t itself2 & ! magnific5ce ( ! orbs ) :i* x is light$1 supply exhau/less mat]ials = contemplation1 & /imulate ! m9d to its noble/ ef=ts4 ,! emotion felt by ! a/ronom] is n t sudd5 excitem5t or ec/asy1 :i* we>s out life1 b x is a cont9u$ gl[ ( exalt$ feel+1 :i* gives ! s5sation ( brea?+ 9 a pur] atmosph]e ?an o!rs enjoy4 ,we %\ld at fir/ imag9e1 t a /udy :i* calls ^u its vot>ies = ! sev]e/ ef=ts ( ! human intellect1 :i* dem&s ! undivid$ toil ( ye>s1 & :i* robs ! night ( its accu/om$ h\rs ( repose1 w\ld abridge ! p]iod ( life2 b x is a s+ul> fact1 t di/+ui%$ a/ronom]s1 z a class1 h be5 rem>kable = longevity4 ,i "k n h[ to acc\nt = ?is fact1 unless we suppose t ! /udy ( a/ronomy itself has some?+ inh]5t 9 x1 :i* su/a9s its vot>ies by a peculi> alim5t4 ,x is ! privilege ( ! /ud5t ( ?is dep>tm5t ( ,nature1 t 8 cab9et is already collect$1 & is ev] be=e him2 & he is exempt$ f ! toil ( collect+ 8 mat]ials ( /udy & illu/ration1 by trav]s+ l& & sea1 or by p5etrat+ into ! dep?s ( ! e>?4 ,nor are !y 9 _! nature frail & p]i%able4 ,no soon] is ! veil ( cl\ds remov$1 t occasionally conceals ! firmam5t by night1 ?an 8 specim5s are display$ to view1 bright & *angeless4 ,! r5ew$ pleasure :i* he feels1 at e new survey ( ! con/ellations1 gr[s into an affection = objects :i* h s (t5 m9i/]$ to 8 happ9ess4 ,8 imag9ation aids him 9 giv+ !m a p]sonification1 l t :i* ! anci5ts gave to ! con/ellations2 7z is evid5t f ! names :i* !y h transmitt$ to u27 & he walks abroad1 b5ea? ! ev5+ canopy1 ) ! consci\s satisfaction & delight ( be+ 9 ! pres5ce ( old fri5ds4 ,?is emotion becomes /rong] :5 he w&]s f> f home4 ,o!r objects ( 8 atta*m5t des]t him2 ! face ( society *anges2 ! e>? pres5ts new features2 b ! same sun illum9es ! day1 ! same moon adorns ! night1 & ! same bright />s /ill att5d him4 ,:51 moreov]1 ! /ud5t ( ! heav5s c comm& ! aid ( telescopes1 ( high] & high] p[]s1 new acqua9tances are made e ev5+4 ,! sight ( ea* new memb] ( ! />ry tra91 t ! telescope successively reveals to him1 inspires a peculi> emotion ( pleasure2 & he at l5g? f9ds himself1 :5ev] he sweeps 8 telescope ov] ! firmam5t1 greet$ by smiles1 unp]ceiv$ & unkn[n to 8 fell[-mortals4 ,! same p]sonification is giv5 to ^! objects z to ! con/ellations1 & he seems to himself1 at times1 :5 he has p5etrat$ into ! remote/ dep?s ( e!r1 to enjoy ! high pr]ogative ( hold+ conv]se ) ! cele/ials4 ,x is no small enc\ragem5t1 to "o :o wi%es to acquire a k ( ! heav5s1 t ! subject is emb>rass$ ) f> less t is te*nical ?an mo/ o!r bran*es ( natural hi/ory4 ,hav+ fir/ le>n$ a few def9itions1 & ! pr9cipal circles into :i*1 = conv5i5ce1 ! sph]e is divid$1 & receiv+ ! great laws ( a/ronomy on ! au?ority ( ! em95t p]sons :o h inve/igat$ !m1 y w f9d few h>d t]ms1 or te*nical di/9ctions1 to repel or p]plex y2 & y w1 ,i hope1 f9d t no?+ b an intellig5t m9d & fix$ att5tion are requisite = p]us+ ! ,lett]s :i* ,i propose to address to y4 ,i %all inde$ be greatly disappo9t$1 if ! p]usal does n inspire y ) "s portion ( t pleasure1 :i* ,i h describ$ z enjoy$ by ! a/ronom] himself4 ,! dignity ( ! /udy ( ! heav5ly bodies1 & its suitabl5ess to ! mo/ ref9$ & cultivat$ m9d1 has be5 recognis$ 9 all ages4 ,virgil celebrates x 9 ! beautiful /ra9s ) :i* ,i h head$ ?is ,lett]1 & simil> s5tim5ts h ev] be5 *]i%$ by ! greate/ m9ds4 ,z1 9 ! c\rse ( ^! ,lett]s1 ,i propose to trace an outl9e ( ! hi/ory ( a/ronomy1 f ! e>lie/ ages to ! pres5t "t1 y may ?9k ?is ! mo/ suitable place = introduc+ x2 b ! successive discov]ies 9 ! sci5ce _c be fully und]/ood & appreciat$1 until aft] an acqua9tance has be5 =m$ ) ! sci5ce itself4 ,we mu/ !re=e res]ve ! details ( ?is subject = a future opportunity2 b x may be /at$1 "h1 t a/ronomy 0 cultivat$ ! e>lie/ ( all ! sci5ces2 t great att5tion 0 paid to x by sev]al v anci5t nations1 z ! ,egyptians & ,*aldeans1 & ! p ( ,india & ,*9a1 be=e x took its rise 9 ,greece4 ,m ?an six hundr$ ye>s be=e ! ,*ri/ian era1 h[ev]1 x began to be /udi$ 9 ?is latt] c\ntry4 ,?ales & ,py?agoras 7 p>ticul>ly di/+ui%$ = _! devotion to ?is sci5ce2 & ! celebrat$ s*ool ( ,alex&ria1 9 ,egypt1 :i* took its rise ab\t ?ree hundr$ ye>s be=e ! ,*ri/ian era1 & fl\ri%$ = sev]al hundr$ ye>s1 numb]$ among its disciples a succession ( em95t a/ronom]s1 among :om 7 ,hipp>*us1 ,erato/h5es1 & ,ptolemy4 ,! la/ ( ^! compos$ a great "w on a/ronomy1 call$ ! ',almage/1' 9 :i* is transmitt$ to u an acc\nt ( all t 0 kn[n ( ! sci5ce by ! ,alex&rian s*ool4 ,! ',almage/' 0 ! pr9cipal text-book 9 a/ronomy1 = _m c5turies aft]w>ds1 & comp>atively few improvem5ts 7 made until ! age ( ,cop]nicus4 ,cop]nicus 0 born at ,?orn1 9 ,prussia1 9 #adgc4 ,previ\s to 8 "t1 ! doctr9e 0 held1 t ! e>? is at re/ 9 ! c5tre ( ! univ]se1 & t ! sun1 moon1 & />s1 revolve ab\t x1 e day1 f ea/ to we/2 9 %ort1 t ! app>5t motions ( ! heav5ly bodies are ! same ) _! real motions4 ,b ,cop]nicus exp\nd$ :at is n[ kn[n to be ! true !ory ( ! cele/ial motions1 9 :i* ! sun is plac$ 9 ! c5tre ( ! sol> sy/em1 & ! e>? & all ! planets are made to revolve ar\nd him1 f we/ to ea/1 :ile ! app>5t diurnal motion ( ! heav5ly bodies1 f ea/ to we/1 is expla9$ by ! revolution ( ! e>? on its axis1 9 ! same "t1 f we/ to ea/2 a motion ( :i* we are unconsci\s1 & :i* we errone\sly ascribe to ext]nal objects1 z we imag9e ! %ore is rec$+ f u1 :5 we are unconsci\s ( ! motion ( ! %ip t c>ries u f x4 ,al?\gh _m ( ! appe>ances1 pres5t$ by ! motions ( ! heav5ly bodies1 may be expla9$ on ! =m] errone\s hypo!sis1 yet1 l o!r hypo!ses f\nd$ 9 error1 x 0 cont9ually lead+ its vot>ies into difficulties1 & bl9d+ _! m9ds to ! p]ception ( tru?4 ,!y _h advanc$ ne>ly z f> z x 0 practicable to g 9 ! wrong road2 & ! great & sublime discov]ies ( mod]n times are ow+1 9 no small degree1 to ! fact1 t1 s9ce ! days ( ,cop]nicus1 a/ronom]s h be5 pursu+ ! pla9 & simple pa? ( tru?1 in/ead ( ?read+ _! way ?r\gh ! mazes ( error4 ,ne> ! close ( ! sixte5? c5tury1 ,ty*o ,brahe1 a native ( ,sw$51 b a resid5t ( ,d5m>k1 c>ri$ a/ronomical obs]vations 7:i* con/itute ! basis ( all t is valuable 9 a/ronomy7 to a f> great] degree ( p]fection ?an _h ev] be5 done be=e4 ,kepl]1 a native ( ,g]many1 "o ( ! greate/ g5iuses ! _w has ev] se51 0 contempor>y ) ,ty*o ,brahe1 & 0 associat$ ) him 9 a "p ( 8 labors4 ,galileo1 an ,italian a/ronom] ( great em95ce1 fl\ri%$ only a little lat] ?an ,ty*o ,brahe4 ,he inv5t$ ! telescope1 &1 bo? by 8 discov]ies & reason+s1 contribut$ greatly to e/abli% ! true sy/em ( ! _w4 ,soon aft] ! comm5cem5t ( ! sev5te5? c5tury1 7#afbj17 ,"l ,bacon1 a celebrat$ ,engli% philosoph]1 po9t$ out ! true me?od ( conduct+ all inquiries into ! ph5om5a ( ,nature1 & introduc$ ! inductive me?od ( philosophiz+4 ,accord+ to ! inductive me?od1 we are to beg9 our inquiries into ! causes ( any ev5ts by fir/ exam9+ & classify+ all ! facts t relate to x1 &1 f ! comp>ison ( ^!1 to d$uce our conclusions4 ,b ! greate/ s+le discov]y1 t has ev] be5 made 9 a/ronomy1 0 ! law ( univ]sal gravitation1 a discov]y made by ,sir ,isaac ,newton1 9 ! latt] "p ( ! sev5te5? c5tury4 ,! discov]y ( ?is law made u acqua9t$ ) ! hidd5 =ces t move ! great ma*9]y ( ! univ]se4 ,x furni%$ ! key :i* unlocks ! inn] temple ( ,nature2 & f ?is "t we may reg>d a/ronomy z fix$ on a sure & immovable basis4 ,i %all h]eaft] endeavor to expla9 to y ! lead+ pr9ciples ( univ]sal gravitation1 :5 we come to ! prop] place = inquir+ into ! causes ( ! cele/ial motions1 z exemplifi$ 9 ! motion ( ! e>? ar\nd ! sun4 ,,lett] ,,ii4 ,,doctr9e ,,( ,,! ,,sph]e4 ,all are b p>ts ( "o /up5d\s :ole1 ,^: body ,nature is1 & ,god ! s\l4--,pope4 ,,let u n[ consid] :at a/ronomy is1 & into :at great divisions x is di/ribut$2 & !n we w take a cursory view ( ! doctr9e ( ! sph]e4 ,?is subject w probably be less int]e/+ to y ?an _m t are to foll[2 b /ill1 p]mit me to urge ^u y ! necessity ( /udy+ x ) att5tion1 & reflect+ ^u ea* def9ition1 until y fully und]/& x2 =1 unless y fully & cle>ly compreh5d ! circles ( ! sph]e1 & ! use t is made ( !m 9 a/ronomy1 a mi/ w hang ov] e subsequ5t portion ( ! sci5ce4 ,i beg y1 !re=e1 to pause ^u e p>agraph ( ?is ,lett]2 & if !re is any po9t 9 ! :ole :i* y _c cle>ly und]/&1 ,i w\ld advise y to m>k x1 & to recur to x repeat$ly2 &1 if y f9ally _c obta9 a cle> idea ( x y\rself1 ,i w\ld recomm5d to y to apply = aid to "s ( y\r fri5ds1 :o may be able to assi/ y4 ,a/ronomy is t sci5ce :i* treats ( ! heav5ly bodies4 ,m p>ticul>ly1 its object is to tea* :at is kn[n respect+ ! sun1 moon1 planets1 comets1 & fix$ />s2 & also to expla9 ! me?ods by :i* ?is k is acquir$4 ,a/ronomy is sometimes divid$ into descriptive1 physical1 & practical4 ,descriptive a/ronomy respects facts2 physical a/ronomy1 causes2 practical a/ronomy1 ! means ( inve/igat+ ! facts1 :e!r by in/rum5ts or by calculation4 ,x is ! prov9ce ( descriptive a/ronomy to obs]ve1 classify1 & record1 all ! ph5om5a ( ! heav5ly bodies1 :e!r p]ta9+ to ^? bodies individually1 or result+ f _! motions & mutual relations4 ,x is ! "p ( physical a/ronomy to expla9 ! causes ( ^! ph5om5a1 by inve/igat+ ! g5]al laws on :i* !y dep5d2 especially1 by trac+ out all ! consequ5ces ( ! law ( univ]sal gravitation4 ,practical a/ronomy l5ds its aid to bo? ! o!r dep>tm5ts4 ,! def9itions ( ! diff]5t l9es1 po9ts1 & circles1 :i* are us$ 9 a/ronomy1 & ! propositions f\nd$ ^u !m1 compose ! doctr9e ( ! sph]e4 ,be=e ^! def9itions are giv51 ,i mu/ recall to y\r recollection a few p>ticul>s respect+ ! me?od ( measur+ angles4 7,see ,fig4 #a1 page #ah47 ,a l9e drawn f ! c5tre to ! circumf]5ce ( a circle is call$ a radius1 z ,c ,d1 ,c ,b1 or ,c ,k4 ,any "p ( ! circumf]5ce ( a circle is call$ an arc1 z ,a ,b1 or ,b ,d4 ,an angle is measur$ by an arc includ$ betwe5 two radii4 ,?us1 9 ,fig4 #a1 ! angle conta9$ betwe5 ! two radii1 ,c ,a & ,c ,b1 t is1 ! angle ,a ,c ,b1 is measur$ by ! arc ,a ,b4 ,e circle1 x w be recollect$1 is divid$ into ?ree hundr$ & sixty equal p>ts1 call$ degrees2 & any arc1 z ,a ,b1 conta9s a c]ta9 numb] ( degrees1 accord+ to its l5g?4 ,?us1 if ! arc ,a ,b conta9s =ty degrees1 !n ! opposite angle ,a ,c ,b is said to be an angle ( =ty degrees1 & to be measur$ by ,a ,b4 ,b ?is arc is ! same "p ( ! small] circle t ,e ,f is ( ! great]4 ,! arc ,a ,b1 !re=e1 conta9s ! same numb] ( degrees z ! arc ,e ,f1 & ei!r may be tak5 z ! measure ( ! angle ,a ,c ,b4 ,z ! :ole circle conta9s ?ree hundr$ & sixty degrees1 x is evid5t1 t ! qu>t] ( a circle1 or quadrant1 conta9s n9ety degrees1 & t ! semicircle ,a ,b ,d ,g conta9s "o hundr$ & eighty degrees4 ,illu/ration ,fig4 #a4 ,! complem5t ( an arc1 or angle1 is :at x wants ( n9ety degrees4 ,?us1 s9ce ,a ,d is an arc ( n9ety degrees1 ,b ,d is ! complem5t ( ,a ,b1 & ,a ,b is ! complem5t ( ,b ,d4 ,if ,a ,b d5otes a c]ta9 numb] ( degrees ( latitude1 ,b ,d w be ! complem5t ( ! latitude1 or ! colatitude1 z x is commonly writt54 ,! supplem5t ( an arc1 or angle1 is :at x wants ( "o hundr$ & eighty degrees4 ,?us1 ,b ,a is ! supplem5t ( ,g ,d ,b1 & ,g ,d ,b is ! supplem5t ( ,b ,a4 ,if ,b ,a 7 tw5ty degrees ( longitude1 ,g ,d ,b1 its supplem5t1 w\ld be "o hundr$ & sixty degrees4 ,an angle is said to be subt5d$ by ! side :i* is opposite to x4 ,?us1 9 ! triangle ,a ,c ,k1 ! angle at ,c is subt5d$ by ! side ,a ,k1 ! angle at ,a by ,c ,k1 & ! angle at ,k by ,c ,a4 ,9 l mann]1 a side is said to be subt5d$ by an angle1 z ,a ,k by ! angle at ,c4 ,let u n[ proce$ ) ! doctr9e ( ! sph]e4 ,a section ( a sph]e1 by a plane cutt+ x 9 any mann]1 is a circle4 ,great circles are ^? :i* pass ?r\gh ! c5tre ( ! sph]e1 & divide x into two equal hemisph]es4 ,small circles are su* z d n pass ?r\gh ! c5tre1 b divide ! sph]e into two unequal p>ts4 ,! axis ( a circle is a /raight l9e pass+ ?r\gh its c5tre at "r angles to its plane4 ,! pole ( a great circle is ! po9t on ! sph]e :]e its axis cuts ?r\gh ! sph]e4 ,e great circle has two poles1 ea* ( :i* is e :]e n9ety degrees f ! great circle4 ,all great circles ( ! sph]e cut ea* o!r 9 two po9ts diametrically opposite1 & consequ5tly _! po9ts ( section are "o hundr$ & eighty degrees ap>t4 ,a great circle1 :i* passes ?r\gh ! pole ( ano!r great circle1 cuts ! latt] at "r angles4 ,! great circle :i* passes ?r\gh ! pole ( ano!r great circle1 & is at "r angles to x1 is call$ a second>y to t circle4 ,! angle made by two great circles on ! surface ( ! sph]e is measur$ by an arc ( ano!r great circle1 ( :i* ! angul> po9t is ! pole1 be+ ! arc ( t great circle int]cept$ betwe5 ^? two circles4 ,9 ord] to fix ! position ( any place1 ei!r on ! surface ( ! e>? or 9 ! heav5s1 bo? ! e>? & ! heav5s are conceiv$ to be divid$ into sep>ate portions1 by circles1 :i* are imag9$ to cut ?r\gh !m1 9 v>i\s ways4 ,! e>? ?us int]sect$ is call$ ! t]re/rial1 & ! heav5s ! cele/ial1 sph]e4 ,we mu/ be> 9 m9d1 t ^! circles h no exi/5ce 9 ,nature1 b are m]e l&m>ks1 artificially contriv$ = conv5i5ce ( ref]5ce4 ,on acc\nt ( ! imm5se di/ances ( ! heav5ly bodies1 !y appe> to u1 :]ev] we are plac$1 to be fix$ 9 ! same concave surface1 or cele/ial vault4 ,! great circles ( ! globe1 ext5d$ e way to meet ! concave sph]e ( ! heav5s1 become circles ( ! cele/ial sph]e4 ,! horizon is ! great circle :i* divides ! e>? into upp] & l[] hemisph]es1 & sep>ates ! visible heav5s f ! invisible4 ,?is is ! rational horizon4 ,! s5sible horizon is a circle t\*+ ! e>? at ! place ( ! spectator1 & is b\nd$ by ! l9e 9 :i* ! e>? & skies seem to meet4 ,! s5sible horizon is p>allel to ! rational1 b is di/ant f x by ! semidiamet] ( ! e>?1 or ne>ly f\r ?\s& miles4 ,/ill1 s va/ is ! di/ance ( ! />ry sph]e1 t bo? ^! planes appe> to cut ! sph]e 9 ! same l9e2 s t we see ! same hemisph]e ( />s t we %\ld see1 if ! upp] half ( ! e>? 7 remov$1 & we /ood on ! rational horizon4 ,! poles ( ! horizon are ! z5i? & nadir4 ,! z5i? is ! po9t directly ov] our heads2 & ! nadir1 t directly "u our feet4 ,! plumb-l9e 7su* z is =m$ by susp5d+ a bullet by a /r+7 is 9 ! axis ( ! horizon1 & consequ5tly direct$ t[>ds its poles4 ,e place on ! surface ( ! e>? has its own horizon2 & ! travell] has a new horizon at e /ep1 always ext5d+ n9ety degrees f him1 9 all directions4 ,v]tical circles are ^? :i* pass ?r\gh ! poles ( ! horizon1 7! z5i? & nadir17 p]p5dicul> to x4 ,! m]idian is t v]tical circle :i* passes ?r\gh ! nor? & s\? po9ts4 ,! prime v]tical is t v]tical circle :i* passes ?r\gh ! ea/ & we/ po9ts4 ,! altitude ( a body is its elevation above ! horizon1 measur$ on a v]tical circle4 ,! azimu? ( a body is its di/ance1 measur$ on ! horizon1 f ! m]idian to a v]tical circle pass+ ?r\gh t body4 ,! amplitude ( a body is its di/ance1 on ! horizon1 f ! prime v]tical to a v]tical circle pass+ ?r\gh ! body4 ,azimu? is reckon$ n9ety degrees f ei!r ! nor? or s\? po9t2 & amplitude n9ety degrees f ei!r ! ea/ or we/ po9t4 ,azimu? & amplitude are mutually complem5ts ( ea* o!r1 = "o makes up :at ! o!r wants ( n9ety degrees4 ,:5 a po9t is on ! horizon1 x is only necess>y to c\nt ! numb] ( degrees ( ! horizon betwe5 t po9t & ! m]idian1 9 ord] to f9d its azimu?2 b if ! po9t is above ! horizon1 !n its azimu? is e/imat$ by pass+ a v]tical circle ?r\gh x1 & reckon+ ! azimu? f ! po9t :]e ?is circle cuts ! horizon4 ,! z5i? di/ance ( a body is measur$ on a v]tical circle pass+ ?r\gh t body4 ,x is ! complem5t ( ! altitude4 ,! axis ( ! e>? is ! diamet] on :i* ! e>? is conceiv$ to turn 9 its diurnal revolution4 ,! same l9e1 cont9u$ until x meets ! />ry concave1 con/itutes ! axis ( ! cele/ial sph]e4 ,! poles ( ! e>? are ! extremities ( ! e>?'s axis3 ! poles ( ! heav5s1 ! extremities ( ! cele/ial axis4 ,! equator is a great circle cutt+ ! axis ( ! e>? at "r angles4 ,h5ce1 ! axis ( ! e>? is ! axis ( ! equator1 & its poles are ! poles ( ! equator4 ,! int]section ( ! plane ( ! equator ) ! surface ( ! e>? con/itutes ! t]re/rial1 & its int]section ) ! concave sph]e ( ! heav5s1 ! cele/ial1 equator4 ,! latt]1 by way ( di/9ction1 is sometimes d5om9at$ ! equ9octial4 ,! second>ies to ! equator1--t is1 ! great circles pass+ ?r\gh ! poles ( ! equator1--are call$ m]idians1 because t second>y :i* passes ?r\gh ! z5i? ( any place is ! m]idian ( t place1 & is at "r angles bo? to ! equator & ! horizon1 pass+1 z x does1 ?r\gh ! poles ( bo?4 ,^! second>ies are also call$ h\r circles because ! arcs ( ! equator int]cept$ betwe5 !m are us$ z measures ( "t4 ,! latitude ( a place on ! e>? is its di/ance f ! equator nor? or s\?4 ,! pol> di/ance1 or angul> di/ance f ! ne>e/ pole1 is ! complem5t ( ! latitude4 ,! longitude ( a place is its di/ance f "s /&>d m]idian1 ei!r ea/ or we/1 measur$ on ! equator4 ,! m]idian1 usually tak5 z ! /&>d1 is t ( ! ,obs]vatory ( ,gre5wi*1 9 ,london4 ,if a place is directly on ! equator1 we h only to inquire1 h[ _m degrees ( ! equator !re are betwe5 t place & ! po9t :]e ! m]idian ( ,gre5wi* cuts ! equator4 ,if ! place is nor? or s\? ( ! equator1 !n its longitude is ! arc ( ! equator int]cept$ betwe5 ! m]idian :i* passes ?r\gh ! place & ! m]idian ( ,gre5wi*4 ,! ecliptic is a great circle1 9 :i* ! e>? p]=ms its annual revolutions ar\nd ! sun4 ,x passes ?r\gh ! c5tre ( ! e>? & ! c5tre ( ! sun4 ,x is f\nd1 by obs]vation1 t ! e>? does n lie ) its axis at "r angles to ! plane ( ! ecliptic1 s z to make ! equator co9cide ) x1 b t x is turn$ ab\t tw5ty-?ree & a half degrees out ( a p]p5dicul> direction1 mak+ an angle ) ! plane itself ( sixty-six & a half degrees4 ,! equator1 !re=e1 mu/ be turn$ ! same di/ance out ( a co9cid5ce ) ! ecliptic1 ! two circles mak+ an angle ) ea* o!r ( tw5ty-?ree & a half degrees4 ,x is p>ticul>ly important t we %\ld =m correct ideas ( ! ecliptic1 & ( its relations to ! equator1 s9ce to ^! two circles a great numb] ( a/ronomical measurem5ts & ph5om5a are ref]r$4 ,! equ9octial po9ts1 or equ9oxes1 are ! int]sections ( ! ecliptic & equator4 ,! "t :5 ! sun crosses ! equator1 9 go+ nor?w>d1 is call$ ! v]nal1 & 9 return+ s\?w>d1 ! autumnal1 equ9ox4 ,! v]nal equ9ox occurs ab\t ! tw5ty-fir/ ( ,m>*1 & ! autumnal1 ab\t ! tw5ty-second ( ,septemb]4 ,! sol/itial po9ts are ! two po9ts ( ! ecliptic mo/ di/ant f ! equator4 ,! times :5 ! sun comes to !m are call$ sol/ices4 ,! ,summ] sol/ice occurs ab\t ! tw5ty-second ( ,june1 & ! ,w9t] sol/ice ab\t ! tw5ty-second ( ,decemb]4 ,! ecliptic is divid$ into twelve equal p>ts1 ( ?irty degrees ea*1 call$ signs1 :i*1 beg9n+ at ! v]nal equ9ox1 succe$ ea* o!r1 9 ! foll[+ ord]3 #a4 ,aries1 ,zodiac3 ,aries #b4 ,taurus1 ,zodiac3 ,taurus #c4 ,gem9i1 ,zodiac3 ,gem9i #d4 ,canc]1 ,zodiac3 ,canc] #e4 ,leo1 ,zodiac3 ,leo #f4 ,virgo1 ,zodiac3 ,virgo #g4 ,libra1 ,zodiac3 ,libra #h4 ,scorpio1 ,zodiac3 ,scorpio #i4 ,sagitt>ius1 ,zodiac3 ,sagitt>ius #aj4 ,capricornus1 ,zodiac3 ,capricornus #aa4 ,aqu>ius1 ,zodiac3 ,aqu>ius #ab4 ,pisces4 ,zodiac3 ,pisces ,! mode ( reckon+ on ! ecliptic is by signs1 degrees1 m9utes1 & seconds4 ,! sign is d5ot$ ei!r by its "n or its numb]4 ,?us1 "o hundr$ degrees may be express$ ei!r z ! t5? degree ( ,canc]1 or z #cs #aj4 ,x w be f\nd an advantage to repeat ! signs 9 _! prop] ord]1 until !y are well fix$ 9 ! memory1 & to be able to recognise ea* sign by its appropriate "*4 ,( ! v>i\s m]idians1 two are di/+ui%$ by ! "n ( colures4 ,! equ9octial colure is ! m]idian :i* passes ?r\gh ! equ9octial po9ts4 ,f ?is m]idian1 "r asc5sion & cele/ial longitude are reckon$1 z longitude on ! e>? is reckon$ f ! m]idian ( ,gre5wi*4 ,! sol/itial colure is ! m]idian :i* passes ?r\gh ! sol/itial po9ts4 ,! position ( a cele/ial body is ref]r$ to ! equator by its "r asc5sion & decl9ation4 ,"r asc5sion is ! angul> di/ance f ! v]nal equ9ox measur$ on ! equator4 ,if a /> is situat$ on ! equator1 !n its "r asc5sion is ! numb] ( degrees ( ! equator betwe5 ! /> & ! v]nal equ9ox4 ,b if ! /> is nor? or s\? ( ! equator1 !n its "r asc5sion is ! numb] ( degrees ( ! equator1 int]cept$ betwe5 ! v]nal equ9ox & t second>y to ! equator :i* passes ?r\gh ! />4 ,decl9ation is ! di/ance ( a body f ! equator measur$ on a second>y to ! latt]4 ,!re=e1 "r asc5sion & decl9ation correspond to t]re/rial longitude & latitude1--"r asc5sion be+ reckon$ f ! equ9octial colure1 9 ! same mann] z longitude is reckon$ f ! m]idian ( ,gre5wi*4 ,on ! o!r h&1 cele/ial longitude & latitude are ref]r$1 n to ! equator1 b to ! ecliptic4 ,cele/ial longitude is ! di/ance ( a body f ! v]nal equ9ox measur$ on ! ecliptic4 ,cele/ial latitude is ! di/ance f ! ecliptic measur$ on a second>y to ! latt]4 ,or1 m briefly1 longitude is di/ance on ! ecliptic3 latitude1 di/ance f ! ecliptic4 ,! nor? pol> di/ance ( a /> is ! complem5t ( its decl9ation4 ,p>allels ( latitude are small circles p>allel to ! equator4 ,!y con/antly dim9i% 9 size1 z we g f ! equator to ! pole4 ,! tropics are ! p>allels ( latitude :i* pass ?r\gh ! sol/ices4 ,! nor!rn tropic is call$ ! tropic ( ,canc]2 ! s\!rn1 ! tropic ( ,capricorn4 ,! pol> circles are ! p>allels ( latitude t pass ?r\gh ! poles ( ! ecliptic1 at ! di/ance ( tw5ty-?ree & a half degrees f ! poles ( ! e>?4 ,! elevation ( ! pole ( ! heav5s above ! horizon ( any place is always equal to ! latitude ( ! place4 ,?us1 9 =ty degrees ( nor? latitude we see ! nor? /> =ty degrees above ! nor!rn horizon2 :]eas1 if we %\ld travel s\?w>d1 its elevation w\ld gr[ less & less1 until we rea*$ ! equator1 :]e x w\ld appe> 9 ! horizon4 ,or1 if we %\ld travel nor?w>ds1 ! nor? /> w\ld rise cont9ually high] & high]1 until1 if we c\ld rea* ! pole ( ! e>?1 t /> w\ld appe> directly ov] head4 ,! elevation ( ! equator above ! horizon ( any place is equal to ! complem5t ( ! latitude4 ,?us1 at ! latitude ( =ty degrees nor?1 ! equator is elevat$ fifty degrees above ! s\!rn horizon4 ,! e>? is divid$ into five zones4 ,t portion ( ! e>? :i* lies betwe5 ! tropics is call$ ! torrid zone2 t betwe5 ! tropics & ! pol> circles1 ! temp]ate zones2 & t betwe5 ! pol> circles & ! poles1 ! frigid zones4 ,! zodiac is ! "p ( ! cele/ial sph]e :i* lies ab\t eight degrees on ea* side ( ! ecliptic4 ,?is portion ( ! heav5s is ?us m>k$ (f by itself1 because all ! planets move )9 x4 ,aft] endeavor+ to =m1 f ! def9itions1 z cle> an idea z we c ( ! v>i\s circles ( ! sph]e1 we may next resort to an artificial globe1 & see h[ !y are sev]ally repres5t$ !re4 ,i d n advise to beg9 le>n+ ! def9itions f ! globe2 ! m9d is m improv$1 & a p[] ( conceiv+ cle>ly h[ ?+s are 9 ,nature is m effectually acquir$1 by ref]r+ e ?+1 at fir/1 to ! gr& sph]e ( ,nature itself1 & aft]w>ds resort+ to artificial repres5tations to aid our conceptions4 ,we c get b a v imp]fect idea ( a man f a pr(ile cut 9 pap]1 unless we "k ! orig9al4 ,if we are acqua9t$ ) ! individual1 ! pr(ile w assi/ u to recall 8 appe>ance m di/9ctly ?an we c d )\t x4 ,9 l mann]1 orr]ies1 globes1 & o!r artificial aids1 w be f\nd v useful1 9 assi/+ u to =m di/9ct conceptions ( ! relations exi/+ betwe5 ! diff]5t circles ( ! sph]e1 & ( ! arrangem5ts ( ! heav5ly bodies2 b1 unless we h already acquir$ "s correct ideas ( ^! ?+s1 by contemplat+ !m z !y are 9 ,nature1 artificial globes1 & especially orr]ies1 w be apt to mislead u4 ,i tru/ y w be able to obta9 ! use ( a globe1#a to aid y 9 ! /udy ( ! =ego+ def9itions1 or doctr9e ( ! sph]e2 b if n1 ,i w\ld recomm5d ! foll[+ easy device4 ,to repres5t ! e>?1 select a l>ge apple1 7a melon1 :5 9 season1 w be f\nd /ill bett]47 ,! eye & ! /em ( ! apple w indicate ! position ( ! two poles ( ! e>?4 ,apply+ ! ?umb & f+] ( ! left h& to ! poles1 & hold+ ! apple s t ! poles may be 9 a nor? & s\? l9e1 turn ?is globe f we/ to ea/1 & its motion w correspond to ! diurnal movem5t ( ! e>?4 ,pass a wire or a knitt+ ne$le ?r\gh ! poles1 & x w repres5t ! axis ( ! sph]e4 ,a circle cut ar\nd ! apple1 half way betwe5 ! poles1 w be ! equator2 & sev]al o!r circles cut betwe5 ! equator & ! poles1 p>allel to ! equator1 w repres5t p>allels ( latitude2 ( :i*1 two1 drawn tw5ty-?ree & a half degrees f ! equator1 w be ! tropics1 & two o!rs1 at ! same di/ance f ! poles1 w be ! pol> circles4 ,a great circle cut ?r\gh ! poles1 9 a nor? & s\? direction1 w =m ! m]idian1 & sev]al o!r great circles drawn ?r\gh ! poles1 & ( c\rse p]p5dicul>ly to ! equator1 w be second>ies to ! equator1 con/itut+ m]idians1 or h\r circles4 ,a great circle cut ?r\gh ! c5tre ( ! e>?1 f "o tropic to ! o!r1 w\ld repres5t ! plane ( ! ecliptic2 & consequ5tly a l9e cut r\nd ! apple :]e su* a section meets ! surface1 w be ! t]re/rial ecliptic4 ,! po9ts :]e ?is circle meets ! tropics indicate ! position ( ! sol/ices2 & its int]section ) ! equator1 t ( ! equ9octial po9ts4 ,! horizon is be/ repres5t$ by a circul> piece ( pa/ebo>d1 cut s z to fit closely to ! apple1 be+ movable ^u x4 ,:5 ?is horizon is pass$ ?r\gh ! poles1 x becomes ! horizon ( ! equator2 :5 x is s plac$ z to co9cide ) ! e>?'s equator1 x becomes ! horizon ( ! poles2 & 9 e o!r situation x repres5ts ! horizon ( a place on ! globe n9ety degrees e way f x4 ,suppose we are 9 latitude =ty degrees2 !n let u place our movable pap] p>allel to our own horizon1 & elevate ! pole =ty degrees above x1 z ne> z we c judge by ! eye4 ,if we cut a circle ar\nd ! apple1 pass+ ?r\gh its highe/ "p1 & ?r\gh ! ea/ & we/ po9ts1 x w repres5t ! prime v]tical4 ,simple z ! =ego+ device is1 if y w take ! tr\ble to con/ruct "o = y\rself1 x w lead y to m correct views ( ! doctr9e ( ! sph]e1 ?an y w\ld be apt to obta9 f ! mo/ exp5sive artificial globes1 al?\gh !re are _m o!r useful purposes :i* su* globes s]ve1 = :i* ! apple w\ld be inadequate4 ,:5 y h ?us made a sph]e = y\rself1 or1 ) an artificial globe be=e y1 if y h access to "o1 proce$ to po9t out on x ! v>i\s arcs ( azimu? & altitude1 "r asc5sion & decl9ation1 t]re/rial & cele/ial latitude & longitude1--^! la/ be+ ref]r$ to ! equator on ! e>?1 & to ! ecliptic 9 ! heav5s4 ,:5 ! circles ( ! sph]e are well le>n$1 we may advantage\sly employ projections ( !m 9 v>i\s illu/rations4 ,by ! projection ( ! sph]e is meant a repres5tation ( all its p>ts on a plane4 ,! plane itself is call$ ! plane ( projection4 ,let u take any circul> r+1 z a wire b5t into a circle1 & hold x 9 diff]5t positions be=e ! eye4 ,if we hold x p>allel to ! face1 ) ! :ole bread? opposite to ! eye1 we see x z an entire circle4 ,if we turn x a little sideways1 x appe>s oval1 or z an ellipse2 &1 z we cont9ue to turn x m & m r\nd1 ! ellipse gr[s n>r[] & n>r[]1 until1 :5 ! edge is pres5t$ to ! eye1 we see no?+ b a l9e4 ,n[ imag9e ! r+ to be ne> a p]p5dicul> wall1 & ! eye to be remov$ at su* a di/ance f x1 z n to di/+ui% any int]val betwe5 ! r+ & ! wall2 !n ! sev]al figures "u :i* ! r+ is se5 w appe> to be inscrib$ on ! wall1 & we %all see ! r+ z a circle1 :5 p]p5dicul> to a /raight l9e jo9+ ! c5tre ( ! r+ & ! eye1 or z an ellipse1 :5 oblique to ?is l9e1 or z a /raight l9e1 :5 its edge is t[>ds u4 ,illu/ration3 ,fig4 #b4 ,x is 9 ?is mann] t ! circles ( ! sph]e are project$1 z repres5t$ 9 ! foll[+ diagram1 ,fig4 #b4 ,"h1 v>i\s circles are repres5t$ z project$ on ! m]idian1 :i* is suppos$ to be situat$ directly be=e ! eye1 at "s di/ance f x4 ,! horizon ,h ,o1 be+ p]p5dicul> to ! m]idian1 is se5 edgewise1 & consequ5tly is project$ into a /raight l9e4 ,! same is ! case ) ! prime v]tical ,z ,n1 ) ! equator ,e ,q1 & ! sev]al small circles p>allel to ! equator1 :i* repres5t ! two tropics & ! two pol> circles4 ,9 fact1 all circles :atsoev]1 :i* are p]p5dicul> to ! plane ( projection1 w be repres5t$ by /raight l9es4 ,b e circle :i* is p]p5dicul> to ! horizon1 except ! prime v]tical1 be+ se5 obliquely1 z ,z ,m ,n1 w be project$ into an ellipse1 "o half only ( :i* is se51--! o!r half be+ on ! o!r side ( ! plane ( projection4 ,9 ! same mann]1 ,p ,r ,p1 an h\r circle1 is repres5t$ by an ellipse on ! plane ( projection4 ,,footnote3 #a ,a small pair ( globes1 t w answ] e purpose requir$ by ! read]s ( ^! ,lett]s1 may be _h ( ! publi%]s ( ?is ,"w1 at a price n exce$+ t5 doll>s2 or half t sum = a cele/ial globe1 :i* w s]ve alone = /udy+ a/ronomy4 ,,lett] ,,iii4 ,,a/ronomical ,,in/rum5ts4----,,telescope4 ,"h tru?s sublime1 & sacr$ sci5ce *>m1 ,creative arts new faculties supply1 ,me*anic p[]s give m ?an giant's arm1 ,& pi]c+ optics m ?an eagle's eye2 ,eyes t explore creation's wondr\s laws1 ,& tea* u to adore ! great ,design+ ,cause4--,beattie4 ,if1 z ,i tru/1 y h ga9$ a cle> & famili> k ( ! circles & divisions ( ! sph]e1 & ( ! mode ( e/imat+ ! position ( a heav5ly body by its azimu? & altitude1 or by its "r asc5sion & decl9ation1 or by its longitude & latitude1 y w n[ ent] ) advantage ^u an acc\nt ( ^? in/rum5ts1 by means ( :i* our k ( a/ronomy has be5 greatly promot$ & p]fect$4 ,! mo/ anci5t a/ronom]s employ$ no in/rum5ts ( obs]vation1 b acquir$ _! k ( ! heav5ly bodies by long-cont9u$ & mo/ att5tive inspection ) ! nak$ eye4 ,in/rum5ts = measur+ angles 7 fir/ us$ 9 ! ,alex&rian s*ool1 ab\t ?ree hundr$ ye>s be=e ! ,*ri/ian era4 ,:]ev] we are situat$ on ! e>?1 we appe> to be 9 ! c5tre ( a va/ sph]e1 on ! concave surface ( :i* all cele/ial objects are inscrib$4 ,if we take any two po9ts on ! surface ( ! sph]e1 z two />s1 = example1 & imag9e /raight l9es to be drawn to !m f ! eye1 ! angle includ$ betwe5 ^! l9es w be measur$ by ! arc ( ! sky conta9$ betwe5 ! two po9ts4 ,?us1 if ,d ,b ,h1 ,fig4 #c1 page #cj1 repres5ts ! concave surface ( ! sph]e1 ,a1 ,b1 two po9ts on x1 z two />s1 & ,c ,a1 ,c ,b1 /raight l9es drawn f ! spectator to ^? po9ts1 !n ! angul> di/ance betwe5 !m is measur$ by ! arc ,a ,b1 or ! angle ,a ,c ,b4 ,b ?is angle may be measur$ on a mu* small] circle1 hav+ ! same c5tre1 z ,g ,f ,k1 s9ce ! arc ,e ,f w h ! same numb] ( degrees z ! arc ,a ,b4 ,! simple/ mode ( tak+ an angle betwe5 two />s is by means ( an arm op5+ at a jo9t l ! blade ( a p5knife1 ! end ( ! arm mov+ l ,c ,e ^u ! graduat$ circle ,k ,f ,g4 ,9 fact1 an in/rum5t con/ruct$ on ?is pr9ciple1 resembl+ a c>p5t]'s rule ) a fold+ jo9t1 ) a semicircle atta*$1 con/itut$ ! fir/ rude app>atus = measur+ ! angul> di/ance betwe5 two po9ts on ! cele/ial sph]e4 ,?us ! sun's elevation above ! horizon might be asc]ta9$1 by plac+ "o arm ( ! rule on a level ) ! horizon1 & br++ ! edge ( ! o!r into a l9e ) ! sun's c5tre4 ,illu/ration ,fig4 #c4 ,! common surveyor's compass af=ds a simple example ( angul> measurem5t4 ,"h1 ! ne$le lies 9 a nor? & s\? l9e1 :ile ! circul> rim ( ! compass1 :5 ! in/rum5t is level1 corresponds to ! horizon4 ,h5ce ! compass %[s ! azimu? ( an object1 or h[ _m degrees x lies ea/ or we/ ( ! m]idian4 ,x is obvi\s1 t ! l>g] ! graduat$ circle is1 ! m m9utely its limb may be divid$4 ,if ! circle is "o foot 9 diamet]1 ea* degree w occupy "o t5? ( an in*4 ,if ! circle is tw5ty feet 9 diamet]1 a degree w occupy ! space ( two in*es1 & c\ld be easily divid$ into m9utes1 s9ce ea* m9ute w\ld cov] a space "o ?irtie? ( an in*4 ,ref9$ a/ronomical circles are n[ divid$ ) v great skill & accuracy1 ! spaces betwe5 ! divisions be+1 :5 read (f1 magnifi$ by a microscope2 b 9 =m] times1 a/ronom]s _h no mode ( measur+ small angles b by employ+ v l>ge circles4 ,b ! telescope & microscope enable u at pres5t to measure cele/ial arcs mu* m accurately ?an 0 done by ! old] a/ronom]s4 ,9 ! be/ in/rum5ts1 ! measurem5ts ext5d to a s+le second ( space1 or "o ?irty-six hundr$? "p ( a degree1--a space1 on a circle twelve feet 9 diamet]1 no great] ?an "o fifty-sev5 hundr$? "p ( an in*4 ,to divide1 or graduate1 a/ronomical in/rum5ts1 to su* a degree ( nicety1 requires ! highe/ ef=ts ( me*anical skill4 ,inde$1 ! :ole art ( in/rum5t-mak+ is reg>d$ z ! mo/ difficult & ref9$ ( all ! me*anical arts2 & a few em95t arti/s1 :o h produc$ in/rum5ts ( peculi> p[] & accuracy1 take rank ) a/ronom]s ( ! highe/ celebrity4 ,i w endeavor to make y acqua9t$ ) sev]al ( ! pr9cipal in/rum5ts employ$ 9 a/ronomical obs]vations1 b especially ) ! telescope1 :i* is ! mo/ important & int]e/+ ( !m all4 ,i ?9k ,i %all consult y\r wi%es1 z well z y\r improvem5t1 by giv+ y a cle> insight into ! pr9ciples ( ?is pr9ce ( in/rum5ts1 & by recit+ a few p>ticul>s1 at lea/1 respect+ its inv5tion & subsequ5t hi/ory4 ,! ,telescope1 z its "n implies1 is an in/rum5t employ$ = view+ di/ant objects4#b ,x aids ! eye 9 two ways2 fir/1 by enl>g+ ! visual angle "u :i* objects are se51 &1 secondly1 by collect+ & convey+ to ! eye a mu* l>g] am\nt ( ! light t emanates f ! object1 ?an w\ld ent] ! nak$ pupil4 ,a complete k ( ! telescope _c be acquir$1 )\t an acqua9tance ) ! sci5ce ( optics2 b "o unacqua9t$ ) t sci5ce may obta9 "s idea ( ! lead+ pr9ciples ( ?is noble in/rum5t4 ,its ma9 pr9ciple is z foll[s3 ,by means ( ! telescope1 we fir/ =m an image ( a di/ant object1--z ! moon1 = example1--& !n magnify t image by a microscope4 ,illu/ration ,fig4 #d4 ,let u fir/ see h[ ! image is =m$4 ,?is may be done ei!r by a convex l5s1 or by a concave mirror4 ,a convex l5s is a flat piece ( glass1 hav+ its two faces convex1 or sph]ical1 z is se5 9 a common sun-glass1 or a pair ( spectacles4 ,e "o :o has se5 a sun-glass1 kn[s1 t1 :5 held t[>ds ! sun1 x collects ! sol> rays into a small bright circle 9 ! focus4 ,?is is 9 fact a small image ( ! sun4 ,9 ! same mann]1 ! image ( any di/ant object1 z a />1 may be =m$1 z is repres5t$ 9 ! foll[+ diagram4 ,let ,a ,b ,c ,d1 ,fig4 #d1 repres5t ! tube ( ! telescope4 ,at ! front end1 or at ! end :i* is direct$ t[>ds ! object1 7:i* we w suppose to be ! moon17 is ins]t$ a convex l5s1 ,l1 :i* receives ! rays ( light f ! moon1 & collects !m into ! focus at a1 =m+ an image ( ! moon4 ,?is image is view$ by a magnifi] atta*$ to ! end ,b ,c4 ,! l5s1 ,l1 is call$ ! object-glass1 & ! microscope 9 ,b ,c1 ! eyeglass4 ,we apply a microscope to ?is image j z we w\ld to any object2 &1 by greatly enl>g+ its dim5sions1 we may r5d] its v>i\s p>ts f> m di/9ct ?an !y w\ld o!rwise be2 :ile1 at ! same "t1 ! l5s collects & conveys to ! eye a mu* great] quantity ( light ?an w\ld proce$ directly f ! body "u exam9ation4 ,a v few rays ( light only1 f a di/ant object1 z a />1 c ent] ! eye directly2 b a l5s "o foot 9 diamet] w collect a beam ( light ( ! same dim5sions1 & convey x to ! eye4 ,by ^! means1 _m obscure cele/ial objects become di/9ctly visible1 :i* w\ld o!rwise be ei!r too m9ute1 or n suffici5tly lum9\s1 to be se5 by u4 ,b ! image may also be =m$ by means ( a concave mirror1 :i*1 z well z ! concave l5s1 has ! prop]ty ( collect+ ! rays ( light :i* proce$ f any lum9\s body1 & ( =m+ an image ( t body4 ,! image =m$ by a concave mirror is magnifi$ by a microscope1 9 ! same mann] z :5 =m$ by ! concave l5s4 ,:5 ! l5s is us$ to =m an image1 ! in/rum5t is call$ a refract+ telescope2 :5 a concave mirror is us$1 x is call$ a reflect+ telescope4 ,! (fice ( ! object-glass is simply to collect ! light1 & to =m an image ( ! object1 b n to magnify x3 ! magnify+ p[] is :olly 9 ! eyeglass4 ,h5ce ! pr9ciple ( ! telescope is z foll[s3 ,by means ( ! object-glass1 79 ! refract+ telescope17 or by ! concave mirror1 79 ! reflect+ telescope17 we =m an image ( ! object1 & magnify t image by a microscope4 ,! inv5tion ( ?is noble in/rum5t is g5]ally ascrib$ to ! great philosoph] ( ,flor5ce1 ,galileo4 ,he _h he>d t a spectacle mak] ( ,holl& _h accid5tally hit ^u a discov]y1 by :i* di/ant objects might be br\ght app>5tly ne>]2 &1 )\t fur!r in=mation1 he pursu$ ! inquiry1 9 ord] to asc]ta9 :at =ms & comb9ations ( glasses w\ld produce su* a result4 ,by a v philosophical process ( reason+1 he 0 l$ to ! discov]y ( t peculi> =m ( ! telescope :i* be>s 8 "n4 ,al?\gh ! telescopes made by ,galileo 7 no l>g] ?an a common spyglass ( ! k9d n[ us$ on bo>d ( %ips1 yet1 z !y gave new views ( ! heav5ly bodies1 reveal+ ! m\nta9s & valleys ( ! moon1 ! satellites ( ,jupit]1 & multitudes ( />s :i* are invisible to ! nak$ eye1 x 0 reg>d$ ) inf9ite delight & a/oni%m5t4 ,reflect+ telescopes 7 fir/ con/ruct$ by ,sir ,isaac ,newton1 al?\gh ! use ( a concave reflector1 in/ead ( an object-glass1 to =m ! image1 _h be5 previ\sly sugge/$ by ,gregory1 an em95t ,scot* a/ronom]4 ,! fir/ telescope made by ,newton 0 only six in*es long4 ,its reflector1 too1 0 only a little m ?an an in*4 ,not)/&+ its small dim5sions1 x p]=m$ s well1 z to enc\rage fur!r ef=ts2 & ?is illu/ri\s philosoph] aft]w>ds con/ruct$ mu* l>g] in/rum5ts1 "o ( :i*1 made ) 8 own h&s1 0 pres5t$ to ! ,royal ,society ( ,london1 & is n[ c>efully pres]v$ 9 _! libr>y4 ,newton 0 induc$ to und]take ! con/ruction ( reflect+ telescopes1 f ! belief t refract+ telescopes 7 necess>ily limit$ to a v small size1 ) only mod]ate illum9at+ p[]s1 :]eas ! dim5sions & p[]s ( ! =m] admitt$ ( be+ indef9itely increas$4 ,consid]able magnify+ p[]s might1 inde$1 be obta9$ f refractors1 by mak+ !m v long2 b ! brightness ) :i* telescopic objects are se51 dep5ds greatly on ! dim5sions ( ! beam ( light :i* is collect$ by ! object-glass1 or by ! mirror1 & convey$ to ! eye2 & !re=e1 small object-glasses _c h a v high illum9at+ p[]4 ,n[1 ! exp]im5ts ( ,newton on colors l$ him to believe1 t x w\ld be impossible to employ l>ge l5ses 9 ! con/ruction ( telescopes1 s9ce su* glasses w\ld give to ! images1 !y =m$1 ! colors ( ! ra9b[4 ,b lat] opticians h f\nd means ( correct+ ^! imp]fections1 s t we are n[ able to use object-glasses a foot or m 9 diamet]1 :i* give v cle> & bright images4 ,su* in/rum5ts are call$ a*romatic telescopes1--a "n imply+ ! abs5ce ( prismatic or ra9b[ colors 9 ! image4 ,x is1 h[ev]1 f> m difficult to con/ruct l>ge a*romatic ?an l>ge reflect+ telescopes4 ,v l>ge pieces ( glass c seldom be f\nd1 t are suffici5tly pure = ! purpose2 s9ce e inequality 9 ! glass1 su* z waves1 te>s1 ?reads1 & ! l1 spoils x = optical purposes1 z x di/orts ! light1 & produces no?+ b confus$ images4 ,! a*romatic telescope 7t is1 ! refract+ telescope1 hav+ su* an object-glass z to give a colorless image7 0 inv5t$ by ,dollond1 a di/+ui%$ ,engli% arti/1 ab\t ! ye> #ageg4 ,he _h 9 8 possession a quantity ( glass ( a rem>kably f9e quality1 :i* enabl$ him to c>ry 8 inv5tion at once to a high degree ( p]fection4 ,x has ev] s9ce be51 ) ! manufactur]s ( telescopes1 a matt] ( ! greate/ difficulty to f9d pieces ( glass1 ( a suitable quality = object-glasses1 m ?an two or ?ree in*es 9 diamet]4 ,h5ce1 l>ge a*romatic telescopes are v exp5sive1 be+ valu$ 9 proportion to ! cubes ( _! diamet]s2 t is1 if a telescope ^: ap]ture 7z ! bread? ( ! object-glass is te*nically call$7 is two in*es1 co/ "o hundr$ doll>s1 "o ^: ap]ture is eight in*es w\ld co/ six ?\s& f\r hundr$ doll>s4 ,s9ce x is s mu* easi] to make l>ge reflect+ ?an l>ge refract+ telescopes1 y may ask1 :y ! latt] are ev] attempt$1 & :y reflectors are n exclusively employ$8 ,i answ]1 t ! a*romatic telescope1 :5 l>ge & well con/ruct$1 is a m p]fect & m durable in/rum5t ?an ! reflect+ telescope4 ,mu* m ( ! light t falls on ! mirror is absorb$ ?an is lo/ 9 pass+ ?r\gh ! object-glass ( a refractor2 & h5ce ! l>g] a*romatic telescopes af=d a /rong] light ?an ! reflect+1 unless ! latt] are made ( an enorm\s & unwieldy size4 ,moreov]1 ! mirror is v liable to t>ni%1 & w nev] reta9 its full lu/re = _m ye>s toge!r2 & x is no easy matt] to re/ore ! lu/re1 :5 once impair$4 ,9 my next ,lett]1 ,i w give y an acc\nt ( "s ( ! mo/ celebrat$ telescopes t h ev] be5 con/ruct$1 & po9t out ! me?od ( us+ ?is excell5t in/rum5t1 s z to obta9 ) x ! f9e/ views ( ! heav5ly bodies4 ,,footnote3 #b ,f two ,greek words1 tle1 7tele17 f>1 & s*ope1 7skopeo17 to see4 ,,lett] ,,iv ,,telescope ,,cont9u$4 ----! broad circumf]5ce ,hung on 8 %\ld]s l ! moon1 ^: orb ,?r\gh optic glass ! ,tuscan arti/ views ,at ev5+1 f ! top ( ,fesol ,or 9 ,vald>no1 to descry new l&s1 ,riv]s or m\nta9s1 9 h] spott$ globe4--,milton4 ,! two mo/ celebrat$ telescopes1 hi!rto made1 are ,h]s*el's =ty-feet reflector1 & ! great ,dorpat refractor4 ,h]s*el 0 a ,hanov]ian by bir?1 b settl$ 9 ,engl& 9 ! y\ng] "p ( 8 life4 ,z e>ly z #aggd1 he began to make telescopes = 8 own use2 &1 dur+ 8 life1 he made m ?an f\r hundr$1 ( v>i\s sizes & p[]s4 ,"u ! patronage ( ,george ! ,?ird1 he complet$1 9 #aghi1 8 great telescope1 hav+ a tube ( iron1 =ty feet long1 & a speculum1 =ty-n9e & a half in*es or m ?an f\r feet 9 diamet]4 ,let u endeavor to =m a j conception ( ?is gigantic in/rum5t1 :i* we c d only by dwell+ on its dim5sions1 & comp>+ !m ) ^? ( o!r objects ) :i* we are famili>1 z ! l5g? or height ( a h\se1 & ! bread? ( a hog%ead or ci/]n1 ( kn[n dim5sions4 ,! reflector alone weigh$ ne>ly a ton4 ,s l>ge & pond]\s an in/rum5t mu/ require a va/ deal ( ma*9]y to "w x1 & to keep x /eady2 &1 accord+ly1 ! framework surr\nd+ x 0 =m$ ( heavy timb]s1 & resembl$ ! frame ( a l>ge build+4 ,:5 "o ( ! l>ge/ ( ! fix$ />s1 z ,sirius1 is ent]+ ! field ( ?is telescope1 its approa* is ann\nc$ by a bright dawn1 l t :i* prec$es ! ris+ sun2 & :5 ! /> itself ent]s ! field1 ! light is insupportable to ! nak$ eye4 ,! planets are exp&$ into brilliant lum9>ies1 l ! moon2 & innum]able multitudes ( />s are scatt]$ l glitt]+ du/ ov] ! cele/ial vault4 ,! great ,dorpat telescope is ( m rec5t con/ruction4 ,x 0 made by ,fraunh(]1 a ,g]man optician ( ! greate/ em95ce1 at ,muni*1 9 ,bav>ia1 & takes its "n f its be+ atta*$ to ! obs]vatory at ,dorpat1 9 ,russia4 ,x is ( mu* small] dim5sions ?an ! great telescope ( ,h]s*el4 ,its object-glass is n9e & a half in*es 9 diamet]1 & its l5g?1 f\rte5 feet4 ,al?\gh ! price ( ?is in/rum5t 0 ne>ly five ?\s& doll>s1 yet x is said t ?is sum b>ely cov]$ ! actual exp5ses4 ,x weighs five ?\s& p\nds1 & yet is turn$ ) ! f+]4 ,9 facility ( managem5t1 x has greatly ! advantage ( ,h]s*el's telescope4 ,moreov]1 ! sky ( ,engl& is s mu* ( ! "t unfavorable = a/ronomical obs]vation1 t "o hundr$ good h\rs 7or ^? 9 :i* ! high] p[]s c be us$7 are all t c be obta9$ 9 a :ole ye>4 ,on ?is acc\nt1 & on acc\nt ( ! difficulty ( %ift+ ! position ( ! in/rum5t1 ,h]s*el e/imat$ t x w\ld take ab\t six hundr$ ye>s to obta9 ) x ev5 a mom5t>y glimpse ( e "p ( ! heav5s4 ,?is rem>k %[s t su* great telescopes are unsuit$ to ! common purposes ( a/ronomical obs]vation4 ,inde$1 mo/ ( ,h]s*el's discov]ies 7 made ) 8 small telescopes2 & al?\gh1 = c]ta9 r>e purposes1 p[]s 7 appli$ :i* magnifi$ sev5 ?\s& times1 yet1 9 mo/ ( 8 obs]vations1 p[]s magnify+ only two or ?ree hundr$ times 7 employ$4 ,! highe/ p[] ( ! ,dorpat telescope is only sev5 hundr$1 & yet ! director ( ?is in/rum5t1 ,pr(essor ,/ruve1 is ( ! op9ion1 t x is ne>ly or q equal 9 quality1 all ?+s consid]$1 to ,h]s*el's =ty-feet reflector4 ,x is n g5]ally und]/ood 9 :at way greatness ( size 9 a telescope increases its p[]s2 & x conveys b an imp]fect idea ( ! excell5ce ( a telescope1 to tell h[ mu* x magnifies4 ,9 ! same in/rum5t1 an increase ( magnify+ p[] is always att5d$ ) a dim9ution ( ! light & ( ! field ( view4 ,h5ce1 ! l[] p[]s g5]ally af=d ! mo/ agreeable views1 because !y give ! cle>e/ light1 & take 9 ! l>ge/ space4 ,! sev]al circum/ances :i* influ5ce ! qualities ( a telescope are1 illum9at+ p[]1 di/9ctness1 field ( view1 & magnify+ p[]4 ,l>ge mirrors & l>ge object-glasses are sup]ior to small] ones1 because !y collect a l>g] beam ( light1 & transmit x to ! eye4 ,/>s :i* are invisible to ! nak$ eye are r5d]$ visible by ! telescope1 because ?is in/rum5t collects & conveys to ! eye a l>ge beam ( ! few rays :i* emanate f ! />s2 :]eas a beam ( ^! rays ( only ! diamet] ( ! pupil ( ! eye1 w\ld af=d too little light = di/9ct vision4 ,9 ?is p>ticul>1 l>ge telescopes h great advantages ov] small ones4 ,! great mirror ( ,h]s*el's =ty-feet reflector collects & conveys to ! eye a beam m ?an f\r feet 9 diamet]4 ,! ,dorpat telescope also transmits to ! eye a beam n9e & "o half in*es 9 diamet]4 ,?is seems small1 9 comp>ison ) ! reflector2 b mu* less ( ! light is lo/ on pass+ ?r\gh ! glass ?an is absorb$ by ! mirror1 & ! mirror is v liable to be cl\d$ or t>ni%$2 s t !re is n s great a diff]5ce 9 ! two in/rum5ts1 9 reg>d to illum9at+ p[]1 z might be suppos$ f ! diff]5ce ( size4 ,di/9ctness ( view is all-important to ! p]=mance ( an in/rum5t4 ,! object may be suffici5tly bright1 yet1 if ! image is di/ort$1 or ill-def9$1 ! illum9ation is ( little consequ5ce4 ,?is prop]ty dep5ds ma9ly on ! skill ) :i* all ! imp]fections ( figure & color 9 ! glass or mirror are correct$1 & c exi/ 9 p]fection only :5 ! image is r5d]$ completely a*romatic1 & :5 all ! rays t proce$ f ea* po9t 9 ! object are collect$ into correspond+ po9ts ( ! image1 unaccompani$ by any o!r rays4 ,di/9ctness is v mu* affect$ by ! /ead9ess ( ! in/rum5t4 ,e "o kn[s h[ indi/9ct a page becomes1 :5 a book is pass$ rapidly backw>ds & =w>ds be=e ! eyes1 & h[ difficult x is to read 9 a c>riage 9 rapid motion on a r\gh road4 ,field ( view is ano!r important consid]ation4 ,! f9e/ in/rum5ts exhibit ! moon1 = example1 n only bright & di/9ct1 9 all its p>ts1 b !y take 9 ! :ole disk at once2 :]eas1 ! inf]ior in/rum5ts1 :5 ! high] p[]s1 especially1 are appli$1 p]mit u to see only a small "p ( ! moon at once4 ,i hope1 my fri5d1 t1 :5 y h p]us$ ^! ,lett]s1 or r1 :ile y are p]us+ !m1 y w h frequ5t opportunities ( look+ ?r\gh a good telescope4 ,i ev5 anticipate t y w acquire su* a ta/e = view+ ! heav5ly bodies ) ! aid ( a good glass1 t y w deem a telescope a mo/ suitable app5dage to y\r libr>y1 & z c]ta9ly n less an ornam5t to x ?an ! m exp5sive /atues ) :i* "s p ( =tune adorn !irs4 ,i w !re=e1 be=e conclud+ ?is lett]1 (f] y a few directions = us+ ! telescope4 ,"s /ates ( wea!r1 ev5 :5 ! sky is cle>1 are f> m favorable = a/ronomical obs]vation ?an o!rs4 ,aft] sudd5 *anges ( temp]ature 9 ! atmosph]e1 ! m$ium is usually v un/eady4 ,if ! sun %9es out w>m aft] a cl\dy season1 ! gr\nd fir/ becomes heat$1 & ! air t is ne>e/ to x is exp&$1 & rises1 :ile ! cold] air desc5ds1 & ?us asc5d+ & desc5d+ curr5ts ( air1 m+l+ toge!r1 create a confus$ & wavy m$ium4 ,! same cause op]ates :5 a curr5t ( hot air rises f a *imney2 & h5ce ! /ate ( ! atmosph]e 9 cities & l>ge t[ns is v unfavorable to ! a/ronom]1 on ?is acc\nt1 z well z on acc\nt ( ! smoky condition 9 :i* x is usually f\nd4 ,aft] a long season ( dry wea!r1 also1 ! air becomes smoky1 & unfit = obs]vation4 ,inde$1 foggy1 mi/y1 or smoky1 air is s preval5t 9 "s c\ntries1 t only a v few times 9 ! :ole ye> c be f\nd1 :i* are entirely suit$ to obs]vation1 especially ) ! high] p[]s2 = we mu/ recollect1 t ^! inequalities & imp]fections are magnifi$ by telescopes1 z well z ! objects !mselves4 ,?us1 z ,i h already m5tion$1 n m ?an "o hundr$ good h\rs 9 a ye> c\ld be obta9$ = obs]vation ) ,h]s*el's great telescope4 ,by good h\rs1 ,h]s*el means t ! sky mu/ be v cle>1 ! moon abs5t1 no twilight1 no haz9ess1 no viol5t w9d1 & no sudd5 *ange ( temp]ature4 ,z a g5]al fact1 ! w>m] climates enjoy a mu* f9] sky = ! a/ronom] ?an ! cold]1 hav+ _m m cle> ev5+s1 a %ort twilight1 & less *ange ( temp]ature4 ,! wat]y vapor ( ! atmosph]e1 also1 is m p]fectly dissolv$ 9 hot ?an 9 cold air1 & ! m wat] air conta9s1 provid$ x is 9 a /ate ( p]fect solution1 ! cle>] x is4 ,a c]ta9 prep>ation ( ! obs]v] himself is also requisite = ! nice/ obs]vations ) ! telescope4 ,he mu/ be free f all agitation1 & ! eye mu/ n rec5tly h be5 expos$ to a /rong light1 :i* contracts ! pupil ( ! eye4 ,inde$1 = delicate obs]vations1 ! obs]v] %\ld rema9 = "s "t be=eh& 9 a d>k room1 to let ! pupil ( ! eye dilate4 ,by ?is means1 x w be enabl$ to admit a l>g] numb] ( ! rays ( light4 ,9 asc5d+ ! /airs ( an obs]vatory1 visitors frequ5tly get out ( brea?1 & hav+ p]haps rec5tly em]g$ f a /rongly-light$ ap>tm5t1 ! eye is n 9 a favorable /ate = obs]vation4 ,"u ^! disadvantages1 !y take a ha/y look into ! telescope1 & x is no wond] t disappo9tm5t usually foll[s4 ,want ( /ead9ess is a great difficulty att5d+ ! use ( ! highe/ magnifi]s2 = ! motions ( ! in/rum5t are magnifi$ z well z ! object4 ,h5ce1 9 ! /ructure ( obs]vatories1 ! greate/ pa9s is requisite1 to avoid all tremor1 & to give to ! in/rum5ts all possible /ead9ess2 & ! same c>e is to be ex]cis$ by obs]v]s4 ,9 ! m ref9$ obs]vations1 only "o or two p]sons ought to be ne> ! in/rum5t4 ,9 g5]al1 l[ p[]s af=d bett] views ( ! heav5ly bodies ?an v high magnifi]s4 ,x may be ?\ght absurd1 to recomm5d ! use ( l[ p[]s1 9 respect to l>ge in/rum5ts especially1 s9ce x is commonly suppos$ t ! advantage ( l>ge in/rum5ts is1 t !y w be> high magnify+ p[]s4 ,b ?is is n _! only1 nor ev5 _! pr9cipal1 advantage4 ,a good light & l>ge field are qualities1 = mo/ purposes1 m important ?an great magnify+ p[]2 & x mu/ be borne 9 m9d1 t1 z we increase ! magnify+ p[] 9 a giv5 in/rum5t1 we dim9i% bo? ! illum9ation & ! field ( view4 ,/ill1 diff]5t objects require diff]5t magnify+ p[]s2 & a telescope is usually furni%$ ) sev]al v>ieties ( p[]s1 "o ( :i* is be/ fitt$ = view+ ! moon1 ano!r = ,jupit]1 & a /ill high] p[] = ,saturn4 ,comets require only ! l[e/ magnifi]s2 = "h1 our object is to comm& z mu* light1 & z l>ge a field1 z possible1 :ile x avails little to increase ! dim5sions ( ! object4 ,on ! o!r h&1 = c]ta9 d\ble />s1 7/>s :i* appe> s+le to ! nak$ eye1 b d\ble to ! telescope17 we require v high magnifi]s1 9 ord] to sep>ate ^! m9ute objects s f> f ea* o!r1 t ! int]val c be di/9ctly se54 ,:5ev] we exhibit cele/ial objects to inexp]i5c$ obs]v]s1 x is useful to prec$e ! view ) good draw+s ( ! objects1 accompani$ by an explanation ( :at ea* appe>ance1 exhibit$ 9 ! telescope1 indicates4 ,! novice is told1 t m\nta9s & valleys c be se5 9 ! moon by ! aid ( ! telescope2 b1 on look+1 he sees a confus$ mass ( light & %ade1 & no?+ :i* looks to him l ei!r m\nta9s or valleys4 ,_h 8 att5tion be5 previ\sly direct$ to a pla9 draw+ ( ! moon1 & ea* p>ticul> appe>ance int]pret$ to him1 he w\ld !n h look$ ?r\gh ! telescope ) intellig5ce & satisfaction4 ,,lett] ,v4 ,,obs]vatories4 ,we1 ?\gh f heav5 remote1 to heav5 w move1 ,) /r5g? ( m9d1 & tread ! abyss above2 ,& p5etrate1 ) an int]ior light1 ,^? upp] dep?s :i* ,nature hid f sight4 ,pleas$ we w be1 to walk along ! sph]e ,( %9+ />s1 & travel ) ! ye>4--,ovid4 ,an obs]vatory is a /ructure fitt$ up expressly = a/ronomical obs]vations1 & furni%$ ) suitable in/rum5ts = t purpose4 ,! two mo/ celebrat$ obs]vatories1 hi!rto built1 are t ( ,ty*o ,brahe1 & t ( ,gre5wi*1 ne> ,london4 ,! obs]vatory ( ,ty*o ,brahe1 ,fig4 #e1 0 con/ruct$ at ! exp5se ( ! ,k+ ( ,d5m>k1 9 a /yle ( royal magnific5ce1 & co/ no less ?an two hundr$ ?\s& cr[ns4 ,x 0 situat$ on ! isl& ( ,hu5na1 at ! entrance ( ! ,baltic1 & 0 call$ ,uraniburg1 or ! palace ( ! skies4 ,be=e ,i give y an acc\nt ( ,ty*o's obs]vatory1 ,i w recite a few p>ticul>s respect+ ?is great a/ronom] himself4 ,ty*o ,brahe 0 ( ,sw$i% desc5t1 & ( noble family2 b hav+ receiv$ 8 education at ! ,univ]sity ( ,cop5hag51 & sp5t a l>ge "p ( 8 life 9 ,d5m>k1 he is usually consid]$ z a ,dane1 & quot$ z a ,dani% a/ronom]4 ,he 0 born 9 ! ye> #aedf4 ,:5 he 0 ab\t f\rte5 ye>s old1 !re happ5$ a great eclipse ( ! sun1 :i* awak5$ 9 him a high int]e/1 especially :5 he saw h[ ,illu/ration ,fig4 #e4 accurately all ! circum/ances ( x answ]$ to ! pr$iction ) :i* he _h be5 be=e made acqua9t$4 ,he 0 imm$iately seiz$ ) an irresi/ible passion to acquire a k ( ! sci5ce :i* c\ld s successfully lift ! veil ( futurity4 ,8 fri5ds _h de/9$ him = ! pr(ession ( law1 &1 f ! sup]ior tal5ts ( :i* he gave e>ly promise1 & ) ! advantage ( p[]ful family connexions1 !y _h m>k$ out = him a di/+ui%$ c>e] 9 public life4 ,!y !re=e endeavor$ to disc\rage him f pursu+ a pa? :i* !y deem$ s mu* less glori\s ?an t1 & va9ly s\ght1 by v>i\s means1 to ext+ui% ! zeal = a/ronomy :i* 0 k9dl$ 9 8 y\?ful bosom4 ,despis+ all ! attractions ( a c\rt1 he contract$ an alliance ) a peasant girl1 &1 9 ! peaceful retirem5t ( dome/ic life1 desir$ no happi] lot ?an to p]use ! gr& volume :i* ! nocturnal heav5s display$ to 8 en?usia/ic imag9ation4 ,he soon e/abli%$ 8 fame z "o ( ! greate/ a/ronom]s ( ! age1 & mon>*s did homage to 8 g5ius4 ,! ,k+ ( ,d5m>k became 8 munific5t patron1 & ,james ! ,fir/1 ,k+ ( ,engl&1 :5 he w5t to ,d5m>k to complete 8 m>riage ) a ,dani% ,pr9cess1 pass$ eight days ) ,ty*o 9 8 obs]vatory1 &1 at 8 dep>ture1 address$ to ! a/ronom] a ,lat9 ode1 accompani$ ) a magnific5t pres5t4 ,he gave him also 8 royal lic5se to pr9t 8 works 9 ,engl&1 & add$ to x ! foll[+ complim5t>y lett]3 ,nor am ,i acqua9t$ ) ^! ?+s on ! relation ( o!rs1 or f a m]e p]usal ( y\r works1 b ,i h se5 !m ) my own eyes1 & he>d !m ) my own e>s1 9 y\r resid5ce at ,uraniburg1 dur+ ! v>i\s le>n$ & agreeable conv]sations :i* ,i !re held ) y1 :i* ev5 n[ affect my m9d to su* a degree1 t x is difficult to decide1 :e!r ,i recollect !m ) great] pleasure or admiration4 ,admir+ disciples also cr[d$ to ?is sanctu>y ( ! sci5ces1 to acquire a k ( ! heav5s4 ,! obs]vatory consi/$ ( a ma9 build+1 :i* 0 squ>e1 ea* side be+ sixty feet1 & ( l>ge w+s 9 ! =m ( r\nd t[]s4 ,! :ole 0 execut$ 9 a /yle ( great magnific5ce1 & ,ty*o1 :o 0 a nobleman by desc5t1 gratifi$ 8 ta/e = spl5dor & ornam5t1 by giv+ to e "p ( ! /ructure an air ( ! mo/ f9i%$ elegance4 ,nor 7 ! in/rum5ts ) :i* x 0 furni%$ less magnific5t ?an ! build+s4 ,!y 7 va/ly l>g] ?an _h be=e be5 employ$ 9 ! survey ( ! heav5s1 & _m ( !m 7 adorn$ ) co/ly ornam5ts4 ,! cut on page #df1 ,fig4 #f1 repres5ts "o ( ,ty*o's l>ge & spl5did in/rum5ts1 7an a/ronomical quadrant17 on "o side ( :i* 0 figur$ a repres5tation ( ! a/ronom] & 8 assi/ants1 9 ! mid/ ( _! in/rum5ts1 & int5tly engag$ 9 mak+ & record+ obs]vations4 ,x conveys to u a /rik+ idea ( ! magnific5ce ( 8 arrangem5ts1 & ( ! ext5t ( 8 op]ations4 ,"h ,ty*o sat 9 /ate1 clad 9 ! robes ( nobility1 & support$ ?r\gh\t 8 e/abli%m5t ! etiquette due to 8 rank4 ,8 obs]vations 7 m num]\s ?an all t _h ev] be5 made be=e1 & !y 7 c>ri$ to a degree ( accuracy t is a/oni%+1 :5 we consid] t !y 7 made )\t ! use ( ! telescope1 :i* 0 n yet inv5t$4 ,ty*o c>ri$ on 8 obs]vations at ,uraniburg = ab\t tw5ty ye>s1 dur+ :i* "t he accumulat$ an imm5se /ore ( accurate & valuable facts1 :i* af=d$ ! gr\ndwork ( ! discov]y ( ! great laws ( ! sol> sy/em e/abli%$ by ,kepl]1 ( :om ,i %all tell y m h]eaft]4 ,b ! high m>ks ( di/9ction :i* ,ty*o enjoy$1 n only f 8 own ,sov]eign1 b also f =eign pot5tates1 provok$ ! envy ( ! c\rti]s ( 8 royal patron4 ,!y did n inde$ v5ture to make _! attacks ^u him :ile 8 g5]\s patron 0 liv+2 b ! ,k+ 0 no soon] dead1 & succe$$ by a "y mon>*1 :o did n feel ! same ,illu/ration ,fig4 #f4 int]e/ 9 protect+ & enc\rag+ ?is great ornam5t ( ! k+dom1 ?an 8 envi\s foes c>ri$ into execution _! long-m$itat$ plot = 8 ru94 ,!y repres5t$ to ! "y ,k+1 t ! treasury 0 exhau/$1 & t x 0 necess>y to retr5* a numb] ( p5sions1 :i* _h be5 grant$ = useless purposes1 & 9 p>ticul> t ( ,ty*o1 :i*1 !y ma9ta9$1 ought to be conf]r$ ^u "s p]son capable ( r5d]+ great] s]vices to ! /ate4 ,by ^! means1 !y succe$$ 9 depriv+ him ( 8 support1 & he 0 compell$ to retreat "u ! hospitable mansion ( a fri5d 9 ,g]many4 ,"h he became kn[n to ! ,emp]or1 :o invit$ him to ,prague1 :]e1 ) an ample /ip5d1 he resum$ 8 labors4 ,b1 ?\gh surr\nd$ ) affectionate fri5ds & admir+ disciples1 he 0 /ill an exile 9 a =eign l&4 ,al?\gh 8 c\ntry _h be5 base 9 its +ratitude1 x 0 yet ! l& :i* he lov$2 ! sc5e ( 8 e>lie/ affection2 ! !atre ( 8 sci5tific glory4 ,^! feel+s cont9ually prey$ ^u 8 m9d1 & 8 unsettl$ _s 0 ev] hov]+ among 8 native m\nta9s4 ,9 ?is condition he 0 attack$ by a disease ( ! mo/ pa9ful k9d1 &1 ?\gh its agoniz+ p>oxysms _h l5g!n$ int]missions1 yet he saw t dea? 0 approa*+4 ,he implor$ 8 pupils to p]sev]e 9 _! sci5tific labors2 he conv]s$ ) ,kepl] on "s ( ! pr(\nde/ po9ts ( a/ronomy2 & ) ^! secul> occupations he m+l$ frequ5t acts ( piety & devotion4 ,9 ?is happy condition he expir$1 )\t pa91 at ! age ( fifty-five4#c ,! obs]vatory at ,gre5wi* 0 n built until a hundr$ ye>s aft] t ( ,ty*o ,brahe1 namely1 9 #afgf4 ,! great int]e/s ( ! ,briti% nation1 :i* are involv$ 9 navigation1 con/itut$ ! rul+ motive ) ! gov]nm5t to l5d _! aid 9 erect+ & ma9ta9+ ?is obs]vatory4 ,! site ( ! obs]vatory at ,gre5wi* is on a comm&+ em95ce fac+ ! ,riv] ,?ames1 five miles ea/ ( ! c5tral p>ts ( ,london4 ,be+ "p ( a royal p>k1 ! neighbor+ gr\nds are 9 no dang] ( be+ occupi$ by build+s1 s z to ob/ruct ! view4 ,x is also 9 full view ( ! %ipp+ on ! ,?ames2 &1 accord+ to a /&+ regulation ( ! obs]vatory1 at ! in/ant ( "o o'clock1 e day1 a huge ball is dropp$ f ov] ! h\se1 z a signal to ! comm&]s ( vessels = regulat+ _! *ronomet]s4 ,! build+s comprise a s]ies ( rooms1 ( suffici5t numb] & ext5t to accommodate ! diff]5t in/rum5ts1 ! inmates ( ! e/abli%m5t1 & ! libr>y2 & on ! top is a celebrat$ cam]a obscura1 exhibit+ a mo/ di/9ct & p]fect picture ( ! gr& & unrivall$ sc5]y :i* ?is em95ce comm&s4 ,?is e/abli%m5t1 by ! accuracy & ext5t ( its obs]vations1 has contribut$ m ?an all o!r in/itutions to p]fect ! sci5ce ( a/ronomy4 ,to preside ov] & direct ?is great in/itution1 a man ( ! highe/ em95ce 9 ! sci5ce is appo9t$ by ! gov]nm5t1 ) ! title ( ,a/ronom] ,royal4 ,he is paid an ample sal>y1 ) ! und]/&+ t he is to devote himself exclusively to ! bus9ess ( ! obs]vatory4 ,! a/ronom]s royal ( ! ,gre5wi* obs]vatory1 f ! "t ( its fir/ e/abli%m5t1 9 #afgf1 to ! pres5t "t1 h con/itut$ a s]ies ( ! pr\de/ names ( :i* ,briti% sci5ce c boa/4 ,a m detail$ sket* ( _! int]e/+ hi/ory w be giv5 t[>ds ! close ( ^! ,lett]s4 ,six assi/ants1 besides inf]ior labor]s1 are con/antly 9 att5dance2 & ! bus9ess ( mak+ & record+ obs]vations is conduct$ ) ! utmo/ sy/em & ord]4 ,! great objects to be atta9$ 9 ! con/ruction ( an obs]vatory are1 a comm&+ & unob/ruct$ view ( ! heav5s2 fre$om f causes t affect ! transp>5cy & uni=m /ate ( ! atmosph]e1 su* z fires1 smoke1 or m>%y gr\nds2 me*anical facilities = ! managem5t ( in/rum5ts1 &1 especially1 e precaution t is necess>y to secure p]fect /ead9ess4 ,?is la/ consid]ation is "o ( ! greate/ importance1 p>ticul>ly 9 ! use ( v l>ge magnifi]s2 = we mu/ recollect1 t any motion 9 ! in/rum5t is magnifi$ by ! full p[] ( ! glass1 & gives a proportional un/ead9ess to ! object4 ,a situation is !re=e select$ z remote z possible f public roads1 7= ev5 ! pass+ ( c>riages w\ld give a tremul\s motion to ! gr\nd1 :i* w\ld be s5sible 9 l>ge in/rum5ts17 & /ructures ( solid masonry are comm5c$ deep en\gh 9 ! gr\nd to be unaffect$ by fro/1 & built up to ! height requir$1 )\t any connexion ) ! o!r p>ts ( ! build+4 ,_m obs]vatories are furni%$ ) a movable dome = a ro(1 capable ( revolv+ on roll]s1 s t in/rum5ts p5etrat+ ?r\gh ! ro( may be easily br\ght to be> ^u any po9t at or ne> ! z5i?4 ,y w n p]haps desire me to g into a m9ute description ( all ! v>i\s in/rum5ts t are us$ 9 a well-con/ruct$ obs]vatory4 ,nor is ?is necess>y1 s9ce a v l>ge proportion ( all a/ronomical obs]vations are tak5 on ! m]idian1 by means ( ! transit in/rum5t & clock4 ,:5 a body1 9 its diurnal revolution1 comes to ! m]idian1 x is at its highe/ po9t above ! horizon1 & is !n lea/ affect$ by refraction & p>allax4 ,?is1 !n1 is ! mo/ favorable position = tak+ obs]vations ^u x4 ,moreov]1 x is peculi>ly easy to take obs]vations on a body :5 9 ?is situation4 ,h5ce ! transit in/rum5t & clock are ! mo/ important memb]s ( an a/ronomical obs]vatory4 ,y w1 !re=e1 expect me to give y "s acc\nt ( ^! in/rum5ts4 ,illu/ration ,fig4 #g4 ,! transit in/rum5t is a telescope :i* is fix$ p]man5tly 9 ! m]idian1 & moves only 9 t plane4 ,! accompany+ diagram1 ,fig4 #g1 repres5ts a side view ( a portable transit in/rum5t1 exhibit+ ! telescope support$ on a firm horizontal axis1 on :i* x turns 9 ! plane ( ! m]idian1 f ! s\? po9t ( ! horizon ?r\gh ! z5i? to ! nor? po9t4 ,x c !re=e be s direct$ z to obs]ve ! passage ( a /> across ! m]idian at any altitude4 ,! accompany+ graduat$ circle enables ! obs]v] to set ! in/rum5t at any requir$ altitude1 correspond+ to ! kn[n altitude at :i* ! body to be obs]v$ crosses ! m]idian4 ,or x may be us$ to measure ! altitude ( a body1 or its z5i? di/ance1 at ! "t ( its m]idian passage4 ,ne> ! circle may be se5 a _s-level1 :i* s]ves to %[ :5 ! axis is exactly on a level ) ! horizon4 ,! framework is made ( solid metal1 7usually brass17 e ?+ be+ arrang$ ) ref]5ce to keep+ ! in/rum5t p]fectly /eady4 ,x /&s on screws1 :i* n only af=d a /eady support1 b are useful = adju/+ ! in/rum5t to a p]fect level4 ,! transit in/rum5t is sometimes fix$ immovably to a solid f\ndation1 z a pill> ( /one1 :i* is built up f a dep? 9 ! gr\nd bel[ ! rea* ( fro/4 ,:5 enclos$ 9 a build+1 z 9 an obs]vatory1 ! /one pill> is c>ri$ up sep>ate f ! walls & floors ( ! build+1 s z to be entirely free f ! agitations to :i* !y are liable4 ,! use ( ! transit in/rum5t is to %[ ! precise in/ant :5 a heav5ly body is on ! m]idian1 or to measure ! "t x occupies 9 cross+ ! m]idian4 ,! a/ronomical clock is ! con/ant companion ( ! transit in/rum5t4 ,?is clock is s regulat$ z to keep exact pace ) ! />s1 & ( c\rse ) ! revolution ( ! e>? on its axis2 t is1 x is regulat$ to sid]eal "t4 ,x measures ! progress ( a />1 indicat+ an h\r = e fifte5 degrees1 & tw5ty-f\r h\rs = ! :ole p]iod ( ! revolution ( ! />4 ,sid]eal "t comm5ces :5 ! v]nal equ9ox is on ! m]idian1 j z sol> "t comm5ces :5 ! sun is on ! m]idian4 ,h5ce ! h\r by ! sid]eal clock has no correspond5ce ) ! h\r ( ! day1 b simply indicates h[ long x is s9ce ! equ9octial po9t cross$ ! m]idian4 ,= example1 ! clock ( an obs]vatory po9ts to ?ree h\rs & tw5ty m9utes2 ?is may be 9 ! morn+1 at noon1 or any o!r "t ( ! day1--= x m]ely %[s t x is ?ree h\rs & tw5ty m9utes s9ce ! equ9ox 0 on ! m]idian4 ,h5ce1 :5 a /> is on ! m]idian1 ! clock itself %[s its "r asc5sion1 :i* y w recollect is ! angul> di/ance measur$ on ! equ9octial1 f ! po9t ( int]section ( ! ecliptic & equ9octial1 call$ ! v]nal equ9ox1 reckon+ fifte5 degrees = e h\r1 & a proportional numb] ( degrees & m9utes = a less p]iod4 ,i h be=e rem>k$1 t a v l>ge portion ( all a/ronomical obs]vations are tak5 :5 ! bodies are on ! m]idian1 by means ( ! transit in/rum5t & clock4 ,hav+ n[ describ$ ^! in/rum5ts1 ,i w next expla9 ! mann] ( us+ !m = diff]5t obs]vations4 ,any ?+ becomes a measure ( "t1 :i* divides duration equally4 ,! equ9octial1 !re=e1 is peculi>ly adapt$ to ?is purpose1 s9ce1 9 ! daily revolution ( ! heav5s1 equal portions ( ! equ9octial pass "u ! m]idian 9 equal times4 ,! only difficulty is1 to asc]ta9 ! am\nt ( ^! portions = giv5 int]vals4 ,n[1 ! clock %[s u exactly ?is am\nt2 =1 :5 regulat$ to sid]eal "t1 7z x easily may be17 ! h\r-h& keeps exact pace ) ! equator1 revolv+ once on ! dial-plate ( ! clock :ile ! equator turns once by ! revolution ( ! e>?4 ,! same is true1 also1 ( all ! small circles ( diurnal revolution2 !y all turn exactly at ! same rate z ! equ9octial1 & a /> situat$ any :]e betwe5 ! equator & ! pole w move 9 its diurnal circle along ) ! clock1 9 ! same mann] z ?\gh x 7 9 ! equ9octial4 ,h5ce1 if we note ! int]val ( "t betwe5 ! passage ( any two />s1 z %[n by ! clock1 we h a measure ( ! numb] ( degrees by :i* !y are di/ant f ea* o!r 9 "r asc5sion4 ,h5ce we see h[ easy x is to take arcs ( "r asc5sion3 ! transit in/rum5t %[s u :5 a body is on ! m]idian2 ! clock indicates h[ long x is s9ce ! v]nal equ9ox pass$ x1 :i* is ! "r asc5sion itself2 or x tells u ! diff]5ce ( "r asc5sion betwe5 any two bodies1 simply by indicat+ ! diff]5ce 9 "t betwe5 _! p]iods ( pass+ ! m]idian4 ,aga91 x is easy to take ! decl9ation ( a body :5 on ! m]idian4 ,by decl9ation1 y w recollect1 is meant ! di/ance ( a heav5ly body f ! equ9octial2 ! same1 inde$1 z latitude on ! e>?4 ,:5 a /> is pass+ ! m]idian1 if1 on ! in/ant ( cross+ ! m]idian wire ( ! telescope1 we take its di/ance f ! nor? pole1 7:i* may readily be done1 because ! position ( ! pole is always kn[n1 be+ equal to ! latitude ( ! place17 & subtract ?is di/ance f n9ety degrees1 ! rema9d] w be ! di/ance f ! equator1 :i* is ! decl9ation4 ,y w ask1 :y we take ?is indirect me?od ( f9d+ ! decl9ation8 ,:y we d n r take ! di/ance ( ! /> f ! equ9octial1 at once8 ,i answ]1 t x is easy to po9t an in/rum5t to ! nor? pole1 & to asc]ta9 its exact position1 & ( c\rse to measure any di/ance f x on ! m]idian1 :ile1 z !re is no?+ to m>k ! exact situation ( ! equ9octial1 x is n s easy to take direct measurem5ts f x4 ,:5 we h ?us det]m9$ ! situation ( a heav5ly body1 ) respect to two great circles at "r angles ) ea* o!r1 z 9 ! pres5t case1 ! di/ance ( a body f ! equator & f ! equ9octial colure1 or t m]idian :i* passes ?\gh ! v]nal equ9ox1 we "k its relative position 9 ! heav5s2 & :5 we h ?us det]m9$ ! relative positions ( all ! />s1 we may lay !m d[n on a map or a globe1 exactly z we d places on ! e>?1 by means ( _! latitude & longitude4 ,! =ego+ is only a specim5 ( ! v>i\s uses ( ! transit in/rum5t1 9 f9d+ ! relative places ( ! heav5ly bodies4 ,ano!r use ( ?is excell5t in/rum5t is1 to regulate our clocks & wat*es4 ,by an obs]vation ) ! transit in/rum5t1 we f9d :5 ! sun's c5tre is on ! m]idian4 ,?is is ! exact "t ( app>5t noon4 ,b wat*es & clocks usually keep mean "t1 & !re=e1 9 ord] to set our timepiece by ! transit in/rum5t1 we mu/ apply to ! app>5t "t ( noon ! equation ( "t1 z w be expla9$ 9 my next ,lett]4 ,a noon-m>k may easily be made by ! aid ( ! transit in/rum5t4 ,a w9d[ sill is frequ5tly select$ z a suitable place = ! m>k1 advantage be+ tak5 ( ! %ad[ project$ ^u x by ! p]p5dicul> cas+ ( ! w9d[4 ,let an assi/ant /&1 ) a rule laid on ! l9e ( %ad[1 & ) a knife ready to make ! m>k1 ! in/ant :5 ! obs]v] at ! transit in/rum5t ann\nces t ! c5tre ( ! sun is on ! m]idian4 ,by a conc]t$ signal1 z ! /roke ( a bell1 ! inhabitants ( a t[n may all fix a noon-m>k f ! same obs]vation4 ,if ! signal be giv5 on "o ( ! days :5 app>5t "t & mean "t become equal to ea* o!r1 z on ! tw5ty-f\r? ( ,decemb]1 no equation ( "t is requir$4 ,z a noon-m>k is conv5i5t = regulat+ timepieces1 ,i w po9t out a me?od ( mak+ "o1 :i* may be practis$ )\t ! aid ( ! telescope4 ,^u a smoo?1 level plane1 freely expos$ to ! sun1 ) a pair ( compasses describe a circle4 ,9 ! c5tre1 :]e ! leg ( ! compasses /ood1 erect a p]p5dicul> wire ( su* a l5g?1 t ! t]m9ation ( its %ad[ %all fall ^u ! circumf]5ce ( ! circle at "s h\r be=e noon1 z ab\t t5 o'clock4 ,make a small dot at ! po9t :]e ! end ( ! %ad[ falls ^u ! circle1 & d ! same :]e x falls ^u x aga9 9 ! aft]noon4 ,take a po9t half-way betwe5 ^! two po9ts1 & f x draw a l9e to ! c5tre1 & x w be a true m]idian l9e4 ,! direction ( ?is l9e w\ld be ! same1 :e!r x 7 made 9 ! ,summ] or 9 ! ,w9t]2 b x is exp$i5t to draw x ab\t ! fifte5? ( ,june1 = !n ! %ad[ alt]s its l5g? mo/ rapidly1 & ! mom5t ( its cross+ ! wire w be m def9ite1 ?an 9 ! ,w9t]4 ,at ?is "t ( ye>1 also1 ! sun & clock agree1 or are toge!r1 z w be m fully expla9$ 9 my next ,lett]2 :]eas1 at o!r times ( ! ye>1 ! "t ( noon1 z indicat$ by a common clock1 w\ld n agree ) t indicat$ by ! sun4 ,if ! upp] end ( ! wire is flatt5$1 & a small hole is made 9 x1 ?r\gh :i* ! sun may %9e1 ! in/ant :5 ?is bright spot falls ^u ! circle w be bett] def9$ ?an ! t]m9ation ( ! %ad[4 ,ano!r important in/rum5t ( ! obs]vatory is ! mural circle4 ,x is a graduat$ circle1 usually ( v l>ge size1 fix$ p]man5tly 9 ! plane ( ! m]idian1 & atta*$ firmly to a p]p5dicul> wall2 & on its c5tre is a telescope1 :i* revolves along ) x1 & is easily br\ght to be> on any object 9 any po9t 9 ! m]idian4 ,x is made ( l>ge size1 sometimes tw5ty feet 9 diamet]1 9 ord] t v small angles may be measur$ on its limb2 = x is obvi\s t a small angle1 z "o second1 w be a l>g] space on ! limb ( an in/rum5t1 9 proportion z ! in/rum5t itself is l>g]4 ,! v]tical circle usually connect$ ) ! transit in/rum5t1 z 9 ,fig4 #g1 may inde$ be employ$ = ! same purposes z ! mural circle1 namely1 to measure arcs ( ! m]idian1 z m]idian altitudes1 z5i? di/ances1 nor? pol> di/ances1 & decl9ations2 b z t circle mu/ necess>ily be small1 & !re=e incapable ( measur+ v m9ute angles1 ! mural circle is p>ticul>ly useful 9 measur+ ^! important arcs4 ,x is v difficult to keep s l>ge an in/rum5t p]fectly /eady2 & !re=e x is atta*$ to a massive wall ( solid masonry1 & is h5ce call$ a mural circle1 f a ,lat9 ^w1 7murus17 :i* signifies a wall4 ,! diagram1 ,fig4 #h1 page #ef1 repres5ts a mural circle fix$ to its wall1 & ready = obs]vations4 ,x w be se51 t e exp$i5t is employ$ to give ! in/rum5t firmness ( p>ts & /ead9ess ( position4 ,! circle is ( solid metal1 usually ( brass1 & x is /r5g!n$ by num]\s radii1 :i* keep x f w>p+ or b5d+2 & ^! are made 9 ! =m ( holl[ cones1 because t is ! figure :i* unites 9 ! highe/ degree lightness & /r5g?4 ,on ! rim ( ! in/rum5t1 at ,a1 y may obs]ve a microscope4 ,?is is atta*$ to a micromet]1--a delicate piece ( app>atus1 us$ = read+ ! m9ute subdivisions ( angles2 =1 aft] divid+ ! limb ( ! in/rum5t z m9utely z possible1 x w !n be necess>y to magnify ^? divisions ) ! microscope1 & subdivide ea* ( ^! p>ts ) ! micromet]4 ,?us1 if we h a mural circle tw5ty feet 9 diamet]1 & ( c\rse ne>ly sixty-?ree feet 9 circumf]5ce1 s9ce !re are tw5ty-"o ?\s& & six hundr$ m9utes 9 ! :ole circle1 we %all f9d1 by calculation1 t "o m9ute w\ld occupy1 on ! limb ( su* an in/rum5t1 only ab\t "o ?irtie? ( an in*1 & a second1 only "o eighte5 hundr$? ( an in*4 ,we c\ld n1 !re=e1 hope to c>ry ! actual divisions to a great] degree ( m9ut5ess ?an m9utes2 b ea* ( ^! spaces may aga9 be subdivid$ into seconds by ! micromet]4 ,illu/ration ,fig4 #h4 ,f ^! /atem5ts1 y w acquire "s fa9t idea ( ! extreme difficulty ( mak+ p]fect a/ronomical in/rum5ts1 especially :]e !y are int5d$ to measure su* m9ute angles z "o second4 ,inde$1 ! art ( con/ruct+ a/ronomical in/rum5ts is "o :i* requires su* ref9$ me*anical g5ius1--s sup]ior a m9d to devise1 & s delicate a h& to execute1--t ! mo/ celebrat$ in/rum5t-mak]s take rank ) ! mo/ di/+ui%$ a/ronom]s2 supply+1 z !y d1 ! means by :i* only ! latt] are enabl$ to make ^! great discov]ies4 ,a/ronom]s h sometimes made _! own telescopes2 b !y h seldom1 if ev]1 possess$ ! ref9$ manual skill :i* is requisite = graduat+ delicate in/rum5ts4 ,! sextant is also "o ( ! mo/ valuable in/rum5ts = tak+ cele/ial arcs1 or ! di/ance betwe5 any two po9ts on ! cele/ial sph]e1 be+ applicable to a mu* great] numb] ( purposes ?an ! in/rum5ts already describ$4 ,x is p>ticul>ly valuable = measur+ cele/ial arcs at sea1 because x is n1 l mo/ a/ronomical in/rum5ts1 affect$ by ! motion ( ! %ip4 ,! pr9ciple ( ! sextant may be briefly describ$1 z foll[s3 x gives ! angul> di/ance betwe5 any two bodies on ! cele/ial sph]e1 by reflect+ ! image ( "o ( ! bodies s z to co9cide ) ! o!r body1 z se5 directly4 ,! arc ?r\gh :i* ! reflector is turn$1 to br+ ! reflect$ body to co9cide ) ! o!r body1 becomes a measure ( ! angul> di/ance betwe5 !m4 ,by keep+ ?is pr9ciple 9 view1 y w be able to und]/& ! use ( ! sev]al p>ts ( ! in/rum5t1 z !y are exhibit$ 9 ! diagram1 ,fig4 #i1 page #eh4 ,x is1 y obs]ve1 ( a triangul> %ape1 & x is made /rong & firm by metallic cross-b>s4 ,x has two reflectors1 ,i & ,h1 call$1 respectively1 ! index glass & ! horizon glass1 bo? ( :i* are firmly fix$ p]p5dicul> to ! plane ( ! in/rum5t4 ,! index glass is atta*$ to ! movable arm1 ,,id1 & turns z ?is is mov$ along ! graduat$ limb1 ,,ef4 ,?is arm also c>ries a v]ni]1 at ,d1 a contrivance :i*1 l ! micromet]1 enables u to take (f m9ute p>ts ( ! spaces into :i* ! limb is divid$4 ,! horizon glass1 ,h1 consi/s ( two p>ts2 ! upp] "p be+ transp>5t or op51 s t ! eye1 look+ ?r\gh ! telescope1 ,t1 c see ?r\gh x a di/ant body1 z a /> at ,s1 :ile ! l[] "p is a reflector4 ,illu/ration ,fig4 #i4 ,suppose x 7 requir$ to measure ! angul> di/ance betwe5 ! moon & a c]ta9 />1--! moon be+ at ,m1 & ! /> at ,s4 ,! in/rum5t is held firmly 9 ! h&1 s t ! eye1 look+ ?r\gh ! telescope1 sees ! />1 ,s1 ?r\gh ! transp>5t "p ( ! horizon glass4 ,!n ! movable arm1 ,,id1 is mov$ f ,f t[>ds ,e1 until ! image ( ,m is reflect$ d[n to ,s1 :5 ! numb] ( degrees & p>ts ( a degree reckon$ on ! limb1 f ,f to ! index at ,d1 w %[ ! angul> di/ance betwe5 ! two bodies4 ,,footnote3 #c ,brew/]'s ,life ( ,newton ,,lett] ,,vi4 ,,"t ,,& ,,! ,,cal5d>4 ,f old ,et]nity's my/]i\s orb ,0 ,"t cut (f1 & ca/ b5ea? ! skies4--,"y4 ,,hav+ hi!rto be5 conv]sant only ) ! _m f9e & s5tim5tal ?+s :i* ! poets h sung respect+ ,old ,"t1 p]haps y w f9d "s difficulty 9 br++ d[n y\r m9d to ! calm] consid]ation ( :at "t really is1 & accord+ to :at diff]5t /&>ds x is measur$ = diff]5t purposes4 ,y w n1 h[ev]1 ,i ?9k1 f9d ! subject ev5 9 our matt]-(-fact & unpoetical way ( treat+ x1 altoge!r un9t]e/+4 ,:at1 !n1 is "t8 ,"t is a measur$ portion ( indef9ite duration4 ,x consi/s ( equal portions cut (f f et]nity1 z a l9e on ! surface ( ! e>? is sep>at$ f its contigu\s portions t con/itute a great circle ( ! sph]e1 by apply+ to x a two-foot scale2 or z a few y>ds ( clo? are measur$ (f f a piece ( unkn[n or indef9ite ext5t4 ,any ?+1 or any ev5t :i* takes place at equal int]vals1 may become a measure ( "t4 ,?us1 ! pulsations ( ! wri/1 ! fl[+ ( a giv5 quantity ( s& f "o vessel to ano!r1 z 9 ! h\rglass1 ! beat+ ( a p5dulum1 & ! revolution ( a />1 h be5 sev]ally employ$ z measures ( "t4 ,b ! great /&>d ( "t is ! p]iod ( ! revolution ( ! e>? on its axis1 :i*1 by ! mo/ exact obs]vations1 is f\nd to be always ! same4 ,i h anticipat$ a little ( ?is subject1 9 giv+ an acc\nt ( ! transit in/rum5t & clock1 b ,i propose1 9 ?is lett]1 to ent] into x m at l>ge4 ,! "t ( ! e>?'s revolution on its axis1 z already expla9$1 is call$ a sid]eal day1 & is det]m9$ by ! revolution ( a /> 9 ! heav5s4 ,?is int]val is divid$ into tw5ty-f\r sid]eal h\rs4 ,obs]vations tak5 on num]\s />s1 9 diff]5t ages ( ! _w1 %[ t !y all p]=m _! diurnal revolution 9 ! same "t1 & t _! motion1 dur+ any "p ( ! revolution1 is always uni=m4 ,"h1 !n1 we h an exact measure ( "t1 probably m exact ?an any ?+ :i* c be devis$ by art4 ,sol> "t is reckon$ by ! app>5t revolution ( ! sun f ! m]idian r\nd to ! m]idian aga94 ,7 ! sun /ation>y 9 ! heav5s1 l a fix$ />1 ! "t ( its app>5t revolution w\ld be equal to ! revolution ( ! e>? on its axis1 & ! sol> & ! sid]eal days w\ld be equal4 ,b1 s9ce ! sun passes f we/ to ea/1 ?r\gh ?ree hundr$ & sixty degrees1 9 ?ree hundr$ & sixty-five & "o f\r? days1 x moves ea/w>d ne>ly "o degree a day4 ,:ile1 !re=e1 ! e>? is turn+ r\nd on its axis1 ! sun is mov+ 9 ! same direction1 s t1 :5 we h come r\nd "u ! same cele/ial m]idian f :i* we />t$1 we d n f9d ! sun !re1 b he has mov$ ea/w>d ne>ly a degree1 & ! e>? mu/ p]=m s mu* m ?an "o complete revolution1 be=e we come "u ! sun aga94 ,n[1 s9ce we move1 9 ! diurnal revolution1 fifte5 degrees 9 sixty m9utes1 we mu/ pass ov] "o degree 9 f\r m9utes4 ,x takes1 !re=e1 f\r m9utes = u to cat* up ) ! sun1 aft] we h made "o complete revolution4 ,h5ce ! sol> day is ab\t f\r m9utes long] ?an ! sid]eal2 & if we 7 to reckon ! sid]eal day tw5ty-f\r h\rs1 we %\ld reckon ! sol> day tw5ty-f\r h\rs f\r m9utes4 ,to suit ! purposes ( society at l>ge1 h[ev]1 x is f\nd m conv5i5t to reckon ! sol> days tw5ty-f\r h\rs1 & ?r[ ! fraction into ! sid]eal day4 ,!n1 #bd;h4 #dm4 3 #bd;h4 33 #bd;h4 3 #bc;h4 #efm4 #ds4 ,t is1 :5 we r$uce tw5ty-f\r h\rs & f\r m9utes to tw5ty-f\r h\rs1 ! same proportion w require t we r$uce ! sid]eal day f tw5ty-f\r h\rs to tw5ty-?ree h\rs fifty-six m9utes f\r seconds2 or1 9 o!r words1 a sid]eal day is su* a "p ( a sol> day4 ,! sol> days1 h[ev]1 d n always diff] f ! sid]eal by precisely ! same fraction1 s9ce !y are n con/antly ( ! same l5g?4 ,"t1 z measur$ by ! sun1 is call$ app>5t "t1 & a clock s regulat$ z always to keep exactly ) ! sun1 is said to keep app>5t "t4 ,mean "t is "t reckon$ by ! av]age l5g? ( all ! sol> days ?r\gh\t ! ye>4 ,?is is ! p]iod :i* con/itutes ! civil day ( tw5ty-f\r h\rs1 beg9n+ :5 ! sun is on ! l[] m]idian1 namely1 at twelve o'clock at night1 & c\nt$ by twelve h\rs f ! l[] to ! upp] m]idian1 & f ! upp] to ! l[]4 ,! a/ronomical day is ! app>5t sol> day c\nt$ ?r\gh ! :ole tw5ty-f\r h\rs1 7in/ead ( by p]iods ( twelve h\rs ea*1 z 9 ! civil day17 & beg9s at noon4 ,?us x is n[ ! t5? ( ,june1 at n9e o'clock1 ,a4,m41 accord+ to civil "t2 b we h n yet rea*$ ! t5? ( ,june by a/ronomical "t1 nor %all we1 until noon to-day2 consequ5tly1 x is n[ ,june n9?1 tw5ty-fir/ h\r ( a/ronomical "t4 ,a/ronom]s1 s9ce s _m ( _! obs]vations are tak5 on ! m]idian1 are always suppos$ to look t[>ds ! s\?4 ,geograph]s1 hav+ =m]ly be5 conv]sant only ) ! nor!rn hemisph]e1 are always und]/ood to be look+ t[>ds ! nor?4 ,h5ce1 left & "r1 :5 appli$ to ! a/ronom]1 mean ea/ & we/1 respectively2 b to ! geograph] ! "r is ea/1 & ! left1 we/4 ,clocks are usually regulat$ s z to indicate mean sol> "t2 yet1 z ?is is an artificial p]iod n m>k$ (f1 l ! sid]eal day1 by any natural ev5t1 x is necess>y to "k h[ mu* is to be add$ to1 or subtract$ f1 ! app>5t sol> "t1 9 ord] to give ! correspond+ mean "t4 ,! int]val1 by :i* app>5t "t diff]s f mean "t1 is call$ ! equation ( "t4 ,if "o clock is s con/ruct$ z to keep exactly ) ! sun1 go+ fa/] or sl[]1 accord+ z ! l5g?s ( ! sol> days v>y1 & ano!r clock is regulat$ to mean "t1 !n ! diff]5ce ( ! two clocks1 at any p]iod1 w\ld be ! equation ( "t = t mom5t4 ,if ! app>5t clock 7 fa/] ?an ! mean1 !n ! equation ( "t mu/ be subtract$2 b if ! app>5t clock 7 sl[] ?an ! mean1 !n ! equation ( "t mu/ be add$1 to give ! mean "t4 ,! two clocks w\ld diff] mo/ ab\t ! ?ird ( ,novemb]1 :5 ! app>5t "t is sixte5 & "o f\r? m9utes great] ?an ! mean4 ,b s9ce app>5t "t is sometimes great] & sometimes less ?an mean "t1 ! two mu/ obvi\sly be sometimes equal to ea* o!r4 ,?is is1 9 fact1 ! case f\r times a ye>1 namely1 ,april fifte5?1 ,june fifte5?1 ,septemb] fir/1 & ,decemb] tw5ty-f\r?4 ,a/ronomical clocks are made ( ! be/ workman%ip1 ) e advantage t c promote _! regul>ity4 ,al?\gh !y are br\ght to an a/oni%+ degree ( accuracy1 yet !y are n z regul> 9 _! movem5ts z ! />s are1 & _! accuracy requires to be frequ5tly te/$4 ,! transit in/rum5t itself1 :5 once accurately plac$ 9 ! m]idian1 af=ds ! means ( te/+ ! correctness ( ! clock1 s9ce "o revolution ( a />1 f ! m]idian to ! m]idian aga91 ought to correspond exactly to tw5ty-f\r h\rs by ! clock1 & to cont9ue ! same1 f day to day2 & ! "r asc5sions ( v>i\s />s1 z !y cross ! m]idian1 ought to be su* by ! clock1 z !y are giv5 9 ! tables1 :]e !y are /at$ accord+ to ! accurate det]m9ations ( a/ronom]s4 ,or1 by tak+ ! diff]5ce ( any two />s1 on successive days1 x w be se5 :e!r ! go+ ( ! clock is uni=m = t "p ( ! day2 & by tak+ ! "r asc5sions ( diff]5t pairs ( />s1 we may le>n ! rate ( ! clock at v>i\s p>ts ( ! day4 ,we ?us le>n1 n only :e!r ! clock accurately measures ! l5g? ( ! sid]eal day1 b also :e!r x goes uni=mly f h\r to h\r4 ,al?\gh a/ronomical clocks h be5 br\ght to a great degree ( p]fection1 s z h>dly to v>y a second = _m mon?s1 yet none are absolutely p]fect1 & mo/ are s f> f x1 z to require to be correct$ by means ( ! transit in/rum5t1 e few days4 ,inde$1 = ! nice/ obs]vations1 x is usual n to attempt to br+ ! clock to a /ate ( absolute correctness1 b1 aft] br++ x z ne> to su* a /ate z c conv5i5tly be done1 to asc]ta9 h[ mu* x ga9s or loses 9 a day2 t is1 to asc]ta9 ! rate ( its go+1 & to make all[ance accord+ly4 ,hav+ consid]$ ! mann] 9 :i* ! small] divisions ( "t are measur$1 let u n[ take a ha/y glance at ! l>g] p]iods :i* compose ! cal5d>4 ,z a day is ! p]iod ( ! revolution ( ! e>? on its axis1 s a ye> is ! p]iod ( ! revolution ( ! e>? ar\nd ! sun4 ,?is "t1 :i* con/itutes ! a/ronomical ye>1 has be5 asc]ta9$ ) great exactness1 & f\nd to be ?ree hundr$ & sixty-five days five h\rs =ty-eight m9utes & fifty-"o seconds4 ,! mo/ anci5t nations det]m9$ ! numb] ( days 9 ! ye> by means ( ! /ylus1 a p]p5dicul> rod :i* ca/s its %ad[ on a smoo? plane be>+ a m]idian l9e4 ,! "t :5 ! %ad[ 0 %orte/1 w\ld indicate ! day ( ! ,summ] sol/ice2 & ! numb] ( days :i* elaps$1 until ! %ad[ return$ to ! same l5g? aga91 w\ld %[ ! numb] ( days 9 ! ye>4 ,?is 0 f\nd to be ?ree hundr$ & sixty-five :ole days1 & accord+ly1 ?is p]iod 0 adopt$ = ! civil ye>4 ,su* a diff]5ce1 h[ev]1 betwe5 ! civil & a/ronomical ye>s1 at l5g? ?rew all dates into confusion4 ,= if1 at fir/1 ! ,summ] sol/ice happ5$ on ! tw5ty-fir/ ( ,june1 at ! end ( f\r ye>s1 ! sun w\ld n h rea*$ ! sol/ice until ! tw5ty-second ( ,june2 t is1 x w\ld h be5 beh9d its "t4 ,at ! end ( ! next f\r ye>s1 ! sol/ice w\ld fall on ! tw5ty-?ird2 & 9 process ( "t1 x w\ld fall successively on e day ( ! ye>4 ,! same w\ld be true ( any o!r fix$ date4 ,julius ,cs>1 :o 0 di/+ui%$ alike = ! v>iety & ext5t ( 8 k1 & 8 skill 9 arms1 fir/ attempt$ to make ! cal5d> con=m to ! motions ( ! sun4 ,amid/ ! hurry ( tumultu\s w>1 ,! />s1 ! gods1 ! heav5s1 7 /ill 8 c>e4 ,aid$ by ,sosig5es1 an ,egyptian a/ronom]1 he made ! fir/ correction ( ! cal5d>1 by introduc+ an additional day e f\r? ye>1 mak+ ,febru>y to consi/ ( tw5ty-n9e in/ead ( tw5ty-eight days1 & ( c\rse ! :ole ye> to consi/ ( ?ree hundr$ & sixty-six days4 ,?is f\r? ye> 0 d5om9at$ ,bissextile1 because ! six? day be=e ! ,kal5ds ( ,m>* 0 reckon$ twice4 ,x is also call$ ,leap ,ye>4 ,! ,julian ye> 0 introduc$ into all ! civiliz$ nations t submitt$ to ! ,roman p[]1 & cont9u$ 9 g5]al use until ! ye> #aehb4 ,b ! true correction 0 n six h\rs1 b five h\rs =ty-n9e m9utes2 h5ce ! addition 0 too great by elev5 m9utes4 ,?is small fraction w\ld am\nt 9 "o hundr$ ye>s to ?ree f\r?s ( a day1 & 9 "o ?\s& ye>s to m ?an sev5 days4 ,f ! ye> #cbe to ! ye> #aehb1 x _h1 9 fact1 am\nt$ to m ?an t5 days2 = x 0 kn[n t1 9 #cbe1 ! v]nal equ9ox fell on ! tw5ty-fir/ ( ,m>*1 :]eas1 9 #aehb1 x fell on ! elev5?4 ,x 0 ord]$ by ! ,c\ncil ( ,nice1 a celebrat$ ecclesia/ical c\ncil1 held 9 ! ye> #cbe1 t ,ea/] %\ld be celebrat$ ^u ! fir/ ,sunday aft] ! fir/ full moon1 next foll[+ ! v]nal equ9ox2 & z c]ta9 o!r fe/ivals ( ! ,romi% ,*ur* 7 appo9t$ at p>ticul> seasons ( ! ye>1 confusion w\ld result f su* a want ( con/ancy betwe5 any fix$ date & a p>ticul> season ( ! ye>4 ,suppose1 = example1 a fe/ival accompani$ by num]\s religi\s c]emonies1 0 decre$ by ! ,*ur* to be held at ! "t :5 ! sun cross$ ! equator 9 ! ,spr+1 7an ev5t hail$ ) great joy1 z ! h>b+] ( ! return ( ,summ]17 & t1 9 ! ye> #cbe1 ,m>* tw5ty-fir/ 0 designat$ z ! "t = hold+ ! fe/ival1 s9ce1 at t p]iod1 x 0 on ! tw5ty-fir/ ( ,m>* :5 ! sun rea*$ ! equ9ox2 ! next ye>1 ! sun w\ld rea* ! equ9ox a little soon] ?an ! tw5ty-fir/ ( ,m>*1 only elev5 m9utes1 inde$1 b /ill am\nt+ 9 twelve hundr$ ye>s to t5 days2 t is1 9 #aehb1 ! sun rea*$ ! equ9ox on ! elev5? ( ,m>*4 ,if1 !re=e1 !y %\ld cont9ue to obs]ve ! tw5ty-fir/ z a religi\s fe/ival 9 honor ( ?is ev5t1 !y w\ld commit ! absurdity ( celebrat+ x t5 days aft] x _h pass$ by4 ,pope ,gregory ! ,?irte5?1 :o 0 !n at ! head ( ! ,roman ,see1 0 a man ( sci5ce1 & und]took to re=m ! cal5d>1 s t fix$ dates w\ld always correspond to ! same seasons ( ! ye>4 ,he fir/ decre$1 t ! ye> %\ld be br\ght =w>d t5 days1 by reckon+ ! fif? ( ,octob] ! fifte5?2 &1 9 ord] to prev5t ! cal5d> f fall+ into confusion aft]w>ds1 he prescrib$ ! foll[+ rule3 ,e ye> ^: numb] is n divisible by f\r1 )\t a rema9d]1 consi/s ( ?ree hundr$ & sixty-five days2 e ye> :i* is s divisible1 b is n divisible by "o hundr$1 ( ?ree hundr$ & sixty-six2 e ye> divisible by "o hundr$1 b n by f\r hundr$1 aga91 ( ?ree hundr$ & sixty-five2 & e ye> divisible by f\r hundr$1 ( ?ree hundr$ & sixty-six4 ,?us ! ye> #ahch1 n be+ divisible by f\r1 conta9s ?ree hundr$ & sixty-five days1 :ile #ahcf & #ahdj are leap ye>s4 ,yet1 to make e f\r? ye> consi/ ( ?ree hundr$ & sixty-six days w\ld increase x too mu*1 by ab\t ?ree f\r?s ( a day 9 a c5tury2 !re=e e hundr$? ye> has only ?ree hundr$ & sixty-five days4 ,?us #ahjj1 al?\gh divisible by f\r1 0 n a leap ye>1 b a common ye>4 ,b we h all[$ a :ole day 9 a hundr$ ye>s1 :]eas we ought to h all[$ only ?ree f\r?s ( a day4 ,h5ce1 9 f\r hundr$ ye>s1 we %\ld all[ a day too mu*1 & !re=e1 we let ! f\r hundr$? rema9 a leap ye>4 ,?is rule involves an error ( less ?an a day 9 f\r ?