,transcrib]'s ,note3 ,! angle symbol has be5 replac$ ) angle4 ,greek lett]s h be5 replac$ ) _! translit]ations 9 brackets1 e4 g4 a = alpha4 ,! upside-d[n ,omega symbol has be5 replac$ ) mho4 ,,tw5tie? ,,c5tury ,,text-,,books ,,edit$ ,,by ,a4 ,f4 ,,night+ale1 ,,ph4,d41 ,,ll4,d4 ,,=m]ly ,,sup]9t5d5t ,,( ,,high ,,s*ools1 ,,*icago ,illu/ration3 ,a ,,total ,,sol> ,,eclipse4 ,aft] ,burckhalt]'s photographs ( ! eclipse ( ,may #bh1 #aijj4 ,,tw5tie? ,,c5tury ,,text-,,books ,a ,,text-,,book ,,( ,,a/ronomy ,,by ,,george ,c4 ,,com/ock ,,director ,,( ,,! ,,wa%burn ,,obs]vatory ,,& ,,pr(essor ,,( ,,a/ronomy ,,9 ,,! ,,univ]sity ,,( ,,wiscons9 ,illu/ration ,,new ,,york ,d4 ,,appleton ,,& ,,company #aijc ,,copyright1 #aija ,,by ,d4 ,,appleton ,,& ,,company ,,preface ,! pres5t "w is n a comp5dium ( a/ronomy or an outl9e c\rse ( popul> read+ 9 t sci5ce4 ,x has be5 prep>$ z a text-book1 & ! au?or has purposely omitt$ f x mu* matt] int]e/+ z well z important to a complete view ( ! sci5ce1 & has endeavor$ to conc5trate att5tion ^u ^? p>ts ( ! subject t possess special educational value4 ,f ?is po9t ( view matt] :i* p]mits ( exp]im5tal treatm5t ) simple app>atus is ( peculi> value & is giv5 a prom95ce 9 ! text beyond its j due 9 a well-balanc$ exposition ( ! elem5ts ( a/ronomy1 :ile topics1 su* z ! results ( spectrum analysis1 :i* dep5d ^u elaborate app>atus1 are 9 ! exp]im5tal "p ( ! "w accord$ mu* less space ?an _! intr9sic importance w\ld ju/ify4 ,tea*] & /ud5t are alike urg$ to magnify ! obs]vational side ( ! subject & to /rive to obta9 9 _! "w ! maximum degree ( precision ( :i* _! app>atus is capable4 ,! in/rum5ts requir$ are few & easily obta9$4 ,) exception ( a wat* & a protractor1 all ( ! app>atus ne$$ may be built by any "o ( fair me*anical tal5t :o w foll[ ! illu/rations & descriptions ( ! text4 ,9 ord] t prop] opportunity = obs]vations may be _h1 ! /udy %\ld be pursu$ dur+ ! mild] portion ( ! ye>1 betwe5 ,april & ,novemb] 9 nor!rn latitudes1 us+ cle> wea!r = a direct /udy ( ! sky & cl\dy days = book "w4 ,! illu/rations conta9$ 9 ! pres5t "w are wor?y ( z c>eful /udy z is ! text1 & _m ( !m are int5d$ z an aid to exp]im5tal "w & accurate measurem5t1 e4 g41 ! /> maps1 ! diagrams ( ! planet>y orbits1 pictures ( ! moon1 sun1 etc4 ,if ! s*ool possesses a projection lant]n1 a set ( a/ronomical slides to be us$ 9 connection ) x may be made ( great advantage1 if ! pictures are /udi$ z an auxili>y to ,nature4 ,m]e display & sc5ic effect are ( little value4 ,a brief bibliography ( popul> lit]ature ^u a/ronomy may be f\nd at ! end ( ?is book1 & x w be well if at lea/ a "p ( ^! works c be plac$ 9 ! s*ool libr>y & sy/ematically us$ = supplem5t>y read+4 ,an add$ int]e/ may be giv5 to ! /udy if "o or m ( ! popul> p]iodicals :i* deal ) a/ronomy are tak5 regul>ly by ! s*ool & kept )9 easy rea* ( ! /ud5ts4 ,f "t to "t ! tea*] may well assign topics treat$ 9 ^! p]iodicals to be read by individual /ud5ts & pres5t$ to ! class 9 ! =m ( an essay4 ,! au?or is "u obligations to _m ( 8 pr(essional fri5ds :o h contribut$ illu/rative matt] = 8 text1 & 8 ?anks are 9 an especial mann] due to ! editors ( ! ,a/rophysical ,j\rnal1 ,a/ronomy & ,a/rophysics1 & ,popul> ,a/ronomy = p]mission to reproduce "h plates :i* h appe>$ 9 ^? p]iodicals1 & to ,dr4 ,*>les ,boynton1 :o has k9dly read & criticis$ ! pro(s4 ,,george ,c4 ,,com/ock4 ,,univ]sity ,,( ,,wiscons91 ,febru>y1 #aija4 ,,cont5ts ,,*apt] ,,page ,i4--,,diff]5t ,,k9ds ,,( ,,measurem5t #a ,! measurem5t ( angles & "t4 ,,ii4--,,! ,,/>s ,,& ,,_! ,,diurnal ,,motion #aj ,f9d+ ! />s--,_! app>5t motion-- ,latitude--,direction ( ! m]idian--,sid]eal "t--,def9itions4 ,,iii4--,,fix$ ,,& ,,w&]+ ,,/>s #bi ,app>5t motion ( ! sun1 moon1 & planets--,orbits ( ! planets--,h[ to f9d ! planets4 ,,iv4--,,cele/ial ,,me*anics #df ,kepl]'s laws--,newton's laws ( motion--,! law ( gravitation--,orbital motion--,p]turbations-- ,masses ( ! planets--,discov]y ( ,neptune-- ,! tides4 ,v4--,,! ,,e>? ,,z ,a ,,planet #gj ,size--,mass--,precession--,! w>m+ ( ! e>?--,! atmosph]e--,twilight4 ,,vi4--,,! ,,measurem5t ,,( ,,"t #hf ,sol> & sid]eal "t--,longitude--,! cal5d>--,*ronology4 ,,vii4--,,eclipses #aja ,_! cause & nature--,eclipse limits--,eclipse maps--,recurr5ce & pr$iction ( eclipses4 ,,viii4--,,in/rum5ts ,,& ,,! ,,pr9ciples ,,involv$ ,,9 ,,_! ,,use #aba ,! clock--,radiant en]gy--,mirrors & l5ses-- ,! telescope--,cam]a--,spectroscope--,pr9ci ples ( spectrum analysis4 ,,ix4--,,! ,,moon #aej ,num]ical data--,phases--,motion--,librations--,lu n> topography--,physical condition4 ,x4--,,! ,,sun #agh ,num]ical data--,*emical nature--,temp]ature-- ,visible & invisible p>ts--,photosph]e--,spots-- ,facul--,*romosph]e--,prom95ces--,corona --,! sun-spot p]iod--,! sun's rotation--,me*anical !ory ( ! sun4 ,,xi4--,,! ,,planets #bab ,arrangem5t ( ! sol> sy/em--,bode's law-- ,physical condition ( ! planets--,jupit]-- ,saturn--,uranus & ,neptune--,v5us--,m]cury-- ,m>s--,! a/]oids4 ,,xii4--,,comets ,,& ,,meteors #bea ,motion1 size1 & mass ( comets--,meteors--,_! numb] & di/ribution--,meteor %[]s--,relation ( comets & meteors--,p]iodic comets--,comet families & gr\ps--,comet tails--,physical nature ( comets--,collisions4 ,,xiii4--,,! ,,fix$ ,,/>s #bia ,numb] ( ! />s--,brightness--,di/ance--,prop] motion--,motion 9 l9e ( sight--,d\ble />s-- ,v>iable />s--,new />s4 ,,xiv4--,,/>s ,,& ,,nebul #ccj ,/ell> colors & spectra--,classes ( />s-- ,clu/]s--,nebul--,_! spectra & physical condition--,! ,milky ,way--,con/ruction ( ! heav5s--,ext5t ( ! /ell> sy/em4 ,,xv4--,,gr[? ,,& ,,decay #ceh ,logical bases & limitations--,developm5t ( ! sun--,! nebul> hypo!sis--,tidal friction--,ro*e's limit--,developm5t ( ! moon--,developm5t ( />s & nebul--,! future4 ,,app5dix #chc ,,index #chg ,,li/ ,,( ,,li?ographic ,,plates ,,fac+ ,,page ,i4--,nor!rn ,con/ellations #abd ,,ii4--,equatorial ,con/ellations #aij ,,iii4--,map ( ,m>s #bdf ,,iv4--,! ,pleiades #cdd ,protractor ,9 pocket at back ( book ,,li/ ,,( ,,full-,,page ,,illu/rations ,,fac+ ,,page ,a ,total ,sol> ,eclipse ,frontispiece ,! ,h>v>d ,college ,obs]vatory1 ,cambridge1 ,mass4 #bd ,isaac ,newton #df ,galileo ,galilei #eb ,! ,lick ,obs]vatory1 ,m\nt ,hamilton1 ,cal4 #fj ,! ,y]kes ,obs]vatory1 ,williams ,bay1 ,wis4 #ajj ,! ,moon1 "o day aft] ,fir/ ,qu>t] #aej ,william ,h]s*el #bcd ,pi]re ,simon ,laplace #cfd ,,a/ronomy ,,*apt] ,i ,,diff]5t ,,k9ds ,,( ,,measurem5t #a4 ,,accurate ,,measurem5t4--,accurate measurem5t is ! f\ndation ( exact sci5ce1 & at ! v beg9n+ ( 8 /udy 9 a/ronomy ! /ud5t %\ld le>n some?+ ( ! a/ronom]'s k9d ( measurem5t4 ,he %\ld practice measur+ ! />s ) all possible c>e1 & %\ld seek to atta9 ! mo/ accurate results ( :i* 8 in/rum5ts & app>atus are capable4 ,! ord9>y affairs ( life furni% abundant illu/ration ( "s ( ^! measurem5ts1 su* z f9d+ ! l5g? ( a bo>d 9 in*es or ! weight ( a load ( coal 9 p\nds & measurem5ts ( bo? l5g? & weight are ( importance 9 a/ronomy1 b ( f> great] a/ronomical importance ?an ^! are ! measurem5t ( angles & ! measurem5t ( "t4 ,a kit*5 clock or a *eap wat* is usually ?\ght ( z a ma*9e to tell ! "t ( day1 b x may be us$ to "t a horse or a bicycl] ^u a race c\rse1 & !n x becomes an in/rum5t to measure ! am\nt ( "t requir$ = cov]+ ! l5g? ( ! c\rse4 ,a/ronom]s use a clock 9 bo? ( ^! ways--to tell ! "t at :i* some?+ happ5s or is done1 & to measure ! am\nt ( "t requir$ = some?+2 & 9 us+ a clock = ei!r purpose ! /ud5t %\ld le>n to take ! "t f x to ! ne>e/ second or bett]1 if x has a seconds h&1 or to a small fraction ( a m9ute1 by e/imat+ ! position ( ! m9ute h& betwe5 ! m9ute m>ks on ! dial4 ,e/imate ! fraction 9 t5?s ( a m9ute1 n 9 halves or qu>t]s4 ,,ex]cise #a4--;,if sev]al wat*es are available1 let "o p]son tap %>ply ^u a desk ) a p5cil & let ea* ( ! o!rs note ! "t by ! m9ute h& to ! ne>e/ t5? ( a m9ute & record ! obs]vations z foll[s3 #b;h4 #dd4em4 ,fir/ tap4 #b;h4 #df4dm4 #a4im4 #b;h4 #dd4im4 ,second tap4 #b;h4 #df4gm4 #a4hm4 #b;h4 #df4fm4 ,?ird tap4 #b;h4 #dh4fm4 #b4jm4 ,! lett]s h & m are us$ z abbreviations = h\r & m9ute4 ,! fir/ & second columns ( ! table are ! record made by "o /ud5t1 & second & ?ird ! record made by ano!r4 ,aft] all ! obs]vations h be5 made & record$ !y %\ld be br\ght toge!r & comp>$ by tak+ ! diff]5ces betwe5 ! times record$ = ea* tap1 z is %[n 9 ! la/ column4 ,?is diff]5ce %[s h[ mu* fa/] "o wat* is ?an ! o!r1 & ! agreem5t or disagreem5t ( ^! diff]5ces %[s ! degree ( accuracy ( ! obs]vations4 ,keep up ?is practice until t5?s ( a m9ute c be e/imat$ ) fair precision4 #b4 ,,angles ,,& ,,_! ,,use4--,an angle is ! am\nt ( op5+ or diff]5ce ( direction betwe5 two l9es t cross ea* o!r4 ,at twelve o'clock ! h\r & m9ute h& ( a wat* po9t 9 ! same direction & ! angle betwe5 !m is z]o4 ,at "o o'clock ! m9ute h& is aga9 at ,,xii1 b ! h\r h& has mov$ to ,i1 "o twelf? "p ( ! circumf]5ce ( ! dial1 & ! angle betwe5 ! h&s is "o twelf? ( a circumf]5ce4 ,x is cu/om>y to imag9e ! circumf]5ce ( a dial to be cut up into #cfj equal p>ts--i4 e41 ea* m9ute space ( an ord9>y dial to be subdivid$ into six equal p>ts1 ea* ( :i* is call$ a degree1 & ! measurem5t ( an angle consi/s 9 f9d+ h[ _m ( ^! degrees are includ$ 9 ! op5+ betwe5 its sides4 ,at "o o'clock ! angle betwe5 ! h&s ( a wat* is ?irty degrees1 :i* is usually writt5 #cj1 at ?ree o'clock x is #ij1 at six o'clock #ahj1 etc4 ,a wat* may be us$ to measure angles4 ,h[8 ,b a m conv5i5t in/rum5t is ! protractor1 :i* is %[n 9 ,fig4 #a1 appli$ to ! angle ,a ,b ,c & %[+ t ,a ,b ,c #he z ne>ly z ! protractor scale c be read4 ,! /ud5t %\ld h & use a protractor1 su* z is furni%$ ) ?is book1 = ! num]\s ex]cises :i* are to foll[4 ,illu/ration3 ,,fig4 #a4--;,a protractor4 ,,ex]cise #b4--;,draw neatly a triangle ) sides ab\t #ajj millimet]s long1 measure ea* ( its angles & take _! sum4 ,no matt] :at may be ! %ape ( ! triangle1 ?is sum %\ld be v ne>ly #ahj--;exactly #ahj if ! "w 7 p]fect--b p]fection c seldom be atta9$ & "o ( ! fir/ lessons to be le>n$ 9 any sci5ce :i* deals ) measurem5t is1 t h[ev] c>eful we may be 9 our "w "s m9ute error w cl+ to x & our results c be only approximately correct4 ,?is1 h[ev]1 %\ld n be tak5 z an excuse = c>eless "w1 b r z a /imulus to extra ef=t 9 ord] t ! unavoidable errors may be made z small z possible4 ,9 ! pres5t case ! measur$ angles may be improv$ a little by add+ 7algebraically7 to ea* ( !m "o ?ird ( ! am\nt by :i* _! sum falls %ort ( #ahj1 z 9 ! foll[+ example3 ,measur$ angles4 ,correction4 ,correct$ angles4 ,a #gc4d #j4a #gc4e ,b #di4c #j4a #di4d ,c #eg4j #j4a #eg4a ----- ----- ,sum #agi4g #ahj4j ,defect #j4c ,?is process is 9 v common use among a/ronom]s1 & is call$ adju/+ ! obs]vations4 ,illu/ration3 ,,fig4 #b4--,triangulation4 #c4 ,,triangles4--,! in/rum5ts us$ by a/ronom]s = ! measurem5t ( angles are usually provid$ ) a telescope1 :i* may be po9t$ at diff]5t objects1 & ) a scale1 l t ( ! protractor1 to measure ! angle ?r\gh :i* ! telescope is turn$ 9 pass+ f "o object to ano!r4 ,9 ?is way x is possible to measure ! angle betwe5 l9es drawn f ! in/rum5t to two di/ant objects1 su* z two *ur* /eeples or ! sun & moon1 & ?is is usually call$ ! angle betwe5 ! objects4 ,by measur+ angles 9 ?is way x is possible to det]m9e ! di/ance to an inaccessible po9t1 z %[n 9 ,fig4 #b4 ,a surveyor at ,a desires to "k ! di/ance to ,c1 on ! opposite side ( a riv] :i* he c n cross4 ,he measures ) a tape l9e along 8 own side ( ! /ream ! di/ance ,a ,b #ajj y>ds & !n1 ) a suitable in/rum5t1 measures ! angle at ,a betwe5 ! po9ts ,c & ,b1 & ! angle at ,b betwe5 ,c & ,a1 f9d+ ,b ,a ,c #gc4d1 ,a ,b ,c #di4c4 ,to det]m9e ! di/ance ,a ,c he draws ^u pap] a l9e #ajj millimet]s long1 & m>ks ! ends a & b2 ) a protractor he con/ructs at a ! angle b a c #gc4d1 & at b ! angle a b c #di4c1 & m>ks by c ! po9t :]e ! two l9es ?us drawn meet4 ,) ! millimet] scale he n[ measures ! di/ance a c #ij4b millimet]s1 :i* det]m9es ! di/ance ,a ,c across ! riv] to be #ij4b y>ds1 s9ce ! triangle on pap] has be5 made simil> to ! "o across ! riv]1 & millimet]s on ! "o correspond to y>ds on ! o!r4 ,:at is ! proposition ( geometry ^u :i* ?is dep5ds8 ,! measur$ di/ance ,a ,b 9 ! surveyor's problem is call$ a base l9e4 ,,ex]cise #c4--,) a foot rule & a protractor measure a base l9e & ! angles necess>y to det]m9e ! l5g? ( ! s*oolroom4 ,aft] ! l5g? has be5 ?us f\nd1 measure x directly ) ! foot rule & comp>e ! measur$ l5g? ) ! "o f\nd f ! angles4 ,if any "p ( ! "w has be5 c>elessly done1 ! /ud5t ne$ n expect ! results to agree4 ,illu/ration3 ,,fig4 #c4--;,f9d+ ! moon's di/ance f ! e>?4 ,9 ! same mann]1 by sight+ at ! moon f widely diff]5t p>ts ( ! e>?1 z 9 ,fig4 #c1 ! moon's di/ance f u is f\nd to be ab\t a qu>t] ( a million miles4 ,:at is ! base l9e 9 ?is case8 #d4 ,,! ,,horizon--,,altitudes4--,9 _! obs]vations a/ronom]s & sailors make mu* use ( ! plane ( ! horizon1 & practically any flat & level surface1 su* z t ( a smoo? pond1 may be reg>d$ z a "p ( ?is plane & us$ z su*4 ,a v common obs]vation relat+ to ! plane ( ! horizon is call$ tak+ ! sun's altitude1 & consi/s 9 measur+ ! angle betwe5 ! sun's rays & ! plane ( ! horizon ^u :i* !y fall4 ,?is angle betwe5 a l9e & a plane appe>s slightly diff]5t f ! angle betwe5 two l9es1 b is really ! same ?+1 s9ce x means ! angle betwe5 ! sun's rays & a l9e drawn 9 ! plane ( ! horizon t[>d ! po9t directly "u ! sun4 ,comp>e ?is ) ! def9ition giv5 9 ! geographies1 ,! latitude ( a po9t on ! e>?'s surface is its angul> di/ance nor? or s\? ( ! equator1 & note t ! latitude is ! angle betwe5 ! plane ( ! equator & a l9e drawn f ! e>?'s c5t] to ! giv5 po9t on its surface4 ,a conv5i5t me?od ( obta9+ a "p ( ! plane ( ! horizon = use 9 obs]vation is z foll[s3 ,place a slate or a pane ( glass ^u a table 9 ! sun%9e4 ,slightly moi/5 its :ole surface & !n p\r a little m wat] ^u x ne> ! c5t]4 ,if ! wat] runs t[>d "o side1 ?ru/ ! edge ( a ?9 wood5 w$ge "u ?is side & block x up until ! wat] %[s no t5d5cy to run "o way r ?an ano!r2 x is !n level & a "p ( ! plane ( ! horizon4 ,get sev]al w$ges ready be=e comm5c+ ! exp]im5t4 ,aft] !y h be5 prop]ly plac$1 drive a p9 or tack beh9d ea* "o s t x may n slip4 #e4 ,,tak+ ,,! ,,sun',s ,,altitude4 ,,ex]cise #d4--,prep>e a piece ( bo>d #bj c5timet]s1 or m1 squ>e1 plan$ smoo? on "o face & "o edge4 ,drive a p9 p]p5dicul>ly into ! face ( ! bo>d1 ne> ! middle ( ! plan$ edge4 ,set ! bo>d on edge on ! horizon plane & turn x edgewise t[>d ! sun s t a %ad[ ( ! p9 is ca/ on ! plane4 ,/ick ano!r p9 into ! bo>d1 ne> its upp] edge1 s t its %ad[ %all fall exactly ^u ! %ad[ ( ! fir/ p91 & ) a wat* or clock obs]ve ! "t at :i* ! two %ad[s co9cide4 ,)\t lift+ ! bo>d f ! plane1 turn x ar\nd s t ! opposite edge is direct$ t[>d ! sun & set a ?ird p9 j z ! second "o 0 plac$1 & aga9 take ! "t4 ,remove ! p9s & draw f9e p5cil l9es1 connect+ ! holes1 z %[n 9 ,fig4 #d1 & ) ! protractor measure ! angle ?us m>k$4 ,! /ud5t :o has /udi$ elem5t>y geometry %\ld be able to demon/rate t at ! mean ( ! two record$ times ! sun's altitude 0 equal to "o half ( ! angle measur$ 9 ! figure4 ,illu/ration3 ,,fig4 #d4--,tak+ ! sun's altitude4 ,:5 ! bo>d is turn$ edgewise t[>d ! sun s t its %ad[ is z ?9 z possible1 rule a p5cil l9e alongside x on ! horizon plane4 ,! angle :i* ?is l9e makes ) a l9e po9t+ due s\? is call$ ! sun's azimu?4 ,:5 ! sun is s\?1 its azimu? is z]o2 :5 we/1 x is #ij2 :5 ea/1 #bgj1 etc4 ,,ex]cise #e4--,let a numb] ( diff]5t /ud5ts take ! sun's altitude dur+ bo? ! morn+ & aft]noon session & note ! "t ( ea* obs]vation1 to ! ne>e/ m9ute4 ,v]ify ! sett+ ( ! plane ( ! horizon f "t to "t1 to make sure t no *ange has occurr$ 9 x4 #f4 ,,graphical ,,repres5tations4--,make a graph 7draw+7 ( all ! obs]vations1 simil> to ,fig4 #e1 & f9d by bisect+ a set ( *ords g to g1 e to e1 d to d1 drawn p>allel to ,b ,b1 ! "t at :i* ! sun's altitude 0 greate/4 ,9 ,fig4 #e we see f ! int]section ( ,m ,m ) ,b ,b t ?is "t 0 #aa;h4 #ejm4 ,! me?od ( graphs :i* is "h introduc$ is ( great importance 9 physical sci5ce1 & ! /ud5t %\ld c>efully obs]ve 9 ,fig4 #e t ! l9e ,b ,b is a scale ( times1 :i* may be made long or %ort1 provid$ only ! int]vals betwe5 consecutive h\rs #i to #aj1 #aj to #aa1 #aa to #ab1 etc41 are equal4 ,! di/ance ( ea* little circle f ,b ,b is tak5 proportional to ! sun's altitude1 & may be ^u any desir$ scale--e4 g41 a millimet] to a degree--provid$ ! same scale is us$ = all obs]vations4 ,ea* circle is plac$ accurately ov] t "p ( ! base l9e :i* corresponds to ! "t at :i* ! altitude 0 tak54 ,squ>e rul$ pap] is v conv5i5t1 al?\gh n necess>y1 = su* diagrams4 ,x is especially to be not$ t f ! few obs]vations :i* are repres5t$ 9 ! figure a smoo? curve has be5 drawn ?r\gh ! circles :i* repres5t ! sun's altitude1 & ?is curve %[s ! altitude ( ! sun at e mom5t betwe5 #i ,a4 ,m4 & #c ,p4 ,m4 ,9 ,fig4 #e ! sun's altitude at noon 0 #eg4 ,:at 0 x at half pa/ two8 ,illu/ration3 ,,fig4 #e4--;,a graph ( ! sun's altitude4 #g4 ,,diamet] ,,( ,a ,,di/ant ,,object4--,by sight+ ov] a protractor1 measure ! angle betwe5 imag9>y l9es drawn f x to ! opposite sides ( a w9d[4 ,c>ry ! protractor f>!r away f ! w9d[ & repeat ! exp]im5t1 to see h[ mu* ! angle *anges4 ,! angle ?us measur$ is call$ ! angle subt5d$ by ! w9d[ at ! place :]e ! measurem5t 0 made4 ,if ?is place 0 squ>ely 9 front ( ! w9d[ we may draw ^u pap] an angle equal to ! measur$ "o & lay (f f ! v]tex along its sides a di/ance proportional to ! di/ance ( ! w9d[--e4 g41 a millimet] = ea* c5timet] ( real di/ance4 ,if a cross l9e be n[ drawn connect+ ! po9ts ?us f\nd1 its l5g? w be proportional to ! wid? ( ! w9d[1 & ! wid? may be read (f to scale1 a c5timet] = e millimet] 9 ! l5g? ( ! cross l9e4 ,! a/ronom] :o measures ) an appropriate in/rum5t ! angle subt5d$ by ! moon may 9 an entirely simil> mann] f9d ! moon's diamet] & has1 9 fact1 f\nd x to be #b1afc miles4 ,c ! same me?od be us$ to f9d ! diamet] ( ! sun8 ,a planet8 ,! e>?8 ,,*apt] ,,ii ,,! ,,/>s ,,& ,,_! ,,diurnal ,,motion #h4 ,,! ,,/>s4--,f ! v beg9n+ ( 8 /udy 9 a/ronomy1 & z frequ5tly z possible1 ! /ud5t %\ld practice wat*+ ! />s by night1 to become acqua9t$ ) ! con/ellations & _! movem5ts4 ,z an introduction to ?is /udy he may face t[>d ! nor?1 & comp>e ! />s :i* he sees 9 t "p ( ! sky ) ! map ( ! nor!rn heav5s1 giv5 on ,plate ,i1 opposite page #abd4 ,turn ! map ar\nd1 upside d[n if necess>y1 until ! />s ^u x mat* ! bright] ones 9 ! sky4 ,note h[ ! />s are gr\p$ 9 su* conspicu\s con/ellations z ! ,big ,dipp] 7,ursa ,major71 ! ,little ,dipp] 7,ursa ,m9or71 & ,cassiopeia4 ,^! ?ree con/ellations %\ld be le>n$ s t !y c be recogniz$ at any "t4 ,! names ( ! />s4--,fac+ ! /> map is a key :i* conta9s ! names ( ! m important con/ellations & ! names ( ! bright] />s 9 _! con/ellations4 ,^! names are = ! mo/ "p a ,greek lett] prefix$ to ! g5itive case ( ! ,lat9 "n ( ! con/ellation4 7,see ! ,greek alphabet pr9t$ at ! end ( ! book47 #i4 ,,magnitudes ,,( ,,! ,,/>s4--,ne>ly n9ete5 c5turies ago ,/4 ,paul not$ t "o /> diff]e? f ano!r /> 9 glory1 & no m apt words c be f\nd to m>k ! diff]5ce ( brightness :i* ! />s pres5t4 ,ev5 prior to ,/4 ,paul's day ! anci5t ,greek a/ronom]s _h divid$ ! />s 9 respect ( brightness into six gr\ps1 :i* ! mod]n a/ronom]s /ill use1 call+ ea* gr\p a magnitude4 ,?us a few ( ! brighte/ />s are said to be ( ! fir/ magnitude1 ! great mass ( fa9t ones :i* are j visible to ! unaid$ eye are said to be ( ! six? magnitude1 & int]m$iate degrees ( brilliancy are repres5t$ by ! int]m$iate magnitudes1 second1 ?ird1 f\r?1 & fif?4 ,! /ud5t mu/ n be misl$ by ! ^w magnitude4 ,x has no ref]5ce to ! size ( ! />s1 b only to _! brightness1 & on ! /> maps ( ?is book ! l>g] & small] circles by :i* ! />s are repres5t$ indicate only ! brightness ( ! />s accord+ to ! sy/em ( magnitudes4 ,foll[+ ! indications ( ^! maps1 ! /ud5t %\ld1 9 le>n+ ! pr9cipal />s & con/ellations1 le>n also to recognize h[ bright is a /> ( ! second1 f\r?1 or o!r magnitude4 #aj4 ,,obs]v+ ,,! ,,/>s4--,f9d on ! map & 9 ! sky ! />s a ,urs ,m9oris1 a ,urs ,majoris1 b ,urs ,majoris4 ,:at geometrical figure w fit on to ^! />s8 ,9 addition to its regul> "n1 a ,urs ,m9oris is frequ5tly call$ by ! special "n ,pol>is1 or ! pole />4 ,:y are ! o!r two />s call$ ! ,po9t]s8 ,:at lett] ( ! alphabet d ! five bright />s 9 ,cassiopeia sugge/8 ,,ex]cise #f4--,/& 9 su* a position t ,pol>is is j hidd5 beh9d ! corn] ( a build+ or "s o!r v]tical l9e1 & m>k ^u ! key map z accurately z possible ! position ( ?is l9e ) respect to ! o!r />s1 %[+ :i* />s are to ! "r & :i* are to ! left ( x4 ,record ! "t 7date1 h\r1 & m9ute7 at :i* ?is obs]vation 0 made4 ,an h\r or two lat] repeat ! obs]vation at ! same place1 draw ! l9e & note ! "t1 & y w f9d t ! l9e la/ drawn ^u ! map does n agree ) ! fir/ "o4 ,! />s h *ang$ _! positions1 & ) respect to ! v]tical l9e ! ,po9t]s are n[ 9 a diff]5t direction f ,pol>is4 ,measure ) a protractor ! angle betwe5 ! two l9es drawn 9 ! map1 & use ?is angle & ! record$ times ( ! obs]vation to f9d h[ _m degrees p] h\r ?is direction is *ang+4 ,x %\ld be ab\t #ae p] h\r4 ,if ! obs]vation 7 repeat$ #ab h\rs aft] ! fir/ record$ "t1 :at w\ld be ! position ( ! v]tical l9e among ! />s8 ,:at w\ld x be #bd h\rs lat]8 ,a week lat]8 ,repeat ! obs]vation on ! next cle> night1 & all[+ = ! numb] ( :ole revolutions made by ! />s betwe5 ! two dates1 aga9 det]m9e f ! "t int]val a m accurate value ( ! rate at :i* ! />s move4 ,! motion ( ! />s :i* ! /ud5t has "h detect$ is call$ _! diurnal motion4 ,:at is ! significance ( ! ^w diurnal8 ,9 ! prec$+ p>agraph !re is introduc$ a me?od ( great importance 9 a/ronomical practice--i4 e41 det]m9+ some?+--9 ?is case ! rate p] h\r1 f obs]vations sep>at$ by a long int]val ( "t1 9 ord] to get a m accurate value ?an c\ld be f\nd f a %ort int]val4 ,:y is x m accurate8 ,to det]m9e ! rate at :i* ! planet ,m>s rotates ab\t its axis1 a/ronom]s use obs]vations sep>at$ by an int]val ( m ?an #bjj ye>s1 dur+ :i* ! planet made m ?an #ge1jjj revolutions ^u its axis4 ,if we 7 to write out 9 algebraic =m an equation = det]m9+ ! l5g? ( "o revolution ( ,m>s ab\t its axis1 ! l>ge numb]1 #ge1jjj1 w\ld appe> 9 ! equation z a divisor1 & 9 ! f9al result w\ld greatly r$uce :atev] errors exi/$ 9 ! obs]vations employ$4 ,repeat ,ex]cise #f night aft] night1 & note :e!r ! />s come back to ! same position at ! same h\r & m9ute e night4 ,illu/ration3 ,,fig4 #f4 ,! plumb-l9e app>atus4 ,illu/ration3 ,,fig4 #g4 ,! plumb-l9e app>atus4 #aa4 ,,! ,,plumb-,,l9e ,,app>atus4--,?is exp]im5t1 & _m o!rs1 may be conv5i5tly & accurately made ) no o!r app>atus ?an a plumb l9e1 & a device = sight+ pa/ x4 ,9 ,figs4 #f & #g !re is %[n a simple =m ( su* app>atus1 consi/+ ess5tially ( a bo>d :i* re/s 9 a horizontal position ^u ! po9ts ( ?ree screws t pass ?r\gh x4 ,?is bo>d c>ries a small box1 to "o side ( :i* is nail$ 9 v]tical position ano!r bo>d #e or #f feet long to c>ry ! plumb l9e4 ,?is consi/s ( a wire or fi% l9e ) any heavy weight--e4 g41 a brick or flatiron--ti$ to its l[] end & imm]s$ 9 a vessel ( wat] plac$ inside ! box1 s z to *eck any sw++ motion ( ! weight4 ,9 ! cov] ( ! box is a small hole ?r\gh :i* ! wire passes1 & by turn+ ! screws 9 ! basebo>d ! app>atus may be readily level$1 s t ! wire %all sw+ freely 9 ! c5t] ( ! hole )\t t\*+ ! cov] ( ! box4 ,guy wires1 %[n 9 ! figure1 are appli$ s z to /iff5 ! :ole app>atus4 ,a bo>d ) a screw eye at ea* end may be pivot$ to ! upright1 z 9 ,fig4 #f1 = measur+ altitudes2 or to ! box1 z 9 ,fig4 #g1 = obs]v+ ! "t at :i* a /> 9 its diurnal motion passes ?r\gh ! plane det]m9$ by ! plumb l9e & ! c5t] ( ! screw eye ?r\gh :i* ! obs]v] looks4 ,! :ole app>atus may be con/ruct$ by any p]son ( ord9>y me*anical skill at a v small co/1 & x or some?+ equival5t %\ld be provid$ = e class beg9n+ obs]vational a/ronomy4 ,to use ! app>atus = ! exp]im5t ( #aj1 x %\ld be level$1 & ! bo>d ) ! screw eyes1 atta*$ z 9 ,fig4 #g1 %\ld be turn$ until ! obs]v]1 look+ ?r\gh ! screw eye1 sees ,pol>is exactly beh9d ! wire4 ,use a bicycle lamp to illum9e ! wire by night4 ,! app>atus is n[ adju/$1 & ! obs]v] has only to wait = ! />s :i* he desires to obs]ve1 & to note by 8 wat* ! "t at :i* !y pass beh9d ! wire4 ,x w be se5 t ! wire takes ! place ( ! v]tical edge ( ! build+1 & t ! bo>d ) ! screw eyes is introduc$ solely to keep ! obs]v] 9 ! "r place relative to ! wire4 #ab4 ,a ,,sid]eal ,,clock4--,clocks are sometimes s made & regulat$ t !y %[ always ! same h\r & m9ute :5 ! />s come back to ! same place1 & su* a timepiece is call$ a sid]eal clock--i4 e41 a />-"t clock4 ,w\ld su* a clock ga9 or lose 9 comp>ison ) an ord9>y wat*8 ,c\ld an ord9>y wat* be turn$ into a sid]eal wat* by mov+ ! regulator8 ,illu/ration3 ,,fig4 #h4--,photograph+ ! circumpol> />s4--,,b>n>d4 #ac4 ,,photograph+ ,,! ,,/>s4--,,ex]cise #g4--;,= any /ud5t :o uses a cam]a4 ,^u "s cle> & moonless night po9t ! cam]a1 prop]ly focus$1 at ,pol>is1 & expose a plate = ?ree or f\r h\rs4 ,^u develop+ ! plate y %\ld f9d a s]ies ( circul> trails su* z are %[n 9 ,fig4 #h1 only long]4 ,ea* "o ( ^! is produc$ by a /> mov+ sl[ly ov] ! plate1 9 consequ5ce ( its *ang+ position 9 ! sky4 ,! c5t] indicat$ by ^! curv$ trails is call$ ! pole ( ! heav5s4 ,x is t "p ( ! sky t[>d :i* is po9t$ ! axis ab\t :i* ! e>? rotates1 & ! motion ( ! />s ar\nd ! c5t] is only an app>5t motion due to ! rotation ( ! e>? :i* daily c>ries ! obs]v] & 8 cam]a ar\nd ?is axis :ile ! />s /& /ill1 j z trees & f5ces & telegraph poles /& /ill1 al?\gh to ! pass5g] ^u a railway tra9 !y appe> to be 9 rapid motion4 ,s f> z simple obs]vations are conc]n$1 !re is no me?od by :i* ! pupil c tell = himself t ! motion ( ! />s is an app>5t r ?an a real "o1 &1 foll[+ ! cu/om ( a/ronom]s1 we %all habitually speak z if x 7 a real movem5t ( ! />s4 ,h[ long 0 ! plate expos$ 9 photograph+ ,fig4 #h8 #ad4 ,,f9d+ ,,! ,,/>s4--,on ,plate ,i1 opposite page #abd1 ! pole ( ! heav5s is at ! c5t] ( ! map1 ne> ,pol>is1 & ! heavy trail ne> ! c5t] ( ,fig4 #h is made by ,pol>is4 ,see if y c id5tify f ! map any ( ! />s ^: trails %[ 9 ! photograph4 ,! bright] ! /> ! bold] & heavi] its trail4 ,f9d f ! map & locate 9 ! sky ! two bright />s ,capella & ,vega1 :i* are on opposite sides ( ,pol>is & ne>ly equidi/ant f x4 ,d ^! />s %>e 9 ! motion ar\nd ! pole8 ,are !y visible on e cle> night1 & all night8 ,obs]ve o!r bright />s f>!r f ,pol>is ?an are ,vega & ,capella & note _! movem5t4 ,d !y move l ! sun & moon8 ,d !y rise & set8 ,9 :at "p ( ! sky d ! />s move mo/ rapidly1 ne> ! pole or f> f x8 ,h[ long does x take ! fa/e/ mov+ />s to make ! circuit ( ! sky & come back to ! same place8 ,h[ long does x take ! sl[ />s8 #ae4 ,,ris+ ,,& ,,sett+ ,,( ,,! ,,/>s4--,a /udy ( ! sky along ! l9es indicat$ 9 ^! que/ions w %[ t !re is a consid]able "p ( x surr\nd+ ! pole ^: />s are visible on e cle> night4 ,! same /> is sometimes high 9 ! sky1 sometimes l[1 sometimes to ! ea/ ( ! pole & at o!r times we/ ( x1 b is always above ! horizon4 ,su* />s are said to be circumpol>4 ,a little f>!r f ! pole ea* />1 :5 at ! l[e/ po9t ( its circul> pa?1 dips = a "t bel[ ! horizon & is lo/ to view1 & ! f>!r x is away f ! pole ! long] does x rema9 invisible1 until1 9 ! case ( />s #ij away f ! pole1 we f9d !m hidd5 bel[ ! horizon = twelve h\rs out ( e tw5ty-f\r 7see ,fig4 #i74 ,! sun is su* a />1 & 9 its ris+ & sett+ acts precisely z does e o!r /> at a simil> di/ance f ! pole--only1 z we %all f9d lat]1 ea* /> keeps always at 7ne>ly7 ! same di/ance f ! pole1 :ile ! sun 9 ! c\rse ( a ye> *anges its di/ance f ! pole v greatly1 & ?us *anges ! am\nt ( "t x sp5ds above & bel[ ! horizon1 produc+ 9 ?is way ! long days ( summ] & ! %ort ones ( w9t]4 ,illu/ration3 ,,fig4 #i4--;,diurnal motion ( ! nor!rn con/ellations4 ,h[ mu* "t d />s :i* are m ?an #ij f ! pole sp5d above ! horizon8 ,we say 9 common spee* t ! sun rises 9 ! ea/1 b ?is is /rictly true only at ! "t :5 x is #ij di/ant f ! pole--i4 e41 9 ,m>* & ,septemb]4 ,at o!r seasons x rises nor? or s\? ( ea/ accord+ z its di/ance f ! pole is less or great] ?an #ij1 & ! same is true = ! />s4 #af4 ,,! ,,geography ,,( ,,! ,,sky4--,f9d f a map ! latitude & longitude ( y\r s*oolh\se4 ,f9d on ! map ! place ^: latitude is #ci & longitude #gg we/ ( ! m]idian ( ,gre5wi*4 ,is !re any o!r place 9 ! _w :i* has ! same latitude & longitude z y\r s*oolh\se8 ,! places ( ! />s 9 ! sky are locat$ 9 exactly ! mann] :i* is illu/rat$ by ^! geographical que/ions1 only diff]5t names are us$4 ,in/ead ( latitude ! a/ronom] says decl9ation1 9 place ( longitude he says "r asc5sion1 9 place ( m]idian he says h\r circle1 b he means by ^! new names ! same ideas t ! geograph] expresses by ! old ones4 ,imag9e ! e>? swoll5 up until x fills ! :ole sky2 ! e>?'s equator w\ld meet ! sky along a l9e 7a great circle7 ev]y:]e #ij di/ant f ! pole1 & ?is l9e is call$ ! cele/ial equator4 ,trace its position along ! middle ( ! map opposite page #aij & notice ne> :at />s x runs4 ,e m]idian ( ! swoll5 e>? w\ld t\* ! sky along an h\r circle--i4 e41 a great circle pass+ ?r\gh ! pole & !re=e p]p5dicul> to ! equator4 ,note t 9 ! map "o ( ^! h\r circles is m>k$ #j4 ,x plays ! same "p 9 measur+ "r asc5sions z does ! m]idian ( ,gre5wi* 9 measur+ longitudes2 x is ! beg9n+1 f :i* !y are reckon$4 ,note also1 at ! extreme left end ( ! map1 ! f\r bright />s 9 ! =m ( a squ>e1 "o side ( :i* is p>allel & close to ! h\r circle1 :i* is m>k$ #j4 ,?is is famili>ly call$ ! ,great ,squ>e 9 ,pegasus1 & may be f\nd high up 9 ! s\!rn sky :5ev] ! ,big ,dipp] lies bel[ ! pole4 ,:y c x n be se5 :5 ,ursa ,major is above ! pole8 ,a/ronom]s use ! "r asc5sions ( ! />s n only to tell 9 :at "p ( ! sky ! /> is plac$1 b also 9 "t reckon+s1 to regulate _! sid]eal clocks1 & ) reg>d to ?is use !y f9d x conv5i5t to express "r asc5sion n 9 degrees b 9 h\rs1 #bd ( :i* fill up ! circuit ( ! sky & ea* ( :i* is equal to #ae ( arc1 #bd #ae #cfj4 ,! "r asc5sion ( ,capella is #e;h4 #im4 #gg4b1 b ! /ud5t %\ld accu/om himself to us+ x 9 h\rs & m9utes z giv5 & n to *ange x into degrees4 ,he %\ld also note t "s />s lie on ! side ( ! cele/ial equator t[>d ,pol>is1 & o!rs are on ! opposite side1 s t ! a/ronom] has to di/+ui% betwe5 nor? decl9ations & s\? decl9ations1 j z ! geograph] di/+ui%es betwe5 nor? latitudes & s\? latitudes4 ,?is is done by ! use ( ! & - signs1 a d5ot+ t ! /> lies nor? ( ! cele/ial equator1 i4 e41 t[>d ,pol>is4 ,illu/ration3 ,,fig4 #aj4--;,f a photograph ( ! ,pleiades4 ,f9d on ,plate ,,ii1 opposite page #aij1 ! ,pleiades 7,pleades71 ,r4 ,a4 #c;h4 #dbm41 ,dec4 #bc4h4 ,:y d !y n %[ on ,plate ,i1 opposite page #abd8 ,9 :at direction are !y f ,pol>is8 ,?is is "o ( ! f9e/ /> clu/]s 9 ! sky1 b x ne$s a telescope to br+ out its ri*ness4 ,see h[ _m />s y c c\nt 9 x ) ! nak$ eye1 & aft]w>d exam9e x ) an op]a glass4 ,comp>e :at y see ) ,fig4 #aj4 ,f9d ,ant>es1 ,r4 ,a4 #af;h4 #bcm4 ,dec4 -#bf4b4 ,h[ f> is x1 9 degrees1 f ! pole8 ,is x visible 9 y\r sky8 ,if s1 :at is its color8 ,f9d ! ,r4 ,a4 & ,dec4 ( a ,urs ,majoris2 ( b ,urs ,majoris2 ( ,pol>is4 ,f9d ! ,nor!rn ,cr[n1 ,corona ,borealis1 ,r4 ,a4 #ae;h4 #cjm41 ,dec4 #bg4j2 ! ,beehive1 ,prsepe1 ,r4 ,a4 #h;h4 #ccm41 ,dec4 #bj4d4 ,^! %\ld be look$ up1 n only on ! map1 b also 9 ! sky4 #ag4 ,,ref]5ce ,,l9es ,,& ,,circles4--,z ! />s move across ! sky 9 _! diurnal motion1 !y c>ry ! framework ( h\r circles & equator ) !m1 s t ! "r asc5sion & decl9ation ( ea* /> rema9 un*ang$ by ?is motion1 j z longitudes & latitudes rema9 un*ang$ by ! e>?'s rotation4 ,!y are ! same :5 a /> is ris+ & :5 x is sett+2 :5 x is above ! pole & :5 x is bel[ x4 ,dur+ ea* day ! h\r circle ( e /> 9 ! heav5s passes ov]head1 & at ! mom5t :5 any p>ticul> h\r circle is exactly ov]head all ! />s :i* lie ^u x are said to be on ! m]idian--i4 e41 at t p>ticul> mom5t !y /& directly ov] ! obs]v]'s geographical m]idian & ^u ! correspond+ cele/ial m]idian4 ,an eye plac$ at ! c5t] ( ! e>? & capable ( look+ ?r\gh its solid sub/ance w\ld see y\r geographical m]idian aga9/ ! backgr\nd ( ! sky exactly cov]+ y\r cele/ial m]idian & pass+ f "o pole ?r\gh y\r z5i? to ! o!r pole4 ,9 ,fig4 #aa ! inn] circle repres5ts ! t]re/rial m]idian ( a c]ta9 place1 ,o1 z se5 f ! c5t] ( ! e>?1 ,c1 & ! out] circle repres5ts ! cele/ial m]idian ( ,o z se5 f ,c1 only we mu/ imag9e1 :at c n be %[n on ! figure1 t ! out] circle is s l>ge t ! inn] "o %r9ks to a m]e po9t 9 comp>ison ) x4 ,if ,c ,p repres5ts ! direction 9 :i* ! e>?'s axis passes ?r\gh ! c5t]1 !n ,c ,e at "r angles to x mu/ be ! direction ( ! equator :i* we suppose to be turn$ edgewise t[>d u2 & if ,c ,o is ! direction ( "s p>ticul> po9t on ! e>?'s surface1 !n ,z directly ov]head is call$ ! z5i? ( t po9t1 ^u ! cele/ial sph]e4 ,! l9e ,c ,h repres5ts a direction p>allel to ! horizon plane at ,o1 & ,h ,c ,p is ! angle :i* ! axis ( ! e>? makes ) ?is horizon plane4 ,! arc ,o ,e measures ! latitude ( ,o1 & ! arc ,z ,e measures ! decl9ation ( ,z1 & s9ce by elem5t>y geometry ea* ( ^! arcs conta9s ! same numb] ( degrees z ! angle ,e ,c ,z1 we h ! ,!orem4--,! latitude ( any place is equal to ! decl9ation ( its z5i?4 ,coroll>y4--,any /> ^: decl9ation is equal to y\r latitude w once 9 ea* day pass ?r\gh y\r z5i?4 ,illu/ration3 ,,fig4 #aa4--,ref]5ce l9es & circles4 #ah4 ,,latitude4--,f ! con/ruction ( ! figure angle ,e ,c ,z angle ,z ,c ,p #ij angle ,h ,c ,p angle ,z ,c ,p #ij f :i* we f9d by subtraction & transposition angle ,e ,c ,z angle ,h ,c ,p & ?is gives ! fur!r ,!orem4--,! latitude ( any place is equal to ! elevation ( ! pole above its horizon plane4 ,an obs]v] :o travels nor? or s\? ov] ! e>? *anges 8 latitude1 & !re=e *anges ! angle betwe5 8 horizon plane & ! axis ( ! e>?4 ,:at effect w ?is h ^u ! position ( />s 9 8 sky8 ,if y 7 to g to ! e>?'s equator1 9 :at "p ( ! sky w\ld y look = ,pol>is8 ,c ,pol>is be se5 f ,au/ralia8 ,f ,s\? ,am]ica8 ,if y 7 to g f ,m9nesota to ,texas1 9 :at respect w\ld ! appe>ance ( />s 9 ! nor!rn sky be *ang$8 ,h[ w\ld ! appe>ance ( />s 9 ! s\!rn sky be *ang$8 ,illu/ration3 ,,fig4 #ab4--;,diurnal pa? ( ,pol>is4 ,,ex]cise #h4--;,det]m9e y\r latitude by tak+ ! altitude ( ,pol>is :5 x is at "s "o ( ! f\r po9ts ( its diurnal pa?1 %[n 9 ,fig4 #ab4 ,:5 x is at #a x is said to be at upp] culm9ation1 & ! /> z ,urs ,majoris 9 ! h&le ( ! ,big ,dipp] w be directly bel[ x4 ,:5 at #b x is at we/]n elongation1 & ! /> ,ca/or is ne> ! m]idian4 ,:5 x is at #c x is at l[] culm9ation1 & ! /> ,spica is on ! m]idian4 ,:5 x is at #d x is at ea/]n elongation1 & ,altair is ne> ! m]idian4 ,all ( ^! />s are conspicu\s ones1 :i* ! /ud5t %\ld f9d ^u ! map & le>n to recognize 9 ! sky4 ,! altitude obs]v$ at ei!r #b or #d may be consid]$ equal to ! latitude ( ! place1 b ! altitude obs]v$ :5 ,pol>is is at ! positions m>k$ #a & #c mu/ be correct$ = ! />'s di/ance f ! pole1 :i* may be assum$ equal to #a4c4 ,! plumb-l9e app>atus describ$ at page #ab is %[n 9 ,fig4 #f slightly modifi$1 s z to adapt x to measur+ ! altitudes ( />s4 ,note t ! bo>d ) ! screw eye at "o end has be5 transf]r$ f ! box to ! v]tical /&>d1 & has a screw eye at ea* end4 ,:5 ! app>atus has be5 prop]ly level$1 s t ! plumb l9e hangs at ! middle ( ! hole 9 ! box cov]1 ! bo>d is to be po9t$ at ! /> by sight+ ?r\gh ! c5t]s ( ! two screw eyes1 & a p5cil l9e is to be rul$ along its edge ^u ! face ( ! v]tical /&>d4 ,aft] ?is has be5 done turn ! app>atus halfway ar\nd s t :at 0 ! nor? side n[ po9ts s\?1 level x aga9 & revolve ! bo>d ab\t ! screw :i* holds x to ! v]tical /&>d1 until ! screw eyes aga9 po9t to ! />4 ,rule ano!r l9e along ! same edge ( ! bo>d z be=e & ) a protractor measure ! angle betwe5 ^! l9es4 ,use a bicycle lamp if y ne$ artificial light = y\r "w4 ,! /ud5t :o has /udi$ plane geometry %\ld be able to prove t "o half ( ! angle betwe5 ^! l9es is equal to ! altitude ( ! />4 ,aft] y h det]m9$ y\r latitude f ,pol>is1 comp>e ! result ) y\r position z %[n ^u ! be/ map available4 ,) a little practice & consid]able c>e ! latitude may be ?us det]m9$ )9 "o t5? ( a degree1 :i* is equival5t to ab\t #g miles4 ,if y g #aj miles nor? or s\? f y\r fir/ /ation y %\ld f9d ! pole high] up or l[] d[n 9 ! sky by an am\nt :i* c be measur$ ) y\r app>atus4 #ai4 ,,! ,,m]idian ,,l9e4--,to e/abli% a true nor? & s\? l9e ^u ! gr\nd1 use ! app>atus z describ$ at page #ac1 & :5 ,pol>is is at upp] or l[] culm9ation drive into ! gr\nd two /akes 9 l9e ) ! /> & ! plumb l9e4 ,su* a m]idian l9e is ( great conv5i5ce 9 obs]v+ ! />s & %\ld be laid out & p]man5tly m>k$ 9 "s conv5i5t op5 space f :i*1 if possible1 all p>ts ( ! sky are visible4 ,june & ,novemb] are conv5i5t mon?s = ?is ex]cise1 s9ce ,pol>is !n comes to culm9ation e>ly 9 ! ev5+4 #bj4 ,,"t4--,:at is ! "t at :i* s*ool beg9s 9 ! morn+8 ,:at d y mean by ! "t8 ,! sid]eal "t at any mom5t is ! "r asc5sion ( ! h\r circle :i* at t mom5t co9cides ) ! m]idian4 ,:5 ! h\r circle pass+ ?r\gh ,sirius co9cides ) ! m]idian1 ! sid]eal "t is #f;h4 #djm41 s9ce t is ! "r asc5sion ( ,sirius1 & 9 a/ronomical language ,sirius is on ! m]idian at #f;h4 #djm4 sid]eal "t4 ,z may be se5 f ! map1 ?is #f;h4 #djm4 is ! "r asc5sion ( ,sirius1 & if a clock be set to indicate #f;h4 #djm4 :5 ,sirius crosses ! m]idian1 x w %[ sid]eal "t4 ,if ! clock is prop]ly regulat$1 e o!r /> 9 ! heav5s w come to ! m]idian at ! mom5t :5 ! "t %[n by ! clock is equal to ! "r asc5sion ( ! />4 ,a clock prop]ly regulat$ = ?is purpose w ga9 ab\t f\r m9utes p] day 9 comp>ison ) ord9>y clocks1 & :5 s regulat$ x is call$ a sid]eal clock4 ,! /ud5t %\ld be provid$ ) su* a clock = 8 future "w1 b "o su* clock w s]ve = sev]al p]sons1 & a nutmeg clock or a wat* ( ! *eape/ k9d is q suffici5t4 ,illu/ration3 ,,! ,,h>v>d ,,college ,,obs]vatory1 ,,cambridge1 ,,mass4 ,,ex]cise #i4--,set su* a clock to sid]eal "t by means ( ! transit ( a /> ov] y\r m]idian4 ,= ?is exp]im5t x is presuppos$ t a m]idian l9e has be5 m>k$ out on ! gr\nd z 9 #ai1 & ! simple/ mode ( p]=m+ ! exp]im5t requir$ is = ! obs]v]1 hav+ *os5 a suitable /> 9 ! s\!rn "p ( ! sky1 to place 8 eye accurately ov] ! nor!rn end ( ! m]idian l9e & to e/imate z ne>ly z possible ! beg9n+ & end ( ! p]iod dur+ :i* ! /> appe>s to /& exactly above ! s\!rn end ( ! l9e4 ,! middle ( ?is p]iod may be tak5 z ! "t at :i* ! /> cross$ ! m]idian & at ?is mom5t ! sid]eal "t is equal to ! "r asc5sion ( ! />4 ,! diff]5ce betwe5 ?is "r asc5sion & ! obs]v$ middle in/ant is ! error ( ! clock or ! am\nt by :i* its h&s mu/ be set back or =w>d 9 ord] to indicate true sid]eal "t4 ,a m accurate mode ( p]=m+ ! exp]im5t consi/s 9 us+ ! plumb-l9e app>atus c>efully adju/$1 z 9 ,fig4 #g1 s t ! l9e jo9+ ! wire to ! c5t] ( ! screw eye %all be p>allel to ! m]idian l9e4 ,obs]ve ! "t by ! clock at :i* ! /> disappe>s beh9d ! wire z se5 ?r\gh ! c5t] ( ! screw eye4 ,if ! /> is too high up 9 ! sky = conv5i5t obs]vation1 place a mirror1 face up1 j nor? ( ! screw eye & obs]ve />1 wire & screw eye by reflection 9 x4 ,! num]ical "r asc5sion ( ! obs]v$ /> is ne$$ = ?is exp]im5t1 & x may be measur$ f ! /> map1 b x w usually be be/ to obs]ve "o ( ! />s ( ! table at ! end ( ! book1 & to obta9 its "r asc5sion z foll[s3 ,! table gives ! "r asc5sion & decl9ation ( ea* /> z !y 7 at ! beg9n+ ( ! ye> #aijj1 b on acc\nt ( ! precession 7see ,*apt] ,v71 ^! numb]s all *ange sl[ly ) ! lapse ( "t1 & on ! av]age ! "r asc5sion ( ea* /> ( ! table mu/ be increas$ by "o tw5tie? ( a m9ute = ea* ye> aft] #aijj--;i4 e41 9 #aiaj ! "r asc5sion ( ! fir/ /> ( ! table w be #j;h4 #ch4fm4 7#aj_/bj7m4 #j;h4 #ci4am4 ,! decl9ations also *ange slightly1 b z !y are only int5d$ to help 9 f9d+ ! /> on ! /> maps1 _! *ange may be ignor$4 ,hav+ set ! clock approximately to sid]eal "t1 obs]ve "o or two m />s 9 ! same way z above4 ,! diff]5ce betwe5 ! obs]v$ "t & ! "r asc5sion1 if any is f\nd1 is ! correction ( ! clock4 ,?is correction ought n to exce$ a m9ute if due c>e has be5 tak5 9 ! sev]al op]ations prescrib$4 ,! relation ( ! clock to ! "r asc5sion ( ! />s is express$ 9 ! foll[+ equation1 ) :i* ! /ud5t %\ld become ?or\ghly famili>3 ,a ,t ,u ,t /&s = ! "t by ! clock at :i* ! /> cross$ ! m]idian4 ,a is ! "r asc5sion ( ! />1 & ,u is ! correction ( ! clock4 ,use ! sign 9 ! equation :5ev] ! clock is too sl[1 & ! - sign :5 x is too fa/4 ,u may be f\nd f ?is equation :5 ,a & ,t are giv51 or ,a may be f\nd :5 ,t & ,u are giv54 ,x is 9 ?is way t a/ronom]s measure ! "r asc5sions ( ! />s & planets4 ,det]m9e ,u f ea* /> y h obs]v$1 & note h[ ! sev]al results agree "o ) ano!r4 #ba4 ,,def9itions4--,to def9e a ?+ or an idea is to give a description suffici5t to id5tify x & di/+ui% x f e o!r possible ?+ or idea4 ,if a def9ition does n come up to ?is /&>d x is insuffici5t4 ,any?