,a ,,prelim9>y ,,diss]tation ,,on ,,! ,,me*anism ,,( ,,! ,,heav5s4 ,,by ,,mrs4 ,,somm]ville ,,philadelphia3 ,,c>ey ,,lea #ahcb ,9 ord] to convey "s idea ( ! object ( ?is "w1 x may be useful to (f] a few prelim9>y obs]vations on ! nature ( ! subject :i* x is int5d$ to inve/igate1 & ( ! means t h already be5 adopt$ ) s mu* success to br+ )9 ! rea* ( our faculties1 ^? tru?s :i* might seem to be plac$ s f> beyond !m4 ,all ! k we possess ( ext]nal objects is f\nd$ ^u exp]i5ce1 :i* furni%es a k ( facts1 & ! comp>ison ( ^! facts e/abli%es relations1 f :i*1 induction1 ! intuitive belief t l causes w produce l effects1 leads u to g5]al laws4 ,?us1 exp]i5ce tea*es t bodies fall at ! surface ( ! e>? ) an accel]at$ velocity1 & proportional to _! masses4 ,newton prov$1 by comp>ison1 t ! =ce :i* occasions ! fall ( bodies at ! e>?'s surface1 is id5tical ) t :i* reta9s ! moon 9 h] orbit2 & induction l$ him to conclude t z ! moon is kept 9 h] orbit by ! attraction ( ! e>?1 s ! planets might be reta9$ 9 _! orbits by ! attraction ( ! sun4 ,by su* /eps he 0 l$ to ! discov]y ( "o ( ^? p[]s ) :i* ! ,creator has orda9$ t matt] %\ld reciprocally act ^u matt]4 ,physical a/ronomy is ! sci5ce :i* comp>es & id5tifies ! laws ( motion obs]v$ on e>? ) ! motions t take place 9 ! heav5s1 & :i* traces1 by an un9t]rupt$ *a9 ( d$uction f ! great pr9ciple t gov]ns ! univ]se1 ! revolutions & rotations ( ! planets1 & ! oscillations ( ! fluids at _! surfaces1 & :i* e/imates ! *anges ! sy/em has hi!rto und]gone or may h]eaft] exp]i5ce1 *anges :i* require millions ( ye>s = _! accompli%m5t4 ,! comb9$ ef=ts ( a/ronom]s1 f ! e>lie/ dawn ( civilization1 h be5 requisite to e/abli% ! me*anical !ory ( a/ronomy3 ! c\rses ( ! planets h be5 obs]v$ = ages ) a degree ( p]sev]ance t is a/oni%+1 if we consid] ! imp]fection1 & ev5 ! want ( in/rum5ts4 ,! real motions ( ! e>? h be5 sep>at$ f ! app>5t motions ( ! planets2 ! laws ( ! planet>y revolutions h be5 discov]$2 & ! discov]y ( ^! laws has l$ to ! k ( ! gravitation ( matt]4 ,on ! o!r h&1 desc5d+ f ! pr9ciple ( gravitation1 e motion 9 ! sy/em ( ! _w has be5 s completely expla9$1 t no a/ronomical ph5om5on c n[ be transmitt$ to po/]ity ( :i* ! laws h n be5 det]m9$4 ,sci5ce1 reg>d$ z ! pursuit ( tru?1 :i* c only be atta9$ by pati5t & unprejudic$ inve/igation1 :]e9 no?+ is too great to be attempt$1 no?+ s m9ute z to be ju/ly disreg>d$1 mu/ ev] af=d occupation ( consummate int]e/ & ( elevat$ m$itation4 ,! contemplation ( ! works ( creation elevates ! m9d to ! admiration ( :atev] is great & noble1 accompli%+ ! object ( all /udy1 :i* 9 ! elegant language ( ,sir ,james ,mack9to% is to inspire ! love ( tru?1 ( wisdom1 ( beauty1 especially ( goodness1 ! highe/ beauty1 & ( t supreme & et]nal m9d1 :i* conta9s all tru? & wisdom1 all beauty & goodness4 ,by ! love or delightful contemplation & pursuit ( ^! transc5d5t aims = _! own sake only1 ! m9d ( man is rais$ f l[ & p]i%able objects1 & prep>$ = ^? high de/9ies :i* are appo9t$ = all ^? :o are capable ( !m4 ,! heav5s af=d ! mo/ sublime subject ( /udy :i* c be d]iv$ f sci5ce3 ! magnitude & spl5d\r ( ! objects1 ! inconceivable rapidity ) :i* !y move1 & ! enorm\s di/ances betwe5 !m1 impress ! m9d ) "s notion ( ! en]gy t ma9ta9s !m 9 _! motions ) a durability to :i* we c see no limits4 ,equally conspicu\s is ! goodness ( ! great ,fir/ ,cause 9 hav+ end[$ man ) faculties by :i* he c n only appreciate ! magnific5ce ( 8 works1 b trace1 ) precision1 ! op]ation ( 8 laws1 use ! globe he inhabits u a base :]e) to measure ! magnitude & di/ance ( ! sun & planets1 & make ! diamet] ( ! e>?'s orbit ! fir/ /ep ( a scale by :i* he may asc5d to ! />ry firmam5t4 ,su* pursuits1 :ile !y ennoble ! m9d1 at ! same "t inculcate humility1 by %[+ t !re is a b>ri]1 :i* no en]gy1 m5tal or physical1 c ev] enable u to pass3 t h[ev] pr(\ndly we may p5etrate ! dep?s ( space1 !re /ill rema9 innum]able sy/ems comp>$ ) :i* ^? :i* seem s mighty to u mu/ dw9dle into insignificance1 or ev5 become invisible2 & t n only man1 b ! globe he inhabits1 nay ! :ole sy/em ( :i* x =ms s small a "p1 might be annihilat$1 & its ext9ction be unp]ceiv$ 9 ! imm5sity or creation4 ,a complete acqua9tance ) ,physical ,a/ronomy c only be atta9$ by ^? :o are well v]s$ 9 ! high] bran*es ( ma!matical & me*anical sci5ce3 su* alone c appreciate ! extreme beauty ( ! results1 & ( ! means by :i* ^! results are obta9$4 ,nev]!less a suffici5t skill 9 analysis to foll[ ! g5]al outl9e1 to see ! mutual dep5d5ce ( ! diff]5t p>ts ( ! sy/em1 & to compreh5d by :at means "s ( ! mo/ extraord9>y conclusions h be5 arriv$ at1 is )9 ! rea* ( _m :o %r9k f ! task1 appall$ by difficulties1 :i* p]haps are n m =midable ?an ^? incid5t to ! /udy ( ! elem5ts ( e bran* ( k1 & possibly ov]rat+ !m by n mak+ a suffici5t di/9ction betwe5 ! degree ( ma!matical acquirem5t necess>y = mak+ discov]ies1 & t :i* is requisite = und]/&+ :at o!rs h done4 ,t ! /udy ( ma!matics & _! application to a/ronomy are full ( int]e/ w be all[$ by all :o h devot$ _! "t & att5tion to ^! pursuits1 & !y only c e/imate ! delight ( arriv+ at tru?1 :e!r x be 9 ! discov]y ( a _w1 or ( a new prop]ty ( numb]s4 ,x has be5 prov$ by ,newton t a p>ticle ( matt] plac$ )\t ! surface ( a holl[ sph]e is attract$ by x 9 ! "n mann] z if its mass1 or ! :ole matt] x conta9s1 7 collect$ 9 its c5tre4 ,! same is !re=e true ( a solid sph]e :i* may be suppos$ to consi/ ( an inf9ite numb] ( conc5tric holl[ sph]es4 ,?is h[ev] is n ! case ) a sph]oid1 b ! cele/ial bodies are s ne>ly sph]ical1 & at su* remote di/ances f ea* o!r1 t !y attract & are attract$ z if ea* 7 a d5se po9t situate 9 its c5tre ( gravity1 a circum/ance :i* greatly facilitates ! inve/igation ( _! motions4 ,! attraction ( ! e>? on bodies at its surface 9 t latitude1 ! squ>e ( ^: s9e is 1 is ! same z if x 7 a sph]e2 & exp]i5ce %[s t bodies !re fall ?r\gh #af4jfig feet 9 a second4 ,! mean di/ance ( ! moon f ! e>? is ab\t sixty times ! mean radius ( ! e>?4 ,:5 ! numb] #af4jfig is dim9i%$ 9 ! ratio ( #a to #cfjj1 :i* is ! squ>e ( ! moon's di/ance f ! e>?1 x is f\nd to be exactly ! space ! moon w\ld fall ?r\gh 9 ! fir/ second ( h] desc5t to ! e>?1 7 %e n prev5t$ by h] c5trifugal =ce1 aris+ f ! velocity ) :i* %e moves 9 h] orbit4 ,s t ! moon is reta9$ 9 h] orbit by a =ce hav+ ! same orig9 & regulat$ by ! same law ) t :i* causes a /one to fall at ! e>?'s surface4 ,! e>? may !re=e be reg>d$ z ! c5tre ( a =ce :i* ext5ds to ! moon2 b z exp]i5ce %[s t ! action & reaction ( matt] are equal & contr>y1 ! moon mu/ attract ! e>? ) an equal & contr>y =ce4 ,newton prov$ t a body project$ 9 space w move 9 a conic section1 if x be attract$ by a =ce direct$ t[>ds a fix$ po9t1 & hav+ an int5sity inv]sely z ! squ>e ( ! di/ance2 b t any deviation f t law w cause x to move 9 a curve ( a diff]5t nature4 ,kepl] asc]ta9$ by direct obs]vation t ! planets describe ellipses r\nd ! sun1 & lat] obs]vations %[ t comets also move 9 conic sections3 x consequ5tly foll[s t ! sun attracts all ! planets & comets inv]sely z ! squ>e ( _! di/ances f 8 c5tre2 ! sun !re=e is ! c5tre ( a =ce ext5d+ indef9itely 9 space1 & includ+ all ! bodies ( ! sy/em 9 its action4 ,kepl] also d$uc$ f obs]vation1 t ! squ>es ( ! p]iodic times ( ! planets1 or ! times ( _! revolutions r\nd ! sun1 are proportional to ! cubes ( _! mean di/ances f 8 c5tre3 :5ce x foll[s1 t ! int5sity ( gravitation ( all ! bodies t[>ds ! sun is ! same at equal di/ances2 consequ5tly gravitation is proportional to ! masses1 = if ! planets & comets be suppos$ to be at equal di/ances f ! sun & left to ! effects ( gravity1 !y w\ld arrive at 8 surface at ! same "t4 ,! satellites also gravitate to _! prim>ies accord+ to ! same law t _! prim>ies d to ! sun4 ,h5ce1 by ! law ( action & reaction1 ea* body is itself ! c5tre ( an attractive =ce ext5d+ indef9itely 9 space1 :5ce proce$ all ! mutual di/urbances t r5d] ! cele/ial motions s complicat$1 & _! inve/igation s difficult4 ,! gravitation ( matt] direct$ to a c5tre1 & attract+ directly z ! mass1 & inv]sely z ! squ>e ( ! di/ance1 does n belong to x :5 tak5 9 mass2 p>ticle acts on p>ticle accord+ to ! same law :5 at s5sible di/ances f ea* o!r4 ,if ! sun act$ on ! c5tre ( ! e>? )\t attract+ ea* ( its p>ticles1 ! tides w\ld be v mu* great] ?an !y n[ are1 & 9 o!r respects !y also w\ld be v diff]5t4 ,! gravitation ( ! e>? to ! sun results f ! gravitation ( all its p>ticles1 :i* 9 _! turn attract ! sun 9 ! ratio ( _! respective masses4 ,!re is a reciprocal action likewise betwe5 ! e>? & e p>ticle at its surface2 7 ?is n ! case1 & 7 any portion ( ! e>?1 h[ev] small1 to attract ano!r portion & n be itself attract$1 ! c5tre ( gravity ( ! e>? w\ld be mov$ 9 space1 :i* is impossible4 ,! =m ( ! planets results f ! reciprocal attraction ( _! compon5t p>ticles4 ,a deta*$ fluid mass1 if at re/1 w\ld assume ! =m ( a sph]e1 f ! reciprocal attraction ( its p>ticles2 b if ! mass revolves ab\t an axis1 x becomes flatt5$ at ! poles1 & bulges at ! equator1 9 consequ5ce ( ! c5trifugal =ce aris+ f ! velocity ( rotation4 ,=1 ! c5trifugal =ce dim9i%es ! gravity ( ! p>ticles at ! equator1 & equilibrium c only exi/ :5 ^! two =ces are balanc$ by an increase ( gravity2 !re=e1 z ! attractive =ce is ! same on all p>ticles at equal di/ances f ! c5tre ( a sph]e1 ! equatorial p>ticles w\ld rec$e f ! c5tre till _! increase 9 numb] balanc$ ! c5trifugal =ce by _! attraction1 consequ5tly ! sph]e w\ld become an oblate sph]oid2 & a fluid p>tially or entirely cov]+ a solid1 z ! ocean & atmosph]e cov] ! e>?1 mu/ assume t =m 9 ord] to rema9 9 equilibrio4 ,! surface ( ! sea is !re=e sph]oidal1 & ! surface ( ! e>? only deviates f t figure :]e x rises above or s9ks bel[ ! level ( ! sea2 b ! deviation is s small t x is unimportant :5 comp>$ ) ! magnitude ( ! e>?4 ,su* is ! =m ( ! e>? & planets1 b ! compression or flatt5+ at _! poles is s small1 t ev5 ,jupit]1 ^: rotation is ! mo/ rapid1 diff]s b little f a sph]e4 ,al?\gh ! planets attract ea* o!r z if !y 7 sph]es on acc\nt ( _! imm5se di/ances1 yet ! satellites are ne> en\gh to be s5sibly affect$ 9 _! motions by ! =ms ( _! prim>ies4 ,! moon = example is s ne> ! e>?1 t ! reciprocal attraction betwe5 ea* ( h] p>ticles & ea* ( ! p>ticles 9 ! prom95t mass at ! t]re/rial equator1 occasions consid]able di/urbances 9 ! motions ( bo? bodies4 ,=1 ! action ( ! moon on ! matt] at ! e>?'s equator produces a nutation 9 ! axis ( rotation1 & ! reaction ( t matt] on ! moon is ! cause ( a correspond+ nutation 9 ! lun> orbit4 ,if a sph]e at re/ 9 space receives an impulse pass+ ?r\gh its c5tre ( gravity1 all its p>ts w move ) an equal velocity 9 a /raight l9e2 b if ! impulse does n pass ?r\gh ! c5tre ( gravity1 its p>ticles hav+ unequal velocities1 w give x a rotatory motion at ! same "t t x is translat$ 9 space4 ,^! motions are indep5d5t ( "o ano!r1 s t a contr>y impulse pass+ ?r\gh its c5tre ( gravity w imp$e its progression1 )\t int]f]+ ) its rotation4 ,z ! sun rotates ab\t an axis1 x seems probable if an impulse 9 a contr>y direction has n be5 giv5 to 8 c5tre ( gravity1 t he moves 9 space accompani$ by all ^? bodies :i* compose ! sol> sy/em1 a circum/ance t w\ld 9 no way int]f]e ) _! relative motions2 =1 9 consequ5ce ( our exp]i5ce t =ce is proportional to velocity1 ! reciprocal attractions ( a sy/em rema9 ! same1 :e!r its c5tre ( gravity be at re/1 or mov+ uni=mly 9 space4 ,x is comput$ t _h ! e>? receiv$ its motion f a s+le impulse1 su* impulse mu/ h pass$ ?r\gh a po9t ab\t tw5ty-five miles f its c5tre4 ,s9ce ! motions ( ! rotation & translation ( ! planets are indep5d5t ( ea* o!r1 ?\gh probably communicat$ by ! same impulse1 !y =m sep>ate subjects ( inve/igation4 ,a planet moves 9 its elliptical orbit ) a velocity v>y+ e in/ant1 9 consequ5ce ( two =ces1 "o t5d+ to ! c5tre ( ! sun1 & ! o!r 9 ! direction ( a tang5t to its orbit1 aris+ f ! primitive impulse giv5 at ! "t :5 x 0 laun*$ into space3 %\ld ! =ce 9 ! tang5t cease1 ! planet w\ld fall to ! sun by its gravity2 7 ! sun n to attract x1 ! planet w\ld fly (f 9 ! tang5t4 ,?us1 :5 a planet is 9 its aphelion or at ! po9t :]e ! orbit is f>!/ f ! sun1 8 action ov]comes its velocity1 & br+s x t[>ds him ) su* an accel]at$ motion1 t x at la/ ov]comes ! sun's attraction1 & %oots pa/ him2 !n1 gradually decreas+ 9 velocity1 x arrives at ! aphelion :]e ! sun's attraction aga9 prevails4 ,9 ?is motion ! radii vectores1 or imag9>y l9es jo9+ ! c5tres ( ! sun & planets1 pass ov] equal areas 9 equal times4 ,if ! planets 7 attract$ by ! sun only1 ?is w\ld ev] be _! c\rse2 & because 8 action is proportional to 8 mass1 :i* is imm5sely l>g] ?an t ( all ! planets put toge!r1 ! elliptical is ! ne>e/ approximation to _! true motions1 :i* are extremely complicat$1 9 consequ5ce ( _! mutual attraction1 s t !y d n move 9 any kn[n or symmetrical curve1 b 9 pa?s n[ approa*+ to1 & n[ rec$+ f ! elliptical =m1 & _! radii vectores d n describe areas exactly proportional to ! "t4 ,?us ! areas become a te/ ( ! exi/5ce ( di/urb+ =ces4 ,to det]m9e ! motion ( ea* body :5 di/urb$ by all ! re/ is beyond ! p[] ( analysis2 x is !re=e necess>y to e/imate ! di/urb+ action ( "o planet at a "t1 :5ce arises ! celebrat$ problem ( ! ?ree bodies1 :i* orig9ally 0 t ( ! moon1 ! e>?1 & ! sun1 namely1--! masses be+ giv5 ( ?ree bodies project$ f ?ree giv5 po9ts1 ) velocities giv5 bo? 9 quantity & direction2 & suppos+ ! bodies to gravitate to "o ano!r ) =ces t are directly z _! masses1 & inv]sely z ! squ>es ( ! di/ances1 to f9d ! l9es describ$ by ^! bodies1 & _! position at any giv5 in/ant4 ,by ?is problem ! motions ( translation ( all ! cele/ial bodies are det]m9$4 ,x is "o ( extreme difficulty1 & w\ld be ( inf9itely great] difficulty1 if ! di/urb+ action 7 n v small1 :5 comp>$ ) ! c5tral =ce4 ,z ! di/urb+ influ5ce ( ea* body may be f\nd sep>ately1 x is assum$ t ! action ( ! :ole sy/em 9 di/urb+ any "o planet is equal to ! sum ( all ! p>ticul> di/urbances x exp]i5ces1 on ! g5]al me*anical pr9ciple1 t ! sum ( any numb] ( small oscillations is ne>ly equal to _! simultane\s & jo9t effect4 ,on acc\nt ( ! reciprocal action ( matt]1 ! /ability ( ! sy/em dep5ds on ! int5sity ( ! primitive mom5tum ( ! planets1 & ! ratio ( _! masses to t ( ! sun3 = ! nature ( ! conic sections 9 :i* ! cele/ial bodies move1 dep5ds on ! velocity ) :i* !y 7 fir/ propell$ 9 space2 _h t velocity be5 su* z to make ! planets move 9 orbits ( un/able equilibrium1 _! mutual attractions might h *ang$ !m into p>abolas or ev5 hyp]bolas2 s t ! e>? & planets might ages ago h be5 sweep+ ?r\gh ! abyss ( space3 b z ! orbits diff] v little f circles1 ! mom5tum ( ! planets :5 project$1 mu/ h be5 exactly suffici5t to ensure ! p]man5cy & /ability ( ! sy/em4 ,besides ! mass ( ! sun is imm5sely great] ?an ^? ( ! planets2 & z _! inequalities be> ! same ratio to _! elliptical motions z _! masses d to t ( ! sun1 _! mutual di/urbances only increase or dim9i% ! ecc5tricities ( _! orbits by v m9ute quantities2 consequ5tly ! magnitude ( ! sun's mass is ! pr9cipal cause ( ! /ability ( ! sy/em4 ,!re is n 9 ! physical _w a m spl5did example ( ! adaptation ( means to ! accompli%m5t ( ! end1 ?an is exhibit$ 9 ! nice adju/m5t ( ^! =ces4 ,! orbits ( ! planets h a v small incl9ation to ! plane ( ! ecliptic 9 :i* ! e>? moves2 & on t acc\nt1 a/ronom]s ref] _! motions to x at a giv5 epo* z a kn[n & fix$ position4 ,! pa?s ( ! planets1 :5 _! mutual di/urbances are omitt$1 are ellipses ne>ly approa*+ to circles1 ^: planes1 slightly incl9$ to ! ecliptic3 cut x 9 /raight l9es pass+ ?r\gh ! c5tre ( ! sun2 ! po9ts :]e ! orbit int]sects ! plane ( ! ecliptic are its nodes4 ,! orbits ( ! rec5tly discov]$ planets deviate m f ! ecliptic3 t ( ,pallas has an incl9ation ( #ce to x3 on t acc\nt x w be m difficult to det]m9e _! motions4 ,^! little planets h no s5sible effect 9 di/urb+ ! re/1 ?