\s& two hundr$ & ?irty-sev5 ye>s4 ,! ,pope1 :o1 y w recollect1 at t age assum$ au?ority ov] all secul> pr9ces1 issu$ 8 decree to ! reign+ sov]eigns ( ,*ri/5dom1 comm&+ ! obs]vance ( ! cal5d> z re=m$ by him4 ,! decree met ) great opposition among ! ,prote/ant ,/ates1 z !y recognis$ 9 x a new ex]cise ( ecclesia/ical tyranny2 & "s ( !m1 :5 !y receiv$ x1 made x expressly und]/ood1 t _! acquiesc5ce %\ld n be con/ru$ z a submission to ! ,papal au?ority4 ,9 #ageb1 ! ,gregorian ye>1 or ,new ,/yle1 0 e/abli%$ 9 ,great ,brita9 by act ( ,p>liam5t2 & ! dates ( all de$s1 & o!r legal pap]s1 7 to be made accord+ to x4 ,z above a c5tury _h !n pass$ s9ce ! fir/ introduction ( ! new /yle1 elev5 days 7 suppress$1 ! ?ird ( ,septemb] be+ call$ ! f\rte5?4 ,by ! same act1 ! beg9n+ ( ! ye> 0 *ang$ f ,m>* tw5ty-fif? to ,janu>y fir/4 ,a few p]sons born previ\sly to #ageb h come d[n to our day1 & we frequ5tly see inscriptions on tomb/ones ( ^? ^: "t ( bir? is record$ 9 old /yle4 ,9 ord] to make ?is correspond to our pres5t mode ( reckon+1 we mu/ add elev5 days to ! date4 ,?us ! same ev5t w\ld be ,june twelf? ( old /yle1 or ,june tw5ty-?ird ( new /yle2 & if an ev5t occurr$ betwe5 ,janu>y fir/ & ,m>* tw5ty-fif?1 ! date ( ! ye> w\ld be advanc$ "o1 s9ce ,febru>y #a/1 #agdj1 ,o4,s4 w\ld be ,febru>y #a/1 #agda1 ,n4,s4 ,?us1 ,g5]al ,wa%+ton 0 born ,febru>y #aa?1 #agca1 ,o4,s41 or ,febru>y #bb;d1 #agcb1 ,n4,s4 ,if we inquire h[ any pres5t ev5t may be made to correspond 9 date to ! old /yle1 we mu/ subtract twelve days1 & put ! ye> back "o1 if ! ev5t lies betwe5 ,janu>y fir/ & ,m>* tw5ty-fif?4 ,?us1 ,june t5?1 ,n4,s4 corresponds to ,may tw5ty-n9?1 ,o4,s42 & ,m>* #bj?1 #ahdj1 to ,m>* #h?1 #ahci4 ,france1 be+ a ,roman ,ca?olic c\ntry1 adopt$ ! new /yle soon aft] x 0 decre$ by ! ,pope2 b ,prote/ant c\ntries1 z we h se51 7 mu* sl[] 9 adopt+ x2 & ,russia1 & ! ,greek ,*ur* g5]ally1 /ill adh]e to ! old /yle4 ,9 ord]1 !re=e1 to make ! ,russian dates correspond to ours1 we mu/ add to !m twelve days4 ,x may seem to y v rem>kable1 t s mu* pa9s %\ld h be5 be/[$ ^u ?is subject2 b )\t a correct & uni=m /&>d ( "t1 ! dates ( de$s1 commissions1 & all legal pap]s2 ( fa/s & fe/ivals1 appo9t$ by ecclesia/ical au?ority2 ! returns ( seasons1 & ! records ( hi/ory1--mu/ all fall into inextricable confusion4 ,to *ange ! obs]vance ( c]ta9 religi\s fea/s1 :i* h be5 long fix$ to p>ticul> days1 is look$ ^u z an impi\s innovation2 & ?\gh ! times ( ! ev5ts1 ^u :i* ^! c]emonies dep5d1 are utt]ly unkn[n1 x is /ill insi/$ ^u by c]ta9 classes 9 ,engl&1 t ! ,gla/5bury ?orn blooms on ,*ri/mas day4 ,al?\gh ! anci5t ,grecian cal5d> 0 extremely defective1 yet ! common p 7 entirely av]se to its re=mation4 ,_! sup]/iti\s adh]5ce to ^! errors 0 satiriz$ by ,ari/ophanes1 9 8 com$y ( ! ,cl\ds4 ,an actor1 :o _h j come f ,a!ns1 rec\nts t he met ) ,diana1 or ! moon1 & f\nd h] extremely inc5s$1 t !y did n regulate h] c\rse bett]4 ,%e compla9$1 t ! ord] ( ,nature 0 *ang$1 & e ?+ turn$ topsyturvy4 ,! gods no long] knew :at belong$ to !m2 b1 aft] pay+ _! visits on c]ta9 fea/-days1 & expect+ to meet ) good *e]1 z usual1 !y 7 "u ! disagreeable necessity ( return+ back to heav5 )\t _! supp]s4 ,among ! ,greeks1 & o!r anci5t nations1 ! l5g? ( ! ye> 0 g5]ally regulat$ by ! c\rse ( ! moon4 ,?is planet1 on acc\nt ( ! diff]5t appe>ances :i* %e exhibits at h] full1 *ange1 & qu>t]s1 0 consid]$ by !m z be/ adapt$ ( any ( ! cele/ial bodies = ?is purpose4 ,z "o lunation1 or revolution ( ! moon ar\nd ! e>?1 0 f\nd to be complet$ 9 ab\t tw5ty-n9e & "o half days1 & twelve ( ^! p]iods be+ suppos$ equal to "o revolution ( ! sun1 _! mon?s 7 made to consi/ ( tw5ty-n9e & ?irty days alt]nately1 & _! ye> ( ?ree hundr$ & fifty-f\r days4 ,b ?is disagre$ ) ! annual revolution ( ! sun1 :i* mu/ evid5tly gov]n ! seasons ( ! ye>1 m ?an elev5 days4 ,! irregul>ities1 :i* su* a mode ( reckon+ w\ld occasion1 mu/ h be5 too obvi\s n to h be5 obs]v$4 ,=1 suppos+ x to h be5 settl$1 at any p>ticul> "t1 t ! beg9n+ ( ! ye> %\ld be 9 ! ,spr+2 9 ab\t sixte5 ye>s aft]w>ds1 ! beg9n+ w\ld h be5 9 ,autumn2 & 9 ?irty-?ree or ?irty-f\r ye>s1 x w\ld h gone backw>ds ?r\gh all ! seasons1 to ,spr+ aga94 ,?is defect !y attempt$ to rectify1 by introduc+ a numb] ( days1 at c]ta9 times1 into ! cal5d>1 z occasion requir$1 & putt+ ! beg9n+ ( ! ye> =w>ds1 9 ord] to make x agree ) ! c\rse ( ! sun4 ,b z ^! additions1 or int]calations1 z !y 7 call$1 7 g5]ally consign$ to ! c>e ( ! prie/s1 :o1 f motives ( int]e/ or sup]/ition1 frequ5tly omitt$ !m1 ! ye> 0 made long or %ort at pleasure4 ,! week is ano!r division ( "t1 ( ! highe/ antiquity1 :i*1 9 almo/ all c\ntries1 has be5 made to consi/ ( sev5 days2 a p]iod suppos$ by "s to h be5 traditionally d]iv$ f ! creation ( ! _w2 :ile o!rs imag9e x to h be5 regulat$ by ! phases ( ! moon4 ,! names1 ,saturday1 ,sunday1 & ,monday1 are obvi\sly d]iv$ f ,saturn1 ! ,sun1 & ! ,moon2 :ile ,tuesday1 ,w$nesday1 ,?ursday1 & ,friday1 are ! days ( ,tuisco1 ,wod51 ,?or1 & ,friga1 :i* are ,saxon names = ,m>s1 ,m]cury1 ,jupit]1 & ,v5us4#d ,! common ye> beg9s & ends on ! same day ( ! week2 b leap ye> ends "o day lat] ?an x began4 ,fifty-two weeks conta9 ?ree hundr$ & sixty-f\r days2 if1 !re=e1 ! ye> beg9s on ,tuesday1 = example1 we %\ld complete fifty-two weeks on ,monday1 leav+ "o day1 7,tuesday17 to complete ! ye>1 & ! foll[+ ye> w\ld beg9 on ,w$nesday4 ,h5ce1 any day ( ! mon? is "o day lat] 9 ! week1 ?an ! correspond+ day ( ! prec$+ ye>4 ,?us1 if ! sixte5? ( ,novemb]1 #ahch1 falls on ,friday1 ! sixte5? ( ,novemb]1 #ahcg1 fell on ,?ursday1 & w fall1 9 #ahci1 on ,saturday4 ,b if leap ye> beg9s on ,sunday1 x ends on ,monday1 & ! foll[+ ye> beg9s on ,tuesday2 :ile any giv5 day ( ! mon? is two days lat] 9 ! week ?an ! correspond+ date ( ! prec$+ ye>4 ,,footnote3 #d ,bonnyca/le's ,a/ronomy4 ,,lett] ,,vii4 ,,figure ,,( ,,! ,,e>?4 ,he took ! gold5 compasses1 prep>$ ,9 ,god's et]nal /ore1 to circumscribe ,?is univ]se1 & all creat$ ?+s2 ,"o foot he c5tr$1 & ! o!r turn$ ,r\nd ?r\gh ! va/ pr(undity obscure1 ,& said1 ',?us f> ext5d1 ?us f> ?y b\nds1 ,?is be ?y j circumf]5ce1 ,o ,_w6'--,milton4 ,,9 ! e>lie/ ages1 ! e>? 0 reg>d$ z "o cont9u$ plane2 b1 at a comp>atively remote p]iod1 z five hundr$ ye>s be=e ! ,*ri/ian era1 a/ronom]s began to ent]ta9 ! op9ion t ! e>? is r\nd4 ,we are able n[ to adduce v>i\s argum5ts :i* sev]ally prove ?is tru?4 ,fir/1 :5 a %ip is com+ 9 f sea1 we fir/ obs]ve only ! v highe/ p>ts ( ! %ip1 :ile ! l[] portions come successively into view4 ,7 ! e>? a cont9u$ plane1 ! l[] p>ts ( ! %ip w\ld be visible z soon z ! high]1 z is evid5t f ,fig4 #aj1 page #gj4 ,illu/ration ,fig4 #aj4 ,illu/ration ,fig4 #aa4 ,s9ce light comes to ! eye 9 /raight l9es1 by :i* objects become visible1 x is evid5t1 t no reason exi/s :y ! p>ts ( ! %ip ne> ! wat] %\ld n be se5 z soon z ! upp] p>ts4 ,b if ! e>? be a sph]e1 !n ! l9e ( sight w\ld pass above ! deck ( ! %ip1 z is repres5t$ 9 ,fig4 #aa2 & z ! %ip drew ne>] to l&1 ! l[] p>ts w\ld successively rise above ?is l9e & come into view exactly 9 ! mann] kn[n to obs]vation4 ,secondly1 9 a lun> eclipse1 :i* is occasion$ by ! moon's pass+ ?r\gh ! e>?'s %ad[1 ! figure ( ! %ad[ is se5 to be sph]ical1 :i* c\ld n be ! case unless ! e>? itself 7 r\nd4 ,?irdly1 navigators1 by /e]+ cont9ually 9 "o direction1 z ea/ or we/1 h 9 fact come r\nd to ! po9t f :i* !y />t$1 & ?us confirm$ ! fact ( ! e>?'s rotundity beyond all "q4 ,"o may also rea* a giv5 place on ! e>?1 by tak+ directly opposite c\rses4 ,?us1 he may rea* ,canton 9 ,*9a1 by a we/]ly r\te ar\nd ,cape ,horn1 or by an ea/]ly r\te ar\nd ! ,cape ( ,good ,hope4 ,all ^! argum5ts sev]ally prove t ! e>? is r\nd4 ,b ,i propose1 9 ?is ,lett]1 to give y "s acc\nt ( ! unwe>i$ labors :i* h be5 p]=m$ to asc]ta9 ! exact figure ( ! e>?2 = al?\gh ! e>? is prop]ly describ$ 9 g5]al language z r\nd1 yet x is n an exact sph]e4 ,7 x s1 all its diamet]s w\ld be equal2 b x is kn[n t a diamet] drawn ?r\gh ! equator exce$s "o drawn f pole to pole1 giv+ to ! e>? ! =m ( a sph]oid1--a figure resembl+ an orange1 :]e ! ends are flatt5$ a little & ! c5tral p>ts are swell$ out4 ,al?\gh x w\ld be a matt] ( v rational curiosity1 to inve/igate ! precise %ape ( ! planet on :i* ,heav5 has fix$ our abode1 yet ! imm5se pa9s :i* has be5 be/[$ on ?is subject has n all aris5 f m]e curiosity4 ,no accurate measurem5ts c be tak5 ( ! di/ances & magnitudes ( ! heav5ly bodies1 nor any exact det]m9ations made ( _! motions1 )\t a k ( ! exact figure ( ! e>?2 & h5ce is d]iv$ a p[]ful motive = asc]ta9+ ?is elem5t ) all possible precision4 ,! fir/ satisfactory evid5ce t 0 obta9$ ( ! exact figure ( ! e>? 0 d]iv$ f reason+ on ! effects ( ! e>?'s c5trifugal =ce1 occasion$ by its rapid revolution on its own axis4 ,:5 wat] is :irl$ 9 a pail1 we see x rec$e f ! c5tre & accumulate ^u ! sides ( ! vessel2 & :5 a mill/one is :irl$ rapidly1 s9ce ! portions ( ! /one fur!/ f ! c5tre revolve mu* m rapidly ?an ^? ne> to x1 _! great] t5d5cy to rec$e sometimes makes !m fly (f ) a viol5t explosion4 ,a case1 :i* comes /ill ne>] to t ( ! e>?1 is exhibit$ by a mass ( clay revolv+ on a pott]'s :eel1 z se5 9 ! process ( mak+ e>!n vessels4 ,! mass swells out 9 ! middle1 9 consequ5ce ( ! c5trifugal =ce ex]t$ ^u x by a rapid motion4 ,n[1 9 ! diurnal revolution1 ! equatorial p>ts ( ! e>? move at ! rate ( ab\t "o ?\s& miles p] h\r1 :ile ! poles d n move at all2 & s9ce1 z we take po9ts at successive di/ances f ! equator t[>ds ! pole1 ! rate at :i* ^! po9ts move gr[s con/antly less & less2 & s9ce1 9 revolv+ bodies1 ! c5trifugal =ce is proportion$ to ! velocity1 consequ5tly1 ^? p>ts :i* move ) ! greate/ rapidity w be m affect$ by ?is =ce ?an ^? :i* move m sl[ly4 ,h5ce1 ! equatorial regions mu/ be high] f ! c5tre ?an ! pol> regions2 =1 7 n ?is ! case1 ! wat]s on ! surface ( ! e>? w\ld be ?r[n t[>ds ! equator1 & be pil$ up !re1 j z wat] is accumulat$ on ! sides ( a pail :5 made to revolve rapidly4 ,huygh5s1 an em95t a/ronom] ( ,holl&1 :o inve/igat$ ! laws ( c5trifugal =ces1 0 ! fir/ to inf] t su* mu/ be ! actual %ape ( ! e>?2 b to ,sir ,isaac ,newton we owe ! full developem5t ( ?is doctr9e4 ,by comb9+ ! reason+ d]iv$ f ! kn[n laws ( ! c5trifugal =ce ) argum5ts d]iv$ f ! pr9ciples ( univ]sal gravitation1 he conclud$ t ! di/ance ?r\gh ! e>?1 9 ! direction ( ! equator1 is great] ?an t 9 ! direction ( ! poles4 ,he e/imat$ ! diff]5ce to be ab\t ?irty-f\r miles4 ,b x 0 soon aft]w>ds det]m9$ by ! a/ronom]s ( ,france1 to asc]ta9 ! figure ( ! e>? by actual measurem5ts1 specially in/itut$ = t purpose4 ,let u see h[ ?is c\ld be effect$4 ,if we set out at ! equator & travel t[>ds ! pole1 x is easy to see :5 we h advanc$ "o degree ( latitude1 = ?is w be indicat$ by ! ris+ ( ! nor? />1 :i* appe>s 9 ! horizon :5 ! spectator /&s on ! equator1 b rises 9 ! same proportion z he rec$es f ! equator1 until1 on rea*+ ! pole1 ! nor? /> w\ld be se5 directly ov] head4 ,n[1 7 ! e>? a p]fect sph]e1 ! m]idian ( ! e>? w\ld be a p]fect circle1 & ! di/ance betwe5 any two places1 diff]+ "o degree 9 latitude1 w\ld be exactly equal to ! di/ance betwe5 any o!r two places1 diff]+ 9 latitude to ! same am\nt4 ,b if ! e>? be a sph]oid1 flatt5$ at ! poles1 !n a l9e encompass+ ! e>? f nor? to s\?1 con/itut+ ! t]re/rial m]idian1 w\ld n be a p]fect circle1 b an ellipse or oval1 hav+ its long] diamet] ?r\gh ! equator1 & its %ort] ?r\gh ! poles4 ,! "p ( ?is curve includ$ betwe5 two radii1 drawn f ! c5tre ( ! e>? to ! cele/ial m]idian1 at angles "o degree asund]1 w\ld be great] 9 ! pol> ?an 9 ! equatorial region2 t is1 ! degrees ( ! m]idian w\ld l5g!n t[>ds ! poles4 ,! ,fr5* a/ronom]s1 !re=e1 und]took to asc]ta9 by actual measurem5ts ( arcs ( ! m]idian1 9 diff]5t latitudes1 :e!r ! degrees ( ! m]idian are ( uni=m l5g?1 or1 if n1 9 :at mann] !y diff] f ea* o!r4 ,aft] sev]al indecisive measurem5ts ( an arc ( ! m]idian 9 ,france1 x 0 det]m9$ to effect simultane\s measurem5ts ( arcs ( ! m]idian ne> ! equator1 & z ne> z possible to ! nor? pole1 presum+ t if degrees ( ! m]idian1 9 diff]5t latitudes1 are really ( diff]5t l5g?s1 !y w diff] mo/ 9 po9ts mo/ di/ant f ea* o!r4 ,accord+ly1 9 #agce1 ! ,fr5* ,academy1 aid$ by ! gov]nm5t1 s5t out two exp$itions1 "o to ,p]u & ! o!r to ,lapl&4 ,?ree di/+ui%$ ma!maticians1 ,b\gu]1 ,la ,condam9e1 & ,god91 7 despat*$ to ! =m] place1 & f\r o!rs1 ,maup]tius1 ,camus1 ,clairault1 & ,lemoni]1 7 s5t to ! "p ( ,sw$i% ,lapl& :i* lies at ! head ( ! ,gulf ( ,tornea1 ! nor!rn arm ( ! ,baltic4 ,?is commission complet$ its op]ations sev]al ye>s soon] ?an ! o!r1 :i* met ) great] difficulties 9 ! way ( _! ent]prise4 ,/ill1 ! nor!rn deta*m5t _h great ob/acles to cont5d )1 aris+ p>ticul>ly f ! extreme l5g? & sev]ity ( _! ,w9t]s4 ,! measurem5ts1 h[ev]1 7 conduct$ ) c>e & skill1 & ! result1 :5 comp>$ ) t obta9$ = ! l5g? ( a degree 9 ,france1 pla9ly indicat$1 by its great] am\nt1 a compression ( ! e>? t[>ds ! poles4 ,mean-:ile1 ,b\gu] & 8 p>ty 7 prosecut+ a simil> "w 9 ,p]u1 "u extraord9>y difficulties4 ,^! 7 caus$1 p>tly by ! localities1 & p>tly by ! ill-w & indol5ce ( ! inhabitants4 ,! place select$ = _! op]ations 0 9 an elevat$ valley betwe5 two pr9cipal *a9s ( ! ,&es4 ,! l[e/ po9t ( _! arc 0 at an elevation ( a mile & a half above ! level ( ! sea2 &1 9 "s in/ances1 ! heights ( two neighbor+ signals diff]$ m ?an a mile4 ,encamp$ ^u l(ty m\nta9s1 !y _h to /ruggle aga9/ /orms1 cold1 & privations ( e description1 :ile ! inv9cible indiff]5ce ( ! ,indians1 !y 7 =c$ to employ1 0 n to be %ak5 by ! fe> ( puni%m5t or ! hope ( rew>d4 ,yet1 by pati5ce & +5uity1 !y ov]came all ob/acles1 & execut$ ) great accuracy "o ( ! mo/ important op]ations1 ( ?is nature1 ev] und]tak54 ,to accompli% ?is1 h[ev]1 took !m n9e ye>s2 ( :i*1 ?ree 7 occupi$ 9 det]m9+ ! latitudes alone4#e ,i h recit$ ! =ego+ facts1 9 ord] to give y "s idea ( ! unwe>i$ pa9s :i* a/ronom]s h tak5 to asc]ta9 ! exact figure ( ! e>?4 ,y w f9d1 inde$1 t all _! labors are *>act]iz$ by ! same love ( accuracy4 ,ye>s ( toilsome wat*+s1 & incr$ible labor ( computation1 h be5 und]gone1 = ! sake ( arriv+ only a few seconds ne>] to ! tru?4 ,! l5g? ( a degree ( ! m]idian1 z measur$ 9 ,p]u1 0 less ?an t be=e det]m9$ 9 ,france1 & ( c\rse less ?an t ( ,lapl&2 s t ! sph]oidal figure ( ! e>? appe>$ n[ to be asc]ta9$ by actual measurem5t4 ,/ill1 ^! measures 7 too few 9 numb]1 & cov]$ too small a portion ( ! :ole quadrant f ! equator to ! pole1 to enable a/ronom]s to asc]ta9 ! exact law ( curvature ( ! m]idian1 & !re=e simil> measurem5ts h s9ce be5 prosecut$ ) great zeal by diff]5t nations1 p>ticul>ly by ! ,fr5* & ,engli%4 ,9 #agfd1 two ,engli% ma!maticians ( great em95ce1 ,mason & ,dixon1 und]took ! measurem5t ( an arc 9 ,p5nsylvania1 ext5d+ m ?an "o hundr$ miles4 ,illu/ration ,fig4 #ab4 ,illu/ration ,fig4 #ac4 ,^! op]ations are c>ri$ on by :at is call$ a sy/em ( triangulation4 ,)\t "s k ( trigonometry1 y w n be able fully to und]/& ?is process2 b1 z x is 9 its nature some:at curi\s1 & is appli$ to v>i\s o!r geographical measurem5ts1 z well z to ! det]m9ation ( arcs ( ! m]idian1 ,i am desir\s t y %\ld und]/& its g5]al pr9ciples4 ,let u reflect1 !n1 t x mu/ be a matt] ( ! greate/ difficulty1 to execute ) exactness ! measurem5t ( a l9e ( any great l5g? 9 "o cont9u$ direction on ! e>?'s surface4 ,ev5 if we select a level & op5 c\ntry1 m or less inequalities ( surface w occur2 riv]s mu/ be cross$1 morasses mu/ be trav]s$1 ?ickets mu/ be p5etrat$1 & innum]able o!r ob/acles mu/ be surm\nt$2 & f9ally1 e "t we apply an artificial measure1 z a rod1 = example1 we obta9 a result n absolutely p]fect4 ,ea* error may inde$ be v small1 b small errors1 (t5 repeat$1 may produce a =midable aggregate4 ,n[1 "o unacqua9t$ ) trigonometry c easily und]/& ! fact1 t1 :5 we "k c]ta9 p>ts ( a triangle1 we c f9d ! o!r p>ts by calculation2 z1 9 ! rule ( ?ree 9 ari?metic1 we c obta9 ! f\r? t]m ( a proportion1 f hav+ ! fir/ ?ree t]ms giv54 ,?us1 9 ! triangle ,a ,b ,c1 ,fig4 #ab1 if we "k ! side ,a ,b1 & ! angles at ,a & ,b1 we c f9d by computation1 ! o!r sides1 ,a ,c & ,b ,c1 & ! rema9+ angle at ,c4 ,suppose1 !n1 t 9 measur+ an arc ( ! m]idian ?r\gh any c\ntry1 ! l9e 7 to pass directly ?r\gh ,a ,b1 b ! gr\nd 0 s ob/ruct$ betwe5 ,a & ,b1 t we c\ld n possibly c>ry our measurem5t ?r\gh x4 ,we might !n measure ano!r l9e1 z ,a ,c1 :i* 0 accessible1 & ) a compass take ! be>+ ( ,b f ! po9ts ,a & ,c1 by :i* means we %\ld le>n ! value ( ! angles at ,a & ,c4 ,f ^! data we might calculate1 by ! rules ( trigonometry1 ! exact l5g? ( ! l9e ,a ,b4 ,p]haps ! gr\nd might be s situat$1 t we c\ld n rea* ! po9t ,b1 by any r\te2 /ill1 if x c\ld be se5 f ,a & ,c1 x w\ld be all we %\ld want4 ,?us1 9 conduct+ a trigonometrical survey ( any c\ntry1 conspicu\s signals are plac$ on elevat$ po9ts1 & ! be>+s ( ^! are tak5 f ! extremities ( a kn[n l9e1 call$ ! base1 & ?us ! relative situation ( v>i\s places is accurately det]m9$4 ,7 we to und]take to run an exact nor? & s\? l9e ?r\gh any c\ntry1 z ,new ,engl&1 we %\ld select1 ne> "o extremity1 a spot ( gr\nd favorable = actual measurem5t1 z a level1 unob/ruct$ pla92 we %\ld provide a measure ^: l5g? 9 feet & in*es 0 det]m9$ ) ! greate/ possible precision1 & %\ld apply x ) ! utmo/ c>e4 ,we %\ld ?us obta9 a base l9e4 ,f ! extremities ( ?is l9e1 we %\ld take 7) "s appropriate in/rum5t7 ! be>+ ( "s signal at a great] or less di/ance1 & ?us we %\ld obta9 "o side & two angles ( a triangle1 f :i* we c\ld f9d1 by ! rules ( trigonometry1 ei!r ( ! unkn[n sides4 ,tak+ ?is z a new base1 we might take ! be>+ ( ano!r signal1 /ill fur!r on our way1 & ?us proce$ to run ! requir$ nor? & s\? l9e1 )\t actually measur+ any ?+ m ?an ! fir/1 or base l9e4 ,?us1 9 ,fig4 #ac1 we wi% to measure ! di/ance betwe5 ! two po9ts ,a & ,o1 :i* are bo? on ! same m]idian1 z is kn[n by _! hav+ ! same longitude2 b1 on acc\nt ( v>i\s ob/acles1 x w\ld be f\nd v inconv5i5t to measure ?is l9e directly1 ) a rod or *a91 & ev5 if we c\ld d x1 we c\ld n by ?is me?od obta9 ne>ly s accurate a result1 z we c\ld by a s]ies ( triangles1 :]e1 aft] ! base l9e 0 measur$1 we %\ld h no?+ else to measure except angles1 :i* c be det]m9$1 by obs]vation1 to a great] degree ( exactness1 ?an l9es4 ,we !re=e1 9 ! fir/ place1 measure ! base l9e1 ,a ,b1 ) ! utmo/ precision4 ,!n1 tak+ ! be>+ ( "s signal at ,c f ,a & ,b1 we obta9 ! means ( calculat+ ! side ,b ,c1 z has be5 already expla9$4 ,tak+ ,b ,c z a new base1 we proce$1 9 l mann]1 to det]m9e successively ! sides ,c ,d1 ,d ,e1 & ,e ,f1 & also ,a ,c1 & ,c ,e4 ,al?\gh ,a ,c is n 9 ! direction ( ! m]idian1 b consid]ably to ! ea/ ( x1 yet x is easy to f9d ! correspond+ di/ance on ! m]idian1 ,a ,m2 & 9 ! same mann] we c f9d ! portions ( ! m]idian ,m ,n & ,n ,o1 correspond+ respectively to ,c ,e & ,e ,f4 ,add+ ^! sev]al p>ts ( ! m]idian toge!r1 we obta9 ! l5g? ( ! arc f ,a to ,o1 9 miles2 & by obs]vations on ! nor? />1 at ea* extremity ( ! arc1 namely1 at ,a & at ,o1 we c\ld det]m9e ! diff]5ce ( latitude betwe5 ^! two po9ts4 ,suppose1 = example1 t ! di/ance betwe5 ,a & ,o is exactly five degrees1 & t ! l5g? ( ! int]v5+ l9e is ?ree hundr$ & =ty-sev5 miles2 !n1 divid+ ! latt] by ! =m] numb]1 we f9d ! l5g? ( a degree to be sixty-n9e miles & f\r t5?s4 ,to take1 h[ev]1 a few ( ! results actually obta9$1 !y are z foll[s3 ,places ( obs]vation4 ,latitude4 ,l5g? ( a deg4 9 miles4 ,p]u1 #jj #jj' #jj #fh4gcb ,p5nsylvania1 #ci #ab #jj #fh4hif ,france1 #df #ab #jj #fi4jed ,engl&1 #ea #bi #ed-a_/b #fi4adf ,sw$51 #ff #bj #aj #fi4bib ,?is comp>ison %[s1 t ! l5g? ( a degree gradually increases1 z we proce$ f ! equator t[>ds ! pole4 ,comb9+ ! results ( v>i\s e/imates1 ! dim5sions ( ! t]re/rial sph]oid are f\nd to be z foll[s3 ,equatorial diamet]1 #gibe4fdh miles4 ,pol> diamet]1 #ghii4agj ,av]age diamet]1 #giab4dji ,! diff]5ce betwe5 ! greate/ & ! lea/ is ab\t tw5ty-six & "o half miles1 :i* is ab\t "o two hundr$ & n9ety-n9? "p ( ! greate/4 ,?is fraction is d5om9at$ ! ellipticity ( ! e>?1--be+ ! excess ( ! equatorial ov] ! pol> diamet]4 ,! op]ations1 und]tak5 = ! purpose ( det]m9+ ! figure ( ! e>?1 h be5 conduct$ ) ! mo/ ref9$ exactness4 ,at any /age ( ! process1 ! l5g? ( ! la/ side1 z obta9$ by calculation1 may be actually measur$ 9 ! same mann] z ! base f :i* ! s]ies ( triangles comm5c$4 ,:5 ?us measur$1 x is call$ ! base ( v]ification4 ,9 "s surveys1 ! base ( v]ification1 :5 tak5 at a di/ance ( f\r hundr$ miles f ! />t+ po9t1 has n diff]$ m ?an "o foot f ! same l9e1 z det]m9$ by calculation4 ,ano!r me?od ( arriv+ at ! exact figure ( ! e>? is1 by obs]vations ) ! p5dulum4 ,if a p5dulum1 l t ( a clock1 be susp5d$1 & ! numb] ( its vibrations p] h\r be c\nt$1 !y w be f\nd to be diff]5t 9 diff]5t latitudes4 ,a p5dulum t vibrates ?irty-six hundr$ times p] h\r1 at ! equator1 w vibrate ?irty-six hundr$ & five & two ?irds times1 at ,london1 & a /ill great] numb] ( times ne>] ! nor? pole4 ,n[1 ! vibrations ( ! p5dulum are produc$ by ! =ce ( gravity4 ,h5ce _! comp>ative numb] at diff]5t places is a measure ( ! relative =ces ( gravity at ^? places4 ,b :5 we "k ! relative =ces ( gravity at diff]5t places1 we "k _! relative di/ances f ! c5tre ( ! e>?2 because ! ne>] a place is to ! c5tre ( ! e>?1 ! great] is ! =ce ( gravity4 ,suppose1 = example1 we %\ld c\nt ! numb] ( vibrations ( a p5dulum at ! equator1 & !n c>ry x to ! nor? pole1 & c\nt ! numb] ( vibrations made !re 9 ! same "t1--we %\ld be able1 f ^! two obs]vations1 to e/imate ! relative =ces ( gravity at ^! two po9ts2 &1 hav+ ! relative =ces ( gravity1 we c !nce d$uce _! relative di/ances f ! c5tre ( ! e>?1 & ?us obta9 ! pol> & equatorial diamet]s4 ,obs]vations ( ?is k9d h be5 tak5 ) ! greate/ accuracy1 9 _m places on ! surface ( ! e>?1 at v>i\s di/ances f ea* o!r1 & !y lead to ! same conclusions respect+ ! figure ( ! e>?1 z ^? d]iv$ f measur+ arcs ( ! m]idian4 ,x is pleas+ ?us to see a great tru?1 & "o app>5tly beyond ! pale ( human inve/igation1 rea*$ by two r\tes entirely indep5d5t ( ea* o!r4 ,nor1 inde$1 are ^! ! only pro(s :i* h be5 discov]$ ( ! sph]oidal figure ( ! e>?4 ,9 consequ5ce ( ! accumulation ( matt] above ! equatorial regions ( ! e>?1 a body weighs less !re ?an t[>ds ! poles1 be+ fur!r remov$ f ! c5tre ( ! e>?4 ,! same accumulation ( matt]1 by ! =ce ( attraction :i* x ex]ts1 causes slight inequalities 9 ! motions ( ! moon2 & s9ce ! am\nt ( ^! becomes a measure ( ! =ce :i* produces !m1 a/ronom]s are able1 f ^! inequalities1 to calculate ! exact quantity ( ! matt] ?us accumulat$1 & h5ce to det]m9e ! figure ( ! e>?4 ,! result is n ess5tially diff]5t f t obta9$ by ! o!r me?ods4 ,f9ally1 ! %ape ( ! e>?'s %ad[ is alt]$1 by its sph]oidal figure1--a circum/ance :i* affects ! "t & duration ( a lun> eclipse4 ,all ^! diff]5t & indep5d5t ph5om5a af=d a pleas+ example ( ! h>mony ( tru?4 ,! kn[n effects ( ! c5trifugal =ce ^u a body revolv+ on its axis1 l ! e>?1 lead u to inf] t ! e>? is ( a sph]oidal figure2 b if ?is be ! fact1 ! p5dulum ought to vibrate fa/] ne> ! pole ?an at ! equator1 because x w\ld !re be ne>] ! c5tre ( ! e>?4 ,on trial1 su* is f\nd to be ! case4 ,if1 aga91 !re be su* an accumulation ( matt] ab\t ! equatorial regions1 its effects ought to be visible 9 ! motions ( ! moon1 :i* x w\ld influ5ce by its gravity2 & !re1 also1 its effects are trac$4 ,at l5g?1 we apply our measures to ! surface ( ! e>? itself1 & f9d ! same fact1 :i* _h ?us be5 se>*$ out among ! hidd5 ?+s ( ,nature1 "h palpably exhibit$ be=e our eyes4 ,f9ally1 on e/imat+ f ^! diff]5t s\rces1 :at ! exact am\nt ( ! compression at ! poles mu/ be1 all br+ out ne>ly "o & ! same result4 ,?is tru?1 s h>moni\s 9 itself1 takes along ) x1 & e/abli%es1 a ?\s& o!r tru?s on :i* x re/s4 ,,footnote3 #e ,libr>y ( ,useful ,k3 ,hi/ory ( ,a/ronomy1 page #ie4 ,,lett] ,,viii4 ,,diurnal ,,revolutions4 ,to "s %e taught ! fabric ( ! sph]e1 ,! *angeful moon1 ! circuit ( ! />s1 ,! gold5 zones ( heav54--,ak5side4 ,,) ! elem5t>y k already acquir$1 y w n[ be able to ent] ) pleasure & pr(it on ! v>i\s int]e/+ ph5om5a dep5d5t on ! revolution ( ! e>? on its axis & ar\nd ! sun4 ,! app>5t diurnal revolution ( ! heav5ly bodies1 f ea/ to we/1 is ow+ to ! actual revolution ( ! e>? on its own axis1 f we/ to ea/4 ,if we conceive ( a radius ( ! e>?'s equator ext5d$ until x meets ! concave sph]e ( ! heav5s1 !n1 z ! e>? revolves1 ! extremity ( ?is l9e w\ld trace out a curve on ! face ( ! sky2 namely1 ! cele/ial equator4 ,9 curves p>allel to ?is1 call$ ! circles ( diurnal revolution1 ! heav5ly bodies actually appe> to move1 e /> hav+ its own peculi> circle4 ,aft] y h fir/ r5d]$ famili> ! real motion ( ! e>? f we/ to ea/1 y may !n1 )\t dang] ( misappreh5sion1 adopt ! common language1 t all ! heav5ly bodies revolve ar\nd ! e>? once a day1 f ea/ to we/1 9 circles p>allel to ! equator & to ea* o!r4 ,i mu/ rem9d y1 t ! "t occupi$ by a />1 9 pass+ f any po9t 9 ! m]idian until x comes r\nd to ! same po9t aga91 is call$ a sid]eal day1 & measures ! p]iod ( ! e>?'s revolution on its axis4 ,if we wat* ! returns ( ! same /> f day to day1 we %all f9d ! int]vals exactly equal to ea* o!r2 t is1 ! sid]eal days are all equal4 ,:atev] /> we select = ! obs]vation1 ! same result w be obta9$4 ,! />s1 !re=e1 always keep ! same relative position1 & h a common movem5t r\nd ! e>?1--a consequ5ce t naturally fl[s f ! hypo!sis t _! app>5t motion is all produc$ by a s+le real motion2 namely1 t ( ! e>?4 ,! sun1 moon1 & planets1 z well z ! fix$ />s1 revolve 9 l mann]2 b _! returns to ! m]idian are n1 l ^? ( ! fix$ />s1 at exactly equal int]vals4 ,! appe>ances ( ! diurnal motions ( ! heav5ly bodies are diff]5t 9 diff]5t p>ts ( ! e>?1--s9ce e place has its own horizon1 & diff]5t horizons are v>i\sly incl9$ to ea* o!r4 ,no?+ 9 a/ronomy is m apt to mislead u1 ?an ! ob/9ate habit ( consid]+ ! horizon z a fix$ & immutable plane1 & ( ref]r+ e ?+ to x4 ,we %\ld contemplate ! e>? z a huge globe1 occupy+ a small portion ( space1 & encircl$ on all sides1 at an imm5se di/ance1 by ! />ry sph]e4 ,we %\ld free our m9ds f _! habitual pron5ess to consid] "o "p ( space z naturally up & ano!r d[n1 & view ourselves z subject to a =ce 7gravity7 :i* b9ds u to ! e>? z truly z ?\gh we 7 fa/5$ to x by "s invisible cords or wires1 z ! ne$le atta*es itself to all sides ( a sph]ical load/one4 ,we %\ld dwell on ?is po9t1 until x appe>s to u z truly up1 9 ! direction ,b ,b1 ,c ,c1 ,d ,d1 :5 "o is at ,b1 ,c1 ,d1 respectively1 z 9 ! direction ,a ,a1 :5 he is at ,a1 ,fig4 #ad4 ,let u n[ suppose ! spectator view+ ! diurnal revolutions f sev]al diff]5t positions on ! e>?4 ,on ! equator1 8 horizon w\ld pass ?r\gh bo? poles2 = ! horizon cuts ! cele/ial vault at n9ety degrees 9 e direction f ! z5i? ( ! spectator2 b ! pole is likewise n9ety degrees f 8 z5i?1 :5 he /&s on ! equator2 & consequ5tly1 ! pole mu/ be 9 ! horizon4 ,"h1 also1 ! cele/ial equator w\ld co9cide ) ! prime v]tical1 be+ a great circle pass+ ?r\gh ! ea/ & we/ po9ts4 ,s9ce all ! diurnal circles are p>allel to ! equator1 consequ5tly1 !y w\ld all1 l ! equator be p]p5dicul> to ! horizon4 ,su* a view ( ! heav5ly bodies is call$ a "r sph]e1 :i* may be ?us def9$3 a "r sph]e is "o 9 :i* all ! daily revolutions ( ! />s are 9 circles p]p5dicul> to ! horizon4 ,illu/ration ,fig4 #ad4 ,a "r sph]e is se5 only at ! equator4 ,any /> situat$ 9 ! cele/ial equator w\ld appe> to rise directly 9 ! ea/1 at midnight to be 9 ! z5i? ( ! spectator1 & to set directly 9 ! we/4 ,9 proportion z />s are at a great] di/ance f ! equator t[>ds ! pole1 !y describe small] & small] circles1 until1 ne> ! pole1 _! motion is h>dly p]ceptible4 ,if ! spectator advances "o degree f ! equator t[>ds ! nor? pole1 8 horizon rea*es "o degree beyond ! pole ( ! e>?1 & cuts ! />ry sph]e "o degree bel[ ! pole ( ! heav5s1 or bel[ ! nor? />1 if t be tak5 z ! place ( ! pole4 ,z he moves onw>d t[>ds ! pole1 8 horizon cont9ually rea*es fur!r & fur!r beyond x1 until1 :5 he comes to ! pole ( ! e>?1 & "u ! pole ( ! heav5s1 8 horizon rea*es on all sides to ! equator1 & co9cides ) x4 ,moreov]1 s9ce all ! circles ( daily motion are p>allel to ! equator1 !y become1 to ! spectator at ! pole1 p>allel to ! horizon4 ,or1 a p>allel sph]e is t 9 :i* all ! circles ( daily motion are p>allel to ! horizon4 ,to r5d] ?is view ( ! heav5s famili>1 ,i w\ld advise y to foll[ r\nd 9 m9d a numb] ( sep>ate />s1 9 _! diurnal revolution1 "o ne> ! horizon1 "o a few degrees above x1 & a ?ird ne> ! z5i?4 ,to "o :o /ood ^u ! nor? pole1 ! />s ( ! nor!rn hemisph]e w\ld all be p]petually 9 view :5 n obscur$ by cl\ds1 or lo/ 9 ! sun's light1 & none ( ^? ( ! s\!rn hemisph]e w\ld ev] be se54 ,! sun w\ld be con/antly above ! horizon = six mon?s 9 ! ye>1 & ! rema9+ six cont9ually out ( sight4 ,t is1 at ! pole1 ! days & nights are ea* six mon?s long4 ,! appe>ances at ! s\? pole are simil> to ^? at ! nor?4 ,a p]fect p>allel sph]e c nev] be se51 except at "o ( ! poles1--a po9t :i* has nev] be5 actually rea*$ by man2 yet ! ,briti% discov]y %ips p5etrat$ )9 a few degrees ( ! nor? pole1 & ( c\rse enjoy$ ! view ( a sph]e ne>ly p>allel4 ,z ! circles ( daily motion are p>allel to ! horizon ( ! pole1 & p]p5dicul> to t ( ! equator1 s at all places betwe5 ! two1 ! diurnal motions are oblique to ! horizon4 ,?is aspect ( ! heav5s con/itutes an oblique sph]e1 :i* is ?us def9$3 an oblique sph]e is t 9 :i* ! circles ( daily motion are oblique to ! horizon4 ,suppose1 = example1 t ! spectator is at ! latitude ( fifty degrees4 ,8 horizon rea*es fifty degrees beyond ! pole ( ! e>?1 & gives ! same app>5t elevation to ! pole ( ! heav5s4 ,x cuts ! equator & all ! circles ( daily motion1 at an angle ( =ty degrees1--be+ always equal to :at ! altitude ( ! pole lacks ( n9ety degrees3 t is1 x is always equal to ! co-altitude ( ! pole4 ,?us1 let ,h ,o1 ,fig4 #ae1 repres5t ! horizon1 ,e ,q ! equator1 & ,p ,p ! axis ( ! e>?4 ,also1 l l1 m m1 n n1 p>allels ( latitude4 ,!n ! horizon ( a spectator at ,z1 9 latitude fifty degrees1 rea*es to fifty degrees beyond ! pole2 & ! angle ,e ,c ,h1 :i* ! equator makes ) ! horizon1 is =ty degrees1--! complem5t ( ! latitude4 ,z we advance /ill fur!r nor?1 ! elevation ( ! diurnal circle above ! horizon gr[s less & less1 & consequ5tly1 ! motions ( ! heav5ly bodies m & m oblique to ! horizon1 until f9ally1 at ! pole1 :]e ! latitude is n9ety degrees1 ! angle ( elevation ( ! equator vani%es1 & ! horizon & ! equator co9cide ) ea* o!r1 z be=e /at$4 ,illu/ration ,fig4 #ae4 ,! circle ( p]petual app>ition is ! b\nd>y ( t space ar\nd ! elevat$ pole1 :]e ! />s nev] set4 ,its di/ance f ! pole is equal to ! latitude ( ! place4 ,=1 s9ce ! altitude ( ! pole is equal to ! latitude1 a />1 ^: pol> di/ance is j equal to ! latitude1 w1 :5 at its l[e/ po9t1 only j rea* ! horizon2 & all ! />s ne>] ! pole ?an ?is w evid5tly n desc5d s f> z ! horizon4 ,?us m m1 ,fig4 #ae1 is ! circle ( p]petual app>ition1 betwe5 :i* & ! nor? pole1 ! />s nev] set1 & its di/ance f ! pole1 ,o ,p1 is evid5tly equal to ! elevation ( ! pole1 & ( c\rse to ! latitude4 ,9 ! opposite hemisph]e1 a simil> "p ( ! sph]e adjac5t to ! depress$ pole nev] rises4 ,h5ce1 ! circle ( p]petual occultation is ! b\nd>y ( t space ar\nd ! depress$ pole1 )9 :i* ! />s nev] rise4 ,?us m m1 ,fig4 #ae1 is ! circle ( p]petual occultation1 betwe5 :i* & ! s\? pole1 ! />s nev] rise4 ,9 an oblique sph]e1 ! horizon cuts ! circles ( daily motion unequally4 ,t[>ds ! elevat$ pole1 m ?an half ! circle is above ! horizon1 & a great] & great] portion1 z ! di/ance f ! equator is increas$1 until f9ally1 )9 ! circle ( p]petual app>ition1 ! :ole circle is above ! horizon4 ,j ! opposite takes place 9 ! hemisph]e next ! depress$ pole4 ,accord+ly1 :5 ! sun is 9 ! equator1 z ! equator & horizon1 l all o!r great circles ( ! sph]e1 bisect ea* o!r1 ! days & nights are equal all ov] ! globe4 ,b :5 ! sun is nor? ( ! equator1 ! days become long] ?an ! nights1 b %ort]1 :5 ! sun is s\? ( ! equator4 ,moreov]1 ! high] ! latitude1 ! great] is ! inequality 9 ! l5g?s ( ! days & nights4 ,by exam9+ ,fig4 #ae1 y w easily see h[ ea* ( ^! cases mu/ hold good4 ,mo/ ( ! appe>ances ( ! diurnal revolution c be expla9$1 ei!r on ! supposition t ! cele/ial sph]e actually turns ar\nd ! e>? once 9 tw5ty-f\r h\rs1 or t ?is motion ( ! heav5s is m]ely app>5t1 aris+ f ! revolution ( ! e>? on its axis1 9 ! opposite direction1--a motion ( :i* we are ins5sible1 z we sometimes lose ! consci\sness ( our own motion 9 a %ip or /eam-boat1 & obs]ve all ext]nal objects to be rec$+ f u1 ) a common motion4 ,pro(s1 entirely conclusive & satisfactory1 e/abli% ! fact1 t x is ! e>?1 & n ! cele/ial sph]e1 t turns2 b ^! pro(s are drawn f v>i\s s\rces1 & "o is n prep>$ to appreciate _! value1 or ev5 to und]/& "s ( !m1 until he has made consid]able pr(ici5cy 9 ! /udy ( a/ronomy1 & become famili> ) a great v>iety ( a/ronomical ph5om5a4 ,to su* a p]iod we w !re=e po/pone ! discussion ( ! e>?'s rotation on its axis4 ,:ile we reta9 ! same place on ! e>?1 ! diurnal revolution occasions no *ange 9 our horizon1 b our horizon goes r\nd1 z well z ourselves4 ,let u fir/ take our /ation on ! equator1 at sunrise2 our horizon n[ passes ?r\gh bo? ! poles & ?r\gh ! sun1 :i* we are to conceive ( z at a great di/ance f ! e>?1 & !re=e z cut1 n by ! t]re/rial1 b by ! cele/ial1 horizon4 ,z ! e>? turns1 ! horizon dips m & m bel[ ! sun1 at ! rate ( fifte5 degrees = e h\r2 &1 z 9 ! case ( ! pol> />1 ! sun appe>s to rise at ! same rate4 ,9 six h\rs1 !re=e1 x is depress$ n9ety degrees bel[ ! sun1 br++ u directly "u ! sun1 :i*1 = our pres5t purpose1 we may consid] z hav+ all ! :ile ma9ta9$ ! same fix$ position 9 space4 ,! e>? cont9ues to turn1 & 9 six h\rs m1 x completely rev]ses ! position ( our horizon1 s t ! we/]n "p ( ! horizon1 :i* at sunrise 0 diametrically opposite to ! sun1 n[ cuts ! sun1 & soon aft]w>ds x rises above ! level ( ! sun1 & ! sun sets4 ,dur+ ! next twelve h\rs1 ! sun cont9ues on ! invisible side ( ! sph]e1 until ! horizon returns to ! position f :i* x set out1 & a new day beg9s4 ,let u next contemplate ! simil> ph5om5a at ! poles4 ,"h ! horizon1 co9cid+1 z x does1 ) ! equator1 w\ld cut ! sun ?r\gh its c5tre & ! sun w\ld appe> to revolve along ! surface ( ! sea1 "o half above & ! o!r half bel[ ! horizon4 ,?is supposes ! sun 9 its annual revolution to be at "o ( ! equ9oxes4 ,:5 ! sun is nor? ( ! equator1 x revolves cont9ually r\nd 9 a circle1 :i*1 dur+ a s+le revolution1 appe>s p>allel to ! equator1 & x is con/antly day2 & :5 ! sun is s\? ( ! equator1 x is1 = ! same reason1 cont9ual night4 ,:5 we h ga9$ a cle> idea ( ! appe>ances ( ! diurnal revolutions1 z exhibit$ to a spectator at ! equator & at ! pole1 t is1 9 a "r & 9 a p>allel sph]e1 !re w be little difficulty 9 imag9+ h[ !y mu/ be 9 ! int]m$iate latitudes1 :i* h an oblique sph]e4 ,! appe>ances ( ! sun & />s1 pres5t$ to ! inhabitants ( diff]5t c\ntries1 are su* z correspond to ! sph]e 9 :i* !y live4 ,?us1 9 ! f]vid climates ( ,india1 ,africa1 & ,s\? ,am]ica1 ! sun m\nts up to ! highe/ regions ( ! heav5s1 & desc5ds directly d[nw>ds1 sudd5ly plung+ b5ea? ! horizon4 ,8 rays1 d>t+ almo/ v]tically ^u ! heads ( ! inhabitants1 /rike ) a =ce unkn[n to ! p ( ! cold] climates2 :ile 9 places remote f ! equator1 z 9 ! nor? ( ,europe1 ! sun1 9 ,summ]1 rises v f> 9 ! nor?1 takes a long circuit t[>ds ! s\?1 & sets z f> nor?w>d 9 ! we/ z ! po9t :]e x rose on ! o!r side ( ! m]idian4 ,z we g /ill fur!r nor?1 to ! nor!rn p>ts ( ,norway & ,sw$51 = example1 to ! conf9es ( ! frigid zone1 ! ,summ]'s sun j grazes ! nor!rn horizon1 & at noon appe>s only tw5ty-?ree & "o half degrees above ! s\!rn4 ,on ! o!r h&1 9 mid-w9t]1 9 ! nor? ( ,europe1 z at ,/4 ,pet]sburgh1 ! day dw9dles almo/ to no?+1--la/+ only :ile ! sun describes a v %ort arc 9 ! extreme s\?4 ,9 "s p>ts ( ,sib]ia & ,icel&1 ! only day consi/s ( a little glimm]+ ( ! sun on ! v]ge ( ! s\!rn horizon1 at noon4 ,,lett] ,,ix4 ,,p>allax ,,& ,,refraction4 ,g1 wondr\s creature6 m\nt :]e sci5ce guides1 ,g measure e>?1 weigh air1 & /ate ! tides2 ,in/ruct ! planets 9 :at orbs to run1 ,correct old ,"t1 & regulate ! sun4--,pope4 ,i ,,?9k y mu/ h felt "s a/oni%m5t1 t a/ronom]s are able to calculate ! exact di/ances & magnitudes ( ! sun1 moon1 & planets4 ,we %\ld1 at ! fir/ ?\ght1 imag9e t su* k z ?is mu/ be beyond ! rea* ( ! human faculties1 & we might be incl9$ to suspect t a/ronom]s practise "s deception 9 ?is matt]1 = ! purpose ( excit+ ! admiration ( ! unle>n$4 ,i w !re=e1 9 ! pres5t ,lett]1 endeavor to give y "s cle> & correct views respect+ ! mann] 9 :i* a/ronom]s acquire ?is k4 ,9 our *ildhood1 we all probably adopt ! notion t ! sky is a real dome ( def9ite surface1 9 :i* ! heav5ly bodies are fix$4 ,:5 any objects are beyond a c]ta9 di/ance f ! eye1 we lose all p[] ( di/+ui%+1 by our sight alone1 betwe5 diff]5t di/ances1 & _c tell :e!r a giv5 object is "o million or a ?\s& millions ( miles (f4 ,al?\gh ! bodies se5 9 ! sky are 9 fact at di/ances extremely v>i\s1--"s1 z ! cl\ds1 only a few miles (f2 o!rs1 z ! moon1 b a few ?\s& miles2 & o!rs1 z ! fix$ />s1 innum]able millions ( miles f u1--yet1 z our eye _c di/+ui% ^! diff]5t di/ances1 we acquire ! habit ( ref]r+ all objects beyond a mod]ate height to "o & ! same surface1 namely1 an imag9>y sph]ical surface1 d5om9at$ ! cele/ial vault4 ,?us1 ! v>i\s objects repres5t$ 9 ! diagram on next page1 ?\gh diff]+ v mu* 9 %ape & diamet]1 w\ld all be project$ ^u ! sky alike1 & compose a "p1 inde$1 ( ! imag9>y vault itself4 ,! place :i* ea* object occupies is det]m9$ by l9es drawn f ! eye ( ! spectator ?r\gh ! extremities ( ! body1 to meet ! imag9>y concave sph]e4 ,?us1 to a spectator at ,o1 ,fig #af1 ! sev]al l9es ,a ,b1 ,c ,d1 & ,e ,f1 w\ld all be project$ into ar*es on ! face ( ! sky1 & be se5 z p>ts ( ! sky itself1 z repres5t$ by ! l9es ,a ,b1 ,c ,d1 & ,e ,f4 ,& 7 a body actually to move 9 ! sev]al directions indicat$ by ^! l9es1 !y w\ld appe> to ! spectator to describe portions ( ! cele/ial vault4 ,?us1 ev5 :5 mov+ ?r\gh ! crook$ l9e1 f a to b1 a body w\ld appe> to be mov+ along ! face ( ! sky1 & ( c\rse 9 a regul> curve l9e1 f c to d4 ,illu/ration ,fig4 #af4 ,b1 al?\gh all objects1 beyond a c]ta9 mod]ate height1 are project$ on ! imag9>y surface ( ! sky1 yet diff]5t spectators w project ! same object on diff]5t p>ts ( ! sky4 ,?us1 a spectator at ,a1 ,fig4 #ag1 w\ld see a body1 ,c1 at ,m1 :ile a spectator at ,b w\ld see ! same body at ,n4 ,?is *ange ( place 9 a body1 z se5 f diff]5t po9ts1 is call$ p>allax1 :i* is ?us def9$3 p>allax is ! app>5t *ange ( place :i* bodies und]go by be+ view$ f diff]5t po9ts4 ,illu/ration ,fig4 #ag4 ,! arc ,m ,n is call$ ! p>allactic arc1 & ! angle ,a ,c ,b1 ! p>allactic angle4 ,x is pla91 f ! figure1 t ne> objects are mu* m affect$ by p>allax ?an di/ant ones4 ,?us1 ! body ,c1 ,fig4 #ag1 makes a mu* great] p>allax ?an ! m di/ant body ,d1--! =m] be+ measur$ by ! arc ,m ,n1 & ! latt] by ! arc ,o ,p4 ,we may easily imag9e bodies to be s di/ant1 t !y w\ld appe> project$ at v ne>ly ! same po9t ( ! heav5s1 :5 view$ f places v remote f ea* o!r4 ,inde$1 ! fix$ />s1 z we %all see m fully h]eaft]1 are s di/ant1 t spectators1 a hundr$ millions ( miles ap>t1 see ea* /> 9 "o & ! same place 9 ! heav5s4 ,x is by means ( p>allax1 t a/ronom]s f9d ! di/ances & magnitudes ( ! heav5ly bodies4 ,9 ord] fully to und]/& ?is subject1 "o requires to "k some?+ ( trigonometry1 :i* sci5ce enables u to f9d c]ta9 unkn[n p>ts ( a triangle f c]ta9 o!r p>ts :i* are kn[n4 ,al?\gh y may n be acqua9t$ ) ! pr9ciples ( trigonometry1 yet y w readily und]/&1 f y\r k ( ari?metic1 t f c]ta9 ?+s giv5 9 a problem o!rs may be f\nd4 ,e triangle has ( c\rse ?ree sides & ?ree angles2 &1 if we "k two ( ! angles & "o ( ! sides1 we c f9d all ! o!r p>ts1 namely1 ! rema9+ angle & ! two unkn[n sides4 ,?us1 9 ! triangle ,a ,b ,c1 ,fig4 #ah1 if we "k ! l5g? ( ! side ,a ,b1 & h[ _m degrees ea* ( ! angles ,a ,b ,c & ,b ,c ,a conta9s1 we c f9d ! l5g? ( ! side ,b ,c1 or ( ! side ,a ,c1 & ! rema9+ angle at ,a4 ,n[1 let u apply ^! pr9ciples to ! measurem5ts ( "s ( ! heav5ly bodies4 ,illu/ration ,fig4 #ah4 ,illu/ration ,fig4 #ai4 ,9 ,fig4 #ai1 let ,a repres5t ! e>?1 ,c ,h ! horizon1 & ,h ,z a quadrant ( a great circle ( ! heav5s1 ext5d+ f ! horizon to ! z5i?2 & let ,e1 ,f1 ,g1 ,o1 be successive positions ( ! moon1 at diff]5t elevations1 f ! horizon to ! m]idian4 ,n[1 a spectator on ! surface ( ! e>?1 at ,a1 w\ld ref] ! moon1 :5 at ,e1 to h1 on ! face ( ! sky1 :]eas1 if se5 f ! c5tre ( ! e>?1 x w\ld appe> at ,h4 ,s1 :5 ! moon 0 at ,f1 a spectator at ,a w\ld see x at p1 :ile1 if se5 f ! c5tre1 x w\ld h appe>$ at ,p4 ,! p>allactic arcs1 ,h h1 ,p p1 ,r r1 gr[ cont9ually small] & small]1 z a body is situat$ high] above ! horizon2 & :5 ! body is 9 ! z5i?1 !n ! p>allax vani%es altoge!r1 = at ,o ! moon w\ld be se5 at ,z1 :e!r view$ f ,a or ,c4 ,s9ce1 !n1 a heav5ly body is liable to be ref]r$ to diff]5t po9ts on ! cele/ial vault1 :5 se5 f diff]5t p>ts ( ! e>?1 & ?us "s confusion be occasion$ 9 ! det]m9ation ( po9ts on ! cele/ial sph]e1 a/ronom]s h agre$ to consid] ! true place ( a cele/ial object to be t :]e x w\ld appe>1 if se5 f ! c5tre ( ! e>?2 & ! doctr9e ( p>allax tea*es h[ to r$uce obs]vations made at any place on ! surface ( ! e>?1 to su* z !y w\ld be1 if made f ! c5tre4 ,:5 ! moon1 or any heav5ly body1 is se5 9 ! horizon1 z at ,e1 ! *ange ( place is call$ ! horizontal p>allax4 ,?us1 ! angle ,a ,e ,c1 measures ! horizontal p>allax ( ! moon4 ,7 a spectator to view ! e>? f ! c5tre ( ! moon1 he w\ld see ! semidiamet] ( ! e>? "u ?is same angle2 h5ce1 ! horizontal p>allax ( any body is ! angle subt5d$ by ! semidiamet] ( ! e>?1 z se5 f ! body4 ,please to rememb] ?is fact4 ,x is evid5t f ! figure1 t ! effect ( p>allax ^u ! place ( a cele/ial body is to depress x4 ,?us1 9 consequ5ce ( p>allax1 ,e is depress$ by ! arc ,h h2 ,f1 by ! arc ,p p2 ,g1 by ! arc ,r r2 :ile ,o su/a9s no *ange4 ,h5ce1 9 all calculations respect+ ! altitude ( ! sun1 moon1 or planets1 ! am\nt ( p>allax is to be add$3 ! />s1 z we %all see h]eaft]1 h no s5sible p>allax4 ,x is n[ v easy to see h[1 :5 ! p>allax ( a body is kn[n1 we may f9d its di/ance f ! c5tre ( ! e>?4 ,?us1 9 ! triangle ,a ,c ,e1 ,fig4 #ai1 ! side ,a ,c is kn[n1 be+ ! semidiamet] ( ! e>?2 ! angle ,c ,a ,e1 be+ a "r angle1 is also kn[n2 & ! p>allactic angle1 ,a ,e ,c1 is f\nd f obs]vation2 & x is a well-kn[n pr9ciple ( trigonometry1 t :5 we h any two angles ( a triangle1 we may f9d ! rema9+ angle by subtract+ ! sum ( ^! two f "o hundr$ & eighty degrees4 ,consequ5tly1 9 ! triangle ,a ,e ,c1 we "k all ! angles & "o side1 namely1 ! side ,a ,c2 h5ce1 we h ! means ( f9d+ ! side ,c ,e1 :i* is ! di/ance f ! c5tre ( ! e>? to ! c5tre ( ! moon4 ,illu/ration ,fig4 #bj4 ,:5 ! di/ance ( a heav5ly body is kn[n1 & we c measure1 ) in/rum5ts1 its angul> bread?1 we c easily det]m9e its magnitude4 ,?us1 if we h ! di/ance ( ! moon1 ,e ,s1 ,fig4 #bj1 & half ! bread? ( its disk ,s ,c1 7:i* is measur$ by ! angle ,s ,e ,c17 we c f9d ! l5g? ( ! l9e1 ,s ,c1 9 miles4 ,twice ?is l9e is ! diamet] ( ! body2 & :5 we "k ! diamet] ( a sph]e1 we c1 by well-kn[n rules1 f9d ! cont5ts ( ! surface1 & its solidity4 ,y w p]haps be curi\s to "k1 h[ ! moon's horizontal p>allax is f\nd2 = x mu/ h be5 previ\sly asc]ta9$1 be=e we c\ld apply ?is me?od to f9d+ ! di/ance ( ! moon f ! e>?4 ,suppose t two a/ronom]s take _! /ations on ! same m]idian1 b "o s\? ( ! equator1 z at ! ,cape ( ,good ,hope1 & ano!r nor? ( ! equator1 z at ,b]l91 9 ,prussia1 :i* two places lie ne>ly on ! same m]idian4 ,! obs]v]s w\ld sev]ally ref] ! moon to diff]5t po9ts on ! face ( ! sky1--! s\!rn obs]v] c>ry+ x fur!r nor?1 & ! nor!rn obs]v] fur!r s\?1 ?an its true place1 z se5 f ! c5tre ( ! e>?4 ,?is w be pla9 f ! diagram1 ,fig4 #ba4 ,if ,a & ,b repres5t ! positions ( ! spectators1 ,m ! moon1 & ,c ,d an arc ( ! sky1 !n x is evid5t1 t ,c ,d w\ld be ! p>allactic arc4 ,illu/ration ,fig4 #ba4 ,^! obs]vations furni% mat]ials = calculat+1 by ! aid ( trigonometry1 ! moon's horizontal p>allax1 & we h be=e se5 h[1 :5 we "k ! p>allax ( a heav5ly body1 we c f9d bo? its di/ance f ! e>? & its magnitude4 ,beside ! *ange ( place :i* ^! heav5ly bodies und]go1 9 consequ5ce ( p>allax1 !re is ano!r1 ( an opposite k9d1 aris+ f ! effect ( ! atmosph]e1 call$ refraction4 ,refraction elevates ! app>5t place ( a body1 :ile p>allax depresses x4 ,x affects alike ! mo/ di/ant z well z ne>] bodies4 ,9 ord] to und]/& ! nature ( refraction1 we mu/ consid]1 t an object always appe>s 9 ! direction 9 :i* ! la/ ray ( light comes to ! eye4 ,if ! light :i* comes f a /> 7 b5t into fifty directions be=e x rea*$ ! eye1 ! /> w\ld nev]!less appe> 9 ! l9e describ$ by ! ray ne>e/ ! eye4 ,! op]ation ( ?is pr9ciple is se5 :5 an o>1 or any /ick1 is ?ru/ into wat]4 ,z ! rays ( light by :i* ! o> is se5 h _! direction *ang$ z !y pass out ( wat] into air1 ! app>5t direction 9 :i* ! body is se5 is *ang$ 9 ! same degree1 giv+ x a b5t appe>ance1--! "p bel[ ! wat] hav+ app>5tly a diff]5t direction f ! "p above4 ,?us1 9 ,fig4 #bb1 page #if1 if ,s a x be ! o>1 ,s a b w be ! b5t appe>ance1 z affect$ by refraction4 ,! transp>5t sub/ance ?r\gh :i* any ray ( light passes is call$ a m$ium4 ,x is a g5]al fact 9 optics1 t1 :5 light passes out ( a r>] into a d5s] m$ium1 z out ( air into wat]1 or out ( space into air1 x is turn$ t[>ds a p]p5dicul> to ! surface ( ! m$ium2 & :5 x passes out ( a d5s] into a r>] m$ium1 z out ( wat] into air1 x is turn$ f ! p]p5dicul>4 ,9 ! above case1 ! light1 pass+ out ( space into air1 is turn$ t[>ds ! radius ( ! e>?1 ?is be+ p]p5dicul> to ! surface ( ! atmosph]e2 & x is turn$ m & m t[>ds t radius ! ne>] x approa*es to ! e>?1 because ! d5sity ( ! air rapidly increases ne> ! e>?4 ,illu/ration ,fig4 #bb4 ,let u n[ conceive ( ! atmosph]e z made up ( a great numb] ( p>allel /rata1 z ,a ,a1 ,b ,b1 ,c ,c1 & ,d ,d1 increas+ rapidly 9 d5sity 7z is kn[n to be ! fact7 9 approa*+ ne> to ! surface ( ! e>?4 ,let ,s be a />1 f :i* a ray ( light1 ,s a1 ent]s ! atmosph]e at a1 :]e1 be+ mu* turn$ t[>ds ! radius ( ! convex surface1 x w\ld *ange its direction into ! l9e a b1 & aga9 into b c1 & c ,o1 rea*+ ! eye at ,o4 ,n[1 s9ce an object always appe>s 9 ! direction 9 :i* ! light f9ally /rikes ! eye1 ! /> w\ld be se5 9 ! direction ,o c1 &1 consequ5tly1 ! /> w\ld app>5tly *ange its place1 by refraction1 f ,s to ,s1 be+ elevat$ out ( its true position4 ,moreov]1 s9ce1 on acc\nt ( ! cont9ual increase ( d5sity 9 desc5d+ ?r\gh ! atmosph]e1 ! light w\ld be cont9ually turn$ out ( its c\rse m & m1 x w\ld !re=e move1 n 9 ! polygon repres5t$ 9 ! figure1 b 9 a correspond+ curve l9e1 ^: curvature is rapidly increas$ ne> ! surface ( ! e>?4 ,:5 a body is 9 ! z5i?1 s9ce a ray ( light f x ent]s ! atmosph]e at "r angles to ! refract+ m$ium1 x suff]s no refraction4 ,consequ5tly1 ! position ( ! heav5ly bodies1 :5 9 ! z5i?1 is n *ang$ by refraction1 :ile1 ne> ! horizon1 :]e a ray ( light /rikes ! m$ium v obliquely1 & trav]ses ! atmosph]e ?r\gh its d5se/ "p1 ! refraction is greate/4 ,! :ole am\nt ( refraction1 :5 a body is 9 ! horizon1 is ?irty-f\r m9utes2 :ile1 at only an elevation ( "o degree1 ! refraction is b tw5ty-f\r m9utes2 & at =ty-five degrees1 x is sc>cely a s+le m9ute4 ,h5ce x is always important to make our obs]vations on ! heav5ly bodies :5 !y are at z great an elevation z possible above ! horizon1 be+ !n less affect$ by refraction ?an at l[] altitudes4 ,s9ce ! :ole am\nt ( refraction ne> ! horizon exce$s ?irty-?ree m9utes1 & ! diamet]s ( ! sun & moon are sev]ally less ?an ?is1 ^! lum9>ies are 9 view bo? be=e !y h actually ris5 & aft] !y h set4 ,! rapid increase ( refraction ne> ! horizon is /rik+ly ev9c$ by ! oval figure :i* ! sun assumes :5 ne> ! horizon1 & :i* is se5 to ! greate/ advantage :5 light cl\ds enable u to view ! sol> disk4 ,7 all p>ts ( ! sun equally rais$ by refraction1 !re w\ld be no *ange ( figure2 b1 s9ce ! l[] side is m refract$ ?an ! upp]1 ! effect is to %ort5 ! v]tical diamet]1 & ?us to give ! disk an oval =m4 ,?is effect is p>ticul>ly rem>kable :5 ! sun1 at 8 ris+ or sett+1 is obs]v$ f ! top ( a m\nta91 or at an elevation ne> ! sea%ore2 = 9 su* situations1 ! rays ( light make a great] angle ?an ord9>y ) a p]p5dicul> to ! refract+ m$ium1 & ! am\nt ( refraction is proportionally great]4 ,9 "s cases ( ?is k9d1 ! %ort5+ ( ! v]tical diamet] ( ! sun has be5 obs]v$ to am\nt to six m9utes1 or ab\t "o fif? ( ! :ole4 ,! app>5t enl>gem5t ( ! sun & moon1 :5 ne> ! horizon1 arises f an optical illusion4 ,^! bodies1 9 fact1 are n se5 "u s great an angle :5 9 ! horizon z :5 on ! m]idian1 = !y are ne>] to u 9 ! latt] case ?an 9 ! =m]4 ,! di/ance ( ! sun1 inde$1 is s great1 t x makes v little diff]5ce 9 8 app>5t diamet] :e!r he is view$ 9 ! horizon or on ! m]idian2 b ) ! moon1 ! case is o!rwise2 its angul> diamet]1 :5 measur$ ) in/rum5ts1 is p]ceptibly l>g] :5 at its culm9ation1 or highe/ elevation above ! horizon4 ,:y1 !n1 d ! sun & moon appe> s mu* l>g] :5 ne> ! horizon8 ,x is ow+ to a habit ( ! m9d1 by :i* we judge ( ! magnitudes ( di/ant objects1 n m]ely by ! angle !y subt5d at ! eye1 b also by our impressions respect+ _! di/ance1 all[+1 "u a giv5 angle1 a great] magnitude z we imag9e ! di/ance ( a body to be great]4 ,n[1 on acc\nt ( ! num]\s objects usually 9 sight betwe5 u & ! sun1 :5 he is ne> ! horizon1 he appe>s mu* fur!r remov$ f u ?an :5 on ! m]idian2 & we unconsci\sly assign to him a proportionally great] magnitude4 ,if we view ! sun1 9 ! two positions1 ?r\gh a smok$ glass1 no su* diff]5ce ( size is obs]v$2 = "h no objects are se5 b ! sun himself4 ,twilight is ano!r ph5om5on dep5d+ on ! ag5cy ( ! e>?'s atmosph]e4 ,x is t illum9ation ( ! sky :i* takes place j be=e sunrise & :i* cont9ues aft] sunset4 ,x is ow+ p>tly to refraction1 & p>tly to reflection1 b mo/ly to ! latt]4 ,:ile ! sun is )9 eighte5 degrees ( ! horizon1 be=e x rises or aft] x sets1 "s portion ( its light is convey$ to u1 by means ( num]\s reflections f ! atmosph]e4 ,at ! equator1 :]e ! circles ( daily motion are p]p5dicul> to ! horizon1 ! sun desc5ds ?r\gh eighte5 degrees 9 an h\r & twelve m9utes4 ,! light ( day1 !re=e1 decl9es rapidly1 & z rapidly advances aft] daybreak 9 ! morn+4 ,at ! pole1 a con/ant twilight is enjoy$ :ile ! sun is )9 eighte5 degrees ( ! horizon1 occupy+ ne>ly two ?irds ( ! half ye> :5 ! direct light ( ! sun is )drawn1 s t ! progress f cont9ual day to con/ant night is exce$+ly gradual4 ,to an inhabitant ( an oblique sph]e1 ! twilight is long] 9 proportion z ! place is ne>] ! elevat$ pole4 ,7 x n = ! p[] ! atmosph]e has ( disp]s+ ! sol> light1 & scatt]+ x 9 v>i\s directions1 no objects w\ld be visible to u out ( direct sun%9e2 e %ad[ ( a pass+ cl\d w\ld involve u 9 midnight d>kness2 ! />s w\ld be visible all day2 & e ap>tm5t into :i* ! sun _h n direct admission w\ld be involv$ 9 ! obscurity ( night4 ,?is scatt]+ action ( ! atmosph]e on ! sol> light is greatly increas$ by ! irregul>ity ( temp]ature caus$ by ! sun1 :i* ?r[s ! atmosph]e into a con/ant /ate ( undulation2 & by ?us br++ toge!r masses ( air ( diff]5t temp]atures1 produces p>tial reflections & refractions at _! common b\nd>ies1 by :i* means mu* light is turn$ aside f a direct c\rse1 & div]t$ to ! purposes ( g5]al illum9ation4#f ,9 ! upp] regions ( ! atmosph]e1 z on ! tops ( v high m\nta9s1 :]e ! air is too mu* r>efi$ to reflect mu* light1 ! sky assumes a black appe>ance1 & />s become visible 9 ! day "t4 ,al?\gh ! atmosph]e is usually s transp>5t1 t x is invisible to u1 yet we z truly move & live 9 a fluid z fi%es t swim 9 ! sea4 ,consid]$ 9 comp>ison ) ! :ole e>?1 ! atmosph]e is to be reg>d$ z a ?9 lay] inve/+ ! surface1 l a film ( wat] cov]+ ! surface ( an orange4 ,its actual height1 h[ev]1 is ov] a hundr$ miles1 ?\gh we _c assign its precise b\nd>ies4 ,be+ p]fectly ela/ic1 ! l[] portions1 be>+ z !y d1 ! weight ( all ! mass above !m1 are greatly compress$1 :ile ! upp] portions hav+ little to oppose ! natural t5d5cy ( air to exp&1 diffuse !mselves widely4 ,! consequ5ce is1 t ! atmosph]e und]goes a rapid dim9ution ( d5sity1 z we asc5d f ! e>?1 & soon becomes exce$+ly r>e4 ,at s mod]ate a height z sev5 miles1 x is f\r times r>] ?an at ! surface1 & cont9ues to gr[ r>e 9 ! same proportion1 namely1 be+ f\r times less = e sev5 miles ( asc5t4 ,x is only1 !re=e1 )9 a few miles ( ! e>?1 t ! atmosph]e is suffici5tly d5se to su/a9 cl\ds & vapors1 :i* seldom rise s high z eight miles1 & are usually mu* ne>] to ! e>? ?an ?is4 ,s r>e does ! air become on ! top ( ,m\nt ,*imborazo1 9 ,s\? ,am]ica1 t x is incompet5t to support mo/ ( ! birds t fly ne> ! level ( ! sea4 ,! condor1 a bird :i* has rem>kably long w+s1 & a light body1 is ! only bird se5 t[]+ above ?is l(ty summit4 ,! transp>5cy ( ! atmosph]e1--a quality s ess5tial to f9e views ( ! />ry heav5s1--is mu* increas$ by conta9+ a l>ge proportion ( wat]1 provid$ x is p]fectly dissolv$1 or 9 a /ate ( invisible vapor4 ,a c\ntry at once hot & humid1 l "s portions ( ! torrid zone1 pres5ts a mu* bright] & m beautiful view ( ! moon & />s1 ?an is se5 9 cold climates4 ,be=e a copi\s ra91 especially 9 hot wea!r1 :5 ! atmosph]e is unusually humid1 we sometimes obs]ve ! sky to be rem>kably respl5d5t1 ev5 9 our own latitude4 ,accord+ly1 ?is unusual cle>ness ( ! sky1 :5 ! />s %9e ) unwont$ brilliancy1 is reg>d$ z a sign ( approa*+ ra92 & :51 aft] ! ra9 is app>5tly ov]1 ! air is rem>kably transp>5t1 & di/ant objects on ! e>? are se5 ) uncommon di/9ctness1 :ile ! sky exhibits an unusually deep azure1 we may conclude t ! s]5ity is only tempor>y1 & t ! ra9 w probably soon return4 ,,footnote3 #f ,sir ,j4 ,h]s*el4 ,,lett] ,x4 ,,! ,,sun4 ,great s\rce ( day6 be/ image "h bel[ ,( ?y ,creator1 ev] p\r+ wide1 ,f _w to _w1 ! vital ocean r\nd1 ,on ,nature write1 ) e beam1 ,8 praise4--,?omson4 ,,! subjects :i* h occupi$ ! prec$+ ,lett]s are by no means ! mo/ int]e/+ p>ts ( our sci5ce4 ,!y con/itute1 inde$1 little m ?an an introduction to our ma9 subject1 b comprise su* matt]s z are v necess>y to be cle>ly und]/ood1 be=e "o is prep>$ to ent] ) pr(it & delight ^u ! m sublime & int]e/+ field :i* n[ op5s be=e u4 ,we w beg9 our survey ( ! heav5ly bodies ) ! ,,sun1 :i* fir/ claims our homage1 z ! natural mon>* ( ! skies4 ,! moon w next occupy our att5tion2 !n ! o!r bodies :i* compose ! sol> sy/em1 namely1 ! planets & comets2 &1 f9ally1 we %all leave beh9d ?is little prov9ce 9 ! great empire ( ,nature1 & w+ a bold] flight to ! fix$ />s4 ,! di/ance ( ! sun f ! e>? is ab\t n9ety-five millions ( miles4 ,x may p]haps seem incr$ible to y1 t a/ronom]s %\ld be able to det]m9e ?is fact ) any degree ( c]ta9ty4 ,"s1 inde$1 n s well in=m$ z y\rself1 h look$ ^u ! m>vell\s ?+s t are told respect+ ! di/ances1 magnitudes1 & velocities1 ( ! heav5ly bodies1 z attempts ( a/ronom]s to impose on ! cr$ulity ( ! _w at l>ge2 b ! c]ta9ty & exactness ) :i* ! pr$ictions ( a/ronom]s are fulfill$1 z an eclipse1 = example1 ought to inspire full confid5ce 9 _! /atem5ts4 ,i c assure y1 my de> fri5d1 t ! evid5ce on :i* ^! /atem5ts are f\nd$ is p]fectly satisfactory to ^? ^: atta9m5ts 9 ! sci5ces qualify !m to und]/& !m2 &1 s f> are a/ronom]s f wi%+ to impose on ! unle>n$1 by ann\nc+ su* wond]ful discov]ies z !y h made among ! heav5ly bodies1 no class ( m5 h ev] %[n a /rict] reg>d & zeal ?an !y = ! exact tru?1 :]ev] x is atta9able4 ,n9ety-five millions ( miles is inde$ a va/ di/ance4 ,no human m9d is adequate to compreh5d x fully2 b ! ne>e/ approa*es we c make t[>ds x are ga9$ by successive ef=ts ( ! m9d to conceive ( great di/ances1 beg9n+ ) su* z are cle>ly )9 our grasp4 ,let u1 !n1 fir/ take s small a di/ance z t ( ! bread? ( ! ,atlantic ocean1 & foll[1 9 m9d1 a %ip1 z %e leaves ! port ( ,new ,york1 &1 aft] tw5ty days' /eady sail1 rea*es ,liv]pool4 ,hav+ =m$ ! be/ idea we are able ( ?is di/ance1 we may !n reflect1 t x w\ld take a %ip1 mov+ con/antly at ! rate ( t5 miles p] h\r1 m ?an a ?\s& ye>s to rea* ! sun4 ,! diamet] ( ! sun is t[>ds a million ( miles2 or1 m exactly1 x is eight hundr$ & eighty-five ?\s& miles4 ,"o hundr$ & twelve bodies z l>ge z ! e>?1 ly+ side by side1 w\ld be requir$ to rea* across ! sol> disk2 & our %ip1 sail+ at ! same rate z be=e1 w\ld be t5 ye>s 9 pass+ ov] ! same space4 ,imm5se z is ! sun1 we c readily und]/& :y x appe>s no l>g] ?an x does1 :5 we reflect1 t its di/ance is /ill m va/4 ,ev5 l>ge objects on ! e>?1 :5 se5 on a di/ant em95ce1 or ov] a wide expanse ( wat]1 dw9dle almo/ to a po9t4 ,c\ld we approa* ne>] & ne>] to ! sun1 x w\ld con/antly exp& its volume1 until f9ally x w\ld fill ! :ole vault ( heav54 ,we c\ld1 h[ev]1 approa* b little ne>] to ! sun )\t be+ consum$ by ! int5sity ( 8 heat4 ,:5ev] we come ne>] to any fire1 ! heat rapidly increases1 be+ f\r times z great at half ! di/ance1 & "o hundr$ times z great at "o t5? ! di/ance4 ,?is fact is express$ by say+1 t ! heat increases z ! squ>e ( ! di/ance decreases4 ,our globe is situat$ at su* a di/ance f ! sun1 z exactly suits ! animal & vegetable k+doms4 ,7 x ei!r mu* ne>] or mu* m remote1 !y c\ld n exi/1 con/itut$ z !y are4 ,! int5sity ( ! sol> light also foll[s ! same law4 ,consequ5tly1 7 we ne>] to ! sun ?an we are1 its blaze w\ld be insuff]able2 or1 7 we mu* fur!r (f1 ! light w\ld be too dim to s]ve all ! purposes ( vision4 ,! sun is "o million f\r hundr$ ?\s& times z l>ge z ! e>?2 b its matt] is n m ?an ab\t "o f\r? z d5se z t ( ! e>?1 be+ only a little heavi] ?an wat]1 :ile ! av]age d5sity ( ! e>? is m ?an five times t ( wat]4 ,/ill1 on acc\nt ( ! imm5se magnitude ( ! sun1 its entire quantity ( matt] is ?ree hundr$ & fifty ?\s& times z great z t ( ! e>?4 ,n[1 ! =ce ( gravity 9 a body is great]1 9 proportion z its quantity ( matt] is great]4 ,consequ5tly1 we might suppose1 t ! weight ( a body 7weight be+ no?+ else ?an ! measure ( ! =ce ( gravity7 w\ld be increas$ 9 ! same proportion2 or1 t a body1 :i* weighs only "o p\nd at ! surface ( ! e>?1 w\ld weigh ?ree hundr$ & fifty ?\s& p\nds at ! sun4 ,b we mu/ consid]1 t ! attraction ex]t$ by any body is ! same z ?\gh all ! matt] 7 conc5trat$ 9 ! c5tre4 ,?us1 ! attraction ex]t$ by ! e>? & by ! sun is ! same z ?\gh ! entire matt] ( ea* body 7 9 its c5tre4 ,h5ce1 on acc\nt ( ! va/ dim5sions ( ! sun1 its surface is "o hundr$ & twelve times fur!r f its c5tre ?an ! surface ( ! e>? is f its c5tre2 &1 s9ce ! =ce ( gravity dim9i%es z ! squ>e ( ! di/ance increases1 t ( ! sun1 ex]t$ on bodies at its surface1 is 7s f> z ?is cause op]ates7 ! squ>e ( "o hundr$ & twelve1 or twelve ?\s& five hundr$ & =ty-f\r times less ?an t ( ! e>?4 ,if1 !re=e1 we increase ! weight ( a body ?ree hundr$ & fifty-f\r ?\s& times1 9 consequ5ce ( ! great] am\nt ( matt] 9 ! sun1 & dim9i% x twelve ?\s& five hundr$ & =ty-f\r times1 9 consequ5ce ( ! =ce act+ at a great] di/ance f ! body1 we %all f9d t ! body w\ld weigh ab\t tw5ty-eight times m on ! sun ?an on ! e>?4 ,h5ce1 a man weigh+ ?ree hundr$ p\nds w\ld1 if convey$ to ! surface ( ! sun1 weigh eight ?\s& f\r hundr$ p\nds1 or ne>ly ?ree tons & ?ree qu>t]s4 ,a limb ( our bodies1 weigh+ =ty p\nds1 w\ld require to lift x a =ce ( "o ?\s& "o hundr$ & tw5ty p\nds1 :i* w\ld be beyond ! ord9>y p[] ( ! muscles4 ,at ! surface ( ! e>?1 a body falls f re/ by ! =ce ( gravity1 9 "o second1 sixte5 & "o twelf? feet2 b at ! surface ( ! sun1 a body w\ld1 9 ! same "t1 fall ?r\gh f\r hundr$ & =ty-eight & sev5 t5?s feet4 ,! sun turns on 8 own axis once 9 a little m ?an tw5ty-five days4 ,?is fact is kn[n by obs]v+ c]ta9 d>k places se5 by ! telescope on ! sun's disk1 call$ sol> spots4 ,^! are v v>iable 9 size & numb]4 ,sometimes1 ! sun's disk1 :5 view$ ) a telescope1 is q free f spots1 :ile at o!r times we may see a doz5 or m di/9ct clu/]s1 ea* conta9+ a great numb] ( spots1 "s l>ge & "s v m9ute4 ,occasionally1 a s+le spot is s l>ge z to be visible to ! nak$ eye1 especially :5 ! sun is ne> ! horizon1 & ! gl>e ( 8 light is tak5 (f4 ,"o measur$ by ,dr4 ,h]s*el 0 no less ?an fifty ?\s& miles 9 diamet]4 ,a sol> spot usually consi/s ( two p>ts1 ! nucleus & ! umbra4 ,! nucleus is black1 ( a v irregul> %ape1 & is subject to great & sudd5 *anges1 bo? 9 =m & size4 ,spots h sometimes seem$ to bur/ asund]1 & to project fragm5ts 9 diff]5t directions4 ,! umbra is a wide m>g91 ( light] %ade1 & is (t5 ( great] ext5t ?an ! nucleus4 ,! spots are usually conf9$ to a zone ext5d+ across ! c5tral regions ( ! sun1 n exce$+ sixty degrees 9 bread?4 ,fig4 #bc exhibits ! appe>ance ( ! sol> spots4 ,z ^! spots h all a common motion f day to day1 across ! sun's disk2 z !y g (f at "o limb1 &1 aft] a c]ta9 int]val1 sometimes come on aga9 on ! opposite limb1 x is inf]r$ t ?is app>5t motion is imp>t$ to !m by an actual revolution ( ! sun on 8 own axis4 ,we "k t ! spots mu/ be 9 contact1 or v ne>ly s1 at lea/1 ) ! body ( ! sun1 & _c be bodies revolv+ ar\nd x1 :i* are project$ on ! sol> disk :5 !y are betwe5 u & ! sun2 =1 9 t case1 !y w\ld n be s long 9 view z out ( view1 z w be evid5t f inspect+ ! foll[+ diagram4 ,let ,s1 ,fig4 #bd1 page #ajf1 repres5t ! sun1 & b a body revolv+ r\nd x 9 ! orbit a b c2 & let ,e repres5t ! e>?1 :]e1 ( c\rse1 ! spectator is situat$4 ,! body w\ld be se5 project$ on ! sun only :ile pass+ f b to c1 :ile1 ?r\gh\t ! rema9d] ( its orbit1 x w\ld be out ( view1 :]eas no su* inequality exi/s 9 respect to ! two p]iods4 ,illu/ration ,fig4 #bc4 ,illu/ration ,fig4 #bd4 ,if y ask1 :at is ! cause ( ! sol> spots1 ,i c only tell y :at diff]5t a/ronom]s h suppos$ respect+ !m4 ,!y attract$ ! notice ( ,galileo soon aft] ! inv5tion ( ! telescope1 & he =m$ an hypo!sis respect+ _! nature4 ,suppos+ ! sun to consi/ ( a solid body embosom$ 9 a sea ( liquid fire1 he believ$ t ! spots are compos$ ( black c9d]s1 =m$ 9 ! int]ior ( ! sun by volcanic action1 :i* rise & float on ! surface ( ! fi]y sea4 ,! *ief objections to ?is hypo!sis are1 fir/1 ! va/ ext5t ( "s ( ! spots1 cov]+1 z !y d1 two ?\s& millions ( squ>e miles1 or m1--a space :i* x is incr$ible %\ld be fill$ by lava 9 s %ort a "t z t 9 :i* ! spots are sometimes =m$2 &1 secondly1 ! sudd5 disappe>ance :i* ! spots sometimes und]go1 a fact :i* c h>dly be acc\nt$ = by suppos+1 z ,galileo did1 t su* a va/ accumulation ( matt] all at once sunk b5ea? ! fi]y flood4 ,moreov]1 we h _m reasons = believ+ t ! spots are depressions bel[ ! g5]al surface4 ,la ,l&e1 an em95t ,fr5* a/ronom] ( ! la/ c5tury1 held t ! sun is a solid1 opaque body1 hav+ its ext]ior div]sifi$ ) high m\nta9s & deep valleys1 & cov]$ all ov] ) a burn+ sea ( liquid matt]4 ,! spots he suppos$ to be produc$ by ! flux & reflux ( ?is fi]y sea1 retreat+ occasionally f ! m\nta9s1 & expos+ to view a portion ( ! d>k body ( ! sun4 ,b x is inconsi/5t ) ! nature ( fluids1 t a liquid1 l ! sea suppos$1 %\ld dep>t s f> f its equilibrium & rema9 s long fix$1 z to lay b>e ! imm5se spaces occupi$ by "s ( ! sol> spots4 ,dr4 ,h]s*el's views respect+ ! nature & con/itution ( ! sun1 embrac+ an explanation ( ! sol> spots1 h1 ( late ye>s1 be5 v g5]ally receiv$ by ! a/ronomical _w4 ,?is great a/ronom]1 aft] att5tively view+ ! surface ( ! sun1 = a long "t1 ) 8 l>ge telescopes1 came to ! foll[+ conclusions respect+ ! nature ( ?is lum9>y4 ,he supposes ! sun to be a planet>y body l our e>?1 div]sifi$ ) m\nta9s & valleys1 to :i*1 on acc\nt ( ! magnitude ( ! sun1 he assigns a prodigi\s ext5t1 "s ( ! m\nta9s be+ six hundr$ miles high1 & ! valleys proportionally deep4 ,he employs 9 8 explanation no volcanic fires1 b supposes two sep>ate regions ( d5se cl\ds float+ 9 ! sol> atmosph]e1 at diff]5t di/ances f ! sun4 ,! ext]ior /ratum ( cl\ds he consid]s z ! depository ( ! sun's light & heat1 :ile ! inf]ior /ratum s]ves z an awn+ or scre5 to ! body ( ! sun itself1 :i* ?us becomes fitt$ to be ! resid5ce ( animals4 ,! pro(s (f]$ 9 support ( ?is hypo!sis are *iefly ! foll[+3 fir/1 t ! appe>ances1 z pres5t$ to ! telescope1 are su* z accord bett] ) ! idea t ! fluctuations arise f ! motions ( cl\ds1 ?an t !y are ow+ to ! agitations ( a liquid1 :i* c\ld n dep>t f> en\gh f its g5]al level to enable u to see its waves at s great a di/ance1 :]e a l9e =ty miles 9 l5g? w\ld subt5d an angle at ! eye ( only ! t5? "p ( a second2 secondly1 t1 s9ce cl\ds are easily disp]s$ to any ext5t1 ! great dim5sions :i* ! sol> spots occasionally exhibit are m consi/5t ) ?is ?an ) any o!r hypo!sis2 &1 f9ally1 t a l[] /ratum ( cl\ds1 simil> to ^? ( our atmosph]e1 0 frequ5tly se5 by ! ,doctor1 f> bel[ ! lum9\s cl\ds :i* are ! f\nta9s ( light & heat4 ,su* are ! views ( "o :o _h1 x mu/ be ackn[l$g$1 great p[]s ( obs]vation1 & means ( obs]vation 9 high] p]fection ?an h ev] be5 enjoy$ by any o!r individual2 b1 ) all def]5ce to su* au?ority1 ,i am compell$ to ?9k t ! hypo!sis is encumb]$ ) v s]i\s objections4 ,cl\ds analog\s to ^? ( our atmosph]e 7& ! ,doctor expressly ass]ts t 8 l[] /ratum ( cl\ds are analog\s to ours1 & reasons respect+ ! upp] /ratum accord+ to ! same analogy7 _c exi/ 9 hot air2 !y are t5ants only ( cold regions4 ,h[ c !y be suppos$ to exi/ 9 ! imm$iate vic9ity ( a fire s int5se1 t !y are ev5 dissipat$ by x at ! di/ance ( n9ety-five millions ( miles8 ,mu* less c !y be suppos$ to be ! depositories ( su* dev\r+ fire1 :5 any ?+ 9 ! =m ( cl\ds1 float+ 9 our atmosph]e1 is at once scatt]$ & dissolv$ by ! accession ( only a few degrees ( heat4 ,no?+1 moreov]1 c be imag9$ m unfavorable = radiat+ heat to su* a di/ance1 ?an ! light1 incon/ant matt] ( :i* cl\ds are compos$1 float+ loosely 9 ! sol> atmosph]e4 ,!re is a logical difficulty 9 ! case3 x is ascrib+ to ?+s prop]ties :i* !y are n kn[n to possess2 nay1 m1 :i* !y are kn[n n to possess4 ,f v>iations ( light & %ade 9 objects se5 at mod]ate di/ances on ! e>?1 we are (t5 deceiv$ 9 reg>d to _! appe>ances2 & we mu/ di/ru/ ! p[] ( an a/ronom] to decide ^u ! nature ( matt] se5 at ! di/ance ( n9ety-five millions ( miles4 ,i ?9k1 !re=e1 we mu/ confess our ignorance ( ! nature & con/itution ( ! sun2 nor c we1 z a/ronom]s1 obta9 mu* m satisfactory k respect+ x ?an ! common appreh5sion1 namely1 t x is an imm5se globe ( fire4 ,we h n yet le>n$ :at causes are 9 op]ation to ma9ta9 its undecay+ fires2 b our confid5ce 9 ! ,div9e wisdom & goodness leads u to believe1 t ^? causes are su* z w pres]ve ^? fires f ext9ction1 & at a ne>ly uni=m degree ( int5sity4 ,any mat]ial *ange 9 ?is respect w\ld jeop>dize ! safety ( ! animal & vegetable k+doms1 :i* c\ld n exi/ )\t ! enliv5+ influ5ce ( ! sol> heat1 nor1 inde$1 7 t heat any m or less int5se ?an x is at pres5t4 ,if we inquire :e!r ! surface ( ! sun is 9 a /ate ( actual combu/ion1 l burn+ fuel1 or m]ely 9 a /ate ( int5se ignition1 l a /one heat$ to r$ness 9 a furnace1 we %all f9d x mo/ reasonable to conclude t x is 9 a /ate ( ignition4 ,if ! body ( ! sun 7 compos$ ( combu/ible matt] & 7 actually on fire1 ! mat]ial ( ! sun w\ld be cont9ually wa/+ away1 :ile ! products ( combu/ion w\ld fill all ! va/ surr\nd+ regions1 & obscure ! sol> light4 ,b solid bodies may atta9 a v int5se /ate ( ignition1 & gl[ ) ! mo/ f]v5t heat1 :ile none ( _! mat]ial is consum$1 & no cl\ds or fumes rise to obscure _! brightness1 or to imp$e _! fur!r emission ( heat4 ,an ignit$ surface1 moreov]1 is f> bett] adapt$ ?an flame to ! radiation ( heat4 ,flame1 :5 made to act 9 contact ) ! surfaces ( solid bodies1 heats !m rapidly & p[]fully2 b x s5ds =?1 or radiates1 v little heat1 comp>$ ) solid matt] 9 a high /ate ( ignition4 ,^! v>i\s consid]ations r5d] x highly probable to my m9d1 t ! body ( ! sun is n 9 a /ate ( actual combu/ion1 b m]ely 9 a /ate ( high ignition4 ,! sol> beam consi/s ( a mixture ( sev]al diff]5t sorts ( rays4 ,fir/1 !re are ! calorific rays1 :i* af=d heat1 & are entirely di/9ct f ^? :i* af=d light1 & may be sep>at$ f !m4 ,secondly1 !re are ! colorific rays1 :i* give light1 consi/+ ( rays ( sev5 di/9ct colors1 namely1 violet1 indigo1 blue1 gre51 yell[1 orange1 r$4 ,^!1 :5 sep>at$1 z !y may be by a glass prism1 compose ! prismatic spectrum4 ,!y appe> also 9 ! ra9b[4 ,:5 unit$ aga91 9 due proportions1 !y con/itute :ite light1 z se5 9 ! light ( ! sun4 ,?irdly1 !re are f\nd 9 ! sol> beam a class ( rays :i* af=d nei!r heat nor light1 b :i* produce *emical *anges 9 c]ta9 bodies expos$ to _! influ5ce1 & h5ce are call$ *emical rays4 ,f\r?ly1 !re is /ill ano!r class1 call$ magnetiz+ rays1 because !y are capable ( imp>t+ magnetic prop]ties to /eel4 ,^! diff]5t sorts ( rays are s5t =? f ! sun1 to ! remote/ regions ( ! planet>y worlds1 invigorat+ all ?+s by _! life-giv+ influ5ce1 & dispell+ ! d>kness t naturally fills all space4 ,b x 0 n alone to give heat & light1 t ! sun 0 plac$ 9 ! firmam5t4 ,by 8 p[] ( attraction1 also1 he s]ves z ! great regulator ( ! planet>y motions1 b5d+ !m cont9ually f ! /raight l9e 9 :i* !y t5d to move1 & compell+ !m to circulate ar\nd him1 ea* at ne>ly a uni=m di/ance1 & all 9 p]fect h>mony4 ,i w h]eaft] expla9 to y ! mann] 9 :i* ! gravity ( ! sun ?us acts1 to control ! planet>y motions4 ,= ! pres5t1 let u cont5t ourselves ) reflect+ ^u ! wond]ful =ce :i* ! sun mu/ put =?1 9 ord] to b5d out ( _! c\rses1 into circul> orbits1 su* a numb] ( planets1 "s ( :i* are m ?an a ?\s& times z l>ge z ! e>?4 ,7 a %ip ( w> "u full sail1 & x %\ld be requir$ to turn h] aside f h] c\rse by a rope atta*$ to h] b[1 we c easily imag9e t x w\ld take a great =ce to d x1 especially 7 x requir$ t ! =ce %\ld rema9 /ation>y & ! %ip be s con/antly div]t$ f h] c\rse1 z to be made to g r\nd ! =ce z r\nd a c5tre4 ,some:at simil> to ?is is ! action :i* ! sun ex]ts on ea* ( ! planets by "s invisible influ5ce1 call$ gravitation4 ,! bodies :i* he ?us turns out ( _! c\rse1 & b5ds into a circul> orbit ar\nd himself1 are1 h[ev]1 _m millions ( times z pond]\s z ! %ip1 & are mov+ _m ?\s& times z swiftly4 ,,lett] ,,xi4 ,,annual ,,revolution4--,,seasons ,^!1 z !y *ange1 ,almighty ,fa!r1 ^! ,are b ! v>i$ ,god4 ,! roll+ ye> ,is full ( ,!e4--,?omson4 ,,we h se5 t ! app>5t revolution ( ! heav5ly bodies1 f ea/ to we/1 e tw5ty-f\r h\rs1 is ow+ to a real revolution ( ! e>? on its own axis1 9 ! opposite direction4 ,?is motion is v easily und]/ood1 resembl+1 z x does1 ! sp9n+ ( a top4 ,we mu/1 h[ev]1 conceive ( ! top z turn+ )\t any visible support1 & n z re/+ 9 ! usual mann] on a plane4 ,! annual motion ( ! e>? ar\nd ! sun1 :i* gives rise to an app>5t motion ( ! sun ar\nd ! e>? once a ye>1 & occasions ! *ange ( seasons1 is some:at m difficult to und]/&2 & x may co/ y "s reflection1 be=e y w settle all ! po9ts respect+ ! *anges ( ! seasons cle>ly 9 y\r m9d4 ,we sometimes see ^! two motions exemplifi$ 9 a top4 ,:51 z ! /r+ is pull$1 ! top is ?r[n =w>ds on ! floor1 we may see x move =w>d 7sometimes 9 a circle7 at ! same "t t x sp9s on its axis4 ,let a c&le be plac$ on a table1 to repres5t ! sun1 & let ^! two motions be imag9$ to be giv5 to a top ar\nd x1 & we %all h a case some:at resembl+ ! actual motions ( ! e>? ar\nd ! sun4 ,:5 bodies are at su* a di/ance f ea* o!r z ! e>? & ! sun1 a spectator on ei!r w\ld project ! o!r body ^u ! concave sph]e ( ! heav5s1 always see+ x on ! opposite side ( a great circle "o hundr$ & eighty degrees f himself4 ,recollect t ! pa? 9 :i* ! e>? moves r\nd ! sun is call$ ! ecliptic4 ,we are n to conceive ( ?is1 or ( any o!r cele/ial circle1 z hav+ any real1 palpable exi/5ce1 any m ?an ! pa? ( a bird ?r\gh ! sky4 ,y w p]haps ?9k x q sup]flu\s = me to rem9d y ( ?is2 b1 f ! habit ( see+ ! orbits ( ! heav5ly bodies repres5t$ 9 diagrams & orr]ies1 by palpable l9es & circles1 we are apt inadv]t5tly to acquire ! notion1 t ! orbits ( ! planets1 & o!r repres5tations ( ! artificial sph]e1 h a real1 palpable exi/5ce 9 ,nature2 :]eas1 !y d5ote ! places :]e m]e geometrical or imag9>y l9es run4 ,y might h expect$ to see an orr]y1 exhibit+ a view ( ! sun & planets1 ) _! v>i\s motions1 p>ticul>ly describ$ 9 my ,lett] on a/ronomical in/rum5ts & app>atus4 ,i mu/ ackn[l$ge1 t ,i ent]ta9 a v l[ op9ion ( ! utility ( ev5 ! be/ orr]ies1 & ,i _c recomm5d !m z auxili>ies 9 ! /udy ( a/ronomy4 ,! num]\s app5dages usually connect$ ) !m1 "s to support !m 9 a prop] position1 & "s to communicate to !m ! requisite motions1 ent] into ! ideas :i* ! le>n] =ms respect+ ! ma*9]y ( ! heav5s2 & x co/s mu* labor aft]w>ds to dive/ ! m9d ( su* errone\s impressions4 ,a/ronomy c be exhibit$ mu* m cle>ly & beautifully to ! m5tal eye ?an to ! visual organ4 ,x is mu* easi] to conceive ( ! sun exi/+ 9 b\ndless space1 & ( ! e>? z mov+ ar\nd him at a great di/ance1 ! m9d hav+ no?+ 9 view b simply ^! two bodies1 ?an x is1 9 an orr]y1 to contemplate ! motion ( a ball repres5t+ ! e>?1 c>ri$ by a complicat$ app>atus ( :eels ar\nd ano!r ball1 support$ by a cyl9d] or wire1 to repres5t ! sun4 ,i w\ld advise y1 :5ev] x is practicable1 to ?9k h[ ?+s are 9 ,nature1 r ?an h[ !y are repres5t$ by art4 ,! ma*9]y ( ! heav5s is mu* simpl] ?an t ( an orr]y4 ,9 endeavor+ to obta9 a cle> idea ( ! revolution ( ! e>? ar\nd ! sun1 imag9e to y\rself a plane 7a geometrical plane1 hav+ m]ely l5g? & bread?1 b no ?ickness7 pass+ ?r\gh ! c5tres ( ! sun & ! e>?1 & ext5d$ f> beyond ! e>? till x rea*es ! firmam5t ( />s4 ,al?\gh1 inde$1 no su* dome actually exi/s z t "u :i* we figure to ourselves ! vault ( ! sky1 yet1 z ! fix$ />s appe> to be set 9 su* a dome1 we may imag9e t ! circles ( ! sph]e1 :5 indef9itely enl>g$1 f9ally rea* su* an imag9>y vault4 ,all t is ess5tial is1 t we %\ld imag9e ?is to exi/ f> beyond ! b\nds ( ! sol> sy/em1 ! v>i\s bodies t compose ! latt] be+ situat$ close ar\nd ! sun1 at ! c5tre4 ,along ! l9e :]e ?is great circle meets ! />ry vault1 are situat$ a s]ies ( con/ellations1--,aries1 ,taurus1 ,gem9i1 c41--:i* occupy successively ?is portion ( ! heav5s4 ,:5 bodies are at su* a di/ance f ea* o!r z ! sun & ! e>?1 ,i h said t a spectator on ei!r w\ld project ! o!r body ^u ! concave sph]e ( ! heav5s1 always see+ x on ! opposite side ( a great circle "o hundr$ & eighty degrees f himself4 ,! place ( a body1 :5 view$ f any po9t1 is d5ot$ by ! position x occupies among ! />s4 ,?us1 9 ! diagram1 ,fig4 #be1 page #aad1 :5 ! e>? arrives at ,e1 x is said to be 9 ,aries1 because1 if view$ f ! sun1 x w\ld be project$ on t "p ( ! heav5s2 &1 = ! same reason1 to a spectator at ,e1 ! sun w\ld be 9 ,libra4 ,:5 ! e>? %ifts its position f ,aries to ,taurus1 z we are unconsci\s ( our own motion1 ! sun x is t appe>s to move f ,libra to ,scorpio1 9 ! opposite "p ( ! heav5s4 ,h5ce1 z we g =w>d1 9 ! ord] ( ! signs1 on "o side ( ! ecliptic1 ! sun seems to be mov+ =w>d at ! same rate on ! opposite side ( ! same great circle2 & !re=e1 al?\gh we are unconsci\s ( our own motion1 we c read x1 f day to day1 9 ! motions ( ! sun4 ,if we c\ld see ! />s at ! same "t ) ! sun1 we c\ld actually obs]ve1 f day to day1 ! sun's progress ?r\gh !m1 z we obs]ve ! progress ( ! moon at night2 only ! sun's rate ( motion w\ld be ne>ly f\rte5 times sl[] ?an t ( ! moon4 ,al?\gh we d n see ! />s :5 ! sun is pres5t1 we c obs]ve t x makes daily progress ea/w>d1 z is app>5t f ! con/ellations ( ! zodiac occupy+1 successively1 ! we/]n sky imm$iately aft] sunset1 prov+ t ei!r all ! />s h a common motion we/w>d1 indep5d5t ( _! diurnal motion1 or t ! sun has a motion pa/ !m f we/ to ea/4 ,we %all see1 h]eaft]1 abundant evid5ce to prove1 t ?is *ange 9 ! relative position ( ! sun & />s1 is ow+ to a *ange 9 ! app>5t place ( ! sun1 & n to any *ange 9 ! />s4 ,illu/ration ,fig4 #be4 ,to =m a cle> idea ( ! two motions ( ! e>?1 imag9e y\rself /&+ on a circul> plat=m :i* turns sl[ly r\nd its c5tre4 ,:ile y are c>ri$ sl[ly r\nd ! entire ( ! circuit ( ! heav5s1 along ) ! plat=m1 y may turn r\nd ^u y\r heel ! same way ?ree hundr$ & sixty-five times4 ,! =m] is analog\s to our annual motion ) ! e>? ar\nd ! sun2 ! latt]1 to our diurnal revolution 9 common ) ! e>? ar\nd its own axis4 ,al?\gh ! app>5t revolution ( ! sun is 9 a direction opposite to ! real motion ( ! e>?1 z reg>ds absolute space1 yet bo? are nev]!less f we/ to ea/1 s9ce ^! t]ms d n ref] to any directions 9 absolute space1 b to ! ord] 9 :i* c]ta9 con/ellations 7! con/ellations ( ! ,zodiac7 succe$ "o ano!r4 ,! e>? itself1 on opposite sides ( its orbit1 does 9 fact move t[>ds directly opposite po9ts ( space2 b x is all ! :ile pursu+ its c\rse 9 ! ord] ( ! signs4 ,9 ! same mann]1 al?\gh ! e>? turns on its axis f we/ to ea/1 yet any place on ! surface ( ! e>? is mov+ 9 a direction 9 space exactly opposite to its direction twelve h\rs be=e4 ,if ! sun left a visible trace on ! face ( ! sky1 ! ecliptic w\ld ( c\rse be di/9ctly m>k$ on ! cele/ial sph]e1 z x is on an artificial globe2 & 7 ! equator del9eat$ 9 a simil> mann]1 we %\ld !n see1 at a glance1 ! relative position ( ^! two circles1--! po9ts :]e !y int]sect "o ano!r1 con/itut+ ! equ9oxes2 ! po9ts :]e !y are at ! greate/ di/ance asund]1 t is1 ! sol/ices2 & v>i\s o!r p>ticul>s1 :i*1 = want ( su* visible traces1 we are n[ oblig$ to se>* = by indirect & circuit\s me?ods4 ,x w aid y1 to h con/antly be=e y\r m5tal vision an imag9>y del9eation ( ^! two important circles on ! face ( ! sky4 ,! equator makes an angle ) ! ecliptic ( tw5ty-?ree degrees & tw5ty-eight m9utes4 ,?is is call$ ! obliquity ( ! ecliptic4 ,z ! sun & e>? are bo? always 9 ! ecliptic1 & z ! motion ( ! e>? 9 "o "p ( x makes ! sun appe> to move 9 ! opposite "p1 at ! same rate1 ! sun app>5tly desc5ds1 9 ,w9t]1 tw5ty-?ree degrees & tw5ty-eight m9utes to ! s\? ( ! equator1 & asc5ds1 9 ,summ]1 ! same numb] ( degrees nor? ( x4 ,we mu/ keep 9 m9d1 t ! cele/ial equator & cele/ial ecliptic are "h und]/ood1 & we may imag9e !m to be two great circles del9eat$ on ! face ( ! sky4 ,on comp>+ obs]vations made at diff]5t p]iods1 = m ?an two ?\s& ye>s1 x is f\nd1 t ! obliquity ( ! ecliptic is n con/ant1 b t x und]goes a slight dim9ution1 f age to age1 am\nt+ to fifty-two seconds 9 a c5tury1 or ab\t half a second annually4 ,we might appreh5d t1 by successive approa*es to ea* o!r1 ! equator & ecliptic w\ld f9ally co9cide2 b a/ronom]s h discov]$1 by a mo/ pr(\nd inve/igation1 bas$ on ! pr9ciples ( univ]sal gravitation1 t ?is irregul>ity is conf9$ )9 c]ta9 n>r[ limits2 & t ! obliquity1 aft] dim9i%+ = "s ?\s&s ( ye>s1 w !n increase = a simil> p]iod1 & w ?us vibrate =ev] ab\t a mean value4 ,z ! e>? trav]ses e "p ( h] orbit 9 ! c\rse ( a ye>1 %e w be once at ea* sol/ice1 & once at ea* equ9ox4 ,! be/ way ( obta9+ a correct idea ( h] two motions is1 to conceive ( h] z /&+ /ill = a s+le day1 at "s po9t 9 h] orbit1 until %e has turn$ once on h] axis1 !n mov+ ab\t a degree1 & halt+ aga91 until ano!r diurnal revolution is complet$4 ,let u suppose ! e>? at ! ,autumnal equ9ox1 ! sun1 ( c\rse1 be+ at ! ,v]nal equ9ox1--= we mu/ always ?9k ( ^! two bodies z diametrically opposite to ea* o!r4 ,suppose ! e>? to /& /ill 9 its orbit = tw5ty-f\r h\rs4 ,! revolution ( ! e>? on its axis1 f we/ to ea/1 w make ! sun appe> to describe a great circle ( ! heav5s f ea/ to we/1 co9cid+ ) ! equator4 ,at ! end ( ?is p]iod1 suppose ! sun to move nor?w>d "o degree1 & to rema9 !re = tw5ty-f\r h\rs2 9 :i* "t1 ! revolution ( ! e>?1 w make ! sun appe> to describe ano!r circle1 f ea/ to we/1 p>allel to ! equator1 b "o degree nor? ( x4 ,?us1 we may conceive ( ! sun z mov+ "o degree nor?1 e day1 = ab\t ?ree mon?s1 :5 x w rea* ! po9t ( ! ecliptic fur!/ f ! equator1 :i* po9t is call$ ! tropic1 f a ,greek ^w1 signify+ to turn2 because1 aft] ! sun has pass$ ?is po9t1 8 motion 9 8 orbit c>ries him cont9ually t[>ds ! equator1 & !re=e he seems to turn ab\t4 ,! same po9t is also call$ ! sol/ice1 f a ,lat9 ^w1 signify+ to /& /ill2 s9ce1 :5 ! sun has rea*$ its greate/ nor!rn or s\!rn limit1 :ile its decl9ation is at ! po9t :]e x ceases to increase1 b beg9s to decrease1 !re ! sun seems = a %ort "t /ation>y1 ) reg>d to ! equator1 appe>+ = sev]al days to describe ! same p>allel ( latitude4 ,:5 ! sun is at ! nor!rn tropic1 :i* happ5s ab\t ! tw5ty-fir/ ( ,june1 8 elevation above ! s\!rn horizon at noon is ! greate/ 9 ! ye>2 & :5 he is at ! s\!rn tropic1 ab\t ! tw5ty-fir/ ( ,decemb]1 8 elevation at noon is ! lea/ 9 ! ye>4 ,! diff]5ce betwe5 ^! two m]idian altitudes w give ! :ole di/ance f "o tropic to ! o!r1 & consequ5tly1 twice ! di/ance f ea* tropic to ! equator4 ,by ?is means1 we f9d h[ f> ! tropic is f ! equator1 & t gives u ! angle :i* ! equator & ecliptic make ) ea* o!r2 = ! greate/ di/ance betwe5 any two great circles on ! sph]e is always equal to ! angle :i* !y make ) ea* o!r4 ,?us1 ! anci5t a/ronom]s 7 able to det]m9e ! obliquity ( ! ecliptic ) a great degree ( accuracy4 ,x 0 easy to f9d ! situation ( ! z5i?1 because ! direction ( a plumb-l9e %[s u :]e t is2 & x 0 easy to f9d ! di/ances f ! z5i? :]e ! sun 0 at ! greate/ & lea/ di/ances2 respectively4 ,! diff]5ce ( ^! two arcs is ! angul> di/ance f "o tropic to ! o!r2 & half ?is arc is ! di/ance ( ei!r tropic f ! equator1 & ( c\rse1 equal to ! obliquity ( ! ecliptic4 ,all ?is w be v easily und]/ood f ! annex$ diagram1 ,fig4 #bf4 ,let ,z be ! z5i? ( a spectator situat$ at ,c2 ,z n ! lea/1 & ,z s ! greate/ di/ance ( ! sun f ! z5i?4 ,f ,z s subtract ,z n1 & !n s n1 ! diff]5ce1 divid$ by two1 w give ! obliquity ( ! ecliptic4 ,illu/ration ,fig4 #bf4 ,! motion ( ! e>? 9 its orbit is ne>ly sev5ty times z great z its greate/ motion ar\nd its axis4 ,9 its revolution ar\nd ! sun1 ! e>? moves no less ?an "o million six hundr$ & =ty ?\s& miles p] day1 sixty-eight ?\s& miles p] h\r1 elev5 hundr$ miles p] m9ute1 & ne>ly n9ete5 miles e second2 a velocity ne>ly sixty times z great z ! greate/ velocity ( a cannon ball4 ,places on ! e>? turn ) v diff]5t degrees ( velocity 9 diff]5t latitudes4 ,^? ne> ! equator are c>ri$ r\nd on ! circumf]5ce ( a l>ge circle2 ^? t[>ds ! poles1 on ! circumf]5ce ( a small circle2 :ile "o /&+ on ! pole itself w\ld n turn at all4 ,^? :o live on ! equator are c>ri$ ab\t "o ?\s& miles an h\r4 ,9 our latitude1 7=ty-"o degrees & eighte5 m9utes17 ! diurnal velocity is ab\t sev5 hundr$ & fifty miles p] h\r4 ,x w\ld seem1 at fir/ view1 q incr$ible1 t we %\ld be :irl$ r\nd at s rapid a rate1 & yet be entirely ins5sible ( any motion2 & mu* m1 t we c\ld be go+ s swiftly ?r\gh space1 9 our circuit ar\nd ! sun1 :ile all ?