+ beyond ?is requirem5t is c]ta9ly useless & probably mis*iev\s4 ,let ! /ud5t def9e ! foll[+ geographical t]ms1 & let him also criticise ! def9itions (f]$ by 8 fell[-/ud5ts3 ,equator1 poles1 m]idian1 latitude1 longitude1 nor?1 s\?1 ea/1 we/4 ,comp>e ! foll[+ a/ronomical def9itions ) y\r geographical def9itions1 & criticise !m 9 ! same way4 ,if y are n able to improve ^u !m1 commit !m to memory3 ,! ,poles ( ! heav5s are ^? po9ts 9 ! sky t[>d :i* ! e>?'s axis po9ts4 ,h[ _m are !re8 ,! "o ne> ,pol>is is call$ ! nor? pole4 ,! ,cele/ial ,equator is a great circle ( ! sky di/ant #ij f ! poles4 ,! ,z5i? is t po9t ( ! sky1 ov]head1 t[>d :i* a plumb l9e po9ts4 ,:y is ! ^w ov]head plac$ 9 ! def9ition8 ,is !re m ?an "o z5i?8 ,! ,horizon is a great circle ( ! sky #ij di/ant f ! z5i?4 ,an ,h\r ,circle is any great circle ( ! sky :i* passes ?r\gh ! poles4 ,e /> has its own h\r circle4 ,! ,m]idian is t h\r circle :i* passes ?r\gh ! z5i?4 ,a ,v]tical ,circle is any great circle t passes ?r\gh ! z5i?4 ,is ! m]idian a v]tical circle8 ,! ,decl9ation ( a /> is its angul> di/ance nor? or s\? ( ! cele/ial equator4 ,! ,"r ,asc5sion ( a /> is ! angle includ$ betwe5 its h\r circle & ! h\r circle ( a c]ta9 po9t on ! equator :i* is call$ ! ,v]nal ,equ9ox4 ,f sph]ical geometry we le>n t ?is angle is to be measur$ ei!r at ! pole :]e ! two h\r circles int]sect1 z is done 9 ! /> map opposite page #abd1 or along ! equator1 z is done 9 ! map opposite page #aij4 ,"r asc5sion is always measur$ f ! v]nal equ9ox 9 ! direction opposite to t 9 :i* ! />s appe> to travel 9 _! diurnal motion--i4 e41 f we/ t[>d ea/4 ,! ,altitude ( a /> is its angul> di/ance above ! horizon4 ,! ,azimu? ( a /> is ! angle betwe5 ! m]idian & ! v]tical circle pass+ ?r\gh ! />4 ,a /> due s\? has an azimu? ( #j4 ,due we/1 #ij4 ,due nor?1 #ahj4 ,due ea/1 #bgj4 ,:at is ! azimu? ( ,pol>is 9 degrees8 ,:at is ! azimu? ( ! sun at sunrise8 ,at sunset8 ,at noon8 ,are ^! azimu?s ! same on diff]5t days8 ,! ,h\r ,angle ( a /> is ! angle betwe5 its h\r circle & ! m]idian4 ,x is measur$ f ! m]idian 9 ! direction 9 :i* ! />s appe> to travel 9 _! diurnal motion--i4 e41 f ea/ t[>d we/4 ,:at is ! h\r angle ( ! sun at noon8 ,:at is ! h\r angle ( ,pol>is :5 x is at ! l[e/ po9t 9 its daily motion8 #bb4 ,,ex]cises4--,! /ud5t mu/ n be satisfi$ ) m]ely le>n+ ^! def9itions4 ,he mu/ le>n to see ^! po9ts & l9es 9 8 m9d z if !y 7 visibly pa9t$ ^u ! sky4 ,to ?is end x w help him to note t ! poles1 ! z5i?1 ! m]idian1 ! horizon1 & ! equator seem to /& /ill 9 ! sky1 always 9 ! same place ) respect to ! obs]v]1 :ile ! h\r circles & ! v]nal equ9ox move ) ! />s & keep ! same place among !m4 ,does ! app>5t motion ( a /> *ange its decl9ation or "r asc5sion8 ,:at is ! h\r angle ( ! sun :5 x has ! greate/ altitude8 ,w y\r answ] to ! prec$+ "q be true = a />8 ,:at is ! altitude ( ! sun aft] sunset8 ,9 :at direction is ! nor? pole f ! z5i?8 ,f ! v]nal equ9ox8 ,:]e are ! po9ts 9 :i* ! m]idian & equator respectively int]sect ! horizon8 ,,*apt] ,,iii ,,fix$ ,,& ,,w&]+ ,,/>s #bc4 ,,/> ,,maps4--,select f ! map "s conspicu\s con/ellation t w be conv5i5tly plac$ = obs]vation 9 ! ev5+1 & make on a l>ge scale a copy ( all ! />s ( ! con/ellation t are %[n ^u ! map4 ,at night comp>e ?is copy ) ! sky1 & m>k 9 ^u y\r pap] all ! />s ( ! con/ellation :i* are n already !re4 ,bo? ! orig9al draw+ & ! additions made to x by night %\ld be c>efully done1 & = ! latt] purpose :at is call$ ! me?od ( all9eations may be us$ ) advantage--i4 e41 ! new /> is 9 l9e ) two already on ! draw+ & is midway betwe5 !m1 or x makes an equilat]al triangle ) two o!rs1 or a squ>e ) ?ree o!rs1 etc4 ,a s]ies ( maps ( ! m prom95t con/ellations1 su* z ,ursa ,major1 ,cassiopea1 ,pegasus1 ,taurus1 ,orion1 ,gem9i1 ,canis ,major1 ,leo1 ,corvus1 ,bootes1 ,virgo1 ,h]cules1 ,lyra1 ,aquila1 ,scorpius1 %\ld be con/ruct$ 9 ?is mann] ^u a uni=m scale & pres]v$ z a "p ( ! /ud5t's "w4 ,let ! magnitude ( ! />s be repres5t$ on ! maps z accurately z may be1 & note ! peculi>ity ( color :i* "s />s pres5t4 ,= ! mo/ "p _! color is a v pale yell[1 b occasionally "o may be f\nd ( a decid$ly ruddy hue--e4 g41 ,aldeb>an or ,ant>es4 ,su* a /> map1 n q complete1 is %[n 9 ,fig4 #ac4 ,s1 too1 a %>p eye may detect t "s />s d n rema9 always ( ! same magnitude1 b *ange _! brightness f night to night1 & ?is n on acc\nt ( cl\d or mi/ 9 ! atmosph]e1 b f some?+ 9 ! /> itself4 ,algol is "o ( ! mo/ conspicu\s ( ^! v>iable />s1 z !y are call$4 ,illu/ration3 ,,fig4 #ac4--,/> map ( ! region ab\t ,orion4 #bd4 ,,! ,,moon',s ,,motion ,,among ,,! ,,/>s4--,:5ev] ! moon is visible note its position among ! />s by all9eations1 & plot x on ! key map opposite page #aij4 ,keep a record ( ! day & h\r correspond+ to ea* su* obs]vation4 ,y w f9d1 if ! "w is correctly done1 t ! positions ( ! moon all fall ne> ! curv$ l9e %[n on ! map4 ,?is l9e is call$ ! ecliptic4 ,aft] sev]al su* obs]vations h be5 made & plott$1 f9d by measurem5t f ! map h[ _m degrees p] day ! moon moves4 ,h[ long w\ld x require to make ! circuit ( ! heav5s & come back to ! />t+ po9t8 ,on ea* night :5 y obs]ve ! moon1 make on a sep>ate piece ( pap] a draw+ ( x ab\t #aj c5timet]s 9 diamet] & %[ 9 ! draw+ e feature ( ! moon's face :i* y c see--e4 g41 ! %ape ( ! illum9at$ surface 7phase72 ! direction among ! />s ( ! l9e jo9+ ! horns2 any spots :i* y c see ^u ! moon's face1 etc4 ,an op]a glass w prove ( great assi/ance 9 ?is "w4 ,use y\r draw+s & ! positions ( ! moon plott$ ^u ! map to answ] ! foll[+ que/ions3 ,does ! direction ( ! l9e jo9+ ! horns h any special relation to ! ecliptic8 ,does ! am\nt ( illum9at$ surface ( ! moon h any relation to ! moon's angul> di/ance f ! sun8 ,does x h any relation to ! "t at :i* ! moon sets8 ,d ! spots on ! moon :5 visible rema9 always 9 ! same place8 ,d !y come & g8 ,d !y *ange _! position ) relation to ea* o!r8 ,c y det]m9e f ^! spots t ! moon rotates ab\t an axis1 z ! e>? does8 ,9 :at direction does its axis po9t8 ,h[ long does x take to make "o revolution ab\t ! axis8 ,is !re any day & night ^u ! moon8 ,ea* ( ^! que/ions c be correctly answ]$ f ! /ud5t's own obs]vations )\t rec\rse to any book4 #be4 ,,! ,,sun ,,& ,,its ,,motion4--,exam9e ! face ( ! sun ?r\gh a smok$ glass to see if !re is any?+ !re t y c sket*4 ,by day z well z by night ! sky is /udd$ ) />s1 only !y c n be se5 by day on acc\nt ( ! ov]:elm+ gl>e ( sunlight1 b ! position ( ! sun among ! />s may be f\nd q z accurately z 0 t ( ! moon1 by obs]v+ f day to day its "r asc5sion & decl9ation1 & ?is %\ld be practic$ at noon on cle> days by diff]5t memb]s ( ! class4 ,,ex]cise #aj4--,! "r asc5sion ( ! sun may be f\nd by obs]v+ ) ! sid]eal clock ! "t ( its transit ov] ! m]idian4 ,use ! equation 9 #bj1 & sub/itute 9 place ( ,u ! value ( ! clock correction f\nd f obs]vations ( />s on a prec$+ or foll[+ night4 ,if ! clock ga9s or loses ) respect to sid]eal "t1 take ?is into acc\nt 9 ! value ( ,u4 ,,ex]cise #aa4--,to det]m9e ! sun's decl9ation1 measure its altitude at ! "t x crosses ! m]idian4 ,use ei!r ! me?od ( ,ex]cise #d1 or t us$ ) ,pol>is 9 ,ex]cise #h4 ,! /ud5t %\ld be able to %[ f ,fig4 #aa t ! decl9ation is equal to ! sum ( ! altitude & ! latitude ( ! place dim9i%$ by #ij1 or 9 an equation ,decl9ation ,altitude ,latitude - #ij4 ,if ! decl9ation z f\nd f ?is equation is a negative numb] x indicates t ! sun is on ! s\? side ( ! equator4 ,! "r asc5sion & decl9ation ( ! sun z obs]v$ on ea* day %\ld be plott$ on ! map & ! date1 writt5 opposite x4 ,if ! "w has be5 correctly done1 ! plott$ po9ts %\ld fall ^u ! curv$ l9e 7ecliptic7 :i* runs l5g?wise ( ! map4 ,?is l9e1 9 fact1 repres5ts ! sun's pa? among ! />s4 ,note t ! h\rs ( "r asc5sion increase f #j up to #bd1 :ile ! numb]s on ! clock dial g only f #j to #ab1 & !n repeat #j to #ab aga9 dur+ ! same day4 ,:5 ! sid]eal "t is #ac h\rs1 #ad h\rs1 etc41 ! clock w indicate #a h\r1 #b h\rs1 etc41 & #ab h\rs mu/ !n be add$ to ! "t %[n on ! dial4 ,if obs]vations ( ! sun's "r asc5sion & decl9ation are made 9 ! latt] "p ( ei!r ,m>* or ,septemb] ! /ud5t w f9d t ! sun crosses ! equator at ^! times1 & he %\ld det]m9e f 8 obs]vations1 z accurately z possible1 ! date & h\r ( ?is cross+ & ! po9t on ! equator at :i* ! sun crosses x4 ,^! po9ts are call$ ! equ9oxes1 ,v]nal ,equ9ox & ,autumnal ,equ9ox = ! spr+ & autumn cross+s respectively1 & ! /ud5t w recall t ! v]nal equ9ox is ! po9t f :i* "r asc5sions are measur$4 ,its position among ! />s is f\nd by a/ronom]s f obs]vations l ^? above describ$1 only made ) mu* m elaborate app>atus4 ,simil> obs]vations made 9 ,june & ,decemb] %[ t ! sun's midday altitude is ab\t #dg great] 9 summ] ?an 9 w9t]4 ,!y %[ also t ! sun is z f> nor? ( ! equator 9 ,june z he is s\? ( x 9 ,decemb]1 f :i* x is easily inf]r$ t 8 pa?1 ! ecliptic1 is incl9$ to ! equator at an angle ( #bc4e1 "o half ( #dg4 ,?is angle is call$ ! obliquity ( ! ecliptic4 ,! /ud5t may recall t 9 ! geographies ! torrid zone is said to ext5d #bc4e on ei!r side ( ! e>?'s equator4 ,is !re any connection betwe5 ^! limits & ! obliquity ( ! ecliptic8 ,w\ld x be correct to def9e ! torrid zone z t "p ( ! e>?'s surface )9 :i* ! sun may at "s season ( ! ye> pass ?r\gh ! z5i?8 ,,ex]cise #ab4--;,aft] a half doz5 obs]vations ( ! sun h be5 plott$ ^u ! map1 f9d by measurem5t ! rate1 9 degrees p] day1 at :i* ! sun moves along ! ecliptic4 ,h[ _m days w be requir$ = x to move completely ar\nd ! ecliptic f v]nal equ9ox back to v]nal equ9ox aga98 ,accurate obs]vations ) ! elaborate app>atus us$ by pr(essional a/ronom]s %[ t ?is p]iod1 :i* is call$ a tropical ye>1 is #cfe days #e h\rs #dh m9utes #df seconds4 ,is ?is ! same z ! ord9>y ye> ( our cal5d>s8 #bf4 ,,! ,,planets4--,any "o :o has wat*$ ! sky & :o has made ! draw+s prescrib$ 9 ?is *apt] c h>dly fail to h f\nd 9 ! c\rse ( 8 obs]vations "s bright />s n set d[n on ! pr9t$ /> maps1 & to h f\nd also t ^! />s d n rema9 fix$ 9 position among _! fell[s1 b w&] ab\t f "o con/ellation to ano!r4 ,obs]ve ! motion ( "o ( ^! planets f night to night & plot its positions on ! /> map1 precisely z 0 done = ! moon4 ,:at k9d ( pa? does x foll[8 ,bo? ! anci5t ,greeks & ! mod]n ,g]mans h call$ ^! bodies w&]+ />s1 & 9 ,engli% we "n !m planets1 :i* is simply ! ,greek ^w = w&]]1 b5t to our use4 ,besides ! sun & moon !re are 9 ! heav5s five planets easily visible to ! nak$ eye &1 z we %all see lat]1 a great numb] ( small] ones visible only 9 ! telescope4 ,m ?an #b1jjj ye>s ago a/ronom]s began obs]v+ ! motion ( sun1 moon1 & planets among ! />s1 & endeavor$ to acc\nt = ^! motions by ! !ory t ea* w&]+ /> mov$ 9 an orbit ab\t ! e>?4 ,classical & m$ival lit]ature are p]meat$ ) ?is idea1 :i* 0 displac$ only aft] a long /ruggle begun by ,cop]nicus 7#aedc ,a4 ,d471 :o taught t ! moon alone ( ^! bodies revolves ab\t ! e>?1 :ile ! e>? & ! o!r planets revolve ar\nd ! sun4 ,! ecliptic is ! int]section ( ! plane ( ! e>?'s orbit ) ! sky1 & ! sun appe>s to move along ! ecliptic because1 z ! e>? moves ar\nd its orbit1 ! sun is always se5 project$ aga9/ ! opposite side ( x4 ,! moon & planets all appe> to move ne> ! ecliptic because ! planes ( _! orbits ne>ly co9cide ) ! plane ( ! e>?'s orbit1 & a n>r[ /rip on ei!r side ( ! ecliptic1 foll[+ its c\rse completely ar\nd ! sky1 is call$ ! zodiac1 a ^w :i* may be reg>d$ z ! "n ( a n>r[ /reet 7#af wide7 )9 :i* all ! w&]+s ( ! visible planets are conf9$ & outside ( :i* !y nev] v5ture4 ,inde$1 ,m>s is ! only planet :i* ev] approa*es ! edge ( ! /reet1 ! o!rs travel+ ne> ! middle ( ! road4 ,illu/ration3 ,,fig4 #ad4--,! app>5t motion ( a planet4 #bg4 ,a ,,typical ,,case ,,( ,,planet>y ,,motion4--,! ,cop]nican !ory1 enorm\sly ext5d$ & develop$ ?r\gh ! ,newtonian law ( gravitation 7see ,*apt] ,,iv71 has completely supplant$ ! old] ,ptolemaic doctr9e1 & an illu/ration ( ! simple mann] 9 :i* x acc\nts = ! app>5tly complicat$ motions ( a planet among ! />s is f\nd 9 ,figs4 #ad & #ae1 ! fir/ ( :i* repres5ts ! app>5t motion ( ! planet ,m>s ?r\gh ! con/ellations ,aries & ,pisces dur+ ! latt] "p ( ! ye> #ahid1 :ile ! second %[s ! true motions ( ,m>s & ! e>? 9 _! orbits ab\t ! sun dur+ ! same p]iod4 ,! /raight l9e 9 ,fig4 #ad1 ) cross rul+ ^u x1 is a "p ( ! ecliptic1 & ! numb]s plac$ opposite x repres5t ! di/ance1 9 degrees1 f ! v]nal equ9ox4 ,9 ,fig4 #ae ! /raight l9e repres5ts ! direction f ! sun t[>d ! v]nal equ9ox1 & ! angle :i* ?is l9e makes ) ! l9e jo9+ e>? & sun is call$ ! e>?'s longitude4 ,! imag9>y l9e jo9+ ! e>? & sun is call$ ! e>?'s radius vector1 & ! pupil %\ld note t ! longitude & l5g? ( ! radius vector tak5 toge!r %[ ! direction & di/ance ( ! e>? f ! sun--i4 e41 !y fix ! relative positions ( ! two bodies4 ,! same is ne>ly true = ,m>s & w\ld be :olly true if ! orbit ( ,m>s lay 9 ! same plane ) t ( ! e>?4 ,h[ does ,fig4 #ad %[ t ! orbit ( ,m>s does n lie exactly 9 ! same plane ) ! orbit ( ! e>?8 ,,ex]cise #ac4--;,f9d f ,fig4 #ae :at ought to h be5 ! app>5t c\rse ( ,m>s among ! />s dur+ ! p]iod %[n 9 ! two figures1 & comp>e :at y f9d ) ,fig4 #ad4 ,! app>5t position ( ,m>s among ! />s is m]ely its direction f ! e>?1 & ?is direction is repres5t$ 9 ,fig4 #ad by ! di/ance ( ! planet f ! ecliptic & by its longitude4 ,illu/ration3 ,,fig4 #ae4--,! real motion ( a planet4 ,! longitude ( ,m>s = ea* date c be f\nd f ,fig4 #ae by measur+ ! angle betwe5 ! /raight l9e ,s ,v & ! l9e drawn f ! e>? to ,m>s4 ,?us = ,octob] #ab? we may f9d ) ! protractor t ! angle betwe5 ! l9e ,s ,v & ! l9e jo9+ ! e>? to ,m>s is a little m ?an #cj1 & 9 ,fig4 #ad ! position ( ,m>s = ?is date is %[n ne>ly opposite ! cross l9e correspond+ to #cj on ! ecliptic4 ,j h[ f> bel[ ! ecliptic ?is position ( ,m>s %\ld fall c n be told f ,fig4 #ae1 :i* f necessity is con/ruct$ z if ! orbits ( ,m>s & ! e>? lay 9 ! same plane1 & ,m>s 9 ?is case w\ld always appe> to /& exactly on ! ecliptic & to oscillate back & =? z %[n 9 ,fig4 #ad1 b )\t ! up-&-d[n motion !re %[n4 ,9 ?is way plot 9 ,fig4 #ad ! longitudes ( ,m>s z se5 f ! e>? = o!r dates & obs]ve h[ ! =w>d motion ( ! two planets 9 _! orbits acc\nts = ! app>5tly caprici\s motion ( ,m>s to & fro among ! />s4 ,illu/ration3 ,,fig4 #af4--,! orbits ( ,jupit] & ,saturn4 #bh4 ,,! ,,orbits ,,( ,,! ,,planets4--,ea* planet1 great or small1 moves 9 its own appropriate orbit ab\t ! sun1 & ! exact det]m9ation ( ^! orbits1 _! sizes1 %apes1 positions1 etc41 has be5 "o ( ! great problems ( a/ronomy = m ?an #b1jjj ye>s1 9 :i* successive g5]ations ( a/ronom]s h /riv5 to pu% to a /ill high] degree ( accuracy ! k atta9$ by _! pr$ecessors4 ,)\t attempt+ to ent] into ! details ( ?is problem we may say1 g5]ally1 t e planet moves 9 a plane pass+ ?r\gh ! sun1 & = ! six planets visible to ! nak$ eye ^! planes ne>ly co9cide1 s t ! six orbits may all be %[n )\t mu* error z ly+ 9 ! flat surface ( "o map4 ,x is1 h[ev]1 m conv5i5t to use two maps1 su* z ,figs4 #af & #ag1 "o ( :i* %[s ! gr\p ( planets1 ,m]cury1 ,v5us1 ! e>?1 & ,m>s1 :i* are ne> ! sun1 & on ?is acc\nt are sometimes call$ ! inn] planets1 :ile ! o!r %[s ! m di/ant planets1 ,jupit] & ,saturn1 toge!r ) ! e>?1 ^: orbit is ?us made to s]ve z a connect+ l9k betwe5 ! two diagrams4 ,^! diagrams are accurately drawn to scale1 & are int5d$ to be us$ by ! /ud5t = accurate measurem5t 9 connection ) ! ex]cises & problems :i* foll[4 ,9 addition to ! six planets %[n 9 ! figures ! sol> sy/em conta9s two l>ge planets & sev]al hundr$ small ones1 = ! mo/ "p invisible to ! nak$ eye1 :i* are omitt$ 9 ord] to avoid confus+ ! diagrams4 #bi4 ,,jupit] ,,& ,,saturn4--,9 ,fig4 #af ! sun at ! c5t] is encircl$ by ! orbits ( ! ?ree planets1 & inclos+ all ( ^! is a circul> bord] %[+ ! directions f ! sun ( ! con/ellations :i* lie along ! zodiac4 ,! /ud5t mu/ note c>efully t x is only ! directions ( ^! con/ellations t are correctly %[n1 & t 9 ord] to %[ !m at all !y h be5 plac$ v mu* too close to ! sun4 ,! cross l9es ext5d+ f ! orbit ( ! e>? t[>d ! sun ) ,roman num]als opposite !m %[ ! positions ( ! e>? 9 its orbit on ! fir/ day ( ,janu>y 7,i71 fir/ day ( ,febru>y 7,,ii71 etc41 & ! simil> l9es atta*$ to ! orbits ( ,jupit] & ,saturn ) ,arabic num]als %[ ! positions ( ^? planets on ! fir/ day ( ,janu>y ( ea* ye> indicat$1 s t ! figure s]ves to %[ n only ! orbits ( ! planets1 b _! actual positions 9 _! orbits = some?+ m ?an ! fir/ decade ( ! tw5tie? c5tury4 ,! l9e drawn f ! sun t[>d ! "r ( ! figure %[s ! direction to ! v]nal equ9ox4 ,x =ms "o side ( ! angle :i* measures a planet's longitude4 ,illu/ration3 ,,fig4 #ag4--,! orbits ( ! inn] planets4 ,,ex]cise #ad4--,measure ) y\r protractor ! longitude ( ! e>? on ,janu>y #a/4 ,is ?is longitude ! same 9 all ye>s8 ,measure ! longitude ( ,jupit] on ,janu>y #a1 #aijj2 on ,july #a1 #aijj2 on ,septemb] #be1 #aijf4 ,draw neatly on ! map a p5cil l9e connect+ ! position ( ! e>? = ,janu>y #a1 #aijj1 ) ! position ( ,jupit] = ! same date1 & produce ! l9e beyond ,jupit] until x meets ! circle ( ! con/ellations4 ,?is l9e repres5ts ! direction ( ,jupit] f ! e>?1 & po9ts t[>d ! con/ellation 9 :i* ! planet appe>s at t date4 ,b ?is repres5tation ( ! place ( ,jupit] 9 ! sky is n a v accurate "o1 s9ce on ! scale ( ! diagram ! />s are 9 fact m ?an #ajj1jjj times z f> (f z !y are %[n 9 ! figure1 & ! p5cil m>k does n meet ! l9e ( con/ellations at ! same int]section x w\ld h if ?is l9e 7 pu%$ back to its true position4 ,to rem$y ?is defect we mu/ draw ano!r l9e f ! sun p>allel to ! "o fir/ drawn1 & its int]section ) ! con/ellations w give v approximately ! true position ( ,jupit] 9 ! sky4 ,,ex]cise #ae4--;,f9d ! pres5t positions ( ,jupit] & ,saturn1 & look !m up 9 ! sky by means ( y\r /> maps4 ,! planets w appe> 9 ! indicat$ con/ellations z v bright />s n %[n on ! map4 ,:i* ( ! planets1 ,jupit] & ,saturn1 *anges its direction f ! sun m rapidly8 ,:i* travels ! great] numb] ( miles p] day8 ,:5 w ,jupit] & ,saturn be 9 ! same con/ellation8 ,does ! e>? move fa/] or sl[] ?an ,jupit]8 ,! di/ance ( ,jupit] or ,saturn f ! e>? at any "t may be readily obta9$ f ! figure4 ,?us1 by direct measurem5t ) ! millimet] scale we f9d = ,janu>y #a1 #aijj1 ! di/ance ( ,jupit] f ! e>? is #f4a times ! di/ance ( ! sun f ! e>?1 & ?is may be turn$ into miles by multiply+ x by #ic1jjj1jjj1 :i* is approximately ! di/ance ( ! sun f ! e>?4 ,= mo/ purposes x is q z well to disp5se ) ?is multiplication & call ! di/ance #f4a a/ronomical units1 rememb]+ t ! a/ronomical unit is ! di/ance ( ! sun f ! e>?4 ,,ex]cise #af4--,:at is ,jupit]'s di/ance f ! e>? at its ne>e/ approa*8 ,:at is ! greate/ di/ance x ev] atta9s8 ,is ,jupit]'s lea/ di/ance f ! e>? great] or less ?an its lea/ di/ance f ,saturn8 ,on :at day 9 ! ye> #aijf w ! e>? be on l9e betwe5 ,jupit] & ! sun8 ,on ?is day ,jupit] is said to be 9 opposition--i4 e41 ! planet & ! sun are on opposite sides ( ! e>?1 & ,jupit] !n comes to ! m]idian ( any & e place at midnight4 ,:5 ! sun is betwe5 ! e>? & ,jupit] 7at :at date 9 #aijf87 ! planet is said to be 9 conjunction ) ! sun1 & ( c\rse passes ! m]idian ) ! sun at noon4 ,c y det]m9e f ! figure ! "t at :i* ,jupit] comes to ! m]idian at o!r dates ?an opposition & conjunction8 ,c y det]m9e :5 x is visible 9 ! ev5+ h\rs8 ,tell f ! figure :at con/ellation is on ! m]idian at midnight on ,janu>y #a/4 ,w x be ! same con/ellation 9 e ye>8 #cj4 ,,m]cury1 ,,v5us1 ,,& ,,m>s4--,fig4 #ag1 :i* repres5ts ! orbits ( ! inn] planets1 diff]s f ,fig4 #af only 9 ! me?od ( fix+ ! positions ( ! planets 9 _! orbits at any giv5 date4 ,! motion ( ^! planets is s rapid1 on acc\nt ( _! proximity to ! sun1 t x w\ld n d to m>k _! positions z 0 done = ,jupit] & ,saturn1 & ) ! exception ( ! e>? !y d n always return to ! same place on ! same day 9 ea* ye>4 ,x is !re=e necess>y to adopt a slightly diff]5t me?od1 z foll[s3 ,! /raight l9e ext5d+ f ! sun t[>d ! v]nal equ9ox1 ,v1 is call$ ! prime radius1 & we "k f pa/ obs]vations t ! e>? 9 its motion ar\nd ! sun crosses ?is l9e on ,septemb] #bc;d 9 ea* ye>1 & to fix ! e>?'s position = ,septemb] #bc;d 9 ! diagram we h only to take ! po9t at :i* ! prime radius int]sects ! e>?'s orbit4 ,a mon? lat]1 on ,octob] #bc;d1 ! e>? w no long] be at ?is po9t1 b w h mov$ on along its orbit to ! po9t m>k$ #cj 7?irty days aft] ,septemb] #bc;d74 ,sixty days aft] ,septemb] #bc;d x w be at ! po9t m>k$ #fj1 etc41 & = any date we h only to f9d ! numb] ( days int]v5+ betwe5 x & ! prec$+ ,septemb] #bc;d1 & ?is numb] w %[ at once ! position ( ! e>? 9 its orbit4 ,?us = ! date ,july #d1 #aijj1 we f9d #aijj1 ,july #d - #ahii1 ,septemb] #bc #bhd days1 & ! little circle m>k$ ^u ! e>?'s orbit betwe5 ! numb]s #bgj & #cjj %[s ! position ( ! e>? on t date4 ,9 :at con/ellation 0 ! sun on ,july #d1 #aijj8 ,:at zodiacal con/ellation came to ! m]idian at midnight on t date8 ,:at o!r con/ellations came to ! m]idian at ! same "t8 ,! positions ( ! o!r planets 9 _! orbits are f\nd 9 ! same mann]1 save t !y d n cross ! prime radius on ! same date 9 ea* ye>1 & ! times at :i* !y d cross x mu/ be tak5 f ! foll[+ table3 ,,table ,,( ,,epo*s ---------------------------------------- ------------------- ,a4 ,d4 ,m]cury4 ,v5us4 ,e>?4 ,m>s4 ---------------------------------------- --------------- ,p]iod #hh4j days4 #bbd4g days4#cfe4be days4 #fhg4a days4 #aijj ,feb4 #ah?4 ,jan4 #aa?4 ,sept4 #bc;d4 ,april #bh?4 #aija ,feb4 #e?4 ,april #e?4 ,sept4 #bc;d4 444 #aijb ,jan4 #bc;d4 ,june #bi?4 ,sept4 #bc;d4 ,m>* #af?4 #aijc ,april #h?4 ,feb4 #h?4 ,sept4 #bc;d4 444 #aijd ,m>* #be?4 ,may #c;d4 ,sept4 #bc;d4 ,feb4 #a/4 #aije ,m>* #ab?4 ,july #bf?4 ,sept4 #bc;d4 ,dec4 #ai?4 #aijf ,feb4 #bg?4 ,m>* #h?4 ,sept4 #bc;d4 444 #aijg ,feb4 #ad?4 ,may #ca/4 ,sept4 #bc;d4 ,nov4 #f?4 #aijh ,feb4 #a/4 ,jan4 #aa?4 ,sept4 #bc;d4 444 #aiji ,jan4 #ah?4 ,april #d?4 ,sept4 #bc;d4 ,sept4 #bc;d4 #aiaj ,jan4 #e?4 ,june #bh?4 ,sept4 #bc;d4 444 ---------------------------------------- ------------------- ,! fir/ l9e ( figures 9 ?is table %[s ! numb] ( days t ea* ( ^! planets requires to make a complete revolution ab\t ! sun1 & x appe>s f ^! numb]s t ,m]cury makes ab\t f\r revolutions 9 its orbit p] ye>1 & !re=e crosses ! prime radius f\r times 9 ea* ye>1 :ile ! o!r planets are decid$ly sl[] 9 _! movem5ts4 ,! foll[+ l9es ( ! table %[ = ea* ye> ! date at :i* ea* planet fir/ cross$ ! prime radius 9 t ye>2 ! dates ( subsequ5t cross+s 9 any ye> c be f\nd by add+ once1 twice1 or ?ree times ! p]iod to ! giv5 date1 & ! table may be ext5d$ to lat] ye>s1 if ne$ be1 by cont9u\sly add+ multiples ( ! p]iod4 ,9 ! case ( ,m>s x appe>s t !re is only ab\t "o ye> out ( two 9 :i* ?is planet crosses ! prime radius4 ,aft] ! date at :i* ! planet crosses ! prime radius has be5 det]m9$ its position = any requir$ date is f\nd exactly z 9 ! case ( ! e>?1 & ! con/ellation 9 :i* ! planet w appe> f ! e>? is f\nd z expla9$ above 9 connection ) ,jupit] & ,saturn4 ,! brok5 l9es 9 ! figure repres5t ! con/ruction = f9d+ ! places 9 ! sky occupi$ by ,m]cury1 ,v5us1 & ,m>s on ,july #d1 #aijj4 ,let ! /ud5t make a simil> con/ruction & f9d ! positions ( ^! planets at ! pres5t "t4 ,look !m up 9 ! sky & see if !y are :]e y\r "w puts !m4 #ca4 ,,ex]cises4--,! ev5+ /> is a t]m loosely appli$ to any planet :i* is visible 9 ! we/]n sky soon aft] sunset4 ,x is easy to see t su* a planet mu/ be f>!r t[>d ! ea/ 9 ! sky ?an is ! sun1 & 9 ei!r ,fig4 #af or ,fig4 #ag any planet :i* view$ f ! position ( ! e>? lies to ! left ( ! sun & n m ?an #ej away f x w be an ev5+ />4 ,if to ! "r ( ! sun x is a morn+ />1 & may be se5 9 ! ea/]n sky %ortly be=e sunrise4 ,:at planet is ! ev5+ /> n[8 ,is !re m ?an "o ev5+ /> at a "t8 ,:at is ! morn+ /> n[8 ,d ,m]cury1 ,v5us1 or ,m>s ev] appe> 9 opposition8 ,:at is ! maximum angul> di/ance f ! sun at :i* ,v5us c ev] be se58 ,:y is ,m]cury a m difficult planet to see ?an ,v5us8 ,9 :at mon? ( ! ye> does ,m>s come ne>e/ to ! e>?8 ,w x always be bright] 9 ?is mon? ?an 9 any o!r8 ,:i* ( all ! planets comes ne>e/ to ! e>?8 ,! e>? always comes to ! same longitude on ! same day ( ea* ye>4 ,:y is n ?is true ( ! o!r planets8 ,! /ud5t %\ld rememb] t 9 "o respect ,figs4 #af & #ag are n altoge!r correct repres5tations1 s9ce !y %[ ! orbits z all ly+ 9 ! same plane4 ,if ?is 7 /rictly true1 e planet w\ld move1 l ! sun1 always along ! ecliptic2 b 9 fact all ( ! orbits are tilt$ a little out ( ! plane ( ! ecliptic & e planet 9 its motion deviates a little f ! ecliptic1 fir/ to "o side !n to ! o!r2 b n ev5 ,m>s1 :i* is ! mo/ erratic 9 ?is respect1 ev] gets m ?an eight degrees away f ! ecliptic1 & = ! mo/ "p all ( !m are mu* clos] to ! ecliptic ?an ?is limit4 ,,*apt] ,,iv ,,cele/ial ,,me*anics #cb4 ,,! ,,beg9n+s ,,( ,,cele/ial ,,me*anics4--,f ! e>lie/ dawn ( civilization1 long be=e ! beg9n+s ( writt5 hi/ory1 ! motions ( sun & moon & planets among ! />s f con/ellation to con/ellation _h comm&$ ! att5tion ( ?9k+ m51 p>ticul>ly ( ! class ( prie/s4 ,! religions ( :i* !y 7 ! gu>dians & tea*]s /ood 9 close/ relations ) ! movem5ts ( ! />s1 & _! own p[] & influ5ce 7 increas$ by a k ( !m4 ,illu/ration3 ,,isaac ,,newton 7#afdc-agbg74 ,out ( ^! pr(essional ne$s1 z well z f a _s ( sci5tific rese>*1 !re grew up & fl\ri%$ = _m c5turies a /udy ( ! motions ( ! planets1 simple & crude at fir/1 because ! obs]vations t c\ld !n be made 7 at be/ b r\gh ones1 b gr[+ m accurate & m complex z ! developm5t ( ! me*anic arts put bett] & m precise in/rum5ts into ! h&s ( a/ronom]s & enabl$ !m to obs]ve ) increas+ accuracy ! movem5ts ( ^! bodies4 ,x 0 e>ly se5 t :ile = ! mo/ "p ! planets1 includ+ ! sun & moon1 travel$ ?r\gh ! con/ellations f we/ to ea/1 "s ( !m sometimes rev]s$ _! motion & = a "t travel$ 9 ! opposite way4 ,?is cle>ly c n be expla9$ by ! simple !ory :i* _h e>ly be5 adopt$ t a planet moves always 9 ! same direction ar\nd a circul> orbit hav+ ! e>? at its c5t]1 & s x 0 said to move ar\nd 9 a small circul> orbit1 call$ an epicycle1 ^: c5t] 0 situat$ ^u & mov$ along a circul> orbit1 call$ ! def]5t1 )9 :i* ! e>? 0 plac$1 z is %[n 9 ,fig4 #ah1 :]e ! small circle is ! epicycle1 ! l>ge circle is ! def]5t1 ,p is ! planet1 & ,e ! e>?4 ,:5 ?is prov$ inadequate to acc\nt = ! really complicat$ movem5ts ( ! planets1 ano!r epicycle 0 put on top ( ! fir/ "o1 & !n ano!r & ano!r1 until ! suppos$ sy/em became s complicat$ t ,cop]nicus1 a ,poli% a/ronom]1 repudiat$ its fundam5tal !orem & taught t ! motions ( ! planets take place 9 circles ar\nd ! sun in/ead ( ab\t ! e>?1 & t ! e>? itself is only "o ( ! planets mov+ ar\nd ! sun 9 its own appropriate orbit & itself l>gely responsible = ! seem+ly erratic movem5ts ( ! o!r planets1 s9ce f day to day we see !m & obs]ve _! positions f diff]5t po9ts ( view4 ,illu/ration3 ,,fig4 #ah4--;,epicycle & def]5t4 #cc4 ,,kepl]',s ,,laws4--,two g5]ations lat] came ,kepl] ) 8 ?ree fam\s laws ( planet>y motion3 ,i4 ,e planet moves 9 an ellipse :i* has ! sun at "o ( its foci4 ,,ii4 ,! radius vector ( ea* planet moves ov] equal areas 9 equal times4 ,,iii4 ,! squ>es ( ! p]iodic times ( ! planets are proportional to ! cubes ( _! mean di/ances f ! sun4 ,^! laws are ! cr[n+ glory1 n only ( ,kepl]'s c>e]1 b ( all a/ronomical discov]y f ! beg9n+ up to 8 "t1 & !y well des]ve c>eful /udy & explanation1 al?\gh m mod]n progress has %[n t !y are only approximately true4 ,,ex]cise #ag4--;,drive two p9s into a smoo? bo>d an in* ap>t & fa/5 to !m ! ends ( a /r+ a foot long4 ,take up ! slack ( ! /r+ ) ! po9t ( a lead p5cil &1 keep+ ! /r+ drawn taut1 move ! p5cil po9t ov] ! bo>d into e possible position4 ,! curve ?us trac$ w be an ellipse hav+ ! p9s at ! two po9ts :i* are call$ its foci4 ,9 ! case ( ! planet>y orbits "o focus ( ! ellipse is vacant1 &1 9 accordance ) ! fir/ law1 ! c5t] ( ! sun is at ! o!r focus4 ,9 ,fig4 #ag ! dot1 inside ! orbit ( ,m]cury1 :i* is m>k$ a1 %[s ! position ( ! vacant focus ( ! orbit ( ,m>s1 & ! dot b is ! vacant focus ( ,m]cury's orbit4 ,! orbits ( ,v5us & ! e>? are s ne>ly circul> t _! vacant foci lie v close to ! sun & are n m>k$ 9 ! figure4 ,! l9e drawn f ! sun to any po9t ( ! orbit 7! /r+ f p9 to p5cil po9t7 is a radius vector4 ,! po9t midway betwe5 ! p9s is ! c5t] ( ! ellipse1 & ! di/ance ( ei!r p9 f ! c5t] measures ! ecc5tricity ( ! ellipse4 ,draw sev]al ellipses ) ! same l5g? ( /r+1 b ) ! p9s at diff]5t di/ances ap>t1 & note t ! great] ! ecc5tricity ! flatt] is ! ellipse1 b t all ( !m h ! same l5g?4 ,if bo? p9s 7 driv5 into ! same hole1 :at k9d ( an ellipse w\ld y get8 ,! ,second ,law 0 work$ out by ,kepl] z 8 answ] to a problem sugge/$ by ! fir/ law4 ,9 ,fig4 #ag x is app>5t f a m]e inspection ( ! orbit ( ,m]cury t ?is planet travels mu* fa/] on "o side ( its orbit ?an on ! o!r1 ! di/ance cov]$ 9 t5 days betwe5 ! numb]s #aj & #bj be+ m ?an fifty p] c5t great] ?an t betwe5 #ej & #fj4 ,! same diff]5ce is f\nd1 ?\gh usually 9 less degree1 = e o!r planet1 & ,kepl]'s problem 0 to discov] a means by :i* to m>k ^u ! orbit ! figures %[+ ! positions ( ! planet at ! end ( equal int]vals ( "t4 ,8 solution ( ?is problem1 conta9$ 9 ! second law1 ass]ts t if we draw radii vectors f ! sun to ea* ( ! m>k$ po9ts tak5 at equal "t int]vals ar\nd ! orbit1 !n ! area ( ! sector =m$ by two adjac5t radii vectores & ! arc includ$ betwe5 !m is equal to ! area ( ea* & e o!r su* sector1 ! %ort radii vectores be+ spread ap>t s z to include a long arc betwe5 !m :ile ! long radii vectores h a %ort arc4 ,9 ,kepl]'s =m ( /at+ ! law ! radius vector is suppos$ to travel ) ! planet & 9 ea* day to sweep ov] ! same fractional "p ( ! total area ( ! orbit4 ,! spac+ ( ! numb]s 9 ,fig4 #ag 0 done by means ( ?is law4 ,= ! prop] und]/&+ ( ,kepl]'s ,?ird ,law we mu/ note t ! mean di/ance :i* appe>s 9 x is "o half ( ! long diamet] ( ! orbit & t ! p]iodic "t means ! numb] ( days or ye>s requir$ by ! planet to make a complete circuit 9 its orbit4 ,repres5t+ ! fir/ ( ^! by a & ! second by ,t1 we h1 z ! ma!matical equival5t ( ! law1 a#c ,t#b ,c :]e ! quoti5t1 ,c1 is a numb] :i*1 z ,kepl] f\nd1 is ! same = e planet ( ! sol> sy/em4 ,if we take ! mean di/ance ( ! e>? f ! sun z ! unit ( di/ance1 & ! ye> z ! unit ( "t1 we %all f9d by apply+ ! equation to ! e>?'s motion1 ,c #a4 ,apply+ ?is value to any o!r planet we %all f9d 9 ! same units1 a ,t#b_/c1 by means ( :i* we may det]m9e ! di/ance ( any planet f ! sun :5 its p]iodic "t1 ,t1 has be5 le>n$ f obs]vation4 ,,ex]cise #ah4--,uranus requires #hd ye>s to make a revolution 9 its orbit4 ,:at is its mean di/ance f ! sun8 ,:at are ! mean di/ances ( ,m]cury1 ,v5us1 & ,m>s8 7,see ,*apt] ,,iii = _! p]iodic times47 ,w\ld x be possible = two planets at diff]5t di/ances f ! sun to move ar\nd _! orbits 9 ! same "t8 ,a circle is an ellipse 9 :i* ! two foci h be5 br\ght toge!r4 ,w\ld ,kepl]'s laws hold true = su* an orbit8 #cd4 ,,newton',s ,,laws ,,( ,,motion4--,kepl] /udi$ & describ$ ! motion ( ! planets4 ,newton1 ?ree g5]ations lat] 7#agbg ,a4 ,d471 /udi$ & describ$ ! me*anism :i* controls t motion4 ,to ,kepl] & 8 age ! heav5s 7 sup]natural1 :ile to ,newton & 8 successors !y are a "p ( ,nature1 gov]n$ by ! same laws :i* obta9 ^u ! e>?1 & we turn to ! ord9>y ?+s ( ev]yday life z ! f\ndation ( cele/ial me*anics4 ,e "o :o has ridd5 a bicycle kn[s t he c coa/ f>!r ^u a level road if x is smoo? ?an if x is r\gh2 b h[ev] smoo? & h>d ! road may be & h[ev] fa/ ! :eel may h be5 />t$1 x is soon] or lat] /opp$ by ! resi/ance :i* ! road & ! air (f] to its motion1 & :5 once /opp$ or *eck$ x c be />t$ aga9 only by apply+ fre% p[]4 ,we h "h a famili> illu/ration ( :at is call$ ,,! ,,fir/ ,,law ,,( ,,motion4--,e body cont9ues 9 its /ate ( re/ or ( uni=m motion 9 a /raight l9e except 9 s f> z x may be compell$ by =ce to *ange t /ate4 ,a gu/ ( w9d1 a /one1 a c>eless movem5t ( ! rid] may turn ! bicycle to ! "r or ! left1 b unless "s di/urb+ =ce is appli$ x w g /raight ahead1 & if all resi/ance to its motion c\ld be remov$ x w\ld g always at ! spe$ giv5 x by ! la/ p[] appli$1 sw]v+ nei!r to ! "o h& nor ! o!r4 ,:5 a sl[ rid] increases 8 spe$ we recognize at once t he has appli$ additional p[] to ! :eel1 & :5 ?is spe$ is slack5$ x equally %[s t =ce has be5 appli$ aga9/ ! motion4 ,x is =ce alone :i* c produce a *ange 9 ei!r velocity or direction ( motion2 b simple z ?is law n[ appe>s x requir$ ! g5ius ( ,galileo to discov] x & ( ,newton to give x ! =m 9 :i* x is /at$ above4 #ce4 ,,! ,,second ,,law ,,( ,,motion1 :i* is also due to ,galileo & ,newton1 is3 ,*ange ( motion is proportional to =ce appli$ & takes place 9 ! direction ( ! /raight l9e 9 :i* ! =ce acts4 ,suppose a man to fall f a balloon at "s great elevation 9 ! air2 8 own weight is ! =ce :i* pulls him d[n1 & t =ce op]at+ at e in/ant is suffici5t to give him at ! end ( ! fir/ second ( 8 fall a d[nw>d velocity ( #cb feet p] second--i4 e41 x has *ang$ 8 /ate f re/1 to motion at ?is rate1 & ! motion is t[>d ! e>? because ! =ce acts 9 t direction4 ,dur+ ! next second ! ceaseless op]ation ( ?is =ce w h ! same effect z 9 ! fir/ second & w add ano!r #cb feet to 8 velocity1 s t two seconds f ! "t he comm5c$ to fall he w be mov+ at ! rate ( #fd feet p] second1 etc4 ,! column ( figures m>k$ v 9 ! table bel[ %[s :at 8 velocity w be at ! end ( subsequ5t seconds4 ,! *ang+ velocity "h %[n is ! *ange ( motion to :i* ! law ref]s1 & ! velocity is proportional to ! "t %[n 9 ! fir/ column ( ! table1 because ! am\nt ( =ce ex]t$ 9 ?is case is proportional to ! "t dur+ :i* x op]at$4 ,! di/ance ?r\gh :i* ! man w fall 9 ea* second is %[n 9 ! column m>k$ d1 & is f\nd by tak+ ! av]age ( 8 velocity at ! beg9n+ & end ( ?is second1 & ! total di/ance ?r\gh :i* he has fall5 at ! end ( ea* second1 m>k$ s 9 ! table1 is f\nd by tak+ ! sum ( all ! prec$+ values ( d4 ,! velocity1 #cb feet p] second1 :i* measures ! *ange ( motion 9 ea* second1 also measures ! accel]at+ =ce :i* produces ?is motion1 & x is usually repres5t$ 9 =mul by ! lett] g4 ,let ! /ud5t %[ f ! numb]s 9 ! table t ! accel]at+ =ce1 ! "t1 t1 dur+ :i* x op]ates1 & ! space1 s1 fall5 ?r\gh1 satisfy ! relation s #a_/b gt#b1 :i* is usually call$ ! law ( fall+ bodies4 ,h[ does ! table %[ t g is equal to #cb8 ,,table t v d s #j #j #j #j #a #cb #af #af #b #fd #dh #fd #c #if #hj #add #d #abh #aab #bef #e #afj #add #djj etc4 etc4 etc4 etc4 ,if ! balloon 7 half a mile high h[ long w\ld x take to fall to ! gr\nd8 ,:at w\ld be ! velocity j be=e rea*+ ! gr\nd8 ,illu/ration3 ,,galileo ,,galilei 7#aefd-afdb74 ,fig4 #ai %[s ! pa? ?r\gh ! air ( a ball :i* has be5 /ruck by a bat at ! po9t ,a1 & />t$ (f 9 ! direction ,a ,b ) a velocity ( #bjj feet p] second4 ,9 accordance ) ! fir/ law ( motion1 if x 7 act$ ^u by no o!r =ce ?an ! impulse giv5 by ! bat1 x %\ld travel along ! /raight l9e ,a ,b at ! uni=m rate ( #bjj feet p] second1 & at ! end ( ! f\r? second x %\ld be #hjj feet f ,a1 at ! po9t m>k$ #d1 b dur+ ^! f\r seconds its weight has caus$ x to fall #bef feet1 & its actual position1 #d'1 is #bef feet bel[ ! po9t #d4 ,9 ?is way we f9d its position at ! end ( ea* second1 #a'1 #b'1 #c'1 #d'1 etc41 & draw+ a l9e ?r\gh ^! po9ts we %all f9d ! actual pa? ( ! ball "u ! influ5ce ( ! two =ces to be ! curv$ l9e ,a ,c4 ,no matt] h[ f> ! ball may g be=e /rik+ ! gr\nd1 x c n get back to ! po9t ,a1 & ! curve ,a ,c !re=e c n be a "p ( a circle1 s9ce t curve returns into itself4 ,x is1 9 fact1 a "p ( a p>abola1 :i*1 z we %all see lat]1 is a k9d ( orbit 9 :i* comets & "s o!r heav5ly bodies move4 ,a skyrocket moves 9 ! same k9d ( a pa?1 & s does a /one1 a bullet1 or any o!r object hurl$ ?r\gh ! air4 ,illu/ration3 ,,fig4 #ai4--,! pa? ( a ball4 #cf4 ,,! ,,?ird ,,law ,,( ,,motion4--,to e action !re is always an equal & contr>y reaction2 or ! mutual actions ( any two bodies are always equal & oppositely direct$4 ,?is is well illu/rat$ 9 ! case ( a man climb+ a rope h& ov] h&4 ,! direct =ce or action :i* he ex]ts is a d[nw>d pull ^u ! rope1 & x is ! reaction ( ! rope to ?is pull :i* lifts him along x4 ,we %all f9d 9 a lat] *apt] a curi\s application ( ?is law to ! hi/ory ( ! e>? & moon4 ,x is ! great glory ( ,sir ,isaac ,newton t he fir/ ( all m5 recogniz$ t ^! simple laws ( motion hold true 9 ! heav5s z well z ^u ! e>?2 t ! complicat$ motion ( a planet1 a comet1 or a /> is det]m9$ 9 accordance ) ^! laws by ! =ces :i* act ^u ! bodies1 & t ^! =ces are ess5tially ! same z t :i* we call weight4 ,! =mal /atem5t ( ! pr9ciple la/ nam$ is includ$ 9-- #cg4 ,,newton',s ,,law ,,( ,,gravitation4--,e p>ticle ( matt] 9 ! univ]se attracts e o!r p>ticle ) a =ce ^: direction is t ( a l9e jo9+ ! two1 & ^: magnitude is directly z ! product ( _! masses1 & inv]sely z ! squ>e ( _! di/ance f ea* o!r4 ,we "k t we ourselves & ! ?+s ab\t u are pull$ t[>d ! e>? by a =ce 7weight7 :i* is call$1 9 ! ,lat9 t ,newton wrote1 gravitas1 & ! ^w m>ks well ! true significance ( ! law ( gravitation4 ,newton did n discov] a new =ce 9 ! heav5s1 b he ext5d$ an old & famili> "o f a limit$ t]re/rial sph]e ( action to an unlimit$ & cele/ial "o1 & furni%$ a precise /atem5t ( ! way 9 :i* ! =ce op]ates4 ,:e!r a body be hot or cold1 wet or dry1 solid1 liquid1 or gase\s1 is ( no acc\nt 9 det]m9+ ! =ce :i* x ex]ts1 s9ce ?is dep5ds solely ^u mass & di/ance4 ,! /ud5t %\ld p]haps be w>n$ aga9/ /ra9+ too f> ! language :i* x is cu/om>y to employ 9 ?is connection4 ,! law ( gravitation is c]ta9ly a f>-rea*+ "o1 & x may op]ate 9 e remote/ corn] ( ! univ]se precisely z /at$ above1 b additional in=mation ab\t ^? corn]s w\ld be welcome to supplem5t our r scanty /ock ( k conc]n+ :at happ5s !re4 ,we may n controv]t ! words ( a popul> prea*] :o says1 ,:5 ,i lift my h& ,i move ! />s 9 ,ursa ,major1 b we %\ld n wi% to /& sponsor = !m1 ev5 ?\gh !y are ju/ifi$ by a rigor\s int]pretation ( ! ,newtonian law4 ,! ^w mass1 9 ! /atem5t ( ! law ( gravitation1 means ! quantity ( matt] conta9$ 9 ! body1 & if we repres5t by ! lett]s m & m ! respective quantities ( matt] conta9$ 9 ! two bodies ^: di/ance f ea* o!r is r1 we %all h1 9 accordance ) ! law ( gravitation1 ! foll[+ ma!matical expression = ! =ce1 ,f1 :i* acts betwe5 !m3 ,f k mm_/r#b4 ,?is equation1 :i* is ! g5]al ma!matical expression = ! law ( gravitation1 may be made to yield "s curi\s results4 ,?us1 if we select two bullets1 ea* hav+ a mass ( #a gram1 & place !m s t _! c5t]s are #a c5timet] ap>t1 ! above expression = ! =ce ex]t$ betwe5 !m becomes ,f k 7#a #a7_/ab k1 f :i* x appe>s t ! coeffici5t k is ! =ce ex]t$ betwe5 ^! bodies4 ,?is is call$ ! gravitation con/ant1 & x evid5tly furni%es a measure ( ! specific int5sity ) :i* "o p>ticle ( matt] attracts ano!r4 ,elaborate exp]im5ts :i* h be5 made to det]m9e ! am\nt ( ?is =ce %[ t x is surpris+ly small1 = 9 ! case ( ! two bullets ^: mass ( #a gram ea* is suppos$ to be conc5trat$ into an indef9itely small space1 gravity w\ld h to op]ate betwe5 !m cont9u\sly = m ?an =ty m9utes 9 ord] to pull !m toge!r1 al?\gh !y 7 sep>at$ by only #a c5timet] to />t )1 & no?+ save _! own in]tia oppos$ _! movem5ts4 ,x is only :5 "o or bo? ( ! masses m1 m are v great t ! =ce ( gravity becomes l>ge1 & ! weight ( bodies at ! surface ( ! e>? is consid]able because ( ! great quantity ( matt] :i* goes to make up ! e>?4 ,_m ( ! heav5ly bodies are mu* m massive ?an ! e>?1 z ! ma!matical a/ronom]s h f\nd by apply+ ! law ( gravitation to det]m9e num]ically _! masses1 or1 9 m popul> language1 to weigh !m4 ,! /ud5t %\ld obs]ve t ! two t]ms mass & weight are n synonym\s2 mass is def9$ above z ! quantity ( matt] conta9$ 9 a body1 :ile weight is ! =ce ) :i* ! e>? attracts t body1 & 9 accordance ) ! law ( gravitation its weight dep5ds ^u its di/ance f ! c5t] ( ! e>?1 :ile its mass is q indep5d5t ( its position ) respect to ! e>?4 ,by ! ?ird law ( motion ! e>? is pull$ t[>d a fall+ body j z /rongly z ! body is pull$ t[>d ! e>?--i4 e41 by a =ce equal to ! weight ( ! body4 ,h[ mu* does ! e>? rise t[>d ! body8 #ch4 ,,! ,,motion ,,( ,a ,,planet4--,9 ,fig4 #bj ,s repres5ts ! sun & ,p a planet or o!r cele/ial body1 :i* = ! mom5t is mov+ along ! /raight l9e ,p #a4 ,9 accordance ) ! fir/ law ( motion x w\ld cont9ue to move along ?is l9e ) uni=m velocity if no ext]nal =ce act$ ^u x2 b su* a =ce1 ! sun's attraction1 is act+1 & by virtue ( ?is attraction ! body is pull$ aside f ! l9e ,p #a4 ,kn[+ ! velocity & direction ( ! body's motion & ! =ce ) :i* ! sun attracts x1 ! ma!matician is able to apply ,newton's laws ( motion s z to det]m9e ! pa? ( ! body1 & a few ( ! possible orbits are %[n 9 ! figure :]e ! %ort cross /roke m>ks ! po9t ( ea* orbit :i* is ne>e/ to ! sun4 ,?is po9t is call$ ! p]ihelion4 ,)\t any =mal application ( ma!matics we may readily see t ! swift] ! motion ( ! body at ,p ! %ort] w be ! "t dur+ :i* x is subject$ to ! sun's attraction at close range1 & !re=e ! =ce ex]t$ by ! sun1 & ! result+ *ange ( motion1 w be small1 z 9 ! orbits ,p #a & ,p #b4 ,on ! o!r h&1 ,p #e & ,p #f repres5t orbits 9 :i* ! velocity at ,p 0 comp>atively small1 & ! result+ *ange ( motion great] ?an w\ld be possible = a m swiftly mov+ body4 ,:at w\ld be ! orbit if ! velocity at ,p 7 r$uc$ to no?+ at all8 ,:at w\ld be ! effect if ! body />t+ at ,p mov$ directly away f #a8 ,illu/ration3 ,,fig4 #bj4--;,diff]5t k9ds ( orbits4 ,! /ud5t %\ld n fail to obs]ve t ! sun's attraction t5ds to pull ! body at ,p =w>d along its pa?1 & !re=e increases its velocity1 & t ?is influ5ce cont9ues until ! planet rea*es p]ihelion1 at :i* po9t x atta9s its greate/ velocity1 & ! =ce ( ! sun's attraction is :olly exp5d$ 9 *ang+ ! direction ( its motion4 ,aft] ! planet has pass$ p]ihelion ! sun beg9s to pull backw>d & to ret>d ! motion 9 j ! same measure t be=e p]ihelion passage x increas$ x1 s t ! two halves ( ! orbit on opposite sides ( a l9e drawn f ! p]ihelion ?r\gh ! sun are exactly alike4 ,we may "h note ! explanation ( ,kepl]'s second law3 :5 ! planet is ne> ! sun x moves fa/]1 & ! radius vector *anges its direction m rapidly ?an :5 ! planet is remote f ! sun on acc\nt ( ! great] =ce ) :i* x is attract$1 & ! exact relation betwe5 ! rates at :i* ! radius vector turns 9 diff]5t p>ts ( ! orbit1 z giv5 by ! second law1 dep5ds ^u ! *anges 9 ?is =ce4 ,:5 ! velocity is n too great1 ! sun's backw>d pull1 aft] a planet has pass$ p]ihelion1 f9ally ov]comes x & turns ! planet t[>d ! sun aga91 9 su* a way t x comes back to ! po9t ,p1 mov+ 9 ! same direction & ) ! same spe$ z be=e--i4 e41 x has gone ar\nd ! sun 9 an orbit l ,p #f or ,p #d1 an ellipse1 along :i* x w cont9ue to move ev] aft]4 ,b we mu/ n fail to note t ?is return into ! same orbit is a consequ5ce ( ! la/ l9e 9 ! /atem5t ( ! law ( gravitation 7p4 #ed71 & t1 if ! magnitude ( ?is =ce 7 inv]sely z ! cube ( ! di/ance or any o!r proportion ?an ! squ>e1 ! orbit w\ld be some?