\gh _! own motions are r5d]$ v irregul> by ! proximity ( ,jupit] & ,saturn4 ,! planets are subject to di/urbances ( two di/9ct k9ds1 bo? result+ f ! con/ant op]ation ( _! reciprocal attraction1 "o k9d dep5d+ ^u _! positions ) reg>d to ea* o!r1 beg9s f z]o1 increases to a maximum1 decreases & becomes z]o aga91 :5 ! planets return to ! same relative positions4 ,9 consequ5ce ( ^!1 ! tr\bl$ planet is sometimes drawn away f ! sun1 sometimes br\ght ne>] to him2 at "o "t x is drawn above ! plane ( its orbit1 at ano!r "t bel[ x1 accord+ to ! position ( ! di/urb+ body4 ,all su* *anges1 be+ accompli%$ 9 %ort p]iods1 "s 9 a few mon?s1 o!rs 9 ye>s1 or 9 hundr$s ( ye>s1 are d5om9at$ ,p]iodic ,inequalities4 ,! inequalities ( ! o!r k9d1 ?\gh occasion$ likewise by ! di/urb+ en]gy ( ! planets1 are entirely indep5d5t ( _! relative positions2 !y dep5d on ! relative positions ( ! orbits alone1 ^: =ms & places 9 space are alt]$ by v m9ute quantities 9 imm5se p]iods ( "t1 & are !re=e call$ ,secul> ,inequalities4 ,9 consequ5ce ( di/urbances ( ?is k9d1 ! apsides1 or extremities ( ! major axes ( all ! orbits1 h a direct1 b v>iable motion 9 space1 except+ ^? ( ,v5us1 :i* are retrograde2 & ! l9es ( ! nodes move ) a v>iable velocity 9 ! contr>y direction4 ,! motions ( bo? are extremely sl[2 x requires m ?an #ajiggj ye>s = ! major axis ( ! e>?'s orbit to accompli% a sid]eal revolution1 & #bjice ye>s to complete its tropical motion4 ,! major axis ( ,jupit]'s orbit requires no less ?an #aigefa ye>s to p]=m its revolution f ! di/urb+ action ( ,saturn alone4 ,! p]iods 9 :i* ! nodes revolve are also v great4 ,beside ^!1 ! incl9ation & ecc5tricity ( e orbit are 9 a /ate ( p]petual1 b sl[ *ange4 ,at ! pres5t "t1 ! incl9ations ( all ! orbits are decreas+2 b s sl[ly1 t ! incl9ation ( ,jupit]'s orbit is only six m9utes less n[ ?an x 0 9 ! age ( ,ptolemy4 ,! t]re/rial ecc5tricity is decreas+ at ! rate ( #ciad miles 9 a c5tury2 & if x 7 to decrease equably1 x w\ld be #cfcjj ye>s be=e ! e>?'s orbit became a circle4 ,b 9 ! mid/ ( all ^! vicissitudes1 ! major axes & mean motions ( ! planets rema9 p]man5tly indep5d5t ( secul> *anges2 !y are s connect$ by ,kepl]'s law ( ! squ>es ( ! p]iodic times be+ proportional to ! cubes ( ! mean di/ances ( ! planets f ! sun1 t "o _c v>y )\t affect+ ! o!r4 ,) ! exception ( ^! two elem5ts1 x appe>s1 t all ! bodies are 9 motion1 & e orbit is 9 a /ate ( p]petual *ange4 ,m9ute z ^! *anges are1 !y might be suppos$ liable to accumulate 9 ! c\rse ( ages suffici5tly to d]ange ! :ole ord] ( nature1 to alt] ! relative positions ( ! planets1 to put an end to ! vicissitudes ( ! seasons1 & to br+ ab\t collisions1 :i* w\ld involve our :ole sy/em1 n[ s h>moni\s1 9 *aotic confusion4 ,! consequ5ces be+ s dreadful1 x is natural to inquire1 :at pro( exi/s t creation w be pres]v$ f su* a cata/rophe8 ,= no?+ c be kn[n f obs]vation1 s9ce ! exi/5ce ( ! human race has occupi$ b a po9t 9 duration1 :ile ^! vicissitudes embrace myriads ( ages4 ,! pro( is simple & conv9c+4 ,all ! v>iations ( ! sol> sy/em1 z well secul> z p]iodic1 are express$ analytically by ! s9es & cos9es ( circul> arcs1 :i* increase ) ! "t2 & z a s9e or cos9e nev] c exce$ ! radius1 b mu/ oscillate betwe5 z]o & unity1 h[ev] mu* ! "t may increase1 x foll[s1 t :5 ! v>iations h by sl[ *anges accumulat$ 9 h[ev] long a "t to a maximum1 !y decrease by ! same sl[ degrees1 till !y arrive at _! smalle/ value1 & !n beg9 a new c\rse1 ?us = ev] oscillat+ ab\t a mean value4 ,?is1 h[ev]1 w\ld n be ! case if ! planets mov$ 9 a resi/+ m$ium1 = !n bo? ! ecc5tricity & ! major axes ( ! orbits w\ld v>y ) ! "t1 s t ! /ability ( ! sy/em w\ld be ultimately de/roy$4 ,b if ! planets d move 9 an e!real m$ium1 x mu/ be ( extreme r>ity1 s9ce its resi/ance has hi!rto be5 q ins5sible4 ,?ree circum/ances h g5]ally be5 suppos$ necess>y to prove ! /ability ( ! sy/em3 ! small ecc5tricities ( ! planet>y orbits1 _! small incl9ations1 & ! revolution ( all ! bodies1 z well planets z satellites1 9 ! same direction4 ,^!1 h[ev]1 are n necess>y conditions3 ! p]iodicity ( ! t]ms 9 :i* ! inequalities are express$ is suffici5t to assure u1 t ?\gh we d n "k ! ext5t ( ! limits1 nor ! p]iod ( t gr& cycle :i* probably embraces millions ( ye>s1 yet !y nev] w exce$ :at is requisite = ! /ability & h>mony ( ! :ole1 = ! pres]vation ( :i* e circum/ance is s beautifully & wond]fully adapt$4 ,! plane ( ! ecliptic itself1 ?\gh assum$ to be fix$ at a giv5 epo* = ! conv5i5ce ( a/ronomical computation1 is subject to a m9ute secul> v>iation ( #ebaji1 occasion$ by ! reciprocal action ( ! planets2 b z ?is is also p]iodical1 ! t]re/rial equator1 :i* is incl9$ to x at an angle ( ab\t #bc #bh'1 w nev] co9cide ) ! plane ( ! ecliptic2 s !re nev] c be p]petual spr+4 ,! rotation ( ! e>? is uni=m2 !re=e day & night1 summ] & w9t]1 w cont9ue _! vicissitudes :ile ! sy/em endures1 or is untr\bl$ by =eign causes4 ,yond] />ry sph]e ,( planets1 & ( fix'd1 9 all h] :eels ,resembles ne>e/1 mazes intricate1 ,ecc5tric1 int]volv'd1 yet regul> ,!n mo/1 :5 mo/ irregul> !y seem4 ,! /ability ( our sy/em 0 e/abli%$ by ,la ,grange1 'a discov]y1' says ,pr(essor ,playfair1 't mu/ r5d] ! "n = ev] memorable 9 sci5ce1 & rev]$ by ^? :o delight 9 ! contemplation ( :atev] is excell5t & sublime4 ,aft] ,newton's discov]y ( ! elliptical orbits ( ! planets1 ,la ,grange's discov]y ( _! p]iodical inequalities is )\t d\bt ! noble/ tru? 9 physical a/ronomy2 &1 9 respect ( ! doctr9e ( f9al causes1 x may be reg>d$ z ! greate/ ( all4' ,not)/&+ ! p]man5cy ( our sy/em1 ! secul> v>iations 9 ! planet>y orbits w\ld h be5 extremely emb>rass+ to a/ronom]s1 :5 x became necess>y to comp>e obs]vations sep>at$ by long p]iods4 ,?is difficulty is obviat$ by ,la ,place1 :o has %[n t :atev] *anges "t may induce ei!r 9 ! orbits !mselves1 or 9 ! plane ( ! ecliptic1 !re exi/s an inv>iable plane pass+ ?r\gh ! c5tre ( gravity ( ! sun1 ab\t :i* ! :ole sy/em oscillates )9 n>r[ limits1 & :i* is det]m9$ by ?is prop]ty2 t if e body 9 ! sy/em be project$ on x1 & if ! mass ( ea* be multipli$ by ! area describ$ 9 a giv5 "t by its projection on ?is plane1 ! sum ( all ^! products w be a maximum4 ,?is plane ( greate/ in]tia1 by no means peculi> to ! sol> sy/em1 b exi/+ 9 e sy/em ( bodies submitt$ to _! mutual attractions only1 always rema9s p>allel to itself1 & ma9ta9s a fix$ position1 :5ce ! oscillations ( ! sy/em may be e/imat$ ?r\gh unlimit$ "t4 ,x is situate ne>ly half way betwe5 ! orbits ( ,jupit] & ,saturn1 & is incl9$ to ! ecliptic at an angle ( ab\t #a #ce' #ca4 ,all ! p]iodic & secul> inequalities d$uc$ f ! law ( gravitation are s p]fectly confirm$ by obs]vations1 t analysis has become "o ( ! mo/ c]ta9 means ( discov]+ ! planet>y irregul>ities1 ei!r :5 !y are too small1 or too long 9 _! p]iods1 to be detect$ by o!r me?ods4 ,jupit] & ,saturn1 h[ev]1 exhibit inequalities :i* = a long "t seem$ discordant ) t law4 ,all obs]vations1 f ^? ( ! ,*9ese & ,arabs d[n to ! pres5t day1 prove t = ages ! mean motions ( ,jupit] & ,saturn h be5 affect$ by great inequalities ( v long p]iods1 =m+ :at appe>$ an anomaly 9 ! !ory ( ! planets4 ,x 0 long kn[n by obs]vation1 t five times ! mean motion ( ,saturn is ne>ly equal to twice t ( ,jupit]2 a relation :i* ! sagacity ( ,la ,place p]ceiv$ to be ! cause ( a p]iodic inequality 9 ! mean motion ( ea* ( ^! planets1 :i* completes its p]iod 9 ne>ly #ibi ,julian ye>s1 ! "o be+ ret>d$1 :ile ! o!r is accel]at$4 ,^! inequalities are /rictly p]iodical1 s9ce !y dep5d on ! configuration ( ! two planets2 & ! !ory is p]fectly confirm$ by obs]vation1 :i* %[s t 9 ! c\rse ( tw5ty c5turies1 ,jupit]'s mean motion has be5 accel]at$ by #c #bc'1 & ,saturn's ret>d$ by #e #ac'4 ,x might be imag9$ t ! reciprocal action ( su* planets z h satellites w\ld be diff]5t f ! influ5ce ( ^? t h none2 b ! di/ances ( ! satellites f _! prim>ies are incomp>ably less ?an ! di/ances ( ! planets f ! sun1 & f "o ano!r1 s t ! sy/em ( a planet & its satellites moves ne>ly z if all ^? bodies 7 unit$ 9 _! common c5tre ( gravity2 ! action ( ! sun h[ev] di/urbs 9 "s degree ! motion ( ! satellites ab\t _! prim>y4 ,! *anges t take place 9 ! planet>y sy/em are exhibit$ on a small scale by ,jupit] & 8 satellites2 & z ! p]iod requisite = ! developm5t ( ! inequalities ( ^! little moons only ext5ds to a few c5turies1 x may be reg>d$ z an epitome ( t gr& cycle :i* w n be accompli%$ by ! planets 9 myriads ( c5turies4 ,! revolutions ( ! satellites ab\t ,jupit] are precisely simil> to ^? ( ! planets ab\t ! sun2 x is true !y are di/urb$ by ! sun1 b 8 di/ance is s great1 t _! motions are ne>ly ! same z if !y 7 n "u 8 influ5ce4 ,! satellites l ! planets1 7 probably project$ 9 elliptical orbits1 b ! compression ( ,jupit]'s sph]oid is v great 9 consequ5ce ( 8 rapid rotation2 & z ! masses ( ! satellites are ne>ly #ajjjjj times less ?an t ( ,jupit]1 ! imm5se quantity ( prom95t matt] at 8 equator mu/ soon h giv5 ! circul> =m obs]v$ 9 ! orbits ( ! fir/ & second satellites1 :i* its sup]ior attraction w always ma9ta94 ,! ?ird & f\r? satellites be+ fur!r remov$ f its influ5ce1 move 9 orbits ) a v small ecc5tricity4 ,! same cause occasions ! orbits ( ! satellites to rema9 ne>ly 9 ! plane ( ,jupit]'s equator1 on acc\nt ( :i* !y are always se5 ne>ly 9 ! same l9e2 & ! p[]ful action ( t quantity ( prom95t matt] is ! reason :y ! motion ( ! nodes ( ^! little bodies is s mu* m rapid ?an ^? ( ! planet4 ,! nodes ( ! f\r? satellite accompli% a revolution 9 #ebj ye>s1 :ile ^? ( ,jupit]'s orbit require no less ?an #ejfgc ye>s1 a pro( ( ! reciprocal attraction betwe5 ea* p>ticle ( ,jupit]'s equator & ( ! satellites4 ,al?\gh ! two fir/ satellites s5sibly move 9 circles1 !y acquire a small ellipticity f ! di/urbances !y exp]i5ce4 ,! orbits ( ! satellites d n reta9 a p]man5t incl9ation1 ei!r to ! plane ( ,jupit]'s equator1 or to t ( 8 orbit1 b to c]ta9 planes pass+ betwe5 ! two1 & ?r\gh _! int]section2 ^! h a great] incl9ation to 8 equator ! fur!r ! satellite is remov$1 a circum/ance entirely ow+ to ! influ5ce ( ,jupit]'s compression4 ,a s+ul> law obta9s among ! mean motions & mean longitudes ( ! ?ree fir/ satellites4 ,x appe>s f obs]vation1 t ! mean motion ( ! fir/ satellite1 plus twice t ( ! ?ird1 is equal to ?ree times t ( ! second1 & t ! mean longitude ( ! fir/ satellite1 m9us ?ree times t ( ! second1 plus twice t ( ! ?ird1 is always equal to two "r angles4 ,x is prov$ by !ory1 t if ^! relations _h only be5 approximate :5 ! satellites 7 fir/ laun*$ into space1 _! mutual attractions w\ld h e/abli%$ & ma9ta9$ !m4 ,!y ext5d to ! synodic motions ( ! satellites1 consequ5tly !y affect _! eclipses1 & h a v great influ5ce on _! :ole !ory4 ,! satellites move s ne>ly 9 ! plane ( ,jupit]'s equator1 :i* has a v small incl9ation to 8 orbit1 t !y are frequ5tly eclips$ by ! planet4 ,! in/ant ( ! beg9n+ or end ( an eclipse ( a satellite m>ks ! same in/ant ( absolute "t to all ! inhabitants ( ! e>?2 !re=e ! "t ( ^! eclipses obs]v$ by a travell]1 :5 comp>$ ) ! "t ( ! eclipse comput$ = ,gre5wi* or any o!r fix$ m]idian1 gives ! diff]5ce ( ! m]idians 9 "t1 & consequ5tly ! longitude ( ! place ( obs]vation4 ,x has requir$ all ! ref9em5ts ( mod]n in/rum5ts to r5d] ! eclipses ( ^! remote moons available to ! m>9]2 n[ h[ev]1 t sy/em ( bodies invisible to ! nak$ eye1 kn[n to man by ! aid ( sci5ce alone1 enables him to trav]se ! ocean1 spread+ ! light ( k & ! bless+s ( civilization ov] ! mo/ remote regions1 & to return load$ ) ! productions ( ano!r hemisph]e4 ,nor is ?is all3 ! eclipses ( ,jupit]'s satellites h be5 ! means or a discov]y1 :i*1 ?\gh n s imm$iately applicable to ! wants ( man1 unfolds a prop]ty ( light1 t m$ium1 )\t ^: *e]+ influ5ce all ! beauties ( ! creation w\ld h be5 to u a blank4 ,x is obs]v$1 t ^? eclipses ( ! fir/ satellite :i* happ5 :5 ,jupit] is ne> conjunction1 are lat] by #af' #bf ?an ^? :i* take place :5 ! planet is 9 opposition4 ,b z ,jupit] is ne>] to u :5 9 opposition by ! :ole bread? ( ! e>?'s orbit ?an :5 9 conjunction1 ?is circum/ance 0 attribut$ to ! "t employ$ by ! rays ( light 9 cross+ ! e>?'s orbit1 a di/ance ( #aib millions ( miles2 :5ce x is e/imat$1 t light travels at ! rate ( #aibjjj miles 9 "o second4 ,su* is its velocity1 t ! e>?1 mov+ at ! rate ( n9ete5 miles 9 a second1 w\ld take two mon?s to pass ?r\gh a di/ance :i* a ray ( light w\ld d>t ov] 9 eight m9utes4 ,! subsequ5t discov]y ( ! ab]ration ( light confirm$ ?is a/oni%+ result4 ,objects appe> to be situate 9 ! direction ( ! rays t proce$ f !m4 ,7 light propagat$ in/antane\sly1 e object1 :e!r at re/ or 9 motion1 w\ld appe> 9 ! direction ( ^! rays2 b z light takes "s "t to travel1 :5 ,jupit] is 9 conjunction1 we see him by means ( rays t left him #af' #bf be=e2 b dur+ t "t we h *ang$ our position1 9 consequ5ce ( ! motion ( ! e>? 9 its orbit2 we !re=e ref] ,jupit] to a place 9 :i* he is n4 ,8 true position is 9 ! diagonal ( ! p>allelogram1 ^: sides are 9 ! ratio ( ! velocity ( light to ! velocity ( ! e>? 9 its orbit1 :i* is z #aibjjj to #ai4 ,9 consequ5ce ( ab]ration1 none ( ! heav5ly bodies are 9 ! place 9 :i* !y seem to be4 ,9 fact1 if ! e>? 7 at re/1 rays f a /> w\ld pass along ! axis ( a telescope direct$ to x2 b if ! e>? 7 to beg9 to move 9 its orbit ) its usual velocity1 ^! rays w\ld /rike aga9/ ! side ( ! tube2 x w\ld !re=e be necess>y to incl9e ! telescope a little1 9 ord] to see ! />4 ,! angle conta9$ betwe5 ! axis ( ! telescope & a l9e drawn to ! true place ( ! />1 is its ab]ration1 :i* v>ies 9 quantity & direction 9 diff]5t p>ts ( ! e>?'s orbit2 b z x nev] exce$s tw5ty seconds1 9 ord9>y cases4 ,! velocity ( light d$uc$ f ! obs]v$ ab]ration ( ! fix$ />s1 p]fectly corresponds ) t giv5 by ! eclipses ( ! fir/ satellite4 ,! same result obta9$ f s\rces s diff]5t1 leaves n a d\bt ( its tru?4 ,_m su* beautiful co9cid5ces1 d]iv$ f app>5tly ! mo/ unpromis+ & dissimil> circum/ances1 occur 9 physical a/ronomy1 & prove dep5d5ces :i* we might o!rwise be unable to trace4 ,! id5tity ( ! velocity ( light at ! di/ance ( ,jupit] & on ! e>?'s surface %[s t its velocity is uni=m2 & if light consi/s 9 ! vibrations ( an ela/ic fluid or e!r fill+ space1 :i* hypo!sis accords be/ ) obs]v$ ph5om5a1 ! uni=mity ( its velocity %[s t ! d5sity ( ! fluid ?r\gh\t ! :ole ext5t ( ! sol> sy/em1 mu/ be proportional to its ela/icity4 ,among ! =tunate conjectures :i* h be5 confirm$ by subsequ5t exp]i5ce1 t ( ,bacon is n ! lea/ rem>kable4 ,x produces 9 me1 says ! re/or] ( true philosophy1 a d\bt1 :e!r ! face ( ! s]5e & />ry heav5s be se5 at ! in/ant x really exi/s1 or n till "s "t lat]2 & :e!r !re be n1 ) respect to ! heav5ly bodies1 a true "t & an app>5t "t1 no less ?an a true place & an app>5t place1 z a/ronom]s say1 on acc\nt ( p>allax4 ,= x seems incr$ible t ! species or rays ( ! cele/ial bodies c pass ?r\gh ! imm5se int]val betwe5 !m & u 9 an in/ant2 or t !y d n ev5 require "s consid]able portion ( "t4 ,z great discov]ies g5]ally lead to a v>iety ( conclusions1 ! ab]ration ( light af=ds a direct pro( ( ! motion ( ! e>? 9 its orbit2 & its rotation is prov$ by ! !ory ( fall+ bodies1 s9ce ! c5trifugal =ce x induces ret>ds ! oscillations ( ! p5dulum 9 go+ f ! pole to ! equator4 ,?us a high degree ( sci5tific k has be5 requisite to dispel ! errors ( ! s5ses4 ,! little t is kn[n ( ! !ories ( ! satellites ( ,saturn & ,uranus is 9 all respects simil> to t ( ,jupit]4 ,! great compression ( ,saturn occasions its satellites to move ne>ly 9 ! plane ( its equator4 ,( ! situation ( ! equator ( ,uranus we "k no?