+s1 :5 unaffect$ by local causes1 appe> to be 9 su* a /ate ( quiesc5ce4 ,yet we h ! mo/ unque/ionable evid5ce ( ! fact2 nor is x difficult to acc\nt = x1 9 consi/5cy ) ! g5]al /ate ( repose among bodies on ! e>?1 :5 we reflect t _! relative motions1 ) respect to ea* o!r1 are n 9 ! lea/ di/urb$ by any motions :i* !y may h 9 common4 ,:5 we are on bo>d a /eam-boat1 we move ab\t 9 ! same mann] :5 ! boat is 9 rapid motion1 z :5 x is ly+ /ill2 & su* w\ld be ! case1 if x mov$ /eadily a hundr$ times fa/] ?an x does4 ,7 ! e>?1 h[ev]1 sudd5ly to /op its diurnal revolution1 all movable bodies on its surface w\ld be ?r[n (f 9 tang5ts to ! surface ) velocities proportional to t ( _! diurnal motion2 & 7 ! e>? sudd5ly to halt 9 its orbit1 we %\ld be hurl$ =w>d into space ) inconceivable rapidity4 ,i w next endeavor to expla9 to y ! ph5om5a ( ! ,seasons4 ,^! dep5d on two causes2 fir/1 ! incl9ation ( ! e>?'s axis to ! plane ( its orbit2 &1 secondly1 to ! circum/ance1 t ! axis always rema9s p>allel to itself4 ,imag9e to y\rself a c&le plac$ 9 ! c5tre ( a r+1 to repres5t ! sun 9 ! c5tre ( ! e>?'s orbit1 & an apple ) a knitt+ne$le runn+ ?r\gh x 9 ! direction ( ! /em4 ,run a knife ar\nd ! c5tral "p ( ! apple1 to m>k ! situation ( ! equator4 ,! circumf]5ce ( ! r+ repres5ts ! e>?'s orbit 9 ! plane ( ! ecliptic4 ,place ! apple s t ! equator %all co9cide ) ! wire2 !n ! axis w lie directly across ! plane ( ! ecliptic2 t is1 at "r angles to x4 ,let ! apple be c>ri$ q r\nd ! r+1 con/antly pres]v+ ! axis p>allel to itself1 & ! equator all ! :ile co9cid+ ) ! wire t repres5ts ! orbit4 ,n[1 s9ce ! sun enlight5s half ! globe at once1 s ! c&le1 :i* "h repres5ts ! sun1 w %9e on ! half ( ! apple t is turn$ t[>ds x2 & ! circle :i* divides ! enlight5$ f ! un5light5$ side ( ! apple1 call$ ! t]m9ator1 w pass ?r\gh bo? ! poles4 ,if ! apple be turn$ sl[ly r\nd on its axis1 ! t]m9ator w successively pass ov] all places on ! e>?1 giv+ ! appe>ance ( sunrise to places at :i* x arrives1 & ( sunset to places f :i* x dep>ts4 ,if1 !re=e1 ! equator _h co9cid$ ) ! ecliptic1 z w\ld h be5 ! case1 _h ! e>?'s axis be5 p]p5dicul> to ! plane ( its orbit1 ! diurnal motion ( ! sun w\ld always h be5 9 ! equator1 & ! days & nights w\ld h be5 equal all ov] ! globe4 ,to ! inhabitants ( ! equatorial p>ts ( ! e>?1 ! sun w\ld always h appe>$ to move 9 ! prime v]tical1 ris+ directly 9 ! ea/1 pass+ ?r\gh ! z5i? at noon1 & sett+ 9 ! we/4 ,9 ! pol> regions1 ! sun w\ld always h appe>$ to revolve 9 ! horizon2 :ile1 at any place betwe5 ! equator & ! pole1 ! c\rse ( ! sun w\ld h be5 oblique to ! horizon1 b always oblique 9 ! same degree4 ,!re w\ld h be5 no?+ ( ^? agreeable vicissitudes ( ! seasons :i* we n[ enjoy2 b "s regions ( ! e>? w\ld h be5 cr[n$ ) p]petual spr+1 o!rs w\ld h be5 scor*$ ) ! unremitt+ f]vor ( a v]tical sun1 :ile ext5sive regions t[>ds ei!r pole w\ld h be5 consign$ to ev]la/+ fro/ & /]ility4 ,to und]/&1 !n1 cle>ly1 ! causes ( ! *ange ( seasons1 use ! same app>atus z be=e2 b1 in/ead ( plac+ ! axis ( ! e>? at "r angles to ! plane ( its orbit1 turn x out ( a p]p5dicul> position a little1 7tw5ty-?ree degrees & tw5ty-eight m9utes17 !n ! equator w be turn$ j ! same numb] ( degrees out ( a co9cid5ce ) ! ecliptic4 ,let ! apple be c>ri$ ar\nd ! r+1 always hold+ ! axis incl9$ at ! same angle to ! plane ( ! r+1 & always p>allel to itself4 ,y w f9d t !re w be two po9ts 9 ! circuit :]e ! plane ( ! equator1 t y _h m>k$ ar\nd ! c5tre ( ! apple1 w pass ?r\gh ! c5tre ( ! sun2 ^! w be ! po9ts :]e ! cele/ial equator & ! ecliptic cut "o ano!r1 or ! equ9oxes4 ,:5 ! e>? is at ei!r ( ^! po9ts1 ! sun %9es on bo? poles alike2 &1 if we conceive ( ! e>?1 :ile 9 ?is situation1 z turn+ once r\nd on its axis1 ! app>5t diurnal motion ( ! sun w be ! same z x w\ld be1 7 ! e>?'s axis p]p5dicul> to ! plane ( ! equator4 ,= t day1 ! sun w\ld revolve 9 ! equator1 & ! days & nights w\ld be equal all ov] ! globe4 ,if ! apple 7 c>ri$ r\nd 9 ! mann] suppos$1 !n1 at ! di/ance ( n9ety degrees f ! equ9oxes1 ! same pole w\ld be turn$ f ! sun on "o side1 j z mu* z x 0 turn$ t[>ds him on ! o!r4 ,9 ! =m] case1 ! sun's light w\ld fall %ort ( ! pole tw5ty-?ree & "o half degrees1 & 9 ! o!r case1 x w\ld rea* beyond x ! same numb] ( degrees4 ,i w\ld recomm5d to y to obta9 z cle> an idea z y c ( ! cause ( ! *ange ( seasons1 by ?9k+ ov] ! =ego+ illu/ration4 ,y may !n cle> up any rema9+ difficulties1 by /udy+ ! diagram1 ,fig4 #bg1 on page #abb4 ,illu/ration ,fig4 #bg4 ,let ,a ,b ,c ,d repres5t ! e>?'s place 9 diff]5t p>ts ( its orbit1 hav+ ! sun 9 ! c5tre4 ,let ,a1 ,c1 be ! positions ( ! e>? at ! equ9oxes1 & ,b1 ,d1 its positions at ! tropics1--! axis n s be+ always p>allel to itself4 ,x is difficult to repres5t ?+s ( ?is k9d correctly1 all on ! same plane2 b y w readily see1 t ! figure ( ! e>?1 "h1 answ]s to ! apple 9 ! =m] illu/ration2 t ! hemisph]e t[>ds n is above1 & t t[>ds s is bel[1 ! plane ( ! pap]4 ,:5 ! e>? is at ,a & ,c1 ! ,v]nal & ,autumnal equ9oxes1 ! sun1 y w p]ceive1 %9es on bo? ! poles n & s2 &1 if y conceive ( ! globe1 :ile 9 ?is position1 z turn$ r\nd on its axis1 z x is 9 ! diurnal revolution1 y w readily und]/&1 t ! sun w\ld describe ! cele/ial equator4 ,?is may n at fir/ appe> s obvi\s1 by inspect+ ! figure2 b if y consid] ! po9t n z rais$ above ! plane ( ! pap]1 & ! po9t s z depress$ bel[ x1 y w readily see h[ ! plane ( ! equator w\ld pass ?r\gh ! c5tre ( ! sun4 ,aga91 at ,b1 :5 ! e>? is at ! s\!rn tropic1 ! sun %9es tw5ty-?ree & a half degrees beyond ! nor? pole1 n1 & falls ! same di/ance %ort ( ! s\? pole1 s4 ,! case is exactly rev]s$ :5 ! e>? is at ! nor!rn tropic1 & ! sun at ! s\!rn4 ,:ile ! e>? is at "o ( ! tropics1 at ,b1 = example1 let u conceive ( x z turn+ on its axis1 & we %all readily see1 t all t "p ( ! e>? :i* lies )9 ! nor? pol> circle w enjoy cont9ual day1 :ile t )9 ! s\? pol> circle w h cont9ual night2 & t all o!r places w h _! days long] z !y are ne>] to ! enlight5$ pole1 & %ort] z !y are ne>] to ! un5light5$ pole4 ,?is figure likewise %[s ! successive positions ( ! e>?1 at diff]5t p]iods ( ! ye>1 ) respect to ! signs1 & :at mon?s correspond to p>ticul> signs4 ,?us1 ! e>? ent]s ,libra1 & ! sun ,aries1 on ! tw5ty-fir/ ( ,m>*1 & on ! tw5ty-fir/ ( ,june1 ! e>? is j ent]+ ,capricorn1 & ! sun1 ,canc]4 ,y w call to m9d :at is meant by ?is phraseology1--t by say+ ! e>? ent]s ,libra1 we mean t a spectator plac$ on ! sun w\ld see ! e>? 9 t "p ( ! cele/ial ecliptic1 :i* is occupi$ by ! sign ,libra2 & t a spectator on ! e>? sees ! sun at ! same "t project$ on ! opposite "p ( ! heav5s1 occupi$ by ! sign ,canc]4 ,_h ! axis ( ! e>? be5 p]p5dicul> to ! plane ( ! ecliptic1 !n ! sun w\ld always h appe>$ to move 9 ! equator1 ! days w\ld e :]e h be5 equal to ! nights1 & !re c\ld h be5 no *ange ( seasons4 ,on ! o!r h&1 _h ! incl9ation ( ! ecliptic to ! equator be5 mu* great] ?an x is1 ! vicissitudes ( ! seasons w\ld h be5 proportionally great]1 ?an at pres5t4 ,suppose1 = in/ance1 ! equator _h be5 at "r angles to ! ecliptic1 9 :i* case1 ! poles ( ! e>? w\ld h be5 situat$ 9 ! ecliptic itself2 !n1 9 diff]5t p>ts ( ! e>?1 ! appe>ances w\ld h be5 z foll[s3 ,to a spectator on ! equator1 7:]e all ! circles ( diurnal revolution are p]p5dicul> to ! horizon17 ! sun1 z he left ! v]nal equ9ox1 w\ld e day p]=m 8 diurnal revolution 9 a small] & small] circle1 until he rea*$ ! nor? pole1 :5 he w\ld halt = a mom5t1 & !n :eel ab\t & return to ! equator1 9 a rev]se ord]4 ,! progress ( ! sun ?r\gh ! s\!rn signs1 to ! s\? pole1 w\ld be simil> to t already describ$4 ,su* w\ld be ! appe>ances to an inhabitant ( ! equatorial regions4 ,to a spectator liv+ 9 an oblique sph]e1 9 our own latitude1 = example1 ! sun1 :ile nor? ( ! equator1 w\ld advance cont9ually nor?w>d1 mak+ 8 diurnal circuit 9 p>allels fur!r & fur!r di/ant f ! equator1 until he rea*$ ! circle ( p]petual app>ition2 aft] :i*1 he w\ld climb1 by a spiral c\rse1 to ! nor? />1 & !n z rapidly return to ! equator4 ,by a simil> progress s\?w>d1 ! sun w\ld at l5g? pass ! circle ( p]petual occultation1 & = "s "t 7:i* w\ld be long] or %ort]1 accord+ to ! latitude ( ! place ( obs]vation7 !re w\ld be cont9ual night4 ,to a spectator on ! pole ( ! e>? & "u ! pole ( ! heav51 dur+ ! long day ( six mon?s1 ! sun w\ld w9d its way to a po9t directly ov] head1 p\r+ d[n ^u ! e>? b5ea? n m]ely ! heat ( ! torrid zone1 b ! heat ( a torrid noon1 accumulat+ )\t int]mission4 ,! great vicissitudes ( heat & cold1 :i* w\ld att5d ^! sev]al movem5ts ( ! sun1 w\ld be :olly incompatible ) ! exi/5ce ( ei!r ! animal or ! vegetable k+dom1 & all t]re/rial ,nature w\ld be doom$ to p]petual /]ility & desolation4 ,! happy provision :i* ! ,creator has made aga9/ su* extreme vicissitudes1 by conf9+ ! *anges ( ! seasons )9 su* n>r[ b\nds1 conspires ) _m o!r express arrangem5ts 9 ! economy ( ,nature1 to secure ! safety & com=t ( ! human race4 ,p]haps y h nev] reflect$ ^u all ! reasons1 :y ! sev]al *anges ( position1 ) respect to ! horizon1 :i* ! sun und]goes 9 ! c\rse ( ! ye>1 occasion su* a diff]5ce 9 ! am\nt ( heat receiv$ f him4 ,two causes contribute to increase ! heat ( ,summ] & ! cold ( ,w9t]4 ,! high] ! sun asc5ds above ! horizon1 ! m directly 8 rays fall ^u ! e>?2 & _! heat+ p[] is rapidly augm5t$1 z !y approa* a p]p5dicul> direction4 ,:5 ! sun is ne>ly ov] head1 8 rays /rike u ) f> great] =ce ?an :5 !y meet u obliquely2 & ! e>? absorbs a f> great] numb] ( ^? rays ( heat :i* /rike x p]p5dicul>ly1 ?an ( ^? :i* meet x 9 a slant+ direction4 ,:5 ! sun is ne> ! horizon1 8 rays m]ely glance along ! gr\nd1 & _m ( !m1 be=e !y rea* x1 are absorb$ & disp]s$ 9 pass+ ?r\gh ! atmosph]e4 ,^? :o h felt only ! oblique sol> rays1 z !y fall ^u objects 9 ! high latitudes1 h a v inadequate idea ( ! p[] ( a v]tical1 noonday sun1 z felt 9 ! region ( ! equator4 ,! increas$ l5g? ( ! day 9 ,summ] is ano!r cause ( ! heat ( ?is season ( ! ye>4 ,?is cause m s5sibly affects places f> remov$ f ! equator1 because at su* places ! days are long] & ! nights %ort] ?an 9 ! torrid zone4 ,by ! op]ation ( ?is cause1 ! sol> heat accumulates !re s mu*1 dur+ ! longe/ days ( ,summ]1 t ! temp]ature rises to a high] degree ?an is (t5 kn[n 9 ! torrid climates4 ,b ! temp]ature ( a place is influ5c$ v mu* by sev]al o!r causes1 z well z by ! =ce & duration ( ! sun's heat4 ,fir/1 ! elevation ( a c\ntry above ! level ( ! sea has a great influ5ce ^u its climate4 ,elevat$ di/ricts ( c\ntry1 ev5 9 ! torrid zone1 (t5 enjoy ! mo/ agreeable climate 9 ! _w4 ,! cold ( ! upp] regions ( ! atmosph]e modifies & temp]s ! sol> heat1 s z to give a mo/ delightful s(tness1 :ile ! uni=mity ( temp]ature excludes ^? sudd5 & excessive *anges :i* are (t5 exp]i5c$ 9 less favor$ climes4 ,9 asc5d+ c]ta9 high m\nta9s situat$ )9 ! torrid zone1 ! travell] passes1 9 a %ort "t1 ?r\gh e v>iety ( climate1 f ! mo/ oppressive & sultry heat1 to ! s(t & balmy air ( ,spr+1 :i* aga9 is succe$$ by ! cool] breezes ( ,autumn1 & !n by ! sev]e/ fro/s ( ,w9t]4 ,a correspond+ diff]5ce is se5 9 ! products ( ! vegetable k+dom4 ,:ile ,w9t] reigns on ! summit ( ! m\nta91 its c5tral regions may be encircl$ ) ! v]dure ( ,spr+1 & its base ) ! fl[]s & fruits ( ,summ]4 ,secondly1 ! proximity ( ! ocean also has a great effect to equalize ! temp]ature ( a place4 ,z ! ocean *anges its temp]ature dur+ ! ye> mu* less ?an ! l&1 x becomes a s\rce ( w>m? to contigu\s c\ntries 9 ,w9t]1 & a f\nta9 ( cool breezes 9 ,summ]4 ,?irdly1 ! relative humidity or dryness ( ! atmosph]e ( a place is ( great importance1 9 reg>d to its effects on ! animal sy/em4 ,a dry air ( n9ety degrees is n s insupportable z a humid air ( eighty degrees2 & x may be ass]t$ z a g5]al pr9ciple1 t a hot & humid atmosph]e is unheal?y1 al?\gh a hot air1 :5 dry1 may be v salubri\s4 ,9 a w>m atmosph]e :i* is dry1 ! evaporation ( moi/ure f ! surface ( ! body is rapid1 & its cool+ influ5ce af=ds a mo/ /rik+ relief to an int5se heat )\t2 b :5 ! surr\nd+ atmosph]e is already fill$ ) moi/ure1 no su* evaporation takes place f ! surface ( ! sk91 & no su* refre%+ effects are exp]i5c$ f ?is cause4 ,moi/ure collects on ! sk92 a sultry1 oppressive s5sation is felt2 & *ills & fev]s are usually 9 ! tra94 ,,lett] ,,xii4 ,,laws ,,( ,,motion4 ,:at ?\gh 9 solemn sil5ce1 all ,move r\nd ?is d>k1 t]re/rial ball6 ,9 reason's e> !y all rejoice1 ,& utt] =? a glori\s voice2 ,= ev] s++1 z !y %9e1 ',! h& t made u is div9e4'--,addison4 ,,h[ev] incr$ible x may seem1 no fact is m c]ta91 ?an t ! e>? is con/antly on ! w+1 fly+ ar\nd ! sun ) a velocity s prodigi\s1 t1 = e brea? we draw1 we advance on our way =ty or fifty miles4 ,if1 :5 pass+ across ! wat]s 9 a /eam-boat1 we c wake1 aft] a night's repose1 & f9d ourselves conduct$ on our voyage a hundr$ miles1 we exult 9 ! triumphs ( art1 :i* c\ld h mov$ s pond]\s a body z a /eam-%ip ov] su* a space 9 s %ort a "t1 & s quietly1 too1 z n to di/urb our slumb]s2 b1 ) a motion va/ly m quiet & uni=m1 we h1 9 ! same int]val1 be5 c>ri$ along ) ! e>? 9 its orbit m ?an half a million ( miles4 ,9 ! case ( ! /eam-%ip1 h[ev] p]fect ! ma*9]y may be1 we /ill1 9 our wak+ h\rs at lea/1 are made s5sible ( ! action ( ! =ces by :i* ! motion is ma9ta9$1--z ! ro>+ ( ! fire1 ! beat+ ( ! pi/on1 & ! da%+ ( ! paddle-:eels2 b 9 ! m p]fect ma*9]y :i* c>ries ! e>? =w>d on h] gr&] voyage1 no s\nd is he>d1 nor ! lea/ intimation af=d$ ( ! /up5d\s =ces by :i* ?is motion is a*iev$4 ,to ! pi\s obs]v] ( ,nature x might seem suffici5t1 )\t any inquiry into second causes1 to ascribe ! motions ( ! sph]es to ! direct ag5cy ( ! ,supreme ,be+4 ,if1 h[ev]1 we c succe$ 9 f9d+ ! secret spr+s & cords1 by :i* ! motions ( ! heav5ly bodies are imm$iately produc$ & controll$1 x w detract no?+ f our j admiration ( ! ,great ,fir/ ,cause ( all ?+s4 ,we may !re=e n[ ent] ^u ! inquiry into ! nature or laws ( ! =ces by :i* ! e>? is made to revolve on h] axis & 9 h] orbit2 & hav+ le>n$ :at x is1 t causes & ma9ta9s ! motions ( ! e>?1 y w !n acquire1 at ! same "t1 a k ( all ! cele/ial ma*9]y4 ,! subject w involve an explanation ( ! laws ( motion1 & ( ! pr9ciples ( univ]sal gravitation4 ,x 0 once suppos$1 t we c\ld nev] reason respect+ ! laws t gov]n ! heav5ly bodies f :at we obs]ve 9 bodies ar\nd u1 b t motion is "o ?+ on ! e>? & q ano!r ?+ 9 ! skies2 & h5ce1 t x is impossible = u1 by any inquiries into ! laws ( t]re/rial ,nature1 to asc]ta9 h[ ?+s take place among ! heav5ly bodies4 ,galileo & ,newton1 h[ev]1 proce$$ on ! contr>y supposition1 t ,nature is uni=m 9 all h] works2 t ! same ,almighty arm rules ov] all2 & t ,he works by ! same fix$ laws ?r\gh all p>ts ( ,8 b\ndless realm4 ,! c]ta9ty ) :i* all ! pr$ictions ( a/ronom]s1 made on ^! suppositions1 are fulfill$1 atte/s ! s\ndness ( ! hypo!sis4 ,accord+ly1 ^? laws1 :i* all exp]i5ce1 endlessly multipli$ & v>i$1 proves to be ! laws ( t]re/rial motion1 are held to be ! laws t gov]n also ! motions ( ! mo/ di/ant planets & />s1 & to prevail ?r\gh\t ! univ]se ( matt]4 ,let u1 !n1 briefly review ^! great laws ( motion1 :i* are ?ree 9 numb]4 ,! ,,fir/ ,,law is z foll[s3 e body p]sev]es 9 a /ate ( re/1 or ( uni=m motion 9 a /raight l9e1 unless compell$ by "s =ce to *ange its /ate4 ,by =ce is meant any ?+ :i* produces motion4 ,! =ego+ law has be5 fully e/abli%$ by exp]im5t1 & is con=mable to all exp]i5ce4 ,x embraces sev]al p>ticul>s4 ,fir/1 a body1 :5 at re/1 rema9s s1 unless "s =ce puts x 9 motion2 & h5ce x is inf]r$1 :5 a body is f\nd 9 motion1 t "s =ce mu/ h be5 appli$ to x suffici5t to h caus$ its motion4 ,?us1 ! fact1 t ! e>? is 9 motion ar\nd ! sun & ar\nd its own axis1 is to be acc\nt$ = by assign+ to ea* ( ^! motions a =ce adequate1 bo? 9 quantity & direction1 to produce ^! motions1 respectively4 ,secondly1 :5 a body is once 9 motion1 x w cont9ue to move = ev]1 unless some?+ /ops x4 ,:5 a ball is /ruck on ! surface ( ! e>?1 ! friction ( ! e>? & ! resi/ance ( ! air soon /op its motion2 :5 /ruck on smoo? ice1 x w g mu* fur!r be=e x comes to a /ate ( re/1 because ! ice opposes mu* less resi/ance ?an ! gr\nd2 &1 7 !re no imp$im5t to its motion1 x w\ld1 :5 once set 9 motion1 cont9ue to move )\t end4 ,! heav5ly bodies are actually 9 ?is condition3 !y cont9ue to move1 n because any new =ces are appli$ to !m2 b1 hav+ be5 once set 9 motion1 !y cont9ue 9 motion because !re is no?+ to /op !m4 ,?is prop]ty 9 bodies to p]sev]e 9 ! /ate !y are actually 91--if at re/1 to rema9 at re/1 or1 if 9 motion1 to cont9ue 9 motion1--is call$ in]tia4 ,! in]tia ( a body 7:i* is measur$ by ! =ce requir$ to ov]come x7 is proportion$ to ! quantity ( matt] x conta9s4 ,a /eam-boat manife/s its in]tia1 on fir/ />t+ x1 by ! enorm\s exp5diture ( =ce requir$ to br+ x to a giv5 rate ( motion2 & x aga9 manife/s its in]tia1 :5 9 rapid motion1 by ! great difficulty ( /opp+ x4 ,! heav5ly bodies1 hav+ be5 once put 9 motion1 & meet+ ) no?+ to /op !m1 move on by _! own in]tia4 ,a top af=ds a beautiful illu/ration ( in]tia1 cont9u+1 z x does1 to sp9 aft] ! mov+ =ce is )drawn4 ,?irdly1 ! motion to :i* a body naturally t5ds is uni=m2 t is1 ! body moves j z f> ! second m9ute z x did ! fir/1 & z f> ! ?ird z ! second2 & passes ov] equal spaces 9 equal times4 ,i d n ass]t t ! motion ( all mov+ bodies is 9 fact uni=m1 b t su* is _! t5d5cy4 ,if x is o!rwise ?an uni=m1 !re is "s cause op]at+ to di/urb ! uni=mity to :i* x is naturally prone4 ,f\r?ly1 a body 9 motion w move 9 a /raight l9e1 unless div]t$ out ( t l9e by "s ext]nal =ce2 & ! body w resume its /raight-=w>d motion1 :5ev] ! =ce t turns x aside is )drawn4 ,e body t is revolv+ 9 an orbit1 l ! moon ar\nd ! e>?1 or ! e>? ar\nd ! sun1 t5ds to move 9 a /raight l9e :i* is a tang5t#g to its orbit4 ,?us1 if ,a ,b ,c1 ,fig4 #bh1 repres5ts ! orbit ( ! moon ar\nd ! e>?1 7 x n = ! con/ant action ( "s =ce t draws h] t[>ds ! e>?1 %e w\ld move (f 9 a /raight l9e4 ,if ! =ce t c>ries h] t[>ds ! e>? 7 susp5d$ at ,a1 %e w\ld imm$iately des]t ! circul> motion1 & proce$ 9 ! direction ,a ,d4 ,9 ! same mann]1 a boy :irls a /one ar\nd 8 head 9 a sl+1 & !n lett+ g "o ( ! /r+s1 & releas+ ! =ce t b9ds x to ! circle1 x flies (f 9 a /raight l9e :i* is a tang5t to t "p ( ! circle :]e x 0 releas$4 ,?is t5d5cy :i* a body revolv+ 9 an orbit exhibits1 to rec$e f ! c5tre & to fly (f 9 a tang5t1 is call$ ! c5trifugal =ce4 ,we see x manife/$ :5 a pail ( wat] is :irl$4 ,! wat] rises on ! sides ( ! vessel1 leav+ a holl[ 9 ! c5tral p>ts4 ,we see an example ( ! effects ( c5trifugal action1 :5 a horse turns swiftly r\nd a corn]1 & ! rid] is ?r[n outw>ds2 also1 :5 a :eel passes rapidly ?r\gh a small collection ( wat]1 & portions ( ! wat] are ?r[n (f f ! top ( ! :eel 9 /raight l9es :i* are tang5ts to ! :eel4 ,illu/ration ,fig4 #bh4 ,! c5trifugal =ce is increas$ z ! velocity is increas$4 ,?us1 ! p>ts ( a mill/one mo/ remote f ! c5tre sometimes acquire a c5trifugal =ce s mu* great] ?an ! c5tral p>ts1 :i* move mu* sl[]1 t ! /one is divid$1 & ! ext]ior portions are project$ ) great viol5ce4 ,9 l mann]1 z ! equatorial p>ts ( ! e>?1 9 ! diurnal revolution1 revolve mu* fa/] ?an ! p>ts t[>ds ! poles1 s ! c5trifugal =ce is felt mo/ at ! equator1 & becomes /rik+ly manife/ by ! dim9i%$ weight ( bodies1 s9ce x acts 9 opposition to ! =ce ( gravity4 ,al?\gh ! =ego+ law ( motion1 :5 fir/ pres5t$ to ! m9d1 appe>s to convey no new tru?1 b only to enunciate 9 a =mal mann] :at we knew be=e2 yet a j und]/&+ ( ?is law1 9 all its be>+s1 leads u to a cle> compreh5sion ( no small %>e ( all ! ph5om5a ( motion4 ,! second & ?ird laws may be expla9$ 9 few] t]ms4 ,! ,,second ,,law ( motion is z foll[s3 motion is proportion$ to ! =ce impress$1 & 9 ! direction ( t =ce4 ,! mean+ ( ?is law is1 t e =ce t is appli$ to a body produces its full effect1 proportion$ to its int5sity1 ei!r 9 caus+ or 9 prev5t+ motion4 ,let !re be ev] s _m bl[s appli$ at once to a ball1 ea* w produce its own effect 9 its own direction1 & ! ball w move (f1 n inde$ 9 ! zigzag1 complex l9es correspond+ to ! directions ( ! sev]al =ces1 b 9 a s+le l9e express+ ! unit$ effect ( all4 ,if y place a ball at ! corn] ( a table1 & give x an impulse1 at ! same in/ant1 ) ! ?umb & f+] ( ea* h&1 "o impell+ x 9 ! direction ( "o side ( ! table1 & ! o!r 9 ! direction ( ! o!r side1 ! ball w move diagonally across ! table4 ,if ! bl[s be exactly proportion$ ea* to ! l5g? ( ! side ( ! table on :i* x is direct$1 ! ball w run exactly f corn] to corn]1 & 9 ! same "t t x w\ld h pass$ ov] ea* side by ! bl[ giv5 9 ! direction ( t side4 ,?is pr9ciple is express$ by say+1 t a body impell$ by two =ces1 act+ respectively 9 ! directions ( ! two sides ( a p>allelogram1 & proportion$ 9 int5sity to ! l5g?s ( ! sides1 w describe ! diagonal ( ! p>allelogram 9 ! same "t 9 :i* x w\ld h describ$ ! sides by ! =ces act+ sep>ately4 ,! conv]se ( ?is proposition is also true1 namely1 t any s+le motion may be consid]$ z ! resultant ( two o!rs1--! motion itself be+ repres5t$ by ! diagonal1 :ile ! two compon5ts are repres5t$ by ! sides1 ( a p>allelogram4 ,?is r$uction ( a motion to ! individual motions t produce x1 is call$ ! resolution ( motion1 or ! resolution ( =ces4 ,nor c a giv5 motion be resolv$ into two compon5ts1 m]ely4 ,^!1 aga91 may be resolv$ into o!rs1 v>y+ indef9itely1 9 direction & int5sity1 f all :i* ! giv5 motion may be consid]$ z hav+ result$4 ,?is composition & resolution ( motion or =ces is (t5 ( great use1 9 inquiries into ! motions ( ! heav5ly bodies4 ,! composition (t5 enables u to sub/itute a s+le =ce = a great numb] ( o!rs1 ^: individual op]ations w\ld be too complicat$ to be foll[$4 ,by ?is means1 ! inve/igation is greatly simplifi$4 ,on ! o!r h&1 x is frequ5tly v conv5i5t to resolve a giv5 motion into two or m o!rs1 "s ( :i* may be ?r[n out ( ! acc\nt1 z n influ5c+ ! p>ticul> po9t :i* we are inquir+ ab\t1 :ile o!rs are f> m easily und]/ood & manag$ ?an ! s+le =ce w\ld h be54 ,x is *>act]i/ic ( great m9ds1 to simplify ^! inquiries4 ,!y ga9 an insight into complicat$ & difficult subjects1 n s mu* by any extraord9>y faculty ( see+ 9 ! d>k1 z by ! p[] ( remov+ f ! object all incid5tal causes ( obscurity1 until x %9es 9 its own cle> & simple light4 ,if e =ce1 :5 appli$ to a body1 produces its full & legitimate effect1 h[ _m o!r =ces soev] may act ^u x1 impell+ x diff]5t ways1 !n x mu/ foll[1 t ! smalle/ =ce ought to move ! l>ge/ body2 & su* is 9 fact ! case4 ,a snap ( a f+] ^u a sev5ty-f\r "u full sail1 if appli$ 9 ! direction ( its motion1 w\ld actually increase its spe$1 al?\gh ! effect might be too small to be visible4 ,/ill x is some?+1 & may be truly express$ by a fraction4 ,?us1 suppose a globe1 weigh+ a million ( p\nds1 7 susp5d$ f ! ceil+ by a /r+1 & we %\ld apply to x ! snap ( a f+]1--x is grant$ t ! motion w\ld be q ins5sible4 ,let u !n divide ! body into a million equal p>ts1 ea* weigh+ "o p\nd2 !n ! same impulse1 appli$ to ea* "o sep>ately1 w\ld produce a s5sible effect1 mov+ x1 say "o in*4 ,x w be f\nd1 on trial1 t ! same impulse giv5 to a mass ( two p\nds w move x half an in*2 & h5ce x is inf]r$1 t1 if appli$ to a mass weigh+ a million ( p\nds1 x w\ld move x ! million? "p ( an in*4 ,x is "o ( ! curi\s results ( ! second law ( motion1 t an unlimit$ numb] ( motions may exi/ toge!r 9 ! same body4 ,?us1 at ! same mom5t1 we may be walk+ ar\nd a po/ 9 ! cab9 ( a /eam-boat1 accompany+ ! boat 9 its passage ar\nd an isl&1 revolv+ ) ! e>? on its axis1 fly+ ?r\gh space 9 our annual circuit ar\nd ! sun1 & possibly :eel+1 along ) ! sun & 8 :ole ret9ue ( planets1 ar\nd "s c5tre 9 common ) ! />ry worlds4 ,! ,,?ird ,,law ( motion is ?is3 action & reaction are equal1 & 9 contr>y directions4 ,:5ev] ,i give a bl[1 ! body /ruck ex]ts an equal =ce on ! /rik+ body4 ,if ,i /rike ! wat] ) an o>1 ! wat] communicates an equal impulse to ! o>1 :i*1 be+ communicat$ to ! boat1 drives x =w>d 9 ! opposite direction4 ,if a magnet attracts a piece ( iron1 ! iron attracts ! magnet j z mu*1 9 ! opposite direction2 &1 9 %ort1 e portion ( matt] 9 ! univ]se attracts & is attract$ by e o!r1 equally1 9 an opposite direction4 ,?is br+s u to ! doctr9e ( univ]sal gravitation1 :i* is ! v key t unlocks all ! secrets ( ! skies4 ,?is w =m ! subject ( my next ,lett]4 ,,footnote3 #g ,a tang5t is a /raight l9e t\*+ a circle1 z ,a ,d1 9 ,fig4 #bh ,,lett] ,,xiii4 ,,t]re/rial ,,gravity4 ,to ,him no high1 no l[1 no great1 no small1 ,he fills1 ,he b\nds1 connects1 & equals all4--,pope4 ,,we discov] 9 ,nature a t5d5cy ( e portion ( matt] t[>ds e o!r4 ,?is t5d5cy is call$ gravitation4 ,9 ob$i5ce to ?is p[]1 a /one falls to ! gr\nd1 & a planet revolves ar\nd ! sun4 ,we may contemplate ?is subject z x relates ei!r to ph5om5a t take place ne> ! surface ( ! e>?1 or 9 ! cele/ial regions4 ,! =m]1 gravity1 is exemplifi$ by fall+ bodies2 ! latt]1 univ]sal gravitation1 by ! motions ( ! heav5ly bodies4 ,! laws ( t]re/rial gravity 7 fir/ inve/igat$ by ,galileo2 ^? ( univ]sal gravitation1 by ,sir ,isaac ,newton4 ,t]re/rial gravity is only an individual example ( univ]sal gravitation2 be+ ! t5d5cy ( bodies t[>ds ! c5tre ( ! e>?4 ,we are s mu* accu/om$1 f our e>lie/ ye>s1 to see bodies fall to ! e>?1 t we imag9e bodies mu/ ( necessity fall d[nw>ds2 b :5 we reflect t ! e>? is r\nd1 & t bodies fall t[>ds ! c5tre on all sides ( x1 & t ( c\rse bodies on opposite sides ( ! e>? fall 9 precisely opposite directions1 & t[>ds ea* o!r1 we p]ceive t !re mu/ be "s =ce act+ to produce ?is effect2 nor is x en\gh to say1 z ! anci5ts did1 t bodies naturally fall to ! e>?4 ,e motion implies "s =ce :i* produces x2 & ! fact t bodies fall t[>ds ! e>?1 on all sides ( x1 leads u to inf] t t =ce1 :atev] x is1 resides 9 ! e>? itself4 ,we !re=e call x attraction4 ,we d n1 h[ev]1 say :at attraction is1 b :at x does4 ,we mu/ be> 9 m9d1 also1 t1 accord+ to ! ?ird law ( motion1 ?is attraction is mutual2 t :5 a /one falls t[>ds ! e>?1 x ex]ts ! same =ce on ! e>? t ! e>? ex]ts on ! /one2 b ! motion ( ! e>? t[>ds ! /one is z mu* less ?an t ( ! /one t[>ds ! e>?1 z its quantity ( matt] is great]2 & !re=e its motion is q ins5sible4 ,b al?\gh we are compell$ to ackn[l$ge ! exi/5ce ( su* a =ce z gravity1 caus+ a t5d5cy 9 all bodies t[>ds ea* o!r1 yet we "k no?+ ( its nature1 nor c we conceive by :at m$ium bodies at su* a di/ance z ! moon & ! e>? ex]cise ?is influ5ce on ea* o!r4 ,/ill1 we may trace ! modes 9 :i* ?is =ce acts2 t is1 its laws2 = ! laws ( ,nature are no?+ else ?an ! modes 9 :i* ! p[]s ( ,nature act4 ,we owe *iefly to ! great ,galileo ! fir/ inve/igation ( ! laws ( t]re/rial gravity1 z exemplifi$ 9 fall+ bodies2 & ,i w avail myself ( ?is opportunity to make y bett] acqua9t$ ) "o ( ! mo/ int]e/+ ( m5 & greate/ ( philosoph]s4 ,galileo 0 born at ,pisa1 9 ,italy1 9 ! ye> #aefd4 ,he 0 ! son ( a ,flor5t9e nobleman1 & 0 de/9$ by 8 fa!r = ! m$ical pr(ession1 & to ?is 8 e>li] /udies 7 devot$4 ,b a fondness & a g5ius = me*anical inv5tions _h develop$ itself1 at a v e>ly age1 9 ! con/ruction ( 8 toys1 & a love ( draw+2 & z he grew old]1 a passion = ma!matics1 & = exp]im5tal rese>*1 pr$om9at$ ov] 8 zeal = ! /udy ( m$ic9e1 & he =tunately ab&on$ t = ! m cong5ial pursuits ( natural philosophy & a/ronomy4 ,9 ! tw5ty-fif? ye> ( 8 age1 he 0 appo9t$1 by ! ,gr& ,duke ( ,tuscany1 pr(essor ( ma!matics 9 ! ,univ]sity ( ,pisa4 ,at t p]iod1 !re prevail$ 9 all ! s*ools a mo/ extraord9>y rev]5ce = ! writ+s ( ,ari/otle1 ! preceptor ( ,alex&] ! ,great1--a philosoph] :o fl\ri%$ 9 ,greece1 ab\t ?ree hundr$ ye>s be=e ! ,*ri/ian era4 ,ari/otle1 by 8 great g5ius & le>n+1 ga9$ a wond]ful asc5d5cy ov] ! m9ds ( m51 & became ! oracle ( ! :ole read+ _w = tw5ty c5turies4 ,x 0 held1 on ! "o h&1 t all tru?s wor? kn[+ 7 conta9$ 9 ! writ+s ( ,ari/otle2 &1 on ! o!r1 t an ass]tion :i* contradict$ any ?+ 9 ,ari/otle c\ld n be true4 ,b ,galileo _h a greatness ( m9d :i* so>$ above ! prejudices ( ! age 9 :i* he liv$1 & d>$ to int]rogate ,nature by ! two great & only successful me?ods ( discov]+ h] secrets1--exp]im5t & obs]vation4 ,galileo 0 inde$ ! fir/ philosoph] t ev] fully employ$ exp]im5ts z ! means ( le>n+ ! laws ( ,nature1 by imitat+ on a small :at %e p]=ms on a great scale1 & ?us detect+ h] modes ( op]ation4 ,ar*im$es1 ! great ,sicilian philosoph]1 _h 9 anci5t times introduc$ ma!matical or geometrical reason+ into natural philosophy2 b x 0 res]v$ = ,galileo to unite ! advantages ( bo? ma!matical & exp]im5tal reason+s 9 ! /udy ( ,nature1--bo? sure & ! only sure guides to tru?1 9 ?is dep>tm5t ( k1 at lea/4 ,exp]im5t & obs]vation furni% mat]ials ^u :i* geometry builds h] reason+s1 & f :i* %e d]ives _m tru?s t ei!r lie = ev] hidd5 f ! eye ( obs]vation1 or :i* x w\ld require ages to unfold4 ,?is me?od1 ( int]rogat+ ,nature by exp]im5t & obs]vation1 0 matur$ into a sy/em by ,"l ,bacon1 a celebrat$ ,engli% philosoph]1 e>ly 9 ! sev5te5? c5tury1--inde$1 dur+ ! life ( ,galileo4 ,previ\s to t "t1 ! inquir]s into ,nature did n op5 _! eyes to see h[ ! facts really are2 b1 by metaphysical processes1 9 imitation ( ,ari/otle1 det]m9$ h[ !y ought to be1 & ha/ily conclud$ t !y 7 s4 ,?us1 !y did n /udy into ! laws ( motion1 by obs]v+ h[ motion actually takes place1 "u v>i\s circum/ances1 b fir/1 9 _! closets1 con/ruct$ a def9ition ( motion1 & !nce inf]r$ all its prop]ties4 ,! sy/em ( reason+ respect+ ! ph5om5a ( ,nature1 introduc$ by ,"l ,bacon1 0 ?is3 9 ! fir/ place1 to exam9e all ! facts ( ! case1 & !n f ^! to det]m9e ! laws ( ,nature4 ,to d]ive g5]al conclusions f ! comp>ison ( a great numb] ( individual in/ances con/itutes ! peculi>ity ( ! ,baconian philosophy4 ,x is call$ ! inductive sy/em1 because its conclusions 7 built on ! induction1 or comp>ison1 ( a great _m s+le facts4 ,previ\s to ! "t ( ,"l ,bacon1 h>dly any insight _h be5 ga9$ into ! causes ( natural ph5om5a1 & h>dly "o ( ! laws ( ,nature _h be5 cle>ly e/abli%$1 because all ! inquir]s into ,nature 7 ^u a wrong road1 grop+ _! way ?r\gh ! labyr9? ( error4 ,bacon po9t$ out to !m ! true pa?1 & held be=e !m ! tor*-light ( exp]im5t & obs]vation1 "u ^: guidance all successful /ud5ts ( ,nature h s9ce walk$1 & by ^: illum9ation !y h ga9$ s wond]ful an insight into ! my/]ies ( ! natural _w4 ,x is a rem>kable fact1 t two su* *>act]s z ,bacon & ,galileo %\ld appe> on ! /age at ! same "t1 :o1 )\t any communication ) ea* o!r1 or p]haps )\t any p]sonal k ( ea* o!r's exi/5ce1 %\ld h ea* develop$ ! true me?od ( inve/igat+ ! laws ( ,nature4 ,galileo practis$ :at ,bacon only taught2 & "s1 !re=e1 ) mu* reason1 consid] ,galileo z a great] philosoph] ?an ,bacon4 ,bacon1 says ,hume1 po9t$ out1 at a great di/ance1 ! road to philosophy2 ,galileo bo? po9t$ x out to o!rs1 & made1 himself1 consid]able advances 9 x4 ,! ,engli%man 0 ignorant ( geometry2 ! ,flor5t9e reviv$ t sci5ce1 excell$ 9 x1 & 0 ! fir/ :o appli$ x1 toge!r ) exp]im5t1 to natural philosophy4 ,! =m] reject$1 ) ! mo/ positive disda91 ! sy/em ( ,cop]nicus2 ! latt] =tifi$ x ) new pro(s1 d]iv$ bo? f reason & ! s5ses4 ,:5 we reflect t geometry is a sci5ce built ^u self-evid5t tru?s1 & t all its conclusions are ! result ( pure demon/ration1 & c admit ( no controv]sy2 :5 we fur!r reflect1 t exp]im5tal evid5ce re/s on ! te/imony ( ! s5ses1 & we inf] a ?+ to be true because we actually see x to be s2 x %[s u ! extreme bigotry1 ! d>kness visible1 t becl\d$ ! human intellect1 :5 x n only refus$ to admit conclusions fir/ e/abli%$ by pure geometrical reason+1 & aft]w>ds confirm$ by exp]im5ts exhibit$ 9 ! light ( day1 b in/itut$ ! mo/ cruel p]secutions aga9/ ! great philosoph] :o fir/ proclaim$ ^! tru?s4 ,galileo 0 hat$ & p]secut$ by two di/9ct bodies ( m51 bo? possess+ great influ5ce 9 _! respective sph]es1--! "o consi/+ ( ! le>n$ doctors ( philosophy1 :o did no?+ m1 f age to age1 ?an reit]ate ! doctr9es ( ,ari/otle1 & 7 consequ5tly al>m$ at ! promulgation ( pr9ciples subv]sive ( ^? doctr9es2 ! o!r consi/+ ( ! ,romi% prie/hood1 compris+ ! t]rible ,inquisition1 :o d5\nc$ ! tru?s taught by ,galileo1 z inconsi/5t ) c]ta9 decl>ations ( ! ,holy ,scriptures4 ,we %all see1 z we advance1 :at a fe>ful w>f>e he _h to wage aga9/ ^! comb9$ p[]s ( d>kness4 ,ari/otle _h ass]t$1 t1 if two diff]5t weights ( ! same mat]ial 7 let fall f ! same height1 ! heavi] "o w\ld rea* ! gr\nd soon] ?an ! o!r1 9 proportion z x 0 m weighty4 ,= example3 if a t5-p\nd lead5 weight & a "o-p\nd 7 let fall f a giv5 height at ! same in/ant1 ! =m] w\ld rea* ! gr\nd t5 times z soon z ! latt]4 ,no "o ?\ght ( mak+ ! trial1 b x 0 deem$ suffici5t t ,ari/otle _h said s2 & accord+ly ?is ass]tion _h long be5 receiv$ z an axiom 9 ! sci5ce ( motion4 ,galileo v5tur$ to appeal f ! au?ority ( ,ari/otle to t ( 8 own s5ses1 & ma9ta9$1 t bo? weights w\ld fall 9 ! same "t4 ,! le>n$ doctors ridicul$ ! idea4 ,galileo tri$ ! exp]im5t 9 _! pres5ce1 by lett+ fall1 at ! same in/ant1 l>ge & small weights f ! top ( ! celebrat$ lean+ t[] ( ,pisa4 ,yet1 ) ! s\nd ( ! two weights click+ ^u ! pavem5t at ! same mom5t1 !y /ill ma9ta9$ t ! t5-p\nd weight w\ld rea* ! gr\nd 9 "o t5? "p ( ! "t ( ! o!r1 because !y c\ld quote ! *apt] & v]se ( ,ari/otle :]e ! fact 0 ass]t$4 ,we>i$ & disgu/$ ) ! malice & folly ( ^! ,ari/otelian philosoph]s1 ,galileo1 at ! age ( tw5ty-eight1 resign$ 8 situation 9 ! univ]sity ( ,pisa1 & remov$ to ,padua1 9 ! univ]sity ( :i* place he 0 elect$ pr(essor ( ma!matics4 ,up to ?is p]iod1 ,galileo _h devot$ himself *iefly to ! /udies ( ! laws ( motion1 & ! o!r bran*es ( me*anical philosophy4 ,soon aft]w>ds1 he began to publi% 8 writ+s1 9 rapid succession1 & became at once among ! mo/ conspicu\s ( 8 age1--a rank :i* he aft]w>ds well su/a9$ & greatly exalt$1 by ! inv5tion ( ! telescope1 & by 8 num]\s a/ronomical discov]ies4 ,i w res]ve an acc\nt ( ^! great a*ievem5ts until we come to t "p ( a/ronomy to :i* !y 7 m imm$iately relat$1 & proce$1 n[1 to expla9 to y ! lead+ pr9ciples ( t]re/rial gravity1 z exemplifi$ 9 fall+ bodies4 ,fir/1 all bodies ne> ! e>?'s surface fall 9 /raight l9es t[>ds ! c5tre ( ! e>?4 ,we are n to inf] f ?is fact1 t !re resides at ! c5tre any peculi> =ce1 z a great load/one1 = example1 :i* attracts bodies t[>ds itself2 b bodies fall t[>ds ! c5tre ( ! sph]e1 because ! comb9$ attractions ( all ! p>ticles ( matt] 9 ! e>?1 ea* ex]t+ its prop] =ce ^u ! body1 w\ld c>ry x t[>ds ! c5tre4 ,?is may be easily illu/rat$ by a diagram4 ,let ,b1 ,fig4 #bi1 page #adj1 be ! c5tre ( ! e>?1 & ,a a body )\t x4 ,e portion ( matt] 9 ! e>? ex]ts "s =ce on ,a1 to draw x d[n to ! e>?4 ,b s9ce !re is j z mu* matt] on "o side ( ! l9e ,a ,b1 z on ! o!r side1 ea* half ex]ts an equal =ce to draw ! body t[>ds itself2 !re=e x falls 9 ! direction ( ! diagonal betwe5 ! two =ces4 ,?us1 if we comp>e ! effects ( any two p>ticles ( matt] at equal di/ances f ! l9e ,a ,b1 b on opposite sides ( x1 z a1 b1 :ile ! =ce ( ! p>ticle at a w\ld t5d to draw ,a 9 ! direction ( ,a a1 t ( b w\ld draw x 9 ! direction ( ,a b1 & x w\ld fall 9 ! l9e ,a ,b1 half way betwe5 ! two4 ,! same w\ld hold true ( any o!r two correspond+ p>ticles ( matt] on diff]5t sides ( ! e>?1 9 respect to a body situat$ 9 any place )\t x4 ,illu/ration ,fig4 #bi4 ,secondly1 all bodies fall t[>ds ! e>?1 f ! same height1 ) equal velocities4 ,a musket-ball1 & ! f9e/ p>ticle ( d[n1 if let fall f a c]ta9 height t[>ds ! e>?1 t5d to desc5d t[>ds x at ! same rate1 & w\ld proce$ ) equal spe$1 7 x n = ! resi/ance ( ! air1 :i* ret>ds ! d[n m ?an x does ! ball1 & f9ally /ops x4 ,if1 h[ev]1 ! air be remov$ out ( ! way1 z x may be by means ( ! air-pump1 ! two bodies keep side by side 9 fall+ f ! greate/ height at :i* we c try ! exp]im5t4 ,?irdly1 bodies1 9 fall+ t[>ds ! e>?1 h _! rate ( motion cont9ually accel]at$4 ,suppose we let fall a musket-ball f ! top ( a high t[]1 & wat* its progress1 disreg>d+ ! resi/ance ( ! air3 ! fir/ second1 x w pass ov] sixte5 feet & "o in*1 b its spe$ w be con/antly increas$1 be+ all ! :ile urg$ onw>d by ! same =ce1 & reta9+ all t x has already acquir$2 s t ! long] x is 9 fall+1 ! swift] its motion becomes4 ,consequ5tly1 :5 bodies fall f a great height1 !y acquire an imm5se velocity be=e !y rea* ! e>?4 ,?us1 a man fall+ f a balloon1 or f ! ma/-head ( a %ip1 is brok5 9 pieces2 & ^? meteoric /ones1 :i* sometimes fall f ! sky1 bury !mselves deep 9 ! e>?4 ,on measur+ ! spaces ?r\gh :i* a body falls1 x is f\nd1 t x w fall f\r times z f> 9 two seconds z 9 "o1 & "o hundr$ times z f> 9 t5 seconds z 9 "o2 & univ]sally1 ! space describ$ by a fall+ body is proportion$ to ! "t multipli$ into itself2 t is1 to ! squ>e ( ! "t4 ,f\r?ly1 gravity is proportion$ to ! quantity ( matt]4 ,a body :i* has twice z mu* matt] z ano!r ex]ts a =ce ( attraction twice z great1 & also receives twice z mu* f ! same body z x w\ld d1 if x 7 only j z heavy z t body4 ,?us ! e>?1 conta9+1 z x does1 =ty times z mu* matt] z ! moon1 ex]ts ^u ! moon =ty times z mu* =ce z x w\ld d1 7 its mass ! same ) t ( ! moon2 b x is also capable ( receiv+ =ty times z mu* gravity f ! moon z x w\ld d1 7 its mass ! same z ! moon's2 s t ! p[] ( attract+ & t ( be+ attract$ are reciprocal2 & x is !re=e correct to say1 t ! moon attracts ! e>? j z mu* z ! e>? attracts ! moon2 & ! same may be said ( any two bodies1 h[ev] diff]5t 9 quantity ( matt]4 ,fif?ly1 gravity1 :5 act+ at a di/ance f ! e>?1 is n z int5se z x is ne> ! e>?4 ,at su* a di/ance z we are accu/om$ to asc5d above ! g5]al level ( ! e>?1 no great diff]5ce is obs]v$4 ,on ! tops ( high m\nta9s1 we f9d bodies fall+ t[>ds ! e>?1 ) ne>ly ! same spe$ z !y d f ! smalle/ elevations4 ,x is f\nd1 nev]!less1 t !re is a real diff]5ce2 s t1 9 fact1 ! weight ( a body 7:i* is no?+ m ?an ! measure ( its =ce ( gravity7 is n q s great on ! tops ( high m\nta9s z at ! g5]al level ( ! sea4 ,?us1 a ?\s& p\nds' weight1 on ! top ( a m\nta9 half a mile high1 w\ld weigh a qu>t] ( a p\nd less ?an at ! level ( ! sea2 & if elevat$ f\r ?\s& miles above ! e>?1--t is1 twice z f> f ! c5tre ( ! e>? z ! surface is f ! c5tre1--x w\ld weigh only "o f\r? z mu* z be=e2 if ?ree times z f>1 x w\ld weigh only "o n9? z mu*4 ,s t ! =ce ( gravity decreases1 z we rec$e f ! e>?1 9 ! same proportion z ! squ>e ( ! di/ance increases4 ,?is fact is g5]aliz$ by say+1 t ! =ce ( gravity1 at diff]5t di/ances f ! e>?1 is inv]sely z ! squ>e ( ! di/ance4 ,7 a body to fall f a great di/ance1--suppose a ?\s& times t ( ! radius ( ! e>?1--! =ce ( gravity be+ "o million times less ?an t at ! surface ( ! e>?1 ! motion ( ! body w\ld be exce$+ly sl[1 c>ry+ x ov] only ! six? "p ( an in* 9 a day4 ,x w\ld be a long "t1 !re=e1 9 mak+ any s5sible approa*es t[>ds ! e>?2 b at l5g?1 z x drew ne> to ! e>? x w\ld acquire a v great velocity1 & w\ld f9ally ru% t[>ds x ) prodigi\s viol5ce4 ,fall+ s f>1 & be+ cont9ually accel]at$ on ! way1 we might suppose t x w\ld at l5g? atta9 a velocity inf9itely great2 b x c be demon/rat$1 t1 if a body 7 to fall f an inf9ite di/ance1 attract$ to ! e>? only by gravity1 x c\ld nev] acquire a velocity great] ?an ab\t sev5 miles p] second4 ,?is1 h[ev]1 is a spe$ inconceivably great1 be+ ab\t eighte5 times ! greate/ velocity t c be giv5 to a cannon-ball1 & m ?an tw5ty-five ?\s& miles p] h\r4 ,b ! ph5om5a ( fall+ bodies mu/ h long be5 obs]v$1 & _! laws _h be5 fully inve/igat$ by ,galileo & o!rs1 be=e ! cause ( _! fall+ 0 und]/ood1 or any su* pr9ciple z gravity1 inh]5t 9 ! e>? & 9 all bodies1 0 appli$ to !m4 ,! developem5t ( ?is great pr9ciple 0 ! "w ( ,sir ,isaac ,newton2 & ,i w give y1 9 my next ,lett]1 "s p>ticul>s respect+ ! life & discov]ies ( ?is wond]ful man4 ,,lett] ,,xiv4 ,,sir ,,isaac ,,newton4--,,univ]sal ,,gravitation4--,,figure ,,( ,,! ,,e>?',s ,,orbit4--,,precession ,,( ,,! ,,equ9oxes4 ,! heav5s are all 8 own2 f ! wild rule ,( :irl+ vortices1 & circl+ sph]es1 ,to _! fir/ great simplicity re/or$4 ,! s*ools a/oni%$ /ood2 b f\nd x va9 ,to combat long ) demon/ration cle>1 ,&1 unawak5$1 dream b5ea? ! blaze ,( tru?4 ,at once _! pleas+ visions fl$1 ,) ! light %ad[s ( ! morn+ mix$1 ,:5 ,newton rose1 our philosophic sun4--,?omson's ,elegy4 ,,sir ,,isaac ,,newton 0 born 9 ,l9coln%ire1 ,engl&1 9 #afdb1 j "o ye> aft] ! dea? ( ,galileo4 ,8 fa!r di$ be=e he 0 born1 & he 0 a helpless infant1 ( a dim9utive size1 & s feeble a frame1 t 8 att5dants h>dly expect$ 8 life = a s+le h\r4 ,! family dwell+ 0 ( humble ar*itecture1 situat$ 9 a retir$ b beautiful valley1 & 0 surr\nd$ by a small f>m1 :i* af=d$ b a scanty liv+ to ! wid[$ "m & h] preci\s *>ge4 ,! cut on page #add1 ,fig #cj1 repres5ts ! mode/ mansion1 & ! emblems ( ru/ic life t fir/ met ! eyes ( ?is pride ( ! ,briti% nation1 & ornam5t ( human nature4 ,x w probably be f\nd1 t g5ius has (t5] emanat$ f ! cottage ?an f ! palace4 ,illu/ration ,fig4 #cj4 ,! boyhood ( ,newton 0 di/+ui%$ *iefly = 8 +5i\s me*anical contrivances4 ,among o!r pieces ( me*anism1 he con/ruct$ a w9dmill s curi\s & complete 9 its workman%ip1 z to excite univ]sal admiration4 ,aft] c>ry+ x a :ile by ! =ce ( ! w9d1 he resolv$ to sub/itute animal p[]1 & = ?is purpose he inclos$ 9 x a m\se1 :i* he call$ ! mill]1 & :i* kept ! mill a-go+ by act+ on a tread-:eel4 ,! p[] ( ! m\se 0 br\ght into action by unavail+ attempts to rea* a portion ( corn plac$ above ! :eel4 ,a wat]-clock1 a f\r-:eel$ c>riage propell$ by ! rid] himself1 & kites ( sup]ior workman%ip1 7 among ! productions ( ! me*anical g5ius ( ?is gift$ boy4 ,at a little lat] p]iod1 he began to turn 8 att5tion to ! motions ( ! heav5ly bodies1 & con/ruct$ sev]al sun-dials on ! walls ( ! h\se :]e he liv$4 ,all ?is 0 be=e he _h rea*$ 8 fifte5? ye>4 ,at ?is age1 he 0 s5t by 8 "m1 9 company ) an old family s]vant1 to a neighbor+ m>ket-t[n1 to dispose ( products ( _! f>m1 & to buy articles ( m]*&ise = _! family use2 b ! "y philosoph] left all ^! negotiations to 8 wor?y p>tn]1 occupy+ himself1 mean-:ile1 ) a collection ( old books1 :i* he _h f\nd 9 a g>ret4 ,at o!r times1 he /opp$ on ! road1 & took %elt] ) 8 book "u a h$ge1 until ! s]vant return$4 ,!y endeavor$ to educate him z a f>m]2 b ! p]usal ( a book1 ! con/ruction ( a wat]-mill1 or "s o!r me*anical or sci5tific amusem5t1 absorb$ all 8 ?\ghts1 :5 ! %eep 7 go+ a/ray1 & ! cattle 7 dev\r+ or tread+ d[n ! corn4 ,"o ( 8 uncles hav+ f\nd him "o day "u a h$ge1 ) a book 9 8 h&1 & entirely absorb$ 9 m$itation1 took x f him1 & f\nd t x 0 a ma!matical problem :i* s engross$ 8 att5tion4 ,8 fri5ds1 !re=e1 wisely resolv$ to favor ! b5t ( 8 g5ius1 & remov$ him f ! f>m to ! s*ool1 to prep>e = ! univ]sity4 ,9 ! eighte5? ye> ( 8 age1 ,newton 0 admitt$ into ,tr9ity ,college1 ,cambridge4 ,he made rapid & extraord9>y advances 9 ! ma!matics1 & soon af=d$ unequivocal presages ( t greatness :i* aft]w>ds plac$ him at ! head ( ! human intellect4 ,9 #affi1 at ! age ( tw5ty-sev51 he became pr(essor ( ma!matics at ,cambridge1 a po/ :i* he occupi$ = _m ye>s aft]w>ds4 ,dur+ ! f\r or five ye>s previ\s to ?is he _h1 9 fact1 made mo/ ( ^? great discov]ies :i* h immortaliz$ 8 "n4 ,we are at pres5t *iefly int]e/$ 9 "o ( ^!1 namely1 t ( univ]sal gravitation2 & let u see by :at /eps he 0 conduct$ to ?is greate/ ( sci5tific discov]ies4 ,9 ! ye> #afff1 :5 ,newton 0 ab\t tw5ty-f\r ye>s ( age1 ! plague 0 prevail+ at ,cambridge1 & he retir$ into ! c\ntry4 ,"o day1 :ile he sat 9 a g>d51 mus+ on ! ph5om5a ( ,nature ar\nd him1 an apple *anc$ to fall to ! gr\nd4 ,reflect+ on ! my/]i\s p[] t makes all bodies ne> ! e>? fall t[>ds its c5tre1 & consid]+ t ?is p[] rema9s unimpair$ at consid]able heights above ! e>?1 z on ! tops ( trees & m\nta9s1 he ask$ himself1--,may n ! same =ce ext5d its influ5ce to a great di/ance f ! e>?1 ev5 z f> z ! moon8 ,inde$1 may n ?is be ! v reason1 :y ! moon is drawn away cont9ually f ! /raight l9e 9 :i* e body t5ds to move1 & is ?us made to circulate ar\nd ! e>?8 ,y w recollect t x 0 m5tion$1 9 my ,lett] :i* conta9$ an acc\nt ( ! fir/ law ( motion1 t if a body is put 9 motion by any =ce1 x w always move =w>d 9 a /raight l9e1 unless "s o!r =ce compels x to turn aside f su* a direction2 & t1 :5 we see a body mov+ 9 a curve1 z a circul> orbit1 we are au?oriz$ to conclude t !re is "s =ce exi/+ )9 ! circle1 :i* cont9ually draws ! body away f ! direction 9 :i* x t5ds to move4 ,accord+ly1 x 0 a v natural sugge/ion1 to "o s well acqua9t$ ) ! laws ( motion z ,newton1 t ! moon %\ld con/antly b5d t[>ds ! e>?1 f a t5d5cy to fall t[>ds x1 z any o!r heavy body w\ld d1 if c>ri$ to su* a di/ance f ! e>?4 ,newton _h already prov$1 t if su* a p[] z gravity ext5ds f ! e>? to di/ant bodies1 x mu/ decrease1 z ! squ>e ( ! di/ance f ! c5tre ( ! e>? increases2 t is1 at d\ble ! di/ance1 x w\ld be f\r times less2 at t5 times ! di/ance1 "o hundr$ times less2 & s on4 ,n[1 x 0 kn[n t ! moon is ab\t sixty times z f> f ! c5tre ( ! e>? z ! surface ( ! e>? is f ! c5tre1 & consequ5tly1 ! =ce ( attraction at ! moon mu/ be ! squ>e ( sixty1 or ?irty-six hundr$ times less ?an x is at ! e>?2 s t a body at ! di/ance ( ! moon w\ld fall t[>ds ! e>? v sl[ly1 only "o ?irty-six hundr$? "p z f> 9 a giv5 "t1 z at ! e>?4 ,does ! moon actually fall t[>ds ! e>? at ?is rate2 or1 :at is ! same ?+1 does %e dep>t at ?is rate cont9ually f ! /raight l9e 9 :i* %e t5ds to move1 & 9 :i* %e w\ld move1 if no ext]nal =ce div]t$ h] f x8 ,on mak+ ! calculation1 su* 0 f\nd to be ! fact4 ,h5ce gravity1 & no o!r =ce ?an gravity1 acts ^u ! moon1 & compels h] to revolve ar\nd ! e>?4 ,by reason+s equally conclusive1 x 0 aft]w>ds prov$1 t a simil> =ce compels all ! planets to circulate ar\nd ! sun2 & n[1 we may asc5d f ! contemplation ( ?is =ce1 z we h se5 x exemplifi$ 9 fall+ bodies1 to t ( a univ]sal p[] ^: influ5ce ext5ds to all ! mat]ial creation4 ,x is 9 ?is s5se t we recognise ! pr9ciple ( univ]sal gravitation1 ! law ( :i* may be ?us enunciat$2 all bodies 9 ! univ]se1 :e!r great or small1 attract ea* o!r1 ) =ces proportion$ to _! respective quantities ( matt]1 & inv]sely z ! squ>es ( _! di/ances f ea* o!r4 ,?is law ass]ts1 fir/1 t attraction reigns ?r\gh\t ! mat]ial _w1 affect+ alike ! smalle/ p>ticle ( matt] & ! greate/ body2 secondly1 t x acts ^u e mass ( matt]1 precisely 9 proportion to its quantity2 &1 ?irdly1 t its int5sity is dim9i%$ z ! squ>e ( ! di/ance is increas$4 ,obs]vation has fully confirm$ ! preval5ce ( ?is law ?r\gh\t ! sol> sy/em2 & rec5t discov]ies among ! fix$ />s1 to be m fully detail$ h]eaft]1 indicate t ! same law prevails !re4 ,! law ( univ]sal gravitation is !re=e held to be ! gr& pr9ciple :i* gov]ns all ! cele/ial motions4 ,n only is x consi/5t ) all ! obs]v$ motions ( ! heav5ly bodies1 ev5 ! mo/ irregul> ( ^? motions1 b1 :5 foll[$ out into all its consequ5ces1 x w\ld be compet5t to ass]t t su* irregul>ities mu/ take place1 ev5 if !y _h nev] be5 obs]v$4 ,newton fir/ publi%$ ! doctr9e ( univ]sal gravitation 9 ! ',pr9cipia1' 9 #afhg4 ,! "n implies t ! "w conta9s ! fundam5tal pr9ciples ( natural philosophy & a/ronomy4 ,be+ f\nd$ ^u ! immutable basis ( ma!matics1 its conclusions mu/ ( c\rse be true & unalt]able1 & !nce=? we may reg>d ! great laws ( ! univ]se z trac$ to _! remote/ pr9ciple4 ,! greate/ a/ronom]s & ma!maticians h s9ce occupi$ !mselves 9 foll[+ out ! plan :i* ,newton began1 by apply+ ! pr9ciples ( univ]sal gravitation to all ! subord9ate z well z to ! gr& movem5ts ( ! sph]es4 ,?is great labor has be5 especially a*iev$ by ,la ,place1 a ,fr5* ma!matician ( ! highe/ em95ce1 9 8 pr(\nd "w1 ! ',mecanique ,cele/e4' ,( ?is "w1 our di/+ui%$ c\ntryman1 ,dr4 ,b[dit*1 has giv5 a magnific5t translation1 & accompani$ x ) a comm5t>y1 :i* bo? illu/rates ! orig9al1 & adds a great am\nt ( matt] h>dly less pr(\nd ?an t4 ,illu/ration ,fig4 #ca4 ,we h ?us f> tak5 ! e>?'s orbit ar\nd ! sun z a great circle1 su* be+ its projection on ! sph]e con/itut+ ! cele/ial ecliptic4 ,! real pa? ( ! e>? ar\nd ! sun is le>n$1 z ,i be=e expla9$ to y1 by ! app>5t pa? ( ! sun ar\nd ! e>? once a ye>4 ,n[1 :5 a body revolves ab\t ! e>? at a great di/ance f u1 z is ! case ) ! sun & moon1 we _c c]ta9ly inf] t x moves 9 a circle because x appe>s to describe a circle on ! face ( ! sky1 = su* might be ! appe>ance ( its orbit1 7 x ev] s irregul> a curve4 ,?us1 if ,e1 ,fig4 #ca1 repres5ts ! e>?1 & ,,acb1 ! irregul> pa? ( a body revolv+ ab\t x1 s9ce we %\ld ref] ! body cont9ually to "s place on ! cele/ial sph]e1 ,,xyz1 det]m9$ by l9es drawn f ! eye to ! concave sph]e ?r\gh ! body1 ! body1 :ile mov+ f ,a to ,b ?r\gh ,c1 w\ld appe> to move f ,x to ,z1 ?r\gh ,y4 ,h5ce1 we mu/ det]m9e f o!r circum/ances ?an ! actual appe>ance1 :at is ! true figure ( ! orbit4 ,illu/ration ,fig4 #cb4 ,7 ! e>?'s pa? a circle1 hav+ ! sun 9 ! c5tre1 ! sun w\ld always appe> to be at ! same di/ance f u2 t is1 ! radius ( ! orbit1 or radius vector1 7! "n giv5 to a l9e drawn f ! c5tre ( ! sun to ! orbit ( any planet17 w\ld always be ( ! same l5g?4 ,b ! e>?'s di/ance f ! sun is con/antly v>y+1 :i* %[s t its orbit is n a circle4 ,we le>n ! true figure ( ! orbit1 by asc]ta9+ ! relative di/ances ( ! e>? f ! sun1 at v>i\s p]iods ( ! ye>4 ,^! di/ances all be+ laid d[n 9 a diagram1 accord+ to _! respective l5g?s1 ! extremities1 on be+ connect$1 give u our fir/ idea ( ! %ape ( ! orbit1 :i* appe>s ( an oval =m1 & at lea/ resembles an ellipse2 &1 on fur!r trial1 we f9d t x has ! prop]ties ( an ellipse4 ,?us1 let ,e1 ,fig4 #cb1 be ! place ( ! e>?1 & a1 b1 c1 c41 successive positions ( ! sun2 ! relative l5g?s ( ! l9es ,e a1 ,e b1 c41 be+ kn[n1 on connect+ ! po9ts a1 b1 c1 c41 ! result+ figure indicates ! true figure ( ! e>?'s orbit4 ,^! relative di/ances are f\nd 9 two diff]5t ways2 fir/1 by *anges 9 ! sun's app>5t diamet]1 &1 secondly1 by v>iations 9 8 angul> velocity4 ,! same object appe>s to u small] 9 proportion z x is m di/ant2 & if we see a heav5ly body v>y+ 9 size1 at diff]5t times1 we inf] t x is at diff]5t di/ances f u2 t :5 l>ge/1 x is ne>e/ to u1 & :5 smalle/1 fur!/ (f4 ,n[1 :5 ! sun's diamet] is accurately measur$ by in/rum5ts1 x is f\nd to v>y f day to day2 be+1 :5 greate/1 m ?an ?irty-two m9utes & a half1 & :5 smalle/1 only ?irty-"o m9utes & a half1--diff]+1 9 all1 ab\t sev5ty-five seconds4 ,:5 ! diamet] is greate/1 :i* happ5s 9 ,janu>y1 we "k t ! sun is ne>e/ to u2 & :5 ! diamet] is lea/1 :i* occurs 9 ,july1 we inf] t ! sun is at ! greate/ di/ance f u4 ,! po9t :]e ! e>?1 or any planet1 9 its revolution1 is ne>e/ ! sun1 is call$ its p]ihelion2 ! po9t :]e x is fur!/ f ! sun1 its aphelion4 ,suppose1 !n1 t1 ab\t ! fir/ ( ,janu>y1 :5 ! diamet] ( ! sun is greate/1 we draw a l9e1 ,e a1 ,fig4 #cb1 to repres5t x1 & aft]w>ds1 e t5 days1 draw o!r l9es1 ,e b1 ,e c1 c42 increas+ 9 ! same ratio z ! app>5t diamet]s ( ! sun decrease4 ,^! l9es mu/ be drawn at su* a di/ance f ea* o!r1 t ! triangles1 ,e a b1 ,e b c1 c41 %all be all equal to ea* o!r1 = a reason t w be expla9$ h]eaft]4 ,on connect+ ! extremities ( ^! l9es1 we %all obta9 ! figure ( ! e>?'s orbit4 ,simil> conclusions may be drawn f obs]vations on ! sun's angul> velocity4 ,a body appe>s to move mo/ rapidly :5 ne>e/ to u4 ,inde$1 ! app>5t velocity increases rapidly1 z x approa*es u1 & z rapidly dim9i%es1 :5 x rec$es f u4 ,if x comes twice z ne> z be=e1 x appe>s to move n m]ely twice z swiftly1 b f\r times z swiftly2 if x comes t5 times ne>]1 its app>5t velocity is "o hundr$ times z great z be=e4 ,we say1 !re=e1 t ! velocity v>ies inv]sely z ! squ>e ( ! di/ance2 =1 z ! di/ance is dim9i%$ t5 times1 ! velocity is increas$ ! squ>e ( t52 t is1 "o hundr$ times4 ,n[1 by not+ ! "t x takes ! sun1 f day to day1 to cross ! c5tral wire ( ! transit-in/rum5t1 we le>n ! comp>ative velocities ) :i* x moves at diff]5t times2 & f ^! we d]ive ! comp>ative di/ances ( ! sun at ! correspond+ times2 & lay+ d[n ^! relative di/ances 9 a diagram1 z be=e1 we get our fir/ notions ( ! actual figure ( ! e>?'s orbit1 or ! pa? :i* x describes 9 its annual revolution ar\nd ! sun4 ,hav+ n[ le>n$ ! fact1 t ! e>? moves ar\nd ! sun1 n 9 a circul> b 9 an elliptical orbit1 y w desire to "k by :at =ces x is impell$1 to make x describe ?is figure1 ) su* uni=mity & con/ancy1 f age to age4 ,x is commonly said1 t gravity causes ! e>? & ! planets to circulate ar\nd ! sun2 & x is true t x is gravity :i* turns !m aside f ! /raight l9e 9 :i*1 by ! fir/ law ( motion1 !y t5d to move1 & ?us causes !m to revolve ar\nd ! sun4 ,b :at =ce is t :i* gave to !m ?is orig9al impulse1 & impress$ ^u !m su* a t5d5cy to move =w>d 9 a /raight l9e8 ,! "n projectile =ce is giv5 to x1 because x is ! same z ?\gh ! e>? 7 orig9ally project$ into space1 :5 fir/ creat$2 & !re=e its motion is ! result ( two =ces1 ! projectile =ce1 :i* w\ld cause x to move =w>d 9 a /raight l9e :i* is a tang5t to its orbit1 & gravitation1 :i* b5ds x t[>ds ! sun4 ,b be=e y c cle>ly und]/& ! nature ( ?is motion1 & ! action ( ! two =ces t produce x1 ,i mu/ expla9 to y a few elem5t>y pr9ciples ^u :i* ?is & all ! o!r planet>y motions dep5d4 ,y h already le>n$1 t :5 a body is act$ on by two =ces1 9 diff]5t directions1 x moves 9 ! direction ( nei!r1 b 9 "s direction betwe5 !m4 ,if ,i ?r[ a /one horizontally1 ! attraction ( ! e>? w cont9ually draw x d[nw>d1 out ( ! l9e ( direction 9 :i* x 0 ?r[n1 & make x desc5d to ! e>? 9 a curve4 ,! p>ticul> =m ( ! curve w dep5d on ! velocity ) :i* x is ?r[n4 ,x w always beg9 to move 9 ! l9e ( direction 9 :i* x is project$2 b x w soon be turn$ f t l9e t[>ds ! e>?4 ,x w1 h[ev]1 cont9ue ne>] to ! l9e ( projection 9 proportion z ! velocity ( projection is great]4 ,?us1 let ,a ,c1 ,fig4 #cc1 be p]p5dicul> to ! horizon1 & ,a ,b p>allel to x1 & let a /one be ?r[n f ,a1 9 ! direction ( ,a ,b4 ,x w1 9 e case1 comm5ce its motion 9 ! l9e ,a ,b1 :i* w !re=e be a tang5t to ! curve x describes2 b1 if x is ?r[n ) a small velocity1 x w soon dep>t f ! tang5t1 describ+ ! l9e ,a ,d2 ) a great] velocity1 x w describe a curve ne>] ! tang5t1 z ,a ,e2 & ) a /ill great] velocity1 x w describe ! curve ,a ,f4 ,illu/ration ,fig4 #cc4 ,z an example ( a body revolv+ 9 an orbit "u ! influ5ce ( two =ces1 suppose a body plac$ at any po9t1 ,p1 ,fig4 #cd1 above ! surface ( ! e>?1 & let ,p ,a be ! direction ( ! e>?'s c5tre2 t is1 a l9e p]p5dicul> to ! horizon4 ,if ! body 7 all[$ to move1 )\t receiv+ any impulse1 x w\ld desc5d to ! e>? 9 ! direction ,p ,a ) an accel]at$ motion4 ,b suppose t1 at ! mom5t ( its dep>ture f ,p1 x receives a bl[ 9 ! direction ,p ,b1 :i* w\ld c>ry x to ,b 9 ! "t ! body w\ld fall f ,p to ,a2 !n1 "u ! influ5ce ( bo? =ces1 x w\ld desc5d along ! curve ,p ,d4 ,if a /rong] bl[ 7 giv5 to x 9 ! direction ,p ,b1 x w\ld describe a l>g] curve1 ,p ,e2 or1 f9ally1 if ! impulse 7 suffici5tly /rong1 x w\ld circulate q ar\nd ! e>?1 & return aga9 to ,p1 describ+ ! circle ,p ,f ,g4 ,) a velocity ( projection /ill great]1 x w\ld describe an ellipse1 ,p ,i ,k2 & if ! velocity be increas$ to a c]ta9 degree1 ! figure becomes a p>abola1 ,l ,p ,m1--a curve :i* nev] returns into itself4 ,illu/ration ,fig4 #cd4 ,9 ,fig4 #ce1 page #aed1 suppose ! planet to h pass$ ! po9t ,c1 at ! aphelion1 ) s small a velocity1 t ! attraction ( ! sun b5ds its pa? v mu*1 & causes x imm$iately to beg9 to approa* t[>ds ! sun4 ,! sun's attraction w increase its velocity1 z x moves ?r\gh ,d1 ,e1 & ,f1 = ! sun's attractive =ce on ! planet1 :5 at ,d1 is act+ 9 ! direction ,d ,s2 &1 on acc\nt ( ! small angle made betwe5 ,d ,e & ,d ,s1 ! =ce act+ 9 ! l9e ,d ,s helps ! planet =w>d 9 ! pa? ,d ,e1 & ?us increases its velocity4 ,9 l mann]1 ! velocity ( ! planet w be cont9ually increas+ z x passes ?r\gh ,d1 ,e1 & ,f2 & ?\gh ! attractive =ce1 on acc\nt ( ! planet's ne>ness1 is s mu* increas$1 & t5ds1 !re=e1 to make ! orbit m curv$1 yet ! velocity is also s mu* increas$1 t ! orbit is n m curv$ ?an be=e2 = ! same increase ( velocity1 occasion$ by ! planet's approa* to ! sun1 produces a great] increase ( c5trifugal =ce1 :i* c>ries x (f aga94 ,we may see1 also1 ! reason :y1 :5 ! planet has rea*$ ! mo/ di/ant p>ts ( its orbit1 x does n entirely fly (f1 & nev] return to ! sun2 =1 :5 ! planet passes along ,h1 ,k1 ,a1 ! sun's attraction ret>ds ! planet1 j z gravity ret>ds a ball roll$ up hill2 & :5 x has rea*$ ,c1 its velocity is v small1 & ! attraction to ! c5tre ( =ce causes a great deflection f ! tang5t1 suffici5t to give its orbit a great curvature1 & ! planet :eels ab\t1 returns to ! sun1 & goes ov] ! same orbit aga94 ,z ! planet rec$es f ! sun1 its c5trifugal =ce dim9i%es fa/] ?an ! =ce ( gravity1 s t ! latt] f9ally prepond]ates4 ,illu/ration ,fig4 #ce4 ,i %all conclude :at ,i h to say at pres5t1 respect+ ! motion ( ! e>? ar\nd ! sun1 by add+ a few words respect+ ! precession ( ! equ9oxes4 ,! precession ( ! equ9oxes is a sl[ b cont9ual %ift+ ( ! equ9octial po9ts1 f ea/ to we/4 ,suppose t we m>k ! exact place 9 ! heav5s :]e1 dur+ ! pres5t ye>1 ! sun crosses ! equator1 & t ?is po9t is close to a c]ta9 />2 next ye>1 ! sun w cross ! equator a little way we/w>d ( t />1 & s e ye>1 a little fur!r we/w>d1 until1 9 a long c\rse ( ages1 ! place ( ! equ9ox w occupy successively e "p ( ! ecliptic1 until we come r\nd to ! same /> aga94 ,z1 !re=e1 ! sun revolv+ f we/ to ea/1 9 8 app>5t orbit1 comes r\nd to ! po9t :]e x left ! equ9ox1 x meets ! equ9ox be=e x rea*es t po9t4 ,! appe>ance is z ?\gh ! equ9ox goes =w>d to meet ! sun1 & h5ce ! ph5om5on is call$ ! precession ( ! equ9oxes2 & ! fact is express$ by say+1 t ! equ9oxes retrograde on ! ecliptic1 until ! l9e ( ! equ9oxes 7a /raight l9e drawn f "o equ9ox to ! o!r7 makes a complete revolution1 f ea/ to we/4 ,?is is ( c\rse a retrograde motion1 s9ce x is contr>y to ! ord] ( ! signs4 ,! equator is conceiv$ z slid+ we/w>d on ! ecliptic1 always pres]v+ ! same incl9ation to x1 z a r+1 plac$ at a small angle ) ano!r ( ne>ly ! same size :i* rema9s fix$1 may be slid q ar\nd x1 giv+ a correspond+ motion to ! two po9ts ( int]section4 ,x mu/ be obs]v$1 h[ev]1 t ?is mode ( conceiv+ ( ! precession ( ! equ9oxes is purely imag9>y1 & is employ$ m]ely = ! conv5i5ce ( repres5tation4 ,! am\nt ( precession annually is fifty seconds & "o t5?2 :5ce1 s9ce !re are ?irty-six hundr$ seconds 9 a degree1 & ?ree hundr$ & sixty degrees 9 ! :ole circumf]5ce ( ! ecliptic1 & consequ5tly "o million two hundr$ & n9ety-six ?\s& seconds1 ?is sum1 divid$ by fifty seconds & "o t5?1 gives tw5ty-five ?\s& eight hundr$ & sixty-eight ye>s = ! p]iod ( a complete revolution ( ! equ9oxes4 ,suppose we n[ fix to ! c5tre ( ea* ( ! two r+s1 be=e m5tion$1 a wire repres5t+ its axis1 "o correspond+ to ! axis ( ! ecliptic1 ! o!r to t ( ! equator1 ! extremity ( ea* be+ ! pole ( its circle4 ,z ! r+ d5ot+ ! equator turns r\nd on ! ecliptic1 :i*1 ) its axis1 rema9s fix$1 x is easy to conceive t ! axis ( ! equator revolves ar\nd t ( ! ecliptic1 & ! pole ( ! equator ar\nd ! pole ( ! ecliptic1 & con/antly at a di/ance equal to ! incl9ation ( ! two circles4 ,to transf] our conceptions to ! cele/ial sph]e1 we may easily see t ! axis ( ! diurnal sph]e 7t ( ! e>? produc$7 w\ld n h its pole con/antly 9 ! same place among ! />s1 b t ?is pole w\ld p]=m a sl[ revolution ar\nd ! pole ( ! ecliptic1 f ea/ to we/1 complet+ ! circuit 9 ab\t tw5ty-six ?\s& ye>s4 ,h5ce ! /> :i* we n[ call ! pole-/> has n always enjoy$ t di/9ction1 nor w x always enjoy x1 h]eaft]4 ,:5 ! e>lie/ catalogues ( ! />s 7 made1 ?is /> 0 twelve degrees f ! pole4 ,x is n[ "o degree tw5ty-f\r m9utes1 & w approa* /ill ne>]2 or1 to speak m accurately1 ! pole w come /ill ne>] to ?is />1 aft] :i* x w leave x1 & successively pass by o!rs4 ,9 ab\t ?irte5 ?\s& ye>s1 ! bright /> ,lyra 7:i* lies ne> ! circle 9 :i* ! pole ( ! equator revolves ab\t ! pole ( ! ecliptic1 on ! side opposite to ! pres5t pole-/>7 w be )9 five degrees ( ! pole1 & w con/itute ! pole-/>4 ,z ,lyra n[ passes ne> our z5i?1 y might suppose t ! *ange ( position ( ! pole among ! />s w\ld be att5d$ ) a *ange ( altitude ( ! nor? pole above ! horizon4 ,?is mi/ak5 idea is "o ( ! _m misappreh5sions :i* result f ! habit ( consid]+ ! horizon z a fix$ circle 9 space4 ,h[ev] ! pole might %ift its position 9 space1 we %\ld /ill be at ! same di/ance f x1 & our horizon w\ld always rea* ! same di/ance beyond x4 ,! "t occupi$ by ! sun1 9 pass+ f ! equ9octial po9t r\nd to ! same po9t aga91 is call$ ! tropical ye>4 ,z ! sun does n p]=m a complete revolution 9 ?is int]val1 b falls %ort ( x fifty seconds & "o t5?1 ! tropical ye> is %ort] ?an ! sid]eal by tw5ty m9utes & tw5ty seconds1 9 mean sol> "t1 ?is be+ ! "t ( describ+ an arc ( fifty seconds & "o t5?1 9 ! annual revolution4 ,! *anges produc$ by ! precession ( ! equ9oxes1 9 ! app>5t places ( ! circumpol> />s1 h l$ to "s int]e/+ results 9 *ronology4 ,9 consequ5ce ( ! retrograde motion ( ! equ9octial po9ts1 ! signs ( ! ecliptic d n correspond1 at pres5t1 to ! con/ellations :i* be> ! same names1 b lie ab\t "o sign1 or ?irty degrees1 we/w>d ( !m4 ,?us1 t division ( ! ecliptic :i* is call$ ! sign ,taurus lies 9 ! con/ellation ,aries1 & ! sign ,gem9i1 9 ! con/ellation ,taurus4 ,und\bt$ly1 h[ev]1 :5 ! ecliptic 0 ?us fir/ divid$1 & ! divisions nam$1 ! sev]al con/ellations lay 9 ! respective divisions :i* be> _! names4 ,,lett] ,,xv4 ,,! ,,moon4 ,soon z ! ev5+ %ades prevail ,! ,moon takes up ! wondr\s tale1 ,& nightly to ! li/5+ e>? ,repeats ! /ory ( h] bir?4--,addison4 ,,hav+ n[ le>n$ s mu* ( a/ronomy z relates to ! e>? & ! sun1 & ! mutual relations :i* exi/ betwe5 !m1 y are prep>$ to ent] ) advantage ^u ! survey ( ! o!r bodies t compose ! sol> sy/em4 ,?is be+ done1 we %all !n h /ill be=e u ! b\ndless range ( ! fix$ />s4 ,! moon1 :i* next claims our notice1 has be5 /udi$ by a/ronom]s ) great] att5tion ?an any o!r ( ! heav5ly bodies1 s9ce h] comp>ative ne>ness to ! e>? br+s h] peculi>ly )9 ! range ( our telescopes1 & h] p]iodical *anges & v irregul> motions1 af=d curi\s subjects1 bo? = obs]vation & speculation4 ,! mild light ( ! moon also invites our gaze1 :ile h] v>y+ aspects s]ve b>b>\s tribes1 especially1 = a k9d ( dial-plate inscrib$ on ! face ( ! sky1 = weeks1 & mon?s1 & times1 & seasons4 ,! moon is di/ant f ! e>? ab\t two hundr$ & =ty ?\s& miles2 or1 m exactly1 two hundr$ & ?irty-eight ?\s& five hundr$ & =ty-five miles4 ,h] angul> or app>5t diamet] is ab\t half a degree1 & h] real diamet]1 two ?\s& "o hundr$ & sixty miles4 ,%e is a companion1 or satellite1 to ! e>?1 revolv+ ar\nd x e mon?1 & accompany+ u 9 our annual revolution ar\nd ! sun4 ,al?\gh h] ne>ness to u makes h] appe> z a l>ge & conspicu\s object 9 ! heav5s1 yet1 9 comp>ison ) mo/ ( ! o!r cele/ial bodies1 %e is 9 fact v small1 be+ only "o =ty-n9? "p z l>ge z ! e>?1 & only ab\t "o sev5ty million? "p z l>ge z ! sun4 ,! moon %9es by light borr[$ f ! sun1 be+ itself an opaque body1 l ! e>?4 ,:5 ! disk1 or any portion ( x1 is illum9at$1 we c pla9ly disc]n1 ev5 ) ! nak$ eye1 v>ieties ( light & %ade1 indicat+ inequalities ( surface :i* we imag9e to be l& & wat]4 ,i believe x is ! common impression1 t ! d>k] portions are l& & ! light] portions wat]2 b if ei!r "p is wat]1 x mu/ be ! d>k] regions4 ,a smoo? poli%$ surface1 l wat]1 w\ld reflect ! sun's light l a mirror4 ,x w\ld1 l a convex mirror1 =m a dim9i%$ image ( ! sun1 b w\ld n itself appe> lum9\s l an unev5 surface1 :i* multiplies ! light by num]\s reflections )9 itself4 ,?us1 f ?is cause1 high brok5 m\nta9\s di/ricts appe> m lum9\s ?an ext5sive pla9s4 ,illu/ration ,figures #cf1 #cg4 ,,telescopic ,,views ,,( ,,! ,,moon4 ,by ! aid ( ! telescope1 we may see und\bt$ indications ( m\nta9s & valleys4 ,inde$1 ) a good glass1 we c discov] ! mo/ decisive evid5ce t ! surface ( ! moon is exce$+ly v>i$1--"o "p asc5d+ 9 l(ty peaks1 ano!r clu/]+ 9 huge m\nta9 gr\ps1 or long ranges1 & ano!r be>+ all ! m>ks ( deep cav]ns or valleys4 ,y w n1 inde$1 at ! fir/ sight ( ! moon ?r\gh a telescope1 recognise all ^! diff]5t objects4 ,if y look at ! moon :5 half h] disk is enlight5$1 7:i* is ! be/ "t = see+ h] v>ieties ( surface17 y w1 at ! fir/ glance1 obs]ve a motley appe>ance1 p>ticul>ly along ! l9e call$ ! t]m9ator1 :i* sep>ates ! enlight5$ f ! un5light5$ "p ( ! disk4 7,fig4 #cg47 ,on "o side ( ! t]m9ator1 )9 ! d>k "p ( ! disk1 y w see illum9at$ po9ts1 & %ort1 crook$ l9es1 l rude *>act]s m>k$ ) *alk on a black gr\nd4 ,on ! o!r side ( ! t]m9ator y w see a succession ( little circul> gr\ps1 appe>+ l num]\s bubbles ( oil on ! surface ( wat]4 ,! fur!r y c>ry y\r eye f ! t]m9ator1 on ! same side ( x1 ! m indi/9ctly =m$ ^! bubbles appe>1 until t[>ds ! edge ( ! moon !y assume q a diff]5t aspect4 ,"s p]sons1 :5 !y look into a telescope = ! fir/ "t1 hav+ he>d t m\nta9s & valleys are to be se51 & discov]+ no?+ b ^! unmean+ figures1 break (f 9 disappo9tm5t1 & h _! fai? 9 ^! ?+s r dim9i%$ ?an increas$4 ,i w\ld advise y1 !re=e1 be=e y take ev5 y\r fir/ view ( ! moon ?r\gh a telescope1 to =m z cle> an idea z y c1 h[ m\nta9s1 & valleys1 & cav]ns1 situat$ at su* a di/ance f ! eye1 ought to look1 & by :at m>ks !y may be recognis$4 ,seize1 if possible1 ! mo/ favorable p]iod1 7ab\t ! "t ( ! fir/ qu>t]17 & previ\sly le>n f draw+s & explanations1 h[ to int]pret e ?+ y see4 ,:at1 !n1 ought to be ! respective appe>ances ( m\nta9s1 valleys1 & deep crat]s1 or cav]ns1 9 ! moon8 ,! sun %9es on ! moon 9 ! same way z x %9es on ! e>?2 & let1 u reflect1 !n1 ^u ! mann] 9 :i* x /rikes simil> objects "h4 ,"o half ! globe is con/antly enlight5$2 &1 by ! revolution ( ! e>? on its axis1 ! t]m9ator1 or ! l9e :i* sep>ates ! enlight5$ f ! un5light5$ "p ( ! e>?1 travels along f ea/ to we/1 ov] diff]5t places1 z we see ! moon's t]m9ator travel ov] h] disk f new to full moon2 al?\gh1 9 ! case ( ! e>?1 ! motion is m rapid1 & dep5ds on a diff]5t cause4 ,9 ! morn+1 ! sun's light fir/ /rikes ^u ! tops ( ! m\nta9s1 &1 if !y are v high1 !y may be brightly illum9at$ :ile x is yet night 9 ! valleys bel[4 ,by degrees1 z ! sun rises1 ! circle ( illum9ation travels d[n ! m\nta91 until at l5g? x rea*es ! bottom ( ! valleys2 & ^! 9 turn enjoy ! full light ( day4 ,aga91 a m\nta9 ca/s a %ad[ opposite to ! sun1 :i* is v long :5 ! sun fir/ rises1 & %ort5s cont9ually z ! sun asc5ds1 its l5g? at a giv5 "t1 h[ev]1 be+ proportion$ to ! height ( ! m\nta92 s t1 if ! %ad[ be /ill v long :5 ! sun is f> above ! horizon1 we inf] t ! m\nta9 is v l(ty4 ,we may1 moreov]1 =m "s judgm5t ( ! %ape ( a m\nta91 by obs]v+ t ( its %ad[4 ,n[1 ! moon is s di/ant t we c\ld n easily di/+ui% places simply by _! elevations1 s9ce !y w\ld be project$ into ! same imag9>y plane :i* con/itutes ! app>5t disk ( ! moon2 b ! =ego+ consid]ations w\ld enable u to inf] _! exi/5ce4 ,?us1 :5 y view ! moon at any "t )9 h] fir/ qu>t]1 b bett] ne> ! end ( t p]iod1 y w obs]ve1 on ! side ( ! t]m9ator )9 ! d>k "p ( ! disk1 ! tops ( m\nta9s :i* ! light ( ! sun is j /rik+1 z ! morn+ sun /rikes ! tops ( m\nta9s on ! e>?4 ,^! y w recognise by ^? :ite specks & little crook$ l9es1 be=e m5tion$1 z is repres5t$ 9 ,fig4 #cg4 ,^! bright po9ts & l9es y w see alt]+ _! figure1 e h\r1 z !y come m & m into ! sun's light2 &1 mean-:ile1 o!r bright po9ts1 v m9ute at fir/1 w />t into view1 :i* also 9 turn gr[ l>g] z ! t]m9ator approa*es !m1 until !y fall into ! enlight5$ "p ( ! disk4 ,z !y fall fur!r & fur!r )9 ?is "p1 y w h additional pro(s t !y are m\nta9s1 f ! %ad[s :i* !y ca/ on ! pla91 always 9 a direction opposite to ! sun4 ,! m\nta9 itself may entirely disappe>1 or become conf\nd$ ) ! o!r enlight5$ portions ( ! surface2 b its position & its %ape may /ill be recognis$ by ! d>k l9e :i* x projects on ! plane4 ,?is l9e w correspond 9 %ape to t ( ! m\nta91 pres5t+ at "o "t a long s]p5t9e /ripe ( black1 d5ot+ t ! m\nta9 is a cont9u$ range2 at ano!r "t exhibit+ a conical figure tap]+ to a po9t1 or a s]ies ( su* %>p po9ts2 or a s]rat$1 unev5 t]m9ation1 indicat+1 9 ea* case respectively1 a conical m\nta91 or a gr\p ( peaks1 or a range ) l(ty cliffs4 ,all ^! appe>ances w inde$ be se5 9 m9iature2 b a little famili>ity ) !m w enable y to give !m1 9 imag9ation1 _! prop] dim5sions1 z y give to ! pictures ( kn[n animals _! due sizes1 al?\gh drawn on a scale f> bel[ t ( real life4 ,9 ! next place1 let u see h[ valleys & deep crat]s 9 ! moon might be expect$ to appe>4 ,we c\ld n expect to see depressions any m ?an elevations1 s9ce bo? w\ld alike be project$ on ! same imag9>y disk4 ,b we may recognise su* depressions1 f ! mann] 9 :i* ! light ( ! sun %9es into !m4 ,:5 we hold a *9a tea-cup at "s di/ance f a c&le1 9 ! night1 ! c&le be+ elevat$ b little above ! level ( ! top ( ! cup1 a lum9\s cresc5t w be =m$ on ! side ( ! cup opposite to ! c&le1 :ile ! side next to ! c&le w be cov]$ by a deep %ad[4 ,z we gradually elevate ! c&le1 ! cresc5t enl>ges & travels d[n ! side ( ! cup1 until f9ally ! :ole int]ior becomes illum9at$4 ,we obs]ve simil> appe>ances 9 ! moon1 :i* we recognise z deep depressions4 ,!y are ^? circul> spots ne> ! t]m9ator be=e spok5 (1 :i* look l bubbles ( oil float+ on wat]4 ,!y are no?+ else ?an circul> crat]s or deep valleys4 ,:5 !y are s situat$ t ! light ( ! sun is j beg9n+ to %9e into !m1 y may see1 z 9 ! tea-cup1 a lum9\s cresc5t ar\nd ! side fur!/ f ! sun1 :ile a deep black %ad[ is ca/ on ! side next to ! sun4 ,z ! cavity is turn$ m & m t[>ds ! light1 ! cresc5t enl>ges1 until at l5g? ! :ole int]ior is illum9at$4 ,if ! tea-cup be plac$ on a table1 & a c&le be held at "s di/ance f x1 ne>ly on a level ) ! top1 b a little above x1 ! cup itself w ca/ a %ad[ on ! table1 l any o!r elevat$ object4 ,9 l mann]1 _m ( ^! circul> spots on ! moon ca/ deep %ad[s beh9d !m1 indicat+ t ! tops ( ! crat]s are elevat$ f> above ! g5]al level ( ! moon4 ,! regul>ity ( "s ( ^! circul> spots is v rem>kable4 ,! circle1 9 "s in/ances1 appe>s z well =m$ z c\ld be describ$ by a pair ( compasses1 :ile 9 ! c5tre !re n unfrequ5tly is se5 a conical m\nta9 ca/+ its po9t$ %ad[ on ! bottom ( ! crat]4 ,i hope y w enjoy repeat$ opportunities to view ! moon ?r\gh a telescope4 ,all[ me to recomm5d to y1 n to re/ satisfi$ ) a ha/y or ev5 ) a s+le view1 b to v]ify ! prec$+ rem>ks by repeat$ & c>eful inspection ( ! lun> disk1 at diff]5t ages ( ! moon4 ,! v>i\s places on ! moon's disk h receiv$ appropriate names4 ,! dusky regions be+ =m]ly suppos$ to be seas1 7 nam$ accord+ly2 & o!r rem>kable places h ea* two names1 "o d]iv$ f "s well-kn[n spot on ! e>?1 & ! o!r f "s di/+ui%$ p]sonage4 ,?us1 ! same bright spot on ! surface ( ! moon is call$ ,m\nt ,s9ai or ,ty*o1 & ano!r1 ,m\nt ,etna or ,cop]nicus4 ,! names ( individuals1 h[ev]1 are m us$ ?an ! o!rs4 ,! diagram1 ,fig4 #cf1 7see page #aei17 repres5ts rudely1 ! telescopic appe>ance ( ! full moon4 ,! reality is f> m beautiful4 ,a few ( ! mo/ rem>kable po9ts h ! foll[+ names correspond+ to ! numb]s & lett]s on ! map4 #a4 ,ty*o1 #f4 ,erato/h5es1 #b4 ,kepl]1 #g4 ,plato1 #c4 ,cop]nicus1 #h4 ,ar*im$es1 #d4 ,ari/>*us1 #i4 ,eudoxus1 #e4 ,helicon1 #aj4 ,ari/otle4 ,a4 ,m>e ,humorum1 ,sea ( ,humors1 ,b4 ,m>e ,nubium1 ,sea ( ,cl\ds1 ,c4 ,m>e ,imbrium1 ,sea ( ,ra9s1 ,d4 ,m>e ,nect>is1 ,sea ( ,nect>1 ,e4 ,m>e ,tranquillitatis1 ,sea ( ,tranquillity1 ,f4 ,m>e ,s]5itatis1 ,sea ( ,s]5ity1 ,g4 ,m>e ,fecunditatis1 ,sea ( ,pl5ty1 ,h4 ,m>e ,crisium1 ,crisian ,sea4 ,! heights ( ! lun> m\nta9s1 & ! dep?s ( ! valleys1 c be e/imat$ ) a consid]able degree ( accuracy4 ,"s ( ! m\nta9s are z high z five miles1 & ! valleys1 9 "s in/ances1 are f\r miles deep4 ,h5ce x is inf]r$1 t ! surface ( ! moon is m brok5 & irregul> ?an t ( ! e>?1 its m\nta9s be+ high] & its valleys deep]1 9 proportion to its magnitude1 ?an ^? ( ! e>?4 ,! v>ieties ( surface 9 ! moon1 z se5 by ! aid ( l>ge telescopes1 h be5 well describ$ by ,dr4 ,dick1 9 8 ',cele/ial ,sc5]y1' & ,i _c give y a bett] idea ( !m1 ?an to add a few extracts f 8 "w4 ,! lun> m\nta9s 9 g5]al exhibit an arrangem5t & an aspect v diff]5t f ! m\nta9 sc5]y ( our globe4 ,!y may be arrang$ "u ! f\r foll[+ v>ieties3 ,fir/1 insulat$ m\nta9s1 :i* rise f pla9s ne>ly level1 %ap$ l a sug> loaf1 :i* may be suppos$ to pres5t an appe>ance some:at simil> to ,m\nt ,etna1 or ! ,peak ( ,t5]iffe4 ,! %ad[s ( ^! m\nta9s1 9 c]ta9 phases ( ! moon1 are z di/9ctly p]ceiv$ z ! %ad[ ( an upright /aff1 :5 plac$ opposite to ! sun2 & ^! heights c be calculat$ f ! l5g? ( _! %ad[s4 ,"s ( ^! m\nta9s be+ elevat$ 9 ! mid/ ( ext5sive pla9s1 w\ld pres5t to a spectator on _! summits magnific5t views ( ! surr\nd+ regions4 ,secondly1 m\nta9 ranges1 ext5d+ 9 l5g? two or ?ree hundr$ miles4 ,^! ranges be> a di/ant resemblance to our ,alps1 ,ap5n9es1 & ,&es2 b !y are mu* less 9 ext5t4 ,"s ( !m appe> v rugg$ & precipit\s2 & ! highe/ ranges are 9 "s places m ?an f\r miles 9 p]p5dicul> altitude4 ,9 "s in/ances1 !y are ne>ly 9 a /raight l9e f nor!a/ to s\?we/1 z 9 ! range call$ ! ,ap5n9es2 9 o!r cases1 !y assume ! =m ( a semicircle1 or cresc5t4 ,?irdly1 circul> ranges1 :i* appe> on almo/ e "p ( ! moon's surface1 p>ticul>ly 9 its s\!rn regions4 ,?is is "o gr& peculi>ity ( ! lun> ranges1 to :i* we h no?+ simil> on ! e>?4 ,a pla91 & sometimes a l>ge cavity1 is surr\nd$ ) a circul> ridge ( m\nta9s1 :i* encompasses x l a mighty ramp>t4 ,^! annul> ridges & pla9s are ( all dim5sions1 f a mile to =ty or fifty miles 9 diamet]1 & are to be se5 9 great numb]s ov] e region ( ! moon's surface2 !y are mo/ conspicu\s1 h[ev]1 ne> ! upp] & l[] limbs1 ab\t ! "t ( ! half moon4 ,! m\nta9s :i* =m ^! circul> ridges are ( diff]5t elevations1 f "o fif? ( a mile to ?ree miles & a half1 & _! %ad[s cov] "o half ( ! pla9 at ! base4 ,^! pla9s are sometimes on a level ) ! g5]al surface ( ! moon1 & 9 o!r cases !y are sunk a mile or m bel[ ! level ( ! gr\nd :i* surr\nds ! ext]ior circle ( ! m\nta9s4 ,f\r?ly1 c5tral m\nta9s1 or ^? :i* are plac$ 9 ! middle ( circul> pla9s4 ,9 _m ( ! pla9s & cavities surr\nd$ by circul> ranges ( m\nta9s !re /&s a s+le insulat$ m\nta91 :i* rises f ! c5tre ( ! pla91 & ^: %ad[ sometimes ext5ds1 9 ! =m ( a pyramid1 half across ! pla9 to ! opposite ridges4 ,^! c5tral m\nta9s are g5]ally f half a mile to a mile & a half 9 p]p5dicul> altitude4 ,9 "s in/ances1 !y h two1 & sometimes ?ree1 diff]5t tops1 ^: %ad[s c be easily di/+ui%$ f ea* o!r4 ,sometimes !y are situat$ t[>ds "o side ( ! pla91 or cavity2 b 9 ! great majority ( in/ances _! position is ne>ly or exactly c5tral4 ,! l5g?s ( _! bases v>y f five to ab\t fifte5 or sixte5 miles4 ,! lun> cav]ns =m a v peculi> & prom95t feature ( ! moon's surface1 & are to be se5 ?r\gh\t almo/ e region1 b are mo/ num]\s 9 ! s\?we/ "p ( ! moon4 ,ne>ly a hundr$ ( !m1 great & small1 may be di/+ui%$ 9 t qu>t]4 ,!y are all ne>ly ( a circul> %ape1 & appe> l a v %all[ egg-cup4 ,! small] cavities appe>1 )91 almo/ l a holl[ cone1 ) ! sides tap]+ t[>ds ! c5tre2 b ! l>g] ones h1 = ! mo/ "p1 flat bottoms1 f ! c5tre ( :i* !re frequ5tly rises a small1 /eep1 conical hill1 :i* gives !m a resemblance to ! circul> ridges & c5tral m\nta9s be=e describ$4 ,9 "s in/ances1 _! m>g9s are level ) ! g5]al surface ( ! moon2 b1 9 mo/ cases1 !y are encircl$ ) a high annul> ridge ( m\nta9s1 m>k$ ) l(ty peaks4 ,"s ( ! l>g] ( ^! cavities conta9 small] cavities ( ! same k9d & =m1 p>ticul>ly 9 _! sides4 ,! m\nta9\s ridges :i* surr\nd ^! cavities reflect ! greate/ quantity ( light2 & h5ce t region ( ! moon 9 :i* !y ab\nd appe>s bright] ?an any o!r4 ,f _! ly+ 9 e possible direction1 !y appe>1 at & ne> ! "t ( full moon1 l a numb] ( brilliant /reaks1 or radiations4 ,^! radiations appe> to conv]ge t[>ds a l>ge brilliant spot1 surr\nd$ by a fa9t %ade1 ne> ! l[] "p ( ! moon1 :i* is nam$ ,ty*o1--a spot easily di/+ui%$ ev5 by a small telescope4 ,! spots nam$ ,kepl] & ,cop]nicus are ea* compos$ ( a c5tral spot ) lum9\s radiations4#h ,! brok5 surface & app>5t geological /ructure ( ! moon has sugge/$ ! op9ion1 t ! moon has be5 subject to p[]ful volcanic action4 ,?is op9ion receives support f c]ta9 actual appe>ances ( volcanic fires1 :i* h at diff]5t times be5 obs]v$4 ,9 a total eclipse ( ! sun1 ! moon comes directly betwe5 u & t lum9>y1 & pres5ts h] d>k side t[>ds u "u circum/ances v favorable = obs]vation4 ,at su* times1 sev]al a/ronom]s1 at diff]5t p]iods1 h notic$ bright spots1 :i* !y took to be volcanoes4 ,x mu/ evid5tly require a l>ge fire to be visible at all1 at su* a di/ance2 & ev5 a burn+ sp>k1 or po9t b j visible 9 a l>ge telescope1 might be 9 fact a volcano rag+ l ,etna or ,vesuvius4 ,/ill1 z fires might be suppos$ to exi/ 9 ! moon f diff]5t causes1 we %\ld require "s m>ks peculi> to volcanic fires1 to assure u t su* 0 _! orig9 9 a giv5 case4 ,dr4 ,h]s*el exam9$ ?is po9t ) great att5tion1 & ) bett] means ( obs]vation ?an any ( 8 pr$ecessors enjoy$1 & fully embrac$ ! op9ion t :at he saw 7 volcanoes4 ,9 ,april1 #aghg1 he records 8 obs]vations z foll[s3 ,i p]ceive ?ree volcanoes 9 diff]5t places 9 ! d>k "p ( ! moon4 ,two ( !m are already ne>ly ext9ct1 or o!rwise 9 a /ate ( go+ to break out2 ! ?ird %[s an eruption ( fire or lum9\s matt]4 ,on ! next night1 he says3 ,! volcano burns ) great] viol5ce ?an la/ night2 its diamet] _c be less ?an ?ree seconds2 & h5ce ! %9+ or burn+ matt] mu/ be above ?ree miles 9 diamet]4 ,! appe>ance resembles a small piece ( burn+ *>coal1 :5 x is cov]$ ) a v ?9 coat ( :ite a%es2 & x has a degree ( brightness ab\t z /rong z t ) :i* su* a coal w\ld be se5 to gl[ 9 fa9t daylight4 ,t ^! 7 really volcanic fires1 he consid]$ fur!r evid5t f ! fact1 t :]e a fire1 suppos$ to h be5 volcanic1 _h be5 burn+1 !re 0 se51 aft] its ext9ction1 an accumulation ( matt]1 su* z w\ld arise f ! production ( a great quantity ( lava1 suffici5t to =m a m\nta94 ,x is probable t ! moon has an atmosph]e1 al?\gh x is difficult to obta9 p]fectly satisfactory evid5ce ( its exi/5ce2 = grant+ ! exi/5ce ( an atmosph]e be>+ ! same proportion to t planet z our atmosph]e be>s to ! e>?1 its dim5sions & its d5sity w\ld be s small1 t we c\ld detect its pres5ce only by ! mo/ ref9$ obs]vations4 ,z our twilight is ow+ to ! ag5cy ( our atmosph]e1 s1 c\ld we disc]n any appe>ance ( twilight 9 ! moon1 we %\ld reg>d t fact z indicat+ t %e is surr\nd$ by an atmosph]e4 ,or1 :5 ! moon cov]s ! sun 9 a sol> eclipse1 c\ld we see ar\nd h] circumf]5ce a fa9t lum9\s r+1 indicat+ t ! sunlight %one ?r\gh an a]ial m$ium1 we might likewise inf] ! exi/5ce ( su* a m$ium4 ,su* a fa9t r+ ( light has sometimes1 z is suppos$1 be5 obs]v$4 ,s*roet]1 a ,g]man a/ronom]1 di/+ui%$ = ! acut5ess ( 8 vision & 8 p[]s ( obs]vation 9 g5]al1 0 v confid5t ( hav+ obta9$1 f diff]5t s\rces1 cle> evid5ce ( a lun> atmosph]e4 ,he conclud$1 t ! inf]ior or m d5se "p ( ! moon's atmosph]e is n m ?an fifte5 hundr$ feet high1 & t ! entire height1 at lea/ to ! limit :]e x w\ld be too r>e to produce any ( ! ph5om5a :i* are reli$ on z pro(s ( its exi/5ce1 is n m ?an a mile4 ,x has be5 a "q1 mu* agitat$ among a/ronom]s1 :e!r !re is wat] 9 ! moon4 ,analogy /rongly incl9es u to reply 9 ! affirmative4 ,b ! analogy betwe5 ! e>? & ! moon1 z d]iv$ f all ! p>ticul>s 9 :i* we c comp>e ! two bodies1 is too feeble to w>rant su* a conclusion1 & we mu/ h rec\rse to o!r evid5ce1 be=e we c decide ! po9t4 ,9 ! fir/ place1 !n1 !re is no positive evid5ce 9 favor ( ! exi/5ce ( wat] 9 ! moon4 ,^? ext5sive level regions1 be=e spok5 (1 & d5om9at$ seas 9 ! geography ( ?is planet1 h no o!r signs ( be+ wat]1 except t !y are level & d>k4 ,b bo? ^! p>ticul>s w\ld *>act]ize an e>?ly pla91 l ! des]ts ( ,arabia & ,africa4 ,9 ! second place1 7 ^? d>k regions compos$ ( wat]1 ! t]m9ator w\ld be entirely smoo? :]e x pass$ ov] ^! oceans or seas4 ,x is inde$ ind5t$ by few inequalities1 comp>$ ) ^? :i* x exhibits :]e x passes ov] ! m\nta9\s regions2 b /ill1 ! inequalities are too consid]able to p]mit ! conclusion1 t ^! level spots are su* p]fect levels z wat] w\ld =m4 ,!y d n appe> to be m p]fect levels ?an _m pla9 c\ntries on ! globe4 ,! deep cav]ns1 moreov]1 se5 9 ^? dusky spots :i* 7 suppos$ to be seas1 are unfavorable to ! supposition t ^? regions are cov]$ by wat]4 ,9 ! ?ird place1 ! face ( ! moon1 :5 illum9at$ by ! sun & n obscur$ by ! /ate ( our own atmosph]e1 is always s]5e1 & !re=e free f cl\ds4 ,cl\ds are objects ( great ext5t2 !y frequ5tly int]cept light1 l solid bodies2 & did !y exi/ ab\t ! moon1 we %\ld c]ta9ly see !m1 & %\ld lose sight ( c]ta9 p>ts ( ! lun> disk :i* !y cov]$4 ,b nei!r position is true2 we nei!r see any cl\ds ab\t ! moon1 ) our be/ telescopes1 nor d we1 by ! int]v5tion ( cl\ds1 ev] lose sight ( any portion ( ! moon :5 our own atmosph]e is cle>4 ,b ! want ( cl\ds 9 ! lun> atmosph]e almo/ necess>ily implies ! abs5ce ( wat] 9 ! moon4 ,?is planet is at ! same di/ance f ! sun z our own1 & has1 9 ?is respect1 an equal opportunity to feel ! influ5ce ( 8 rays4 ,its days are also tw5ty-sev5 times z long z ours1 a circum/ance :i* w\ld augm5t ! sol> heat4 ,:5 ! pressure ( ! atmosph]e is dim9i%$ on ! surface ( wat]1 its t5d5cy to pass into ! /ate ( vapor is increas$4 ,7 ! :ole pressure ( ! atmosph]e remov$ f ! surface ( a lake1 9 a ,summ]'s day1 :5 ! temp]ature 0 no high] ?an sev5ty-two degrees1 ! wat] w\ld beg9 to boil4 ,n[ x is well asc]ta9$1 t if !re be any atmosph]e ab\t ! moon1 x is mu* light] ?an ours1 & presses on ! surface ( t body ) a proportionally small =ce4 ,?is circum/ance1 !re=e1 w\ld conspire ) ! o!r causes m5tion$1 to conv]t all ! wat] ( ! moon into vapor1 if we c\ld suppose x to h exi/$ at any giv5 "t4 ,b ^?1 :o are anxi\s to furni% ! moon & o!r planets ) all ! accommodations :i* !y f9d 9 our own1 h a subt]fuge 9 read9ess1 to :i* !y inv>iably resort 9 all cases l ! =ego+4 ,!re may be1 say !y1 "s means1 unkn[n to u1 provid$ = reta9+ wat] on ! surface ( ! moon1 & = prev5t+ its be+ wa/$ by evaporation3 p]haps x rema9s unalt]$ 9 quantity1 imp>t+ to ! lun> regions p]petual v]dure & f]tility4 ,to ?is ,i reply1 t ! b>e possibility ( a ?+ is b slight evid5ce ( its reality2 nor is su* a condition possible1 except by miracle4 ,if !y grant t ! laws ( ,nature are ! same 9 ! moon z 9 ! e>?1 !n1 accord+ to ! =ego+ reason+1 !re _c be wat] 9 ! moon2 b if !y say t ! laws ( ,nature are n ! same !re z "h1 !n we _c reason at all respect+ !m4 ,"o :o resorts to a subt]fuge ( ?is k9d ru9s 8 own cause4 ,he argues ! exi/5ce ( wat] 9 ! moon1 f ! analogy ( t planet to ?is4 ,b if ! laws ( ,nature are n ! same !re z "h1 :at becomes ( 8 analogy8 ,a liquid sub/ance :i* w\ld n evaporate by su* a degree ( sol> heat z falls on ! moon1 :i* w\ld n evaporate ! fa/]1 9 consequ5ce ( ! dim9i%$ atmosph]ic pressure :i* prevails !re1 c\ld n be wat]1 = x w\ld n h ! prop]ties ( wat]1 & ?+s are kn[n by _! prop]ties4 ,:5ev] we des]t ! c>d9al pr9ciple ( ! ,newtonian philosophy1--t ! laws ( ,nature are uni=m ?r\gh\t all h] realms1--we w&] 9 a labyr9?2 all analogies are made void2 all physical reason+s cease2 & imag9>y possibilities or direct miracles take ! place ( legitimate natural causes4 ,on ! supposition t ! moon is inhabit$1 ! "q has (t5 be5 rais$1 :e!r we may hope t our telescopes w ev] be s mu* improv$1 & our o!r means ( obs]vation s mu* augm5t$1 t we %all be able to discov] ei!r ! lun> inhabitants or any ( _! works4 ,! improbability ( our ev] id5tify+ artificial /ructures 9 ! moon may be inf]r$ f ! fact1 t a space a mile 9 diamet] is ! lea/ space t c\ld be di/9ctly se54 ,ext5sive works ( art1 z l>ge cities1 or ! cle>+ up ( l>ge tracts ( c\ntry = settlem5t or tillage1 might inde$ af=d "s v>ieties ( surface2 b !y w\ld be m]ely v>ieties ( light & %ade1 & ! individual objects t occasion$ !m w\ld probably nev] be recognis$ by _! di/9ctive *>act]s4 ,?us1 a build+ equal to ! great pyramid ( ,egypt1 :i* cov]s a space less ?an ! fif? ( a mile 9 diamet]1 w\ld n be di/+ui%$ by its figure2 inde$1 x w\ld be a m]e po9t4 ,/ill less is x probable t we %all ev] discov] any inhabitants 9 ! moon4 ,7 we to view ! moon ) a telescope t magnifies t5 ?\s& times1 x w\ld br+ ! moon app>5tly t5 ?\s& times ne>]1 & pres5t x to ! eye l a body tw5ty-f\r miles (f4 ,b ev5 ?is is a di/ance too great = u to see ! works ( man ) di/9ctness4 ,moreov]1 f ! nature ( ! telescope itself1 we c nev] hope to apply a magnify+ p[] s high z t "h suppos$4 ,z ,i expla9$ to y1 :5 speak+ ( ! telescope1 :5ev] we increase ! magnify+ p[] ( ?is in/rum5t we dim9i% its field ( view1 s t ) v high magnifi]s we c see no?+ b a po9t1 su* z a fix$ />4 ,we at ! same "t1 also1 magnify ! vapors & smoke ( ! atmosph]e1 & all ! imp]fections ( ! m$ium1 :i* greatly obscures ! object1 & prev5ts our see+ x di/9ctly4 ,h5ce x is g5]ally mo/ satisfactory to view ! moon ) l[ p[]s1 :i* af=d a l>ge field ( view & give a cle> light4 ,) ,cl>k's telescope1 belong+ to ,yale ,college1 we seldom ga9 any ?+ by apply+ to ! moon a high] p[] ?an "o hundr$ & eighty1 al?\gh ! in/rum5t admits ( magnifi]s z high z f\r hundr$ & fifty4 ,"s writ]s1 h[ev]1 suppose t possibly we may trace indications ( lun> inhabitants 9 _! works1 & t !y may 9 l mann] recognise ! exi/5ce ( ! inhabitants ( our planet4 ,an au?or1 :o has reflect$ mu* on subjects ( ?is k9d1 reasons z foll[s3 ,a navigator :o approa*es )9 a c]ta9 di/ance ( a small isl&1 al?