+ v diff]5t4 ,if ! velocity is too great = ! sun's attraction to ov]come1 ! orbit w be a hyp]bola1 l ,p #b1 along :i* ! body w move away nev] to return1 :ile a velocity j at ! limit ( :at ! sun c control gives an orbit l ,p #c1 a p>abola1 along :i* ! body moves ) p>abolic velocity1 :i* is ev] dim9i%+ z ! body gets f>!r f ! sun1 b is always j suffici5t to keep x f return+4 ,if ! e>?'s velocity c\ld be increas$ #da p] c5t1 f #ai up to #bg miles p] second1 x w\ld h p>abolic velocity1 & w\ld quit ! sun's company4 ,! summation ( ! :ole matt] is t ! orbit 9 :i* a body moves ar\nd ! sun1 or pa/ ! sun1 dep5ds ^u its velocity & if ?is velocity & ! direction ( ! motion at any "o po9t 9 ! orbit are kn[n ! :ole orbit is det]m9$ by !m1 & ! position ( ! planet 9 its orbit = pa/ z well z future times c be det]m9$ ?r\gh ! application ( ,newton's laws2 & ! same is true = any o!r heav5ly body--moon1 comet1 meteor1 etc4 ,x is 9 ?is way t a/ronom]s are able to pr$ict1 ye>s 9 advance1 9 :at p>ticul> "p ( ! sky a giv5 planet w appe> at a giv5 "t4 ,x is sometimes a s\rce ( wond] t ! planets move 9 ellipses in/ead ( circles1 b x is easily se5 f ,fig4 #bj t ! planet1 ,p1 c\ld n by any possibility move 9 a circle1 s9ce ! direction ( its motion at ,p is n at "r angles ) ! l9e jo9+ x to ! sun z x mu/ be 9 a circul> orbit1 & ev5 if x 7 p]p5dicul> to ! radius vector ! planet mu/ ne$s h exactly ! "r velocity giv5 to x at ?is po9t1 s9ce ei!r m or less spe$ w\ld *ange ! circle into an ellipse4 ,9 ord] to produce circul> motion !re mu/ be a balanc+ ( conditions z nice z is requir$ to make a p9 /& ^u its po9t1 & ! really surpris+ ?+ is t ! orbits ( ! planets %\ld be s ne>ly circul> z !y are4 ,if ! orbit ( ! e>? 7 drawn accurately to scale1 ! untra9$ eye w\ld n detect ! slighte/ deviation f a true circle1 & ev5 ! orbit ( ,m]cury 7,fig4 #ag71 :i* is mu* m ecc5tric ?an t ( ! e>?1 might almo/ pass = a circle4 ,illu/ration3 ,,fig4 #ba4 ,an impossible orbit4 ,! orbit ,p #b1 :i* lies betwe5 ! p>abola & ! /raight l9e1 is call$ 9 geometry a hyp]bola1 & ,newton succe$$ 9 prov+ f ! law ( gravitation t a body might move "u ! sun's attraction 9 a hyp]bola z well z 9 a p>abola or ellipse2 b x mu/ move 9 "s "o ( ^! curves2 no o!r orbit is possible4#a ,?us x w\ld n be possible = a body mov+ "u ! law ( gravitation to describe ab\t ! sun any su* orbit z is %[n 9 ,fig4 #ba4 ,if ! body passes a second "t ?r\gh any po9t ( its orbit1 su* z ,p 9 ! figure1 !n x mu/ retrace1 "t aft] "t1 ! :ole pa? t x fir/ trav]s$ 9 gett+ f ,p ar\nd to ,p aga9--i4 e41 ! orbit mu/ be an ellipse4 #a ,! circle & /raight l9e are consid]$ to be special cases ( ^! curves1 :i*1 tak5 collectively1 are call$ ! conic sections4 ,newton also prov$ t ,kepl]'s ?ree laws are m]e coroll>ies f ! law ( gravitation1 & t to be /rictly correct ! ?ird law mu/ be slightly alt]$ s z to take into acc\nt ! masses ( ! planets4 ,^! are1 h[ev]1 s small 9 comp>ison ) t ( ! sun1 t ! correction is ( comp>atively little mom5t4 #ci4 ,,p]turbations4--,9 :at prec$es we h consid]$ ! motion ( a planet "u ! influ5ce ( no o!r =ce ?an ! sun's attraction1 :ile 9 fact1 z ! law ( gravitation ass]ts1 e o!r body 9 ! univ]se is 9 "s measure attract+ x & *ang+ its motion4 ,! result+ di/urbances 9 ! motion ( ! attract$ body are call$ p]turbations1 b = ! mo/ "p ^! are insignificant1 because ! bodies by ^: di/urb+ attractions !y are caus$ are ei!r v small or v remote1 & x is only :5 our mov+ planet1 ,p1 comes "u ! influ5ce ( "s great di/urb+ p[] l ,jupit] or "o ( ! o!r planets t ! p]turbations caus$ by _! influ5ce ne$ to be tak5 into acc\nt4 ,! problem ( ! motion ( ?ree bodies--sun1 ,jupit]1 planet--:i* mu/ !n be dealt ) is va/ly m complicat$ ?an t :i* we h consid]$1 & ! able/ ma!maticians & a/ronom]s h n be5 able to furni% a complete solution = x1 al?\gh !y h work$ ^u ! problem = two c5turies1 & h develop$ an imm5se am\nt ( detail$ in=mation conc]n+ x4 ,illu/ration3 ,,! ,,lick ,,obs]vatory1 ,,m\nt ,,hamilton1 ,,cal4 ,9 g5]al ea* planet works ceaselessly ^u ! orbit ( e o!r1 *ang+ its size & %ape & position1 backw>d & =w>d 9 accordance ) ! law ( gravitation1 & x is a "q ( s]i\s mom5t h[ f> ?is process may ext5d4 ,if ! diamet] ( ! e>?'s orbit 7 v mu* increas$ or dim9i%$ by ! p]turb+ action ( ! o!r planets1 ! am\nt ( heat receiv$ f ! sun w\ld be correspond+ly *ang$1 & ! e>?1 p]haps1 be r5d]$ unfit = ! support ( life4 ,! tipp+ ( ! plane ( ! e>?'s orbit into a new position might also produce s]i\s consequ5ces2 b ! great ,fr5* ma!matician ( a c5tury ago1 ,laplace1 succe$$ 9 prov+ f ! law ( gravitation t al?\gh bo? ( ^! *anges are actually 9 progress !y c n1 at lea/ = millions ( ye>s1 g f> en\gh to prove ( s]i\s consequ5ce1 & ! same is true = all ! o!r planets1 unless "h & !re an a/]oid may prove an exception to ! rule4 ,! precession 7,*apt] ,v7 is a /rik+ illu/ration ( a p]turbation ( slightly diff]5t "* f ! above1 & ano!r is f\nd 9 connection ) ! plane ( ! moon's orbit4 ,x w be rememb]$ t ! moon 9 its motion among ! />s nev] goes f> f ! ecliptic1 b 9 a complete circuit ( ! heav5s crosses x twice1 once 9 go+ f s\? to nor? & once 9 ! opposite direction4 ,! po9ts at :i* x crosses ! ecliptic are call$ ! nodes1 & "u ! p]turb+ influ5ce ( ! sun ^! nodes move we/w>d along ! ecliptic ab\t tw5ty degrees p] ye>1 an extraord9>ily rapid p]turbation1 & "o ( great consequ5ce 9 ! !ory ( eclipses4 ,illu/ration3 ,,fig4 #bb4--;,a planet subject to great p]turbations by ,jupit]4 #dj4 ,,weigh+ ,,! ,,planets4--,al?\gh ^! p]turbations c n be consid]$ dang]\s1 !y are int]e/+ s9ce !y furni% a me?od = weigh+ ! planets :i* produce !m4 ,f ! law ( gravitation we le>n t ! ability ( a planet to produce p]turbations dep5ds directly ^u its mass1 s9ce ! =ce ,f :i* x ex]ts conta9s ?is mass1 m1 z a factor4 ,s1 too1 ! divisor r#b 9 ! expression = ! =ce %[s t ! di/ance betwe5 ! di/urb+ & di/urb$ bodies is a matt] ( great consequ5ce1 = ! small] ! di/ance ! great] ! =ce4 ,:51 !re=e1 ! mass ( a planet su* z ,jupit] is to be det]m9$ f ! p]turbations x produces1 x is cu/om>y to select "s su* opportunity z is pres5t$ 9 ,fig4 #bb1 :]e "o ( ! small planets1 call$ a/]oids1 is repres5t$ z mov+ 9 a v ecc5tric orbit1 :i* at "o po9t approa*es close to ! orbit ( ,jupit]1 & at ano!r place comes ne> to ! orbit ( ! e>?4 ,= ! mo/ "p ,jupit] w n ex]t any v great di/urb+ influ5ce ^u a planet mov+ 9 su* an orbit z ?is1 s9ce x is only at r>e int]vals t ! a/]oid & ,jupit] approa* s close to ea* o!r1 z is %[n 9 ! figure4 ,! "t dur+ :i* ! a/]oid is little affect$ by ! attraction ( ,jupit] is us$ to /udy ! motion giv5 to x by ! sun's attraction--t is1 to det]m9e c>efully ! undi/urb$ orbit 9 :i* x moves2 b !re comes a "t at :i* ! a/]oid passes close to ,jupit]1 z %[n 9 ! figure1 & ! orbital motion :i* ! sun imp>ts to x w !n be greatly di/urb$1 & :5 ! planet next comes r\nd to ! "p ( its orbit ne> ! e>? ! effect ( ^! di/urbances ^u its app>5t position 9 ! sky w be exagg]at$ by its close proximity to ! e>?4 ,if n[ ! a/ronom] obs]ves ! actual position ( ! a/]oid 9 ! sky1 its "r asc5sion & decl9ation1 & comp>es ^! ) ! position assign$ to ! planet by ! law ( gravitation :5 ! attraction ( ,jupit] is ignor$1 ! diff]5ces betwe5 ! obs]v$ "r asc5sions & decl9ations & ^? comput$ ^u ! !ory ( undi/urb$ motion w measure ! influ5ce t ,jupit] has _h ^u ! a/]oid1 & ! am\nt by :i* ,jupit] has %ift$ x1 comp>$ ) ! am\nt by :i* ! sun has mov$ x--t is1 ) ! motion 9 its orbit--furni%es ! mass ( ,jupit] express$ z a fractional "p ( ! mass ( ! sun4 ,!re has be5 det]m9$ 9 ?is mann] ! mass ( e planet 9 ! sol> sy/em :i* is l>ge en\gh to produce any appreciable p]turbation1 & all ^! masses prove to be exce$+ly small fractions ( ! mass ( ! sun1 z may be se5 f ! foll[+ table1 9 :i* is giv5 opposite ! "n ( ea* planet ! numb] by :i* ! mass ( ! sun mu/ be divid$ 9 ord] to get ! mass ( ! planet3 ,m]cury #g1jjj1jjj 787 ,v5us #djh1jjj ,e>? #cbi1jjj ,m>s #c1jic1ejj ,jupit] #a1jdg4d ,saturn #c1ejb ,uranus #bb1hjj ,neptune #ai1gjj ,x is to be especially not$ t ! mass giv5 = ea* planet includes ! mass ( all ! satellites :i* att5d x1 s9ce _! influ5ce 0 felt 9 ! p]turbations f :i* ! mass 0 d]iv$4 ,?us ! mass assign$ to ! e>? is ! comb9$ mass ( e>? & moon4 #da4 ,,discov]y ,,( ,,neptune4--,! mo/ fam\s example ( p]turbations is f\nd 9 connection ) ! discov]y1 9 ! ye> #ahdf1 ( ,neptune1 ! out]mo/ planet ( ! sol> sy/em4 ,= _m ye>s ! motion ( ,uranus1 8 next neighbor1 _h prov$ a puzzle to a/ronom]s4 ,9 accordance ) ,kepl]'s fir/ law ?is planet %\ld move 9 an ellipse hav+ ! sun at "o ( its foci1 b no ellipse c\ld be f\nd :i* exactly fitt$ its obs]v$ pa? among ! />s1 al?\gh1 to be sure1 ! misfit 0 n v pron\nc$4 ,a/ronom]s surmis$ t ! small deviations ( ,uranus f ! be/ pa? :i* !ory comb9$ ) obs]vation c\ld assign1 7 due to p]turbations 9 its motion caus$ by an unkn[n planet m remote f ! sun--a ?+ easy to conjecture b h>d to prove1 & h>d] /ill to f9d ! unkn[n di/urb]4 ,b almo/ simultane\sly two "y m51 ,adams 9 ,engl& & ,le ,v]ri] 9 ,france1 attack$ ! problem q indep5d5tly ( ea* o!r1 & c>ri$ x to a successful solution1 %[+ t if ! irregul>ities 9 ! motion ( ,uranus 7 inde$ caus$ by an unkn[n planet1 !n t planet mu/1 9 ,septemb]1 #ahdf1 be 9 ! direction ( ! con/ellation ,aqu>ius2 & !re x 0 f\nd on ,septemb] #bc;d by ! a/ronom]s ( ! ,b]l9 ,obs]vatory :om ,le ,v]ri] _h invit$ to se>* = x1 & f\nd )9 a degree ( ! exact po9t :i* ! law ( gravitation 9 8 h&s _h assign$ to x4 ,?is work+ backw>d f ! p]turbations exp]i5c$ by ,uranus to ! cause :i* produc$ !m is ju/ly reg>d$ z "o ( ! greate/ sci5tific a*ievem5ts ( ! human intellect1 & x is wor?y ( note t we are approa*+ ! "t at :i* x may be repeat$1 = ,neptune n[ behaves mu* z did ,uranus ?ree qu>t]s ( a c5tury ago1 & ! mo/ plausible explanation :i* c be (f]$ = ^! anomalies 9 its pa? is t ! b\nds ( ! sol> sy/em mu/ be aga9 enl>g$ to include ano!r di/urb+ planet4 #db4 ,,! ,,%ape ,,( ,a ,,planet4--,!re is an effect ( gravitation n yet t\*$ ^u1 :i* is ( consid]able int]e/ & wide application 9 a/ronomy--viz41 its influ5ce 9 det]m9+ ! %ape ( ! heav5ly bodies4 ,! e>? is a globe because e "p ( x is drawn t[>d ! c5t] by ! attraction ( ! o!r p>ts1 & if ?is attraction on its surface 7 ev]y:]e ( equal =ce ! mat]ial ( ! e>? w\ld be cru%$ by x into a truly sph]ical =m1 no matt] :at may h be5 ! %ape 9 :i* x 0 orig9ally made4 ,b su* is n ! real condition ( ! e>?1 = its diurnal rotation develops 9 e p>ticle ( its body a =ce :i* is sometimes call$ c5trifugal1 b :i* is really no?+ m ?an ! in]tia ( its p>ticles1 :i* t5d at e mom5t to keep un*ang$ ! direction ( _! motion & :i* ?us resi/ ! attraction t pulls !m into a circul> pa? m>k$ out by ! e>?'s rotation1 j z a /one ti$ at ! end ( a /r+ & swung swiftly 9 a circle pulls ^u ! /r+ & opposes ! con/ra9t :i* keeps x mov+ 9 a circle4 ,a few exp]im5ts ) su* a /one w %[ t ! fa/] x goes ! h>d] does x pull ^u ! /r+1 & ! same is true ( ea* p>ticle ( ! e>?1 ! swiftly mov+ ones ne> ! equator hav+ a great] c5trifugal =ce ?an ! sl[ ones ne> ! poles4 ,at ! equator ! c5trifugal =ce is directly oppos$ to ! =ce ( gravity1 & 9 effect dim9i%es x1 s t1 comp>atively1 !re is an excess ( gravity at ! poles :i* compresses ! e>? along its axis & causes x to bulge out at ! equator until a balance is ?us re/or$4 ,z we h le>n$ f ! /udy ( geography1 9 ! case ( ! e>?1 ?is compression am\nts to ab\t #bg miles1 b 9 ! l>g] planets1 ,jupit] & ,saturn1 x is mu* great]1 am\nt+ to sev]al ?\s& miles4 ,b rotation is n ! only influ5ce t t5ds to pull a planet out ( %ape4 ,! attraction :i* ! e>? ex]ts ^u ! moon is /rong] on ! ne> side & weak] on ! f> side ( our satellite ?an at its c5t]1 & ?is diff]5ce ( attraction t5ds to w>p ! moon1 z is illu/rat$ 9 ,fig4 #bc :]e #a1 #b1 & #c repres5t pieces ( iron ( equal mass plac$ 9 l9e on a table ne> a horse%oe magnet1 ,h4 ,ea* piece ( iron is attract$ by ! magnet & is held back by a weight to :i* x is fa/5$ by means ( a cord runn+ ov] a pulley1 ,p1 at ! edge ( ! table4 ,^! weights are all to be suppos$ equally heavy & ea* ( !m pulls ^u its piece ( iron ) a =ce j suffici5t to balance ! attraction ( ! magnet = ! middle piece1 ,no4 #b4 ,x is cle> t "u ?is arrangem5t ,no4 #b w move nei!r to ! "r nor to ! left1 s9ce ! =ces ex]t$ ^u x by ! magnet & ! weight j balance ea* o!r4 ,^u ,no4 #a1 h[ev]1 ! magnet pulls h>d] ?an ^u ,no4 #b1 because x is ne>] & its pull !re=e m ?an balances ! =ce ex]t$ by ! weight1 s t ,no4 #a w be pull$ away f ,no4 #b & w /ret* ! ela/ic cords1 :i* are repres5t$ by ! l9es jo9+ #a & #b1 until _! t5sion1 toge!r ) ! =ce ex]t$ by ! weight1 j balances ! attraction ( ! magnet4 ,= ,no4 #c1 ! =ce ex]t$ by ! magnet is less ?an t ( ! weight1 & x w also be pull$ away f ,no4 #b until its ela/ic cords are /ret*$ to ! prop] t5sion4 ,! net result is t ! ?ree blocks :i*1 )\t ! magnet's influ5ce1 w\ld be held close toge!r by ! ela/ic cords1 are pull$ ap>t by ?is outside =ce z f> z ! resi/ance ( ! cords w p]mit4 ,illu/ration3 ,,fig4 #bc4--,tide-rais+ =ces4 ,an entirely analog\s set ( =ces produces a simil> effect ^u ! %ape ( ! moon4 ,! ela/ic cords ( ,fig4 #bc /& = ! attraction ( gravitation by :i* all ! p>ts ( ! moon are b\nd toge!r4 ,! magnet repres5ts ! e>? pull+ ) unequal =ce ^u diff]5t p>ts ( ! moon4 ,! weights are ! in]tia ( ! moon 9 its orbital motion :i*1 z we h se5 9 a previ\s section1 ^u ! :ole j balances ! e>?'s attraction & keeps ! moon f fall+ into x4 ,! effect ( ^! =ces is to /ret* out ! moon along a l9e po9t+ t[>d ! e>?1 j z ! blocks 7 /ret*$ out along ! l9e ( ! magnet1 & to make ?is diamet] ( ! moon slightly b p]man5tly long] ?an ! o!rs4 ,illu/ration3 ,,fig4 #bd4--,! tides4 ,,! ,,tides4--,simil>ly ! moon & ! sun attract opposite sides ( ! e>? ) diff]5t =ces & feebly t5d to pull x out ( %ape4 ,b "h a new elem5t comes into play3 ! e>? turns s rapidly ^u its axis t its solid p>ts h no "t 9 :i* to yield s5sibly to ! /ra9s1 :i* %ift rapidly f "o diamet] to ano!r z diff]5t p>ts ( ! e>? are turn$ t[>d ! moon1 & x is *iefly ! wat]s ( ! sea :i* respond to ! di/ort+ effect ( ! sun's & moon's attraction4 ,^! are heap$ up on opposite sides ( ! e>? s z to produce a slight elongation ( its diamet]1 & ,fig4 #bd %[s h[ by ! e>?'s rotation ?is swell+ ( ! wat]s is swept out f "u ! moon & is pull$ back by ! moon until x f9ally takes up "s su* position z t %[n 9 ! figure :]e ! effect ( ! e>?'s rotation 9 c>ry+ x "o way is j balanc$ by ! moon's attraction urg+ x back on l9e ) ! moon4 ,?is heap+ up ( ! wat]s is call$ a tide4 ,if ,i 9 ! figure repres5ts a little isl& 9 ! sea ! wat]s :i* surr\nd x w ( c\rse accompany x 9 its diurnal rotation ab\t ! e>?'s axis1 b :5ev] ! isl& comes back to ! position ,i1 ! wat]s w swell up z a "p ( ! tidal wave & w encroa* ^u ! l& 9 :at is call$ high tide or flood tide4 ,s too :5 !y rea* ,i1 half a day lat]1 !y w aga9 rise 9 flood tide1 & midway betwe5 ^! po9ts1 at ,i1 ! wat]s mu/ subside1 giv+ l[ or ebb tide4 ,! height ( ! tide rais$ by ! moon 9 ! op5 sea is only a v few feet1 & ! tide rais$ by ! sun is ev5 less1 b along ! coa/ ( a cont95t1 9 bays & angles ( ! %ore1 x (t5 happ5s t a broad b l[ tidal wave is =c$ into a n>r[ corn]1 & !n ! rise ( ! wat] may be _m feet1 especially :5 ! sol> tide & ! lun> tide come 9 toge!r1 z !y d twice 9 e mon?1 at new & full moon4 ,:y d !y come toge!r at ^! times in/ead ( "s o!r8 ,small z are ^! tidal effects1 x is wor? not+ t !y may 9 c]ta9 cases be v mu* great]--e4 g41 if ! moon 7 z massive z is ! sun its tidal effect w\ld be "s millions ( times great] ?an x n[ is & w\ld suffice to gr9d ! e>? into fragm5ts4 ,al?\gh ! e>? escapes ?is fate1 "s o!r bodies are n s =tunate1 & we %all see 9 lat] *apt]s "s evid5ce ( _! dis9tegration4 #dc4 ,,! ,,scope ,,( ,,! ,,law ,,( ,,gravitation4--,9 all ! doma9 ( physical sci5ce !re is no o!r law s fam\s z ! ,newtonian law ( gravitation2 none o!r t has be5 s dwelt ^u1 /udi$1 & elaborat$ by a/ronom]s & ma!maticians1 & p]haps none t c be consid]$ s indisputably prov$4 ,ov] & ov] aga9 ma!matical analysis1 bas$ ^u ?is law1 has po9t$ out conclusions :i*1 ?\gh hi!rto unsuspect$1 h aft]w>d be5 f\nd true1 z :5 ,newton himself d]iv$ z a coroll>y f ?is law t ! e>? ought to be flatt5$ at ! poles--a ?+ n kn[n at t "t1 & n prov$ by actual measurem5t until long aft]w>d4 ,x is1 9 fact1 ?is capacity = pr$ict+ ! unkn[n & = expla9+ 9 m9ute/ detail ! complicat$ ph5om5a ( ! heav5s & ! e>? t con/itutes ! real pro( ( ! law ( gravitation1 & x is !re=e wor? :ile to note t at ! pres5t "t !re are a v few po9ts at :i* ! law fails to furni% a satisfactory acc\nt ( ?+s obs]v$4 ,*ief among ^! is ! case ( ! planet ,m]cury1 ! long diamet] ( ^: orbit is sl[ly turn+ ar\nd 9 a way = :i* ! law ( gravitation z yet furni%es no explanation4 ,:e!r ?is is because ! law itself is inaccurate or incomplete1 or :e!r x only m>ks a case 9 :i* a/ronom]s h n yet prop]ly appli$ ! law & trac$ out its consequ5ces1 we d n "k2 b :e!r x be ! "o or ! o!r1 ?is & o!r simil> cases %[ t ev5 "h1 9 its mo/ p]fect *apt]1 a/ronomy /ill rema9s an incomplete sci5ce4 ,,*apt] ,v ,,! ,,e>? ,,z ,a ,,planet #dd4 ,,! ,,size ,,( ,,! ,,e>?4--,! /ud5t is presum$ to h le>n$1 9 8 /udy ( geography1 t ! e>? is a globe ab\t #h1jjj miles 9 diamet] &1 )\t dwell+ ^u ! pro(s :i* are commonly giv5 = ^! /atem5ts1 we proce$ to consid] ! pr9ciples ^u :i* ! measurem5t ( ! e>?'s size & %ape are bas$4 ,illu/ration3 ,,fig4 #be4--,measur+ ! size ( ! e>?4 ,9 ,fig4 #be ! circle repres5ts a m]idian section ( ! e>?2 ,p ,p is ! axis ab\t :i* x rotates1 & ! dott$ l9es repres5t a beam ( light com+ f a /> 9 ! plane ( ! m]idian1 & s di/ant t ! dott$ l9es are all practically p>allel to ea* o!r4 ,! sev]al radii drawn ?r\gh ! po9ts #a1 #b1 #c1 repres5t ! direction ( ! v]tical at ^! po9ts1 & ! angles :i* ^! radii produc$1 make ) ! rays ( />light are ea* equal to ! angul> di/ance ( ! /> f ! z5i? ( ! place at ! mom5t ! /> crosses ! m]idian4 ,we h already se51 9 ,*apt] ,,ii1 h[ ^! angles may be measur$1 & x is app>5t f ! figure t ! diff]5ce betwe5 any two ( ^! angles--e4 g41 ! angles at #a & #b--;is equal to ! angle at ! c5t]1 ,o1 betwe5 ! po9ts #a & #b4 ,by measur+ ^! angul> di/ances ( ! /> f ! z5i?1 ! a/ronom] f9ds ! angles at ! c5t] ( ! e>? betwe5 ! /ations #a1 #b1 #c1 etc41 at :i* 8 obs]vations are made4 ,if ! m]idian 7 a p]fect circle ! *ange ( z5i? di/ance ( ! />1 z "o travel$ along a m]idian f ! equator to ! pole1 w\ld be p]fectly uni=m--! same numb] ( degrees = ea* hundr$ miles travel$--& obs]vations made 9 _m p>ts ( ! e>? %[ t ?is is v ne>ly true1 b t1 on ! :ole1 z we approa* ! pole x is necess>y to travel a little great] di/ance ?an is requir$ = a giv5 *ange 9 ! angle at ! equator4 ,! e>? is1 9 fact1 flatt5$ at ! poles to ! am\nt ( ab\t #bg miles 9 ! l5g? ( its diamet]1 & by ?is am\nt1 z well z by small] v>iations due to m\nta9s & valleys1 ! %ape ( ! e>? diff]s f a p]fect sph]e4 ,^! a/ronomical measurem5ts ( ! curvature ( ! e>?'s surface furni% by f> ! mo/ satisfactory pro( t x is v approximately a sph]e1 & furni% z its equatorial diamet] #g1ibf miles4 ,neglect+ ! compression1 z x is call$1 i4 e41 ! #bg miles by :i* ! equatorial diamet] exce$s ! pol>1 ! size ( ! e>? may easily be f\nd by measur+ ! di/ance #a--b along ! surface & by comb9+ ) ?is ! angle #a ,o #b obta9$ ?r\gh measur+ ! m]idian altitudes ( any /> z se5 f #a & #b4 ,draw on pap] an angle equal to ! measur$ diff]5ce ( altitude & f9d h[ f> y mu/ g f its v]tex 9 ord] to h ! di/ance betwe5 ! sides1 measur$ along an arc ( a circle1 equal to ! measur$ di/ance betwe5 #a & #b4 ,?is di/ance f ! v]tex w be ! e>?'s radius4 ,,ex]cise #ai4--,measure ! diamet] ( ! e>? by ! me?od giv5 above4 ,9 ord] t ?is may be done satisfactorily1 ! two /ations at :i* obs]vations are made mu/ be sep>at$ by a consid]able di/ance--i4 e41 #bjj miles4 ,!y ne$ n be on ! same m]idian1 b if !y are on diff]5t m]idians 9 place ( ! actual di/ance betwe5 !m1 !re mu/ be us$ ! projection ( t di/ance ^u ! m]idian--i4 e41 ! nor? & s\? "p ( ! di/ance4 ,by co-op]ation betwe5 s*ools 9 ! ,nor!rn & ,s\!rn ,/ates1 us+ a good map to obta9 ! requir$ di/ances1 ! diamet] ( ! e>? may be measur$ ) ! plumb-l9e app>atus describ$ 9 ,*apt] ,,ii & det]m9$ )9 a small p]c5tage ( its true value4 #de4 ,,! ,,mass ,,( ,,! ,,e>?4--,we h se5 9 ,*apt] ,,iv ! possibility ( det]m9+ ! masses ( ! planets z fractional p>ts ( ! sun's mass1 b no?+ 0 !re %[n1 or c\ld be %[n1 ab\t measur+ ^! masses aft] ! common fa%ion 9 kilogrammes or tons4 ,to d ?is we mu/ fir/ get ! mass ( ! e>? 9 tons or kilogrammes1 & :ile ! pr9ciples involv$ 9 ?is det]m9ation are simple en\gh1 _! actual application is delicate & difficult4 ,illu/ration3 ,,fig4 #bf4--;,illu/rat+ ! pr9ciples involv$ 9 weigh+ ! e>?4 ,9 ,fig4 #bf we suppose a long plumb l9e to be susp5d$ above ! surface ( ! e>? & to be attract$ t[>d ! c5t] ( ! e>?1 ,c1 by a =ce ^: int5sity is 7,*apt] ,,iv7 ,f k m,e_/,r#b1 :]e ,e d5otes ! mass ( ! e>?1 :i* is to be det]m9$ by exp]im5t1 & ,r is ! radius ( ! e>?1 #c1ifc miles4 ,if !re is no di/urb+ influ5ce pres5t1 ! plumb l9e w po9t directly d[nw>d1 b if a massive ball ( lead or o!r heavy sub/ance is plac$ at "o side1 #a1 x w attract ! plumb l9e ) a =ce equal to f k m,b_/r#b1 :]e r is ! di/ance ( its c5t] f ! plumb bob & ,b is its mass :i* we may suppose1 = illu/ration1 to be a ton4 ,9 consequ5ce ( ?is attraction ! plumb l9e w be pull$ a little to "o side1 z %[n by ! dott$ l9e1 & if we repres5t by l ! l5g? ( ! plumb l9e & by d ! di/ance betwe5 ! orig9al & ! di/urb$ positions ( ! plumb bob we may write ! proportion ,f 3 f 33 l 3 d2 & introduc+ ! values ( ,f & f giv5 above1 & solv+ = ,e ! proportion ?us trans=m$1 we f9d ,e ,b l_/d 7,r_/r7#b4 ,9 ?is equation ! mass ( ! ball1 ,b1 ! l5g? ( ! plumb l9e1 l1 ! di/ance betwe5 ! c5t] ( ! ball & ! c5t] ( ! plumb bob1 r1 & ! radius ( ! e>?1 ,r1 c all be measur$ directly1 & d1 ! am\nt by :i* ! plumb bob is pull$ to "o side by ! ball1 is readily f\nd by %ift+ ! ball ov] to ! o!r side1 at #b1 & measur+ ) a microscope h[ f> ! plumb bob moves4 ,?is di/ance w1 ( c\rse1 be equal to #b d4 ,by me?ods involv+ ^! pr9ciples1 b appli$ 9 a mann] m complicat$ z well z m precise1 ! mass ( ! e>? is f\nd to be1 9 tons1 #f1fdb #ajah--;i4 e41 #f1fdb foll[$ by #ah ciph]s1 or 9 kilogrammes #fj1beh #ajbj4 ,! e>?'s atmosph]e makes up ab\t a million? "p ( ?is mass4 ,if ! l5g? ( ! plumb l9e 7 #ajj feet1 ! weight ( ! ball a ton1 & ! di/ance betwe5 ! two positions ( ! ball1 #a & #b1 six feet1 h[ _m in*es1 d1 w\ld ! plumb bob be pull$ out ( place8 ,f9d f ! mass ( ! e>? & ! data ( #dj ! mass ( ! sun 9 tons4 ,f9d also ! mass ( ,m>s4 ,! computation c be v greatly abridg$ by ! use ( log>i?ms4 #df4 ,,precession4--,t ! e>? is isolat$ 9 space & has no support ^u :i* to re/1 is suffici5tly %[n by ! fact t ! />s are visible ^u e side ( x1 & no support c be se5 /ret*+ out t[>d !m4 ,we mu/ !n consid] ! e>? to be a globe travel+ freely ab\t ! sun 9 a circuit :i* x completes once e ye>1 & rotat+ once 9 e tw5ty-f\r h\rs ab\t an axis :i* rema9s at all seasons direct$ v ne>ly t[>d ! /> ,pol>is4 ,! /ud5t %\ld be able to %[ f 8 own obs]vations ( ! sun t1 ) ref]5ce to ! />s1 ! direction ( ! sun f ! e>? *anges ab\t a degree a day4 ,does ?is prove t ! e>? revolves ab\t ! sun8 ,b x is only 9 appe>ance t ! pole ma9ta9s its fix$ position among ! />s4 ,if photographs are tak5 ye> aft] ye>1 aft] ! mann] ( ,ex]cise #g1 x w be f\nd t sl[ly ! pole is mov+ 7ne>ly7 t[>d ,pol>is1 & mak+ ?is /> describe a small] & small] circle 9 its diurnal pa?1 :ile />s on ! o!r side ( ! pole 79 "r asc5sion #ab;h47 become m di/ant f x & describe l>g] circles 9 _! diurnal motion2 b ! process takes place s sl[ly t ! space ( a lifetime is requir$ = ! motion ( ! pole to equal ! angul> diamet] ( ! full moon4 ,sp9 a top & note h[ its rapid :irl ab\t its axis corresponds to ! e>?'s diurnal rotation4 ,:5 ! axis ab\t :i* ! top sp9s is truly v]tical ! top sleeps2 b if ! axis is tipp$ ev] s little away f ! v]tical x beg9s to wobble1 s t if we imag9e ! axis prolong$ out to ! sky & provid$ ) a p5cil po9t z a m>k]1 ?is w\ld trace a circle ar\nd ! z5i?1 along :i* ! pole ( ! top w\ld move1 & a little obs]vation w %[ t ! m ! top is tipp$ f ! v]tical ! l>g] does ?is circle become & ! m rapidly does ! wobbl+ take place4 ,7 x n = ! sp9n+ ( ! top ab\t its axis1 x w\ld promptly fall ov] :5 tipp$ f ! v]tical position1 b ! sp9 comb9es ) ! =ce :i* pulls ! top ov] & produces ! wobbl+ motion4 ,sp9 ! top 9 opposite directions1 ) ! h&s ( a wat* & contr>y to ! h&s ( a wat*1 & note ! effect :i* is produc$ ^u ! wobbl+4 ,! e>? pres5ts _m po9ts ( resemblance to ! top4 ,its diurnal rotation is ! sp9 ab\t ! axis4 ,?is axis is tipp$ #bc4e away f ! p]p5dicul> to its orbit 7obliquity ( ! ecliptic7 j z ! axis ( ! top is tipp$ away f ! v]tical l9e4 ,9 consequ5ce ( its rapid sp91 ! body ( ! e>? bulges out at ! equator 7#bg miles71 & ! sun & moon1 by virtue ( _! attraction 7see ,*apt] ,,iv71 lay hold ( ?is protub]ance & pull x d[n t[>d ! plane ( ! e>?'s orbit1 s t if x 7 n = ! sp9 ?is =ce w\ld /raight5 ! axis up & set x p]p5dicul> to ! orbit plane4 ,b "h1 z 9 ! case ( ! top1 ! sp9 & ! tipp+ =ce comb9e to produce a wobble :i* is call$ precession1 & ^: effect we recognize 9 ! %ift+ position ( ! pole among ! />s4 ,! motion ( precession is v mu* sl[] ?an ! wobbl+ ( ! top1 s9ce ! tipp+ =ce = ! e>? is relatively v small1 & a p]iod ( ne>ly #bf1jjj ye>s is requir$ = a complete circuit ( ! pole ab\t its c5t] ( motion4 ,friction ultimately /ops bo? ! sp9 & ! wobble ( ! top1 b ?is influ5ce seems :olly abs5t 9 ! case ( ! e>?1 & bo? rotation & precession g on un*ang$ f c5tury to c5tury1 save = c]ta9 m9or =ces :i* = a "t *ange ! direction or rate ( ! precessional motion1 fir/ 9 "o way & !n 9 ano!r1 )\t 9 ! long run produc+ any results ( consequ5ce4 ,! c5t] ( motion1 ab\t :i* ! pole travels 9 a small circle hav+ an angul> radius ( #bc4e1 is at t po9t ( ! heav5s t[>d :i* a p]p5dicul> to ! plane ( ! e>?'s orbit po9ts1 & may be f\nd on ! /> map 9 "r asc5sion #ah;h4 #jm4 & decl9ation #ff4e4 ,,ex]cise #bj4--;,f9d ?is po9t on ! map1 & draw z well z y c ! pa? ( ! pole ab\t x4 ,! motion ( ! pole along its pa? is t[>d ! con/ellation ,cepheus4 ,m>k ! position ( ! pole along ?is pa? at int]vals ( #a1jjj ye>s1 & ref] to ^! positions 9 deal+ ) "s ( ! foll[+ que/ions3 ,does ! wobbl+ ( ! top occur 9 ! same direction z ! motion ( precession8 ,d ! tipp+ =ces appli$ to ! e>? & top act 9 ! same direction8 ,:at w be ! pol> /> #ab1jjj ye>s h5ce8 ,! ,great ,pyramid ( ,egypt is ?\ght to h be5 us$ z an obs]vatory :5 ,alpha ,draconis 0 ! bright /> ne>e/ ! pole4 ,h[ long ago 0 t8 ,! motion ( ! pole ( c\rse c>ries ! equator & ! equ9oxes ) x1 & ?us sl[ly *anges ! "r asc5sions & decl9ations ( all ! />s4 ,on ?is acc\nt x is frequ5tly call$ ! precession ( ! equ9oxes1 & ?is motion ( ! equ9ox1 sl[ ?\gh x is1 is a matt] ( "s consequ5ce 9 connection ) *ronology & ! l5g? ( ! ye>4 ,w ! precession ev] br+ back ! "r asc5sions & decl9ations to be aga9 :at !y n[ are8 ,9 :at direction is ! pole mov+ ) respect to ! ,big ,dipp]8 ,w its motion ev] br+ x exactly to ,pol>is8 ,h[ f> away f ,pol>is w ! precession c>ry ! pole8 ,:at o!r bright />s w be br\ght ne> ! pole by ! precession8 #dg4 ,,! ,,w>m+ ,,( ,,! ,,e>?4--,w9t] & summ] alike ! day is on ! av]age w>m] ?an ! night1 & x is easy to see t ?is surplus ( heat comes f ! sun by day & is lo/ by night ?r\gh radiation into ! void :i* surr\nds ! e>?2 j z ! heat conta9$ 9 a mass ( molt5 iron is radiat$ away & ! iron cool$ :5 x is tak5 out f ! furnace & plac$ amid cold] surr\nd+s4 ,! e>?'s loss ( heat by radiation goes on ceaselessly day & night1 & 7 x n = ! influx ( sol> heat ?is radiation w\ld /eadily dim9i% ! temp]ature t[>d :at is call$ ! absolute z]o--i4 e41 a /ate 9 :i* all heat has be5 tak5 away & beyond :i* !re c be no great] degree ( cold4 ,?is mu/ n be conf\nd$ ) ! z]o temp]atures %[n by our !rmomet]s1 s9ce x lies ne>ly #ejj bel[ ! z]o ( ! ,fahr5heit scale 7-#bgc ,c5tigrade71 a temp]ature :i* by comp>ison makes ! colde/ w9t] wea!r seem w>m1 al?\gh ! ord9>y !rmomet] may regi/] _m degrees bel[ its z]o4 ,! heat radiat$ by ! sun into ! surr\nd+ space on e side ( x is ano!r example ( ! same cool+ process1 a hot body giv+ up its heat to ! cold] space ab\t x1 & x is ! m9ute fraction ( ?is heat p\r$ out by ! sun1 & 9 small "p int]cept$ by ! e>?1 :i* w>ms ! latt] & produces :at we call wea!r1 climate1 ! seasons1 etc4 ,obs]ve ! fluctuations1 ! ebb & fl[1 :i* are inh]5t 9 ?is process4 ,f sunset to sunrise !re is no?+ to comp5sate ! /eady outfl[ ( heat1 & air & gr\nd gr[ /eadily cold]1 b ) ! sunrise !re comes an influx ( sol> heat1 feeble at fir/ because x /rikes ! e>?'s surface v obliquely1 b becom+ m & m effici5t z ! sun rises high] 9 ! sky4 ,b z ! air & ! gr\nd gr[ w>m dur+ ! morn+ h\rs !y "p m & m readily & rapidly ) _! /ore ( heat1 j z a /eam pipe or a cup ( c(fee radiates heat m rapidly :5 v hot4 ,! w>me/ h\r ( ! day is rea*$ :5 ^! oppos+ t5d5cies ( income & exp5diture ( heat are j balanc$2 & b>r+ su* di/urb+ factors z w9d & cl\ds1 ! ga9 9 temp]ature usually ext5ds to ! "t--an h\r or two beyond noon--at :i* ! dim9i%+ altitude ( ! sun r5d]s 8 rays less effici5t1 :5 radiation ga9s ! upp] h& & ! temp]ature becomes = a %ort "t /ation>y1 & !n comm5ces to fall /eadily until ! next sunrise4 ,we h "h an example ( :at is call$ a p]iodic *ange--i4 e41 "o :i*1 )9 a def9ite & uni=m p]iod 7#bd h\rs71 oscillates f a m9imum up to a maximum temp]ature & !n back aga9 to a m9imum1 repeat+ sub/antially ! same v>iation day aft] day4 ,b x mu/ be und]/ood t m9or causes n tak5 into acc\nt above1 su* z w9ds1 wat]1 etc41 produce o!r fluctuations f day to day :i* sometimes obscure or ev5 oblit]ate ! diurnal v>iation ( temp]ature caus$ by ! sun4 ,expose ! back ( y\r h& to ! sun1 hold+ ! h& 9 su* a position t ! sunlight /rikes p]p5dicul>ly ^u x2 !n turn ! h& s t ! light falls q obliquely ^u x & note h[ mu* m vigor\s is ! w>m+ effect ( ! sun 9 ! fir/ position ?an 9 ! second4 ,x is *iefly ?is diff]5ce ( angle t makes ! sun's w>m? m effective :5 he is high up 9 ! sky ?an :5 he is ne> ! horizon1 & m effective 9 summ] ?an 9 w9t]4 ,we h se5 9 ,*apt] ,,iii t ! sun's motion among ! />s takes place along a pa? :i* c>ries x alt]nately nor? & s\? ( ! equator to a di/ance ( #bc4e1 & ! />s %[ by _! e>li] ris+s & lat] sett+s1 z we pass f ! equator t[>d ! nor? pole ( ! heav5s1 t z ! sun moves nor?w>d f ! equator1 ea* day 9 ! nor!rn hemisph]e w become a little long]1 ea* night a little %ort]1 & e day ! sun w rise high] t[>d ! z5i? until ?is process culm9ates t[>d ! end ( ,june1 :5 ! sun beg9s to move s\?w>d1 br++ %ort] days & small] altitudes until ! ,*ri/mas season1 :5 aga9 x is rev]s$ & ! sun moves nor?w>d4 ,we h "h ano!r p]iodic v>iation1 :i* runs its complete c\rse 9 a p]iod ( a ye>1 & x is easy to see t ?is v>iation mu/ h a m>k$ effect on ! w>m+ ( ! e>?1 ! long days & great altitudes ( summ] produc+ ! great] w>m? ( t season1 :ile ! %ort] days & l[] altitudes ( ,decemb]1 by dim9i%+ ! daily supply ( sol> heat1 br+ on ! w9t]'s cold4 ,! succession ( ! seasons1 w9t] foll[+ summ] & summ] w9t]1 is caus$ by ! v>y+ altitude ( ! sun1 & ?is 9 turn is due to ! obliquity ( ! ecliptic1 or1 :at is ! same ?+1 ! am\nt by :i* ! axis ( ! e>? is tipp$ f be+ p]p5dicul> to ! plane ( its orbit1 & ! seasons are simply a p]iodic *ange 9 ! w>m+ ( ! e>?1 q comp>able ) ! diurnal *ange b ( long] p]iod4 ,x is evid5t t ! p]iod )9 :i* ! succession ( w9t] & summ] is complet$1 ! ye>1 z we commonly call x1 mu/ equal ! "t requir$ by ! sun to g f ! v]nal equ9ox ar\nd to ! v]nal equ9ox aga91 s9ce ?is furni%es a complete cycle ( ! sun's motions nor? & s\? f ! equator4 ,on acc\nt ( ! we/w>d motion ( ! equ9ox 7precession7 ?is is n q ! same z ! "t requir$ = a complete revolution ( ! e>? 9 its orbit1 b is a little %ort] 7#bjm4 #bcs471 s9ce ! equ9ox moves back to meet ! sun4 #dh4 ,,relation ,,( ,,! ,,sun ,,to ,,climate4--,x is cle> t bo? ! nor!rn & s\!rn hemisph]es ( ! e>? mu/ h sub/antially ! same k9d ( seasons1 s9ce ! motion ( ! sun nor? & s\? affects bo? alike2 b :5 ! sun is nor? ( ! equator & w>m+ our hemisph]e mo/ effectively1 8 light falls m obliquely ^u ! o!r hemisph]e1 ! days !re are %ort & w9t] reigns at ! "t we are enjoy+ summ]1 :ile six mon?s lat] ! conditions are rev]s$4 ,9 ^? p>ts ( ! e>? ne> ! equator--! torrid zone--!re is no su* m>k$ *ange f cold to w>m z we exp]i5ce1 because1 z ! sun nev] gets m ?an #bc4e away f ! cele/ial equator1 on e day ( ! ye> he m\nts high 9 ! tropic skies1 always com+ )9 #bc4e ( ! z5i?1 & usually clos] ?an ?is1 s t !re is no su* p]iodic *ange 9 ! heat supply z is exp]i5c$ 9 high] latitudes1 & )9 ! tropics ! temp]ature is !re=e bo? high] & m uni=m ?an 9 our latitude4 ,9 ! frigid zones1 on ! contr>y1 ! sun nev] rises high 9 ! sky2 at ! poles 8 greate/ altitude is only #bc4e1 & dur+ ! w9t] season he does n rise at all1 s t ! temp]ature is "h l[ ! :ole ye> r\nd1 & dur+ ! w9t] season1 :5 = weeks or mon?s at a "t ! supply ( sol> light is entirely cut (f1 ! temp]ature falls to a degree unkn[n 9 m favor$ climes4 ,if ! obliquity ( ! ecliptic 7 made #aj great]1 :at w\ld be ! effect ^u ! seasons 9 ! temp]ate zones8 ,:at if x 7 made #aj less8 ,does ! precession ( ! equ9oxes h any effect ^u ! seasons or ^u ! climate ( diff]5t p>ts ( ! e>?8 ,if ! axis ( ! e>? po9t$ t[>d ,arcturus in/ead ( ,pol>is1 w\ld ! seasons be any diff]5t f :at !y are n[8 #di4 ,,! ,,atmosph]e4--,al?\gh we live ^u its surface1 we are n outside ! e>?1 b at ! bottom ( a sea ( air :i* =ms ! e>?'s out]mo/ lay] & ext5ds above our heads to a height ( _m miles4 ,! /udy ( mo/ ( ! ph5om5a ( ! atmosph]e belongs to t bran* ( physics call$ meteorology1 b !re are a few matt]s :i* fairly come )9 our consid]ation ( ! e>? z a planet4 ,we c n see ! />s save z we look ?r\gh ?is atmosph]e1 & ! light :i* comes ?r\gh x is b5t & (t5times di/ort$ s z to pres5t s]i\s ob/acles to any accurate telescopic /udy ( ! heav5ly bodies4 ,frequ5tly ?is di/urbance is visible to ! nak$ eye1 & ! />s are said to tw9kle--i4 e41 to quiv] & *ange color _m times p] second1 solely 9 consequ5ce ( a di/urb$ condition ( ! air & n f any?+ :i* goes on 9 ! />4 ,?is effect is m m>k$ l[ d[n 9 ! sky ?an ne> ! z5i?1 & x is wor? not+ t ! planets %[ v little ( x because ! light !y s5d to ! e>? comes f a disk ( s5sible area1 :ile a />1 be+ mu* small] & f>!r f ! e>?1 has its disk r$uc$ practically to a m]e po9t ^: light is m easily affect$ by local di/urbances 9 ! atmosph]e ?an is ! broad] beam :i* comes f ! planets' disk4 #ej4 ,,refraction4--,at all times1 :e!r ! />s tw9kle or n1 _! light is b5t 9 its passage ?r\gh ! atmosph]e1 s t ! />s appe> to /& high] up 9 ! sky ?an _! true positions4 ,?is effect1 :i* ! a/ronom] calls refraction1 mu/ be all[$ = 9 obs]vations ( ! m precise class1 al?\gh save at l[ altitudes its am\nt is a v small fraction ( a degree1 b ne> ! horizon x is mu* exagg]at$ 9 am\nt & becomes easily visible to ! nak$ eye by di/ort+ ! disks ( ! sun & moon f circles into ovals ) _! long diamet]s horizontal4 ,! refraction lifts bo? upp] & l[] edge ( ! sun1 b lifts ! l[] edge m ?an ! upp]1 ?us %ort5+ ! v]tical diamet]4 ,see ,fig4 #bg1 :i* %[s n only ?is effect1 b also ! reflection ( ! sun f ! curv$ surface ( ! sea1 /ill fur!r flatt5+ ! image4 ,if ! surface ( ! wat] 7 flat1 ! reflect$ image w\ld h ! same %ape z ! sun's disk1 & its alt]$ appe>ance is sometimes cit$ z a pro( t ! e>?'s surface is curv$4 ,! total am\nt ( ! refraction at ! horizon is a little m ?an half a degree1 & s9ce ! diamet]s ( ! sun & moon subt5d an angle ( ab\t half a degree1 we h ! rem>kable result t 9 reality ! :ole disk ( ei!r sun or moon is bel[ ! horizon at ! in/ant t ! l[] edge appe>s to t\* ! horizon & sunset or moonset beg9s4 ,! same effect exi/s at sunrise1 & z a consequ5ce ! duration ( sun%9e or ( moon%9e is on ! av]age ab\t six m9utes long] ea* day ?an x w\ld be if !re 7 no atmosph]e & no refraction4 ,a p>tial (fset to ?is b5efit is f\nd 9 ! fact t ! atmosph]e absorbs ! light ( ! heav5ly bodies1 s t />s appe> mu* less bright :5 ne> ! horizon ?an :5 !y are high] up 9 ! sky1 & by reason ( ?is absorption ! sett+ sun c be look$ at ) ! nak$ eye )\t ! discom=t :i* its dazzl+ lu/] causes at noon4 ,illu/ration3 ,,fig4 #bg4--;,flatt5+ ( ! sun's disk by refraction & by reflection f ! surface ( ! sea4 #ea4 ,,! ,,twilight4--,ano!r effect ( ! atmosph]e1 ev5 m m>k$ ?an ! prec$+1 is ! twilight4 ,z at sunrise ! m\nta9 top cat*es ! rays ( ! com+ sun be=e !y rea* ! l[l&1 & at sunset x keeps !m aft] !y h fad$ f ! regions bel[1 s ! p>ticles ( du/ & vapor1 :i* always float 9 ! atmosph]e1 cat* ! sunlight & reflect x to ! surface ( ! e>? :ile ! sun is /ill bel[ ! horizon1 giv+ at ! beg9n+ & end ( day t vague & diffuse light :i* we call twilight4 ,illu/ration3 ,,fig4 #bh4--,twilight ph5om5a4 ,fig4 #bh %[s a "p ( ! e>? surr\nd$ by su* a du/-lad5 atmosph]e1 :i* is illum9at$ on ! left by ! rays ( ! sun1 b :i*1 on ! "r ( ! figure1 lies 9 ! %ad[ ca/ by ! e>?4 ,to an obs]v] plac$ at #a ! sun is j sett+1 & all ! atmosph]e above him is illum9$ ) its rays1 :i* furni% a bright twilight4 ,:51 by ! e>?'s rotation1 ?is obs]v] has be5 c>ri$ to #b1 all ! region to ! ea/ ( 8 z5i? lies 9 ! %ad[1 :ile to ! we/ !re is a "p ( ! atmosph]e f :i* !re /ill comes a twilight1 b n[ comp>atively fa9t1 because ! l[] "p ( ! atmosph]e ab\t our obs]v] lies 9 ! %ad[1 & x is ma9ly its upp] regions f :i* ! light comes1 & "h ! du/ & moi/ure are mu* less abundant ?an 9 ! l[] /rata4 ,/ill lat]1 :5 ! obs]v] has be5 c>ri$ by ! e>?'s rotation to ! po9t #c1 e ve/ige ( twilight w h vani%$ f 8 sky1 because all ( ! illum9at$ "p ( ! atmosph]e is n[ bel[ 8 horizon1 :i* is repres5t$ by ! l9e #c ,l4 ,9 ! figure ! sun is repres5t$ to be #gh bel[ ?is horizon l9e at ! end ( twilight1 b ?is is a gross exagg]ation1 made = ! sake ( cle>ness 9 ! draw+--9 fact1 twilight is usually said to end :5 ! sun is #ah bel[ ! horizon4 ,let ! /ud5t r$raw ,fig4 #bh on a l>ge scale1 s t ! po9ts #a & #c %all be only #ah ap>t1 z se5 f ! e>?'s c5t]4 ,he w f9d t ! po9t ,l is br\ght d[n mu* clos] to ! surface ( ! e>?1 & measur+ ! l5g? ( ! l9e #b ,l1 he %\ld f9d = ! height ( ! atmosph]e ab\t "o-eightie? "p ( ! radius ( ! e>?--i4 e41 a little less ?an #ej miles4 ,?is1 h[ev]1 is n ! true height ( ! atmosph]e4 ,! air ext5ds f> beyond ?is1 b ! p>ticles ( du/ & vapor :i* are capable ( s5d+ sunlight d[n to ! e>? seem all to lie bel[ ?is limit4 ,! /ud5t %\ld n fail to wat* ! ea/]n sky aft] sunset1 & see ! %ad[ ( ! e>? rise up & fill x :ile ! twilight ar* retreats /eadily t[>d ! we/4 ,illu/ration3 ,,fig4 #bi4--,! cause ( long & %ort twilights4 ,duration ( twilight4--,s9ce twilight ends :5 ! sun is #ah bel[ ! horizon1 any circum/ance :i* makes ! sun g d[n rapidly w %ort5 ! duration ( twilight1 & any?+ :i* ret>ds ! d[nw>d motion ( ! sun w correspond+ly prolong x4 ,*ief among influ5ces ( ?is k9d is ! angle :i* ! sun's c\rse makes ) ! horizon4 ,if x goes /raight d[n1 z at a1 ,fig4 #bi1 a mu* %ort] "t w suffice to c>ry x to a depression ( #ah ?an is ne$$ 9 ! case %[n at b 9 ! same figure1 :]e ! motion is v oblique to ! horizon4 ,if we consid] diff]5t latitudes & diff]5t seasons ( ! ye>1 we %all f9d e possible v>iety ( circum/ance f a to b1 & correspond+ to ^!1 ! duration ( twilight v>ies f an all-night duration 9 ! summ]s ( ,scotl& & m nor!rn l&s to an h\r or less 9 ! m\nta9s ( ,p]u4 ,= ! sake ( graphical effect1 ! %ortness ( tropical twilight is some:at exagg]at$ by ,col]idge 9 ! l9es1 ,! sun's rim dips2 ! />s ru% out3 ,at "o /ride comes ! d>k4 ,! ,anci5t ,m>9]4 ,9 ! ,unit$ ,/ates ! longe/ twilights come at ! end ( ,june1 & la/ = a little m ?an two h\rs1 :ile ! %orte/ ones are 9 ,m>* & ,septemb]1 am\nt+ to a little m ?an an h\r & a half2 b at all times ! la/ half h\r ( twilight is h>dly to be di/+ui%$ f night1 s small is ! quantity ( reflect+ matt] 9 ! upp] regions ( ! atmosph]e4 ,= practical conv5i5ce x is cu/om>y to assume 9 ! c\rts ( law t twilight ends an h\r aft] sunset4 ,h[ long does twilight la/ at ! nor? pole8 ,! ,aurora4--,"o o!r ph5om5on ( ! atmosph]e may be m5tion$1 only to po9t out t x is n ( an a/ronomical "*4 ,! ,aurora1 or nor!rn lights1 is z purely an affair ( ! e>? z is a ?und]/orm1 & its explanation belongs to ! subject ( t]re/rial magnetism4 ,,*apt] ,,vi ,,! ,,measurem5t ,,( ,,"t #eb4 ,,sol> ,,"t4--,to measure any quantity we ne$ a unit 9 t]ms ( :i* x mu/ be express$4 ,angles are measur$ 9 degrees1 & ! degree is ! unit = angul> measurem5t4 ,= mo/ sci5tific purposes ! c5timet] is adopt$ z ! unit ) :i* to measure di/ances1 & simil>ly a day is ! fundam5tal unit = ! measurem5t ( "t4 ,h\rs1 m9utes1 & seconds are aliquot p>ts ( ?is unit conv5i5t = use 9 deal+ ) %ort] p]iods ?an a day1 & ! week1 mon?1 & ye> :i* we use 9 our cal5d>s are multiples ( ! day4 ,/rictly speak+1 a day is n ! "t requir$ by ! e>? to make "o revolution ^u its axis1 b x is be/ def9$ z ! am\nt ( "t requir$ = a p>ticul> "p ( ! sky to make ! complete circuit f ! m]idian ( a p>ticul> place ?r\gh we/ & ea/ back to ! m]idian aga94 ,! day beg9s at ! mom5t :5 ?is specifi$ "p ( ! sky is on ! m]idian1 & ! "t at any mom5t is ! h\r angle ( ?is p>ticul> "p ( ! sky--i4 e41 ! numb] ( h\rs1 m9utes1 etc41 t h elaps$ s9ce x 0 on ! m]idian4 ,! /ud5t has already become famili> ) ! k9d ( day :i* is bas$ ^u ! motion ( ! v]nal equ9ox1 & :i* furni%es sid]eal "t1 & he has se5 t sid]eal "t1 :ile v conv5i5t 9 deal+ ) ! motions ( ! />s1 is decid$ly inconv5i5t = ! ord9>y affairs ( life s9ce 9 ! reckon+ ( ! h\rs x takes no acc\nt ( daylight & d>kness4 ,"o c n tell (f-h& :e!r #aj h\rs1 sid]eal "t1 falls 9 ! day or 9 ! night4 ,we mu/ 9 "s way obta9 a day & a sy/em ( "t reckon+ bas$ ^u ! app>5t diurnal motion ( ! sun1 & we may1 if we *oose1 take ! sun itself z ! po9t 9 ! heav5s ^: transit ov] ! m]idian %all m>k ! beg9n+ & ! end ( ! day4 ,9 ?is sy/em ! "t is ! numb] ( h\rs1 m9utes1 etc41 :i* h elaps$ s9ce ! sun 0 on ! m]idian1 & ?is is ! k9d ( "t :i* is %[n by a sun dial1 & :i* 0 9 g5]al use1 ye>s ago1 be=e clocks & wat*es became common4 ,s9ce ! sun moves among ! />s ab\t a degree p] day1 x is easily se5 t ! rotat+ e>? w h to turn f>!r 9 ord] to c>ry any p>ticul> m]idian f ! sun ar\nd to ! sun aga91 ?an to c>ry x f a /> ar\nd to ! same />1 or f ! v]nal equ9ox ar\nd to ! v]nal equ9ox aga92 j z ! m9ute h& ( a clock turns f>!r 9 go+ f ! h\r h& r\nd to ! h\r h& aga9 ?an x turns 9 go+ f ,,xii to ,,xii4 ,^! sol> days & h\rs & m9utes are !re=e a little long] ?an ! correspond+ sid]eal ones1 & ?is furni%es ! explanation :y ! />s come to ! m]idian a little e>li]1 by sol> "t1 e night ?an on ! night be=e1 & :y sid]eal "t ga9s /eadily ^u sol> "t1 ?is ga9 am\nt+ to approximately #cm4 #ef4es4 p] day1 or exactly "o day p] ye>1 s9ce ! sun makes ! complete circuit ( ! con/ellations once 9 a ye>4 ,) ! g5]al introduction ( clocks & wat*es into use ab\t a c5tury ago ?is k9d ( sol> "t w5t out ( common use1 s9ce no well-regulat$ clock c\ld keep ! "t correctly4 ,! e>? 