+1 nor ( its compression4 ,! orbits ( its satellites are ne>ly p]p5dicul> to ! plane ( ! ecliptic4 ,our con/ant companion ! moon next claims att5tion4 ,sev]al circum/ances concur to r5d] h] motions ! mo/ int]e/+1 & at ! same "t ! mo/ difficult to inve/igate ( all ! bodies ( our sy/em4 ,9 ! sol> sy/em planet tr\bles planet1 b 9 ! lun> !ory ! sun is ! great di/urb+ cause2 8 va/ di/ance be+ comp5sat$ by 8 enorm\s magnitude1 s t ! motions ( ! moon are m irregul> ?an ^? ( ! planets2 & on acc\nt ( ! great ellipticity ( h] orbit & ! size ( ! sun1 ! approximations to h] motions are t$i\s & difficult1 beyond :at ^? unaccu/om$ to su* inve/igations c\ld imag9e4 ,nei!r ! ecc5tricity ( ! lun> orbit1 nor its incl9ation to ! plane ( ! ecliptic1 h exp]i5c$ any *anges f secul> inequalities2 b ! mean motion1 ! nodes1 & ! p]igee1 are subject to v rem>kable v>iations4 ,f an eclipse obs]v$ at ,babylon by ! ,*aldeans1 on ! #ai? ( ,m>*1 sev5 hundr$ & tw5ty-"o ye>s be=e ! ,*ri/ian era1 ! place ( ! moon is kn[n f t ( ! sun at ! in/ant ( opposition2 :5ce h] mean longitude may be f\nd2 b ! comp>ison ( ?is mean longitude ) ano!r mean longitude1 comput$ back = ! in/ant ( ! eclipse f mod]n obs]vations1 %[s t ! moon p]=ms h] revolution r\nd ! e>? m rapidly & 9 a %ort] "t n[1 ?an %e did =m]ly2 & t ! accel]ation 9 h] mean motion has be5 increas+ f age to age z ! squ>e ( ! "t2 all ! anci5t & int]m$iate eclipses confirm ?is result4 ,z ! mean motions ( ! planets h no secul> inequalities1 ?is seem$ to be an unacc\ntable anomaly1 & x 0 at "o "t attribut$ to ! resi/ance ( an e!real m$ium p]vad+ space2 at ano!r to ! successive transmission ( ! gravitat+ =ce3 b z ,la ,place prov$ t nei!r ( ^! causes1 ev5 if !y exi/1 h any influ5ce on ! motions ( ! lun> p]igee or nodes1 !y c\ld n affect ! mean motion1 a v>iation 9 ! latt] f su* a cause be+ insep>ably connect$ ) v>iations 9 ! two =m] ( ^! elem5ts4 ,t great ma!matician1 h[ev]1 9 /udy+ ! !ory ( ,jupit]'s satellites1 p]ceiv$ t ! secul> v>iations 9 ! elem5ts ( ,jupit]'s orbit1 f ! action ( ! planets1 occasion correspond+ *anges 9 ! motions ( ! satellites3 ?is l$ him to suspect t ! accel]ation 9 ! mean motion ( ! moon might be connect$ ) ! secul> v>iation 9 ! ecc5tricity ( ! t]re/rial orbit2 & analysis has prov$ t he assign$ ! true cause4 ,if ! ecc5tricity ( ! e>?'s orbit 7 inv>iable1 ! moon w\ld be expos$ to a v>iable di/urbance f ! action ( ! sun1 9 consequ5ce ( ! e>?'s annual revolution2 b x w\ld be p]iodic1 s9ce x w\ld be ! same z (t5 z ! sun1 ! e>?1 & ! moon return$ to ! same relative positions3 on acc\nt h[ev] ( ! sl[ & incessant dim9ution 9 ! ecc5tricity ( ! t]re/rial orbit1 ! revolution ( our planet is p]=m$ at diff]5t di/ances f ! sun e ye>4 ,! position ( ! moon ) reg>d to ! sun1 und]goes a correspond+ *ange2 s t ! mean action ( ! sun on ! moon v>ies f "o c5tury to ano!r1 & occasions ! secul> increase 9 ! moon's velocity call$ ! accel]ation1 a "n :i* is v appropriate 9 ! pres5t age1 & :i* w cont9ue to be s = a va/ numb] ( ages to come2 because1 z long z ! e>?'s ecc5tricity dim9i%es1 ! moon's mean motion w be accel]at$2 b :5 ! ecc5tricity has pass$ its m9imum & beg9s to increase1 ! mean motion w be ret>d$ f age to age4 ,at pres5t ! secul> accel]ation is ab\t #aj1 b its effect on ! moon's place increases z ! squ>e ( ! "t4 ,x is rem>kable t ! action ( ! planets ?us reflect$ by ! sun to ! moon1 is mu* m s5sible ?an _! direct action1 ei!r on ! e>? or moon4 ,! secul> dim9ution 9 ! ecc5tricity1 :i* has n alt]$ ! equation ( ! c5tre ( ! sun by eight m9utes s9ce ! e>lie/ record$ eclipses1 has produc$ a v>iation ( #a #dh' 9 ! moon's longitude1 & ( #g #ab' 9 h] mean anomaly4 ,! action ( ! sun occasions a rapid b v>iable motion 9 ! nodes & p]igee ( ! lun> orbit2 ! =m]1 ?\gh !y rec$e dur+ ! great] "p ( ! moon's revolution1 & advance dur+ ! small]1 p]=m _! sid]eal revolutions 9 #fgic;days4#dbab1 & ! latt]1 ?\gh its motion is sometimes retrograde & sometimes direct1 9 #cbcb;days4#ehjg1 or a little m ?an n9e ye>s3 b su* is ! diff]5ce betwe5 ! di/urb+ en]gy ( ! sun & t ( all ! planets put toge!r1 t x requires no less ?an #ajiggj ye>s = ! great] axis ( ! t]re/rial orbit to d ! same4 ,x is evid5t t ! same secul> v>iation :i* *anges ! sun's di/ance f ! e>?1 & occasions ! accel]ation 9 ! moon's mean motion1 mu/ affect ! motion ( ! nodes & p]igee2 & x consequ5tly appe>s1 f !ory z well z obs]vation1 t bo? ^! elem5ts are subject to a secul> inequality1 aris+ f ! v>iation 9 ! ecc5tricity ( ! e>?'s orbit1 :i* connects !m ) ! accel]ation2 s t bo? are ret>d$ :5 ! mean motion is anticipat$4 ,! secul> v>iations 9 ^! ?ree elem5ts are 9 ! ratio ( ! numb]s #c1 #j4gce1 & #a2 :5ce ! ?ree motions ( ! moon1 ) reg>d to ! sun1 to h] p]igee1 & to h] nodes1 are cont9ually accel]at$1 & _! secul> equations are z ! numb]s #a1 #d1 & #j4bfe1 or accord+ to ! mo/ rec5t inve/igations z #a1 #d1 #fggf & #j4cia4 ,a comp>ison ( anci5t eclipses obs]v$ by ! ,arabs1 ,greeks1 & ,*aldeans1 imp]fect z !y are1 ) mod]n obs]vations1 p]fectly confirms ^! results ( analysis4 ,future ages w develop ^! great inequalities1 :i* at "s mo/ di/ant p]iod w am\nt to _m circumf]5ces4 ,!y are inde$ p]iodic2 b :o %all tell _! p]iod8 ,millions ( ye>s mu/ elapse be=e t great cycle is accompli%$2 b 'su* *anges1 ?\gh r>e 9 "t1 are frequ5t 9 et]nity4' ,! moon is s ne>1 t ! excess ( matt] at ! e>?'s equator occasions p]iodic v>iations 9 h] longitude & latitude2 &1 z ! cause mu/ be proportional to ! effect1 a comp>ison ( ^! inequalities1 comput$ f !ory1 ) ! same giv5 by obs]vation1 %[s t ! compression ( ! t]re/rial sph]oid1 or ! ratio ( ! diff]5ce betwe5 ! pol> & equatorial diamet] to ! diamet] ( ! equator is #a_/cje4je4 ,x is prov$ analytically1 t if a fluid mass ( homog5e\s matt]1 ^: p>ticles attract ea* o!r inv]sely z ! squ>e ( ! di/ance1 7 to revolve ab\t an axis1 z ! e>?1 x w\ld assume ! =m ( a sph]oid1 ^: compression is #a_/bcj4 ,:5ce x appe>s1 t ! e>? is n homog5e\s1 b decreases 9 d5sity f its c5tre to its circumf]5ce4 ,?us ! moon's eclipses %[ ! e>? to be r\nd1 & h] inequalities n only det]m9e ! =m1 b ! int]nal /ructure ( our planet2 results ( analysis :i* c\ld n h be5 anticipat$4 ,simil> inequalities 9 ,jupit]'s satellites prove t 8 mass is n homog5e\s1 & t 8 compression is #a_/ach4 ,! motions ( ! moon h n[ become ( m importance to ! navigator & geograph] ?an ^? ( any o!r body1 f ! precision ) :i* ! longitude is det]m9$ by ! occultations ( />s & lun> di/ances4 ,! lun> !ory is br\ght to su* p]fection1 t ! times ( ^! ph5om5a1 obs]v$ "u any m]idian1 :5 comp>$ ) t comput$ = ,gre5wi* 9 ! ,nautical ,almanack1 gives ! longitude ( ! obs]v] )9 a few miles4 ,! accuracy ( t "w is obvi\sly ( extreme importance to a m>itime nation2 we h reason to hope t ! new ,ephem]is1 n[ 9 prep>ation1 w be by f> ! mo/ p]fect "w ( ! k9d t ev] has be5 publi%$4 ,f ! lun> !ory1 ! mean di/ance ( ! sun f ! e>?1 & !nce ! :ole dim5sions ( ! sol> sy/em are kn[n2 = ! =ces :i* reta9 ! e>? & moon 9 _! orbits1 are respectively proportional to ! radii vectores ( ! e>? & moon1 ea* be+ divid$ by ! squ>e ( its p]iodic "t2 & z ! lun> !ory gives ! ratio ( ! =ces1 ! ratio ( ! di/ance ( ! sun & moon f ! e>? is obta9$3 :5ce x appe>s t ! sun's di/ance f ! e>? is ne>ly #cif times great] ?an t ( ! moon4 ,! me?od h[ev] ( f9d+ ! absolute di/ances ( ! cele/ial bodies 9 miles1 is 9 fact ! same ) t employ$ 9 measur+ di/ances ( t]re/rial objects4 ,f ! extremities ( a kn[n base ! angles :i* ! visual rays f ! object =m ) x1 are measur$2 _! sum subtract$ f two "r-angles gives ! angle opposite ! base2 !re=e by trigonometry1 all ! angles & sides ( ! triangle may be comput$2 consequ5tly ! di/ance ( ! object is f\nd4 ,! angle "u :i* ! base ( ! triangle is se5 f ! object1 is ! p>allax ( t object2 x evid5tly increases & decreases ) ! di/ance2 !re=e ! base mu/ be v great inde$1 to be visible at all f ! cele/ial bodies4 ,b ! globe itself ^: dim5sions are asc]ta9$ by actual admeasurem5t1 furni%es a /&>d ( measures1 ) :i* we comp>e ! di/ances1 masses1 d5sities1 & volumes ( ! sun & planets4 ,! c\rses ( ! great riv]s1 :i* are 9 g5]al navigable to a consid]able ext5t1 prove t ! curvature ( ! l& diff]s b little f t ( ! ocean2 & z ! heights ( ! m\nta9s & cont95ts are1 at any rate1 q inconsid]able :5 comp>$ ) ! magnitude ( ! e>?1 its figure is und]/ood to be det]m9$ by a surface at e po9t p]p5dicul> to ! direction ( gravity1 or ( ! plumb-l9e1 & is ! same :i* ! sea w\ld h if x 7 cont9u$ all r\nd ! e>? b5ea? ! cont95ts4 ,su* is ! figure t has be5 measur$ 9 ! foll[+ mann]3-- ,a t]re/rial m]idian is a l9e pass+ ?r\gh bo? poles1 all ! po9ts ( :i* h contemporane\sly ! same noon4 ,7 ! l5g?s & curvatures ( diff]5t m]idians kn[n1 ! figure ( ! e>? might be det]m9$2 b ! l5g? ( "o degree is suffici5t to give ! figure ( ! e>?1 if x be measur$ on diff]5t m]idians1 & 9 a v>iety ( latitudes2 = if ! e>? 7 a sph]e1 all degrees w\ld be ( ! same l5g?1 b if n1 ! l5g?s ( ! degrees w be greate/ :]e ! curvature is lea/2 a comp>ison ( ! l5g? ( ! degrees 9 diff]5t p>ts ( ! e>?'s surface w !re=e det]m9e its size & =m4 ,an arc ( ! m]idian may be measur$ by obs]v+ ! latitude ( its extreme po9ts1 & !n measur+ ! di/ance betwe5 !m 9 feet or fa?oms2 ! di/ance ?us det]m9$ on ! surface ( ! e>?1 divid$ by ! degrees & p>ts ( a degree conta9$ 9 ! diff]5ce ( ! latitudes1 w give ! exact l5g? ( "o degree1 ! diff]5ce ( ! latitudes be+ ! angle conta9$ betwe5 ! v]ticals at ! extremities ( ! arc4 ,?is w\ld be easily accompli%$ 7 ! di/ance unob/ruct$1 & on a level ) ! sea2 b on acc\nt ( ! innum]able ob/acles on ! surface ( ! e>?1 x is necess>y to connect ! extreme po9ts ( ! arc by a s]ies ( triangles1 ! sides & angles ( :i* are ei!r measur$ or comput$1 s t ! l5g? ( ! arc is asc]ta9$ ) mu* labori\s computation4 ,9 consequ5ce ( ! inequalities ( ! surface1 ea* triangle is 9 a diff]5t plane2 !y mu/ !re=e be r$uc$ by computation to :at !y w\ld h be51 _h !y be5 measur$ on ! surface ( ! sea2 & z ! e>? is sph]ical1 !y require a correction to r$uce !m f plane to sph]ical triangles4 ,arcs ( ! m]idian h be5 measur$ 9 a v>iety ( latitudes1 bo? nor? & s\?1 z well z arcs p]p5dicul> to ! m]idian4 ,f ^! measurem5ts x appe>s t ! l5g? ( ! degrees increase f ! equator to ! poles1 ne>ly z ! squ>e ( ! s9e ( ! latitude2 consequ5tly1 ! convexity ( ! e>? dim9i%es f ! equator to ! poles4 ,_m discrepancies occur1 b ! figure t mo/ ne>ly foll[s ?is law is an ellipsoid ( revolution1 ^: equatorial radius is #cifb4f miles1 & ! pol> radius #cidi4g2 ! diff]5ce1 or #ab4i miles1 divid$ by ! equatorial radius1 is #a_/cjhg1 or #a_/cji ne>ly2 ?is fraction is call$ ! compression ( ! e>?1 because1 accord+ z x is great] or less1 ! t]re/rial ellipsoid is m or less flatt5$ at ! poles2 x does n diff] mu* f t giv5 by ! lun> inequalities4 ,if we assume ! e>? to be a sph]e1 ! l5g? ( a degree ( ! m]idian is #fi #a_/bb ,briti% miles2 !re=e #cfj degrees1 or ! :ole circumf]5ce ( ! globe is #bdhef1 & ! diamet]1 :i* is some?+ less ?an a ?ird ( ! circumf]5ce1 is #giaf or #hjjj miles ne>ly4 ,erato/h5es1 :o di$ #aid ye>s be=e ! ,*ri/ian era1 0 ! fir/ to give an approximate value ( ! e>?'s circumf]5ce1 by ! m5suration ( an arc betwe5 ,alex&ria & ,sy5e4 ,b !re is ano!r me?od ( f9d+ ! figure ( ! e>?1 totally indep5d5t ( ei!r ( ! prec$+4 ,if ! e>? 7 a homog5e\s sph]e )\t rotation1 its attraction on bodies at its surface w\ld be ev]y:]e ! same2 if x be elliptical1 ! =ce ( gravity !oretically ought to increase1 f ! equator to ! pole z ! squ>e ( ! s9e ( ! latitude2 b = a sph]oid 9 rotation1 by ! laws ( me*anics ! c5trifugal =ce v>ies z ! squ>e ( ! s9e ( ! latitude f ! equator :]e x is greate/1 to ! pole :]e x vani%es2 & z x t5ds to make bodies fly (f ! surface1 x dim9i%es ! effects ( gravity by a small quantity4 ,h5ce by gravitation1 :i* is ! diff]5ce ( ^! two =ces1 ! fall ( bodies ought to be accel]at$ 9 go+ f ! equator to ! poles1 proportionably to ! squ>e ( ! s9e ( ! latitude2 & ! weight ( ! same body ought to increase 9 t ratio4 ,?is is directly prov$ by ! oscillations ( ! p5dulum2 = if ! fall ( bodies be accel]at$1 ! oscillations w be m rapid2 & t !y may always be p]=m$ 9 ! same "t1 ! l5g? ( ! p5dulum mu/ be alt]$4 ,n[1 by num]\s & v c>eful exp]im5ts1 x is prov$ t a p5dulum1 :i* makes #hfdjj oscillations 9 a mean day at ! equator1 w d ! same at e po9t ( ! e>?'s surface1 if its l5g? be increas$ 9 go+ to ! pole1 z ! squ>e ( ! s9e ( ! latitude4 ,f ! mean ( ^! x appe>s t ! compression ( ! t]re/rial sph]oid is ab\t #a_/cdb1 :i* does n diff] mu* f t giv5 by ! lun> inequalities1 & f ! arcs ( ! m]idian4 ,! ne> co9cid5ce ( ^! ?ree values1 d$uc$ by me?ods s entirely indep5d5t ( ea* o!r1 %[s t ! mutual t5d5cies ( ! c5tres ( ! cele/ial bodies to "o ano!r1 & ! attraction ( ! e>? = bodies at its surface1 result f ! reciprocal attraction ( all _! p>ticles4 ,ano!r pro( may be add$2 ! nutation ( ! e>?'s axis1 & ! precession ( ! equ9oxes1 are occasion$ by ! action ( ! sun & moon on ! protub]ant matt] at ! e>?'s equator2 & al?\gh ^! inequalities d n give ! absolute value ( ! t]re/rial compression1 !y %[ t ! fraction express+ x is compris$ betwe5 ! limits #a_/bgi & #a_/egh4 ,x might be expect$ t ! same compression %\ld result f ea*1 if ! diff]5t me?ods ( obs]vation c\ld be made )\t error4 ,?is1 h[ev]1 is n ! case2 = su* discrepancies are f\nd bo? 9 ! degrees ( ! m]idian & 9 ! l5g? ( ! p5dulum1 z %[ t ! figure ( ! e>? is v complicat$2 b !y are s small :5 comp>$ ) ! g5]al results1 t !y may be disreg>d$4 ,! compression d$uc$ f ! mean ( ! :ole1 appe>s to be ab\t #a_/cbj2 t giv5 by ! lun> !ory has ! advantage ( be+ indep5d5t ( ! irregul>ities at ! e>?'s surface1 & ( local attractions4 ,! =m & size ( ! e>? be+ det]m9$1 x furni%es a /&>d ( measure ) :i* ! dim5sions ( ! sol> sy/em may be comp>$4 ,! p>allax ( a cele/ial body is ! angle "u :i* ! radius ( ! e>? w\ld be se5 if view$ f ! c5tre ( t body2 x af=ds ! means ( asc]ta9+ ! di/ances ( ! sun1 moon1 & planets4 ,suppose t1 :5 ! moon is 9 ! horizon at ! in/ant ( ris+ or sett+1 l9es 7 drawn f h] c5tre to ! spectator & to ! c5tre ( ! e>?1 ^! w\ld =m a "r-angl$ triangle ) ! t]re/rial radius1 :i* is ( a kn[n l5g?2 & z ! p>allax or angle at ! moon c be measur$1 all ! angles & "o side are giv52 :5ce ! di/ance ( ! moon f ! c5tre ( ! e>? may be comput$4 ,! p>allax ( an object may be f\nd1 if two obs]v]s "u ! same m]idian1 b at a v great di/ance f "o ano!r1 obs]ve its z5i? di/ances on ! same day at ! "t ( its passage ov] ! m]idian4 ,by su* contemporane\s obs]vations at ! ,cape ( ,good ,hope & at ,b]l91 ! mean horizontal p>allax ( ! moon 0 f\nd to be #cdedb2 :5ce ! mean di/ance ( ! moon is ab\t sixty times ! mean t]re/rial radius1 or #bdjjjj miles ne>ly4 ,s9ce ! p>allax is equal to ! radius ( ! e>? divid$ by ! di/ance ( ! moon2 "u ! same p>allel ( latitude x v>ies ) ! di/ance ( ! moon f ! e>?1 & proves ! ellipticity ( ! lun> orbit2 & :5 ! moon is at h] mean di/ance1 x v>ies ) ! t]re/rial radii1 ?us %[+ t ! e>? is n a sph]e4 ,al?