\gh he p]ceives no human be+ ^u x1 c judge ) c]ta9ty t x is inhabit$1 if he p]ceives human habitations1 villages1 corn-fields1 or o!r traces ( cultivation4 ,9 l mann]1 if we c\ld p]ceive *anges or op]ations 9 ! moon1 :i* c\ld be trac$ to ! ag5cy ( intellig5t be+s1 we %\ld !n obta9 satisfactory evid5ce t su* be+s exi/ on t planet2 & x is ?\ght possible t su* op]ations may be trac$4 ,a telescope :i* magnifies twelve hundr$ times w enable u to p]ceive1 z a visible po9t on ! surface ( ! moon1 an object ^: diamet] is only ab\t ?ree hundr$ feet4 ,su* an object is n l>g] ?an _m ( our public edifices2 & !re=e1 7 any su* edifices re>+ 9 ! moon1 or 7 a t[n or city ext5d+ its b\nd>ies1 or 7 op]ations ( ?is description c>ry+ on1 9 a di/rict :]e no su* edifices _h previ\sly be5 erect$1 su* objects & op]ations might probably be detect$ by a m9ute inspection4 ,7 a multitude ( liv+ creatures mov+ f place to place1 9 a body1 or 7 !y ev5 encamp+ 9 an ext5sive pla91 l a l>ge army1 or l a tribe ( ,arabs 9 ! des]t1 & aft]w>ds remov+1 x is possible su* *anges might be trac$ by ! diff]5ce ( %ade or color1 :i* su* movem5ts w\ld produce4 ,9 ord] to detect su* m9ute objects & op]ations1 x w\ld be requisite t ! surface ( ! moon %\ld be di/ribut$ among at lea/ a hundr$ a/ronom]s1 ea* hav+ a spot or two allott$ to him1 z ! object ( 8 m p>ticul> inve/igation1 & t ! obs]vations be cont9u$ = a p]iod ( at lea/ ?irty or =ty ye>s1 dur+ :i* "t c]ta9 *anges w\ld probably be p]ceiv$1 aris+ ei!r f physical causes1 or f ! op]ations ( liv+ ag5ts4#i ,,footnote3 #h ,dick's ',cele/ial ,sc5]y1' ,*apt] ,,iv ,,lett] ,,xvi4 ,,! ,,moon4--,,phases4--,,h>ve/ ,,moon4--,,librations4 ,fir/ to ! neighbor+ ,moon ?is mighty key ,( nature he appli$4 ,behold6 x turn$ ,! secret w>ds1 x op5$ wide ! c\rse ,& v>i\s aspects ( ! que5 ( night3 ,:e!r %e wanes into a scanty orb1 ,or1 wax+ broad1 ) h] pale %ad[y light1 ,9 a s(t deluge ov]fl[s ! sky4--,?omson's ,elegy4 ,,let u n[ inquire into ! revolutions ( ! moon ar\nd ! e>?1 & ! v>i\s *anges %e und]goes e mon?1 call$ h] phases1 :i* dep5d on ! diff]5t positions %e assumes1 ) respect to ! e>? & ! sun1 9 ! c\rse ( h] revolution4 ,! moon revolves ab\t ! e>? f we/ to ea/4 ,h] app>5t orbit1 z trac$ out on ! face ( ! sky1 is a great circle2 b ?is fact w\ld n c]ta9ly prove t ! orbit is really a circle1 s9ce1 if x 7 an ellipse1 or ev5 a m irregul> curve1 ! projection ( x on ! face ( ! sky w\ld be a circle1 z expla9$ to y be=e4 7,see page #adh47 ,! moon is comp>atively s ne> to ! e>?1 t h] app>5t movem5ts are v rapid1 s t1 by att5tively wat*+ h] progress 9 a cle> night1 we may see h] move f /> to />1 *ang+ h] place p]ceptibly1 e few h\rs4 ,! int]val dur+ :i* %e goes ?r\gh ! entire circuit ( ! heav5s1 f any /> until %e comes r\nd to ! same /> aga91 is call$ a sid]eal mon?1 & consi/s ( ab\t tw5ty-sev5 & "o f\r? days4 ,! "t :i* int]v5es betwe5 "o new moon & ano!r is call$ a synodical mon?1 & consi/s ( ne>ly tw5ty-n9e & a half days4 ,a new moon occurs :5 ! sun & moon meet 9 ! same "p ( ! heav5s2 b ! sun z well z ! moon is app>5tly travell+ ea/w>d1 & ne>ly at ! rate ( "o degree a day1 & consequ5tly1 dur+ ! tw5ty-sev5 days :ile ! moon has be5 go+ r\nd ! e>?1 ! sun has be5 go+ =w>d ab\t ! same numb] ( degrees 9 ! same direction4 ,h5ce1 :5 ! moon comes r\nd to ! "p ( ! heav5s :]e %e pass$ ! sun la/1 %e does n f9d him !re1 b mu/ g on m ?an two days1 be=e %e comes up ) him aga94 ,! moon does n pursue precisely ! same track ar\nd ! e>? z ! sun does1 9 8 app>5t annual motion1 ?\gh %e nev] deviates f> f t track4 ,! incl9ation ( h] orbit to ! ecliptic is only ab\t five degrees1 & ( c\rse ! moon is nev] se5 fur!r f ! ecliptic ?an ab\t t di/ance1 & %e is commonly mu* ne>] to ! ecliptic ?an five degrees4 ,we may !re=e see ne>ly :at is ! situation ( ! ecliptic 9 our ev5+ sky at any p>ticul> "t ( ye>1 j by wat*+ ! pa? :i* ! moon pursues1 f night to night1 f new to full moon4 ,! two po9ts :]e ! moon's orbit crosses ! ecliptic are call$ h] nodes4 ,!y are ! int]sections ( ! lun> & sol> orbits1 z ! equ9oxes are ! int]sections ( ! equ9octial & ecliptic1 &1 l ! latt]1 are "o hundr$ & eighty degrees ap>t4 ,! *anges ( ! moon1 commonly call$ h] phases1 arise f diff]5t portions ( h] illum9at$ side be+ turn$ t[>ds ! e>? at diff]5t times4 ,:5 ! moon is fir/ se5 aft] ! sett+ sun1 h] =m is t ( a bright cresc5t1 on ! side ( ! disk next to ! sun1 :ile ! o!r portions ( ! disk %9e ) a feeble light1 reflect$ to ! moon f ! e>?4 ,e night1 we obs]ve ! moon to be fur!r & fur!r ea/w>d ( ! sun1 until1 :5 %e has rea*$ an elongation f ! sun ( n9ety degrees1 half h] visible disk is enlight5$1 & %e is said to be 9 h] fir/ qu>t]4 ,! t]m9ator1 or l9e :i* sep>ates ! illum9at$ f ! d>k "p ( ! moon1 is convex t[>ds ! sun f ! new to ! fir/ qu>t]1 & ! moon is said to be horn$4 ,! extremities ( ! cresc5t are call$ cusps4 ,at ! fir/ qu>t]1 ! t]m9ator becomes a /raight l9e1 co9cid+ ) ! diamet] ( ! disk2 b aft] pass+ ?is po9t1 ! t]m9ator becomes concave t[>ds ! sun1 b\nd+ t side ( ! moon by an elliptical curve1 :5 ! moon is said to be gibb\s4 ,:5 ! moon arrives at ! di/ance ( "o hundr$ & eighty degrees f ! sun1 ! entire circle is illum9at$1 & ! moon is full4 ,%e is !n 9 opposition to ! sun1 ris+ ab\t ! "t ! sun sets4 ,= a week aft] ! full1 ! moon appe>s gibb\s aga91 until1 hav+ arriv$ )9 n9ety degrees ( ! sun1 %e resumes ! same =m z at ! fir/ qu>t]1 be+ !n at h] ?ird qu>t]4 ,f ?is "t until new moon1 %e exhibits aga9 ! =m ( a cresc5t be=e ! ris+ sun1 until1 approa*+ h] conjunction ) ! sun1 h] n>r[ ?read ( light is lo/ 9 ! sol> blaze2 & f9ally1 at ! mom5t ( pass+ ! sun1 ! d>k side is :olly turn$ t[>ds u1 & = "s "t we lose sight ( ! moon4 ,by inspect+ ,fig4 #ch1 7:]e ,t repres5ts ! e>?1 ,a1 ,b1 ,c1 c41 ! moon 9 h] orbit1 & a1 b1 c1 c41 h] phases1 z se5 9 ! heav5s17 we %all easily see h[ all ^! *anges occur4 ,illu/ration ,fig4 #ch4 ,y h d\btless obs]v$1 t ! moon appe>s mu* fur!r 9 ! s\? at "o "t ?an at ano!r1 :5 ( ! same age4 ,?is is ow+ to ! fact t ! ecliptic1 & ( c\rse ! moon's pa?1 :i* is always v ne> x1 is diff]5tly situat$ ) respect to ! horizon1 at a giv5 "t ( night1 at diff]5t seasons ( ! ye>4 ,?is y w see at once1 by turn+ to an artificial globe1 & obs]v+ h[ ! ecliptic /&s ) respect to ! horizon1 at diff]5t p]iods ( ! revolution4 ,?us1 if we place ! two equ9octial po9ts 9 ! ea/]n & we/]n horizon1 ,libra be+ 9 ! we/1 x w repres5t ! position ( ! ecliptic at sunset 9 ! mon? ( ,septemb]1 :5 ! sun is cross+ ! equator2 & at t season ( ! ye>1 ! moon's pa? ?r\gh our ev5+ sky1 "o ev5+ aft] ano!r1 f new to full1 w be ne>ly along ! same r\te1 cross+ ! m]idian ne>ly at "r angles4 ,b if we place ! ,w9t] sol/ice1 or fir/ degree ( ,capricorn1 9 ! we/]n horizon1 & ! fir/ degree ( ,canc] 9 ! ea/]n1 !n ! position ( ! ecliptic w be v oblique to ! m]idian1 ! ,w9t] sol/ice be+ v f> 9 ! s\?we/1 & ! ,summ] sol/ice v f> 9 ! nor!a/2 & ! c\rse ( ! moon f new to full w be ne>ly along ?is track4 ,keep+ ^! ?+s 9 m9d1 we may easily see :y ! moon runs sometimes high & sometimes l[4 ,recollect1 also1 t ! new moon is always 9 ! same "p ( ! heav5s ) ! sun1 & t ! full moon is 9 ! opposite "p ( ! heav5s f ! sun4 ,n[1 :5 ! sun is at ! ,w9t] sol/ice1 x sets f> 9 ! s\?we/1 & accord+ly ! new moon runs v l[2 b ! full moon1 be+ 9 ! opposite tropic1 :i* rises f> 9 ! nor!a/1 runs v high1 z is kn[n to be ! case 9 mid-w9t]4 ,b n[ take ! position ( ! ecliptic 9 mid-summ]4 ,!n1 at sunset1 ! tropic ( ,canc] is 9 ! nor?we/1 & ! tropic ( ,capricorn 9 ! s\!a/2 consequ5tly1 ! new moons run high & ! full moons l[4 ,x is a natural consequ5ce ( ?is arrangem5t1 to r5d] ! moon's light ! mo/ b5eficial to u1 by giv+ x to u 9 greate/ abundance1 :5 we h lea/ ( ! sun's light1 & giv+ x to u mo/ sp>+ly1 :5 ! sun's light is greate/4 ,?us1 dur+ ! long nights ( ,w9t]1 ! full moon runs high1 & cont9ues a v long "t above ! horizon2 :ile 9 mid-summ]1 ! full moon runs l[1 & is above ! horizon = a mu* %ort] p]iod4 ,?is arrangem5t op]ates v favorably to ! inhabitants ( ! pol> regions4 ,at ! season :5 ! sun is abs5t1 & !y h con/ant night1 !n ! moon1 dur+ ! second & ?ird qu>t]s1 embrac+ ! season ( full moon1 is cont9ually above ! horizon1 comp5sat+ 9 no small degree = ! abs5ce ( ! sun2 :ile1 dur+ ! ,summ] mon?s1 :5 ! sun is con/antly above ! horizon1 & ! light ( ! moon is n ne$$1 !n %e is above ! horizon dur+ ! fir/ & la/ qu>t]s1 :5 h] light is lea/1 af=d+ at t "t h] greate/ light to ! inhabitants ( ! o!r hemisph]e1 f :om ! sun is )drawn4 ,ab\t ! "t ( ! ,autumnal equ9ox1 ! moon1 :5 ne> h] full1 rises ab\t sunset a numb] ( nights 9 succession4 ,?is occasions a rem>kable numb] ( brilliant moonlight ev5+s2 & z ?is is1 9 ,engl&1 ! p]iod ( h>ve/1 ! ph5om5on is call$ ! h>ve/ moon4 ,its return is celebrat$1 p>ticul>ly among ! peasantry1 by fe/ive dances1 & kept z a fe/ival1 call$ ! h>ve/ home1--an occasion (t5 allud$ to by ! ,briti% poets4 ,?us ,h5ry ,kirke ,:ite3 ,moon ( h>ve/1 h]ald mild ,( pl5ty1 ru/ic labor's *ild1 ,hail1 ,o hail6 ,i greet ?y beam1 ,z s(t x trembles o'er ! /ream1 ,& gilds ! /raw-?at*'d hamlet wide1 ,:]e innoc5ce & peace reside2 ',tis ?\ t glad'/ ) joy ! ru/ic ?rong1 ,prompte/ ! tripp+ dance1 ?' exhil>at+ song4 ,to und]/& ! reason ( ! h>ve/ moon1 we w1 z be=e1 consid] ! moon's orbit z co9cid+ ) ! ecliptic1 because we may !n take ! ecliptic1 z x is drawn on ! artificial globe1 to repres5t t orbit4 ,we w also be> 9 m9d1 7:at has be5 fully illu/rat$ "u ! la/ head17 t1 s9ce ! ecliptic cuts ! m]idian obliquely1 :ile all ! circles ( diurnal revolution cut x p]p5dicul>ly1 diff]5t portions ( ! ecliptic w cut ! horizon at diff]5t angles4 ,?us1 :5 ! equ9oxes are 9 ! horizon1 ! ecliptic makes a v small angle ) ! horizon2 :]eas1 :5 ! sol/itial po9ts are 9 ! horizon1 ! same angle is f> great]4 ,9 ! =m] case1 a body mov+ ea/w>d 9 ! ecliptic1 & be+ at ! ea/]n horizon at sunset1 w\ld desc5d b a little way bel[ ! horizon 9 mov+ ov] _m degrees ( ! ecliptic4 ,n[1 ?is is j ! case ( ! moon at ! "t ( ! h>ve/ home1 ab\t ! "t ( ! ,autumnal equ9ox4 ,! sun be+ !n 9 ,libra1 & ! moon1 :5 full1 be+ ( c\rse opposite to ! sun1 or 9 ,aries2 & mov+ ea/w>d1 9 or ne> ! ecliptic1 at ! rate ( ab\t ?irte5 degrees p] day1 w\ld desc5d b a small di/ance bel[ ! horizon = five or six days 9 succession2 t is = two or ?ree days be=e1 & ! same numb] ( days aft]1 ! full2 & w\ld consequ5tly rise dur+ all ^! ev5+s ne>ly at ! same "t1 namely1 a little be=e1 or a little aft]1 sunset1 s z to af=d a rem>kable succession ( f9e moonlight ev5+s4 ,! moon turns on h] axis 9 ! same "t 9 :i* %e revolves ar\nd ! e>?4 ,?is is kn[n by ! moon's always keep+ ne>ly ! same face t[>ds u1 z is indicat$ by ! telescope1 :i* c\ld n happ5 unless h] revolution on h] axis kept pace ) h] motion 9 h] orbit4 ,take an apple1 to repres5t ! moon2 /ick a knitt+ne$le ?r\gh x1 9 ! direction ( ! /em1 to repres5t ! axis1 9 :i* case ! two eyes ( ! apple w aptly repres5t ! poles4 ,?r\gh ! poles cut a l9e ar\nd ! apple1 divid+ x into two hemisph]es1 & m>k !m1 s z to be readily di/+ui%$ f ea* o!r4 ,n[ place a c&le on ! table1 to repres5t ! e>?1 & hold+ ! apple by ! knitt+ne$le1 c>ry x r\nd ! c&le1 & y w see t1 unless y make ! apple turn r\nd on ! axis z y c>ry x ab\t ! c&le1 x w pres5t diff]5t sides t[>ds ! c&le2 & t1 9 ord] to make x always pres5t ! same side1 x w be necess>y to make x revolve exactly once on its axis1 :ile x is go+ r\nd ! circle1--! revolution on its axis always keep+ exact pace ) ! motion 9 its orbit4 ,! same ?+ w be obs]v$1 if y walk ar\nd a tree1 always keep+ y\r face t[>ds ! tree4 ,if y h y\r face t[>ds ! tree :5 y set out1 & walk r\nd )\t turn+1 :5 y h rea*$ ! opposite side ( ! tree1 y\r back w be t[>ds x1 & y w f9d t1 9 ord] to keep y\r face con/antly t[>ds ! tree1 x w be necess>y to turn y\rself r\nd on y\r heel at ! same rate z y g =w>d4 ,s9ce1 h[ev]1 ! motion ( ! moon on its axis is uni=m1 :ile ! motion 9 its orbit is unequal1 ! moon does 9 fact reveal to u a little sometimes ( "o side & sometimes ( ! o!r4 ,?us if1 :ile c>ry+ ! apple r\nd ! c&le1 y c>ry x =w>d a little fa/] ?an ! rate at :i* x turns on its axis1 a portion ( ! hemisph]e usually out ( sight is br\ght into view on "o side2 or if ! apple is mov$ =w>d sl[] ?an x is turn$ on its axis1 a portion ( ! same hemisph]e comes into view on ! o!r side4 ,^! appe>ances are call$ ! moon's librations 9 longitude4 ,! moon has also a libration 9 latitude2--s call$1 because 9 "o "p ( h] revolution m ( ! region ar\nd "o ( ! poles comes into view1 &1 9 ano!r "p ( ! revolution1 m ( ! region ar\nd ! o!r pole1 :i* gives ! appe>ance ( a tilt+ motion to ! moon's axis4 ,?is is ow+ to ! fact1 t ! moon's axis is incl9$ to ! plane ( h] orbit4 ,if1 9 ! exp]im5t ) ! apple1 y hold ! knitt+ne$le p>allel to ! c&le1 79 :i* case ! axis w be p]p5dicul> to ! plane ( revolution17 ! c&le w %9e ^u bo? poles dur+ ! :ole circuit1 & an eye situat$ :]e ! c&le is w\ld con/antly see bo? poles2 b n[ incl9e ! ne$le t[>ds ! plane ( revolution1 & c>ry x r\nd1 always keep+ x p>allel to itself1 & y w obs]ve t ! two poles w be alt]nately 9 & out ( sight4 ,! moon exhibits ano!r appe>ance ( ?is k9d1 call$ h] diurnal libration1 dep5d+ on ! daily rotation ( ! spectator4 ,%e turns ! same face t[>ds ! c5tre ( ! e>? only1 :]eas we view h] f ! surface4 ,:5 %e is on ! m]idian1 we view h] disk ne>ly z ?\gh we view$ x f ! c5tre ( ! e>?1 & h5ce1 9 ?is situation1 x is subject to little *ange2 b :5 %e is ne> ! horizon1 our circle ( vision takes 9 m ( ! upp] limb ?an w\ld be pres5t$ to a spectator at ! c5tre ( ! e>?4 ,h5ce1 f ?is cause1 we see a portion ( "o limb :ile ! moon is ris+1 :i* is gradually lo/ sight (1 & we see a portion ( ! opposite limb1 z ! moon decl9es to ! we/4 ,y w rem>k t nei!r ( ! =ego+ *anges implies any actual motion 9 ! moon1 b t ea* arises f a *ange ( position 9 ! spectator4 ,s9ce ! succession ( day & night dep5ds on ! revolution ( a planet on its own axis1 & x takes ! moon tw5ty-n9e & a half days to p]=m ?is revolution1 s t ! sun %all g f ! m]idian ( any place & return to ! same m]idian aga91 ( c\rse ! lun> day occupies ?is long p]iod4 ,s protract$ an exposure to ! sun's rays1 especially 9 ! equatorial regions ( ! moon1 mu/ occasion an excessive accumulation ( heat2 & s long an abs5ce ( ! sun mu/ occasion a correspond+ degree ( cold4 ,a spectator on ! side ( ! moon :i* is opposite to u w\ld nev] see ! e>?1 b "o on ! side next to u w\ld see ! e>? con/antly 9 8 firmam5t1 und]go+ a gradual succession ( *anges1 correspond+ to ^? :i* ! moon exhibits to ! e>?1 b 9 ! rev]se ord]4 ,?us1 :5 x is full moon to u1 ! e>?1 z se5 f ! moon1 is !n 9 conjunction ) ! sun1 & ( c\rse pres5ts h] d>k side to ! moon4 ,soon aft] ?is1 an inhabitant ( ! moon w\ld see a cresc5t1 resembl+ our new moon1 :i* w\ld 9 l mann] increase & g ?r\gh all ! *anges1 f new to full1 & f full to new1 z we see !m 9 ! moon4 ,!re are1 h[ev]1 9 ! two cases1 sev]al /rik+ po9ts ( diff]5ce4 ,9 ! fir/ place1 in/ead ( tw5ty-n9e & a half days1 all ^! *anges occur 9 "o lun> day & night4 ,dur+ ! fir/ & la/ qu>t]s1 ! *anges w\ld occur 9 ! day-"t2 b dur+ ! second & ?ird qu>t]s1 dur+ ! night4 ,by ?is arrangem5t1 ! lun>ians w\ld enjoy ! greate/ possible b5efit f ! light af=d$ by ! e>?1 s9ce 9 ! half ( h] revolution :]e %e appe>s to !m z full1 %e w\ld be pres5t :ile ! sun 0 abs5t1 & w\ld af=d h] lea/ light :ile ! sun 0 pres5t4 ,9 ! second place1 ! e>? w\ld appe> ?irte5 times z l>ge to a spectator on ! moon z ! moon appe>s to u1 & w\ld af=d ne>ly ! same proportion ( light1 s t _! long nights mu/ be cont9ually *e]$ by an extraord9>y degree ( light d]iv$ f ?is s\rce2 & if ! full moon is hail$ by our poets z refulg5t lamp ( night1#aj ) h[ mu* m reason might a lun>ian exult ?us1 9 view ( ! spl5did orb t adorns 8 nocturnal sky6 ,9 ! ?ird place1 ! e>?1 z view$ f any p>ticul> place on ! moon1 w\ld occupy inv>iably ! same "p ( ! heav5s4 ,= :ile ! rotation ( ! moon on h] axis f we/ to ea/ w\ld appe> to make ! e>? 7z ! moon does to u7 revolve f ea/ to we/1 ! correspond+ progress ( ! moon 9 h] orbit w\ld make ! e>? appe> to revolve f we/ to ea/2 & z ^! two motions are equal1 _! unit$ effect w\ld be to keep ! moon app>5tly /ation>y 9 ! sky4 ,?us1 a spectator at ,e1 ,fig4 #ch1 page #age1 9 ! middle ( ! disk t is turn$ t[>ds ! e>?1 w\ld h ! e>? con/antly on 8 m]idian1 & at ,e1 ! conjunction ( ! e>? & sun w\ld occur at mid-day2 b :5 ! moon arriv$ at ,g1 ! same place w\ld be on ! m>g9 ( ! circle ( illum9ation1 & w h ! sun 9 ! horizon2 b ! e>? w\ld /ill be on 8 m]idian & 9 quadrature4 ,9 l mann]1 a place situat$ on ! m>g9 ( ! circle ( illum9ation1 :5 ! moon is at ,e1 w\ld h ! e>? 9 ! horizon2 & ! same place w\ld always see ! e>? 9 ! horizon1 except ! slight v>iations t w\ld occur f ! librations ( ! moon4 ,9 ! f\r? place1 ! e>? w\ld pres5t to a spectator on ! moon none ( t uni=mity ( aspect :i* ! moon pres5ts to u1 b w\ld exhibit an appe>ance exce$+ly div]sifi$4 ,! comp>atively rapid rotation ( ! e>?1 repeat$ fifte5 times dur+ a lun> night1 w\ld pres5t1 9 rapid succession1 a view ( our seas1 oceans1 cont95ts1 & m\nta9s1 all div]sifi$ by our cl\ds1 /orms1 & volcanoes4 ,,footnotes3 #i ,dick's ',cele/ial ,sc5]y4' #aj ,z :5 ! moon1 refulg5t lamp ( night1 ,o'er heav5's cle> azure %$s h] sacr$ light1 ,:5 n a brea? di/urbs ! deep s]5e1 ,& n a cl\d o'erca/s ! solemn sc5e1 ,ar\nd h] ?rone ! vivid planets roll1 ,& />s unnumb]$ gild ! gl[+ pole2 ,o'er ! d>k trees a yell[] v]dure %$1 ,& tip ) silv] e m\nta9's head2 ,!n %9e ! vales1 ! rocks 9 prospect rise1 ,a flood ( glory bur/s f all ! skies2 ,! consci\s swa9s1 rejoic+ 9 ! sight1 ,eye ! blue vault1 & bless ! useful light4 ,pope's ,hom]4 ,,lett] ,,xvii4 ,,moon',s ,,orbit4--,,h] ,,irregul>ities4 ,"s say ! zodiac con/ellations ,h long s9ce left _! antique /ations1 ,above a sign1 & prove ! same ,9 ,taurus n[1 once 9 ! ,ram2 ,t 9 twelve hundr$ ye>s & odd1 ,! sun has left 8 anci5t road1 ,& ne>] to ! e>? is come1 ',bove fifty ?\s& miles f home4--,hudibras4 ,,we h ?us f> contemplat$ ! revolution ( ! moon ar\nd ! e>? z ?\gh ! e>? 7 at re/4 ,b 9 ord] to h j ideas respect+ ! moon's motions1 we mu/ recollect t ! moon likewise revolves along ) ! e>? ar\nd ! sun4 ,x is sometimes said t ! e>? c>ries ! moon along ) h]1 9 h] annual revolution4 ,?is language may convey an errone\s idea2 = ! moon1 z well z ! e>?1 revolves ar\nd ! sun "u ! influ5ce ( two =ces1 :i* are indep5d5t ( ! e>?1 & w\ld cont9ue h] motion ar\nd ! sun1 7 ! e>? remov$ out ( ! way4 ,inde$1 ! moon is attract$ t[>ds ! sun two & "o fif? times m ?an t[>ds ! e>?1 & w\ld ab&on ! e>?1 7 n ! latt] also c>ri$ along ) h] by ! same =ces4 ,s f> z ! sun acts equally on bo? bodies1 ! motion ) respect to ea* o!r w\ld n be di/urb$4 ,because ! gravity ( ! moon t[>ds ! sun is f\nd to be great]1 at ! conjunction1 ?an h] gravity t[>ds ! e>?1 "s h appreh5d$ t1 if ! doctr9e ( univ]sal gravitation is true1 ! moon ought necess>ily to ab&on ! e>?4 ,9 ord] to und]/& ! reason :y x does n d ?us1 we mu/ reflect1 t1 :5 a body is revolv+ 9 its orbit "u ! influ5ce ( ! projectile =ce & gravity1 :atev] dim9i%es ! =ce ( gravity1 :ile t ( projection rema9s ! same1 causes ! body to approa* ne>] to ! tang5t ( h] orbit1 & ( c\rse to rec$e f ! c5tre2 & :atev] increases ! am\nt ( gravity1 c>ries ! body t[>ds ! c5tre4 ,?us1 9 ,fig4 #cc1 page #aeb1 if1 ) a c]ta9 =ce ( projection act+ 9 ! direction ,a ,b1 & ( attraction1 9 ! direction ,a ,c1 ! attraction :i* caus$ a body to move 9 ! l9e ,a ,d 7 dim9i%$1 x w\ld move ne>] to ! tang5t1 z 9 ,a ,e1 or ,a ,f4 ,n[1 :5 ! moon is 9 conjunction1 h] gravity t[>ds ! e>? acts 9 opposition to t t[>ds ! sun1 7see ,fig4 #ch1 page #age17 :ile h] velocity rema9s too great to c>ry h] ) :at =ce rema9s1 9 a circle ab\t ! sun1 & %e !re=e rec$es f ! sun1 & comm5ces h] revolution ar\nd ! e>?4 ,on arriv+ at ! opposition1 ! gravity ( ! e>? conspires ) t ( ! sun1 & ! moon's projectile =ce be+ less ?an t requir$ to make h] revolve 9 a circul> orbit1 :5 attract$ t[>ds ! sun by ! sum ( ^! =ces1 %e accord+ly beg9s to approa* ! sun1 & desc5ds aga9 to ! conjunction4 ,! attraction ( ! sun1 h[ev]1 be+ e :]e great] ?an t ( ! e>?1 ! actual pa? ( ! moon ar\nd ! sun is e :]e concave t[>ds ! latt]4 ,/ill1 ! elliptical pa? ( ! moon ar\nd ! e>? is to be conceiv$ (1 9 ! same way z ?\gh bo? bodies 7 at re/ ) respect to ! sun4 ,?us1 :ile a /eam-boat is pass+ swiftly ar\nd an isl&1 & a man is walk+ sl[ly ar\nd a po/ 9 ! cab91 ! l9e :i* he describes 9 space betwe5 ! =w>d motion ( ! boat & 8 circul> motion ar\nd ! po/1 may be e :]e concave t[>ds ! isl&1 :ile 8 pa? ar\nd ! po/ w /ill be ! same z ?\gh bo? 7 at re/4 ,a nail 9 ! rim ( a coa*-:eel w turn ar\nd ! axis ( ! :eel1 :5 ! coa* has a =w>d motion1 9 ! same mann] z :5 ! coa* is at re/1 al?\gh ! l9e actually describ$ by ! nail w be ! resultant ( bo? motions1 & v diff]5t f ei!r4 ,we h hi!rto reg>d$ ! moon z describ+ a great circle on ! face ( ! sky1 su* be+ ! visible orbit1 z se5 by projection4 ,b1 on a m exact inve/igation1 x is f\nd t h] orbit is n a circle1 & t h] motions are subject to v num]\s irregul>ities4 ,^! w be be/ und]/ood 9 connexion ) ! causes on :i* !y dep5d4 ,! law ( univ]sal gravitation has be5 appli$ ) wond]ful success to _! developem5t1 & its results h conspir$ ) ^? ( long-cont9u$ obs]vation1 to furni% ! means ( asc]ta9+ ) great exactness ! place ( ! moon 9 ! heav5s1 at any giv5 in/ant ( "t1 pa/ or future1 & ?us to enable a/ronom]s to det]m9e longitudes1 to calculate eclipses1 & to solve o!r problems ( ! highe/ int]e/4 ,! :ole numb] ( irregul>ities to :i* ! moon is subject is n less ?an sixty1 b ! great] "p are s small z to be h>dly des]v+ ( att5tion2 b z _m z ?irty require to be e/imat$ & all[$ =1 be=e we c asc]ta9 ! exact place ( ! moon at any giv5 "t4 ,y w be able to und]/& some?+ ( ! cause ( ^! irregul>ities1 if y fir/ ga9 a di/9ct idea ( ! mutual actions ( ! sun1 ! moon1 & ! e>?4 ,! irregul>ities 9 ! moon's motions are due *iefly to ! di/urb+ influ5ce ( ! sun1 :i* op]ates 9 two ways2 fir/1 by act+ unequally on ! e>? & moon2 & secondly1 by act+ obliquely on ! moon1 on acc\nt ( ! incl9ation ( h] orbit to ! ecliptic4 ,if ! sun act$ equally on ! e>? & moon1 & always 9 p>allel l9es1 ?is action w\ld s]ve only to re/ra9 !m 9 _! annual motions ar\nd ! sun1 & w\ld n affect _! actions on ea* o!r1 or _! motions ab\t _! common c5tre ( gravity4 ,9 t case1 if !y 7 all[$ to fall t[>ds ! sun1 !y w\ld fall equally1 & _! respective situations w\ld n be affect$ by _! desc5d+ equally t[>ds x4 ,b1 because ! moon is ne>] ! sun 9 "o half ( h] orbit ?an ! e>? is1 & 9 ! o!r half ( h] orbit is at a great] di/ance ?an ! e>? f ! sun1 :ile ! p[] ( gravity is always great] at a less di/ance2 x foll[s1 t 9 "o half ( h] orbit ! moon is m attract$ ?an ! e>? t[>ds ! sun1 &1 9 ! o!r half1 less attract$ ?an ! e>?4 ,to see ! effects ( ?is process1 let u suppose t ! projectile motions ( ! e>? & moon 7 de/roy$1 & t !y 7 all[$ to fall freely t[>ds ! sun4 7,see ,fig4 #ch1 page #age47 ,if ! moon 0 9 conjunction ) ! sun1 or 9 t "p ( h] orbit :i* is ne>e/ to him1 ! moon w\ld be m attract$ ?an ! e>?1 & fall ) great] velocity t[>ds ! sun2 s t ! di/ance ( ! moon f ! e>? w\ld be increas$ by ! fall4 ,if ! moon 0 9 opposition1 or 9 ! "p ( h] orbit :i* is fur!/ f ! sun1 %e w\ld be less attract$ ?an ! e>? by ! sun1 & w\ld fall ) a less velocity1 & be left beh9d2 s t ! di/ance ( ! moon f ! e>? w\ld be increas$ 9 ?is case1 also4 ,if ! moon 0 9 "o ( ! qu>t]s1 !n ! e>? & ! moon be+ bo? attract$ t[>ds ! c5tre ( ! sun1 !y w\ld bo? desc5d directly t[>ds t c5tre1 &1 by approa*+ x1 !y w\ld necess>ily at ! same "t approa* ea* o!r1 & 9 ?is case _! di/ance f ea* o!r w\ld be dim9i%$4 ,n[1 :5ev] ! action ( ! sun w\ld increase _! di/ance1 if !y 7 all[$ to fall t[>ds ! sun1 !n ! sun's action1 by endeavor+ to sep>ate !m1 dim9i%es _! gravity to ea* o!r2 :5ev] ! sun's action w\ld dim9i% ! di/ance1 !n x increases _! mutual gravitation4 ,h5ce1 9 ! conjunction & opposition1 _! gravity t[>ds ea* o!r is dim9i%$ by ! action ( ! sun1 :ile 9 ! quadratures x is increas$4 ,b x mu/ be rememb]$1 t x is n ! total action ( ! sun on !m t di/urbs _! motions1 b only t "p ( x :i* t5ds at "o "t to sep>ate !m1 & at ano!r "t to br+ !m ne>] toge!r4 ,! o!r & f> great] "p has no o!r effect ?an to reta9 !m 9 _! annual c\rse ar\nd ! sun4 ,! cause ( ! lun> irregul>ities 0 fir/ inve/igat$ by ,sir ,isaac ,newton1 9 con=mity ) 8 doctr9e ( univ]sal gravitation1 & ! explanation 0 fir/ publi%$ 9 ! ',pr9cipia2' b1 z x 0 giv5 9 a ma!matical dress1 !re 7 at t age v few p]sons capable ( read+ or und]/&+ x4 ,sev]al em95t individuals1 !re=e1 und]took to give a popul> explanation ( ^! difficult po9ts4 ,among ,newton's contempor>ies1 ! be/ comm5tator 0 ,m',laur91 a ,scotti% a/ronom]1 :o publi%$ a l>ge "w entitl$ ',m',laur9's ,acc\nt ( ,sir ,isaac ,newton's ,discov]ies4' ,no writ] ( 8 own day1 &1 9 my op9ion1 no lat] comm5tator1 has equall$ ,m',laur91 9 r$uc+ to common appreh5sion ! lead+ pr9ciples ( ! doctr9e ( gravitation1 & ! explanation x af=ds ( ! motions ( ! heav5ly bodies4 ,to ?is writ] ,i am indebt$ = ! prec$+ easy explanation ( ! irregul>ities ( ! moon's motions1 z well z = sev]al o!r illu/rations ( ! same sublime doctr9e4 ,! figure ( ! moon's orbit is an ellipse4 ,we h be=e se51 t ! e>?'s orbit ar\nd ! sun is ( ! same figure2 & we %all h]eaft] see ?is to be true ( all ! planet>y orbits4 ,! pa? ( ! e>?1 h[ev]1 dep>ts v little f a circle2 t ( ! moon diff]s mat]ially f a circle1 be+ consid]ably long] "o way ?an ! o!r4 ,7 ! orbit a circle hav+ ! e>? 9 ! c5tre1 !n ! radius vector1 or l9e drawn f ! c5tre ( ! moon to ! c5tre ( ! e>?1 w\ld always be ( ! same l5g?2 b x is f\nd t ! l5g? ( ! radius vector is only fifty-six times ! radius ( ! e>? :5 ! moon is ne>e/ to u1 :ile x is sixty-f\r times t radius :5 ! moon is fur!/ f u4 ,! po9t 9 ! moon's orbit ne>e/ ! e>? is call$ h] p]igee2 ! po9t fur!/ f ! e>?1 h] apogee4 ,we always "k :5 ! moon is at "o ( ^! po9ts1 by h] app>5t diamet] or app>5t velocity2 =1 :5 at ! p]igee1 h] diamet] is great] ?an at any "t1 & h] motion mo/ rapid2 &1 on ! o!r h&1 h] diamet] is lea/1 & h] motion sl[e/1 :5 %e is at h] apogee4 ,! moon's nodes con/antly %ift _! positions 9 ! ecliptic1 f ea/ to we/1 at ! rate ( ab\t n9ete5 & a half degrees e ye>1 return+ to ! same po9ts once 9 eighte5 & a half ye>s4 ,9 ord] to und]/& :at is meant by ?is backw>d motion ( ! nodes1 y mu/ h v di/9ctly 9 m9d ! mean+ ( ! t]ms !mselves2 & if1 at any "t1 y %\ld be at a loss ab\t ! signification ( any ^w t is us$ 9 express+ an a/ronomical proposition1 ,i w\ld advise y to turn back to ! previ\s def9ition ( t t]m1 & revive its mean+ cle>ly 9 ! m9d1 be=e y proce$ any fur!r4 ,9 ! pres5t case1 y w recollect t ! moon's nodes are ! two po9ts :]e h] orbit cuts ! plane ( ! ecliptic4 ,suppose ! great circle ( ! ecliptic m>k$ out on ! face ( ! sky 9 a di/9ct l9e1 & let u obs]ve1 at any giv5 "t1 ! exact mom5t :5 ! moon crosses ?is l9e1 :i* we w suppose to be close to a c]ta9 />2 !n1 on its next return to t "p ( ! heav5s1 we %all f9d t x crosses ! ecliptic s5sibly to ! we/w>d ( t />1 & s on1 fur!r & fur!r to ! we/w>d1 e "t x crosses ! ecliptic at ei!r node4 ,?is fact is express$ by say+ t ! nodes retrograde on ! ecliptic2 s9ce any motion f ea/ to we/1 be+ contr>y to ! ord] ( ! signs1 is call$ retrograde4 ,! l9e :i* jo9s ^! two po9ts1 or ! l9e ( ! nodes1 is also said to h a retrograde motion1 or to revolve f ea/ to we/ once 9 eighte5 & a half ye>s4 ,! l9e ( ! apsides ( ! moon's orbit revolves f we/ to ea/1 ?r\gh h] :ole c\rse1 9 ab\t n9e ye>s4 ,y w recollect t ! apsides ( an elliptical orbit are ! two extremities ( ! long] axis ( ! ellipse2 correspond+ to ! p]ihelion & aphelion ( bodies revolv+ ab\t ! sun1 or to ! p]igee & apogee ( a body revolv+ ab\t ! e>?4 ,if1 9 any revolution ( ! moon1 we %\ld accurately m>k ! place 9 ! heav5s :]e ! moon is ne>e/ ! e>?1 7:i* may be kn[n by ! moon's app>5t diamet] be+ !n greate/17 we %\ld f9d t1 at ! next revolution1 x w\ld come to its p]igee a little fur!r ea/w>d ?an be=e1 & s on1 at e revolution1 until1 aft] n9e ye>s1 x w\ld come to its p]igee ne>ly at ! same po9t z at fir/4 ,?is fact is express$ by say+1 t ! p]igee1 & ( c\rse ! apogee1 revolves1 & t ! l9e :i* jo9s ^! two po9ts1 or ! l9e ( ! apsides1 also revolves4 ,^! are only a few ( ! irregul>ities t att5d ! motions ( ! moon4 ,^! & a few o!rs 7 fir/ discov]$ by actual obs]vation & h be5 long kn[n2 b a f> great] numb] ( lun> irregul>ities h be5 made kn[n by foll[+ out all ! consequ5ces ( ! law ( univ]sal gravitation4 ,! moon may be reg>d$ z a body endeavor+ to make its way ar\nd ! e>?1 b z subject to be cont9ually imp$$1 or div]t$ f its ma9 c\rse1 by ! action ( ! sun & ( ! e>?2 sometimes act+ 9 conc]t & sometimes 9 opposition to ea* o!r4 ,n[1 by exactly e/imat+ ! am\nt ( ^! respective =ces1 & asc]ta9+ _! resultant or comb9$ effect1 9 any giv5 case1 ! direction & velocity ( ! moon's motion may be accurately det]m9$4 ,b to d ?is has requir$ ! highe/ p[]s ( ! human m9d1 aid$ by all ! wond]ful res\rces ( ma!matics4 ,yet1 s consi/5t is tru? ) itself1 t1 :]e "s m9ute inequality 9 ! moon's motions is develop$ at ! end ( a long & intricate ma!matical process1 x inv>iably happ5s1 t1 on po9t+ ! telescope to ! moon1 & wat*+ its progress ?r\gh ! skies1 we may actually see h] commit ! same irregul>ities1 unless 7z is ! case ) _m ( !m7 !y are too m9ute to be matt]s ( obs]vation1 be+ beyond ! p[]s ( our vision1 ev5 :5 aid$ by ! be/ telescopes4 ,b ! tru? ( ! law ( gravitation1 & ( ! results x gives1 :5 foll[$ out by a *a9 ( ma!matical reason+1 is fully confirm$1 ev5 9 ^! m9ute/ matt]s1 by ! fact t ! moon's place 9 ! heav5s1 :5 ?us det]m9$1 always corresponds1 ) wond]ful exactness1 to ! place :i* %e is actually obs]v$ to occupy at t "t4 ,! m9d1 t 0 fir/ able to elicit f ! op]ations ( ,nature ! law ( univ]sal gravitation1 & aft]w>ds to apply x to ! complete explanation ( all ! irregul> w&]+s ( ! moon1 mu/ h giv5 evid5ce ( intellectual p[]s f> elevat$ above ^? ( ! majority ( ! human race4 ,we ne$ n wond]1 !re=e1 t su* homage is n[ paid to ! g5ius ( ,newton1--an admiration :i* has be5 cont9ually increas+1 z new discov]ies h be5 made by trac+ out new consequ5ces ( ! law ( univ]sal gravitation4 ,! *ief object ( a/ronomical tables is to give ! am\nt ( all ! irregul>ities t att5d ! motions ( ! heav5ly bodies1 by e/imat+ ! sep>ate value ( ea*1 "u all ! diff]5t circum/ances 9 :i* a body c be plac$4 ,?us1 ) respect to ! moon1 be=e we c det]m9e accurately ! di/ance ( ! moon f ! v]nal equ9ox1 t is1 h] longitude at any giv5 mom5t1 we mu/ be able to make exact all[ances = all h] irregul>ities :i* w\ld affect h] longitude4 ,^! are 9 all no less ?an sixty1 ?\gh mo/ ( !m are s exce$+ly m9ute1 t x is n common to take into ! acc\nt m ?an tw5ty-eight or ?irty4 ,! values ( ^! are all giv5 9 ! lun> tables2 & 9 f9d+ ! moon's place1 at any giv5 "t1 we proce$ z foll[s3 ,we fir/ f9d :at h] place w\ld be on ! supposition t %e moves uni=mly 9 a circle4 ,?is gives h] mean place4 ,we next apply ! v>i\s corrections = h] irregul> motions2 t is1 we apply ! equations1 subtract+ "s & add+ o!rs1 & ?us we f9d h] true place4 ,! a/ronomical tables h be5 c>ri$ to su* an a/oni%+ degree ( accuracy1 t x is said1 by ! highe/ au?ority1 t an a/ronom] c\ld n[ pr$ict1 = a ?\s& ye>s to come1 ! precise mom5t ( ! passage ( any "o ( ! />s ov] ! m]idian wire ( ! telescope ( 8 transit-in/rum5t1 ) su* a degree ( accuracy1 t ! error w\ld n be s great z to remove ! object ?r\gh an angul> space correspond+ to ! semidiamet] ( ! f9e/ wire t c\ld be made2 & a body :i*1 by ! tables1 ought to appe> 9 ! transit-in/rum5t 9 ! middle ( t wire1 w\ld 9 no case be remov$ to its out] edge4 ,! a/ronom]1 ! ma!matician1 & ! arti/1 h unit$ _! p[]s to produce ?is great result4 ,! a/ronom] has collect$ ! data1 by long-cont9u$ & mo/ accurate obs]vations on ! actual motions ( ! heav5ly bodies1 f night to night1 & f ye> to ye>2 ! ma!matician has tak5 ^! data1 & appli$ to !m ! b\ndless res\rces ( geometry & ! calculus2 &1 f9ally1 ! in/rum5t-mak] has furni%$ ! means1 n only ( v]ify+ ^! conclusions1 b ( discov]+ new tru?s1 z ! f\ndation ( future reason+s4 ,s9ce ! po9ts :]e ! moon crosses ! ecliptic1 or ! moon's nodes1 con/antly %ift _! positions ab\t n9ete5 & a half degrees to ! we/w>d1 e ye>1 ! sun1 9 8 annual progress 9 ! ecliptic1 w g f ! node r\nd to ! same node aga9 9 less "t ?an a ye>1 s9ce ! node goes to meet him n9ete5 & a half degrees to ! we/ ( ! po9t :]e !y met be=e4 ,x w\ld h tak5 ! sun ab\t n9ete5 days to h pass$ ov] ?is arc2 & consequ5tly1 ! int]val betwe5 two successive conjunctions betwe5 ! sun & ! moon's node is ab\t n9ete5 days %ort] ?an ! sol> ye> ( ?ree hundr$ & sixty-five days2 t is1 x is ab\t ?ree hundr$ & =ty-six days2 or1 m exactly1 x is #cdf4faihea days4 ,! "t f "o new moon to ano!r is #bi4ecjehhg days4 ,n[1 n9ete5 ( ! =m] p]iods are almo/ exactly equal to two hundr$ & tw5ty-?ree ( ! latt]3 ,= #cdf4faihea #aifehe4gh days#ah y4 #aj d4 ,& #bi4ecjehhg #bbcfehe4cb ,h5ce1 if ! sun & moon 7 to leave ! moon's node toge!r1 aft] ! sun _h be5 r\nd to ! same node n9ete5 times1 ! moon w\ld h made v ne>ly two hundr$ & tw5ty-?ree conjunctions ) ! sun4 ,if1 !re=e1 %e 0 9 conjunction ) ! sun at ! beg9n+ ( ?is p]iod1 %e w\ld be 9 conjunction aga9 at ! end ( x2 & all ?+s relat+ to ! sun1 ! moon1 & ! node1 w\ld be re/or$ to ! same relative situation z be=e1 & ! sun & moon w\ld />t aga91 to repeat ! same ph5om5a1 aris+ out ( ^! relations1 z occurr$ 9 ! prec$+ p]iod1 & 9 ! same ord]4 ,n[1 :5 ! sun & moon meet at ! moon's node1 an eclipse ( ! sun happ5s2 & dur+ ! entire p]iod ( eighte5 & a half ye>s eclipses w happ51 ne>ly 9 ! same mann] z !y did at correspond+ times 9 ! prec$+ p]iod4 ,?us1 if !re 0 a great eclipse ( ! sun on ! fif? ye> ( "o ( ^! p]iods1 a simil> eclipse 7usually diff]+ some:at 9 magnitude7 might be expect$ on ! fif? ye> ( ! next p]iod4 ,h5ce ?is p]iod1 consi/+ ( ab\t eighte5 ye>s & t5 days1 "u ! "n ( ! ,s>os1 0 us$ by ! ,*aldeans1 & o!r anci5t nations1 9 pr$ict+ eclipses4 ,x 0 probably by ?is means t ,?ales1 a ,grecian a/ronom] :o fl\ri%$ six hundr$ ye>s be=e ! ,*ri/ian era1 pr$ict$ an eclipse ( ! sun4 ,h]odotus1 ! old hi/orian ( ,greece1 relates t ! day 0 sudd5ly *ang$ into night1 & t ,?ales ( ,miletus _h =etold t a great eclipse 0 to happ5 ?is ye>4 ,x 0 !re=e1 at t age1 consid]$ z a di/+ui%$ feat to pr$ict ev5 ! ye> 9 :i* an eclipse 0 to happ54 ,?is eclipse is memorable 9 anci5t hi/ory1 f its hav+ t]m9at$ ! w> betwe5 ! ,lydians & ! ,m$es1 bo? p>ties be+ smitt5 ) su* indications ( ! wra? ( ! gods4 ,! ,metonic ,cycle has sometimes be5 conf\nd$ ) ! ,s>os1 b x is n ! same ) x1 nor 0 ! p]iod us$1 l ! ,s>os1 = =etell+ eclipses1 b = asc]ta9+ ! age ( ! moon at any giv5 p]iod4 ,x consi/$ ( n9ete5 tropical ye>s1 dur+ :i* "t !re are exactly two hundr$ & ?irty-five new moons2 s t1 at ! end ( ?is p]iod1 ! new moons w recur at seasons ( ! ye> correspond+ exactly to ^? ( ! prec$+ cycle4 ,if1 = example1 a new moon fell at ! "t ( ! v]nal equ9ox1 9 "o cycle1 n9ete5 ye>s aft]w>ds x w\ld occur aga9 at ! same equ9ox2 or1 if x _h happ5$ t5 days aft] ! equ9ox1 9 "o cycle1 x w\ld also happ5 t5 days aft] ! equ9ox1 n9ete5 ye>s aft]w>ds4 ,by regi/]+1 !re=e1 ! exact days ( any cycle at :i* ! new or full moons occurr$1 su* a cal5d> w\ld %[ on :at days ^! ev5ts w\ld occur 9 any o!r cycle2 &1 s9ce ! regulation ( games1 fea/s1 & fa/s1 has be5 made v ext5sively1 bo? 9 anci5t & mod]n times1 accord+ to new or full moons1 su* a cal5d> becomes v conv5i5t = f9d+ ! day on :i* ! new or full moon requir$ takes place4 ,suppose1 = example1 x 7 decre$ t a fe/ival %\ld be held on ! day ( ! fir/ full moon aft] ! ,v]nal equ9ox4 ,!n1 to f9d on :at day t w\ld happ51 9 any giv5 ye>1 we h only to see :at ye> x is ( ! lun> cycle2 = ! day w be ! same z x 0 9 ! correspond+ ye> ( ! cal5d> :i* records all ! full moons ( ! cycle = ea* ye>1 & ! respective days on :i* !y happ54 ,! ,a!nians adopt$ ! metonic cycle f\r hundr$ & ?irty-?ree ye>s be=e ! ,*ri/ian era1 = ! regulation ( _! cal5d>s1 & _h x inscrib$ 9 lett]s ( gold on ! walls ( ! temple ( ,m9]va4 ,h5ce ! t]m gold5 numb]1 /ill f\nd 9 our almanacs1 :i* d5otes ! ye> ( ! lun> cycle4 ,?us1 f\rte5 0 ! gold5 numb] = #ahcg1 be+ ! f\rte5? ye> ( ! lun> cycle4 ,! inequalities ( ! moon's motions are divid$ into p]iodical & secul>4 ,p]iodical inequalities are ^? :i* are complet$ 9 comp>atively %ort p]iods4 ,secul> inequalities are ^? :i* are complet$ only 9 v long p]iods1 su* z c5turies or ages4 ,h5ce ! correspond+ t]ms p]iodical equations & secul> equations4 ,z an example ( a secul> inequality1 we may m5tion ! accel]ation ( ! moon's mean motion4 ,x is discov]$ t ! moon actually revolves ar\nd ! e>? 9 a less p]iod n[ ?an %e did 9 anci5t times4 ,! diff]5ce1 h[ev]1 is exce$+ly small1 be+ only ab\t t5 seconds 9 a c5tury4 ,9 a lun> eclipse1 ! moon's longitude diff]s f t ( ! sun1 at ! middle ( ! eclipse1 by exactly "o hundr$ & eighty degrees2 & s9ce ! sun's longitude at any giv5 "t ( ! ye> is kn[n1 if we c le>n ! day & h\r :5 an eclipse occurr$ at any p]iod ( ! _w1 we ( c\rse "k ! longitude ( ! sun & moon at t p]iod4 ,n[1 9 ! ye> #gba1 be=e ! ,*ri/ian era1 ,ptolemy records a lun> eclipse to h happ5$1 & to h be5 obs]v$ by ! ,*aldeans4 ,! moon's longitude1 !re=e1 = t "t1 is kn[n2 & z we "k ! mean motions ( ! moon1 at pres5t1 />t+ f t epo*1 & comput+1 z may easily be done1 ! place :i* ! moon ought to occupy at pres5t1 at any giv5 "t1 %e is f\nd to be actually ne>ly a degree & a half 9 advance ( t place4 ,moreov]1 ! same conclusion is d]iv$ f a comp>ison ( ! ,*aldean obs]vations ) ^? made by an ,arabian a/ronom] ( ! t5? c5tury4 ,?is ph5om5on at fir/ l$ a/ronom]s to appreh5d t ! moon enc\nt]$ a resi/+ m$ium1 :i*1 by de/roy+ at e revolution a small portion ( h] projectile =ce1 w\ld h ! effect to br+ h] ne>] & ne>] to ! e>?1 & ?us to augm5t h] velocity4 ,b1 9 #aghf1 ,la ,place demon/rat$ t ?is accel]ation is "o ( ! legitimate effects ( ! sun's di/urb+ =ce1 & is s connect$ ) *anges 9 ! ecc5tricity ( ! e>?'s orbit1 t ! moon w cont9ue to be accel]at$ :ile t ecc5tricity dim9i%es2 b :5 ! ecc5tricity has rea*$ its m9imum1 or l[e/ po9t1 7z x w d1 aft] _m ages17 & beg9s to increase1 !n ! moon's motions w beg9 to be ret>d$1 & ?us h] mean motions w oscillate = ev] ab\t a mean value4 ,,lett] ,,xviii4 ,,eclipses4 ----,z :5 ! sun1 new ris51 ,looks ?r\gh ! horizontal mi/y air1 ,%orn ( 8 beams1 or f beh9d ! moon1 ,9 dim eclipse1 disa/r\s twilight %$s ,on half ! nations1 & ) fe> ( *ange ,p]plexes mon>*s3 d>k5$ s1 yet %one1 ,above !m all1 ! ,ar*angel4--,milton4 ,,hav+ n[ le>n$ v>i\s p>ticul>s respect+ ! e>?1 ! sun1 & ! moon1 y are prep>$ to und]/& ! explanation ( sol> & lun> eclipses1 :i* h 9 all ages excit$ a high degree ( int]e/4 ,inde$1 :at is m admirable1 ?an t a/ronom]s %\ld be able to tell u1 ye>s be=eh&1 ! exact in/ant ( ! comm5cem5t & t]m9ation ( an eclipse1 & describe all ! att5dant circum/ances ) ! greate/ fidelity4 ,y h d\btless1 my de> fri5d1 p>ticipat$ 9 ?is admiration1 & felt a /rong desire to le>n h[ x is t a/ronom]s are able to look s f> into futurity4 ,i w endeavor1 9 ?is ,lett]1 to expla9 to y ! lead+ pr9ciples ( ! calculation ( eclipses1 ) z mu* pla9ness z possible4 ,an eclipse ( ! moon happ5s :5 ! moon1 9 its revolution ar\nd ! e>?1 falls into ! e>?'s %ad[4 ,an eclipse ( ! sun happ5s :5 ! moon1 com+ betwe5 ! e>? & ! sun1 cov]s ei!r a "p or ! :ole ( ! sol> disk4 ,! e>? & ! moon be+ bo? opaque1 globul> bodies1 expos$ to ! sun's light1 !y ca/ %ad[s opposite to ! sun1 l any o!r bodies on :i* ! sun %9es4 ,7 ! sun ( ! same size ) ! e>? & ! moon1 !n ! l9es drawn t\*+ ! surface ( ! sun & ! surface ( ! e>? or moon 7:i* l9es =m ! b\nd>ies ( ! %ad[7 w\ld be p>allel to ea* o!r1 & ! %ad[ w\ld be a cyl9d] inf9ite 9 l5g?2 & 7 ! sun less ?an ! e>? or ! moon1 ! %ad[ w\ld be an increas+ cone1 its n>r[] end re/+ on ! e>?2 b z ! sun is va/ly great] ?an ei!r ( ^! bodies1 ! %ad[ ( ea* is a cone ^: base re/s on ! body itself1 & :i* comes to a po9t1 or v]tex1 at a c]ta9 di/ance beh9d ! body4 ,^! sev]al cases are repres5t$ 9 ! foll[+ diagrams1 ,figs4 #ci1 #dj1 #da4 ,illu/ration ,figs4 #ci1 #dj1 #da4 ,x is f\nd1 by calculation1 t ! l5g? ( ! moon's %ad[1 on an av]age1 is j ab\t suffici5t to rea* to ! e>?2 b ! moon is sometimes fur!r f ! e>? ?an at o!rs1 & :5 %e is ne>] ?an usual1 ! %ad[ rea*es consid]ably beyond ! surface ( ! e>?4 ,also1 ! moon1 z well z ! e>?1 is at diff]5t di/ances f ! sun at diff]5t times1 & its %ad[ is longe/ :5 x is fur!/ f ! sun4 ,n[1 :5 bo? ^! circum/ances conspire1 t is1 :5 ! moon is 9 h] p]igee & along ) ! e>? 9 h] aphelion1 h] %ad[ ext5ds ne>ly fifte5 ?\s& miles beyond ! c5tre ( ! e>?1 & cov]s a space on ! surface "o hundr$ & sev5ty miles broad4 ,! e>?'s %ad[ is ne>ly a million ( miles 9 l5g?1 & consequ5tly m ?an ?ree & a half times z long z ! di/ance ( ! e>? f ! moon2 & x is also1 at ! di/ance ( ! moon1 ?ree times z broad z ! moon itself4 ,an eclipse ( ! sun c take place only at new moon1 :5 ! sun & moon meet 9 ! same "p ( ! heav5s1 = !n only c ! moon come betwe5 u & ! sun2 & an eclipse ( ! moon c occur only :5 ! sun & moon are 9 opposite p>ts ( ! heav5s1 or at full moon2 = !n only c ! moon fall into ! %ad[ ( ! e>?4 ,illu/ration ,fig4 #db4 ,! nature ( eclipses w be cle>ly und]/ood f ! foll[+ repres5tation4 ,! diagram1 ,fig4 #db1 exhibits ! relative position ( ! sun1 ! e>?1 & ! moon1 bo? 9 a sol> & 9 a lun> eclipse4 ,"h1 ! moon is fir/ repres5t$1 :ile revolv+ r\nd ! e>?1 z pass+ betwe5 ! e>? & ! sun1 & ca/+ its %ad[ on ! e>?4 ,z ! moon is "h suppos$ to be at h] av]age di/ance f ! e>?1 ! %ad[ b j rea*es ! e>?'s surface4 ,7 ! moon 7z is sometimes ! case7 ne>] ! e>? h] %ad[ w\ld n t]m9ate 9 a po9t1 z is repres5t$ 9 ! figure1 b at a great] or less di/ance ne>] ! base ( ! cone1 s z to cov] a consid]able space1 :i*1 z ,i h already m5tion$1 sometimes ext5ds to "o hundr$ & sev5ty miles 9 bread?1 b is commonly mu* less ?an ?is4 ,on ! o!r side ( ! e>?1 ! moon is repres5t$ z trav]s+ ! e>?'s %ad[1 z is ! case 9 a lun> eclipse4 ,z ! moon is sometimes ne>] ! e>? & sometimes fur!r (f1 x is evid5t t x w trav]se ! %ad[ at a broad] or a n>r[] "p1 accord+ly4 ,! figure1 h[ev]1 repres5ts ! moon z pass+ ! %ad[ fur!r f ! e>? ?an is ev] actually ! case1 s9ce ! di/ance f ! e>? is nev] s mu* z "o ?ird ( ! :ole l5g? ( ! %ad[4 ,x is evid5t f ! figure1 t if a spectator 7 situat$ :]e ! moon's %ad[ /rikes ! e>?1 ! moon w\ld cut (f f him ! view ( ! sun1 or ! sun w\ld be totally eclips$4 ,or1 if he 7 )9 a c]ta9 di/ance ( ! %ad[ on ei!r side1 ! moon w\ld be p>tly betwe5 him & ! sun1 & w\ld int]cept f him m or less ( ! sun's light1 accord+ z he 0 ne>] to ! %ad[ or fur!r f x4 ,if he 7 at c or d1 he w\ld j see ! moon ent]+ ^u ! sun's disk2 if he 7 ne>] ! %ad[ ?an ei!r ( ^! po9ts1 he w\ld h a portion ( ?is light cut (f f 8 view1 & m1 9 proportion z he drew ne>] ! %ad[2 & ! mom5t he ent]$ ! %ad[1 he w\ld lose sight ( ! sun4 ,to all places betwe5 a or b & ! %ad[1 ! sun w\ld ca/ a p>tial %ad[ ( ! moon1 gr[+ deep] & deep]1 z x approa*$ ! true %ad[4 ,?is p>tial %ad[ is call$ ! moon's p5umbra4 ,9 l mann]1 z ! moon approa*es ! e>?'s %ad[1 9 a lun> eclipse1 z soon z %e arrives at a1 ! e>? beg9s to int]cept f h] a portion ( ! sun's light1 or %e falls 9 ! e>?'s p5umbra4 ,%e cont9ues to lose m & m ( ! sun's light1 z %e draws ne> to ! %ad[1 & h5ce h] disk becomes gradually obscur$1 until x ent]s ! %ad[1 :5 ! sun's light is entirely lo/4 ,z ! sun & e>? are bo? situat$ 9 ! plane ( ! ecliptic1 if ! moon also revolv$ ar\nd ! e>? 9 ?is plane1 we %\ld h a sol> eclipse at e new moon1 & a lun> eclipse at e full moon2 =1 9 ! =m] case1 ! moon w\ld come directly betwe5 u & ! sun1 & 9 ! latt] case1 ! e>? w\ld come directly betwe5 ! sun & ! moon4 ,b ! moon is incl9$ to ! ecliptic ab\t five degrees1 & ! c5tre ( ! moon may be all ?is di/ance f ! c5tre ( ! sun at new moon1 & ! same di/ance f ! c5tre ( ! e>?'s %ad[ at full moon4 ,x is true1 ! moon ext5ds across h] pa?1 "o half h] bread? ly+ on ea* side ( x1 & ! sun likewise rea*es f ! ecliptic a di/ance equal to half 8 bread?4 ,b ^! lum9>ies toge!r make b little m ?an a degree1 & consequ5tly1 _! two semidiamet]s w\ld occupy only ab\t half a degree ( ! five degrees f "o orbit to ! o!r :]e !y are fur!/ ap>t4 ,also1 ! e>?'s %ad[1 :]e ! moon crosses x1 ext5ds f ! ecliptic less ?an ?ree f\r?s ( a degree1 s t ! semidiamet] ( ! moon & ( ! e>?'s %ad[ w\ld toge!r rea* b little way across ! space t may1 9 c]ta9 cases1 sep>ate ! two lum9>ies f ea* o!r :5 !y are 9 opposition4 ,?us1 suppose we c\ld take hold ( ! circle 9 ! figure t repres5ts ! moon's orbit1 7,fig4 #db1 page #aig17 & lift ! moon up five degrees above ! plane ( ! pap]1 x is evid5t t ! moon1 z se5 f ! e>?1 w\ld appe> 9 ! heav5s five degrees above ! sun1 & ( c\rse w\ld cut (f none ( 8 light2 & x is also pla9 t ! moon1 at ! full1 w\ld pass ! %ad[ ( ! e>? five degrees bel[ x1 & w\ld suff] no eclipse4 ,b 9 ! c\rse ( ! sun's app>5t revolution r\nd ! e>? once a ye> he is successively 9 e "p ( ! ecliptic2 consequ5tly1 ! conjunctions & oppositions ( ! sun & moon may occur at any "p ( ! ecliptic1 & ( c\rse at ! two po9ts :]e ! moon's orbit crosses ! ecliptic1--t is1 at ! nodes2 = ! sun mu/ necess>ily come to ea* ( ^! nodes once a ye>4 ,if1 !n1 ! moon ov]takes ! sun j z %e is cross+ 8 pa?1 %e w hide m or less ( 8 disk f u4 ,s9ce1 also1 ! e>?'s %ad[ is always directly opposite to ! sun1 if ! sun is at "o ( ! nodes1 ! %ad[ mu/ ext5d 9 ! direction ( ! o!r node1 s z to lie directly across ! moon's pa?2 & if ! moon ov]takes x !re1 %e w pass ?r\gh x1 & be eclips$4 ,?us1 9 ,fig4 #dc1 let ,,bn repres5t ! sun's pa?1 & ,,an1 ! moon's1--,n be+ ! place ( ! node2 !n x is evid5t1 t if ! two lum9>ies at new moon be s f> f ! node1 t ! di/ances betwe5 _! c5tres is great] ?an _! semidiamet]s1 no eclipse c happ52 b if t di/ance is less ?an ?is sum1 z at ,e1 ,f1 !n an eclipse w take place2 b if ! position be z at ,c1 ,d1 ! two bodies w j t\* "o ano!r4 ,if ,a d5otes ! e>?'s %ad[1 in/ead ( ! sun1 ! same illu/ration w apply to an eclipse ( ! moon4 ,illu/ration ,fig4 #dc4 ,s9ce bodies are def9$ to be 9 conjunction :5 !y are 9 ! same "p ( ! heav5s1 & to be 9 opposition :5 !y are 9 opposite p>ts ( ! heav5s1 x may n appe> h[ ! sun & moon c be 9 conjunction1 z at ,a & ,b1 :5 !y are /ill at "s di/ance f ea* o!r4 ,b x mu/ be recollect$ t bodies are 9 conjunction :5 !y h ! same longitude1 9 :i* case !y are situat$ 9 ! same great circle p]p5dicul> to ! ecliptic1--t is1 9 ! same second>y to ! ecliptic4 ,"o ( ^! bodies may be mu* fur!r f ! ecliptic ?an ! o!r2 /ill1 if ! same second>y to ! ecliptic passes ?r\gh !m bo?1 !y w be 9 conjunction or opposition4 ,9 a total eclipse ( ! moon1 its disk is /ill visible1 %9+ ) a dull1 r$ light4 ,?is light _c be d]iv$ directly f ! sun1 s9ce ! view ( ! sun is completely hidd5 f ! moon2 nor by reflection f ! e>?1 s9ce ! illum9at$ side ( ! e>? is :olly turn$ f ! moon2 b x is ow+ to refraction f ! e>?'s atmosph]e1 by :i* a few scatt]$ rays ( ! sun are b5t r\nd into ! e>?'s %ad[ & convey$ to ! moon1 suffici5t 9 numb] to af=d ! feeble light 9 "q4 ,x is impossible fully to und]/& ! me?od ( calculat+ eclipses1 )\t a k ( trigonometry2 /ill x is n difficult to =m "s g5]al notion ( ! process4 ,x may be readily conceiv$ t1 by long-cont9u$ obs]vations on ! sun & moon1 ! laws ( _! revolution may be s well und]/ood1 t ! exact places :i* !y w occupy 9 ! heav5s at any future times may be =ese5 & laid d[n 9 tables ( ! sun & moon's motions2 t we may ?us asc]ta91 by inspect+ ! tables1 ! in/ant :5 ^! two bodies w be toge!r 9 ! heav5s1 or be 9 conjunction1 & :5 !y w be "o hundr$ & eighty degrees ap>t1 or 9 opposition4 ,moreov]1 s9ce ! exact place ( ! moon's node among ! />s at any p>ticul> "t is kn[n to a/ronom]s1 x _c be difficult to det]m9e :5 ! new or full moon occurs 9 ! same "p ( ! heav5s z t :]e ! node is project$1 z se5 f ! e>?4 ,9 %ort1 z a/ronom]s c easily det]m9e :at w be ! relative position ( ! sun1 ! moon1 & ! moon's nodes1 = any giv5 "t1 !y c tell :5 ^! lum9>ies w meet s ne> ! node z to produce an eclipse ( ! sun1 or :5 !y w be 9 opposition s ne> ! node z to produce an eclipse ( ! moon4 ,a little reflection w enable y to =m a cle> idea ( ! situation ( ! sun1 ! moon1 & ! e>?1 at ! "t ( a sol> eclipse4 ,fir/1 suppose ! conjunction to take place at ! node2 t is1 imag9e ! moon to come directly betwe5 ! e>? & ! sun1 z %e w ( c\rse d1 if %e comes betwe5 ! e>? & ! sun ! mom5t %e is cross+ ! ecliptic2 = !n ! ?ree bodies w all lie 9 "o & ! same /raight l9e4 ,b :5 ! moon is 9 ! ecliptic1 h] %ad[1 or at lea/ ! axis1 or c5tral l9e1 ( ! %ad[1 mu/ co9cide ) ! l9e t jo9s ! c5tres ( ! sun & e>?1 & rea* along ! plane ( ! ecliptic t[>ds ! e>?4 ,! moon's %ad[1 at h] av]age di/ance f ! e>?1 is j ab\t long en\gh to rea* ! surface ( ! e>?2 b :5 ! moon1 at ! new1 is 9 h] apogee1 or at h] greate/ di/ance f ! e>?1 ! %ad[ is n long en\gh to rea* ! e>?4 ,on ! contr>y1 :5 ! moon is ne>] to u ?an h] av]age di/ance1 h] %ad[ is long en\gh to rea* beyond ! e>?1 ext5d+1 :5 ! moon is 9 h] p]igee1 m ?an f\rte5 ?\s& miles beyond ! c5tre ( ! e>?4 ,n[1 z dur+ ! eclipse ! moon moves ne>ly 9 ! plane ( ! ecliptic1 h] %ad[ :i* accompanies h] mu/ also move ne>ly 9 ! same plane1 & mu/ !re=e trav]se ! e>? across its c5tral regions1 along ! t]re/rial ecliptic1 s9ce ?is is no?+ m ?an ! int]section ( ! plane ( ! cele/ial ecliptic ) ! e>?'s surface4 ,! motion ( ! e>?1 too1 on its axis1 9 ! same direction1 w c>ry a place along ) ! %ad[1 ?\gh ) a less velocity by m ?an "o half2 s t ! actual velocity ( ! %ad[1 9 respect to places ov] :i* x passes on ! e>?1 w only equal ! diff]5ce betwe5 its own rate & t ( ! places1 z !y are c>ri$ =w>d 9 ! diurnal revolution4 ,we h ?us f> suppos$ t ! moon comes to h] conjunction precisely at ! node1 or at ! mom5t :5 %e is cross+ ! ecliptic4 ,b1 secondly1 suppose %e is on ! nor? side ( ! ecliptic at ! "t ( conjunction1 & mov+ t[>ds h] desc5d+ node1 & t ! conjunction takes place z f> f ! node z an eclipse c happ54 ,! %ad[ w n fall 9 ! plane ( ! ecliptic1 b a little nor?w>d ( x1 s z j to graze ! e>? ne> ! pole ( ! ecliptic4 ,! ne>] ! conjunction comes to ! node1 ! fur!r ! %ad[ w fall f ! pol> t[>ds ! equatorial regions4 ,9 a sol> eclipse1 ! %ad[ ( ! moon travels ov] a portion ( ! e>?1 z ! %ad[ ( a small cl\d1 se5 f an em95ce 9 a cle> day1 rides along ov] hills & pla9s4 ,let u imag9e ourselves /&+ on ! moon2 !n we %all see ! e>? p>tially eclips$ by ! moon's %ad[1 9 ! same mann] z we n[ see ! moon eclips$ by ! %ad[ ( ! e>?2 & we might calculate ! v>i\s circum/ances ( ! eclipse1--its comm5cem5t1 duration1 & quantity1--9 ! same mann] z we calculate ^! elem5ts 9 an eclipse ( ! moon1 z se5 f ! e>?4 ,b al?\gh ! g5]al *>act]s ( a sol> eclipse might be inve/igat$ on ^! pr9ciples1 s f> z respects ! e>? at l>ge1 yet1 z ! appe>ances ( ! same eclipse ( ! sun are v diff]5t at diff]5t places on ! e>?'s surface1 x is necess>y to calculate its peculi> aspects = ea* place sep>ately1 a circum/ance :i* makes ! calculation ( a sol> eclipse mu* m complicat$ & t$i\s ?an t ( an eclipse ( ! moon4 ,! moon1 :5 %e ent]s ! %ad[ ( ! e>?1 is depriv$ ( ! light ( ! "p imm]s$1 & ! effect ^u its appe>ance is ! same z ?\gh t "p 7 pa9t$ black1 9 :i* case x w\ld be black alike to all places :]e ! moon 0 above ! horizon4 ,b x n s ) a sol> eclipse4 ,we d n see ?is by ! %ad[ ca/ on ! e>?1 z we %\ld d1 if we /ood on ! moon1 b by ! int]position ( ! moon betwe5 u & ! sun2 & ! sun may be hidd5 f "o obs]v]1 :ile he is 9 full view ( ano!r only a few miles di/ant4 ,?us1 a small insulat$ cl\d sail+ 9 a cle> sky w1 = a few mom5ts1 hide ! sun f u1 & f a c]ta9 space ne> u1 :ile all ! region ar\nd is illum9at$4 ,b al?\gh ! analogy betwe5 ! motions ( ! %ad[ ( a small cl\d & ( ! moon 9 a sol> eclipse holds good 9 _m p>ticul>s1 yet ! velocity ( ! lun> %ad[ is f> great] ?an t ( ! cl\d1 be+ no less ?an two ?\s& two hundr$ & eighty miles p] h\r4 ,! moon's %ad[ c nev] cov] a space on ! e>? m ?an "o hundr$ & sev5ty miles broad1 & ! space actually cov]$ commonly falls mu* %ort ( t4 ,! portion ( ! e>?'s surface ev] cov]$ by ! moon's p5umbra is ab\t f\r ?\s& ?ree hundr$ & n9ety-?ree miles4 ,! app>5t diamet] ( ! moon v>ies mat]ially at diff]5t times1 be+ greate/ :5 ! moon is ne>e/ to u1 & lea/ :5 %e is fur!/ (f2 :ile ! sun's app>5t dim5sions rema9 ne>ly ! same4 ,:5 ! moon is at h] av]age di/ance f ! e>?1 %e is j ab\t l>ge en\gh to cov] ! sun's disk2 consequ5tly1 if1 9 a c5tral eclipse ( ! sun1 ! moon is at h] mean di/ance1 %e cov]s ! sun b = an in/ant1 produc+ only a mom5t>y eclipse4 ,if %e is ne>] ?an h] av]age di/ance1 !n ! eclipse may cont9ue total "s "t1 ?\gh nev] m ?an eight m9utes1 & seldom s long z t2 b if %e is fur!r (f ?an usual1 or t[>ds h] apogee1 !n %e is n l>ge en\gh to cov] ! :ole sol> disk1 b we see a r+ ( ! sun encircl+ ! moon1 con/itut+ an annul> eclipse1 z se5 9 ,fig4 #dd4 ,ev5 ! elevation ( ! moon above ! horizon w sometimes s5sibly affect ! dim5sions ( ! eclipse4 ,y w recollect t ! moon is ne>] to u :5 on ! m]idian ?an :5 9 ! horizon by ne>ly f\r ?\s& miles1 or by ne>ly ! radius ( ! e>?2 & consequ5tly1 h] app>5t diamet] is l>ge/ :5 on ! m]idian4 ,! diff]5ce is s consid]able1 t ! same eclipse w appe> total to a spectator :o views x ne> 8 m]idian1 :ile1 at ! same mom5t1 x appe>s annul> to "o :o has ! moon ne> 8 horizon4 ,an annul> eclipse may la/1 at mo/1 twelve m9utes & tw5ty-f\r seconds4 ,illu/ration ,fig4 #dd4 ,eclipses ( ! sun are m frequ5t ?an ^? ( ! moon4 ,yet lun> eclipses be+ visible to e "p ( ! t]re/rial hemisph]e opposite to ! sun1 :ile ^? ( ! sun are visible only to a small portion ( ! hemisph]e on :i* ! moon's %ad[ falls1 x happ5s t1 = any p>ticul> place on ! e>?1 lun> eclipses are m frequ5tly visible ?an sol>4 ,9 any ye>1 ! numb] ( eclipses ( bo? lum9>ies _c be less ?an two nor m ?an sev53 ! mo/ usual numb] is f\r1 & x is v r>e to h m ?an six4 ,a total eclipse ( ! moon frequ5tly happ5s at ! next full moon aft] an eclipse ( ! sun4 ,= s9ce1 9 a sol> eclipse1 ! sun is at or ne> "o ( ! moon's nodes1--t is1 is project$ to ! place 9 ! sky :]e ! moon crosses ! ecliptic1--! e>?'s %ad[1 :i* is ( c\rse directly opposite to ! sun1 mu/ be at or ne> ! o!r node1 & may n h pass$ too f> f ! node be=e ! moon comes r\nd to ! opposition & ov]takes x4 ,9 total eclipses ( ! sun1 !re has sometimes be5 obs]v$ a rem>kable radiation ( light f ! m>g9 ( ! sun1 :i* is ?\ght to be ow+ to ! zodiacal light1 :i* is ( su* dim5sions z to ext5d f> beyond ! sol> orb4 ,a /rik+ appe>ance ( ?is k9d 0 exhibit$ 9 ! total eclipse ( ! sun :i* occurr$ 9 ,june1 #ahjf4 ,a total eclipse ( ! sun is "o ( ! mo/ sublime & impressive ph5om5a ( ,nature4 ,among b>b>\s tribes x is ev] contemplat$ ) fe> & a/oni%m5t1 & z /rongly indicative ( ! displeasure ( ! gods4 ,two anci5t nations1 ! ,lydians & ,m$es1 allud$ to be=e1 :o 7 engag$ 9 a bloody w>1 ab\t six hundr$ ye>s be=e ,*ri/1 7 smitt5 ) su* awe1 on ! appe>ance ( a total eclipse ( ! sun1 j on ! eve ( a battle1 t !y ?rew d[n _! arms1 & made peace4 ,:5 ,columbus fir/ discov]$ ,am]ica1 & 0 9 dang] ( ho/ility f ! ,natives1 he aw$ !m into submission by tell+ !m t ! sun w\ld be d>k5$ on a c]ta9 day1 9 tok5 ( ! ang] ( ! gods at !m1 = _! treatm5t ( him4 ,among cultivat$ nations1 a total eclipse ( ! sun is recognis$1 f ! exactness ) :i* ! "t ( occurr5ce & ! v>i\s appe>ances answ] to ! pr$iction1 z af=d+ "o ( ! pr\de/ triumphs ( a/ronomy4 ,by a/ronom]s !mselves1 x is ( c\rse view$ ) ! highe/ int]e/1 n only z v]ify+ _! calculations1 b z contribut+ to e/abli%1 beyond all d\bt1 ! c]ta9ty ( ^? gr& laws1 ! tru? ( :i* is involv$ 9 ! result4 ,i _h ! good =tune to witness ! total eclipse ( ! sun ( ,june1 #ahjf1 :i* 0 "o ( ! mo/ rem>kable on record4 ,to ! wond]+ gaze ( *ildhood x pres5t$ a spectacle t c nev] be =gott54 ,a bright & beautiful morn+ inspir$ univ]sal joy1 = ! sky 0 entirely cl\dless4 ,e "o 0 busily occupi$ 9 prep>+ smok$ glass1 9 read9ess = ! great sight1 :i* 0 to be fir/ se5 ab\t t5 o'clock4 ,a ?rill ( m+l$ wond] & delight /ruck e m9d :51 at ! appo9t$ mom5t1 a little black ind5tation appe>$ on ! limb ( ! sun4 ,?is gradually exp&$1 cov]+ m & m ( ! sol> disk1 until an increas+ gloom 0 spread ov] ! face ( ,nature2 & :5 ! sun 0 :olly lo/1 ne> mid-day1 a feel+ ( horror p]vad$ almo/ e behold]4 ,! d>kness 0 :olly unlike t ( twilight or night4 ,a ?ick curta91 v diff]5t f cl\ds1 hung ^u ! face ( ! sky1 produc+ a /range & indescribably gloomy appe>ance1 :i* 0 reflect$ f all ?+s on ! e>?1 9 hues equally /range & unnatural4 ,"s ( ! planets1 & ! l>ge/ ( ! fix$ />s1 %one out ?r\gh ! gloom1 yet ) _! usual brightness4 ,! temp]ature ( ! air rapidly decl9$1 & s sudd5 a *ill came ov] ! e>?1 t _m p]sons caught sev]e colds f _! exposure4 ,ev5 ! animal tribes exhibit$ tok5s ( fe> & agitation4 ,birds1 especially1 flutt]$ & flew swiftly ab\t1 & dome/ic f[ls w5t to re/4 ,inde$1 ! ^w eclipse is d]iv$ f a ,greek ^w1 7 ekleipsis1 ekleipsis17 :i* signifies to fail1 to fa9t or swoon away2 s9ce ! moon1 at ! p]iod ( h] greate/ brightness1 fall+ into ! %ad[ ( ! e>?1 0 imag9$ by ! anci5ts to sick5 & swoon1 z if %e 7 go+ to die4 ,by "s v anci5t nations %e 0 suppos$1 at su* times1 to be 9 pa92 &1 9 ord] to relieve h] fanci$ di/ress1 !y lift$ tor*es high 9 ! atmosph]e1 blew horns & trumpets1 beat ^u braz5 vessels1 & ev51 aft] ! eclipse 0 ov]1 !y (f]$ sacrifices to ! moon4 ,! op9ion also ext5sively prevail$1 t x 0 9 ! p[] ( wit*es1 by _! spells & *>ms1 n only to d>k5 ! moon1 b to br+ h] d[n f h] orbit1 & to compel h] to %$ h] baleful influ5ces ^u ! e>?4 ,9 sol> eclipses1 also1 especially :5 total1 ! sun 0 suppos$ to turn away 8 face 9 abhorr5ce ( "s atroci\s crime1 t ei!r _h be5 p]petrat$ or 0 ab\t to be p]petrat$1 & to ?reat5 mank9d ) ev]la/+ night1 & ! de/ruction ( ! _w4 ,to su* sup]/itions ,milton alludes1 9 ! passage :i* ,i h tak5 = ! motto ( ?is ,lett]4 ,! ,*9ese1 :o1 f a v high p]iod ( antiquity1 h be5 great obs]v]s ( eclipses1 al?\gh !y did n take mu* notice ( ^? ( ! moon1 reg>d$ eclipses ( ! sun 9 g5]al z un=tunate1 b especially su* z occurr$ on ! fir/ day ( ! ye>4 ,^! 7 ?\ght to =ebode ! greate/ calamities to ! emp]or1 :o on su* occasions did n receive ! usual complim5ts ( ! season4 ,:51 f ! pr$ictions ( _! a/ronom]s1 an eclipse ( ! sun 0 expect$1 !y made great prep>ation at c\rt = obs]v+ x2 & z soon z x comm5c$1 a bl9d man beat a drum1 a great conc\rse assembl$1 & ! m&>9s1 or nobility1 appe>$ 9 /ate4 ,,lett] ,,xix4 ,,longitude4--,,tides4 ,fir/ 9 8 ea/1 ! glori\s lamp 0 se51 ,reg5t ( day1 & all ! horizon r\nd ,inve/$ ) bright rays1 jocund to run ,8 longitude ?r\gh heav5's high road2 ! gray ,dawn & ! ,pleiades be=e him danc$1 ,%$d+ sweet influ5ce4--,milton4 ,,! anci5ts /udi$ a/ronomy *iefly z subsidi>y to a/rology1 ) ! va9 hope ( ?us p5etrat+ ! veil ( futurity1 & read+ _! de/9ies among ! />s4 ,! mod]ns1 on ! o!r h&1 h 9 view1 z ! great practical object ( ?is /udy1 ! p]fect+ ( ! art ( navigation4 ,:5 we reflect on ! va/ int]e/s emb>k$ on ! ocean1 bo? ( prop]ty & life1 & ^u ! imm5se b5efits t accrue to society f a safe & spe$y int]c\rse betwe5 ! diff]5t nations ( ! e>?1 we _c b see t :atev] t5ds to enable ! m>9] to f9d 8 way on ! pa?less ocean1 & to secure him aga9/ its multipli$ dang]s1 mu/ conf] a signal b5efit on society4 ,9 anci5t times1 to v5ture out ( sight ( l& 0 deem$ an act ( extreme audacity2 & ,horace1 ! ,roman poet1 pron\nces him :o fir/ v5tur$ to tru/ 8 frail b>k to ! /ormy ocean1 endu$ ) a he>t ( oak1 & girt ) triple folds ( brass4 ,b n[1 ! navigator :o fully avails himself ( all ! res\rces ( sci5ce1 & especially ( a/ronomy1 may laun* fe>lessly on ! deep1 & almo/ bid defiance to rocks & tempe/s4 ,by enabl+ ! navigator to f9d 8 place on ! ocean ) almo/ absolute precision1 h[ev] he may h be5 driv5 ab\t by ! w9ds1 & h[ev] long he may h be5 out ( sight ( l&1 a/ronom]s mu/ be held z great b5efactors to all :o commit ei!r _! lives or _! =tunes to ! sea4 ,nor h !y secur$ to ! art ( navigation su* b5efits )\t incr$ible /udy & toil1 9 wat*+ ! motions ( ! heav5ly bodies1 9 inve/igat+ ! laws by :i* _! movem5ts are gov]n$1 & 9 r$uc+ all _! discov]ies to a =m easily available to ! navigator1 s t1 by "s simple obs]vation on "o or two ( ! heav5ly bodies1 ) in/rum5ts :i* ! a/ronom] has inv5t$1 & prep>$ = 8 use1 & by look+ out a few numb]s 9 tables :i* h be5 compil$ = him1 ) imm5se labor1 he may asc]ta9 ! exact place he occupies on ! surface ( ! globe1 ?\s&s ( miles f l&4 ,! situation ( any place is kn[n by its latitude & longitude4 ,z *>ts ( e ocean & sea are furni%$ to ! sailor1 9 :i* are laid d[n ! latitudes & longitudes ( e po9t ( l&1 :e!r on ! %ores ( isl&s or ! ma91 he has1 !re=e1 only to asc]ta9 8 latitude & longitude at any p>ticul> place on ! ocean1 9 ord] to f9d :]e he is1 ) respect to ! ne>e/ po9t ( l&1 al?\gh ?is may be1 & may always h be51 entirely out ( sight to him4 ,to det]m9e ! latitude ( a place is comp>atively an easy matt]1 :5ev] we c see ei!r ! sun or ! />s4 ,! di/ance ( ! sun f ! z5i?1 :5 on ! m]idian1 on a giv5 day ( ! ye>1 7:i* di/ance we may easily take ) ! sextant17 enables u1 ) ! aid ( ! tables1 to f9d ! latitude ( ! place2 or1 by tak+ ! altitude ( ! nor? />1 we at once obta9 ! latitude4 ,! longitude ( a place may be f\nd by any me?od1 by :i* we may asc]ta9 h[ mu* its "t ( day diff]s f t ( ,gre5wi* at ! same mom5t4 ,a place t lies ea/w>d ( ano!r comes to ! m]idian an h\r e>li] = e fifte5 degrees ( longitude1 & ( c\rse has ! h\r ( ! day s mu* 9 advance ( ! o!r1 s t x c\nts "o o'clock :5 ! o!r place c\nts twelve4 ,on ! o!r h&1 a place ly+ we/w>d ( ano!r comes to ! m]idian lat] by "o h\r = e fifte5 degrees1 s t x c\nts only elev5 o'clock :5 ! o!r place c\nts twelve4 ,keep+ ^! pr9ciples 9 view1 x is easy to see t a comp>ison ( ! diff]5ce ( "t betwe5 two places at ! same mom5t1 all[+ fifte5 degrees = an h\r1 sixty m9utes = e f\r m9utes ( "t1 & sixty seconds = e f\r seconds ( "t1 af=ds u an accurate mode ( f9d+ ! diff]5ce ( longitude betwe5 ! two places4 ,?is comp>ison may be made by means ( a *ronomet]1 or f sol> or lun> eclipses1 or by :at is call$ ! lun> me?od ( f9d+ ! longitude4 ,*ronomet]s are di/+ui%$ f clocks1 by be+ regulat$ by means ( a balance-:eel in/ead ( a p5dulum4 ,a wat*1 !re=e1 comes "u ! g5]al def9ition ( a *ronomet]2 b ! "n is m commonly appli$ to l>g] timepieces1 too l>ge to be c>ri$ ab\t ! p]son1 & con/ruct$ ) ! greate/ possible accuracy1 ) special ref]5ce to f9d+ ! longitude4 ,suppose1 !n1 we are furni%$ ) a *ronomet] set to ,gre5wi* "t4 ,we arrive at ,new ,york1 = example1 & comp>e x ) ! "t !re4 ,we f9d x is five h\rs 9 advance ( ! ,new-,york "t1 indicat+ five o'clock1 ,p4,m41 :5 x is noon at ,new ,york4 ,h5ce we f9d t ! longitude ( ,new ,york is #eaege degrees4#aa ,! "t at ,new ,york1 or any individual place1 c be kn[n by obs]vations ) ! transit-in/rum5t1 :i* gives u ! precise mom5t :5 ! sun is on ! m]idian4 ,x w\ld n be necess>y to resort to ,gre5wi*1 = ! purpose ( sett+ our *ronomet] to ,gre5wi* "t1 z x might be set at any place ^: longitude is kn[n1 hav+ be5 previ\sly det]m9$4 ,?us1 if we "k t ! longitude ( a c]ta9 place is exactly sixty degrees ea/ ( ,gre5wi*1 we h only to set our *ronomet] f\r h\rs beh9d ! "t at t place1 & x w be regulat$ to ,gre5wi* "t4 ,h5ce x is a matt] ( ! greate/ importance to navigation1 t ! longitude ( num]\s ports1 9 diff]5t p>ts ( ! e>?1 %\ld be accurately det]m9$1 s t :5 a %ip arrives at any su* port1 x may h ! means ( sett+ or v]ify+ its *ronomet]4 ,?is me?od ( tak+ ! longitude seems s easy1 t y w p]haps ask1 :y x is n suffici5t = all purposes1 & accord+ly1 :y x does n sup]s$e ! move complicat$ & labori\s me?ods8 :y e sailor does n provide himself ) a *ronomet]1 in/ead ( f9d+ 8 longitude at sea by t$i\s & (t-repeat$ calculations1 z he is 9 ! habit ( do+8 ,i answ]1 x is only 9 a few extraord9>y cases t *ronomet]s h be5 con/ruct$ ( su* accuracy z to af=d results z exact z ^? obta9$ by ! o!r me?ods1 to be describ$ %ortly2 & in/rum5ts ( su* p]fection are too exp5sive = g5]al use among sailors4 ,inde$1 ! m common *ronomet]s co/ too mu* to come )9 ! means ( a great majority ( sea-f>+ m54 ,moreov]1 by be+ transport$ f place to place1 *ronomet]s are liable to *ange _! rate4 ,by ! rate ( any timepiece is meant its deviation f p]fect accuracy4 ,?us1 if a clock %\ld ga9 "o second p] day1 "o day ) ano!r1 & we %\ld f9d x impossible to br+ x ne>] to ! tru?1 we may reckon ?is z its rate1 & all[ = x 9 our e/imate ( ! "t ( any p>ticul> obs]vation4 ,if ! error 0 n uni=m1 b sometimes great] & sometimes less ?an "o second p] day1 !n ! am\nt ( su* deviation is call$ its v>iation f its mean rate4 ,i introduce ^! m9ute /atem5ts1 7:i* are m precise ?an ,i usually deem necess>y17 to %[ y to :at an a/oni%+ degree ( accuracy *ronomet]s h 9 "s in/ances be5 br\ght4 ,!y h be5 c>ri$ f ,london to ,baff9's ,bay1 & br\ght back1 aft] a ?ree ye>s' voyage1 & f\nd to h v>i$ f _! mean rate1 dur+ ! :ole "t1 only a second or two1 :ile ! extreme v>iation ( sev]al *ronomet]s1 tri$ at ! ,royal ,obs]vatory at ,gre5wi*1 nev] exce$$ a second & a half4 ,c\ld *ronomet]s always be dep5d$ on to su* a degree ( accuracy z ?is1 we %\ld h>dly desire any ?+ bett] = det]m9+ ! longitude ( diff]5t places on ! e>?4 ,a rec5t det]m9ation ( ! longitude ( ! ,city ,hall 9 ,new ,york1 by means ( ?ree *ronomet]s1 s5t out f ,london expressly = t purpose1 did n diff] f ! longitude z f\nd by a sol> eclipse 7:i* is "o ( ! be/ me?ods7 b a second & a qu>t]4 ,eclipses ( ! sun & moon furni% ! means ( asc]ta9+ ! longitude ( a place1 because ! entrance ( ! moon into ! e>?'s %ad[ 9 a lun> eclipse1 & ! entrance ( ! moon ^u ! disk ( ! sun 9 a sol> eclipse1 are sev]ally examples ( "o ( ^? in/antane\s occurr5ces 9 ! heav5s1 :i* af=d ! means ( comp>+ ! times ( diff]5t places1 & ( ?us det]m9+ _! diff]5ces ( longitude4 ,?us1 if ! comm5cem5t ( a lun> eclipse 0 se5 at "o place an h\r soon] ?an at ano!r1 ! two places w\ld be fifte5 degrees ap>t1 9 longitude2 & if ! longitude ( "o ( ! places 0 kn[n1 t ( ! o!r w\ld become kn[n also4 ,! exact in/ant ( ! moon's ent]+ into ! %ad[ ( ! e>?1 h[ev]1 _c be det]m9$ ) v great precision1 s9ce ! moon1 9 pass+ ?r\gh ! e>?'s p5umbra1 loses its light gradually1 s t ! mom5t :5 x leaves ! p5umbra & ent]s into ! %ad[ _c be v accurately def9$4 ,! fir/ contact ( ! moon ) ! sun's disk1 9 a sol> eclipse1 or ! mom5t ( leav+ x1--t is1 ! beg9n+ & end ( ! eclipse1--are in/ants t c be det]m9$ ) mu* precision1 & accord+ly !y are mu* reli$ on = an accurate det]m9ation ( ! longitude4 ,b1 on acc\nt ( ! complicat$ & labori\s nature ( ! calculation ( ! longitude f an eclipse ( ! sun1 7s9ce ! beg9n+ & end are n se5 at diff]5t places1 at ! same mom5t17 ?is me?od ( f9d+ ! longitude is n adapt$ to common use1 nor available at sea4 ,x is useful1 h[ev]1 = det]m9+ ! longitude ( fix$ obs]vatories4 ,! lun> me?od ( f9d+ ! longitude is ! mo/ ref9$ & accurate ( all ! modes practis$ at sea4 ,! motion ( ! moon ?r\gh ! heav5s is s rapid1 t %e p]ceptibly alt]s h] di/ance f any /> e m9ute2 consequ5tly1 ! mom5t :5 t di/ance is a c]ta9 numb] ( degrees & m9utes is "o ( ^? in/antane\s ev5ts1 :i* may be tak5 advantage ( = comp>+ ! times ( diff]5t places1 & ?us det]m9+ _! diff]5ce ( longitude4 ,n[1 9 a "w call$ ! ',nautical ,almanac1' pr9t$ 9 ,london1 annually1 = ! use ( navigators1 ! di/ance ( ! moon f ! sun by day1 or f kn[n fix$ />s by night1 = e day & night 9 ! ye>1 is calculat$ be=eh&4 ,if1 !re=e1 a sailor wi%es to asc]ta9 8 longitude1 he may take ) 8 sextant ! di/ance ( ! moon f "o ( ^! />s at any "t1--suppose n9e o'clock1 at night1--& !n turn to ! ',nautical ,almanac1' & see :at "t x 0 at ,gre5wi* :5 ! di/ance betwe5 ! moon & t /> 0 ! same4 ,let x be twelve o'clock1 or ?ree h\rs 9 advance ( 8 "t3 8 longitude1 ( c\rse1 is =ty-five degrees we/4 ,?is me?od requires m skill & accuracy ?an are possess$ by ! majority ( seaf>+ m52 b1 :5 practis$ ) ! requisite degree ( skill1 its results are v satisfactory4 ,capta9 ,basil ,hall1 "o ( ! mo/ sci5tific comm&]s 9 ! ,briti% navy1 relates ! foll[+ incid5t1 to %[ ! excell5ce ( ?is me?od4 ,he sail$ f ,san ,blas1 on ! we/ coa/ ( ,mexico1 &1 aft] a voyage ( eight ?\s& miles1 occupy+ eighty-n9e days1 arriv$ (f ,rio de ,janeiro1 hav+1 9 ?is int]val1 pass$ ?r\gh ! ,pacific ,ocean1 r\nd$ ,cape ,horn1 & cross$ ! ,s\? ,atlantic1 )\t mak+ any l&1 or ev5 see+ a s+le sail1 ) ! exception ( an ,am]ican :al] (f ,cape ,horn4 ,:5 )9 a week's sail ( ,rio1 he set s]i\sly ab\t det]m9+1 by lun> obs]vations1 ! precise l9e ( ! %ip's c\rse1 & its situation at a det]m9ate mom5t2 & hav+ asc]ta9$ ?is )9 f five to t5 miles1 ran ! re/ ( ! way by ^? m ready & comp5di\s me?ods1 kn[n to navigators1 :i* c be safely employ$ = %ort trips betwe5 "o kn[n po9t & ano!r1 b :i* _c be tru/$ 9 long voyages1 :]e ! moon is ! only sure guide4 ,!y /e]$ t[>ds ,rio ,janeiro = "s days aft] tak+ ! lun>s1 &1 hav+ arriv$ )9 fifte5 or tw5ty miles ( ! coa/1 !y hove to1 at f\r 9 ! morn+1 till ! day %\ld break1 & !n bore up1 proce$+ cauti\sly1 on acc\nt ( a ?ick fog :i* envelop$ !m4 ,z ?is cle>$ away1 !y _h ! satisfaction ( see+ ! great ,sug>-,loaf ,rock1 :i* /&s on "o side ( ! h>bor's m\?1 s ne>ly "r ahead1 t !y _h n to alt] _! c\rse above a po9t1 9 ord] to hit ! entrance ( ! h>bor4 ,?is 0 ! fir/ l& !y _h se5 = ?ree mon?s1 aft] cross+ s _m seas1 & be+ set backw>ds & =w>ds by innum]able curr5ts & f\l w9ds4 ,! effect on all on bo>d 0 electric2 & ! admiration ( ! sailors 0 unb\nd$4 ,inde$1 :at c\ld be m admirable ?an t a man on ! deck ( a vessel1 by measur+ ! di/ance betwe5 ! moon & a />1 ) a little in/rum5t :i* he held 9 8 h&1 c\ld det]m9e 8 exact place on ! e>?'s surface 9 ! mid/ ( a va/ ocean1 aft] hav+ trav]s$ x 9 all directions1 = ?ree mon?s1 cross+ 8 track _m times1 & all ! :ile out ( sight ( l&8 ,! lun> me?od ( f9d+ ! longitude c\ld nev] h be5 susceptible ( suffici5t accuracy1 _h n ! motions ( ! moon1 ) all _! irregul>ities1 be5 /udi$ & inve/igat$ by ! mo/ labori\s & pr(\nd rese>*es4 ,h5ce ,newton1 :ile wrapt 9 ^? m$itations :i*1 to sup]ficial m9ds1 w\ld p]haps h appe>$ r curi\s ?an useful1 inasmu* z !y respect$ di/ant bodies ( ! univ]se :i* seem$ to h little connexion ) ! affairs ( ?is _w1 0 labor+ night & day = ! b5efit ( ! sailor & ! m]*ant4 ,he 0 guid+ ! vessel ( ! "o1 & secur+ ! m]*&ise ( ! o!r2 & ?us he contribut$ a l>ge %>e to promote ! happ9ess ( 8 fell[-m51 n only 9 exalt+ ! p[]s ( ! human intellect1 b also 9 pres]v+ ! lives & =tunes ( ^? engag$ 9 navigation & comm]ce4 ,pr9ciples 9 sci5ce are rules 9 art2 & ! philosoph] :o is engag$ 9 ! inve/igation ( ^! pr9ciples1 al?\gh 8 pursuits may be ?\ght less practically useful ?an ^? ( ! artisan :o c>ries out ^? pr9ciples into real life1 yet1 )\t ! k ( ! pr9ciples1 ! rules w\ld h nev] be5 kn[n4 ,/udies1 !re=e1 ! mo/ ab/ruse1 are1 :5 view$ z furni%+ rules to act1 (t5 productive ( ! highe/ practical utility4 ,s9ce ! tides are occasion$ by ! influ5ce ( ! sun & moon1 ,i w conclude ?is ,lett] ) a few rem>ks on ?is curi\s ph5om5on4 ,by ! tides are meant ! alt]nate ris+ & fall+ ( ! wat]s ( ! ocean4 ,its greate/ & lea/ elevations are call$ high & l[ wat]2 its ris+ & fall+ are call$ flood & ebb2 & ! extraord9>y high & l[ tides t occur twice e mon? are call$ spr+ & neap tides4 ,x is high or l[ tide on opposite sides ( ! globe at ! same "t4 ,if1 = example1 we h high wat] at noon1 x is also high wat] to ^? :o live on ! m]idian bel[ u1 :]e x is midnight4 ,9 l mann]1 l[ wat] occurs simultane\sly on opposite sides ( ! m]idian4 ,! av]age am\nt ( ! tides = ! :ole globe is ab\t two & a half feet2 b _! actual height at diff]5t places is v v>i\s1 sometimes be+ sc>cely p]ceptible1 & sometimes ris+ to sixty or sev5ty feet4 ,at ! same place1 also1 ! ph5om5a ( ! tides are v diff]5t at diff]5t times4 ,9 ! ,bay ( ,fundy1 :]e ! tide rises sev5ty feet1 x comes 9 a mighty wave1 se5 ?irty miles (f1 & ro>+ ) a l\d noise4 ,at ! m\? ( ! ,sev]n1 9 ,engl&1 ! flood comes up 9 "o head ab\t t5 feet high1 br++ c]ta9 de/ruction to any small craft t has be5 un=tunately left by ! ebb+ wat]s on ! flats & z x passes ! m\? ( ! ,avon1 x s5ds up t small riv] a va/ body ( wat]1 ris+1 at ,bri/ol1 =ty or fifty feet4 ,tides are caus$ by ! unequal attractions ( ! sun & moon ^u diff]5t p>ts ( ! e>?4 ,suppose ! projectile =ce by :i* ! e>? is c>ri$ =w>d 9 h] orbit to be susp5d$1 & ! e>? to fall t[>ds "o ( ^! bodies1--! moon1 = example1--9 consequ5ce ( _! mutual attraction4 ,!n1 if all p>ts ( ! e>? fell equally t[>ds ! moon1 no d]angem5t ( its diff]5t p>ts w\ld result1 any m ?an ( ! p>ticles ( a drop ( wat]1 9 its desc5t to ! gr\nd4 ,b if "o "p fell fa/] ?an ano!r1 ! diff]5t portions w\ld evid5tly be sep>at$ f ea* o!r4 ,n[1 ?is is precisely :at takes place ) respect to ! e>?1 9 its fall t[>ds ! moon4 ,! portions ( ! e>? 9 ! hemisph]e next to ! moon1 on acc\nt ( be+ ne>] to ! c5tre ( attraction1 fall fa/] ?an ^? 9 ! opposite hemisph]e1 & consequ5tly leave !m beh9d4 ,! solid e>?1 on acc\nt ( its cohesion1 _c obey ?is impulse1 s9ce all its diff]5t portions con/itute "o mass1 :i* is act$ on 9 ! same mann] z ?\gh x 7 all collect$ 9 ! c5tre2 b ! wat]s on ! surface1 mov+ freely "u ?is impulse1 endeavor to des]t ! solid mass & fall t[>ds ! moon4 ,= a simil> reason1 ! wat]s 9 ! opposite hemisph]e1 fall+ less t[>ds ! moon ?an ! solid e>? does1 are left beh9d1 or appe> to rise4 ,illu/ration ,fig4 #df4 ,b if ! moon draws ! wat]s ( ! e>? into an oval =m t[>ds h]self1 rais+ !m simultane\sly on ! opposite sides ( ! e>?1 !y mu/ obvi\sly be drawn away f ! int]m$iate p>ts ( ! e>?1 :]e x mu/ at ! same "t be l[ wat]4 ,?us1 9 ,fig4 #df1 ! moon1 ,m1 raises ! wat]s b5ea? itself at ,z & ,n1 at :i* places x is high wat]1 b at ! same "t depresses ! wat]s at ,h & ,r1 at :i* places x is l[ wat]4 ,h5ce1 ! int]val betwe5 ! high & l[ tide1 on successive days1 is ab\t fifty m9utes1 correspond+ to ! progress ( ! moon 9 h] orbit f we/ to ea/1 :i* causes h] to come to ! m]idian ab\t fifty m9utes lat] e day4 ,!re occurs1 h[ev]1 an int]m$iate tide1 :5 ! moon is on ! l[] m]idian1 s t ! int]val betwe5 two high tides is ab\t twelve h\rs1 & tw5ty-five m9utes4 ,7 x n = ! imp$im5ts :i* prev5t ! =ce f produc+ its full effects1 we might expect to see ! great tide-wave1 z ! elevat$ cre/ is call$1 always directly b5ea? ! moon1 att5d+ x regul>ly ar\nd ! globe4 ,b ! in]tia ( ! wat]s prev5ts _! in/antly obey+ ! moon's attraction1 & ! friction ( ! wat]s on ! bottom ( ! ocean /ill fur!r ret>ds its progress4 ,x is n1 !re=e1 until sev]al h\rs 7diff]+ at diff]5t places7 aft] ! moon has pass$ ! m]idian ( a place1 t x is high tide at t place4 ,! sun has an action simil> to t ( ! moon1 b only "o ?ird z great4 ,on acc\nt ( ! great mass ( ! sun1 comp>$ ) t ( ! moon1 we might suppose t 8 action 9 rais+ ! tides w\ld be great] ?an ! moon's2 b ! ne>ness ( ! moon to ! e>? m ?an comp5sates = ! sun's great] quantity ( matt]4 ,z1 h[ev]1 wrong views are frequ5tly ent]ta9$ on ?is subject1 let u endeavor to =m a correct idea ( ! advantage :i* ! moon d]ives f h] proximity4 ,x is n t h] actual am\nt ( attraction is ?us r5d]$ great] ?an t ( ! sun2 b x is t h] attraction = ! diff]5t p>ts ( ! e>? is v unequal1 :ile t ( ! sun is ne>ly uni=m4 ,x is ! inequality ( ?is action1 & n ! absolute =ce1 t produces ! tides4 ,! sun be+ n9ety-five millions ( miles f ! e>?1 :ile ! diamet] ( ! e>? is only "o twelve ?\s&? "p ( ?is di/ance1 ! effects ( ! sun's attraction w be ne>ly ! same on all p>ts ( ! e>?1 & !re=e w n1 z 0 expla9$ ( ! moon1 t5d to sep>ate ! wat]s f ! e>? on ! ne>e/ side1 or ! e>? f ! wat]s on ! remote/ side1 b 9 a degree proportionally small]4 ,b ! diamet] ( ! e>? is "o ?irtie? ! di/ance ( ! moon1 & !re=e ! moon acts ) consid]ably great] p[] on "o "p ( ! e>? ?an on ano!r4 ,z ! sun & moon bo? contribute to produce ! tides1 & z !y sometimes act toge!r & sometimes 9 opposition to ea* o!r1 s correspond+ v>iations occur 9 ! height ( ! tide4 ,! spr+ tides1 or ^? :i* rise to an unusual height twice a mon?1 are produc$ by ! sun & moon's act+ toge!r2 & ! neap tides1 or ^? :i* are unusually l[ twice a mon?1 are produc$ by ! sun & moon's act+ 9 opposition to ea* o!r4 ,! spr+ tides occur at ! syzygies3 ! neap tides at ! quadratures4 ,at ! "t ( new moon1 ! sun & moon bo? be+ on ! same side ( ! e>?1 & act+ ^u x 9 ! same l9e1 _! actions conspire1 & ! sun may be consid]$ z add+ s mu* to ! =ce ( ! moon4 ,we h already se5 h[ ! moon contributes to raise a tide on ! opposite side ( ! e>?4 ,b ! sun1 z well z ! moon1 raises its own tide-wave1 :i* at new moon co9cides ) ! lun> tide-wave4 ,?is w be pla9 on inspect+ ! diagram1 ,fig4 #dg1 on page #bbj1 :]e ,s repres5ts ! sun1 ,c1 ! moon 9 conjunction1 ,o1 ! moon 9 opposition1 & ,z1 ,n1 ! tide-wave4 ,s9ce ! sun & moon sev]ally raise a tide-wave1 & ! two "h co9cide1 x is evid5t t a peculi>ly high tide mu/ occur :5 ! two bodies are 9 conjunction1 or at new moon4 ,at full moon1 also1 ! two lum9>ies conspire 9 ! same way to raise ! tide2 = we mu/ recollect t ea* body contributes to raise a tide on ! opposite side4 ,?us1 :5 ! sun is at ,s & ! moon at ,o1 ! sun draws ! wat]s on ! side next to x away f ! e>?1 & ! moon draws ! e>? away f ! wat]s on t side2 _! unit$ actions1 !re=e1 conspire1 & an unusually high tide is ! result4 ,on ! side next to ,o1 ! two =ces likewise conspire3 = :ile ! moon draws ! wat]s away f ! e>?1 ! sun draws ! e>? away f ! wat]s4 ,9 bo? cases an unusually l[ tide is produc$2 = ! m ! wat] is elevat$ at ,z & ,n1 ! m x w be depress$ at ,h & ,r1 ! places ( l[ tide4 ,illu/ration ,fig4 #dg4 ,twice a mon?1 also1 namely1 at ! quadratures ( ! moon1 ! tides nei!r rise s high nor fall s l[ z at o!r times1 because !n ! sun & moon act aga9/ ea* o!r4 ,?us1 9 ,fig4 #dh1 :ile ,f t5ds to raise ! wat] at ,z1 ,s t5ds to depress x1 & consequ5tly ! high tide is less ?an usual4 ,aga91 :ile ,f t5ds to depress ! wat] at ,r1 ,s t5ds to elevate x1 & !re=e ! l[ tide is less ?an usual4 ,h5ce ! diff]5ce betwe5 high & l[ wat] is only half z great at neap z at spr+ tide4 ,9 ! diagrams1 ! elevation & depression ( ! wat]s is repres5t$1 = ! sake ( illu/ration1 z f> great] ?an x really is2 = y mu/ recollect t ! av]age height ( ! tides = ! :ole globe is only ab\t two & a half feet1 a quantity s small1 9 comp>ison ) ! diamet] ( ! e>?1 t 7 ! due proportions pres]v$ 9 ! figures1 ! effect w\ld be :olly ins5sible4 ,illu/ration ,fig4 #dh4 ,! v>iations ( di/ance 9 ! sun are n great en\gh to influ5ce ! tides v mat]ially1 b ! v>iations 9 ! moon's di/ances h a /rik+ effect4 ,! tides :i* happ51 :5 ! moon is 9 p]igee1 are consid]ably great] ?an :5 %e is 9 apogee2 & if %e happ5s to be 9 p]igee at ! "t ( ! syzygies1 ! spr+ tides are unusually high4 ,! motion ( ! tide-wave is n a progressive motion1 b a m]e undulation1 & is to be c>efully di/+ui%$ f ! curr5ts to :i* x gives rise4 ,if ! ocean completely cov]$ ! e>?1 ! sun & moon be+ 9 ! equator1 ! tide-wave w\ld travel at ! same rate z ! e>? revolves on its axis4 ,inde$1 ! correct way ( conceiv+ ( ! tide-wave1 is to consid] ! moon at re/1 & ! e>?1 9 its rotation f we/ to ea/1 z br++ successive portions ( wat] "u ! moon1 :i* portions be+ elevat$ successively1 at ! same rate z ! e>? revolves on its axis1 h a relative motion we/w>d1 at ! same rate4 ,! tides ( riv]s1 n>r[ bays1 & %ores f> f ! ma9 body ( ! ocean1 are n produc$ 9 ^? places by ! direct action ( ! sun & moon1 b are subord9ate waves propagat$ f ! great tide-wave1 & are call$ d]ivative tides1 :ile ^? rais$ directly by ! sun & moon are call$ primitive tides4 ,illu/ration ,fig4 #di4 ,! velocity ) :i* ! tide moves w dep5d on v>i\s circum/ances1 b pr9cipally on ! dep?1 & probably on ! regul>ity1 ( ! *annel4 ,if ! dep? is ne>ly uni=m ! tides w be regul>2 b if "s p>ts ( ! *annel are deep :ile o!rs are %all[1 ! wat]s w be deta9$ by ! great] friction ( ! %all[ places1 & ! tides w be irregul>4 ,! direction1 also1 ( ! d]ivative tide may be totally diff]5t f t ( ! primitive4 ,?us1 9 ,fig4 #di1 if ! great tide-wave1 mov+ f ea/ to we/1 is repres5t$ by ! l9es #a1 #b1 #c1 #d1 ! d]ivative tide1 :i* is propagat$ up a riv] or bay1 w be repres5t$ by ! l9es #c1 #d1 #e1 #f1 #g4 ,advanc+ fa/] 9 ! *annel ?an next ! bank1 ! tides w lag beh9d t[>ds ! %ores1 & ! tide-wave w take ! =m ( curves1 z repres5t$ 9 ! diagram4 ,on acc\nt ( ! ret>d+ influ5ce ( %oals1 & an unev51 ind5t$ coa/1 ! tide-wave travels m sl[ly along ! %ores ( an isl& ?an 9 ! neighbor+ sea1 assum+ convex figures at a little di/ance f ! isl&1 & on opposite sides ( x4 ,^! convex l9es sometimes meet1 & become bl5d$ 9 su* a way1 z to create s+ul> anomalies 9 a sea mu* brok5 by isl&s1 z well z on coa/s ind5t$ ) num]\s bays & riv]s4 ,peculi> ph5om5a are also produc$1 :5 ! tide fl[s 9 at opposite extremities ( a reef or isl&1 z into ! two opposite ends ( ,long-,isl& ,s\nd4 ,9 c]ta9 cases1 a tide-wave is =c$ into a n>r[ arm ( ! sea1 & produces v rem>kable tides4 ,! tides ( ! ,bay ( ,fundy 7! highe/ 9 ! _w7 are ascrib$ to ?is cause4 ,! tides on ! coa/ ( ,nor? ,am]ica are d]iv$ f ! great tide-wave ( ! ,s\? ,atlantic1 :i* runs /eadily nor?w>d along ! coa/ to ! m\? ( ! ,bay ( ,fundy1 :]e x meets ! nor!rn tide-wave fl[+ 9 ! opposite direction4 ,?is accumulat$ wave be+ =c$ into ! n>r[ space occupi$ by ! ,bay1 produces ! rem>kable tide ( t place4 ,! l>ge/ lakes & inl& seas h no p]ceptible tides4 ,?is is ass]t$ by all writ]s respect+ ! ,caspian & ,eux9e2 & ! same is f\nd to be true ( ! l>ge/ ( ! ,nor?-,am]ican lakes1 ,lake ,sup]ior4 ,al?\gh ^! sev]al tracts ( wat] appe> l>ge1 :5 tak5 by !mselves1 yet !y occupy b small portions ( ! surface ( ! globe1 z w appe> evid5t f ! del9eation ( !m on ! artificial globe4 ,n[1 we mu/ recollect t ! primitive tides are produc$ by ! unequal action ( ! sun & moon ^u ! diff]5t p>ts ( ! e>?2 & t x is only at po9ts ^: di/ance f ea* o!r be>s a consid]able ratio to ! :ole di/ance ( ! sun or moon1 t ! inequality ( action becomes manife/4 ,! space requir$ to make ! effect s5sible is l>g] ?an ei!r ( ^! tracts ( wat]4 ,x is obvi\s1 also1 t !y h no opportunity to be subject to a d]ivative tide4 ,al?\gh all mu/ admit t ! tides h "s connexion ) ! sun & ! moon1 yet !re are s _m seem+ anomalies1 :i* at fir/ appe> irreconcilable ) ! !ory ( gravitation1 t "s are unwill+ to admit ! explanation giv5 by ?is !ory4 ,?us1 ! height ( ! tide is s v>i\s1 t at "s places on ! e>? !re is sc>cely any tide at all1 :ile at o!r places x rises to sev5ty feet4 ,! "t ( occurr5ce is also at _m places :olly uncon=mable to ! motions ( ! moon1 z is requir$ by ! !ory1 be+ l[ wat] :]e x %\ld be high wat]2 or1 in/ead ( appe>+ j b5ea? ! moon1 z ! !ory w\ld lead u to expect1 foll[+ x at ! di/ance ( six1 t51 or ev5 fifte51 h\rs2 & f9ally1 ! moon sometimes appe>s to h no "p at all 9 produc+ ! tide1 b x happ5s uni=mly at noon & midnight1 7z is said to be ! case at ! ,society ,isl&s17 & !re=e seems :olly dep5d5t on ! sun4 ,not)/&+ ^! seem+ inconsi/5cies ) ! law ( univ]sal gravitation1 to :i* ! explanation ( ! tides is ref]r$1 ! correspond5ce ( ! tides to ! motions ( ! sun & moon1 9 ob$i5ce to ! law ( attraction1 is 9 g5]al su* z to w>rant ! application ( t law to !m1 :ile 9 a great majority ( ! cases :i* appe> to be exceptions to ! op]ation ( t law1 local causes & imp$im5ts h be5 discov]$1 :i* modifi$ or ov]rul$ ! uni=m op]ation ( ! law ( gravitation4 ,?us x does n disprove ! reality ( ! exi/5ce ( a =ce :i* c>ries bodies ne> ! surface ( ! e>? t[>ds its c5tre1 t we see !m sometimes compell$1 by ! op]ation ( local causes1 to move 9 ! opposite direction4 ,a ball %ot f a cannon is /ill subject to ! law ( gravitation1 al?