9 its orbital motion ar\nd ! sun goes fa/] 9 "s p>ts ( its orbit ?an 9 o!rs1 & 9 consequ5ce ! sun appe>s to move m rapidly among ! />s 9 w9t] ?an 9 summ]2 moreov]1 on acc\nt ( ! conv]g5ce ( h\r circles z we g away f ! equator1 ! same am\nt ( motion along ! ecliptic produces m effect 9 w9t] & summ] :5 ! sun is nor? or s\?1 ?an x does 9 ! spr+ & autumn :5 ! sun is ne> ! equator1 & z a comb9$ result ( ^! causes & o!r m9or ones true sol> "t1 z x is call$1 is itself n uni=m1 b falls beh9d ! uni=m lapse ( sid]eal "t at a v>iable rate1 sometimes quick]1 sometimes sl[]4 ,a true sol> day1 f noon to noon1 is #ea seconds %ort] 9 ,septemb] ?an 9 ,decemb]4 ,illu/ration3 ,,fig4 #cj4--,! equation ( "t4 #ec4 ,,mean ,,sol> ,,"t4--,to rem$y ^! inconv5i5ces !re has be5 inv5t$ & br\ght into common use :at is call$ mean sol> "t1 :i* is p]fectly uni=m 9 its lapse & :i*1 by comp>ison ) sid]eal "t1 loses exactly "o day p] ye>4 ,! "t 9 ?is sy/em nev] diff]s mu* f true sol> "t1 & ! diff]5ce betwe5 ! two = any p>ticul> day may be f\nd 9 any good almanac1 or may be read f ! curve 9 ,fig4 #cj1 9 :i* ! "p ( ! curve above ! l9e m>k$ #jm %[s h[ _m m9utes mean sol> "t is fa/] ?an true sol> "t4 ,! correct "n = ?is diff]5ce betwe5 ! two k9ds ( sol> "t is ! equation ( "t1 b 9 ! almanacs x is frequ5tly m>k$ sun fa/ or sun sl[4 ,9 sid]eal "t & true sol> "t ! di/9ction betwe5 ,a4 ,m4 h\rs 7ante m]idiem be=e ! sun rea*es ! m]idian7 & ,p4 ,m4 h\rs 7po/ m]idiem aft] ! sun has pass$ ! m]idian7 is n obs]v$1 ! "t be+ c\nt$ f #j h\rs to #bd h\rs1 comm5c+ :5 ! sun or v]nal equ9ox is on ! m]idian4 ,occasionally ! attempt is made to introduce into common use ?is mode ( reckon+ ! h\rs1 beg9n+ ! day 7date7 at midnight & c\nt+ ! h\rs consecutively up to #bd1 :5 ! next date is rea*$ & a new />t made4 ,su* a sy/em w\ld simplify railway "t tables & simil> publications2 b ! ,am]ican public is sl[ to adopt x1 al?\gh ! sy/em has come into practical use 9 ,canada & ,spa94 #ed4 ,,to ,,f9d 7,,approximately7 ,,! ,,sid]eal ,,"t ,,at ,,any ,,mom5t4--,,rule ,i4 ,:5 ! mean sol> "t is kn[n4 ,let ,w repres5t ! "t %[n by an ord9>y wat*1 & repres5t by ,s ! correspond+ sid]eal "t & by ,d ! numb] ( days t h elaps$ f ,m>* #bc;d to ! date 9 "q4 ,!n ,s ,w #fi_/gj ,d #d4 ,! la/ t]m is express$ 9 m9utes1 & %\ld be r$uc$ to h\rs & m9utes4 ,?us at #d ,p4 ,m4 on ,july #d?-- ,d #ajc days4 #fi_/gj ,d #d #djfm4 #f;h4 #dfm4 ,w #d;h4 #jm4 ,s #aj;h4 #dfm4 ,! daily ga9 ( sid]eal ^u mean sol> "t is #fi_/gj ( #d m9utes1 & ,m>* #bc;d is ! date on :i* sid]eal & mean sol> "t are toge!r1 tak+ ! av]age ( "o ye> ) ano!r1 b x v>ies a little f ye> to ye> on acc\nt ( ! extra day introduc$ 9 leap ye>s4 ,,rule ,,ii4 ,:5 ! />s 9 ! nor!rn sky c be se54 ,f9d b ,cassiopei1 & imag9e a l9e drawn f x to ,pol>is1 & ano!r l9e f ,pol>is to ! z5i?4 ,! sid]eal "t is equal to ! angle betwe5 ^! l9es1 provid$ t t angle mu/ be measur$ f ! z5i? t[>d ! we/4 ,turn ! angle f degrees into h\rs by divid+ by #ae4 #ee4 ,,! ,,e>?',s ,,rotation4--,we are famili> ) ! fact t a wat* may run fa/] at "o "t ?an at ano!r1 & x is wor? :ile to inquire if ! same is n true ( our *ief timepiece--! e>?4 ,x is assum$ 9 ! sections ^u ! measurem5t ( "t t ! e>? turns ab\t its axis ) absolute uni=mity1 s t mean sol> "t nev] ga9s or loses ev5 ! smalle/ fraction ( a second4 ,:e!r ?is be absolutely true or n1 no "o has ev] succe$$ 9 f9d+ conv9c+ pro( ( a v>iation l>ge en\gh to be measur$1 al?\gh x has rec5tly be5 %[n t ! axis ab\t :i* x rotates is n p]fectly fix$ )9 ! body ( ! e>?4 ,! solid body ( ! e>? wriggles ab\t ?is axis l a fi% ^u a hook1 s t ! position ( ! nor? pole ^u ! e>?'s surface *anges )9 a ye> to ! ext5t ( #dj or #ej feet 7#ae met]s7 )\t ev] gett+ m ?an ?is di/ance away f its av]age position4 ,?is is probably caus$ by ! p]iodical %ift+ ( masses ( air & wat] f "o "p ( ! e>? to ano!r z ! seasons *ange1 & x seems probable t ^! *anges w produce "s small effect ^u ! rotation ( ! e>?4 ,b 9 spite ( ^!1 = any su* mod]ate int]val ( "t z a ye> or a c5tury1 s f> z pres5t k goes1 we may reg>d ! e>?'s rotation z uni=m & undi/urb$4 ,= long] int]vals--e4 g41 #a1jjj1jjj or #aj1jjj1jjj ye>s--! "q is a v diff]5t "o1 & we %all h to meet x aga9 9 ano!r connection4 #ef4 ,,longitude ,,& ,,"t4--,9 :at prec$es !re has be5 con/ant ref]5ce to ! m]idian4 ,! day beg9s :5 ! sun is on ! m]idian4 ,sol> "t is ! angul> di/ance ( ! sun pa/ ! m]idian4 ,sid]eal "t 0 det]m9$ by obs]v+ transits ( />s ov] a m]idian l9e actually laid out ^u ! gr\nd1 etc4 ,b e place ^u ! e>? has its own m]idian f :i* ! "t may be reckon$1 & 9 ,fig4 #ca1 :]e ! rays ( sunlight are repres5t$ z fall+ ^u a "p ( ! e>?'s equator ?r\gh :i* ! m]idians ( ,new ,york1 ,*icago1 & ,san ,francisco pass1 x is evid5t t ^! rays make diff]5t angles ) ! m]idians1 & t ! sun is f>!r f ! m]idian ( ,new ,york ?an f t ( ,san ,francisco by an am\nt j equal to ! angle at ,o betwe5 ^! m]idians4 ,?is angle is call$ by geograph]s ! diff]5ce ( longitude betwe5 ! two places1 & ! /ud5t %\ld note t ! ^w longitude is "h us$ 9 a diff]5t s5se f t on page #cf4 ,f ,fig4 #ca we obta9 ! ,!orem4--,! diff]5ce betwe5 ! times at any two m]idians is equal to _! diff]5ce ( longitude1 & ! "t at ! ea/]n m]idian is great] ?an at ! we/]n m]idian4 ,a/ronom]s usually express diff]5ces ( longitude 9 h\rs in/ead ( degrees4 #a;h4 #ae4 ,! "n giv5 to any k9d ( "t %\ld di/+ui% all ! elem5ts :i* ent] into x--e4 g41 ,new ,york sid]eal "t means ! h\r angle ( ! v]nal equ9ox measur$ f ! m]idian ( ,new ,york1 ,*icago true sol> "t is ! h\r angle ( ! sun reckon$ f ! m]idian ( ,*icago1 etc4 ,illu/ration3 ,,fig4 #ca4--,longitude & "t ,illu/ration3 ,,fig4 #cb4--,/&>d "t4 #eg4 ,,/&>d ,,"t4--,! requirem5ts ( railroad traffic h l$ to ! use ?r\gh\t ! ,unit$ ,/ates & ,canada ( f\r /&>d times1 ea* ( :i* is a mean sol> "t "s integral numb] ( h\rs sl[] ?an ! "t ( ! m]idian pass+ ?r\gh ! ,royal ,obs]vatory at ,gre5wi*1 ,engl&4 ,ea/]n "t is #e h\rs sl[] ?an t ( ,gre5wi*4 ,c5tral #f ,m\nta9 #g ,pacific #h ,9 ,fig4 #cb ! brok5 l9es indicate r\ghly ! p>ts ( ! ,unit$ ,/ates & ,canada 9 :i* ^! sev]al k9ds ( "t are us$1 & illu/rate h[ irregul> are ! b\nd>ies ( ^! p>ts4 ,/&>d "t is s5t daily into all ( ! m important telegraph (fices ( ! ,unit$ ,/ates1 & s]ves to regulate wat*es & clocks1 to ! almo/ complete exclusion ( local "t4 #eh4 ,,to ,,det]m9e ,,! ,,longitude4--,) an ord9>y wat* obs]ve ! "t ( ! sun's transit ov] y\r local m]idian1 & correct ! obs]v$ "t = ! equation ( "t by means ( ! curve 9 ,fig4 #cj4 ,! diff]5ce betwe5 ! correct$ "t & #ab o'clock w be ! correction ( y\r wat* ref]r$ to local mean sol> "t4 ,comp>e y\r wat* ) ! "t signals 9 ! ne>e/ telegraph (fice & f9d its correction ref]r$ to /&>d "t4 ,! diff]5ce betwe5 ! two corrections is ! diff]5ce betwe5 y\r longitude & t ( ! /&>d m]idian4 ,n4 ,b4--,don't tamp] ) ! wat* by try+ to set x "r4 ,no h>m w be done if x is wrong1 provid$ y take due acc\nt ( ! correction z indicat$ above4 ,if ! correction ( ! wat* *ang$ betwe5 y\r obs]vation & ! comp>ison 9 ! telegraph (fice1 :at effect w\ld x h ^u ! longitude det]m9ation8 ,h[ c y avoid ?is effect8 #ei4 ,,*ronology4--,! ,c5tury ,diction>y def9es *ronology z ! sci5ce ( "t--t is1 ! me?od ( measur+ or comput+ "t by regul> divisions or p]iods accord+ to ! revolutions ( ! sun or moon4 ,we h already se5 t = ! measurem5t ( %ort int]vals ( "t ! day & its subdivisions--h\rs1 m9utes1 seconds--furni% a v complete & conv5i5t sy/em4 ,b = long] p]iods1 ext5d+ to hundr$s & ?\s&s ( days1 a l>g] unit ( "t is requir$1 & = ! mo/ "p ^! long] units h 9 all ages & among all peoples be5 bas$ ^u a/ronomical consid]ations4 ,b to ?is !re is "o m>k$ exception4 ,! week is a simple multiple ( ! day1 z ! dime is a multiple ( ! c5t1 & :ile x may h _h its orig9 9 ! *ang+ phases ( ! moon ?is is at be/ d\btful1 s9ce x does n foll[ ^! ) any consid]able accuracy4 ,if ! /ill long] units ( "t--! mon? & ! ye>--_h equally be5 made to consi/ ( an integral numb] ( days mu* confusion & misund]/&+ might h be5 avoid$1 & ! annals ( anci5t times w\ld h pres5t$ few] pitfalls to ! hi/orian ?an is n[ ! case4 ,! mon? is pla9ly connect$ ) ! motion ( ! moon among ! />s4 ,! ye> is1 ( c\rse1 bas$ ^u ! motion ( ! sun ?r\gh ! heav5s & ! *ange ( seasons :i* is ?us produc$2 al?\gh1 z commonly employ$1 x is n q ! same z ! "t requir$ by ! e>? to make "o complete revolution 9 its orbit4 ,?is "t ( "o revolution is call$ a sid]eal ye>1 :ile1 z we h already se5 9 ,*apt] ,v1 ! ye> :i* measures ! c\rse ( ! seasons is %ort] ?an ?is on acc\nt ( ! precession ( ! equ9oxes4 ,x is call$ a tropical ye> ) ref]5ce to ! circuit :i* ! sun makes f "o tropic to ! o!r & back aga94 ,we c readily und]/& :y primitive peoples %\ld adopt z units ( "t ^! natural p]iods1 b 9 s do+ !y incurr$ mu* ! same k9d ( difficulty t we %\ld exp]i5ce 9 try+ to use bo? ,engli% & ,am]ican money 9 ! ord9>y transactions ( life4 ,h[ _m doll>s make a p\nd /]l+8 ,h[ %all we make *ange ) ,engli% %ill+s & ,am]ican dimes1 etc48 ,h[ mu* is "o unit wor? 9 t]ms ( ! o!r8 ,"o ( ! ,greek poets#b has left u a qua9t acc\nt ( ! confusion :i* exi/$ 9 8 "t ) reg>d to ! place ( mon?s & moons 9 ! cal5d>3 ,! moon by u to y h] greet+ s5ds1 ,b bids u say t %e's an ill-us$ moon ,& takes x mu* amiss t y w /ill ,%uffle h] days & turn !m topsy-turvy1 ,s t :5 gods1 :o "k _! fea/ days well1 ,by y\r false c\nt are s5t home supp]less1 ,!y scold & /orm at h] = y\r neglect4 #b ,ari/ophanes1 ,! ,cl\ds1 ,:ewell's translation4 #fj4 ,,day1 ,,mon?1 ,,& ,,ye>4--,if ! day1 ! mon?1 & ! ye> are to be us$ concurr5tly1 x is necess>y to det]m9e h[ _m days are conta9$ 9 ! mon? & ye>1 & :5 ?is has be5 done by ! a/ronom] ! numb]s are f\nd to be v awkw>d & inconv5i5t = daily use2 & mu* ( ! hi/ory ( *ronology consi/s 9 an acc\nt ( ! v>i\s devices by :i* +5i\s m5 h s\ght to use integral numb]s to replace ! cumbr\s decimal fractions :i* foll[4 ,accord+ to ,pr(essor ,h>kness1 = ! epo* #aijj ,a4 ,d4-- ,"o tropical ye> #cfe4bdbaig mean sol> days4 #cfe;d4 #e;h4 #dhm4 #de4hs4 ,"o lunation #bi4ecjehh mean sol> days4 #bi;d4 #ab;h4 #ddm4 #b4hs4 ,! ^w lunation means ! av]age int]val f "o new moon to ! next "o--i4 e41 ! "t requir$ by ! moon to g f conjunction ) ! sun r\nd to conjunction aga94 ,a v anci5t device 0 to call a ye> equal to #cfe days1 & to h mon?s alt]nately ( #bi & #cj days 9 l5g?1 b ?is 0 unsatisfactory 9 m ?an "o way4 ,at ! end ( f\r ye>s ?is artificial cal5d> w\ld be ab\t "o day ahead ( ! true "o1 at ! end ( =ty ye>s t5 days 9 error1 & )9 a s+le lifetime ! seasons w\ld h appreciably *ang$ _! position 9 ! ye>1 ,april wea!r be+ due 9 ,m>*1 accord+ to ! cal5d>4 ,s1 too1 ! ye> "u ?is arrangem5t did n consi/ ( any integral numb] ( mon?s1 #ab mon?s ( ! av]age l5g? ( #bi4e days be+ #ced days1 & #ac mon?s #chc4e days1 ?us mak+ any p>ticul> mon? *ange its position f ! beg9n+ to ! middle & ! end ( ! ye> )9 a comp>atively %ort "t4 ,"s peoples gave up ! a/ronomical ye> z an indep5d5t unit & adopt$ a conv5tional ye> ( #ab lun> mon?s1 #ced days1 :i* is n[ 9 use 9 c]ta9 ,mohamm$an c\ntries1 :]e x is kn[n z ! w&]+ ye>1 ) ref]5ce to ! *ang+ positions ( ! seasons 9 su* a ye>4 ,o!rs held to ! a/ronomical ye> & adopt$ a sy/em ( conv5tional mon?s1 su* t twelve ( !m w\ld j make up a ye>1 z is done to ?is day 9 our own cal5d>1 ^: mon?s ( arbitr>y l5g? we are compell$ to rememb] by "s su* j+le z ! foll[+3 ,?irty days ha? ,septemb]1 ,april1 ,june1 & ,novemb]2 ,all ! re/ h ?irty-"o ,save ,febru>y1 ,:i* alone ha? tw5ty-eight1 ,till leap ye> gives x tw5ty-n9e4 #fa4 ,,! ,,cal5d>4--,! f\ndations ( our cal5d> may fairly be ascrib$ to ,julius ,cs>1 :o1 "u ! advice ( ! ,egyptian a/ronom] ,sosig9es1 adopt$ ! old ,egyptian device ( a leap ye>1 :]eby e f\r? ye> 0 to consi/ ( #cff days1 :ile ord9>y ye>s 7 only #cfe days long4 ,he also plac$ ! beg9n+ ( ! ye> at ! fir/ ( ,janu>y1 in/ead ( 9 ,m>*1 :]e x _h =m]ly be51 & gave 8 own "n1 ,julius1 to ! mon? :i* we n[ call ,july4 ,augu/ 0 aft]w>d nam$ 9 honor ( 8 successor1 ,augu/us4 ,! names ( ! e>li] mon?s ( ! ye> are drawn f ,roman my?ology2 ^? ( ! lat] mon?s1 ,septemb]1 ,octob]1 etc41 mean+ sev5? mon?1 eigh? mon?1 repres5t ! places ( ^! mon?s 9 ! ye>1 be=e ,cs>'s re=mation1 & also _! places 9 "s ( ! subsequ5t cal5d>s1 = ! wide/ div]sity ( practice exi/$ dur+ m$ival times ) reg>d to ! day on :i* ! new ye> %\ld beg91 ,*ri/mas1 ,ea/]1 ,m>* #be?1 & o!rs hav+ be5 employ$ at diff]5t times & places4 ,! sy/em ( leap ye>s introduc$ by ,cs> makes ! av]age l5g? ( a ye> #cfe4be days1 :i* diff]s by ab\t elev5 m9utes f ! true l5g? ( ! tropical ye>1 a diff]5ce s small t = ord9>y purposes no bett] approximation to ! true l5g? ( ! ye> ne$ be desir$4 ,b any deviation f ! true l5g?1 h[ev] small1 mu/ 9 ! c\rse ( "t %ift ! seasons1 ! v]nal & autumnal equ9ox1 to ano!r "p ( ! ye>1 & ! ecclesia/ical au?orities ( m$ival ,europe f\nd "h gr\nd = objection to ,cs>'s cal5d>1 s9ce ! great ,*ur* fe/ival ( ,ea/] has its date det]m9$ ) ref]5ce to ! v]nal equ9ox1 & ) ! lapse ( c5turies ,ea/] became m & m displac$ 9 ! cal5d>1 until ,pope ,gregory ,,xiii1 late 9 ! sixte5? c5tury1 decre$ ano!r re=mation1 :]eby t5 days 7 dropp$ f ! cal5d>1 ! day aft] ,m>* #aa? be+ call$ ,m>* #ba/1 to br+ back ! v]nal equ9ox to ! date on :i* x fell 9 ,a4 ,d4 #cbe1 ! "t ( ! ,c\ncil ( ,nica1 :i* ,gregory adopt$ z ! fundam5tal epo* ( 8 cal5d>4 ,! cal5d> hav+ ?us be5 br\ght back into agreem5t ) t ( old "t1 ,gregory purpos$ to keep x 9 su* agreem5t = ! future by modify+ ,cs>'s leap-ye> rule s t x %\ld run3 ,e ye> ^: numb] is divisible by #d %all be a leap ye> except ^? ye>s ^: numb]s are divisible by #ajj b n divisible by #djj4 ,^! latt] ye>s--e4 g41 #aijj--;are c\nt$ z common ye>s4 ,! cal5d> ?us alt]$ is call$ ,gregorian to di/+ui% x f ! old]1 ,julian cal5d>1 & x f\nd spe$y acceptance 9 ^? civiliz$ c\ntries ^: ,*ur* adh]$ to ,rome2 b ! ,prote/ant p[]s 7 sl[ to adopt x1 & x 0 introduc$ into ,engl& & h] ,am]ican colonies by act ( ,p>liam5t 9 ! ye> #ageb1 ne>ly two c5turies aft] ,gregory's "t4 ,9 ,russia ! ,julian cal5d> has rema9$ 9 common use to our own day1 b 9 comm]cial affairs x is !re cu/om>y to write ! date accord+ to bo? cal5d>s--e4 g41 ,july #d_/af1 & at ! pres5t "t /r5u\s ex]tions are mak+ 9 t c\ntry = ! adoption ( ! ,gregorian cal5d> to ! complete exclusion ( ! ,julian "o4 ,! ,julian & ,gregorian cal5d>s are frequ5tly repres5t$ by ! abbreviations ,o4 ,s4 & ,n4 ,s41 old /yle1 new /yle1 & z ! old] hi/orical dates are usually express$ 9 ,o4 ,s41 x is sometimes conv5i5t to trans=m a date f ! "o cal5d> to ! o!r4 ,?is is readily done by ! =mula ,g ,j 7,n - #b7 - ,n_/#d1 :]e ,g & ,j are ! respective dates1 ,n is ! numb] ( ! c5tury1 & ! rema9d] is to be neglect$ 9 ! division by #d4 ,= ,septemb] #c1 #ageb1 ,o4 ,s41 we h ,j ,sept4 #c ,n - #b #ae - ,n_/#d - #d ------------------ ,g ,sept4 #ad & ,septemb] #ad is ! date fix$ by act ( ,p>liam5t to correspond to ,septemb] #c1 #ageb1 ,o4 ,s4 ,columbus discov]$ ,am]ica on ,octob] #ab1 #adib1 ,o4 ,s4 ,:at is ! correspond+ date 9 ! ,gregorian cal5d>8 #fb4 ,,! ,,day ,,( ,,! ,,week4--,a problem simil> to ! above b m complicat$ consi/s 9 f9d+ ! day ( ! week on :i* any giv5 date ( ! ,gregorian cal5d> falls--e4 g41 ,octob] #ba1 #adib4 ,! =mula = ?is case is #gq r ,y ,d 7,y - #a7_/d - 7,y - #a7_/ajj 7,y - #a7_/djj :]e ,y d5otes ! giv5 ye>1 ,d ! numb] ( ! day 7date7 9 t ye>1 & q & r are respectively ! quoti5t & ! rema9d] obta9$ by divid+ ! second memb] ( ! equation by #g4 ,if r #a ! date falls on ,sunday1 etc41 & if r #j ! day is ,saturday4 ,= ! example sugge/$ above we h ,jan4 #ca ,feb4 #bi ,m*4 #ca ,april #cj ,may #ca ,june #cj ,july #ca ,aug4 #ca ,sept4 #cj ,oct4 #ba --- ,d #bie ,y #adib ,d #bie 7,y - #a7 #d #cgb - 7,y - #a7 #ajj - #ad 7,y - #a7 #djj #c ------- #g7 #badh q #cjf r #f ,friday4 ,f9d f "s hi/ory ! day ( ! week on :i* ,columbus fir/ saw ,am]ica1 & comp>e ?is ) ! above4 ,on :at day ( ! week did la/ ,*ri/mas fall8 ,on :at day ( ! week 7 y born8 ,9 ! =mula = ! day ( ! week :y does q h ! coeffici5t #g8 ,:at pr9ciples 9 ! cal5d> give rise to ! divisors #d1 #ajj1 #djj8 ,= mu* curi\s & int]e/+ in=mation ab\t me?ods ( reckon+ ! lapse ( "t ! /ud5t may consult ! articles ,cal5d> & ,*ronology 9 any good encyclopdia4 ,illu/ration3 ,,! ,,y]kes ,,obs]vatory1 ,,williams ,,bay1 ,,wis4 ,,*apt] ,,vii ,,eclipses #fc4 ,,! ,,nature ,,( ,,eclipses4--,e planet has a %ad[ :i* travels ) ! planet along its orbit1 always po9t+ directly away f ! sun1 & cutt+ (f f a c]ta9 region ( space ! sunlight :i* o!rwise w\ld fill x4 ,= ! mo/ "p ^! %ad[s are invisible1 b occasionally "o ( !m falls ^u a planet or "s o!r body :i* %9es by reflect$ sunlight1 &1 cutt+ (f its supply ( light1 produces ! /rik+ ph5om5on :i* we call an eclipse4 ,! satellites ( ,jupit]1 ,saturn1 & ,m>s are eclips$ :5ev] !y plunge into ! %ad[s ca/ by _! respective planets1 & ,jupit] himself is p>tially eclips$ :5 "o ( 8 own satellites passes betwe5 him & ! sun1 & ca/s ^u 8 broad surface a %ad[ too small to cov] m ?an a fraction ( x4 ,b ! eclipses ( mo/ int]e/ to u are ^? ( ! sun & moon1 call$ respectively sol> & lun> eclipses4 ,9 ,fig4 #cc ! full moon1 ,m1 is %[n imm]s$ 9 ! %ad[ ca/ by ! e>?1 & !re=e eclips$1 & 9 ! same figure ! new moon1 ,m1 is %[n z ca/+ its %ad[ ^u ! e>? & produc+ an eclipse ( ! sun4 ,f a m]e inspection ( ! figure we may le>n t an eclipse ( ! sun c occur only at new moon--i4 e41 :5 ! moon is on l9e betwe5 ! e>? & sun--& an eclipse ( ! moon c occur only at full moon4 ,:y8 ,also1 ! eclips$ moon1 ,m1 w pres5t sub/antially ! same appe>ance f e "p ( ! e>? :]e x is at all visible--! same f ,nor? ,am]ica z f ,s\? ,am]ica--b ! eclips$ sun w pres5t v diff]5t aspects f diff]5t p>ts ( ! e>?4 ,?us1 at ,l1 )9 ! moon's %ad[1 ! sunlight w be entirely cut (f1 produc+ :at is call$ a total eclipse4 ,at po9ts ( ! e>?'s surface ne> ,j & ,k !re w be no int]f]5ce :atev] ) ! sunlight1 & no eclipse1 s9ce ! moon is q (f ! l9e jo9+ ^! regions to any "p ( ! sun4 ,at places betwe5 ,j & ,l or ,k & ,l ! moon w cut (f a "p ( ! sun's light1 b n all ( x1 & w produce :at is call$ a p>tial eclipse1 :i*1 z se5 f ! nor!rn p>ts ( ! e>?1 w be an eclipse ( ! l[] 7s\!rn7 "p ( ! sun1 & z se5 f ! s\!rn hemisph]e w be an eclipse ( ! nor!rn "p ( ! sun4 ,illu/ration3 ,,fig4 #cc4--;,diff]5t k9ds ( eclipse4 ,! moon revolves ar\nd ! e>? 9 a plane1 :i*1 9 ! figure1 we suppose to be p]p5dicul> to ! surface ( ! pap]1 & to pass ?r\gh ! sun along ! l9e ,m ,m produc$4 ,b x frequ5tly happ5s t ?is plane is turn$ to "o side ( ! sun1 along "s su* l9e z ,p ,q1 & 9 ?is case ! full moon w\ld cut ?r\gh ! edge ( ! e>?'s %ad[ )\t be+ at any "t :olly imm]s$ 9 x1 giv+ a p>tial eclipse ( ! moon1 z is %[n 9 ! figure4 ,9 :at p>ts ( ! e>? w\ld ?is eclipse be visible8 ,:at k9ds ( sol> eclipse w\ld be produc$ by ! new moon at ,q8 ,9 :at p>ts ( ! e>? w\ld !y be visible8 #fd4 ,,! ,,%ad[ ,,cone4--,! %ape & position ( ! e>?'s %ad[ are indicat$ 9 ,fig4 #cc by ! l9es drawn tang5t to ! circles :i* repres5t ! sun & e>?1 s9ce x is only betwe5 ^! l9es t ! e>? int]f]es ) ! free radiation ( sunlight1 & s9ce bo? sun & e>? are sph]es1 & ! e>? is mu* ! small] ( ! two1 x is evid5t t ! e>?'s %ad[ mu/ be1 9 geometrical language1 a cone ^: base is at ! e>?1 & ^: v]tex lies f> to ! "r ( ! figure--9 o!r words1 ! e>?'s %ad[1 al?\gh v long1 tap]s (f f9ally to a po9t & ends4 ,s1 too1 ! %ad[ ( ! moon is a cone1 hav+ its base at ! moon & its v]tex turn$ away f ! sun1 &1 z %[n 9 ! figure1 j ab\t long en\gh to rea* ! e>?4 ,x is easily %[n1 by ! !orem ( simil> triangles 9 connection ) ! kn[n size ( ! e>? & sun1 t ! di/ance f ! c5t] ( ! e>? to ! v]tex ( its %ad[ is always equal to ! di/ance ( ! e>? f ! sun divid$ by #ajh1 &1 simil>ly1 t ! l5g? ( ! moon's %ad[ is equal to ! di/ance ( ! moon f ! sun divid$ by #djj1 ! moon's %ad[ be+ ! small] & %ort] ( ! two1 because ! moon is small] ?an ! e>?4 ,! radius ( ! moon's orbit is j ab\t #a_/djj? "p ( ! radius ( ! e>?'s orbit--i4 e41 ! di/ance ( ! moon f ! e>? is #a_/djj? "p ( ! di/ance ( ! e>? f ! sun1 & x is ?is *ance agreem5t betwe5 ! l5g? ( ! moon's %ad[ & ! di/ance ( ! moon f ! e>? :i* makes ! tip ( ! moon's %ad[ fall v ne> ! e>? at ! "t ( sol> eclipses4 ,inde$1 ! elliptical %ape ( ! moon's orbit produces consid]able v>iations 9 ! di/ance ( ! moon f ! e>?1 & 9 consequ5ce ( ^! v>iations ! v]tex ( ! %ad[ sometimes falls %ort ( rea*+ ! e>?1 & sometimes ev5 projects consid]ably beyond its f>!r side4 ,:5 ! moon's di/ance is too great = ! %ad[ to bridge ! space betwe5 e>? & moon !re c be no total eclipse ( ! sun1 = !re is no %ad[ :i* c fall ^u ! e>?1 ev5 ?\gh ! moon does come directly betwe5 e>? & sun4 ,b !re is !n produc$ a peculi> k9d ( p>tial eclipse call$ annul>1 or r+-%ap$1 because ! moon1 al?\gh eclips+ ! c5tral p>ts ( ! sun1 is n l>ge en\gh to cov] ! :ole ( x1 b leaves ! sun's edge visible z a r+ ( light1 :i* completely surr\nds ! moon4 ,al?\gh1 /rictly speak+1 ?is is only a p>tial eclipse1 x is cu/om>y to put total & annul> eclipses toge!r 9 "o class1 :i* is call$ c5tral eclipses1 s9ce 9 ^! eclipses ! l9e ( c5t]s ( sun & moon /rikes ! e>?1 :ile 9 ord9>y p>tial eclipses x passes to "o side ( ! e>? )\t /rik+ x4 ,9 ?is latt] case we h to consid] ano!r cone call$ ! p5umbra--i4 e41 p>tial %ad[--:i* is %[n 9 ,fig4 #cc by ! brok5 l9es tang5t to ! sun & moon1 & cross+ at ! po9t ,v1 :i* is ! v]tex ( ?is cone4 ,?is p5umbral cone includes )9 its surface all t region ( space )9 :i* ! moon cuts (f any ( ! sunlight1 & ( c\rse x includes ! %ad[ cone :i* produces total eclipses4 ,:]ev] ! p5umbra falls !re w be a sol> eclipse ( "s k9d1 & ! ne>] ! place is to ! axis ( ! p5umbra1 ! m ne>ly total w be ! eclipse4 ,s9ce ! moon /&s ab\t midway betwe5 ! e>? & ! v]tex ( ! p5umbra1 ! diamet] ( ! p5umbra :]e x /rikes ! e>? w be ab\t twice z great z ! diamet] ( ! moon1 & ! /ud5t %\ld be able to %[ f ?is t ! region ( ! e>?'s surface )9 :i* a p>tial sol> eclipse is visible ext5ds 9 a /raight l9e ab\t #b1ajj miles on ei!r side ( ! region :]e ! eclipse is total4 ,measur$ along ! curv$ surface ( ! e>?1 ?is di/ance is frequ5tly mu* great]4 ,is x true t if at any "t ! axis ( ! %ad[ cone comes )9 #b1ajj miles ( ! e>?'s surface a p>tial eclipse w be visible 9 ^? p>ts ( ! e>? ne>e/ ! axis ( ! %ad[8 #fe4 ,,diff]5t ,,*>act]i/ics ,,( ,,lun> ,,& ,,sol> ,,eclipses4--,"o m>k$ diff]5ce betwe5 lun> & sol> eclipses :i* has be5 already sugge/$1 may be le>n$ f ,fig4 #cc4 ,! full moon1 ,m1 w be se5 eclips$ f e "p ( ! e>? :]e x is visible at all at ! "t ( ! eclipse--t is1 f ! :ole night side ( ! e>?2 :ile ! eclips$ sun w be se5 eclips$ only f ^? p>ts ( ! day side ( ! e>? ^u :i* ! moon's %ad[ or p5umbra falls4 ,s9ce ! po9t ( ! %ad[ at be/ b little m ?an rea*es to ! e>?1 ! am\nt ( space ^u ! e>? :i* x c cov] at any "o mom5t is v small1 seldom m ?an #ajj to #bjj miles 9 l5g?1 & x is only )9 ! space ?us actually cov]$ by ! %ad[ t ! sun is at any giv5 mom5t totally eclips$1 b )9 ?is region ! sun disappe>s1 absolutely1 beh9d ! solid body ( ! moon1 leav+ to view only su* outly+ p>ts & app5dages z are too l>ge = ! moon to cov]4 ,at a lun> eclipse1 on ! o!r h&1 ! e>? com+ betwe5 sun & moon cuts (f ! light f ! latt]1 b1 curi\sly en\gh1 does n cut x (f s completely t ! moon disappe>s altoge!r f sight ev5 9 mid-eclipse4 ,! explanation ( ?is cont9u$ visibility is furni%$ by ! brok5 l9es ext5d+1 9 ,fig4 #cc1 f ! e>? ?r\gh ! moon4 ,^! repres5t sunlight1 :i*1 ent]+ ! e>?'s atmosph]e ne> ! edge ( ! e>? 7edge z se5 f sun & moon71 passes ?r\gh x & em]ges 9 a *ang$ direction1 refract$1 into ! %ad[ cone & feebly illum9es ! moon's surface ) a ruddy light l t (t5 %[n 9 our r$ sunsets4 ,eclipse & sunset alike %[ t :5 ! sun's light %9es ?r\gh d5se lay]s ( air x is ! r$ rays :i* come ?r\gh mo/ freely1 & ! att5tive obs]v] may (t5 see at a cle> sunset some?+ :i* corresponds exactly to ! b5d+ ( ! sunlight into ! %ad[ cone2 j be=e ! sun rea*es ! horizon its disk is di/ort$ f a circle into an oval ^: horizontal diamet] is long] ?an ! v]tical "o 7see #ej74 ,,qu]y4--,at a total lun> eclipse :at w\ld be ! effect ^u ! appe>ance ( ! moon if ! atmosph]e ar\nd ! edge ( ! e>? 7 heavily lad5 ) cl\ds8 #ff4 ,,! ,,track ,,( ,,! ,,%ad[4--,we may reg>d ! moon's %ad[ cone z a huge p5cil atta*$ to ! moon1 mov+ ) x along its orbit 9 ! direction ( ! arr[head 7,fig4 #cd71 & z x moves draw+ a black l9e across ! face ( ! e>? at ! "t ( total eclipse4 ,?is black l9e is ! pa? ( ! %ad[ & m>ks out ^? regions )9 :i* ! eclipse w be total at "s /age ( its progress4 ,if ! po9t ( ! %ad[ j rea*es ! e>? its trace w h no s5sible wid?1 :ile1 if ! moon is ne>]1 ! po9t ( ! cone w be brok5 (f1 &1 l a blunt p5cil1 x w draw a broad /reak across ! e>?1 & ?is "u ! mo/ favorable circum/ances may h a bread? ( a little m ?an #afj miles & a l5g? ( #aj1jjj or #ab1jjj miles4 ,! /ud5t %\ld be able to %[ f ! kn[n di/ance ( ! moon 7#bdj1jjj miles7 & ! kn[n int]val betwe5 consecutive new moons 7#bi4e days7 t on ! av]age ! moon's %ad[ sweeps pa/ ! e>? at ! rate ( #b1ajj miles p] h\r1 & t 9 a g5]al way ?is motion is f we/ to ea/1 s9ce t is ! direction ( ! moon's motion 9 its orbit4 ,! actual velocity ) :i* ! moon's %ad[ moves pa/ a giv5 /ation may1 h[ev]1 be consid]ably great] or less ?an ?is1 s9ce on ! "o h& :5 ! %ad[ falls v obliquely1 z :5 ! eclipse occurs ne> sunrise or sunset1 ! %ift+ ( ! %ad[ w be v mu* great] ?an ! actual motion ( ! moon :i* produces x1 & on ! o!r h& ! e>? 9 revolv+ ^u its axis c>ries ! spectator & ! gr\nd ^u :i* he /&s along ! same direction 9 :i* ! %ad[ is mov+4 ,at ! equator1 ) ! sun & moon ov]head1 ?is motion ( ! e>? subtracts ab\t #a1jjj miles p] h\r f ! velocity ) :i* ! %ad[ passes by4 ,x is *iefly on ?is acc\nt1 ! dim9i%$ velocity ) :i* ! %ad[ passes by1 t total sol> eclipses la/ long] 9 ! tropics ?an 9 high] latitudes1 b ev5 "u ! mo/ favorable circum/ances ! duration ( totality does n rea* eight m9utes at any "o place1 al?\gh x may take ! %ad[ sev]al h\rs to sweep ! entire l5g? ( its pa? across ! e>?4 ,accord+ to ,:itmell ! greate/ possible duration ( a total sol> eclipse is #gm4 #djs41 & x c atta9 ?is limit only :5 ! eclipse occurs ne> ! beg9n+ ( ,july & is visible at a place #e nor? ( ! equator4 ,! duration ( a lun> eclipse dep5ds ma9ly ^u ! position ( ! moon ) respect to ! e>?'s %ad[4 ,if x /rikes ! %ad[ c5trally1 z at ,m1 ,fig4 #cc1 a total eclipse may la/ = ab\t two h\rs1 ) an additional h\r at ! beg9n+ & end1 dur+ :i* ! moon is ent]+ & leav+ ! e>?'s %ad[4 ,if ! moon meets ! %ad[ at "o side ( ! axis1 z at ,p1 ! total phase ( ! eclipse may fail altoge!r1 & betwe5 ^! extremes ! duration ( totality may be any?+ f two h\rs d[nw>d4 ,illu/ration3 ,,fig4 #cd4--,relation ( ! lun> nodes to eclipses4 #fg4 ,,relation ,,( ,,! ,,lun> ,,nodes ,,to ,,eclipses4--,to %[ :y ! moon sometimes enc\nt]s ! e>?'s %ad[ c5trally & m frequ5tly at full moon passes by )\t t\*+ x at all1 we resort to ,fig4 #cd1 :i* repres5ts a "p ( ! orbit ( ! e>? ab\t ! sun1 ) dates %[+ ! "t 9 ea* ye> at :i* ! e>? passes ! "p ( its orbit ?us m>k$4 ,! orbit ( ! moon ab\t ! e>?1 ,m ,m1 is also %[n1 ) ! new moon1 ,m1 ca/+ its %ad[ t[>d ! e>? & ! full moon1 ,m1 app>5tly imm]s$ 9 ! e>?'s %ad[4 ,b "h appe>ances are deceptive1 & ! /ud5t :o has made ! obs]vations set =? 9 ,*apt] ,,iii has le>n$ = himself a fact ( :i* c>eful acc\nt mu/ n[ be tak54 ,! app>5t pa?s ( ! moon & sun among ! />s are great circles :i* lie ne> ea* o!r1 b are n exactly ! same2 & s9ce ^! great circles are only ! int]sections ( ! sky ) ! planes ( ! e>?'s orbit & ! moon's orbit1 we see t ^! planes are slightly incl9$ to ea* o!r & mu/ !re=e int]sect along "s l9e pass+ ?r\gh ! c5t] ( ! e>?4 ,?is l9e1 ,n ,n1 is %[n 9 ! figure1 & if we suppose ! surface ( ! pap] to repres5t ! plane ( ! e>?'s orbit1 we %all h to suppose ! moon's orbit to be tipp$ ar\nd ?is l9e1 s t ! left side ( ! orbit lies above & ! "r side bel[ ! surface ( ! pap]4 ,b s9ce ! e>?'s %ad[ lies 9 ! plane ( its orbit--i4 e41 9 ! surface ( ! pap]--! full moon ( ,m>*1 ,m1 mu/ h pass$ bel[ ! %ad[1 & ! new moon1 ,m1 mu/ h ca/ its %ad[ above ! e>?1 s t nei!r a lun> nor a sol> eclipse c\ld occur 9 t mon?4 ,b t[>d ! end ( ,may ! e>? & moon h rea*$ a position :]e ! l9e ,n ,n po9ts almo/ directly t[>d ! sun1 9 l9e ) ! %ad[ cones :i* hide x4 ,note t ! l9e ,n ,n rema9s v ne>ly p>allel to its orig9al position1 :ile ! e>? is mov+ along its orbit4 ,! full moon w n[ be v ne> ?is l9e & !re=e v close to ! plane ( ! e>?'s orbit1 if n actually 9 x1 & mu/ pass ?r\gh ! %ad[ ( ! e>? & be eclips$4 ,s also ! new moon w ca/ its %ad[ 9 ! plane ( ! ecliptic1 & ?is %ad[1 fall+ ^u ! e>?1 produc$ ! total sol> eclipse ( ,may #bh1 #aijj4 ,n ,n is call$ ! l9e ( nodes ( ! moon's orbit 7 #ci71 & ! two positions ( ! e>? 9 its orbit1 diametrically opposite ea* o!r1 at :i* ,n ,n po9ts exactly t[>d ! sun1 we %all call ! nodes ( ! lun> orbit4 ,/rictly speak+1 ! nodes are ^? po9ts ( ! sky aga9/ :i* ! moon's c5t] is project$ at ! mom5t :5 9 its orbital motion x cuts ?r\gh ! plane ( ! e>?'s orbit4 ,be>+ 9 m9d ^! def9itions1 we may cond5se mu* ( :at prec$es into ! proposition3 ,eclipses ( ei!r sun or moon c occur only :5 ! e>? is at or ne> "o ( ! nodes ( ! moon's orbit4 ,correspond+ to ^! positions ( ! e>? !re are 9 ea* ye> two seasons1 ab\t six mon?s ap>t1 at :i* times1 & at ^! only1 eclipses c occur4 ,?us 9 ! ye> #aijj ! e>? pass$ ^! two po9ts on ,june #b;d & ,novemb] #bd? respectively1 & ! foll[+ li/ ( eclipses :i* occurr$ 9 t ye> %[s t all ( !m 7 )9 a few days ( "o or ! o!r ( ^! dates3 ,eclipses ( ! ,ye> #aijj ,total sol> eclipse ,may #bh?4 ,p>tial lun> eclipse ,june #ab?4 ,annul> 7sol>7 eclipse ,novemb] #ba/4 #fh4 ,,eclipse ,,limits4--,if ! e>? is exactly at ! node at ! "t ( new moon1 ! moon's %ad[ w fall c5trally ^u x & w produce an eclipse visible )9 ! torrid zone1 s9ce ?is is t "p ( ! e>?'s surface ne>e/ ! plane ( its orbit4 ,if ! e>? is ne> b n at ! node1 ! new moon w /& a little nor? or s\? ( ! plane ( ! e>?'s orbit1 & its %ad[ w /rike ! e>? f>!r nor? or s\? ?an be=e1 produc+ an eclipse 9 ! temp]ate or frigid zones2 or ! %ad[ may ev5 pass entirely above or bel[ ! e>?1 produc+ no eclipse :atev]1 or at mo/ a p>tial eclipse visible ne> ! nor? or s\? pole4 ,j h[ _m days' motion ! e>? may be away f ! node & /ill p]mit an eclipse is %[n 9 ! foll[+ brief table ( eclipse limits1 z !y are call$3 ,sol> ,eclipse ,limits ,if at any new moon ! e>? is ,less ?an #aj days away f a node1 a c5tral eclipse is c]ta94 ,betwe5 #aj & #af days "s k9d ( eclipse is c]ta94 ,betwe5 #af & #ai days a p>tial eclipse is possible4 ,m ?an #ai days no eclipse is possible4 ,lun> ,eclipse ,limits ,if at any full moon ! e>? is ,less ?an #d days away f a node1 a total eclipse is c]ta94 ,betwe5 #d & #aj days "s k9d ( eclipse is c]ta94 ,betwe5 #aj & #ad days a p>tial eclipse is possible4 ,m ?an #ad days no eclipse is possible4 ,f ?is table ( eclipse limits we may draw "s int]e/+ conclusions ab\t ! frequ5cy ) :i* eclipses occur4 #fi4 ,,numb] ,,( ,,eclipses ,,9 ,a ,,ye>4--,:5ev] ! e>? passes a node ( ! moon's orbit a new moon mu/ occur at "s "t dur+ ! #b #af days t ! e>? rema9s inside ! limits :]e "s k9d ( eclipse is c]ta91 & !re mu/ !re=e be an eclipse ( ! sun e "t ! e>? passes a node ( ! moon's orbit4 ,b1 s9ce !re are two nodes pa/ :i* ! e>? moves at lea/ once 9 ea* ye>1 !re mu/ be at lea/ two sol> eclipses e ye>4 ,c !re be m ?an two8 ,on ! av]age1 w c5tral or p>tial eclipses be ! m num]\s8 ,a simil> l9e ( reason+ w n hold true = eclipses ( ! moon1 s9ce x is q possible t no full moon %\ld occur dur+ ! #bj days requir$ by ! e>? to move pa/ ! node f ! we/]n to ! ea/]n limit4 ,?is omission ( a full moon :ile ! e>? is )9 ! eclipse limits sometimes happ5s at bo? nodes 9 ! same ye>1 & !n we h a ye> ) no eclipse ( ! moon4 ,! /ud5t may note 9 ! li/ ( eclipses = #aijj t ! p>tial lun> eclipse ( ,june #ab? occurr$ #aj days aft] ! e>? pass$ ! node1 & 0 !re=e )9 ! d\btful zone :]e eclipses may occur & may fail1 & correspond+ to ?is position ! eclipse 0 a v small "o1 only a ?\s&? "p ( ! moon's diamet] dipp+ into ! %ad[ ( ! e>?4 ,by s mu* ! ye> #aijj escap$ be+ an illu/ration ( a ye> 9 :i* no lun> eclipse occurr$4 ,a p>tial eclipse ( ! moon w usually occur ab\t a =tnight be=e or aft] a total eclipse ( ! sun1 s9ce ! full moon w !n be )9 ! eclipse limit at ! opposite node4 ,a p>tial eclipse ( ! sun w always occur ab\t a =tnight be=e or aft] a total eclipse ( ! moon4 ,illu/ration3 ,,fig4 #ce4--,! eclipse ( ,may #bh1 #aijj4 #gj4 ,,eclipse ,,maps4--,x is ! cu/om ( a/ronom]s to prep>e1 9 advance ( ! m important eclipses1 maps %[+ ! trace ( ! moon's %ad[ across ! e>?1 & indicat+ ! times ( beg9n+ & end+ ( ! eclipses1 z is %[n 9 ,fig4 #ce4 ,:ile ! actual con/ruction ( su* a map requires mu* te*nical k1 ! pr9ciples involv$ are simple en\gh3 ! /raight l9e pass$ ?r\gh ! c5t] ( sun & moon is ! axis ( ! %ad[ cone1 & ! map conta9s little m ?an a graphical repres5tation ( :5 & :]e ?is cone meets ! surface ( ! e>?4 ,?us 9 ! map1 ! ,pa? ( ,total ,eclipse is ! trace ( ! %ad[ cone across ! face ( ! e>?1 & ! wid? ( ?is pa? %[s t ! e>? enc\nt]$ ! %ad[ consid]ably inside ! v]tex ( ! cone4 ,! g5]al direction ( ! pa? is f we/ to ea/1 & ! slight s9u\sities :i* x pres5ts are = ! mo/ "p due to unavoidable di/ortion ( ! map caus$ by ! attempt to repres5t ! curv$ surface ( ! e>? ^u ! flat surface ( ! pap]4 ,on ei!r side ( ! ,pa? ( ,total ,eclipse is ! region )9 :i* ! eclipse 0 only p>tial1 & ! brok5 l9es m>k$ ,beg9s at #c;h41 ,ends at #c;h41 %[ ! int]section ( ! p5umbral cone ) ! surface ( ! e>? at #c ,p4 ,m41 ,gre5wi* "t4 ,^! two l9es inclose e "p ( ! e>?'s surface f :i* at t "t any eclipse :atev] c\ld be se51 & at ?is mom5t ! p>tial eclipse 0 j beg9n+ at e po9t on ! ea/]n edge ( ! p5umbra & j end+ at e po9t on ! we/]n edge1 :ile at ! c5t] ( ! p5umbra1 on ! ,pa? ( ,total ,eclipse1 lay ! %ad[ ( ! moon1 an oval pat* ^: greate/ diamet] 0 b little m ?an #fj miles 9 l5g?1 & )9 :i* lay e "p ( ! e>? :]e ! eclipse 0 total at t mom5t4 ,! position ( ! p5umbra at o!r h\rs is also %[n on ! map1 al?\gh ) m di/ortion1 because x !n meets ! surface ( ! e>? m obliquely1 & f ^! l9es x is easy to obta9 ! "t ( beg9n+ & end ( ! eclipse at any desir$ place1 & to e/imate by ! di/ance ( ! place f ! ,pa? ( ,total ,eclipse h[ mu* ( ! sun's face 0 obscur$4 ,let ! /ud5t make ^! pr$ictions = ,wa%+ton1 ,*icago1 ,london1 & ,algi]s4 ,! po9ts 9 ! map m>k$ ,fir/ ,contact1 ,la/ ,contact1 %[ ! places at :i* ! p5umbral cone fir/ t\*$ ! e>? & f9ally left x4 ,accord+ to computations made z a basis = ! con/ruction ( ! map ! ,gre5wi* "t ( ,fir/ ,contact 0 #j;h4 #ab4em4 & ( ,la/ ,contact #e;h4 #ce4fm41 & ! diff]5ce betwe5 ^! two times gives ! total duration ( ! eclipse ^u ! e>?--i4 e41 #e h\rs #bc4a m9utes4 ,illu/ration3 ,,fig4 #cf4--;,c5tral eclipses = ! fir/ two decades ( ! tw5tie? c5tury4 ,,oppolz]4 #ga4 ,,future ,,eclipses4--,an eclipse map ( a diff]5t k9d is %[n 9 ,fig4 #cf1 :i* repres5ts ! %ad[ pa?s ( all ! c5tral eclipses ( ! sun1 visible dur+ ! p]iod #aijj-aiah ,a4 ,d41 9 ^? p>ts ( ! e>? nor? ( ! s\? temp]ate zone4 ,ea* cont9u\s black l9e %[s ! pa? ( ! %ad[ 9 a total eclipse1 f its beg9n+1 at sunrise1 at ! we/]n end ( ! l9e to its end1 sunset1 at ! ea/]n end1 ! little circle ne> ! middle ( ! l9e %[+ ! place at :i* ! eclipse 0 total at noon4 ,! brok5 l9es repres5t simil> data = ! annul> eclipses4 ,?is map is "o ( a s]ies prep>$ by ! ,au/rian a/ronom]1 ,oppolz]1 %[+ ! pa? ( e su* eclipse f ! ye> #abjj ,b4 ,c4 to #bafj ,a4 ,d41 a p]iod ( m ?an ?ree ?\s& ye>s4 ,if we exam9e ! dates ( ! eclipses %[n 9 ?is map we %all f9d t !y are n limit$ to ! p>ticul> seasons1 ,may & ,novemb]1 9 :i* ^? ( ! ye> #aijj occurr$1 b are scatt]$ ?r\gh all ! mon?s ( ! ye>1 f ,janu>y to ,decemb]4 ,?is %[s at once t ! l9e ( nodes1 ,n ,n1 ( ,fig4 #cd1 does n rema9 9 a fix$ position1 b turns r\nd 9 ! plane ( ! e>?'s orbit s t 9 diff]5t ye>s ! e>? rea*es ! node 9 diff]5t mon?s4 ,! precession has already furni%$ u an illu/ration ( a simil> *ange1 ! sl[ rotation ( ! e>?'s axis1 produc+ a correspond+ %ift+ ( ! l9e 9 :i* ! planes ( ! equator & ecliptic int]sect2 & 9 mu* ! same way1 ?r\gh ! di/urb+ influ5ce ( ! sun's attraction1 ! l9e ,n ,n is made to revolve we/w>d1 opposite to ! arr[heads 9 ,fig4 #cd1 at ! rate ( ne>ly #bj p] ye>1 s t ! e>? comes to ea* node ab\t #ai days e>li] 9 ea* ye> ?an 9 ! ye> prec$+1 & ! eclipse season 9 ea* ye> comes on ! av]age ab\t #ai days e>li] ?an 9 ! ye> be=e1 al?\gh !re is a good deal ( irregul>ity 9 ! am\nt ( *ange 9 p>ticul> ye>s4 #gb4 ,,recurr5ce ,,( ,,eclipses4--,be=e ! beg9n+ ( ! ,*ri/ian era a/ronom]s _h f\nd out a r\gh-&-ready me?od ( pr$ict+ eclipses1 :i* is /ill ( int]e/ & value4 ,! sub/ance ( ! me?od is t if we />t ) any eclipse :atev]--e4 g41 ! eclipse ( ,may #bh1 #aijj--;& reckon =w>d or backw>d f t date a p]iod ( #ah ye>s & #aj or #aa days1 we %all f9d ano!r eclipse q simil> 9 its g5]al *>act]i/ics to ! "o ) :i* we />t$4 ,?us1 f ! map ( eclipses 7,fig4 #cf71 we f9d t a total sol> eclipse w occur on ,june #h1 #aiah1 #ah ye>s & #aa days aft] ! "o illu/rat$ 9 ,fig4 #ce4 ,?is p]iod ( #ah ye>s & #aa days is call$ s>os1 an anci5t ^w :i* means cycle or repetition1 & s9ce e eclipse is repeat$ aft] ! lapse ( a s>os1 we may f9d ! dates ( all ! eclipses ( #aiah by add+ #aa days to ! dates giv5 9 ! table ( eclipses = #aijj 7 #fg71 & x is to be especially not$ t ea* eclipse ( #aiah w be l its pr$ecessor ( #aijj 9 "*--lun>1 sol>1 p>tial1 total1 etc4 ,! eclipses ( any ye> may be pr$ict$ by a simil> ref]5ce to ^? :i* occurr$ eighte5 ye>s e>li]4 ,consult a file ( old almanacs4 ,! exact l5g? ( a s>os is #bbc lun> mon?s1 ea* ( :i* is a little m ?an #bi4e days long1 & if we multiply ! exact value ( ?is la/ numb] 7see #fj7 by #bbc1 we %all f9d = ! product #f1ehe4cb days1 :i* is equal to #ah ye>s #aa4cb days :5 !re are f\r leap ye>s includ$ 9 ! #ah1 or #ah ye>s #aj4cb days :5 ! numb] ( leap ye>s is five2 & 9 apply+ ! s>os to ! pr$iction ( eclipses1 due he$ mu/ be paid to ! numb] ( int]v5+ leap ye>s4 ,to expla9 :y eclipses are repeat$ at ! end ( ! s>os1 we note t ! occurr5ce ( an eclipse dep5ds solely ^u ! relative positions ( ! e>?1 moon1 & node ( ! moon's orbit1 & ! eclipse w be repeat$ z (t5 z ^! ?ree come back to ! position :i* fir/ produc$ x4 ,?is happ5s at ! end ( e s>os1 s9ce ! s>os is1 approximately1 ! lea/ common multiple ( ! l5g? ( ! ye>1 ! l5g? ( ! lun> mon?1 & ! l5g? ( "t requir$ by ! l9e ( nodes to make a complete revolution ar\nd ! ecliptic4 ,if ! s>os 7 exactly a multiple ( ^! ?ree p]iods1 e eclipse w\ld be repeat$ ov] & ov] aga9 = ?\s&s ( ye>s2 b su* is n ! case1 ! s>os is n an exact multiple ( a ye>1 nor is x an exact multiple ( ! "t requir$ = a revolution ( ! l9e ( nodes1 & 9 consequ5ce ! re/itution :i* comes at ! end ( ! s>os is n a p]fect "o4 ,! e>? at ! #bbc;d new moon is 9 fact ab\t half a day's motion f>!r we/1 relative to ! node1 ?an x 0 at ! beg9n+1 & ! result+ eclipse1 :ile v simil>1 is n precisely ! same z be=e4 ,aft] ano!r #ah ye>s1 at ! second repetition1 ! e>? is a day f>!r f ! node ?an at fir/1 & ! eclipse diff]s /ill m 9 "*1 etc4 ,?is is %[n 9 ,fig4 #cg1 :i* repres5ts ! app>5t positions ( ! disks ( ! sun & moon z se5 f ! c5t] ( ! e>? at ! end ( ea* six? s>os1 #ajh ye>s1 :]e ! upp] r[ ( figures repres5ts ! numb] ( repetitions ( ! eclipse f ! beg9n+1 m>k$ #j1 to ! end1 #gb4 ,! sol> eclipse limits1 #aj1 #af1 #ai days1 are also %[n1 & all ^? eclipses :i* fall betwe5 ! #aj-;day limits w be c5tral z se5 f "s "p ( ! e>?1 ^? betwe5 #af & #ai p>tial :]ev] se51 :ile betwe5 #aj & #af !y may be ei!r total or p>tial4 ,comp>e ! figure ) ! foll[+ description giv5 by ,pr(essor ,newcomb3 ,a s]ies ( su* eclipses comm5ces ) a v small eclipse ne> "o pole ( ! e>?4 ,gradually increas+ = ab\t elev5 recurr5ces1 x w become c5tral ne> ! same pole4 ,=ty or m c5tral eclipses w !n recur1 ! c5tral l9e mov+ sl[ly t[>d ! o!r pole4 ,! s]ies w !n become p>tial1 & f9ally cease4 ,! entire duration ( ! s]ies w be m ?an a ?