\gh ! me?od describ$ is suffici5tly accurate = f9d+ ! p>allax ( an object s ne> z ! moon1 x w n answ] = ! sun :i* is s remote1 t ! smalle/ error 9 obs]vation w\ld lead to a false result2 b by ! transits ( ,v5us t difficulty is obviat$4 ,:5 t planet is 9 h] nodes1 or )9 #a #a_/d ( !m1 t is1 91 or ne>ly 9 ! plane ( ! ecliptic1 %e is occasionally se5 to pass ov] ! sun l a block spot4 ,if we c\ld imag9e t ! sun & ,v5us _h no p>allax1 ! l9e describ$ by ! planet on 8 disc1 & ! duration ( ! transit1 w\ld be ! same to all ! inhabitants ( ! e>?2 b z ! sun is n s remote b t ! semidiamet] ( ! e>? has a s5sible magnitude :5 view$ f 8 c5tre1 ! l9e describ$ by ! planet 9 its passage ov] 8 disc appe>s to be ne>] to 8 c5tre or f>!r f x1 accord+ to ! position ( ! obs]v]2 ,s t ! duration ( ! transit v>ies ) ! diff]5t po9ts ( ! e>?'s surface at :i* x is obs]v$4 ,?is diff]5ce ( "t1 be+ entirely ! effect ( p>allax1 furni%es ! means ( comput+ x f ! kn[n motions ( ! e>? & ,v5us1 by ! same me?od z = ! eclipses ( ! sun4 ,9 fact ! ratio ( ! di/ances ( ,v5us & ! sun f ! e>? at ! "t ( ! transit1 are kn[n f ! !ory ( _! elliptical motion2 consequ5tly1 ! ratio ( ! p>allaxes ( ^! two bodies1 be+ inv]sely z _! di/ances1 is giv52 & z ! transit gives ! diff]5ce ( ! p>allaxes1 t ( ! sun is obta9$4 ,9 #agfi1 ! p>allax ( ! sun 0 det]m9$ by obs]vations ( a transit ( ,v5us made at ,w>dhus 9 ,lapl&1 & at ,otaheite 9 ! ,s\? ,sea1 ! latt] obs]vation be+ ! object ( ,cook's fir/ voyage4 ,! transit la/$ ab\t six h\rs at ,otaheite1 & ! diff]5ce 9 ! duration at ^! two /ations 0 eight m9utes2 :5ce ! sun's p>allax 0 f\nd to be #hgb2 b by o!r consid]ations x has subsequ5tly be5 r$uc$ to #hege2 f :i* ! mean di/ance ( ! sun appe>s to be ab\t #ieiifjjj1 or n9ety-six millions ( miles ne>ly4 ,?is is confirm$ by an inequality 9 ! motion ( ! moon1 :i* dep5ds on ! p>allax ( ! sun1 & :i* :5 comp>$ ) obs]vation gives #hf = ! sun's p>allax4 ,! p>allax ( ,v5us is det]m9$ by h] transits1 t ( ,m>s by direct obs]vation4 ,! di/ances ( ^! two planets f ! e>? are !re=e kn[n 9 t]re/rial radii2 consequ5tly _! mean di/ances f ! sun may be comput$ & z ! ratios ( ! di/ances ( ! planets f ! sun are kn[n by ,kepl]'s law1 _! absolute di/ances 9 miles are easily f\nd4 ,f> z ! e>? seems to be f ! sun1 x is ne> to him :5 comp>$ ) ,uranus2 t planet is no less ?an #ahdc millions ( miles f ! lum9>y t w>ms & enliv5s ! _w2 to x1 situate on ! v]ge ( ! sy/em1 ! sun mu/ appe> n mu* l>g] ?an ,v5us does to u4 ,! e>? _c ev5 be visible z a telescopic object to a body s remote2 yet man1 ! inhabitant ( ! e>?1 so>s beyond ! va/ dim5sions ( ! sy/em to :i* 8 planet belongs1 & assumes ! diamet] ( its orbit z ! base ( a triangle1 ^: apex ext5ds to ! />s4 ,sublime z ! idea is1 ?is assumption proves ineffectual1 = ! app>5t places ( ! fix$ />s are n s5sibly *ang$ by ! e>?'s annual revolution2 & ) ! aid d]iv$ f ! ref9em5ts ( mod]n a/ronomy & ! mo/ p]fect in/rum5ts1 x is /ill a matt] ( d\bt :e!r a s5sible p>allax has be5 detect$1 ev5 9 ! ne>e/ ( ^! remote suns4 ,if a fix$ /> _h ! p>allax ( "o second1 its di/ance f ! sun w\ld be #bjejjjjj millions ( miles4 ,at su* a di/ance n only ! t]re/rial orbit %r9ks to a po9t1 b1 :]e ! :ole sol> sy/em1 :5 se5 9 ! focus ( ! mo/ p[]ful telescope1 might be cov]$ by ! ?ickness ( a spid]'s ?read4 ,light1 fly+ at ! rate ( #bjjjjj miles 9 a second1 w\ld take ?ree ye>s & sev5 days to travel ov] t space2 "o ( ! ne>e/ />s may !re=e h be5 k9dl$ or ext+ui%$ m ?an ?ree ye>s be=e we c\ld h be5 aw>e ( s mighty an ev5t4 ,b ?is di/ance mu/ be small :5 comp>$ ) t ( ! mo/ remote ( ! bodies :i* are visible 9 ! heav5s4 ,! fix$ />s are und\bt$ly lum9\s l ! sun2 x is !re=e probable t !y are n ne>] to "o ano!r ?an ! sun is to ! ne>e/ ( !m4 ,9 ! milky way & ! o!r />ry nebul1 "s ( ! />s t seem to u to be close to o!rs1 may be f> beh9d !m 9 ! b\ndless dep? ( space2 nay1 may rationally be suppos$ to be situat$ _m ?\s& times fur!r (f3 light w\ld !re=e require ?\s&s ( ye>s to come to ! e>? f ^? myriads ( suns1 ( :i* our own is b '! dim & remote companion4' ,! masses ( su* planets z h no satellites are kn[n by comp>+ ! inequalities !y produce 9 ! motions ( ! e>? & ( ea* o!r1 det]m9$ !oretically1 ) ! same inequalities giv5 by obs]vation1 = ! di/urb+ cause mu/ necess>ily be proportional to ! effect x produces4 ,b z ! quantities ( matt] 9 any two prim>y planets are directly z ! cubes ( ! mean di/ances at :i* _! satellites revolve1 & inv]sely z ! squ>es ( _! p]iodic times1 ! mass ( ! sun & ( any planets :i* h satellites1 may be comp>$ ) ! mass ( ! e>?4 ,9 ?is mann] x is comput$ t ! mass ( ! sun is #cedicf times great] ?an t ( ! e>?2 :5ce ! great p]turbations ( ! moon & ! rapid motion ( ! p]igee & nodes ( h] orbit4 ,ev5 ,jupit]1 ! l>ge/ ( ! planets1 is #ajgj4e times less ?an ! sun4 ,! mass ( ! moon is det]m9$ f f\r diff]5t s\rces1--f h] action on ! t]re/rial equator1 :i* occasions ! rotation 9 ! axis ( rotation2 f h] horizontal p>allax1 f an inequality %e produces 9 ! sun's longitude1 & f h] action on ! titles4 ,! ?ree fir/ quantities1 comput$ f !ory1 & comp>$ ) _! obs]v$ values1 give h] mass respectively equal to ! #a_/ga1 #a_/gdb1 & #a_/fib "p ( t ( ! e>?1 :i* d n diff] v mu* f ea* o!r2 b1 f h] action 9 rais+ ! tides1 :i* furni%es ! f\r? me?od1 h] mass appe>s to be ab\t ! sev5ty-fif? "p ( t ( ! e>?1 a value t _c diff] mu* f ! tru?4 ,! app>5t diamet]s ( ! sun1 moon1 & planets are det]m9$ by measurem5t2 !re=e _! real diamet]s may be comp>$ ) t ( ! e>?2 = ! real diamet] ( a planet is to ! real diamet] ( ! e>?1 or #hjjj miles1 z ! app>5t diamet] ( ! planet to ! app>5t diamet] ( ! e>? z se5 f ! planet1 t is1 to twice ! p>allax ( ! planet ,! mean app>5t diamet] ( ! sun is #aibj1 & ) ! sol> p>allax #hfe1 x w be f\nd t ! diamet] ( ! sun is ab\t #hhhjjj miles2 !re=e1 ! c5tre ( ! sun 7 to co9cide ) ! c5tre ( ! e>?1 8 volume w\ld n only include ! orbit ( ! moon1 b w\ld ext5d ne>ly z f> aga91 = ! moon's mean di/ance f ! e>? is ab\t sixty times ! e>?'s mean radius or #bdjjjj miles2 s t twice ! di/ance ( ! moon is #dhjjjj miles1 :i* diff]s b little f ! sol> radius2 8 equatorial radius is probably n mu* less ?an ! major axis ( ! lun> orbit4 ,! diamet] ( ! moon is only #bafj miles2 & ,jupit]'s diamet] ( #hhjjj miles is incomp>ably less ?an t ( ! sun ,! diamet] ( ,pallas does n mu* exce$ #ga miles1 s t an inhabitant ( t planet1 9 "o ( our /eam-c>riages1 might g r\nd 8 _w 9 five or six h\rs4 ,! oblate =m ( ! cele/ial bodies indicates rotatory motion1 & ?is has be5 confirm$1 9 mo/ cases1 by trac+ spots on _! surfaces1 :5ce _! poles & times ( rotation h be5 det]m9$4 ,! rotation ( ,m]cury is unkn[n1 on acc\nt ( 8 proximity to ! sun2 & t ( ! new planets has n yet be5 asc]ta9$4 ,! sun revolves 9 tw5ty-five days t5 h\rs1 ab\t an axis t is direct$ t[>ds a po9t half way betwe5 ! pole /> & ,lyra1 ! plane ( rotation be+ incl9$ a little m ?an #gj to t on :i* ! e>? revolves4 ,f ! rotation ( ! sun1 !re is e reason to believe t he has a progressive motion 9 space1 al?\gh ! direction to :i* he t5ds is z yet unkn[n2 b 9 consequ5ce ( ! reaction ( ! planets1 he describes a small irregul> orbit ab\t ! c5tre ( in]tia ( ! sy/em1 nev] deviat+ f 8 position by m ?an twice 8 own diamet]1 or ab\t sev5 times ! di/ance ( ! moon f ! e>?4 ,! sun & all 8 att5dants rotate f we/ to ea/ on axes t rema9 ne>ly p>allel to !mselves 9 e po9t ( _! orbit1 & ) angul> velocities t are s5sibly uni=m4 ,al?\gh ! uni=mity 9 ! direction ( _! rotation is a circum/ance hi!rto unacc\nt$ = 9 ! economy ( ,nature1 yet f ! design & adaptation ( e o!r "p to ! p]fection ( ! :ole1 a co9cid5ce s rem>kable _c be accid5tal2 & z ! revolutions ( ! planets & satellites are also f we/ to ea/1 x is evid5t t bo? mu/ h aris5 f ! primitive causes :i* h det]m9$ ! planet>y motions4 ,! l>g] planets rotate 9 %ort] p]iods ?an ! small] planets & ! e>?2 _! compression is consequ5tly great]1 & ! action ( ! sun & ( _! satellites occasions a nutation 9 _! axes1 & a precession ( _! equ9oxes1 simil> to t :i* obta9s 9 ! t]re/rial sph]oid f ! attraction ( ! sun & moon on ! prom95t matt] at ! equator4 ,9 comp>+ ! p]iods ( ! revolutions ( ,jupit] & ,saturn ) ! times ( _! rotation1 x appe>s t a ye> ( ,jupit] conta9s ne>ly t5 ?\s& ( 8 days1 & t ( ,saturn ab\t ?irty ?\s& ,saturnian days4 ,! appe>ance ( ,saturn is unp>allel$ 9 ! sy/em ( ! _w2 he is surr\nd$ by a r+ ev5 bright] ?an himself1 :i* always rema9s 9 ! plane ( 8 equator1 & view$ ) a v good telescope1 x is f\nd to consi/ ( two conc5tric r+s1 divid$ by a d>k b&4 ,by ! laws ( me*anics1 x is impossible t ?is body c reta9 its position by ! adhesion ( its p>ticles alone2 x mu/ necess>ily revolve ) a velocity t w g5]ate a c5trifugal =ce suffici5t to balance ! attraction ( ,saturn4 ,obs]vation confirms ! tru? ( ^! pr9ciples1 %[+ t ! r+s rotate ab\t ! planet 9 #aj #a_/b h\rs1 :i* is consid]ably less ?an ! "t a satellite w\ld take to revolve ab\t ,saturn at ! same di/ance4 ,_! plane is incl9$ to ! ecliptic at an angle ( #ca2 & 9 consequ5ce ( ?is obliquity ( position !y always appe> elliptical to u1 b ) an ecc5tricity s v>iable z ev5 to be occasionally l a /raight l9e drawn across ! planet4 ,at pres5t ! app>5t axes ( ! r+s are z #ajjj to #afj2 & on ! #bi? ( ,septemb]1 #ahcb1 ! plane ( ! r+s w pass ?r\gh ! c5tre ( ! e>? :5 !y w be visible only ) sup]ior in/rum5ts1 & w appe> l a f9e l9e across ! disc ( ,saturn4 ,on ! #a/ ( ,decemb] 9 ! same ye>1 ! plane ( ! r+s w pass ?r\gh ! c5tre ( ! sun4 ,x is a s+ul> result ( ! !ory1 t ! r+s c\ld n ma9ta9 _! /ability ( rotation if !y 7 ev]y:]e ( uni=m ?ickness2 = ! smalle/ di/urbance w\ld de/roy ! equilibrium1 :i* w\ld become m & m d]ang$1 till at la/ !y w\ld be precipitat$ on ! surface ( ! planet4 ,! r+s ( ,saturn mu/ !re=e be irregul> solids ( unequal bread? 9 ! diff]5t p>ts ( ! circumf]5ce1 s t _! c5tres ( gravity d n co9cide ) ! c5tres ( _! figures4 ,pr(essor ,/ruve has also discov]$ t ! c5tre ( ! r+ is n conc5tric ) ! c5tre ( ,saturn2 ! int]val betwe5 ! out] edge ( ! globe ( ! planet & ! out] edge ( ! r+ on "o side1 is #aajgc1 & on ! o!r side ! int]val is #aabhh2 consequ5tly !re is an ecc5tricity ( ! globe 9 ! r+ ( #jbae4 ,if ! r+s obey$ diff]5t =ces1 !y w\ld n rema9 9 ! same plane1 b ! p[]ful attraction ( ,saturn always ma9ta9s !m & 8 satellites 9 ! plane ( 8 equator4 ,! r+s1 by _! mutual action1 & t ( ! sun & satellites1 mu/ oscillate ab\t ! c5tre ( ,saturn1 & produce ph5om5a ( light & %ad[1 ^: p]iods ext5d to _m ye>s4 ,! p]iods ( ! rotation ( ! moon & ! o!r satellites are equal to ! times ( _! revolutions1 consequ5tly ^! bodies always turn ! same face to _! prim>ies2 h[ev]1 z ! mean motion ( ! moon is subject to a secul> inequality :i* w ultimately am\nt to _m circumf]5ces1 if ! rotation ( ! moon 7 p]fectly uni=m1 & n affect$ by ! same inequalities1 x w\ld cease exactly to c\nt]balance ! motion ( revolution2 & ! moon1 9 ! c\rse ( ages1 w\ld successively & gradually discov] e po9t o!r surface to ! e>?4 ,b !ory proves t ?is nev] c happ52 = ! rotation ( ! moon1 ?\gh x does n p>take ( ! p]iodic inequalities ( h] revolution1 is affect$ by ! same secul> v>iations1 s t h] motions ( rotation & revolution r\nd ! e>? w always balance ea* o!r1 & rema9 equal4 ,?is circum/ance arises f ! =m ( ! lun> sph]oid1 :i* has ?ree pr9cipal axes ( diff]5t l5g?s at "r angles to ea* o!r4 ,! moon is flatt5$ at ! poles f h] c5trifugal =ce1 !re=e h] pol> axis is lea/2 ! o!r two are 9 ! plane ( h] equator1 b t direct$ t[>ds ! e>? is ! greate/4 ,! attraction ( ! e>?1 z if x _h drawn out t "p ( ! moon's equator1 con/antly br+s ! greate/ axis1 & consequ5tly ! same hemisph]e t[>ds u1 :i* makes h] rotation p>ticipate 9 ! secul> v>iations 9 h] mean motion ( revolution4 ,ev5 if ! angul> velocities ( rotation & revolution _h n be5 nicely balanc$ 9 ! beg9n+ ( ! moon's motion1 ! attraction ( ! e>? w\ld h recall$ ! greate/ axis to ! direction ( ! l9e jo9+ ! c5tres ( ! e>? & moon2 s t x w\ld vibrate on ea* side ( t l9e 9 ! same mann] z a p5dulum oscillates on ea* side ( ! v]tical f ! influ5ce ( gravitation4 ,no su* libration is p]ceptible2 & z ! smalle/ di/urbance w\ld make x evid5t1 x is cle> t if ! moon has ev] be5 t\*$ by a comet1 ! mass ( ! latt] mu/ h be5 extremely small2 = if x _h be5 only ! hundr$-?\s&? "p ( t ( ! e>?y x w\ld h r5d]$ ! libration s5sible4 ,a simil> libration exi/s 9 ! motions ( ,jupit]'s satellites2 b al?\gh ! comet ( #agfg & #aggi pass$ ?r\gh ! mid/ ( !m1 _! libration /ill rema9s ins5sible4 ,x is true1 ! moon is liable to librations dep5d+ on ! position ( ! spectator2 at h] ris+1 "p ( ! we/]n edge ( h] disc is visible1 :i* is invisible at h] sett+1 & ! contr>y takes place ) reg>d to h] ea/]n edge4 ,!re are also librations aris+ f ! relative positions ( ! e>? & moon 9 _! respective orbits1 b z !y are only optical appe>ances1 "o hemisph]e w be et]nally conceal$ f ! e>?4 ,= ! same reason1 ! e>?1 :i* mu/ be s spl5did an object to "o lun> hemisph]e1 w be = ev] veil$ f ! o!r4 ,on acc\nt ( ^! circum/ances1 ! remot] hemisph]e ( ! moon has its day a =tnight long1 & a night ( ! same duration n ev5 enlight5$ by a moon1 :ile ! fav\r$ side is illum9at$ by ! reflection ( ! e>? dur+ its long night4 ,a moon exhibit+ a surface ?irte5 times l>g] ?an ours1 ) all ! v>ieties ( cl\ds1 l&1 & wat] com+ successively into view1 w\ld be a spl5did object to a lun> travell] 9 a j\rney to 8 antipodes4 ,! great height ( ! lun> m\nta9s probably has a consid]able influ5ce on ! ph5om5a ( h] motion1 ! m s z h] compression is small1 & h] mass consid]able4 ,9 ! curve pass+ ?r\gh ! poles1 & t diamet] ( ! moon :i* always po9ts to ! e>?1 nature has furni%$ a p]man5t m]idian1 to :i* ! diff]5t spots on h] surface h be5 ref]r$1 & _! positions det]m9$ ) z mu* accuracy z ^? ( _m ( ! mo/ rem>kable places on ! surface ( our globe4 ,! rotation ( ! e>? :i* det]m9es ! l5g? ( ! day may be reg>d$ z "o ( ! mo/ important elem5ts 9 ! sy/em ( ! _w4 ,x s]ves z a measure ( "t1 & =ms ! /&>d ( comp>ison = ! revolutions ( ! cele/ial bodies1 :i* by _! proportional increase or decrease w\ld soon disclose any *anges x might su/a94 ,!ory & obs]vation concur 9 prov+1 t among ! innum]able vicissitudes t prevail ?r\gh\t creation1 ! p]iod ( ! e>?'s diurnal rotation is immutable4 ,a fluid1 z ,mr4 ,babbage obs]ves1 9 fall+ f a high] to a l[] level1 c>ries ) x ! velocity due to its revolution ) ! e>? at a great] di/ance f its c5tre4 ,x w !re=e accel]ate1 al?\gh to an almo/ inf9itesimal ext5t1 ! e>?'s daily rotation4 ,! sum ( all ^! increm5ts ( velocity1 aris+ f ! desc5t ( all ! riv]s on ! e>?'s surface1 w\ld 9 "t become p]ceptible1 did n nature1 by ! process ( evaporation1 raise ! wat]s back to _! s\rces2 & ?us aga9 by remov+ matt] to a great] di/ance f ! c5tre1 de/roy ! velocity g5]at$ by its previ\s approa*2 s t ! desc5t ( ! riv]s does n affect ! e>?'s rotation4 ,enorm\s masses project$ by volcanoes f ! equator to ! poles1 & ! contr>y1 w\ld inde$ affect x1 b !re is no evid5ce ( su* convulsions4 ,! di/urb+ action ( ! moon & planets1 :i* has s p[]ful an effect on ! revolution ( ! e>?1 9 no way influ5ces its rotation3 ! con/ant friction ( ! trade w9ds on ! m\nta9s & cont95ts betwe5 ! tropics does n imp$e its velocity1 :i* !ory ev5 proves to be ! same1 z if ! sea toge!r ) ! e>? =m$ "o solid mass4 ,b al?\gh ^! circum/ances be ineffici5t1 a v>iation 9 ! mean temp]ature w\ld c]ta9ly occasion a correspond+ *ange 9 ! velocity ( rotation3 = 9 ! sci5ce ( dynamics1 x is a pr9ciple 9 a sy/em ( bodies1 or ( p>ticles revolv+ ab\t a fix$ c5tre1 t ! mom5tum1 or sum ( ! products ( ! mass ( ea* into its angul> velocity & di/ance f ! c5tre is a con/ant quantity1 if ! sy/em be n d]ang$ by an ext]nal cause4 ,n[ s9ce ! numb] ( p>ticles 9 ! sy/em is ! same :atev] its temp]ature may be1 :5 _! di/ances f ! c5tre are dim9i%$1 _! angul> velocity mu/ be increas$ 9 ord] t ! prec$+ quantity may /ill rema9 con/ant4 ,x foll[s !n1 t z ! primitive mom5tum ( rotation ) :i* ! e>? 0 project$ into space mu/ necess>ily rema9 ! same1 ! smalle/ decrease 9 heat1 by contract+ ! t]re/rial sph]oid1 w\ld accel]ate its rotation1 & consequ5tly dim9i% ! l5g? ( ! day4 ,not)/&+ ! con/ant accession ( heat f ! sun's rays1 geologi/s h be5 induc$ to believe f ! nature ( fossil rema9s1 t ! mean temp]ature ( ! globe is decreas+4 ,! high temp]ature ( m9es1 hot spr+s1 & above all1 ! int]nal fires t h produc$1 & d /ill occasion su* deva/ation on our planet1 indicate an augm5tation ( heat t[>ds its c5tre ! increase ( d5sity 9 ! /rata correspond+ to ! dep? & ! =m ( ! sph]oid1 be+ :at !ory assigns to a fluid mass 9 rotation1 concur to induce ! idea t ! temp]ature ( ! e>? 