\gh1 = a c]ta9 "t1 9 ob$i5ce to ! impulse giv5 x1 x may proce$ 9 a l9e contr>y to t 9 :i* gravity alone w\ld c>ry x4 ,! fact t wat] may be made to run up hill does n disprove ! fact t x usually runs d[n hill by ! =ce ( gravity1 or t x is /ill subject to ?is =ce1 al?\gh1 f ! action ( modify+ or sup]ior =ces1 x may be proce$+ 9 a direction contr>y to t giv5 by gravity4 ,inde$1 ^? :o h /udi$ ! doctr9e ( ! tides mo/ pr(\ndly consid] !m z af=d+ a /rik+ & palpable exhibition ( ! tru? ( ! doctr9e ( univ]sal gravitation4 ,,footnote3 #aa ,! exact longitude ( ! ,city ,hall1 9 ! city ( ,new ,york1 is #d;h4 #efm4 #cc4es4 ,,lett] ,,xx4 ,,planets4--,,m]cury ,,& ,,v5us4 ,fir/1 ,m]cury1 amid/ full tides ( light1 ,rolls next ! sun1 ?r\gh 8 small circle bright2 ,our e>? w\ld blaze b5ea? s fi]ce a ray1 ,& all its m>ble m\nta9s melt away4 ,fair ,v5us next fulfils h] l>g] r\nd1 ,) s(t] beams1 & mild] glory cr[n$2 ,fri5d to mank9d1 %e glitt]s f af>1 ,n[ ! bright ev5+1 n[ ! morn+1 />4--,bak]4 ,,!re is no /udy 9 :i* m is to be hop$ = f a lucid arrangem5t1 ?an 9 ! /udy ( a/ronomy4 ,"s subjects involv$ 9 ?is /udy appe> v difficult & p]plex+ to ! le>n]1 be=e he has fully le>n$ ! doctr9e ( ! sph]e1 & ga9$ a c]ta9 famili>ity ) a/ronomical doctr9es1 :i* w\ld seem v easy to him aft] he _h made su* atta9m5ts4 ,su* an ord] ought to be obs]v$1 z %all br+ out ! facts & doctr9es ( ! sci5ce j 9 ! place :]e ! m9d ( ! le>n] is prep>$ to receive !m4 ,"s writ]s on a/ronomy introduce _! read]s at once to ! mo/ p]plex+ "p ( ! :ole subject1--! planet>y motions4 ,i h ?\ght a diff]5t c\rse advisable1 & h !re=e comm5c$ ^! ,lett]s ) an acc\nt ( ^? bodies :i* are mo/ famili>ly kn[n to u1 ! e>?1 ! sun1 & ! moon4 ,9 connexion ) ! e>?1 we are able to acquire a good k ( ! artificial divisions & po9ts ( ref]5ce t are e/abli%$ on ! e>? & 9 ! heav5s1 con/itut+ ! doctr9e ( ! sph]e4 ,y ?us became famili> ) _m t]ms & def9itions :i* are us$ 9 a/ronomy4 ,^! ought to be always v cle>ly borne 9 m9d2 & if y n[ meet ) any t]m1 ! def9ition ( :i* y h ei!r p>tially or :olly =gott51 let me /rongly recomm5d to y1 to turn back & review x1 until x becomes z famili> to y z h\sehold words4 ,inde$1 y w f9d x mu* to y\r advantage to g back frequ5tly1 & reit]ate ! e>li] p>ts ( ! subject1 be=e y advance to subjects ( a m intricate nature4 ,if ?is process %\ld appe> to y a little t$i\s1 /ill y w f9d y\rself fully comp5sat$ by ! cle> light 9 :i* all ! succe$+ subjects w appe>4 ,?is cle> & di/9ct p]ception ( ! gr\nd we h be5 ov] %[s u j :]e we are on our j\rney1 & helps u to f9d ! rema9d] ( ! way ) f> great] ease ?an we c\ld o!rwise d4 ,i d n1 h[ev]1 propose by any devices to relieve y f ! tr\ble ( ?9k+4 ,^? :o are n will+ to incur ?is tr\ble c nev] le>n mu* ( a/ronomy4 ,9 introduc+ y to ! planets1 7:i* next claim our att5tion17 ,i w1 9 ! fir/ place1 endeavor to convey to y "s cle> views ( ^! bodies individually1 & aft]w>ds help y to =m z correct a notion z possible ( _! motions & mutual relations4 ,! "n planet is d]iv$ f a ,greek ^w1 7 plants1 planetes17 :i* signifies a w&]]1 & is appli$ to ?is class ( bodies1 because !y %ift _! positions 9 ! heav5s1 :]eas ! fix$ />s con/antly ma9ta9 ! same places ) respect to ea* o!r4 ,! planets kn[n f a high antiquity are1 ,m]cury1 ,v5us1 ,e>?1 ,m>s1 ,jupit]1 & ,saturn4 ,to ^!1 9 #agha1 0 add$ ,uranus1 7or ,h]s*el1 z x is sometimes call$1 f ! "n ( its discov]]27 &1 z late z ! comm5cem5t ( ! pres5t c5tury1 f\r m 7 add$1 namely1 ,c]es1 ,pallas1 ,juno1 & ,ve/a4 ,^! bodies are designat$ by ! foll[+ *>act]s3 #a4 ,m]cury1 ,planet3 ,m]cury #b4 ,v5us1 ,planet3 ,v5us #c4 ,e>?1 ,planet3 ,e>? #d4 ,m>s1 ,planet3 ,m>s #e4 ,ve/a1 ,planet3 ,ve/a #f4 ,juno1 ,planet3 ,juno #g4 ,c]es1 ,planet3 ,c]es #h4 ,pallas1 ,planet3 ,pallas #i4 ,jupit]1 ,planet3 ,jupit] #aj4 ,saturn1 ,planet3 ,saturn #aa4 ,uranus1 ,planet3 ,uranus ,! =ego+ are call$ ! prim>y planets4 ,sev]al ( ^! h "o or m att5dants1 or satellites1 :i* revolve ar\nd !m z !y revolve ar\nd ! sun4 ,! ,e>? has "o satellite1 namely1 ! ,moon2 ,jupit] has f\r2 ,saturn1 sev52 & ,uranus1 six4 ,^! bodies are also planets1 b1 9 di/9ction f ! o!rs1 !y are call$ second>y planets4 ,h5ce1 ! :ole numb] ( planets are tw5ty-n9e1 namely1 elev5 prim>y1 & eighte5 second>y1 planets4 ,y ne$ nev] look = a planet ei!r v f> 9 ! nor? or v f> 9 ! s\?1 s9ce !y are always ne> ! ecliptic4 ,m]cury1 :i* deviates fur!/ f t great circle1 nev] is se5 m ?an sev5 degrees f x2 & y w h>dly ev] see "o ( ! planets s f> f x z ?is1 b !y all pursue ne>ly ! same great r\te ?r\gh ! skies1 9 _! revolutions ar\nd ! sun4 ,! new planets1 h[ev]1 make wid] excursions f ! plane ( ! ecliptic1 am\nt+1 9 ! case ( ,pallas1 to ?irty-f\r & a half degrees4 ,m]cury & ,v5us are call$ inf]ior planets1 because !y h _! orbits ne>] to ! sun ?an t ( ! e>?2 :ile all ! o!rs1 be+ m di/ant f ! sun ?an ! e>?1 are call$ sup]ior planets4 ,! planets pres5t great div]sities among !mselves1 9 respect to di/ance f ! sun1 magnitude1 "t ( revolution1 & d5sity4 ,!y diff]1 also1 9 reg>d to satellites1 ( :i*1 z we h se51 ?ree h respectively f\r1 six1 & sev51 :ile m ?an half h none at all4 ,x w aid ! memory1 & r5d] our view ( ! planet>y sy/em m cle> & compreh5sive1 if we classify1 z f> z possible1 ! v>i\s p>ticul>s compreh5d$ "u ! =ego+ heads4 ,z y h _h an opportunity1 9 prec$+ ,lett]s1 ( le>n+ some?+ respect+ ! means :i* a/ronom]s h ( asc]ta9+ ! di/ances & magnitudes ( ^! bodies1 y w n d\bt t !y are really z great z !y are repres5t$2 b :5 y attempt to conceive ( spaces s va/1 y w f9d ! m9d :olly inadequate to ! task4 ,x is inde$ b a comp>atively small space t we c fully compreh5d at "o grasp4 ,/ill1 by cont9ual & repeat$ ef=ts1 we may1 f "t to "t1 some:at enl>ge ! b\nd>ies ( our m5tal vision4 ,let u beg9 ) "s kn[n & famili> space1 z ! di/ance betwe5 two places we are accu/om$ to trav]se4 ,suppose ?is to be "o hundr$ miles4 ,tak+ ?is z our measure1 let u apply x to "s great] di/ance1 z t across ! ,atlantic ,ocean1--say ?ree ?\s& miles4 ,f ?is /ep we may advance to "s fa9t conception ( ! diamet] ( ! e>?2 & tak+ t z a new measure1 we may apply x to su* great] spaces z ! di/ance ( ! planets f ! sun4 ,i hope y w make trial ( ?is me?od on ! foll[+ comp>ative /atem5ts respect+ ! planets4 ,di/ances f ! ,sun1 9 miles4 #a4 ,m]cury1 #cg1jjj1jjj #b4 ,v5us1 #fh1jjj1jjj #c4 ,e>?1 #ie1jjj1jjj #d4 ,m>s1 #adb1jjj1jjj #e4 ,ve/a1 #bbe1jjj1jjj #f4 ,juno1 #g4 ,c]es1 #bfa1jjj1jjj #h4 ,pallas1 #i4 ,jupit]1 #dhe1jjj1jjj #aj4 ,saturn1 #hij1jjj1jjj #aa4 ,uranus1 or ,h]s*el1 #ahjj1jjj1jjj ,! dim5sions ( ! planet>y sy/em are se5 f ?is table to be va/1 compreh5d+ a circul> space ?irty-six hundr$ millions ( miles 9 diamet]4 ,a rail-way c>1 travell+ con/antly at ! rate ( tw5ty miles an h\r1 w\ld require m ?an tw5ty ?\s& ye>s to cross ! orbit ( ,uranus4 ,magnitudes4 ,diam4 9 miles4 #a4 ,m]cury1 #cadj #b4 ,v5us1 #ggjj #c4 ,e>?1 #giab #d4 ,m>s1 #dbjj #e4 ,c]es1 #afj #f4 ,jupit]1 #hi1jjj #g4 ,saturn1 #gi1jjj #h4 ,uranus1 #ce1jjj ,we rem>k "h a great div]sity 9 reg>d to magnitude1--a div]sity :i* does n appe> to be subject to any def9ite law4 ,:ile ,v5us1 an inf]ior planet1 is n9e t5?s z l>ge z ! e>?1 ,m>s1 a sup]ior planet1 is only "o sev5?1 :ile ,jupit] is twelve hundr$ & eighty-"o times z l>ge4 ,al?\gh sev]al ( ! planets1 :5 ne>e/ to u1 appe> brilliant & l>ge1 :5 comp>$ ) mo/ ( ! fix$ />s1 yet ! angle :i* !y subt5d is v small1--t ( ,v5us1 ! greate/ ( all1 nev] exce$+ ab\t "o m9ute1 :i* is less ?an "o ?irtie? ! app>5t diamet] ( ! sun or moon4 ,jupit]1 also1 by 8 sup]ior brightness1 sometimes makes a /rik+ figure among ! />s2 yet 8 greate/ app>5t diamet] is less ?an "o =tie? t ( ! sun4 ,p]iodic ,times4 ,m]cury revolves ar\nd ! sun 9 ne>ly #c mon?s4 ,v5us1 #g-a_/b ,e>?1 #a ye>4 ,m>s1 #b ye>s4 ,c]es1 #d-b_/c ,jupit]1 #ab ,saturn1 #bi ,uranus1 #hd ,f ?is view1 x appe>s t ! planets ne>e/ ! sun move mo/ rapidly4 ,?us1 ,m]cury p]=ms ne>ly ?ree hundr$ & fifty revolutions :ile ,uranus p]=ms "o4 ,! app>5t progress ( ! mo/ di/ant planets ar\nd ! sun is exce$+ly sl[4 ,uranus advances only a little m ?an f\r degrees 9 a :ole ye>2 s t we f9d ?is planet occupy+ ! same sign1 & ( c\rse rema9+ ne>ly 9 ! same "p ( ! heav5s1 = sev]al ye>s 9 succession4 ,aft] ?is comp>ative view ( ! planets 9 g5]al1 let u n[ look at !m individually2 & fir/1 ( ! inf]ior planets1 ,m]cury & ,v5us4 ,,m]cury & ,,v5us1 hav+ _! orbits s f> )9 t ( ! e>?1 appe> to u z att5dants ^u ! sun4 ,m]cury nev] appe>s fur!r f ! sun ?an tw5ty-n9e degrees1 & seldom s f>2 & ,v5us1 nev] m ?an ab\t =ty-sev5 degrees4 ,bo? planets1 !re=e1 appe> ei!r 9 ! we/ soon aft] sunset1 or 9 ! ea/ a little be=e sunrise4 ,9 high latitudes1 :]e ! twilight is long1 ,m]cury c seldom be se5 ) ! nak$ eye1 & !n only :5 its angul> di/ance f ! sun is greate/4 ,cop]nicus1 ! great ,prussian a/ronom]1 7:o fir/ di/9ctly e/abli%$ ! ord] ( ! sol> sy/em1 z at pres5t receiv$17 lam5t$1 on 8 dea?-b$1 t he _h nev] be5 able to obta9 a sight ( ,m]cury2 & ,delambre1 a di/+ui%$ a/ronom] ( ,france1 saw x b twice4 ,9 our latitude1 h[ev]1 we may see ?is planet = sev]al ev5+s & morn+s1 if we w wat* ! "t 7z usually giv5 9 ! almanac7 :5 x is at its greate/ elongations f ! sun4 ,x w n1 h[ev]1 rema9 long = our gaze1 b w soon run back to ! sun4 ,! reason ( ?is w be readily und]/ood f ! foll[+ diagram1 ,fig4 #ej4 ,let ,s repres5t ! sun1 ,e1 ! e>?1 & ,m1 ,n1 ,m]cury at its greate/ elongations f ! sun1 & ,o ,z ,p1 a portion ( ! sky4 ,!n1 s9ce we ref] all di/ant bodies to ! same concave sph]e ( ! heav5s1 x is evid5t t we %\ld see ! sun at ,z1 & ,m]cury at ,o1 :5 at its greate/ ea/]n elongation1 & at ,p1 :5 at its greate/ we/]n elongation2 & :ile pass+ f ,m to ,n ?r\gh ,q1 x w\ld appe> to describe ! arc ,o ,p2 & :ile pass+ f ,n to ,m ?r\gh ,r1 x w\ld appe> to run back across ! sun on ! same arc4 ,x is fur!r evid5t t x w\ld be visible only :5 at or ne> "o ( its greate/ elongations2 be+ at all o!r times s ne> ! sun z to be lo/ 9 8 light4 ,illu/ration ,fig4 #ej4 ,a planet is said to be 9 conjunction ) ! sun :5 x is se5 9 ! same "p ( ! heav5s ) ! sun4 ,m]cury & ,v5us h ea* two conjunctions1 ! inf]ior & ! sup]ior conjunction4 ,! inf]ior conjunction is its position :5 9 conjunction on ! same side ( ! sun ) ! e>?1 z at ,q1 9 ! figure2 ! sup]ior conjunction is its position :5 on ! side ( ! sun mo/ di/ant f ! e>?1 z at ,r4 ,! "t :i* a planet occupies 9 mak+ "o entire circuit ( ! heav5s1 f any />1 until x comes r\nd to ! same /> aga91 is call$ its sid]eal revolution4 ,! p]iod occupi$ by a planet betwe5 two successive conjunctions ) ! e>? is call$ its synodical revolution4 ,bo? ! planet & ! e>? be+ 9 motion1 ! "t ( ! synodical revolution ( ,m]cury or ,v5us exce$s t ( ! sid]eal2 = :5 ! planet comes r\nd to ! place :]e x be=e ov]took ! e>?1 x does n f9d ! e>? at t po9t1 b f> 9 advance ( x4 ,?us1 let ,m]cury come into inf]ior conjunction ) ! e>? at ,c1 ,fig4 #ea4 ,9 ab\t eighty-eight days1 ! planet w come r\nd to ! same po9t aga92 b1 mean-:ile1 ! e>? has mov$ =w>d ?r\gh ! arc ,e ,e1 & w cont9ue to move :ile ! planet is mov+ m rapidly to ov]take h]2 ! case be+ analog\s to t ( ! h\r & m9ute h& ( a clock4 ,illu/ration ,fig4 #ea4 ,! synodical p]iod ( ,m]cury is "o hundr$ & sixte5 days1 & t ( ,v5us five hundr$ & eighty-f\r days4 ,! =m] is increas$ tw5ty-eight days1 & ! latt]1 ?ree hundr$ & sixty days1 by ! motion ( ! e>?2 s t ,v5us1 aft] be+ 9 conjunction ) ! e>?1 goes m ?an twice r\nd ! sun be=e %e comes into conjunction aga94 ,=1 s9ce ! e>? is likewise 9 motion1 & moves m ?an half z fa/ z ,v5us1 by ! "t ! latt] has gone r\nd & return$ to ! place :]e ! two bodies 7 toge!r1 ! e>? is m ?an half way r\nd1 & cont9ues mov+1 s t x w be a long "t be=e ,v5us comes up ) x4 ,! motion ( an inf]ior planet is direct 9 pass+ ?r\gh its sup]ior conjunction1 & retrograde 9 pass+ ?r\gh its inf]ior conjunction4 ,y w recollect t ! motion ( a heav5ly body is said to be direct :5 x is 9 ! ord] ( ! signs f we/ to ea/1 & retrograde :5 x is contr>y to ! ord] ( ! signs1 or f ea/ to we/4 ,n[ ,v5us1 :ile go+ f ,b ?r\gh ,d to ,a1 7,fig4 #ea17 moves f we/ to ea/1 & w\ld appe> to trav]se ! cele/ial vault ,b ,s ,a1 f "r to left2 b 9 pass+ f ,a ?r\gh ,c to ,b1 h] c\rse w\ld be retrograde1 return+ on ! same arc f left to "r4 ,if ! e>? 7 at re/1 !re=e1 7& ! sun1 ( c\rse1 at re/17 ! inf]ior planets w\ld appe> to oscillate backw>ds & =w>ds across ! sun4 ,b x mu/ be recollect$ t ! e>? is mov+ 9 ! same direction ) ! planet1 z respects ! signs1 b ) a sl[] motion4 ,?is modifies ! motions ( ! planet1 accel]at+ x 9 ! sup]ior1 & ret>d+ x 9 ! inf]ior1 conjunction4 ,?us1 9 ,fig4 #ea1 ,v5us1 :ile mov+ ?r\gh ,b ,d ,a1 w\ld seem to move 9 ! heav5s f ,b to ,a1 7 ! e>? at re/2 b1 mean-:ile1 ! e>? *anges its position f ,e to ,e1 on :i* acc\nt ! planet is n se5 at ,a1 b at ,a1 be+ accel]at$ by ! arc ,a ,a1 9 consequ5ce ( ! e>?'s motion4 ,on ! o!r h&1 :5 ! planet is pass+ ?r\gh its inf]ior conjunction ,a ,c ,b1 x appe>s to move backw>ds 9 ! heav5s f ,a to ,b1 if ! e>? is at re/1 b f ,a to ,b1 if ! e>? has 9 ! mean "t mov$ f ,e to ,e1 be+ ret>d$ by ! arc ,b ,b4 ,al?\gh ! motions ( ! e>? h ! effect to accel]ate ! planet 9 ! sup]ior conjunction1 & to ret>d x 9 ! inf]ior1 yet1 on acc\nt ( ! great] di/ance1 ! app>5t motion ( ! planet is mu* sl[] 9 ! sup]ior ?an 9 ! inf]ior conjunction1 ,v5us be+ ! :ole bread? ( h] orbit1 or "o hundr$ & ?irty-six millions ( miles fur!r f u :5 at h] greate/1 ?an :5 at h] lea/1 di/ance1 z is evid5t f ,fig4 #ea4 ,:5 pass+ f ! sup]ior to ! inf]ior conjunction1 or f ! inf]ior to ! sup]ior1 ?r\gh ! greate/ elongations1 ! inf]ior planets are /ation>y4 ,?us1 7,fig4 #ea17 :5 ! planet is at ,a1 ! e>? be+ at ,e1 z ! planet's motion is directly t[>ds ! spectator1 he w\ld con/antly project x at ! same po9t 9 ! heav5s1 namely1 ,a2 consequ5tly1 x w\ld appe> to /& /ill4 ,or1 :5 at its greate/ elongation on ! o!r side1 at ,b1 z its motion w\ld be directly f ! spectator1 x w\ld be se5 con/antly at ,b4 ,if ! e>? 7 at re/1 ! /ation>y po9ts w\ld be at ! greate/ elongations1 z at ,a & ,b2 b ! e>? itself is mov+ ne>ly at "r angles to ! planet's motion1 :i* makes ! planet appe> to move 9 ! opposite direction4 ,its direct motion w !re=e cont9ue long] on ! "o side1 & its retrograde motion long] on ! o!r side1 ?an w\ld be ! case1 7 x n = ! motion ( ! e>?4 ,m]cury1 ^: greate/ angul> di/ance f ! sun is ne>ly tw5ty-n9e degrees1 is /ation>y at an elongation ( f fifte5 to tw5ty degrees2 & ,v5us1 at ab\t tw5ty-n9e degrees1 al?\gh h] greate/ elongation is ab\t =ty-sev5 degrees4 ,m]cury & ,v5us exhibit to ! telescope phases simil> to ^? ( ! moon4 ,:5 on ! side ( _! inf]ior conjunction1 z f ,b to ,c ?r\gh ,d1 ,fig4 #eb1 less ?an half _! enlight5$ disk is turn$ t[>ds u1 & !y appe> horn$1 l ! moon 9 h] fir/ & la/ qu>t]s2 & :5 on ! side ( ! sup]ior conjunction1 z f ,c to ,b ?r\gh ,a1 m ?an half ! enlight5$ disk is turn$ t[>ds u1 & !y appe> gibb\s4 ,at ! mom5t ( sup]ior conjunction1 ! :ole enlight5$ orb ( ! planet is turn$ t[>ds ! e>?1 & ! appe>ance w\ld be t ( ! full moon2 b ! planet is too ne> ! sun to be commonly visible4 ,illu/ration ,fig4 #eb4 ,we %\ld at fir/ ?\ght expect1 t ea* ( ^! planets w\ld be l>ge/ & brighte/ ne> _! inf]ior conjunction1 be+ !n s mu* ne>] to u ?an at o!r times2 b we mu/ recollect t1 :5 9 ?is situation1 only a small "p ( ! enlight5$ disk is turn$ t[>d u4 ,/ill1 ! p]iod ( greate/ brilliancy _c be :5 mo/ ( ! illum9at$ side is turn$ t[>ds u1 = !n1 be+ at ! sup]ior conjunction1 its light w be dim9i%$1 bo? by its great di/ance1 & by its be+ s ne> ! sun z to be p>tially lo/ 9 ! twilight4 ,h5ce1 :5 ,v5us is a little )9 h] place ( greate/ elongation1 ab\t =ty degrees f ! sun1 al?\gh less ?an half h] disk is enlight5$1 yet1 be+ comp>atively ne> to u1 & %9+ at a consid]able altitude aft] ! ev5+ or be=e ! morn+ twilight1 %e !n appe>s 9 greate/ spl5dor1 & pres5ts an object admir$ = its beauty 9 all ages4 ,?us ,milton1 ,faire/ ( />s1 la/ 9 ! tra9 ( night1 ,if bett] ?\ belong n to ! dawn1 ,sure pl$ge ( day t cr[n'/ ! smil+ morn ,) ?y bright circlet4 ,m]cury & ,v5us bo? revolve on _! axes 9 ne>ly ! same "t ) ! e>?4 ,! diurnal p]iod ( ,m]cury is a little great]1 & t ( ,v5us a little less1 ?an tw5ty-f\r h\rs4 ,^! revolutions h be5 det]m9$ by means ( "s spot or m>k se5 by ! telescope1 z ! revolution ( ! sun on 8 axis is asc]ta9$ by means ( 8 spots4 ,m]cury owes mo/ ( its peculi>ities to its proximity to ! sun4 ,its light & heat1 d]iv$ f ! sun1 are e/imat$ to be neatly sev5 times z great z on ! e>?1 & ! app>5t magnitude ( ! sun to a spectator on ,m]cury w\ld be sev5 times great] ?an to u4 ,h5ce ! sun w\ld pres5t to an inhabitant ( t planet1 ) eyes l ours1 an object ( insuff]able brightness2 & all objects on ! surface w\ld be array$ 9 a light m glori\s ?an we c well imag9e4 7,see ,fig4 #ec47 ,! av]age heat on ! great] portion ( ?is planet w\ld exce$ t ( boil+ wat]1 & !re=e be incompatible ) ! exi/5ce bo? ( an animal & a vegetable k+dom con/itut$ l ours4 ,! motion ( ,m]cury1 9 8 revolution r\nd ! sun1 is swift] ?an t ( any o!r planet1 be+ m ?an "o hundr$ ?\s& miles e h\r2 :]eas t ( ! e>? is less ?an sev5ty ?\s&4 ,eighte5 hundr$ miles e m9ute1--cross+ ! ,atlantic ocean 9 less ?an two m9utes1--?is is a velocity ( :i* we c =m b a v inadequate conception1 al?\gh1 z we %all see h]eaft]1 x is f> less ?an comets sometimes exhibit4 ,v5us is reg>d$ z ! mo/ beautiful ( ! planets1 & is well kn[n z ! morn+ & ev5+ />4 ,! mo/ anci5t nations1 inde$1 did n recognise ! morn+ & ev5+ /> z "o & ! same body1 b suppos$ !y 7 diff]5t planets1 & accord+ly gave !m diff]5t names1 call+ ! morn+ /> ,lucif]1 & ! ev5+ /> ,hesp]us4 ,at h] p]iod ( greate/ spl5dor1 ,v5us ca/s a %ad[1 & is sometimes visible 9 broad daylight4 ,h] light is !n e/imat$ z equal to t ( tw5ty />s ( ! fir/ magnitude4 ,9 ! equatorial regions ( ! e>?1 :]e ! twilight is %ort1 & ,v5us1 at h] greate/ elongation1 appe>s v high above ! horizon1 h] spl5dors are said to be f> m conspicu\s ?an 9 our latitude4 ,illu/ration ,fig4 #ec4 ,,app>5t ,,magnitudes ,,( ,,! ,,sun1 ,,z ,,se5 ,,f ,,! ,,diff]5t ,,planets4 ,illu/ration ,figures #ed1 #ee1 #ef4 ,,v5us ,,& ,,m>s4 ,e eight ye>s1 ,v5us =ms h] conjunction ) ! sun 9 ! same "p ( ! heav5s4 ,:atev] appe>ances1 !re=e1 arise f h] position ) respect to ! e>? & ! sun1 !y are repeat$ e eight ye>s1 9 ne>ly ! same =m4 ,?us1 e eight ye>s1 ,v5us is rem>kably conspicu\s1 s z to be visible 9 ! day-"t1 be+ !n mo/ favorably situat$1 on sev]al acc\nts2 namely1 be+ ne>e/ ! e>?1 & at ! po9t 9 h] orbit :]e %e gives h] greate/ brilliancy1 t is1 a little )9 ! place ( greate/ elongation4 ,?is is ! p]iod = obta9+ f9e telescopic views ( ,v5us1 :5 %e is se5 ) spots on h] disk4 ,?us two figures ( ! annex$ diagram 7,fig4 #ed7 repres5t ,v5us z se5 ne> h] inf]ior conjunction1 & at ! p]iod ( maximum brilliancy4 ,! =m] situation is favorable = view+ h] inequalities ( surface1 z indicat$ by ! r\ghness ( ! l9e :i* sep>ates ! enlight5$ f ! un5light5$ "p1 7! t]m9ator47 ,accord+ to ,s*roet]1 a ,g]man a/ronom]1 ,v5us has m\nta9s tw5ty-two miles high4 ,h] m\nta9s1 h[ev]1 are mu* m difficult to be se5 ?an ^? ( ! moon4 ,! sun w\ld appe>1 z se5 f ,v5us1 twice z l>ge z on ! e>?1 & its light & heat w\ld be augm5t$ 9 ! same proportion4 7,see ,fig4 #ec47 ,9 _m respects1 h[ev]1 ! ph5om5a ( ?is planet are simil> to ^? ( our own2 & ! g5]al lik5ess betwe5 ,v5us & ! e>?1 9 reg>d to dim5sions1 revolutions1 & seasons1 is great] ?an exi/s betwe5 any o!r two bodies ( ! sy/em4 ,i w only add to ! pres5t ,lett] a few words on ! transits ( ! inf]ior planets4 ,! transit ( ,m]cury or ,v5us is its passage across ! sun's disk1 z ! moon passes ov] x 9 a sol> eclipse4 ,! planet is se5 project$ on ! sun's disk 9 a small1 black1 r\nd spot1 mov+ sl[ly ov] ! face ( ! sun4 ,z ! transit takes place only :5 ! planet is 9 inf]ior conjunction1 at :i* "t h] motion is retrograde1 x is always f left to "r2 &1 on acc\nt ( its motion be+ ret>d$ by ! motion ( ! e>?1 7z 0 expla9$ by ,fig4 #ea1 page #bcb17 x rema9s sometimes a long "t on ! sol> disk4 ,m]cury1 :5 x makes its transit across ! sun's c5tre1 may rema9 on ! sun f five to sev5 h\rs4 ,y may ask1 :y we d n obs]ve ?is appe>ance e "t "o ( ! inf]ior planets comes into inf]ior conjunction1 = !n1 ( c\rse1 x passes betwe5 u & ! sun4 ,x mu/1 inde$1 at ?is "t1 cross ! m]idian at ! same "t ) ! sun2 b1 because its orbit is incl9$ to t ( ! sun1 x may cross x 7& g5]ally does7 a little above or a little bel[ ! sun4 ,x is only :5 ! conjunction takes place at or v ne> ! po9t :]e ! two orbits cross "o ano!r1 t is1 ne> ! node1 t a transit c occur4 ,?us1 if ! orbit ( ,m]cury1 ,n ,m ,r1 ,fig4 #ej1 7page #bca17 7 9 ! same plane ) ! e>?'s orbit1 7& ( c\rse ) ! sun's app>5t orbit17 !n1 :5 ! planet 0 at ,q1 9 its inf]ior conjunction1 ! e>? be+ at ,e1 x w\ld always be project$ on ! sun's disk at ,z1 on ! concave sph]e ( ! heav5s1 & a transit w\ld happ5 at e inf]ior conjunction4 ,b n[ let u take hold ( ! po9t ,r1 & lift ! circle :i* repres5ts ! orbit ( ,m]cury upw>ds sev5 degrees1 lett+ x turn ^u ! diamet] d b2 !n1 we may easily see t a spectator at ,e w\ld project ! planet high] 9 ! heav5s ?an ! sun2 & su* w\ld always be ! case1 except :5 ! conjunction takes place at ! node4 ,!n ! po9t ( int]section ( ! two orbits be+ 9 "o & ! same plane1 bo? bodies w\ld be ref]r$ to ! same po9t on ! cele/ial sph]e4 ,z ! sun1 9 8 app>5t revolution ar\nd ! e>? e ye>1 passes ?r\gh e po9t 9 ! ecliptic1 ( c\rse he mu/ e ye> be at ea* ( ! po9ts :]e ! orbit ( ,m]cury or ,v5us crosses ! ecliptic1 t is1 at ea* ( ! nodes ( "o ( ^! planets2#ab & z ^! nodes are on opposite sides ( ! ecliptic1 consequ5tly1 ! sun w pass ?r\gh !m at opposite seasons ( ! ye>1 z 9 ,janu>y & ,july1 ,febru>y & ,augu/4 ,n[1 %\ld ,m]cury or ,v5us happ5 to come betwe5 u & ! sun1 j z ! sun is pass+ "o ( ! planet's nodes1 a transit w\ld happ54 ,h5ce ! transits ( ,m]cury take place 9 ,may & ,novemb]1 & ^? ( ,v5us1 9 ,june & ,decemb]4 ,transits ( ,m]cury occur m frequ5tly ?an ^? ( ,v5us4 ,! p]iodic times ( ,m]cury & ! e>? are s adju/$ to ea* o!r1 t ,m]cury p]=ms ne>ly tw5ty-n9e revolutions :ile ! e>? p]=ms sev54 ,if1 !re=e1 ! two bodies meet at ! node 9 any giv5 ye>1 sev5 ye>s aft]w>ds !y w meet ne>ly at ! same node1 & a transit may take place1 accord+ly1 at int]vals ( sev5 ye>s4 ,b fifty-f\r revolutions ( ,m]cury correspond /ill ne>] to ?irte5 revolutions ( ! e>?2 & !re=e a transit is /ill m probable aft] int]vals ( ?irte5 ye>s4 ,at int]vals ( ?irty-?ree ye>s1 transits ( ,m]cury are exce$+ly probable1 because 9 t "t ,m]cury makes almo/ exactly "o hundr$ & ?irty-sev5 revolutions4 ,int]m$iate transits1 h[ev]1 may occur at ! o!r node4 ,?us1 transits ( ,m]cury happ5$ at ! asc5d+ node 9 #ahae1 & #ahbb1 at int]vals ( sev5 ye>s2 & at ! desc5d+ node 9 #ahcb1 :i* w return 9 #ahde1 aft] ?irte5 ye>s4 ,transits ( ,v5us are ev5ts ( v unfrequ5t occurr5ce4 ,eight revolutions ( ! e>? are complet$ 9 ne>ly ! same "t z ?irte5 revolutions ( ,v5us2 & h5ce two transits ( ,v5us may occur aft] an int]val ( eight ye>s1 z 0 ! case at ! la/ return ( ! ph5om5on1 "o transit hav+ occurr$ 9 #agfa1 & ano!r 9 #agfi4 ,b if a transit does n happ5 aft] eight ye>s1 x w n happ5 at ! same node1 until an int]val ( two hundr$ & ?irty-five ye>s3 b int]m$iate transits may occur at ! o!r node4 ,! next transit ( ,v5us w take place 9 #ahgd1 be+ two hundr$ & ?irty-five ye>s aft] ! fir/ t 0 ev] obs]v$1 :i* occurr$ 9 #afci4 ,?is 0 se51 = ! fir/ "t by mortal eyes1 by two y\?ful ,engli% a/ronom]s1 ,horrox & ,crabtree4 ,horrox 0 a "y man ( extraord9>y promise1 & indicat$ e>ly tal5ts = practical a/ronomy1 :i* augur$ ! highe/ em95ce2 b he di$ 9 ! tw5ty-?ird ye> ( 8 age4 ,he 0 only tw5ty :5 ! transit appe>$1 & he _h made ! calculations & obs]vations1 by :i* he 0 enabl$ to anticipate its arrival sev]al ye>s be=e4 ,at ! approa* ( ! desir$ "t = obs]v+ ! transit1 he receiv$ ! sun's image ?r\gh a telescope 9 a d>k room ^u a :ite piece ( pap]1 & aft] wait+ _m h\rs ) great impati5ce1 7z 8 calculation did n lead him to a k ( ! precise "t ( ! occurr5ce17 at la/1 on ! tw5ty-f\r? ( ,novemb]1 #afci1 old /yle1 at ?ree & a qu>t] h\rs pa/ twelve1 j z he return$ f *ur*1 he _h ! pleasure to f9d a l>ge r\nd spot ne> ! limb ( ! sun's image4 ,x mov$ sl[ly across ! sun's disk1 b _h n entirely left x :5 ! sun set4 ,! great int]e/ atta*$ by a/ronom]s to a transit ( ,v5us arises f its furni%+ ! mo/ accurate means 9 our p[] ( det]m9+ ! sun's horizontal p>allax1--an elem5t ( great importance1 s9ce x leads u to a k ( ! di/ance ( ! e>? f ! sun1 :i* aga9 af=ds ! means ( e/imat+ ! di/ances ( all ! o!r planets1 & possibly1 ( ! fix$ />s4 ,h5ce1 9 #agfi1 great ef=ts 7 made ?r\gh\t ! civiliz$ _w1 "u ! patronage ( diff]5t gov]nm5ts1 to obs]ve ?is ph5om5on "u circum/ances ! mo/ favorable = det]m9+ ! p>allax ( ! sun4 ,! common me?ods ( f9d+ ! p>allax ( a heav5ly body _c be reli$ on to a great] degree ( accuracy ?an f\r seconds4 ,9 ! case ( ! moon1 ^: greate/ p>allax am\nts to ab\t "o degree1 ?is deviation f absolute accuracy is n v mat]ial2 b x am\nts to ne>ly half ! entire p>allax ( ! sun4 ,if ! sun & ,v5us 7 equally di/ant f u1 !y w\ld be equally affect$ by p>allax1 z view$ by spectators 9 diff]5t p>ts ( ! e>?1 & h5ce _! relative situation w\ld n be alt]$ by x2 b s9ce ,v5us1 at ! inf]ior conjunction1 is only ab\t "o ?ird z f> (f z ! sun1 h] p>allax is proportionally great]1 & !re=e spectators at di/ant po9ts w see ,v5us project$ on diff]5t p>ts ( ! sol> disk1 z ! planet trav]ses ! disk4 ,a/ronom]s avail !mselves ( ?is circum/ance to asc]ta9 ! sun's horizontal p>allax1 :i* !y are enabl$ to d by comp>+ x ) t ( ,v5us1 9 a mann] :i*1 )\t a k ( trigonometry1 y w n fully und]/&4 ,9 ord] to make ! diff]5ce 9 ! app>5t places ( ,v5us on ! sun's disk z great z possible1 v di/ant places are select$ = obs]vation4 ,?us1 9 ! transits ( #agfa & #agfi1 sev]al ( ! ,european gov]nm5ts fitt$ out exp5sive exp$itions to p>ts ( ! e>? remote f ea* o!r4 ,= ?is purpose1 ! celebrat$ ,capta9 ,cook1 9 #agfi1 w5t to ! ,s\? ,pacific ,ocean1 & obs]v$ ! transit at ! isl& ( ,otaheite1 :ile o!rs w5t to ,lapl&1 = ! same purpose1 & o!rs /ill1 to _m o!r p>ts ( ! globe4 ,?us1 suppose two obs]v]s took _! /ations on opposite sides ( ! e>?1 z at ,a1 & ,b1 ,fig4 #eg1 page #bdb2 at ,a1 ! planet ,v w\ld be se5 on ! sun's disk at a1 :ile at ,b1 x w\ld be se5 at b4 ,! appe>ance ( ,v5us on ! sun's disk be+ t ( a well-def9$ black spot1 & ! exactness ) :i* ! mom5t ( ext]nal or int]nal contact may be det]m9$1 are circum/ances favorable to ! exactness ( ! result2 & a/ronom]s repose s mu* confid5ce 9 ! e/imation ( ! sun's horizontal p>allax1 z d]iv$ f obs]vations on ! transit ( #agfi1 t ?is important elem5t is ?\ght to be asc]ta9$ )9 "o t5? ( a second4 ,! g5]al result ( all ^! obs]vations gives ! sun's horizontal p>allax eight seconds & six t5?s1--a result :i* %[s at once t ! sun mu/ be a great way (f1 s9ce ! semidiamet] ( ! e>?1 a l9e ne>ly f\r ?\s& miles 9 l5g?1 w\ld appe> at ! sun "u an angle less ?an "o f\r hundr$? ( a degree4 ,dur+ ! transits ( ,v5us ov] ! sun's disk1 9 #agfa & #agfi1 a sort ( p5umbral light 0 obs]v$ ar\nd ! planet1 by sev]al a/ronom]s1 :i* 0 ?\ght to indicate an atmosph]e4 ,?is appe>ance 0 p>ticul>ly obs]vable :ile ! planet 0 com+ on or go+ (f ! sol> disk4 ,! total imm]sion & em]sion 7 n in/antane\s2 b z two drops ( wat]1 :5 ab\t to sep>ate1 =m a ligam5t betwe5 !m1 s !re 0 a d>k %ade /ret*$ out betwe5 ,v5us & ! sun2 & :5 ! ligam5t broke1 ! planet seem$ to h got ab\t an eigh? "p ( h] diamet] f ! limb ( ! sun4 ,! v>i\s acc\nts ( ! two transits ab\nd ) rem>ks l ^!1 :i* indicate ! exi/5ce ( an atmosph]e ab\t ,v5us ( ne>ly ! d5sity & ext5t ( ! e>?'s atmosph]e4 ,simil> pro(s ( ! exi/5ce ( an atmosph]e ar\nd ?is planet are d]iv$ f appe>ances ( twilight4 ,illu/ration ,fig4 #eg4 ,! eld] a/ronom]s imag9$ t !y _h discov]$ a satellite accompany+ ,v5us 9 h] transit4 ,if ,v5us _h 9 reality any satellite1 ! fact w\ld be obvi\s at h] transits1 z1 9 "s ( !m at lea/1 x is probable t ! satellite w\ld be project$ ne> ! prim>y on ! sun's disk2 b lat] a/ronom]s h se>*$ 9 va9 = any appe>ances ( ! k9d1 & ! inf]5ce is1 t =m] a/ronom]s 7 deceiv$ by "s optical illusion4 ,,footnote3 #ab ,y w recollect t ! sun is said to be at ! node1 :5 ! places ( ! node & ! sun are bo? project$1 by a spectator on ! e>?1 ^u ! same "p ( ! heav5s4 ,,lett] ,,xxi4 ,,sup]ior ,,planets3 ,,m>s1 ,,jupit]1 ,,saturn1 ,,& ,,uranus4 ,) :at an awful1 _w-revolv+ p[]1 ,7 fir/ ! unwieldy planets laun*$ along ,! illimitable void6 ,!re to rema9 ,amid/ ! flux ( _m ?\s& ye>s1 ,t (t has swept ! toil+ race ( m51 ,& all _! labor$ monum5ts1 away4--,?omson4 ,,m]cury ,,& ,,v5us1 z we h se51 are always obs]v$ ne> ! sun1 & f ?is circum/ance1 z well z f ! *anges ( magnitude & =m :i* !y und]go1 we "k t !y h _! orbits )9 t ( ! e>?1 & h5ce we call !m inf]ior planets4 ,on ! o!r h&1 ,m>s1 ,jupit]1 ,saturn1 & ,uranus1 exhibit su* appe>ances1 at diff]5t times1 z %[ t !y revolve ar\nd ! sun at a great] di/ance ?an ! e>?1 & h5ce we d5om9ate !m sup]ior planets4 ,we "k t !y nev] come betwe5 u & ! sun1 because !y nev] und]go ^? *anges :i* ,m]cury & ,v5us1 z well z ! moon1 su/a91 9 consequ5ce ( _! com+ into su* a position4 ,!y1 h[ev]1 w&] to ! greate/ angul> di/ance f ! sun1 be+ sometimes se5 "o hundr$ & eighty degrees f him1 s z to rise :5 ! sun sets4 ,all ^! diff]5t appe>ances mu/ naturally result f _! orbits' be+ ext]ior to t ( ! e>?1 z w be evid5t f ! foll[+ repres5tation4 ,let ,e1 ,fig4 #eh1 page #bdd1 be ! e>?1 & ,m1 "o ( ! sup]ior planets1 ,m>s1 = example1 ea* body be+ se5 9 its pa? ar\nd ! sun4 ,at ,m1 ! planet w\ld be 9 opposition to ! sun1 l ! moon at ! full2 at ,q & ,q1 x w\ld be se5 n9ety degrees (f1 or 9 quadrature2 & at ,m1 9 conjunction4 ,we "k1 h[ev]1 t ?is mu/ be a sup]ior & n an inf]ior conjunction1 = ! illum9at$ disk is /ill turn$ t[>ds u2 :]eas1 if x came betwe5 u & ! sun1 l ,m]cury1 or ,v5us1 9 its inf]ior conjunction1 its d>k side w\ld be pres5t$ to u4 ,illu/ration ,fig4 #eh4 ,! sup]ior planets d n exhibit to ! telescope diff]5t phases1 b1 ) a s+le exception1 !y always pres5t ! side t is turn$ t[>ds ! e>? fully enlight5$4 ,?is is ow+ to _! great di/ance f ! e>?2 = 7 ! spectator to /& ^u ! sun1 he w\ld ( c\rse always h ! illum9at$ side ( ea* ( ! planets turn$ t[>ds him2 b s di/ant are all ! sup]ior planets1 except ,m>s1 t !y are view$ by u v ne>ly1 9 ! same mann] z !y w\ld be if we actually /ood on ! sun4 ,m>s1 h[ev]1 is suffici5tly ne> to appe> some:at gibb\s :5 at or ne> "o ( its quadratures4 ,?us1 :5 ! planet is at ,q1 x is pla9 t1 ( ! hemisph]e t is turn$ t[>ds ! e>?1 a small "p is unillum9at$4 ,m>s is a small planet1 8 diamet] be+ only ab\t half t ( ! e>?1 or f\r ?\s& two hundr$ miles4 ,he also1 at times1 comes ne>] to ! e>? ?an any o!r planet1 except ,v5us4 ,8 mean di/ance f ! sun is "o hundr$ & =ty-two millions ( miles2 b 8 orbit is s elliptical1 t 8 di/ance v>ies mu* 9 diff]5t p>ts ( 8 revolution4 ,m>s is always v ne> ! ecliptic1 nev] v>y+ f x m ?an two degrees4 ,he is di/+ui%$ f all ! planets by 8 deep r$ color1 & fi]y aspect2 b 8 brightness & app>5t magnitude v>y mu*1 at diff]5t times1 be+ sometimes ne>] to u ?an at o!rs by ! :ole diamet] ( ! e>?'s orbit2 t is1 by ab\t "o hundr$ & n9ety millions ( miles4 ,:5 ,m>s is on ! same side ( ! sun ) ! e>?1 or at 8 opposition1 he comes )9 =ty-sev5 millions ( miles ( ! e>?1 &1 ris+ ab\t ! "t ! sun sets1 surprises u by 8 magnitude & spl5dor2 b :5 he passes to ! o!r side ( ! sun1 to 8 sup]ior conjunction1 he dw9dles to ! appe>ance ( a small />1 be+ !n two hundr$ & ?irty-sev5 millions ( miles f u4 ,?us1 let ,m1 ,fig1 #eh1 repres5t ,m>s 9 opposition1 & ,m1 9 ! sup]ior conjunction1 :ile ,e repres5ts ! e>?4 ,x is obvi\s t1 9 ! =m] situation1 ! planet mu/ be ne>] to ! e>? ?an 9 ! latt]1 by ! :ole diamet] ( ! e>?'s orbit4 ,:5 view$ ) a p[]ful telescope1 ! surface ( ,m>s appe>s div]sifi$ ) num]\s v>ieties ( light & %ade4 ,! region ar\nd ! poles is m>k$ by :ite spots1 7see ,fig4 #ef1 page #bcg17 :i* v>y _! appe>ances ) ! *anges ( seasons 9 ! planet4 ,h5ce ,dr4 ,h]s*el conjectur$ t !y 7 ow+ to ice & sn[1 :i* alt]nately accumulate & melt away1 accord+ z x is ,w9t] or ,summ]1 9 t region4 ,!y are greate/ & mo/ conspicu\s :5 t "p ( ! planet has j em]g$ f a long ,w9t]1 & !y gradually wa/e away1 z !y are expos$ to ! sol> heat4 ,fig4 #ef1 repres5ts ! planet1 z exhibit$1 "u ! mo/ favorable circum/ances1 to a p[]ful telescope1 at ! "t :5 its gibb\s =m is /rik+ly obvi\s4 ,x has be5 common to ascribe ! ruddy light ( ,m>s to an ext5sive & d5se atmosph]e1 :i* 0 said to be di/9ctly indicat$ by ! gradual dim9ution ( light obs]v$ 9 a />1 z x approa*es v ne> to ! planet1 9 und]go+ an occultation2 b m rec5t obs]vations af=d no su* evid5ce ( an atmosph]e4 ,by obs]vations on ! spots1 we le>n t ,m>s revolves on 8 axis 9 v ne>ly ! same "t ) ! e>?1 7tw5ty-f\r h\rs ?irty-n9e m9utes tw5ty-"o seconds & ?ree t5?s17 & t ! incl9ation ( 8 axis to t ( 8 orbit is also ne>ly ! same1 be+ ?irty degrees eighte5 m9utes t5 seconds & eight t5?s4 ,h5ce ! *anges ( day & night mu/ be ne>ly ! same !re z "h1 & ! seasons also v simil> to ours4 ,s9ce1 h[ev]1 ! di/ance ( ,m>s f ! sun is "o hundr$ & =ty-two :ile t ( ! e>? is only n9ety-five millions ( miles1 ! sun w appe> m ?an twice z small on t planet z on ours1 7see ,fig4 #ec1 page #bcf17 & its light & heat w be dim9i%$ 9 ! same proportion4 ,only ! equatorial regions1 !re=e1 w be suitable = ! exi/5ce ( animals & vegetables4 ,! e>? w be se5 f ,m>s z an inf]ior planet1 always ne> ! sun1 pres5t+ appe>ances simil>1 9 _m respects1 to ^? :i* ,v5us pres5ts to u4 ,x w be to t planet ! ev5+ & morn+ />1 sung by _! poets 7if poets !y h7 ) a l en?usiasm4 ,! moon w att5d ! e>? z a little />1 be+ nev] se5 fur!r f h] side ?an ab\t ! diamet] "u :i* we view ! moon4 ,to ! telescope1 ! e>? w exhibit phases simil> to ^? ( ,v5us2 &1 f9ally1 %e w1 at long int]vals1 make h] transits ov] ! sol> disk4 ,mean-:ile1 ,v5us w /& to ,m>s 9 a relation simil> to t ( ,m]cury ,illu/ration ,figures #ei1 #fj4 ,,jupit] ,,& ,,saturn4 to u1 reveal+ h]self only :5 at ! p]iods ( h] greate/ elongation1 & at all o!r times hid+ h]self )9 ! sol> blaze4 ,m]cury w nev] be visible to an inhabitant ( ,m>s4 ,jupit] is di/+ui%$ f all ! o!r planets by 8 great magnitude4 ,8 diamet] is eighty-n9e ?\s& miles1 & 8 volume "o ?\s& two hundr$ & eighty times t ( ! e>?4 ,8 figure is /rik+ly sph]oidal1 ! equatorial be+ m ?an six ?\s& miles long] ?an ! pol> diamet]4 ,su* a figure might naturally be expect$ f ! rapidity ( 8 diurnal rotation1 :i* is accompli%$ 9 ab\t t5 h\rs4 ,a place on ! equator ( ,jupit] mu/ turn tw5ty-sev5 times z fa/ z on ! t]re/rial equator4 ,! di/ance ( ,jupit] f ! sun is ne>ly f\r hundr$ & n9ety millions ( miles1 & 8 revolution ar\nd ! sun occupies ne>ly twelve ye>s4 ,e ?+ app]ta9+ to ,jupit] is on a gr& scale4 ,a _w 9 itself1 equal 9 dim5sions to twelve hundr$ & eighty ( ours2 ! :ole firmam5t roll+ r\nd x 9 ! %ort space ( t5 h\rs1 a movem5t s rapid t ! eye c\ld probably p]ceive ! heav5ly bodies to *ange _! places e mom5t2 its ye> dragg+ out a l5g? ( m ?an f\r ?\s& days1 & m ?an t5 ?\s& ( its own days1 :ile its nocturnal skies are light$ up ) f\r brilliant moons2--^! are "s ( ! peculi>ities :i* *>act]ize ?is magnific5t planet4 ,! view ( ,jupit] ?r\gh a good telescope is "o ( ! mo/ spl5did & int]e/+ spectacles 9 a/ronomy4 ,! disk exp&s into a l>ge & bright orb1 l ! full moon2 ! sph]oidal figure :i* !ory assigns to revolv+ sph]es1 especially to ^? :i* turn ) great velocity1 is "h palpably exhibit$ to ! eye2 across ! disk1 arrang$ 9 p>allel /ripes1 are disc]n$ sev]al dusky b&s1 call$ belts2 & f\r bright satellites1 always 9 att5dance1 & ev] v>y+ _! positions1 compose a spl5did ret9ue4 ,inde$1 a/ronom]s gaze ) peculi> int]e/ on ,jupit] & 8 moons1 z af=d+ a m9iature repres5tation ( ! :ole sol> sy/em1 repeat+1 on a small] scale1 ! same revolutions1 & exemplify+ m )9 ! compass ( our obs]vation1 ! same laws z regulate ! entire assemblage ( sun & planets4 ,figure #ei1 fac+ page #bdg1 gives a correct view ( ,jupit]1 z exhibit$ to a p[]ful telescope 9 a cle> ev5+4 ,y w rem>k 8 flatt5$ or sph]oidal figure1 ! belts :i* appe> 9 p>allel /ripes across 8 disk1 & ! f\r satellites1 t are se5 l little />s 9 a /raight l9e ) ! equator ( ! planet4 ,! belts ( ,jupit] are v>iable 9 _! numb] & dim5sions4 ,) ! small] telescopes only "o or two are se51 & ^? across ! equatorial regions2 b ) m p[]ful in/rum5ts1 ! numb] is increas$1 cov]+ a l>ge "p ( ! entire disk4 ,diff]5t op9ions h be5 ent]ta9$ by a/ronom]s respect+ ! cause ( ^! belts2 b !y h g5]ally be5 reg>d$ z cl\ds =m$ 9 ! atmosph]e ( ! planet1 agitat$ by w9ds1 z is indicat$ by _! frequ5t *anges1 & made to assume ! =m ( belts p>allel to ! equator1 l curr5ts t circulate ar\nd our globe4 ,sir ,john ,h]s*el supposes t ! belts are n ranges ( cl\ds1 b portions ( ! planet itself1 br\ght into view by ! removal ( cl\ds & mi/s1 t exi/ 9 ! atmosph]e ( ! planet1 ?r\gh :i* are op5+s made by curr5ts circulat+ ar\nd ,jupit]4 ,! satellites ( ,jupit] may be se5 ) a telescope ( v mod]ate p[]s4 ,ev5 a common spyglass w enable u to disc]n !m4 ,inde$1 "o or two ( !m h be5 occasionally se5 ) ! nak$ eye4 ,9 ! l>ge/ telescopes !y sev]ally appe> z bright z ,sirius4 ,) su* an in/rum5t1 ! view ( ,jupit]1 ) 8 moons & belts1 is truly a magnific5t spectacle4 ,z ! orbits ( ! satellites d n deviate f> f ! plane ( ! ecliptic1 & b little f ! equator ( ! planet1 !y are usually se5 9 ne>ly a /raight l9e ) ea* o!r1 ext5d+ across ! c5tral "p ( ! disk4 7,see ,fig4 #ei1 fac+ page #bdg47 ,jupit] & 8 satellites exhibit 9 m9iature all ! ph5om5a ( ! sol> sy/em4 ,! satellites p]=m1 ar\nd _! prim>y1 revolutions v analog\s to ^? :i* ! planets p]=m ar\nd ! sun1 hav+1 9 l mann]1 motions alt]nately direct1 /ation>y1 & retrograde4 ,!y are all1 ) "o exception1 a little l>g] ?an ! moon2 & ! second satellite1 :i* is ! smalle/1 is ne>ly z l>ge z ! moon1 be+ two ?\s& & sixty-eight miles 9 diamet]4 ,!y are all v small comp>$ ) ! prim>y1 ! l>ge/ be+ only "o tw5ty-six? "p ( ! prim>y4 ,! out]mo/ satellite ext5ds to ! di/ance f ! planet ( f\rte5 times 8 diamet]4 ,! :ole sy/em1 !re=e1 occupies a region ( space m ?an "o million miles 9 bread?4 ,rapidity ( motion1 z well z greatness ( dim5sions1 is *>act]i/ic ( ! sy/em ( ,jupit]4 ,i h already m5tion$ t ! planet itself has a motion on its own axis mu* swift] ?an t ( ! e>?1 & ! motions ( ! satellites are also mu* m rapid ?an t ( ! moon4 ,! inn]mo/1 :i* is a little fur!r (f ?an ! moon is f ! e>?1 goes r\nd its prim>y 9 ab\t a day & ?ree qu>t]s2 & ! out]mo/ occupies less ?an sev5te5 days4 ,! orbits ( ! satellites are ne>ly or q circul>1 & deviate b little f ! plane ( ! planet's equator1 & ( c\rse are b slightly incl9$ to ! plane ( 8 orbit4 ,!y are !re=e 9 a simil> situation ) respect to ,jupit]1 z ! moon w\ld be ) respect to ! e>?1 if h] orbit ne>ly co9cid$ ) ! ecliptic1 9 :i* case1 %e w\ld und]go an eclipse at e opposition4 ,! eclipses ( ,jupit]'s satellites1 9 _! g5]al circum/ances1 are p]fectly analog\s to ^? ( ! moon1 b 9 _! details !y diff] 9 sev]al p>ticul>s4 ,ow+ to ! mu* great] di/ance ( ,jupit] f ! sun1 & its great] magnitude1 ! cone ( its %ad[ is mu* long] & l>g] ?an t ( ! e>?4 ,on ?is acc\nt1 z well z on acc\nt ( ! little incl9ation ( _! orbit to t ( ! prim>y1 ! ?ree inn] satellites ( ,jupit] pass ?r\gh 8 %ad[1 & are totally eclips$1 at e revolution4 ,! f\r? satellite1 ow+ to ! great] incl9ation ( its orbit1 sometimes1 ?\gh r>ely1 escapes eclipse1 & sometimes m]ely grazes ! limits ( ! %ad[1 or suff]s a p>tial eclipse4 ,^! eclipses1 moreov]1 are n se51 z is ! case ) ^? ( ! moon1 f ! c5tre ( _! motion1 b f a remote /ation1 & "o ^: situation ) respect to ! l9e ( ! %ad[ is v>iable4 ,?is makes no diff]5ce 9 ! times ( ! eclipses1 b x makes a v great "o 9 _! visibility1 & 9 _! app>5t situations ) respect to ! planet at ! mom5t ( _! ent]+ or quitt+ ! %ad[4 ,illu/ration ,fig4 #fa4 ,! eclipses ( ,jupit]'s satellites pres5t "s curi\s ph5om5a1 :i* y w easily und]/& by /udy+ ! foll[+ diagram4 ,let ,a1 ,b1 ,c1 ,d1 ,fig4 #fa1 repres5t ! e>? 9 diff]5t p>ts ( its orbit2 ,j1 ,jupit]1 9 8 orbit1 surr\nd$ by 8 f\r satellites1 ! orbits ( :i* are m>k$ #a1 #b1 #c1 #d4 ,at a1 ! fir/ satellite ent]s ! %ad[ ( ! planet1 em]ges f x at b1 & advances to its greate/ elongation at c4 ,! o!r satellites trav]se ! %ad[ 9 a simil> mann]4 ,! app>5t place1 ) respect to ! planet1 at :i* ^! eclipses w be se5 to occur1 w be alt]$ by ! position ! e>? happ5s at t mom5t to h 9 its orbit2 b _! appe>ances = any giv5 night1 z exhibit$ at ,gre5wi*1 are calculat$ & accurately laid d[n 9 ! ,nautical ,almanac4 ,:5 "o ( ! satellites is pass+ betwe5 ,jupit] & ! sun1 x ca/s its %ad[ on ! prim>y1 z ! moon ca/s its %ad[ on ! e>? 9 a sol> eclipse4 ,we see ) ! telescope ! %ad[ trav]s+ ! disk4 ,sometimes1 ! satellite itself is se5 project$ on ! disk2 b1 be+ illum9at$ z well z ! prim>y1 x is n s easily di/+ui%$ z ,v5us or ,m]cury1 :5 se5 on ! sun's disk 9 "o ( _! transits1 s9ce ^! bodies h _! d>k sides turn$ t[>ds u2 b ! satellite is illum9at$ by ! sun1 z well z ! prim>y1 & !re=e is n easily di/+ui%able f x4 ,! eclipses ( ,jupit]'s satellites h be5 /udi$ ) great att5tion by a/ronom]s1 on acc\nt ( _! af=d+ "o ( ! easie/ me?ods ( det]m9+ ! longitude4 ,on ?is subject1 ,sir ,john ,h]s*el rem>ks3 ,! discov]y ( ,jupit]'s satellites by ,galileo1 :i* 0 "o ( ! fir/ fruits ( ! inv5tion ( ! telescope1 =ms "o ( ! mo/ memorable epo*s 9 ! hi/ory ( a/ronomy4 ,! fir/ a/ronomical solution ( ! problem ( '! longitude1'--! mo/ important problem = ! int]e/s ( mank9d t has ev] be5 br\ght "u ! dom9ion ( /rict sci5tific pr9ciples1--dates imm$iately f ?is discov]y4 ,! f9al & conclusive e/abli%m5t ( ! ,cop]nican sy/em ( a/ronomy may also be consid]$ z ref]able to ! discov]y & /udy ( ?is exquisite m9iature sy/em1 9 :i* ! laws ( ! planet>y motions1 z asc]ta9$ by ,kepl]1 & especially t :i* connects _! p]iods & di/ances1 7 spe$ily trac$1 & f\nd to be satisfactorily ma9ta9$4 ,! entrance ( "o ( ,jupit]'s satellites into ! %ad[ ( ! prim>y1 be+ se5 l ! entrance ( ! moon into ! e>?'s %ad[ at ! same mom5t ( absolute "t1 at all places :]e ! planet is visible1 & be+ :olly indep5d5t ( p>allax1 t is1 pres5t+ ! same ph5om5on to places remote f ea* o!r2 be+1 moreov]1 pr$ict$ be=eh&1 ) great accuracy1 = ! in/ant ( its occurr5ce at ,gre5wi*1 & giv5 9 ! ,nautical ,almanac2 ?is w\ld seem to be "o ( ^? ev5ts :i* are peculi>ly adapt$ = f9d+ ! longitude4 ,= y w recollect1 t any in/antane\s appe>ance 9 ! heav5s1 visible at ! same mom5t ( absolute "t at any two places1 may be employ$ = det]m9+ ! diff]5ce ( longitude betwe5 ^? places2 = ! diff]5ce 9 _! local times1 z indicat$ by clocks or *ronomet]s1 all[+ fifte5 degrees = e h\r1 w %[ _! diff]5ce ( longitude4 ,) respect to ! me?od by ! eclipses ( ,jupit]'s satellites1 x mu/ be rem>k$1 t ! ext9ction ( light 9 ! satellite1 at its imm]sion1 & ! recov]y ( its light at its em]sion1 are n in/antane\s1 b gradual2 = ! satellite1 l ! moon1 occupies "s "t 9 ent]+ into ! %ad[1 or 9 em]g+ f x1 :i* occasions a progressive dim9ution or increase ( light4 ,two obs]v]s 9 ! same room1 obs]v+ ) diff]5t telescopes ! same eclipse1 w frequ5tly disagree1 9 not+ its "t1 to ! am\nt ( fifte5 or tw5ty seconds4 ,bett] me?ods1 !re=e1 ( f9d+ ! longitude1 are n[ employ$1 al?\gh ! facility ) :i* ! necess>y obs]vations c be made1 & ! little calculation requir$1 /ill r5d] ?is me?od eligible 9 _m cases :]e extreme accuracy is n important4 ,z a telescope is ess5tial = obs]v+ an eclipse ( "o ( ! satellites1 x is obvi\s t ?is me?od _c be practis$ at sea1 s9ce ! telescope _c be us$ on bo>d ( %ip1 = want ( ! requisite /ead9ess4 ,! gr& discov]y ( ! progressive motion ( light 0 fir/ made by obs]vations on ! eclipses ( ,jupit]'s satellites4 ,9 ! ye> #afge1 x 0 rem>k$ by ,roem]1 a ,dani% a/ronom]1 on comp>+ toge!r obs]vations ( ^! eclipses dur+ _m successive ye>s1 t !y take place soon] by ab\t sixte5 m9utes1 :5 ! e>? is on ! same side ( ! sun ) ! planet1 ?an :5 %e is on ! opposite side4 ,! diff]5ce he ascribes to ! progressive motion ( light1 :i* takes t "t to pass ?r\gh ! diamet] ( ! e>?'s orbit1 mak+ ! velocity ( light ab\t "o hundr$ & n9ety-two ?\s& miles p] second4 ,s great a velocity />tl$ a/ronom]s at fir/1 & produc$ "s degree ( di/ru/ ( ?is explanation ( ! ph5om5on2 b ! subsequ5t discov]y ( :at is call$ ! ab]ration ( light1 l$ to an indep5d5t e/imation ( ! velocity ( light1 ) almo/ precisely ! same result4 ,few great] feats h ev] be5 p]=m$ by ! human m9d1 ?an to measure ! spe$ ( light1--a spe$ s great1 z w\ld c>ry x across ! ,atlantic ,ocean 9 ! sixty-f\r? "p ( a second1 & ar\nd ! globe 9 less ?an ! sev5? "p ( a second6 ,?us has man appli$ 8 scale to ! motions ( an elem5t1 t lit]ally leaps f _w to _w 9 ! tw9kl+ ( an eye4 ,?is is "o example ( ! great p[] :i* ! inv5tion ( ! telescope conf]r$ on man4 ,c\ld we plant ourselves on ! surface ( ?is va/ planet1 we %\ld see ! same />ry firmam5t exp&+ ov] our heads z we see n[2 & ! same w\ld be true if we c\ld fly f "o planet>y _w to ano!r1 until we made ! circuit ( !m all2 b ! sun & ! planet>y sy/em w\ld pres5t !mselves to u "u new & /range aspects4 ,! sun himself w\ld dw9dle to "o tw5ty-sev5? ( 8 pres5t surface1 7,fig4 #ec1 fac+ page #bcf17 & af=d a degree ( light & heat proportionally dim9i%$2 ,m]cury1 ,v5us1 & ev5 ! ,e>?1 w\ld all disappe>1 be+ too ne> ! sun to be visible2 ,m>s w\ld be z seldom se5 z ,m]cury is by u1 & con/itute ! only inf]ior planet4 ,on ! o!r h&1 ,saturn w\ld %9e ) greatly augm5t$ size & spl5dor4 ,:5 9 opposition to ! sun1 7at :i* "t x comes ne>e/ to ,jupit]17 x w\ld be a gr& object1 appe>+ l>g] ?an ei!r ,v5us or ,jupit] does to u4 ,:51 h[ev]1 pass+ to ! o!r side ( ! sun1 ?r\gh its sup]ior conjunction1 x w\ld gradually dim9i% 9 size & brightness1 & at l5g? become mu* less ?an x ev] appe>s to u1 s9ce x w\ld !n be f\r hundr$ millions ( miles fur!r f ,jupit] ?an x ev] is f u4 ,al?\gh ,jupit] comes f\r hundr$ millions ( miles ne>] to ,uranus ?an ! e>? does1 yet x is /ill ?irte5 hundr$ millions ( miles di/ant f t planet4 ,h5ce ! augm5tation ( ! magnitude & light ( ,uranus w\ld be b>ely suffici5t to r5d] x di/+ui%able by ! nak$ eye4 ,x appe>s1 !re=e1 t ,saturn is ! peculi> ornam5t ( ! firmam5t ( ,jupit]1 & w\ld pres5t to ! telescope mo/ int]e/+ & sublime ph5om5a4 ,z we owe ! revelation ( ! sy/em ( ,jupit] & 8 att5dant worlds :olly to ! telescope1 & z ! discov]y & obs]vation ( !m con/itut$ a l>ge portion ( ! glory ( ,galileo1 ,i am n[ =cibly rem9d$ ( 8 labors1 & w recur to 8 hi/ory1 & f9i% ! sket* :i* ,i comm5c$ 9 a previ\s ,lett]4 ,,lett] ,,xxii4 ,,cop]nicus4--,,galileo4 ,!y leave at l5g? ! ne!r gloom1 & /& ,be=e ! portals ( a bett] l&2 ,to happi] pla9s !y come1 & fair] groves1 ,! seats ( ^? :om ,heav51 b5ignant1 loves2 ,a bright] day1 a blu] e!r1 spreads ,its lucid dep?s above _! favor$ heads2 ,&1 purg$ f mi/s t veil our e>?ly skies1 ,%9e suns & />s unse5 by mortal eyes4--,virgil4 ,,9 ord] to appreciate ! value ( ! contributions :i* ,galileo made to a/ronomy1 soon aft] ! inv5tion ( ! telescope1 x is necess>y to glance at ! /ate ( ! sci5ce :5 he comm5c$ 8 discov]ies ,= _m c5turies1 dur+ ! middle ages1 a d>k night _h hung ov] a/ronomy1 ?r\gh :i* h>dly a ray ( light p5etrat$1 :51 9 ! ea/]n "p ( civiliz$ ,europe1 a lum9>y appe>$1 t prov$ ! h>b+] ( a bright & glori\s day4 ,?is 0 ,cop]nicus1 a native ( ,?orn1 9 ,prussia4 ,he 0 born 9 #adgc4 ,?\gh de/9$ = ! pr(ession ( m$ic9e1 f 8 e>lie/ ye>s he display$ a great fondness & g5ius = ma!matical /udies1 & pursu$ !m ) di/+ui%$ success 9 ! ,univ]sity ( ,crac[4 ,at ! age ( tw5ty-five ye>s1 he resort$ to ,italy1 = ! purpose ( /udy+ a/ronomy1 :]e he resid$ a numb] ( ye>s4 ,?us prep>$1 he return$ to 8 native c\ntry1 &1 hav+ acquir$ an ecclesia/ical liv+ t 0 adequate to 8 support 9 8 frugal mode ( life1 he e/abli%$ himself at ,frau5b]g1 a small t[n ne> ! m\? ( ! ,vi/ula1 :]e he sp5t ne>ly =ty ye>s 9 obs]v+ ! heav5s1 & m$itat+ on ! cele/ial motions4 ,he occupi$ ! upp] "p ( a humble f>m-h\se1 ?r\gh ! ro( ( :i* he c\ld f9d access to an unob/ruct$ sky1 & !re he c>ri$ on 8 obs]vations4 ,8 in/rum5ts1 h[ev]1 7 few & imp]fect1 & x does n appe> t he add$ any ?+ to ! art ( practical a/ronomy4 ,?is 0 res]v$ = ,ty*o ,brahe1 :o came a half a c5tury aft] him4 ,nor did ,cop]nicus enri* ! sci5ce ) any important discov]ies4 ,x 0 n s mu* 8 g5ius or ta/e to se>* = new bodies1 or new ph5om5a among ! />s1 z x 0 to expla9 ! reasons ( ! mo/ obvi\s & well-kn[n appe>ances & motions ( ! heav5ly bodies4 ,) ?is view1 he gave 8 m9d to long-cont9u$ & pr(\nd m$itation4 ,cop]nicus tells u t he 0 fir/ l$ to ?9k t ! app>5t motions ( ! heav5ly bodies1 9 _! diurnal revolution1 7 ow+ to ! real motion ( ! e>? 9 ! opposite direction1 f obs]v+ in/ances ( ! same k9d among t]re/rial objects2 z :5 ! %ore seems to ! m>9] to rec$e1 z he rapidly sails f x2 & z trees & o!r objects seem to glide by u1 :51 on rid+ swiftly pa/ !m1 we lose ! consci\sness ( our own motion4 ,he 0 also smitt5 ) ! simplicity preval5t 9 all ! works & op]ations ( ,nature1 :i* is m & m conspicu\s ! m !y are und]/ood2 & he h5ce conclud$ t ! planets d n move 9 ! complicat$ pa?s :i* mo/ prec$+ a/ronom]s assign$ to !m4 ,i %all expla9 to y1 h]eaft]1 ! details ( 8 sy/em4 ,i ne$ only at pres5t rem9d y t ! hypo!sis :i* he esp\s$ & def5d$1 7be+ sub/antially ! same z t propos$ by ,py?agoras1 five hundr$ ye>s be=e ! ,*ri/ian era17 supposes1 fir/1 t ! app>5t movem5ts ( ! sun by day1 & ( ! moon & />s by night1 f ea/ to we/1 result f ! actual revolution ( ! e>? on its own axis f we/ to ea/2 &1 secondly1 t ! e>? & all ! planets revolve ab\t ! sun 9 circul> orbits4 ,?is hypo!sis1 :5 he fir/ assum$ x1 0 ) him1 z x _h be5 ) ,py?agoras1 little m ?an m]e conjecture4 ,! argum5ts by :i* its tru? 0 to be f9ally e/abli%$ 7 n yet develop$1 & c\ld n be1 )\t ! aid ( ! telescope1 :i* 0 n yet inv5t$4 ,^u ?is hypo!sis1 h[ev]1 he set out to expla9 all ! ph5om5a ( ! visible heav5s1--z ! diurnal revolutions ( ! sun1 moon1 & />s1 ! sl[ progress ( ! planets ?r\gh ! signs ( ! zodiac1 & ! num]\s irregul>ities to :i* ! planet>y motions are subject4 ,^! la/ are app>5tly s caprici\s1--be+ = "s "t =w>d1 !n /ation>y1 !n backw>d1 !n /ation>y aga91 & f9ally direct1 a second "t1 9 ! ord] ( ! signs1 & con/antly v>y+ 9 ! velocity ( _! movem5ts1--t no?+ b long-cont9u$ & sev]e m$itation c\ld h solv$ all ^! appe>ances1 9 con=mity ) ! idea t ea* planet is pursu+ its simple way all ! :ile 9 a circle ar\nd ! sun4 ,al?\gh1 !re=e1 ,py?agoras fa?om$ ! pr(\nd doctr9e t ! sun is ! c5tre ar\nd :i* ! e>? & all ! planets revolve1 yet we h no evid5ce t he ev] solv$ ! irregul> motions ( ! planets 9 con=mity ) 8 hypo!sis1 al?\gh ! explanation ( ! diurnal revolution ( ! heav5s1 by t hypo!sis1 involv$ no difficulty4 ,ignorant z ,cop]nicus 0 ( ! pr9ciple ( gravitation1 & ( mo/ ( ! laws ( motion1 he c\ld g b little way 9 foll[+ out ! consequ5ces ( 8 own hypo!sis2 & all t c be claim$ = him is1 t he solv$1 by means ( x1 mo/ ( ! common ph5om5a ( ! cele/ial motions4 ,he inde$ got ^u ! road to tru?1 & advanc$ "s way 9 its sure pa?2 b he 0 able to adduce b few indep5d5t pro(s1 to %[ t x 0 ! tru?4 ,x 0 only q at ! close ( 8 life t he publi%$ 8 sy/em to ! _w1 & t only at ! urg5t reque/ ( 8 fri5ds2 anticipat+1 p]haps1 ! opposition ( a bigot$ prie/hood1 ^: fury 0 aft]w>ds p\r$ ^u ! head ( ,galileo1 = ma9ta9+ ! same doctr9es4 ,al?\gh1 !re=e1 ! sy/em ( ,cop]nicus af=d$ an explanation ( ! cele/ial motions1 f> m simple & rational ?an ! previ\s sy/ems :i* made ! e>? ! c5tre ( ^? motions1 yet ?is fact alone 0 n suffici5t to compel ! ass5t ( a/ronom]s2 = ! great] "p1 to say ! lea/1 ( ! same ph5om5a1 c\ld be expla9$ on ei!r hypo!sis4 ,) ! old doctr9e a/ronom]s 7 already famili>1 a circum/ance :i* made x seem easi]2 :ile ! new doctr9es w\ld seem m difficult1 f _! be+ imp]fectly und]/ood4 ,accord+ly1 = ne>ly a c5tury aft] ! publication ( ! sy/em ( ,cop]nicus1 he ga9$ few disciples4 ,ty*o ,brahe reject$ x1 & propos$ "o ( 8 own1 ( :i* ,i %all h]eaft] give y "s acc\nt2 & x w\ld probably h fall5 q into oblivion1 _h n ! obs]vations ( ,galileo1 ) 8 newly-inv5t$ telescope1 br\ght to light innum]able pro(s ( its tru?1 f> m cog5t ?an any :i* ,cop]nicus himself _h be5 able to devise4 ,galileo no soon] _h complet$ 8 telescope1 & direct$ x to ! heav5s1 ?an a _w ( wond]s sudd5ly bur/ ^u 8 enraptur$ sight4 ,po9t+ x to ! moon1 he 0 pres5t$ ) a sight ( h] mottl$ disk1 & ( h] m\nta9s & valleys4 ,! sun exhibit$ 8 spots2 ,v5us1 h] phases2 & ,jupit]1 8 exp&$ orb1 & 8 ret9ue ( moons4 ,^! la/ he nam$1 9 honor ( 8 patron1 ,cosmo d',m$ici1 ,m$icean />s4 ,s great 0 ?is honor deem$ ( associat+ "o's "n ) ! />s1 t express application 0 made to ,galileo1 by ! c\rt ( ,france1 to aw>d ?is di/9ction to ! reign+ ,mon>*1 ,h5ry ! ,f\r?1 ) pla9 intimations1 t by s do+ he w\ld r5d] himself & 8 family ri* & p[]ful = ev]4 ,galileo publi%$ ! result ( 8 discov]ies 9 a pap]1 d5om9at$ ',nuncius ,sid]eus1' ! ',mess5g] ( ! ,/>s4' ,9 t ignorant & m>vell\s age1 ?is publication produc$ a wond]ful excitem5t4 ,_m d\bt$1 _m positively refus$ to believe1 s novel an ann\ncem5t2 all 7 /ruck ) ! greate/ a/oni%m5t1 accord+ to _! respective op9ions1 ei!r at ! new view ( ! univ]se ?us (f]$ to !m1 or at ! high audacity ( ,galileo1 9 inv5t+ su* fables4 ,ev5 ,kepl]1 ! great ,g]man a/ronom]1 ( :om ,i %all tell y m by & by1 wrote to ,galileo1 & desir$ him to supply him ) argum5ts1 by :i* he might answ] ! objections to ^! pret5d$ discov]ies ) :i* he 0 cont9ually assail$4 ,galileo answ]$ him z foll[s3 ,9 ! fir/ place1 ,i return y my ?anks t y fir/1 & almo/ alone1 be=e ! "q _h be5 sift$1 7su* is y\r c&or1 & ! l(t9ess ( y\r m9d17 put fai? 9 my ass]tions4 ,y tell me y h "s telescopes1 b n suffici5tly good to magnify di/ant objects ) cle>ness1 & t y anxi\sly expect a sight ( m9e1 :i* magnifies images m ?an a ?\s& times4 ,x is m9e no long]1 = ! ,gr& ,duke ( ,tuscany has ask$ x ( me1 & int5ds to lay x up 9 8 museum1 among 8 mo/ r>e & preci\s curiosities1 9 et]nal remembrance ( ! inv5tion4 ,y ask1 my de> ,kepl]1 = o!r te/imonies4 ,i produce1 = "o1 ! ,gr& ,duke1 :o1 aft] obs]v+ ! ,m$icean planets sev]al times ) me at ,pisa1 dur+ ! la/ mon?s1 made me a pres5t1 at p>t+1 ( m ?an a ?\s& flor9s1 & has n[ invit$ me to atta* myself to him1 ) ! annual sal>y ( "o ?\s& flor9s1 & ) ! title ( ',philosoph] & ,pr9cipal ,ma!matician to ,8 ,highness2' )\t ! duties ( any (fice to p]=m1 b ) ! mo/ complete leisure4 ,i produce1 = ano!r witness1 myself1 :o1 al?\gh already end[$ 9 ?is ,college ) ! noble sal>y ( "o ?\s& flor9s1 su* z no pr(essor ( ma!matics ev] be=e receiv$1 & :i* ,i might securely enjoy dur+ my life1 ev5 if ^! planets %\ld deceive me & %\ld disappe>1 yet quit ?is situation1 & take me :]e want & disgrace w be my puni%m5t1 %\ld ,i prove to h be5 mi/ak54 ,! le>n$ pr(essors 9 ! univ]sities1 :o1 9 ^? days1 7 unaccu/om$ to employ _! s5ses 9 inquir+ into ! ph5om5a ( ,nature1 b satisfi$ !mselves ) ! au?ority ( ,ari/otle1 on all subjects1 7 among ! mo/ incr$ul\s ) respect to ! discov]ies ( ,galileo4 ,oh1 my de> ,kepl]1 says ,galileo1 h[ ,i wi% t we c\ld h "o he>ty laugh toge!r4 ,"h1 at ,padua1 is ! pr9cipal ,pr(essor ( ,philosophy1 :om ,i h repeat$ly & urg5tly reque/$ to look at ! moon & planets ?r\gh my glass1 :i* he p]t9aci\sly refuses to d4 ,:y are y n "h8 ,:at %\ts ( laught] we %\ld h at ?is glori\s folly1 & to he> ! ,pr(essor ( ,philosophy at ,pisa labor+ be=e ! ,gr& ,duke1 ) logical argum5ts1 z if ) magical incantations1 to *>m ! new planets out ( ! sky4 ,! foll[+ argum5t by ,sizzi1 a contempor>y a/ronom] ( "s note1 to prove t !re c be only sev5 planets1 is a specim5 ( ! logic ) :i* ,galileo 0 assail$4 ,!re are sev5 w9d[s giv5 to animals 9 ! domicile ( ! head1 ?r\gh :i* ! air is admitt$ to ! tab]nacle ( ! body1 to enlight51 to w>m1 & to n\ri% x2 :i* w9d[s are ! pr9cipal p>ts ( ! microcosm1 or little _w1--two no/rils1 two eyes1 two e>s1 & "o m\?4 ,s 9 ! heav5s1 z 9 a macrocosm1 or great _w1 !re are two favorable />s1 ,jupit] & ,v5us2 two unpropiti\s1 ,m>s & ,saturn2 two lum9>ies1 ! ,sun & ,moon2 & ,m]cury alone1 undecid$ & indiff]5t4 ,f :i*1 & f _m o!r ph5om5a ( ,nature1 su* z ! sev5 metals1 c41 :i* x 7 t$i\s to enum]ate1 we ga!r t ! numb] ( planets is necess>ily sev54 ,moreov]1 ! satellites are invisible to ! nak$ eye1 & !re=e c ex]cise no influ5ce ov] ! e>?1 & !re=e w\ld be useless1 & !re=e d n exi/4 ,besides1 z well ! ,jews & o!r anci5t nations1 z mod]n ,europeans1 h adopt$ ! division ( ! week into sev5 days1 & h nam$ !m f ! sev5 planets4 ,n[1 if we increase ! numb] ( planets1 ?is :ole sy/em falls to ! gr\nd4 ,:51 at l5g?1 ! a/ronom]s ( ! s*ools f\nd x useless to d5y ! fact t ,jupit] is att5d$ by small] bodies1 :i* revolve ar\nd him1 !y %ift$ _! gr\nd ( w>f>e1 & ass]t$ t ,galileo _h n told ! :ole tru?2 t !re 7 n m]ely f\r satellites1 b a /ill great] numb]2 "o said five2 ano!r1 n9e2 & ano!r1 twelve2 b1 9 a little "t1 ,jupit] mov$ =w>d 9 8 orbit1 & left all beh9d him1 save ! f\r ,m$icean />s4 ,x _h be5 object$ to ! ,cop]nican sy/em1 t 7 ,v5us a body :i* revolv$ ar\nd ! sun 9 an orbit int]ior to t ( ! e>?1 %e w\ld und]go *anges simil> to ^? ( ! moon4 ,z no su* *anges c\ld be detect$ by ! nak$ eye1 no satisfactory answ] c\ld be giv5 to ?is objection2 b ! telescope set all "r1 by %[+1 9 fact1 ! phases ( ,v5us4 ,! same in/rum5t1 disclos$1 also1 9 ! sy/em ( ,jupit] & 8 moons1 a m9iature exhibition ( ! sol> sy/em itself4 ,x %[$ ! actual exi/5ce ( ! motion ( a numb] ( bodies ar\nd "o c5tral orb1 exactly simil> to t :i* 0 pr$icat$ ( ! sun & planets4 ,e "o1 !re=e1 ( ^! new & int]e/+ discov]ies1 help$ to confirm ! tru? ( ! sy/em ( ,cop]nicus4 ,b a fe>ful cl\d 0 n[ ris+ ov] ,galileo1 :i* spread itself1 & grew d>k] e h\r4 ,! ,*ur* ( ,rome _h tak5 al>m at ! new doctr9es respect+ ! e>?'s motion1 z contr>y to ! decl>ations ( ! ,bible1 & a =midable difficulty pres5t$ itself1 namely1 h[ to publi% & def5d ^! doctr9es1 )\t invok+ ! t]rible puni%m5ts inflict$ by ! ,inquisition on h]etics4 ,no "w c\ld be pr9t$ )\t lic5se f ! c\rt ( ,rome2 & any op9ions suppos$ to be held & mu* m kn[n to be taught by any "o1 :i*1 by an ignorant & sup]/iti\s prie/hood1 c\ld be int]pret$ z contr>y to ,scripture1 w\ld expose ! (f5d] to ! sev]e/ puni%m5ts1 ev5 to imprisonm5t1 sc\rg+1 & dea?4 ,we1 :o live 9 an age s di/+ui%$ = fre$om ( ?\ght & op9ion1 c =m b a v inadequate conception ( ! bondage 9 :i* ! m9ds ( m5 7 held by ! *a9s ( ! ,inquisition4 ,x 0 necess>y1 !re=e1 = ,galileo to proce$ ) ! greate/ caution 9 promulgat+ tru?s :i* 8 own discov]ies _h confirm$4 ,he did n1 l ! ,*ri/ian m>tyrs1 proclaim ! tru? 9 ! face ( p]secutions & tortures2 b :ile he s\ght to give curr5cy to ! ,cop]nican doctr9es1 he labor$1 at ! same "t1 by cunn+ artifices1 to bl9d ! ecclesia/ics to 8 real designs1 & ?us to escape ! effects ( _! ho/ility4 ,be=e ,galileo publi%$ 8 doctr9es 9 =m1 he _h express$ himself s freely1 z to h excit$ mu* al>m among ! ecclesia/ics4 ,"o ( !m prea*$ publicly aga9/ him1 tak+ = 8 text1 ! passage1 ,ye m5 ( ,galilee1 :y /& ye "h gaz+ up into heav58 ,he !re=e ?\ght x prud5t to resort to ,rome1 & confront 8 enemies face to face4 ,a contempor>y describes 8 appe>ance !re 9 ! foll[+ t]ms1 9 a lett] address$ to a ,romi% ,c>d9al3 ,y\r ,em95ce w\ld be delight$ ) ,galileo1 if y he>d him hold+ =?1 z he (t5 does1 9 ! mid/ ( fifte5 or tw5ty1 all viol5tly attack+ him1 sometimes 9 "o h\se1 sometimes 9 ano!r4 ,b he is arm$ aft] su* fa%ion1 t he laughs all ( !m to scorn2 & ev5 if ! novelty ( 8 op9ions prev5ts entire p]suasion1 at lea/ he convicts ( empt9ess mo/ ( ! argum5ts ) :i* 8 adv]s>ies endeavor to ov]:elm him4 ,9 #afaf1 ,galileo1 z he himself /ates1 _h a mo/ graci\s audi5ce ( ! ,pope1 ,paul ! ,fif?1 :i* la/$ = ne>ly an h\r1 at ! end ( :i* 8 ,hol9ess assur$ him1 t ! ,congregation 7 no long] 9 a humor to li/5 lightly to calumnies aga9/ him1 & t s long z he occupi$ ! ,papal *air1 ,galileo might ?9k himself out ( all dang]4 ,nev]!less1 he 0 n all[$ to return home1 )\t receiv+ =mal notice n to tea* ! op9ions ( ,cop]nicus1 t ! sun is 9 ! c5tre ( ! sy/em1 & t ! e>? moves ab\t x1 f t "t =w>d1 9 any mann]4 ,galileo _h a mo/ s>ca/ic ve91 & (t5 ralli$ 8 p]secutors ) ! ke5e/ irony4 ,?is he exhibit$1 "s "t aft] quitt+ ,rome1 9 an epi/le :i* he s5t to ! ,ar* ,duke ,leopold1 accompany+ 8 ',!ory ( ! ,tides4' ,?is !ory1 says he1 occurr$ to me :5 9 ,rome1 :il/ ! !ologians 7 debat+ on ! prohibition ( ,cop]nicus's book1 & ( ! op9ion ma9ta9$ 9 x ( ! motion ( ! e>?1 :i* ,i at t "t believ$2 until x pleas$ ^? g5tlem5 to susp5d ! book1 & to decl>e ! op9ion false & repugnant to ! ,holy ,scriptures4 ,n[1 z ,i "k h[ well x becomes me to obey & believe ! decisions ( my sup]iors1 :i* proce$ out ( m pr(\nd k ?an ! weakness ( my intellect c atta9 to1 ?is !ory1 :i* ,i s5d y1 :i* is f\nd$ on ! motion ( ! e>?1 ,i n[ look ^u z a fiction & a dream1 & beg y\r ,highness to receive x z su*4 ,b1 z poets (t5 le>n to prize ! creations ( _! fancy1 s1 9 l mann]1 d ,i set "s value on ?is absurdity ( m9e4 ,x is true1 t :5 ,i sket*$ ?is little "w1 ,i did hope t ,cop]nicus w\ld n1 aft] eighty ye>s1 be convict$ ( error2 & ,i _h int5d$ to develope & amplify x fur!r2 b a voice f heav5 sudd5ly awak5$ me1 & at once annihilat$ all my confus$ & entangl$ fancies4 ,x is difficult1 h[ev]1 sometimes to decide :e!r ! language ( ,galileo is ironical1 or :e!r he uses x ) subtlety1 ) ! hope ( evad+ ! ana!mas ( ! ,inquisition4 ,?us he ends "o ( 8 writ+s ) ! foll[+ passage3 ,9 conclusion1 s9ce ! motion attribut$ to ! e>?1 :i* ,i1 z a pi\s & ,ca?olic p]son1 consid] mo/ false1 & n to exi/1 accommodates itself s well to expla9 s _m & su* diff]5t ph5om5a1 ,i %all n feel sure t1 false z x is1 x may n j z delud+ly correspond ) ! ph5om5a ( comets4 ,9 ! ye> #afbd1 soon aft] ! accession ( ,urban ! ,eigh? to ! ,pontifical *air1 ,galileo w5t to ,rome aga91 to (f] 8 congratulations to ! new ,pope1 z well z to propitiate 8 favor4 ,he seems to h be5 receiv$ ) unexpect$ cordiality2 &1 on 8 dep>ture1 ! ,pope comm5d$ him to ! good graces ( ,f]d9&1 ,gr& ,duke ( ,tuscany1 9 ! foll[+ t]ms3 ,we f9d 9 him n only lit]>y di/9ction1 b also ! love ( piety1 & he is /rong 9 ^? qualities by :i* ,pontifical good-w is easily obta9$4 ,& n[1 :5 he has be5 br\ght to ?is city1 to congratulate ,u on ,our elevation1 ,we h lov+ly embrac$ him2 nor c ,we suff] him to return to ! c\ntry :i!r y\r lib]ality recalls him1 )\t an ample provision ( ,pontifical love4 ,& t y may "k h[ de> he is to ,u1 we h will$ to give him ?is honorable te/imonial ( virtue & piety4 ,& ,we fur!r signify1 t e b5efit :i* y %all conf] ^u him w conduce to ,our gratification4 ,9 ! ye> #afcj1 ,galileo f9i%$ a great "w1 on :i* he _h be5 long engag$1 entitl$1 ',! ,dialogue on ! ,ptolemaic & ,cop]nican ,sy/ems4' ,f ! notion :i* prevail$1 t he /ill c\nt5anc$ ! ,cop]nican doctr9e ( ! e>?'s motion1 :i* _h be5 condemn$ z h]etical1 x 0 "s "t be=e he c\ld obta9 p]mission f ! ,inquisitors 7^: lic5se 0 necess>y to e book7 to publi% x4 ,?is he 0 able to d1 only by employ+ aga9 t duplicity or artifice :i* w\ld ?r[ du/ 9 ! eyes ( ! va9 & sup]/iti\s prie/hood4 ,9 #afcb1 ! "w appe>$ "u ! foll[+ title3 ',a ,dialogue1 by ,galileo ,galilei1 ,extraord9>y ,ma!matician ( ! ,univ]sity ( ,pisa1 & ,pr9cipal ,philosoph] & ,ma!matician ( ! ,mo/ ,s]5e ,gr& ,duke ( ,tuscany2 9 :i*1 9 a ,conv]sation ( f\r days1 are discuss$ ! two pr9cipal ,sy/ems ( ! ,_w1 ! ,ptolemaic & ,cop]nican1 indet]m9ately propos+ ! ,philosophical ,argum5ts z well on "o side z on ! o!r4' ,! subtle disguise :i* he wore1 may be se5 f ! foll[+ extract f 8 ',introduction1' address$ ',to ! discreet ,read]4' ,"s ye>s ago1 a salut>y edict 0 promulgat$ at ,rome1 :i*1 9 ord] to obviate ! p]il\s sc&als ( ! pres5t age1 enjo9$ an opportune sil5ce on ! ,py?agorean op9ion ( ! e>?'s motion4 ,"s 7 n want+1 :o ra%ly ass]t$ t ?is decree orig9at$1 n 9 a judici\s exam9ation1 b 9 ill-in=m$ passion2 & compla9ts 7 he>d1 t c\nsellors totally inexp]i5c$ 9 a/ronomical obs]vations ought n1 by ha/y prohibitions1 to clip ! w+s ( speculative m9ds4 ,my zeal c\ld n keep sil5ce :5 ,i he>d ^! ra% lam5tations1 & ,i ?\ght x prop]1 z be+ fully in=m$ ) reg>d to t mo/ prud5t det]m9ation1 to appe> publicly on ! !atre ( ! _w1 z a witness ( ! actual tru?4 ,i happ5$ at t "t to be 9 ,rome3 ,i 0 admitt$ to ! audi5ces1 & enjoy$ ! approbation1 ( ! mo/ em95t prelates ( t c\rt2 nor did ! publication ( t decree occur )\t my receiv+ "s prior intimation ( x4 ,:]e=e1 x is my int5tion1 9 ?is pres5t "w1 to %[ to =eign nations1 t z mu* is kn[n ( ?is matt] 9 ,italy1 & p>ticul>ly 9 ,rome1 z ultramontane dilig5ce c ev] h =m$ any notion (1 & collect+ toge!r all my own speculations on ! ,cop]nican sy/em1 to give !m to und]/& t ! k ( all ^! prec$$ ! ,roman c5sures2 & t f ?is c\ntry proce$ n only dogmas = ! salvation ( ! s\l1 b also +5i\s discov]ies = ! gratification ( ! und]/&+4 ,) ?is object1 ,i h tak5 up 9 ! ',dialogue' ! ,cop]nican side ( ! "q1 treat+ x z a pure ma!matical hypo!sis2 & endeavor+1 9 e artificial mann]1 to repres5t x z hav+ ! advantage1 n ov] ! op9ion ( ! /ability ( ! e>? absolutely1 b accord+ to ! mann] 9 :i* t op9ion is def5d$ by "s1 :o inde$ pr(ess to be ,ari/otelians1 b reta9 only ! "n1 & are cont5t$1 )\t improvem5t1 to wor%ip %ad[s1 n philosophiz+ ) _! own reason1 b only f ! recollection ( ! f\r pr9ciples imp]fectly und]/ood4 ,al?\gh ! ,pope himself1 z well z ! ,inquisitors1 _h exam9$ ,galileo's manuscript1 &1 n hav+ ! sagacity to detect ! real motives ( ! au?or1 _h cons5t$ to its publication1 yet1 :5 ! book 0 out1 ! enemies ( ,galileo f\nd means to al>m ! c\rt ( ,rome1 & ,galileo 0 summon$ to appe> be=e ! ,inquisition4 ,! philosoph] 0 !n sev5ty ye>s old1 & v infirm1 & x 0 ) great difficulty t he p]=m$ ! j\rney4 ,8 unequall$ dignity & celebrity1 h[ev]1 comm&$ ! involunt>y respect ( ! tribunal be=e :i* he 0 summon$1 :i* !y manife/$ by p]mitt+ him to reside at ! palace ( 8 fri5d1 ! ,tuscan ,ambassador2 & :5 x became necess>y1 9 ! c\rse ( ! inquiry1 to exam9e him 9 p]son1 al?\gh 8 removal to ! ,holy ,(fice 0 !n insi/$ ^u1 yet he 0 n1 l o!r h]etics1 committ$ to close & solit>y conf9em5t4 ,on ! contr>y1 he 0 lodg$ 9 ! ap>tm5ts ( ! ,head ( ! ,inquisition1 :]e he 0 all[$ ! att5dance ( 8 own s]vant1 :o 0 also p]mitt$ to sleep 9 an adjo9+ room1 & to come & g at pleasure4 ,^! 7 deem$ extraord9>y indulg5ces 9 an age :5 ! puni%m5t ( h]etics usually began be=e _! trial4 ,ab\t f\r mon?s aft] ,galileo's arrival 9 ,rome1 he 0 summon$ to ! ,holy ,(fice4 ,he 0 deta9$ !re dur+ ! :ole ( t day2 & on ! next day 0 conduct$1 9 a p5it5tial dress1 to ! ,conv5t ( ,m9]va1 :]e ! ,c>d9als & ,prelates1 8 judges1 7 assembl$ = ! purpose ( pass+ judgem5t ^u him1 by :i* ?is v5]able old man 0 solemnly call$ ^u to r5\nce & abjure1 z impi\s & h]etical1 ! op9ions :i* 8 :ole exi/5ce _h be5 consecrat$ to =m & /r5g!n4 ,probably !re is n a m curi\s docum5t 9 ! hi/ory ( sci5ce1 ?an t :i* conta9s ! s5t5ce ( ! ,inquisition on ,galileo1 & 8 consequ5t abjuration4 ,x tea*es u s mu*1 bo? ( ! d>kness & bigotry ( ! t]rible ,inquisition1 & ( ! suff]+s enc\nt]$ by ^? e>ly m>tyrs ( sci5ce1 t ,i w transcribe = y\r p]usal1 f ! excell5t ',life ( ,galileo' 9 ! ',libr>y ( ,useful ,k1' 7f :i* ,i h borr[$ mu* already17 ! entire record ( ?is transaction4 ,! s5t5ce ( ! ,inquisition is z foll[s3 ,we1 ! und]sign$1 by ! grace ( ,god1 ,c>d9als ( ! ,holy ,roman ,*ur*1 ,inquisitors ,g5]al ?r\gh\t ! :ole ,*ri/ian ,republic1 ,special ,deputies ( ! ,holy ,apo/olical ,*air aga9/ h]etical depravity3 ,:]eas1 y1 ,galileo1 son ( ! late ,v9c5zo ,galilei ( ,flor5ce1 ag$ sev5ty ye>s1 7 d5\nc$ 9 #afae1 to ?is ,holy ,(fice1 = hold+ z true a false doctr9e taught by _m1 namely1 t ! sun is immovable 9 ! c5tre ( ! _w1 & t ! e>? moves1 & also ) a diurnal motion2 also1 = hav+ pupils :i* y in/ruct$ 9 ! same op9ions2 also1 = ma9ta9+ a correspond5ce on ! same ) "s ,g]man ma!maticians2 also1 = publi%+ c]ta9 lett]s on ! sol> spots1 9 :i* y develop$ ! same doctr9e z true2 also1 = answ]+ ! objections :i* 7 cont9ually produc$ f ! ,holy ,scriptures1 by gloz+ ! said ,scriptures1 accord+ to y\r own mean+2 & :]eas1 !reupon 0 produc$ ! copy ( a writ+1 9 =m ( a lett]1 pr(ess$ly writt5 by y to a p]son =m]ly y\r pupil1 9 :i*1 foll[+ ! hypo!sis ( ,cop]nicus1 y include sev]al propositions contr>y to ! true s5se & au?ority ( ! ,holy ,scriptures3 !re=e1 ?is ,holy ,tribunal1 be+ desir\s ( provid+ aga9/ ! disord] & mis*ief :i* 0 !nce proce$+ & increas+1 to ! detrim5t ( ! holy fai?1 by ! desire ( ,8 ,hol9ess1 & ( ! ,mo/ ,em95t ,lords ,c>d9als ( ?is supreme & univ]sal ,inquisition1 ! two propositions ( ! /ability ( ! sun1 & motion ( ! e>?1 7 qualifi$ by ! ,!ological ,qualifi]s1 z foll[s3 #a4 ,! proposition t ! sun is 9 ! c5tre ( ! _w1 & immovable f its place1 is absurd1 philosophically false1 & =mally h]etical2 because x is expressly contr>y to ! ,holy ,scriptures4 #b4 ,! proposition t ! e>? is n ! c5tre ( ! _w1 nor immovable1 b t x moves1 & also ) a diurnal motion1 is also absurd1 philosophically false1 &1 !ologically consid]$1 equally errone\s 9 fai?4 ,b :]eas1 be+ pleas$ at t "t to deal mildly ) y1 x 0 decre$ 9 ! ,holy ,congregation1 held be=e ,8 ,hol9ess on ! tw5ty-fif? day ( ,febru>y1 #afaf1 t ,8 ,em95ce ! ,"l ,c>d9al ,bell>m9e %\ld enjo9 y to give up altoge!r ! said false doctr9e2 if y %\ld refuse1 t y %\ld be ord]$ by ! ,commiss>y ( ! ,holy ,(fice to rel9qui% x1 n to tea* x to o!rs1 nor to def5d x1 & 9 default ( ! acquiesc5ce1 t y %\ld be imprison$2 & 9 execution ( ?is decree1 on ! foll[+ day1 at ! palace1 9 pres5ce ( ,8 ,em95ce ! said ,"l ,c>d9al ,bell>m9e1 aft] y _h be5 mildly admoni%$ by ! said ,"l ,c>d9al1 y 7 comm&$ by ! act+ ,commiss>y ( ! ,holy ,(fice1 be=e a not>y & witnesses1 to rel9qui% altoge!r ! said false op9ion1 & 9 future nei!r to def5d nor tea* x 9 any mann]1 nei!r v]bally nor 9 writ+1 & ^u y\r promis+ ob$i5ce1 y 7 dismiss$4 ,&1 9 ord] t s p]nici\s a doctr9e might be altoge!r root$ out1 nor ins9uate itself fur!r to ! heavy detrim5t ( ! ,ca?olic tru?1 a decree emanat$ f ! ,holy ,congregation ( ! ,index1 prohibit+ ! books :i* treat ( ?is doctr9e2 & x 0 decl>$ false1 & altoge!r contr>y to ! ,holy & ,div9e ,scripture4 ,& :]eas1 a book has s9ce appe>$1 publi%$ at ,flor5ce la/ ye>1 ! title ( :i* %[$ t y 7 ! au?or1 :i* title is1 ',! ,dialogue ( ,galileo ,galilei1 on ! two pr9cipal ,sy/ems ( ! ,_w1 ! ,ptolemaic & ,cop]nican2' & :]eas1 ! ,holy ,congregation has he>d t1 9 consequ5ce ( pr9t+ ! said book1 ! false op9ion ( ! e>?'s motion & /ability ( ! sun is daily ga9+ gr\nd2 ! said book has be5 tak5 into c>eful consid]ation1 & 9 x has be5 detect$ a gl>+ violation ( ! said ord]1 :i* _h be5 intimat$ to y2 inasmu* z 9 ?is book y h def5d$ ! said op9ion1 already1 & 9 y\r pres5ce1 condemn$2 al?\gh 9 ! said book y labor1 ) _m circumlocutions1 to induce ! belief t x is left by y undecid$1 & 9 express t]ms probable2 :i* is equally a v grave error1 s9ce an op9ion c 9 no way be probable :i* has be5 already decl>$ & f9ally det]m9$ contr>y to ! ,div9e ,scripture4 ,!re=e1 by ,our ord]1 y h be5 cit$ to ?is ,holy ,(fice1 :]e1 on y\r exam9ation ^u oa?1 y h ackn[l$g$ ! said book z writt5 & pr9t$ by y4 ,y also confess$ t y began to write ! said book t5 or twelve ye>s ago1 aft] ! ord] a=esaid _h be5 giv54 ,also1 t y dem&$ lic5se to publi% x1 b )\t signify+ to ^? :o grant$ y ?is p]mission1 t y _h be5 comm&$ n to hold1 def5d1 or tea*1 ! said doctr9e 9 any mann]4 ,y also confess$1 t ! /yle ( said book 01 9 _m places1 s compos$1 t ! read] might ?9k ! argum5ts adduc$ on ! false side to be s word$1 z m effectually to entangle ! und]/&+ ?an to be easily solv$1 alleg+1 9 excuse1 t y h ?us run into an error1 =eign 7z y say7 to y\r int5tion1 f writ+ 9 ! =m ( a dialogue1 & 9 consequ5ce ( ! natural complac5cy :i* e "o feels ) reg>d to 8 own subtilties1 & 9 %[+ himself m skilful ?an ! g5]ality ( mank9d 9 contriv+1 ev5 9 favor ( false propositions1 +5i\s & app>5tly probable argum5ts4 ,&1 ^u a conv5i5t "t be+ giv5 y = mak+ y\r def5ce1 y produc$ a c]tificate 9 ! h&writ+ ( ,8 ,em95ce1 ! ,"l ,c>d9al ,bell>m9e1 procur$1 z y said1 by y\rself1 t y might def5d y\rself aga9/ ! calumnies ( y\r enemies1 :o report$ t y _h abjur$ y\r op9ions1 & _h be5 puni%$ by ! ,holy ,(fice2 9 :i* c]tificate x is decl>$1 t y _h n abjur$1 nor _h be5 puni%$1 b m]ely t ! decl>ation made by 8 ,hol9ess1 & promulgat$ by ! ,holy ,congregation ( ! ,index1 _h be5 ann\nc$ to y1 :i* decl>es t ! op9ion ( ! motion ( ! e>?1 & /ability ( ! sun1 is contr>y to ! ,holy ,scriptures1 & !re=e _c be held or def5d$4 ,:]e=e1 s9ce no m5tion is !re made ( two articles ( ! ord]1 to wit1 ! ord] 'n to tea*1' & '9 any mann]1' y argu$ t we ought to believe t1 9 ! lapse ( f\rte5 or sixte5 ye>s1 !y _h escap$ y\r memory1 & t ?is 0 also ! reason :y y 7 sil5t z to ! ord]1 :5 y s\ght p]mission to publi% y\r book1 & t ?is is said by y1 n to excuse y\r error1 b t x may be attribut$ to va9-glori\s ambition r ?an to malice4 ,b ?is v c]tificate1 produc$ on y\r behalf1 has greatly aggravat$ y\r (f5ce1 s9ce x is !re9 decl>$1 t ! said op9ion is contr>y to ! ,holy ,scriptures1 & yet y h d>$ to treat ( x1 & to argue t x is probable2 nor is !re any ext5uation 9 ! lic5se artfully & cunn+ly extort$ by y1 s9ce y did n intimate ! comm& impos$ ^u y4 ,b :]eas1 x appe>$ to ,u t y _h n disclos$ ! :ole tru? ) reg>d to y\r int5tions1 ,we ?\ght x necess>y to proce$ to ! rigor\s exam9ation ( y1 9 :i* 7)\t any prejudice to :at y _h confess$1 & :i* is above detail$ aga9/ y1 ) reg>d to y\r said int5tion7 y answ]$ l a good ,ca?olic4 ,!re=e1 hav+ se5 & maturely consid]$ ! m]its ( y\r cause1 ) y\r said confessions & excuses1 & e ?+ else :i* ought to be se5 & consid]$1 ,we h come to ! und]writt5 f9al s5t5ce aga9/ y3 ,invok+1 !re=e1 ! mo/ holy "n ( our ,"l ,jesus ,*ri/1 & ( 8 ,mo/ ,glori\s ,virg9 ,"m1 ,m>y1 by ?is ,our f9al s5t5ce1 :i*1 sitt+ 9 c\ncil & judgem5t = ! tribunal ( ! ,rev]5d ,ma/]s ( ,sacr$ ,!ology1 & ,doctors ( bo? ,laws1 ,our ,assessors1 ,we put =? 9 ?is writ+ t\*+ ! matt]s & controv]sies be=e ,u1 betwe5 ! ,magnific5t ,*>les ,s9c]us1 ,doctor ( bo? ,laws1 ,fiscal ,proctor ( ?is ,holy ,(fice1 ( ! "o "p1 & y1 ,galileo ,galilei1 an exam9$ & confess$ crim9al f ?is pres5t writ+ n[ 9 progress1 z above1 ( ! o!r "p1 ,we pron\nce1 judge1 & decl>e1 t y1 ! said ,galileo1 by reason ( ^! ?+s :i* h be5 detail$ 9 ! c\rse ( ?is writ+1 & :i*1 z above1 y h confess$1 h r5d]$ y\rself vehem5tly suspect$1 by ?is ,holy ,(fice1 ( h]esy2 t is to say1 t y believe & hold ! false doctr9e1 & contr>y to ! ,holy & ,div9e ,scriptures1 namely1 t ! sun is ! c5tre ( ! _w1 & t x does n move f ea/ to we/1 & t ! e>? does move1 & is n ! c5tre ( ! _w2 also1 t an op9ion c be held & support$1 z probable1 aft] x has be5 decl>$ & f9ally decre$ contr>y to ! ,holy ,scripture1 & consequ5tly1 t y h incurr$ all ! c5sures & p5alties enjo9$ & promulgat$ 9 ! sacr$ canons1 & o!r g5]al & p>ticul> con/itutions aga9/ del9qu5ts ( ?is description4 ,f :i* x is ,our pleasure t y be absolv$1 provid$ t1 ) a s9c]e he>t & unfeign$ fai?1 9 ,our pres5ce1 y abjure1 curse1 & dete/1 ! said errors & h]esies1 & e o!r error & h]esy1 contr>y to ! ,ca?olic & ,apo/olic ,*ur* ( ,rome1 9 ! =m n[ %[n to y4 ,b t y\r griev\s & p]nici\s error & transgression may n g altoge!r unpuni%$1 & t y may be made m cauti\s 9 future1 & may be a w>n+ to o!rs to ab/a9 f del9qu5cies ( ?is sort1 ,we decree1 t ! book ( ! ,dialogues ( ,galileo ,galilei be prohibit$ by a public edict1 & ,we condemn y to ! =mal prison ( ?is ,holy ,(fice = a p]iod det]m9able at ,our pleasure2 &1 by way ( salut>y p5ance1 ,we ord] y1 dur+ ! next ?ree ye>s1 to recite1 once a week1 ! sev5 p5it5tial psalms1 res]v+ to ,ourselves ! p[] ( mod]at+1 commut+1 or tak+ (f ! :ole or "p ( ! said puni%m5t1 or p5ance4 ,& s ,we say1 pron\nce1 & by ,our s5t5ce decl>e1 decree1 & res]ve1 9 ?is & 9 e o!r bett] =m & mann]1 :i* lawfully ,we may & c use4 ,s ,we1 ! subscrib+ ,c>d9als1 pron\nce4 ,subscrib$ by sev5 ,c>d9als4 ,9 con=mity ) ! =ego+ s5t5ce1 ,galileo 0 made to kneel be=e ! ,inquisition1 & make ! foll[+ ,abjuration3 ,i1 ,galileo ,galilei1 son ( ! late ,v9c5zo ,galilei1 ( ,flor5ce1 ag$ sev5ty ye>s1 be+ br\ght p]sonally to judgem5t1 & kneel+ be=e y1 ,mo/ ,em95t & ,mo/ ,rev]5d ,lords ,c>d9als1 ,g5]al ,inquisitors ( ! ,univ]sal ,*ri/ian ,republic aga9/ h]etical depravity1 hav+ be=e my eyes ! ,holy ,gospels1 :i* ,i t\* ) my own h&s1 swe>1 t ,i h always believ$1 & ) ! help ( ,god w 9 future believe1 e article :i* ! ,holy ,ca?olic & ,apo/olic ,*ur* ( ,rome holds1 tea*es1 & prea*es4 ,b because ,i _h be5 enjo9$1 by ?is ,holy ,(fice1 altoge!r to ab&on ! false op9ion :i* ma9ta9s t ! sun is ! c5tre & immovable1 & =bidd5 to hold1 def5d1 or tea*1 ! said false doctr9e1 9 any mann]3 & aft] x _h be5 signifi$ to me t ! said doctr9e is repugnant to ! ,holy ,scripture1 ,i h writt5 & pr9t$ a book1 9 :i* ,i treat ( ! same doctr9e n[ condemn$1 & adduce reasons ) great =ce 9 support ( ! same1 )\t giv+ any solution1 & !re=e h be5 judg$ griev\sly suspect$ ( h]esy2 t is to say1 t ,i held & believ$ t ! sun is ! c5tre ( ! _w & immovable1 & t ! e>? is n ! c5tre & movable2 will+1 !re=e1 to remove f ! m9ds ( ,y\r ,em95ces1 & ( e ,ca?olic ,*ri/ian1 ?is vehem5t suspicion rightfully ent]ta9$ t[>ds me1 ) a s9c]e he>t & unfeign$ fai?1 ,i abjure1 curse1 & defeat1 ! said errors & h]esies1 & g5]ally e o!r error & sect contr>y to ! said ,holy ,*ur*2 & ,i swe>1 t ,i w nev] m 9 future say or ass]t any ?+1 v]bally or 9 writ+1 :i* may give rise to a simil> suspicion ( me3 b if ,i %all "k any h]etic1 or any "o suspect$ ( h]esy1 t ,i w d5\nce him to ?is ,holy ,(fice1 or to ! ,inquisitor & ,ord9>y ( ! place 9 :i* ,i may be4 ,i swe>1 moreov]1 & promise1 t ,i w fulfil & obs]ve fully1 all ! p5ances :i* h be5 or %all be laid on me by ?is ,holy ,(fice4 ,b if x %all happ5 t ,i violate any ( my said promises1 oa?s1 & prote/ations1 7:i* ,god av]t67 ,i subject myself to all ! pa9s & puni%m5ts :i* h be5 decre$ & promulgat$ by ! sacr$ canons1 & o!r g5]al & p>ticul> con/itutions1 aga9/ del9qu5ts ( ?is description4 ,s may ,god help me1 & 8 ,holy ,gospels1 :i* ,i t\* ) my own h&s4 ,i1 ! above-nam$ ,galileo ,galilei1 h abjur$1 sworn1 promis$1 & b\nd myself1 z above2 & 9 witness !re(1 ) my own h& h subscrib$ ?is pres5t writ+ ( my abjuration1 :i* ,i h recit$1 ^w = ^w4 ,at ,rome1 9 ! ,conv5t ( ,m9]va1 tw5ty-second ,june1 #afcc1 ,i1 ,galileo ,galilei1 h abjur$ z above1 ) my own h&4 ,f ! c\rt ,galileo 0 conduct$ to prison1 to be immur$ = life 9 "o ( ! dungeons ( ! ,inquisition4 ,8 s5t5ce 0 aft]w>ds mitigat$1 & he 0 p]mitt$ to return to ,flor5ce2 b ! humiliation to :i* he _h be5 subject$ press$ heavily on 8 spirits1 beset z he 0 ) infirmities1 & totally bl9d1 & he nev] m talk$ or wrote on ! subject ( a/ronomy4 ,!re 0 en\gh 9 ! "* ( ,galileo to comm& a high admiration4 ,!re 0 mu*1 also1 9 8 suff]+s 9 ! cause ( sci5ce1 to excite ! deepe/ sympa?y1 & ev5 compassion4 ,he is moreov] univ]sally repres5t$ to h be5 a man ( great equanimity1 & ( a noble & g5]\s disposition4 ,no sci5tific "* ( ! age1 or p]haps ( any age1 =ms a /ructure ( f9] proportions1 or we>s 9 a high] degree ! grace ( symmetry4 ,/ill1 we _c approve ( 8 employ+ artifice 9 ! promulgation ( tru?2 & we are compell$ to lam5t t 8 l(ty _s b[$ 9 ! f9al conflict4 ,h[ f>1 !re=e1 he s9ks bel[ ! dignity ( ! ,*ri/ian m>tyr6 ,at ! age ( sev5ty1 says ,dr4 ,brew/]1 9 8 life ( ,sir ,isaac ,newton1 on 8 b5d$ knees1 & ) 8 "r h& re/+ on ! ,holy ,evangeli/s1 did ?is patri>* ( sci5ce av[ 8 pres5t & pa/ belief 9 ! dogmas ( ! ,romi% ,*ur*1 ab&on z false & h]etical ! doctr9e ( ! e>?'s motion & ( ! sun's immobility1 & pl$ge himself to d5\nce to ! ,inquisition any o!r p]son :o 0 ev5 suspect$ ( h]esy4 ,he abjur$1 curs$1 & dete/$1 ^? et]nal & immutable tru?s :i* ! ,almighty _h p]mitt$ him to be ! fir/ to e/abli%4 ,_h ,galileo b add$ ! c\rage ( ! m>tyr to ! wisdom ( ! sage2 _h he c>ri$ ! glance ( 8 indignant eye r\nd ! circle ( 8 judges2 _h he lift$ 8 h&s to heav51 & call$ ! liv+ ,god to witness ! tru? & immutability ( 8 op9ions2 ! bigotry ( 8 enemies w\ld h be5 dis>m$1 & sci5ce w\ld h enjoy$ a memorable triumph4 ,,lett] ,,xxiii4 ,,saturn4--,,uranus4--,,a/]oids4 ,into ! ,heav5 ( ,heav5s ,i h presum$1 ,an e>?ly gue/1 & drawn empyreal air4--,milton4 ,,! consid]ation ( ! sy/em ( ,jupit] & 8 satellites l$ u to review ! int]e/+ hi/ory ( ,galileo1 :o fir/1 by means ( ! telescope1 disclos$ ! k ( t sy/em to ! _w4 ,i w n[ proce$ ) ! o!r sup]ior planets4 ,saturn1 z well z ,jupit]1 has )9 itself a sy/em on a scale ( great magnific5ce4 ,9 size x is next to ,jupit] ! l>ge/ ( ! planets1 be+ sev5ty-n9e ?\s& miles 9 diamet]1 or ab\t "o ?\s& times z l>ge z ! e>?4 ,x has likewise belts on its surface1 & is att5d$ by sev5 satellites4 ,b a /ill m wond]ful app5dage is its ,r+1 a broad :eel1 encompass+ ! planet at a great di/ance f x4 ,z ,saturn is n9e hundr$ millions ( miles f u1 we require a m p[]ful telescope to see 8 glories1 9 all _! magnific5ce1 ?an we d to enjoy a full view ( ! sy/em ( ,jupit]4 ,:5 we are privileg$ ) a view ( ,saturn1 9 8 mo/ favorable positions1 ?r\gh a telescope ( ! l>g] class1 ! me*anism appe>s m wond]ful ?an ev5 t ( ,jupit]4 ,saturn's r+1 :5 view$ ) telescopes ( a high p[]1 is f\nd to consi/ ( two conc5tr$ r+s1 sep>at$ f ea* o!r by a d>k space4 ,al?\gh ?is division ( ! r+s appe>s to u1 on acc\nt ( our imm5se di/ance1 z only a f9e l9e1 yet x is1 9 reality1 an int]val ( n less ?an eighte5 hundr$ miles4 ,! dim5sions ( ! :ole sy/em are1 9 r\nd numb]s1 z foll[s3 ,miles4 ,diamet] ( ! planet1 #gi1jjj ,f ! surface ( ! planet to ! inn] r+1 #bj1jjj ,bread? ( ! inn] r+1 #ag1jjj ,int]val betwe5 ! r+s1 #a1hjj ,bread? ( ! out] r+1 #aj1ejj ,extreme dim5sions f outside to outside1 #agf1jjj ,figure #fj1 fac+ page #bdg1 repres5ts ,saturn1 z x appe>s to a p[]ful telescope1 surr\nd$ by its r+s1 & hav+ its body /rip$ ) d>k belts1 some:at simil>1 b broad] & less /rongly m>k$ ?an ^? ( ,jupit]4 ,9 telescopes ( inf]ior p[]1 b /ill suffici5t to see ! r+ di/9ctly1 we %\ld sc>cely disc]n ! belts at all4 ,we might1 h[ev]1 obs]ve ! %ad[ ca/ ^u ! r+ by ! planet1 7z se5 9 ! figure on ! "r1 on ! upp] side27 &1 9 favorable situations ( ! planet1 we might disc]n glimpses ( ! %ad[ ( ! r+ on ! body ( ! planet1 on ! l[] side b5ea? ! r+4 ,to see ! division ( ! r+ & ! satellites requires a bett] telescope ?an is 9 possession ( mo/ obs]v]s4 ,) small] telescopes1 we may discov] an oval figure ( peculi> appe>ance1 :i* x w\ld be difficult to int]pret4 ,galileo1 :o fir/ saw x 9 ! ye> #afaj1 recognis$ ?is peculi>ity1 b did n "k :at x meant4 ,see+ some?