\s& ye>s4 ,a new s]ies comm5ces1 on ! av]age1 at int]vals ( ?irty ye>s4 ,illu/ration3 ,,fig4 #cg4--;,graphical illu/ration ( ! s>os4 ,a simil> figure may be con/ruct$ to repres5t ! recurr5ce ( lun> eclipses2 b "h1 9 consequ5ce ( ! small] eclipse limits1 we %all f9d t a s]ies is ( %ort] duration1 a little ov] eight c5turies z comp>$ ) twelve c5turies1 :i* is ! av]age duration ( a s]ies ( sol> eclipses4 ,"o fur!r matt] connect$ ) ! s>os des]ves att5tion4 ,dur+ ! p]iod ( #f1ehe4cb days ! e>? has #f1ehe times turn$ t[>d ! sun ! same face ^u :i* ! moon's %ad[ fell at ! beg9n+ ( ! s>os1 b at ! end ( ! s>os ! odd #j4cb ( a day gives ! e>? "t to make ab\t a ?ird ( a revolution m be=e ! eclipse is repeat$1 & 9 consequ5ce ! eclipse is se5 9 a diff]5t region ( ! e>?1 on ! av]age ab\t #aaf f>!r we/ 9 longitude4 ,comp>e 9 ,fig4 #cf ! regions 9 :i* ! eclipses ( #aijj & #aiah are visible4 ,is ?is *ange 9 ! region :]e ! repeat$ eclipse is visible1 true ( lun> eclipses z well z sol>8 #gc4 ,,use ,,( ,,eclipses4--,at all times & among all peoples eclipses1 & p>ticul>ly total eclipses ( ! sun1 h be5 reckon$ among ! mo/ impressive ph5om5a ( ,nature4 ,9 e>ly times & among uncultivat$ p !y 7 usually reg>d$ ) appreh5sion1 (t5 am\nt+ to a t]ror & fr5zy1 :i* civiliz$ travel]s h n scrupl$ to use = _! own purposes ) ! aid ( ! eclipse pr$ictions conta9$ 9 _! almanacs1 ?reat5+ at ! prop] "t to de/roy ! sun or moon1 & po9t+ to ! advanc+ eclipse z pro( t _! ?reats 7 n va94 ,9 our own day & our own l& ^! feel+s ( awe h n q disappe>$1 b = ! mo/ "p eclipses are n[ await$ ) an int]e/ & pleasure :i*1 contra/$ ) ! =m] feel+s ( mank9d1 furni% "o ( ! mo/ /rik+ illu/rations ( ! effect ( sci5tific k 9 trans=m+ human fe> & mis]y into a s5se ( security & enjoym5t4 ,b to ! a/ronom] an eclipse is m ?an a beautiful illu/ration ( ! work+ ( natural laws2 x is 9 v>y+ degree an opportunity ( add+ to 8 /ore ( k respect+ ! heav5ly bodies4 ,! region imm$iately surr\nd+ ! sun is at mo/ times clos$ to rese>* by ! bl9d+ gl>e ( ! sun's own light1 s t a planet z l>ge z ! moon might exi/ "h unse5 7 x n = ! occasional opportunity pres5t$ by a total eclipse :i* %uts (f ! excessive light & p]mits n only a se>* = unkn[n planets b = any?+ & ev]y?+ :i* may exi/ ar\nd ! sun4 ,m ?an "o a/ronom] has report$ ! discov]y ( su* planets1 & at lea/ "o ( ^! has f\nd a "n & a description 9 "s ( ! books1 b at ! pres5t "t mo/ a/ronom]s are v skeptical ab\t ! exi/5ce ( any su* object ( consid]able size1 al?\gh !re is "s reason to believe t an enorm\s numb] ( little bodies1 rang+ 9 size f gra9s ( s& upw>d1 d move 9 ?is region1 z yet unse5 & (f]+ to ! future problems = inve/igation4 ,b 9 o!r directions ! /udy ( ?is region at ! times ( total eclipse has yield$ f> l>g] returns1 & 9 ! *apt] on ! sun we %all h to consid] ! m>vel\s appe>ances pres5t$ by ! sol> prom95ces & by ! corona1 an app5dage ( ! sun :i* rea*es out f 8 surface = millions ( miles b is nev] se5 save at an eclipse4 ,photographs ( ! corona are tak5 by a/ronom]s at e opportunity1 & reproductions ( "s ( ^! may be f\nd 9 ,*apt] ,x4 ,annul> eclipses & lun> eclipses are ( comp>atively little consequ5ce1 b any record$ eclipse may become ( value 9 connection ) *ronology4 ,we date our lett]s 9 a p>ticul> ye> ( ! tw5tie? c5tury1 & commonly suppose t ! ye>s are reckon$ f ! bir? ( ,*ri/2 b ?is is an error1 = ! eclipses :i* 7 obs]v$ ( old & by ! *ronicl]s h be5 associat$ ) ev5ts ( 8 life1 :5 exam9$ by ! a/ronom]s are f\nd q inconsi/5t ) a/ronomic !ory4 ,!y are1 h[ev]1 reconcil$ ) x if we assume t our sy/em ( dates has its orig9 f\r ye>s aft] ! bir? ( ,*ri/1 or1 9 o!r words1 t ,*ri/ 0 born 9 ! ye> #d ,b4 ,c4 ,a mi/ake 0 d\btless made at ! "t ! ,*ri/ian era 0 introduc$ into *ronology4 ,at _m o!r po9ts ! *ance record ( an eclipse 9 ! e>ly annals ( civilization furni%es a simil> means ( controll+ & correct+ ! dates assign$ by ! hi/orian to ev5ts long pa/4 ,,*apt] ,,viii ,,in/rum5ts ,,& ,,! ,,pr9ciples ,,involv$ ,,9 ,,_! ,,use #gd4 ,,two ,,famili> ,,in/rum5ts4--,9 previ\s *apt]s we h se5 t a clock & a divid$ circle 7protractor7 are ne$$ = ! obs]vations :i* an a/ronom] makes1 & x is wor? :ile to note "h t ! geography ( ! sky & ! sci5ce ( cele/ial motions dep5d fundam5tally ^u ^! two in/rum5ts4 ,! protractor is a simple in/rum5t1 a humble memb] ( ! family ( divid$ circles1 b untold labor & +5uity h be5 exp5d$ on ?is family to make possible ! con/ruction ( a circle s accurately divid$ t ) x angles may be measur$ to ! t5? ( a second in/ead ( to ! t5? ( a degree--i4 e41 #c1fjj times z accurate z ! protractor furni%es4 ,! build+ ( a good clock is equally important & has co/ a l am\nt ( labor & pa9s1 s t x is a f> cry f ,galileo & 8 discov]y t a p5dulum keeps "t to ! mod]n clock ) its accurate con/ruction & elaborate provision aga9/ di/urb+ influ5ces ( e k9d4 ,e su* timepiece1 :e!r x be ( ! nutmeg v>iety :i* sells = a doll>1 or :e!r x be ! /&>d clock ( a great national obs]vatory1 is made up ( ! same ess5tial p>ts t fall naturally into f\r classes1 :i* we may comp>e ) ! dep>tm5ts ( a well-ord]$ factory3 ,i4 ,a timekeep+ dep>tm5t1 ! p5dulum or balance spr+1 ^: oscillations mu/ all be ( equal duration4 ,,ii4 ,a p[] dep>tm5t1 ! weights or ma9spr+1 :i*1 :5 w\nd1 /ore up ! p[] appli$ f outside & give x out piecemeal z requir$ to keep ! fir/ dep>tm5t runn+4 ,,iii4 ,a publication dep>tm5t1 ! dial & h&s1 :i* give out ! "t furni%$ by ,dep>tm5t ,i4 ,,iv4 ,a transportation dep>tm5t1 ! :eels1 :i* connect ! o!r ?ree & s]ve z a means ( transmitt+ p[] & "t f "o to ! o!r4 ,! case ( ei!r clock or wat* is m]ely ! ro( :i* %elt]s x & =ms no dep>tm5t ( its indu/ry4 ,( ^! dep>tm5ts ! fir/ is by f> ! mo/ important1 & its good or bad p]=mance makes or m>s ! cr$it ( ! clock4 ,bew>e ( m$dl+ ) ! balance :eel ( y\r wat*4 #ge4 ,,radiant ,,en]gy4--,b we h n[ to consid] o!r in/rum5ts :i* 9 practice supplem5t or displace ! simple app>atus hi!rto employ$4 ,among ! mo/ important ( ^! mod]n in/rum5ts are ! telescope1 ! spectroscope1 & ! photographic cam]a2 & s9ce all ^! in/rum5ts deal ) ! light :i* comes f ! />s to ! e>?1 we mu/ = _! prop] und]/&+ take acc\nt ( ! nature ( t light1 or1 m /rictly speak+1 we mu/ take acc\nt ( ! radiant en]gy emitt$ by ! sun & />s1 :i* en]gy1 com+ f ! sun1 is translat$ by our n]ves into ! two diff]5t s5sations ( light & heat4 ,! radiant en]gy :i* comes f ! />s is n fundam5tally diff]5t f t ( ! sun1 b ! am\nt ( en]gy furni%$ by any /> is s small t x is unable to produce ?r\gh our n]ves any s5sible p]ception ( heat1 & = ! same reason ! va/ majority ( />s are invisible to ! unaid$ eye2 !y d n furni% a suffici5t am\nt ( en]gy to affect ! optic n]ves4 ,a hot brick tak5 into ! h& reveals its pres5ce by ! two diff]5t s5sations ( heat & pressure 7weight72 b z !re is only "o brick to produce ! two s5sations1 s !re is only "o en]gy to produce ?r\gh its action ^u diff]5t n]ves ! two s5sations ( light & heat1 & ?is en]gy is call$ radiant because x appe>s to /ream =? radially f ev]y?+ :i* has ! capacity ( emitt+ x4 ,= ! detail$ /udy ( radiant en]gy ! /ud5t is ref]r$ to t bran* ( sci5ce call$ physics2 b "s ( its elem5t>y pr9ciples may be le>n$ ?r\gh ! foll[+ simple exp]im5t1 :i* ! /ud5t %\ld n fail to p]=m = himself3 ,drop a bullet or o!r simil> object into a bucket ( wat] & obs]ve ! circul> waves :i* spread f ! place :]e x ent]s ! wat]4 ,^! waves are a =m ( radiant en]gy1 b diff]+ f light or heat 9 t !y are visibly conf9$ to a s+le plane1 ! surface ( ! wat]1 in/ead ( fill+ ! entire surr\nd+ space4 ,by v>y+ ! size ( ! bucket1 ! dep? ( ! wat]1 ! weight ( ! bullet1 etc41 diff]5t k9ds ( waves1 big & little1 may be produc$2 b e su* set ( waves may be describ$ & def9$ 9 all its pr9cipal *>act]i/ics by means ( ?ree numb]s--viz41 ! v]tical height ( ! waves f holl[ to cre/2 ! di/ance ( "o wave f ! next2 & ! velocity ) :i* ! waves travel across ! wat]4 ,! la/ ( ^! quantities is call$ ! velocity ( propagation2 ! second is call$ ! wave l5g?2 "o half ( ! fir/ is call$ ! amplitude2 & all ^! t]ms f9d important applications 9 ! !ory ( light & heat4 ,! en]gy ( ! fall+ bullet1 ! di/urbance :i* x produc$ on ent]+ ! wat]1 0 c>ri$ by ! waves f ! c5t] to ! edge ( ! bucket b n beyond1 = ! wave c g only s f> z ! wat] ext5ds4 ,! transf] ( en]gy 9 ?is way requires a p]fectly cont9u\s m$ium ?r\gh :i* ! waves may travel1 & ! :ole visible univ]se is suppos$ to be fill$ ) some?+ call$ e!r1 :i* s]ves ev]y:]e z a m$ium = ! transmission ( radiant en]gy j z ! wat] 9 ! exp]im5t s]v$ z a m$ium = transmitt+ 9 waves ! en]gy furni%$ to x by ! fall+ bullet4 ,! /ud5t may ?9k ( ?is en]gy z be+ transmitt$ 9 sph]ical waves ?r\gh ! e!r1 e gl[+ body1 su* z a />1 a c&le flame1 an arc lamp1 a hot coal1 etc41 be+ ! orig9 & c5t] ( su* sy/ems ( waves1 & det]m9+ by its own physical & *emical prop]ties ! wave l5g? & amplitude ( ! wave sy/ems giv5 (f4 ,! int5sity ( any light dep5ds ^u ! amplitude ( ! correspond+ vibration1 & its color dep5ds ^u ! wave l5g?4 ,by +5i\s devices :i* ne$ n be "h describ$ x has be5 f\nd possible to measure ! wave l5g? correspond+ to diff]5t colors--e4 g41 all ( ! colors ( ! ra9b[1 & "s ( ^! wave l5g?s express$ 9 t5? met]s are z foll[s3 ,a t5? met] is ! l5g? obta9$ by divid+ a met] into #ajaj equal p>ts4 #ajaj #aj1jjj1jjj1jjj4 ,color4 ,wave l5g?4 ,extreme limit ( visible violet #c1ijj ,middle ( ! violet #d1jfj blue #d1gcj gre5 #e1bgj yell[ #e1haj orange #e1igj r$ #g1jjj ,extreme limit ( visible r$ #g1fjj ,illu/ration3 ,,plate ,i4 ,,! ,,nor!rn ,,con/ellations ,! phrase extreme limit ( visible violet or r$ us$ above mu/ be und]/ood to mean t 9 g5]al ! eye is n able to detect radiant en]gy hav+ a wave l5g? less ?an #c1ijj or great] ?an #g1fjj t5? met]s4 ,radiant en]gy1 h[ev]1 exi/s 9 waves ( bo? great] & %ort] l5g? ?an ! above1 & may be readily detect$ by app>atus n subject to ! limitations ( ! human eye--e4 g41 a common !rmomet] w %[ a rise ( temp]ature :5 its bulb is expos$ to radiant en]gy ( wave l5g? mu* great] ?an #g1fjj t5? met]s1 & a photographic plate w be /rongly affect$ by en]gy ( %ort] wave l5g? ?an #c1ijj t5? met]s4 #gf4 ,,reflection ,,& ,,cond5sation ,,( ,,waves4--,:5 ! waves produc$ by dropp+ a bullet into a bucket ( wat] meet ! sides ( ! bucket1 !y appe> to reb\nd & are reflect$ back t[>d ! c5t]1 & if ! bullet is dropp$ v ne> ! c5t] ( ! bucket ! reflect$ waves w meet simultane\sly at ?is po9t & produce !re by _! comb9$ action a wave high] ?an t :i* 0 reflect$ at ! walls ( ! bucket4 ,!re has be5 a cond5sation ( en]gy produc$ by ! reflection1 & ?is increas$ en]gy is %[n by ! great] amplitude ( ! wave4 ,! /ud5t %\ld n fail to notice t ea* portion ( ! wave has travel$ out & back ov] ! radius ( ! bucket1 & t !y meet simultane\sly at ! c5t] because ( ?is equality ( ! pa?s ov] :i* !y travel1 & ! result+ equality ( "t requir$ to g out & back4 ,if ! bullet 7 dropp$ at "o side ( ! c5t]1 w\ld ! reflect$ waves produce at any po9t a cond5sation ( en]gy8 ,if ! bucket 7 ( elliptical in/ead ( circul> cross section & ! bullet 7 dropp$ at "o focus ( ! ellipse !re w\ld be produc$ a cond5sation ( reflect$ en]gy at ! o!r focus1 s9ce ! sum ( ! pa?s trav]s$ by ea* portion ( ! wave be=e & aft] reflection is equal to ! sum ( ! pa?s trav]s$ by e o!r portion1 & all p>ts ( ! wave rea* ! second focus at ! same "t4 ,^u :at geometrical pr9ciple does ?is dep5d8 ,! cond5sation ( wave en]gy 9 ! circul> & elliptical buckets are special cases "u ! g5]al pr9ciple t su* a cond5sation w be produc$ at any po9t :i* is s plac$ t diff]5t p>ts ( ! wave front rea* x simultane\sly1 :e!r by reflection or by "s o!r means1 z %[n bel[4 ,! /ud5t w note t = ! sake ( great] precision we "h say wave front in/ead ( wave4 ,if 9 any wave we imag9e a l9e drawn along ! cre/1 s z to t\* e drop :i* at t mom5t is exactly at ! cre/1 we %all h :at is call$ a wave front1 & simil>ly a l9e drawn ?r\gh ! tr\gh betwe5 two waves1 or ?r\gh any set ( drops simil>ly plac$ on a wave1 con/itutes a wave front4 #gg4 ,,mirrors ,,& ,,l5ses4--,t =m ( radiant en]gy :i* we recognize z light & heat may be reflect$ & cond5s$ precisely z are ! waves ( wat] 9 ! ex]cise consid]$ above1 b ow+ to ! extreme %ortness ( ! wave l5g? 9 ?is case ! reflect+ surface %\ld be v smoo? & highly poli%$4 ,a piece ( glass holl[$ out 9 ! c5t] by gr9d+1 & ) a light film ( silv] *emically deposit$ ^u ! holl[ surface & c>efully poli%$1 is (t5 us$ by a/ronom]s = ?is purpose1 & is call$ a concave mirror4 ,! radiant en]gy com+ f a /> or o!r di/ant object & fall+ ^u ! silv]$ face ( su* a mirror is reflect$ & cond5s$ at a po9t a little 9 front ( ! mirror1 & !re =ms an image ( ! />1 :i* may be se5 ) ! unaid$ eye1 if x is held 9 ! "r place1 or may be exam9$ ?r\gh a magnify+ glass4 ,simil>ly1 an image ( ! sun1 a planet1 or a di/ant t]re/rial object is =m$ by ! mirror1 :i* cond5ses at its appropriate place ! radiant en]gy proce$+ f ea* & e po9t 9 ! surface ( ! object1 & ?is1 9 common phrase1 produces an image ( ! object4 ,ano!r device m frequ5tly us$ by a/ronom]s = ! production ( images 7cond5sation ( en]gy7 is a l5s :i* 9 its simple/ =m is a r\nd piece ( glass1 ?ick 9 ! c5t] & ?9 at ! edge1 ) a cross section1 su* z is %[n at ,a ,b 9 ,fig4 #ch4 ,if we suppose ,e ,g ,d to repres5t a small "p ( a wave front com+ f a v di/ant s\rce ( radiant en]gy1 su* z a />1 ?is wave front w be practically a plane surface repres5t$ by ! /raight l9e ,e ,d1 b 9 pass+ ?r\gh ! l5s ?is surface w become w>p$1 s9ce light travels sl[] 9 glass ?an 9 air1 & ! c5tral "p ( ! beam1 ,g1 9 its onw>d motion w be ret>d$ by ! ?ick c5t] ( ! l5s1 m ?an ,e or ,d w be ret>d$ by ! comp>atively ?9 out] edges ( ,a ,b4 ,on ! "r ( ! l5s ! wave front !re=e w be trans=m$ into a curv$ surface ^: exact "* dep5ds ^u ! %ape ( ! l5s & ! k9d ( glass ( :i* x is made4 ,by prop]ly *oos+ ^! ! new wave front may be made a "p ( a sph]e hav+ its c5t] at ! po9t ,f & ! :ole en]gy ( ! wave front1 ,e ,g ,d1 w !n be cond5s$ at ,f1 because ?is po9t is equally di/ant f all p>ts ( ! w>p$ wave front1 & !re=e is 9 a position to receive !m simultane\sly4 ,! di/ance ( ,f f ,a ,b is call$ ! focal l5g? ( ! l5s1 & ,f itself is call$ ! focus4 ,! significance ( ?is la/ ^w 7,lat91 focus fireplace7 w become pa9fully app>5t to ! /ud5t if he w hold a common read+ glass betwe5 8 h& & ! sun 9 su* a way t ! focus falls ^u 8 h&4 ,illu/ration3 ,,fig4 #ch4--;,illu/rat+ ! !ory ( l5ses4 ,all ! en]gy transmitt$ by ! l5s 9 ! direction ,g ,f is conc5trat$ ^u a v small area at ,f1 & an image ( ! object--e4 g41 a />1 f :i* ! light came--is =m$ "h4 ,o!r />s situat$ ne> ! "o 9 "q w also s5d beams ( light along slightly diff]5t directions to ! l5s1 & ^! w be conc5trat$1 ea* 9 its appropriate place1 9 ! focal plane1 ,f ,h1 pass$ ?r\gh ! focus1 ,f1 p]p5dicul> to ! l9e1 ,f ,g1 & we %all f9d 9 ?is plane a picture ( all ! />s or o!r objects )9 ! range ( ! l5s4 ,illu/ration3 ,,fig4 #ci4--;,ess5tial p>ts ( a reflect+ telescope4 #gh4 ,,telescopes4--,! simple/ k9d ( telescope consi/s ( a concave mirror to produce images1 & a magnify+ glass1 call$ an eyepiece1 ?r\gh :i* to exam9e !m2 b = conv5i5ce' sake1 s t ! obs]v] may n /& 9 8 own light1 a small mirror is frequ5tly add$ to ?is comb9ation1 z at ,h 9 ,fig4 #ci1 :]e ! l9es repres5t ! directions along :i* ! en]gy is propagat$4 ,by reflection f ?is mirror ! focal plane & ! images are %ift$ to ,f1 :]e !y may be exam9$ f "o side ?r\gh ! magnify+ glass ,e4 ,illu/ration3 ,,fig4 #dj4--;,a simple =m ( refract+ telescope4 ,su* a comb9ation ( p>ts is call$ a reflect+ telescope1 :ile "o 9 :i* ! images are produc$ by a l5s or comb9ation ( l5ses is call$ a refract+ telescope1 ! adjective hav+ ref]5ce to ! b5d+1 refraction1 produc$ by ! glass ^u ! direction 9 :i* ! en]gy is propagat$4 ,! cu/om>y arrangem5t ( p>ts 9 su* a telescope is %[n 9 ,fig4 #dj1 :]e ! "p m>k$ ,o is call$ ! objective & ,v ,e 7! magnify+ glass7 is ! eyepiece1 or ocul>1 z x is sometimes call$4 ,mo/ objects ) :i* we h to deal 9 us+ a telescope s5d to x n light ( "o color only1 b a mixture ( light ( _m colors1 _m diff]5t wave l5g?s1 "s ( :i* are refract$ m ?an o!rs by ! glass ( :i* ! l5s is compos$1 & 9 consequ5ce ( ^! diff]5t am\nts ( refraction a s+le l5s does n furni% a s+le image ( a />1 b gives a confus$ jumble ( r$ & yell[ & blue images mu* inf]ior 9 %>pness ( outl9e 7def9ition7 to ! images made by a good concave mirror4 ,to rem$y ?is defect x is cu/om>y to make ! objective ( two or m pieces ( glass ( diff]5t d5sities & gr\nd to diff]5t %apes z is %[n at ,o 9 ,fig4 #dj4 ,! two pieces ( glass ?us m\nt$ 9 "o frame con/itute a comp\nd l5s hav+ its own focal plane1 %[n at ,f 9 ! figure1 & simil>ly ! l5ses compos+ ! eyepiece h a focal plane betwe5 ! eyepiece & ! objective :i* mu/ also fall at ,f1 & 9 ! use ( a telescope ! eyepiece mu/ be pu%$ out or 9 until its focal plane co9cides ) t ( ! objective4 ,?is process1 :i* is call$ focus+1 is :at is accompli%$ 9 ! ord9>y op]a glass by turn+ a screw plac$ betwe5 ! two tubes1 & x mu/ be c>efully done ) e telescope 9 ord] to obta9 di/9ct vision4 #gi4 ,,magnify+ ,,p[]4--,! am\nt by :i* a giv5 telescope magnifies dep5ds ^u ! focal l5g? ( ! objective 7or mirror7 & ! focal l5g? ( ! eyepiece1 & is equal to ! ratio ( ^! two quantities4 ,?us 9 ,fig4 #dj ! di/ance ( ! objective f ! focal plane ,f is ab\t #af times z great z ! di/ance ( ! eyepiece f ! same plane1 & ! magnify+ p[] ( ?is telescope is !re=e #af diamet]s4 ,a magnify+ p[] ( #af diamet]s means t ! diamet] ( any object se5 9 ! telescope looks #af times z l>ge z x appe>s )\t ! telescope1 & is ne>ly equival5t to say+ t ! object appe>s only "o sixte5? z f> (f4 ,sometimes ! magnify+ p[] is assum$ to be ! numb] ( times t ! area ( an object seems increas$2 & s9ce areas are proportional to ! squ>es ( l9es1 ! magnify+ p[] ( #af diamet]s might be call$ a p[] ( #bef4 ,e l>ge telescope is provid$ ) sev]al eyepieces ( diff]5t focal l5g?s1 rang+ f a qu>t] ( an in* to two & a half in*es1 :i* are us$ to furni% diff]5t magnify+ p[]s z may be requir$ = ! diff]5t k9ds ( "w und]tak5 ) ! in/rum5t4 ,high] p[]s c be us$ ) l>ge telescopes ?an ) small ones1 b x is seldom advantage\s to use ) any telescope an eyepiece giv+ a high] p[] ?an #fj diamet]s = ea* in* ( diamet] ( ! objective4 ,! "p play$ by ! eyepiece 9 det]m9+ magnify+ p[] w be readily und]/ood f ! foll[+ exp]im5t3 ,make a p9 hole 9 a piece ( c>dbo>d4 ,br+ a pr9t$ page s close to "o eye t y c no long] see ! lett]s di/9ctly1 & !n place ! p9 hole betwe5 ! eye & ! page4 ,! lett]s :i* 7 be=e blurr$ may n[ be se5 pla9ly ?r\gh ! p9 hole1 ev5 :5 ! page is br\ght ne>] to ! eye ?an be=e4 ,z x is br\ght ne>]1 notice h[ ! lett]s seem to become l>g]1 solely because !y are ne>]4 ,a p9 hole is ! simple/ k9d ( a magnifi]1 & ! eyepiece 9 a telescope plays ! same "p z does ! p9 hole 9 ! exp]im5t2 x enables ! eye to be br\ght ne>] to ! image1 & ! %ort] ! focal l5g? ( ! eyepiece ! ne>] is ! eye br\ght to ! image & ! high] is ! magnify+ p[]4 #hj4 ,,! ,,equatorial ,,m\nt+4--,telescopes are ( all sizes1 f ! mode/ op]a glass :i* may be c>ri$ 9 ! pocket & :i* requires no o!r support ?an ! h&1 to ! giant :i* mu/ h a special ro( to %elt] x & elaborate ma*9]y to support & direct x t[>d ! sky4 ,b = ev5 ! l>ge/ telescopes ?is ma*9]y consi/s ( ! foll[+ p>ts1 :i* are illu/rat$1 ) exception ( ! la/ "o1 9 ! small equatorial telescope %[n 9 ,fig4 #da4 ,x is n cu/om>y to place a driv+ clock on s small a telescope z ?is3 7a7 ,a support+ pi] or tripod4 7b7 ,an axis plac$ p>allel to ! axis ( ! e>?4 7c7 ,ano!r axis at "r angles to b & capable ( revolv+ ^u b z an axle4 7d7 ,! telescope tube atta*$ to c & capable ( revolv+ ab\t c4 7e7 ,graduat$ circles atta*$ to c & b to measure ! am\nt by :i* ! telescope is turn$ on ^! axes4 7f7 ,a driv+ clock s connect$ ) b z to make c 7& d7 revolve ab\t b ) an angul> velocity equal & opposite to t ) :i* ! e>? turns ^u its axis4 ,illu/ration3 ,,fig4 #da4--;,a simple equatorial m\nt+4 ,illu/ration3 ,,fig4 #db4--;,equatorial m\nt+ ( ! great telescope ( ! ,y]kes ,obs]vatory4 ,su* a support is call$ an equatorial m\nt+1 & ! /ud5t %\ld note f ! figure t ! circles1 e1 measure ! h\r angle & decl9ation ( any /> t[>d :i* ! telescope is direct$1 & conv]sely if ! telescope be s set t ^! circles indicate ! h\r angle & decl9ation ( any giv5 />1 ! telescope w !n po9t t[>d t />4 ,9 ?is way x is easy to f9d ) ! telescope any mod]ately bright />1 ev5 9 broad daylight1 al?\gh x is !n absolutely invisible to ! nak$ eye4 ,! rotation ( ! e>? ab\t its axis w spe$ily c>ry ! telescope away f ! />1 b if ! driv+ clock be />t$1 its effect is to turn ! telescope t[>d ! we/ j z fa/ z ! e>?'s rotation c>ries x t[>d ! ea/1 & by ^! comp5sat+ motions to keep x direct$ t[>d ! />4 ,9 ,fig4 #db1 :i* repres5ts ! l>ge/ & "o ( ! mo/ p]fect refract+ telescopes ev] built1 let ! /ud5t pick out & id5tify ! sev]al p>ts ( ! m\nt+ above describ$4 ,a "p ( ! driv+ clock may be se5 )9 ! head ( ! pi]4 ,9 ,fig4 #dc trace out ! correspond+ p>ts 9 ! m\nt+ ( a reflect+ telescope4 ,illu/ration3 ,,fig4 #dc4--,! reflect+ telescope ( ! ,p>is ,obs]vatory4 ,a telescope is (t5 only a subord9ate "p ( "s in/rum5t or app>atus1 & !n its /yle ( m\nt+ is det]m9$ by ! requirem5ts ( ! special case2 b :5 ! telescope is ! *ief ?+1 & ! rema9d] ( ! app>atus is subord9ate to x1 ! equatorial m\nt+ is almo/ always adopt$1 al?\gh sometimes ! arrangem5t ( ! p>ts is v diff]5t 9 appe>ance f any ( ^? %[n above4 ,bew>e ( ! popul> error t an object held close 9 front ( a telescope c be se5 by an obs]v] at ! eyepiece4 ,! num]\s /ories ( a/ronom]s :o saw spid]s crawl+ ov] ! objective ( _! telescope1 & imag9$ !y 7 behold+ /range objects 9 ! sky1 are all fictiti\s1 s9ce no?+ on or ne> ! objective c\ld possibly be se5 ?r\gh ! telescope4 #ha4 ,,photography4--,a photographic cam]a consi/s ( a l5s & a device = hold+ at its focus a specially prep>$ plate or film4 ,?is plate c>ries a *emical deposit :i* is v s5sitive to ! action ( light1 & :i* may be made to pres]ve ! impr9t ( any picture :i* ! l5s =ms ^u x4 ,if su* a s5sitive plate is plac$ at ! focus ( a reflect+ telescope1 ! comb9ation becomes a cam]a available = a/ronomical photography1 & at ! pres5t "t ! t5d5cy is /rong 9 ne>ly e bran* ( a/ronomical rese>* to sub/itute ! s5sitive plate 9 place ( ! obs]v] at a telescope4 ,a refract+ telescope may also be us$ = a/ronomical photography1 & is v mu* us$1 b "s complications occur "h on acc\nt ( ! resolution ( ! light into its con/itu5t colors 9 pass+ ?r\gh ! objective4 ,fig4 #dd %[s su* a telescope1 or r two telescopes1 "o photographic1 ! o!r visual1 support$ side by side ^u ! same equatorial m\nt+4 ,illu/ration3 ,,fig4 #dd4--,photographic telescope ( ! ,p>is ,obs]vatory4 ,"o ( ! great advantages ( photography is f\nd 9 connection ) :at is call$-- #hb4 ,,p]sonal ,,equation4--,x is a rem>kable fact1 fir/ inve/igat$ by ! ,g]man a/ronom] ,bessel1 ?ree qu>t]s ( a c5tury ago1 t :]e extreme accuracy is requir$ ! human s5ses c n be implicitly reli$ ^u4 ,! mo/ skillful obs]v]s w n agree exactly 9 _! measurem5t ( an angle or 9 e/imat+ ! exact in/ant at :i* a /> cross$ ! m]idian2 ! mo/ skillful arti/s c n draw id5tical pictures ( ! same object1 etc4 ,^! m9or deceptions ( ! s5ses are includ$ 9 ! t]m p]sonal equation1 :i* is a fam\s phrase 9 a/ronomy1 d5ot+ t ! obs]vations ( any giv5 p]son require to be correct$ by means ( "s equation involv+ 8 p]sonality4 ,g5]al heal?1 dige/ion1 n]ves1 fatigue1 all influ5ce ! p]sonal equation1 & x 0 9 ref]5ce to su* matt]s t "o ( ! mo/ em95t ( liv+ a/ronom]s has giv5 ?is description ( 8 habits ( obs]v+3 ,9 ord] to avoid e physiological di/urbance1 ,i h adopt$ ! rule to ab/a9 = "o or two h\rs be=e comm5c+ obs]vations f e labori\s occupation2 nev] to g to ! telescope ) /oma* load$ ) food2 to ab/a9 f ev]y?+ :i* c\ld affect ! n]v\s sy/em1 f n>cotics & alcohol1 & especially f ! abuse ( c(fee1 :i* ,i h f\nd to be exce$+ly prejudicial to ! accuracy ( obs]vation4#c ,a regim5 sugge/ive ( prep>ation = an a?letic conte/ r ?an = ! m quiet labors ( an a/ronom]4 #c ,s*iap>elli1 ,oss]vazioni sulle ,/elle ,doppie4 #hc4 ,,visual ,,& ,,photographic ,,"w4--,! photographic plate has no /oma* & no n]ves1 & is ?us free f _m ( ! s\rces ( error :i* inh]e 9 visual obs]vations1 & 9 special classes ( "w x possesses o!r m>k$ advantages1 su* z rapidity :5 _m />s are to be dealt ) simultane\sly1 p]man5ce ( record1 & ow+ to ! cumulative effect ( long exposure ( ! plate x is possible to photograph ) a giv5 telescope />s f> too fa9t to be se5 ?r\gh x4 ,on ! o!r h&1 ! eye has ! advantage 9 "s respects1 su* z /udy+ ! m9ute details ( a fairly bright object--e4 g41 ! surface ( a planet1 or ! sun's corona &1 = ! pres5t at lea/1 nei!r me?od ( obs]v+ c exclude ! o!r4 ,= a rem>kable case ( discordance betwe5 ! results ( photographic & visual obs]vations comp>e ! pictures ( ! great nebula 9 ! con/ellation ,&rom$a1 :i* are giv5 9 ,*apt] ,,xiv4 ,a p>tial explanation ( ^! discordances & o!r simil> ones is t ! eye is mo/ /rongly affect$ by gre5i%-yell[ light1 :ile ! photographic plate responds mo/ /rongly to violet light2 ! photograph1 !re=e1 repres5ts ?+s :i* ! eye has little capacity = see+1 & vice v]sa4 #hd4 ,,! ,,spectroscope4--,9 "s respects ! spectroscope is ! exact c\nt]p>t ( ! telescope4 ,! latt] cond5ses radiant en]gy & ! =m] disp]ses x4 ,z a measur+ in/rum5t ! telescope is ma9ly conc]n$ ) ! direction f :i* light comes1 & ! diff]5t colors ( :i* t light is compos$ affect x only z an ob/acle to be ov]come 9 its con/ruction4 ,on ! o!r h&1 ) ! spectroscope ! direction f :i* ! radiant en]gy comes is ( m9or consequ5ce1 & ! all-important consid]ation is ! intr9sic "* ( t radiation4 ,:at colors are pres5t 9 ! light & 9 :at proportions8 ,:at c ^! colors be made to tell ab\t ! nature & condition ( ! body f :i* !y come1 be x sun1 or />1 or "s t]re/rial s\rce ( light1 su* z an arc lamp1 a c&le flame1 or a furnace 9 bla/8 ,^! are "s ( ! *>act]i/ic que/ions ( ! spectrum analysis1 &1 z ! "n implies1 !y are solv$ by analyz+ ! radiant en]gy into its compon5t p>ts1 sett+ d[n ! blue light 9 "o place1 ! yell[ 9 ano!r1 ! r$ 9 /ill ano!r1 etc41 & int]pret+ ?is array ( colors by means ( pr9ciples :i* we %all h to consid]4 ,some?+ ( ?is process ( color analysis may be se5 9 ! brilliant hues %[n by a soap bubble1 or reflect$ f a piece ( "m-(-pe>l1 & /ill m /rik+ly exhibit$ 9 ! ra9b[1 produc$ by ra9drops :i* break up ! sunlight into its compon5t colors & arrange !m ea* 9 its appropriate place4 ,any ( ^! natural me?ods ( decompos+ light might be employ$ 9 ! con/ruction ( a spectroscope1 b 9 spectroscopes :i* are us$ = analyz+ ! light f feeble s\rces1 su* z a />1 or a c&le flame1 a glass prism ( triangul> cross section is usually employ$ to resolve ! light into its compon5t colors1 :i* x does by refract+ x z %[n at ! edges ( ! l5s 9 ,fig4 #ch4 ,illu/ration3 ,,fig4 #de4--,resolution ( light into its compon5t colors4 ,! c\rse ( a beam ( light 9 pass+ ?r\gh su* a prism is %[n 9 ,fig4 #de4 ,note t ! b5d+ ( ! light f its orig9al c\rse into a new "o1 :i* is "h %[n z produc$ by ! prism1 is q simil> to ! b5d+ %[n at ! edges ( a l5s & comes f ! same cause1 ! sl[] velocity ( light 9 glass ?an 9 air4 ,x takes ! light-waves z long to move ov] ! pa? ,a ,b 9 glass z ov] ! long] pa? #a1 #b1 #c1 #d1 ( :i* only ! middle section lies 9 ! glass4 ,n only does ! prism b5d ! beam ( light transmitt$ by x1 b x b5ds 9 diff]5t degree light ( diff]5t colors1 z is %[n 9 ! figure1 :]e ! beam at ! left ( ! prism is suppos$ to be made up ( a mixture ( blue & r$ light1 :ile at ! "r ( ! prism ! great] deviation imp>t$ to ! blue q sep>ates ! colors1 s t !y fall at diff]5t places on ! scre51 ,s ,s4 ,! comp\nd light has be5 analyz$ into its con/itu5ts1 & 9 ! same way e o!r color w\ld be put d[n at its appropriate place on ! scre51 & a beam ( :ite light fall+ ^u ! prism w\ld be resolv$ by x into a sequ5ce ( colors1 fall+ ^u ! scre5 9 ! ord] r$1 orange1 yell[1 gre51 blue1 indigo1 violet4 ,! initial lett]s ( ^! names make ! ^w ,roygbiv1 & by means ( x _! ord] is easily rememb]$4 ,illu/ration3 ,,fig4 #df4--,pr9cipal p>ts ( a spectroscope4 ,if ! light :i* is to be exam9$ comes f a /> ! analysis made by ! prism is complete1 & :5 view$ ?r\gh a telescope ! image ( ! /> is se5 to be drawn out into a b& ( light1 :i* is call$ a spectrum1 & is r$ at "o end & violet or blue at ! o!r1 ) all ! colors ( ! ra9b[ int]v5+ 9 prop] ord] betwe5 ^! extremes4 ,su* a prism plac$ 9 front ( ! objective ( a telescope is call$ an objective prism1 & has be5 us$ = /ell> "w ) m>k$ success at ! ,h>v>d ,college ,obs]vatory4 ,b if ! light to be analyz$ comes f an object hav+ an appreciable ext5t ( surface1 su* z ! sun or a planet1 ! objective prism c n be successfully employ$1 s9ce ea* po9t ( ! surface w produce its own spectrum1 & ^! w appe> 9 ! view telescope sup]pos$ & confus$ "o ) ano!r 9 a v objectionable mann]4 ,to avoid ?is difficulty !re is plac$ betwe5 ! prism & ! s\rce ( light an opaque scre51 ,s1 ) a v n>r[ slit cut 9 x1 ?r\gh :i* all ! light to be analyz$ mu/ pass & mu/ also g ?r\gh a l5s1 ,a1 plac$ betwe5 ! slit & ! prism1 z %[n 9 ,fig4 #df4 ,! slit & l5s1 toge!r ) ! tube 9 :i* !y are usually support$1 are call$ a collimator4 ,by ?is device a v limit$ am\nt ( light is p]mitt$ to pass f ! object ?r\gh ! slit & l5s to ! prism & is !re resolv$ into a spectrum1 :i* is 9 effect a s]ies ( images ( ! slit 9 light ( diff]5t colors1 plac$ side by side s close z to make practically a cont9u\s ribbon ( light ^: wid? is ! l5g? ( ea* individual picture ( ! slit4 ,! l5g? ( ! ribbon 7disp]sion7 dep5ds ma9ly ^u ! %ape ( ! prism & ! k9d ( glass ( :i* x is made1 & x may be v greatly increas$ & ! effici5cy ( ! spectroscope enhanc$ by putt+ two1 ?ree1 or m prisms 9 place ( ! s+le "o above describ$4 ,:5 ! am\nt ( light is v great1 z 9 ! case ( ! sun or an electric arc lamp1 x is advantage\s to alt] slightly ! arrangem5t ( ! spectroscope & to sub/itute 9 place ( ! prism a grat+--i4 e41 a metallic mirror ) a great numb] ( f9e p>allel l9es rul$ ^u its surface at equal int]vals1 "o f ano!r4 ,x is by virtue ( su* a sy/em ( f9e p>allel grooves t "m-(-pe>l displays its beautiful color effects1 & a brilliant spectrum ( great purity & high disp]sion is furni%$ by a grat+ rul$ ) f #aj1jjj to #bj1jjj l9es to ! in*4 ,fig4 #dg repres5ts1 r crudely1 a "p ( ! spectrum ( an arc light furni%$ by su* a grat+1 or r x %[s ?ree diff]5t spectra arrang$ side by side1 & look+ some?+ l a rude ladd]4 ,! sides ( ! ladd] are ! spectra furni%$ by ! inc&esc5t c>bons ( ! lamp1 & ! cross pieces are ! spectrum ( ! electric arc fill+ ! space betwe5 ! c>bons4 ,fig4 #dh %[s a cont9uation ( ! same spectra into a region :]e ! radiant en]gy is invisible to ! eye1 b is capable ( be+ photograph$4 ,illu/ration3 ,,fig4 #dg4--;,gre5 & blue "p ( ! spectrum ( an electric arc light4 ,x is only :5 a l5s is plac$ betwe5 ! lamp & ! slit ( ! spectroscope t ! ?ree spectra are %[n di/9ct f ea* o!r z 9 ! figure4 ,! purpose ( ! l5s is to make a picture ( ! lamp ^u ! slit1 s t all ! radiant en]gy f any "o po9t ( ! arc may be br\ght to "o "p ( ! slit1 & ?us appe> 9 ! result+ spectrum sep>at$ f ! en]gy :i* comes f e o!r "p ( ! arc4 ,su* an in/rum5t is call$ an analyz+ spectroscope :ile "o )\t ! l5s is call$ an integrat+ spectroscope1 s9ce x furni%es to ea* po9t ( ! slit a sample ( ! radiant en]gy com+ f e "p ( ! s\rce ( light1 & ?us produces only an av]age spectrum ( t s\rce )\t di/9ction ( its p>ts4 ,:5 a spectroscope is atta*$ to a telescope1 z is (t5 done 7see ,fig4 #di71 ! eyepiece is remov$ to make way = x1 & ! telescope objective takes ! "p ( ! analyz+ l5s4 ,a cam]a is frequ5tly comb9$ ) su* an app>atus to photograph ! spectra x furni%es1 & ! :ole in/rum5t is !n call$ a spectrograph4 ,illu/ration3 ,,fig4 #dh4--,violet & ultraviolet p>ts ( spectrum ( an arc lamp4 ,illu/ration3 ,,fig4 #di4--;,a spectroscope atta*$ to ! ,y]kes telescope4 #he4 ,,spectrum ,,analysis4--,hav+ se5 ! me*anism ( ! spectroscope by :i* ! light incid5t ^u x is resolv$ into its con/itu5t p>ts & drawn out into a s]ies ( colors arrang$ 9 ! ord] ( _! wave l5g?s1 we h n[ to consid] ! int]pretation :i* is to be plac$ ^u ! v>i\s k9ds ( spectra :i* may be se51 & "h we rely ^u ! exp]i5ce ( physici/s & *emi/s1 f :om we le>n z foll[s3 ,! radiant en]gy :i* is analyz$ by ! spectroscope has its s\rce 9 ! atoms & molecules :i* make up ! lum9\s body f :i* ! en]gy is radiat$1 & ^! atoms & molecules are able to impress ^u ! e!r _! own peculi>ities 9 ! %ape ( waves ( diff]5t l5g? & amplitude4 ,we h se5 t by v>y+ ! conditions ( ! exp]im5t diff]5t k9ds ( waves may be produc$ 9 a bucket ( wat]2 & z a /udy ( ^! waves might furni% an index to ! conditions :i* produc$ !m1 s ! /udy ( ! waves peculi> to ! light :i* comes f any s\rce may be made to give in=mation ab\t ! molecules :i* make up t s\rce4 ,?us ! molecules ( iron produce a sy/em ( waves peculi> to !mselves & :i* c be duplicat$ by no?+ else1 & e o!r sub/ance gives (f its own peculi> type ( en]gy1 pres5t+ a limit$ & def9ite numb] ( wave l5g?s dep5d5t ^u ! nature & condition ( its molecules4 ,if ^! molecules are free to behave 9 _! own *>act]i/ic fa%ion )\t di/urbance or cr[d+1 !y emit light ( ^! wave l5g?s only1 & we f9d 9 ! spectrum a s]ies ( bright l9es1 pictures ( ! slit produc$ by light ( ^! p>ticul> wave l5g?s1 :ile betwe5 ^! bright l9es lie d>k spaces %[+ ! abs5ce f ! radiant en]gy ( light ( int]m$iate wave l5g?s4 ,su* a spectrum is %[n 9 ! c5tral portion ( ,fig4 #dg1 :i*1 z we h already se51 is produc$ by ! space betwe5 ! c>bons ( ! arc lamp4 ,on ! o!r h&1 if ! molecules are closely pack$ toge!r "u pressure !y s int]f]e ) ea* o!r z to give (f a jumble ( en]gy ( all wave l5g?s1 & ?is is translat$ by ! spectroscope into a cont9u\s ribbon ( light ) no d>k spaces int]v5+1 z 9 ! upp] & l[] p>ts ( ,figs4 #dg & #dh1 produc$ by ! inc&esc5t solid c>bons ( ! lamp4 ,^! two types are kn[n z ! cont9u\s & discont9u\s spectrum1 & we may lay d[n ! foll[+ pr9ciple reg>d+ !m3 ,a discont9u\s spectrum1 or bright-l9e spectrum z x is famili>ly call$1 indicates t ! molecules ( ! s\rce ( light are n cr[d$ toge!r1 & !re=e ! light mu/ come f an inc&esc5t gas4 ,a cont9u\s spectrum %[s only t ! molecules are cr[d$ toge!r1 or are s num]\s t ! body to :i* !y belong is n transp>5t & gives no fur!r in=mation4 ,! body may be solid1 liquid1 or gase\s1 b 9 ! latt] case ! gas mu/ be "u consid]able pressure or ( great ext5t4 ,a second pr9ciple is3 ,! l9es :i* appe> 9 a spectrum are *>act]i/ic ( ! s\rce f :i* ! light came--e4 g41 ! d\ble l9e 9 ! yell[ "p ( ! spectrum at ! extreme left 9 ,fig4 #dg is produc$ by sodium vapor 9 & ar\nd ! electric arc & is nev] produc$ by any?+ b sodium4 ,:5 by laboratory exp]im5ts we h le>n$ ! p>ticul> set ( l9es correspond+ to iron1 we may treat ! pres5ce ( ^! l9es 9 ano!r spectrum z pro( t iron is pres5t 9 ! s\rce f :i* ! light came1 :e!r t s\rce be a :ite-hot pok] 9 ! next room or a /> immeasurably di/ant4 ,! evid5ce t iron is pres5t lies 9 ! nature ( ! light1 & !re is no reason to suppose t nature to be alt]$ on ! way f /> to e>?4 ,x may1 h[ev]1 be alt]$ by some?+ happ5+ to ! s\rce f :i* x comes--e4 g41 *ang+ temp]ature or pressure may affect1 & does affect1 ! spectrum :i* su* a sub/ance z iron emits1 & we mu/ be prep>$ to f9d ! same sub/ance pres5t+ diff]5t spectra "u diff]5t conditions1 only ^! conditions mu/ be greatly alt]$ 9 ord] to produce radical *anges 9 ! spectrum4 ,illu/ration3 ,,fig4 #ej4--,! *ief l9es 9 ! spectrum ( sunlight4--,,h]s*el4 #hf4 ,,wave ,,l5g?s4--,to id5tify a l9e z belong+ to & produc$ by iron or any o!r sub/ance1 its position 9 ! spectrum--i4 e41 its wave l5g?--mu/ be v accurately det]m9$1 & = ! id5tification ( a sub/ance by means ( its spectrum x is (t5 necess>y to det]m9e accurately ! wave l5g?s ( _m l9es4 ,a complicat$ spectrum may consi/ ( hundr$s or ?\s&s ( l9es1 due to ! pres5ce ( _m diff]5t sub/ances 9 ! s\rce ( light1 & unless great c>e is tak5 9 assign+ ! exact position ( ^! l9es 9 ! spectrum1 confusion & wrong id5tifications are sure to result4 ,= ! measurem5t ( ! requir$ wave l5g? a t5? met] 7 #ge7 is ! unit employ$1 & a scale ( wave l5g?s express$ 9 ?is unit is pres5t$ 9 ,fig4 #ej4 ,! accuracy ) :i* "s ( ^! wave l5g?s are det]m9$ is truly a/\nd+2 a t5-billion? ( an in*6 ,^! num]ical wave l5g?s save all necessity = ref]r+ to ! color ( any "p ( ! spectrum1 & pictures ( spectra = sci5tific use are n usually pr9t$ 9 colors4 #hg4 ,,absorption ,,spectra4--,!re is ano!r k9d ( spectrum1 ( great] importance ?an ei!r ( ^? above consid]$1 :i* is well illu/rat$ by ! spectrum ( sunlight 7,fig4 #ej74 ,?is is a ne>ly cont9u\s spectrum cross$ by num]\s d>k l9es due to absorption ( radiant en]gy 9 a comp>atively cool gas ?r\gh :i* x passes on its way to ! spectroscope4 ,fraunh(]1 :o made ! fir/ c>eful /udy ( spectra1 designat$ "s ( ! m conspicu\s ( ^! l9es by lett]s ( ! alphabet :i* are %[n 9 ! plate1 & :i* are /ill 9 common use z names = ! l9es1 n only 9 ! spectrum ( sunlight b :]ev] !y occur 9 o!r spectra4 ,?us ! d\ble l9e m>k$ ,d1 wave l5g? #ehic1 falls at precisely ! same place 9 ! spectrum z does ! d\ble 7sodium7 l9e :i* we h already se5 9 ! yell[ "p ( ! arc-light spectrum1 :i* l9e is also call$ ,d & be>s a v intimate relation to ! d>k ,d l9e ( ! sol> spectrum4 ,! /ud5t :o has access to color$ crayons %\ld color "o edge ( ,fig4 #ej 9 accordance ) ! lett]+ !re giv5 &1 s f> z possible1 he %\ld make ! transition f "o color to ! next a gradual "o1 z x is 9 ! ra9b[4 ,fig4 #ej is f> f be+ a complete repres5tation ( ! spectrum ( sunlight4 ,n only does ?is spectrum ext5d bo? to ! "r & to ! left into regions invisible to ! human eye1 b )9 ! limits ( ! figure1 in/ead ( ! sev5ty-five l9es !re %[n1 !re are lit]ally ?\s&s ^u ?\s&s ( l9es1 ( :i* only ! mo/ conspicu\s c be %[n 9 su* a cut z ?is4 ,! d>k l9es :i* appe> 9 ! spectrum ( sunlight c1 "u prop] conditions1 be made to appe> 9 ! spectrum ( an arc light1 & ,fig4 #ea %[s a magnifi$ repres5tation ( a small "p ( su* a spectrum adjac5t to ! ,d 7sodium7 l9es4 ,d[n ! middle ( ea* ( ^! l9es runs a black /reak ^: position 7wave l5g?7 is precisely t ( ! ,d l9es 9 ! spectrum ( sunlight1 & ^: pres5ce is expla9$ z foll[s3 ,! v hot sodium vapor at ! c5t] ( ! arc gives (f its *>act]i/ic light1 :i*1 %9+ ?r\gh ! out] & cool] lay]s ( sodium vapor1 is p>tially absorb$ by ^!1 result+ 9 a f9e d>k l9e correspond+ exactly 9 position & wave l5g? to ! bright l9es1 & se5 aga9/ ^! z a backgr\nd1 s9ce ! high] temp]ature at ! c5t] ( ! arc t5ds to broad5 ! bright l9es & make !m diffuse4 ,simil>ly ! d>k l9es 9 ! spectrum ( ! sun 7,fig4 #ej7 po9t to ! exi/5ce ( a surr\nd+ envelope ( relatively cool gases1 :i* absorb f ! sunlight precisely ^? k9ds ( radiant en]gy :i* !y w\ld !mselves emit if inc&esc5t4 ,! result+ d>k l9es 9 ! spectrum are to be int]pret$ by ! same set ( pr9ciples :i* we h above appli$ to ! bright l9es ( a discont9u\s spectrum1 & !y may be us$ to det]m9e ! *emical composition ( ! sun1 j z ! bright l9es s]ve to det]m9e ! *emical elem5ts pres5t 9 ! electric arc4 ,) ref]5ce to ! mode ( _! =mation1 bright-l9e & d>k-l9e spectra are sometimes call$ respectively emission & absorption spectra4 ,illu/ration3 ,,fig4 #ea4--,! l9es rev]s$4 #hh4 ,,types ,,( ,,spectrum4--,! sun pres5ts by f> ! mo/ complex spectrum kn[n1 & ,fig4 #ej %[s only a small numb] ( ! m conspicu\s l9es :i* appe> 9 x4 ,spectra ( />s1 p] contra1 appe> relatively simple1 s9ce _! feeble light is insuffici5t to br+ out fa9t details4 ,9 ,*apt]s ,,xiii & ,,xiv !re are %[n types ( ! diff]5t k9ds ( spectra giv5 by />light1 & ^! are to be int]pret$ by ! pr9ciples above e/abli%$4 ,?us ! spectrum ( ! bright /> b ,aurig %[s a cont9u\s spectrum cross$ by a few heavy absorption l9es :i* are kn[n f laboratory exp]im5ts to be produc$ only by hydrog54 ,!re mu/ !re=e be an atmosph]e ( relatively cool hydrog5 surr\nd+ ?is />4 ,! spectrum ( ,pollux is q simil> to t ( ! sun & is to be int]pret$ z %[+ a physical condition simil> to t ( ! sun1 :ile ! spectrum ( a ,h]culis is q diff]5t f ei!r ( ! o!rs4 ,9 subsequ5t *apt]s we %all h occasion to consid] m fully ^! diff]5t types ( spectrum4 #hi4 ,,! ,,doppl] ,,pr9ciple4--,?is important pr9ciple ( ! spectrum analysis is mo/ readily appreciat$ ?r\gh ! foll[+ exp]im5t3 ,li/5 to ! :i/le ( a locomotive rapidly approa*+1 & obs]ve h[ ! pit* *anges & ! note becomes m grave z ! locomotive passes by & comm5ces to rec$e4 ,dur+ ! approa* ( ! :i/le ea* successive s\nd wave has a %ort] di/ance to travel 9 com+ to ! e> ( ! li/5] ?an _h its pr$ecessor1 & 9 consequ5ce ! waves appe> to come 9 quick] succession1 produc+ a high] note ) a correspond+ly %ort] wave l5g? ?an w\ld be he>d if ! same :i/le 7 bl[n ) ! locomotive at re/4 ,on ! o!r h&1 ! wave l5g? is increas$ & ! pit* ( ! note l[]$ by ! rec$+ motion ( ! :i/le4 ,a simil> effect is produc$ ^u ! wave l5g? ( light by a rapid *ange ( di/ance betwe5 ! s\rce f :i* x comes & ! in/rum5t :i* receives x1 s t a dim9i%+ di/ance dim9i%es v slightly ! wave l5g? ( e l9e 9 ! spectrum produc$ by ! light1 & an increas+ di/ance increases ^! wave l5g?s1 & ?is holds true :e!r ! *ange ( di/ance is produc$ by motion ( ! s\rce ( light or by motion ( ! in/rum5t :i* receives x4 ,?is *ange ( wave l5g? is sometimes describ$ by say+ t :5 a body is rapidly approa*+1 ! l9es ( its spectrum are all displac$ t[>d ! violet end ( ! spectrum1 & are correspond+ly displac$ t[>d ! r$ end by a rec$+ motion4 ,! am\nt ( ?is %ift+1 :5 x c be measur$1 measures ! velocity ( ! body along ! l9e ( sight1 b ! obs]vations are exce$+ly delicate1 & x is only 9 rec5t ye>s t x has be5 f\nd possible to make !m ) precision4 ,= ?is purpose !re is made to pass ?r\gh ! spectroscope light f an artificial s\rce :i* conta9s "o or m *emical elem5ts kn[n to be pres5t 9 ! /> :i* is to be obs]v$1 & ! correspond+ l9es 9 ! spectrum ( ?is light & 9 ! spectrum ( ! /> are exam9$ to det]m9e :e!r !y exactly mat* 9 position1 or %[1 z !y sometimes d1 a slight displacem5t1 z if "o spectrum _h be5 slipp$ pa/ ! o!r4 ,! difficulty ( ! obs]vations lies 9 ! extremely small am\nt ( ?is slipp+1 :i* r>ely if ev] 9 ! case ( a mov+ /> am\nts to "o six? "p ( ! int]val betwe5 ! close p>allel l9es m>k$ ,d 9 ,fig4 #ej4 ,! spectral l9es furni%$ by ! headlight ( a locomotive runn+ at ! rate ( a hundr$ miles p] h\r w\ld be displac$ by ?is motion less ?an "o six-?