0 orig9ally s high z to r$uce all ! sub/ances ( :i* x is compos$ to a /ate ( fusion1 & t 9 ! c\rse ( ages x has cool$ d[n to its pres5t /ate2 t x is /ill becom+ cold]1 & t x w cont9ue to d s1 till ! :ole mass arrives at ! temp]ature ( ! m$ium 9 :i* x is plac$1 or r at a /ate ( equilibrium betwe5 ?is temp]ature1 ! cool+ p[] ( its own radiation1 & ! heat+ effect ( ! sun's rays4 ,b ev5 if ?is cause be suffici5t to produce ! obs]v$ effects1 x mu/ be extremely sl[ 9 its op]ation2 = 9 consequ5ce ( ! rotation ( ! e>? be+ a measure ( ! p]iods ( ! cele/ial motions1 x has be5 prov$1 t if ! l5g? ( ! day _h decreas$ by ! ?ree hundr$? "p ( a second s9ce ! obs]vations ( ,hipp>*us two ?\s& ye>s ago1 x w\ld h dim9i%$ ! secul> equation ( ! moon by #dd4 ,x is !re=e beyond a d\bt1 t ! mean temp]ature ( ! e>? _c h s5sibly v>i$ dur+ t "t2 if !n ! appe>ances exhibit$ by ! /rata really ow+ to a decrease ( int]nal temp]ature1 x ei!r %[s ! imm5se p]iods requisite to produce geological *anges to :i* two ?\s& ye>s are z no?+1 or t ! mean temp]ature ( ! e>? _h arriv$ at a /ate ( equilibrium be=e ^! obs]vations4 ,h[ev] /rong ! indication ( ! primitive fluidity ( ! e>?1 z !re is no direct pro(1 x c only be reg>d$ z a v probable hypo!sis2 b "o ( ! mo/ pr(\nd philosoph]s & elegant writ]s ( mod]n times has f\nd1 9 ! secul> v>iation ( ! ecc5tricity ( ! t]re/rial orbit1 an evid5t cause ( decreas+ temp]ature4 ,t accompli%$ au?or1 9 po9t+ out ! mutual dep5d5ces ( ph5om5a1 says--',x is evid5t t ! mean temp]ature ( ! :ole surface ( ! globe1 9 s f> z x is ma9ta9$ by ! action ( ! sun at #h high] degree ?an x w\ld h 7 ! sun ext+ui%$1 mu/ dep5d on ! mean quantity ( ! sun's rays :i* x receives1 or1 :i* comes to ! same ?+1 on ! total quantity receiv$ 9 a giv5 inv>iable "t3 & ! l5g? ( ! ye> be+ un*angeable 9 all ! fluctuations ( ! planet>y sy/em1 x foll[s1 t ! total am\nt ( sol> radiation w det]m9e1 ct]is p>ibus1 ! g5]al climate ( ! e>?4 ,n[ x is n difficult to %[1 t ?is am\nt is inv]sely proportional to ! m9or axis ( ! ellipse describ$ by ! e>? ab\t ! sun1 reg>d$ z sl[ly v>iable2 & t1 !re=e1 ! major axis rema9+1 z we "k x to be1 con/ant1 & ! orbit be+ actually 9 a /ate ( approa* to a circle1 & consequ5tly ! m9or axis be+ on ! increase1 ! mean annual am\nt ( sol> radiation receiv$ by ! :ole e>? mu/ be actually on ! decrease4 ,we h1 !re=e1 an evid5t real cause to acc\nt = ! ph5om5on4' ,! limits ( ! v>iation 9 ! ecc5tricity ( ! e>?'s orbit are unkn[n2 b if its ellipticity has ev] be5 z great z t ( ! orbit ( ,m]cury or ,pallas1 ! mean temp]ature ( ! e>? mu/ h be5 s5sibly high] ?an x is at pres5t2 :e!r x 0 great en\gh to r5d] our nor!rn climates fit = ! production ( tropical plants1 & = ! resid5ce ( ! elephant1 & ! o!r inhabitants ( ! torrid zone1 x is impossible to say4 ,! relative quantity ( heat receiv$ by ! e>? at diff]5t mom5ts dur+ a s+le revolution1 v>ies ) ! position ( ! p]igee ( its orbit1 :i* accompli%es a tropical revolution 9 #bjice ye>s4 ,9 ! ye> #abej ( our era1 & #bifec ye>s be=e x1 ! p]igee co9cid$ ) ! summ] sol/ice2 at bo? ^! p]iods ! e>? 0 ne>] ! sun dur+ ! summ]1 & f>!r f him 9 ! w9t] ?an 9 any o!r position ( ! apsides3 ! extremes ( temp]ature mu/ !re=e h be5 great] ?an at pres5t2 b z ! t]re/rial orbit 0 probably m elliptical at ! di/ant epo*1 ! heat ( ! summ]s mu/ h be5 v great ?\gh possibly comp5sat$ by ! rig\r ( ! w9t]s2 at all ev5ts1 none ( ^! *anges affect ! l5g? ( ! day4 ,x appe>s f ! m>9e %ells f\nd on ! tops ( ! highe/ m\nta9s1 & 9 almo/ e "p ( ! globe1 t imm5se cont95ts h be5 elevat$ above ! ocean1 :i* mu/ h :i* mu/ h engulph$ o!rs4 ,su* a cata/rophe w\ld be occasion$ by a v>iation 9 ! position ( ! axis ( rotation on ! surface ( ! e>?2 = ! seas end+ to ! new equator w\ld leave "s portions ( ! globe1 & ov]:elm o!rs4 ,b !ory proves t nei!r nutation1 precession1 nor any ( ! di/urb+ =ces t affect ! sy/em1 h ! smalle/ influ5ce on ! axis ( rotation1 :i* ma9ta9s a p]man5t position on ! surface1 if ! e>? be n di/urb$ 9 its rotation by "s =eign cause1 z ! collision ( a comet :i* may h happ5$ 9 ! imm5sity ( "t4 ,!n inde$1 ! equilibrium c\ld only h be5 re/or$ by ! ru%+ ( ! seas to ! new equator1 :i* !y w\ld cont9ue to d1 till ! surface 0 e :]e p]p5dicul> to ! direction ( gravity4 ,b x is probable t su* an accumulation ( ! wat]s w\ld n be suffici5t to re/ore equilibrium if ! d]angem5t _h be5 great2 = ! mean d5sity ( ! sea is only ab\t a fif? "p ( ! mean d5sity ( ! e>?1 & ! mean dep? ev5 ( ! ,pacific ocean is n m ?an f\r miles1 :]eas ! equatorial radius ( ! e>? exce$s ! pol> radius by tw5ty-five or ?irty miles2 consequ5tly ! influ5ce ( ! sea on ! direction ( gravity is v small2 & z x appe>s t a great *ange 9 ! position ( ! axes is incompatible ) ! law ( equilibrium1 ! geological ph5om5a mu/ be ascrib$ to an int]nal cause4 ,?us amid/ ! mighty revolutions :i* h swept innum]able races ( organiz$ be+s f ! e>?1 :i* h elevat$ pla9s1 & buri$ m\nta9s 9 ! ocean1 ! rotation ( ! e>?1 & ! position ( ! axis on its surface1 h und]gone b slight v>iations4 ,x is beyond a d\bt t ! /rata increase 9 d5sity f ! surface ( ! e>? to its c5tre1 :i* is ev5 prov$ by ! lun> inequalities2 & x is manife/ f ! m5suration ( arcs ( ! m]idian & ! l5g?s ( ! seconds p5dulum t ! /rata are elliptical & conc5tric4 ,?is c]ta9ly w\ld h happ5$ if ! e>? _h orig9ally be5 fluid1 = ! d5s] p>ts mu/ h subsid$ t[>ds ! c5tre1 z x approa*$ a /ate ( equilibrium2 b ! enorm\s pressure ( ! sup]9cumb5t mass is a suffici5t cause = ^! ph5om5a4 ,pr(essor ,leslie obs]ves1 t air compress$ into ! fiftie? "p ( its volume has its ela/icity fifty times augm5t$2 if x cont9ue to contract at t rate1 x w\ld1 f its own incumb5t weight1 acquire ! d5sity ( wat] at ! dep? ( ?irty-f\r miles4 ,b wat] itself w\ld h its d5sity d\bl$ at ! dep? ( n9ety-?ree miles1 & w\ld ev5 atta9 ! d5sity ( quicksilv] at a dep? ( #cfb miles4 ,9 desc5d+ !re=e t[>ds ! c5tre ?r\gh #djjj miles1 ! cond5sation ( ord9>y mat]ials w\ld surpass ! utmo/ p[]s ( conception4 ,b a d5sity s extreme is n borne out by a/ronomical obs]vation4 ,x might seem !re=e to foll[1 t our planet mu/ h a widely cav]n\s /ructure1 & t we tread on a cru/ or %ell1 ^: ?ickness be>s a v small proportion to ! diamet] ( its sph]e4 ,possibly too ?is great cond5sation at ! c5tral regions may be c\nt]balanc$ by ! increas$ ela/icity due to a v elevat$ temp]ature4 ,dr4 ,"y says t /eel w\ld be compress$ into "o-f\r?1 & /one into "o-eigh? ( its bulk at ! e>?'s c5tre4 ,h[ev] we are yet ignorant ( ! laws ( compression ( solid bodies beyond a c]ta9 limit2 b1 f ! exp]im5ts ( ,mr4 ,p]k9s1 !y appe> to be capable ( a great] degree ( compression ?an has g5]ally be5 imag9$4 ,x appe>s !n1 t ! axis ( rotation is inv>iable on ! surface ( ! e>?1 & obs]vation %[s1 t 7 x n = ! action ( ! sun & moon on ! matt] at ! equator1 x w\ld rema9 p>allel to itself 9 e po9t ( its orbit4 ,! attraction ( an ext]ior body n only draws a sph]oid t[>ds x2 b1 z ! =ce v>ies inv]sely z ! squ>e ( ! di/ance1 x gives x a motion ab\t its c5tre ( gravity1 unless :5 ! attract+ body is situat$ 9 ! prolongation ( "o ( ! axes ( ! sph]oid4 ,! plane ( ! equator is incl9$ to ! plane ( ! ecliptic at an angle ( ab\t #bc #bh'1 & ! incl9ation ( ! lun> orbit on ! same is ne>ly #e2 consequ5tly1 f ! oblate figure ( ! e>?1 ! sun & moon act+ obliquely & unequally on ! diff]5t p>ts ( ! t]re/rial sph]oid1 urge ! plane ( ! equator f its direction1 & =ce x to move f ea/ to we/1 s t ! equ9octial po9ts h a sl[ retrograde motion on ! plane ( ! ecliptic ( ab\t #ejdab annually4 ,! direct t5d5cy ( ?is action w\ld be to make ! planes ( ! equator & ecliptic co9cide2 b 9 consequ5ce ( ! rotation ( ! e>?1 ! incl9ation ( ! two planes rema9s con/ant1 z a top 9 sp9n+ pres]ves ! same incl9ation to ! plane ( ! horizon4 ,7 ! e>? sph]ical ?is effect w\ld n be produc$1 & ! equ9oxes w\ld always correspond to ! same po9ts ( ! ecliptic1 at lea/ z f> z ?is k9d ( action is conc]n$4 ,b ano!r & totally diff]5t cause op]ates on ?is motion1 :i* has already be5 m5tion$4 ,! action ( ! planets on "o ano!r & on ! sun1 occasions a v sl[ v>iation 9 ! position ( ! plane ( ! ecliptic1 :i* affects its incl9ation on ! plane ( ! equator1 & gives ! equ9octial po9ts a sl[ b direct motion on ! ecliptic ( #jcab annually1 :i* is entirely indep5d5t ( ! figure ( ! e>?1 & w\ld be ! same if x 7 a sph]e4 ,?us ! sun & moon1 by mov+ ! plane ( ! equator1 cause ! equ9octial po9ts to retrograde on ! ecliptic2 & ! planets1 by mov+ ! plane ( ! ecliptic1 give !m a direct motion1 b mu* less ?an ! =m]2 consequ5tly ! diff]5ce ( ! two is ! mean precession1 :i* is prov$1 bo? by !ory & obs]vation1 to be ab\t #eja annually4 ,z ! longitudes ( all ! fix$ />s are increas$ by ?is quantity1 ! effects ( precession are soon detect$2 x 0 accord+ly discov]$ by ,hipp>*us1 9 ! ye> #abh be=e ,*ri/1 f a comp>ison ( 8 own obs]vations ) ^? ( ,timo*>is1 #aee ye>s be=e4 ,9 ! "t ( ,hipp>*us ! entrance ( ! sun into ! con/ellation ,aries 0 ! beg9n+ ( spr+1 b s9ce !n ! equ9octial po9ts h rec$$ #cj2 s t ! con/ellations call$ ! signs ( ! zodiac are n[ at a consid]able di/ance f ^? divisions ( ! ecliptic :i* be> _! names4 ,mov+ at ! rate ( #eja annually1 ! equ9octial po9ts w accompli% a revolution 9 #behfh ye>s2 b z ! precession v>ies 9 diff]5t c5turies1 ! ext5t ( ?is p]iod w be slightly modifi$4 ,s9ce ! motion ( ! sun is direct1 & t ( ! equ9octial po9ts retrograde1 he takes a %ort] "t to return to ! equator ?an to arrive at ! same />s2 s t ! tropical ye> ( #cfe4bdbbfd days mu/ be increas$ by ! "t he takes to move ?r\gh an arc ( #eja1 9 ord] to h ! l5g? ( ! sid]eal ye>4 ,by simple proportion x is ! #j4jadaai? "p ( a day1 s t ! sid]eal ye> is #cfe4befchc4 ,! mean annual precession is subject to a secul> v>iation2 = al?\gh ! *ange 9 ! plane ( ! ecliptic :i* is ! orbit ( ! sun1 be indep5d5t ( ! =m ( ! e>?1 yet by br++ ! sun1 moon & e>? into diff]5t relative positions f age to age1 x alt]s ! direct action ( ! two fir/ on ! prom95t matt] at ! equator2 on ?is acc\nt ! motion ( ! equ9ox is great] by #jdee n[ ?an x 0 9 ! lime ( ,hipp>*us2 consequ5tly ! actual l5g? ( ! tropical ye> is ab\t #daed %ort] ?an x 0 at t "t4 ,! utmo/ *ange t x c exp]i5ce f ?is cause am\nts to #dc4 ,su* is ! secul> motion ( ! equ9oxes1 b x is sometimes increas$ & sometimes dim9i%$ by p]iodic v>iations1 ^: p]iods dep5d on ! relative positions ( ! sun & moon ) reg>d to ! e>?1 & occasion$ by ! direct action ( ^! bodies on ! equator4 ,dr4 ,bradley discov]$ t by ?is action ! moon causes ! pole ( ! equator to describe a small ellipse 9 ! heav5s1 ! diamet]s ( :i* are #af & #bj4 ,! p]iod ( ?is inequality is n9ete5 ye>s1 ! "t employ$ by ! nodes ( ! lun> orbit to accompli% a revolution4 ,! sun causes a small v>iation 9 ! description ( ?is ellipse2 x runs ?r\gh its p]iod 9 half a ye>4 ,?is nutation 9 ! e>?'s axis affects bo? ! precession & obliquity ) small p]iodic v>iations2 b 9 consequ5ce ( ! secul> v>iation 9 ! position ( ! t]re/rial orbit1 :i* is *iefly ow+ to ! di/urb+ en]gy ( ,jupit] on ! e>?1 ! oblique ( ! ecliptic is annually dim9i%$ by #jebaji4 ,) reg>d to ! fix$ />s1 ?is v>iation 9 ! c\rse ( ages may am\nt to tea or elev5 degrees2 b ! obliquity ( ! ecliptic to ! equator c nev] v>y m ?an two or ?ree degrees1 s9ce ! equator w foll[ 9 "s measure ! motion ( ! ecliptic4 ,x is evid5t t ! places ( all ! cele/ial bodies are affect$ by precession & nutation1 & !re=e all obs]vations ( !m mu/ be correct$ = ^! inequalities4 ,! d5sities ( bodies are proportional to _! masses divid$ by _! volumes2 h5ce if ! sun & planets be assum$ to be sph]es1 _! volumes w be z ! cubes ( _! diamet]s4 ,n[ ! app>5t diamet]s ( ! sun & e>? at _! mean di/ance1 are #aibb & #agjh1 & ! mass ( ! e>? is ! #a_/cedicf? "p ( t ( ! sun tak5 z ! unit2 x foll[s !re=e1 t ! e>? is ne>ly f\r times z d5se z ! sun2 b ! sun is s l>ge t 8 attractive =ce w\ld cause bodies to fall ?r\gh ab\t #dej feet 9 a second2 consequ5tly if he 7 ev5 habitable by human be+s1 !y w\ld be unable to move1 s9ce _! weight w\ld be ?irty times z great z x is "h4 ,a mod]ate siz$ man w\ld weigh ab\t two tons at ! surface ( ! sun4 ,on ! contr>y1 at ! surface ( ! f\r new planets we %\ld be s light1 t x w\ld be impossible to /& f ! excess ( our muscul> =ce1 = a man w\ld only weigh a few p\nds4 ,all ! planets & satellites appe> to be ( less d5sity ?an ! e>?4 ,! motions ( ,jupit]'s satellites %[ t 8 d5sity increases t[>ds 8 c5tre2 & ! s+ul> irregul>ities 9 ! =m ( ,saturn1 & ! great compression ( ,m>s1 prove ! int]nal /ructure ( ^! two planets to be v f> f uni=m4 ,a/ronomy has be5 ( imm$iate & ess5tial use 9 af=d+ inv>iable /&>ds = measur+ duration1 di/ance1 magnitude1 & velocity4 ,! sid]eal day1 measur$ by ! "t elaps$ betwe5 two consecutive transits ( any /> at ! same m]idian1 & ! sid]eal ye>1 are immutable units ) :i* to comp>e all great p]iods ( "t2 ! oscillations ( ! iso*ron\s p5dulum measure its small] portions4 ,by ^! inv>iable /&>ds alone we c judge ( ! sl[ *anges t o!r elem5ts ( ! sy/em may h und]gone 9 ! lapse ( ages4 ,! returns ( ! sun to ! same m]idian1 & to ! same equ9ox or sol/ice1 h be5 univ]sally adopt$ z ! measure ( our civil days & ye>s4 ,! sol> or a/ronomical day is ! "t t elapses betwe5 two consecutive noons or midnights2 x is consequ5tly long] ?an ! sid]eal day1 on acc\nt ( ! prop] motion ( ! sun dur+ a revolution ( ! cele/ial sph]e2 b z ! sun moves ) great] rapidity at ! w9t] ?an at ! summ] sol/ice1 ! a/ronomical day is m ne>ly equal to ! sid]eal day 9 summ] ?an 9 w9t]4 ,! obliquity ( ! ecliptic also affects its duration1 = 9 ! equ9oxes ! arc ( ! equator is less ?an ! correspond+ arc ( ! ecliptic1 & 9 ! sol/ices x is great]4 ,! a/ronomical day is !re=e dim9i%$ 9 ! fir/ case1 & increas$ 9 ! second4 ,if ! sun mov$ uni=mly 9 ! equator at ! rate ( #ei' #hc e day1 ! sol> days w\ld be all equal2 ! "t !re=e1 :i* is reckon$ by ! arrival ( an imag9>y sun at ! m]idian1 or ( "o :i* is suppos$ to move 9 ! equator1 is d5om9at$ mean sol> "t1 su* z is giv5 by clocks & wat*es 9 common life3 :5 x is reckon$ by ! arrival ( ! real sun at ! m]idian1 x is app>5t "t1 su* z is giv5 by dials4 ,! diff]5ce betwe5 ! "t %[n by a clock & a dial is ! equation ( "t giv5 9 ! ,nautical ,almanac1 & sometimes am\nts to z mu* z sixte5 m9utes4 ,! app>5t & mean "t co9cide f\r times 9 ! ye>4 ,a/ronom]s beg9 ! day at noon1 b 9 common reckon+ ! day beg9s at midnight4 ,9 ,engl& x is divid$ into tw5ty-f\r h\rs1 :i* are c\nt$ by twelve & twelve2 b 9 ,france1 a/ronom]s adopt+ decimal division1 divide ! day into t5 h\rs1 ! h\r into "o hundr$ m9utes1 & ! m9ute into a hundr$ seconds1 because ( ! facility 9 computation1 & 9 con=mity ) _! sy/em ( weights & measures4 ,?is subdivision is n us$ 9 common life1 nor has x be5 adopt$ 9 any o!r c\ntry1 ?\gh _! sci5tific writ]s /ill employ t division ( "t4 ,! mean l5g? ( ! day1 ?