+ 9 ! c5tre ) two project+ arms1 "o on ea* side1 he conclud$ t ! planet 0 triple-%ap$4 ,?is 01 at ! "t1 all he c\ld le>n respect+ x1 z ! telescopes he possess$ 7 v humble1 comp>$ ) ^? n[ us$ by a/ronom]s4 ,! fir/ con/ruct$ by him magnifi$ b ?ree times2 8 second1 eight times2 & 8 be/1 only ?irty times1 :i* is no bett] ?an a common %ip-glass4 ,x 0 ! practice ( ! a/ronom]s ( ^? days to give ! fir/ intimation ( a new discov]y 9 a ,lat9 v]se1 ! lett]s ( :i* 7 transpos$4 ,?is w\ld enable !m to claim priority1 9 case any o!r p]son %\ld conte/ ! honor ( ! discov]y1 & at ! same "t w\ld af=d opportunity to complete _! obs]vations1 be=e !y publi%$ a full acc\nt ( !m4 ,accord+ly1 ,galileo ann\nc$ ! discov]y ( ! s+ul> appe>ance ( ,saturn "u ?is disguise1 9 a l9e :i*1 :5 ! transpos$ lett]s 7 re/or$ to _! prop] places1 signifi$ t he _h obs]v$1 t ! mo/ di/ant planet is triple-=m$4#ac ,he %ortly aft]w>ds1 at ! reque/ ( 8 patron1 ! ,emp]or ,rodolph1 gave ! solution1 & add$1 ,i h1 ) great admiration1 obs]v$ t ,saturn is n a s+le />1 b ?ree toge!r1 :i*1 z x 71 t\* ea* o!r2 !y h no relative motion1 & are con/itut$ ( ?is =m1 o,oo1 ! middle "o be+ some:at l>g] ?an ! two lat]al ones4 ,if we exam9e !m ) an eyeglass :i* magnifies ! surface less ?an "o ?\s& times1 ! ?ree />s d n appe> v di/9ctly1 b ,saturn has an oblong appe>ance1 l t ( an olive1 ?us1 oblong symbol4 ,n[1 ,i h discov]$ a c\rt = ,jupit]1 7allud+ to 8 satellites17 & two s]vants = ?is old man1 7,saturn17 :o aid 8 /eps1 & nev] quit 8 side4 ,x 0 by ?is my/ic light t ,galileo grop$ 8 way ?r\gh an organization :i*1 "u ! m p[]ful glasses ( 8 successors1 0 to exp& into a mighty orb1 encompass$ by spl5did r+s ( va/ dim5sions1 ! :ole att5d$ by sev5 bright satellites4 ,?is sy/em 0 fir/ fully develop$ by ,huygh5s1 a ,dut* a/ronom]1 ab\t =ty ye>s aft]w>ds4#ad ,x requires a sup]ior telescope to see x to advantage2 b1 :5 se5 ?r\gh su* a telescope1 x is "o ( ! mo/ *>m+ spectacles af=d$ to t in/rum5t4 ,to give "s idea ( ! prop]ties ( a telescope suit$ to su* obs]vations1 ,i annex an extract f an acc\nt1 t 0 publi%$ a few ye>s s9ce1 ( a telescope con/ruct$ by ,mr4 ,tully1 a di/+ui%$ ,engli% arti/4 ,! l5g? ( ! in/rum5t 0 twelve feet1 b 0 easily adju/$1 & 0 p]fectly /eady4 ,! magnify+ p[]s rang$ f two hundr$ to sev5 hundr$ & eighty times2 b ! great excell5ce ( ! telescope consi/$ m 9 ! sup]ior di/9ctness & brilliancy ) :i* objects 7 se5 ?r\gh x1 ?an 9 its magnify+ p[]s4 ,) a p[] ( two hundr$ & =ty1 ! light ( ,jupit] 0 almo/ m ?an ! eye c\ld be>1 & 8 satellites appe>$ z bright z ,sirius1 b ) a cle> & /eady light2 & ! belts & spots on ! face ( ! planet 7 mo/ di/9ctly def9$4 ,) a p[] ( ne>ly f\r hundr$1 ,saturn appe>$ l>ge & well def9$1 & 0 "o ( ! mo/ beautiful objects t c well be conceiv$4 ,t ! r+ is a solid opaque sub/ance1 is %[n by its ?r[+ its %ad[ on ! body ( ! planet on ! side ne>e/ ! sun1 & on ! o!r side receiv+ t ( ! body4 ,! r+ encompasses ! equatorial regions ( ! planet1 & ! planet revolves on an axis :i* is p]p5dicul> to ! plane ( ! r+ 9 ab\t t5 & a half h\rs4 ,?is is kn[n by obs]v+ ! rotation ( c]ta9 dusky spots1 :i* sometimes appe> on its surface4 ,?is motion is ne>ly ! same ) ! diurnal motion ( ,jupit]1 subject+ places on ! equator ( ! planet to a v swift revolution1 & occasion+ a high degree ( compression at ! poles1 ! equatorial be+ to ! pol> diamet] 9 ! high ratio ( elev5 to t54 ,saturn's r+1 9 its revolution ar\nd ! sun1 always rema9s p>allel to itself4 ,if we hold opposite to ! eye a circul> r+ or disk1 l a piece ( co91 x w appe> z a complete circle only :5 x is at "r angles to ! axis ( vision4 ,:5 x is oblique to t axis1 x w be project$ into an ellipse m & m flatt5$1 z its obliquity is increas$1 until1 :5 its plane co9cides ) ! axis ( vision1 x is project$ into a /raight l9e4 ,please to take "s circle1 z a flat plate1 7^: rim may well repres5t ! r+ ( ,saturn17 & hold x 9 ^! diff]5t positions be=e ! eye4 ,n[1 place on ! table a lamp to repres5t ! sun1 & hold+ ! r+ at a c]ta9 di/ance1 incl9$ a little t[>ds ! lamp1 c>ry x r\nd ! lamp1 always keep+ x p>allel to itself4 ,dur+ its revolution1 x w twice pres5t its edge to ! lamp at opposite po9ts2 & twice1 at places n9ety degrees di/ant f ^? po9ts1 x w pres5t its broade/ face t[>ds ! lamp4 ,at int]m$iate po9ts1 x w exhibit an ellipse m or less op51 accord+ z x is ne>] "o or ! o!r ( ! prec$+ positions4 ,x w be se51 also1 t 9 "o half ( ! revolution1 ! lamp %9es on "o side ( ! r+1 & 9 ! o!r half ( ! revolution1 on ! o!r side4 ,su* w\ld be ! successive appe>ances ( ,saturn's r+ to a spectator on ! sun2 & s9ce ! e>? is1 9 respect to s di/ant a body z ,saturn1 v ne> ! sun1 ^! appe>ances are pres5t$ to u ne>ly 9 ! same mann] z ?\gh we view$ !m f ! sun4 ,accord+ly1 we sometimes see ,saturn's r+ "u ! =m ( a broad ellipse1 :i* gr[s cont9ually m & m acute1 until x passes into a l9e1 & we ei!r lose sight ( x1 altoge!r1 or1 by ! aid ( ! mo/ p[]ful telescopes1 we see x z a f9e ?read ( light drawn across ! disk1 & project+ out f x on ea* side4 ,z ! :ole revolution occupies ?irty ye>s1 & ! edge is pres5t$ to ! sun twice 9 ! revolution1 ?is la/ ph5om5on1 namely1 ! disappe>ance ( ! r+1 takes place e fifte5 ye>s4 ,illu/ration ,fig4 #fa4 ,y may p]haps ga9 a /ill cle>] idea ( ! =ego+ appe>ances f ! foll[+ diagram1 ,fig4 #fa4 ,let ,a1 ,b1 ,c1 c41 repres5t successive positions ( ,saturn & 8 r+1 9 diff]5t p>ts ( 8 orbit1 :ile a b repres5ts ! orbit ( ! e>?4 ,please to rem>k1 t ^! orbits are drawn s elliptical1 n to repres5t ! ecc5tricity ( ei!r ! e>?'s or ,saturn's orbit1 b m]ely z ! projection ( circles se5 v obliquely4 ,also1 imag9e "o half ( ! body ( ! planet & ( ! r+ to be above ! plane ( ! pap]1 & ! o!r half bel[ x4 ,7 ! r+1 :5 at ,c & ,g1 p]p5dicul> to ,c ,g1 x w\ld be se5 by a spectator situat$ at a or b z a p]fect circle2 b be+ incl9$ to ! l9e ( vision tw5ty-eight degrees f\r m9utes1 x is project$ into an ellipse4 ,?is ellipse contracts 9 bread? z ! r+ passes t[>ds its nodes at ,a & ,e1 :]e x dw9dles into a /raight l9e4 ,f ,e to ,g ! r+ op5s aga91 becomes broade/ at ,g1 & aga9 contracts1 till x becomes a /raight l9e at ,a1 & f ?is po9t exp&s1 till x recov]s its orig9al bread? at ,c4 ,^! successive appe>ances are all exhibit$ to a telescope ( mod]ate p[]s4 ,! r+ is extremely ?91 s9ce ! smalle/ satellite1 :5 project$ on x1 m ?an cov]s x4 ,! ?ickness is e/imat$ at only "o hundr$ miles4 ,saturn's r+ %9es :olly by reflect$ light d]iv$ f ! sun4 ,?is is evid5t f ! fact t t side only :i* is turn$ t[>ds ! sun is enlight5$2 & x is rem>kable1 t ! illum9ation ( ! r+ is great] ?an t ( ! planet itself1 b ! out] r+ is less bright ?an ! inn]4 ,al?\gh we view ,saturn's r+ ne>ly z ?\gh we saw x f ! sun1 yet ! plane ( ! r+ produc$ may pass betwe5 ! e>? & ! sun1 9 :i* case1 also1 ! r+ becomes invisible1 ! illum9at$ side be+ :olly turn$ f u4 ,?us1 :5 ! r+ is approa*+ its node at ,e1 a spectator at a w\ld h ! d>k side ( ! r+ pres5t$ to him4 ,! r+ 0 invisible 9 #ahcc1 & w be invisible aga9 9 #ahdg4 ,! nor!rn side ( ! r+ w be 9 sight until #ahee1 :5 ! s\!rn side w come into view4 ,x appe>s1 !re=e1 t !re are ?ree causes = ! disappe>ance ( ,saturn's r+3 fir/1 :5 ! edge ( ! r+ is pres5t$ to ! sun2 secondly1 :5 ! edge is pres5t$ to ! e>?2 & ?irdly1 :5 ! unillum9at$ side is t[>ds ! e>?4 ,saturn's r+ revolves 9 its own plane 9 ab\t t5 & a half h\rs4 ,la ,place inf]r$ ?is f ! doctr9e ( univ]sal gravitation4 ,he prov$ t su* a rotation 0 necess>y2 o!rwise1 ! matt] ( :i* ! r+ is compos$ w\ld be precipitat$ ^u its prim>y4 ,he %[$ t1 9 ord] to su/a9 itself1 its p]iod ( rotation mu/ be equal to ! "t ( revolution ( a satellite1 circulat+ ar\nd ,saturn at a di/ance f x equal to t ( ! middle ( ! r+1 :i* p]iod w\ld be ab\t t5 & a half h\rs4 ,by means ( spots 9 ! r+1 ,dr4 ,h]s*el foll[$ ! r+ 9 its rotation1 & actually f\nd its p]iod to be ! same z assign$ by ,la ,place1--a co9cid5ce :i* beautifully exemplifies ! h>mony ( tru?4 ,al?\gh ! r+s h v ne>ly ! same c5tre ) ! planet itself1 yet1 rec5t measurem5ts ( extreme delicacy h demon/rat$1 t ! co9cid5ce is n ma!matically exact1 b t ! c5tre ( gravity ( ! r+s describes ar\nd t ( ! body a v m9ute orbit4 ,?is fact1 says ,sir ,j4 ,h]s*el1 unimportant z x may seem1 is ( ! utmo/ consequ5ce to ! /ability ( ! sy/em ( r+s4 ,suppos+ !m ma!matically p]fect 9 _! circul> =m1 & exactly conc5tric ) ! planet1 x is demon/rable t !y w\ld =m 79 spite ( _! c5trifugal =ce7 a sy/em 9 a /ate ( un/able equilibrium1 :i* ! slighte/ ext]nal p[] w\ld subv]t1 n by caus+ a rupture 9 ! sub/ance ( ! r+s1 b by precipitat+ !m unbrok5 ^u ! surface ( ! planet4 ,! r+ may be suppos$ ( an unequal bread? 9 its diff]5t p>ts1 & z consi/+ ( irregul> solids1 ^: common c5tre ( gravity does n co9cide ) ! c5tre ( ! figure4 ,7 x n = ?is di/ribution ( matt]1 its equilibrium w\ld be de/roy$ by ! slighte/ =ce1 su* z ! attraction ( a satellite1 & ! r+ w\ld f9ally precipitate itself ^u ! planet4 ,sir ,j4 ,h]s*el fur!r obs]ves1 t1 z ! smalle/ diff]5ce ( velocity betwe5 ! planet & its r+s mu/ infallibly precipitate ! r+s ^u ! planet1 nev] m to sep>ate1 x foll[s1 ei!r t _! motions 9 _! common orbit r\nd ! sun mu/ h be5 adju/$ to ea* o!r by an ext]nal p[]1 ) ! m9ute/ precision1 or t ! r+s mu/ h be5 =m$ ab\t ! planet :ile subject to _! common orbitual motion1 & "u ! full & free influ5ce ( all ! act+ =ces4 ,! r+s ( ,saturn mu/ pres5t a magnific5t spectacle f ^? regions ( ! planet :i* lie on _! enlight5$ sides1 appe>+ z va/ ar*es spann+ ! sky f horizon to horizon1 & hold+ an inv>iable situation among ! />s4 ,on ! o!r h&1 9 ! region b5ea? ! d>k side1 a sol> eclipse ( fifte5 ye>s 9 duration1 "u _! %ad[1 mu/ af=d 7to our ideas7 an inhospitable abode to animat$ be+s1 b ill comp5sat$ by ! full light ( its satellites4 ,b we %all d wrong to judge ( ! fitness or unfitness ( _! condition1 f :at we see ar\nd u1 :51 p]haps1 ! v comb9ations :i* convey to our m9ds only images ( horror1 may be 9 reality !atres ( ! mo/ /rik+ & glori\s displays ( b5efic5t contrivance4 ,saturn is att5d$ by sev5 satellites4 ,al?\gh !y are bodies ( consid]able size1 _! great di/ance prev5ts _! be+ visible to any telescope b su* z af=d a /rong light & high magnify+ p[]s4 ,! out]mo/ satellite is di/ant f ! planet m ?an ?irty times ! planet's diamet]1 & is by f> ! l>ge/ ( ! :ole4 ,x exhibits1 l ! satellites ( ,jupit]1 p]iodic v>iations ( light1 :i* prove its revolution on its axis 9 ! "t ( a sid]eal revolution ab\t ,saturn1 z is ! case ) our moon1 :ile p]=m+ its circuit ab\t ! e>?4 ,! next satellite 9 ord]1 proce$+ inw>ds1 is tol]ably conspicu\s2 ! ?ree next are v m9ute1 & require p[]ful telescopes to see !m2 :ile ! two int]ior satellites1 :i* j skirt ! edge ( ! r+1 & move exactly 9 its plane1 h nev] be5 discov]$ b ) ! mo/ p[]ful telescopes :i* human art has yet con/ruct$1 & !n only "u peculi> circum/ances4 ,at ! "t ( ! disappe>ance ( ! r+s1 7to ord9>y telescopes17 !y 7 se5 by ,sir ,william ,h]s*el1 ) 8 great telescope1 project$ along ! edge ( ! r+1 & ?read+1 l beads1 ! ?9 fibre ( light to :i* ! r+ is !n r$uc$4 ,ow+ to ! obliquity ( ! r+1 & ( ! orbits ( ! satellites1 to t ( _! prim>y1 !re are no eclipses ( ! satellites1 ! two int]ior ones except$1 until ne> ! "t :5 ! r+ is se5 edgewise4 ,! firmam5t ( ,saturn w unque/ionably pres5t to view a m magnific5t & div]sifi$ sc5e ( cele/ial ph5om5a ?an t ( any o!r planet 9 our sy/em4 ,x is plac$ ne>ly 9 ! middle ( t space :i* int]v5es betwe5 ! sun & ! orbit ( ! remote/ planet4 ,includ+ its r+s & satellites1 x may be consid]$ z ! l>ge/ body or sy/em ( bodies )9 ! limits ( ! sol> sy/em2 & x excels !m all 9 ! sublime & div]sifi$ app>atus ) :i* x is accompani$4 ,9 ^! respects1 ,saturn may ju/ly be consid]$ z ! sov]eign among ! planet>y ho/s4 ,! prom95t p>ts ( its cele/ial sc5]y may be consid]$ z belong+ to its own sy/em ( r+s & satellites1 & ! views :i* w occasionally be op5$ ( ! firmam5t ( ! fix$ />s2 = few ( ! o!r planets w make _! appe>ance 9 its sky4 ,jupit] w appe> alt]nately z a morn+ & an ev5+ />1 ) ab\t ! same degree ( brilliancy x exhibits to u2 b x w seldom be conspicu\s1 except ne> ! p]iod ( its greate/ elongation2 & x w nev] appe> to remove f ! sun fur!r ?an ?irty-sev5 degrees1 & consequ5tly w n appe> s conspicu\s1 nor = su* a l5g? ( "t1 z ,v5us does to u4 ,uranus is ! only o!r planet :i* w be se5 f ,saturn1 & x w !re be di/9ctly p]ceptible1 l a /> ( ! ?ird magnitude1 :5 ne> ! "t ( its opposition to ! sun4 ,b ne> ! "t ( its conjunction x w be completely invisible1 be+ !n eighte5 hundr$ millions ( miles m di/ant ?an at ! opposition1 & eight hundr$ millions ( miles m di/ant f ,saturn ?an x ev] is f ! e>? at any p]iod4#ae ,,uranus4--,uranus is ! remote/ planet belong+ to our sy/em1 & is r>ely visible1 except to ! telescope4 ,al?\gh 8 diamet] is m ?an f\r times t ( ! e>?1 be+ ?irty-five ?\s& "o hundr$ & twelve miles1 yet 8 di/ance f ! sun is likewise n9ete5 times z great z ! e>?'s di/ance1 or ab\t eighte5 hundr$ millions ( miles4 ,8 revolution ar\nd ! sun occupies ne>ly eighty-f\r ye>s1 s t 8 position 9 ! heav5s1 = sev]al ye>s 9 succession1 is ne>ly /ation>y4 ,8 pa? lies v ne>ly 9 ! ecliptic1 be+ incl9$ to x less ?an "o degree4 ,! sun himself1 :5 se5 f ,uranus dw9dles almo/ to a />1 subt5d+1 z x does1 an angle ( only "o m9ute & =ty seconds2 s t ! surface ( ! sun w\ld appe> !re f\r hundr$ times less ?an x does to u4 ,?is planet 0 discov]$ by ,sir ,william ,h]s*el on ! ?irte5? ( ,m>*1 #agha4 ,8 att5tion 0 attract$ to x by ! l>g5ess ( its disk 9 ! telescope2 & f9d+ t x %ift$ its place among ! />s1 he at fir/ took x = a comet1 b soon p]ceiv$ t its orbit 0 n ecc5tric1 l ! orbits ( comets1 b ne>ly circul>1 l ^? ( ! planets4 ,x 0 !n recognis$ z a new memb] ( ! planet>y sy/em1 a conclusion :i* has be5 ju/ifi$ by all succe$+ obs]vations4 ,x 0 nam$ by ! discov]] ! ,george ,/>1 7,georgium ,sidus17 aft] 8 munific5t patron1 ,george ! ,?ird2 9 ! ,unit$ ,/ates1 & 9 "s o!r c\ntries1 x 0 call$ ,h]s*el2 b ! "n ,uranus1 f a ,greek ^w1 7 ,ouranos1 ,ouranos17 signify+ ! olde/ ( ! gods1 has f9ally prevail$4 ,s di/ant is ,uranus f ! sun1 t light itself1 :i* moves ne>ly twelve millions ( miles e m9ute1 w\ld require m ?an two h\rs & a half to pass to x f ! sun4 ,& n[1 hav+ contemplat$ all ! planets sep>ately1 j ca/ y\r eyes on ! diagram fac+ page #bcf1 ,fig4 #ec1 & y w see a comp>ative view ( ! v>i\s magnitudes ( ! sun1 z se5 f ea* ( ! planets4 ,uranus is att5d$ by six satellites4 ,s m9ute objects are !y1 t !y c be se5 only by p[]ful telescopes4 ,inde$1 ! exi/5ce ( m ?an two is /ill consid]$ z some:at d\btful4 ,^! two1 h[ev]1 (f] rem>kable & inde$ q unexpect$ & unexampl$ peculi>ities4 ,contr>y to ! unbrok5 analogy ( ! :ole planet>y sy/em1 ! planes ( _! orbits are ne>ly p]p5dicul> to ! ecliptic1 & 9 ^! orbits _! motions are retrograde2 t is1 in/ead ( advanc+ f we/ to ea/ ar\nd _! prim>y1 z is ! case ) all ! o!r planets & satellites1 !y move 9 ! opposite direction4 ,) ?is exception1 all ! motions ( ! planets1 :e!r ar\nd _! own axes1 or ar\nd ! sun1 are f we/ to ea/4 ,! sun himself turns on 8 axis f we/ to ea/2 all ! prim>y planets revolve ar\nd ! sun f we/ to ea/2 _! revolutions on _! own axes are also 9 ! same direction2 all ! second>ies1 ) ! s+le exception above m5tion$1 move ab\t _! prim>ies f we/ to ea/2 &1 f9ally1 su* ( ! second>ies z h be5 discov]$ to h a diurnal revolution1 foll[ ! same c\rse4 ,su* uni=mity among s _m motions c\ld h result$ only f =ces impress$ ^u !m by ! same ,omnipot5t h&2 & few ?+s 9 ! creation m di/9ctly proclaim t ,god made ! _w4 ,retir+ n[ to ?is fur!/ v]ge ( ! sol> sy/em1 let u = a mom5t glance at ! aspect ( ! firmam5t by night4 ,not)/&+ we h tak5 a flight ( eighte5 hundr$ millions ( miles1 ! same />ry canopy b5ds ov] our heads2 ,sirius /ill %9es ) exactly ! same spl5dor z "h2 ,orion1 ! ,scorpion1 ! ,great & ! ,little ,be>1 all occupy ! same /ations2 & ! ,galaxy spans ! sky ) ! same s(t & my/]i\s light4 ,! planets1 h[ev]1 ) ! exception ( ,saturn1 are all lo/ to ! view1 be+ too ne> ! sun ev] to be se52 & ,saturn himself is visible only at di/ant int]vals1 at p]iods ( fifte5 ye>s1 :5 at its greate/ elongations f ! sun1 & is !n too ne> ! sun to p]mit a cle> view ( 8 r+s1 mu* less ( ! satellites t unite ) ! r+s to compose 8 gorge\s ret9ue4 ,comets1 mov+ sl[ly z !y d :5 s di/ant f ! sun1 w l+] mu* long] 9 ! firmam5t ( ,uranus ?an 9 ours4 ,al?\gh ! sun %$s by day a dim & *e]less light1 yet ! six satellites t enlight5 & div]sify ! nocturnal sky pres5t int]e/+ aspects4 ,let u suppose "o satellite pres5t+ a surface 9 ! sky eight or t5 times l>g] ?an our moon2 a second1 five or six times l>g]2 a ?ird1 ?ree times l>g]2 a f\r?1 twice z l>ge2 a fif?1 ab\t ! same size z ! moon2 a six?1 some:at small]2 &1 p]haps1 ?ree or f\r o!rs ( diff]5t app>5t dim5sions3 let u suppose two or ?ree ( ^?1 ( diff]5t phases1 mov+ along ! concave ( ! sky1 at "o p]iod f\r or five ( !m disp]s$ ?r\gh ! heav5s1 "o ris+ above ! horizon1 "o sett+1 "o on ! m]idian1 "o t[>ds ! nor?1 & ano!r t[>ds ! s\?2 at ano!r p]iod1 five or six ( !m display+ _! lu/re 9 ! =m ( a half moon1 or a cresc5t1 9 "o qu>t] ( ! heav5s2 &1 at ano!r "t1 ! :ole ( ^! moons %9+1 ) full enlight5$ hemisph]es1 9 "o glori\s assemblage1 & we %all h a fa9t idea ( ! beauty1 v>iety1 & sublimity ( ! firmam5t ( ,uranus4#af ,! ,new ,planets1--,c]es1 ,pallas1 ,juno1 & ,ve/a4--,! comm5cem5t ( ! pres5t c5tury 0 r5d]$ memorable 9 ! annals ( a/ronomy1 by ! discov]y ( f\r new planets1 occupy+ ! long vacant tract betwe5 ,m>s & ,jupit]4 ,kepl]1 f "s analogy :i* he f\nd to subsi/ among ! di/ances ( ! planets f ! sun1 _h long be=e suspect$ ! exi/5ce ( "o at ?is di/ance2 & 8 conjecture 0 r5d]$ m probable by ! discov]y ( ,uranus1 :i* foll[s ! analogy ( ! o!r planets4 ,s /rongly1 inde$1 7 a/ronom]s impress$ ) ! idea t a planet w\ld be f\nd betwe5 ,m>s & ,jupit]1 t1 9 ! hope ( discov]+ x1 an association 0 =m$ on ! cont95t ( ,europe1 ( tw5ty-f\r obs]v]s1 :o divid$ ! sky into z _m zones1 "o ( :i* 0 allott$ to ea* memb] ( ! association4 ,! discov]y ( ! fir/ ( ^! bodies 01 h[ev]1 made accid5tally by ,piazzi1 an a/ronom] ( ,pal]mo1 on ! fir/ ( ,janu>y1 #ahja4 ,x 0 %ortly aft]w>ds lo/ sight ( on acc\nt ( its proximity to ! sun1 & 0 n se5 aga9 until ! close ( ! ye>1 :5 x 0 re-discov]$ 9 ,g]many4 ,piazzi call$ x ,c]es1 9 honor ( ! tutel>y goddess ( ,sicily1 & h] emblem1 ! sickle1 7,planet3 ,c]es7 has be5 adopt$ z its appropriate symbol4 ,! difficulty ( f9d+ ,c]es induc$ ,dr4 ,olb]s1 ( ,brem51 to exam9e ) p>ticul> c>e all ! small />s t lie ne> h] pa?1 z se5 f ! e>?2 &1 :ile prosecut+ ^! obs]vations1 9 ,m>*1 #ahjb1 he discov]$ ano!r simil> body1 v ne>ly at ! same di/ance f ! sun1 & resembl+ ! =m] 9 _m o!r p>ticul>s4 ,! discov]] gave to ?is second planet ! "n ( ,pallas1 *oos+ = its symbol ! lance1 7,planet3 ,pallas7 ! *>act]i/ic ( ,m9]va4 ,! mo/ surpris+ circum/ance connect$ ) ! discov]y ( ,pallas 0 ! exi/5ce ( two planets at ne>ly ! same di/ance f ! sun1 & app>5tly cross+ ! ecliptic 9 ! same "p ( ! heav5s1 or hav+ ! same node4 ,on acc\nt ( ?is s+ul>ity1 ,dr4 ,olb]s 0 l$ to conjecture t ,c]es & ,pallas are only fragm5ts ( a l>g] planet1 :i* _h =m]ly circulat$ at ! same di/ance1 & be5 %att]$ by "s int]nal convulsion4 ,! hypo!sis sugge/$ ! probability t !re might be o!r fragm5ts1 ^: orbits might be expect$ to cross ! ecliptic at a common po9t1 or to h ! same node4 ,dr4 ,olb]s1 !re=e1 propos$ to exam9e c>efully1 e mon?1 ! two opposite p>ts ( ! heav5s 9 :i* ! orbits ( ,c]es & ,pallas int]sect "o ano!r1 ) a view to ! discov]y ( o!r planets1 :i* might be s\ght = 9 ^? p>ts ) a great] *ance ( success1 ?an 9 a wid] zone1 embrac+ ! entire limits ( ^! orbits4 ,accord+ly1 9 #ahjd1 ne> "o ( ! nodes ( ,c]es & ,pallas1 a ?ird planet 0 discov]$4 ,?is 0 call$ ,juno1 & ! "* 7,planet3 ,juno7 0 adopt$ = its symbol1 repres5t+ ! />ry sceptre ( ! ,que5 ( ,olympus4 ,pursu+ ! same rese>*es1 9 #ahjg a f\r? planet 0 discov]$1 to :i* 0 giv5 ! "n ( ,ve/a1 & = its symbol ! "* 7,planet3 ,ve/a7 0 *os51--an alt> surm\nt$ ) a c5s] hold+ ! sacr$ fire4 ,! av]age di/ance ( ^! bodies f ! sun is two hundr$ & sixty-"o millions ( miles2 & x is rem>kable t _! orbits are v ne> toge!r4 ,tak+ ! di/ance ( ! e>? f ! sun = unity1 _! respective di/ances are #b4gg1 #b4gg1 #b4fg1 #b4cg4 ,_! times ( revolution ar\nd ! sun are ne>ly equal1 av]ag+ ab\t f\r & a half ye>s4 ,9 respect to ! incl9ation ( _! orbits to ! ecliptic1 !re is also consid]able div]sity4 ,! orbit ( ,ve/a is incl9$ only ab\t sev5 degrees1 :ile t ( ,pallas is m ?an ?irty-f\r degrees4 ,!y all1 !re=e1 h a high] incl9ation ?an ! orbits ( ! old planets1 & ( c\rse make excursions f ! ecliptic beyond ! limits ( ! zodiac4 ,h5ce !y h be5 call$ ! ultra-zodiacal planets4 ,:5 fir/ discov]$1 be=e _! place 9 ! sy/em 0 fully asc]ta9$ x 0 also propos$ to call !m a/]oids1 a "n imply+ t !y 7 planets "u ! =m ( />s4 ,_! title1 h[ev]1 to take _! rank among ! prim>y planets1 is n[ g5]ally conc$$4 ,! ecc5tricity ( _! orbits is also1 9 g5]al1 great] ?an t ( ! old planets4 ,y w recollect t ?is language d5otes t _! orbits are m elliptical1 or dep>t fur!r f ! circul> =m4 ,! ecc5tricities ( ! orbits ( ,pallas & ,juno exce$ t ( ! orbit ( ,m]cury4 ,! a/]oids diff] s mu*1 h[ev]1 9 ecc5tricity1 t _! orbits may cross ea* o!r4 ,! orbits ( ! old planets are s ne>ly circul>1 & at su* a great di/ance ap>t1 t !re is no dang] ( _! int]f]+ ) ea* o!r4 ,! e>?1 = example1 :5 at its ne>e/ di/ance f ! sun1 w nev] come s ne> x z ,v5us is :5 at its greate/ di/ance1 & !re=e c nev] cross ! orbit ( ,v5us4 ,b s9ce ! av]age di/ance ( ,c]es & ,pallas f ! sun is ab\t ! same1 :ile ! ecc5tricity ( ! orbit ( ,pallas is mu* great] ?an t ( ,c]es1 consequ5tly1 ,pallas may come s ne> to ! sun at its p]ihelion1 z to cross ! orbit ( ,c]es4 ,! small size ( ! a/]oids con/itutes "o ( _! mo/ rem>kable peculi>ities4 ,! difficulty ( e/imat+ ! app>5t diamet] ( bodies at once s v small & s f> (f1 w\ld lead u to expect diff]5t results 9 ! actual e/imates4 ,accord+ly1 :ile ,dr4 ,h]s*el e/imates ! diamet] ( ,pallas at only eighty miles1 ,s*roet] places x z high z two ?\s& miles1 or ab\t ! diamet] ( ! moon4 ,! volume ( ,ve/a is e/imat$ at only "o fifte5 ?\s&? "p ( ! e>?'s1 & h] surface is only ab\t equal to t ( ! k+dom ( ,spa94 ,^! little bodies are surr\nd$ by atmosph]es ( great ext5t1 "s ( :i* are uncommonly lum9\s1 & o!rs appe> to consi/ ( nebul\s matt]1 l t ( comets4 ,^! planets %9e ) a m vivid light ?an might be expect$1 f _! great di/ance & dim9utive size2 b a good telescope is ess5tial = obta9+ a di/9ct view ( _! ph5om5a4 ,al?\gh ! great *asm :i* occurs betwe5 ,m>s & ,jupit]1--a *asm ( m ?an ?ree hundr$ millions ( miles1--sugge/$ long ago ! idea ( o!r planet>y bodies occupy+ t "p ( ! sol> sy/em1 yet ! discov]y ( ! a/]oids does n entirely satisfy expectation s9ce !y are bodies s dissimil> to ! o!r memb]s ( ! s]ies 9 size1 9 appe>ance1 & 9 ! =m & incl9ations ( _! orbits4 ,h5ce1 ,dr4 ,olb]s1 ! discov]] ( ?ree ( ^! bodies1 held t !y 7 fragm5ts ( a s+le l>ge planet1 :i* once occupi$ t place 9 ! sy/em1 & :i* explod$ 9 diff]5t directions by "s int]nal viol5ce4 ,( ! fragm5ts ?us project$ into space1 "s w\ld be propell$ 9 su* directions & ) su* velocities1 z1 "u ! =ce ( projection & t ( ! sol> attraction w\ld make !m revolve 9 regul> orbits ar\nd ! sun4 ,o!rs w\ld be s project$ among ! o!r bodies 9 ! sy/em1 z to be ?r[n 9 v irregul> orbits1 app>5tly w&]+ lawless ?r\gh ! skies4 ,! l>g] fragm5ts w\ld receive ! lea/ impetus f ! explosive =ce1 & w\ld !re=e circulate 9 an orbit deviat+ less ?an any o!r ( ! fragm5ts f ! orig9al pa? ( ! l>ge planet2 :ile ! less] fragm5ts1 be+ ?r[n (f ) great] velocity1 w\ld revolve 9 orbits m ecc5tric1 & m incl9$ to ! ecliptic4 ,dr4 ,brew/]1 editor ( ! ',ed9burgh ,encyclop$ia1' & ! well-kn[n au?or ( v>i\s philosophical works1 esp\s$ ?is hypo!sis ) mu* zeal2 &1 aft] summ+ up ! evid5ce 9 favor ( x1 he rem>ks z foll[s3 ,^! s+ul> resemblances 9 ! motions ( ! great] fragm5ts1 & 9 ^? ( ! less] fragm5ts1 & ! /rik+ co9cid5ces betwe5 !ory & obs]vation 9 ! ecc5tricity ( _! orbits1 9 _! incl9ation to ! ecliptic1 9 ! position ( _! nodes1 & 9 ! places ( _! p]ihelia1 are ph5om5a :i* c\ld n possibly result f *ance1 & :i* concur to prove1 ) an evid5ce am\nt+ almo/ to demon/ration1 t ! f\r new planets h div]g$ f "o common node1 & h !re=e compos$ a s+le planet4 ,! same di/+ui%$ writ] supposes t "s ( ! smalle/ fragm5ts might ev5 h come )9 rea* ( ! e>?'s attraction1 & by ! comb9$ effects ( _! projectile =ces & ! attraction ( ! e>?1 be made to revolve ar\nd ?is body z ! l>g] fragm5ts are c>ri$ ar\nd ! sun2 & t ^! are 9 fact ! bodies :i* af=d ^? meteoric /ones :i* are occasionally precipitat$ to ! e>?4 ,x is n[ a well-asc]ta9$ fact1 a fact :i* has be5 _m times v]ifi$ 9 our own c\ntry1 t l>ge meteors1 9 ! %ape ( fire-balls1 trav]s+ ! atmosph]e1 sometimes project to ! e>? masses ( /ony or f]rug9\s matt]4 ,su* 7 ! meteoric /ones :i* fell at ,we/on1 9 ,connecticut1 9 #ahjg1 ( :i* a full & int]e/+ acc\nt 0 publi%$1 aft] a m9ute exam9ation ( ! facts1 by ,pr(essors ,silliman & ,k+sley1 ( ,yale ,college4 ,v>i\s acc\nts ( simil> occurr5ces may be f\nd 9 diff]5t volumes ( ! ,am]ican ,j\rnal ( ,sci5ce4 ,x is = ! production ( ^! wond]ful ph5om5a t ,dr4 ,brew/] supposes ! explosion ( ! planet1 :i*1 accord+ to ,dr4 ,olb]s1 produc$ ! a/]oids1 acc\nts4 ,o!rs1 h[ev]1 z ,sir ,john ,h]s*el1 h be5 dispos$ to ascribe v little weight to ! doctr9e ( ,olb]s4 ,,footnotes3 #ac ,altissimum planetam t]gem9um obs]vavi4 ,or1 z transpos$1 ,smaismrmilme poeta leumi bvne nugttaviras4 #ad ,9 imitation ( ,galileo1 ,huygh5s ann\nc$ 8 discov]y 9 ?is =m3 a a a a a a a c c c c c d e e e e e g h i i i i i i i l l l l m m n n n n n n n n n o o o o p p q r r s t t t t t u u u u u2 :i* he aft]w>ds recompos$ into ?is s5t5ce3 ,annulo c+itur1 t5ui1 plano1 nusquam cohr5te1 ad eclipticam incl9ato4 #ae ,dick's ',cele/ial ,sc5]y4' #af ,dick's ',cele/ial ,sc5]y4' ,,lett] ,,xxiv4 ,,! ,,planet>y ,,motions4----,,kepl]',s ,,laws4----,,kepl]4 ,god ( ! roll+ orbs above6 ,?y "n is writt5 cle>ly bright ,9 ! w>m day's unv>y+ blaze1 ,or ev5+'s gold5 %[] ( light2 ,= e fire t fronts ! sun1 ,& e sp>k t walks alone ,ar\nd ! utmo/ v]ge ( heav51 ,0 k9dl$ at ?y burn+ ?rone4--,peabody4 ,,if we c\ld /& ^u ! sun & view ! planet>y motions1 !y w\ld appe> to u z simple z ! motions ( eque/rians rid+ ) diff]5t degrees ( spe$ ar\nd a l>ge r+1 ( :i* we occupi$ ! c5tre4 ,we %\ld see all ! planets c\rs+ ea* o!r f we/ to ea/1 ?r\gh ! same great highway1 7! ,zodiac17 no "o ( !m1 ) ! exception ( ! a/]oids1 deviat+ m ?an sev5 degrees f ! pa? pursu$ by ! e>?4 ,mo/ ( !m1 inde$1 w\ld always be se5 mov+ mu* ne>] ?an t to ! ecliptic4 ,we %\ld see ! planets mov+ on _! way ) v>i\s degrees ( spe$4 ,m]cury w\ld make ! entire circuit 9 ab\t ?ree mon?s1 hurry+ on 8 c\rse ) a spe$ ab\t "o ?ird z great z t by :i* ! moon revolves ar\nd ! e>?4 ,! mo/ di/ant planets1 on ! o!r h&1 move at s sl[ a pace1 t we %\ld see ,m]cury1 ,v5us1 ! ,e>?1 & ,m>s1 sev]ally ov]tak+ !m a great _m times1 be=e !y _h complet$ _! revolutions4 ,b ?\gh ! movem5ts ( "s 7 comp>atively rapid1 & ( o!rs extremely sl[1 yet !y w\ld n seem to diff] mat]ially1 9 o!r respects3 ea* w\ld be mak+ a /eady & ne>ly uni=m m>* along ! cele/ial vault4 ,su* w\ld be ! simple & h>moni\s motions ( ! planets1 z !y w\ld be se5 f ! sun1 ! c5tre ( _! motions2 & su* !y are1 9 fact4 ,b two circum/ances conspire to make !m appe> exce$+ly diff]5t f ^!1 & va/ly m complicat$2 "o is1 t we view !m out ( ! c5tre ( _! motions2 ! o!r1 t we are ourselves 9 motion4 ,i h already expla9$ to y ! effect :i* ^! two causes produce on ! app>5t motions ( ! inf]ior planets1 ,m]cury & ,v5us4 ,let u n[ see h[ !y effect ^? ( ! sup]ior planets1 ,m>s1 ,jupit]1 ,saturn1 & ,uranus4 ,orr]ies1 or ma*9es int5d$ to exhibit a model ( ! sol> sy/em1 are sometimes employ$ to give a popul> view ( ! planet>y motions2 b !y (t5] mislead ?an give correct ideas4 ,!y may assi/ reflection1 b !y c nev] supply its place4 ,! impossibility ( repres5t+ ?+s 9 _! j proportions w be evid5t1 :5 we reflect t1 to d ?is1 if 9 an orr]y we make ,m]cury z l>ge z a *]ry1 we %\ld h to repres5t ! sun six feet 9 diamet]4 ,if we pres]ve ! same proportions1 9 reg>d to di/ance1 we mu/ place ,m]cury two hundr$ & fifty feet1 & ,uranus twelve ?\s& five hundr$ feet1 or m ?an two miles f ! sun4 ,! m9d ( ! /ud5t ( a/ronomy mu/1 !re=e1 raise itself f su* imp]fect repres5tations ( cele/ial ph5om5a1 z are af=d$ by artificial me*anism1 &1 transf]r+ 8 contemplations to ! cele/ial regions !mselves1 he mu/ conceive ( ! sun & planets z bodies t be> an insignificant ratio to ! imm5se spaces 9 :i* !y circulate1 resembl+ m a few little birds fly+ 9 ! op5 sky1 ?an !y d ! cr[d$ ma*9]y ( an orr]y4 ,! real motions ( ! planets1 inde$1 or su* z orr]ies usually exhibit1 are v easily conceiv$ (1 z be=e expla9$2 b ! app>5t motions are1 = ! mo/ "p1 entirely diff]5t f ^!4 ,! app>5t motions ( ! inf]ior planets h be5 already expla9$4 ,y w recollect t ,m]cury & ,v5us move backw>ds & =w>ds across ! sun1 ! =m] nev] be+ se5 fur!r ?an tw5ty-n9e degrees1 & ! latt] nev] m ?an ab\t =ty-sev5 degrees1 f t lum9>y2 t1 :ile pass+ f ! greate/ elongation on "o side1 to ! greate/ elongation on ! o!r side1 ?r\gh ! sup]ior conjunction1 ! app>5t motions ( ^! planets are accel]at$ by ! motion ( ! e>?2 b t1 :ile mov+ ?r\gh ! inf]ior conjunction1 at :i* "t _! motions are retrograde1 !y are app>5tly ret>d$ by ! e>?'s motion4 ,let u n[ see :at are ! app>5t motions ( ! sup]ior planets4 ,let ,a1 ,b1 ,c1 ,fig4 #fb1 page #bid1 repres5t ! e>? 9 diff]5t positions 9 its orbit1 ,m1 a sup]ior planet1 z ,m>s1 & ,n ,r1 an arc ( ! concave sph]e ( ! heav5s4 ,fir/1 suppose ! planet to rema9 at re/ 9 ,m1 & let u see :at app>5t motions x w receive f ! real motions ( ! e>?4 ,:5 ! e>? is at ,b1 x w see ! planet 9 ! heav5s at ,n2 & z ! e>? moves successively ?r\gh ,c1 ,d1 ,e1 ,f1 ! planet w appe> to move ?r\gh ,o1 ,p1 ,q1 ,r4 ,b & ,f are ! two po9ts ( greate/ elongation ( ! e>? f ! sun1 z se5 f ! planet2 h5ce1 betwe5 ^! two po9ts1 :ile pass+ ?r\gh its orbit mo/ remote f ! planet1 7:5 ! planet is se5 9 sup]ior conjunction17 ! e>?1 by its own motion1 gives an app>5t motion to ! planet 9 ! ord] ( ! signs2 t is1 ! app>5t motion giv5 by ! real motion ( ! e>? is direct4 ,b 9 pass+ f ,f to ,b ?r\gh ,a1 :5 ! planet is se5 9 opposition1 ! app>5t motion giv5 to ! planet by ! e>?'s motion is f ,r to ,n1 & is !re=e retrograde4 ,z ! arc describ$ by ! e>?1 :5 ! motion is direct1 is mu* great] ?an :5 ! motion is retrograde1 :ile ! app>5t arc ( ! heav5s describ$ by ! planet f ,n to ,r1 9 ! "o case1 & f ,r to ,n1 9 ! o!r1 is ! same 9 bo? cases1 ! retrograde motion is mu* swift] ?an ! direct1 be+ p]=m$ 9 mu* less "t4 ,illu/ration ,fig4 #fb4 ,b ! sup]ior planets are n 9 fact at re/1 z we h suppos$1 b are all ! :ile mov+ ea/w>d1 ?\gh ) a sl[] motion ?an ! e>?4 ,inde$1 ) respect to ! remote/ planets1 z ,saturn & ,uranus1 ! =w>d motion is s exce$+ly sl[1 t ! above repres5tation is ne>ly true = a s+le ye>4 ,/ill1 ! effect ( ! real motions ( all ! sup]ior planets1 ea/w>d1 is to increase ! direct app>5t motion communicat$ by ! e>?1 & to dim9i% ! retrograde motion4 ,?is w be evid5t f inspect+ ! figure2 = if ! planet actually moves ea/w>d :ile x is app>5tly c>ri$ ea/w>d by ! e>?'s motion1 ! :ole motion ea/w>d w be equal to ! sum ( ! two2 & if1 :ile x is really mov+ ea/w>d1 x is app>5tly c>ri$ we/w>d /ill m by ! e>?'s motion1 ! retrograde movem5t w equal ! diff]5ce ( ! two4 ,if ,m>s /ood /ill :ile ! e>? w5t r\nd ! sun1 !n a second opposition1 z at ,a1 w\ld occur at ! end ( "o ye> f ! fir/2 b1 :ile ! e>? is p]=m+ ?is circuit1 ,m>s is also mov+ ! same way1 m ?an half z fa/2 s t1 :5 ! e>? returns to ,a1 ! planet has already p]=m$ m ?an half ! same circuit1 & w h complet$ its :ole revolution be=e ! e>? comes up ) x4 ,inde$ ,m>s1 aft] hav+ be5 se5 once 9 opposition1 does n come into opposition aga9 until aft] two ye>s & fifty days4 ,& s9ce ! planet is !n comp>atively ne> to u1 z at ,m1 :ile ! e>? is at ,a1 & appe>s v l>ge & bright1 ris+ unexpect$ly ab\t ! "t ! sun sets1 he surprises ! _w z ?\gh x 7 "s new cele/ial body4 ,b on acc\nt ( ! sl[ progress ( ,saturn & ,uranus1 we f9d1 aft] hav+ p]=m$ "o circuit ar\nd ! sun1 t !y are b little advanc$ beyond :]e we left !m at ! la/ opposition4 ,! "t betwe5 "o opposition ( ,saturn & ano!r is only a ye> & ?irte5 days4 ,x appe>s1 !re=e1 t ! sup]ior planets /eadily pursue _! c\rse ar\nd ! sun1 b t _! app>5t retrograde motion1 :5 9 opposition1 is occasion$ by our pass+ by !m ) a swift] motion1 ( :i* we are unconsci\s1 l ! app>5t backw>d motion ( a vessel1 :5 we ov]take x & pass by x rapidly 9 a /eam-boat4 ,su* are ! real & ! app>5t motions ( ! planets4 ,let u n[ turn our att5tion to ! laws ( ! planet>y orbits4 ,!re are ?ree great pr9ciples1 accord+ to :i* ! motions ( ! e>? & all ! planets ar\nd ! sun are regulat$1 call$ ,,kepl]',s ,,laws1 hav+ be5 fir/ discov]$ by ! a/ronom] ^: "n !y be>4 ,!y may appe> to y1 at fir/1 dry & obscure2 yet !y w be easily und]/ood f ! explanations :i* foll[2 & s important h !y prov$ 9 a/ronomical inquiries1 t !y h acquir$ = _! r5[n$ discov]] ! appellation ( ! ',legislator ( ! ,skies4' ,we w consid] ea* ( ^! laws sep>ately2 &1 = ! sake ( r5d]+ ! explanation cle> & intelligible1 ,i %all p]haps repeat "s ?+s t h be5 briefly m5tion$ be=e4 ,illu/ration ,fig4 #fc4 ,,fir/ ,,law4--,! orbits ( ! e>? & all ! planets are ellipses1 hav+ ! sun 9 ! common focus4 ,9 a circle1 all ! diamet]s are equal to "o ano!r2 b if we take a metallic wire or hoop1 & draw x out on opposite sides1 we elongate x into an ellipse1 ( :i* ! diff]5t diamet]s are v unequal4 ,t :i* connects ! po9ts mo/ di/ant f ea* o!r is call$ ! transv]se1 & t :i* is at "r angles to ?is is call$ ! conjugate1 axis4 ,?us1 ,a ,b1 ,fig4 #fc1 is ! transv]se axis1 & ,c ,d1 ! conjugate ( ! ellipse ,a ,b ,c4 ,by su* a process ( elongat+ ! circle into an ellipse1 ! c5tre ( ! circle may be conceiv$ ( z drawn opposite ways to ,e & ,f1 ea* ( :i* becomes a focus1 & bo? toge!r are call$ ! foci ( ! ellipse4 ,! di/ance ,g ,e1 or ,g ,f1 ( ! focus f ! c5tre is call$ ! ecc5tricity ( ! ellipse2 & ! ellipse is said to be m or less ecc5tric1 z ! di/ance ( ! focus f ! c5tre is great] or less4 ,figure #fd repres5ts su* a collection ( ellipses ar\nd ! common focus ,f1 ! inn]mo/1 ,a ,g ,d1 hav+ a small ecc5tricity1 or v>y+ little f a circle1 :ile ! out]mo/1 ,a ,c ,b1 is an ecc5tric ellipse4 ,! orbits ( all ! bodies t revolve ab\t ! sun1 bo? planets & comets1 h1 9 l mann]1 a common focus1 9 :i* ! sun is situat$1 b !y diff] 9 ecc5tricity4 ,mo/ ( ! planets h orbits ( v little ecc5tricity1 diff]+ little f circles1 b comets move 9 v ecc5tric ellipses4 ,! e>?'s pa? ar\nd ! sun v>ies s little f a circle1 t a diagram repres5t+ x truly w\ld sc>cely be di/+ui%$ f a p]fect circle2 yet1 :5 ! comp>ative di/ances ( ! sun f ! e>? are tak5 at diff]5t seasons ( ! ye>1 we f9d t ! diff]5ce betwe5 _! greate/ & lea/ di/ances is no less ?an ?ree millions ( miles4 ,illu/ration ,fig4 #fd4 ,,second ,,law4--,! radius vector ( ! e>?1 or ( any planet1 describes equal areas 9 equal times4 ,y w recollect t ! radius vector is a l9e drawn f ! c5tre ( ! sun to a planet revolv+ ab\t ! sun4 ,?is def9ition ,i h some:]e giv5 y be=e1 & p]haps x may appe> to y l ne$less repetition to /ate x aga94 ,9 a book design$ = sy/ematic in/ruction1 :]e all ! articles are di/9ctly numb]$1 x is commonly suffici5t to make a ref]5ce back to ! article :]e ! po9t 9 "q is expla9$2 b ,i ?9k1 9 ,lett]s l ^!1 y w be> ) a little repetition1 r ?an be at ! tr\ble ( turn+ to ! ,index & hunt+ up a def9ition long s9ce giv54 ,illu/ration ,fig4 #fe4 ,9 ,figure #fe1 ,e a1 ,e b1 ,e c1 c41 are successive repres5tations ( ! radius vector4 ,n[1 if a planet sets out f a1 & travels r\nd ! sun 9 ! direction ( a b c1 x w move fa/] :5 ne>] ! sun1 z at a1 ?an :5 m remote f x1 z at m2 yet1 if a b & m n be arcs describ$ 9 equal times1 !n1 accord+ to ! =ego+ law1 ! space ,e a b w be equal to ! space ,e m n2 & ! same is true ( all ! o!r spaces describ$ 9 equal times4 ,al?\gh ! figure ,e a b is mu* %ort] ?an ,e m n1 yet its great] bread? exactly c\nt]balances ! great] l5g? ( ^? figures :i* are describ$ by ! radius vector :]e x is long]4 ,,?ird ,,law4--,! squ>es ( ! p]iodical times are z ! cubes ( ! mean di/ances f ! sun4 ,! p]iodical "t ( a body is ! "t x takes to complete its orbit1 9 its revolution ab\t ! sun4 ,?us ! e>?'s p]iodic "t is "o ye>1 & t ( ! planet ,jupit] ab\t twelve ye>s4 ,z ,jupit] takes s mu* long] "t to travel r\nd ! sun ?an ! e>? does1 we might suspect t 8 orbit is l>g] ?an t ( ! e>?1 & ( c\rse1 t he is at a great] di/ance f ! sun2 & our fir/ ?\ght might be1 t he is probably twelve times z f> (f2 b ,kepl] discov]$ t ! di/ance does n increase z fa/ z ! times increase1 b t ! planets :i* are m di/ant f ! sun actually move sl[] ?an ^? :i* are ne>]4 ,aft] try+ a great _m proportions1 he at l5g? f\nd t1 if we take ! squ>es ( ! p]iodic times ( two planets1 ! great] squ>e conta9s ! less1 j z (t5 z ! cube ( ! di/ance ( ! great] conta9s t ( ! less4 ,?is fact is express$ by say+1 t ! squ>es ( ! p]iodic times are to "o ano!r z ! cubes ( ! di/ances4 ,?is law is ( great use 9 det]m9+ ! di/ance ( ! planets f ! sun4 ,suppose1 = example1 t we wi% to f9d ! di/ance ( ,jupit]4 ,we c easily det]m9e1 f obs]vation1 :at is ,jupit]'s p]iodical "t1 = we c actually see h[ long x takes = ,jupit]1 aft] leav+ a c]ta9 "p ( ! heav5s to come r\nd to ! same "p aga94 ,let ?is p]iod be twelve ye>s4 ,! e>?'s p]iod is ( c\rse "o ye>2 & ! di/ance ( ! e>?1 z det]m9$ f ! sun's horizontal p>allax1 z already expla9$1 is ab\t n9ety-five millions ( miles4 ,n[1 we h "h ?ree t]ms ( a proportion to f9d ! f\r?1 & !re=e ! solution is m]ely a simple case ( ! rule ( ?ree4 ,?us3--! squ>e ( #a ye> 3 squ>e ( #ab ye>s 33 cube ( #ie1jjj1jjj 3 cube ( ,jupit]'s di/ance4 ,! ?ree fir/ t]ms be+ kn[n1 we h only to multiply toge!r ! second & ?ird & divide by ! fir/1 to obta9 ! f\r? t]m1 :i* w give u ! cube ( ,jupit]'s di/ance f ! sun2 & by extract+ ! cube root ( ?is sum1 we obta9 ! di/ance itself4 ,9 ! same mann] we may obta9 ! respective di/ances ( all ! o!r planets4 ,s truly is ?is a law ( ! sol> sy/em1 t x holds good 9 respect to ! new planets1 :i* h be5 discov]$ s9ce ,kepl]'s "t1 z well z 9 ! case ( ! old planets4 ,x also holds good 9 respect to comets1 & to all bodies belong+ to ! sol> sy/em1 :i* revolve ar\nd ! sun z _! c5tre ( motion4 ,h5ce1 x is ju/ly reg>d$ z "o ( ! mo/ int]e/+ & important pr9ciples yet develop$ 9 a/ronomy4 ,b :o 0 ?is ,kepl]1 t ga9$ su* an extraord9>y insight into ! laws ( ! planet>y sy/em1 z to be call$ ! ',legislator ( ! ,skies8' ,john ,kepl] 0 "o ( ! mo/ rem>kable ( ! human race1 & ,i ?9k ,i _c gratify or in/ruct y m1 ?an by occupy+ ! rema9d] ( ?is ,lett] ) "s p>ticul>s ( 8 hi/ory4 ,kepl] 0 a native ( ,g]many4 ,he 0 born 9 ! ,du*y ( ,wurtemb]g1 9 #aega4 ,z ,cop]nicus1 ,ty*o ,brahe1 ,galileo1 ,kepl]1 & ,newton1 are names t are mu* associat$ 9 ! hi/ory ( a/ronomy1 let u see h[ !y /ood relat$ to ea* o!r 9 po9t ( "t4 ,cop]nicus 0 born 9 #adgc2 ,ty*o1 9 #aedf2 ,galileo1 9 #aefd2 ,kepl]1 9 #aega2 & ,newton1 9 #afdb4 ,h5ce1 ,cop]nicus 0 sev5ty-?ree ye>s be=e ,ty*o1 & ,ty*o n9ety-six ye>s be=e ,newton4 ,!y all liv$ to an advanc$ age1 s t ,ty*o1 ,galileo1 & ,kepl]1 7 contempor>y = _m ye>s2 & ,newton1 z ,i m5tion$ 9 ! sket* ,i gave y ( 8 life1 0 born ! ye> t ,galileo di$4 ,kepl] 0 born ( p>5ts :o 7 !n 9 humble circum/ances1 al?\gh ( noble desc5t4 ,_! mis=tunes1 :i* _h r$uc$ !m to pov]ty1 seem to h be5 aggravat$ by _! own unhappy dispositions2 = 8 biograph] in=ms u1 t 8 "m 0 treat$ ) a degree ( b>b>ity by h] husb& & bro!r-9-law1 t 0 h>dly exce$$ by h] own p]v]s5ess4 ,x is =tunate1 !re=e1 t ,kepl]1 9 8 *ildhood1 0 remov$ f ! imm$iate society & example ( 8 p>5ts1 & educat$ at a public s*ool at ! exp5se ( ! ,duke ( ,wurtemb]g4 ,he e>ly imbib$ a ta/e = natural philosophy1 b _h conceiv$ a /rong prejudice aga9/ a/ronomy1 & ev5 a contempt = x1 inspir$1 probably1 by ! arrogant & ridicul\s pret5sions ( ! a/rolog]s1 :o con/itut$ ! pr9cipal a/ronom]s ( 8 c\ntry4 ,a vacant po/1 h[ev]1 ( tea*] ( a/ronomy1 occurr$ :5 he 0 ( a suitable age to fill x1 & he 0 compell$ to take x by ! au?ority ( 8 tutors1 ?\gh ) _m prote/ations1 on 8 "p1 wi%+ to be provid$ = 9 "s o!r m brilliant pr(ession4 ,happy is g5ius1 :5 x lights on a pr(ession entirely consonant to its p[]s1 :]e ! objects successively pres5t$ to x are s exactly suit$ to its nature1 t x cl+s to !m z ! load/one to its k9dr$ metal among piles ( =eign ores4 ,no?+ c\ld h be5 m cong5ial to ! v m5tal con/itution ( ,kepl]1 ?an ! /udy ( a/ronomy1--a sci5ce :]e ! mo/ capaci\s und]/&+ may f9d scope 9 unison ) ! mo/ f]vid imag9ation4 ,mu* z has be5 said aga9/ hypo!ses 9 philosophy1 x is nev]!less a fact1 t "s ( ! greate/ tru?s h be5 discov]$ 9 ! pursuit ( hypo!ses1 9 !mselves entirely false2 tru?s1 moreov]1 f> m important ?an ^? assum$ by ! hypo!ses2 z ,columbus1 9 se>*+ = a nor?we/ passage to ,india1 discov]$ a new _w4 ,?us ,kepl] grop$ 8 way ?r\gh _m false & absurd suppositions1 to "s ( ! mo/ sublime discov]ies ev] made by man4 ,! fundam5tal pr9ciple :i* guid$ him 0 n1 h[ev]1 ei!r false or absurd4 ,x 01 t ,god1 :o made ! _w1 _h e/abli%$1 ?r\gh\t all 8 works1 fix$ laws1--laws t are (t5 s def9ite z to be capable ( expression 9 exact num]ical t]ms4 ,9 accordance ) ^! views1 he s\ght = num]ical relations 9 ! disposition & arrangem5t ( ! planets1 9 respect to _! numb]1 ! times ( _! revolution1 & _! di/ances f "o ano!r4 ,_m1 inde$1 ( ! subord9ate suppositions :i* he made1 7 extremely fanciful2 b he tri$ 8 own hypo!ses by a rigor\s ma!matical te/1 :]ev] he c\ld apply x2 & z soon z he discov]$ t a supposition w\ld n abide ?is te/1 he ab&on$ x )\t ! lea/ hesitation1 & adopt$ o!rs1 :i* he submitt$ to ! same sev]e trial1 to %>e1 p]haps1 ! same fate4 ,aft] _m failures1 he says1 ,i 0 com=t$ by obs]v+ t ! motions1 9 e case1 seem$ to be connect$ ) ! di/ances2 & t1 :5 !re 0 a great gap betwe5 ! orbits1 !re 0 ! same betwe5 ! motions4 ,& ,i reason$ t1 if ,god _h adapt$ motions to ! orbits 9 "s relation to ! di/ances1 he _h also arrang$ ! di/ances !mselves 9 relation to some?+ else4 ,9 two ye>s aft] he comm5c$ ! /udy ( a/ronomy1 he publi%$ a book1 call$ ! ',my/]ium ,cosmographicum1' a "n :i* implies an explanation ( ! my/]ies involv$ 9 ! con/ruction ( ! univ]se4 ,?is "w 0 full ( ! wilde/ speculations & mo/ extravagant hypo!ses1 ! mo/ rem>kable ( :i* 01 t ! di/ances ( ! planets f ! sun are regulat$ by ! relations :i* subsi/ betwe5 ! five regul> solids4 ,x is well kn[n to geomet]s1 t !re are & c be only five regul> solids4 ,^! are1 fir/1 ! tetra$ron1 a f\r-sid$ figure1 all ^: sides are equal & simil> triangles2 secondly1 ! cube1 conta9$ by six equal squ>es2 ?irdly1 an octa$ron1 an eight-sid$ figure1 consi/+ ( two f\r-sid$ pyramids jo9$ at _! bases2 f\r?ly1 a dodeca$ron1 hav+ twelve five-sid$ or p5tagonal faces2 &1 fif?ly1 an icosa$ron1 conta9$ by tw5ty equal & simil> triangles4 ,y w be mu* at a loss1 ,i ?9k1 to imag9e :at relation ,kepl] c\ld trace betwe5 ^! /range figures & ! di/ances ( ! sev]al planets f ! sun4 ,he ?\ght he discov]$ a connexion betwe5 ^? di/ances & ! spaces :i* figures ( ?is k9d w\ld occupy1 if int]pos$ 9 c]ta9 ways betwe5 !m4 ,?us1 he says ! ,e>? is a circle1 ! measure ( all2 r\nd x describe a dodeca$ron1 & ! circle includ+ ?is w be ! orbit ( ,m>s4 ,r\nd ?is circle describe a tetra$ron1 & ! circle includ+ ?is w be ! orbit ( ,jupit]4 ,describe a cube r\nd ?is1 & ! circle includ+ x w be ! orbit ( ,saturn4 ,n[1 inscribe 9 ! e>? an icosa$ron1 & ! circle includ$ 9 ?is w give ! orbit ( ,v5us4 ,9 ?is inscribe an octa$ron1 & ! circle includ$ 9 ?is w be ! orbit ( ,m]cury4 ,on ?is suppos$ discov]y ,kepl] exults 9 ! mo/ en?usia/ic expressions4 ,! int5se pleasure ,i h receiv$ f ?is discov]y nev] c be told 9 words4 ,i regrett$ no m "t wa/$2 ,i tir$ ( no labor2 ,i %unn$ no toil ( reckon+2 days & nights ,i sp5t 9 calculations1 until ,i c\ld see :e!r ?is op9ion w\ld agree ) ! orbits ( ,cop]nicus1 or :e!r my joy 0 to vani% into air4 ,i will+ly subjo9 t s5tim5t ( ,ar*ytas1 z giv5 by ,cic]o2 ',if ,i c\ld m\nt up into heav51 & ?or\ghly p]ceive ! nature ( ! _w & ! beauty ( ! />s1 t admiration w\ld be )\t a *>m = me1 unless ,i _h "s "o l y1 read]1 c&id1 att5tive1 & eag] = k1 to :om to describe x4' ,if y ackn[l$ge ?is feel+1 & are c&id1 y w refra9 f blame1 su* z1 n )\t cause1 ,i anticipate2 b if1 leav+ t to itself1 y fe>1 le/ ^! ?+s be n asc]ta9$1 & t ,i h %\t$ triumph be=e victory1 at lea/ approa* ^! pages1 & le>n ! matt] 9 consid]ation3 y w n f9d1 z j n[1 new & unkn[n planets int]pos$2 t boldness ( m9e is n approv$2 b ^? old ones v little loos5$1 & s furni%$ by ! int]position 7h[ev] absurd y may ?9k x7 ( rectil9e> figures1 t 9 future y may give a reason to ! ru/ics1 :5 !y ask = ! hooks :i* keep ! skies f fall+4 ,:5 ,ty*o ,brahe1 :o _h !n retir$ f 8 fam\s ,uraniburg1 & 0 settl$ 9 ,prague1 met ) ?is "w ( ,kepl]'s1 he imm$iately recognis$ "u ?is fanta/ic g>b ! l9eam5ts ( a great a/ronom]4 ,he ne$$ su* an unwe>i$ & pati5t calculator z he p]ceiv$ ,kepl] to be1 to aid him 9 8 labors1 9 ord] t he might devote himself m unres]v$ly to ! tak+ ( obs]vations1--an employm5t 9 :i* he delight$1 & 9 :i*1 z ,i m5tion$1 9 giv+ y a sket* ( 8 hi/ory1 he excell$ all m5 ( t & prec$+ ages4 ,kepl]1 !re=e1 at ! express invitation ( ,ty*o1 w5t to ,prague1 & jo9$ him 9 ! capacity ( assi/ant4 ,_h ,ty*o be5 ( a nature less truly noble1 he might h look$ ) contempt on "o :o _h made s few obs]vations1 & indulg$ s mu* 9 wild speculation2 or he might h be5 jeal\s ( a ris+ g5ius1 9 :i* he descri$ s _m signs ( future em95ce z an a/ronom]2 b1 sup]ior to all ! bas] motives1 he ext5ds to ! "y aspirant ! h& ( enc\ragem5t1 9 ! foll[+ k9d invitation3 ,come n z a /rang]1 b z a v welcome fri5d2 come1 & %>e 9 my obs]vations1 ) su* in/rum5ts z ,i h ) me4 ,sev]al ye>s previ\s to ?is1 ,kepl]1 aft] "o or two unsuccessful trials1 _h f\nd him a wife1 f :om he expect$ a consid]able =tune2 b 9 ?is he 0 disappo9t$2 & s poor 0 he1 t1 :5 on 8 j\rney to ,prague1 9 company ) 8 wife1 be+ tak5 sick1 he 0 unable to defray ! exp5ses ( ! j\rney1 & 0 =c$ to ca/ himself on ! b\nty ( ,ty*o4 ,9 ! c\rse ( ! foll[+ ye>1 :ile abs5t f ,prague1 he fanci$ t ,ty*o _h injur$ him1 & accord+ly address$ to ! noble ,dane a lett] full ( insults & reproa*es4 ,a mild reply f ,ty*o op5$ ! eyes ( ,kepl] to 8 own +ratitude4 ,8 bett] feel+s soon return$1 & he s5t to 8 great patron ?is humble apology3 ,mo/ noble ,ty*o6 ,h[ %all ,i enum]ate1 or rightly e/imate1 y\r b5efits conf]r$ on me6 ,= two mon?s y h lib]ally & gratuit\sly ma9ta9$ me1 & my :ole family2 y h provid$ = all my wi%es2 y h done me e possible k9dness2 y h communicat$ to me e ?+ y hold mo/ de>2 no "o1 by ^w or de$1 has int5tionally injur$ me 9 any ?+2 9 %ort1 n to y\r own *ildr51 y\r wife1 or y\rself1 h y %[n m indulg5ce ?an to me4 ,?is be+ s1 z ,i am anxi\s to put ^u record1 ,i _c reflect1 )\t con/]nation1 t ,i %\ld h be5 s giv5 up by ,god to my own intemp]ance1 z to %ut my eyes on all ^! b5efits2 t1 in/ead ( mode/ & respectful gratitude1 ,i %\ld indulge = ?ree weeks 9 cont9ual moros5ess t[>ds all y\r family1 & 9 headlong passion & ! utmo/ insol5ce t[>ds y\rself1 :o possess s _m claims on my v5]ation1 f y\r noble family1 y\r extraord9>y le>n+1 & di/+ui%$ reputation4 ,:atev] ,i h said or writt5 aga9/ ! p]son1 ! fame1 ! honor1 & ! le>n+1 ( y\r ,excell5cy2 or :atev]1 9 any o!r way1 ,i h injuri\sly spok5 or writt51 7if !y admit no o!r m favorable int]pretation17 z to my grief ,i h spok5 & writt5 _m ?+s1 & m ?an ,i c rememb]2 all & e ?+ ,i recant1 & freely & hone/ly decl>e & pr(ess to be gr\ndless1 false1 & incapable ( pro(4 ,?is 0 ample satisfaction to ! g5]\s ,ty*o4 ,to err is human3 to =give1 div9e4 ,on ,kepl]'s return to ,prague1 he 0 pres5t$ to ! ,emp]or by ,ty*o1 & honor$ ) ! title ( ,imp]ial ,ma!matician4 ,?is 0 9 #afja1 :5 he 0 ?irty ye>s ( age4 ,ty*o di$ %ortly aft]1 & ,kepl] succe$$ him z pr9cipal ma!matician to ! ,emp]or2 b 8 sal>y 0 badly paid1 & he suff]$ mu* f pecuni>y emb>rassm5ts4 ,al?\gh he held ! a/rolog]s1 or ^? :o told =tunes by ! />s1 9 great contempt1 yet he ent]ta9$ notions ( 8 own1 on ! same subject1 q z extravagant1 & practis$ ! art ( ca/+ nativities1 to eke out a support = 8 family4 ,:5 ,galileo began to obs]ve ) 8 telescope1 & ann\nc$1 9 rapid succession1 8 wond]ful discov]ies1 ,kepl] ent]$ into !m ) 8 *>act]i/ic en?usiasm1 al?\gh !y subv]t$ _m ( 8 favorite hypo!ses4 ,b su* 0 8 love ( tru?1 t he 0 among ! fir/ to congratulate ,galileo1 & a mo/ engag+ correspond5ce 0 c>ri$ on betwe5 ^! ma/]-spirits4 ,! fir/ planet1 :i* occupi$ ! p>ticul> att5tion ( ,kepl]1 0 ,m>s1 ! long & assidu\s /udy ( ^: motions conduct$ him at l5g? to ! discov]y ( ^? great pr9ciples call$ ',kepl]'s ,laws4' ,r>ely d we meet ) s rem>kable a union ( a vivid fancy ) a pr(\nd intellect4 ,! ha/y & extravagant sugge/ions ( ! =m] 7 submitt$ to ! mo/ labori\s calculations1 "s ( :i*1 t 7 ( great l5g?1 he repeat$ sev5ty times4 ,?is exub]ance ( fancy frequ5tly appe>s 9 8 /yle ( writ+1 :i* occasionally assumes a tone ludicr\sly figurative4 ,he seems con/antly to contemplate ,m>s z a valiant h]o1 :o _h hi!rto prov$ inv9cible1 & :o w\ld (t5 elude 8 own ef=ts to conqu] him1 ,:ile ?us triumph+ ov] ,m>s1 & prep>+ = him1 z = "o altoge!r vanqui%$1 tabul> prisons1 & equat$1 ecc5tric fett]s1 x is buzz$ "h & !re1 t ! victory is va91 & t ! w> is rag+ anew z viol5tly z be=e4 ,= ! enemy1 left at home a despis$ captive1 has bur/ all ! *a9s ( ! equation1 & brok5 =? ( ! prisons ( ! tables4 ,skirmi%es r\t$ my =ces ( physical causes1 &1 %ak+ (f ! yoke1 rega9$ _! lib]ty4 ,& n[1 !re 0 little to prev5t ! fugitive enemy f effect+ a junction ) 8 own rebelli\s support]s1 & r$uc+ me to despair1 _h ,i n sudd5ly s5t into ! field a res]ve ( new physical reason+s1 on ! r\t & disp]sion ( ! vet]ans1 & dilig5tly foll[$1 )\t all[+ ! slighte/ respite1 9 ! direction 9 :i* he _h brok5 out4 ,b he pursu$ ?is w>f>e ) ! planet until he ga9$ a full conque/1 by ! discov]y ( ! fir/ two ( 8 laws1 namely1 t he revolves 9 an elliptical orbit1 & t 8 radius vector passes ov] equal spaces 9 equal times4 ,dome/ic tr\bles1 h[ev]1 involv$ him 9 ! deepe/ affliction4 ,pov]ty1 ! loss ( a promis+ & favorite son1 ! dea? ( 8 wife1 aft] a long illness2--^! 7 "s ( ! mis=tunes t clu/]$ ar\nd him4 ,al?\gh 8 fir/ m>riage _h be5 an unhappy "o1 x 0 n consonant to 8 g5ius to surr5d] any ?+ ) only a s+le trial4 ,accord+ly1 x 0 n long be=e he endeavor$ to repair 8 loss by a second alliance4 ,he commission$ a numb] ( 8 fri5ds to look out = him1 & he soon obta9$ a tabul> li/ ( elev5 ladies1 among :om 8 affections wav]$4 ,! progress ( 8 c\rt%ip is ?us n>rat$ 9 ! int]e/+ ',life' conta9$ 9 ! ',libr>y ( ,useful ,k4' ,x furni%es s f9e a specim5 ( 8 ecc5tricities1 t ,i _c d5y myself ! pleasure ( transcrib+ ! passage = y\r p]usal4 ,x is tak5 f an acc\nt :i* ,kepl] himself gave 9 a lett] to a fri5d4 ,! fir/ on ! li/ 0 a wid[1 an intimate fri5d ( 8 fir/ wife & :o1 on _m acc\nts1 appe>$ a mo/ eligible mat*4 ,at fir/1 %e seem$ favorably incl9$ to ! proposal3 x is c]ta9 t %e took "t to consid] x1 b at la/ %e v quietly excus$ h]self4 ,f9d+ h] aft]w>ds less agreeable 9 p]son ?an he _h anticipat$1 he consid]$ x a =tunate escape1 m5tion+1 among o!r objections1 t %e _h two m>riageable daught]s1 :om1 by ! way1 he _h got on 8 li/ = exam9ation4 ,he 0 mu* tr\bl$ to reconcile 8 a/rology ) ! fact ( 8 hav+ tak5 s mu* pa9s ab\t a negotiation n de/9$ to succe$4 ,he exam9$ ! case pr(essionally4 ',h ! />s1' says he1 'ex]cis$ any influ5ce "h8 ,=1 j ab\t ?is "t1 ! direction ( ! mid-heav5 is 9 hot opposition to ,m>s1 & ! passage ( ,saturn ?r\gh ! asc5d+ po9t ( ! zodiac1 9 ! s*eme ( my nativity1 w happ5 aga9 next ,novemb] & ,decemb]4 ,b1 if ^! are ! causes1 h[ d !y act8 ,is t explanation ! true "o1 :i* ,i h else:]e giv58 ,= ,i c nev] ?9k ( h&+ ov] to ! />s ! (fice ( deities1 to produce effects4 ,let u1 !re=e1 suppose x acc\nt$ = by ! />s1 t at ?is season ,i am viol5t 9 my temp] & affections1 9 ra%ness ( belief1 9 a %[ ( pitiful t5d]-he>t$ness1 9 cat*+ at reputation by new & p>adoxical notions1 & ! s+ul>ity ( my actions2 9 busily inquir+ into1 & weigh+1 & discuss+1 v>i\s reasons2 9 ! uneas9ess ( my m9d1 ) respect to my *oice4 ,i ?ank ,god1 t t did n happ5 :i* might h happ5$2 t ?is m>riage did n take place4 ,n[ = ! o!rs4' ,( ^!1 "o 0 too old2 ano!r1 9 bad heal?2 ano!r1 too pr\d ( h] bir? & qu>t]+s2 a f\r? _h le>n$ no?+ b %[y accompli%m5ts1 n at all suitable to ! k9d ( life %e w\ld h to lead ) him4 ,ano!r grew impati5t1 & m>ri$ a m decid$ admir] :ile he 0 hesitat+4 ',! mis*ief1' says he1 '9 all ^! atta*m5ts 01 t1 :il/ ,i 0 delay+1 comp>+1 & balanc+1 conflict+ reasons1 e day saw me inflam$ ) a new passion4' ,by ! "t he rea*$ ,no4 #h1 ( 8 li/1 he f\nd 8 mat* 9 ?is respect4 ',=tune has av5g$ h]self at l5g? on my d\btful incl9ations4 ,at fir/1 %e 0 q comply+1 & h] fri5ds also4 ,pres5tly1 :e!r %e did or did n cons5t1 n only ,i1 b %e h]self1 did n "k4 ,aft] ! lapse ( a few days1 came a r5ew$ promise1 :i*1 h[ev]1 _h to be confirm$ a ?ird "t3 &1 f\r days aft] t1 %e aga9 rep5t$ h] con=mation1 & begg$ to be excus$ f x4 ,^u ?is1 ,i gave h] up1 & ?is "t all my c\nsellors 7 ( "o op9ion4' ,?is 0 ! longe/ c\rt%ip 9 ! li/1 hav+ la/$ ?ree :ole mon?s2 &1 q di%e>t5$ by its bad success1 ,kepl]'s next attempt 0 ( a m timid complexion4 ,8 advances to ,no4 #i 7 made by confid+ to h] ! :ole /ory ( 8 rec5t disappo9tm5t1 prud5tly det]m9+ to be guid$ 9 8 behavior1 by obs]v+ :e!r ! treatm5t he exp]i5c$ met ) a prop] degree ( sympa?y4 ,app>5tly1 ! exp]im5t did n succe$2 &1 :5 almo/ r$uc$ to despair1 ,kepl] betook himself to ! advice ( a fri5d1 :o _h = "s "t pa/ compla9$ t %e 0 n consult$ 9 ?is difficult negotiation4 ,:5 %e produc$ ,no4 #aj1 & ! fir/ visit 0 paid1 ! report ^u h] 0 z foll[s3 ',%e has1 und\bt$ly1 a good =tune1 is ( good family1 & ( economical habits3 b h] physiognomy is mo/ horribly ugly2 %e w\ld be />$ at 9 ! /reets1 n to m5tion ! /rik+ disproportion 9 our figures4 ,i am lank1 lean1 & sp>e2 %e is %ort & ?ick4 ,9 a family notori\s = fatness1 %e is consid]$ sup]flu\sly fat4' ,! only objection to ,no4 #aa seems to h be51 h] excessive y\?2 & :5 ?is treaty 0 brok5 (f1 on t acc\nt1 ,kepl] turn$ 8 back ^u all 8 advis]s1 & *ose = himself "o :o _h figur$ z ,no4 #e1 9 8 li/1 to :om he pr(esses to h felt atta*$ ?r\gh\t1 b f :om ! repres5tations ( 8 fri5ds _h hi!rto deta9$ him1 probably on acc\nt ( h] humble /ation4 ,hav+ ?us settl$ 8 dome/ic affairs1 ,kepl] n[ betook himself1 ) 8 usual indu/ry1 to 8 a/ronomical /udies1 & br\ght be=e ! _w ! mo/ celebrat$ ( 8 publications1 entitl$ ',h>monics4' ,9 ! fif? book ( ?is "w he ann\nc$ 8 ,?ird ,law1--t ! squ>es ( ! p]iodical times ( ! planets are z ! cubes ( ! di/ances4 ,kepl]'s rapture on detect+ x 0 unb\nd$4 ,:at1 says he1 ,i prophesi$ two-&-tw5ty ye>s ago1 z soon z ,i discov]$ ! five solids among ! heav5ly orbits2 :at ,i firmly believ$ long be=e ,i _h se5 ,ptolemy's ,h>monics2 :at ,i _h promis$ my fri5ds 9 ! title ( ?is book1 :i* ,i nam$ be=e ,i 0 sure ( my discov]y2 :at1 sixte5 ye>s ago1 ,i urg$ z a ?+ to be s\ght2 t = :i* ,i jo9$ ,ty*o ,brahe1 = :i* ,i settl$ 9 ,prague1 = :i* ,i h devot$ ! be/ "p ( my life to a/ronomical contemplations2--at l5g? ,i h br\ght to light1 & h recognis$ its tru? beyond my mo/ sangu9e expectations4 ,x is n[ eighte5 mon?s s9ce ,i got ! fir/ glimpse ( light1 ?ree mon?s s9ce ! dawn1 v few days s9ce ! unveil$ sun1 mo/ admirable to gaze on1 bur/ out ^u me4 ,no?+ holds me3 ,i w indulge 9 my sacr$ fury2 ,i w triumph ov] mank9d by ! hone/ confession1 t ,i h /ol5 ! gold5 vases ( ! ,egyptians to build up a tab]nacle = my ,god1 f> f ! conf9es ( ,egypt4 ,if y =give me1 ,i rejoice3 if y are angry1 ,i c be> x2 ! die is ca/1 ! book is writt51 to be read ei!r n[ or by po/]ity1--,i c>e n :i*4 ,i may well wait a c5tury = a read]1 z ,god has wait$ six ?\s& ye>s = an obs]v]4 ,9 accordance ) ! notion he ent]ta9$ respect+ ! music ( ! sph]es1 he made ,saturn & ,jupit] take ! bass1 ,m>s ! t5or1 ! ,e>? & ,v5us ! c\nt]1 & ,m]cury ! treble4 ,! mis]y 9 :i* ,kepl] liv$1 says ,sir ,david ,brew/]1 9 8 ',life ( ,newton1' =ms a pa9ful contra/ ) ! s]vices :i* he p]=m$ = sci5ce4 ,! p5sion on :i* he subsi/$ 0 always 9 arre>s2 & ?\gh ! ?ree emp]ors1 ^: reigns he adorn$1 direct$ _! m9i/]s to be m punctual 9 its paym5t1 ! disob$i5ce ( _! comm&s 0 a s\rce ( cont9ual vexation to ,kepl]4 ,:5 he retir$ to ,silesia1 to sp5d ! rema9d] ( 8 days1 8 pecuni>y difficulties became /ill m h>ass+4 ,necessity at l5g? compell$ him to apply p]sonally = ! arre>s :i* 7 due2 & he accord+ly set out1 9 #afcj1 :5 ne>ly sixty ye>s ( age1 = ,ratisbon2 b1 9 consequ5ce ( ! great fatigue :i* s long a j\rney on horseback produc$1 he 0 seiz$ ) a fev]1 :i* put an end to 8 life4 ,pr(essor ,:ewell 79 8 int]e/+ "w on ,a/ronomy & ,g5]al ,physics consid]$ ) ref]5ce to ,natural ,!ology7 expresses ! op9ion t ,kepl]1 not)/&+ 8 con/itutional oddities1 0 a man ( /rong & lively piety4 ,8 ',comm5t>ies on ! ,motions ( ,m>s' he op5s ) ! foll[+ passage3 ,i besee* my read]1 t1 n unm9dful ( ! ,div9e goodness be/[$ on man1 he d ) me praise & celebrate ! wisdom & greatness ( ! ,creator1 :i* ,i op5 to him f a m inw>d explication ( ! =m ( ! _w1 f a se>*+ ( causes1 f a detection ( ! errors ( vision2 & t ?us1 n only 9 ! firmness & /ability ( ! e>?1 he p]ceive ) gratitude ! pres]vation ( all liv+ ?+s 9 ,nature z ! gift ( ,god1 b also t 9 its motion1 s recondite1 s admirable1 he ackn[l$ge ! wisdom ( ! ,creator4 ,b him :o is too dull to receive ?is sci5ce1 or too weak to believe ! ,cop]nican sy/em )\t h>m to 8 piety1--him1 ,i say1 ,i advise t1 leav+ ! s*ool ( a/ronomy1 & condemn+1 if he please1 any doctr9es ( ! philosoph]s1 he foll[ 8 own pa?1 & desi/ f ?is w&]+ ?r\gh ! univ]se2 &1 lift+ up 8 natural eyes1 ) :i* he alone c see1 p\r himself out 9 8 own he>t1 9 praise ( ,god ! ,creator2 be+ c]ta9 t he gives no less wor%ip to ,god ?an ! a/ronom]1 to :om ,god has giv5 to see m cle>ly ) 8 inw>d eye1 & :o1 = :at he has himself discov]$1 bo? c & w glorify ,god4 ,9 a ,life ( ,kepl]1 v rec5tly publi%$ 9 8 native c\ntry1 f\nd$ on manuscripts ( 8 :i* h lately be5 br\ght to light1 !re are giv5 num]\s o!r examples ( a simil> devotional _s4 ,kepl] ?us concludes 8 ,h>monics3 ,i give ,!e ?anks1 ,"l & ,creator1 t ,?\ has giv5 me joy ?r\gh ,?y creation2 = ,i h be5 ravi%$ ) ! "w ( ,?y h&s4 ,i h reveal$ unto mank9d ! glory ( ,?y works1 z f> z my limit$ _s c\ld conceive _! inf9itude4 ,%\ld ,i h br\ght =w>d any ?+ t is unwor?y ( ,!e1 or %\ld ,i h s\ght my own fame1 be graci\sly pleas$ to =give me4 ,z ,galileo exp]i5c$ ! mo/ bitt] p]secutions f ! ,*ur* ( ,rome1 s ,kepl] met ) mu* viol5t opposition & calumny f ! ,prote/ant cl]gy ( 8 own c\ntry1 p>ticul>ly = adopt+1 9 an almanac :i*1 z a/ronom] royal1 he annually publi%$1 ! re=m$ cal5d>1 z giv5 by ! ,pope ( ,rome4 ,8 op9ions respect+ religi\s lib]ty1 also1 appe> to h be5 greatly 9 advance ( ! times 9 :i* he liv$4 ,9 answ] to c]ta9 calumnies ) :i* he 0 assail$1 = 8 boldness 9 reason+ f ! light ( ,nature1 he utt]$ ^! memorable words3 ,! day w soon break1 :5 pi\s simplicity w be a%am$ ( its bl9d sup]/ition2 :5 m5 w recognise tru? 9 ! book ( ,nature z well z 9 ! ,holy ,scriptures1 & rejoice 9 ! two revelations4 ,,lett] ,,xxv4 ,,comets4 ----,fancy n[ no m ,wantons on fickle p9ions ?r\gh ! skies1 ,b1 fix$ 9 aim1 & consci\s ( h] p[]1 ,sublime f cause to cause exults to rise1 ,creation's bl5d$ /ores arrang+ z %e flies4--,beattie4 ,,no?+ 9 a/ronomy is m truly admirable1 ?an ! k :i* a/ronom]s h acquir$ ( ! motions ( comets1 & ! p[] !y h ga9$ ( pr$ict+ _! return4 ,inde$1 e ?+ app]ta9+ to ?is class ( bodies is s wond]ful1 z to seem r a tale ( romance ?an a simple recital ( facts4 ,comets are truly ! knights-errant ( a/ronomy4 ,appe>+ sudd5ly 9 ! nocturnal sky1 & (t5 dragg+ aft] !m a tra9 ( t]rific aspect1 !y 71 9 ! e>li] ages ( ! _w1 & inde$ until a rec5t p]iod1 consid]$ z peculi>ly om9\s ( ! wra? ( ,heav51 & z h>b+]s ( w>s & fam9es1 ( ! de?ronem5t ( mon>*s1 & ! dissolution ( empires4 ,sci5ce has1 x is true1 dis>m$ !m ( _! t]rors1 & demon/rat$ t !y are "u ! guidance ( ! same ,h&1 t directs 9 _! c\rses ! o!r memb]s ( ! sol> sy/em2 b %e has1 at ! same "t1 array$ !m 9 a g>b ( maje/y peculi>ly h] own4 ,al?\gh ! anci5ts paid little att5tion to ! ord9>y ph5om5a ( ,nature1 h>dly deem+ !m wor?y ( a reason1 yet1 :5 a comet blaz$ =?1 fe> & a/oni%m5t conspir$ to make x an object ( ! mo/ att5tive obs]vation4 ,h5ce ! aspects ( rem>kable comets1 t h appe>$ at v>i\s times1 h be5 h&$ d[n to u1 (t5 ) circum/antial m9ut5ess1 by ! hi/orians ( diff]5t ages4 ,! comet :i* appe>$ 9 ! ye> #acj1 be=e ! ,*ri/ian era1 at ! bir? ( ,mi?ridates1 is said to h _h a disk equal 9 magnitude to t ( ! sun4 ,t5 ye>s be=e ?is1 "o 0 se51 :i*1 accord+ to ,ju/91 occupi$ a f\r? "p ( ! sky1 t is1 ext5d$ ov] =ty-five degrees1 & surpass$ ! sun 9 spl5dor4 ,9 ! ye> #djj1 "o 0 se5 :i* resembl$ a sword 9 %ape1 & ext5d$ f ! z5i? to ! horizon4 ,su* are "s ( ! acc\nts ( comets ( pa/ ages2 b x is probable we mu/ all[ mu* = ! exagg]ations naturally accompany+ ! descriptions ( objects 9 !mselves s truly wond]ful4 ,a comet1 :5 p]fectly =m$1 consi/s ( ?ree p>ts1 ! nucleus1 ! envelope1 & ! tail4 ,! nucleus1 or body ( ! comet1 is g5]ally di/+ui%$ by its =m+ a bright po9t 9 ! c5tre ( ! head1 convey+ ! idea ( a solid1 or at lea/ ( a v d5se1 portion ( matt]4 ,?\gh x is usually exce$+ly small1 :5 comp>$ ) ! o!r p>ts ( ! comet1 & is sometimes want+ altoge!r1 yet x occasionally subt5ds an angle capable ( be+ measur$ by ! telescope4 ,! envelope 7sometimes call$ ! coma1 f a ,lat9 ^w signify+ hair1 9 allusion to its hairy appe>ance7 is a d5se nebul\s cov]+1 :i* frequ5tly r5d]s ! edge ( ! nucleus s indi/9ct1 t x is extremely difficult to asc]ta9 its diamet] ) any degree ( precision4 ,_m comets h no nucleus1 b pres5t only a nebul\s mass1 exce$+ly att5uat$ on ! conf9es1 b gradually increas+ 9 d5sity t[>ds ! c5tre4 ,inde$1 !re is a regul> gradation ( comets1 f su* z are compos$ m]ely ( a gase\s or vapory m$ium1 to ^? :i* h a well-def9$ nucleus4 ,9 "s in/ances on record1 a/ronom]s h detect$ ) _! telescopes small />s ?r\gh ! d5se/ "p ( a comet4 ,! tail is reg>d$ z an expansion or prolongation ( ! coma2 & pres5t+1 z x sometimes does1 a tra9 ( appall+ magnitude1 & ( a pale1 port5t\s light1 x conf]s on ?is class ( bodies _! peculi> celebrity4 ,^! sev]al p>ts are exhibit$ 9 ,fig4 #fg1 :i* ,illu/ration ,figures #fg1 #fh4 ,,comets ,,( #afhj ,,& #ahaa4 repres5ts ! appe>ance ( ! comet ( #afhj4 ,fig4 #fh also exhibits t ( ! comet ( #ahaa4 ,! numb] ( comets belong+ to ! sol> sy/em1 is probably v great4 ,_m no d\bt escape obs]vation1 by be+ above ! horizon 9 ! day-"t4 ,s5eca m5tions1 t dur+ a total eclipse ( ! sun1 :i* happ5$ sixty ye>s be=e ! ,*ri/ian era1 a l>ge & spl5did comet sudd5ly made its appe>ance1 be+ v ne> ! sun4 ,! lead+ p>ticul>s ( at lea/ "o hundr$ & ?irty h be5 comput$1 & arrang$ 9 a table1 = future comp>ison4 ,( ^!1 six are p>ticul>ly rem>kable2 namely1 ! comets ( #afhj1 #aggj1 & #ahaa2 & ^? :i* be> ! names ( ,halley1 ,biela1 & ,encke4 ,! comet ( #afhj 0 rem>kable1 n only = its a/oni%+ size & spl5dor1 & its ne> approa* to ! sun1 b is celebrat$ = hav+ submitt$ itself to ! obs]vations ( ,sir ,isaac ,newton1 & = hav+ enjoy$ ! signal honor ( be+ ! fir/ comet ^: elem5ts 7 det]m9$ on ! sure basis ( ma!matics4 ,! comet ( #aggj is memorable = ! *anges its orbit has und]gone by ! action ( ,jupit]1 z ,i %all expla9 to y m p>ticul>ly h]eaft]4 ,! comet ( #ahaa 0 ! mo/ rem>kable 9 its appe>ance ( all t h be5 se5 9 ! pres5t c5tury4 ,x _h sc>cely any p]ceptible nucleus1 b its tra9 0 v long & broad1 z is repres5t$ 9 ,fig4 #fh4 ,halley's comet 7! same :i* reappe>$ 9 #ahce7 is di/+ui%$ z t ^: return 0 fir/ successfully pr$ict$1 & ^: orbit is be/ det]m9$2 & ,biela's & ,encke's comets are well kn[n = _! %ort p]iods ( revolution1 :i* subject !m frequ5tly to ! view ( a/ronom]s4 ,9 magnitude & brightness1 comets exhibit great div]sity4 ,hi/ory in=ms u ( comets s bright1 z to be di/9ctly visible 9 ! day-"t1 ev5 at noon1 & 9 ! brighte/ sun%9e4 ,su* 0 ! comet se5 at ,rome a little be=e ! assass9ation ( ,julius ,cs>4 ,! comet ( #afhj cov]$ an arc ( ! heav5s ( n9ety-sev5 degrees1 & its l5g? 0 e/imat$ at "o hundr$ & tw5ty-?ree millions ( miles4 ,t ( #ahaa _h a nucleus ( only f\r hundr$ & tw5ty-eight miles 9 diamet]1 b a tail "o hundr$ & ?irty-two millions ( miles long4 ,_h x be5 coil$ ar\nd ! e>? l a s]p5t1 x w\ld h rea*$ r\nd m ?an five ?\s& times4 ,o!r comets are exce$+ly small1 ! nucleus be+ 9 "o case e/imat$ at only tw5ty-five miles2 & "s1 :i* are de/itute ( any p]ceptible nucleus1 appe> to ! l>ge/ telescopes1 ev5 :5 ne>e/ to u1 only z a small speck ( fog1 or z a tuft ( d[n4 ,! majority ( comets c be se5 only by ! aid ( ! telescope4 ,inde$1 ! same comet has v diff]5t aspects1 at its diff]5t returns4 ,halley's comet1 9 #acje1 0 describ$ by ! hi/orians ( t age z ! comet ( t]rific magnitude2 7cometa horr5d magnitud9is27 9 #adef its tail rea*$ f ! horizon to ! z5i?1 & inspir$ su* t]ror1 t1 by a decree ( ! ,pope ( ,rome1 public pray]s 7 (f]$ up at noonday 9 all ! ,ca?olic *ur*es1 to deprecate ! wra? ( heav52 :ile 9 #afhb its tail 0 only ?irty degrees 9 l5g?2 & 9 #agei x 0 visible only to ! telescope until aft] x _h pass$ its p]ihelion4 ,at its rec5t return1 9 #ahce1 ! greate/ l5g? ( ! tail 0 ab\t twelve degrees4 ,^! *anges 9 ! appe>ance ( ! same comet are p>tly ow+ to ! diff]5t positions ( ! e>? ) respect to !m1 be+ sometimes mu* ne>] to !m :5 !y cross its track ?an at o!rs2 also1 "o spectator1 s situat$ z to see ! comet at a high] angle ( elevation1 or 9 a pur] sky1 ?an ano!r1 w see ! tra9 long] ?an x appe>s to ano!r less favorably situat$2 b ! ext5t ( ! *anges are su* z indicate also a real *ange 9 magnitude & brightness4 ,! p]iods ( comets 9 _! revolutions ar\nd ! sun are equally v>i\s4 ,encke's comet1 :i* has ! %orte/ kn[n p]iod1 completes its revolution 9 ?ree & "o ?ird ye>s2 or1 m accurately1 9 twelve hundr$ & eight days2 :ile t ( #ahaa is e/imat$ to h a p]iod ( ?irty-?ree hundr$ & eighty ?ree ye>s4 ,! di/ances to :i* diff]5t comets rec$e f ! sun are equally v>i\s4 ,:ile ,encke's comet p]=ms its entire revolution )9 ! orbit ( ,jupit]1 ,halley's comet rec$es f ! sun to twice ! di/ance ( ,uranus2 or ne>ly ?irty-six hundr$ millions ( miles4 ,"s comets1 inde$1 are ?\ght to g a mu* great] di/ance f ! sun ?an ?is1 :ile "s are suppos$ to pass into curves :i* d n1 l ! ellipse1 return into !mselves2 & 9 ?is case !y nev] come back to ! sun4 7,see ,fig4 #cd1 page #aec47 ,comets %9e by reflect+ ! light ( ! sun4 ,9 "o or two in/ances1 !y h be5 ?\ght to exhibit di/9ct phases1 l ! moon1 al?\gh ! nebul\s matt] ) :i* ! nucleus is surr\nd$ w\ld commonly prev5t su* phases f be+ di/9ctly visible1 ev5 :5 !y w\ld o!rwise be app>5t4 ,moreov]1 c]ta9 qualities ( pol>iz$ light1--an affection by :i* a ray ( light seems to h diff]5t prop]ties on diff]5t sides1--enable opticians to decide :e!r ! light ( a giv5 body is direct or reflect$2 & ,m4 ,arago1 ( ,p>is1 by exp]im5ts ( ?is k9d on ! light ( ! comet ( #ahai1 asc]ta9$ x to be reflect$ light4 ,! tail ( a comet usually increases v mu* z x approa*es ! sun2 & x frequ5tly does n rea* its maximum until aft] ! p]ihelion passage4 ,9 rec$+ f ! sun1 ! tail aga9 contracts1 & ne>ly or q disappe>s be=e ! body ( ! comet is entirely out ( sight4 ,! tail is frequ5tly divid$ into two portions1 ! c5tral p>ts1 9 ! direction ( ! axis1 be+ less bright ?an ! m>g9al p>ts4 ,9 #agdd a comet appe>$ :i* _h six tails spread out l a fan4 ,! tails ( comets ext5d 9 a direct l9e f ! sun1 al?\gh m or less curv$1 l a long quill or fea!r1 be+ convex on ! side next to ! direction 9 :i* !y are mov+1--a figure :i* may result f ! less velocity ( ! portion mo/ remote f ! sun4 ,expansions ( ! envelope h also be5 at times obs]v$ on ! side next ! sun2 b ^! seldom atta9 any consid]able l5g?4 ,! quantity ( matt] 9 comets is exce$+ly small4 ,_! tails consi/ ( matt] ( su* t5uity1 t ! smalle/ />s are visible ?r\gh !m4 ,!y c only be reg>d$ z masses ( ?9 vapor1 susceptible ( be+ p5etrat$ ?r\gh _! :ole sub/ance by ! sunbeams1 & reflect+ !m alike f _! int]ior p>ts & f _! surfaces4 ,x appe>s p]haps incr$ible1 t s ?9 a sub/ance %\ld be visible by reflect$ light1 & "s a/ronom]s h held t ! matt] ( comets is self-lum9\s2 b x requires b v little light to r5d] an object visible 9 ! night1 & a light vapor may be visible :5 illum9at$ ?r\gh\t an imm5se /ratum1 :i* c\ld n be se5 if spread ov] ! face ( ! sky l a ?9 cl\d4 ,! highe/ cl\ds t float 9 our atmosph]e1 says ,sir ,john ,h]s*el1 mu/ be look$ ^u z d5se & massive bodies1 comp>$ ) ! filmy & all b spiritual texture ( a comet4 ,! small quantity ( matt] 9 comets is prov$ by ! fact1 t !y h at times pass$ v ne> to "s ( ! planets1 )\t di/urb+ _! motions 9 any appreciable degree4 ,?us ! comet ( #aggj1 9 its way to ! sun1 got entangl$ among ! satellites ( ,jupit]1 & rema9$ ne> !m f\r mon?s2 yet x did n p]ceptibly *ange _! motions4 ,! same comet1 also1 came v ne> ! e>?2 s t1 _h its quantity ( matt] be5 equal to t ( ! e>?1 x w\ld1 by its attraction1 h caus$ ! e>? to revolve 9 an orbit s mu* l>g] ?an at pres5t1 z to h increas$ ! l5g? ( ! ye> two h\rs & =ty-sev5 m9utes4 ,yet x produc$ no s5sible effect on ! l5g? ( ! ye>1 & !re=e its mass1 z is %[n by ,la ,place1 c\ld n h exce$$ #a_/ejjj ( t ( ! e>?1 & might h be5 less ?an ?is to any ext5t4 ,x may inde$ be ask$1 :at pro( we h t comets h any matt]1 & are n m]e reflections ( light4 ,! answ] is1 t1 al?\gh !y are n able by _! own =ce ( attraction to di/urb ! motions ( ! planets1 yet !y are !mselves exce$+ly di/urb$ by ! action ( ! planets1 & 9 exact con=mity ) ! laws ( univ]sal gravitation4 ,a delicate compass may be greatly agitat$ by ! vic9ity ( a mass ( iron1 :ile ! iron is n s5sibly affect$ by ! attraction ( ! ne$le4 ,by approa*+ v ne> to a l>ge planet1 a comet may h its orbit entirely *ang$4 ,?is fact is /rik+ly exemplifi$ 9 ! hi/ory ( ! comet ( #aggj4 ,at its appe>ance 9 #aggj1 its orbit 0 f\nd to be an ellipse1 requir+ = a complete revolution only five & a half ye>s2 & ! wond] 01 t x _h n be5 se5 be=e1 s9ce x 0 a v l>ge & bright comet4 ,a/ronom]s suspect$ t its pa? _h be5 *ang$1 & t x _h be5 rec5tly compell$ to move 9 ?is %ort ellipse1 by ! di/urb+ =ce ( ,jupit] & 8 satellites4 ,! ,fr5* ,in/itute1 !re=e1 (f]$ a high prize = ! mo/ complete inve/igation ( ! elem5ts ( ?is comet1 tak+ into acc\nt any circum/ances :i* c\ld possibly h produc$ an alt]ation 9 its c\rse4 ,by trac+ back ! movem5ts ( ?is comet1 = "s ye>s previ\s to #aggj1 x 0 f\nd t1 at ! beg9n+ ( #agfg1 x _h ent]$ consid]ably )9 ! sph]e ( ,jupit]'s attraction4 ,calculat+ ! am\nt ( ?is attraction f ! kn[n proximity ( ! two bodies1 x 0 f\nd :at mu/ h be5 its orbit previ\s to ! "t :5 x became subject to ! di/urb+ action ( ,jupit]4 ,x 0 !re=e evid5t :y1 z long z x cont9u$ to circulate 9 an orbit s f> f ! c5tre ( ! sy/em1 x 0 nev] visible f ! e>?4 ,9 ,janu>y1 #agfg1 ,jupit] & ! comet happ5$ to be v ne> to "o ano!r1 & z bo? 7 mov+ 9 ! same direction1 & ne>ly 9 ! same plane1 !y rema9$ 9 ! neighborhood ( ea* o!r = sev]al mon?s1 ! planet be+ betwe5 ! comet & ! sun4 ,! consequ5ce 01 t ! comet's orbit 0 *ang$ into a small] ellipse1 9 :i* its revolution 0 accompli%$ 9 five & a half ye>s4 ,b z x approa*$ ! sun1 9 #aggi1 x happ5$ aga9 to fall 9 ) ,jupit]4 ,x 0 9 ! mon? ( ,june t ! attraction ( ! planet began to h a s5sible effect2 & x 0 n until ! mon? ( ,octob] foll[+1 t !y 7 f9ally sep>at$4 ,at ! "t ( _! ne>e/ approa*1 9 ,augu/1 ,jupit] 0 di/ant f ! comet only #a_/dia ( its di/ance f ! sun1 & ex]t$ an attraction ^u x two hundr$ & tw5ty-five times great] ?an t ( ! sun4 ,by reason ( ?is p[]ful attraction1 ,jupit] be+ fur!r f ! sun ?an ! comet1 ! latt] 0 drawn out into a new orbit1 :i* ev5 at its p]ihelion came no ne>] to ! sun ?an ! planet ,c]es4 ,9 ?is ?ird orbit1 ! comet requires ab\t tw5ty ye>s to accompli% its revolution2 & be+ at s great a di/ance f ! e>?1 x is invisible1 & w = ev] rema9 s unless1 9 ! c\rse ( ages1 x may und]go new p]turbations1 & move aga9 9 "s small] orbit1 z be=e4 ,) ! =ego+ lead+ facts respect+ comets 9 view1 ,i w n[ expla9 to y a few ?+s equally rem>kable respect+ _! motions4 ,! pa?s ( ! planets ar\nd ! sun be+ ne>ly circul>1 we are able to see a planet 9 e "p ( its orbit4 ,b ! case is v diff]5t ) comets4 ,= ! great] "p ( _! c\rse1 !y are :olly out ( sight1 & come into view only :ile j 9 ! neighborhood ( ! sun4 ,?is y w readily see mu/ be ! case1 by inspect+ ! frontispiece1 :i* repres5ts ! orbit ( ,biela's comet1 9 #ahcb4 ,sometimes1 ! orbit is s ecc5tric1 t ! place ( ! focus occupi$ by ! sun appe>s almo/ at ! extremity ( ! orbit4 ,?is 0 ! case ) ! orbit ( ! comet ( #afhj4 ,inde$1 ?is comet1 at its p]ihelion1 came 9 fact ne>] to ! sun ?an ! six? "p ( ! sun's diamet]1 be+ only "o hundr$ & =ty-six ?\s& miles f ! surface ( ! sun1 :i*1 y w rem>k1 is only a little m ?an half ! di/ance ( ! moon f ! e>?2 :ile1 at its aphelion1 x 0 e/imat$ to be ?irte5 ?\s& millions ( miles f ! sun1--m ?an elev5 ?\s& millions ( miles beyond ! planet ,uranus4 ,its velocity1 :5 ne>e/ ! sun1 exce$$ a million ( miles an h\r4 ,to describe su* an orbit z 0 assign$ to x by ,sir ,isaac ,newton1 w\ld require five hundr$ & sev5ty-five ye>s4 ,dur+ all ?is p]iod1 x 0 entirely out ( view to ! inhabitants ( ! e>?1 except ! few mon?s1 :ile x 0 runn+ d[n to ! sun f su* a di/ance z ! orbit ( ,jupit] & back4 ,! velocity ( bodies mov+ 9 su* ecc5tric orbits diff]s widely 9 diff]5t p>ts ( _! orbits4 ,9 ! remote/ p>ts x is s sl[1 t ye>s w\ld be requir$ to pass ov] a space equal to t :i* x w\ld run ov] 9 a s+le day1 :5 ne> ! sun4 ,! appe>ances ( ! same comet at diff]5t p]iods ( its return are s v>i\s1 t we c nev] pron\nce a giv5 comet to be ! same ) "o t has appe>$ be=e1 f any peculi>ities 9 its physical aspect1 z f its color1 magnitude1 or %ape2 s9ce1 9 all ^! respects1 x is v diff]5t at diff]5t returns2 b x is judg$ to be ! same if its pa? ?r\gh ! heav5s1 z trac$ among ! />s1 is ! same4 ,! comet ^: hi/ory is ! mo/ int]e/+1 & :i* bo? ( u h be5 privileg$ to see1 is ,halley's4 ,j be=e its late/ visit1 9 #ahce1 its return 0 anticipat$ ) s mu* expectation1 n only by a/ronom]s1 b by all classes ( ! community1 t a great & laudable eag]ness univ]sally prevail$1 to le>n ! p>ticul>s ( its hi/ory4 ,! be/ summ>y ( ^!1 :i* ,i met )1 0 giv5 9 ! ,ed9burgh ,review = ,april1 #ahce4 ,i might cont5t myself ) b>ely ref]r+ y to t well-writt5 article2 b1 z y may n h ! "w at h&1 & w\ld1 moreov]1 probably n desire to read ! :ole article1 ,i w abridge x = y\r p]usal1 int]sp]s+ "s rem>ks ( my own4 ,i h desir$ to give y1 9 ! c\rse ( ^! ,lett]s1 "s specim5 ( ! labors ( a/ronom]s1 & %all probably nev] be able to f9d a bett] "o4 ,x is believ$ t ! fir/ record$ appe>ance ( ,halley's comet 0 t :i* 0 suppos$ to signalize ! bir? ( ,mi?ridates1 "o hundr$ & ?irty ye>s be=e ! bir? ( ,*ri/4 ,x is said to h appe>$ = tw5ty-f\r days2 its light is said to h surpass$ t ( ! sun2 its magnitude to h ext5d$ ov] a f\r? "p ( ! firmam5t2 & x is /at$ to h occupi$1 consequ5tly1 ab\t f\r h\rs 9 ris+ & sett+4 ,9 ! ye> #cbc1 a comet appe>$ 9 ! sign ,virgo4 ,ano!r1 accord+ to ! hi/orians ( ! ,l[] ,empire1 appe>$ 9 ! ye> #cii1 sev5ty-six ye>s aft] ! la/1 at an int]val correspond+ to t ( ,halley's comet4 ,! int]val betwe5 ! bir? ( ,mi?ridates & ! ye> #cbc 0 f\r hundr$ & fifty-?ree ye>s1 :i* w\ld be equival5t to six p]iods ( sev5ty-five & a half ye>s4 ,?us x w\ld seem1 t 9 ! int]im !re 7 five returns ( ?is comet unobs]v$1 or at lea/ unrecord$4 ,! appe>ance 9 ! ye> #cii 0 att5d$ ) extraord9>y circum/ances4 ,x 0 describ$ 9 ! old writ]s z a comet ( mon/r\s size & appall+ aspect1 its tail seem+ to rea* d[n to ! gr\nd4 ,! next record$ appe>ance ( a comet agree+ ) ! asc]ta9$ p]iod m>ks ! tak+ ( ,rome1 9 ! ye> #eej1--;an int]val ( "o hundr$ & fifty-"o ye>s1 or two p]iods ( sev5ty-five & a half ye>s hav+ elaps$4 ,"o unrecord$ return mu/1 !re=e1 h tak5 place 9 ! int]im4 ,! next appe>ance ( a comet1 co9cid+ ) ! assign$ p]iod1 is ?ree hundr$ & eighty ye>s aft]w>ds2 namely1 9 ! ye> #icj1--;five revolutions hav+ be5 complet$ 9 ! int]val4 ,! next appe>ance is record$ 9 ! ye> #ajje1 aft] an int]val ( a s+le p]iod ( sev5ty-five ye>s4 ,?ree revolutions w\ld n[ seem to h pass$ unrecord$1 :5 ! comet aga9 makes its appe>ance 9 #abcj4 ,9 ?is1 z well z 9 =m] appe>ances1 x is prop] to /ate1 t ! sole te/ ( id5tity ( ^! cornets ) t ( ,halley is ! co9cid5ce ( ! times1 z ne> z hi/orical records enable u to asc]ta91 ) ! epo*s at :i* ! comet ( ,halley might be expect$ to appe>4 ,t su* evid5ce1 h[ev]1 is v imp]fect1 mu/ be evid5t1 if ! frequ5cy ( comet>y appe>ances be consid]$1 & if x be rememb]$1 t hi!rto we f9d no record$ obs]vations1 :i* c\ld enable u to trace1 ev5 ) ! rude/ degree ( approximation1 ! pa?s ( ^? comets1 ! times ( ^: appe>ances raise a presumption ( _! id5tity ) t ( ,halley4 ,we n[1 h[ev]1 desc5d to times 9 :i* m satisfactory evid5ce may be expect$4 ,9 ! ye> #acje1 a ye> 9 :i* ! return ( ,halley's comet might h be5 expect$1 !re is record$ a comet ( rem>kable "*3 ,a comet ( t]rific dim5sions made its appe>ance ab\t ! "t ( ! fea/ ( ! ,passov]1 :i* 0 foll[$ by a ,great ,plague4 ,_h ! t]rific appe>ance ( ?is body alone be5 record$1 ?is description might h pass$ )\t ! *>ge ( great exagg]ation2 b :5 we f9d ! ,great ,plague connect$ ) x z a consequ5ce1 x is impossible n to conclude1 t ! comet 0 se5 by its hi/orians ?r\gh ! magnify+ m$ium ( ! calamity :i* foll[$ x4 ,ano!r appe>ance is record$ 9 ! ye> #achj1 unaccompani$ by any o!r circum/ance ?an its m]e date4 ,?is1 h[ev]1 is 9 /rict accordance ) ! asc]ta9$ p]iod ( ,halley's comet4 ,we n[ arrive at ! fir/ appe>ance at :i* obs]vations 7 tak51 possess+ suffici5t accuracy to enable subsequ5t inve/igators to det]m9e ! pa? ( ! comet2 & ?is is accord+ly ! fir/ comet ! id5tity ( :i* ) ! comet ( ,halley c be said to be conclusively e/abli%$4 ,9 ! ye> #adef1 a comet is /at$ to h appe>$ ( unhe>d ( magnitude2 x 0 accompani$ by a tail ( extraord9>y l5g?1 :i* ext5d$ ov] sixty degrees1 7a ?ird "p ( ! heav5s17 & cont9u$ to be se5 dur+ ! :ole mon? ( ,june4 ,! influ5ce :i* 0 attribut$ to ?is appe>ance r5d]s x probable1 t 9 ! record !re is m or less ( exagg]ation4 ,x 0 consid]$ z ! cele/ial indication ( ! rapid success ( ,mohamm$ ! ,second1 :o _h tak5 ,con/ant9ople1 & /ruck t]ror into ! :ole ,*ri/ian _w4 ,pope ,calixtus ! ,second levell$ ! ?und]s ( ! ,*ur* aga9/ ! enemies ( 8 fai?1 t]re/rial & cele/ial2 & 9 ! same ,bull excommunicat$ ! ,turks & ! comet2 &1 9 ord] t ! memory ( ?is manife/ation ( 8 p[] %\ld be = ev] pres]v$1 he orda9$ t ! bells ( all ! *ur*es %\ld be rung at mid-day1--a cu/om :i* is pres]v$ 9 ^? c\ntries to our times4 ,! extraord9>y l5g? & brilliancy :i* 0 ascrib$ to ! tail1 ^u ?is occasion1 h l$ a/ronom]s to inve/igate ! circum/ances "u :i* its brightness & magnitude w\ld be ! greate/ possible2 & ^u trac+ back ! motion ( ! comet to ! ye> #adef1 x has be5 f\nd t x 0 !n actually 9 ! position1 ) respect to ! e>? & sun1 mo/ favorable to magnitude & spl5dor4 ,s f>1 !re=e1 ! result ( a/ronomical calculation corroborates ! records ( hi/ory4 ,! next return took place 9 #aeca4 ,pi]re ,appian1 :o fir/ asc]ta9$ ! fact t ! tails ( comets are usually turn$ f ! sun1 exam9$ ?is comet ) a view to v]ify 8 /atem5t1 & to asc]ta9 ! true direction ( its tail4 ,he made1 accord+ly1 num]\s obs]vations ^u its position1 :i*1 al?