\s&? "p ( ! space betwe5 ! ,d l9es1 an am\nt absolutely imp]ceptible 9 ! mo/ p[]ful spectroscope yet con/ruct$4 ,b _m ( ! cele/ial bodies h velocities s mu* great] ?an a hundr$ miles p] h\r t ^! may be detect$ & measur$ by means ( ! ,doppl] pr9ciple4 #ij4 ,,o!r ,,in/rum5ts4--,o!r in/rum5ts ( importance to ! a/ronom]1 b ( :i* only casual m5tion c "h be made1 are ! m]idian-circle2 ! transit1 "o =m ( :i* is %[n 9 ,fig4 #eb1 & ! z5i? telescope1 :i* furni% ref9$ me?ods = mak+ obs]vations simil> 9 k9d to ^? :i* ! /ud5t has already le>n$ to make ) plumb l9e & protractor2 ! sextant1 :i* is pre-em95tly ! sailor's in/rum5t = f9d+ ! latitude & longitude at sea1 by measur+ ! altitudes ( sun & />s above ! sea horizon2 ! heliomet]1 :i* s]ves = ! v accurate measurem5t ( small angles1 su* z ! angul> di/ance betwe5 two />s n m ?an "o or two degrees ap>t2 & ! photomet]1 :i* is us$ = measur+ ! am\nt ( light receiv$ f ! cele/ial bodies4 ,illu/ration3 ,,fig4 #eb4--;,a comb9$ transit in/rum5t & z5i? telescope4 ,,*apt] ,,ix ,,! ,,moon #ia4 ,,results ,,( ,,obs]vation ,,) ,,! ,,unaid$ ,,eye4--,! /ud5t :o has made ! obs]vations ( ! moon :i* are indicat$ 9 ,*apt] ,,iii has 9 h& data f :i* mu* may be le>n$ ab\t ! e>?'s satellite4 ,p]haps ! mo/ /rik+ feature br\ght out by !m is ! motion ( ! moon among ! />s1 always f we/ t[>d ea/1 accompani$ by t endless s]ies ( *anges 9 %ape & brightness--new moon1 fir/ qu>t]1 full moon1 etc4--^: successive /ages we repres5t by ! words1 ! phase ( ! moon4 ,f 8 own obs]vation ! /ud5t %\ld be able to v]ify1 at lea/ approximately1 ! foll[+ /atem5ts1 al?\gh ! degree ( num]ical precision conta9$ 9 "s ( !m c be rea*$ only by m elaborate app>atus & long] /udy ?an he has giv5 to ! subject3 ,a4 ,! phase ( ! moon dep5ds ^u ! di/ance ap>t ( sun & moon 9 ! sky1 new moon com+ :5 !y are toge!r1 & full moon :5 !y are z f> ap>t z possible4 ,illu/ration3 ,,! ,,moon1 ,,"o ,,day ,,aft] ,,fir/ ,,qu>t]4 ,f a photograph made at ! ,p>is ,obs]vatory4 ,b4 ,! moon is ess5tially a r\nd1 d>k body1 giv+ (f no light ( its own1 b %9+ solely by reflect$ sunlight4 ,! pro( ( ?is is t :5ev] we see a "p ( ! moon :i* is turn$ away f ! sun x looks d>k--e4 g41 at new moon1 sun & moon are 9 ne>ly ! same direction f u & we see little or no?+ ( ! moon1 s9ce ! side ^u :i* ! sun %9es is turn$ away f u4 ,at full moon ! e>? is 9 l9e betwe5 sun & moon1 & we see1 r\nd & bright1 ! face ^u :i* ! sun %9es4 ,at o!r phases1 su* z ! qu>t]s1 ! moon turns t[>d ! e>? a "p ( its night hemisph]e & a "p ( its day hemisph]e1 b 9 g5]al only t "p :i* belongs to ! day side ( ! moon is visible & ! peculi> curv$ l9e :i* =ms ! b\nd>y--! ragg$ edge1 or t]m9ator1 z x is call$1 is ! divid+ l9e betwe5 day & night ^u ! moon4 ,a p>tial exception to :at prec$es is f\nd = a few days aft] new moon :5 ! moon & sun are n v f> ap>t 9 ! sky1 = !n ! :ole r\nd disk ( ! moon may (t5 be se51 a small "p ( x brightly illum9at$ by ! sun & ! l>g] "p feebly illum9at$ by sunlight :i* fell fir/ ^u ! e>? & 0 by x reflect$ back to ! moon1 giv+ ! pleas+ effect :i* is sometimes call$ ! old moon 9 ! new moon's arms4 ,! new moon--i4 e41 ! "p illum9$ by ! sun--usually appe>s to belong to a sph]e ( l>g] radius ?an ! old moon1 b ?is is purely a trick play$ by ! eyes ( ! obs]v]1 & ! effect disappe>s altoge!r 9 a telescope4 ,is !re any simil> effect 9 ! few days be=e new moon8 ,c4 ,! moon makes ! circuit ( ! sky f a giv5 /> ar\nd to ! same /> aga9 9 a little m ?an #bg days 7#bg4cbaff71 b ! int]val betwe5 successive new moons--i4 e41 f ! sun ar\nd to ! sun aga9--is m ?an #bi days 7#bi4ecjei74 ,?is la/ int]val1 :i* is call$ a lun> mon? or synodical mon?1 indicates :at we h le>n$ be=e--t ! sun has *ang$ its place among ! />s dur+ ! mon?1 s t x takes ! moon an extra two days to ov]take him aft] hav+ made ! circuit ( ! sky1 j z x takes ! m9ute h& ( a clock an extra #e m9utes to cat* up ) ! h\r h& aft] hav+ made a complete circuit ( ! dial4 ,d4 ,:]ev] ! moon may be 9 ! sky1 x turns always ! same face t[>d ! e>?1 z is %[n by ! fact t ! d>k m>k+s :i* appe> on its surface /& always ^u 7ne>ly7 ! same "p ( its disk4 ,x does n always turn ! same face t[>d ! sun1 = ! b\nd>y l9e betwe5 ! illum9$ & unillum9$ p>ts ( ! moon %ifts f "o side to ! o!r z ! phase *anges1 divid+ at ea* mom5t day f night ^u ! moon & illu/rat+ by its sl[ progress t ^u ! moon ! day & ! mon? are ( equal l5g? 7#bi4e t]re/rial days71 in/ead ( be+ "t units ( diff]5t l5g?s z ) u4 ,illu/ration3 ,,fig4 #ec4--,motion ( moon & e>? relative to ! sun4 #ib4 ,,! ,,moon',s ,,motion4--,! /ud5t %\ld comp>e ! results ( 8 own obs]vations1 z well z ! prec$+ section1 ) ,fig4 #ec1 9 :i* ! l9es ) dates pr9t$ on !m are all suppos$ to radiate f ! sun & to repres5t ! direction f ! sun ( e>? & moon ^u ! giv5 dates :i* are arbitr>ily assum$ = ! sake ( illu/ration1 any o!r set w\ld d equally well4 ,! black dots1 small & l>ge1 repres5t ! moon revolv+ ab\t ! e>?1 b hav+ ! circul> pa? %[n 9 ,fig4 #cd 7ellipse7 trans=m$ by ! e>?'s =w>d motion into ! peculi> s9u\s l9e "h %[n4 ,) respect to bo? e>? & sun1 ! moon's orbit deviates b little f a circle1 s9ce ! s9u\s curve ( ,fig4 #ec foll[s v closely ! e>?'s orbit ar\nd ! sun & is almo/ id5tical ) x4 ,= cle>ness ( repres5tation ! di/ance betwe5 e>? & moon 9 ! figure has be5 made t5 times too great1 & to get a prop] idea ( ! moon's orbit ) ref]5ce to ! sun1 we mu/ suppose ! moon mov$ up t[>d ! e>? until its di/ance f ! l9e ( ! e>?'s orbit is only a t5? "p ( :at x is 9 ! figure4 ,:5 ?is is done1 ! moon's pa? becomes almo/ indi/+ui%able f t ( ! e>?1 z may be se5 9 ! figure1 :]e ! attempt has be5 made to %[ bo? l9es1 & x is to be especially not$ t ?is real orbit ( ! moon is ev]y:]e concave t[>d ! sun4 ,! phase pres5t$ by ! moon at diff]5t p>ts ( its pa? is indicat$ by ! r[ ( circles at ! "r1 & ! /ud5t %\ld %[ :y a new moon is associat$ ) ,june #cj? & a full moon ) ,july #ae?1 etc4 ,:at 0 ! date ( fir/ qu>t]8 ,?ird qu>t]8 ,we may f9d 9 ,fig4 #ec ano!r effect ( ! same k9d z t not$ above 9 ,c4 ,betwe5 noon1 ,june #cj?1 & noon1 ,july #c;d1 ! e>? makes ^u its axis ?ree complete revolutions ) respect to ! sun1 b ! m]idian :i* po9ts t[>d ! moon at noon on ,june #cj? w n po9t t[>d x at noon on ,july #c;d1 s9ce ! moon has mov$ into a new position & is n[ #cg away f ! m]idian4 ,v]ify ?is /atem5t by measur+1 9 ,fig4 #ec1 ) ! protractor1 ! moon's angul> di/ance f ! m]idian at noon on ,july #c;d4 ,:5 w ! m]idian ov]take ! moon8 #ic4 ,,h>ve/ ,,moon4--,! int]val betwe5 two successive transits ( ! m]idian pa/ ! moon is call$ a lun> day1 & ! /ud5t %\ld %[ f ! figure t on ! av]age a lun> day is #ea m9utes long] ?an a sol> day--i4 e41 ^u ! av]age ea* day ! moon comes to ! m]idian #ea m9utes ( sol> "t lat] ?an on ! day be=e4 ,x is also true t on ! av]age ! moon rises & sets #ea m9utes lat] ea* day ?an on ! day be=e4 ,b !re is a good deal ( irregul>ity 9 ! ret>dation ( ! "t ( moonrise & moonset1 s9ce ! "t ( ris+ dep5ds l>gely ^u ! p>ticul> po9t ( ! horizon at :i* ! moon appe>s1 & betwe5 two days ?is po9t may *ange s mu* on acc\nt ( ! moon's orbital motion z to make ! ret>dation consid]ably great] or less ?an its av]age value4 ,9 nor!rn latitudes ?is effect is p>ticul>ly m>k$ 9 ! mon? ( ,septemb]1 :5 ! ea/]n horizon is ne>ly p>allel ) ! moon's app>5t pa? 9 ! sky1 & ne> ! "t ( full moon 9 t mon? ! moon rises on sev]al successive nights at ne>ly ! same h\r1 & 9 less degree ! same is true = ,octob]4 ,?is highly conv5i5t arrangem5t ( moonlight has caus$ ! full moons ( ^! two mon?s to be *ri/5$ respectively ! ,h>ve/ ,moon & ! ,hunt]'s ,moon4 #id4 ,,size ,,& ,,mass ,,( ,,! ,,moon4--,x has be5 %[n 9 ,*apt] ,i h[ ! di/ance ( ! moon f ! e>? may be measur$ & its diamet] det]m9$ by means ( angles1 & )\t enl>g+ ^u ! details ( ^! obs]vations1 we note z _! result t ! moon is a globe #b1afc miles 9 diamet]1 & di/ant f ! e>? on ! av]age ab\t #bdj1jjj miles4 ,b1 z we h se5 9 ,*apt] ,,vii1 ?is di/ance *anges to ! ext5t ( a few ?\s& miles1 sometimes less1 sometimes great]1 ma9ly on acc\nt ( ! elliptic %ape ( ! moon's orbit ab\t ! e>?1 b also 9 "p f ! di/urb+ influ5ce ( o!r bodies1 su* z ! sun1 :i* pull ! moon to & fro1 backw>d & =w>d1 to q an appreciable ext5t4 ,f ! kn[n diamet] ( ! moon x is a matt] ( elem5t>y geometry to d]ive 9 miles ! area ( its surface & its volume or solid cont5ts4 ,leav+ ?is z an ex]cise = ! /ud5t1 we adopt ! e>? z ! /&>d ( comp>ison & f9d t ! diamet] ( ! moon is r m ?an a qu>t]1 #d_/ae1 t ( ! e>?1 ! area ( its surface is a trifle m ?an #a_/ad t ( ! e>?1 & its volume a little m ?an #a_/di ( ! e>?'s4 ,s mu* is pure geometry1 b we may comb9e ) x "s me*anical pr9ciples :i* enable u to g a /ep f>!r & to weigh ! moon--i4 e41 det]m9e its mass & ! av]age d5sity ( ! mat]ial ( :i* x is made4 ,we h se5 t ! moon moves ar\nd ! sun 9 a pa? diff]+ b little f ! smoo? curve %[n 9 ,fig4 #ec1 ) arr[s indicat+ ! direction ( motion1 & x w\ld foll[ absolutely su* a smoo? pa? 7 x n = ! attraction ( ! e>?1 & 9 less degree ( "s ( ! o!r planets1 :i* sw+ x ab\t fir/ to "o side !n to ! o!r4 ,b action & reaction are equal2 ! moon pulls z /rongly ^u ! e>? z does ! e>? ^u ! moon1 & if e>? & moon 7 ( equal mass1 ! deviation ( ! e>? f ! smoo? curve 9 ! figure w\ld be j z l>ge z t ( ! moon4 ,x is %[n 9 ! figure t ! moon does displace ! e>? f ?is curve1 & we h only to measure ! am\nt ( ?is displacem5t ( ! e>? & comp>e x ) ! displacem5t suff]$ by ! moon to f9d h[ mu* ! mass ( ! "o exce$s t ( ! o!r4 ,x may be se5 f ! figure t at fir/ qu>t]1 ab\t ,july #g?1 ! e>? is ?ru/ ahead 9 ! direction ( its orbital motion1 :ile at ! ?ird qu>t]1 ,july #bb;d1 x is pull$ back by ! action ( ! moon1 & at all times x is m or less displac$ by ?is action1 s t1 9 ord] to be /rictly correct1 we mu/ am5d our =m] /atem5t ab\t ! moon mov+ ar\nd ! e>? & make x read1 ,bo? e>? & moon revolve ar\nd a po9t on l9e betwe5 _! c5t]s4 ,?is po9t is call$ _! c5t] ( gravity1 & ! e>? & ! moon bo? move 9 ellipses hav+ ?is c5t] ( gravity at _! common focus4 ,comp>e ?is ) ,kepl]'s ,fir/ ,law4 ,^! ellipses are simil>ly %ap$1 b ( v diff]5t size1 correspond+ to ,newton's ?ird law ( motion 7,*apt] ,,iv71 s t ! action ( ! e>? 9 caus+ ! small moon to move ar\nd a l>ge orbit is j equal to ! reaction ( ! moon 9 caus+ ! l>g] e>? to move 9 ! small] orbit4 ,?is is equival5t to say+ t ! dim5sions ( ! two orbits are inv]sely proportional to ! masses ( ! e>? & ! moon4 ,by obs]v+ ?r\gh\t ! mon? ! direction f ! e>? to ! sun or to a ne> planet1 su* z ,m>s or ,v5us1 a/ronom]s h det]m9$ t ! diamet] ( ! ellipse 9 :i* ! e>? moves is ab\t #e1hej miles1 s t ! di/ance ( ! e>? f ! c5t] ( gravity is #b1ibe miles1 & ! di/ance ( ! moon f x is #bdj1jjj-b1ibe #bcg1jge4 ,we may n[ write 9 ! =m ( a proportion-- ,mass ( e>? 3 ,mass ( moon 33 #bcg1jge 3 #b1ibe1 & f9d f x t ! mass ( ! e>? is #ha times z great z ! mass ( ! moon--i4 e41 leav+ k9d & quality out ( acc\nt1 !re is en\gh mat]ial 9 ! e>? to make #ha moons4 ,we may note 9 ?is connection t ! diamet] ( ! e>?1 #g1ibf miles1 is great] ?an ! diamet] ( ! mon?ly orbit 9 :i* ! moon causes x to move1 & !re=e ! c5t] ( gravity ( e>? & moon always lies inside ! body ( ! e>?1 ab\t #a1jjj miles bel[ ! surface4 #ie4 ,,d5sity ,,( ,,! ,,moon4--,x is believ$ t 9 a g5]al way ! moon is made ( mu* ! same k9d ( mat]ial :i* goes to make up ! e>?--metals1 m9]als1 rocks1 etc4--& a "p ( ! evid5ce ^u :i* ?is belief is bas$ lies 9 ! d5sity ( ! moon4 ,by d5sity ( a sub/ance we mean ! am\nt ( x :i* is conta9$ 9 a giv5 volume--i4 e41 ! weight ( a bu%el or a cubic c5timet] ( ! /uff4 ,! d5sity ( *alk is twice z great z ! d5sity ( wat]1 because a cubic c5timet] ( *alk weighs twice z mu* z an equal volume ( wat]1 & simil>ly 9 o!r cases ! d5sity is f\nd by divid+ ! mass or weight ( ! body by ! mass or weight ( an equal volume ( wat]4 ,we "k ! mass ( ! e>? 7 #de71 & kn[+ ! mass ( a cubic foot ( wat]1 x is easy1 al?\gh a trifle t$i\s1 to compute :at w\ld be ! mass ( a volume ( wat] equal 9 size to ! e>?4 ,! quoti5t obta9$ by divid+ "o ( ^! masses by ! o!r 7mass ( e>? mass ( wat]7 is ! av]age d5sity ( ! mat]ial compos+ ! e>?1 & we f9d num]ically t ?is is #e4f--;i4 e41 x w\ld take #e4f wat] e>?s to attract z /rongly z does ! real "o4 ,f direct exp]im5t we "k t ! av]age d5sity ( ! pr9cipal rocks :i* make up ! cru/ ( ! e>? is only ab\t half ( ?is1 %[+ t ! deep-ly+ c5tral p>ts ( ! e>? are d5s] ?an ! surface p>ts1 z we %\ld expect !m to be1 because !y h to be> ! weight ( all t lies above !m & are compress$ by x4 ,turn+ n[ to ! moon1 we f9d 9 ! same way z = ! e>? t its av]age d5sity is #c4d z great z t ( wat]4 #if4 ,,=ce ,,( ,,gravity ,,^u ,,! ,,moon4--,?is numb]1 #c4d1 comp>$ ) ! #e4f :i* we f\nd = ! e>?1 %[s t on ! :ole ! moon is made ( light] /uff ?an is ! body ( ! e>?1 & ?is aga9 is mu* :at we %\ld expect to f9d1 = weight1 ! =ce :i* t5ds to compress ! sub/ance ( ! moon1 is less !re ?an "h4 ,! weight ( a cubic y>d ( rock at ! surface ( ei!r e>? or moon is ! =ce ) :i* ! e>? or moon attracts x1 & ?is by ! law ( gravitation is = ! e>?-- ,w k 7m m7 _/ 7#cifc7b2 & = ! moon-- w k m 7m_/#ha7 _/ 7#ajha7b2 f :i* we f9d by division-- w 7,w _/ #ha7 7#cifc _/ #ajha7b 7,w _/ #f7 7approximately74 ,! cubic y>d ( rock1 :i* ^u ! e>? weighs two tons1 w\ld1 if transport$ to ! moon1 weigh only "o ?ird ( a ton1 & w\ld h only "o six? z mu* influ5ce 9 compress+ ! rocks bel[ x z x _h ^u ! e>?4 ,note t ?is rock :5 transport$ to ! moon w\ld be /ill attract$ by ! e>? & w\ld h weight t[>d ! e>?1 b x is n ?is ( :i* we are speak+2 by its weight 9 ! moon we mean ! =ce ) :i* ! moon attracts x4 ,mak+ due all[ance = ! diff]5ce 9 compression produc$ by weight1 we may say t 9 g5]al1 s f> z d5sity goes1 ! moon is v l a piece ( ! e>? ( equal mass set (f by itself alone4 #ig4 ,,alb$o4--,9 ano!r respect ! lun> /uff is l t ( :i* ! e>? is made3 x reflects ! sunlight 9 mu* ! same way & to ! same am\nt4 ,! contra/ ( light & d>k areas on ! moon's surface %[s1 z we %all see 9 ano!r section1 ! pres5ce ( diff]5t sub/ances ^u ! moon :i* reflect ! sunlight 9 diff]5t degrees4 ,?is capacity = reflect+ a great] or less p]c5tage ( ! incid5t sunlight is call$ alb$o 7,lat91 :it5ess71 & ! brilliancy ( ! full moon might lead "o to suppose t its alb$o is v great1 l t ( sn[ or ^? masses ( summ] cl\d :i* we call ?und]heads4 ,b ?is is only an effect ( contra/ ) ! d>k backgr\nd ( ! sky4 ,! same moon by day looks pale1 & its alb$o is1 9 fact1 n v diff]5t f t ( our common rocks--wea!r-beat5 s&/one accord+ to ,sir ,john ,h]s*el--s t x w\ld be possible to build an artificial moon ( rock or brick :i* w\ld %9e 9 ! sunlight mu* z does ! real moon4 ,! effect produc$ by ! diff]5ces ( alb$o ^u ! moon's face is commonly call$ ! man 9 ! moon1 b1 l ! images pres5t$ by gl[+ coals1 ! face 9 ! moon is any?+ :i* we *oose to make x4 ,among ! ,*9ese x is said to be a monkey p\nd+ rice2 9 ,india1 a rabbit2 9 ,p]sia1 ! e>? reflect$ z 9 a mirror1 etc4 #ih4 ,,librations4--,we h already le>n$ t ! moon turns always ! same face t[>d ! e>?1 & we h n[ to modify ?is /atem5t & to f9d t "h1 z 9 s _m o!r cases1 ! ?+ we le>n fir/ is only approximately true & ne$s to be limit$ or add$ to or modifi$ 9 "s way4 ,9 g5]al1 ,nature is too complex to be completely und]/ood at fir/ sight or to be p]fectly repres5t$ by a simple /atem5t4 ,9 ,fig4 #ee we h two photographs ( ! moon1 tak5 ne>ly ?ree ye>s ap>t1 ! "r-h& "o a little aft] fir/ qu>t] & ! left-h& "o a little be=e ?ird qu>t]4 ,!y !re=e repres5t diff]5t p>ts ( ! moon's surface1 b along ! ragg$ edge ! same region is %[n on bo? photographs1 & features common to bo? pictures may readily be f\nd--e4 g41 ! ?ree r+s :i* =m a "r-angl$ triangle ab\t "o ?ird ( ! way d[n f ! top ( ! cut1 & ! curv$ m\nta9 *a9 j bel[ ^!4 ,if ! moon turn$ exactly ! same face t[>d u 9 ! two pictures1 ! di/ance ( any "o ( ^! m>k+s f any "p ( ! moon's edge mu/ be ! same 9 bo? pictures2 b c>eful measurem5t w %[ t ?is is n ! case1 & t 9 ! left-h& picture ! upp] edge ( ! moon is tipp$ t[>d u & ! l[] edge away f u1 z if ! :ole moon _h be5 rotat$ slightly ab\t a horizontal l9e & mu/ be turn$ back a little 7ab\t #g7 9 ord] to mat* p]fectly ! o!r "p ( ! picture4 ,?is turn+ is call$ a libration1 & x %\ld be borne 9 m9d t ! moon librates n only 9 ! direction above measur$1 nor? & s\?1 b also at "r angles to ?is1 ea/ & we/1 s t we are able to see a little f>!r ar\nd e "p ( ! moon's edge ?an w\ld be possible if x turn$ t[>d u at all times exactly ! same face4 ,b 9 spite ( ! librations !re rema9s on ! f>!r side ( ! moon an area ( #f1jjj1jjj squ>e miles :i* is =ev] hidd5 f u1 & ( ^: "* we h no direct k1 al?\gh !re is no reason to suppose x v diff]5t f t :i* is visible1 despite ! fact t "s ( ! books conta9 qua9t speculations to ! contr>y4 ,! cont95t ( ,s\? ,am]ica is j ab\t equal 9 ext5t to ?is unkn[n region1 :ile ,nor? ,am]ica is a fair equival5t = all ! re/ ( ! moon's surface1 bo? ^? c5tral p>ts :i* are con/antly visible1 & ! zone ar\nd ! edge ^: p>ts sometimes come into sight & are sometimes hidd54 ,an int]e/+ consequ5ce ( ! peculi> rotation ( ! moon is t f our side ( x ! e>? is always visible4 ,sun1 />s1 & planets rise & set !re z well z "h1 b to an obs]v] on ! moon ! e>? sw+s always ov]head1 %ift+ its position a few degrees "o way or ! o!r on acc\nt ( ! libration b runn+ ?r\gh its succession ( phases1 new e>?1 fir/ qu>t]1 etc41 )\t ev] go+ bel[ ! horizon1 provid$ ! obs]v] is any:]e ne> ! c5t] ( ! moon's disk4 ,illu/ration3 ,,fig4 #ed4--;,illu/rat+ ! moon's rotation4 #ii4 ,,cause ,,( ,,librations4--,t ! moon %\ld librate is by no means s rem>kable a fact z t x %\ld at all times turn v ne>ly ! same face t[>d ! e>?4 ,?is latt] fact c h b "o mean+3 ! moon revolves ab\t an axis z does ! e>?1 b ! "t requir$ = ?is revolution is j equal to ! "t requir$ to make a revolution 9 its orbit4 ,place two co9s ^u a table ) _! heads turn$ t[>d ! nor?1 z 9 ,fig4 #ed1 & move ! small] "o ar\nd ! l>g] 9 su* a way t its face %all always look away f ! l>g] "o4 ,9 mak+ "o revolution 9 its orbit ! head on ?is small co9 w be successively direct$ t[>d e po9t ( ! compass1 & :5 x returns to its initial position ! small co9 w h made j "o revolution ab\t an axis p]p5dicul> to ! plane ( its orbit4 ,9 no o!r way c x be made to face always away f ! figure at ! c5t] ( its orbit :ile mov+ ar\nd x4 ,we are n[ 9 a position to und]/& ! moon's librations1 =1 if ! small co9 at any "t moves fa/] or sl[] 9 its orbit ?an x turns ab\t its axis1 a new side w be turn$ t[>d ! c5t]1 & ! same may happ5 if ! c5tral co9 itself %ifts into a new position4 ,?is is :at happ5s to ! moon1 = its orbital motion1 l t ( ,m]cury 7,fig4 #ag71 is alt]nately fa/ & sl[1 & 9 addition to ?is !re are pres5t o!r m9or influ5ces1 su* z ! fact t its rotation axis is n exactly p]p5dicul> to ! plane ( its orbit2 9 addition to ?is ! obs]v] ^u ! e>? is daily c>ri$ by its rotation f "o po9t ( view to ano!r1 etc41 s t x is only 9 a g5]al way t ! rotation ^u ! axis & motion 9 ! orbit keep pace ) ea* o!r4 ,9 a g5]al way a cable keeps a %ip an*or$ 9 ! same place1 al?\gh w9d & waves may cause x to librate ab\t ! an*or4 ,h[ ! moon came to h ?is exact equality betwe5 its times ( revolution & rotation con/itutes a *apt] ( its hi/ory ^u :i* we %all n n[ ent]2 b ! equality hav+ once be5 e/abli%$1 ! me*anism by :i* x is pres]v$ is simple en\gh4 ,! attraction ( ! e>? = ! moon has v slightly pull$ ! latt] out ( %ape 7 #db71 s t ! p>ticul> diamet]1 :i* po9ts t[>d ! e>?1 is a little long] ?an any o!r1 & ?us s]ves z a h&le :i* ! e>? lays hold ( & pulls d[n into its l[e/ possible position--i4 e41 ! position 9 :i* x po9ts t[>d ! c5t] ( ! e>?4 ,j h[ long ?is h&le is1 rema9s unkn[n1 b x may be %[n f ! law ( gravitation t less ?an a hundr$ y>ds ( elongation w\ld suffice = ! "w x has to d4 #ajj4 ,,! ,,moon ,,z ,a ,,_w4--,?us f> we h consid]$ ! moon z a satellite ( ! e>?1 dep5d5t ^u ! e>?1 & int]e/+ *iefly because ( its relation to x4 ,b ! moon is some?+ m ?an ?is2 x is a _w 9 itself1 v diff]5t f ! e>?1 al?\gh n :olly unlike x4 ,! mo/ *>act]i/ic feature ( ! e>?'s surface is its division into l& & wat]1 & no?+ ( ?is k9d c be f\nd ^u ! moon4 ,x is true t ! fir/ g5]ation ( a/ronom]s :o /udi$ ! moon ) telescopes fanci$ t ! l>ge d>k pat*es %[n 9 ,fig4 #ee 7 bodies ( wat]1 & nam$ !m oceans1 seas1 lakes1 & ponds1 & to ! pres5t day we keep ^? names1 al?\gh x is long s9ce recogniz$ t ^! p>ts ( ! moon's surface are z dry z any o!r4 ,_! d>k appe>ance indicates a diff]5t k9d ( mat]ial f t compos+ ! light] p>ts ( ! moon1 mat]ial ) a diff]5t alb$o1 j z ^u ! e>? we h light-color$ & d>k-color$ rocks1 m>ble & slate1 :i* se5 f ! moon mu/ pres5t simil> contra/s ( brightness4 ,al?\gh ^! d>k pat*es are almo/ ! only features di/+ui%able ) ! unaid$ eye1 x is f> o!rwise 9 ! telescope or ! photograph1 especially along ! ragg$ edge :]e great numb]s ( r+s c be se51 :i* are app>5tly depressions 9 ! moon & are call$ crat]s4 ,^! we f9d 9 great numb] all ov] ! moon1 b1 z ! figure %[s1 !y are se5 to ! be/ advantage ne> ! t]m9ator--i4 e41 ! divid+ l9e betwe5 day & night1 s9ce ! long %ad[s ca/ "h by ! ris+ or sett+ sun br+ out ! details ( ! surface bett] ?an else:]e4 ,c>efully exam9e ,fig4 #ee ) ref]5ce to ^! features4 ,illu/ration3 ,,fig4 #ee4--,! moon at fir/ & la/ qu>t]4 ,lick ,obs]vatory photographs4 ,ano!r feature :i* exi/s ^u bo? e>? & moon1 al?\gh f> less common !re ?an "h1 is illu/rat$ 9 ! *a9 ( m\nta9s visible ne> ! t]m9ator1 a little above ! c5t] ( ! moon 9 bo? p>ts ( ,fig4 #ee4 ,?is p>ticul> range ( m\nta9s1 :i* is call$ ! ,lun> ,ap5n9es1 is by f> ! mo/ prom95t "o ^u ! moon1 al?\gh o!rs1 ! ,alps & ,caucasus1 exi/4 ,b = ! mo/ "p ! lun> m\nta9s /& alone1 ea* by itself1 in/ead ( be+ gr\p$ into ranges1 z on ! e>?4 ,note 9 ! figure t "s ( ! lun> m\nta9s /ret* out into ! night side ( ! moon1 _! peaks project+ up into ! sunlight1 & ?us becom+ visible1 :ile ! l[l&s are buri$ 9 ! %ad[4 ,a subord9ate feature ( ! moon's surface is ! sy/em ( rays :i* seem to radiate l spokes f "s ( ! l>g] crat]s1 ext5d+ ov] hill & valley sometimes = hundr$s ( miles4 ,a sugge/ion ( ^! rays may be se5 9 ,fig4 #ee1 ext5d+ f ! great crat] ,cop]nicus a little s\?we/ ( ! end ( ! ,ap5n9es1 b _! mo/ p]fect developm5t is to be se5 at ! "t ( full moon ar\nd ! crat] ,ty*o1 :i* lies ne> ! s\? pole ( ! moon4 ,look = !m ) an op]a glass4 ,ano!r & ev5 less conspicu\s feature is furni%$ by ! rills1 :i*1 "u favorable conditions ( illum9ation1 appe> l long cracks on ! moon's surface1 p]haps analog\s to ! caons ( our ,we/]n c\ntry4 #aja4 ,,! ,,map ,,( ,,! ,,moon4--,fig4 #ee furni%es a fairly good map ( a limit$ portion ( ! moon ne> ! t]m9ator1 b at ! edges little or no detail c be se54 ,?is is always true2 ! :ole ( ! moon c n be se5 to advantage at any "o "t1 & to rem$y ?is we ne$ to con/ruct f _m photographs or draw+s a map :i* %all repres5t ! sev]al p>ts ( ! moon z !y appe> at _! be/4 ,fig4 #ef %[s su* a map photograph$ f a relief model ( ! moon1 & repres5t+ ! pr9cipal features ( ! lun> surface 9 a way !y c nev] be se5 simultane\sly4 ,p]haps its mo/ /rik+ feature is ! %ape ( ! crat]s1 :i* are %[n r\nd 9 ! c5tral p>ts ( ! map & oval at ! edges1 ) _! long diamet]s p>allel to ! moon's edge4 ,?is is1 ( c\rse1 an effect ( ! curvature ( ! moon's surface1 = we look v obliquely at ! edge portions1 & ?us see _! =mations mu* =e%ort5$ 9 ! direction ( ! moon's radius4 ,illu/ration3 ,,fig4 #ef4--,relief map ( ! moon's surface4--,aft] ,,nasmy? & ,,c>p5t]4 ,! nor? & s\? poles ( ! moon are at ! top & bottom ( ! map respectively1 & a m]e inspection ( ! regions ar\nd !m w %[ h[ mu* m rugg$ is ! s\!rn hemisph]e ( ! moon ?an ! nor!rn4 ,x furni%es1 too1 "s indication ( h[ num]\s are ! lun> crat]s1 & h[ 9 cr[d$ regions !y ov]lap "o ano!r4 ,! /ud5t %\ld pick out ^u ! map ^? features :i* he has le>n$ to "k 9 ! photograph 7,fig4 #ee7--! ,ap5n9es1 ,cop]nicus1 & ! cont9uation ( ! ,ap5n9es1 ext5d+ into ! d>k "p ( ! moon4 ,illu/ration3 ,,fig4 #eg4--,m>e ,imbrium4 ,photograph$ by ,g4 ,w4 ,,rit*ey4 #ajb4 ,,size ,,( ,,! ,,lun> ,,features4--,we may measure di/ances "h 9 ! same way z ^u a t]re/rial map1 rememb]+ t ne> ! edges ! scale ( ! map is v mu* di/ort$ p>allel to ! moon's diamet]1 & measurem5ts mu/ n be tak5 9 ?is direction1 b may be tak5 p>allel to ! edge4 ,measur+ ) a millimet] scale1 we f9d on ! map = ! diamet] ( ! crat] ,cop]nicus1 #b4a millimet]s4 ,to turn ?is into ! diamet] ( ! real ,cop]nicus 9 miles1 we measure ^u ! same map ! diamet] ( ! moon1 #gi4g millimet]s1 & !n h ! proportion-- ,diamet] ( ,cop]nicus 9 miles 3 #b1afc 33 #b4a 3 #gi4g1 :i* :5 solv$ gives #eg miles4 ,! real diamet] ( ,cop]nicus is a trifle ov] #ef miles4 ,at ! ea/]n edge ( ! moon1 opposite ! ,ap5n9es1 is a l>ge oval spot call$ ! ,m>e ,crisium 7,lat91 ma-re sea74 ,measure its l5g?4 ,! l>ge crat] to ! nor?we/ ( ! ,ap5n9es is call$ ,ar*im$es4 ,measure its diamet] bo? 9 ! map & 9 ! photograph 7,fig4 #ee71 & see h[ ! two results agree4 ,! true diamet] ( ?is crat]1 ea/ & we/1 is v approximately #ej miles4 ,! great smoo? surface to ! we/ ( ,ar*im$es is ! ,m>e ,imbrium4 ,is x l>g] or small] ?an ,lake ,sup]ior8 ,fig4 #eg is f a photograph ( ! ,m>e ,imbrium1 & ! am\nt ( detail "h %[n at ! bottom ( ! sea is a suffici5t indication t1 9 ?is case at lea/1 ! wat] has be5 drawn (f1 if inde$ any 0 ev] pres5t4 ,illu/ration3 ,,fig4 #eh4--,m>e ,crisium4 ,lick ,obs]vatory photographs4 ,fig4 #eh is a repres5tation ( ! ,m>e ,crisium at a "t :5 night 0 beg9n+ to encroa* ^u its ea/]n bord]1 & x s]ves well to %[ ! rugg$ "* ( ! r+-%ap$ wall :i* incloses ?is area4 ,) ^! pictures ( ! smoo!r p>ts ( ! moon's surface we may comp>e ,fig4 #ei1 :i* %[s a region ne> ! nor? pole ( ! moon1 & ,fig4 #fj1 giv+ an e>ly morn+ view ( ,ar*im$es & ! ,ap5n9es4 ,note h[ long & %>p are ! %ad[s4 ,illu/ration3 ,,fig4 #ei4--;,illu/rat+ ! rugg$ "* ( ! moon's surface4--,,nasmy? & ,,c>p5t]4 #ajc4 ,,! ,,moon',s ,,atmosph]e4--,^u ! e>? ! sun ca/s no %ad[s s %>p & black z ^? ( ,fig4 #fj1 because 8 rays are "h scatt]$ & reflect$ 9 all directions by ! du/ & vapors ( ! atmosph]e 7 #ea71 s t ! place f :i* direct sunlight is cut (f is at lea/ p>tially illum9$ by ?is reflect$ light4 ,! %ad[s ( ,fig4 #fj %[ t ^u ! moon x mu/ be o!rwise1 & sugge/ t if ! moon has any atmosph]e :atev]1 its d5sity mu/ be utt]ly insignificant 9 comp>ison ) t ( ! e>?4 ,9 its motion ar\nd ! e>? ! moon frequ5tly eclipses />s 7occults is ! te*nical ^w71 & if ! moon _h an atmosph]e su* z is %[n 9 ,fig4 #fa1 ! light f ! /> ,a mu/ %9e ?r\gh ?is atmosph]e j be=e ! moon's advanc+ body cuts x (f1 & x mu/ be refract$ by ! atmosph]e s t ! /> w\ld appe> 9 a slightly diff]5t direction 7ne>] to ,b7 ?an be=e4 ,! e>?'s atmosph]e refracts ! />light "u su* circum/ances by m ?an a degree1 b no "o has be5 able to f9d 9 ! case ( ! moon any effect ( ?is k9d am\nt+ to ev5 a fraction ( a second ( arc4 ,:ile ?is h>dly ju/ifies ! /atem5t sometimes made t ! moon has no atmosph]e1 we %all be entirely safe 9 say+ t if x has "o at all its d5sity is less ?an a ?\s&? "p ( t ( ! e>?'s atmosph]e4 ,q 9 keep+ ) ?is abs5ce ( an atmosph]e is ! fact t cl\ds nev] float ov] ! surface ( ! moon4 ,its features always /& out h>d & cle>1 )\t any ( t haze & s(tness ( outl9e :i* our atmosph]e introduces into all t]re/rial l&scapes4 ,illu/ration3 ,,fig4 #fj4--;,ar*im$es & ,ap5n9es4 ,,nasmy? & ,,c>p5t]4 #ajd4 ,,height ,,( ,,! ,,lun> ,,m\nta9s4--,att5tion has already be5 call$ to ! deta*$ m\nta9 peaks1 :i* 9 ,fig4 #ee prolong ! range ( ,ap5n9es into ! lun> night4 ,^! are ! beg9n+s ( ! ,caucasus m\nta9s1 & f ! photograph we may measure z foll[s ! height to :i* !y rise above ! surr\nd+ level ( ! moon3 ,fig4 #fb repres5ts a "p ( ! lun> surface along ! b\nd>y l9e betwe5 night & day1 ! horizontal l9e at ! top ( ! figure repres5t+ a level ray ( sunlight :i* j t\*es ! moon at ,t & b>ely illum9ates ! top ( ! m\nta91 ,m1 ^: height1 h1 is to be det]m9$4 ,if we let ,r /& = ! radius ( ! moon & s = ! di/ance1 ,t ,m1 we %all h 9 ! "r-angl$ triangle ,m ,t ,c1 ,r#b s#b 7,r h7#b1 & we ne$ only to measure s--t is1 ! di/ance f ! t]m9ator to ! deta*$ m\nta9 peak--to make ?is equation det]m9e h1 s9ce ,r is already kn[n1 be+ half ! diamet] ( ! moon--#a1jha miles4 ,practically x is m conv5i5t to use in/ead ( ?is equation ano!r =m1 :i* ! /ud5t :o is exp]t 9 algebra may %[ to be v ne>ly equival5t to x3 h 7miles7 s#b _/ #bafc1 or h 7feet7 #b4dd s#b4 ,! di/ance s mu/ be express$ 9 miles 9 all ( ^! equations4 ,9 ,fig4 #ee ! di/ance f ! t]m9ator to ! fir/ deta*$ peak ( ! ,caucasus m\nta9s is #a4g millimet]s #eb miles1 f :i* we f9d ! height ( ! m\nta9 to be #a4be miles1 or #f1fjj feet4 ,illu/ration3 ,,fig4 #fa4--,occultations & ! moon's atmosph]e4 ,illu/ration3 ,,fig4 #fb4--;,det]m9+ ! height ( a lun> m\nta94 ,two ?+s1 h[ev]1 ne$ to be borne 9 m9d 9 ?is connection4 ,on ! e>? we measure ! heights ( m\nta9s above sea level1 :ile on ! moon !re is no sea1 & our #f1fjj feet is simply ! height ( ! m\nta9 top above ! level ( t p>ticul> po9t 9 ! t]m9ator1 f :i* we measure its di/ance4 ,s too x is evid5t f ! appe>ance ( ?+s1 t ! sunlight1 in/ead ( j t\*+ ! top ( ! p>ticul> m\nta9 ^: height we h measur$1 really ext5ds "s little di/ance d[n f its summit1 & ! #f1fjj feet is !re=e ! elevation ( ! l[e/ po9t on ! m\nta9s to :i* ! sunlight rea*es4 ,! peak itself may be sev]al hundr$ feet high]1 & our photograph mu/ be tak5 at ! exact mom5t :5 ?is peak appe>s 9 ! lun> morn+ or disappe>s 9 ! ev5+ if we are to measure ! altitude ( ! m\nta9's summit4 ,measure ! height ( ! mo/ nor!rn visible m\nta9 ( ! ,caucasus range4 ,?is is "o ( ! outly+ spurs ( ! great m\nta9 ,calippus1 ^: pr9cipal peak1 #ai1jjj feet high1 is %[n 9 ,fig4 #ee z ! brighte/ "p ( ! ,caucasus range4 ,! highe/ peak ( ! lun> ,ap5n9es1 ,huygh5s1 has an altitude ( #ah1jjj feet1 & ! ,leibnitz & ,do]fel ,m\nta9s1 ne> ! s\? pole ( ! moon1 rea* an altitude #ej p] c5t great] ?an ?is1 & are probably ! highe/ peaks on ! moon4 ,?is falls v little %ort ( ! highe/ m\nta9 on ! e>?1 al?\gh ! moon is mu* small] ?an ! e>?1 & ^! m\nta9s are consid]ably high] ?an any?+ on ! we/]n cont95t ( ! e>?4 ,! vagu5ess ( outl9e ( ! t]m9ator makes x difficult to measure f x ) precision1 & some:at m accurate det]m9ations ( ! heights ( lun> m\nta9s c be obta9$ by measur+ ! l5g? ( ! %ad[s :i* !y ca/1 & ! dep?s ( crat]s may also be measur$ by means ( ! %ad[s :i* fall into !m4 #aje4 ,,crat]s4--,fig4 #fc %[s a typical lun> crat]1 & conveys a good idea ( ! rugg$ness ( ! lun> l&scape4 ,comp>e ! appe>ance ( ?is crat] ) ! foll[+ g5]alizations1 :i* are bas$ ^u ! accurate measurem5t ( _m su*3 ,a4 ,a crat] is a real depression 9 ! surface ( ! moon1 surr\nd$ usually by an elevat$ r+ :i* rises above ! g5]al level ( ! region outside1 :ile ! bottom ( ! crat] is ab\t an equal di/ance bel[ t level4 ,b4 ,crat]s are %all[1 _! diamet]s rang+ f five times to m ?an fifty times _! dep?4 ,ar*im$es1 ^: diamet] we f\nd to be #ej miles1 has an av]age dep? ( ab\t #d1jjj feet bel[ ! cre/ ( its surr\nd+ wall1 & is relatively a %all[ crat]4 ,illu/ration3 ,,fig4 #fc4--;,a typical lun> crat]4--,,nasmy? & ,,c>p5t]4 ,c4 ,crat]s frequ5tly h "o or m hills ris+ )9 !m :i*1 h[ev]1 r>ely1 if ev]1 rea* up to ! level ( ! surr\nd+ wall4 ,d4 ,:atev] may h be5 ! mode ( _! =mation1 ! crat]s c n h be5 produc$ by scoop+ out mat]ial f ! c5t] & pil+ x up to make ! wall1 = 9 ?ree cases out ( f\r ! volume ( ! excavation is great] ?an ! volume ( mat]ial conta9$ 9 ! wall4 #ajf4 ,,moon ,,& ,,e>?4--,we h gone f> en\gh n[ to appreciate bo? ! lik5ess & ! unlik5ess ( ! moon & e>?4 ,!y may fairly en\gh be lik5$ to (fspr+ ( ! same p>5t :o h foll[$ v diff]5t c>e]s1 & 9 ! fullness ( "t f9d !mselves 9 v diff]5t circum/ances4 ,! mo/ s]i\s po9t ( diff]5ce 9 ^! circum/ances is ! atmosph]e1 :i* gives to ! e>? a weal? ( ph5om5a altoge!r lack+ 9 ! moon4 ,cl\ds1 w9d1 ra91 sn[1 dew1 fro/1 & hail are all dep5d5t ^u ! atmosph]e & c n be f\nd :]e x is n4 ,!re c be no?+ ^u ! moon at all l t great gr\p ( *anges :i* we call wea!r1 & ! unruffl$ aspect ( ! moon's face contra/s %>ply ) ! succession ( cl\d & sun%9e :i* ! e>? w\ld pres5t if se5 f ! moon4 ,! atmosph]e is ! *ief ag5t 9 ! propagation ( s\nd1 & )\t x ! moon mu/ be wrapp$ 9 sil5ce m absolute ?an c be f\nd ^u ! surface ( ! e>?4 ,s1 too1 ! abs5ce ( an atmosph]e %[s t !re c be no wat] or o!r liquid ^u ! moon1 = if s x w\ld imm$iately evaporate & produce a gase\s envelope :i* we h se5 does n exi/4 ,) air & wat] abs5t !re c be ( c\rse no vegetation or life ( any k9d ^u ! moon1 & we are compell$ to reg>d x z an arid des]t1 utt]ly wa/e4 #ajg4 ,,temp]ature ,,( ,,! ,,moon4--,a *>act]i/ic feature ( t]re/rial des]ts1 :i* is possess$ 9 exagg]at$ degree by ! moon1 is ! great extremes ( temp]ature to :i* !y & x are subject4 ,ow+ to its sl[ rotation ab\t its axis1 a po9t on ! moon receives ! sol> radiation un9t]rupt$ly = m ?an a =tnight1 & t too unmitigat$ by any cl\d or vapor\s cov]+4 ,!n = a l p]iod x is turn$ away f ! sun & all[$ to cool (f1 radiat+ into int]planet>y space )\t h9drance its accumulat$ /ore ( heat4 ,x is easy to see t ! range ( temp]ature betwe5 day & night mu/ be mu* great] "u ^! circum/ances ?an x is ) u :]e %ort] days & cl\d$ skies r5d] day & night m ne>ly alike1 to say no?+ ( ! ocean ^: wat]s s]ve z a great balance :eel = equaliz+ temp]atures4 ,j h[ hot or h[ cold ! moon becomes is h>d to det]m9e1 & v diff]5t e/imates are to be f\nd 9 ! books4 ,p]haps ! mo/ reliable ( ^! are furni%$ by ! rec5t rese>*es ( ,pr(essor ,v1 ^: exp]im5ts lead him to conclude t its rocky surface at midday1 9 latitudes :]e ! sun is high1 is probably hott] ?an boil+ wat] & only ! mo/ t]rible ( e>?'s des]ts1 :]e ! burn+ s&s bli/] ! sk91 & m51 bea/s1 & birds drop dead1 c approa* a noontide on ! cl\dless surface ( our satellite4 ,only ! extreme pol> latitudes ( ! moon c h an endurable temp]ature by day1 to say no?+ ( ! night1 :5 we %\ld h to become troglodytes to pres]ve ourselves f su* int5se cold4 ,:ile ! night temp]ature ( ! moon1 ev5 v soon aft] sunset1 s9ks to some?+ l #bjj bel[ z]o on ! c5tigrade scale1 or #cbj bel[ z]o on ! ,fahr5heit scale1 ! l[e/ kn[n temp]ature ^u ! e>?1 accord+ to ,g5]al ,greely1 is #ij ,fahr4 bel[ z]o1 record$ 9 ,sib]ia 9 ,janu>y1 #ahhe4 ,w9t] & summ] are n m>k$ly diff]5t ^u ! moon1 s9ce its rotation axis is ne>ly p]p5dicul> to ! plane ( ! e>?'s orbit ab\t ! sun1 & ! sun nev] goes f> nor? or s\? ( ! moon's equator4 ,! mon? is ! "o cycle )9 :i* all seasonal *anges 9 its physical condition appe> to run _! complete c\rse4 #ajh4 ,,*anges ,,9 ,,! ,,moon4--,x is evid5tly idle to look = any su* *anges 9 ! condition ( ! moon's surface z ) u m>k ! progress ( ! seasons or ! spread ( civilization ov] ! wild]ness4 ,b m9or *anges !re may be1 & x w\ld seem t ! viol5t oscillations ( temp]ature f day to night ought to h "s effect 9 break+ d[n & crumbl+ ! %>p peaks & crags :i* are !re s common & s pron\nc$4 ,= a c5tury pa/ a/ronom]s h se>*$ c>efully = *anges ( ?is k9d--! fill+ up ( "s crat] or ! fall ( a m\nta9 peak2 b :ile "s ?+s ( ?is k9d h be5 report$ f "t to "t1 ! evid5ce 9 _! behalf has n be5 altoge!r conclusive4 ,at ! pres5t "t x is an op5 "q :e!r *anges ( ?is sort l>ge en\gh to be se5 f ! e>? are 9 progress4 ,a crat] mu* less ?an a mile wide c be se5 9 ! telescope1 b x is n easy to tell :e!r s m9ute an object has *ang$ 9 size or %ape dur+ a ye> or a decade1 & ev5 if *anges are se5 !y may be app>5t r ?an real4 ,fig4 #fd conta9s two views ( ! crat] ,ar*im$es1 tak5 "u a morn+ & an aft]noon sun respectively1 & %[s a v pron\nc$ diff]5ce betwe5 ! two :i* proce$s solely f a diff]5ce ( illum9ation4 ,9 ! pres5ce ( su* l>ge fictiti\s *anges a/ronom]s are sl[ to accept small] ones z real4 ,illu/ration3 ,,fig4 #fd4--;,ar*im$es 9 ! lun> morn+ & aft]noon4--,,we9ek4 ,x is ?is abs5ce ( *ange t is responsible = ! rugg$ & %>p-cut features ( ! moon :i* cont9ue sub/antially z !y 7 made1 :ile ^u ! e>? ra9 & fro/ are cont9ually we>+ d[n ! m\nta9s & spread+ _! sub/ance ^u ! l[l& 9 an un5d+ process ( smoo?+ (f ! r\ghnesses ( its surface4 ,^u ! moon ?is process is almo/ if n :olly want+1 & ! moon abides to-day mu* m l its primitive condition ?an is ! e>?4 #aji4 ,,! ,,moon',s ,,influ5ce ,,^u ,,! ,,e>?4--,!re is a widespread popul> belief t 9 _m ways ! moon ex]cises a consid]able influ5ce ^u t]re/rial affairs3 t x affects ! wea!r = good or ill1 t crops mu/ be plant$ & h>ve/$1 pigs mu/ be kill$1 & timb] cut at ! "r "t ( ! moon1 etc4 ,our common ^w lunatic means moon/ruck--i4 e41 "o ^u :om ! moon has %one :ile sleep+4 ,!re is n ! slighte/ sci5tific basis = any ( ^! beliefs1 & a/ronom]s ev]y:]e class !m ) tales ( wit*craft1 magic1 & popul> delusion4 ,= ! mo/ "p ! moon's influ5ce ^u ! e>? is limit$ to ! light :i* x s5ds & ! effect ( its gravitation1 *iefly exhibit$ 9 ! ocean tides4 ,we receive f ! moon a v small am\nt ( second-h& sol> heat & !re is also a trifl+ magnetic influ5ce1 b nei!r ( ^! la/ effects comes )9 ! range ( ord9>y obs]vation1 & we %all n g f> wrong 9 say+ t1 save ! moonlight & ! tides1 e suppos$ lun> influ5ce ^u ! e>? is ei!r fictiti\s or too small to be readily detect$4 ,,*apt] ,x ,,! ,,sun #aaj4 ,,dep5d5ce ,,( ,,! ,,e>? ,,^u ,,! ,,sun4--,!re is no bett] introduction to ! /udy ( ! sun ?an ,byron's ,ode to ,d>kness1 beg9n+ ) ! l9es-- ,i dream$ a dream ,t 0 n all a dream4 ,! bright sun 0 ext+ui%$1 & proce$+ to depict 9 vivid words ! consequ5ces ( ?is ext9ction4 ,! mo/ matt]-(-fact language ( sci5ce agrees ) ! words ( ! poet 9 decl>+ ! e>?'s dep5d5ce ^u ! sun = all ^? v>i$ =ms ( en]gy :i* make x a fit abode = liv+ be+s4 ,! w9ds bl[ & ! riv]s run2 ! crops gr[1 are ga!r$ & consum$1 by virtue ( ! sol> en]gy4 ,factory1 locomotive1 bea/1 bird1 & ! human body furni% types ( ma*9es run by en]gy d]iv$ f ! sun2 & ! /ud5t w f9d x an in/ructive ex]cise to se>* = k9ds ( t]re/rial en]gy :i* are n d]iv$ ei!r directly or indirectly f ! sun4 ,!re are a few su*1 b !y are nei!r num]\s nor important4 #aaa4 ,,! ,,sun',s ,,di/ance ,,f ,,! ,,e>?4--,to ! a/ronom] ! sun pres5ts problems ( ! highe/ consequ5ce & app>5tly ( v div]se "*1 b all t5d+ t[>d ! same goal3 ! fram+ ( a me*anical explanation ( ! sun consid]$ z a ma*9e2 :at x is1 & h[ x does its "w4 ,9 ! =efront ( ^! problems /& ^? num]ical det]m9ations ( di/ance1 size1 mass1 d5sity1 etc41 :i* we h already enc\nt]$ 9 connection ) ! moon1 b :i* mu/ "h be dealt ) 9 a diff]5t mann]1 because ! imm5sely great] di/ance ( ! sun makes impossible ! resort to any su* simple me?od z ! triangle us$ = det]m9+ ! moon's di/ance4 ,x w\ld be l det]m9+ ! di/ance ( a /eeple a mile away by obs]v+ its direction fir/ f "o eye1 !n f ! o!r2 too %ort a base = ! triangle4 ,9 "o respect1 h[ev]1 we /& ^u a bett] foot+ ?an 9 ! case ( ! moon1 = ! mass ( ! e>? has already be5 f\nd 7,*apt] ,,iv7 z a fractional "p ( ! sun's mass1 & we h only to inv]t ! fraction 9 ord] to f9d t ! sun's mass is #cbi1jjj times t ( ! e>? & moon comb9$1 or #ccc1jjj times t ( ! e>? alone4 ,if we c\ld rely implicitly ^u ?is numb] we might make x det]m9e = u ! di/ance ( ! sun ?r\gh ! law ( gravitation z foll[s3 ,x 0 sugge/$ 9 #ch t ,newton prov$ ,kepl]'s ?ree laws to be imp]fect coroll>ies f ! law ( gravitation1 requir+ a little am5dm5t to make !m /rictly correct1 & bel[ we give 9 ! =m ( an equation ,kepl]'s /atem5t ( ! ,?ird ,law toge!r ) ,newton's am5dm5t ( x4 ,9 ^! equations-- ,t ,p]iodic "t ( any planet2 a ,"o half ! major axis ( its orbit2 m ,its mass2 ,m ,! mass ( ! sun2 k ,! gravitation con/ant correspond+ to ! p>ticul> set ( units 9 :i* ,t1 a1 m1 & ,m are express$4 7,kepl]7 a#c_/,t#b h2 7,newton7 a#c_/,t#b k 7,m m74 ,kepl]'s idea 03 ,= e planet :i* moves ar\nd ! sun1 a#c divid$ by ,t#b always gives ! same quoti5t1 h2 & he did n conc]n himself ) ! significance ( ?is quoti5t fur!r ?an to note t if ! p>ticul> a & ,t :i* belong to any planet--e4 g41 ! e>?--be tak5 z ! units ( l5g? & "t1 !n ! quoti5t w be #a4 ,newton1 on ! o!r h&1 atta*$ a mean+ to ! quoti5t1 & %[$ t x is equal to ! product obta9$ by multiply+ ! sum ( ! two masses1 planet & sun1 by a numb] :i* is always ! same :5 we are deal+ ) ! action ( gravitation1 :e!r x be betwe5 ! sun & planet1 or betwe5 moon & e>?1 or betwe5 ! e>? & a roa/ ( beef 9 ! but*]'s scales1 provid$ only t we use always ! same units ) :i* to measure times1 di/ances1 & masses4 ,num]ically1 ,newton's correction to ,kepl]'s ,?ird ,law does n am\nt to mu* 9 ! motion ( ! planets4 ,jupit]1 :i* %[s ! greate/ effect1 makes ! circuit ( 8 orbit 9 #d1ccc days in/ead ( #d1cce1 :i* x w\ld require if ,kepl]'s law 7 /rictly true4 ,b 9 ano!r respect ! *ange is ( ! utmo/ importance1 s9ce x enables u to ext5d ,kepl]'s law1 :i* relates solely to ! sun & its planets1 to o!r attract+ bodies1 su* z ! e>?1 moon1 & />s4 ,?us = ! moon's motion ar\nd ! e>? we write-- 7#bdj1jjjc7_/7bg4cbb7 k 7#a #a_/ha71 f :i* we may f9d t1 ) ! units "h employ$1 ! e>?'s mass z ! unit ( mass1 ! mean sol> day z ! unit ( "t1 & ! mile z ! unit ( di/ance-- k #ahcj #ajaj4 ,if we introduce ?is value ( k into ! correspond+ equation1 :i* repres5ts ! motion ( ! e>? ar\nd ! sun1 we %all h-- a#c_/7cfe4be7b #ahcj #ajaj 7#ccc1jjj #a71 :]e ! l>ge numb] 9 ! p>5!sis repres5ts ! numb] ( times ! mass ( ! sun is great] ?an ! mass ( ! e>?4 ,we %all f9d by solv+ ?is equation t a1 ! mean di/ance ( ! sun f ! e>?1 is v approximately #ic1jjj1jjj miles4 #aac4 ,,ano!r ,,me?od ,,( ,,det]m9+ ,,! ,,sun',s ,,di/ance4--,?is w be be/ appreciat$ by a ref]5ce to ,fig4 #ag4 ,x appe>s "h t ! e>? makes its ne>e/ approa* to ! orbit ( ,m>s 9 ! mon? ( ,augu/1 & if 9 any ,augu/ ,m>s happ5s to be 9 opposition1 its di/ance f ! e>? w be v mu* less ?an ! di/ance ( ! sun f ! e>?1 & may be measur$ by me?ods n unlike ^? :i* s]v$ = ! moon4 ,if n[ ! orbits ( ,m>s & ! e>? 