\gh accurately det]m9$1 is n suffici5t = ! purposes ei!r ( a/ronomy or civil life4 ,! l5g? ( ! ye> is po9t$ out by nature z a measure ( long p]iods2 b ! incomm5surability t exi/s betwe5 ! l5g?s ( ! day1 & ! revolutions ( ! sun1 r5d]s x difficult to adju/ ! e/imation ( bo? 9 :ole numb]s4 ,if ! revolution ( ! sun 7 accompli%$ 9 #cfe days1 all ! ye>s w\ld be ( precisely ! same numb] ( days1 & w\ld beg9 & end ) ! sun at ! same po9t ( ! ecliptic2 b z ! sun's revolution includes ! fraction ( a day1 a civil ye> & a revolution ( ! sun h n ! same duration4 ,s9ce ! fraction is ne>ly ! f\r? ( a day1 f\r ye>s are ne>ly equal to f\r revolutions ( ! sun1 s t ! addition ( a sup]num]>y day e f\r? ye> ne>ly comp5sates ! diff]5ce2 b 9 process ( "t fur!r correction w be necess>y1 because ! fraction is less ?an ! f\r? ( a day4 ,! p]iod ( sev5 days1 by f> ! mo/ p]man5t division ( "t1 & ! mo/ anci5t monum5t ( a/ronomical k1 0 us$ by ! ,brahm9s 9 ,india ) ! same d5om9ations employ$ by u1 & 0 alike f\nd 9 ! ,cal5d>s ( ! ,jews1 ,egyptians1 ,arabs1 & ,assyrians2 x has surviv$ ! fall ( empires1 & has exi/$ among all successive g5]ations1 a pro( ( _! common orig94 ,! new moon imm$iately foll[+ ! w9t] sol/ice 9 ! #gjg? ye> ( ,rome 0 made ! #a/ ( ,janu>y ( ! fir/ ye> ( ,cs>2 ! #be? ( ,decemb] 9 8 #de? ye>1 is consid]$ z ! date ( ,*ri/'s nativity2 & ,cs>'s #df? ye> is assum$ to be ! fir/ ( our era4 ,! prec$+ ye> is call$ ! fir/ ye> be=e ,*ri/ by *ronologi/s1 b by a/ronom]s x is call$ ! ye> #j4 ,! a/ronomical ye> beg9s on ! #ca/ ( ,decemb] at noon2 & ! date ( an obs]vation expresses ! days & h\rs :i* actually elaps$ s9ce t "t4 ,"s rem>kable a/ronomical eras are det]m9$ by ! position ( ! major axis ( ! sol> ellipse4 ,mov+ at ! rate ( #faijf annually1 x accompli%es a tropical revolution 9 #bjice ye>s4 ,x co9cid$ ) ! l9e ( ! equ9oxes #djjj or #djhi ye>s be=e ! ,*ri/ian era1 mu* ab\t ! "t *ronologi/s assign = ! creation ( man4 ,9 #fdhe ! major axis w aga9 co9cide ) ! l9e ( ! equ9oxes1 b !n ! sol> p]igee w co9cide ) ! equ9ox ( spr+2 :]eas at ! creation ( man x co9cid$ ) ! autumnal equ9ox4 ,9 ! ye> #abej ! major axis 0 p]p5dicul> to ! l9e ( ! equ9oxes1 & !n ! sol> p]igee co9cid$ ) ! sol/ice ( w9t]1 & ! apogee ) ! sol/ice ( summ]4 ,on t acc\nt ,la ,place propos$ ! ye> #abej z a univ]sal epo*1 & t ! v]nal equ9ox ( t ye> %\ld be ! fir/ day ( ! fir/ ye>4 ,! v>iations 9 ! positions ( ! sol> ellipse occasion correspond+ *anges 9 ! l5g? ( ! seasons4 ,9 its pres5t position spr+ is %ort] ?an summ]1 & autumn long] ?an w9t]2 & :ile ! sol> p]igee cont9ues z x n[ is1 betwe5 ! sol/ice ( w9t] & ! equ9ox ( spr+1 ! p]iod includ+ spr+ & summ] w be long] ?an t includ+ autumn & w9t]3 9 ?is c5tury ! diff]5ce is ab\t sev5 days4 ,^! int]vals w be equal t[>ds ! ye> #fdhe1 :5 ! p]igee comes to ! equ9ox ( spr+4 ,7 ! e>?'s orbit circul>1 ! seasons w\ld be equal2 _! diff]5ces arise f ! ecc5tricity ( ! e>?'s orbit1 small z x is2 b ! *anges are s gradual z to be imp]ceptible 9 ! %ort space ( human life4 ,no circum/ance 9 ! :ole sci5ce ( a/ronomy excites a deep] int]e/ ?an its application to *ronology4 ',:ole nations1' says ,la ,place1 'h be5 swept f ! e>?1 ) _! language1 arts & sci5ces1 leav+ b confus$ masses ( ru9 to m>k ! place :]e mighty cities /ood2 _! hi/ory1 ) ! exception ( a few d\btful traditions1 has p]i%$2 b ! p]fection ( _! a/ronomical obs]vations m>ks _! high antiquity1 fixes ! p]iods ( _! exi/5ce1 & proves t ev5 at t e>ly p]iod !y mu/ h made consid]able progress 9 sci5ce4' ,! anci5t /ate ( ! heav5s may n[ be comput$ ) great accuracy2 & by comp>+ ! results ( computation ) anci5t obs]vations1 ! exact p]iod at :i* !y 7 made may be v]ifi$ if true1 or if false1 _! error may be detect$4 ,if ! date be accurate1 & ! obs]vation good1 x w v]ify ! accuracy ( mod]n tables1 & %[ to h[ _m c5turies !y may be ext5d$1 )\t ! fe> ( error4 ,a few examples w %[ ! importance ( ?is subject4 ,at ! sol/ices ! sun is at 8 greate/ di/ance f ! equator1 consequ5tly 8 decl9ation at ^! times is equal to ! obliquity ( ! ecliptic1 :i* 9 =m] times 0 det]m9$ f ! m]idian l5g? ( ! %ad[ ( ! /yle ( a dial on ! day ( ! sol/ice4 ,! l5g?s ( ! m]idian %ad[ at ! summ] & w9t] sol/ice are record$ to h be5 obs]v$ at ! city ( ,layang1 9 ,*9a1 #aajj ye>s be=e ! ,*ri/ian era4 ,f ^!1 ! di/ances ( ! sun f ! z5i? ( ! city ( ,layang are kn[n4 ,half ! sum ( ^! z5i? di/ances det]m9es ! latitude1 & half _! diff]5ce gives ! obliquity ( ! ecliptic at ! p]iod ( ! obs]vation2 & z ! law ( ! v>iation 9 ! obliquity is kn[n1 bo? ! "t & place ( ! obs]vations h be5 v]ifi$ by computation f mod]n tables4 ,?us ! ,*9ese _h made "s advances 9 ! sci5ce ( a/ronomy at t e>ly p]iod2 ! :ole *ronology ( ! ,*9ese is f\nd$ on ! obs]vations ( eclipses1 :i* prove ! exi/5ce ( t empire = m ?an #dgjj ye>s4 ,! epo* ( ! lun> tables ( ! ,indians1 suppos$ by ,bailly to be #cjjj be=e ! ,*ri/ian era1 0 prov$ by ,la ,place f ! accel]ation ( ! moon1 n to be m anci5t ?an ! "t ( ,ptolemy4 ,! great inequality ( ,jupit] & ,saturn ^: cycle embraces #ibi ye>s1 is peculi>ly fitt$ = m>k+ ! civilization ( a p4 ,! ,indians _h det]m9$ ! mean motions ( ^! two planets 9 t "p ( _! p]iods :5 ! app>5t m5u motion ( ,saturn 0 at ! sl[e/1 & t ( ,jupit] ! mo/ rapid4 ,! p]iods 9 :i* t happ5$ 7 #cajb ye>s be=e ! ,*ri/ian era1 & ! ye> #adia aft] x4 ,! returns ( comets to _! p]ihelia may possibly m>k ! pres5t /ate ( a/ronomy to future ages4 ,! places ( ! fix$ />s are affect$ by ! precession ( ! equ9oxes2 & z ! law ( t v>iation is kn[n1 _! positions at any "t may be comput$4 ,n[ ,eudoxus1 a contempor>y ( ,plato1 m5tions a /> situate 9 ! pole ( ! equator1 & f computation x appe>s t ,draconis 0 n v f> f t place ab\t #cjjj ye>s ago2 b z ,eudoxus liv$ only ab\t #baej ye>s ago1 he mu/ h describ$ an ant]ior /ate ( ! heav5s1 suppos$ to be ! same t 0 det]m9$ by ,*iron1 ab\t ! "t ( ! siege ( ,troy4 ,e circum/ance concurs 9 %[+ t a/ronomy 0 cultivat$ 9 ! highe/ ages ( antiquity4 ,a k ( a/ronomy leads to ! int]pretation ( hi]oglyphical *>act]s1 s9ce a/ronomical signs are (t5 f\nd on ! anci5t ,egyptian monum5ts1 :i* 7 probably employ$ by ! prie/s to record dates4 ,on ! ceil+ ( ! portico ( a temple among ! ru9s ( ,t5tyris1 !re is a long r[ ( figures ( m5 & animals1 foll[+ ea* o!r 9 ! "s direction among ^! are ! twelve signs ( ! zodiac1 plac$ accord+ to ! motion ( ! sun3 x is probable t ! fir/ figure 9 ! procession repres5ts ! beg9n+ ( ! ye>4 ,n[ ! fir/ is ! ,lion z if com+ out ( ! temple2 & z x is well kn[n t ! agricultural ye> ( ! ,egyptians comm5c$ at ! sol/ice ( summ]1 ! epo* ( ! inundations ( ! ,nile1 if ! prec$+ hypo!sis be true1 ! sol/ice at ! "t ! temple 0 built mu/ h happ5$ 9 ! con/ellation ( ! lion2 b z ! sol/ice n[ happ5s #ba #f' nor? ( ! con/ellation ( ! ,tw9s1 x is easy to compute t ! zodiac ( ,t5tyris mu/ h be5 made #djjj ye>s ago4 ,! au?or _h occasion to witness an in/ance ( ?is mo/ int]e/+ application ( a/ronomy1 9 asc]ta9+ ! dale ( a papyrus s5t f ,egypt by ,mr4 ,salt1 9 ! hi]oglyphical rese>*es ( ! late ,dr4 ,?omas ,"y1 ^: pr(\nd & v>i$ acquirem5ts d hon\r n only to 8 c\ntry1 b to ! age 9 :i* he liv$4 ,! manuscript 0 f\nd 9 a mummy case2 x prov$ to be a horoscope ( ! age ( ,ptolemy1 & its antiquity 0 det]m9$ f ! configuration ( ! heav5s at ! "t ( its con/ruction4 ,! =m ( ! e>? furni%es a /&>d ( weights & measures = ! ord9>y purposes ( life1 z well z = ! det]m9ation ( ! masses & di/ances ( ! heav5ly bodies4 ,! l5g? ( ! p5dulum vibrat+ seconds 9 ! latitude ( ,london =ms ! /&>d ( ! ,briti% measure ( ext5sion4 ,its l5g? oscillat+ 9 vacuo at ! temp]ature ( #fb ( ,fahr5heit1 & r$uc$ to ! level ( ! sea1 0 det]m9$ by ,capta9 ,kat]1 9 p>ts ( ! imp]ial /&>d y>d1 to be #ci4achg in*es4 ,! weight ( a cubic in* ( wat] at ! temp]ature ( #fb ,fahr5heit1 b>omet] #cj1 0 also det]m9$ 9 p>ts ( ! imp]ial troy p\nd1 :5ce a /&>d bo? ( weight & capacity is d$uc$4 ,! ,fr5* h adopt$ ! metre = _! unit ( l9e> measure1 :i* is ! t5 million? "p ( t quadrant ( ! m]idian pass+ ?r\gh ,=m5t]a & ,gre5wi*1 ! middle ( :i* is ne>ly 9 ! =ty-fif? degree ( latitude4 ,%\ld ! national /&>ds ( ! two c\ntries be lo/ 9 ! vicissitudes ( human affairs1 bo? may be recov]$1 s9ce !y are d]iv$ f natural /&>ds presum$ to be inv>iable4 ,! l5g? ( ! p5dulum w\ld be f\nd aga9 ) m facility ?an ! metre2 b z no measure is ma!matically exact1 an error 9 ! orig9al /&>d may at l5g? become s5sible 9 measur+ a great ext5t1 :]eas ! error t mu/ necess>ily arise 9 measur+ ! quadrant ( ! m]idian is r5d]$ totally ins5sible by subdivision 9 tak+ its t5 million? "p4 ,! ,fr5* h adopt$ ! decimal division n only 9 "t1 b 9 _! degrees1 weights1 & measures1 :i* af=ds v great facility 9 computation4 ,x has n be5 adopt$ by any o!r p2 ?\gh no?+ is m desirable ?an t all nations %\ld concur 9 us+ ! same division & /&>ds1 n only on acc\nt ( ! conv5i5ce1 b z af=d+ a m def9ite idea ( quantity4 ,x is s+ul> t ! decimal division ( ! day1 ( degrees1 weights & measures1 0 employ$ 9 ,*9a #djjj ye>s ago2 & t1 at ! "t ,ibn ,yunus made 8 obs]vations at ,cairo1 ab\t ! ye> #ajjj1 ! ,arabians 7 9 ! habit ( employ+ ! vibrations ( ! p5dulum 9 _! a/ronomical obs]vations4 ,"o ( ! mo/ imm$iate & /rik+ effects ( a gravitat+ =ce ext]nal to ! e>? is ! alt]nate rise & fall ( ! surface ( ! sea twice 9 ! c\rse ( a lun> day1 or #bd;h #ejm #dhs ( mean sol> "t4 ,z x dep5ds on ! action ( ! sun & moon1 x is class$ among a/ronomical problems1 ( :i* x is by f> ! mo/ difficult & ! lea/ satisfactory4 ,! =m ( ! surface ( ! ocean 9 equilibrio1 :5 revolv+ ) ! e>? r\nd its axis1 is an ellipsoid flatt5$ at ! poles2 b ! action ( ! sun & moon1 especially ( ! moon1 di/urbs ! equilibrium ( ! ocean4 ,if ! moon attract$ ! c5tre ( gravity ( ! e>? & all its p>ticles ) equal & p>allel =ces1 ! :ole sy/em ( ! e>? & ! wat]s t cov] x1 w\ld yield to ^! =ces ) a common motion1 & ! equilibrium ( ! seas w\ld rema9 undi/urb$4 ,! diff]5ce ( ! =ces1 & ! inequality ( _! directions1 alone tr\ble ! equilibrium4 ,x is prov$ by daily exp]i5ce1 z well z by /rict me*anical reason+1 t if a numb] ( waves or oscillations be excit$ 9 a fluid by diff]5t =ces1 ea* pursues its c\rse1 & has its effect indep5d5tly ( ! re/4 ,n[ 9 ! tides !re are ?ree di/9ct k9ds ( oscillations1 dep5d+ on diff]5t causes1 produc+ _! effects indep5d5tly ( ea* o!r1 :i* may !re=e be e/imat$ sep>ately4 ,! oscillations ( ! fir/ k9d :i* are v small1 are indep5d5t ( ! rotation ( ! e>?2 & z !y dep5d on ! motion ( ! di/urb+ body 9 its orbit1 !y are ( long p]iods4 ,! second k9d ( oscillations dep5ds on ! rotation ( ! e>?1 !re=e _! p]iod is ne>ly a day3 & ! oscillations ( ! ?ird k9d dep5d on an angle equal to twice ! angul> rotation ( ! e>?2 & consequ5tly happ5 twice 9 tw5ty-f\r h\rs4 ,! fir/ af=d no p>ticul> int]e/1 & are extremely small2 b ! diff]5ce ( two consecutive tides dep5ds on ! second4 ,at ! "t ( ! sol/ices1 ?is diff]5ce :i*1 accord+ to ,newton's !ory1 ought to be v great1 is h>dly s5sible on our %ores4 ,la ,place has %[n t ?is discrepancy arises f ! dep? ( ! sea1 & t if ! dep? 7 uni=m1 !re w\ld be no diff]5ce 9 ! consecutive tides1 7 x n = local circum/ances3 x foll[s !re=e1 t z ?is diff]5ce is extremely small1 ! sea1 consid]$ 9 a l>ge ext5t1 mu/ be ne>ly ( uni=m dep?1 t is to say1 !re is a c]ta9 mean dep? f :i* ! deviation is n great4 ,! mean dep? ( ! ,pacific ,ocean is suppos$ to be ab\t f\r miles1 t ( ! ,atlantic only ?ree4 ,f ! =mul :i* det]m9e ! diff]5ce ( ! consecutive tides x is also prov$ t ! precession ( ! equ9oxes1 & ! nutation 9 ! e>?'s axis1 are ! same z if ! sea =m$ "o solid mass ) ! e>?4 ,! ?ird k9d ( oscillations are ! semidiurnal tides1 s rem>kable on our coa/s2 !y are occasion$ by ! comb9$ action ( ! sun & moon1 b z ! effect ( ea* is indep5d5t ( ! o!r1 !y may be consid]$ sep>ately4 ,! p>ticles ( wat] "u ! moon are m attract$ ?an ! c5tre ( gravity ( ! e>?1 9 ! inv]se ratio ( ! squ>e ( ! di/ances2 h5ce !y h a t5d5cy to leave ! e>?1 b are reta9$ by _! gravitation1 :i* ?is t5d5cy dim9i%es4 ,on ! contr>y1 ! moon attracts ! c5tre ( ! e>? m p[]fully ?an %e attracts ! p>ticles ( wat] 9 ! hemisph]e opposite to h]2 s t ! e>? has a t5d5cy to leave ! wat]s b is reta9$ by gravitation1 :i* ?is t5d5cy aga9 dim9i%es4 ,?us ! wat]s imm$iately "u ! moon are drawn f ! e>? at ! same "t t ! e>? is drawn f ^? :i* are diametrically opposite to h]2 9 bo? in/ances produc+ an elevation ( ! ocean above ! surface ( equilibrium ( ne>ly ! same height2 = ! dim9ution ( ! gravitation ( ! p>ticles 9 ea* position is almo/ ! same1 on acc\nt ( ! di/ance ( ! moon be+ great 9 comp>ison ( ! radius ( ! e>?4 ,7 ! e>? entirely cov]$ by ! sea1 ! wat] ?us attract$ by ! moon w\ld assume ! =m ( an oblong sph]oid1 ^: great] axis w\ld po9t t[>ds ! moon1 s9ce ! columns ( wat] "u ! moon & 9 ! direction diametrically opposite to h] are r5d]$ light]1 9 consequ5ce ( ! dim9ution ( _! gravitation 9 ord] to pres]ve ! equilibrium1 ! axes #ij di/ant w\ld be %ort5$4 ,! elevation1 on acc\nt ( ! small] space to :i* x is conf9$1 is twice z great z ! depression1 because ! cont5ts ( ! sph]oid always rema9 ! same4 ,! effects ( ! sun's attraction are 9 all respects simil> to ^? ( ! moon's1 ?\gh really less 9 degree1 on acc\nt ( 8 di/ance2 he !re=e only modifies ! =m ( ?is sph]oid a little4 ,if ! wat]s 7 capable ( in/antly assum+ ! =m ( equilibrium1 t is1 ! =m ( ! sph]oid1 its summit w\ld always po9t to ! moon1 not)/&+ ! e>?'s rotation2 b on acc\nt ( _! resi/ance1 ! rapid motion produc$ 9 !m by rotation prev5ts !m f assum+ at e in/ant ! =m :i* ! equilibrium ( ! =ces act+ on !m requires4 ,h5ce1 on acc\nt ( ! in]tia ( ! wat]s1 if ! tides be consid]$ relatively to ! :ole e>? & op5 sea1 !re is a m]idian ab\t #cj ea/w>d ( ! moon1 :]e x is always high wat] bo? 9 ! hemisph]e :]e ! moon is1 & 9 t :i* is opposite4 ,on ! we/ side ( ?is circle ! tide is fl[+1 on ! ea/ x is ebb+1 & on ! m]idian at #ij di/ant1 x is ev]y:]e l[ wat]4 ,x is evid5t t ^! tides mu/ happ5 twice 9 a day1 s9ce 9 t "t ! rotation ( ! e>? br+s ! same po9t twice "u ! m]idian ( ! moon1 once "u ! sup]ior & once "u ! inf]ior m]idian4 ,9 ! semidiurnal tides !re are two ph5om5a p>ticul>ly to be di/+ui%$1 "o t happ5s twice 9 a mon?1 & ! o!r twice 9 a ye>4 ,! fir/ ph5om5on is1 t ! tides are mu* increas$ 9 ! syzigies1 or at ! "t ( new & full moon4 ,9 bo? cases ! sun & moon are 9 ! same m]idian1 = :5 ! moon is new !y are 9 conjunction1 & :5 %e is full !y are 9 opposition4 ,9 ea* ( ^! positions _! action is comb9$ to produce ! highe/ or spr+ tides "u t m]idian1 & ! l[e/ 9 ^? po9ts t are #ij di/ant4 ,x is obs]v$ t ! high] ! sea rises 9 ! full tide1 ! l[] x is 9 ! ebb4 ,! neap tides lake place :5 ! moon is 9 quadrature1 !y nei!r rise s high nor s9k s l[ z ! spr+ tides4 ,! spr+ tides are mu* increas$ :5 ! moon is 9 p]igee4 ,x is evid5t t ! spr+ tides mu/ happ5 twice a mon?1 s9ce 9 t "t ! moon is once new & once full4 ,! second ph5om5on 9 ! tides is ! augm5tation :i* occurs at ! "t ( ! equ9oxes :5 ! sun's decl9ation is z]o1 :i* happ5s twice e ye>4 ,! greate/ tides take place :5 a new or full moon happ5s1 ne> ! equ9oxes :ile ! moon is 9 p]igee4 ,! incl9ation ( ! moon's orbit on ! ecliptic is #e #i'2 h5ce 9 ! equ9oxes ! action ( ! moon w\ld be increas$ if h] node 7 to co9cide ) h] p]igee4 ,! equ9octial gales (t5 raise ^! tides to a great height4 ,beside ^! rem>kable v>iations1 !re are o!rs aris+ f ! decl9ation ( ! moon1 :i* has a great influ5ce on ! ebb & fl[ ( ! wat]s4 ,bo? ! height & "t ( high wat] are ?us p]petually *ang+2 !re=e1 9 solv+ ! problem1 x is requir$ to det]m9e ! heights to :i* !y rise1 ! times at :i* !y happ51 & ! daily v>iations4 ,! p]iodic motions ( ! wat]s ( ! ocean on ! hypo!sis ( an ellipsoid ( revolution entirely cov]$ by ! sea1 are v f> f accord+ ) obs]vation2 ?is arises f ! v great irregul>ities 9 ! surface ( ! e>?1 :i* is b p>tially cov]$ by ! sea1 ! v>iety 9 ! dep?s ( ! ocean1 ! mann] 9 :i* x is spread out on ! e>?1 ! position & incl9ation ( ! %ores1 ! curr5ts1 ! resi/ance ! wat]s meet )1 all ( !m causes :i* x is impossible to e/imate1 b :i* modify ! oscillations ( ! great mass ( ! ocean4 ,h[ev]1 amid/ all ^! irregul>ities1 ! ebb & fl[ ( ! sea ma9ta9 a ratio to ! =ces produc+ !m suffici5t to indicate _! nature1 & to v]ify ! law ( ! attraction ( ! sun & moon on ! sea4 ,la ,place obs]ves1 t ! inve/igation ( su* relations betwe5 cause & effect is no less useful 9 natural philosophy ?an ! direct solution ( problems1 ei!r to prove ! exi/5ce ( ! causes1 or trace ! laws ( _! effects4 ,l ! !ory ( probabilities1 x is a happy supplem5t to ! ignorance & weakness ( ! human m9d4 ,?us ! problem ( ! tides does n admit ( a g5]al solution2 x is c]ta9ly necess>y to analyse ! fun]al ph5om5a :i* ought to result f ! attraction ( ! sun & moon1 b ^! mu/ be correct$ 9 ea* p>ticul> case by ^? local obs]vations :i* are modifi$ by ! ext5t & dep? ( ! sea1 & ! peculi> circum/ances ( ! port4 ,s9ce ! di/urb+ action ( ! sun & moon c only become s5sible 9 a v great ext5t ( wat]1 x is evid5t t ! ,pacific ocean is "o ( ! pr9cipal s\rces ( our tides2 b 9 consequ5ce ( ! rotation ( ! e>?1 & ! in]tia ( ! ocean1 high wat] does n happ5 till "s "t aft] ! moon's s\?