\gh rude1 comp>$ ) ! pres5t /&>d ( accuracy1 7 /ill suffici5tly exact to enable ,halley to id5tify ?is comet ) t obs]v$ by himself4 ,! next return took place 9 #afjg1 :5 ! comet 0 obs]v$ by ,kepl]4 ,?is a/ronom] fir/ saw x on ! ev5+ ( ! tw5ty-six? ( ,septemb]1 :5 x _h ! appe>ance ( a /> ( ! fir/ magnitude1 &1 to 8 vision1 0 )\t a tail2 b ! fri5ds :o accompani$ him _h bett] sight1 & di/+ui%$ ! tail4 ,be=e ?ree o'clock ! foll[+ morn+ ! tail _h become cle>ly visible1 & _h acquir$ great magnitude4 ,two days aft]w>ds1 ! comet 0 obs]v$ by ,longomontanus1 a di/+ui%$ philosoph] ( ! "t4 ,he describes its appe>ance1 to ! nak$ eye1 to be l ,jupit]1 b ( a pal] & m obscur$ light2 t its tail 0 ( consid]able l5g?1 ( a pal] light ?an t ( ! head1 & m d5se ?an ! tails ( ord9>y comets4 ,! next appe>ance1 & t :i* 0 obs]v$ by ,halley himself1 took place 9 #afhb1 a little be=e ! publication ( ! ',pr9cipia4' ,9 ! int]val betwe5 #afjg & #afhb1 practical a/ronomy _h made great advances2 in/rum5ts ( obs]vation _h be5 br\ght to a /ate ( comp>ative p]fection2 num]\s obs]vatories _h be5 e/abli%$1 & ! managem5t ( !m _h be5 confid$ to ! mo/ em95t m5 9 ,europe4 ,9 #afhb1 ! sci5tific _w 0 !re=e prep>$ to exam9e ! visitor ( our sy/em ) a degree ( c>e & accuracy be=e unkn[n4 ,9 ! ye> #afhf1 ab\t f\r ye>s aft]w>ds1 ,newton publi%$ 8 ',pr9cipia1' 9 :i* he appli$ to ! comet ( #afhj ! g5]al pr9ciples ( physical inve/igation fir/ promulgat$ 9 t "w4 ,he expla9$ ! me?od ( det]m9+1 by geometrical con/ruction1 ! visible portion ( ! pa? ( a body ( ?is k9d1 & invit$ a/ronom]s to apply ^! pr9ciples to ! v>i\s record$ comets1--to discov] :e!r "s among !m might n h appe>$ at diff]5t epo*s1 ! future returns ( :i* might consequ5tly be pr$ict$4 ,su* 0 ! effect ( ! =ce ( analogy ^u ! m9d ( ,newton1 t1 )\t await+ ! discov]y ( a p]iodic comet1 he boldly assum$ ^! bodies to be analog\s to planets 9 _! revolution r\nd ! sun4 ,extraord9>y z ^! conjectures mu/ h appe>$ at ! "t1 !y 7 soon /rictly realiz$4 ,halley1 :o 0 !n a "y man1 b possess$ "o ( ! be/ m9ds 9 ,engl&1 und]took ! labor ( exam9+ ! circum/ances att5d+ all ! comets previ\sly record$1 ) a view to discov] :e!r any1 & :i* ( !m1 appe>$ to foll[ ! same pa?4 ,antec$5tly to ! ye> #agjj1 f\r hundr$ & tw5ty-five ( ^! bodies _h be5 record$ 9 hi/ory2 b ^? :i* _h appe>$ be=e ! f\rte5? c5tury _h n be5 submitt$ to any obs]vations by :i* _! pa?s c\ld be asc]ta9$1--at lea/1 n ) a suffici5t degree ( precision1 to af=d any hope ( id5tify+ !m ) ^? ( o!r comets4 ,subsequ5tly to ! ye> #acjj1 h[ev]1 ,halley f\nd tw5ty-f\r comets on :i* obs]vations _h be5 made & record$1 ) a degree ( precision suffici5t to enable him to calculate ! actual pa?s :i* ^! bodies foll[$ :ile !y 7 visible4 ,he exam9$1 ) ! mo/ elaborate c>e1 ! c\rses ( ea* ( ^! tw5ty-f\r bodies2 he f\nd ! exact po9ts at :i* ea* "o ( !m cross$ ! ecliptic1 or _! nodes2 also ! angle :i* ! direction ( _! motion made ) t plane1--t is1 ! incl9ation ( _! orbits2 he also calculat$ ! ne>e/ di/ance at :i* ea* ( !m approa*$ ! sun1 or _! p]ihelion di/ance2 & ! exact place ( ! body :5 at t ne>e/ po9t1--t is1 ! longitude ( ! p]ihelion4 ,^! p>ticul>s are call$ ! elem5ts ( a comet1 because1 :5 asc]ta9$1 !y af=d suffici5t data = det]m9+ a comet's pa?4 ,on comp>+ ^! pa?s1 ,halley f\nd t "o1 :i* _h appe>$ 9 #affa1 foll[$ ne>ly ! same pa? z "o :i* _h appe>$ 9 #aecb4 ,suppos+1 !n1 ^! to be two successive appe>ances ( ! same comet1 x w\ld foll[1 t its p]iod w\ld be "o hundr$ & tw5ty-n9e ye>s1 reckon+ f #affa4 ,_h ?is conjecture be5 well f\nd$1 ! comet mu/ h appe>$ ab\t ! ye> #agij4 ,no comet1 h[ev]1 appe>$ at or ne> t "t1 foll[+ a simil> pa?4 ,9 8 second conjecture1 ,halley 0 m =tunate1 z inde$ might be expect$1 s9ce x 0 =m$ ^u m conclusive gr\nds4 ,he f\nd t ! pa?s ( comets :i* _h appe>$ 9 #aeca & #afjg 7 ne>ly id5tical1 & t !y 7 9 fact ! same z ! pa? foll[$ by ! comet obs]v$ by himself 9 #afhb4 ,he suspect$1 !re=e1 t ! appe>ances at ^! ?ree epo*s 7 produc$ by ?ree successive returns ( ! same comet1 & t1 consequ5tly1 its p]iod 9 its orbit mu/ be ab\t sev5ty-five & a half ye>s4 ,! probability ( ?is conclusion is /rik+ly exhibit$ to ! eye1 by pres5t+ ! elem5ts 9 a tabul> =m1 f :i* x w at once be se5 h[ ne>ly !y correspond at ^! regul> int]vals4 ,"t4,incl9ation (,long4 ( ! ,long4 ,p]4,p]4 ,di/4 ,c\rse4 ! orbit4 node4 #adef #agef #dhcj #cjajj #jeh ,retrograde4 #aeca #ag #ef #di #be #cja #ci #j #eg #afjg #ag #jb #ej #ba #cjb #af #j #eh #afhb #ag #db #ej #dh #cja #cf #j #eh ,s little 0 ! sci5tific _w1 at ?is "t1 prep>$ = su* an ann\ncem5t1 t ,halley himself only v5tur$ at fir/ to express 8 op9ion 9 ! =m ( conjecture2 b1 aft] "s fur!r inve/igation ( ! circum/ances ( ! record$ comets1 he f\nd ?ree :i*1 at lea/ 9 po9t ( "t1 agre$ ) ! p]iod assign$ to ! comet ( #afhb4 ,collect+ confid5ce f ^! circum/ances1 he ann\nc$ 8 discov]y z ! result ( obs]vation & calculation comb9$1 & entitl$ to z mu* confid5ce z any o!r consequ5ce ( an e/abli%$ physical law4 ,!re 71 nev]!less1 two circum/ances :i* might be suppos$ to (f] "s difficulty4 ,fir/1 ! int]vals betwe5 ! suppos$ successive returns 7 n precisely equal2 &1 secondly1 ! incl9ation ( ! comet's pa? to ! plane ( ! e>?'s orbit 0 n exactly ! same 9 ea* case4 ,halley1 h[ev]1 ) a degree ( sagacity :i*1 consid]+ ! /ate ( k at ! "t1 _c fail to excite unqualifi$ admiration1 obs]v$1 t x 0 natural to suppose t ! same causes :i* di/urb$ ! planet>y motions mu/ likewise act ^u comets2 & t _! influ5ce w\ld be s mu* ! m s5sible ^u ^! bodies1 because ( _! great di/ances f ! sun4 ,?us1 z ! attraction ( ,jupit] = ,saturn 0 kn[n to affect ! velocity ( ! latt] planet1 sometimes ret>d+ & sometimes accel]at+ x1 accord+ to _! relative position1 s z to affect its p]iod to ! ext5t ( ?irte5 days1 x might well be suppos$1 t ! comet might suff] by a simil> attraction an effect suffici5tly great1 to acc\nt = ! inequality obs]v$ 9 ! int]val betwe5 its successive returns3 & also = ! v>iation to :i* ! direction ( its pa? ^u ! plane ( ! ecliptic 0 f\nd to be subject4 ,he obs]v$1 9 f9e1 t1 z 9 ! int]val betwe5 #afjg & #afhb1 ! comet pass$ s ne> ,jupit] t its velocity mu/ h be5 augm5t$1 & consequ5tly its p]iod %ort5$1 by ! action ( t planet1 ?is p]iod1 !re=e1 hav+ be5 only sev5ty-five ye>s1 he inf]r$ t ! foll[+ p]iod w\ld probably be sev5ty-six ye>s1 or upw>ds2 & consequ5tly1 t ! comet ought n to be expect$ to appe> until ! end ( #ageh1 or ! beg9n+ ( #agei4 ,x is impossible to imag9e any quality ( m9d m enviable ?an t :i*1 9 ! exi/+ /ate ( ma!matical physics1 c\ld h l$ to su* a pr$iction4 ,! imp]fect /ate ( ma!matical sci5ce r5d]$ x impossible = ,halley to (f] to ! _w a demon/ration ( ! ev5t :i* he =etold4 ,! !ory ( gravitation1 :i* 0 9 its infancy 9 ! "t ( ,halley's inve/igations1 _h gr[n to comp>ative maturity be=e ! p]iod at :i* 8 pr$iction c\ld be fulfill$4 ,! exig5cies ( t !ory gave bir? to new & m p[]ful in/rum5ts ( ma!matical inquiry3 ! diff]5tial & integral calculus1 or ! sci5ce ( fluxions1 z x is sometimes call$1--a bran* ( ! ma!matics1 express$ by algebraic symbols1 b capable ( a mu* high] rea*1 z an in/rum5t ( inve/igation1 ?an ei!r algebra or geometry1--0 its fir/ & greate/ (fspr+4 ,?is bran* ( sci5ce 0 cultivat$ ) an ardor & success by :i* x 0 enabl$ to answ] all ! dem&s ( physics1 & x contribut$ l>gely to ! advancem5t ( me*anical sci5ce itself1 build+ ^u ! laws ( motion a /ructure :i* has s9ce be5 d5om9at$ ',cele/ial ,me*anics4' ,newton's discov]ies hav+ obta9$ reception ?r\gh\t ! sci5tific _w1 8 inquiries & 8 !ories 7 foll[$ up2 & ! consequ5ces ( ! great pr9ciple ( univ]sal gravitation 7 rapidly develop$4 ,s9ce1 accord+ to ?is doctr9e1 e body 9 nature attracts & is attract$ by e o!r body1 x foll[s1 t ! comet 0 liable to be act$ on by ea* ( ! planets1 z well z by ! sun1--a circum/ance :i* r5d]$ its movem5ts mu* m difficult to foll[1 ?an w\ld be ! case 7 x subject m]ely to ! projectile =ce & to ! sol> attraction4 ,to e/imate ! "t x w\ld take = a %ip to cross ! ,atlantic w\ld be an easy task1 7 %e subject to only "o con/ant w9d2 b to e/imate1 be=eh&1 ! exact influ5ce :i* all o!r w9ds & ! tides might h ^u h] passage1 "s accel]at+ & "s ret>d+ h] c\rse1 w\ld pres5t a problem ( ! greate/ difficulty4 ,clairaut1 h[ev]1 a celebrat$ ,fr5* ma!matician1 und]took to e/imate ! effects t w\ld be produc$ on ,halley's comet by ! attractions ( all ! planets4 ,8 aim 0 to inve/igate g5]al rules1 by :i* ! computation c\ld be made ari?metically1 & h& !m ov] to ! practical calculator1 to make ! actual computations4 ,lal&e1 a practical a/ronom]1 no less em95t 9 8 own dep>tm5t1 & :o inde$ fir/ urg$ ,clairaut to ?is inquiry1 und]took ! managem5t ( ! a/ronomical & ari?metical "p ( ! calculation4 ,9 ?is prodigi\s labor 7= x 0 "o ( mo/ appall+ magnitude7 he 0 assi/$ by ! wife ( an em95t wat*mak] 9 ,p>is1 nam$ ,lepaute1 ^: ex]tions on ?is occasion h des]v$ly regi/]$ h] "n 9 a/ronomical hi/ory4 ,x is difficult to convey to "o :o is n conv]sant ) su* inve/igations1 an adequate notion ( ! labor :i* su* an inquiry involv$4 ,! calculation ( ! influ5ce ( any "o planet ( ! sy/em ^u any o!r is itself a problem ( "s complexity & difficulty2 b /ill1 "o g5]al computation1 dep5d+ ^u ! calculation ( ! t]ms ( a c]ta9 s]ies1 is suffici5t = its solution4 ,?is comp>ative simplicity arises entirely f two circum/ances :i* *>act]ize ! planet>y orbits4 ,^! are1 t1 ?\gh !y are ellipses1 !y diff] v slightly f circles2 & ?\gh ! planets d n move 9 ! plane ( ! ecliptic1 yet none ( !m deviate consid]ably f t plane4 ,b ^! *>act]s d n belong to ! orbits ( comets1 :i*1 on ! contr>y1 are highly ecc5tric1 & make all possible angles ) ! ecliptic4 ,! consequ5ce ( ?is is1 t ! calculation ( ! di/urbances produc$ 9 ! comet>y orbits by ! action ( ! planets mu/ be conduct$ n l ! planets1 9 "o g5]al calculation applicable to ! :ole orbits1 b 9 a va/ numb] ( sep>ate calculations2 9 :i* ! orbit is consid]$1 z x 71 bit by bit1 ea* bit requir+ a calculation simil> to ! :ole orbit ( ! planet4 ,n[1 :5 x is consid]$ t ! p]iod ( ,halley's comet is ab\t sev5ty-five ye>s1 & t e portion ( its c\rse1 = two successive p]iods1 0 necess>y to be calculat$ sep>ately 9 ?is way1 "s notion may be =m$ ( ! labor enc\nt]$ by ,lal&e & ,madame ,lepaute4 ,dur+ six mon?s1 says ,lal&e1 we calculat$ f morn+ till night1 sometimes ev5 at meals2 ! consequ5ce ( :i* 01 t ,i contract$ an illness :i* *ang$ my con/itution = ! rema9d] ( my life4 ,! assi/ance r5d]$ by ,madame ,lepaute 0 su*1 t1 )\t h]1 we nev] c\ld h d>$ to und]take ?is enorm\s labor1 9 :i* x 0 necess>y to calculate ! di/ance ( ea* ( ! two planets1 ,jupit] & ,saturn1 f ! comet1 & _! attraction ^u t body1 sep>ately1 = e successive degree1 & = "o hundr$ & fifty ye>s4 ,! attraction ( a body is proportion$ to its quantity ( matt]4 ,!re=e1 be=e ! attraction ex]t$ ^u ! comet by ! sev]al planets )9 ^: influ5ce x might fall1 c\ld be correctly e/imat$1 x 0 necess>y to "k ! mass ( ea* planet2 & ?\gh ! planets _h sev]ally be5 weigh$ by me?ods suppli$ by ,newton's ',pr9cipia1' yet ! e/imate _h n !n atta9$ ! same measure ( accuracy z x has n[ rea*$2 nor 0 x c]ta9 t !re 0 n 7z x has s9ce appe>$ t !re actually 07 "o or m planets beyond ,saturn1 ^: attractions might likewise influ5ce ! motions ( ! comet4 ,clairaut1 mak+ ! be/ e/imate he 0 able1 "u all ^! disadvantages1 ( ! di/urb+ influ5ce ( ! planets1 fix$ ! return ( ! comet to ! place ( its ne>e/ di/ance f ! sun on ! f\r? ( ,april1 #agei4 ,9 ! successive appe>ances ( ! comet1 subsequ5tly to #adef1 x 0 f\nd to h gradually decreas$ 9 magnitude & spl5dor4 ,:ile 9 #adef x rea*$ across "o ?ird "p ( ! firmam5t1 & spread t]ror ov] ,europe1 9 #afjg1 its appe>ance1 :5 obs]v$ by ,kepl] & ,longomontanus1 0 t ( a /> ( ! fir/ magnitude2 & s trifl+ 0 its tail t1 ,kepl] himself1 :5 he fir/ saw x1 d\bt$ :e!r x _h any4 ,9 #afhb1 x excit$ little att5tion1 except among a/ronom]s4 ,suppos+ ?is decrease ( magnitude & brilliancy to be progressive1 ,lal&e ent]ta9$ s]i\s appreh5sions t on its expect$ return x might be s inconsid]able1 z to escape ! obs]vation ev5 ( a/ronom]s2 & ?us1 t ?is spl5did example ( ! p[] ( sci5ce1 & unansw]able pro( ( ! pr9ciple ( gravitation1 w\ld be lo/ to ! _w4 ,x is n un9t]e/+ to obs]ve ! misgiv+s ( ?is di/+ui%$ a/ronom] ) respect to ! appe>ance ( ! body1 mix$ up ) 8 un%ak5 fai? 9 ! result ( ! a/ronomical inquiry4 ,we _c d\bt1 says he1 t x w return2 & ev5 if a/ronom]s _c see x1 !y w n !re=e be ! less conv9c$ ( its pres5ce4 ,!y "k t ! fa9tness ( its light1 its great di/ance1 & p]haps ev5 bad wea!r1 may keep x f our view4 ,b ! _w w f9d x difficult to believe u2 !y w place ?is discov]y1 :i* has done s mu* honor to mod]n philosophy1 among ! numb] ( *ance pr$ictions4 ,we %all see discussions spr+ up aga9 9 colleges1 contempt among ! ignorant1 t]ror among ! p2 & sev5ty-six ye>s w roll away1 be=e !re w be ano!r opportunity ( remov+ all d\bt4 ,=tunately = sci5ce1 ! arrival ( ! expect$ visitor did n take place "u su* unt[>d circum/ances4 ,z ! comm5cem5t ( ! ye> #agei approa*$1 a/ronom]s1 says ,voltaire1 h>dly w5t to b$ at all4 ,! honor1 h[ev]1 ( ! fir/ glimpse ( ! /rang] 0 n res]v$ = ! possessors ( sci5tific rank1 nor = ! memb]s ( academies or univ]sities4 ,on ! night ( ,*ri/mas-day1 #ageh1 ,george ,palitz*1 ( ,politz1 ne> ,dresd51--a peasant1 says ,sir ,john ,h]*el1 by /ation1 an a/ronom] by nature1 fir/ saw ! comet4 ,an a/ronom] ( ,leipzic f\nd x soon aft]2 b1 ) ! mean jeal\sy ( a mis]1 he conceal$ 8 treasure1 :ile 8 contempor>ies ?r\gh\t ,europe 7 va9ly direct+ _! anxi\s se>* aft] x to o!r qu>t]s ( ! heav5s4 ,at ?is "t1 ,delisle1 a ,fr5* a/ronom]1 & 8 assi/ant1 ,messi]1 :o1 f 8 unwe>$ assiduity 9 ! pursuit ( comets1 0 call$ ! ,comet-,hunt]1 _h be5 con/antly engag$1 = eighte5 mon?s1 9 wat*+ = ! return ( ,halley's comet4 ,messi] pass$ 8 life 9 se>* ( comets4 ,x is relat$ ( him1 t :5 he 0 9 expectation ( discov]+ a comet1 8 wife 0 tak5 ill & di$4 ,:ile att5d+ on h]1 be+ )drawn f 8 obs]vatory1 ano!r a/ronom] anticipat$ him 9 ! discov]y4 ,messi] 0 9 despair4 ,a fri5d1 visit+ him1 began to (f] "s consolation = ! rec5t affliction he _h suff]$4 ,messi]1 ?9k+ only ( ! comet1 exclaim$1 ,i _h discov]$ twelve3 alas1 t ,i %\ld be robb$ ( ! ?irte5? by ,montague6--& 8 eyes fill$ ) te>s4 ,!n1 rememb]+ t x 0 necess>y to m\rn = 8 wife1 ^: rema9s 7 /ill 9 ! h\se1 he exclaim$1 ,ah6 ?is poor woman6 7ah6 cette pauvre femme17 & aga9 wept = 8 comet4 ,we c easily imag9e h[ eag]ly su* an en?usia/ w\ld wat* = ,halley's comet2 & we c\ld almo/ wi% t x _h be5 8 good =tune to be ! fir/ to ann\nce its arrival3 b1 be+ misl$ by a *>t :i* direct$ 8 att5tion to ! wrong "p ( ! firmam5t1 a :ole mon? elaps$ aft] its discov]y by ,palitz*1 be=e he enjoy$ ! delightful spectacle4 ,! comet arriv$ at its p]ihelion on ! ?irte5? ( ,m>*1 only tw5ty-?ree days f ! "t assign$ by ,clairaut4 ,x appe>$ v r\nd1 ) a brilliant nucleus1 well di/+ui%$ f ! surr\nd+ nebulosity4 ,x _h1 h[ev]1 no appe>ance ( a tail4 ,x became lo/ 9 ! sun1 z x approa*$ its p]ihelion1 & em]g$ aga91 on ! o!r side ( ! sun1 on ! fir/ ( ,april4 ,its exhibit+ an appe>ance1 s inf]ior to :at x pres5t$ on "s ( its previ\s returns1 is p>tly acc\nt$ = by its be+ se5 by ! ,european a/ronom]s "u peculi>ly disadvantage\s circum/ances1 be+ almo/ always )9 ! twilight1 & 9 ! mo/ unfavorable situations4 ,9 ! s\!rn hemisph]e1 h[ev]1 ! circum/ances = obs]v+ x 7 m favorable1 & !re x exhibit$ a tail v>y+ f t5 to =ty-sev5 degrees 9 l5g?4 ,9 my next ,lett] ,i w give y "s p>ticul>s respect+ ! late return ( ,halley's comet4 ,,lett] ,,xxvi4 ,,comets1 ,,cont9u$4 ,inc5s$ ) indignation1 ,satan /ood ,unt]rifi$1 & l a comet burn$1 ,t fires ! l5g? ( ,ophiucus huge ,9 ! ,arctic sky1 & f 8 horrid tra9 ,%akes pe/il5ce & w>4--,milton4 ,,among o!r great results :i* h m>k$ ! hi/ory ( ,halley's comet1 x has itself be5 a crit]ion ( ! exi/+ /ate ( ! ma!matical & a/ronomical sci5ces4 ,we h j se5 h[ f> ! k ( ! great laws ( physical a/ronomy1 & ( ! high] ma!matics1 enabl$ ! a/ronom]s ( #afhb & #agei1 respectively1 to deal ) ?is wond]ful body2 & let u n[ see :at high] advantages 7 possess$ by ! a/ronom]s ( #ahce4 ,dur+ ?is la/ int]val ( sev5ty-six ye>s1 ! sci5ce ( ma!matics1 9 its mo/ pr(\nd & ref9$ bran*es1 has made prodigi\s advances1 m especially 9 its application to ! laws ( ! cele/ial motions1 z exemplifi$ 9 ! ',mecanique ,cele/e' ( ,la ,place4 ,! me?ods ( inve/igation h acquir$ great] simplicity1 & h likewise become m g5]al & compreh5sive2 & me*anical sci5ce1 9 ! l>ge/ s5se ( t t]m1 n[ embraces 9 its =mul>ies ! mo/ complicat$ motions1 & ! mo/ m9ute effects ( ! mutual influ5ces ( ! v>i\s memb]s ( our sy/em4 ,y w probably f9d x difficult to compreh5d1 h[ su* hidd5 facts c be disclos$ by =mul>ies1 consi/+ ( a's & b's1 & x's & y's1 & o!r algebraic symbols2 nor w x be easy to give y a cle> idea ( ?is subject1 )\t a m ext5sive acqua9tance ?an y h =m$ ) algebraic inve/igations2 b y c easily und]/& t ev5 an equation express$ 9 numb]s may be s *ang$ 9 its =m1 by add+1 subtract+1 multiply+ & divid+1 z to express "s new tru? at e trans=mation4 ,"s idea ( ?is may be =m$ by ! simple/ example4 ,take ! foll[+3 #cdg4 ,?is equation expresses ! fact1 t ?ree add$ to f\r is equal to sev54 ,by multiply+ all ! t]ms by #b1 we obta9 a new equation1 9 :i* #fhad4 ,?is expresses a new tru?2 & by v>y+ ! =m1 by simil> op]ations1 an indef9ite numb] ( sep>ate tru?s may be elicit$ f ! simple fundam5tal expression4 ,i w add ano!r illu/ration1 :i* involves a little m algebra1 b n1 ,i ?9k1 m ?an y c und]/&2 or1 if x does1 y w please pass ov] x to ! next p>agraph4 ,accord+ to a rule ( ari?metical progression1 ! sum ( all ! t]ms is equal to half ! sum ( ! extremes multipli$ into ! numb] ( t]ms4 ,call+ ! sum ( ! t]ms s1 ! fir/ t]m a1 ! la/ h1 & ! numb] ( t]ms n1 & we h 7#a_/b7n7ah7s2 or n7ah7#bs2 or ah#bs_/n2 or a7#bs_/n7-h2 or h7#bs_/n7-a4 ,^! are only a few ( ! *anges :i* may be made 9 ! orig9al expression1 /ill pres]v+ ! equality betwe5 ! quantities on ! left h& & ^? on ! "r2 yet ea* ( ^! trans=mations expresses a new tru?1 indicat+ di/9ct & 7z might be ! case7 be=e unkn[n relations betwe5 ! sev]al quantities ( :i* ! :ole expression is compos$4 ,! la/1 = example1 %[s u t ! la/ t]m 9 an ari?metical s]ies is always equal to twice ! sum ( ! :ole s]ies divid$ by ! numb] ( t]ms & dim9i%$ by ! fir/ t]m4 ,9 analytical =mul>ies1 z expressions ( ?is k9d are call$1 ! value ( a s+le unkn[n quantity is sometimes giv5 9 a v complicat$ expression1 consi/+ ( kn[n quantities2 b be=e we c asc]ta9 _! unit$ value1 we mu/ r$uce !m1 by actually p]=m+ all ! additions1 subtractions1 multiplications1 divisions1 rais+ to p[]s1 & extract+ roots1 :i* are d5ot$ by ! symbols4 ,?is makes ! actual calculations d]iv$ f su* =mul>ies imm5sely labori\s4 ,we h already _h an in/ance ( ?is 9 ! calculations made by ,lal&e & ,madame ,lepaute1 f =mul>ies furni%$ by ,clairaut4 ,! analytical =mul>ies1 conta9$ 9 su* works z ,la ,place's ',mecanique ,cele/e1' exhibit to ! eye ( ! ma!matician a record ( all ! evolutions ( ! bodies ( ! sol> sy/em 9 ages pa/1 & ( all ! *anges !y mu/ und]go 9 ages to come4 ,su* has be5 ! result ( ! comb9ation ( transc5d5t ma!matical g5ius & unexampl$ labor & p]sev]ance1 = ! la/ c5tury4 ,! le>n$ societies e/abli%$ 9 v>i\s c5tres ( civilization h m especially direct$ _! att5tion to ! advancem5t ( physical a/ronomy1 & h /imulat$ ! _s ( inquiry by a succession ( prizes1 (f]$ = ! solutions ( problems aris+ out ( ! difficulties :i* 7 progressively develop$ by ! advancem5t ( a/ronomical k4 ,among ^! que/ions1 ! det]m9ation ( ! return ( comets1 & ! di/urbances :i* !y exp]i5ce 9 _! c\rse1 by ! action ( ! planets ne> :i* !y happ5 to pass1 hold a prom95t place4 ,9 #ahbf1 ! ,fr5* ,in/itute (f]$ a prize = ! det]m9ation ( ! exact "t ( ! return ( ,halley's comet to its p]ihelion 9 #ahce4 ,m4 ,pontec\lant aspir$ to ! honor4 ,aft] calculations1 says he1 ( :i* ^? alone :o h engag$ 9 su* rese>*es c e/imate ! ext5t & appreciate ! fa/idi\s monotony1 ,i arriv$ at a result :i* satisfi$ all ! conditions propos$ by ! ,in/itute4 ,i det]m9$ ! p]turbations ( ,halley's comet1 by tak+ into acc\nt ! simultane\s actions ( ,jupit]1 ,saturn1 ,uranus1 & ! ,e>?1 & ,i !n fix$ its return to its p]ihelion = ! sev5? ( ,novemb]4 ,subsequ5tly to ?is1 h[ev]1 ,m4 ,pontec\lant made "s fur!r rese>*es1 :i* l$ him to correct ! =m] result2 & he aft]w>ds alt]$ ! "t to ,novemb] f\rte5?4 ,x actually came to its p]ihelion on ! sixte5?1 )9 two days ( ! "t assign$4 ,no?+ c conv9ce u m fully ( ! complete ma/]y :i* a/ronom]s h at la/ acquir$ ov] ^! erratic bodies1 ?an to read 9 ! ,ed9burgh ,review = ,april1 #ahce1 ! p>agraph conta9+ ! f9al results ( all ! labors & anticipations ( a/ronom]s1 matur$ z !y 71 9 read9ess = ! approa*+ visitant1 & !n to comp>e ! pr$iction ) ! ev5t1 z we saw x fulfill$ a few mon?s aft]w>ds4 ,! p>agraph 0 z foll[s3 ,on ! :ole1 x may be consid]$ z tol]ably c]ta91 t ! comet w become visible 9 e "p ( ,europe ab\t ! latt] end ( ,augu/1 or beg9n+ ( ,septemb]1 next4 ,x w mo/ probably be di/+ui%able by ! nak$ eye1 l a /> ( ! fir/ magnitude1 b ) a dull] light ?an t ( a planet1 & surr\nd$ ) a pale nebulosity1 :i* w slightly impair its spl5dor4 ,on ! night ( ! sev5? ( ,octob]1 ! comet w approa* ! well-kn[n con/ellation ( ! ,great ,be>2 & betwe5 t & ! elev5?1 x w pass directly ?r\gh ! sev5 conspicu\s />s ( t con/ellation1 7! ,dipp]47 ,t[>ds ! end ( ,novemb]1 ! comet w plunge among ! rays ( ! sun1 & disappe>1 & w n issue f !m1 on ! o!r side1 until ! end ( ,decemb]4 ,let u n[ see h[ f> ! actual appe>ances correspond$ to ^! pr$ictions4 ,! comet 0 fir/ discov]$ f ! obs]vatory at ,rome1 on ! morn+ ( ! fif? ( ,augu/2 by ,pr(essor ,/ruve1 at ,dorpat1 on ! tw5tie?2 9 ,engl& & ,france1 on ! tw5ty-?ird2 & at ,yale ,college1 by ,pr(essor ,loomis & myself1 on ! ?irty-fir/4 ,on ! morn+ ( t day1 betwe5 two & ?ree o'clock1 9 ob$i5ce to ! directions :i* ! great m9ds t _h m>k$ out its pa? among ! />s _h prescrib$1 we direct$ ,cl>ke's telescope 7a noble in/rum5t1 belong+ to ,yale ,college7 t[>ds ! nor!a/]n qu>t] ( ! heav5s1 & lo6 !re 0 ! w&]] s long =etold1--a dim speck ( fog on ! conf9es ( creation4 ,x came on sl[ly1 f night to night1 increas+ con/antly 9 magnitude & brightness1 b did n become di/9ctly visible to ! nak$ eye until ! tw5ty-second ( ,septemb]4 ,= a mon?1 !re=e1 a/ronom]s enjoy$ ?is int]e/+ spectacle be=e x exhibit$ itself to ! _w at l>ge4 ,f ?is "t x mov$ rapidly along ! nor!rn sky1 until1 ab\t ! t5? ( ,octob]1 x trav]s$ ! con/ellation ( ! ,great ,be>1 pass+ a little above1 in/ead ( ?r\gh ! sev5 conspicu\s />s con/itut+ ! ,dipp]4 ,at ?is "t x _h a l5g!n$ tra91 & became1 z y d\btless rememb]1 an object ( univ]sal int]e/4 ,e>ly 9 ,novemb]1 ! comet ran d[n to ! sun1 & 0 lo/ 9 8 beams2 b on ! morn+ ( ,decemb] ?irty-fir/1 ,i aga9 obta9$1 ?r\gh ,cl>ke's telescope1 a di/9ct view ( x on ! o!r side ( ! sun1 a mom5t be=e ! morn+ dawn4 ,?is return ( ,halley's comet 0 an a/ronomical ev5t ( transc5d5t importance4 ,x 0 ! *ronicl] ( ages1 & c>ri$ u1 by a few /eps1 up to ! orig9 ( "t4 ,if a gallant %ip1 :i* has sail$ r\nd ! globe1 & comm&$ successively ! admiration ( _m great cities1 div]se 9 language & cu/oms1 is inve/$ ) a peculi> int]e/1 :at int]e/ mu/ atta* to "o t has made ! circuit ( ! sol> sy/em1 & fix$ ! gaze ( successive worlds6 ,s intimate1 moreov]1 is ! bond :i* b9ds toge!r all tru?s 9 "o indissoluble *a91 t ! e/abli%m5t ( "o great tru? (t5 confirms a multitude ( o!rs1 equally important4 ,?us ! return ( ,halley's comet1 9 exact con=mity ) ! pr$ictions ( a/ronom]s1 e/abli%$ ! tru? ( all ^? pr9ciples by :i* ^? pr$ictions 7 made4 ,x af=d$ mo/ triumphant pro( ( ! doctr9e ( univ]sal gravitation1 & ( c\rse ( ! receiv$ laws ( physical a/ronomy2 x inspir$ new confid5ce 9 ! p[] & accuracy ( t in/rum5t 7! calculus7 by means ( :i* its elem5ts _h be5 inve/igat$2 & x prov$ t ! diff]5t planets1 :i* ex]t$ ^u x sev]ally a di/urb+ =ce proportion$ to _! quantity ( matt]1 _h be5 correctly weigh$1 z 9 a balance4 ,i mu/ n[ leave ?is wond]ful body to pursue its sublime m>* f> beyond ! conf9es ( ,uranus1 7a di/ance x has long s9ce rea*$17 & take a ha/y notice ( two o!r comets1 ^: p]iodic returns h also be5 asc]ta9$2 namely1 ^? ( ,biela & ,encke4 ,biela's comet has a p]iod ( six ye>s & ?ree qu>t]s4 ,x has its p]ihelion ne> ! orbit ( ! e>?1 & its aphelion a little beyond t ( ,jupit]4 ,its orbit1 !re=e1 is f> less ecc5tric ?an t ( ,halley's comet2 7see ,frontispiece27 x nei!r approa*es s ne> ! sun1 nor dep>ts s f> f x1 z mo/ o!r kn[n comets3 "s1 inde$1 nev] come ne>] to ! sun ?an ! orbit ( ,jupit]1 :ile !y rec$e to an incompreh5sible di/ance beyond ! remote/ planet4 ,we might ev5 imag9e t !y w\ld get beyond ! limits ( ! sun's attraction2 nor is ?is impossible1 al?\gh1 accord+ to ,la ,place1 ! sol> attraction is s5sible ?r\gh\t a sph]e ^: radius is a hundr$ millions ( times great] ?an ! di/ance ( ! e>? f ! sun1 or ne>ly t5 ?\s& billions ( miles4 ,"s mon?s be=e ! expect$ return ( ,biela's comet1 9 #ahcb1 x 0 ann\nc$ by a/ronom]s1 :o _h calculat$ its pa?1 t x w\ld cross ! plane ( ! e>?'s orbit v ne> to ! e>?'s pa?1 s t1 %\ld ! e>? happ5 at ! "t to be at t po9t ( h] revolution1 a collision might take place4 ,?is ann\ncem5t excit$ s mu* al>m among ! ignorant classes 9 ,france1 t x 0 deem$ exp$i5t by ! ,fr5* academy1 t "o ( _! numb] %\ld prep>e & publi% an article on ! subject1 ) ! express view ( allay+ popul> appreh5sion4 ,?is task 0 execut$ by ,m4 ,arago4 ,he admitt$ t ! e>? w\ld 9 fact pass s ne> ! po9t :]e ! comet cross$ ! plane ( its orbit1 t1 %\ld !y *ance to meet !re1 ! e>? w\ld be envelop$ 9 ! nebul\s atmosph]e ( ! comet4 ,he1 h[ev]1 %[$ t ! e>? w\ld n be ne> t po9t at ! same "t ) ! comet1 b fifty millions ( miles f x4 ,! comet came at ! appo9t$ "t1 b 0 s exce$+ly fa9t & small1 t x 0 visible only to ! l>ge/ telescopes4 ,9 "o respect1 its dim9utive size & feeble light enhanc$ ! int]e/ ) :i* x 0 contemplat$2 = x 0 a sublime spectacle to see a body1 :i*1 z project$ on ! cele/ial vault1 ev5 :5 magnifi$ a ?\s& times1 seem$ b a dim speck ( fog1 /ill pursu+ its way1 9 ob$i5ce to ! laws ( univ]sal gravitation1 ) ! same regul>ity z ,jupit] & ,saturn4 ,we are apt to imag9e t a body1 consi/+ ( su* light mat]ials t x c be comp>$ only to ! ?9ne/ fog1 w\ld be dissipat$ & lo/ 9 ! b\ndless regions ( space2 b s f> is ?is f ! tru?1 t1 :5 subject$ to ! action ( ! same =ces ( projection & sol> attraction1 x w move ?r\gh ! void regions ( space1 & w describe its own orbit ab\t ! sun ) ! same un]r+ c]ta9ty1 z ! d5se/ bodies ( ! sy/em4 ,encke's comet1 by its frequ5t returns1 7once 9 ?ree & a ?ird ye>s17 af=ds peculi> facilities = asc]ta9+ ! laws ( its revolution2 & x has kept ! appo9tm5ts made = x ) great exactness4 ,on its return 9 #ahci1 x exhibit$ to ! telescope a globul> mass ( nebul\s matt]1 resembl+ fog1 & mov$ t[>ds its p]ihelion ) great rapidity4 ,x makes its entire excursions )9 ! orbit ( ,jupit]4 ,b :at has made ,encke's comet p>ticul>ly fam\s1 is its hav+ fir/ reveal$ to u ! exi/5ce ( a resi/+ m$ium 9 ! planet>y spaces4 ,x has long be5 a "q1 :e!r ! e>? & planets revolve 9 a p]fect void1 or :e!r a fluid ( extreme r>ity may n be diffus$ ?r\gh space4 ,a p]fect vacuum 0 deem$ mo/ probable1 because no su* effects on ! motions ( ! planets c\ld be detect$ z indicat$ t !y enc\nt]$ a resi/+ m$ium4 ,b a fea!r1 or a lock ( cotton1 propell$ ) great velocity1 might r5d] obvi\s ! resi/ance ( a m$ium :i* w\ld n be p]ceptible 9 ! motions ( a cannon ball4 ,accord+ly1 ,encke's comet is ?\ght to h pla9ly suff]$ a ret>dation f enc\nt]+ a resi/+ m$ium 9 ! planet>y regions4 ,! effect ( ?is resi/ance1 f ! fir/ discov]y ( ! comet to ! pres5t "t1 has be5 to dim9i% ! "t ( its revolution ab\t two days4 ,su* a resi/ance1 by de/roy+ a "p ( ! projectile =ce1 w\ld cause ! comet to approa* ne>] to ! sun1 & ?us to h its p]iodic "t %ort5$4 ,! ultimate effect ( ?is cause w be to br+ ! comet ne>] to ! sun1 at e revolution1 until x f9ally falls into t lum9>y1 al?\gh _m ?\s& ye>s w be requir$ to produce ?is cata/rophe4 ,x is conceivable1 inde$1 t ! effects ( su* a resi/ance may be c\nt]act$ by ! attraction ( "o or m ( ! planets1 ne> :i* x may pass 9 its successive returns to ! sun4 ,/ill1 x is n probable t ?is cause w exactly c\nt]balance ! o!r2 s t1 if !re is su* an ela/ic m$ium diffus$ ?r\gh ! planet>y regions1 x mu/ foll[ t1 9 ! lapse ( ages1 e comet w fall into ! sun4 ,newton conjectur$ t ?is w\ld be ! case1 al?\gh he did n f\nd 8 op9ion ^u ! exi/5ce ( su* a resi/+ m$ium z is n[ detect$4 ,to su* an op9ion he adh]$ to ! end ( life4 ,at ! age ( eighty-?ree1 9 a conv]sation ) 8 nephew1 he express$ himself ?us3 ,i _c say :5 ! comet ( #afhj w fall into ! sun2 possibly aft] five or six revolutions2 b :5ev] t "t %all arrive1 ! heat ( ! sun w be rais$ by x to su* a po9t1 t our globe w be burn$1 & all ! animals ^u x w p]i%4 ,( ! physical nature ( comets little is und]/ood4 ,! great] "p ( !m are evid5tly m]e masses ( vapor1 s9ce !y p]mit v small />s to be se5 ?r\gh !m4 ,9 ,septemb]1 #ahcb1 ,sir ,john ,h]s*el1 :5 obs]v+ ,biela's comet1 saw t body pass directly betwe5 8 eye & a small clu/] ( m9ute telescopic />s ( ! sixte5? or sev5te5? magnitude4 ,?is little con/ellation occupi$ a space 9 ! heav5s1 ! bread? ( :i* 0 n ! tw5tie? "p ( t ( ! moon2 yet ! :ole ( ! clu/] 0 di/9ctly visible ?r\gh ! comet4 ,a m /rik+ pro(1 says ,sir ,john ,h]s*el1 c\ld n h be5 af=d$1 ( ! extreme transp>5cy ( ! matt] ( :i* ?is comet consi/s4 ,! mo/ trifl+ fog w\ld h entirely effac$ ?is gr\p ( />s1 yet !y cont9u$ visible ?r\gh a ?ickness ( ! comet :i*1 calculat+ on its di/ance & app>5t diamet]1 mu/ h exce$$ fifty ?\s& miles1 at lea/ t[>ds its c5tral p>ts4 ,f ?is & simil> obs]vations1 x is inf]r$1 t ! nebul\s matt] ( comets is va/ly m r>e ?an t ( ! air we brea!1 & h5ce1 t1 7 m or less ( x to be m+l$ ) ! e>?'s atmosph]e1 x w\ld n be p]ceiv$1 al?\gh x might possibly r5d] ! air un:olesome = respiration4 ,m4 ,arago1 h[ev]1 is ( ! op9ion1 t "s comets1 at lea/1 h a solid nucleus4 ,x is difficult1 on any o!r supposition1 to acc\nt = ! /rong light :i* "s ( !m h exhibit$1--a light suffici5tly int5se to r5d] !m visible 9 ! day-"t1 dur+ ! pres5ce ( ! sun4 ,! int5se heat to :i* comets are subject1 9 approa*+ s ne> ! sun z "s ( !m d1 is alleg$ z a suffici5t reason = ! great expansion ( ! ?9 vapory atmosph]es :i* =m _! tails2 & ! inconceivable cold to :i* !y are subject1 9 rec$+ to su* a di/ance f ! sun1 is suppos$ to acc\nt = ! cond5sation ( ! same matt] until x returns to its orig9al dim5sions4 ,?us ! great comet ( #afhj1 at its p]ihelion1 approa*$ )9 "o hundr$ & =ty-six ?\s& miles ( ! surface ( ! sun1 a di/ance ( only "o six? "p ( ! sun's diamet]4 ,! heat :i* x mu/ h receiv$ 0 e/imat$ to be equal to tw5ty-eight ?\s& times t :i* ! e>? receives 9 ! same "t1 & two ?\s& times hott] ?an r$-hot iron4 ,?is temp]ature w\ld be suffici5t to volatilize ! mo/ obdurate sub/ances1 & to exp& ! vapor to va/ dim5sions2 & ! opposite effects ( ! extreme cold to :i* x w\ld be subject 9 ! regions remote f ! sun w\ld be adequate to cond5se x into its =m] volume4 ,?is explanation1 h[ev]1 does n acc\nt = ! direction ( ! tail1 ext5d+1 z x usually does1 only 9 a l9e opposite to ! sun4 ,"s writ]s1 !re=e1 suppose t ! nebul\s matt] ( ! comet1 aft] be+ exp&$ to su* a volume t ! p>ticles are no long] attract$ to ! nucleus1 unless by ! slighte/ conceivable =ce1 are c>ri$ (f 9 a direction f ! sun1 by ! impulse ( ! sol> rays !mselves4 ,b to assign su* a p[] to ! sun's rays1 :ile !y h nev] be5 prov$ to h any mom5tum1 is unphilosophical2 & we are compell$ to place ! ph5om5a ( comets' tails among ! po9ts ( a/ronomy yet to be expla9$4 ,s9ce comets :i* approa* v ne> ! sun1 l ! comet ( #afhj1 cross ! orbits ( all ! planets1 ! possibility t "o ( !m may /rike ! e>? has frequ5tly be5 sugge/$4 ,/ill x may quiet our appreh5sions on ?is subject1 to reflect on ! va/ amplitude ( ! planet>y spaces1 9 :i* ^! bodies are n cr[d$ toge!r1 z we see !m errone\sly repres5t$ 9 orr]ies & diagrams1 b are sp>sely scatt]$ at imm5se di/ances f ea* o!r4 ,!y are l insects fly+1 s+ly1 9 ! expanse ( heav54 ,if a comet's tail lay ) its axis 9 ! plane ( ! ecliptic :5 x 0 ne> ! sun1 we c imag9e t ! tail might sweep ov] ! e>?2 b ! tail may be situat$ at any angle ) ! ecliptic1 z well z 9 ! same plane ) x1 & ! *ances t x w n be 9 ! same plane are almo/ inf9ite4 ,x is also extremely improbable t a comet w cross ! plane ( ! ecliptic precisely at ! e>?'s pa? 9 t plane1 s9ce x may z probably cross x at any o!r po9t ne>] or m remote f ! sun4 ,a ,fr5* writ] ( "s em95ce 7,du ,sej\r7 has discuss$ ?is subject ) ability1 & arriv$ at ! foll[+ conclusions3 ,t ( all ! comets ^: pa?s _h be5 asc]ta9$1 none c\ld pass ne>] to ! e>? ?an ab\t twice ! moon's di/ance2 & t none ev] did pass ne>] to ! e>? ?an n9e times ! moon's di/ance4 ,! comet ( #aggj1 already m5tion$1 :i* became entangl$ among ! satellites ( ,jupit]1 came )9 ?is limit4 ,"s h tak5 al>m at ! idea t a comet1 by approa*+ v ne> to ! e>?1 might raise s high a tide1 z to endang] ! safety ( m>itime c\ntries especially3 b ?is writ] %[s1 t ! comet c\ld n possibly rema9 m ?an two h\rs s ne> ! e>? z a f\r? "p ( ! moon's di/ance2 & x c\ld n rema9 ev5 s long1 unless x pass$ ! e>? "u v peculi> circum/ances4 ,= example1 if its orbit 7 ne>ly p]p5dicul> to t ( ! e>?1 x c\ld n rema9 m ?an half an h\r 9 su* a position4 ,"u su* circum/ances1 ! production ( a tide w\ld be impossible4 ,elev5 h\rs1 at lea/1 w\ld be necess>y to enable a comet to produce an effect on ! wat]s ( ! e>?1 f :i* ! injuri\s effects s mu* dread$ w\ld foll[4 ,! f9al conclusion at :i* he arrives is1 t al?\gh1 9 /rict geometrical rigor1 x is n physically impossible t a comet %\ld enc\nt] ! e>?1 yet ! probability ( su* an ev5t is absolutely no?+4 ,m4 ,arago1 also1 has inve/igat$ ! probability ( su* a collision on ! ma!matical doctr9e ( *ances1 & rem>ks z foll[s3 ,suppose1 n[1 a comet1 ( :i* we "k no?+ b t1 at its p]ihelion1 x w be ne>] ! sun ?an we are1 & t its diamet] is equal to "o f\r? t ( ! e>?2 ! doctr9e ( *ances %[s t1 out ( two hundr$ & eighty-"o millions ( cases1 !re is b "o aga9/ u2 b "o1 9 :i* ! two bodies c\ld meet4 ,la ,place has assign$ ! consequ5ces t w\ld result f a direct collision betwe5 ! e>? & a comet4 ,x is easy1 says he1 to repres5t ! effects ( ! %ock produc$ by ! e>?'s enc\nt]+ a comet4 ,! axis & ! motion ( rotation *ang$2 ! wat]s ab&on+ _! =m] position to precipitate !mselves t[>ds ! new equator2 a great "p ( m5 & animals :elm$ 9 a univ]sal deluge1 or de/roy$ by ! viol5t %ock imp>t$ to ! t]re/rial globe2 entire species annihilat$2 all ! monum5ts ( human indu/ry ov]?r[n2--su* are ! disa/]s :i* ! %ock ( a comet w\ld necess>ily produce4 ,la ,place1 nev]!less1 expresses a decid$ op9ion t ! orbits ( ! planets h nev] yet be5 di/urb$ by ! influ5ce ( comets4 ,comets1 moreov]1 h be51 & are /ill to "s degree1 suppos$ to ex]cise mu* influ5ce 9 ! affairs ( ?is _w1 affect+ ! wea!r1 ! crops1 ! public heal?1 & a great v>iety ( atmosph]ic commotions4 ,ev5 ,halley1 f9d+ t 8 comet mu/ h be5 ne> ! e>? at ! "t ( ! ,deluge1 sugge/$ ! possibility t ! comet caus$ t ev5t1--an idea :i* 0 tak5 up by ,:i/on1 & =m$ into a regul> !ory4 ,9 ,gregory's ,a/ronomy1 an able "w1 publi%$ at ,ox=d 9 #agjb1 ! au?or rem>ks1 t among all nations & 9 all ages1 x has be5 obs]v$1 t ! appe>ance ( a comet has always be5 foll[$ by great calamities2 & he adds1 x does n become philosoph]s lightly to set d[n ^! ?+s z fables4 ,among ! v>i\s ?+s ascrib$ to comets by a late ,engli% writ]1 are hot & cold seasons1 tempe/s1 hurricanes1 viol5t hail-/orms1 great falls ( sn[1 heavy ra9s1 inundations1 dr\ghts1 fam9es1 ?ick fogs1 flies1 gras%opp]s1 plague1 dys5t]y1 contagi\s diseases among animals1 sickness among cats1 volcanic eruptions1 & meteors1 or %oot+ />s4 ,^! notions are too ridicul\s to require a di/9ct refutation2 & ,i w only add1 t we h no evid5ce t comets h hi!rto ev] ex]cis$ ! lea/ influ5ce ^u ! affairs ( ?is _w2 & we /ill rema9 9 d>kness1 ) respect to _! physical nature1 & ! purposes = :i* !y 7 creat$4 ,,lett] ,,xxvii4 ,,meteoric ,,%[]s4 ,(t %alt ?\ see1 ere brood+ /orms arise1 ,/> aft] /> glide headlong d[n ! skies1 ,&1 :]e !y %ot1 long trails ( l+]+ light ,sweep f> beh9d1 & gild ! %ades ( night4--,virgil4 ,,few subjects ( a/ronomy h excit$ a m g5]al int]e/1 = sev]al ye>s pa/1 ?an ^? extraord9>y exhibitions ( %oot+ />s1 :i* h acquir$ ! "n ( meteoric %[]s4 ,my reason = introduc+ ! subject to y\r notice1 9 ?is place1 is1 t ^! small bodies are1 z ,i believe1 d]iv$ f nebul\s or comet>y bodies1 :i* belong to ! sol> sy/em1 & :i*1 !re=e1 ought to be consid]$1 be=e we take our leave ( ?is dep>tm5t ( creation1 & naturally come next 9 ord] to comets4 ,! att5tion ( a/ronom]s 0 p>ticul>ly direct$ to ?is subject by ! extraord9>y %[] ( meteors :i* occurr$ on ! morn+ ( ! ?irte5? ( ,novemb]1 #ahcc4 ,i _h ! good =tune to witness ^! gr& cele/ial fire-works1 & felt a /rong desire t a ph5om5on1 :i*1 z x aft]w>ds appe>$1 0 conf9$ *iefly to ,nor? ,am]ica1 %\ld "h comm& t dilig5t inquiry into its causes1 :i* s sublime a spectacle might ju/ly claim4 ,z ,i ?9k y 7 n s happy z to witness ?is magnific5t display1 ,i w endeavor to give y "s fa9t idea ( x1 z x appe>$ to me a little be=e daybreak4 ,imag9e a con/ant succession ( fire-balls1 resembl+ sky-rockets1 radiat+ 9 all directions f a po9t 9 ! heav5s a few degrees s\!a/ ( ! z5i?1 & foll[+ ! ar* ( ! sky t[>ds ! horizon4 ,!y comm5c$ _! progress at diff]5t di/ances f ! radiat+ po9t2 b _! directions 7 uni=mly su*1 t ! l9es !y describ$1 if produc$ upw>ds1 w\ld all h met 9 ! same "p ( ! heav5s4 ,ar\nd ?is po9t1 or imag9>y radiant1 0 a circul> space ( sev]al degrees1 )9 :i* no meteors 7 obs]v$4 ,! balls1 z !y travell$ d[n ! vault1 usually left aft] !m a vivid /reak ( light2 &1 j be=e !y disappe>$1 explod$1 or sudd5ly resolv$ !mselves into smoke4 ,no report ( any k9d 0 obs]v$1 al?\gh we li/5$ att5tively4 ,beside ! =ego+ di/9ct concretions1 or individual bodies1 ! atmosph]e exhibit$ phosphoric l9es1 foll[+ 9 ! tra9 ( m9ute po9ts1 t %ot (f 9 ! greate/ abundance 9 a nor?we/]ly direction4 ,^! did n s fully copy ! figure ( ! sky1 b mov$ 9 pa?s m ne>ly rectil9e>1 & appe>$ to be mu* ne>] ! spectator ?an ! fire-balls4 ,! light ( _! tra9s 0 also ( a pal] hue1 n unlike t produc$ by writ+ ) a /ick ( phosphorus on ! walls ( a d>k room4 ,! numb] ( ^! lum9\s tra9s increas$ & dim9i%$ alt]nately1 n[ & !n cross+ ! field ( view1 l sn[ drift$ be=e ! w9d1 al?\gh1 9 fact1 _! c\rse 0 t[>ds ! w9d4 ,f ^! two v>ieties1 we 7 pres5t$ ) meteors ( v>i\s sizes & degrees ( spl5dor3 "s 7 m]e po9ts1 :ile o!rs 7 l>g] & bright] ?an ,jupit] or ,v5us2 & "o1 se5 by a cr$ible witness1 at an e>li] h\r1 0 judg$ to be ne>ly z l>ge z ! moon4 ,! fla%es ( light1 al?\gh less int5se ?an lightn+1 7 s bright1 z to awak5 p 9 _! b$s4 ,"o ball t %ot (f 9 ! nor?we/ direction1 & explod$ a little nor?w>d ( ! /> ,capella1 left1 j beh9d ! place ( explosion1 a phosphoresc5t tra9 ( peculi> beauty4 ,?is tra9 0 at fir/ ne>ly /raight1 b x %ortly began to contract 9 l5g?1 to dilate 9 bread?1 & to assume ! figure ( a s]p5t draw+ itself up1 until x appe>$ l a small lum9\s cl\d ( vapor4 ,?is cl\d 0 borne ea/w>d1 7by ! w9d1 z 0 suppos$1 :i* 0 bl[+ g5tly 9 t direction17 opposite to ! direction 9 :i* ! meteor itself _h mov$1 rema9+ 9 sight sev]al m9utes4 ,! po9t f :i* ! meteors seem$ to radiate kept a fix$ position among ! />s1 be+ con/antly ne> a /> 9 ,leo1 call$ ,gamma ,leonis4 ,su* is a brief description ( ?is gr& & beautiful display1 z ,i saw x at ,new ,hav54 ,! newspap]s %ortly br\ght u intellig5ce ( simil> appe>ances 9 all p>ts ( ! ,unit$ ,/ates1 & _m m9ute descriptions 7 publi%$ by v>i\s obs]v]s2 f :i* x appe>$1 t ! exhibition _h be5 m>k$ by v ne>ly ! same *>act]i/ics :]ev] x _h be5 se54 ,probably no cele/ial ph5om5on has ev] occurr$ 9 ?is c\ntry1 s9ce its fir/ settlem5t1 :i* 0 view$ ) s mu* admiration & delight by "o class ( spectators1 or ) s mu* a/oni%m5t & fe> by ano!r class4 ,x /rik+ly ev9c$ ! progress ( k & civilization1 t ! latt] class 0 comp>atively s small1 al?\gh x af=d$ "s few examples ( ! dismay ) :i*1 9 b>b>\s ages ( ! _w1 su* spectacles z ?is 7 wont to be reg>d$4 ,"o or two in/ances 7 report$1 ( p]sons :o di$ ) t]ror2 _m o!rs ?\ght ! la/ great day _h come2 & ! untutor$ black population ( ! ,s\? gave expression to _! fe>s 9 cries & %rieks4 ,aft] collect+ & collat+ ! acc\nts giv5 9 all ! p]iodicals ( ! c\ntry1 & also 9 num]\s lett]s address$ ei!r to my sci5tific fri5ds or to myself1 ! foll[+ appe>$ to be ! lead+ facts att5d+ ! ph5om5on4 ,! %[] p]vad$ ne>ly ! :ole ( ,nor? ,am]ica1 hav+ appe>$ 9 ne>ly equal spl5dor f ! ,briti% possessions on ! nor? to ! ,we/-,india ,isl&s & ,mexico on ! s\?1 & f sixty-"o degrees ( longitude ea/ ( ! ,am]ican coa/1 q to ! ,pacific ,ocean on ! we/4 ,?r\gh\t ?is imm5se region1 ! duration 0 ne>ly ! same4 ,! meteors began to attract att5tion by _! unusual frequ5cy & brilliancy1 f n9e to twelve o'clock 9 ! ev5+2 7 mo/ /rik+ 9 _! appe>ance f two to five2 arriv$ at _! maximum1 9 _m places1 ab\t f\r o'clock2 & cont9u$ until r5d]$ invisible by ! light ( day4 ,! meteors mov$ ei!r 9 "r l9es1 or 9 su* app>5t curves1 z1 ^u optical pr9ciples1 c be resolv$ into "r l9es4 ,_! g5]al t5d5cy 0 t[>ds ! nor?we/1 al?\gh1 by ! effect ( p]spective1 !y appe>$ to move 9 v>i\s directions4 ,su* 7 ! lead+ ph5om5a ( ! great meteoric %[] ( ,novemb] #ac1 #ahcc4 ,= a full] detail ( ! facts1 z well z ( ! reason+s t 7 built on !m1 ,i mu/ beg leave to ref] y to "s pap]s ( m9e 9 ! tw5ty-fif? & tw5ty-six? volumes ( ! ,am]ican ,j\rnal ( ,sci5ce4 ,soon aft] ?is wond]ful occurr5ce1 x 0 asc]ta9$ t a simil> meteoric %[] _h appe>$ 9 #agii1 &1 :at 0 rem>kable1 almo/ at exactly ! same "t ( ye>1 namely1 on ! morn+ ( ! twelf? ( ,novemb]2 & we 7 aga9 surpris$ z well z delight$1 at receiv+ successive acc\nts f diff]5t p>ts ( ! _w ( ! ph5om5on1 z hav+ occurr$ on ! morn+ ( ! same ?irte5? ( ,novemb]1 9 #ahcj1 #ahca1 & #ahcb4 ,h5ce ?is 0 evid5tly an ev5t indep5d5t ( ! casual *anges ( ! atmosph]e2 =1 hav+ a p]iodical return1 x 0 und\bt$ly to be ref]r$ to a/ronomical causes1 & its recurr5ce1 at a c]ta9 def9ite p]iod ( ! ye>1 pla9ly indicat$ "s relation to ! revolution ( ! e>? ar\nd ! sun4 ,x rema9$1 h[ev]1 to develope ! nature ( ?is relation1 by inve/igat+1 if possible1 ! orig9 ( ! meteors4 ,! views to :i* ,i 0 l$ on ?is subject sugge/$ ! probability t ! same ph5om5on w\ld recur on ! correspond+ seasons ( ! ye>1 = at lea/ sev]al ye>s aft]w>ds2 & su* prov$ to be ! fact1 al?\gh ! appe>ances1 at e succe$+ return1 7 less & less /rik+1 until #ahci1 :51 s f> z ,i h he>d1 !y ceas$ altoge!r4 ,mean-:ile1 two o!r di/9ct p]iods ( meteoric %[]s h1 z already intimat$1 be5 det]m9$2 namely1 ab\t ! n9? ( ,augu/1 & sev5? ( ,decemb]4 ,! facts relative to ! hi/ory ( ^! p]iods h be5 collect$ ) great indu/ry by ,mr4 ,edw>d ,c4 ,h]rick2 & sev]al ( ! mo/ +5i\s & mo/ useful conclusions1 respect+ ! laws t regulate ^! s+ul> exhibitions1 h be5 d$uc$ by ,pr(essor ,tw9+4 ,sev]al ( ! mo/ di/+ui%$ a/ronom]s ( ! ,old ,_w1 also1 h engag$ 9 ^! inve/igations ) great zeal1 z ,messrs4 ,arago & ,biot1 ( ,p>is2 ,doctor ,olb]s1 ( ,brem52 ,m4 ,w>tmann1 ( ,g5eva2 & ,m4 ,quetelet1 ( ,brussels4 ,b y w be desir\s to le>n :at are ! conclusions :i* h be5 drawn respect+ ^! new & extraord9>y ph5om5a ( ! heav5s4 ,z ! inf]5ces to :i* ,i 0 l$1 z expla9$ 9 ! tw5ty-six? volume ( ! ',am]ican ,j\rnal ( ,sci5ce1' h1 at lea/ 9 _! mo/ important po9ts1 be5 sanction$ by a/ronom]s ( ! highe/ respectability1 ,i w v5ture to give y a brief ab/ract ( !m1 ) su* modifications z ! progress ( inve/igation s9ce t p]iod has r5d]$ necess>y4 ,! pr9cipal que/ions involv$ 9 ! inquiry 7 ! foll[+3--,0 ! orig9 ( ! meteors )9 ! atmosph]e1 or beyond x8 ,:at 0 ! height ( ! place above ! surface ( ! e>?8 ,by :at =ce 7 ! meteors drawn or impell$ t[>ds ! e>?8 ,9 :at directions did !y move8 ,) :at velocity8 ,:at 0 ! cause ( _! light & heat8 ,( :at size 7 ! l>g] v>ieties8 ,at :at height above ! e>? did !y disappe>8 ,:at 0 ! nature ( ! lum9\s tra9s :i* sometimes rema9$ beh9d8 ,:at sort ( bodies 7 ! meteors !mselves2 ( :at k9d ( matt] con/itut$2 & 9 :at mann] did !y exi/ be=e !y fell to ! e>?8 ,f9ally1 :at relations did ! s\rce f :i* !y emanat$ su/a9 to our e>?8 ,9 ! fir/ place1 ! meteors _h _! orig9 beyond ! limits ( our atmosph]e4 ,we "k :e!r a giv5 appe>ance 9 ! sky is )9 ! atmosph]e or beyond x1 by ?is circum/ance3 all bodies ne> ! e>?1 includ+ ! atmosph]e itself1 h a common motion ) ! e>? ar\nd its axis f we/ to ea/4 ,:5 we see a cele/ial object mov+ regul>ly f we/ to ea/1 at ! same rate z ! e>? moves1 leav+ ! />s beh9d1 we "k x is ne> ! e>?1 & p>takes1 9 common ) ! atmosph]e1 ( its diurnal rotation3 b :5 ! e>? leaves ! object beh9d2 or1 9 o!r words1 :5 ! object moves we/w>d along ) ! />s1 !n we "k t x is s di/ant z n to p>ticipate 9 ! diurnal revolution ( ! e>?1 & ( c\rse to be beyond ! atmosph]e4 ,! s\rce f :i* ! meteors emanat$ ?us kept pace ) ! />s1 & h5ce 0 beyond ! atmosph]e4 ,9 ! second place1 ! height ( ! place :5ce ! meteors proce$$ 0 v great1 b x has n yet be5 accurately det]m9$4 ,reg>d+ ! body :5ce ! meteors emanat$ aft] ! similitude ( a cl\d1 x seem$ possible to obta9 its height 9 ! same mann] z we measure ! height ( a cl\d1 or inde$ ! height ( ! moon4 ,al?\gh we c\ld n see ! body itself1 yet ! "p ( ! heav5s :5ce ! meteors came w\ld indicate its position4 ,?is po9t we call$ ! radiant2 & ! "q 01 :e!r ! radiant 0 project$ by di/ant obs]v]s on diff]5t p>ts ( ! sky2 t is1 :e!r x _h any p>allax4 ,i took mu* pa9s to asc]ta9 ! tru? ( ?is matt]1 by correspond+ ) v>i\s obs]v]s 9 diff]5t p>ts ( ! ,unit$ ,/ates1 :o _h accurately not$ ! position ( ! radiant among ! fix$ />s1 & suppos$ ,i _h obta9$ su* mat]ials z w\ld enable u to det]m9e ! p>allax1 at lea/ approximately2 al?\gh su* discordances exi/$ 9 ! evid5ce z reasonably to create "s di/ru/ ( its validity4 ,putt+ toge!r1 h[ev]1 ! be/ mat]ials ,i c\ld obta91 ,i made ! height ( ! radiant above ! surface ( ! e>? tw5ty-two hundr$ & ?irty-eight miles4 ,:51 h[ev]1 ,i aft]w>ds obta9$1 z ,i suppos$1 "s insight into ! cele/ial orig9 ( ! meteors1 ,i at once saw t ! meteoric body mu/ be mu* fur!r (f ?an ?is di/ance2 & my pres5t impression is1 t we h n ! means ( det]m9+ :at its height really is4 ,we may safely place x at _m ?\s& miles4 ,9 ! ?ird place1 ) respect to ! =ce by :i* ! meteors 7 drawn or impell$ t[>ds ! e>?1 my fir/ impression 01 t !y fell m]ely by ! =ce ( gravity2 b ! velocity :i*1 on c>eful inve/igation by ,pr(essor ,tw9+ & o!rs1 has be5 ascrib$ to !m1 is great] ?an c possibly result f gravity1 s9ce a body c nev] acquire1 by gravity alone1 a velocity great] ?an ab\t sev5 miles p] second4 ,"s o!r cause1 beside gravity1 mu/ !re=e act1 9 ord] to give ! meteors s great an app>5t velocity4 ,9 ! f\r? place1 ! meteors fell t[>ds ! e>? 9 /raight l9es1 & 9 directions :i*1 )9 consid]able di/ances1 7 ne>ly p>allel ) ea* o!r4 ,! c\rses are inf]r$ to h be5 9 /raight l9es1 because no o!rs c\ld h appe>$ to spectators 9 diff]5t situations to h describ$ arcs ( great circles4 ,9 ord] to be project$ into ! arc ( a great circle1 ! l9e ( desc5t mu/ be 9 a plane pass+ ?r\gh ! eye ( ! spectator2 & ! int]section ( su* planes1 pass+ ?r\gh ! eyes ( diff]5t spectators1 mu/ be /raight l9es4 ,! l9es ( direction are inf]r$ to h be5 p>allel1 on acc\nt ( _! app>5t radiation f "o po9t1 t be+ ! vani%+ po9t ( p>allel l9es4 ,?is may appe> to y a little p>adoxical1 to inf] t l9es are p>allel1 because !y div]ge f "o & ! same po9t2 b x is a well-kn[n pr9ciple ( p]spective1 t p>allel l9es1 :5 cont9u$ to a great di/ance f ! eye1 appe> to conv]ge t[>ds ! remot] end4 ,y may obs]ve ?is 9 two long r[s ( trees1 or ( /reet lamps4 ,illu/ration ,fig4 #fi4 ,"s idea ( ! mann] 9 :i* ! meteors fell1 & ( ! reason ( _! app>5t radiation f a common po9t1 may be ga!r$ f ! annex$ diagram4 ,let ,a ,b ,c1 ,fig4 #fi1 repres5t ! vault ( ! sky1 ! c5tre ( :i*1 ,d1 be+ ! place ( ! spectator4 ,let #a1 #b1 #c1 c41 repres5t p>allel l9es direct$ t[>ds ! e>?4 ,a lum9\s body desc5d+ ?r\gh #a' #a1 co9cid+ ) ! l9e ,d ,e1 co9cid5t ) ! axis ( vision1 7or ! l9e drawn f ! meteoric body to ! eye17 w\ld appe> /ation>y all ! :ile at #a1 because di/ant bodies always appe> /ation>y :5 !y are mov+ ei!r directly t[>ds u or directly f u4 ,a body desc5d+ ?r\gh #b #b1 w\ld seem to describe ! %ort arc #b' #b'1 appe>+ to move on ! concave ( ! sky betwe5 ! l9es drawn f ! eye to ! two extremities ( its l9e ( motion2 &1 = a simil> reason1 a body desc5d+ ?r\gh #c #c1 w\ld appe> to describe ! l>g] arc #c' #c'4 ,h5ce1 ^? meteors :i* fell ne>] to ! axis ( vision1 w\ld describe %ort] arcs1 & move sl[]1 :ile ^? :i* 7 fur!r f ! axis & ne>] ! horizon w\ld appe> to describe long] arcs1 & to move ) great] velocity2 ! meteors w\ld all seem to radiate f a common c5tre1 namely1 ! po9t :]e ! axis ( vision met ! cele/ial vault2 & if any meteor *anc$ to move directly 9 ! l9e ( vision1 x w\ld be se5 z a lum9\s body1 /ation>y1 = a few seconds1 at ! c5tre ( radiation4 ,to see h[ exactly ! facts1 z obs]v$1 correspond$ to ^! inf]5ces1 d]iv$ f ! supposition t ! meteors mov$ 9 p>allel l9es1 take ! foll[+ description1 z giv5 imm$iately aft] ! occurr5ce1 by ,pr(essor ,tw9+4 ,9 ! vic9ity ( ! radiant po9t1 a few />-l bodies 7 obs]v$1 possess+ v little motion1 & leav+ v little l5g? ( trace4 ,fur!r (f1 ! motions 7 m rapid & ! traces long]2 & mo/ rapid ( all1 & longe/ 9 _! traces1 7 ^? :i* orig9at$ b a few degrees above ! horizon1 & desc5d$ d[n to x4 ,9 ! fif? place1 _h ! meteors come f a po9t tw5ty-two hundr$ & ?irty-eight miles f ! e>?1 & d]iv$ _! app>5t velocity f gravity alone1 !n x w\ld be f\nd1 by a v easy calculation1 t _! actual velocity 0 ab\t f\r miles p] second2 b1 z already intimat$1 ! velocity obs]v$ 0 e/imat$ mu* great] ?an c\ld be acc\nt$ = on ^! pr9ciples2 n less1 inde$1 ?an f\rte5 miles p] second1 &1 9 "s in/ances1 mu* great] ev5 ?an ?is4 ,! motion ( ! e>? 9 its orbit is ab\t n9ete5 miles p] second2 & ! mo/ reasonable supposition we c make1 at pres5t1 to acc\nt = ! great velocity ( ! meteors1 is1 t !y d]iv$ a relative motion f ! e>?'s pass+ rapidly by !m1--a supposition :i* is c\nt5anc$ by ! fact t !y g5]ally t5d$ we/w>d contr>y to ! e>?'s motion 9 its orbit4 ,9 ! six? place1 ! meteors consi/$ ( combu/ible matt]1 & took fire1 & 7 consum$1 9 trav]s+ ! atmosph]e4 ,t ^! bodies und]w5t combu/ion1 we _h ! direct evid5ce ( ! s5ses1 inasmu* z we saw !m burn4 ,t !y took fire 9 ! atmosph]e1 0 inf]r$ f ! fact t !y 7 n lum9\s 9 _! orig9al situations 9 space1 o!rwise1 we %\ld h se5 ! body f :i* !y emanat$2 & _h !y be5 lum9\s be=e rea*+ ! atmosph]e1 we %\ld h se5 !m = a mu* long] p]iod ?an !y 7 9 sight1 z !y mu/ h occupi$ a consid]able "t 9 desc5d+ t[>ds ! e>? f s great a di/ance1 ev5 at ! rapid rate at :i* !y travell$4 ,! imm$iate consequ5ce ( ! prodigi\s velocity ) :i* ! meteors fell into ! atmosph]e mu/ be a p[]ful cond5sation ( ! air be=e !m1 ret>d+ _! progress1 & produc+1 by a sudd5 compression ( ! air1 a great evolution ( heat4 ,!re is a little in/rum5t call$ ! air-mat*1 consi/+ ( a pi/on & cyl9d]1 l a syr+e1 9 :i* we /rike a light by sudd5ly =c+ d[n ! pi/on ^u ! air bel[4 ,z ! air _c escape1 x is sudd5ly compress$1 & gives a sp>k suffici5t to light a piece ( t9d] at ! bottom ( ! cyl9d]4 ,inde$1 x is a well-kn[n fact1 t1 :5ev] air is sudd5ly & =cibly compress$1 heat is elicit$2 &1 if by su* a compression z may be giv5 by ! h& 9 ! air-mat*1 heat is evolv$ suffici5t to fire t9d]1 :at mu/ be ! heat evolv$ by ! motion ( a l>ge body 9 ! atmosph]e1 ) a velocity s imm5se4 ,x is common to resort to electricity z ! ag5t :i* produces ! heat & light ( %oot+ />s2 b ev5 7 electricity compet5t to produce ?is effect1 its pres5ce1 9 ! case be=e u1 is n prov$2 & its ag5cy is unnecess>y1 s9ce s swift a motion ( ! meteors !mselves1 sudd5ly cond5s+ ! air be=e !m1 is bo? a kn[n & adequate cause ( an int5se light & heat4 ,a combu/ible body fall+ into ! atmosph]e1 "u su* circum/ances1 w\ld become spe$ily ignit$1 b c\ld n burn freely1 until x became envelop$ 9 air ( great] d5sity2 b1 on rea*+ ! l[] portions ( ! atmosph]e1 x w\ld burn ) great rapidity4 ,9 ! sev5? place1 "s ( ! l>g] meteors mu/ h be5 bodies ( great size4 ,accord+ to ! te/imony ( v>i\s individuals1 9 diff]5t p>ts ( ! ,unit$ ,/ates1 a few fire-balls appe>$ z l>ge z ! full moon4 ,dr4 ,smi?1 7!n ( ,nor? ,c>ol9a1 b s9ce surgeon-g5]al ( ! ,texian army17 :o 0 travell+ all night on pr(essional bus9ess1 describes "o :i* he saw 9 ! foll[+ t]ms3 ,9 size x appe>$ some:at l>g] ?an ! full moon ris+4 ,i 0 />tl$ by ! spl5did light 9 :i* ! surr\nd+ sc5e 0 exhibit$1 r5d]+ ev5 small objects q visible2 b ,i he>d no noise1 al?\gh e s5se seem$ to be sudd5ly ar\s$1 9 sympa?y ) ! viol5t impression on ! sight4 ,?is description implies n only t ! body 0 v l>ge1 b t x 0 at a consid]able di/ance f ! spectator4 ,its actual size w dep5d ^u ! di/ance2 =1 z x appe>$ "u ! same angle z ! moon1 its diamet] w be> ! same ratio to ! moon's1 z its di/ance be>s to ! moon's di/ance4 ,we c\ld1 !re=e1 easily asc]ta9 h[ l>ge x 01 provid$ we c\ld f9d h[ f> x 0 f ! obs]v]4 ,if x 0 "o hundr$ & t5 miles di/ant1 its diamet] 0 "o mile1 & 9 ! same proportion = a great] or less di/ance2 &1 if only at ! di/ance ( "o mile1 its diamet] 0 =ty-eight feet4 ,= a mod]ate e/imate1 we w suppose x to h be5 tw5ty-two miles (f2 !n its diamet] 0 elev5 hundr$ & fifty-six feet4 ,^u e view ( ! case1 !re=e1 x mu/ be admitt$1 t ^! 7 bodies ( great size1 comp>$ ) o!r objects :i* trav]se ! atmosph]e4 ,we may fur!r inf] ! great magnitude ( "s ( ! meteors1 f ! dim5sions ( ! tra9s1 or cl\ds1 :i* result$ f _! de/ruction4 ,^! (t5 ext5d$ ov] sev]al degrees1 & at l5g? 7 borne along 9 ! direction ( ! w9d1 exactly 9 ! mann] ( a small cl\d4 ,x 0 an int]e/+ problem to asc]ta91 if possible1 ! height above ! e>? at :i* ^! fire-balls explod$1 or resolv$ !mselves into a cl\d ( smoke4 ,?is w\ld be an easy task1 provid$ we c\ld be c]ta9 t two or m di/ant obs]v]s c\ld be sure t bo? saw ! same meteor2 = z ea* w\ld ref] ! place ( explosion1 or ! position ( ! cl\d t result$ f x1 to a diff]5t po9t ( ! sky1 a p>allax w\ld ?us be obta9$1 f :i* ! height might be det]m9$4 ,! l>ge meteor :i* is m5tion$ 9 my acc\nt ( ! %[]1 7see page #cdh17 z hav+ explod$ ne> ! /> ,capella1 0 s peculi> 9 its appe>ance1 & 9 ! =m & motions ( ! small cl\d :i* result$ f its combu/ion1 t x 0 notic$ & di/+ui%$ by a numb] ( obs]v]s 9 di/ant p>ts ( ! c\ntry4 ,all describ$ ! meteor z exhibit+1 sub/antially1 ! same peculi>ities ( appe>ance2 all agre$ v ne>ly 9 ! "t ( its occurr5ce2 &1 on draw+ l9es1 to repres5t ! c\rse & direction ( ! place :]e x explod$ to ! view ( ea* ( ! obs]v]s respectively1 ^! l9es met 9 ne>ly "o & ! same po9t1 & t 0 ov] ! place :]e x 0 se5 9 ! z5i?4 ,little d\bt1 !re=e1 c\ld rema91 t all saw ! same body2 & on asc]ta9+1 f a comp>ison ( _! obs]vations1 ! am\nt ( p>allax1 & !nce d$uc+ its height1--a task :i* 0 ably execut$ by ,pr(essor ,tw9+1--! foll[+ results 7 obta9$3 t ?is meteor1 & probably all ! meteors1 ent]$ ! atmosph]e ) a velocity n less1 b p]haps great]1 ?an f\rte5 miles 9 a second2 t !y became lum9\s _m miles f ! e>?1--9 ?is case1 ov] eighty miles2 & became ext9ct high above ! surface1--9 ?is case1 ne>ly ?irty miles4 ,9 ! eigh? place1 ! meteors 7 combu/ible bodies1 & 7 con/itut$ ( light & transp>5t mat]ials4 ,! fact t !y burn$ is suffici5t pro( t !y belong$ to ! class ( combu/ible bodies2 & !y mu/ h be5 compos$ ( v light mat]ials1 o!rwise _! mom5tum w\ld h be5 suffici5t to enable !m to make _! way ?r\gh ! atmosph]e to ! surface ( ! e>?4 ,to comp>e great ?+s ) small1 we may lik5 !m to a wad dis*>g$ f a piece ( artill]y1 its velocity be+ suppos$ to be increas$ 7z x may be7 to su* a degree1 t x %all take fire z x moves ?r\gh ! air4 ,al?\gh x w\ld =ce its way to a great di/ance f ! gun1 yet1 if n consum$ too soon1 x w\ld at l5g? be /opp$ by ! resi/ance ( ! air4 ,al?\gh x is suppos$ t ! meteors did 9 fact slightly di/urb ! atmosph]ic equilibrium1 yet1 _h !y be5 con/itut$ ( d5se matt]1 l meteoric /ones1 !y w\ld d\btless h di/urb$ x va/ly m4 ,_! own mom5tum w\ld be lo/ only z x 0 imp>t$ to ! air2 & _h su* a numb] ( bodies1--"s ( !m q l>ge1 p]haps a mile 9 diamet]1 & ent]+ ! atmosph]e ) a velocity m ?an =ty times ! greate/ velocity ( a cannon ball1--_h !y be5 compos$ ( d5se1 pond]\s matt]1 we %\ld h _h appall+ evid5ce ( ?is fact1 n only 9 ! viol5t w9ds :i* !y w\ld h produc$ 9 ! atmosph]e1 b 9 ! calamities !y w\ld h occasion$ on ! surface ( ! e>?4 ,! meteors 7 transp>5t bodies2 o!rwise1 we _c conceive :y ! body f :i* !y emanat$ 0 n di/9ctly visible1 at lea/ by reflect+ ! light ( ! sun4 ,if only ! meteors :i* 7 kn[n to fall t[>ds ! e>? _h be5 collect$ & re/or$ to _! orig9al connexion 9 space1 !y w\ld h compos$ a body ( great ext5t2 & we _c imag9e a body ( su* dim5sions1 "u su* circum/ances1 :i* w\ld n be visible1 unless =m$ ( highly transp>5t mat]ials4 ,by ^! unavoidable inf]5ces respect+ ! k9d ( matt] ( :i* ! meteors 7 compos$1 we are unexpect$ly l$ to recognise a body be>+1 9 its con/itution1 a /rong analogy to comets1 :i* are also compos$ ( exce$+ly light & transp>5t1 &1 z !re is mu* reason to believe1 ( combu/ible matt]4 ,we n[ arrive at ! f9al inquiry1 :at relations did ! body :i* af=d$ ! meteoric %[] su/a9 to ! e>?8 ,0 x ( ! nature ( a satellite1 or t]re/rial comet1 t revolves ar\nd ! e>? z its c5tre ( motion8 ,0 x a collection ( nebul\s1 or comet>y matt]1 :i* ! e>? enc\nt]$ 9 its annual progress8 or 0 x a comet1 :i* *anc$ at ?is "t to be pursu+ its pa? along ) ! e>?1 ar\nd _! common c5tre ( motion8 ,x c\ld n h be5 ( ! nature ( a satellite to ! e>?1 7or "o ( ^? bodies :i* are held by "s to af=d ! meteoric /ones1 :i* sometimes fall to ! e>? f huge meteors t trav]se ! atmosph]e17 because x rema9$ s long /ation>y ) respect to ! e>?4 ,a body s ne> ! e>? z meteors ( ?is class are kn[n to be1 c\ld n rema9 app>5tly /ation>y among ! />s = a mom5t2 :]eas ! body 9 "q occupi$ ! same position1 ) h>dly any p]ceptible v>iation1 = at lea/ two h\rs4 ,nor c we suppose t ! e>?1 9 its annual progress1 came into ! vic9ity ( a nebula1 :i* 0 ei!r /ation>y1 or w&]+ lawless ?r\gh space4 ,su* a collection ( matt] c\ld n rema9 /ation>y )9 ! sol> sy/em1 9 an insulat$ /ate1 =1 if n prev5t$ by a motion ( its own1 or by ! attraction ( "s ne>] body1 x w\ld h proce$$ directly t[>ds ! sun2 & _h x be5 9 motion 9 any o!r direction ?an t 9 :i* ! e>? 0 mov+1 x w\ld soon h be5 sep>at$ f ! e>?2 s9ce1 dur+ ! eight h\rs1 :ile ! meteoric %[] 0 visible1 ! e>? mov$ 9 its orbit ?r\gh ! space ( ne>ly five hundr$ & fifty ?\s& miles4 ,! =ego+ consid]ations conduct u to ! foll[+ tra9 ( reason+4 ,fir/1 if all ! meteors :i* fell on ! morn+ ( ,novemb] #ac1 #ahcc1 _h be5 collect$ & re/or$ to _! orig9al connexion 9 space1 !y w\ld ( !mselves h con/itut$ a nebul\s body ( great ext5t2 b we h reason to suppose t !y1 9 fact1 compos$ b a small "p ( ! mass f :i* !y emanat$1 s9ce1 aft] ! loss ( s mu* matt] z proce$$ f x 9 ! great meteoric %[] ( #agii1 & 9 ! sev]al repetitions ( x t prec$$ ! ye> #ahcc1 x 0 /ill capable ( af=d+ s copi\s a %[] on t ye>2 & simil> %[]s1 m limit$ 9 ext5t1 7 repeat$ = at lea/ five ye>s aft]w>ds4 ,we are !re=e to reg>d ! "p t desc5d$ only z ! extreme portions ( a body or collection ( meteors1 ( unkn[n ext5t1 exi/+ 9 ! planet>y spaces4 ,secondly1 s9ce ! e>? fell 9 ) ?is body 9 ! same "p ( its orbit1 = sev]al ye>s 9 succession1 x mu/ ei!r h rema9$ !re :ile ! e>? 0 p]=m+ its :ole revolution ar\nd ! sun1 or x mu/ itself h _h a revolution1 z well z ! e>?4 ,b ,i h already %[n t x c\ld n h rema9$ /ation>y 9 t "p ( space2 !re=e1 x mu/ h _h a revolution ar\nd ! sun4 ,?irdly1 its p]iod ( revolution mu/ h ei!r be5 great] ?an ! e>?'s1 equal to x1 or less4 ,x c\ld n h be5 great]1 = !n ! two bodies c\ld n h be5 toge!r aga9 at ! end ( ! ye>1 s9ce ! meteoric body w\ld n h complet$ its revolution 9 a ye>4 ,its p]iod might obvi\sly be ! same z ! e>?'s1 = !n !y might easily come toge!r aga9 aft] "o revolution ( ea*2 al?\gh _! orbits might diff] s mu* 9 %ape z to prev5t _! be+ toge!r at any int]m$iate po9t4 ,b ! p]iod ( ! body might also be less ?an t ( ! e>?1 provid$ x 7 "s aliquot "p ( a ye>1 s z to revolve j twice1 or ?ree times1 = example1 :ile ! e>? revolves once4 ,let u suppose t ! p]iod is "o ?ird ( a ye>4 ,!n1 s9ce we h giv5 ! p]iodic times ( ! two bodies1 & ! major axis ( ! orbit ( "o ( !m1 namely1 ( ! e>?1 we c1 by ,kepl]'s law1 f9d ! major axis ( ! o!r orbit2 = ! squ>e ( ! e>?'s p]iodic "t #ab is to ! squ>e ( ! body's "t 7#a_/c7b z ! cube ( ! major axis ( ! e>?'s orbit is to ! cube ( ! major axis ( ! orbit 9 "q4 ,n[1 ! ?ree fir/ t]ms ( ?is proportion are kn[n1 & consequ5tly1 x is only to solve a case 9 ! simple rule ( ?ree1 to f9d ! t]m requir$4 ,on mak+ ! calculation1 x is f\nd1 t ! supposition ( a p]iodic "t ( only "o ?ird ( a ye> gives an orbit ( insuffici5t l5g?2 ! :ole major axis w\ld n rea* f ! sun to ! e>?2 & consequ5tly1 a body revolv+ 9 x c\ld nev] come ne> to ! e>?4 ,on mak+ trial ( six mon?s1 we obta9 an orbit :i* satisfies ! conditions1 be+ su* z is repres5t$ by ! diagram on page #cfb1 ,fig4 #fi'1 :]e ! out] circle d5otes ! e>?'s orbit1 ! sun be+ 9 ! c5tre1 & ! inn] ellipse d5otes ! pa? ( ! meteoric body4 ,! two bodies are toge!r at ! top ( ! figure1 be+ ! place ( ! meteoric body's aphelion on ! ?irte5? ( ,novemb]1 & ! figures #aj1 #bj1 c41 d5ote ! relative positions ( ! e>? & ! body = e t5 days1 = a p]iod ( six mon?s1 9 :i* "t ! body w\ld h return$ to its aphelion4 ,illu/ration ,fig4 #fi'4 ,su* w\ld be ! relation ( ! body t af=ds ! meteoric %[] ( ,novemb]1 provid$ its revolution is accompli%$ 9 six mon?s2 b x is /ill some:at unc]ta9 :e!r ! p]iod be half a ye> or a ye>2 x mu/ be "o or ! o!r4 ,if we inquire1 n[1 :y ! meteors always appe> to radiate f a po9t 9 ! con/ellation ,leo1 recollect+ t ?is is ! po9t to :i* ! body is project$ among ! />s1 ! answ] is1 t ?is is ! v po9t t[>ds :i* ! e>? is mov+ 9 h] orbit at t "t2 s t if1 z we h prov$1 ! e>? pass$ ?r\gh or ne> a nebul\s body on ! ?irte5? ( ,novemb]1 t body mu/ necess>ily h be5 project$ into ! con/ellation ,leo1 else x c\ld n h la9 directly 9 h] pa?4 ,i consid] x !re=e z e/abli%$ by satisfactory pro(1 t ! meteors ( ,novemb] ?irte5? emanate f a nebul\s or comet>y body1 revolv+ ar\nd ! sun1 & com+ s ne> ! e>? at t "t t ! e>? passes ?r\gh its skirts1 or extreme portions1 & ?us attracts to itself "s portions ( its matt]1 giv+ to ! meteors a great] velocity ?an c\ld be imp>t$ by gravity alone1 9 consequ5ce ( pass+ rapidly by !m4 ,all ^! conclusions 7 made out by a process ( reason+ /rictly inductive1 )\t suppos+ t ! meteoric body itself _h ev] be5 se54 ,b !re are "s reasons = believ+ t we d actually see x1 & t x is no o!r ?an t my/]i\s appe>ance long kn[n "u ! "n ( ! zodiacal light4 ,?is is a fa9t light1 :i* at c]ta9 seasons ( ! ye> appe>s 9 ! we/ aft] ev5+ twilight1 & at c]ta9 o!r seasons appe>s 9 ! ea/ be=e ! dawn1 foll[+ or prec$+ ! track ( ! sun 9 a triangul> figure1 ) its broad base next to ! sun1 & its v]tex rea*+ to a great] or less di/ance1 sometimes m ?an n9ety degrees f t lum9>y4 ,y may obta9 a good view ( x 9 ,febru>y or ,m>*1 9 ! we/1 or 9 ,octob]1 9 ! morn+ sky4 ,! v>i\s *anges :i* ?is light und]goes at diff]5t seasons ( ! ye> are su* z to r5d] x probable1 to my m9d1 t ?is is ! v body :i* af=ds ! meteoric %[]s2 its extremity com+1 9 ,novemb]1 )9 ! sph]e ( ! e>?'s attraction4 ,b1 z ! argum5ts = ! exi/5ce ( a body 9 ! planet>y regions1 :i* af=ds ^! %[]s1 7 drawn )\t ! lea/ ref]5ce to ! zodiacal light1 & are good1 %\ld x f9ally be prov$ t ?is light has no connexion ) !m1 ,i w n occupy y\r att5tion ) ! discussion ( ?is po9t1 to ! exclusion ( topics :i* w probably int]e/ y m4 ,x is p]haps mo/ probable1 t ! meteoric %[]s ( ,augu/ & ,decemb] emanate f ! same body4 ,i "k ( no?+ repugnant to ?is conclusion1 al?\gh x has n yet be5 di/9ctly made out4 ,_h ! p]iods ( ! e>? & ( ! meteoric body be5 s adju/$ to ea* o!r t ! latt] 0 conta9$ an exact ev5 numb] ( times 9 ! =m]2 t is1 _h x be5 exactly ei!r a ye> or half a ye>2 !n we might expect a simil> recurr5ce ( ! meteoric %[] e ye>2 b only a slight v>iation 9 su* a proportion betwe5 ! two p]iods w\ld occasion ! repetition ( ! %[] = a few ye>s 9 succession1 & !n an int]mission ( !m1 = an unkn[n l5g? ( "t1 until ! two bodies 7 br\ght into ! same relative situation z be=e4 ,di/urbances1 also1 occasion$ by ! action ( ,v5us & ,m]cury1 might :olly subv]t ?is num]ical relation1 & increase or dim9i% ! probability ( a repetition ( ! ph5om5on4 ,accord+ly1 f ! ye> #ahcj1 :5 ! meteoric %[] ( ,novemb] 0 fir/ obs]v$1 until #ahcc1 !re 0 a regul> increase ( ! exhibition2 9 #ahcc1 x came to its maximum2 & aft] t "t x 0 repeat$ ^u a con/antly dim9i%+ scale1 until #ahch1 s9ce :i* "t x has n be5 obs]v$4 ,p]haps ages may roll away be=e ! _w w be aga9 surpris$ & delight$ ) a display ( cele/ial fire-works equal to t ( ! morn+ ( ,novemb] #ac1 #ahcc4 ,,lett] ,,xxviii4 ,,fix$ ,,/>s4 ----,o1 maje/ic ,night6 ,nature's great ance/or6 ,day's eld] born1 ,& fat$ to survive ! transi5t sun6 ,by mortals & immortals se5 ) awe6 ,a />ry cr[n ?y rav5 br[ adorns1 ,an azure zone ?y wai/2 cl\ds1 9 heav5's loom ,wr\ght1 ?r\gh v>ieties ( %ape & %ade1 ,9 ample folds ( drap]y div9e1 ,?y fl[+ mantle =m2 & heav5 ?r\gh\t ,volum9\sly p\r ?y pomp\s tra94--,"y4 ,,s9ce ! sol> sy/em is b "o among a myriad ( worlds :i* a/ronomy unfolds1 x may appe> to y t ,i h dwelt too long on s dim9utive a "p ( creation1 & res]v$ too little space = ! o!r sy/ems ( ! univ]se4 ,b h[ev] humble a prov9ce our sun & planets compose1 9 ! va/ empire ( ,jehovah1 yet x is t :i* mo/ conc]ns u2 & x is by ! /udy ( ! laws by :i* ?is "p ( creation is gov]n$1 t we le>n ! secrets ( ! skies4 ,until rec5tly1 ! obs]vation & /udy ( ! ph5om5a ( ! sol> sy/em almo/ exclusively occupi$ ! labors ( a/ronom]s4 ,b ,sir ,william ,h]s*el gave 8 *ief att5tion to ! sid]eal heav5s1 & op5$ new & wond]ful fields ( discov]y1 z well z ( speculation4 ,! same subject1 has be5 prosecut$ ) simil> zeal & success by 8 son1 ,sir ,john ,h]s*el1 & ,sir ,james ,s\?1 9 ,engl&1 & by ,pr(essor ,/ruve1 ( ,dorpat1 until m has be5 actually a*iev$ ?an prec$+ a/ronom]s _h v5tur$ to conjecture4 ,a limit$ sket* ( ^! wond]ful discov]ies is all t ,i propose to (f] y4 ,! fix$ />s are s call$1 because1 to common obs]vation1 !y always ma9ta9 ! same situations ) respect to "o ano!r4 ,! />s are class$ by _! app>5t magnitudes4 ,! :ole numb] ( magnitudes record$ are sixte51 ( :i* ! fir/ six only are visible to ! nak$ eye2 ! re/ are telescopic />s4 ,^! magnitudes are n det]m9$ by any v def9ite scale1 b are m]ely rank$ accord+ to _! relative degrees ( brightness1 & ?is is left 9 a great measure to ! decision ( ! eye alone4 ,! brighte/ />s1 to ! numb] ( fifte5 or tw5ty1 are consid]$ z />s ( ! fir/ magnitude2 ! fifty or sixty next brighte/1 ( ! second magnitude2 ! next two hundr$1 ( ! ?ird magnitude2 & ?us ! numb] ( ea* class increases rapidly1 z we desc5d ! scale1 s t no less ?an fifte5 or tw5ty ?\s& are includ$ )9 ! fir/ sev5 magnitudes4 ,! />s h be5 gr\p$ 9 con/ellations f ! mo/ remote antiquity2 a few1 z ,orion1 ,bootes1 & ,ursa ,major1 are m5tion$ 9 ! mo/ anci5t writ+s1 "u ! same names z !y be> at pres5t4 ,! names ( ! con/ellations are sometimes f\nd$ on a suppos$ resemblance to ! objects to :i* !y belong2 z ! ,swan & ! ,scorpion 7 evid5tly s d5om9at$ f _! lik5ess to ^? animals2 b 9 mo/ cases1 x is impossible = u to f9d any reason = designat+ a con/ellation by ! figure ( ! animal or h]o :i* is employ$ to repres5t x4 ,^! repres5tations 7 probably once bl5d$ ) ! fables ( pagan my?ology4 ,! same figures1 absurd z !y appe>1 are /ill reta9$ = ! conv5i5ce ( ref]5ce2 s9ce x is easy to f9d any p>ticul> />1 by specify+ ! "p ( ! figure to :i* x belongs2 z :5 we say1 a /> is 9 ! neck ( ,taurus1 9 ! knee ( ,h]cules1 or 9 ! tail ( ! ,great ,be>4 ,?is me?od furni%es a g5]al clue to its position2 b ! />s belong+ to any con/ellation are di/+ui%$ accord+ to _! app>5t magnitudes1 z foll[s3 ,fir/1 by ! ,greek lett]s1 ,alpha1 ,beta1 ,gamma1 c4 ,?us1 ,alpha ,orionis d5otes ! l>ge/ /> 9 ,orion2 ,beta ,&rom$ ! second /> 9 ,&rom$a2 & ,gamma ,leonis1 ! ?ird brighte/ /> 9 ! ,lion4 ,:5 ! numb] ( ! ,greek lett]s is insuffici5t to include all ! />s 9 a con/ellation1 rec\rse is _h to ! lett]s ( ! ,roman alphabet1 a1 b1 c1 c42 & 9 all cases :]e ^! are exhau/$ ! f9al resort is to numb]s4 ,?is is evid5tly necess>y1 s9ce ! l>ge/ con/ellations conta9 _m hundr$s or ev5 ?\s&s ( />s4 ,catalogues ( p>ticul> />s h also be5 publi%$1 by diff]5t a/ronom]s1 ea* au?or numb]+ ! individual />s embrac$ 9 8 li/ accord+ to ! places !y respectively occupy 9 ! catalogue4 ,^! ref]5ces to p>ticul> catalogues are sometimes ent]$ on l>ge cele/ial globes4 ,?us we meet ) a /> m>k$ #hd ,h41 mean+ t ?is is its numb] 9 ,h]s*el's catalogue2 or #adj ,m41 d5ot+ ! place ! /> occupies 9 ! catalogue ( ,may]4 ,! e>lie/ catalogue ( ! />s 0 made by ,hipp>*us1 ( ! ,alex&rian s*ool1 ab\t "o hundr$ & =ty ye>s be=e ! ,*ri/ian era4 ,a new /> appe>+ 9 ! firmam5t1 he 0 induc$ to c\nt ! />s1 & to record _! positions1 9 ord] t po/]ity might be able to judge ( ! p]man5cy ( ! con/ellations4 ,8 catalogue conta9s all t 7 conspicu\s to ! nak$ eye 9 ! latitude ( ,alex&ria1 be+ "o ?\s& & tw5ty-two4 ,mo/ p]sons1 unacqua9t$ ) ! actual numb] ( ! />s :i* compose ! visible firmam5t1 w\ld suppose x to be mu* great] ?an ?is2 b x is f\nd t ! catalogue ( ,hipp>*us embraces ne>ly all t c n[ be se5 9 ! same latitude2 & t on ! equator1 :]e ! spectator has bo? ! nor!rn & s\!rn hemisph]es 9 view1 ! numb] ( />s t c be c\nt$ does n exce$ ?ree ?\s&4 ,a c>eless view ( ! firmam5t 9 a cle> night gives u ! impression ( an inf9ite numb] ( />s2 b :5 we beg9 to c\nt !m1 !y appe> mu* m sp>sely di/ribut$ ?an we suppos$1 & l>ge portions ( ! sky appe> almo/ de/itute ( />s4 ,by ! aid ( ! telescope1 new fields ( />s pres5t !mselves1 ( b\ndless ext5t2 ! numb] cont9ually augm5t+1 z ! p[]s ( ! telescope are increas$4 ,lal&e1 9 8 ',hi/oire ,cele/e1' has regi/]$ ! positions ( no less ?an fifty ?\s&2 & ! :ole numb] visible 9 ! l>ge/ telescopes am\nts to _m millions4 ,:5 y look at ! firmam5t on a cle> ,autumnal or ,w9t] ev5+1 x appe>s s ?ickly /udd$ ) />s1 t y w\ld p]haps imag9e t ! task ( le>n+ ev5 ! brighte/ ( !m w\ld be almo/ hopeless4 ,let me assure y1 ?is is all a mi/ake4 ,on ! contr>y1 x is a v easy task to become acqua9t$ ) ! names & positions ( ! />s ( ! fir/ magnitude1 & ( ! lead+ con/ellations4 ,if y w give a few ev5+s to ! /udy1 y w be surpris$ to f9d1 bo? h[ rapidly y c =m ^! new acqua9tances1 & h[ deeply y w become int]e/$ 9 !m4 ,i w\ld advise y1 at fir/1 to obta91 = an ev5+ or two1 ! assi/ance ( "s fri5d :o is famili> ) ! />s1 j to po9t out a few ( ! mo/ conspicu\s con/ellations4 ,?is w put y on ! track1 & y w aft]w>ds exp]i5ce no difficulty 9 f9d+ all ! con/ellations & />s t are p>ticul>ly wor? kn[+2 especially if y h be=e y a map ( ! />s1 or1 :at is mu* bett]1 a cele/ial globe4 ,x is a pleasant ev5+ recreation = a small company ( "y a/ronom]s to g out toge!r1 & le>n "o or two con/ellations e favorable ev5+1 until ! :ole are ma/]$4 ,if y h a cele/ial globe1 rectify x = ! ev5+2 t is1 place x 9 su* a position1 t ! con/ellations %all be se5 on x 9 ! same position ) respect to ! horizon1 t !y h at t mom5t 9 ! sky itself4 ,to d ?is1 ,i fir/ elevate ! nor? pole until ! numb] ( degrees on ! brass m]idian f ! pole to ! horizon corresponds to my latitude1 7=ty-"o degrees & eighte5 m9utes47 ,i !n f9d ! sun's place 9 ! ecliptic1 by look+ = ! day ( ! mon? on ! broad horizon1 & aga9/ x not+ ! correspond+ sign & degree4 ,i n[ f9d ! same sign & degree on ! ecliptic itself1 & br+ t po9t to ! brass m]idian4 ,z t w be ! position ( ! sun at noon1 ,i set ! h\r-index at twelve1 & !n turn ! globe we/w>d1 until ! index po9ts to ! giv5 h\r ( ! ev5+4 ,if ,i n[ inspect ! figures ( ! con/ellations1 & !n look upw>d at ! firmam5t1 ,i %all see t ! latt] are spread ov] ! sky 9 ! same mann] z ! pictures ( !m are pa9t$ on ! globe4 ,i w po9t out a few m>ks by :i* ! lead+ con/ellations may be recognis$2 ?is w aid y 9 f9d+ !m1 & y c aft]w>ds le>n ! individual />s ( a con/ellation1 to any ext5t y please1 by means ( ! globes or maps4 ,let u beg9 ) ! ,con/ellations ( ! ,zodiac1 :i*1 succe$+ ea* o!r1 z !y d1 9 a kn[n ord]1 are mo/ easily f\nd4 ,aries 7! ,ram7 is a small con/ellation1 kn[n by two bright />s :i* =m 8 head1 ,alpha & ,beta ,arietis4 ,^! two />s are ab\t f\r degrees ap>t2 & directly s\? ( ,beta1 at ! di/ance ( "o degree1 is a small] />1 ,gamma ,arietis4 ,x has be5 already intimat$ t ! ,v]nal equ9ox probably 0 ne> ! head ( ,aries1 :5 ! signs ( ! zodiac receiv$ _! pres5t names4 ,taurus 7! ,bull7 w be readily f\nd by ! sev5 />s1 or ,pleiades1 :i* lie 9 8 neck4 ,! l>ge/ /> 9 ,taurus is ,aldeb>an1 9 ! ,bull's eye1 a /> ( ! fir/ magnitude1 ( a r$di% color1 some:at resembl+ ! planet ,m>s4 ,aldeb>an & f\r o!r />s1 close toge!r 9 ! face ( ,taurus1 compose ! ,hyades4 ,gem9i 7! ,tw9s7 is kn[n by two v bright />s1 ,ca/or & ,pollux1 five degrees asund]4 ,ca/or 7! nor!rn7 is ( ! fir/1 & ,pollux ( ! second1 magnitude4 ,canc] 7! ,crab47 ,!re are no l>ge />s 9 ?is con/ellation1 & x is reg>d$ z less rem>kable ?an any o!r 9 ! zodiac4 ,x conta9s1 h[ev]1 an int]e/+ gr\p ( small />s1 call$ ,prsepe1 or ! nebula ( ,canc]1 :i* resembles a comet1 & is (t5 mi/ak5 = "o1 by p]sons unacqua9t$ ) ! />s4 ,) a telescope ( v mod]ate p[]s ?is nebula is conv]t$ into a beautiful assemblage ( exce$+ly bright />s4 ,leo 7! ,lion7 is a v l>ge con/ellation1 & has _m int]e/+ memb]s4 ,regulus 7,alpha ,leonis7 is a /> ( ! fir/ magnitude1 :i* lies directly 9 ! ecliptic1 & is mu* us$ 9 a/ronomical obs]vations4 ,nor? ( ,regulus1 lies a semicircle ( bright />s1 =m+ a sickle1 ( :i* ,regulus is ! h&le4 ,d5ebola1 a /> ( ! second magnitude1 is 9 ! ,lion's tail1 tw5ty-five degrees nor!a/ ( ,regulus4 ,virgo 7! ,virg97 ext5ds a consid]able way f we/ to ea/1 b conta9s only a few bright />s4 ,spica1 h[ev]1 is a /> ( ! fir/ magnitude1 & lies a little ea/ ( ! place ( ! ,autumnal equ9ox4 ,eighte5 degrees ea/w>d ( ,d5ebola1 & tw5ty degrees nor? ( ,spica1 is ,v9demiatrix1 9 ! arm ( ,virgo1 a /> ( ! ?ird magnitude4 ,libra 7! ,balance7 is di/+ui%$ by ?ree l>ge />s1 ( :i* ! two brighte/ con/itute ! beam ( ! balance1 & ! smalle/ =ms ! top or h&le4 ,scorpio 7! ,scorpion7 is "o ( ! f9e/ ( ! con/ellations4 ,8 head is =m$ ( five bright />s1 arrang$ 9 ! arc ( a circle1 :i* is cross$ 9 ! c5tre by ! ecliptic ne>ly at "r angles1 ne> ! brighte/ ( ! five1 ,beta ,scorpionis4 ,n9e degrees s\!a/ ( ?is is a rem>kable /> ( ! fir/ magnitude1 ( a r$di% color1 call$ ,cor ,scorpionis1 or ,ant>es4 ,s\? ( ?is1 a succession ( bright />s sweep r\nd t[>ds ! ea/1 t]m9at+ 9 sev]al small />s1 =m+ ! tail ( ! ,scorpion4 ,sagitt>ius 7! ,ar*]47 ,nor!a/ ( ! tail ( ! ,scorpion are ?ree />s 9 ! arc ( a circle1 :i* con/itute ! b[ ( ! ,ar*]1 ! c5tral /> be+ ! brighte/1 directly we/ ( :i* is a bright /> :i* =ms ! arr[4 ,capricornus 7! ,goat7 lies nor!a/ ( ,sagitt>ius1 & is kn[n by two bright />s1 ?ree degrees ap>t1 :i* =m ! head4 ,aqu>ius 7! ,wat]-,be>]7 is recognis$ by two />s 9 a l9e ) ,alpha ,capricorni1 =m+ ! %\ld]s ( ! figure4 ,^! two />s are t5 degrees ap>t2 & ?ree degrees s\!a/ is a ?ird />1 :i*1 toge!r ) ! o!r two1 make an acute triangle1 ( :i* ! we/]nmo/ is ! v]tex4 ,pisces 7! ,fi%es7 lie betwe5 ,aqu>ius & ,aries4 ,!y are n di/+ui%$ by any l>ge />s1 b are connect$ by a s]ies ( small />s1 t =m a crook$ l9e betwe5 !m4 ,piscis ,au/ralia1 ! ,s\!rn ,fi%1 lies directly bel[ ,aqu>ius1 & is kn[n by a s+le bright /> f> 9 ! s\?1 hav+ a decl9ation ( ?irty degrees4 ,! "n ( ?is /> is ,fomalhaut1 & x is mu* us$ 9 a/ronomical measurem5ts4 ,! con/ellations ( ! zodiac1 be+ fir/ well le>n$1 s z to be readily recognis$1 w facilitate ! le>n+ ( o!rs t lie nor? & s\? ( !m4 ,let u1 !re=e1 next review ! pr9cipal ,nor!rn ,con/ellations1 beg9n+ nor? ( ,aries1 & proce$+ f we/ to ea/4 ,&rom$a is *>act]iz$ by ?ree />s ( ! second magnitude1 situat$ 9 a /raight l9e1 ext5d+ f we/ to ea/4 ,! middle /> is ab\t sev5te5 degrees nor? ( ,beta ,arietis4 ,x is 9 ! girdle ( ,&rom$a1 & is nam$ ,mira*4 ,! o!r two lie at ab\t equal di/ances1 f\rte5 degrees we/ & ea/ ( ,mira*4 ,! we/]n />1 9 ! head ( ,&rom$a1 lies 9 ! equ9octial colure4 ,! ea/]n />1 ,alamak1 is situat$ 9 ! foot4 ,p]seus lies directly nor? ( ! ,pleiades1 & conta9s sev]al bright />s4 ,ab\t eighte5 degrees f ! ,pleiades is ,algol1 a /> ( ! second magnitude1 9 ! head ( ,m$usa1 :i* =ms a "p ( ! figure2 & n9e degrees nor!a/ ( ,algol is ,alg5ib1 ( ! same magnitude1 9 ! back ( ,p]seus4 ,betwe5 ,alg5ib & ! ,pleiades are ?ree bright />s1 at ne>ly equal int]vals1 :i* compose ! "r leg ( ,p]seus4 ,auriga 7! ,wagon]7 lies directly ea/ ( ,p]seus1 & ext5ds ne>ly p>allel to t con/ellation1 f nor? to s\?4 ,capella1 a v :ite & beautiful /> ( ! fir/ magnitude1 di/+ui%es ?is con/ellation4 ,! feet ( ,auriga are ne> ! ,bull's horns4 ,! ,lynx comes next1 b pres5ts no?+ p>ticul>ly int]e/+1 conta9+ no />s above ! f\r? magnitude4 ,leo ,m9or consi/s ( a collection ( small />s nor? ( ! sickle 9 ,leo1 & s\? ( ! ,great ,be>4 ,its l>ge/ /> is only ( ! ?ird magnitude4 ,coma ,b]5ices is a clu/] ( small />s1 nor? ( ,d5ebola1 9 ! tail ( ! ,lion1 & ( ! head ( ,virgo4 ,ab\t twelve degrees directly nor? ( ,b]5ice's hair1 is a s+le bright />1 call$ ,cor ,c>oli1 or ,*>les's ,he>t4 ,bootes1 :i* comes next1 is easily f\nd by means ( ,arcturus1 a /> ( ! fir/ magnitude1 ( a r$di% color1 :i* is situat$ ne> ! knee ( ! figure4 ,arcturus is accompani$ by ?ree small />s1 =m+ a triangle a little to ! s\?we/4 ,two bright />s1 ,gamma & ,delta ,bootis1 =m ! %\ld]s1 & ,beta1 ( ! ?ird magnitude1 is 9 ! head1 ( ! figure4 ,corona ,borealis1 7! ,cr[n17 :i* is situat$ ea/ ( ,bootes1 is v easily recognis$1 compos$ z x is ( a semicircle ( bright />s4 ,9 ! c5tre ( ! bright cr[n is a /> ( ! second magnitude1 call$ ,gemma3 ! rema9+ />s are all mu* small]4 ,h]cules1 ly+ betwe5 ! ,cr[n on ! we/ & ! ,lyre on ! ea/1 is v ?ickly set ) />s1 mo/ ( :i* are q small4 ,?is con/ellation cov]s a great ext5t ( ! sky1 especially f nor? to s\?1 ! head t]m9at+ )9 fifte5 degrees ( ! equator1 & m>k$ by a /> ( ! ?ird magnitude1 call$ ,ras ,alge?i1 :i* is ! l>ge/ 9 ! con/ellation4 ,ophiucus is situat$ directly s\? ( ,h]cules1 ext5d+ "s di/ance on bo? sides ( ! equator1 ! feet re/+ on ! ,scorpion4 ,! head t]m9ates ne> ! head ( ,h]cules1 &1 l t1 is m>k$ by a bright /> )9 five degrees ( ,alpha ,h]culis ,ophiucus is repres5t$ z hold+ 9 8 h&s ! ,s]p5t1 ! head ( :i*1 consi/+ ( ?ree bright />s1 is situat$ a little s\? ( ! ,cr[n4 ,! folds ( ! s]p5t w be easily foll[$ by a succession ( bright />s1 :i* ext5d a great way to ! ea/4 ,aquila 7! ,eagle7 is conspicu\s = ?ree bright />s 9 its neck1 ( :i* ! c5tral "o1 ,altair1 is a v brilliant :ite /> ( ! fir/ magnitude4 ,ant9\s lies directly s\? ( ! ,eagle1 & nor? ( ! head ( ,capricornus4 ,delph9us 7! ,dolph97 is a small b beautiful con/ellation1 a few degrees ea/ ( ! ,eagle1 & is *>act]iz$ by f\r bright />s ne> to "o ano!r1 =m+ a small rhombic squ>e4 ,ano!r /> ( ! same magnitude1 five degrees s\?1 makes ! tail4 ,pegasus lies betwe5 ,aqu>ius on ! s\?we/ & ,&rom$a on ! nor!a/4 ,x conta9s b few l>ge />s4 ,a v regul> squ>e ( bright />s is compos$ ( ,alpha ,&rom$ & ! ?ree l>ge/ />s 9 ,pegasus2 namely1 ,s*eat1 ,m>kab1 & ,alg5ib4 ,! sides compos+ ?is squ>e are ea* ab\t fifte5 degrees4 ,alg5ib is situat$ 9 ! equ9octial colure4 ,we may n[ review ! ,con/ellations :i* surr\nd ! nor? pole1 )9 ! circle ( p]petual app>ition4 ,ursa ,m9or 7! ,little ,be>7 lies ne>e/ ! pole4 ,! pole-/>1 ,pol>is1 is 9 ! extremity ( ! tail1 & is ( ! ?ird magnitude4 ,?ree />s 9 a /raight l9e1 f\r degrees or five degrees ap>t1 comm5c+ ) ! pole-/>1 lead to a trapezium ( f\r />s1 & ! :ole sev5 =m toge!r a dipp]1--! trapezium be+ ! body & ! ?ree />s ! h&le4 ,ursa ,major 7! ,great ,be>7 is situat$ betwe5 ! pole & ! ,less] ,lion1 & is usually recognis$ by ! figure ( a l>g] & m p]fect dipp] :i* con/itutes ! h9d] "p ( ! animal4 ,?is has also sev5 />s1 f\r 9 ! body ( ! ,dipp] & ?ree 9 ! h&le4 ,all ^! are />s ( mu* celebrity4 ,! two 9 ! we/]n side ( ! ,dipp]1 ,alpha & ,beta1 are call$ ,po9t]s1 on acc\nt ( _! always be+ 9 a "r l9e ) ! pole-/>1 & !re=e af=d+ an easy mode ( f9d+ t4 ,! fir/ /> 9 ! tail1 next ! body1 is nam$ ,alio?1 & ! second1 ,miz>4 ,! head ( ! ,great ,be> lies f> to ! we/w>d ( ! ,po9t]s1 & is compos$ ( num]\s small />s2 & ! feet are sev]ally compos$ ( two small />s v ne> to ea* o!r4 ,draco 7! ,dragon7 w9ds r\nd betwe5 ! ,great & ! ,little ,be>2 &1 comm5c+ ) ! tail1 betwe5 ! ,po9t]s & ! pole-/>1 x is easily trac$ by a succession ( bright />s ext5d+ f we/ to ea/4 ,pass+ "u ,ursa ,m9or1 x returns we/w>d1 & t]m9ates 9 a triangle :i* =ms ! head ( ,draco1 ne> ! feet ( ,h]cules1 nor?we/ ( ,lyra4 ,cepheus lies ea/w>d ( ! brea/ ( ! ,dragon1 b has no />s above ! ?ird magnitude4 ,cassiopeia is kn[n by ! figure ( a *air1 compos$ ( f\r />s :i* =m ! legs1 & two :i* =m ! back4 ,?is con/ellation lies betwe5 ,p]seus & ,cepheus1 9 ! ,milky ,way4 ,cygnus 7! ,swan7 is situat$ also 9 ! ,milky ,way1 "s di/ance s\?we/ ( ,cassiopeia1 t[>ds ! ,eagle4 ,?ree bright />s1 :i* lie along ! ,milky ,way1 =m ! body & neck ( ! ,swan1 & two o!rs1 9 a l9e ) ! middle "o ( ! ?ree1 "o above & "o bel[1 con/itute ! w+s4 ,?is con/ellation is among ! few t exhibit "s resemblance to ! animals ^: names !y be>4 ,lyra 7! ,lyre7 is directly we/ ( ! ,swan1 & is easily di/+ui%$ by a beautiful :ite /> ( ! fir/ magnitude1 ,alpha ,lyr4 ,! ,s\!rn ,con/ellations are comp>atively few 9 numb]4 ,i %all notice only ! ,:ale1 ,orion1 ! ,great] & ,less] ,dog1 ,hydra1 & ! ,cr[4 ,cetus 7! ,:ale7 is di/+ui%$ r = its ext5t ?an its brilliancy1 rea*+ z x does ?r\gh =ty degrees ( longitude1 :ile none ( its />s1 except "o1 are above ! ?ird magnitude4 ,m5k> 7,alpha ,ceti7 9 ! m\?1 is a /> ( ! second magnitude2 & sev]al o!r bright />s1 directly s\? ( ,aries1 make ! head & neck ( ! ,:ale4 ,mira1 7,omicron ,ceti17 9 ! neck ( ! ,:ale1 is a v>iable />4 ,orion is "o ( ! l>ge/ & mo/ beautiful ( ! con/ellations1 ly+ s\!a/ ( ,taurus4 ,a clu/] ( small />s =ms ! head2 two l>ge />s1 ,betalgeus ( ! fir/ & ,bellatrix ( ! second magnitude1 make ! %\ld]s2 ?ree m bright />s compose ! buckl]1 & ?ree ! sword2 & ,rigel1 ano!r /> ( ! fir/ magnitude1 makes "o ( ! feet4 ,9 ?is con/ellation !re are sev5ty />s pla9ly visible to ! nak$ eye1 includ+ two ( ! fir/ magnitude1 f\r ( ! second1 & ?ree ( ! ?ird4 ,canis ,major lies s\!a/ ( ,orion1 & is di/+ui%$ *iefly by its conta9+ ! l>ge/ ( ! fix$ />s1 ,sirius4 ,canis ,m9or1 a little nor? ( ! equator1 betwe5 ,canis ,major & ,gem9i1 is a small con/ellation1 consi/+ *iefly ( two />s1 ( :i*1 ,procyon is ( ! fir/ magnitude4 ,hydra has its head ne> ,procyon1 consi/+ ( a numb] ( />s ( ord9>y brightness4 ,ab\t fifte5 degrees s\!a/ ( ! head is a /> ( ! second magnitude1 =m+ ! he>t1 7,cor ,hydr27 & ea/w>d ( ?is is a long succession ( />s ( ! f\r? & fif? magnitudes1 compos+ ! body & tail1 & rea*+ a few degrees s\? ( ,spica ,virg9is4 ,corvus 7! ,cr[7 is repres5t$ z /&+ on ! tail ( ,hydra4 ,x consi/s ( small />s1 only ?ree ( :i* are z l>ge z ! ?ird magnitude4 ,9 assign+ ! places ( individual />s1 ,i h n aim$ at great precision2 b su* a k z y w acquire ( ! con/ellations & l>g] />s1 by no?+ m ev5 ?an y c obta9 f ! =ego+ sket*1 w n only add greatly to ! int]e/ ) :i* y w ev] aft]w>ds look at ! />ry heav5s1 b x w enable y to locate any ph5om5on t may pres5t itself 9 ! nocturnal sky1 & to und]/& ! position ( any object t may be describ$1 by assign+ its true place among ! />s2 al?\gh ,i hope y w g mu* fur!r ?an ?is m]e outl9e1 9 cultivat+ an actual acqua9tance ) ! />s4 ,leav+1 n[1 ^! great divisions ( ! bodies ( ! firmam5t1 let u asc5d to ! next ord] ( />s1 compos+ ,,clu/]s4 ,9 v>i\s p>ts ( ! nocturnal heav5s are se5 l>ge gr\ps :i*1 ei!r by ! nak$ eye1 or by ! aid ( ! smalle/ telescope1 are p]ceiv$ to consi/ ( a great numb] ( small />s4 ,su* are ! ,pleiades1 ,coma ,b]5ices1 & ,prsepe1 or ! ,bee-hive1 9 ,canc]4 ,! ,pleiades1 or ,sev5 ,/>s1 z !y are call$1 9 ! neck ( ,taurus1 is ! mo/ conspicu\s clu/]4 ,:5 we look directly at ?is gr\p1 we _c di/+ui% m ?an six />s2 b by turn+ ! eye sideways ^u x1 we discov] t !re are _m m2 = x is a rem>kable fact t indirect vision is f> m delicate ?an direct4 ,?us we c see ! zodiacal light or a comet's tail mu* m di/9ctly & bett] def9$1 if we fix "o eye on a "p ( ! heav5s at "s di/ance & turn ! o!r eye obliquely ^u ! object1 ?an we c by look+ directly t[>ds x4 ,telescopes %[ ! ,pleiades to conta9 fifty or sixty />s1 cr[d$ toge!r1 & app>5tly insulat$ f ! o!r p>ts ( ! heav5s4 ,coma ,b]5ices has few] />s1 b !y are ( a l>g] class ?an ^? :i* compose ! ,pleiades4 ,! ,bee-hive1 or ,nebula ( ,canc]1 z x is call$1 is "o ( ! f9e/ objects ( ?is k9d = a small telescope1 be+ by its aid conv]t$ into a ri* cong]ies ( %9+ po9ts4 ,! head ( ,orion af=ds an example ( ano!r clu/]1 ?\gh less rem>kable ?an ^? already m5tion$4 ,^! clu/]s are pleas+ objects to ! telescope2 & s9ce a common spyglass w s]ve to give a di/9ct view ( mo/ ( !m1 e "o may h ! p[] ( tak+ ! view4 ,b we pass1 n[1 to ! ?ird ord] ( />s1 :i* pres5t !mselves mu* m obscurely to ! gaze ( ! a/ronom]1 & require l>ge in/rum5ts = ! full developem5t ( _! wond]ful organization4 ,^! are ! ,,nebul4 ,illu/ration ,figures #gj1 #ga1 #gb1 #gc4 ,,clu/]s ,,( ,,/>s ,,& ,,nebul4 ,nebul are fa9t mi/y appe>ances :i* are dimly se5 among ! />s1 resembl+ comets1 or a speck ( fog4 ,!y are usually resolv$ by ! telescope into myriads ( small />s2 ?\gh 9 "s in/ances1 no p[]s ( ! telescope h be5 f\nd suffici5t ?us to resolve !m4 ,! ,galaxy or ,milky ,way1 pres5ts a cont9u$ succession ( l>ge nebulas4 ,! telescope reveals to u innum]able objects ( ?is k9d4 ,sir ,william ,h]s*el has giv5 catalogues ( two ?\s& nebul1 & has %[n t ! nebul\s matt] is di/ribut$ ?r\gh ! imm5sity ( space 9 quantities inconceivably great1 & 9 sep>ate p>cels1 ( all %apes & sizes1 & ( all degrees ( brightness betwe5 a m]e milky appe>ance & ! cond5s$ light ( a fix$ />4 ,9 fact1 m di/9ct nebul h be5 hunt$ out by ! aid ( telescopes ?an ! :ole numb] ( />s visible to ! nak$ eye 9 a cle> ,w9t]'s night4 ,_! appe>ances are extremely div]sifi$4 ,9 _m ( !m we c easily di/+ui% ! individual />s2 9 ^? app>5tly m remote1 ! int]val betwe5 ! />s dim9i%es1 until x becomes q imp]ceptible2 & 9 _! fa9te/ aspect !y dw9dle to po9ts s m9ute1 z to be appropriately d5om9at$ />-du/4 ,beyond ?is1 no />s are di/9ctly visible1 b only /reaks or pat*es ( milky light4 ,! diagram fac+ page #cgi repres5ts a magnific5t nebula 9 ! ,galaxy4 ,9 objects s di/ant z ! fix$ />s1 any app>5t int]val mu/ d5ote an imm5se space2 & j imag9e y\rself situat$ any :]e )9 ! gr& assemblage ( />s1 & a firmam5t w\ld exp& itself ov] y\r head l t ( our ev5+ sky1 only a ?