7 circles hav+ _! c5t]s at ! sun ?is di/ance betwe5 !m1 :i* we may repres5t by ,d1 w\ld be ! diff]5ce ( ! radii ( ^! orbits-- ,d a - a1 :]e ! acc5ts 1 repres5t ,m>s & ! e>? respectively4 ,kepl]'s ,?ird ,law furni%es ! relation-- 7a7#c_/7,t7#b 7a7#c_/7,t7#b2 & s9ce ! p]iodic times ( ! e>? & ,m>s1 ,t1 ,t1 are kn[n to a high degree ( accuracy1 ^! two equations are suffici5t to det]m9e ! two unkn[n quantities1 a1 a--i4 e41 ! di/ance ( ! sun f ,m>s z well z f ! e>?4 ,! fir/ ( ^! equations is1 ( c\rse1 n /rictly true1 on acc\nt ( ! elliptical %ape ( ! orbits1 b ?is c be all[$ = easily en\gh4 ,9 practice x is f\nd bett] to apply ?is me?od ( det]m9+ ! sun's di/ance ?r\gh obs]vations ( an a/]oid r ?an obs]vations ( ,m>s1 & great int]e/ has be5 ar\s$ among a/ronom]s by ! discov]y1 9 #ahih1 ( an a/]oid1 or planet1 ,eros1 :i* at times comes mu* clos] to ! e>? ?an does ,m>s or any o!r heav5ly body except ! moon1 & :i* w at future oppositions furni% a m accurate det]m9ation ( ! sun's di/ance ?an any hi!rto available4 ,obs]vations = ?is purpose are be+ made at ! pres5t "t 7,octob]1 #aijj74 ,_m o!r me?ods ( measur+ ! sun's di/ance h be5 devis$ by a/ronom]s1 "s ( !m extremely +5i\s & int]e/+1 b e "o ( !m has its weak po9t--e4 g41 ! det]m9ation ( ! mass ( ! e>? 9 ! fir/ me?od giv5 above & ! measurem5t ( ,d 9 ! second me?od1 s t ev5 ! be/ results at pres5t are unc]ta9 to ! ext5t ( #bjj1jjj miles or m1 & a/ronom]s1 in/ead ( rely+ ^u any "o me?od1 mu/ use all ( !m1 & take an av]age ( _! results4 ,accord+ to ,pr(essor ,h>kness1 ?is av]age value is #ib1gif1iej miles1 & x seems c]ta9 t a l9e ( ?is l5g? drawn f ! e>? t[>d ! sun w\ld end some:]e )9 ! body ( ! sun1 b :e!r on ! ne>] or ! f>!r side ( ! c5t]1 or exactly at x1 no man kn[s4 #aad4 ,,p>allax ,,& ,,di/ance4--,x is q cu/om>y among a/ronom]s to speak ( ! sun's p>allax1 in/ead ( its di/ance f ! e>?1 mean+ by p>allax its diff]5ce ( direction z se5 f ! c5t] & surface ( ! e>?--i4 e41 ! angle subt5d$ at ! sun by a radius ( ! e>? plac$ at "r angles to ! l9e ( sight4 ,! great] ! sun's di/ance ! small] w ?is angle be1 & x !re=e makes a sub/itute = ! di/ance :i* has ! advantage ( be+ repres5t$ by a small numb]1 #h4h1 in/ead ( a l>ge "o4 ,! books ab\nd ) illu/rations int5d$ to help ! read] compreh5d h[ great is a di/ance ( #ic1jjj1jjj miles1 b a s+le "o ( ^! mu/ suffice "h4 ,to ride #ajj miles a day #cfe days 9 ! ye> w\ld be c\nt$ a good bicycl+ record1 b ! rid] :o />t$ at ! beg9n+ ( ! ,*ri/ian era & rode at t rate t[>d ! sun f ! ye> #a ,a4 ,d4 d[n to ! pres5t mom5t w\ld n yet h rea*$ 8 de/9ation1 al?\gh 8 j\rney w\ld be ab\t ?ree qu>t]s done4 ,he w\ld h cross$ ! orbit ( ,v5us ab\t ! "t ( ,*>lemagne1 & t ( ,m]cury soon aft] ! discov]y ( ,am]ica4 #aae4 ,,size ,,& ,,d5sity ,,( ,,! ,,sun4--,kn[+ ! di/ance ( ! sun1 x is easy to f9d f ! angle subt5d$ by its diamet] 7#cb m9utes ( arc7 t ! l5g? ( t diamet] is #hfe1jjj miles4 ,we recall 9 ?is connection t ! diamet] ( ! moon's orbit is only #dhj1jjj miles1 b little m ?an half ! diamet] ( ! sun1 ?us af=d+ abundant room inside ! sun1 & to sp>e1 = ! moon to p]=m ! mon?ly revolution ab\t its orbit1 z %[n 9 ,fig4 #fe4 ,illu/ration3 ,,fig4 #fe4--,! sun's size4--,,"y4 ,9 ! same mann] 9 :i* ! d5sity ( ! moon 0 f\nd f its mass & diamet]1 ! /ud5t may f9d f ! mass & diamet] ( ! sun giv5 above t its mean d5sity is #a4d times t ( wat]4 ,?is is ab\t ! same z ! d5sity ( gravel or s(t coal1 & is j ab\t "o qu>t] ( ! av]age d5sity ( ! e>?4 ,we recall t ! small d5sity ( ! moon 0 acc\nt$ = by ! dim9i%$ weight ( objects ^u x1 b ?is explanation c n hold 9 ! case ( ! sun1 = n only is ! d5sity less b ! =ce ( gravity 7weight7 is !re #bh times z great z ^u ! e>?4 ,! a?lete :o "h weighs #age p\nds1 if transport$ to ! surface ( ! sun w\ld weigh m ?an an elephant does "h1 & w\ld f9d 8 bones break "u 8 own weight if 8 muscles 7 /rong en\gh to hold him upright4 ,! trem5d\s pressure ex]t$ by gravity at ! surface ( ! sun mu/ be surpass$ bel[ ! surface1 & z x does n pack ! mat]ial toge!r & make x d5se1 we are driv5 to "o ( two conclusions3 ,ei!r ! /uff ( :i* ! sun is made is altoge!r unlike t ( ! e>?1 n s readily compress$ by pressure1 or !re is "s oppos+ influ5ce at "w :i* m ?an balances ! effect ( gravity & makes ! sol> /uff mu* light] ?an ! t]re/rial4 #aaf4 ,,mat]ial ,,( ,,:i* ,,! ,,sun ,,is ,,made4--,z to ! fir/ ( ^! alt]natives1 ! spectroscope comes to our aid & %[s 9 ! sun's spectrum 7,fig4 #ej7 ! *>act]i/ic l9e m>k$ ,d1 :i* we "k always indicates ! pres5ce ( sodium & id5tifies at lea/ "o t]re/rial sub/ance z pres5t 9 ! sun 9 consid]able quantity4 ,! l9es m>k$ ,c & ,f are produc$ by hydrog51 :i* is "o ( ! con/itu5ts ( wat]1 ,e %[s calcium to be pres5t 9 ! sun1 b magnesium1 etc4 ,9 ?is way x has be5 %[n t ab\t "o half ( our t]re/rial elem5ts1 ma9ly ! metallic ones1 are pres5t z gases on or ne> ! sun's surface1 b x mu/ n be inf]r$ t elem5ts n f\nd 9 ?is way are abs5t f ! sun4 ,!y may be !re1 probably are !re1 b ! spectroscopic pro( ( _! pres5ce is m difficult to obta94 ,pr(essor ,r[l&1 :o has be5 prom95t 9 ! /udy ( ! sol> spectrum1 says3 ,7 ! :ole e>? heat$ to ! temp]ature ( ! sun1 its spectrum w\ld probably resemble t ( ! sun v closely4 ,"s ( ! common t]re/rial elem5ts f\nd 9 ! sun are3 ,alum9ium4 ,calcium4 ,c>bon4 ,copp]4 ,hydrog54 ,iron4 ,lead4 ,nickel4 ,potassium4 ,silicon4 ,silv]4 ,sodium4 ,t94 ,z9c4 ,oxyg5 787 ,:atev] diff]5ces ( *emical /ructure may exi/ betwe5 ! sun & ! e>?1 x seems t we mu/ reg>d ^! bodies z m l ?an unlike to ea* o!r 9 sub/ance1 & we are br\ght back to ! second ( our alt]natives3 !re mu/ be "s influ5ce oppos+ ! =ce ( gravity & mak+ ! sub/ance ( ! sun light in/ead ( heavy1 & we ne$ n seek f> to f9d x 9-- #aag4 ,,! ,,heat ,,( ,,! ,,sun4--,t ! sun is hot is too evid5t to require pro(1 & x is a famili> fact t heat exp&s mo/ sub/ances & makes !m less d5se4 ,! sun's heat fall+ ^u ! e>? exp&s x & dim9i%es its d5sity 9 "s small degree1 & we h only to imag9e ?is process ( expansion cont9u$ until ! e>?'s diamet] becomes #eh p] c5t l>g] ?an x n[ is1 to f9d ! e>?'s d5sity r$uc$ to a level ) t ( ! sun4 ,j h[ mu* ! temp]ature ( ! e>? mu/ be rais$ to produce ?is am\nt ( expansion we d n "k1 nei!r d we "k accurately ! temp]ature ( ! sun1 b !re c be no d\bt t heat is ! cause ( ! sun's l[ d5sity & t ! correspond+ temp]ature is v high4 ,be=e we inquire m closely into ! sun's temp]ature1 x w be well to draw a %>p di/9ction betwe5 ! two t]ms heat & temp]ature1 :i* are (t5 us$ z if !y meant ! same ?+4 ,heat is a =m ( en]gy :i* may be f\nd 9 v>y+ degree 9 e sub/ance1 :e!r w>m or cold--a block ( ice conta9s a consid]able am\nt ( heat--:ile temp]ature corresponds to our s5sations ( w>m & cold1 & measures ! ext5t to :i* heat is conc5trat$ 9 ! body4 ,x is ! am\nt ( heat p] molecule ( ! body4 ,a b>rel ( w>m wat] conta9s m heat ?an ! flame ( a mat*1 b its temp]ature is n s high4 ,be>+ 9 m9d ?is di/9ction1 we seek to det]m9e n ! am\nt ( heat conta9$ 9 ! sun b ! sun's temp]ature1 & ?is involves ! same difficulty z does ! "q1 ,:at is ! temp]ature ( a locomotive8 ,x is "o ?+ 9 ! fire box & ano!r ?+ 9 ! driv+ :eels1 & /ill ano!r at ! headlight2 & s ) ! sun1 its temp]ature is c]ta9ly diff]5t 9 diff]5t p>ts--"o ?+ at ! c5t] & ano!r at ! surface4 ,ev5 ^? p>ts :i* we see are cov]$ by a veil ( gases :i* produce by absorption ! d>k l9es ( ! sol> spectrum1 & s]i\sly int]f]e bo? ) ! emission ( en]gy f ! sun & ) our attempts at measur+ ! temp]ature ( ^? p>ts ( ! surface f :i* t en]gy /reams4 ,9 view ( ^! & o!r difficulties we ne$ n be surpris$ t ! wilde/ discordance has be5 f\nd 9 e/imates ( ! sol> temp]ature made by diff]5t inve/igators1 :o h assign$ to x values rang+ f #a1djj ,c4 to m ?an #e1jjj1jjj ,c4 ,q rec5tly1 h[ev]1 improv$ me?ods & a bett] und]/&+ ( ! problem h br\ght ab\t a bett] agreem5t ( results1 & x n[ seems probable t ! temp]ature ( ! visible surface ( ! sun lies some:]e betwe5 #e1jjj & #aj1jjj ,c41 say #ae1jjj ( ! ,fahr5heit scale4 #aah4 ,,det]m9+ ,,! ,,sun',s ,,temp]ature4--,"o +5i\s me?od :i* has be5 us$ = det]m9+ ?is temp]ature is bas$ ^u ! pr9ciple /at$ above1 t e object1 :e!r w>m or cold1 conta9s heat & gives x (f 9 ! =m ( radiant en]gy4 ,! radiation f a body ^: temp]ature is l[] ?an #ejj ,c4 is made up exclusively ( en]gy ^: wave l5g? is great] ?an #g1fjj t5? met]s1 & is !re=e invisible to ! eye1 al?\gh a !rmomet] or ev5 ! human h& c (t5 detect x z radiant heat4 ,a brick wall 9 ! summ] sun%9e gives (f en]gy :i* c be felt z heat b c n be se54 ,:5 su* a body is fur!r heat$ x cont9ues to s5d (f ! same k9ds 7wave l5g?s7 ( en]gy z be=e1 b new & %ort] waves are add$ to its radiation1 & :5 x beg9s to emit en]gy ( wave l5g? #g1ejj or #g1fjj t5? met]s1 x also beg9s to %9e ) a dull-r$ light1 :i* pres5tly becomes bright] & less ruddy & *anges to :ite z ! temp]ature rises1 & waves ( /ill %ort] l5g? are !reby add$ to ! radiation4 ,we say1 9 common spee*1 ! body becomes fir/ r$ hot & !n :ite hot1 & we ?us recognize 9 a g5]al way t ! k9d or color ( ! radiation :i* a body gives (f is an index to its temp]ature4 ,! great] ! proportion ( en]gy ( %ort wave l5g?s ! high] is ! temp]ature ( ! radiat+ body4 ,9 sunlight ! maximum ( brilliancy to ! eye lies at or ne> ! wave l5g?1 #e1fjj t5? met]s1 b ! greate/ int5sity ( radiation ( all k9ds 7light includ$7 is e/imat$ to fall some:]e betwe5 gre5 & blue 9 ! spectrum at or ne> ! wave l5g? #e1jjj t5? met]s1 & if we c apply to ?is wave l5g? ,pas*5's law--temp]ature reckon$ 9 degrees c5tigrade f ! absolute z]o is always equal to ! quoti5t obta9$ by divid+ ! numb] #bg1jjj1jjj by ! wave l5g? correspond+ to maximum radiation--we %all f9d at once = ! absolute temp]ature ( ! sun's surface #e1djj ,c4 ,pas*5's law has be5 %[n to hold true1 at lea/ approximately1 = l[] temp]atures & long] wave l5g?s ?an are "h involv$1 b z x is n yet c]ta9 t x is /rictly true & holds = all temp]atures1 too great reliance mu/ n be atta*$ to ! num]ical result furni%$ by x4 ,illu/ration3 ,,fig4 #ff4--,! sun1 ,augu/ #aa1 #ahid4 ,photograph$ at ! ,goodsell ,obs]vatory4 ,illu/ration3 ,,fig4 #fg4--,! sun1 ,augu/ #ad1 #ahid4 ,photograph$ at ! ,goodsell ,obs]vatory4 #aai4 ,,! ,,sun',s ,,surface4--,a m>k$ contra/ exi/s betwe5 ! faces ( sun & moon 9 respect ( ! am\nt ( detail to be se5 ^u !m1 ! sun %[+ no?+ :atev] to correspond ) ! m\nta9s1 crat]s1 & seas ( ! moon4 ,! unaid$ eye 9 g5]al f9ds 9 ! sun only a blank bright circle z smoo? & unm>k$ z ! surface ( /ill wat]1 & ev5 ! telescope at fir/ sight seems to %[ b little m4 ,!re may usually be f\nd ^u ! sun's face a c]ta9 numb] ( black pat*es call$ sun spots1 su* z are %[n 9 ,figs4 #ff to #fi1 & occasionally ^! are l>ge en\gh to be se5 ?r\gh a smok$ glass )\t ! aid ( a telescope4 ,:5 se5 ne> ! edge ( ! sun !y are q frequ5tly accompani$1 z 9 ,fig4 #fi1 by vague pat*es call$ facul 7,lat91 facula a little tor*71 :i* look a little bright] ?an ! surr\nd+ p>ts ( ! sun4 ,s1 too1 a good photograph ( ! sun usually %[s t ! c5tral p>ts ( ! disk are r bright] ?an ! edge1 z inde$ we %\ld expect !m to be1 s9ce ! absorption l9es 9 ! sun's spectrum h already taught u t ! visible surface ( ! sun is envelop$ by invisible vapors :i* 9 "s measure absorb ! emitt$ light & r5d] x feebl] at ! edge :]e x passes ?r\gh a great] ?ickness ( ?is envelope ?an at ! c5t]4 ,see ,fig4 #gj1 :]e x is %[n t ! en]gy com+ f ! edge ( ! sun to ! e>? has to trav]se a mu* long] pa? inside ! vapors ?an does t com+ f ! c5t]4 ,illu/ration3 ,,fig4 #fh4--,! sun1 ,augu/ #ah1 #ahid4 ,photograph$ at ! ,goodsell ,obs]vatory4 ,exam9e ! sun spots 9 ! f\r photographs1 ,figs4 #ff to #fi1 & note t ! two spots :i* appe> at ! extreme left ( ! fir/ photograph1 v mu* di/ort$ & =e%ort5$ by ! curvature ( ! sun's surface1 are se5 9 a diff]5t "p ( ! second picture1 & are n only m conspicu\s b %[ bett] _! true %ape4 ,illu/ration3 ,,plate ,,ii4 ,,! ,,equatorial ,,con/ellations #abj4 ,,! ,,sun',s ,,rotation4--,! *ang$ position ( ^! spots %[s t ! sun rotates ab\t an axis at "r angles to ! direction ( ! spot's motion1 & ! position ( ?is axis is %[n 9 ! figure by a fa9t l9e rul$ obliquely across ! face ( ! sun ne>ly nor? & s\? 9 ea* ( ! f\r photographs4 ,?is rotation 9 ! space ( ?ree days has c>ri$ ! spots f ! edge halfway to ! c5t] ( ! disk1 & ! /ud5t %\ld note ! progress ( ! spots 9 ! two lat] photographs1 t ( ,augu/ #ba/ %[+ !m j ready to disappe> ar\nd ! f>!r edge ( ! sun4 ,illu/ration3 ,,fig4 #fi4--,! sun1 ,augu/ #ba1 #ahid4 ,photograph$ at ! ,goodsell ,obs]vatory4 ,plot accurately 9 "o ( ^! figures ! positions ( ! spots z %[n 9 ! o!r ?ree1 & obs]ve :e!r ! pa? ( ! spots across ! sun's face is a /raight l9e4 ,is !re any reason :y x %\ld n be /raight8 ,^! f\r pictures may be made to illu/rate _m ?+s ab\t ! sun4 ,?us ! sun's axis is n p>allel to t ( ! e>?1 = ! lett]s ,n ,s m>k ! direction ( a nor? & s\? l9e across ! face ( ! sun1 & ?is l9e1 ( c\rse1 is p>allel to ! e>?'s axis1 :ile x is evid5tly n p>allel to ! sun's axis4 ,! gr\p ( spots took m ?an t5 days to move across ! sun's face1 & z at lea/ an equal "t mu/ be requir$ to move ar\nd ! opposite side ( ! sun1 x is evid5t t ! p]iod ( ! sun's rotation is some?+ m ?an #bj days4 ,x is1 9 fact1 r m ?an #be days1 = ?is same gr\p ( spots reappe>$ aga9 on ! left-h& edge ( ! sun on ,septemb] #e?4 ,illu/ration3 ,,fig4 #gj4--;,absorption at ! sun's edge4 #aba4 ,,sun ,,spots4--,ano!r significant fact comes out pla9ly f ! photographs4 ,! spots are n p]man5t features ( ! sun's face1 s9ce !y *ang$ _! size & %ape v appreciably 9 ! few days cov]$ by ! pictures4 ,comp>e p>ticul>ly ! photographs ( ,augu/ #ad? & ,augu/ #ah?1 :]e ! spots are lea/ di/ort$ by ! curvature ( ! sun's surface4 ,by ,septemb] #af? ?is gr\p ( spots _h disappe>$ absolutely f ! sun's face1 al?\gh :5 at its l>ge/ ! gr\p ext5d$ m ?an #hj1jjj miles 9 l5g?1 & sev]al ( ! individual spots 7 l>ge en\gh to conta9 ! e>? if x _h be5 dropp$ ^u !m4 ,f ,fig4 #fg det]m9e 9 miles ! l5g? ( ! gr\p on ,augu/ #ad?4 ,fig4 #ga %[s an enl>g$ view ( ^! spots z !y appe>$ on ,augu/ #ag?1 & 9 ?is we f9d "s details n s well %[n 9 ! prec$+ pictures4 ,! l>g] spots consi/ ( a black "p call$ ! nucleus or umbra 7,lat91 %ad[71 :i* is surr\nd$ by an irregul> bord] call$ ! p5umbra 7p>tial %ad[71 :i* is int]m$iate 9 brightness betwe5 ! nucleus & ! surr\nd+ p>ts ( ! sun4 ,x %\ld n be inf]r$ f ! picture t ! nucleus is really black or ev5 d>k4 ,x %9es1 9 fact1 ) a brilliancy great] ?an t ( an electric lamp1 b ! backgr\nd furni%$ by ! sun's surface is s mu* bright] t by contra/ ) x ! nucleus & p5umbra appe> relatively d>k4 ,illu/ration3 ,,fig4 #ga4--,sun spots1 ,augu/ #ag1 #ahid4 ,goodsell ,obs]vatory4 ,illu/ration3 ,,fig4 #gb4--,sun spot ( ,m>* #e1 #ahgc4--;,f ,,langley1 ,! ,new ,a/ronomy4 ,by p]mission ( ! publi%]s4 ,! bright %9+ surface ( ! sun1 ! backgr\nd = ! spots1 is call$ ! photosph]e 7,greek1 light sph]e71 &1 z ,fig4 #ga %[s1 x assumes "u a suitable magnify+ p[] a mottl$ aspect q diff]5t f ! featureless expanse %[n 9 ! e>li] pictures4 ,! photosph]e is1 9 fact1 a lay] ( little cl\ds ) d>k] spaces betwe5 !m1 & ! f9e detail ( ^! cl\ds1 _! complicat$ /ructure1 & ! way 9 :i*1 :5 project$ aga9/ ! backgr\nd ( a sun spot1 !y produce its p5umbra1 are all br\ght out 9 ,fig4 #gb4 ,note t ! little pat* 9 "o corn] ( ?is picture repres5ts ,nor? & ,s\? ,am]ica drawn to ! same scale z ! sun spots4 ,illu/ration3 ,,fig4 #gc4--,spectroheliograph1 %[+ di/ribution ( facul ^u ! sun4--,,hale4 ,illu/ration3 ,,fig4 #gd4--;,eclipse ( ,july #bj1 #ahgh4--,,tr\velot4 #abb4 ,,facul4--,we h se5 9 ,fig4 #fi a few ( ! bright spots call$ facul4 ,at ! telescope or 9 ! ord9>y photograph ^! c be se5 only at ! edge ( ! sun1 because else:]e ! backgr\nd furni%$ by ! photosph]e is s bright t !y are lo/ 9 x4 ,x is possible1 h[ev]1 by an +5i\s application ( ! spectroscope to break up ! sunlight into a spectrum 9 su* a way z to dim9i% ! brightness ( ?is backgr\nd1 mu* m ?an ! brightness ( ! facul is dim9i%$1 & 9 ?is way to obta9 a photograph ( ! sun's surface :i* %all %[ !m :]ev] !y occur1 & su* a photograph1 %[+ fa9tly ! spectral l9es1 is reproduc$ 9 ,fig4 #gc4 ,! facul are ! bright pat*es :i* /ret* inconspicu\sly across ! face ( ! sun1 9 two r irregul> belts ) a comp>atively empty lane betwe5 !m4 ,?is lane lies along ! sun's equator1 & x is ^u ei!r side ( x betwe5 latitudes #e & #dj t facul seem to be produc$4 ,x is significant ( _! connection ) sun spots t ! spots occur 9 ^! p>ticul> zones & are r>ely f\nd outside !m4 ,illu/ration3 ,,fig4 #ge4--;,eclipse ( ,april #af1 #ahic4--,,s*aeb]le4 #abc4 ,,invisible ,,p>ts ,,( ,,! ,,sun4 ,,! ,,corona4--,?us f> we h be5 deal+ ) p>ts ( ! sun t may be se5 & photograph$ "u all ord9>y conditions4 ,b outside ( & surr\nd+ ^! p>ts is an envelope1 or r sev]al envelopes1 ( mu* great] ext5t ?an ! visible sun4 ,^! envelopes are = ! mo/ "p invisible save at ^? times :5 ! bright] c5tral portions ( ! sun are hidd5 9 a total eclipse4 ,illu/ration3 ,,fig4 #gf4--;,eclipse ( ,janu>y #ba1 #ahih4--;,,campbell4 ,fig4 #gd is f a draw+1 & ,figs4 #ge & #gf are f eclipse photographs %[+ ?is region1 9 :i* ! mo/ conspicu\s object is ! halo ( s(t light call$ ! corona1 t completely surr\nds ! sun b is se5 to be ( diff]+ %apes & diff]+ ext5t at ! sev]al eclipses "h %[n1 al?\gh a l>ge "p ( ^! app>5t diff]5ces is due to te*nical difficulties 9 photograph+1 & reproduc+ an object ) outl9es s vague z ^? ( ! corona4 ,! outl9e ( ! corona is s indef9ite & its out] portions s fa9t t x is impossible to assign to x precise dim5sions1 b at its greate/ ext5t x rea*es out = sev]al millions ( miles & fills a space m ?an tw5ty times z l>ge z ! visible "p ( ! sun4 ,despite its huge bulk1 x is ( mo/ unsub/antial "*1 an airy no?+ ?r\gh :i* comets h be5 kn[n to =ce _! way ar\nd ! sun f "o side to ! o!r1 lit]ally = millions ( miles1 )\t hav+ _! c\rse influ5c$ or _! velocity *eck$ to any appreciable ext5t4 ,?is w\ld h>dly be possible if ! d5sity ev5 at ! bottom ( ! corona 7 great] ?an t ( ! be/ vacuum :i* we are able to produce 9 laboratory exp]im5ts4 ,x seems odd t a vacuum %\ld give (f s bright a light z ! coronal pictures %[1 & ! exact "* ( t light & ! nature ( ! corona are /ill subjects ( dispute among a/ronom]s1 al?\gh x is g5]ally agre$ t1 9 "p at lea/1 its light is ord9>y sunlight fa9tly reflect$ f ! widely scatt]$ molecules compos+ ! sub/ance ( ! corona4 ,x is also probable t 9 "p ! light has its orig9 9 ! corona itself4 ,a curi\s & at pres5t unconfirm$ result ann\nc$ by "o ( ! obs]v]s ( ! eclipse ( ,may #bh1 #aijj1 is t ! corona is n hot1 its effective temp]ature be+ l[] ?an t ( ! in/rum5t us$ = ! obs]vation4 ,illu/ration3 ,,fig4 #gg4--,sol> prom95ce ( ,m>* #be1 #ahie4--;,,hale4 #abd4 ,,! ,,*romosph]e4--,betwe5 ! corona & ! photosph]e !re is a ?9 sep>at+ lay] call$ ! *romosph]e 7,greek1 color sph]e71 because :5 se5 at an eclipse x %9es ) a brilliant r$ light q unlike any?+ else ^u ! sun save ! prom95ces :i* are !mselves only p>ts ( ! *romosph]e tempor>ily ?r[n above its surface1 z 9 a f\nta9 a jet ( wat] is ?r[n up f ! bas9 & rema9s = a few mom5ts susp5d$ 9 mid-air4 ,n infrequ5tly 9 su* a f\nta9 =eign matt] is swept up by ! ru% ( ! wat]--dirt1 twigs1 small fi%1 etc4--& 9 l mann] ! prom95ces (t5 c>ry along ) !m p>ts ( ! und]ly+ lay]s ( ! sun1 photosph]e1 facul1 etc41 :i* reveal _! pres5ce 9 ! prom95ce by add+ _! *>act]i/ic l9es to ! spectrum1 l t ( ! *romosph]e1 :i* ! prom95ce pres5ts :5 !y are abs5t4 ,none ( ! eclipse photographs 7,figs4 #gd to #gf7 %[ ! *romosph]e1 because ! color effect is lack+ 9 !m1 b a great curv+ prom95ce may be se5 ne> ! bottom ( ,fig4 #ge1 & small] ones at o!r p>ts ( ! sun's edge4 ,illu/ration3 ,,fig4 #gh4--;,a sol> prom95ce4--,,hale4 #abe4 ,,prom95ces4--,fig4 #gg %[s ^u a l>g] scale "o ( ^! prom95ces ris+ to a height ( #afj1jjj miles above ! photosph]e2 & ano!r photograph1 tak5 #ah m9utes lat]1 b n reproduc$ "h1 %[$ ! same prom95ce gr[n 9 ?is brief int]val to a /ature ( #bhj1jjj miles4 ,^! pictures 7 n tak5 dur+ an eclipse1 b 9 full sunlight1 us+ ! same spectroscopic app>atus :i* 0 employ$ 9 connection ) ! facul to dim9i% ! brightness ( ! backgr\nd )\t mu* enfeebl+ ! brilliancy ( ! prom95ce itself4 ,! d>k base f :i* ! prom95ce seems to spr+ is n ! sun's edge1 b a "p ( ! app>atus us$ to cut (f ! direct sunlight4 ,fig4 #gh conta9s a s]ies ( photographs ( ano!r prom95ce tak5 )9 an int]val ( #a h\r #dg m9utes & %[+ *anges 9 size & %ape :i* are mu* m ne>ly typical ( ! ord9>y prom95ce ?an 0 ! v unusual *ange 9 ! case ( ,fig4 #gg4 ,illu/ration3 ,,fig4 #gi4--;,contra/$ =ms ( sol> prom95ces4--,,zoelln]4 ,! prec$+ pictures are f photographs1 & ) !m ! /ud5t may comp>e ,fig4 #gi1 :i* is con/ruct$ f draw+s made at ! spectroscope by ! ,g]man a/ronom] ,zoelln]4 ,! *anges "h %[n are mo/ m>k$ 9 ! prom95ce at ! left1 :i* is %ap$ l a brok5 tree trunk1 & :i* appe>s to be vibrat+ f "o side to ! o!r l a re$ %ak5 9 ! w9d4 ,su* a prom95ce is frequ5tly call$ an eruptive "o1 a "n sugge/$ by its appe>ance ( hav+ be5 bl[n out f ! sun by some?+ l an explosion1 :ile ! prom95ce at ! "r 9 ?is s]ies ( draw+s1 :i* appe>s mu* less agitat$1 is call$ by contra/ ) ! o!r a quiesc5t prom95ce4 ,^! quiesc5t prom95ces are1 z a rule1 mu* long]-liv$ ?an ! eruptive ones4 ,"o m picture ( prom95ces 7,fig4 #hj7 is introduc$ to %[ ! cont9u\s /ret* ( *romosph]e out ( :i* !y spr+4 ,illu/ration3 ,,fig4 #hj4--,prom95ces & *romosph]e4--,,hale4 ,prom95ces are se5 only at ! edge ( ! sun1 because x is !re alone t ! necess>y backgr\nd c be obta9$1 b !y mu/ occur at ! c5t] ( ! sun & else:]e q z well z at ! edge1 & x is probable t quiesc5t prom95ces are di/ribut$ ov] all p>ts ( ! sun's surface1 b eruptive prom95ces %[ a /rong t5d5cy t[>d ! regions ( sun spots & facul z if all ?ree 7 intimately relat$ ph5om5a4 #abf4 ,,! ,,sun ,,z ,a ,,ma*9e4--,?us f> we h consid]$ ! anatomy ( ! sun1 dissect+ x into its sev]al p>ts1 & our next /ep %\ld be a consid]ation ( its physiology1 ! relation ( ! p>ts to ea* o!r1 & _! function 9 c>ry+ on ! "w ( ! sol> organism1 b ?is /ep1 un=tunately1 mu/ be a lame "o4 ,! sci5ce ( a/ronomy to-day possesses no compreh5sive & well-e/abli%$ !ory ( ?is k9d1 b looks to ! future = ! solution ( ?is ! greate/ p5d+ problem ( sol> physics4 ,progress has be5 made t[>d its solution1 & among ! /eps ( ?is progress t we %all h to consid]1 ! fir/ & mo/ important is ! conception ( ! sun z a k9d ( heat eng9e4 ,9 a /eam eng9e coal is burn$ "u ! boil]1 & its *emical en]gy1 trans=m$ into heat1 is tak5 up by ! wat] & deliv]$1 ?r\gh /eam z a m$ium1 to ! eng9e1 :i* aga9 trans=ms & gives x out z me*anical "w 9 ! turn+ ( %afts1 ! driv+ ( ma*9]y1 etc4 ,n[1 ! function ( ! sun is exactly opposite to t ( ! eng9e & boil]3 x gives out1 in/ead ( receiv+1 radiant en]gy2 b1 l ! eng9e1 x mu/ be f$ f "s s\rce2 x c n be run ^u no?+ at all any m ?an ! eng9e c run day aft] day )\t fre% supplies ( fuel "u its boil]4 ,we "k t = "s ?\s&s ( ye>s ! sun has be5 furni%+ light & heat to ! e>? 9 practically unv>y+ am\nt1 & n to ! e>? alone1 b x has be5 p\r+ =? ^! =ms ( en]gy 9 e direction1 )\t app>5t reg>d to ei!r use or economy4 ,( all ! radiant en]gy giv5 (f by ! sun1 only two p>ts out ( e ?\s& million fall ^u any planet ( ! sol> sy/em1 & ( ?is small fraction ! e>? takes ab\t "o t5? = ! ma9t5ance ( its v>i$ =ms ( life & action4 ,a/ronom]s & physici/s h s\ght on e h& = an explanation ( ! means by :i* ?is trem5d\s output ( en]gy is ma9ta9$ c5tury aft] c5tury )\t s5sible dim9ution1 & h come ) almo/ "o m9d to ! conclusion t ! gravitative =ces :i* reside 9 ! sun's own mass furni% ! only adequate explanation = x1 al?\gh !y may be 9 "s small measure re-en=c$ by m9or influ5ces1 su* z ! fall ( meteoric du/ & /ones into ! sun4 ,e boy :o has inflat$ a bicycle tire ) a h& pump kn[s t ! pump gr[s w>m dur+ ! op]ation1 on acc\nt ( ! compression ( ! air )9 ! cyl9d]4 ,a "p ( ! muscul> =ce 7en]gy7 exp5d$ 9 work+ ! pump reappe>s 9 ! heat :i* w>ms bo? air & pump1 & a simil> process is =ev] go+ on 9 ! sun1 only 9 place ( muscul> =ce we mu/ !re sub/itute ! trem5d\s attraction ( gravitation1 #bh times z great z ^u ! e>?4 ,! matt] 9 ! int]ior ( ! sun mu/ be z a %uttlecock betwe5 ! /up5d\s pressure & ! enorm\sly high temp]ature1 ! "o t5d+ to compress & ! o!r to exp& x1 b ) ?is important diff]5ce betwe5 !m3 ! temp]ature /eadily t5ds to fall z ! heat en]gy is wa/$ away1 :ile ! gravitative =ce suff]s no correspond+ dim9ution1 & 9 ! long run mu/ ga9 ! upp] h&1 caus+ ! sun to %r9k & become m d5se4 ,x is ?is progressive %r9k+ & compression ( its molecules into a small] space :i* supplies ! en]gy conta9$ 9 ! sun's output ( light & heat4 ,accord+ to ,"l ,kelv91 ea* c5timet] ( %r9kage 9 ! sun's diamet] furni%es ! en]gy requir$ to keep up its radiation = some?+ m ?an an h\r1 &1 on acc\nt ( ! sun's great di/ance1 ! %r9kage might g on at ?is rate = _m c5turies )\t produc+ any measurable effect 9 ! sun's appe>ance4 #abg4 ,,gase\s ,,con/itution ,,( ,,! ,,sun4--,b ,helmholtz's dynamical !ory ( ! ma9t5ance ( ! sun's heat1 :i* we are "h consid]+1 includes "o ess5tial feature t is n suffici5tly /at$ above4 ,9 ord] t ! explanation may hold true1 x is necess>y t ! sun %\ld be 9 ! ma9 a gase\s body1 compos$ f c5t] to circumf]5ce ( gases in/ead ( solid or liquid p>ts4 ,pump+ air w>ms ! bicycle pump 9 a way t pump+ wat] or oil w n4 ,! high temp]ature ( ! sun itself furni%es suffici5t reason = suppos+ ! sol> mat]ial to be 9 ! gase\s /ate1 b ! gas compos+ ^? p>ts ( ! sun bel[ ! photosph]e mu/ be v diff]5t 9 "s ( its *>act]i/ics f ! air or o!r gases ) :i* we are famili> at ! e>?1 s9ce its av]age d5sity is #a1jjj times z great z t ( air1 & its consi/5ce & me*anical behavior mu/ be m l t ( honey or t> ?an t ( any gas ) :i* we are famili>4 ,x is wor? not+1 h[ev]1 t if a hole 7 dug into ! cru/ ( ! e>? to a dep? ( #ae or #bj miles ! air at ! bottom ( ! hole w\ld be compress$ by t above x to a d5sity comp>able ) t ( ! sol> gases4 #abh4 ,,! ,,sun',s ,,circulation4--,x is pla9 t "u ! conditions :i* exi/ 9 ! sun ! out] portions1 :i* c radiate _! heat freely into space1 mu/ be cool] ?an ! inn] c5tral p>ts1 & ?is diff]5ce ( temp]ature mu/ set up curr5ts ( hot matt] drift+ upw>d & outw>d f )9 ! sun & c\nt] curr5ts ( cool] matt] settl+ d[n to take its place4 ,s1 too1 !re mu/ be "s level at :i* ! free radiation into out] space *ills ! hot matt] suffici5tly to cond5se its less refractory gases into cl\ds made up ( liquid drops1 j z on a cl\dy day !re is a level 9 our own atmosph]e at :i* ! vapor ( wat] cond5ses into liquid drops :i* =m ! ?9 %ell ( cl\ds t hov]s above ! e>?'s surface1 :ile above & bel[ is ! gase\s atmosph]e4 ,9 ! case ( ! sun ?is cl\d lay] is always pres5t & is t "p :i* we h le>n$ to call ! photosph]e4 ,above ! photosph]e lies ! *romosph]e1 compos$ ( gases less easily liquefi$1 hydrog5 is ! *ief "o1 :ile betwe5 photosph]e & *romosph]e is a ?9 lay] ( metallic vapors1 p]haps indi/+ui%able f ! top cru/ ( ! photosph]e itself1 :i* by absorb+ ! light giv5 (f f ! liquid photosph]e produces ! great] "p ( ! ,fraunh(] l9es 9 ! sol> spectrum4 ,f "t to "t ! hot matt] /ruggl+ up f bel[ breaks ?r\gh ! photosph]e &1 c>ry+ ) x a c]ta9 am\nt ( ! metallic vapors1 is laun*$ into ! upp] & cool] regions ( ! sun1 :]e1 p>t+ ) its heat1 x falls back aga9 ^u ! photosph]e & is absorb$ into x4 ,x is altoge!r probable t ! corona is *iefly compos$ ( f9e p>ticles eject$ f ! sun ) velocities suffici5t to c>ry !m to a height ( millions ( miles1 or ev5 suffici5t to c>ry !m (f nev] to return4 ,! matt] ( ! corona mu/ c]ta9ly be 9 a /ate ( ! mo/ lively agitation1 its p>ticles be+ alt]nately hurl$ up f ! photosph]e & fall+ back aga9 l fireworks1 ! p>ticles :i* make up ! corona ( to-day be+ q a diff]5t set f ^? ( ye/]day or la/ week4 ,x seems beyond "q t ! prom95ces & facul too are produc$ 9 "s way by ?is up-&-d[n circulation ( ! sun's matt]1 & t any me*anical explanation ( ! sun mu/ be work$ out along ^! l9es2 b ! problem is an exce$+ly difficult "o1 & mu/ include & expla9 _m o!r features ( ! sun's activity ( :i* only a few c be consid]$ "h4 #abi4 ,,! ,,sun-,,spot ,,p]iod4--,sun spots come & g1 & at be/ any p>ticul> spot is b %ort-liv$1 r>ely la/+ m ?an a mon? or two1 & m (t5 its duration is a matt] ( only a few days4 ,!y are n equally num]\s at all times1 b1 l sw>ms ( locu/s1 !y seem to come & ab\nd = a season & !n almo/ to disappe>1 z if ! =ces :i* produc$ !m 7 ( a p]iodic "* alt]nately active & quiet4 ,! effect ( ?is p]iodic activity s9ce #ahgj is %[n 9 ,fig4 #ha1 :]e ! horizontal l9e is a scale ( times1 & ! di/ance ( ! curve above ?is l9e = any ye> %[s ! relative numb] ( spots :i* appe>$ ^u ! sun 9 t ye>4 ,?is indicates v pla9ly t #ahgj1 #ahhc1 & #ahic 7 ye>s ( great sun-spot activity1 :ile #ahgi & #ahhi 7 ye>s 9 :i* few spots appe>$4 ,! old] records1 cov]+ a p]iod ( two c5turies1 %[ ! same fluctuations 9 ! frequ5cy ( sun spots & f ^! records curves 7:i* may be f\nd 9 ,"y's1 ,! ,sun7 h be5 plott$1 %[+ a succession ( waves ext5d+ back = _m ye>s4 ,illu/ration3 ,,fig4 #ha4--,! curve ( sun-spot frequ5cy4 ,! sun-spot p]iod is ! int]val ( "t f ! cre/ or holl[ ( "o wave to ! correspond+ "p ( ! next "o1 & on ! av]age ?is appe>s to be a little m ?an elev5 ye>s1 b is subject to consid]able v>iation4 ,9 accordance ) ?is p]iod !re is drawn 9 brok5 l9es at ! "r ( ,fig4 #ha a pr$ict$ cont9uation ( ! sun-spot curve = ! fir/ decade ( ! tw5tie? c5tury4 ,! irregul>ity %[n by ! ?ree prec$+ waves is su* t we mu/ n expect ! actual c\rse ( future sun spots to correspond v closely to ! pr$iction "h made2 b 9 a g5]al way #aija & #aiaa w probably be ye>s ( few sun spots1 :ile !y w be num]\s 9 #aije1 b :e!r m or less num]\s ?an at prec$+ epo*s ( greate/ frequ5cy c n be =etold ) any approa* to c]ta9ty s long z we rema9 9 our pres5t ignorance ( ! causes :i* make ! sun-spot p]iod4 ,det]m9e f ,fig4 #ha z accurately z possible ! l5g? ( ! sun-spot p]iod4 ,x is h>d to tell ! exact position ( a cre/ or holl[ ( ! curve4 ,w\ld x d to draw a horizontal l9e midway betwe5 top & bottom ( ! curve & det]m9e ! l5g? ( ! p]iod f its int]sections ) ! curve--e4 g41 9 #ahgd & #ahhe8 ,illu/ration3 ,,fig4 #hb4--;,illu/rat+ *ange ( ! sun-spot zones4 #acj4 ,,! ,,sun-,,spot ,,zones4--,x has be5 already not$ t sun spots are f\nd only 9 c]ta9 zones ( latitude ^u ! sun1 & t facul & eruptive prom95ces ab\nd 9 ^! zones m ?an else:]e1 al?\gh n /rictly conf9$ to !m4 ,we h n[ to note a peculi>ity ( ^! zones :i* ought to furni% a clew to ! sun's me*anism1 al?\gh up to ! pres5t "t x has n be5 successfully trac$ out4 ,j be=e a sun-spot m9imum ! few spots :i* appe> are = ! mo/ "p clu/]$ ne> ! sun's equator4 ,z ^! spots die out two new gr\ps appe>1 "o nor? ! o!r s\? ( ! sun's equator & ab\t #be or #cj di/ant f x1 & z ! p]iod advances t[>d a maximum ^! gr\ps %ift _! positions m & m t[>d ! equator1 ?us approa*+ ea* o!r b leav+ betwe5 !m a vacant lane1 :i* becomes /eadily n>r[] until at ! close ( ! p]iod1 :5 ! next m9imum is at h&1 x rea*es its n>r[e/ dim5sions1 b does n altoge!r close up ev5 !n4 ,9 ,fig4 #hb ^! relations are %[n = ! p]iod fall+ betwe5 #ahgi & #ahij1 by means ( ! horizontal l9es2 = ea* ye> "o l9e 9 ! nor!rn & "o 9 ! s\!rn hemisph]e ( ! sun1 _! l5g?s be+ proportional to ! numb] ( spots :i* appe>$ 9 ! correspond+ hemisph]e dur+ ! ye>1 & _! positions on ! sun's disk %[+ ! av]age latitude ( ! spots 9 "q4 ,x is v app>5t f ! figure t dur+ ?is decade ! sun's s\!rn hemisph]e 0 mu* m active ?an ! nor!rn "o 9 ! production ( spots1 & ?is appe>s to be g5]ally ! case1 al?\gh ! diff]5ce is n usually z great z 9 ?is p>ticul> decade4 #aca4 ,,influ5ce ,,( ,,! ,,sun-,,spot ,,p]iod4--,sun spots are c]ta9ly less hot ?an ! surr\nd+ p>ts ( ! sun's surface1 &1 9 view ( ! intimate dep5d5ce ( ! e>? ^u ! sol> radiation1 x w\ld be 9 no way surpris+ if _! pres5ce or abs5ce f ! sun's face %\ld make itself felt 9 "s degree ^u ! e>?1 rais+ & l[]+ its temp]ature & q possibly affect+ x 9 o!r ways4 ,+5i\s m5 h sugge/$ _m su* k9ds ( influ5ce1 :i*1 accord+ to _! inve/igations1 appe> to run 9 cycles ( elev5 ye>s4 ,abundant & scanty h>ve/s1 cyclones1 tornadoes1 epidemics1 ra9fall1 etc41 are among ^! alleg$ effects1 & x is possible t !re may be a real connection betwe5 any or all ( !m & ! sun-spot p]iod1 b = ! mo/ "p a/ronom]s are incl9$ to hold t !re is only "o case 9 :i* ! evid5ce is /rong en\gh to really e/abli% a connection ( ?is k9d4 ,! magnetic condition ( ! e>? & its di/urbances1 :i* are call$ magnetic /orms1 d c]ta9ly foll[ 9 a v m>k$ mann] ! c\rse ( sun-spot activity1 & p]haps !re %\ld be add$ to ?is ! /atem5t t auroras 7nor!rn lights7 /& 9 close relation to ^! magnetic di/urbances & are mo/ frequ5t at ! times ( sun-spot maxima4 ,^u ! sun1 h[ev]1 ! influ5ce ( ! spot p]iod is n limit$ to ?+s 9 & ne> ! photosph]e1 b ext5ds to ! out]mo/ limits ( ! corona4 ,det]m9e f ,fig4 #ha ! p>ticul> "p ( ! sun-spot p]iod correspond+ to ! date ( ea* picture ( ! corona & note h[ ! pictures :i* 7 tak5 ne> times ( sun-spot m9ima pres5t a g5]al agreem5t 9 ! %ape & ext5t ( ! corona1 :ile ! pictures tak5 at a "t ( maximum activity ( ! sun spots %[ a v diff]5tly %ap$ & mu* small] corona4 #acb4 ,,! ,,law ,,( ,,! ,,sun',s ,,rotation4--,we h se5 9 a previ\s "p ( ! *apt] h[ ! "t requir$ by ! sun to make a complete rotation ^u its axis may be det]m9$ f photographs %[+ ! progress ( a spot or gr\p ( spots across its disk1 & we h n[ to add t :5 ?is is done sy/ematically by means ( _m spots situat$ 9 diff]5t sol> latitudes x leads to a v peculi> & extraord9>y result4 ,ea* p>ticul> p>allel ( latitude has its own p]iod ( rotation diff]5t f t ( its neighbors on ei!r side1 s t !re c be no su* ?+ z a fix$ geography ( ! sun's surface4 ,e "p ( x is con/antly tak+ up a new position ) respect to e o!r "p1 mu* z if ! ,gulf ( ,mexico %\ld be s\? ( ! ,unit$ ,/ates ?is ye>1 s\!a/ ( x next ye>1 & at ! end ( a decade %\ld h %ift$ ar\nd to ! opposite side ( ! e>? f u4 ,a m]idian ( longitude drawn d[n ! ,mississippi ,valley rema9s always a /raight l9e1 or1 r1 great circle1 ^u ! surface ( ! e>?1 :ile ,fig4 #hc %[s :at w\ld become ( su* a m]idian drawn ?r\gh ! equatorial p>ts ( ! sun's disk4 ,9 ! fir/ diagram x appe>s z a /raight l9e runn+ d[n ! middle ( ! sun's disk4 ,tw5ty-five days lat]1 :5 ! same face ( ! sun comes back into view aga91 aft] mak+ a complete revolution ab\t ! axis1 ! equatorial p>ts w h mov$ s mu* fa/] & f>!r ?an ^? 9 high] latitudes t ! m]idian w be w>p$ z 9 ! second diagram1 & /ill m w>p$ aft] ano!r & ano!r revolution1 z %[n 9 ! figure4 ,illu/ration3 ,,fig4 #hc4--;,effect ( ! sun's peculi> rotation 9 w>p+ a m]idian1 orig9ally /raight4 ,at lea/ su* is ! case if ! spots truly repres5t ! way 9 :i* ! sun turns r\nd4 ,!re is1 h[ev]1 a possibility t ! spots !mselves drift ) v>y+ spe$s across ! face ( ! sun1 & t ! diff]5ces :i* we f9d 9 _! rates ( motion belong to !m r ?an to ! photosph]e4 ,j :at happ5s 9 ! regions ne> ! poles is h>d to say1 = ! sun spots only ext5d ab\t halfway f ! equator to ! poles1 & ! spectroscope1 :i* may be made to furni% a c]ta9 am\nt ( in=mation be>+ ^u ! case1 is n z yet altoge!r conclusive1 nor are ! facul :i* h also be5 obs]v$ = ?is purpose4 ,! simple !ory t ! sol> ph5om5a are caus$ by an int]*ange ( hott] & cool] matt] betwe5 ! photosph]e & ! l[] /rata ( ! sun furni%es 9 its pres5t %ape little or no explanation ( su* features z ! sun-spot p]iod1 ! v>iations 9 ! corona1 ! peculi> "* ( ! sun's rotation1 etc41 & we h /ill unsolv$ 9 ! me*anical !ory ( ! sun "o ( ! noble/ problems ( a/ronomy1 & "o ^u :i* bo? obs]v]s & !oretical a/ronom]s are assidu\sly work+ at ! pres5t "t4 ,a close wat* is kept ^u sun spots & prom95ces1 ! corona is obs]v$ at e total eclipse1 & num]\s are ! +5i\s me?ods :i* are be+ sugge/$ & tri$ = obs]v+ x )\t an eclipse 9 ord9>y daylight4 ,attempts1 m or less plausible1 h be5 made & are n[ p5d+ to expla9 photosph]e1 spots & ! rev]s+ lay] by means ( ! refraction ( light )9 ! sun's out] envelope ( gases1 & x seems altoge!r probable1 9 view ( ^! comb9$ activities1 t a consid]able addition to our /ore ( k conc]n+ ! sun may be expect$ 9 ! n di/ant future4 ,,*apt] ,,xi ,,! ,,planets #acc4 ,,planets4--,circl+ ab\t ! sun1 "u ! influ5ce ( 8 attraction1 is a family ( planets ea* memb] ( :i* is1 l ! moon1 a d>k body %9+ by reflect$ sunlight1 & !re=e pres5t+ phases2 al?\gh only two ( !m1 ,m]cury & ,v5us1 run ?r\gh ! complete s]ies--new1 fir/ qu>t]1 full1 la/ qu>t]--:i* ! moon pres5ts4 ,! way 9 :i* _! orbits are gr\p$ ab\t ! sun has be5 consid]$ 9 ,*apt] ,,iii1 & ,figs4 #af & #ag ( t *apt] may be complet$ s z to repres5t all ( ! planets by draw+ 9 ,fig4 #af two circles ) radii ( #g4i & #ab4d c5timet]s respectively1 to repres5t ! orbits ( ! planets ,uranus & ,neptune1 :i* are m remote f ! sun ?an ,saturn1 & by introduc+ a little inside ! orbit ( ,jupit] ab\t #ejj ellipses ( diff]5t sizes1 %apes1 & positions to repres5t a gr\p ( m9or planets or a/]oids z !y are (t5 call$4 ,x is conv5i5t to reg>d ^! a/]oids z compos+ by !mselves a class ( v small planets1 :ile ! rema9+ #h l>g] planets fall naturally into two o!r classes1 a gr\p ( m$ium-siz$ ones--,m]cury1 ,v5us1 ,e>?1 & ,m>s--call$ inn] planets by reason ( _! ne>ness to ! sun2 & ! out] planets--,jupit]1 ,saturn1 ,uranus1 ,neptune--ea* ( :i* is mu* l>g] & m massive ?an any planet ( ! inn] gr\p4 ,comp>e 9 ,figs4 #hd & #he _! relative sizes4 ,! e>?1 ,e1 is introduc$ into ,fig4 #he z a connect+ l9k betwe5 ! two figures4 ,"s ( ^! planets1 l ! e>?1 are att5d$ by "o or m moons1 te*nically call$ satellites1 :i* also %9e by reflect$ sunlight & :i* move ab\t _! respective planets 9 accordance ) ! law ( gravitation1 mu* z ! moon moves ar\nd ! e>?4 ,illu/ration3 ,,fig4 #hd4--,! inn] planets & ! moon4 ,illu/ration3 ,,fig4 #he4--,! out] planets4 #acd4 ,,di/ances ,,( ,,! ,,planets ,,f ,,! ,,sun4--,x is a comp>atively simple matt] to obs]ve ^! planets ye> aft] ye> z !y move among ! />s1 & to f9d f ^! obs]vations h[ long ea* "o ( !m requires to make its circuit ar\nd ! sun--t is1 its p]iodic "t1 ,t1 :i* figures 9 ,kepl]'s ,?ird ,law1 & :5 ^! p]iodic times h be5 asc]ta9$1 to use !m 9 connection ) t law to det]m9e ! mean di/ance ( ea* planet f ! sun4 ,?us1 ,jupit] requires #d1ccc days to move completely ar\nd its orbit2 & comp>+ ?is ) ! p]iodic "t & mean di/ance ( ! e>? we f9d-- a#c _/ 7#dcccb7 7#ic1jjj1jjjc7 _/ 7#cfe4beb71 :i* :5 solv$ gives z ! mean di/ance ( ,jupit] f ! sun1 #dhc1gcj1jjj miles1 or #e4bj times z di/ant z ! e>?4 ,if we make a simil> computation = ea* planet1 we %all f9d t _! di/ances f ! sun %[ a rem>kable agreem5t ) an artificial s]ies ( numb]s call$ ,bode's law4 ,we write d[n ! numb]s conta9$ 9 ! fir/ l9e ( figures bel[1 ea* ( :i*1 aft] ! second1 is obta9$ by d\bl+ ! prec$+ "o1 add #d to ea* numb] & po9t (f "o place ( decimals2 ! result+ numb] is 7approximately7 ! di/ance ( ! correspond+ planet f ! sun4 ,m]cury4 ,v5us4 ,e>?4 ,m>s4 ,jupit]4 ,saturn4 ,uranus4 ,neptune4 #j #c #f #ab #bd #dh #if #aib #chd #d #d #d #d #d #d #d #d #d ---------------------------------------- ------------------------------- #j4d #j4g #a4j #a4f #b4h #e4b #aj4j #ai4f #ch4h #j4d #j4g #a4j #a4e #b4h #e4b #i4e #ai4b #cj4a ,! la/ l9e ( figures %[s ! real di/ance ( ! planet z det]m9$ f ,kepl]'s law1 ! e>?'s mean di/ance f ! sun be+ tak5 z ! unit = ?is purpose4 ,) exception ( ,neptune1 ! agreem5t betwe5 ,bode's law & ! true di/ances is v /rik+1 b mo/ rem>kable is ! pres5ce 9 ! s]ies ( a numb]1 #b4h1 ) no planet correspond+ to x4 ,?is l$ a/ronom]s at ! "t ,bode publi%$ ! law1 some?+ m ?an a c5tury ago1 to give new he$ to a sugge/ion made long be=e by ,kepl]1 t !re might be an unkn[n planet mov+ betwe5 ! orbits ( ,m>s & ,jupit]1 & a numb] ( !m agre$ to se>* = su* a planet1 ea* 9 a "p ( ! sky assign$ him = t purpose4 ,b !y 7 anticipat$ by ,piazzi1 an ,italian1 :o f\nd ! new planet1 by accid5t1 on ! fir/ day ( ! n9ete5? c5tury1 mov+ at a di/ance f ! sun repres5t$ by ! numb] #b4gg4 ,?is planet 0 ! fir/ ( ! a/]oids1 & 9 ! c5tury t has elaps$ hundr$s ( !m h be5 discov]$1 :ile at ! pres5t "t no ye> passes by )\t sev]al m be+ add$ to ! numb]4 ,:ile "s ( ^! are ne>] to ! sun ?an is ! fir/ "o discov]$1 & o!rs are f>!r f x1 _! av]age di/ance is fairly repres5t$ by ! numb] #b4h4 ,:y ,bode's law %\ld hold true1 or ev5 s ne>ly true z x does1 is an unexpla9$ riddle1 & _m a/ronom]s are incl9$ to call x no law at all1 b only a *ance co9cid5ce--an illu/ration ( ! inh]5t capacity ( figures to be juggl$ )2 b if s1 x is pass+ /range t x %\ld repres5t ! di/ance ( ! a/]oids & ( ,uranus1 :i* 0 also an undiscov]$ planet at ! "t ! law 0 publi%$4 #ace4 ,,! ,,planets ,,comp>$ ,,) ,,ea* ,,o!r4--,:5 we pass f g5]al consid]ations to a /udy ( ! individual peculi>ities ( ! planets1 we f9d great diff]5ces 9 ! ext5t ( k conc]n+ !m1 & ! reason = ?is is n f> to seek4 ,neptune & ,uranus1 at ! outskirts ( ! sol> sy/em1 are s remote f u & s feebly illum9$ by ! sun t any detail$ /udy ( !m c g b little beyond det]m9+ ! numb]s :i* repres5t _! size1 mass1 d5sity1 ! "* ( _! orbits1 etc4 ,! a/]oids are s small t 9 ! telescope !y look l m]e po9ts ( light1 absolutely indi/+ui%able 9 appe>ance f ! fa9t] />s4 ,m]cury1 al?\gh clos] at h& & pres5t+ a disk ( consid]able size1 always /&s s ne> ! sun t its obs]vation is difficult on ?is acc\nt4 ,some?+ ( ! same k9d is true = ,v5us1 al?\gh 9 mu* less degree2 :ile ,m>s1 ,jupit]1 & ,saturn are comp>atively easy objects = telescopic /udy1 & our k ( !m1 :ile f> f complete1 is consid]ably great] ?an = ! o!r planets4 ,figs4 #hd & #he %[ ! relative sizes ( ! planets compos+ ! inn] & out] gr\ps respectively1 & furni% ! num]ical data conc]n+ _! diamet]s1 masses1 d5sities1 etc41 :i* are ( mo/ importance 9 judg+ ( _! physical condition4 ,ea* planet1 save ,saturn1 is repres5t$ by two circles1 ( :i* ! out] is drawn proportional to ! size ( ! planet1 & ! inn] %[s ! am\nt ( mat]ial t mu/ be subtract$ f ! int]ior 9 ord] t ! rema9+ %ell %all j float 9 wat]4 ,note ! great diff]5ce 9 ?ickness ( %ell betwe5 ! two gr\ps4 ,saturn1 hav+ a mean d5sity less ?an t ( wat]1 mu/ h some?