+4 ,! tide rais$ 9 t _w ( wat]s is transmitt$ to ! ,atlantic1 & f t sea x moves 9 a nor!rly direction along ! coa/s ( ,africa & ,europe1 arriv+ lat] & lat] at ea* place4 ,?is great wave h[ev] is modifi$ by ! tide rais$ 9 ! ,atlantic1 :i* sometimes comb9es ) t f ! ,pacific 9 rais+ ! sea1 & sometimes is 9 opposition to x1 s t ! tides only rise 9 proportion to _! diff]5ce4 ,?is great comb9$ wave1 reflect$ by ! %ores ( ! ,atlantic1 ext5d+ ne>ly f pole to pole1 /ill com+ nor?w>d1 occurs ?r\gh ! ,iri% & ,briti% *annels into ! ,nor? sea1 s t ! tides 9 our ports are modifi$ by ^? ( ano!r hemisph]e4 ,?us ! !ory ( ! tides 9 ea* port1 bo? z to _! height & ! times at :i* !y take place1 is really a matt] ( exp]im5t1 & c only be p]fectly det]m9$ by ! mean ( a v great numb] ( obs]vations includ+ sev]al revolutions ( ! moon's nodes4 ,! height to :i* ! tides rise is mu* great] 9 n>r[ *annels ?an 9 ! op5 sea1 on acc\nt ( ! ob/ructions !y meet )4 ,9 high latitudes :]e ! ocean is less directly "u ! influ5ce ( ! lum9>ies1 ! rise & fall ( ! sea is inconsid]able1 s t1 9 all probability1 !re is no tide at ! poles1 or only a small annual & mon?ly "o4 ,! ebb & fl[ ( ! sea are p]ceptible 9 riv]s to a v great di/ance f _! e/u>ies4 ,9 ! /raits ( ,pauxis1 9 ! riv] ( ! ,amazons1 m ?an five hundr$ miles f ! sea1 ! tides are evid5t4 ,x requires s _m days = ! tide to asc5d ?is mighty /ream1 t ! return+ tides meet a succession ( ^? :i* are com+ up2 s t e possible v>iety occurs 9 "s "p or o!r ( its %ores1 bo? z to magnitude & "t4 ,x requires a v wide expanse ( wat] to accumulate ! impulse ( ! sun & moon1 s z to r5d] _! influ5ce s5sible2 on t acc\nt ! tides 9 ! ,m$it]ranean & ,black ,sea are sc>cely p]ceptible4 ,^! p]petual commotions 9 ! wat]s ( ! ocean are occasion$ by =ces t be> a v small proportion to t]re/rial gravitation3 ! sun's action 9 rais+ ! ocean is only ! #a_/chddhjjj ( gravitation at ! e>?'s surface1 & ! action ( ! moon is little m ?an twice z mu* ^! =ces be+ 9 ! ratio ( #a to #b4ceccc4 ,f ?is ratio ! mass ( ! moon is f\nd to be only #a_/ae "p ( t ( ! e>?4 ,! initial /ate ( ! ocean has no influ5ce on ! tides2 = :atev] its primitive conditions may h be51 !y mu/ soon h vani%$ by ! friction & mobility ( ! fluid4 ,"o ( ! mo/ rem>kable circum/ances 9 ! !ory ( ! tides is ! assurance t 9 consequ5ce ( ! d5sity ( ! sea be+ only "o-fif? ( ! mean d5sity ( ! e>?1 ! /ability ( ! equilibrium ( ! ocean nev] c be subv]t$ by any physical cause :atev]4 ,a g5]al inundation aris+ f ! m]e in/ability ( ! ocean is !re=e impossible4 ,! atmosph]e :5 9 equilibrio is an ellipsoid flatt5$ at ! poles f its rotation ) ! e>?3 9 t /ate its /rata are ( uni=m d5sity at equal heights above ! level ( ! sea1 & x is s5sibly ( f9ite ext5t1 :e!r x consi/s ( p>ticles inf9itely divisible or n4 ,on ! latt] hypo!sis x mu/ really be f9ite2 & ev5 if ! p>ticles ( matt] be inf9itely divisible1 x is kn[n by exp]i5ce to be ( extreme t5uity at v small heights4 ,! b>omet] rises 9 proportion to ! sup]9cumb5t pressure4 ,n[ at ! temp]ature ( melt+ ice1 ! d5sity ( m]cury is to t ( air z #ajcbj to #a2 & z ! mean height ( ! b>omet] is #bi4ebh in*es1 ! height ( ! atmosph]e by simple proportion is #cjdjg feet1 at ! mean temp]ature ( #fb1 or #cdaec feet1 :i* is extremely small1 :5 comp>$ ) ! radius ( ! e>?4 ,! action ( ! sun & moon di/urbs ! equilibrium ( ! atmosph]e1 produc+ oscillations simil> to ^? 9 ! ocean1 :i* occasion p]iodic v>iations 9 ! heights ( ! b>omet]4 ,^!1 h[ev]1 are s extremely small1 t _! exi/5ce 9 latitudes s f> remov$ f ! equator is d\btful2 a s]ies ( obs]vations )9 ! tropics c alone decide ?is delicate po9t4 ,la ,place seems to ?9k t ! flux & reflux di/+ui%able at ,p>is may be occasion$ by ! rise & fall ( ! ocean1 :i* =ms a v>iable base to s great a portion ( ! atmosph]e4 ,! attraction ( ! sun & moon has no s5sible effect on ! trade w9ds2 ! heat ( ! sun occasions ^! a]ial curr5ts1 by r>efy+ ! air at ! equator1 :i* causes ! cool] & m d5se "p ( ! atmosph]e to ru% along ! surface ( ! e>? to ! equator1 :ile t :i* is heat$ is c>ri$ along ! high] /rata to ! poles1 =m+ two curr5ts 9 ! direction ( ! m]idian4 ,b ! rotatory velocity ( ! air correspond+ to its geographical situation decreases t[>ds ! poles2 9 approa*+ ! equator x mu/ !re=e revolve m sl[ly ?an ! correspond+ p>ts ( ! e>?1 & ! bodies on ! surface ( ! e>? mu/ /rike aga9/ x ) ! excess ( _! velocity1 & by its reaction !y w meet ) a resi/ance contr>y to _! motion ( rotation2 s t ! w9d w appe>1 to a p]son suppos+ himself to be at re/1 to bl[ 9 a contr>y direction to ! e>?'s rotation1 or f ea/ to we/1 :i* is ! direction ( ! trade w9ds4 ,! atmosph]e scatt]s ! sun's rays1 & gives all ! beautiful t9ts & *e]fulness ( day4 ,x transmits ! blue light 9 greate/ abundance2 ! high] we asc5d1 ! sky assumes a deep] hue1 b 9 ! expanse ( space ! sun & />s mu/ appe> l brilliant specks 9 pr(\nd blackness4 ,! sun & mo/ ( ! planets appe> to be surr\nd$ ) atmosph]es ( consid]able d5sity4 ,! attraction ( ! e>? has probably depriv$ ! moon ( h]s1 = ! refraction ( ! air at ! surface ( ! e>? is at lea/ a ?\s& times z great z at ! moon4 ,! lun> atmosph]e1 !re=e1 mu/ be ( a great] degree ( r>ity ?an c be produc$ by our be/ air-pumps2 consequ5tly no t]re/rial animal c\ld exi/ 9 x4 ,_m philosoph]s ( ! highe/ au?ority concur 9 ! belief t light consi/s 9 ! undulations ( a highly ela/ic e!real m$ium p]vad+ space1 :i*1 communicat$ to ! optic n]ves produce ! ph5om5a ( vision4 ,! exp]im5ts ( our illu/ri\s c\ntryman1 ,dr4 ,?omas ,"y1 & ^? ( ! celebrat$ ,fresnel1 %[ t ?is !ory accords bett] ) all ! obs]v$ ph5om5a ?an t ( ! emission ( p>ticles f ! lum9\s body4 ,z s\nd is propagat$ by ! undulations ( ! air1 its !ory is 9 a great _m respects simil> to t ( light4 ,! grave or l[ tones are produc$ by v sl[ vibrations1 :i* increase 9 frequ5cy progressively z ! note becomes m acute4 ,:5 ! vibrations ( a musical *ord1 = example1 are less ?an sixte5 9 a second1 x w n communicate a cont9u$ s\nd to ! e>2 ! vibrations or pulses increase 9 numb] ) ! acut5ess ( ! note1 till at la/ all s5se ( pit* is lo/4 ,! :ole ext5t ( human he>+1 f ! l[e/ notes ( ! organ to ! highe/ kn[n cry ( insects1 z ( ! cricket1 includes ab\t n9e octaves4 ,! undulations ( light are mu* m rapid ?an ^? ( s\nd1 b !y are analog\s 9 ?is respect1 t z ! frequ5cy ( ! pulsations 9 s\nd increases f ! l[ tones to ! high]1 s ^? ( light augm5t 9 frequ5cy1 f ! r$ rays ( ! sol> spectrum to ! extreme violet4 ,by ! exp]im5ts ( ,sir ,william ,h]s*el1 x appe>s t ! heat communicat$ by ! spectrum increases f ! violet to ! r$ rays2 b t ! maximum ( ! hot invisible rays is beyond ! extreme r$4 ,heat 9 all probability consi/s1 l light & s\nd1 9 ! undulations ( an ela/ic m$ium4 ,all ! pr9cipal ph5om5a ( heat may actually be illu/rat$ by a comp>ison ) ^? ( s\nd4 ,! excitation ( heat & s\nd are n only simil>1 b (t5 id5tical1 z 9 friction & p]cussion2 !y are bo? communicat$ by contact & by radiation2 & ,dr4 ,"y obs]ves1 t ! effect ( radiant heat 9 rais+ ! temp]ature ( a body ^u :i* x falls1 resembles ! sympa!tic agitation ( a /r+1 :5 ! s\nd ( ano!r /r+1 :i* is 9 unison ) x1 is transmitt$ to x ?r\gh ! air4 ,light1 heat1 s\nd1 & ! waves ( fluids are all subject to ! same laws ( reflection1 &1 inde$1 _! undulat+ !ories are p]fectly simil>4 ,if1 !re=e1 we may judge f analogy1 ! undulations ( ! heat produc+ rays mu/ be less frequ5t ?an ^? ( ! extreme r$ ( ! sol> spectrum2 b if ! analogy 7 p]fect1 ! int]f]5ce ( two hot rays ought to produce cold1 s9ce d>kness results f ! int]f]5ce ( two undulations ( light1 sil5ce ensues f ! int]f]5ce ( two undulations ( s\nd2 & /ill wat]1 or no tide1 is ! consequ5ce ( ! int]f]5ce ( two tides4 ,! propagation ( s\nd requires a mu* d5s] m$ium ?an t ( ei!r light or heat2 its int5sity dim9i%es z ! r>ity ( ! air increases2 s t1 at a v small height above ! surface ( ! e>?1 ! noise ( ! tempe/ ceases1 & ! ?und] is he>d no m 9 ^? b\ndless regions :]e ! heav5ly bodies accompli% _! p]iods 9 et]nal & sublime sil5ce4 ,:at ! body ( ! sun may be1 x is impossible to conjecture2 b he seems to be surr\nd$ by an ocean ( flame ?r\gh :i* 8 d>k nucleus appe>s l black spots1 (t5 ( enorm\s size4 ,! sol> rays1 :i* probably arise f ! *emical processes t cont9ually take place at 8 surface1 are transmitt$ ?r\gh space 9 all directions2 b1 not)/&+ ! sun's magnitude1 & ! inconceivable heat t mu/ exi/ :]e su* combu/ion is go+ on1 z ! int5sity bo? ( 8 light & heat dim9i%es ) ! squ>e ( ! di/ance1 8 k9dly influ5ce c h>dly be felt at ! b\nd>ies ( our sy/em4 ,mu* dep5ds on ! mann] 9 :i* ! rays fall1 z we readily p]ceive f ! diff]5t climates on our globe4 ,9 w9t] ! e>? is ne>] ! sun by #a_/cj? ?an 9 summ]1 b ! rays /rike ! nor!rn hemisph]e m obliquely 9 w9t] ?an 9 ! o!r half ( ! ye>4 ,9 ,uranus ! sun mu/ be se5 l a small b brilliant />1 n above ! hundr$ & fiftie? "p s bright z he appe>s to u2 t is h[ev] #bjjj times bright] ?an our moon to u1 s t he really is a sun to ,uranus1 & probably imp>ts "s degree ( w>m?4 ,b if we consid] t wat] w\ld n rema9 fluid 9 any "p ( ,m>s1 ev5 at 8 equator1 & t 9 ! temp]ate zones ( ! same planet ev5 alcohol & quicksilv] w\ld freeze1 we may =m "s idea ( ! cold t mu/ reign 9 ,uranus1 unless inde$ ! e!r has a temp]ature4 ,! climate ( ,v5us m ne>ly resembles t ( ! e>?1 ?\gh1 except+ p]haps at h] poles1 mu* too hot = animal & vegetable life z !y exi/ "h2 b 9 ,m]cury ! mean heat1 aris+ only f ! int5sity ( ! sun's rays1 mu/ be above t ( boil+ quick-silv]1 & wat] w\ld boil ev5 at 8 poles4 ,?us ! planets1 ?\gh k9dr$ ) ! e>? 9 motion & /ructure1 are totally unfit = ! habitation ( su* a be+ z man4 ,! direct light ( ! sun has be5 e/imat$ to be equal to t ( #eefc wax c&les ( a mod]ate size1 suppos$ to be plac$ at ! di/ance ( "o foot f ! object3 t ( ! moon is probably only equal to ! light ( "o c&le at ! di/ance ( twelve feet2 consequ5tly ! light ( ! sun is m ?an ?ree hundr$ ?\s& times great] ?an t ( ! moon2 = :i* reason ! light ( ! moon imp>ts no heat1 ev5 :5 br\ght to a focus by a mirror4 ,9 adv]t+ to ! peculi>ities 9 ! =m & nature ( ! e>? & planets1 x is impossible to pass 9 sil5ce ! magnetism ( ! e>?1 ! director ( ! m>9]'s compass1 & 8 guide ?r\gh ! ocean4 ,?is prop]ty probably arises f metallic iron 9 ! int]ior ( ! e>?1 or f ! circulation ( curr5ts ( electricity r\nd x3 its influ5ce ext5ds ov] e "p ( its surface1 b its accumulation & defici5cy det]m9e ! two poles ( ?is great magnet1 :i* are by no means ! same z ! poles ( ! e>?'s rotation4 ,9 consequ5ce ( _! attraction & repulsion1 a ne$le freely susp5d$1 :e!r x be magnetic or n1 only rema9s 9 equilibrio :5 9 ! magnetic m]idian1 t is1 9 ! plane :i* passes ?r\gh ! nor? & s\? magnetic poles4 ,!re are places :]e ! magnetic m]idian co9cides ) ! t]re/rial m]idian2 9 ^! a magnetic ne$le freely susp5d$1 po9ts to ! true nor?1 b if x be c>ri$ successively to diff]5t places on ! e>?'s surface1 its direction w deviate sometimes to ! ea/ & sometimes to ! we/ ( nor?4 ,l9es drawn on ! globe ?r\gh all ! places :]e ! ne$le po9ts due nor? & s\?1 are call$ l9es ( no v>iation1 & are extremely complicat$4 ,! direction ( ! ne$le is n ev5 con/ant 9 ! same place1 b *anges 9 a few ye>s1 accord+ to a law n yet det]m9$4 ,9 #afeg1 ! l9e ( no v>iation pass$ ?r\gh ,london4 ,9 ! ye> #ahai1 ,capta9 ,p>ry1 9 8 voyage to discov] ! nor?-we/ passage r\nd ,am]ica1 sail$ directly ov] ! magnetic pole2 & 9 #ahbd1 ,capta9 ,lyon1 :5 on en exp$ition = ! same purpose1 f\nd t ! v>iation ( ! compass 0 #cg #cj' we/1 & t ! magnetic pole 0 !n situate 9 #fc #bf' #ea nor? latitude1 & 9 #hj #ea' #be we/ longitude4 ,x appe>s h[ev] f lat] rese>*es t ! law ( t]re/rial magnetism is ( consid]able complication1 & ! exi/5ce ( m ?an "o magnetic pole 9 ei!r hemisph]e has be5 r5d]$ highly probable4 ,! ne$le is also subject to diurnal v>iations2 9 our latitudes x moves sl[ly we/w>d f ab\t ?ree 9 ! morn+ till two1 & returns to its =m] position 9 ! ev5+4 ,a ne$le susp5d$ s z only to be moveable 9 ! v]tical plane1 dips or become m & m incl9$ to ! horizon ! ne>] x is br\ght to ! magnetic pole4 ,capta9 ,lyon f\nd t ! dip 9 ! latitude & longitude m5tion$ 0 #hf #cb'4 ,:at prop]ties ! planets may h 9 ?is respect1 x is impossible to "k1 b x is probable t ! moon has become highly magnetic1 9 consequ5ce ( h] proximity to ! e>?1 & because h] greate/ diamet] always po9ts t[>ds x4 ,! passage ( comets has nev] s5sibly di/urb$ ! /ability ( ! sol> sy/em2 _! nucleus is r>e1 & _! transit s rapid1 t ! "t has n be5 long en\gh to admit ( a suffici5t accumulation ( impetus to produce a p]ceptible effect4 ,! comet ( #aggj pass$ )9 #hjjjj miles ( ! e>? )\t ev5 affect+ our tides1 & swept ?r\gh ! mid/ ( ,jupit]'s satellites )\t d]ang+ ! motions ( ^? little moons4 ,_h ! mass ( t comet be5 equal to ! mass ( ! e>?1 its di/urb+ action w\ld h %ort5$ ! ye> by ! n9? ( a day2 b1 z ,delambre's computations f ! ,gre5wi* obs]vations ( ! sun1 %[ t ! l5g? ( ! ye> has n be5 s5sibly affect$ by ! approa* ( ! comet4 ,la ,place prov$ t its mass c\ld n be s mu* z ! #ejjj? "p ( t ( ! e>?4 ,! pa?s ( comets h e possible incl9ation to ! plane ( ! ecliptic1 & unlike ! planets1 _! motion is frequ5tly retrograde4 ,comets are only visible :5 ne> _! p]ihelia4 ,!n _! velocity is su* t its squ>e is twice z great z t ( a body mov+ 9 a circle at ! same di/ance2 !y consequ5tly rema9 a v %ort "t )9 ! planet>y orbits2 & z all ! conic sections ( ! same focal di/ance s5sibly co9cide ?r\gh a small arc on ea* side ( ! extremity ( _! axis1 x is difficult to asc]ta9 9 :i* ( ^! curves ! comets move1 f obs]vations made1 z !y necess>ily mu/ be1 at _! p]ihelia3 b probably !y all move 9 extremely ecc5tric ellipses1 al?