\s& times m ri* & spl5did4 ,_m ( ! nebul exhibit a t5d5cy t[>ds a globul> =m1 & indicate a rapid cond5sation t[>ds ! c5tre4 ,?is *>act]i/ic is exhibit$ 9 ! =ms repres5t$ 9 ,figs4 #gj & #ga4 ,we h "h two specim5s ( nebul ( ! ne>] class1 :]e ! />s are easily discrim9at$4 ,9 ,figs4 #gb & #gc we h examples ( two o!rs ( ! remot] k9d1 "o ( :i* is ( ! v>iety call$ />-du/4 ,^! wond]ful objects1 h[ev]1 are n conf9$ to ! sph]ical =m1 b exhibit great v>ieties ( figure4 ,sometimes !y appe> z ovals2 sometimes !y are %ap$ l a fan2 & ! unresolvable k9d (t5 affect ! mo/ fanta/ic =ms4 ,! opposite diagram1 ,fig4 #gd1 z well z ! prec$+1 af=ds a specim5 ( ^! v>ieties1 z giv5 9 ,pr(essor ,ni*ols's ',ar*itecture ( ! ,heav5s1' :]e !y are fai?fully copi$ f ! pap]s ( ,h]s*el1 9 ! ',philosophical ,transactions4' ,illu/ration ,figure #gd4 ,,v>i\s ,,=ms ,,( ,,nebul4 ,sir ,john ,h]s*el has rec5tly return$ f a resid5ce ( five ye>s at ! ,cape ( ,good ,hope1 ) ! express view ( explor+ ! hidd5 treasures ( ! s\!rn hemisph]e4 ,! k9ds ( nebul are 9 g5]al simil> to ^? ( ! nor!rn hemisph]e1 & ! =ms are equally v>i\s & s+ul>4 ,! ,magellan ,cl\ds1 two rem>kable objects se5 among ! />s ( t hemisph]e1 & celebrat$ among navigators1 appe>$ to ! great telescope ( ,h]s*el 7z we are in=m$ by ,pr(essor ,ni*ols7 no long] z simple milky spots1 or p]man5t light flocculi ( cl\d1 z !y appe> to ! unassi/$ eye1 b %one ) inconceivable spl5dor4 ,! ,nubecula ,major1 z ! l>g] object is call$1 is a cong]ies ( clu/]s ( />s1 ( irregul> =m1 globul> clu/]s & nebul ( v>i\s magnitudes & degrees ( cond5sation1 among :i* is int]sp]s$ a l>ge portion ( irresolvable nebul\s matt]1 :i* may be1 & probably is1 />-du/1 b :i* ! p[] ( ! tw5ty-feet telescope %[s only z a g5]al illum9ation ( ! field ( view1 =m+ a bright gr\nd on :i* ! o!r objects are scatt]$4 ,! ,nubecula ,m9or 7! less] cl\d7 exhibit$ appe>ances simil>1 ?\gh inf]ior 9 degree4 ,illu/ration ,figure #ge4 ,a ,,nebula ,,9 ,,! ,,milky ,,way4 ,x is a gr& idea1 fir/ conceiv$ by ,sir ,william ,h]s*el1 & g5]ally adopt$ by a/ronom]s1 t ! :ole ,galaxy1 or ,milky ,way1 is no?+ else ?an a nebula1 & appe>s s ext5d$1 m]ely because x happ5s to be t p>ticul> nebula to :i* we belong4 ,accord+ to ?is view1 our sun1 ) 8 att5dant planets & comets1 con/itutes b a s+le /> ( ! ,galaxy1 & our firmam5t ( />s1 or visible heav5s1 is compos$ ( ! />s ( our nebula alone4 ,an inhabitant ( any ( ! o!r nebul w\ld see spread+ ov] him a firmam5t equally spaci\s1 & 9 "s cases inconceivably m brilliant4 ,x is an exalt$ spectacle to travel ov] ! ,galaxy 9 a cle> night1 ) a p[]ful telescope1 ) ! he>t full ( ! idea t e /> is a _w4 ,sir ,william ,h]s*el1 by c\nt+ ! />s 9 a s+le field ( 8 telescope1 e/imat$ t fifty ?\s& _h pass$ "u 8 review 9 a zone two degrees 9 bread?1 dur+ a s+le h\r's obs]vation4 ,not)/&+ ! app>5t contiguity ( ! />s :i* cr[d ! ,galaxy1 x is c]ta9 t _! mutual di/ances mu/ be inconceivably great4 ,x is ) "s reluctance t ,i leave1 = ! pres5t1 ?is fairy l& ( a/ronomy2 b ,i mu/ n omit1 be=e br++ ^! ,lett]s to a conclusion1 to tell y some?+ respect+ o!r curi\s & int]e/+ objects to be f\nd among ! />s4 ,,v>iable ,,/>s are ^? :i* und]go a p]iodical *ange ( brightness4 ,"o ( ! mo/ rem>kable is ! /> ,mira1 9 ! ,:ale1 7,omicron ,ceti47 ,x appe>s once 9 elev5 mon?s1 rema9s at its greate/ brightness ab\t a =tnight1 be+ !n1 on "s occasions1 equal to a /> ( ! second magnitude4 ,x !n decreases ab\t ?ree mon?s1 until x becomes completely invisible1 & rema9s s ab\t five mon?s1 :5 x aga9 becomes visible1 & cont9ues increas+ dur+ ! rema9+ ?ree mon?s ( its p]iod4 ,ano!r v rem>kable v>iable /> is ,algol1 7,beta ,p]sei47 ,x is usually visible z a /> ( ! second magnitude1 & cont9ues su* = two days & f\rte5 h\rs1 :5 x sudd5ly beg9s to dim9i% 9 spl5dor1 & 9 ab\t ?ree & a half h\rs is r$uc$ to ! f\r? magnitude4 ,x !n beg9s aga9 to increase1 & 9 ?ree & a half h\rs m is re/or$ to its usual brightness1 go+ ?r\gh all its *anges 9 less ?an ?ree days4 ,?is rem>kable law ( v>iation appe>s /rongly to sugge/ ! revolution r\nd x ( "s opaque body1 :i*1 :5 int]pos$ betwe5 u & ,algol1 cuts (f a l>ge portion ( its light4 ,x is1 says ,sir ,j4 ,h]s*el1 an indication ( a high degree ( activity 9 regions :]e1 b = su* evid5ces1 we might conclude all lifeless4 ,our sun requires almo/ n9e times ?is p]iod to p]=m a revolution on its axis4 ,on ! o!r h&1 ! p]iodic "t ( an opaque revolv+ body1 suffici5tly l>ge1 :i* w\ld produce a simil> tempor>y obscuration ( ! sun1 se5 f a fix$ />1 w\ld be less ?an f\rte5 h\rs4 ,! duration ( ^! p]iods is extremely v>i\s4 ,:ile t ( ,beta ,p]sei1 above m5tion$1 is less ?an ?ree days1 o!rs are m ?an a ye>2 & o!rs1 _m ye>s4 ,,tempor>y ,,/>s are new />s1 :i* h appe>$ sudd5ly 9 ! firmam5t1 &1 aft] a c]ta9 int]val1 z sudd5ly disappe>$1 & return$ no m4 ,x 0 ! appe>ance ( a new /> ( ?is k9d1 "o hundr$ & tw5ty-five ye>s be=e ! ,*ri/ian era1 t prompt$ ,hipp>*us to draw up a catalogue ( ! />s1 ! fir/ on record4 ,su*1 also1 0 ! /> :i* sudd5ly %one out1 ,a4,d4 #chi1 9 ! ,eagle1 z bright z ,v5us1 &1 aft] rema9+ ?ree weeks1 disappe>$ entirely4 ,at o!r p]iods1 at di/ant int]vals1 simil> ph5om5a h pres5t$ !mselves4 ,?us ! appe>ance ( a /> 9 #aegb 0 s sudd51 t ,ty*o ,brahe1 return+ home "o day1 0 surpris$ to f9d a collection ( c\ntry p gaz+ at a /> :i* he 0 sure did n exi/ half an h\r be=e4 ,x 0 !n z bright z ,sirius1 & cont9u$ to increase until x surpass$ ,jupit] :5 brighte/1 & 0 visible at mid-day4 ,9 a mon? x began to dim9i%2 &1 9 ?ree mon?s aft]w>ds1 x _h entirely disappe>$4 ,x has be5 suppos$ by "s t1 9 a few in/ances1 ! same /> has return$1 con/itut+ "o ( ! p]iodical or v>iable />s ( a long p]iod4 ,moreov]1 on a c>eful reexam9ation ( ! heav5s1 & a comp>ison ( catalogues1 _m />s are n[ discov]$ to be miss+4 ,,d\ble ,,/>s are ^? :i* appe> s+le to ! nak$ eye1 b are resolv$ into two by ! telescope2 or1 if n visible to ! nak$ eye1 are se5 9 ! telescope s close toge!r z to be recognis$ z objects ( ?is class4 ,sometimes1 ?ree or m />s are f\nd 9 ?is ne> connexion1 con/itut+ triple1 or multiple />s4 ,ca/or1 = example1 :5 se5 by ! nak$ eye1 appe>s z a s+le />1 b 9 a telescope ev5 ( mod]ate p[]s1 x is resolv$ into two />s1 ( betwe5 ! ?ird & f\r? magnitudes1 )9 five seconds ( ea* o!r4 ,^! two />s are ne>ly ( equal size2 b m commonly1 "o is exce$+ly small 9 comp>ison ) ! o!r1 resembl+ a satellite ne> its prim>y1 al?\gh 9 di/ance1 9 light1 & 9 o!r *>act]i/ics1 ea* has all ! attributes ( a />1 & ! comb9ation1 !re=e1 _c be t ( a planet ) a satellite4 ,9 mo/ in/ances1 also1 ! di/ance betwe5 ^! objects is mu* less ?an five seconds2 &1 9 _m cases1 x is less ?an "o second4 ,! extreme clos5ess1 toge!r ) ! exce$+ m9ut5ess1 ( mo/ ( ! d\ble />s1 requires ! be/ telescopes unit$ ) ! mo/ acute p[]s ( obs]vation4 ,inde$1 c]ta9 ( ^! objects are reg>d$ z ! sev]e/ te/s bo? ( ! excell5ce ( ! in/rum5ts & ( ! skill ( ! obs]v]4 ,! diagram on page #chb1 ,fig4 #gf1 repres5ts f\r d\ble />s1 z se5 ) appropriate magnifi]s4 ,no4 #a1 exhibits ,epsilon ,bootis ) a p[] ( ?ree hundr$ & fifty2 ,no4 #b1 ,rigel1 ) a p[] ( "o hundr$ & ?irty2 ,no4 #c1 ! ,pole-/>1 ) a p[] ( "o hundr$2 & ,no4 #d1 ,ca/or1 ) a p[] ( ?ree hundr$4 ,our k ( ! d\ble />s almo/ comm5c$ ) ,sir ,william ,h]s*el1 ab\t ! ye> #aghj4 ,at ! "t he began 8 se>* = !m1 he 0 acqua9t$ ) only f\r4 ,)9 five ye>s he discov]$ ne>ly sev5 hundr$ d\ble />s1 & dur+ 8 life1 he obs]v$ no less ?an tw5ty-f\r hundr$4 ,9 8 ,memoirs1 publi%$ 9 ! ,philosophical ,transactions1 he gave mo/ accurate measurem5ts ( ! di/ances betwe5 ! two />s1 & ( ! angle :i* a l9e jo9+ ! two =m$ ) a circle p>allel to ! equator4 ,^! data w\ld enable him1 or at lea/ po/]ity1 to judge :e!r ^! m9ute bodies ev] *ange _! position ) respect to ea* o!r4 ,s9ce #ahba1 ^! rese>*es h be5 prosecut$1 ) great zeal & indu/ry1 by ,sir ,james ,s\? & ,sir ,john ,h]s*el1 9 ,engl&2 :ile ,pr(essor ,/ruve1 ( ,dorpat1 ) ! celebrat$ telescope ( ,fraunh(]1 has publi%$1 f 8 own obs]vations1 a catalogue ( ?ree ?\s& d\ble />s1 ! det]m9ation ( :i* involv$ ! di/9ct & mo/ m9ute inspection ( at lea/ "o hundr$ & tw5ty ?\s& />s4 ,sir ,john ,h]s*el1 9 8 rec5t survey ( ! s\!rn hemisph]e1 is said to h add$ to ! catalogue ( d\ble />s ne>ly ?ree ?\s& m4 ,illu/ration ,fig4 #gf4 ,two circum/ances add a high degree ( int]e/ to ! ph5om5a ( d\ble />s3 ! fir/ is1 t a few ( !m1 at lea/1 are f\nd to h a revolution ar\nd ea* o!r2 ! second1 t !y are suppos$ to af=d ! means ( asc]ta9+ ! p>allax ( ! fix$ />s4 ,b ,i mu/ def] ^! topics till my next ,lett]4 ,,lett] ,,xxix4 ,,fix$ ,,/>s ,,cont9u$4 ,o h[ can/ ?\ r5\nce ! b\ndless /ore ,( *>ms t ,nature to h] vot>y yields8 ,! w>bl+ woodl&1 ! res\nd+ %ore1 ,! pomp ( groves1 & g>niture ( fields2 ,all t ! g5ial ray ( morn+ yields1 ,& all t e*oes to ! song ( ev51 ,all t ! m\nta9's %elt]+ bosom %ields1 ,& all ! dread magnific5ce ( heav51-- ,o h[ can/ ?\ r5\nce1 & hope to be =giv56--,beattie4 ,9 #ahjc1 ,sir ,william ,h]s*el fir/ det]m9$ & ann\nc$ to ! _w1 t !re exi/ among ! />s sep>ate sy/ems1 compos$ ( two />s revolv+ ab\t ea* o!r 9 regul> orbits4 ,^! he d5om9at$ b9>y />s1 to di/+ui% !m f o!r d\ble />s :]e no su* motion is detect$1 & ^: proximity to ea* o!r may possibly arise f casual juxtaposition1 or f "o be+ 9 ! range ( ! o!r4 ,betwe5 fifty & sixty in/ances ( *anges1 to a great] or less am\nt1 ( ! relative positions ( d\ble />s1 are m5tion$ by ,sir ,william ,h]s*el2 & a few ( !m _h *ang$ _! places s mu*1 )9 tw5ty-five ye>s1 & 9 su* ord]1 z to lead him to ! conclusion t !y p]=m$ revolutions1 "o ar\nd ! o!r1 9 regul> orbits4 ,^! conclusions h be5 fully confirm$ by lat] obs]v]s2 s t x is n[ consid]$ z fully e/abli%$1 t !re exi/ among ! fix$ />s b9>y sy/ems1 9 :i* two />s p]=m to ea* o!r ! (fice ( sun & planet1 & t ! p]iods ( revolution ( m ?an "o su* pair h be5 asc]ta9$ ) "s degree ( exactness4 ,imm]sions & em]sions ( />s beh9d ea* o!r h be5 obs]v$1 & real motions among !m detect$1 rapid en\gh to become s5sible & measurable 9 v %ort int]vals ( "t4 ,! p]iods ( ! d\ble />s are v v>i\s1 rang+1 9 ! case ( ^? already asc]ta9$1 f =ty-?ree ye>s to "o ?\s&4 ,_! orbits are v small ellipses1 only a few seconds 9 ! longe/ direction1 & m ecc5tric ?an ^? ( ! planets4 ,a d\ble /> 9 ! ,nor!rn ,cr[n 7,eta ,coron7 has made a complete revolution s9ce its fir/ discov]y1 & is n[ f> advanc$ 9 its second p]iod2 :ile a /> 9 ! ,lion 7,gamma ,leonis7 requires twelve hundr$ ye>s to complete its circuit4 ,y may n at once see ! reason :y ^! revolutions ( "o memb] ( a d\ble /> ar\nd ! o!r1 %\ld be deem$ facts ( su* extraord9>y int]e/2 to y !y may appe> r 9 ! light ( a/ronomical curiosities4 ,b rem>k1 t ! revolutions ( ! b9>y />s h assur$ u ( ?is mo/ int]e/+ fact1 t ! law ( gravitation ext5ds to ! fix$ />s4 ,be=e ^! discov]ies1 we c\ld n decide1 except by a feeble analogy1 t ?is law transc5d$ ! b\nds ( ! sol> sy/em4 ,inde$1 our belief ( ! fact re/$ m ^u our idea ( unity ( design 9 ! works ( ! ,creator1 ?an ^u any c]ta9 pro(2 b ! revolution ( "o /> ar\nd ano!r1 9 ob$i5ce to =ces :i* are prov$ to be simil> to ^? :i* gov]n ! sol> sy/em1 e/abli%es ! gr& conclusion1 t ! law ( gravitation is truly ! law ( ! mat]ial univ]se4 ,we h ! same evid5ce1 says ,sir ,john ,h]s*el1 ( ! revolutions ( ! b9>y />s ab\t ea* o!r1 t we h ( ^? ( ,saturn & ,uranus ab\t ! sun2 & ! correspond5ce betwe5 _! calculat$ & obs]v$ places1 9 su* elongat$ ellipses1 mu/ be admitt$ to c>ry ) x a pro( ( ! preval5ce ( ! ,newtonian law ( gravity 9 _! sy/ems1 ( ! v same nature & cog5cy z t ( ! calculat$ & obs]v$ places ( comets r\nd ! c5tre ( our own sy/em4 ,b x is n ) ! revolution ( bodies ( a comet>y or planet>y nature r\nd a sol> c5tre1 t we are n[ conc]n$2 x is ) t ( sun ar\nd sun1 ea*1 p]haps1 accompani$ ) its tra9 ( planets & _! satellites1 closely %r\d$ f our view by ! spl5dor ( _! respective suns1 & cr[d$ into a space1 be>+ h>dly a great] proportion to ! enorm\s int]val :i* sep>ates !m1 ?an ! di/ances ( ! satellites ( our planets f _! prim>ies be> to _! di/ances f ! sun itself4 ,_m ( ! d\ble />s are ( diff]5t colors2 & ,sir ,john ,h]s*el is ( ! op9ion t !re exi/ 9 nature suns ( diff]5t colors4 ,x may1 says he1 be easi] sugge/$ 9 words ?an conceiv$ 9 imag9ation1 :at v>iety ( illum9ation two suns1 a r$ & a gre51 or a yell[ & a blue "o1 mu/ af=d to a planet circulat+ ab\t ei!r2 & :at *>m+ contra/s & 'grateful vicissitudes' a r$ & a gre5 day1 = in/ance1 alt]nat+ ) a :ite "o & ) d>kness1 might arise f ! pres5ce or abs5ce ( "o or o!r or bo? above ! horizon4 ,insulat$ />s ( a r$ color1 almo/ z deep z t ( blood1 occur 9 _m p>ts ( ! heav5s2 b no gre5 or blue />1 ( any decid$ hue1 has ev] be5 notic$ unassociat$ ) a companion bright] ?an itself4 ,beside ^! revolutions ( ! b9>y />s1 "s ( ! fix$ />s appe> to h a real motion 9 space4 ,!re are sev]al app>5t *anges ( place among ! />s1 aris+ f real *anges 9 ! e>?1 :i*1 z we are n consci\s ( !m1 we ref] to ! />s2 b !re are o!r motions among ! />s :i* _c result f any *anges 9 ! e>?1 b mu/ arise f *anges 9 ! />s !mselves4 ,su* motions are call$ ! prop] motions ( ! />s4 ,ne>ly two ?\s& ye>s ago1 ,hipp>*us & ,ptolemy made ! mo/ accurate det]m9ations 9 _! p[] ( ! relative situations ( ! />s1 & _! obs]vations h be5 transmitt$ to u 9 ,ptolemy's ',almage/2' f :i* x appe>s t ! />s reta9 at lea/ v ne>ly ! same places n[ z !y did at t p]iod4 ,/ill1 ! m accurate me?ods ( mod]n a/ronom]s h br\ght to light m9ute *anges 9 ! places ( c]ta9 />s1 :i* =ce ^u u ! conclusion1 ei!r t our sol> sy/em causes an app>5t displacem5t ( c]ta9 />s1 by a motion ( its own 9 space1 or t !y h !mselves a prop] motion4 ,possibly1 inde$1 bo? ^! causes may op]ate4 ,if ! sun1 & ( c\rse ! e>? :i* accompanies him1 is actually 9 motion1 ! fact may become manife/ f ! app>5t approa* ( ! />s 9 ! region :i* he is leav+1 & ! recession ( ^? :i* lie 9 ! "p ( ! heav5s t[>ds :i* he is travell+4 ,7 two groves ( trees situat$ on a pla9 at "s di/ance ap>t1 & we %\ld g f "o to ! o!r1 ! trees be=e u w\ld gradually appe> fur!r & fur!r asund]1 :ile ^? we left beh9d w\ld appe> to approa* ea* o!r4 ,"s ye>s s9ce1 ,sir ,william ,h]s*el suppos$ he _h detect$ *anges ( ?is k9d among two sets ( />s 9 opposite po9ts ( ! heav5s1 & ann\nc$ t ! sol> sy/em 0 9 motion t[>ds a po9t 9 ! con/ellation ,h]cules2 b o!r a/ronom]s h n f\nd ! *anges 9 "q su* z w\ld correspond to ?is motion1 or to any motion ( ! sun2 &1 :ile x is a matt] ( g5]al belief t ! sun has a motion 9 space1 ! fact is n consid]$ z yet entirely prov$4 ,9 mo/ cases1 :]e a prop] motion 9 c]ta9 />s has be5 suspect$1 its annual am\nt has be5 s small1 t _m ye>s are requir$ to assure u1 t ! effect is n ow+ to "s o!r cause ?an a real progressive motion 9 ! />s !mselves2 b 9 a few in/ances ! fact is too obvi\s to admit ( any d\bt4 ,?us1 ! two />s1 #fa ,cygni1 :i* are ne>ly equal1 h rema9$ con/antly at ! same or ne>ly at ! same di/ance ( fifte5 seconds1 = at lea/ fifty ye>s pa/4 ,mean-:ile1 !y h %ift$ _! local situation 9 ! heav5s f\r m9utes tw5ty-?ree seconds1 ! annual prop] motion ( ea* /> be+ five seconds & ?ree t5?s1 by :i* quantity ?is sy/em is e ye> c>ri$ along 9 "s unkn[n pa?1 by a motion :i* = _m c5turies mu/ be reg>d$ z uni=m & rectil9e>4 ,a great] proportion ( ! d\ble />s ?an ( any o!r indicate prop] motions1 especially ! b9>y />s1 or ^? :i* h a revolution ar\nd ea* o!r4 ,among />s n d\ble1 & no way diff]+ f ! re/ 9 any o!r obvi\s p>ticul>1 a /> 9 ! con/ellation ,cassiopeia1 7,mu ,cassiopei7 has ! greate/ prop] motion ( any yet asc]ta9$1 am\nt+ to ne>ly f\r seconds annually4 ,y h d\btless he>d mu* respect+ ! immeasurable di/ances ( ! fix$ />s1 & w desire to le>n :at is kn[n to a/ronom]s respect+ ?is int]e/+ subject4 ,we _c asc]ta9 ! actual di/ance ( any ( ! fix$ />s1 b we c c]ta9ly det]m9e t ! ne>e/ /> is m ?an tw5ty millions ( millions ( miles f ! e>?1 7#bj1jjj1jjj1jjj1jjj47 ,= all measurem5ts relat+ to ! di/ances ( ! sun & planets1 ! radius ( ! e>? furni%es ! base l9e4 ,! l5g? ( ?is l9e be+ kn[n1 & ! horizontal p>allax ( ! sun or any planet1 we h ! means ( calculat+ ! di/ance ( ! body f u1 by me?ods expla9$ 9 a previ\s ,lett]4 ,b any />1 view$ f ! opposite sides ( ! e>?1 w\ld appe> f bo? /ations to occupy precisely ! same situation 9 ! cele/ial sph]e1 & ( c\rse x w\ld exhibit no horizontal p>allax4 ,b a/ronom]s h endeavor$ to f9d a p>allax 9 "s ( ! fix$ />s1 by tak+ ! diamet] ( ! e>?'s orbit z a base l9e4 ,yet ev5 a *ange ( position am\nt+ to "o hundr$ & n9ety millions ( miles prov$1 until v rec5tly1 insuffici5t to alt] ! place ( a s+le />1 s f> z to be capable ( detection by v ref9$ obs]vations2 f :i* x 0 conclud$ t ! />s h n ev5 any annual p>allax2 t is1 ! angle subt5d$ by ! semidiamet] ( ! e>?'s orbit1 at ! ne>e/ fix$ />1 is ins5sible4 ,! errors to :i* in/rum5tal measurem5ts are subject1 aris+ f ! defects ( in/rum5ts !mselves1 f refraction1 & f v>i\s o!r s\rces ( inaccuracy1 are su*1 t ! angul> det]m9ations ( arcs ( ! heav5s _c be reli$ on to less ?an "o second1 & !re=e _c be appreciat$ by direct measurem5t4 ,x foll[s1 t1 :5 view$ f ! ne>e/ />1 ! diamet] ( ! e>?'s orbit w\ld be ins5sible2 ! spid]-l9e ( ! telescope w\ld m ?an cov] x4 ,tak+1 h[ev]1 ! annual p>allax ( a fix$ /> at "o second1 x c be demon/rat$1 t ! di/ance ( ! ne>e/ fix$ /> mu/ exce$ #iejjjjjj #bjjjjj #aijjjjjjj #ajjjjj1 or "o hundr$ ?\s& times "o hundr$ & n9ety millions ( miles4 ,( a di/ance s va/ we c =m no adequate conceptions1 & ev5 seek to measure x only by ! "t t light 7:i* moves m ?an "o hundr$ & n9ety-two ?\s& miles p] second1 & passes f ! sun to ! e>? 9 eight m9utes & sev5 seconds7 w\ld take to trav]se x1 :i* is f\nd to be m ?an ?ree & a half ye>s4 ,if ^! conclusions are drawn ) respect to ! l>ge/ ( ! fix$ />s1 :i* we suppose to be va/ly ne>] to u ?an ^? ( ! smalle/ magnitude1 ! idea ( di/ance swells ^u u :5 we attempt to e/imate ! remot5ess ( ! latt]4 ,z x is unc]ta91 h[ev]1 :e!r ! diff]5ce 9 ! app>5t magnitudes ( ! />s is ow+ to a real diff]5ce1 or m]ely to _! be+ at v>i\s di/ances f ! eye1 m or less unc]ta9ty mu/ att5d all ef=ts to det]m9e ! relative di/ances ( ! />s2 b a/ronom]s g5]ally believe1 t ! l[] ord]s ( />s are va/ly m di/ant f u ?an ! high]4 ,( "s />s x is said1 t ?\s&s ( ye>s w\ld be requir$ = _! light to travel d[n to u4 ,i h said t ! />s h always be5 held1 until rec5tly1 to h no annual p>allax2 yet x may be obs]v$ t a/ronom]s 7 n exactly agre$ on ?is po9t4 ,dr4 ,br9kley1 a late em95t ,iri% a/ronom]1 suppos$ t he _h detect$ an annual p>allax 9 ,alpha ,lyr1 am\nt+ to "o second & ?irte5 hundre?s1 & 9 ,alpha ,aquil1 ( "o second & =ty-two hundre?s4 ,^! results 7 controv]t$ by ,mr4 ,pond1 ( ! ,royal ,obs]vatory ( ,gre5wi*2 & ,mr4 ,/ruve1 ( ,dorpat1 has %[n t1 9 a numb] ( cases1 ! suppos$ p>allax is 9 a direction opposite to t :i* w\ld arise f ! motion ( ! e>?4 ,h5ce x is consid]$ d\btful :e!r1 9 all cases ( an app>5t p>allax1 ! effect is n :olly due to errors ( obs]vation4 ,b z if no?+ 0 to be hidd5 f our times1 ! long s\ght = p>allax among ! fix$ />s has at l5g? be5 f\nd1 & consequ5tly ! di/ance ( "s ( ^! bodies1 at lea/1 is no long] veil$ 9 my/]y4 ,9 ! ye> #ahch1 ,pr(essor ,bessel1 ( ,kn+sb]g1 ann\nc$ ! discov]y ( a p>allax 9 "o ( ! />s ( ! ,swan1 7#fa ,cygni17 am\nt+ to ab\t "o ?ird ( a second4 ,?is seems1 inde$1 s small an angle1 t we might h reason to suspect ! reality ( ! det]m9ation2 b ! mo/ compet5t judges :o h ?or\ghly exam9$ ! process by :i* ! discov]y 0 made1 ass5t to its validity4 ,:at1 !n1 d a/ronom]s und]/&1 :5 !y say t a p>allax has be5 discov]$ 9 "o ( ! fix$ />s1 am\nt+ to "o ?ird ( a second8 ,!y mean t ! /> 9 "q app>5tly %ifts its place 9 ! heav5s1 to t am\nt1 :5 view$ at opposite extremities ( ! e>?'s orbit1 namely1 at po9ts 9 space di/ant f ea* o!r "o hundr$ & n9ety millions ( miles4 ,on calculat+ ! di/ance ( ! /> f u f ^! data1 x is f\nd to be six hundr$ & fifty-sev5 ?\s& sev5 hundr$ times n9ety-five millions ( miles1--a di/ance :i* x w\ld take light m ?an t5 ye>s to trav]se4 ,indirect me?ods h be5 propos$1 = asc]ta9+ ! p>allax ( ! fix$ />s1 by means ( obs]vations on ! d\ble />s4 ,if ! two />s compos+ a d\ble /> are at diff]5t di/ances f u1 p>allax w\ld affect !m unequally1 & *ange _! relative positions ) respect to ea* o!r2 & s9ce ! ord9>y s\rces ( error aris+ f ! imp]fection ( in/rum5ts1 f precession1 & f refraction1 w\ld be avoid$1 7z !y w\ld affect bo? objects alike1 & !re=e w\ld n di/urb _! relative positions17 measurem5ts tak5 ) ! micromet] ( *anges mu* less ?an "o second may be reli$ on4 ,sir ,john ,h]s*el propos$ a me?od1 by :i* *anges may be det]m9$ t am\nt to only "o =tie? ( a second4 ,! imm5se di/ance ( ! fix$ />s is inf]r$ also f ! fact1 t ! l>ge/ telescopes d n increase _! app>5t magnitude4 ,!y are /ill po9ts1 :5 view$ ) glasses t magnify five ?\s& times4 ,) respect to ! ,,nature ,,( ,,! ,,/>s1 x w\ld seem fruitless to inquire into ! nature ( bodies s di/ant1 & :i* reveal !mselves to u only z %9+ po9ts 9 space4 ,/ill1 !re are a few v satisfactory inf]5ces t c be made out respect+ !m4 ,fir/1 ! fix$ />s are bodies great] ?an our e>?4 ,if ?is 7 n ! case1 !y w\ld n be visible at su* an imm5se di/ance4 ,dr4 ,wolla/on1 a di/+ui%$ ,engli% philosoph]1 attempt$ to e/imate ! magnitudes ( c]ta9 ( ! fix$ />s f ! light :i* !y af=d4 ,by means ( an accurate photomet]1 7an in/rum5t = measur+ ! relative int5sities ( light17 he comp>$ ! light ( ,sirius ) t ( ! sun4 ,he next inquir$ h[ f> ! sun mu/ be remov$ f u1 9 ord] to appe> no bright] ?an ,sirius4 ,he f\nd ! di/ance to be "o hundr$ & =ty-"o ?\s& times its pres5t di/ance4 ,b ,sirius is m ?an two hundr$ ?\s& times z f> (f z ! sun2 h5ce he inf]r$ t1 ^u ! l[e/ computation1 x mu/ actually give out twice z mu* light z ! sun2 or t1 9 po9t ( spl5dor1 ,sirius mu/ be at lea/ equal to two suns4 ,inde$1 he has r5d]$ x probable1 t its light is equal to t ( f\rte5 suns4 ,!re is reason1 h[ev]1 to believe t ! />s are actually ( v>i\s magnitudes1 & t _! app>5t diff]5ce is n ow+ m]ely to _! diff]5t di/ances4 ,bessel e/imates ! quantity ( matt] 9 ! two memb]s ( a d\ble /> 9 ! ,swan1 z less ?an half t ( ! sun4 ,secondly1 ! fix$ />s are suns4 ,we h already se5 t !y are l>ge bodies2 t !y are imm5sely fur!r (f ?an ! fur!/ planet2 t !y %9e by _! own light2 9 %ort1 t _! appe>ance is1 9 all respects1 ! same z ! sun w\ld exhibit if remov$ to ! region ( ! />s4 ,h5ce we inf] t !y are bodies ( ! same k9d ) ! sun4 ,we are ju/ifi$1 !re=e1 by a s\nd analogy1 9 conclud+ t ! />s 7 made = ! same end z ! sun1 namely1 z ! c5tres ( attraction to o!r planet>y worlds1 to :i* !y sev]ally disp5se light & heat4 ,al?\gh ! />ry heav5s pres5t1 9 a cle> night1 a spectacle ( unrivall$ gr&eur & beauty1 yet x mu/ be admitt$ t ! *ief purpose ( ! />s c\ld n h be5 to adorn ! night1 s9ce by f> ! great] "p ( !m are invisible to ! nak$ eye2 nor z l&m>ks to ! navigator1 = only a v small proportion ( !m are adapt$ to ?is purpose2 nor1 f9ally1 to influ5ce ! e>? by _! attractions1 s9ce _! di/ance r5d]s su* an effect entirely ins5sible4 ,if !y are suns1 & if !y ex]t no important ag5cies ^u our _w1 b are bodies evid5tly adapt$ to ! same purpose z our sun1 !n x is z rational to suppose t !y 7 made to give light & heat1 z t ! eye 0 made = see+ & ! e> = he>+4 ,x is obvi\s to inquire1 next1 to :at !y disp5se ^! gifts1 if n to planet>y worlds2 & :y to planet>y worlds1 if n = ! use ( p]cipi5t be+s8 ,we are ?us l$1 almo/ inevitably1 to ! idea ( a plurality ( worlds2 & ! conclusion is =c$ ^u u1 t ! spot :i* ! ,creator has assign$ to u is b a humble prov9ce 9 8 b\ndless empire4 ,,lett] ,,xxx4 ,,sy/em ,,( ,,! ,,_w ,o h[ unlike ! complex works ( man1 ,heav5's easy1 artless1 un9cumb]$1 plan4--,c[p]4 ,,hav+ n[ expla9$ to y1 z f> z ,i am able to d x 9 s %ort a space1 ! lead+ ph5om5a ( ! heav5ly bodies1 x only rema9s to in=m y ( ! diff]5t sy/ems ( ! _w :i* h prevail$ 9 diff]5t ages1--a subject :i* w necess>ily involve a sket* ( ! hi/ory ( a/ronomy4 ,by a sy/em ( ! _w1 ,i und]/& an explanation ( ! arrangem5t ( all ! bodies t compose ! mat]ial univ]se1 & ( _! relations to ea* o!r4 ,x is o!rwise call$ ! ',me*anism ( ! ,heav5s2' & inde$1 9 ! sy/em ( ! _w1 we figure to ourselves a ma*9e1 all p>ts ( :i* h a mutual dep5d5ce1 & conspire to "o great end4 ,! ma*9es t 7 fir/ inv5t$1 says ,adam ,smi?1 to p]=m any p>ticul> movem5t1 are always ! mo/ complex2 & succe$+ arti/s g5]ally discov] t1 ) few] :eels1 & ) few] pr9ciples ( motion1 ?an _h orig9ally be5 employ$1 ! same effects may be m easily produc$4 ,! fir/ sy/ems1 9 ! same mann]1 are always ! mo/ complex2 & a p>ticul> connect+ *a9 or pr9ciple is g5]ally ?\ght necess>y1 to unite e two seem+ly disjo9t$ appe>ances2 b x (t5 happ5s1 t "o great connect+ pr9ciple is aft]w>ds f\nd to be suffici5t to b9d toge!r all ! discordant ph5om5a t occur 9 a :ole species ( ?+s6 ,?is rem>k is /rik+ly applicable to ! orig9 & progress ( sy/ems ( a/ronomy4 ,x is a rem>kable fact 9 ! hi/ory ( ! human m9d1 t a/ronomy is ! olde/ ( ! sci5ces1 hav+ be5 cultivat$1 ) no small success1 long be=e any att5tion 0 paid to ! causes ( ! common t]re/rial ph5om5a4 ,! op9ion has always prevail$ among ^? :o 7 un5light5$ by sci5ce1 t v extraord9>y appe>ances 9 ! sky1 z comets1 fi]y meteors1 & eclipses1 are om5s ( ! wra? ( heav54 ,!y h1 !re=e1 9 all ages1 be5 wat*$ ) ! greate/ att5tion3 & _! appe>ances h be5 m9utely record$ by ! hi/orians ( ! times4 ,! idea1 moreov]1 t ! aspects ( ! />s are connect$ ) ! de/9ies ( individuals & ( empires1 has be5 rem>kably preval5t f ! e>lie/ records ( hi/ory d[n to a v late p]iod1 &1 inde$1 /ill l+]s among ! un$ucat$ & cr$ul\s4 ,?is notion gave rise to ,,a/rology1--an art :i* pr(ess$ to be able1 by a k ( ! v>y+ aspects ( ! planets & />s1 to p5etrate ! veil ( futurity1 & to =etel approa*+ irregul>ities ( ,nature h]self1 & ! =tunes ( k+doms & ( individuals4 ,t dep>tm5t ( a/rology :i* took cognizance ( extraord9>y occurr5ces 9 ! natural _w1 z tempe/s1 e>?quakes1 eclipses1 & volcanoes1 bo? to pr$ict _! approa* & to int]pret _! mean+1 0 call$ natural a/rology3 t :i* relat$ to ! =tunes ( m5 & ( empires1 judicial a/rology4 ,among _m anci5t nations1 a/rolog]s 7 held 9 ! highe/ e/imation1 & 7 kept ne> ! p]sons ( mon>*s2 & ! practice ( ! art con/itut$ a lucrative pr(ession ?r\gh\t ! middle ages4 ,nor 7 ! ignorant & un$ucat$ portions ( society alone ! dupes ( its pret5sions4 ,hippocrates1 ! ',fa!r ( ,m$ic9e1' ranks a/rology among ! mo/ important bran*es ( k to ! physician2 & ,ty*o ,brahe1 & ,"l ,bacon1 7 firm believ]s 9 its my/]ies4 ,a/rology1 fallaci\s z x 01 mu/ be ackn[l$g$ to h r5d]$ ! greate/ s]vices to a/ronomy1 by lead+ to ! accurate obs]vation & dilig5t /udy ( ! />s4 ,at a p]iod ( v remote antiquity1 a/ronomy 0 cultivat$ 9 ,*9a1 ,india1 ,*aldea1 & ,egypt4 ,! ,*aldeans 7 p>ticul>ly di/+ui%$ = ! accuracy & ext5t ( _! a/ronomical obs]vations4 ,cali/h5es1 ! ,greek philosoph] :o accompani$ ,alex&] ! ,great 9 8 ,ea/]n conque/s1 transmitt$ to ,ari/otle a s]ies ( obs]vations made at ,babylon n9ete5 c5turies be=e ! capture ( t city by ,alex&]2 & ! wise m5 ( ,babylon & ! ,*aldean a/rolog]s are ref]r$ to 9 ! ,sacr$ ,writ+s4 ,!y enjoy$ a cle> sky & a mild climate1 & _! pursuits z %eph]ds favor$ long-cont9u$ obs]vations2 :ile ! admiration & respect accord$ to ! pr(ession1 r5d]$ x an object ( /ill high] ambition4 ,9 ! sev5? c5tury be=e ! ,*ri/ian era1 a/ronomy began to be cultivat$ 9 ,greece2 & !re arose successively ?ree celebrat$ a/ronomical s*ools1--! s*ool ( ,miletus1 ! s*ool ( ,crotona1 & ! s*ool ( ,alex&ria4 ,! fir/ 0 e/abli%$ by ,?ales1 six hundr$ & =ty ye>s be=e ,*ri/2 ! second1 by ,py?agoras1 "o hundr$ & =ty ye>s aft]w>ds2 & ! ?ird1 by ! ,ptolemies ( ,egypt1 ab\t ?ree hundr$ ye>s be=e ! ,*ri/ian era4 ,z ,egypt & ,babylon 7 r5[n$ among ! mo/ anci5t nations1 = _! k ( ! sci5ces1 long be=e !y 7 cultivat$ 9 ,greece1 x 0 ! practice ( ! ,greeks1 :5 !y aspir$ to ! "* ( philosoph]s & sages1 to resort to ^! c\ntries to imbibe wisdom at its f\nta9s4 ,?ales1 aft] ext5sive travels 9 ,crete & ,egypt1 return$ to 8 native place1 ,miletus1 a t[n on ! coa/ ( ,asia ,m9or1 :]e he e/abli%$ ! fir/ s*ool ( a/ronomy 9 ,greece4 ,al?\gh ! m9ds ( ^! anci5t a/ronom]s 7 becl\d$ ) mu* error1 yet ,?ales taught a few tru?s :i* d honor to 8 sagacity4 ,he held t ! />s are =m$ ( fire2 t ! moon receives h] light f ! sun1 & is invisible at h] conjunctions because %e is hid 9 ! sun's rays4 ,he taught ! sph]icity ( ! e>?1 b adopt$ ! common error ( plac+ x 9 ! c5tre ( ! _w4 ,he introduc$ ! division ( ! sph]e into five zones1 & taught ! obliquity ( ! ecliptic4 ,he 0 acqua9t$ ) ! ,s>os1 or sacr$ p]iod ( ! ,*aldeans1 7see page #aib17 & employ$ x 9 calculat+ eclipses4 ,x 0 ,?ales t pr$ict$ ! fam\s eclipse ( ! sun :i* t]m9at$ ! w> betwe5 ! ,lydians & ! ,m$es1 z m5tion$ 9 a =m] ,lett]4 ,inde$1 ,?ales is univ]sally reg>d$ z a bright b solit>y />1 glimm]+ ?r\gh mi/s on ! di/ant horizon4 ,to ,?ales succe$$1 9 ! s*ool ( ,miletus1 two o!r a/ronom]s ( mu* celebrity1 ,anaxim&] & ,anaxagoras4 ,among _m absurd ?+s held by ,anaxim&]1 he fir/ taught ! sublime doctr9e t ! planets are inhabit$1 & t ! />s are suns ( o!r sy/ems4 ,anaxagoras attempt$ to expla9 all ! secrets ( ! skies by natural causes4 ,8 reason+s1 inde$1 7 alloy$ ) _m absurd notions2 b /ill he alone1 among ! a/ronom]s1 ma9ta9$ ! exi/5ce ( "o ,god4 ,8 doctr9es al>m$ 8 c\ntrym51 by _! audacity & impiety to _! gods1 ^: pr]ogatives he 0 ?\ght to invade2 &1 to deprecate _! wra?1 s5t5ce ( dea? 0 pron\nc$ on ! philosoph] & all 8 family1--a s5t5ce :i* 0 commut$ only = ! sad alt]native ( p]petual bani%m5t4 ,! v g5ius ( ! hea!n my?ology 0 at w> ) ! tru?4 ,false 9 itself1 x tra9$ ! m9d to ! love ( :at 0 false 9 ! int]pretation ( nature2 x array$ itself aga9/ ! simplicity ( tru?1 & p]secut$ & put to dea? its mo/ ard5t vot>ies4 ,! religion ( ! ,bible1 on ! o!r h&1 l5ds all its aid to tru? 9 nature z well z 9 morals & religion4 ,9 its v g5ius x inculcates & inspires ! love ( tru?2 x sugge/s1 by its analogies1 ! exi/5ce ( e/abli%$ laws 9 ! sy/em ( ! _w2 & holds out ! moon & ! />s1 :i* ! ,creator has orda9$1 z fit objects to give u exalt$ views ( 8 glory & wisdom4 ,py?agoras 0 ! f\nd] ( ! celebrat$ s*ool ( ,crotona4 ,he 0 a native ( ,samos1 an isl& 9 ! gean sea1 & fl\ri%$ ab\t five hundr$ ye>s be=e ! ,*ri/ian era4 ,aft] travell+ m ?an ?irty ye>s 9 ,egypt & ,*aldea1 & sp5d+ sev]al ye>s m at ,sp>ta1 to le>n ! laws & in/itutions ( ,lycurgus1 he return$ to 8 native isl& to disp5se ! ri*es he _h acquir$ to 8 c\ntrym54 ,b !y1 probably fe>ful ( incurr+ ! displeasure ( ! gods by ! fre$om ) :i* he inquir$ into ! secrets ( ! skies1 gave him s unwelcome a reception1 t he retir$ f !m1 9 disgu/1 & e/abli%$ 8 s*ool at ,crotona1 on ! s\!a/]n coa/ ( ,italy4 ,hi!r1 z to an oracle1 ! fame ( 8 wisdom attract$ hundr$s ( admir+ pupils1 :om he in/ruct$ 9 e species ( k4 ,f ! vision>y notions :i* are g5]ally und]/ood to h be5 ent]ta9$ on ! subject ( a/ronomy1 by ! anci5ts1 we are apt to imag9e t !y knew less ?an !y actually did ( ! tru?s ( ?is sci5ce4 ,b ,py?agoras 0 acqua9t$ ) _m important facts 9 a/ronomy1 & ent]ta9$ _m op9ions respect+ ! sy/em ( ! _w1 :i* are n[ held to be true4 ,among o!r ?+s well kn[n to ,py?agoras1 ei!r d]iv$ f 8 own inve/igations1 or receiv$ f 8 pr$ecessors1 7 ! foll[+2 & we may note !m z a synopsis ( ! /ate ( a/ronomical k at t age ( ! _w4 ,fir/1 ! pr9cipal con/ellations4 ,^! _h begun to be =m$ 9 ! e>lie/ ages ( ! _w4 ,sev]al ( !m1 be>+ ! same "n z at pres5t1 are m5tion$ 9 ! writ+s ( ,hesiod & ,hom]2 & ! sweet influ5ces ( ! ,pleiades1 & ! b&s ( ,orion1 are beautifully allud$ to 9 ! book ( ,job4 ,secondly1 eclipses4 ,py?agoras knew bo? ! causes ( eclipses & h[ to pr$ict !m2 n1 inde$1 9 ! accurate mann] n[ practis$1 b by means ( ! ,s>os4 ,?irdly1 ,py?agoras _h div9$ ! true sy/em ( ! _w1 hold+ t ! sun1 & n ! e>?1 7z 0 g5]ally held by ! anci5ts1 ev5 = _m ages aft] ,py?agoras17 is ! c5tre ar\nd :i* all ! planets revolve2 & t ! />s are s _m suns1 ea* ! c5tre ( a sy/em l our own4 ,among less] ?+s1 he knew t ! e>? is r\nd2 t its surface is naturally divid$ into five zones2 & t ! ecliptic is incl9$ to ! equator4 ,he also held t ! e>? revolves daily on its axis1 & ye>ly ar\nd ! sun2 t ! galaxy is an assemblage ( small />s2 & t x is ! same lum9>y1 namely1 ,v5us1 t con/itutes bo? ! morn+ & ev5+ />2 :]eas all ! anci5ts be=e him _h suppos$ t ea* 0 a sep>ate planet1 & accord+ly ! morn+ /> 0 call$ ,lucif]1 & ! ev5+ />1 ,hesp]us4 ,he held1 also1 t ! planets 7 inhabit$1 & ev5 w5t s f> z to calculate ! size ( "s ( ! animals 9 ! moon4 ,py?agoras 0 also s great an en?usia/ 9 music1 t he n only assign$ to x a conspicu\s place 9 8 sy/em ( education1 b ev5 suppos$ t ! heav5ly bodies !mselves 7 arrang$ at di/ances correspond+ to ! int]vals ( ! diatonic scale1 & imag9$ !m to pursue _! sublime m>* to notes creat$ by _! own h>moni\s movem5ts1 call$ ! 'music ( ! sph]es2' b he ma9ta9$ t ?is cele/ial conc]t1 ?\gh l\d & gr&1 is n audible to ! feeble organs ( man1 b only to ! gods4 ,) few exceptions1 h[ev]1 ! op9ions ( ,py?agoras on ! sy/em ( ! _w 7 f\nd$ 9 tru?4 ,yet !y 7 reject$ by ,ari/otle1 & by mo/ succe$+ a/ronom]s1 d[n to ! "t ( ,cop]nicus2 & 9 _! place 0 sub/itut$ ! doctr9e ( cry/all9e sph]es1 fir/ taught by ,eudoxus1 :o liv$ ab\t ?ree hundr$ & sev5ty ye>s be=e ,*ri/4 ,accord+ to ?is sy/em1 ! heav5ly bodies are set l gems 9 holl[ solid orbs1 compos$ ( cry/al s transp>5t1 t no ant]ior orb ob/ructs 9 ! lea/ ! view ( any ( ! orbs t lie beh9d x4 ,! sun & ! planets h ea* its sep>ate orb2 b ! fix$ />s are all set 9 ! same gr& orb2 & beyond ?is is ano!r /ill1 ! primum mobile1 :i* revolves daily1 f ea/ to we/1 & c>ries along ) x all ! o!r orbs4 ,above ! :ole spreads ! gr& empyrean1 or ?ird heav5s1 ! abode ( p]petual s]5ity4 ,to acc\nt = ! planet>y motions1 x 0 suppos$ t ea* ( ! planet>y orbs1 z well z t ( ! sun1 has a motion ( its own1 ea/w>d1 :ile x p>takes ( ! common diurnal motion ( ! />ry sph]e4 ,ari/otle taught t ^! motions are effect$ by a tutel>y g5ius ( ea* planet1 resid+ 9 x1 & direct+ its motions1 z ! m9d ( man directs 8 movem5ts4 ,two hundr$ ye>s aft] ,py?agoras1 arose ! fam\s s*ool ( ,alex&ria1 "u ! ,ptolemies4 ,^! 7 a succession ( ,egyptian k+s1 & are n to be conf\nd$ ) ,ptolemy1 ! a/ronom]4 ,by ! munific5t patronage ( ?is enlight5$ family1 = ! space ( ?ree hundr$ ye>s1 beg9n+ at ! dea? ( ,alex&] ! ,great1 f :om ! elde/ ( ! ,ptolemies _h receiv$ 8 k+dom1 ! s*ool ( ,alex&ria conc5trat$ 9 its va/ libr>y & pr9cely halls1 erect$ = ! accommodation ( ! philosoph]s1 ne>ly all ! sci5ce & le>n+ ( ! _w4 ,9 w&]+ ov] ! imm5se t]ritories ( ignorance & b>b>ism :i* cov]$1 at t "t1 almo/ ! entire face ( ! e>?1 ! eye reposes ^u ?is little spot1 z ^u a v]dant isl& 9 ! mid/ ( ! des]t4 ,among ! *oice fruits t grew 9 ?is g>d5 ( a/ronomy 7 sev]al ( ! mo/ di/+ui%$ ornam5ts ( anci5t sci5ce1 ( :om ! mo/ em95t 7 ,hipp>*us & ,ptolemy4 ,hipp>*us is ju/ly consid]$ z ! ,newton ( antiquity4 ,he s\ght 8 k ( ! heav5ly bodies n 9 ! illusory sugge/ions ( a f]vid imag9ation1 b 9 ! vigor\s application ( an intellect ( ! fir/ ord]4 ,previ\s to ?is p]iod1 cele/ial obs]vations 7 made *iefly ) ! nak$ eye3 b ,hipp>*us 0 9 possession ( in/rum5ts = measur+ angles1 & knew h[ to resolve sph]ical triangles4 ,^! 7 great /eps beyond all 8 pr$ecessors4 ,he asc]ta9$ ! l5g? ( ! ye> )9 six m9utes ( ! tru?4 ,he discov]$ ! ecc5tricity1 or elliptical figure1 ( ! sol> orbit1 al?\gh he suppos$ ! sun actually to move uni=mly 9 a circle1 b ! e>? to be plac$ out ( ! c5tre4 ,he also det]m9$ ! positions ( ! po9ts among ! />s :]e ! e>? is ne>e/ to ! sun1 & :]e x is mo/ remote f x4 ,he =m$ v accurate e/imates ( ! obliquity ( ! ecliptic & ( ! precession ( ! equ9oxes4 ,he comput$ ! exact p]iod ( ! synodic revolution ( ! moon1 & ! incl9ation ( ! lun> orbit2 discov]$ ! backw>d motion ( h] node & ( h] l9e ( apsides2 & made ! fir/ attempts to asc]ta9 ! horizontal p>allaxes ( ! sun & moon4 ,^u ! appe>ance ( a new /> 9 ! firmam5t1 he und]took1 z already m5tion$1 to numb] ! />s1 & to assign to ea* its true place 9 ! heav5s1 9 ord] t po/]ity might h ! means ( judg+ :at *anges1 if any1 7 go+ =w>d among ^! app>5tly unalt]able bodies4 ,al?\gh ,hipp>*us is g5]ally consid]$ z belong+ to ! ,alex&rian s*ool1 yet he liv$ at ,rhodes1 & !re made 8 a/ronomical obs]vations1 ab\t "o hundr$ & =ty ye>s be=e ! ,*ri/ian era4 ,"o ( 8 treatises has come d[n to u2 b 8 pr9cipal discov]ies h be5 transmitt$ ?r\gh ! ',almage/' ( ,ptolemy4 ,ptolemy fl\ri%$ at ,alex&ria ne>ly ?ree c5turies aft] ,hipp>*us1 9 ! second c5tury aft] ,*ri/4 ,8 great "w1 ! ',almage/1' :i* has convey$ to u mo/ t we "k respect+ ! a/ronomical k ( ! anci5ts1 0 ! univ]sal text-book ( a/ronom]s = f\rte5 c5turies4 ,illu/ration ,fig4 #gg4 ,! "n ( ?is celebrat$ a/ronom] has also desc5d$ to u1 associat$ ) ! sy/em ( ! _w :i* prevail$ f ,ptolemy to ,cop]nicus1 call$ ! ,ptolemaic ,sy/em4 ,! doctr9es ( ! ,ptolemaic sy/em did n orig9ate ) ,ptolemy1 b1 be+ dige/$ by him out ( mat]ials furni%$ by v>i\s h&s1 x has come d[n to u "u ! sanction ( 8 "n4 ,accord+ to ?is sy/em1 ! e>? is ! c5tre ( ! univ]se1 & all ! heav5ly bodies daily revolve ar\nd x1 f ea/ to we/4 ,b al?\gh ?is hypo!sis w\ld acc\nt = ! app>5t diurnal motion ( ! firmam5t1 yet x w\ld n acc\nt = ! app>5t annual motion ( ! sun1 nor = ! sl[ motions ( ! planets f we/ to ea/4 ,9 ord] to expla9 ^! ph5om5a1 rec\rse 0 _h to def]5ts & epicycles1--an explanation devis$ by ,apollonius1 "o ( ! greate/ geomet]s ( antiquity4 ,he conceiv$ t1 9 ! circumf]5ce ( a circle1 hav+ ! e>? = its c5tre1 !re moves ! c5tre ( a small] circle 9 ! circumf]5ce ( :i* ! planet revolves4 ,! circle surr\nd+ ! e>? 0 call$ ! def]5t1 :ile ! small] circle1 ^: c5tre 0 always 9 ! circumf]5ce ( ! def]5t1 0 call$ ! epicycle4 ,?us1 if ,e1 ,fig4 #gg1 repres5ts ! e>?1 ,,abc w be ! def]5t1 & ,,dfg1 ! epicycle2 & x is obvi\s t ! motion ( a body f we/ to ea/1 9 ?is small circle1 w\ld be alt]nately direct1 /ation>y1 & retrograde1 z 0 expla9$1 9 a previ\s ,lett]1 to be actually ! case ) ! app>5t motions ( ! planets4 ,! hypo!sis1 h[ev]1 is inconsi/5t ) ! phases ( ,m]cury & ,v5us1 :i*1 be+ betwe5 u & ! sun1 on bo? sides ( ! epicycle1 w\ld pres5t _! d>k sides t[>ds u at bo? conjunctions ) ! sun1 :]eas1 at "o ( ! conjunctions1 x is kn[n t !y exhibit _! disks illum9at$4 ,x is1 moreov]1 absurd to speak ( a geometrical c5tre1 :i* has no bodily exi/5ce1 mov+ r\nd ! e>? on ! circumf]5ce ( ano!r circle4 ,9 addition to ^! absurdities1 ! :ole ,ptolemaic sy/em is encumb]$ ) ! foll[+ difficulties3 ,fir/1 x is a m]e hypo!sis1 hav+ no evid5ce 9 its favor except t x expla9s ! ph5om5a4 ,?is evid5ce is insuffici5t ( itself1 s9ce x frequ5tly happ5s t ea* ( two hypo!ses1 :i* are directly opposite to ea* o!r1 w expla9 all ! kn[n ph5om5a4 ,b ! ,ptolemaic sy/em does n ev5 d ?is1 z x is inconsi/5t ) ! phases ( ,m]cury & ,v5us1 z already obs]v$4 ,secondly1 n[ t we are acqua9t$ ) ! di/ances ( ! remot] planets1 & especially ! fix$ />s1 ! swiftness ( motion1 impli$ 9 a daily revolution ( ! />ry firmam5t ar\nd ! e>?1 r5d]s su* a motion :olly incr$ible4 ,?irdly1 ! c5trifugal =ce :i* w\ld be g5]at$ 9 ^! bodies1 especially 9 ! sun1 r5d]s x impossible t !y c cont9ue to revolve ar\nd ! e>? z a c5tre4 ,absurd1 h[ev]1 z ! sy/em ( ,ptolemy 01 = _m c5turies no great philosophic g5ius appe>$ to expose its fallacies1 & x !re=e guid$ ! fai? ( a/ronom]s ( all c\ntries d[n to ! "t ( ,cop]nicus4 ,aft] ! age ( ,ptolemy1 ! sci5ce made little progress4 ,) ! decl9e ( ,grecian lib]ty1 ! arts & sci5ces decl9$ also2 & ! ,romans1 !n ma/]s ( ! _w1 7 ev] m ambiti\s to ga9 conque/s ov] man ?an ov] matt]2 & !y accord+ly nev] produc$ a s+le great a/ronom]4 ,dur+ ! middle ages1 ! ,arabians 7 almo/ ! only a/ronom]s1 & !y cultivat$ ?is noble /udy *iefly z subsidi>y to a/rology4 ,at l5g?1 9 ! fifte5? c5tury1 ,cop]nicus arose1 & aft] =ty ye>s ( int5se /udy & m$itation1 div9$ ! true sy/em ( ! _w4 ,y w recollect t ! ,cop]nican sy/em ma9ta9s1 #a4 ,t ! app>5t diurnal motions ( ! heav5ly bodies1 f ea/ to we/1 is ow+ to ! real revolution ( ! e>? on its own axis f we/ to ea/2 &1 #b4 ,t ! sun is ! c5tre ar\nd :i* ! e>? & planets all revolve f we/ to ea/4 ,x re/s on ! foll[+ argum5ts3 ,9 ! fir/ place1 ! e>? revolves on its own axis4 ,fir/1 because ?is supposition is va/ly m simple4 ,secondly1 x is agreeable to analogy1 s9ce all ! o!r planets t af=d any means ( det]m9+ ! "q1 are se5 to revolve on _! axes4 ,?irdly1 ! sph]oidal figure ( ! e>? is ! figure ( equilibrium1 t results f a revolution on its axis4 ,f\r?ly1 ! dim9i%$ weight ( bodies at ! equator indicates a c5trifugal =ce aris+ f su* a revolution4 ,fif?ly1 bodies let fall f a high em95ce1 fall ea/w>d ( _! base1 indicat+ t :5 fur!r f ! c5tre ( ! e>? !y 7 subject to a great] velocity1 :i*1 9 consequ5ce ( _! in]tia1 !y d n entirely lose 9 desc5d+ to ! l[] level4 ,9 ! second place1 ! planets1 includ+ ! e>?1 revolve ab\t ! sun4 ,fir/1 ! phases ( ,m]cury & ,v5us are precisely su*1 z w\ld result f _! circulat+ ar\nd ! sun 9 orbits )9 t ( ! e>?2 b !y are nev] se5 9 opposition1 z !y w\ld be1 if !y circulate ar\nd ! e>?4 ,secondly1 ! sup]ior planets d inde$ revolve ar\nd ! e>?2 b !y also revolve ar\nd ! sun1 z is evid5t f _! phases1 & f ! kn[n dim5sions ( _! orbits2 & t ! sun1 & n ! e>?1 is ! c5tre ( _! motions1 is inf]r$ f ! great] symmetry ( _! motions1 z ref]r$ to ! sun1 ?an z ref]r$ to ! e>?2 & especially f ! laws ( gravitation1 :i* =bid our suppos+ t bodies s mu* l>g] ?an ! e>?1 z "s ( ^! bodies are1 c circulate p]man5tly ar\nd ! e>?1 ! latt] rema9+ all ! :ile at re/4 ,9 ! ?ird place1 ! annual motion ( ! e>? itself is indicat$ also by ! mo/ conclusive argum5ts4 ,=1 fir/1 s9ce all ! planets1 ) _! satellites & ! comets1 revolve ab\t ! sun1 analogy leads u to inf] ! same respect+ ! e>? & its satellite1 z ^? ( ,jupit] & ,saturn1 & indicates t x is a law ( ! sol> sy/em t ! small] bodies revolve ab\t ! l>g]4 ,secondly1 on ! supposition t ! e>? p]=ms an annual revolution ar\nd ! sun1 x is embrac$ along ) ! planets1 9 ,kepl]'s law1 t ! squ>es ( ! times are z ! cubes ( ! di/ances2 o!rwise1 x =ms an exception1 & ! only kn[n exception1 to ?is law4 ,su* are ! lead+ argum5ts ^u :i* re/s ! ,cop]nican sy/em ( a/ronomy4 ,!y 71 h[ev]1 only v p>tially kn[n to ,cop]nicus himself1 z ! /ate bo? ( me*anical sci5ce1 & ( a/ronomical obs]vation1 0 n !n suffici5tly matur$ to %[ him ! /r5g? ( 8 own doctr9e1 s9ce he knew no?+ ( ! telescope1 & no?+ ( ! pr9ciple ( univ]sal gravitation4 ,! evid5ce ( ?is beautiful sy/em be+ left by ,cop]nicus 9 s imp]fect a /ate1 & inde$ 8 own reason+s 9 support ( x be+ t9ctur$ ) "s errors1 we ne$ n s mu* wond] t ,ty*o ,brahe1 :o imm$iately foll[$ ,cop]nicus1 did n give x 8 ass5t1 b1 influ5c$ by c]ta9 passages ( ,scripture1 he /ill ma9ta9$1 ) ,ptolemy1 t ! e>? is 9 ! c5tre ( ! univ]se2 & he acc\nt$ = ! diurnal motions 9 ! same mann] z ,ptolemy _h done1 namely1 by an actual revolution ( ! :ole ho/ ( heav5 ar\nd ! e>? e tw5ty-f\r h\rs4 ,b he reject$ ! s*eme ( def]5ts & epicycles1 & held t ! moon revolves ab\t ! e>? z ! c5tre ( h] motions2 b t ! sun & n ! e>? is ! c5tre ( ! planet>y motions2 & t ! sun1 accompani$ by ! planets1 moves ar\nd ! e>? once a ye>1 some:at 9 ! mann] 9 :i* we n[ conceive ( ,jupit] & 8 satellites z revolv+ ar\nd ! sun4 ,?is sy/em is liable to mo/ ( ! objections t lie aga9/ ! ,ptolemaic sy/em1 ) ! disadvantage ( be+ m complex4 ,kepl] & ,galileo1 h[ev]1 z appe>$ 9 ! sket* ( _! lives1 embrac$ ! !ory ( ,cop]nicus ) great avidity1 & all _! labors contribut$ to swell ! evid5ce ( its tru?4 ,:5 we see ) :at imm5se labor & difficulty ! disciples ( ,ptolemy s\ght to reconcile e new ph5om5on ( ! heav5s ) _! sy/em1 & !n see h[ easily & naturally all ! successive discov]ies ( ,galileo & ,kepl] fall 9 ) ! !ory ( ,cop]nicus1 we feel ! full =ce ( ^? beautiful l9es ( ,c[p] :i* ,i h *os5 = ! motto ( ?is ,lett]4 ,newton receiv$ ! tor* ( tru? f ,galileo1 & transmitt$ x to 8 successors1 ) its light enl>g$ & purifi$2 & s9ce t p]iod1 e new discov]y1 :e!r ! fruit ( ref9$ in/rum5tal obs]vation or ( pr(\nd ma!matical analysis1 has only add$ lu/re to ! glory ( ,cop]nicus4 ,) ,newton comm5c$ a new & wond]ful era 9 a/ronomy1 di/+ui%$ above all o!rs1 n m]ely = ! production ( ! greate/ ( m51 b also = ! e/abli%m5t ( ^? mo/ important auxili>ies to our sci5ce1 ! ,royal ,society ( ,london1 ! ,academy ( ,sci5ces at ,p>is1 & ! ,obs]vatory ( ,gre5wi*4 ,i may add ! comm5cem5t ( ! ,transactions ( ! ,royal ,society1 & ! ,memoirs ( ! ,academy ( ,sci5ces1 :i* h be5 cont9u$ to ! pres5t "t1--bo? preci\s /oreh\ses ( a/ronomical ri*es4 ,! ,obs]vatory ( ,gre5wi*1 moreov]1 has be5 "u ! direction ( an extraord9>y succession ( great a/ronom]s4 ,_! names are ,flam/ead1 ,halley1 ,bradley1 ,maskeleyne1 ,pond1 & ,airy1--! la/ be+ /ill at 8 po/1 & wor?y ( cont9u+ a l9e s truly illu/ri\s4 ,! obs]vations accumulat$ at ?is celebrat$ ,obs]vatory are s num]\s1 & s mu* sup]ior to ^? ( any o!r in/itution 9 ! _w1 t x has be5 said t a/ronomy w\ld suff] little1 if all o!r contempor>y obs]vations ( ! same k9d 7 annihilat$4 ,sir ,william ,h]s*el1 h[ev]1 labor$ *iefly 9 a diff]5t sph]e4 ,! ,a/ronom]s ,royal devot$ !mselves n s mu* to ! discov]y ( new objects among ! heav5ly bodies1 z to ! exact det]m9ation ( ! places ( ! bodies already kn[n1 & to ! developem5t ( new laws or facts among ! cele/ial motions4 ,b ,h]s*el1 hav+ con/ruct$ telescopes ( f> great] rea* ?an any ev] us$ be=e1 employ$ !m to s\nd new & untri$ dep?s 9 ! pr(undities ( space4 ,we h already se5 :at int]e/+ & amaz+ discov]ies he made ( d\ble />s1 clu/]s1 & nebul4 ,! ,engli% h done mo/ = a/ronomy 9 obs]vation & discov]y2 b ! ,fr5* & ,g]mans1 9 develop+1 by ! mo/ pr(\nd ma!matical inve/igation1 ! great laws ( physical a/ronomy4 ,x only rema9s to inquire1 :e!r ! ,cop]nican sy/em is n[ to be reg>d$ z a full exposition ( ! ',me*anism ( ! ,heav5s1' or :e!r !re subsi/ high] ord]s ( relations betwe5 ! fix$ />s !mselves4 ,! revolutions ( ! b9>y />s af=d conclusive evid5ce ( at lea/ subord9ate sy/ems ( suns1 gov]n$ by ! same laws z ^? :i* regulate ! motions ( ! sol> sy/em4 ,! nebul also compose peculi> sy/ems1 9 :i* ! memb]s are evid5tly b\nd toge!r by "s common relation4 ,9 ^! m>ks ( organization1--( />s associat$ toge!r 9 clu/]s2 ( sun revolv+ ar\nd sun2 & ( nebul dispos$ 9 regul> figures1--we recognise diff]5t memb]s ( "s gr& sy/em1 l9ks 9 "o great *a9 t b9ds toge!r all p>ts ( ! univ]se2 z we see ,jupit] & 8 satellites comb9$ 9 "o subord9ate sy/em1 & ,saturn & 8 satellites 9 ano!r1--ea* a va/ k+dom1 & bo? unit+ ) a numb] ( o!r individual p>ts1 to compose an empire /ill m va/4 ,?is fact be+ n[ e/abli%$1 t ! />s are imm5se bodies1 l ! sun1 & t !y are subject to ! laws ( gravitation1 we _c conceive h[ !y c be pres]v$ f fall+ into f9al disord] & ru91 unless !y move 9 h>moni\s conc]t1 l ! memb]s ( ! sol> sy/em4 ,o!rwise1 ^? t are situat$ on ! conf9es ( creation1 be+ reta9$ by no =ces f )\t1 :ile !y are subject to ! attraction ( all ! bodies )91 mu/ leave _! /ations1 & move inw>d ) accel]at$ velocity2 & ?us all ! bodies 9 ! univ]se w\ld at l5g? fall toge!r 9 ! common c5tre ( gravity4 ,! imm5se di/ance at :i* ! />s are plac$ f ea* o!r w\ld inde$ delay su* a cata/rophe2 b ?is mu/ be ! ultimate t5d5cy ( ! mat]ial _w1 unless su/a9$ 9 "o h>moni\s sy/em by nicely-adju/$ motions4 ,to leave entirely out ( view our confid5ce 9 ! wisdom & pres]v+ goodness ( ! ,creator1 & reason+ m]ely f :at we "k ( ! /ability ( ! sol> sy/em1 we %\ld be ju/ifi$ 9 inf]r+1 t o!r worlds are n subject to =ces :i* op]ate only to ha/5 _! decay1 & to involve !m 9 f9al ru94 ,we conclude1 !re=e1 t ! mat]ial univ]se is "o great sy/em2 t ! comb9ation ( planets ) _! satellites con/itutes ! fir/ or l[e/ ord] ( worlds2 t next to ^!1 planets are l9k$ to suns2 t ^! are b\nd to o!r suns1 compos+ a /ill high] ord] 9 ! scale ( be+2 & f9ally1 t all ! diff]5t sy/ems ( worlds move ar\nd _! common c5tre ( gravity4 ,,lett] ,,xxxi4 ,,natural ,,!ology4 ----,philosophy1 baptiz$ ,9 ! pure f\nta9 ( ,et]nal ,love1 ,has eyes inde$2 &1 view+ all %e sees ,z meant to indicate a ,god to man1 ,gives ,him ! praise1 & =feits n h] own4--,c[p]4 ,i ,,int5d$1 my de> ,fri5d1 to comply ) y\r reque/ t ,i w\ld discuss ! argum5ts :i* a/ronomy af=ds to natural !ology2 b ^! ,lett]s h be5 already ext5d$ s mu* fur!r ?an ,i anticipat$1 t ,i %all conclude ) sugge/+ a few ( ^? moral & religi\s reflections1 :i* ought always to foll[ 9 ! tra9 ( su* a survey ( ! heav5ly bodies z we h n[ tak54 ,al?\gh !re is evid5ce en\gh 9 ! /ructure1 arrangem5t1 & laws1 :i* prevail among ! heav5ly bodies1 to prove ! exi/5ce ( ,god1 yet ,i ?9k !re are _m subord9ate p>ts ( ,8 works f> bett] adapt$ to ?is purpose ?an ^!1 be+ m fully )9 our compreh5sion4 ,x 0 int5d$1 no d\bt1 t ! evid5ce ( ,8 be+ %\ld be accessible to all ,8 creatures1 & %\ld n dep5d on a k9d ( k possess$ by comp>atively few4 ,! me*anism ( ! eye is probably n m p]fect ?an t ( ! univ]se2 b we c analyze x bett]1 & m fully und]/& ! design ( ea* "p4 ,b ! exi/5ce ( ,god be+ once prov$1 & x be+ admitt$ t ,he is ! ,creator & ,gov]nor ( ! _w1 !n ! discov]ies ( a/ronomy are admirably adapt$ to p]=m j t (fice 9 relation to ! ,great ,fir/ ,cause1 :i* is assign$ to !m 9 ! ,bible1 namely1 to decl>e ! glory ( ,god1 & to %[ ,8 h&iwork4 ,9 o!r words1 ! discov]ies ( a/ronomy are peculi>ly fitt$1--m s1 p]haps1 ?an any o!r dep>tm5t ( creation1--to exhibit ! unity1 p[]1 & wisdom1 ( ! ,creator4 ,! mo/ mod]n discov]ies h multipli$ ! pro(s ( ! unity ( ,god4 ,x has usually be5 (f]$ z suffici5t evid5ce ( ! tru? ( ?is doctr9e1 t ! laws ( ,nature are f\nd to be uni=m :5 appli$ to ! utmo/ b\nds ( ! sol> sy/em2 t ! law ( gravitation controls alike ! motions ( ,m]cury1 & ^? ( ,uranus2 & t its op]ation is "o & ! same ^u ! moon & ^u ! satellites ( ,saturn4 ,x 01 h[ev]1 impossible1 until rec5tly1 to pr$icate ! same uni=mity 9 ! great laws ( ! univ]se respect+ ! />ry worlds1 except by a feeble analogy4 ,h[ev] improbable1 x 0 /ill possible1 t 9 ^! di/ant worlds o!r laws might prevail1 & o!r ,lords ex]cise dom9ion4 ,b ! discov]y ( ! revolutions ( ! b9>y />s1 9 exact accordance ) ! law ( gravitation1 n m]ely 9 a s+le in/ance1 b 9 _m in/ances1 9 all cases1 inde$1 :]ev] ^? revolutions h advanc$ s f> z to det]m9e _! law ( action1 gives u demon/ration1 in/ead ( analogy1 ( ! preval5ce ( ! same law among ! o!r sy/ems z t :i* rules 9 ours4 ,! m>ks ( a /ill high] organization 9 ! /ructure ( clu/]s & nebul1 all be>+ t same *>act]i/ic union ( resemblance & v>iety :i* belongs to all ! o!r works ( creation t fall "u our notice1 speak l\dly ( "o1 & only "o1 gr& design4 ,e new discov]y ( ! telescope1 !re=e1 has add$ new pro(s to ! great tru? t ,god is "o3 nor1 s f> z ,i "k1 has a s+le fact appe>$1 t is n entirely consonant ) x4 ,light1 moreov]1 :i* br+s u intellig5ce1 &1 9 mo/ cases1 ! only intellig5ce we h1 ( ^! remote orbs1 te/ifies to ! same tru?1 be+ simil> 9 its prop]ties & uni=m 9 its motions1 f :atev] /> x emanates4 ,9 displays ( ! p[] ( ,jehovah1 no?+ c comp>e ) ! />ry heav5s4 ,! magnitudes1 di/ances1 & velocities1 ( ! heav5ly bodies are s mu* beyond e ?+ ( ?is k9d :i* belongs to ?+s ar\nd u1 f :i* we borr[$ our fir/ ideas ( ^! qualities1 t we c sc>cely avoid look+ ) incr$ulity at ! num]ical results to :i* ! un]r+ pr9ciples ( ma!matics h conduct$ u4 ,& :5 we attempt to apply our measures to ! fix$ />s1 & especially to ! nebul1 ! result is absolutely ov]:elm+3 ! m9d refuses its aid 9 our attempts to grasp ! great ideas4 ,nor less conspicu\s1 among ! ph5om5a ( ! heav5ly bodies1 is ! wisdom ( ! ,creator4 ,9 ! fir/ place1 ?is attribute is e :]e exhibit$ 9 ! happy adaptation ( means to _! ends4 ,no pr9ciple c be imag9$ m simple1 & at ! same "t m effectual to answ] ! purposes :i* x s]ves1 ?an gravitation4 ,no position c be giv5 to ! sun & planets s fitt$1 z f> z we c judge1 to fulfil _! mutual relations1 z t :i* ! ,creator has giv5 !m4 ,i say1 z f> z we c judge2 = we f9d ?is to be ! case 9 respect to our own planet & its att5dant satellite1 & h5ce h reason to inf] t ! same is ! case 9 ! o!r planets1 evid5tly hold+1 z !y d1 a simil> relation to ! sun4 ,?us ! position ( ! e>? at j su* a di/ance f ! sun z suits ! nature ( its animal & vegetable k+doms1 & conf9+ ! range ( sol> heat1 va/ z x might easily become1 )9 su* n>r[ b\nds2 ! incl9ation ( ! e>?'s axis to ! plane ( its orbit1 s z to produce ! agreeable vicissitudes ( ! seasons1 & increase ! v>ieties ( animal & vegetable life1 /ill conf9+ ! degree ( incl9ation s exactly )9 ! b\nds ( safety1 t1 7 x mu* to transc5d its pres5t limits1 ! *anges ( temp]ature ( ! diff]5t seasons w\ld be too sudd5 & viol5t = ! exi/5ce ( ei!r animals or vegetables2 ! revolution ( ! e>? on its axis1 s happily divid+ "t into h\rs ( bus9ess & ( repose2 ! adaptation ( ! moon to ! e>?1 s z to af=d to u h] greate/ am\nt ( light j at ! times :5 x is ne$$ mo/1 & giv+ to ! moon j su* a quantity ( matt]1 & plac+ h] at j su* a di/ance f ! e>?1 z s]ves to raise a tide productive ( e conceivable advantage1 )\t ! evils :i* w\ld result f a /agnation ( ! wat]s on ! "o h&1 or f _! ov]fl[ on ! o!r2--^! are a few examples ( ! wisdom display$ 9 ! mutual relations in/itut$ betwe5 ! sun1 ! e>?1 & ! moon4 ,9 ! second place1 simil> m>ks ( wisdom are exhibit$ 9 ! _m useful & important purposes :i* ! same ?+ is made to s]ve4 ,?us ! sun is at once ! great regulator ( ! planet>y motions1 & ! f\nta9 ( light & heat4 ,! moon bo? gives light by night & raises ! tides4 ,or1 if we w\ld foll[ out ?is pr9ciple :]e its op]ations are m )9 our compreh5sion1 we may in/ance ! atmosph]e4 ,:5 man con/ructs an in/rum5t1 he deems x suffici5t if x fulfils "o s+le purpose z ! wat*1 to tell ! h\r ( ! day1 or ! telescope1 to enable him to see di/ant objects2 & _h a be+ l ourselves made ! atmosph]e1 he w\ld h ?\ght x en\gh to h creat$ a m$ium s ess5tial to animal life1 t to live is to brea!1 & to cease to brea! is to die4 ,b beside ?is1 ! atmosph]e has manifold uses1 ea* entirely di/9ct f all ! o!rs4 ,x conveys to plants1 z well z animals1 _! n\ri%m5t & life2 x temp]s ! heat ( ,summ] ) its breezes2 x b9ds d[n all fluids1 & prev5ts _! pass+ into ! /ate ( vapor2 x supports ! cl\ds1 di/ils ! dew1 & wat]s ! e>? ) %[]s2 x multiplies ! light ( ! sun1 & diffuses x ov] e>? & sky2 x fe$s our fires1 turns our ma*9es1 wafts our %ips1 & conveys to ! e> all ! s5tim5ts ( language1 & all ! melodies ( music4 ,9 ! ?ird place1 ! wisdom ( ! ,creator is /rik+ly manife/$ 9 ! provision he has made = ! /ability ( ! univ]se4 ,! p]turbations occasion$ by ! motions ( ! planets1 f _! action on ea* o!r1 are v num]\s1 s9ce e body 9 ! sy/em ex]ts an attraction on e o!r1 9 con=mity ) ! law ( univ]sal gravitation4 ,v5us & ,m]cury1 approa*+1 z !y d at times1 comp>atively ne> to ! e>?1 s5sibly di/urb its motions2 & ! satellites ( ! remot] planets greatly di/urb ea* o!r's movem5ts4 ,nor 0 x possible to end[ ?is pr9ciple ) ! prop]ties x has1 & make x op]ate z x does 9 regulat+ ! motions ( ! _w1 )\t involv+ su* an incid5t4 ,on ?is subject1 ,pr(essor ,:ewell1 9 8 excell5t "w compos+ "o ( ! ,bridgewat] ,treatises1 rem>ks3 ,! d]angem5t :i* ! planets produce 9 ! motion ( "o ( _! numb] w be v small1 9 ! c\rse ( "o revolution2 b ?is gives u no security t ! d]angem5t may n become v l>ge1 9 ! c\rse ( _m revolutions4 ,! cause acts p]petually1 & x has ! :ole ext5t ( "t to "w 94 ,is x n easily conceivable1 !n1 t1 9 ! lapse ( ages1 ! d]angem5ts ( ! motions ( ! planets may accumulate1 ! orbits may *ange _! =m1 & _! mutual di/ances may be mu* increas$ or dim9i%$8 ,is x n possible t ^! *anges may g on )\t limit1 & end 9 ! complete subv]sion & ru9 ( ! sy/em8 ,if1 = in/ance1 ! result ( ?is mutual gravitation %\ld be to increase consid]ably ! ecc5tricity ( ! e>?'s orbit1 or to make ! moon approa* cont9ually ne>] & ne>] to ! e>?1 at e revolution1 x is easy to see t1 9 ! "o case1 our ye> w\ld *ange its "*1 produc+ a f> great] irregul>ity 9 ! di/ribution ( ! sol> heat2 9 ! o!r1 our satellite mu/ fall to ! e>?1 occasion+ a dreadful cata/rophe4 ,if ! positions ( ! planet>y orbits1 ) respect to t ( ! e>?1 7 to *ange mu*1 ! planets might sometimes come v ne> u1 & ?us increase ! effect ( _! attraction beyond calculable limits4 ,"u su* circum/ances1 'we might h ye>s ( unequal l5g?1 & seasons ( caprici\s temp]ature2 planets & moons1 ( port5t\s size & aspect1 gl>+ & disappe>+ at unc]ta9 int]vals2 tides1 l deluges1 sweep+ ov] :ole cont95ts2 & p]haps ! collision ( two ( ! planets1 & ! consequ5t de/ruction ( all organization on bo? ( !m4' ,! fact really is1 t *anges are tak+ place 9 ! motions ( ! heav5ly bodies1 :i* h gone on progressively1 f ! fir/ dawn ( sci5ce4 ,! ecc5tricity ( ! e>?'s orbit has be5 dim9i%+ f ! e>lie/ obs]vations to our times4 ,! moon has be5 mov+ quick] f ! "t ( ! fir/ record$ eclipses1 & is n[ 9 advance1 by ab\t f\r times h] own bread?1 ( :at h] own place w\ld h be51 if x _h n be5 affect$ by ?is accel]ation4 ,! obliquity ( ! ecliptic1 also1 is 9 a /ate ( dim9ution1 & is n[ ab\t two fif?s ( a degree less ?an x 0 9 ! "t ( ,ari/otle4 ,b amid s _m seem+ causes ( irregul>ity & ru91 x is wor?y ( a grateful notice1 t effectual provision is made = ! /ability ( ! sol> sy/em4 ,! full confirmation ( ?is fact is among ! gr& results ( physical a/ronomy4 ,newton did n und]take to demon/rate ei!r ! /ability or in/ability ( ! sy/em4 ,! decision ( ?is po9t requir$ a great numb] ( prep>atory /eps & simplifications1 & su* progress 9 ! inv5tion & improvem5t ( ma!matical me?ods1 z occupi$ ! be/ ma!maticians ( ,europe = ! great] "p ( ! la/ c5tury4 ,t[>ds ! end ( t "t1 x 0 %[n by ,la ,grange & ,la ,place1 t ! arrangem5ts ( ! sol> sy/em are /able2 t1 9 ! long run1 ! orbits & motions rema9 un*ang$2 & t ! *anges 9 ! orbits1 :i* take place 9 %ort] p]iods1 nev] transgress c]ta9 v mod]ate limits4 ,ea* orbit und]goes deviations on ?is side & on t side ( its av]age /ate2 b ^! deviations are nev] v great1 & x f9ally recov]s f !m1 s t ! av]age is pres]v$4 ,! planets produce p]petual p]turbations 9 ea* o!r's motions2 b ^! p]turbations are n indef9itely progressive1 b p]iodical1 rea*+ a maximum value1 & !n dim9i%+4 ,! p]iods :i* ?is re/oration requires are1 = ! mo/ "p1 enorm\s1--n less ?an ?\s&s1 & 9 "s in/ances1 millions1 ( ye>s4 ,inde$1 "s ( ^! app>5t d]angem5ts h be5 go+ on 9 ! same direction f ! creation ( ! _w4 ,b ! re/oration is 9 ! sequel z complete z ! d]angem5t2 & 9 ! mean "t ! di/urbance nev] atta9s a suffici5t am\nt s]i\sly to affect ! /ability ( ! sy/em4 ',i h succe$$ 9 demon/rat+1' says ,la ,place1 't1 :atev] be ! masses ( ! planets1 9 consequ5ce ( ! fact t !y all move 9 ! same direction1 9 orbits ( small ecc5tricity1 & b slightly incl9$ to ea* o!r1 _! secul> irregul>ities are p]iodical1 & includ$ )9 n>r[ limits2 s t ! planet>y sy/em w only oscillate ab\t a mean /ate1 & w nev] deviate f x1 except by a v small quantity4 ,! ellipses ( ! planets h be5 & always w be ne>ly circul>4 ,! ecliptic w nev] co9cide ) ! equator2 & ! entire ext5t ( ! v>iation1 9 its incl9ation1 _c exce$ ?ree degrees4' ,to ^! obs]vations ( ,la ,place1 ,pr(essor ,:ewell adds ! foll[+1 on ! importance1 to ! /ability ( ! sol> sy/em1 ( ! fact t ^? planets :i* h great masses h orbits ( small ecc5tricity4 ,! planets ,m]cury & ,m>s1 :i* h mu* ! l>ge/ ecc5tricity among ! old planets1 are ^? ( :i* ! masses are mu* ! smalle/4 ,! mass ( ,jupit] is m ?an two ?\s& times t ( ei!r ( ^! planets4 ,if ! orbit ( ,jupit] 7 z ecc5tric z t ( ,m]cury1 all ! security = ! /ability ( ! sy/em1 :i* analysis has yet po9t$ out1 w\ld disappe>4 ,! e>? & ! small] planets might1 by ! ne> approa* ( ,jupit] at 8 p]ihelion1 *ange _! ne>ly circul> orbits into v long ellipses1 & ?us might fall into ! sun1 or fly (f into remot] space4 ,x is fur!r rem>kable1 t 9 ! newly-discov]$ planets1 ( :i* ! orbits are /ill m ecc5tric ?an t ( ,m]cury1 ! masses are /ill small]1 s t ! same provision is e/abli%$ 9 ?is case1 also4 ,) ?is ha/y glance at ! unity1 p[]1 & wisdom1 ( ! ,creator1 z manife/$ 9 ! greate/ ( ,8 works1 ,i close4 ,i hope en\gh has be5 said to v9dicate ! s5tim5t t call$ ',devotion1 daught] ( ,a/ronomy6' ,i d n pret5d t ?is1 or any o!r sci5ce1 is adequate ( itself to purify ! he>t1 or to raise x to its ,mak]2 b ,i fully believe t1 :5 ! he>t is already "u ! p[] ( religion1 !re is some?+ 9 ! frequ5t & habitual contemplation ( ! heav5ly bodies "u all ! lights ( mod]n a/ronomy1 v favorable to devotional feel+s1 inspir+1 z x does1 humility1 9 unison ) an exalt$ s5tim5t ( grateful adoration4 ,,lett] ,,xxxii4 ,,rec5t ,,discov]ies4 ,all are b p>ts ( "o /up5d\s :ole4--,pope4 ,,)9 a few ye>s1 a/ronomy has be5 enri*$ ) a numb] ( valuable discov]ies1 ( :i* ,i w endeavor to give y a summ>y acc\nt 9 ?is lett]4 ,! heav5s h be5 explor$ ) f> m p[]ful telescopes ?an be=e2 in/rum5tal measurem5ts h be5 c>ri$ to an a/oni%+ degree ( accuracy2 num]\s additions h be5 made to ! li/ ( small planets or a/]oids2 a comet has appe>$ ( extraord9>y spl5dor1 rem>kable1 above all o!rs1 = its ne> approa* to ! sun2 ! di/ances ( sev]al ( ! fix$ />s1 an elem5t long s\ght = 9 va91 h be5 det]m9$2 a l>ge planet1 compos+ 9 itself a magnific5t _w1 has be5 add$ to ! sol> sy/em1 at su* a di/ance f ! c5tral lum9>y z ne>ly to d\ble ! suppos$ dim5sions ( t sy/em2 v>i\s nebul1 be=e held to be irresolvable1 h be5 resolv$ into />s2 & a new satellite has be5 add$ to ,saturn4 ,,improvem5ts ,,9 ,,! ,,telescope4--,h]s*el's =ty-feet telescope1 ( :i* ,i gave an acc\nt 9 my f\r? lett] 7see page #cf71 rema9$ = half a c5tury unequall$ 9 magnitude & p[]2 b 9 #ahdb1 ,"l ,rosse1 an ,iri% nobleman1 comm5c$ a telescope on a scale /ill m gigantic4 ,l ,h]s*el's1 x 0 a reflector1 ! image be+ =m$ by a concave mirror4 ,?is 0 six feet 9 diamet]1 & weigh$ ?ree tons2 & ! tube 0 fifty feet 9 l5g?4 ,! entire co/ ( ! in/rum5t 0 sixty ?\s& doll>s4 ,its reflect+ surface is ne>ly twice z great z ! great ,h]s*elian1 & consequ5tly x greatly exce$s all in/rum5ts hi!rto con/ruct$ 9 ! am\nt ( light :i* x collects & transmits to ! eye2 & ?is adapts x peculi>ly to view+ ^? objects1 z nebul1 ^: light is exce$+ly fa9t4 ,accord+ly1 x has reveal$ to u new wond]s 9 ?is curi\s dep>tm5t ( a/ronomy4 ,"s idea ( ! great dim5sions ( ! ,levia?an telescope 7z ?is in/rum5t has be5 call$7 may be =m$ :5 x is said t ! ,dean ( ,ely1 a full-siz$ man1 walk$ ?r\gh ! tube f "o end to ! o!r1 ) an umbrella ov] 8 head4 ,b /ill great] advances h be5 made 9 refract+ ?an 9 reflect+ telescopes4 ,su* 0 ! difficulty ( obta9+ l>ge pieces ( glass :i* are free f impurities1 & su* ! liability ( l>ge l5ses to =m obscure & color$ images1 t x 0 =m]ly suppos$ impossible to make a refract+ telescope l>g] 9 diamet] ?an five or six in*es2 b _! size has be5 increas$ f "o /ep to ano!r1 until !y are n[ made m ?an fifte5 in*es 9 diamet]2 & s completely h all ! difficulties aris+ f ! imp]fections ( glass1 & f optical defects inh]5t 9 l5ses1 be5 surm\nt$1 t ! great telescopes ( ,pulkova1 at ,/4 ,pet]sburgh1 & ( ,h>v>d ,univ]sity 7! two f9e/ refractors 9 ! _w7 are consid]$ among ! mo/ p]fect productions ( ! arts4 ,a l5s ( only #ae in*es 9 diamet] seems1 inde$1 dim9utive :5 comp>$ ) a concave reflector ( six feet2 b = mo/ purposes ( ! a/ronom]1 ! ,pulkova & ,cambridge in/rum5ts are m useful ?an su* great reflectors z ^? ( ,h]s*el & ,rosse4 ,if !re is any p>ticul> 9 :i* ^! are m effective1 x is 9 obs]vations on ! fa9te/ nebul1 :]e x is necess>y to collect & convey to ! eye ! greate/ possible beam ( light4 ,,in/rum5tal ,,measurem5ts4--,:5 a/ronomical in/rum5ts 7 fir/ employ$ to measure ! angul> di/ance betwe5 two po9ts on ! cele/ial sph]e1 x 0 n attempt$ to measure spaces small] ?an t5 m9utes--a space equal to ! ?ird "p ( ! bread? ( ! full moon4 ,ty*o ,brahe1 h[ev]1 c>ri$ 8 measures to sixty times t degree ( m9ut5ess1 hav+ devis$ means ( det]m9+ angles no l>g] ?an t5 seconds1 or ! "o hundr$ & eightie? "p ( ! bread? ( ! lun> disk4 ,= _m ye>s pa/1 a/ronom]s h c>ri$ ^! measures to s+le seconds1 or h det]m9$ spaces no great] ?an ! eighte5 hundr$? "p ( ! diamet] ( ! moon4 ,?is is consid]$ ! smalle/ arc :i* c be accurately measur$ directly on ! limb ( an in/rum5t2 b diff]5ces betwe5 spaces may be e/imat$ to a f> great] degree ( accuracy ?an ?is1 ev5 to ! hundr$? "p ( a second--a space less ?an t int]cept$ by a spid]'s web held be=e ! eye4 ,,discov]y ,,( ,,new ,,planets4--,9 my tw5ty-?ird lett] 7see page #bhf71 ,i gave an acc\nt ( ! small planets call$ a/]oids1 :i* lie betwe5 ! orbits ( ,m>s & ,jupit]4 ,:5 t lett] 0 writt51 no long] ago ?an #ahdj1 only f\r ( ^? bodies _h be5 discov]$1 namely1 ,c]es1 ,pallas1 ,juno1 & ,ve/a4 ,)9 a few ye>s pa/1 n9ete5 m h be5 add$1 mak+ ! numb] ( ! a/]oids kn[n at pres5t tw5ty-?ree1 & e ye> adds "o or m to ! li/4#ag ,! idea fir/ sugge/$ by ,olb]s1 "o ( ! e>lie/ discov]]s ( a/]oids1 t !y are fragm5ts ( a l>ge s+le planet once revolv+ betwe5 ,m>s & ,jupit]1 has ga9$ cr$it s9ce ! discov]y ( s _m additional bodies ( ! same class1 all1 l ! =m]1 exce$+ly small & irregul> 9 _! motions1 al?\gh !re are /ill great difficulties 9 trac+ !m to a common orig94 ,,great ,,comet ,,( #ahdc4--,?is is ! mo/ wond]ful body t has appe>$ 9 ! heav5s 9 mod]n times2 fir/1 on acc\nt ( its appe>+1 :5 fir/ se51 9 ! broad light ( noonday2 &1 secondly1 on acc\nt ( its approa*+ s ne> ! sun z almo/ to graze 8 surface4 ,x 0 fir/ discov]$1 9 ,new ,engl&1 on ! #bh? ( ,febru>y1 a little ea/w>d ( ! sun1 %9+ l a :ite cl\d illum9at$ by ! sol> rays4 ,x arre/$ ! att5tion ( _m individuals f half pa/ sev5 9 ! morn+ until ?ree o'clock 9 ! aft]noon1 :5 ! sky became obscur$ by cl\ds4 ,9 ,mexico1 x 0 obs]v$ f n9e 9 ! morn+ until sunset4 ,at a s+le /ation 9 ,s\? ,am]ica1 x 0 said to h be5 se5 on ! #bg? ( ,febru>y1 almo/ 9 contact ) ! sun4 ,e>ly 9 ,m>*1 x _h rec$$ s f> to ! ea/w>d ( t body z to be visible 9 ! s\?we/ aft] sunset1 ?r[+ upw>d a long tra91 :i* increas$ 9 l5g? f night to night until x cov]$ a space ( #dj degrees4 ,its position may be se5 on a cele/ial globe adju/$ to ! latitude ( ,new ,hav5 7#da #ah7 = ! #bj? ( ,m>*1 by trac+ a l9e1 or1 r1 a broad b& proce$+ f ! place ( ! sun t[>ds ! bright /> ,sirius1 9 ! s\?1 betwe5 ! e>s ( ! ,h>e & ! feet ( ,orion4 ,! comet pass$ its p]ihelion on ! #bg? ( ,febru>y1 at :i* "t x almo/ came 9 contact ) ! sun4 ,to prev5t its fall+ into ! sun x 0 endu$ ) a prodigi\s velocity2 a velocity s great t1 _h x cont9u$ at ! same rate z at ! in/ant ( p]ihelion passage1 x w\ld h :irl$ r\nd ! sun 9 two h\rs & a half4 ,x did1 9 fact1 complete m ?an half its revolution ar\nd ! sun 9 t %ort p]iod1 & x made m ?an ?ree qu>t]s ( its circuit ar\nd ! sun 9 "o day4 ,its velocity1 :5 ne>e/ ! sun1 exce$$ a million ( miles p] h\r1 & its tail1 at its greate/ elongation1 0 "o hundr$ & eight millions ( miles2 a l5g? m ?an suffici5t to h rea*$ f ! sun to ! e>?4 ,its heat 0 e/imat$ to be #dg1jjj times great] ?an t receiv$ by ! e>? f a v]tical sun1 & consequ5tly x 0 m int5se ?an t produc$ by ! mo/ p[]ful bl[pipes1 & suffici5t to melt l wax ! mo/ infusible bodies4 ,no d\bt1 :5 9 ! vic9ity ( ! sun1 ! solid matt] ( ! comet 0 fir/ melt$ & !n conv]t$ into vapor1 :i* itself became r$ hot1 or1 m prop]ly speak+1 :ite hot4 ,mu* discussion has aris5 among a/ronom]s respect+ ! p]iodic "t ( ?is comet4 ,its mo/ probable p]iod is ab\t #age ye>s4 ,,di/ances ,,( ,,! ,,/>s4--,i h already m5tion$ 7page #chi7 t ! di/ance ( at lea/ "o ( ! fix$ />s has at l5g? be5 det]m9$1 al?\gh at s great a di/ance t its annual p>allax is only ab\t "o ?ird ( a second1 imply+ a di/ance f ! sun ( ne>ly sixty millions ( millions ( miles4 ,( a di/ance s imm5se ! m9d c =m no adequate conception4 ,! mo/ successful ef=t t[>ds x is made by gradual & successive approximations4 ,let u1 !re=e1 take ! motion ( a rail-way c> z ! mo/ rapid ) :i* we are famili>1 & apply x fir/ to ! planet>y spaces1 & !n to ! va/ int]val t sep>ates ^! ne!r worlds f ! fix$ />s4 ,a rail-way c>1 travell+ con/antly night & day at ! rate ( tw5ty miles p] h\r1 w\ld make #dhj miles p] day4 ,at ?is rate1 to travel ar\nd ! e>? on a great circle w\ld require ab\t #ej days1 & #ejj days to rea* ! moon4 ,if we took our dep>ture f ! sun1 & j\rney$ night & day1 we %\ld rea* ,m]cury 9 a little m ?an #bjj ye>s1 ,v5us 9 ne>ly #djj1 & ! ,e>? 9 #edg ye>s2 b to rea* ,neptune1 ! out]mo/ planet1 w\ld require #af1jjj ye>s4 ,great z appe> ! dim5sions ( ! sol> sy/em1 :5 we imag9e ourselves ?us borne along f _w to _w1 yet ?is space is small comp>$ ) t :i* sep>ates u f ! fix$ />s2 = to rea* #fa ,cygni x w\ld take #cbd1jjj1jjj ye>s4 ,b ?is is believ$1 = c]ta9 satisfactory reasons1 to be "o ( ! ne>e/ ( ! />s4 ,sev]al o!r />s ^: p>allax has be5 det]m9$ are at a mu* great] di/ance ?an #fa ,cygni4 ,! pole /> is five times z f> (f2 & ! great] "p ( ! />s are at di/ances inconceivably m remote4 ,su*1 especially1 are ^? :i* compose ! fa9te/ nebul4 ,,discov]y ,,( ,,! ,,planet ,,neptune4--,f ! e>lie/ ages d[n to ! ye> #agha1 ! sol> sy/em 0 suppos$ to t]m9ate ) ! planet ,saturn1 at ! di/ance ( n9e hundr$ millions ( miles f ! sun2 b ! discov]y ( ,uranus add$ ano!r _w1 & d\bl$ ! dim5sions ( ! sol> sy/em4 ,x seem$ improbable t any m planets %\ld exi/ at a di/ance /ill m remote1 s9ce su* a body c\ld h>dly receive any ( ! vivify+ influ5ces ( ! c5tral lum9>y4 ,/ill1 c]ta9 irregul>ities to :i* ! ,uranus 0 subject1 l$ to ! suspicion t !re exi/s a planet beyond x1 :i*1 by its attractions1 caus$ ^! irregul>ities4 ,impress$ ) ?is belief1 two "y a/ronom]s ( great g5ius1 ,le ,v]ri]1 ( ,france1 & ,adams1 ( ,engl&1 appli$ !mselves to ! task ( f9d+ ! hidd5 planet4 ,! direction 9 :i* ! di/urb$ body 0 mov$ af=d$ "s clue to ! "p ( ! heav5s :]e ! di/urb+ body lay conceal$2 ! k9d ( action x excit$ at diff]5t times indicat$ t x 0 beyond ,uranus1 & n ?is side ( t planet2 & ! magnitude ( ! =ces x ex]t$ gave "s intimation ( its size & mass4 ,! law ( di/ances f ! sun :i* ! sup]ior planets obs]ve 7,saturn be+ ne>ly twice ! di/ance ( ,jupit]1 & ,uranus twice t ( ,saturn71 l$ bo? ^! a/ronom]s to assume t ! body s\ght 0 ne>ly d\ble ! di/ance ( ,uranus f ! sun4 ,) ^! few & imp]fect data1 z s _m lead+-/r+s proce$+ f ! planet ,uranus1 !y felt _! way into ! abysses ( space by ! aid ( two sure guides--! law ( gravitation & ! high] geometry4 ,bo? a/ronom]s arriv$ at ne>ly ! same results1 al?\gh !y wr\ght indep5d5tly ( ea* o!r1 & ea*1 inde$1 )\t ! k ( ! o!r4 ,le ,v]ri] 0 ! fir/ to make public 8 conclusions1 :i* he communicat$ to ! ,fr5* ,academy at _! sitt+1 ,augu/ #ca1 #ahdf4 ,!y saw t !re exi/$1 at ne>ly d\ble ! di/ance ( ,uranus f ! sun1 a planet l>g] ?an t body2 t x lay ne> a c]ta9 /> se5 at t season 9 ! s\?we/1 9 ! ev5+ sky2 t1 on acc\nt ( its imm5se di/ance1 x 0 invisible to ! nak$ eye1 & c\ld be di/9ctly se5 ) a p]ceptible disk only by ! mo/ p[]ful telescopes2 be+ no bright] ?an a /> ( ! n9? magnitude1 & subt5d+ an angle ( only ?ree seconds4 ,le ,v]ri] communicat$ ^! results to ,dr4 ,galle1 ( ,b]l91 ) ! reque/ t he w\ld se>* = ! /rang] ) 8 p[]ful telescope1 po9t+ out ! exact spot 9 ! heav5s :]e x w\ld be f\nd4 ,on ! same ev5+1 ,dr4 ,galle direct$ 8 in/rum5t to t "p ( ! heav5s1 & imm$iately ! planet pres5t$ itself to view1 )9 "o degree ( ! v spot assign$ to x by ,le ,v]ri]4 ,subsequ5t inve/igations h %[n t its app>5t size is )9 half a second ( t :i* ! same sagaci\s m9d =esaw1 & t its diamet] is ne>ly equal to t ( ,uranus1 be+ #ca1jjj1 :ile ,uranus is #ce1jjj miles4#ah ,! di/ance f ! sun is less ?an 0 pr$ict$1 be+ only ab\t #cjjj1 in/ead ( #cfjj millions ( miles2 & its p]iodic "t is #afd-a_/b1 in/ead ( #bag ye>s1 z 0 suppos$ by ,le ,v]ri]4 ,"o satellite only has yet be5 discov]$1 & ?is 0 fir/ se5 by ,pr(essor ,bond ) ! great telescope ( ,h>v>d ,univ]sity4 ,,rec5t ,,telescopic ,,discov]ies4--,! great reflect+ telescope ( ,"l ,rosse1 & ! p[]ful refract+ telescopes ( ,pulkova & ,cambridge1 h op5$ new fields ( discov]y to ! delight$ a/ronom]4 ,a new satellite has be5 add$ to ,saturn1 fir/ reveal$ to ! ,cambridge in/rum5t1 mak+ ! entire numb] ( moons t adorn ! nocturnal sky ( t rem>kable planet no less ?an eight4 ,/ill m wond]ful ?+s h be5 disclos$ among ! remote/ ,nebul4 ,a numb] ( ^! objects be=e plac$ among ! irresolvable nebul1 & suppos$ to consi/ n ( />s1 b ( m]e nebul\s matt]1 h be5 resolv$ into />s2 o!rs1 ( :i* we be=e saw only a "p1 h reveal$ !mselves "u new & /range =ms1 "o resembl+ an animal ) huge bran*+ arms1 & h5ce call$ ! crab nebula2 ano!r imitat+ a scroll or vortex1 & call$ ! :irlpool nebula2 & o!r figures1 :i* to ord9>y telescopes appe> only z dim specks on ! conf9es ( creation1 are pres5t$ to ^! wond]ful in/rum5ts z glori\s firmam5ts ( />s4 ,9 ! ye> #ahcc1 ,sir ,john ,h]s*el left ,engl& = ! ,cape ( ,good ,hope1 furni%$ ) p[]ful in/rum5ts = obs]v+ ! />s & nebul ( ! s\!rn hemisph]e1 :i* _h nev] be5 exam9$ 9 a mann] suit$ to disclose _! full glories4 ,?is great a/ronom] & b5efactor to sci5ce devot$ five ye>s ( ! mo/ assidu\s toil 9 obs]v+ & del9eat+ ! a/ronomical objects ( t portion ( ! heav5s4 ,he _h be=e ext5d$ ! catalogue ( nebul begun by 8 illu/ri\s fa!r1 ,sir ,william ,h]s*el1 to ! numb] ( #bcjg2 & beg9n+ at t po9t1 he swell$ ! numb]1 by 8 labors at ! ,cape ( ,good ,hope1 to #djae4 ,he ext5d$ also ! li/ ( d\ble />s f #ccdf to #eddi1 & %[$ t ! lum9\s spots ne> ! ,s\? ,pole1 kn[n to sailors by ! "n ( ! ,magellan ,cl\ds1 consi/ ( an assemblage ( sev]al hundr$ brilliant nebul4 ,! ,unit$ ,/ates h contribut$ _! full %>e to ! rec5t progress ( a/ronomy4 ,p[]ful telescopes h be5 import$1 made by ! fir/ ,european arti/s1 & num]\s o!rs1 ( sc>cely inf]ior workman%ip & p[]1 h be5 produc$ by arti/s ( our own4 ,! ,am]ican a/ronom]s h also be5 ! fir/ to br+ ! electric telegraph into use 9 a/ronomical obs]vations2 electric clocks h be5 s con/ruct$ z to beat simultane\sly at places di/ant _m hundr$ miles f ea* o!r1 & ?us to furni% means ( det]m9+ ! diff]5ce ( longitude betwe5 places ) an a/oni%+ degree ( accuracy2 & facilities = record+ obs]vations on ! />s h be5 devis$ :i* r5d] ! "w va/ly m rapid z well z m accurate ?an be=e4 ,inde$1 ! inv5tive g5ius = :i* ,am]icans h be5 di/+ui%$ 9 all ! useful arts seems n[ de/9$ to be equally conspicu\s 9 promot+ ! rese>*es ( sci5ce4 ,,footnotes3 #ag ,! names ( all ! a/]oids kn[n at pres5t are z foll[s3 #a4 ,c]es4 #i4 ,metis4 #ag4 ,psy*e4 #b4 ,pallas4 #aj4 ,hygeia4 #ah4 ,melpom5e4 #c4 ,juno4 #aa4 ,p>!nope4 #ai4 ,=tuna4 #d4 ,ve/a4 #ab4 ,victoria4 #bj4 ,massalia4 #e4 ,a/ra4 #ac4 ,eg]ia4 #ba4 ,lutetia4 #f4 ,hebe4 #ad4 ,ir5e4 #bb4 ,calliope4 #g4 ,iris4 #ae4 ,eunomia4 #bc4 ,un-nam$4 #h4 ,flora4 #af4 ,!tis4 #ah ,sir ,john ,h]s*el1 h[ev]1 /ates its diamet] at #da1ejj miles ,,index4 ,a4 ,alamak1 #cga ,aldeb>an1 #cfi ,alex&rian s*ool1 #cid ,alg5ib1 #cga ,algol1 #cga ,alio?1 #cgd ,almage/1 #ad ,altair1 #cgc ,altitude1 #bj ,amplitude1 #bj ,anaxagoras1 #cie ,anaxim&]1 #cie ,&rom$a1 #cga ,ant>es1 #cgj ,ant9\s1 #cgc ,apogee1 #ahg ,apsides1 #ahh ,aqu>ius1 #cga ,aquila1 #cgc ,ar*im$es1 #acf ,arcturus1 #cgb ,aries1 #cfi ,ari/otle1 #acf ,a/rology1 #cic ,a/ronom]s royal1 #dh1 #djd ,a/ronomical clock1 #ea ,a/ronomical tables1 #aij ,a/ronomy1 #ag hi/ory (1 #ad1 #cib ,atmosph]e1 #ajj1 #daj ,attraction1 #ace ,auriga1 #cga ,axis ( ! ,e>?1 #ba ,azimu?1 #bj ,b4 ,bacon1 #af1 #acf ,base l9e1 #gf ,base ( v]ification1 #gi ,bellatrix1 #cge ,betalgeus1 #cge ,bissextile1 #fd ,bootes1 #cgb ,b\gu]1 #gd ,b[dit*1 #adh ,brahean sy/em1 #djc ,c4 ,cs>1 ,julius1 #fd ,cal5d>1 ,grecian1 #fg ,gregorian1 #fe ,canc]1 #cfi ,canis ,major1 #cge ,canis ,m9or1 #cge ,capella1 #cgb ,capricorn1 #cgj ,cassiopeia1 #cgd ,catalogues ( ! />s1 #cfg ,c5tral =ces1 #acj ,cepheus1 #cgd ,c]es1 #bhg ,cetus1 #cgd ,*ronology1 #aeg ,*ronomet]s1 #baj ,circles1 great & small1 #ai ( diurnal revolution1 #ha ( p]petual app>ition1 #he ( p]petual occultation1 #he v]tical1 #bj ,clu/]s1 #cgf ,colures1 #bc ,coma ,b]5ices1 #cgb ,comet1 ,biela's1 #cci ,encke's1 #cdj ,halley's1 #cbc ,comets1 #cac brightness (1 #cae ,comets1 di/ances (1 #cag light (1 #cag magnitude (1 #cae mass (1 #cah motions (1 #cbj numb] (1 #cae p]iods (1 #caf p]turbations (1 #cai /ructure (1 #cad tails (1 #cag ,complem5t1 #ah ,conjunction1 #bjj ,con/ellations1 #cff ,cop]nican sy/em1 #bef1 #dja ,cop]nicus1 #ad1 #bee ,cor ,c>oli1 #cgb ,cor ,hydr1 #cge ,corona ,borealis1 #cgb ,corvus1 #cge ,crotona1 #cid ,cry/all9e sph]es1 #cig ,cygnus1 #cgd ,d4 ,day1 a/ronomical1 #fa sid]eal1 #fj sol>1 #fj ,days ( ! week1 #fh ,decl9ation1 #bd ,def]5ts1 #djj ,d5ebola1 #cgj ,di/ances ( ! heav5ly bodies1 h[ measur$1 #id ,di/ances ( ! />s1 #chg ,dolph91 #cgc ,d\ble />s1 #cha ,draco1 #cgd ,e4 ,e>?1 diamet] ( !1 #gh ellipticity ( !1 #gh figure ( !1 #fi motion ( !1 #abf orbit ( !1 #adi ,eclipses1 annul>1 #bjd calculation (1 #bja ( ! moon1 #aie ( ! sun1 #bjc ,ecliptic1 #bb ,epicycles1 #djj ,equation ( "t1 #fa ,equations1 p]iodical1 #aic secul>1 #aic tabul>1 #aij ,equator1 #ba ,equ9oxes1 #bb precession ( !1 #aed ,eudoxus1 #cig ,f4 ,fomalhaut1 #cga ,fraunh(]1 #cg ,g4 ,galaxy1 #cgi ,galileo1 #ae abjuration (1 #bgb condemnation (1 #bff life (1 #beh p]secutions (1 #bfe ,gem9i1 #cfi ,gemma1 #cgb ,globes1 artificial1 #be ,gravitation1 univ]sal1 #ade ,gravity1 t]re/rial1 #acd ,h4 ,h]cules1 #cgb ,h]s*el1 ,sir ,wm41 #cf1 #aje1 #chc ,hesp]us1 #cig ,hipp>*us1 #cih ,horizon1 rational1 #bj s5sible1 #bj ,h\r-circles1 #ba ,huygh5s1 #gb ,i4 ,inductive sy/em1 #acg ,inquisition1 #ach ,in/rum5ts1 a/ronomical1 #bi ,j4 ,juno1 #bhh ,jupit]1 #bdg belts (1 #bdh diamet] (1 #bdg di/ance (1 #bdg eclipses (1 #bej magnitude (1 #bdg satellites (1 #bej sc5]y (1 #bdg telescopic view (1 #bdg ,k4 ,kepl]1 #cjj ,kepl]'s laws1 #bif ,l4 ,latitude1 #bb h[ f\nd1 #baj ,laws ( motion1 #abf t]re/rial gravity1 #aci ,leap ye>1 #fd ,leo1 #cgj ,leo ,m9or1 #cgb ,libra1 #cgj ,librations ( ! moon1 #agi ,light1 velocity (1 h[ measur$1 #beb ,longitude1 cele/ial1 #bd t]re/rial1 #bb its importance1 #bjh h[ f\nd1 #baj by *ronomet]s1 #baj by eclipses1 #bab by ,jupit]'s satellites1 #bea by lun> me?od1 #bac ,lucif]1 #cig ,lynx1 #cgb ,m4 ,magnitudes1 h[ measur$1 #id ,magellan cl\ds1 #cgh ,m>s1 #bde *anges (1 #bde di/ance (1 #bde revolutions (1 #bdf ,mecanique ,cele/e1 #adh ,m]cury1 #bcj conjunctions (1 #bca diurnal revolution (1 #bce phases (1 #bcd sid]eal revolut'n (1 #bca synodical revolut'n (1 #bca transits (1 #bcg ,m]idian1 #bj ,meteoric %[]s1 #cdf orig9 (1 #cej ,meteoric /ones1 #bij ,metonic cycle1 #aib ,miletus1 s*ool (1 #cid ,milky ,way1 #cgi ,mira1 #cge ,mira*1 #cga ,miz>1 #cgd ,mon?1 sid]eal1 #agc synodical1 #agc ,moon1 #aeg atmosph]e ( !1 #afg cusps ( !1 #agd diamet] ( !1 #aeh di/ance ( !1 #aeh eclipses ( !1 #aie h>ve/1 #agg irregul>ities ( !1 #ahf librations ( !1 #agi light ( !1 #aeh m\nta9s 9 !1 #aei nodes ( !1 #agc phases ( !1 #agd revolutions ( !1 #agh-ahb sc5]y ( !1 #afc telescopic appe>ance ( !1 #aeh volcanoes 9 !1 #aff volume ( !1 #aeh ,motion1 laws (1 #abf ,motions ( ! planets1 #bia ,mural circle1 #ed ,n4 ,nadir1 #bj ,nature ( ! />s1 #cij ,nebul1 #cgg ,new planets1 #bhf di/ances (1 #bhh orig9 (1 #bhi p]iods (1 #bhh size (1 #bhi ,new /yle1 #ff ,newton1 #af1 #adc ,o4 ,oblique sph]e1 #hd ,obliquity ( ! ecliptic1 #aae effect (1 on ! ,seasons1 #abc h[ f\nd1 #aag ,obs]vatory1 #db ,gre5wi*1 #db-dh ,ty*o's1 #db ,old /yle1 #ff ,ophiucus1 #cgb ,opposition1 #bjj ,orion1 #cge ,orr]ies1 #aab1 #bib ,p4 ,pallas1 #bhg ,p>allactic arc1 #ia ,p>allax1 #ij1 #chi annual1 #chg horizontal1 #ic h[ f\nd1 #id ,p>allel sph]e1 #hd ,p>allels ( latitude1 #bd ,pegasus1 #cgc ,p5dulum1 #gi ,p]igee1 #ahg ,p]iodical inequalities1 #aic ,p]seus1 #cga ,pisces1 #cga ,piscis ,au/ralis1 #cga ,planets1 #bbe di/ances (1 #bbh inf]ior1 #bbg magnitudes (1 #bbi p]iods1 #bbi sup]ior1 #bdc ,pleiades1 #cfi ,po9t]s1 #cgd ,pol> di/ance1 #bb ,pol>is1 #cgc ,pole1 #ai ( ! e>?1 #ba ,pollux1 #cfi ,p[] ( ! ,deity1 #djh ,prsepe1 #cfi ,precession1 #aee ,prime v]tical1 #bj ,primum mobile1 #cih ,pr9cipia1 #adg ,procyon1 #cge ,projection ( ! sph]e1 #bg ,prop] motions ( ! />s1 #chd ,ptolemaic sy/em1 #cii ,ptolemy1 #cih ,py?agoras1 #cid ,q4 ,quadrant1 #ah ,r4 ,radius1 #ag ,refraction1 #ie ,regulus1 #cgj ,resolution ( motion1 #acb ,resultant1 #acb ,revolution1 annual1 #aaa diurnal1 #aaa ,rigel1 #cge ,"r asc5sion1 #bc ,"r sph]e1 #hc ,s4 ,sagitt>ius1 #cgj ,s>os1 #aib ,saturn1 #bgd diamet] (1 #bgd r+ (1 #bge satellites (1 #bhb sc5]y (1 #bhc ,scorpio1 #cgj ,seasons1 #aai ,second>y1 #ai ,secul> inequalities1 #aic ,s]p5t1 #cgc ,sextant1 #eg ,sid]eal day1 #ha mon?1 #agc ,signs1 #bc ,sirius1 #cge ,sol/ices1 #bc ,sph]e1 cele/ial1 #ai doctr9e ( !1 #af oblique1 #hd p>allel1 #hd "r1 #hc t]re/rial1 #ai ,spica1 #cgj ,spots on ! sun1 #ajd cause (1 #ajf dim5sions (1 #aje numb] (1 #ajd ,/ability ( ! univ]se1 #daj ,/>s1 fix$1 #cfe ,/ylus1 #fc ,sun1 #aja attraction ( !1 #aaj d5sity ( !1 #ajc diamet] ( !1 #ajb di/ance ( !1 #aja mass ( !1 #ajc nature & con/itution ( !1 #ajg revolutions ( !1 #ajd ,sun1 spots on !1 #ajd volume ( !1 #ajc ,supplem5t1 #ah ,sy/em ( ! _w1 #cib-djf ,brahean1 #djc ,cop]nican1 #dja ,ptolemaic1 #cii ,t4 ,tang5t1 #abi ,taurus1 #cfi ,telescope1 !1 #ca a*romatic1 #cd directions = us+1 #ci ,dorpat1 #cg ,h]s*elian1 #cf hi/ory (1 #cc reflect+1 #cd ,temp]ature1 *anges (1 #abd ,tempor>y />s1 #chj ,t]m9ator1 #aai1 #aei ,?ales1 #cid ,tides1 #baf cause (1 #baf spr+ & neap1 #bai ,"t1 #ei app>5t1 #fa equation (1 #fa mean1 #fa sid]eal1 #fj ,transits1 #bcg ,triangulation1 #ge ,tropic1 #aag ,twilight1 #ih ,u4 ,unity ( ! ,deity1 #djg ,uranus1 #bhc diamet] (1 #bhc di/ance (1 #bhd hi/ory (1 #bhd p]iod (1 #bhd satellites (1 #bhd sc5]y (1 #bhe ,ursa ,major1 #cgc ,ursa ,m9or1 #cgc ,v4 ,v>iable />s1 #cgi ,v5us1 #bcj conjunctions (1 #bca m\nta9s (1 #bcg phases (1 #bcd revolutions (1 #bcb transits (1 #bci ,ve/a1 #bhh ,v9demiatrix1 #cgj ,virgo1 #cgj ,y4 ,ye>1 a/ronomical1 #fc tropical1 #aef ,z4 ,z5i?1 #bj ,z5i? di/ance1 #ba ,zodiac1 #be ,zodiacal light1 #cfc ,zones1 #be ,,rec5t ,,discov]ies4 ,improvem5ts 9 ! ,telescope1 #dad ,rosse's ,levia?an ,telescope1 #dae ,pulkova & ,cambridge ,telescopes1 #dae ,improvem5ts 9 in/rum5tal ,measurem5ts1 #daf ,new ,planets & ,a/]oids1 #daf ,great ,comet ( #ahdc1 #dag ,di/ances ( ! ,/>s1 #dah ,discov]y ( ,neptune1 #dai ,rec5t telescopic discov]ies1 #dbj ,longitude by ! ,electric ,telegraph1 #dbb 99 99 99 99 99 ,transcrib]'s ,notes ,obvi\s punctuation & spell+ errors repair$4 ,greek translit]ations are inclos$ by equals signs4 ,inconsi/5t hyph5ation has be5 repair$4 ,*>act]s t c\ld n be fully express$ are unpack$ & %[n )9 braces1 e4g4 oblong symbol4 ,9 ambigu\s cases1 ! text has be5 left z x appe>s 9 ! orig9al book4 ,9 p>ticul> _m mismat*$ quotation m>ks1 h n be5 *ang$4 ,page #bf1 knitt+ne$le *ang$ to knitt+ ne$le4 ,page #bda1 trignometry *ang$ to trigonometry4 ,page #cjc1 d$eca$ron *ang$ to dodeca$ron4 ,page #cib1 g5]rally *ang$ to g5]ally4