\gh1 9 mo/ cases1 ! p>abolic curve co9cides mo/ ne>ly ) _! obs]v$ motions4 ,ev5 if ! orbit be det]m9$ ) all ! accuracy t ! case admits (1 x may be difficult1 or ev5 impossible1 to recognise a comet on its return1 because its orbit w\ld be v mu* *ang$ if x pass$ ne> any ( ! l>ge planets ( ?is or ( any o!r sy/em1 9 consequ5ce ( _! di/urb+ en]gy1 :i* w\ld be v great on bodies ( s r>e a nature4 ,halley & ,clairaut pr$ict$ t1 9 consequ5ce ( ! attraction ( ,jupit] & ,saturn1 ! return ( ! comet ( #agei w\ld be ret>d$ #fah days1 :i* 0 v]ifi$ by ! ev5t z ne>ly z c\ld be expect$4 ,! nebul\s appe>ance ( comets is p]haps occasion$ by ! vap\rs :i* ! sol> heat raises at _! surfaces 9 _! passage at ! p]ihelia1 & :i* are aga9 cond5s$ z !y rec$e f ! sun4 ,! comet ( #afhj :5 9 its p]ihelion 0 only at ! di/ance ( "o-six? ( ! sun's diamet]1 or ab\t #adhjjj miles f its surface2 x consequ5tly w\ld be expos$ to a heat #bgejj times great] ?an t receiv$ by ! e>?4 ,z ! sun's heat is suppos$ to be 9 proportion to ! int5sity ( 8 height1 x is probable t a degree ( heat s v int5se w\ld be suffici5t to conv]t into vap\r e t]re/rial sub/ance ) :i* we are acqua9t$4 ,9 ^? positions ( comets :]e only half ( _! enlight5$ hemisph]e ought to be se51 !y exhibit no phases ev5 :5 view$ ) high magnify+ p[]s4 ,"s slight indications h[ev] 7 once obs]v$ by ,hevelius & ,la ,hire 9 #afhb2 & 9 #ahaa ,sir ,william ,h]s*el discov]$ a small lum9\s po9t1 :i* he conclud$ to be ! disc ( ! comet4 ,9 g5]al _! masses are s m9ute1 t !y h no s5sible diamet]s1 ! nucleus be+ pr9cipally =m$ ( d5s] /rata ( ! nebul\s matt]1 b s r>e t />s h be5 se5 ?r\gh !m4 ,! transit ( a comet ov] ! sun's disc w\ld af=d ! be/ in=mation on ?is po9t4 ,x 0 comput$ t su* an ev5t 0 to take place 9 ! ye> #afbg2 un=tunately ! sun 0 hid by cl\ds 9 ?is c\ntry1 b x 0 obs]v$ at ,vivi]s & at ,m>seilles at ! "t ! comet mu/ h be5 on x1 b no spot 0 se54 ,! tails are (t5 ( v great l5g?1 & are g5]ally situate 9 ! planes ( _! orbits2 !y foll[ !m 9 _! desc5t t[>ds ! sun1 b prec$e !m 9 _! return1 ) a small degree ( curvature2 b _! ext5t & =m mu/ v>y 9 appe>ance1 accord+ to ! position ( _! orbits ) reg>d to ! ecliptic4 ,! tail ( ! comet ( #afhj appe>$1 at ,p>is1 to ext5d ov] sixty-two degrees4 ,! matt] ( :i* ! tail is compos$ mu/ be extremely buoyant to prec$e a body mov+ ) su* velocity2 inde$ ! rapidity ( its asc5t _c be acc\nt$ =4 ,! nebul\s "p ( comets dim9i%es e "t !y return to _! p]ihelia2 aft] frequ5t returns !y ought to lose x altoge!r1 & pres5t ! appe>ance ( a fix$ nucleus2 ?is ought to happ5 soon] 9 comets ( %ort p]iods4 ,la ,place supposes t ! comet ( #afhb mu/ be approa*+ rapidly to t /ate4 ,%\ld ! sub/ances be altoge!r or ev5 to a great degree evaporat$1 ! comet wilt disappe> = ev]4 ,possibly comets may h vani%$ f our view soon] ?an !y o!rwise w\ld h done f ?is cause4 ,( ab\t six hundr$ comets t h be5 se5 at diff]5t times1 ?ree are n[ p]fectly asc]ta9$ to =m "p ( our sy/em2 t is to say1 !y return to ! sun at int]vals ( #gf1 #f #a_/c1 & #c #a_/d ye>s ne>ly4 ,a hundr$ & =ty comets h appe>$ )9 ! e>?'s orbit dur+ ! la/ c5tury t h n aga9 be5 se52 if a ?\s& ye>s be all[$ z ! av]age p]iod ( ea*1 x may be comput$ by ! !ory ( probabilities1 t ! :ole numb] t range )9 ! e>?'s orbit mu/ be #adjj2 b ,uranus be+ tw5ty times m di/ant1 !re may be no less ?an #aa1bjj1jjj comets t come )9 ! kn[n ext5t ( our sy/em4 ,9 su* a multitude ( w&]+ bodies x is j possible t "o ( !m may come 9 collision ) ! e>?2 b ev5 if x %\ld1 ! mis*ief w\ld be local1 & ! equilibrium soon re/or$4 ,x is h[ev] m probable t ! e>? w\ld only be deflect$ a little f its c\rse by ! ne> approa* ( ! comet1 )\t be+ t\*$4 ,great z ! numb] ( comets appe>s to be1 x is absolutely no?+ :5 comp>$ to ! numb] ( ! fix$ />s4 ,ab\t two ?\s& only are visible to ! nak$ eye1 b :5 we view ! heav5s ) a telescope1 _! numb] seems to be limit$ only by ! imp]fection ( ! in/rum5t4 ,9 "o qu>t] ( an h\r ,sir ,william ,h]s*el e/imat$ t #aafjjj />s pass$ ?r\gh ! field ( 8 telescope1 :i* subt5d$ an angle ( #ae'4 ,?is h[ev] 0 /at$ z a specim5 ( extraord9>y cr[d+2 b at an av]age ! :ole expanse ( ! heav5s mu/ exhibit ab\t a hundr$ millions ( fix$ />s t come )9 ! rea* ( telescopic vision4 ,_m ( ! />s h a v small progressive motion1 especially ,cassiopeia & #fa ,cygni1 bo? small />s2 &1 z ! sun is decid$ly a />1 x is an additional reason = suppos+ ! sol> sy/em to be 9 motion4 ,! di/ance ( ! fix$ />s is too great to admit ( _! exhibit+ a s5sible disc2 b 9 all probability !y are sph]ical1 & mu/ c]ta9ly be s1 if gravitation p]vades all space4 ,) a f9e telescope !y appe> l a po9t ( light2 _! tw9kl+ arises f sudd5 *anges 9 ! refractive p[] ( ! air1 :i* w\ld n be s5sible if !y _h discs l ! planets4 ,?us we c le>n no?+ ( ! relative di/ances ( ! />s f u & f "o ano!r1 by _! app>5t diamet]s2 b _! annual p>allax be+ ins5sible1 %[s t we mu/ be "o hundr$ millions ( millions ( miles f ! ne>e/2 _m ( !m h[ev] mu/ be va/ly m remote1 = ( two />s t appe> close toge!r1 "o may be f> beyond ! o!r 9 ! dep? ( space4 ,! light ( ,sirius1 accord+ to ! obs]vations ( ,mr4 ,h]s*el1 is #cbd times great] ?an t ( a /> ( ! six? magnitude2 if we suppose ! two to be really ( ! same size1 _! di/ances f u mu/ be 9 ! ratio ( #eg4c to #a1 because light dim9i%es z ! squ>e ( ! di/ance ( ! lum9\s body increases4 ,( ! absolute magnitude ( ! />s1 no?+ is kn[n1 only t _m ( !m mu/ be mu* l>g] ?an ! sun1 f ! quantity ( light emitt$ by !m4 ,dr4 ,wolla/on det]m9$ ! approximate ratio t ! light ( a wax c&le be>s to t ( ! sun1 moon1 & />s1 by comp>+ _! respective images reflect$ f small glass globes fill$1 ) m]cury1 :5ce a comp>ison 0 e/abli%$ betwe5 ! quantities ( light emitt$ by ! cele/ial bodies !mselves4 ,by ?is me?od he f\nd t ! light ( ! sun is ab\t tw5ty millions ( millions ( times great] ?an t ( ,sirius1 ! brighte/1 & suppos$ to be ! ne>e/ ( ! fix$ />s4 ,if ,sirius _h a p>allax ( half a second1 its di/ance f ! e>? w\ld be #ebedha times ! di/ance ( ! sun f ! e>?2 & !re=e ,sirius1 plac$ :]e ! sun is1 w\ld appe> to u to be #c4g times z l>ge z ! sun1 & w\ld give #ac4h times m light2 b _m ( ! fix$ />s mu/ be imm5sely great] ?an ,sirius4 ,sometimes />s h all at once appe>$1 %one ) a brilliant light1 & !n vani%$4 ,9 #aegb a /> 0 discov]$ 9 ,cassiopeia1 :i* rapidly increas$ 9 brightness till x ev5 surpass$ t ( ,jupit]2 x !n gradually dim9i%$ 9 spl5d\r1 & aft] exhibit+ all ! v>iety ( t9ts t indicates ! *anges ( combu/ion1 vani%$ sixte5 mon?s aft] its discov]y1 )\t alt]+ its position4 ,x is impossible to imag9e any ?+ m trem5d\s ?an a conflagration t c\ld be visible at su* a di/ance4 ,"s />s are p]iodic1 possibly f ! int]v5tion ( opaque bodies revolv+ ab\t !m1 or f ext5sive spots on _! surfaces4 ,_m ?\s&s ( />s t seem to be only brilliant po9ts1 :5 c>efully exam9$ are f\nd to be 9 reality sy/ems ( two or m suns revolv+ ab\t a common c5tre4 ,^! d\ble & multiple />s are extremely remote1 requir+ ! mo/ p[]ful telescopes to %[ !m sep>ately4 ,! fir/ catalogue ( d\ble />s 9 :i* _! places & relative positions are det]m9$1 0 accompli%$ by ! tal5ts & indu/ry ( ,sir ,william ,h]s*el1 to :om a/ronomy is indebt$ = s _m brilliant discov]ies1 & ) :om orig9at$ ! idea ( _! comb9ation 9 b9>y & multiple sy/ems1 an idea :i* 8 own obs]vations _h completely e/abli%$1 b :i* has s9ce receiv$ additional confirmation f ^? ( 8 son & ,sir ,james ,s\?1 ! =m] ( :om1 z well z ,pr(essor ,/ruve ( ,dorpat1 h add$ _m ?\s&s to _! numb]s4 ,! motions ( revolution r\nd a common c5tre ( _m h be5 cle>ly e/abli%$1 & _! p]iods det]m9$ ) consid]able accuracy4 ,"s h already s9ce _! fir/ discov]y accompli%$ ne>ly a :ole revolution1 & "o1 if ! late/ obs]vations c be dep5d$ on1 is actually consid]ably advanc$ 9 its second p]iod4 ,^! int]e/+ sy/ems ?us pres5t a species ( sid]eal *ronomet]1 by :i* ! *ronology ( ! heav5s w be m>k$ out to future ages by epo*s ( _! own1 liable to no fluctuations f planet>y di/urbances su* z obta9 9 our sy/em4 ,possibly among ! multitudes ( small />s1 :e!r d\ble or insulat$1 "s may be f\nd ne> en\gh to exhibit di/9ct p>allactic motions1 or p]haps some?+ approa*+ to planet>y motion1 :i* may prove t sol> attraction is n conf9$ to our sy/em1 or may lead to ! discov]y ( ! prop] motion ( ! sun4 ,! d\ble />s are ( v>i\s hues1 b mo/ frequ5tly exhibit ! contra/$ col\rs4 ,! l>ge /> is g5]ally yell[1 orange1 or r$2 & ! small /> blue1 purple1 or gre54 ,sometimes a :ite /> is comb9$ ) a blue or purple1 & m r>ely a r$ & :ite are unit$4 ,9 _m cases1 ^! appe>ances are due to ! influ5ces ( contra/ on our judgm5t ( col\rs4 ,= example1 9 obs]v+ a d\ble /> :]e ! l>ge "o is ( a full ruby r$1 or almo/ blood col\r1 & ! small "o a f9e gre51 ! latt] lo/ its col\r :5 ! =m] 0 hid by ! cross wires ( ! telescope4 ,b !re are a va/ numb] ( in/ances :]e ! col\rs are too /rongly m>k$ to be m]ely imag9>y4 ,mr4 ,h]s*el obs]ves 9 "o ( 8 pap]s 9 ! ,philosophical ,transactions1 z a v rem>kable fact1 t al?\gh r$ s+le />s are common en\gh1 no example ( an insulat$ blue1 gre51 or purple "o has z yet be5 produc$4 ,9 "s p>ts ( ! heav5s1 ! />s are s ne> toge!r z to =m clu/]s1 :i* to ! unassi/$ eye appe> l ?9 :ite cl\ds2 su* is ! milky way1 :i* has its brightness f ! diffus$ light ( myriads ( />s4 ,_m ( ^! cl\ds1 h[ev]1 are nev] resolv$ into sep>ate />s1 ev5 by ! highe/ magnify+ p[]s4 ,?is nebul\s matt] exi/s 9 va/ abundance 9 space4 ,no few] ?an #bejj nebul 7 obs]v$ by ,sir ,william ,h]s*el1 ^: places h be5 comput$ f 8 obs]vations1 r$uc$ to a common epo*1 & arrang$ into a catalogue 9 ord] ( "r asc5sion by 8 si/] ,miss ,c>ol9e ,h]s*el1 a lady s ju/ly celebrat$ = a/ronomical k & discov]y4 ,! nature & use ( ?is matt] scatt]$ ov] ! heav5s 9 su* a v>iety ( =ms is involv$ 9 ! greate/ obscurity4 ,t x is a self-lum9\s1 phosphoresc5t mat]ial sub/ance1 9 a highly dilat$ or gase\s /ate1 b gradually subsid+ by ! mutual gravitation ( its p>ticles into />s & sid]eal sy/ems1 is ! hypo!sis :i* seems to be mo/ g5]ally receiv$2 b ! only way t any real k on ?is my/]i\s subject c be obta9$1 is by ! det]m9ation ( ! =m1 place1 & pres5t /ate ( ea* individual nebula1 & a comp>ison ( ^! ) future obs]vations w %[ g5]ations to come ! *anges t may n[ be go+ on 9 ^! rudim5ts ( future sy/ems4 ,) ?is view1 ,mr4 ,h]s*el is n[ engag$ 9 ! difficult & labori\s inve/igation1 :i* is und]/ood to be ne>ly approa*+ its completion1 & ! results ( :i* we may !re=e hope ere long to see made public4 ,! mo/ conspicu\s ( ^! appe>ances are f\nd 9 ,orion1 & 9 ! girdle ( ,&rom$a4 ,x is probable t light mu/ be millions ( ye>s travell+ to ! e>? f "s ( ! nebul4 ,s num]\s are ! objects :i* meet our view 9 ! heav5s1 t we _c imag9e a "p ( space :]e "s light w\ld n /rike ! eye3 b z ! fix$ />s w\ld n be visible at su* di/ances1 if !y did n %9e by _! own light1 x is reasonable to inf] t !y are suns2 & if s1 !y are 9 all probability att5d$ by sy/ems ( opaque bodies1 revolv+ ab\t !m z ! planets d ab\t ours4 ,b al?\gh !re be no pro( t planets n se5 by u revolve ab\t ^! remote suns1 c]ta9 x is1 t !re are _m invisible bodies w&]+ 9 space1 :i*1 occasionally com+ )9 ! sph]e ( ! e>?'s attraction1 are ignit$ by ! velocity ) :i* !y pass ?r\gh ! atmosph]e1 & are precipitat$ ) great viol5ce on ! e>?4 ,! obliquity ( ! desc5t ( meteorites1 ! peculi> matt] ( :i* !y are compos$1 & ! explosion ) :i* _! fall is inv>iably accompani$1 %[ t !y are =eign to our planet4 ,lum9\s spots altoge!r indep5d5t ( ! phases h occasionally appe>$ on ! d>k "p ( ! moon1 :i* h be5 ascrib$ to ! light aris+ f ! eruption ( volcanoes2 :5ce x has be5 suppos$ t meteorites h be5 project$ f ! moon by ! impetus ( volcanic eruption2 x has ev5 be5 comput$1 t if a /one 7 project$ f ! moon 9 a v]tical l9e1 & ) an initial velocity ( #ajiib feet 9 a second1 :i* is m ?an f\r times ! velocity ( a ball :5 fir/ dis*>g$ f a cannon1 in/ead ( fall+ back to ! moon by ! attraction ( gravity1 x w\ld come )9 ! sph]e ( ! e>?'s attraction1 & revolve ab\t x l a satellite4 ,^! bodies1 impell$ ei!r by ! direction ( ! primitive impulse1 or by ! di/urb+ action ( ! sun1 might ultimately p5etrate ! e>?'s atmosph]e1 & arrive at its surface4 ,b f :atev] s\rce meteoric /ones may come1 x seems highly probable1 t !y h a common orig91 f ! uni=mity1 we may almo/ say id5tity1 ( _! *emical composition4 ,! kn[n quantity ( matt] be>s a v small proportion to ! imm5sity ( space4 ,l>ge z ! bodies are1 ! di/ances t sep>ate !m are immeasurably great]2 b z design is manife/ 9 e "p ( creation1 x is probable t if ! v>i\s sy/ems 9 ! univ]se _h be5 ne>] to "o ano!r1 _! mutual di/urbances w\ld h be5 inconsi/5t ) ! h>mony & /ability ( ! :ole4 ,x is cle> t space is n p]vad$ by atmosph]ic air1 s9ce its resi/ance w\ld long ere ?is h de/roy$ ! velocity ( ! planets2 nei!r c we affirm x to be void1 :5 x is trav]s$ 9 all directions by light1 heat1 gravitation1 & possibly by influ5ces ( :i* we c =m no idea2 b :e!r x be replete ) an e!real m$ium1 "t alone w %[4 ,?\gh totally ignorant ( ! laws :i* obta9 9 ! m di/ant regions ( creation1 we are assur$1 t "o alone regulates ! motions ( our own sy/em2 & z g5]al laws =m ! ultimate object ( philosophical rese>*1 we _c conclude ^! rem>ks )\t consid]+ ! nature ( t extraord9>y p[]1 ^: effects we h be5 endeav\r+ to trace ?r\gh "s ( _! mazes4 ,x 0 at "o "t imag9$1 t ! accel]ation 9 ! moon's mean motion 0 occasion$ by ! successive transmission ( ! gravitat+ =ce2 b x has be5 prov$1 t1 9 ord] to produce ?is effect1 its velocity mu/ be ab\t fifty millions ( times great] ?an t ( light1 :i* flies at ! rate ( #bjjjjj miles 9 a second2 its action ev5 at ! di/ance ( ! sun may !re=e be reg>d$ z in/antane\s2 yet s remote are ! ne>e/ ( ! fix$ />s1 t x may be d\bt$ :e!r ! sun has any s5sible influ5ce on !m4 ,! analytical expression = ! gravitat+ =ce is a /raight l9e2 ! curves 9 :i* ! cele/ial bodies move by ! =ce ( gravitation are only l9es ( ! second ord]2 ! attraction ( sph]oids accord+ to any o!r law w\ld be mu* m complicat$2 & z x is easy to prove t matt] might h be5 mov$ accord+ to an inf9ite v>iety ( laws1 x may be conclud$1 t gravitation mu/ h be5 select$ by ,div9e wisdom out ( an inf9ity ( o!r laws1 its be+ ! mo/ simple1 & t :i* gives ! greate/ /ability to ! cele/ial motions4 ,x is a s+ul> result ( ! simplicity ( ! laws ( nature1 :i* admit only ( ! obs]vation & comp>ison ( ratios1 t ! gravitation & !ory ( ! motions ( ! cele/ial bodies are indep5d5t ( _! absolute magnitudes & di/ances2 consequ5tly if all ! bodies 9 ! sol> sy/em1 _! mutual di/ances1 & _! velocities1 7 to dim9i% proportionally1 !y w\ld describe curves 9 all respect simil> to ^? 9 :i* !y n[ move2 & ! sy/em might be successively r$uc$ to ! smalle/ s5sible dim5sions1 & /ill exhibit ! same appe>ances4 ,exp]i5ce %[s t a v diff]5t law ( attraction prevails :5 ! p>ticles ( matt] are plac$ )9 inappreciable di/ances f ea* o!r1 z 9 *emical & capill>y attractions1 & ! attraction ( cohesion2 :e!r x be a modification ( gravity1 or t "s new & unkn[n p[] comes into action1 does n appe>2 b z a *ange 9 ! law ( ! =ce takes place at "o end ( ! scale1 x is possible t gravitation may n rema9 ! same at ! imm5se di/ance ( ! fix$ />s4 ,p]haps ! day may come :5 ev5 gravitation1 no long] reg>d$ z an ultimate pr9ciple1 may be resolv$ into a yet m g5]al cause1 embrac+ e law t regulates ! mat]ial _w4 ,! action ( ! gravitat+ =ce is n imp$$ by ! int]v5tion ev5 ( ! d5se/ sub/ances4 ,if ! attraction ( ! sun = ! c5tre ( ! e>?y & = ! hemisph]e diametrically opposite to him1 0 dim9i%$ by a difficulty 9 p5etrat+ ! int]pos$ matt]1 ! tides w\ld be m obvi\sly affect$4 ,its attraction is ! same also1 :atev] ! sub/ances ( ! cele/ial bodies may be1 = if ! action ( ! sun on ! e>? diff]$ by a million? "p f 8 action on ! moon1 ! diff]5ce w\ld occasion a v>iation 9 ! sun's p>allax am\nt+ to sev]al seconds1 :i* is prov$ to be impossible by ! agreem5t ( !ory ) obs]vation4 ,?us all matt] is p]vi\s to gravitation1 & is equally attract$ by x4 ,z f> z human k goes1 ! int5sity ( gravitation1 has nev] v>i$ )9 ! limits ( ! sol> sy/em2 nor does ev5 analogy lead u to expect t x %\ld2 on ! contr>y1 !re is e reason to be assur$1 t ! great laws ( ! univ]se are immutable l _! ,au?or4 ,n only ! sun & planets1 b ! m9ute/ p>ticles 9 all ! v>ieties ( _! attractions & repulsions1 nay ev5 ! impond]able matt] ( ! electric1 galvanic1 & magnetic fluids are ob$i5t to p]man5t laws1 ?\gh we may n be able 9 e case to resolve _! ph5om5a into g5]al pr9ciples4 ,nor c we suppose ! /ructure ( ! globe alone to be exempt f ! univ]sal fiat1 ?\gh ages may pass be=e ! *anges x has und]gone1 or t are n[ 9 progress1 c be ref]r$ to exi/+ causes ) ! same c]ta9ty ) :i* ! motions ( ! planets & all _! secul> v>iations are ref]able to ! law ( gravitation4 ,! traces ( extreme antiquity p]petually occurr+ to ! geologi/1 give t in=mation z to ! orig9 ( ?+s :i* we 9 va9 look = 9 ! o!r p>ts ( ! univ]se4 ,!y date ! beg9n+ ( "t2 s9ce !re is e reason to believe1 t ! =mation ( ! e>? 0 contemporane\s ) t ( ! re/ ( ! planets2 b !y %[ t creation is ! "w ( ,him ) :om 'a ?\s& ye>s are z "o day1 & "o day z a ?\s& ye>s4'