+ load$ ^u x1 in/ead ( remov$1 9 ord] t x %\ld float j subm]g$4 ,,jupit] #acf4 ,,appe>ance4--,comm5c+ our consid]ation ( ! individual planets ) ,jupit]1 :i* is by f> ! l>ge/ ( !m1 exce$+ bo? 9 bulk & mass all ! o!rs comb9$1 we h 9 ,fig4 #hf f\r repres5tations ( ,jupit] & 8 family ( satellites z !y may be se5 9 a v small telescope--e4 g41 an op]a glass--save t ! little dots :i* "h repres5t ! satellites are numb]$ #a1 #b1 #c1 #d1 9 ord] to pres]ve _! id5tity 9 ! successive pictures4 ,! *ief int]e/ ( ^! pictures lies 9 ! satellites1 b1 res]v+ !m = future consid]ation1 we note t ! planet itself resembles 9 %ape ! full moon1 al?\gh 9 respect ( brightness x s5ds to u less ?an #a_/fjjj "p z mu* light z ! moon4 ,f a consid]ation ( ! motion ( ,jupit] & ! e>? 9 ,fig4 #af1 %[ t ,jupit] c n pres5t any su* phases z does ! moon1 b t its disk mu/ be at all times ne>ly full4 ,z se5 f ,saturn1 :at k9d ( phases w\ld ,jupit] pres5t8 #acg4 ,,! ,,belts4--,ev5 ^u ! small scale ( ,fig4 #hf we detect ! mo/ *>act]i/ic feature ( ,jupit]'s appe>ance 9 ! telescope1 ! two b&s ext5d+ across 8 face p>allel to ! l9e ( ! satellites1 & 9 ,fig4 #hg ^! same d>k b&s may be recogniz$ amid ! abundance ( detail :i* is "h br\ght out by a l>ge telescope4 ,photography does n succe$ z a means ( reproduc+ ?is detail1 & = x we h to rely ^u ! skill ( ! arti/ a/ronom]4 ,! lett]+ %[s ! ,pacific ,/&>d "t at :i* ! sket*es 7 made1 & also ! longitude ( ! m]idian ( ,jupit] pass+ d[n ! c5t] ( ! planet's disk4 ,illu/ration3 ,,fig4 #hf4--;,jupit] & 8 satellites4 ,illu/ration3 ,,fig4 #hg4--;,draw+s ( ,jupit] made at ! #cf-;in* telescope ( ! ,lick ,obs]vatory4--,,keel]4 ,! d>k b&s are call$ te*nically ! belts ( ,jupit]2 & a comp>ison ( ^! belts 9 ! second & ?ird pictures ( ! gr\p1 9 :i* ne>ly ! same face ( ! planet is turn$ t[>d u1 w %[ t !y are subject to consid]able *anges ( =m & position ev5 )9 ! space ( a few days4 ,s1 too1 by a comp>ison ( su* m>k+s z ! r\nd :ite spots 9 ! upp] p>ts ( ! disks1 & ! ind5tations 9 ! edges ( ! belts1 we may recognize t ! planet is 9 ! act ( turn+ r\nd1 & mu/ !re=e h an axis ab\t :i* x turns1 & poles1 an equator1 etc4 ,! belts are 9 fact p>allel to ! planet's equator2 & g5]aliz+ f :at appe>s 9 ! pictures1 we may say t !re is always a /rongly m>k$ belt on ea* side ( ! equator ) a light] color$ /reak betwe5 !m1 & t f>!r f ! equator are o!r belts v>iable 9 numb]1 less conspicu\s1 & less p]man5t ?an ! two fir/ se54 ,comp>e ! position ( ! pr9cipal belts ) ! position ( ! zones ( sun-spot activity 9 ! sun4 ,a feature ( ! planet's surface1 :i* c n be "h reproduc$1 is ! ri* color effect to be f\nd ^u x4 ,! pr9cipal belts are a brick-r$ or salmon color1 ! int]v5+ spaces 9 g5]al :ite b ri*ly mottl$1 & /reak$ ) purples1 br[ns1 & gre5s4 ,! draw+s %[ ! planet z x appe>$ 9 ! telescope1 inv]t$1 & !y mu/ be turn$ upside d[n if we wi% ! po9ts ( ! compass to appe> z ^u a t]re/rial map4 ,be>+ ?is 9 m9d1 note 9 ! la/ picture ! great oval spot 9 ! s\!rn hemisph]e ( ,jupit]4 ,?is is a fam\s m>k+1 kn[n f its color z ! great r$ spot1 :i* appe>$ fir/ 9 #ahgh & has p]si/$ to ! pres5t day 7#aijj71 sometimes ! mo/ conspicu\s m>k+ on ! planet1 at o!rs r$uc$ to a m]e gho/ ( itself1 almo/ invisible save = ! ind5tation :i* x makes 9 ! s\!rn edge ( ! belt ne> x4 #ach4 ,,rotation ,,& ,,flatt5+ ,,at ,,! ,,poles4--,"o fur!r significant fact ) respect to ,jupit] may be obta9$ f a c>eful measurem5t ( ! draw+s2 ! planet is flatt5$ at ! poles1 s t its pol> diamet] is ab\t "o sixte5? "p %ort] ?an ! equatorial diamet]4 ,! flatt5+ ( ! e>? am\nts to only "o ?ree-hundr$? "p1 & ! m>k$ diff]5ce betwe5 ^! two numb]s f9ds its explanation 9 ! great] swiftness ( ,jupit]'s rotation ab\t its axis1 s9ce 9 bo? cases x is ?is rotation :i* makes ! flatt5+4 ,x is n easy to det]m9e ! precise dim5sions ( ! planet1 s9ce ?is involves a k bo? ( its di/ance f u & ( ! angle subt5d$ by its diamet]1 b ! mo/ rec5t det]m9ations ( ?is k9d assign z ! equatorial diamet] #ij1bjj miles1 & = ! pol> diamet] #hd1djj miles4 ,det]m9e f ei!r ( ^! numb]s ! size ( ! great r$ spot4 ,! e>? turns on its axis once 9 #bd h\rs b no su* def9ite "t c be assign$ to ,jupit]1 :i*1 l ! sun1 seems to h diff]5t rotation p]iods 9 diff]5t latitudes--#i;h4 #ejm4 9 ! equatorial belt & #i;h4 #efm4 9 ! d>k belts & high] latitudes4 ,!re is "s indication t ! l>g] "p ( ! visible surface rotates 9 #i;h4 #ee4fm41 :ile a broad /ream along ! equator fl[s ea/w>d "s #bgj miles p] h\r1 & ?us comes back to ! c5t] ( ! planet1 z se5 f ! e>?1 five or six m9utes e>li] ?an ! p>ts :i* d n %>e 9 ?is motion4 ,judg$ by t]re/rial /&>ds1 #bgj miles p] h\r is a great velocity1 b ,jupit] is con/ruct$ on a colossal scale1 &1 too1 we h to comp>e ?is movem5t1 n to a curr5t fl[+ 9 ! ocean1 b to a w9d bl[+ 9 ! upp] regions ( ! e>?'s atmosph]e4 ,! visible surface ( ,jupit] is only ! top ( a cl\d =mation1 & conta9s no?+ solid or p]man5t1 if inde$ !re is any?+ solid ev5 at ! core ( ! planet4 ,! great r$ spot dur+ ! fir/ doz5 ye>s ( its exi/5ce1 in/ead ( rema9+ fix$ relative to ! surr\nd+ =mations1 drift$ two ?irds ( ! way ar\nd ! planet1 & hav+ come to a /&/ill ab\t #ahia1 x is n[ sl[ly retrac+ its pa?4 #aci4 ,,physical ,,condition4--,= a bett] und]/&+ ( ! physical condition ( ,jupit]1 we h n[ to consid] "s indep5d5t l9es ( evid5ce :i* agree 9 po9t+ to ! conclusion t ,jupit]1 al?\gh class$ ) ! e>? z a planet1 is 9 its ess5tial "* mu* m l ! sun4 ,appe>ance4--,! =mations :i* we see 9 ,fig4 #hg look l cl\ds4 ,!y ga!r & disappe>1 & ! only elem5t ( p]man5ce ab\t !m is _! t5d5cy to gr\p !mselves along zones ( latitude4 ,if we measure ! light reflect$ f ! planet we f9d t its alb$o is v high1 l t ( sn[ or our own cumulus cl\ds1 & x is ( c\rse great] f ! light p>ts ( ! disk ?an f ! d>k] b&s4 ,! spectroscope %[s t ! sunlight reflect$ f ^! d>k] belts is l t reflect$ f ! light] p>ts1 save t a l>g] portion ( ! blue & violet rays has be5 absorb$ out ( x1 ?us produc+ ! ruddy t9t ( ! belts1 z sunset colors are produc$ on ! e>?1 & %[+ t "h ! light has p5etrat$ f>!r into ! planet's atmosph]e be=e be+ ?r[n back by reflection f l[]-ly+ cl\d surfaces4 ,! d>k b&s are !re=e to be reg>d$ z rifts 9 ! cl\ds1 rea*+ d[n to "s consid]able di/ance & indicat+ an atmosph]e ( great dep?4 ,! great r$ spot1 #bh1jjj miles long1 & obvi\sly ?ru/+ back ! :ite cl\ds on e side ( x1 ye> aft] ye>1 c h>dly be a m]e pat* on ! face ( ! planet1 b indicates "s consid]able dep? ( atmosph]e4 ,d5sity4--,s1 too1 ! small mean d5sity ( ! planet1 only #a4c times t ( wat] & actually less ?an ! d5sity ( ! sun1 sugge/s t ! l>g] "p ( ! planet's bulk may be made ( gases & cl\ds1 ) v little solid matt] ev5 at ! c5t]2 b "h we get into a difficulty f :i* !re seems b "o escape4 ,! =ce ( gravity at ! visible surface ( ,jupit] may be f\nd f its mass & dim5sions to be #b4f times z great z at ! surface ( ! e>?1 & ! pressure ex]t$ ^u its atmosph]e by ?is =ce ought to compress ! l[] /rata into some?+ m d5se ?an we f9d 9 ! planet4 ,"s idea ( ?is compression may be obta9$ f ,fig4 #hh1 :]e ! l9e m>k$ ,e %[s approximately h[ ! d5sity ( ! air increases z we move f its upp] /rata d[n t[>d ! surface ( ! e>? ?r\gh a di/ance ( #af miles1 ! d5sity at any level be+ proportional to ! di/ance ( ! curv$ l9e f ! /raight "o ne> x4 ,! l9e m>k$ ,j 9 ! same figure %[s h[ ! d5sity w\ld increase if ! =ce ( gravity 7 z great "h z x is 9 ,jupit]1 & indicates a mu* great] rate ( increase4 ,/>t+ f ! upp] surface ( ! cl\d 9 ,jupit]'s atmosph]e1 if we desc5d1 n #af miles1 b #a1fjj or #af1jjj1 :at mu/ ! d5sity ( ! atmosph]e become & h[ is ?is to be reconcil$ ) :at we "k to be ! v small mean d5sity ( ! planet8 ,we are "h 9 a dilemma betwe5 d5sity on ! "o h& & ! effects ( gravity on ! o!r1 & ! only escape f x lies 9 ! assumption t ! int]ior ( ,jupit] is trem5d\sly hot1 & t ?is heat exp&s ! sub/ance ( ! planet 9 spite ( ! pressure to :i* x is subject1 mak+ a l>ge planet ) a l[ d5sity1 possibly gase\s at ! v c5t]1 b 9 its out] "p surr\nd$ by a %ell ( cl\ds cond5s$ f ! gases by radiat+ _! heat into ! cold ( out] space4 ,illu/ration3 ,,fig4 #hh4--;,increase ( d5sity 9 ! atmosph]es ( ,jupit] & ! e>?4 ,?is is ess5tially ! same physical condition t we f\nd = ! sun1 & we may add1 z fur!r po9ts ( resemblance betwe5 x & ,jupit]1 t !re seems to be a circulation ( matt] f ! hot int]ior ( ! planet to its cool] surface t is m pron\nc$ 9 ! s\!rn hemisph]e ?an 9 ! nor!rn1 & t has its p]iods ( maximum & m9imum activity1 :i*1 curi\sly en\gh1 seem to co9cide ) p]iods ( maximum & m9imum sun-spot developm5t4 ,( ?is1 h[ev]1 we c n be entirely sure1 s9ce x is only 9 rec5t ye>s t x has be5 /udi$ ) suffici5t c>e1 & fur!r obs]vations are requir$ to %[ :e!r ! agreem5t is some?+ m ?an an accid5tal & %ort-liv$ co9cid5ce4 ,temp]ature4--,! temp]ature ( ,jupit] mu/1 ( c\rse1 be mu* l[] ?an t ( ! sun1 s9ce ! surface :i* we see is n lum9\s l ! sun's2 b bel[ ! cl\ds x is n improbable t ,jupit] may be inc&esc5t1 :ite hot1 & x is surmis$ ) "s %[ ( probability t a little ( its light escapes ?r\gh ! cl\ds f "t to "t1 & helps to produce ! /rik+ brilliancy ) :i* ?is planet %9es4 #adj4 ,,! ,,satellites ,,( ,,jupit]4--,! satellites be> mu* ! same relation to ,jupit] t ! moon be>s to ! e>?1 revolv+ ab\t ! planet 9 accordance ) ! law ( gravitation1 & con=m+ to ,kepl]'s ?ree laws1 z d ! planets 9 _! c\rses ab\t ! sun4 ,obs]ve 9 ,fig4 #hf ! position ( satellite ,no4 #a on ! f\r dates1 & note h[ x oscillates back & =? f left to "r ( ,jupit]1 app>5tly mak+ a complete revolution 9 ab\t two days1 :ile ,no4 #d moves /eadily f left to "r dur+ ! entire p]iod1 & has evid5tly made only a fraction ( a revolution 9 ! "t cov]$ by ! pictures4 ,?is quick] motion1 ( c\rse1 means t ,no4 #a is ne>] to ,jupit] ?an ,no4 #d1 & ! numb]s giv5 to ! satellites %[ ! ord] ( _! di/ances f ! planet4 ,! peculi> way 9 :i* ! satellites are gr\p$1 always /&+ ne>ly 9 a /raight l9e1 %[s t _! orbits mu/ lie ne>ly 9 ! same plane1 & t ?is plane1 :i* is also ! plane ( ! planets' equator1 is turn$ edgewise t[>d ! e>?4 ,^! satellites enjoy ! di/9ction ( be+ ! fir/ objects ev] discov]$ ) ! telescope1 hav+ be5 f\nd by ,galileo almo/ imm$iately aft] its inv5tion1 ,a4 ,d4 #afaj4 ,x is q possible t be=e ?is "t !y may h be5 se5 ) ! nak$ eye1 = 9 m rec5t ye>s reports are curr5t t !y h be5 se5 "u favorable circum/ances by %>p-ey$ p]sons1 & v little telescopic aid is requir$ to %[ !m4 ,look = !m ) an op]a or field glass4 ,!y be> ! names ,io1 ,europa1 ,ganym$e1 ,calli/o1 :i*1 h[ev]1 are r>ely us$1 &1 foll[+ ! cu/om ( a/ronom]s1 we %all designate !m by ! ,roman num]als ,i1 ,,ii1 ,,iii1 ,,iv4 ,illu/ration3 ,,fig4 #hi4--,orbits ( ,jupit]'s satellites4 ,= ne>ly ?ree c5turies 7#afaj to #ahib7 a/ronom]s spoke ( ! f\r satellites ( ,jupit]2 b 9 ,septemb]1 #ahib1 a fif? "o 0 add$ to ! numb] by ,pr(essor ,b>n>d1 :o1 obs]v+ ) ! l>ge/ telescope !n extant1 f\nd v close to ,jupit] a t9y object only #a_/fjj "p z bright z ! o!r satellites1 b1 l !m1 revolv+ ar\nd ,jupit]1 a p]man5t memb] ( 8 sy/em4 ,?is is call$ ! fif? satellite1 & ,fig4 #hi %[s ! orbits ( ^! satellites ar\nd ,jupit]1 :i* is "h repres5t$ on ! same scale z ! orbits !mselves4 ,! brok5 l9e j inside ! orbit ( ,i repres5ts ! size ( ! moon's orbit4 ,! cut %[s also ! p]iodic times ( ! satellites express$ 9 days1 & furni%es 9 ?is respect a /rik+ illu/ration ( ! great mass ( ,jupit]4 ,satellite ,i is a little f>!r f ,jupit] ?an is ! moon f ! e>?1 b "u ! influ5ce ( a great] attraction x makes ! circuit ( its orbit 9 #a4gg days1 in/ead ( tak+ #bi4ec days1 z does ! moon4 ,det]m9e f ! figure by ! me?od employ$ 9 #aaa h[ mu* m massive is ,jupit] ?an ! e>?4 ,small z ^! satellites seem 9 ,fig4 #hf1 !y are really bodies ( consid]able size1 z appe>s f ,fig4 #ij1 :]e _! dim5sions are comp>$ ) ^? ( ! e>? & moon1 save t ! fif? satellite is n includ$4 ,?is "o is s small z to escape all attempts at measur+ its diamet]1 b1 judg+ f ! am\nt ( light x reflects1 ! p]iod pr9t$ ) ! leg5d ( ! figure repres5ts a gross exagg]ation ( ?is satellite's size4 ,illu/ration3 ,,fig4 #ij4--;,jupit]'s satellites comp>$ ) ! e>? & moon4 ,l ! moon1 ea* ( ^! satellites may fairly be consid]$ a _w 9 itself1 & z su* a fitt+ object ( detail$ /udy1 b1 un=tunately1 _! great di/ance f u makes x impossible1 ev5 ) ! mo/ p[]ful telescope1 to see m ^u _! surfaces ?an occasional vague m>k+s1 :i* h>dly suffice to %[ ! rotations ( ! satellites ^u _! axes4 ,"o /rik+ feature1 h[ev]1 comes out f a /udy ( _! influ5ce 9 di/urb+ ea* o!r's motion ab\t ,jupit]4 ,_! masses & ! result+ d5sities ( ! satellites are small] ?an we %\ld h expect$ to f9d1 ! d5sity be+ less ?an t ( ! moon1 & av]ag+ only a little great] ?an ! d5sity ( ,jupit] itself4 ,at ! surface ( ! ?ird satellite ! =ce ( gravity is b little less ?an on ! moon1 al?\gh ! moon's d5sity is ne>ly twice z great z t ( ,,iii1 & !re c be no "q "h ( acc\nt+ = ! l[ d5sity ?r\gh expansion by great heat1 z 9 ! case ( ! sun & ,jupit]4 ,x has be5 surmis$ t ^! satellites are n solid bodies1 l ! e>? & moon1 b only %oals ( rock & /one1 loosely pil$ toge!r & kept f pack+ into a solid mass by ! action ( ,jupit] 9 rais+ tides )9 !m4 ,b ! explanation c h>dly be reg>d$ z an accept$ article ( a/ronomical belief1 al?\gh x is support$ by "s obs]vations :i* t5d to %[ t ! app>5t %apes ( ! satellites *ange "u ! influ5ce ( ! tidal =ces impress$ ^u !m4 #ada4 ,,eclipses ,,( ,,! ,,satellites4--,x may be se5 f ,fig4 #hi t 9 _! motion ar\nd ! planet ,jupit]'s satellites mu/ f "t to "t pass ?r\gh 8 %ad[ & be eclips$1 & t ! %ad[s ( ! satellites w occasionally fall ^u ! planet1 produc+ to an obs]v] ^u ,jupit] an eclipse ( ! sun1 b to an obs]v] on ! e>? pres5t+ only ! appe>ance ( a r\nd black spot mov+ sl[ly across ! face ( ! planet4 ,occasionally also a satellite w pass exactly betwe5 ! e>? & ,jupit]1 & may be se5 project$ aga9/ ! planet z a backgr\nd4 ,all ( ^! ph5om5a are duly pr$ict$ & obs]v$ by a/ronom]s1 b ! eclipses are ! only ones we ne$ consid] "h4 ,! importance ( ^! eclipses 0 e>ly recogniz$1 & a/ronom]s endeavor$ to con/ruct a !ory ( _! recurr5ce :i* w\ld p]mit accurate pr$ictions ( !m to be made4 ,b 9 ?is !y met ) no great success1 = :ile x 0 easy en\gh to =etell on :at night an eclipse ( a giv5 satellite w\ld occur1 & ev5 to assign ! h\r ( ! night1 x 0 n possible to make ! pr$ict$ m9ute agree ) ! actual "t ( eclipse until aft] ,roem]1 a ,dani% a/ronom] ( ! sev5te5? c5tury1 f\nd :]e lay ! tr\ble4 ,8 discov]y 01 t :5ev] ! e>? 0 on ! side ( its orbit t[>d ,jupit] ! eclipses really occurr$ be=e ! pr$ict$ "t1 & :5 ! e>? 0 on ! f> side ( its orbit !y came a few m9utes lat] ?an ! pr$ict$ "t4 ,he correctly inf]r$ t ?is 0 to be expla9$1 n by any influ5ce :i* ! e>? ex]t$ ^u ,jupit] & 8 satellites1 b ?r\gh ! fact t ! light by :i* we see ! satellite & its eclipse requires an appreciable "t to cross ! int]v5+ space1 & a long] "t :5 ! e>? is f> f ,jupit] ?an :5 x is ne>4 ,= half a c5tury ,roem]'s views f\nd little cr$5ce1 b we "k n[ t he 0 "r1 & t on ! av]age ! eclipses come #hm4 #ahs4 e>ly :5 ! e>? is ne>e/ to ,jupit]1 & #hm4 #ahs4 late :5 x is on ! opposite side ( its orbit4 ,?is is equival5t to say+ t light takes #hm4 #ahs4 to cov] ! di/ance f ! sun to ! e>?1 s t at any mom5t we see ! sun n z x !n is1 b z x 0 #h m9utes e>li]4 ,x has be5 f\nd possible 9 rec5t ye>s to measure by direct exp]im5t ! velocity ) :i* light travels--#ahf1ccg miles p] second--& multiply+ ?is numb] by ! #dihs4 7 #hm4 #ahs47 we obta9 a new det]m9ation ( ! sun's di/ance f ! e>?4 ,! product ( ! two numb]s is #ib1gie1hbf1 9 v fair agreem5t ) ! #ic1jjj1jjj miles f\nd 9 ,*apt] ,x2 b1 z not$ !re1 ?is me?od1 l e o!r1 has its weak side1 & ! result may be a good _m ?\s&s ( miles 9 error4 ,x is wor?y ( note 9 ?is connection t bo? me?ods ( obta9+ ! sun's di/ance :i* 7 giv5 9 ,*apt] ,x involve ,kepl]'s ,?ird ,law1 :ile ! result obta9$ f ,jupit]'s satellites is entirely indep5d5t ( ?is law1 & ! agreem5t ( ! sev]al results is !re=e good evid5ce bo? = ! tru? ( ,kepl]'s laws & = ! s\ndness ( ,roem]'s explanation ( ! eclipses4 ,?is mode ( pro(1 by comp>+ ! num]ical results furni%$ by two or m diff]5t pr9ciples1 & %[+ t !y agree or disagree1 is ( wide application & great importance 9 physical sci5ce4 ,,saturn #adb4 ,,! ,,r+ ,,( ,,saturn4--,9 respect ( size & mass ,saturn /&s next to ,jupit]1 & al?\gh f> inf]ior to him 9 ^! respects1 x conta9s m mat]ial ?an all ! rema9+ planets comb9$4 ,b ! unique feature ( ,saturn :i* di/+ui%es x f e o!r kn[n body 9 ! heav5s is its r+1 :i* 0 long a puzzle to ! a/ronom]s :o fir/ /udi$ ! planet ) a telescope 7"o ( !m call$ ,saturn a planet ) e>s71 b1 0 aft] ne>ly half a c5tury correctly und]/ood & describ$ by ,huygh5s1 ^: ,lat9 text we translate into--,x is surr\nd$ by a r+1 ?91 flat1 n[h]e t\*+ x1 & mak+ q an angle ) ! ecliptic4 ,illu/ration3 ,,fig4 #ia4--;,aspects ( ,saturn's r+s4 ,comp>e ) ?is description ,fig4 #ia1 :i* %[s "s ( ! appe>ances pres5t$ by ! r+ at diff]5t positions ( ,saturn 9 its orbit4 ,x 0 _! v>y+ aspects t l$ ,huygh5s to ins]t ! la/ words ( 8 description1 =1 if ! plane ( ! r+ co9cid$ ) ! plane ( ! e>?'s orbit1 !n at all times ! r+ mu/ be turn$ edgewise t[>d ! e>?1 z %[n 9 ! middle picture ( ! gr\p4 ,fig4 #ib %[s ! sun & ! orbit ( ! e>? plac$ ne> ! c5t] ( ,saturn's orbit1 across ^: circumf]5ce are rul$ "s oblique l9es repres5t+ ! plane ( ! r+1 ! "r end always tilt$ up1 no matt] :]e ! planet is 9 its orbit4 ,x is evid5t t an obs]v] ^u ! e>? w see ! ,n side ( ! r+ :5 ! planet is at ,n & ! ,s side :5 x is at ,s1 z is %[n 9 ! fir/ & ?ird pictures ( ,fig4 #ia1 :ile midway betwe5 ^! positions ! edge ( ! r+ w be pres5t$ to ! e>?4 ,illu/ration3 ,,fig4 #ib4--;,aspects ( ! r+ 9 _! relation to ,saturn's orbital motion4 ,! la/ occasion ( ?is k9d 0 9 ,octob]1 #ahia1 & ) ! l>ge telescope ( ! ,wa%burn ,obs]vatory ! writ] at t "t saw ,saturn )\t a trace ( a r+ surr\nd+ x4 ,! r+ is s ?9 t x disappe>s altoge!r :5 turn$ edgewise4 ,! names ( ! zodiacal con/ellations are ins]t$ 9 ,fig4 #ib 9 _! prop] direction f ! sun1 & f ^! we le>n t ! r+ w disappe>1 or be exce$+ly n>r[1 :5ev] ,saturn is 9 ! con/ellation ,pisces or ne> ! b\nd>y l9e betwe5 ,leo & ,virgo4 ,x w be broad & %[ its nor!rn side :5 ,saturn is 9 ,scorpius or ,sagitt>ius1 & its s\!rn face :5 ! planet is 9 ,gem9i4 ,:at w be its appe>ance 9 #aijg at ! date m>k$ 9 ! figure8 #adc4 ,,nature ,,( ,,! ,,r+4--,x is app>5t f ,figs4 #ia & #ic t ,saturn's r+ is really made up ( two or m r+s ly+ "o inside ( ! o!r & completely sep>at$ by a d>k space :i*1 ?\gh n>r[1 is z clean & %>p z if cut ) a knife4 ,also1 ! inn] edge ( ! r+ fades (f into an obscure bord] call$ ! dusky r+ or crape r+4 ,?is requires a pretty good telescope to %[ x1 z may be inf]r$ f ! fact t x escap$ notice = m ?an two c5turies dur+ :i* ! planet 0 assidu\sly /udi$ ) telescopes1 & 0 discov]$ at ! ,h>v>d ,college ,obs]vatory z rec5tly z #ahej4 ,al?\gh ! r+s appe> oval 9 all ( ! pictures1 ?is is ma9ly an effect ( p]spective1 & !y are 9 fact ne>ly circul> ) ! planet at _! c5t]4 ,! extreme diamet] ( ! r+ is #agb1jjj miles1 & f ?is numb]1 by me?ods already expla9$ 7,*apt] ,,ix71 ! /ud5t %\ld obta9 ! wid? ( ! r+s1 _! di/ance f ! ball ( ! planet1 & ! diamet] ( ! ball4 ,z to ?ickness1 x is evid5t1 f ! disappe>ance ( ! r+ :5 its edge is turn$ t[>d ! e>?1 t x is v ?9 9 comp>ison ) its diamet]1 probably n m ?an #ajj miles ?ick1 al?\gh no exact measurem5t ( ?is c be made4 ,illu/ration3 ,,fig4 #ic4--,saturn4 ,f !oretical reasons bas$ ^u ! law ( gravitation a/ronom]s h held t ! r+s ( ,saturn c\ld n possibly be solid or liquid bodies4 ,! /ra9s impress$ ^u !m by ! planet's attraction w\ld te> into fragm5ts /eel r+s made aft] _! size & %ape4 ,q rec5tly ,pr(essor ,keel] has %[n1 by apply+ ! spectroscope 7,doppl]'s pr9ciple7 to det]m9e ! velocity ( ! r+'s rotation ab\t ,saturn1 t ! inn] p>ts ( ! r+ move1 z ,kepl]'s ,?ird ,law requires1 m rapidly ?an d ! out] p>ts1 ?us furni%+ a direct pro( t !y are n solid1 & leav+ no d\bt t !y are made up ( sep>ate fragm5ts1 ea* mov+ ab\t ! planet 9 its own orbit1 l an indep5d5t satellite1 b /&+ s close to its neighbors t ! :ole space reflects ! sunlight z completely z if x 7 solid4 ,) ?is und]/&+ ( ! r+s x is easy to see :y !y are s ?94 ,l ,jupit]1 ,saturn is greatly flatt5$ at ! poles1 & ?is flatt5+1 or r ! protub]ant mass ab\t ! equator1 lays hold ( e satellite ne> ! planet & ex]ts ^u x a direct =ce t5d+ to ?ru/ x d[n into ! plane ( ! planet's equator & hold x !re4 ,! r+ lies 9 ! plane ( ,saturn's equator because ea* p>ticle is con/ra9$ to move !re4 ,! division ( ! r+ into two p>ts1 an out] & an inn] r+1 is usually expla9$ z foll[s3 ,saturn is surr\nd$ by a num]\s brood ( satellites1 :i* by _! attractions produce p]turbations 9 ! mat]ial compos+ ! r+s1 & ! divid+ l9e betwe5 ! out] & inn] r+s falls at ! place :]e by ! law ( gravitation ! p]turbations w\ld h _! greate/ effect4 ,! divid+ l9e betwe5 ! r+s is !re=e a n>r[ lane1 #b1djj miles wide1 f :i* ! fragm5ts h be5 swept clean away by ! p]turb+ action ( ! satellites4 ,less conspicu\s divisions are se5 f "t to "t 9 o!r p>ts ( ! r+1 :]e ! p]turbations1 ?\gh less1 are /ill appreciable4 ,b x is op5 to "s "q :e!r ?is explanation is suffici5t4 ,! curi\s d>kness ( ! inn] or crape r+ is easily expla9$4 ,! p>ticles compos+ x are n pack$ toge!r s closely z 9 ! out] r+1 & !re=e reflect less sunlight4 ,inde$1 s sp>sely /rewn are ! p>ticles 9 ?is r+ t x is 9 great measure transp>5t to ! sunlight1 z is %[n by a record$ obs]vation ( "o ( ! satellites :i* 0 di/9ctly al?\gh fa9tly se5 :ile mov+ ?r\gh ! %ad[ ( ! d>k r+1 b disappe>$ 9 total eclipse :5 x ent]$ ! %ad[ ca/ by ! bright r+4 #add4 ,,! ,,ball ,,( ,,saturn4--,! ball ( ! planet is 9 mo/ respects a small] copy ( ,jupit]4 ,) an equatorial diamet] ( #gf1jjj miles1 a pol> diamet] ( #fi1jjj miles1 & a mass #ie times t ( ! e>?1 its d5sity is f\nd to be ! lea/ ( any planet 9 ! sol> sy/em1 only #j4gj ( ! d5sity ( wat]1 & ab\t "o half z great z is ! d5sity ( ,jupit]4 ,! =ce ( gravity at its surface is only a little great] 7#a4ah7 ?an on ! e>?2 & ?is1 9 connection ) ! l[ d5sity1 leads1 z 9 ! case ( ,jupit]1 to ! conclusion t ! planet mu/ be ma9ly compos$ ( gases & vapors1 v hot )91 b inclos$ by a %ell ( cl\ds :i* cuts (f _! gl[ f our eyes4 ,l ,jupit] 9 ano!r respect1 ! planet turns v swiftly ^u its axis1 mak+ a revolution 9 #aj h\rs #ad m9utes1 b up to ! pres5t x rema9s unkn[n :e!r diff]5t p>ts ( ! surface h diff]5t rotation times4 #ade4 ,,! ,,satellites4--,saturn is att5d$ by a family ( n9e satellites1 a l>g] numb] ?an belongs to any o!r planet1 b ) "o exception !y are exce$+ly small & difficult to obs]ve save ) a v l>ge telescope4 ,inde$1 ! late/ "o is said to h be5 discov]$ 9 #ahih by means ( ! image :i* x impress$ ^u a photographic plate1 & x has nev] be5 se54 ,titan1 ! l>ge/ ( !m1 is di/ant #gga1jjj miles f ! planet & be>s mu* ! same relation to ,saturn t ,satellite ,,iii be>s to ,jupit]1 ! simil>ity 9 di/ance1 size & mass be+ r /rik+1 al?\gh1 ( c\rse1 ! small] mass ( ,saturn z comp>$ ) ,jupit] makes ! p]iodic "t ( ,titan--#ae days #bc h\rs--mu* great] ?an t ( ,,iii4 ,c y apply ,kepl]'s ,?ird ,law to ! motion ( ,titan s z to det]m9e f ! data giv5 above1 ! "t requir$ = a p>ticle at ! out] or inn] edge ( ! r+ to revolve once ar\nd ,saturn8 ,japetus1 ! second satellite 9 po9t ( size1 ^: di/ance f ,saturn is ab\t t5 times z great z ! moon's di/ance f ! e>?1 pres5ts ! rem>kable peculi>ity ( be+ always bright] 9 "o "p ( its orbit ?an 9 ano!r1 ?ree or f\r times z bright :5 we/ ( ,saturn z :5 ea/ ( x4 ,?is probably indicates t1 l our own moon1 ! satellite turns always ! same face t[>d its planet1 & fur!r1 t "o side ( ! satellite reflects ! sunlight mu* bett] ?an ! o!r side--i4 e41 has a high] alb$o4 ,) ^! two assumptions x is easily se5 t ! satellite w always turn t[>d ! e>? "o face :5 we/1 & ! o!r face :5 ea/ ( ,saturn1 & ?us give ! obs]v$ diff]5ce ( brightness4 ,,uranus ,,& ,,neptune #adf4 ,,*ief ,,*>act]i/ics4--,! two rema9+ l>ge planets are int]e/+ *iefly z mod]n additions to ! kn[n memb]s ( ! sun's family4 ,! circum/ances lead+ to ! discov]y ( ,neptune h be5 t\*$ ^u 9 ,*apt] ,,iv1 & = ,uranus we ne$ only note t x 0 f\nd by accid5t 9 ! ye> #agha by ,william ,h]s*el1 :o = "s "t aft] ! discov]y consid]$ x to be only a comet4 ,x 0 ! fir/ planet ev] discov]$1 all ( its pr$ecessors hav+ be5 kn[n f prehi/oric times4 ,illu/ration3 ,,william ,,h]s*el 7#agch-ahbb74 ,uranus has f\r satellites1 all ( !m v fa9t1 :i* pres5t only "o feature ( special importance4 ,in/ead ( mov+ 9 orbits :i* are approximately p>allel to ! plane ( ! ecliptic1 z d ! satellites ( ! inn] planets1 _! orbit planes are tipp$ up ne>ly p]p5dicul> to ! planes ( ! orbits ( bo? ,uranus & ! e>?4 ,! "o satellite :i* ,neptune possesses has ! same peculi>ity 9 ev5 great] degree1 = its motion ar\nd ! planet takes place 9 ! direction opposite to t 9 :i* all ! planets move ar\nd ! sun1 mu* z if ! orbit ( ! satellite _h be5 tipp$ ov] ?r\gh an angle ( #aej4 ,turn a wat* face d[n & note h[ ! h&s g r\nd 9 ! direction opposite to t 9 :i* !y mov$ be=e ! face 0 turn$ ?r\gh #ahj4 ,bo? ,uranus & ,neptune are too di/ant to all[ mu* detail to be se5 ^u _! surfaces1 b ! pres5ce ( broad absorption b&s 9 _! spectra %[s t !y mu/ possess d5se atmosph]es q diff]5t 9 con/itution f ! atmosph]e ( ! e>?4 ,9 respect ( d5sity & ! =ce ( gravity at _! surfaces1 !y are n v unlike ,saturn1 al?\gh _! d5sity is great] & gravity less ?an 81 lead+ to ! supposition t !y are = ! mo/ "p gase\s bodies1 b cool] & probably m ne>ly solid ?an ei!r ,jupit] or ,saturn4 ,"u favorable circum/ances ,uranus may be se5 ) ! nak$ eye by "o :o kn[s j :]e to look = x4 ,neptune is nev] visible save 9 a telescope4 #adg4 ,,! ,,inn] ,,planets4--,9 %>p contra/ ) ! giant planets :i* we h be5 consid]+ /&s ! gr\p ( f\r inn] planets1 or five if we c\nt ! moon z an indep5d5t body1 :i* resemble ea* o!r 9 be+ all small1 d5se1 & solid bodies1 :i* by comp>ison ) ! great di/ances sep>at+ ! out] planets may fairly be describ$ z huddl$ toge!r close to ! sun4 ,_! relative sizes are %[n 9 ,fig4 #hd1 toge!r ) ! num]ical data conc]n+ size1 mass1 d5sity1 etc41 :i* we h already f\nd important = ! und]/&+ ( a planet's physical condition4 ,,v5us ,illu/ration3 ,,fig4 #id4--,! phases ( ,v5us4--,,antoniadi4 #adh4 ,,appe>ance4--,omitt+ ! e>?1 ,v5us is by f> ! mo/ conspicu\s memb] ( ?is gr\p1 & :5 at its brighte/ is1 ) exception ( ! sun & moon1 ! mo/ brilliant object 9 ! sky1 & may be se5 ) ! nak$ eye 9 broad daylight if ! obs]v] kn[s j :]e to look = x4 ,b its brilliancy is subject to consid]able v>iations on acc\nt ( its *ang+ di/ance f ! e>?1 & ! app>5t size ( its disk v>ies = ! same reason1 z may be se5 f ,fig4 #id4 ,^! draw+s br+ out well ! phases ( ! planet1 & ! /ud5t %\ld det]m9e f ,fig4 #ag :at are ! relative positions 9 _! orbits ( ! e>? & ,v5us at :i* ! planet w\ld pres5t ea* ( ^! phases4 ,z a guide to ?is1 obs]ve t ! d>k "p ( ,v5us's e>?w>d side is always proportional 9 area to ! angle at ,v5us betwe5 ! e>? & sun4 ,9 ! fir/ picture ( ,fig4 #id ab\t two ?irds ( ! surface correspond+ to ! full hemisph]e ( ! planet is d>k1 & ! angle at ,v5us betwe5 e>? & sun is !re=e two ?irds ( #ahj--;i4 e41 #abj4 ,9 ,fig4 #ag f9d a place on ! orbit ( ,v5us f :i* if l9es be drawn to ! sun & e>?1 z !re %[n1 ! angle betwe5 !m w be #abj4 ,make a simil> con/ruction = ! f\r? picture 9 ,fig4 #id4 ,:i* ( ^! two positions is f>!r f ! e>?8 ,h[ d ! di/ances comp>e ) ! app>5t size ( ,v5us 9 ! two pictures8 ,:at is ! phase ( ,v5us to-day8 ,! irregul>ities 9 ! %ad+ ( ! illum9at$ p>ts ( ! disk are too conspicu\s 9 ,fig4 #id1 on acc\nt ( difficulties ( reproduction2 ^! %ad+s are at ! be/ h>d to see 9 ! telescope1 & di/9ct p]man5t m>k+s ^u ! planet are :olly lack+4 ,?is abs5ce ( m>k+s makes almo/ impossible a det]m9ation ( ! planet's "t ( rotation ab\t its axis1 & a/ronom]s are divid$ 9 ?is respect into two p>ties1 "o ( :i* ma9ta9s t ,v5us1 l ! e>?1 turns ^u its axis 9 "s p]iod n v diff]5t f #bd h\rs1 :ile ! o!r cont5ds t1 l ! moon1 x turns always ! same face t[>d ! c5t] ( its orbit1 mak+ a rotation ^u its axis 9 ! same p]iod 9 :i* x makes a revolution ab\t ! sun4 ,! reason :y no p]man5t m>k+s are to be se5 on ?is planet is easily f\nd4 ,l ,jupit] & ,saturn1 its atmosph]e is at all times heavily cl\d-lad51 s t we seldom1 if ev]1 see d[n to ! level ( its solid p>ts4 ,!re is1 h[ev]1 no reason "h to suppose ! int]ior p>ts hot & gase\s4 ,x is mu* m probable t ,v5us1 l ! e>?1 possesses a solid cru/ ^: temp]ature we %\ld expect to be consid]ably high] ?an t ( ! e>?1 because ,v5us is ne>] ! sun4 ,b ! cl\d lay] 9 its atmosph]e mu/ modify ! temp]ature 9 "s degree1 & we h practically no k ( ! real temp]ature conditions at ! surface ( ! planet4 ,x is ! cl\ds ( ,v5us :i* 9 great measure are responsible = its m>k$ brilliancy1 s9ce !y are an excell5t m$ium = reflect+ ! sunlight1 & give to its surface an alb$o great] ?an t ( any o!r planet1 al?\gh ,saturn is ne>ly equal to x4 ,( c\rse1 ! pres5ce ( su* cl\d =mations indicates t ,v5us is surr\nd$ by a d5se atmosph]e1 & we h indep5d5t evid5ce ( ?is 9 ! %ape ( its disk :5 ! planet is v ne>ly betwe5 ! e>? & sun4 ,! illum9at$ "p1 f tip to tip ( ! horns1 !n /ret*es m ?an halfway ar\nd ! planet's circumf]5ce1 & %[s t a c]ta9 am\nt ( light mu/ h be5 refract$ ?r\gh its atmosph]e1 ?us mak+ ! horns ( ! cresc5t appe> unduly prolong$4 ,?is atmosph]e is %[n by ! spectroscope to be n unlike t ( ! e>?1 al?\gh1 possibly1 m d5se4 ,,m]cury #adi4 ,,*ief ,,*>act]i/ics4--,m]cury1 on acc\nt ( its ne>ness to ! sun1 is at all times a difficult object to obs]ve1 & ,cop]nicus1 :o sp5t mo/ ( 8 life 9 ,pol&1 is said1 despite all 8 ef=ts1 to h gone to 8 grave )\t ev] see+ x4 ,9 our m s\!rn latitude x c usually be se5 = ab\t a =tnight at ! "t ( ea* elongation--i4 e41 :5 at its greate/ angul> di/ance f ! sun--& ! /ud5t %\ld f9d f ,fig4 #af ! "t at :i* ! next elongation occurs & look = ! planet1 %9+ l a /> ( ! fir/ magnitude1 l[ d[n 9 ! sky j aft] sunset or be=e sunrise1 accord+ z ! elongation is to ! ea/ or we/ ( ! sun4 ,:5 se5 9 ! morn+ sky ! planet gr[s bright] day aft] day until x disappe>s 9 ! sun's rays1 :ile 9 ! ev5+ sky its brilliancy z /eadily dim9i%es until ! planet is lo/4 ,x %\ld !re=e be look$ = 9 ! ev5+ z soon z possible aft] x em]ges f ! sun's rays4 ,m]cury1 z ! smalle/ ( ! planets1 is be/ comp>$ ) ! moon1 :i* x does n greatly surpass 9 size & :i* x /rongly resembles 9 o!r respects4 ,c>eful comp>isons ( ! am\nt ( light reflect$ by ! planet 9 diff]5t p>ts ( its orbit %[ n only t its alb$o agrees v closely ) t ( ! moon1 b also t its light *anges ) ! v>y+ phase ( ! planet 9 almo/ exactly ! same way z ! am\nt ( moonlight *anges4 ,we may !re=e inf] t its surface is l t ( ! moon1 a r\gh & solid "o1 ) few or no cl\ds hang+ ov] x1 & mo/ probably cov]$ ) v little or no atmosph]e4 ,l ,v5us1 its rotation p]iod is unc]ta91 ) ! balance ( probability favor+ ! view t x rotates ^u its axis once 9 #hh days1 & !re=e always turns ! same face t[>d ! sun4 ,if su* is ! case1 its climate mu/ be v peculi>3 "o side roa/$ 9 a p]petual day1 :]e ! direct heat+ p[] ( ! sun's rays1 :5 ! planet is at p]ihelion1 is t5 times z great z on ! moon1 & :i* six weeks lat]1 :5 ! planet is at its f>!/ f ! sun1 has fall5 (f to less ?an half ( ?is4 ,on ! opposite side ( ! planet !re mu/ reign p]petual night & p]petual cold1 mitigat$ by "s slight access ( w>m? f ! day side1 & p]haps feebly imitat+ ! rapid *ange ( season :i* takes place on ! day side ( ! planet4 ,?is view1 h[ev]1 takes no acc\nt ( a possible deviation ( ! planet's axis f be+ p]p5dicul> to ! plane ( its orbit1 or ( ! librations :i* mu/ be produc$ by ! great ecc5tricity ( ! orbit1 ei!r ( :i* w\ld complicate )\t entirely de/roy+ ! ideal conditions outl9$ above4 ,,m>s #aej4 ,,appe>ance4--,! "o rema9+ memb] ( ! inn] gr\p1 ,m>s1 has 9 rec5t ye>s receiv$ m att5tion ?an any o!r planet1 & ! newspap]s & magaz9es h ann\nc$ m>vel\s ?+s conc]n+ x3 t x is inhabit$ by a race ( be+s sup]ior 9 intellig5ce to m52 t ! "w ( _! h&s may be se5 ^u ! face ( ! planet2 t we %\ld endeavor to communicate ) !m1 if inde$ !y are n already s5d+ messages to u1 etc4--all ( :i* is c]ta9ly important1 if true1 b x re/s ^u a v sl5d] f\ndation ( evid5ce1 a "p ( :i* we %all h to consid]4 ,beg9n+ ) facts ( :i* !re is no d\bt1 ?is ruddy-color$ planet1 :i* usually %9es ab\t z brightly z a /> ( ! fir/ magnitude1 sometimes displays m ?an t5fold ?is brilliancy1 surpass+ e o!r planet save ,v5us & pres5t+ at ^! times especially favorable opportunities = ! /udy ( its surface4 ,! explanation ( ?is increase ( brilliancy is1 ( c\rse1 t ! planet approa*es unusually ne> to ! e>?1 & we h already se5 f a consid]ation ( ,fig4 #ag t ?is c only happ5 9 ! mon?s ( ,augu/ & ,septemb]4 ,! la/ favorable epo* ( ?is k9d 0 9 #ahid4 ,f ,fig4 #ag ! /ud5t %\ld det]m9e :5 ! next "o w come4 ,illu/ration3 ,,fig4 #ie4--,m>s4--,,s*aeb]le4 ,fig4 #ie pres5ts n9e draw+s ( ! planet made at "o ( ! epo*s ( close approa* to ! e>?1 & %[s t its face be>s c]ta9 fa9t m>k+s :i*1 ?\gh inconspicu\s1 are fix$ & p]man5t features ( ! planet4 ,! d>k triangul> projection 9 ! l[] half ( ! second draw+ 0 se5 & sket*$ by ,huygh5s1 #afei ,a4 ,d4 ,9 ,fig4 #if "s ( ^! m>k+s are %[n mu* m pla9ly1 b ,fig4 #ie gives a bett] idea ( _! usual appe>ance 9 ! telescope4 ,illu/ration3 ,,fig4 #if4--;,f\r views ( ,m>s diff]+ #ij 9 longitude4--,,b>n>d4 #aea4 ,,rotation4--,x may be se5 readily en\gh1 f a comp>ison ( ! fir/ two sket*es ( ,fig4 #ie1 t ! planet rotates ab\t an axis1 & f a m ext5sive /udy x is f\nd to be v l ! e>? 9 ?is respect1 turn+ once 9 #bd;h4 #cgm4 ar\nd an axis tipp$ f be+ p]p5dicul> to ! plane ( its orbit ab\t a degree & a half m ?an is ! e>?'s axis4 ,s9ce x is ?is incl9ation ( ! axis :i* is ! cause ( *ang+ seasons ^u ! e>?1 !re mu/ be simil> *anges1 w9t] & summ]1 z well z day & night1 ^u ,m>s1 only ea* season is long] !re ?an "h 9 ! same proportion t its ye> is long] ?an ours--i4 e41 ne>ly two to "o4 ,x is summ] 9 ! nor!rn hemisph]e ( ,m>s :5ev] ! sun1 z se5 f ,m>s1 /&s 9 t con/ellation :i* is ne>e/ ! po9t ( ! sky t[>d :i* ! planet's axis po9ts4 ,b ?is axis po9ts t[>d ! con/ellation ,cygnus1 & ,alpha ,cygni is ! bright /> ne>e/ ! nor? pole ( ,m>s4 ,z ,pisces is ! zodiacal con/ellation ne>e/ to ,cygnus1 x mu/ be summ] 9 ! nor!rn hemisph]e ( ,m>s :5 ! sun is 9 ,pisces1 or1 turn+ ! proposition ab\t1 x mu/ be summ] 9 ! s\!rn hemisph]e ( ,m>s :5 ! planet1 z se5 f ! sun1 lies 9 ! direction ( ,pisces4 #aeb4 ,,! ,,pol> ,,caps4--,"o effect ( ! *ang+ seasons ^u ,m>s is %[n 9 ,fig4 #ig1 :]e we h a s]ies ( draw+s ( ! region ab\t its s\? pole made 9 #ahid1 on dates betwe5 ,may #ba/ & ,decemb] #aj?4 ,%[ f ,fig4 #ag t dur+ ?is "t x 0 summ] 9 ! region "h %[n4 ,m>s cross$ ! prime radius 9 #ahid on ,septemb] #e?4 ,! /rik+ ?+ 9 ^! pictures is ! :ite spot surr\nd+ ! pole1 :i* %r9ks 9 size f ! beg9n+ to ne> ! end ( ! s]ies1 & !n disappe>s altoge!r4 ,! spot came back aga9 a ye> lat]1 & l a simil> spot at ! nor? pole ( ! planet x waxes 9 ! w9t] & wanes dur+ ! summ] ( ,m>s 9 endless succession4 ,illu/ration3 ,,fig4 #ig4--,! s\? pol> cap ( ,m>s 9 #ahid4--;,,b>n>d4 ,sir ,w4 ,h]s*el1 :o /udi$ ^! appe>ances a c5tury ago1 comp>$ !m ) ! sn[ fields :i* e w9t] spread out f ! region ar\nd ! t]re/rial pole1 & 9 ! summ] melt & %r9k1 al?\gh ) u !y d n entirely disappe>4 ,?is explanation ( ! pol> caps ( ,m>s has be5 g5]ally accept$ among a/ronom]s1 & f x we may draw "o int]e/+ conclusion3 ! temp]ature ^u ,m>s betwe5 summ] & w9t] oscillates above & bel[ ! freez+ po9t ( wat]1 z x does 9 ! temp]ate zones ( ! e>?4 ,b ?is conclusion plunges u into a s]i\s difficulty4 ,! temp]ature ( ! e>? is made by ! sun1 & at ! di/ance ( ,m>s f ! sun ! heat+ effect ( ! latt] is r$uc$ to less ?an half :at x is at ! e>?1 s t1 if ,m>s is to be kept at ! same temp]ature z ! e>?1 !re mu/ be "s peculi> means = /or+ ! sol> heat & us+ x m economically ?an is done "h4 ,possibly !re is "s su* me*anism1 al?\gh no "o has yet f\nd x1 & "s a/ronom]s are v confid5t t x does n exi/1 & ass]t t ! comp>ison ( ! pol> caps ) sn[ fields is mislead+1 & t ! temp]ature ^u ,m>s mu/ be at lea/ #ajj1 & p]haps #bjj or m1 bel[ z]o4 #aec4 ,,atmosph]e ,,& ,,climate4--,9 ?is connection "o feature ( ,m>s is ( importance4 ,! m>k+s ^u its surface are always visible :5 turn$ t[>d ! e>?1 ?us %[+ t ! atmosph]e conta9s no su* am\nt ( cl\d z does our own1 b on ! :ole is decid$ly cle> & sunny1 & presumably mu* less d5se ?an ours4 ,we h se5 9 comp>+ ! e>? & ! moon h[ important is ! s]vice :i* ! e>?'s atmosph]e r5d]s 9 /or+ ! sun's heat & *eck+ ^? great vicissitudes ( temp]ature to :i* ! moon is subject2 & ) ?is 9 m9d we mu/ reg>d ! small] d5sity & cl\dless "* ( ! atmosph]e ( ,m>s z unfavorable to ! ma9t5ance !re ( a temp]ature l t ( ! e>?4 ,inde$1 ?is cl\dlessness mu/ mean "o ( two ?+s3 ei!r ! temp]ature is s l[ t vapors c n exi/ 9 any consid]able quantity1 or ! surface ( ,m>s is s dry t !re is little wat] or o!r liquid to be evaporat$4 ,! latt] alt]native is adopt$ by ^? a/ronom]s :o look ^u ! pol> caps z true sn[ fields1 :i* s]ve z ! *ief res]voir ( ! planet's wat] supply1 & :o f9d 9 ,fig4 #ih evid5ce t z ! sn[ melts & ! wat] fl[s away ov] ! flat1 dry surface ( ! planet1 vegetation spr+s up1 z %[n by ! d>k m>k+s on ! disk1 & gradually dies out ) ! advanc+ season4 ,note t 9 ! fir/ ( ^! pictures ! season ^u ,m>s corresponds to ! end ( ,may ) u1 & 9 ! la/ picture to ! beg9n+ ( ,augu/1 a p]iod dur+ :i* 9 mu* ( our we/]n c\ntry ! luxuriant vegetation ( spr+ is burn$ out by ! scor*+ sun4 ,f ?is po9t ( view ! p]man5t d>k spots are ! l[-ly+ p>ts ( ! planet's surface1 9 :i* at all times !re is a suffici5t accumulation ( wat] to support vegetable life4 ,illu/ration3 ,,fig4 #ih4--,! same face ( ,m>s at ?ree diff]5t seasons4--,,l[ell4 #aed4 ,,! ,,canals4--,9 ,fig4 #ih ! l[] "p ( ! disk ( ,m>s %[s c]ta9 fa9t d>k l9es :i* are g5]ally call$ canals1 & 9 ,plate ,,iii !re is giv5 a map ( ,m>s %[+ _m ( ^! canals runn+ 9 n>r[1 dusky /reaks across ! face ( ! planet accord+ to a patt]n almo/ z geometrical z t ( a spid]'s web4 ,?is mu/ n be tak5 = a picture ( ! planet's appe>ance 9 a telescope4 ,no man ev] saw ,m>s look l ?is1 b ! map is useful z a pla9 repres5tation ( ?+s dimly se54 ,"s ( ! regions ( ?is map are m>k$ ,m>e 7sea71 9 accordance ) ! old] view :i* reg>d$ ! d>k] p>ts ( ! planet--& ( ! moon--z bodies ( wat]1 b ?is is n[ kn[n to be an error 9 bo? cases4 ,! curv$ surface ( a planet c n be accurately reproduc$ ^u ! flat surface ( pap]1 b is always m or less di/ort$ by ! v>i\s me?ods ( project+ x :i* are 9 use4 ,comp>e ! map ( ,m>s 9 ,plate ,,iii ) ,fig4 #ii1 9 :i* ! projection repres5ts v well ! equatorial p>ts ( ! planet1 b enorm\sly exagg]ates ! region ar\nd ! poles4 ,x is a rem>kable feature ( ! canals t !y all beg9 & end 9 "o ( ^! d>k p>ts ( ! planet's surface2 !y %[ no loose ends ly+ on ! bright p>ts ( ! planet4 ,ano!r ev5 m rem>kable feature is t :ile ! l>g] canals are p]man5t features ( ! planet's surface1 !y at times appe> d\bl$--i4 e41 9 place ( "o canal two p>allel ones side by side1 la/+ = a "t & !n giv+ place aga9 to a s+le canal4 ,x is exce$+ly difficult to frame any reasonable explanation ( ^! canals & ! v>i$ appe>ances :i* !y pres5t4 ,! s\rce ( ! wild speculations ab\t ,m>s1 to :i* ref]5ce is made above1 is to be f\nd 9 ! sugge/ion frequ5tly made1 half 9 je/ & half 9 e>ne/1 t ! canals are artificial wat] c\rses con/ruct$ ^u a scale va/ly exce$+ any public works ^u ! e>?1 & te/ify+ to ! pres5ce 9 ,m>s ( an advanc$ civilization4 ,! di/+ui%$ ,italian a/ronom]1 ,s*iap>elli1 :o has /udi$ ^! =mations long] ?an any "o else1 seems incl9$ to reg>d !m z wat] c\rses l9$ on ei!r side by vegetation1 :i* fl\ri%es z f> back f ! c5tral *annel z wat] c be suppli$ f x--a plausible en\gh explanation if ! fundam5tal difficulty ab\t temp]ature c be ov]come4 ,illu/ration3 ,,fig4 #ii4--;,a *>t ( ,m>s1 #ahih-'ii4--;,,c]ulli4 ,illu/ration3 ,,plate ,,iii4 ,,map ,,( ,,m>s 7,,aft] ,,s*iap>elli7 #aee4 ,,satellites4--,9 #ahgg1 "o ( ! times ( ne> approa*1 ,pr(essor ,hall1 ( ,wa%+ton1 discov]$ two t9y satellites revolv+ ab\t ,m>s 9 orbits s small t ! ne>] "o1 ,phobos1 pres5ts ! rem>kable anomaly ( complet+ ! circuit ( its orbit 9 less "t ?an ! planet takes = a rotation ab\t its axis4 ,?is satellite1 9 fact1 makes ?ree revolutions 9 its orbit :ile ! planet turns once ^u its axis1 & x !re=e rises 9 ! we/ & sets 9 ! ea/1 z se5 f ,m>s1 go+ f "o horizon to ! o!r 9 a little less ?an #f h\rs4 ,! o!r satellite1 ,deimos1 takes a few h\rs m ?an a day to make ! circuit ( its orbit1 b ! diff]5ce is s small t x rema9s cont9u\sly above ! horizon ( any giv5 place ^u ,m>s = m ?an #fj h\rs at a "t1 & dur+ ?is p]iod runs twice ?r\gh its complete set ( phases--new1 fir/ qu>t]1 full1 etc4 ,9 ord9>y telescopes ^! satellites c be se5 only "u especially favorable circum/ances1 & are f> too small to p]mit ( any direct measurem5t ( _! size4 ,! am\nt ( light :i* !y reflect has be5 comp>$ ) t ( ,m>s & f\nd to be z mu* inf]ior to x z is ,pol>is to two full moons1 &1 judg+ f ?is comp>ison1 _! diamet]s c n mu* exce$ a half doz5 miles1 unless _! alb$o is f> less ?an t ( ,m>s1 :i* does n seem probable4 ,,! ,,a/]oids #aef4 ,,m9or ,,planets4--,^! may be dismiss$ ) few words4 ,!re are ab\t #ejj ( !m kn[n1 all discov]$ s9ce ! beg9n+ ( ! n9ete5? c5tury1 & new ones are /ill f\nd e ye>4 ,no "o pret5ds to rememb] ! names :i* h be5 assign$ !m1 & !y are commonly repres5t$ by a numb] inclos$ 9 a circle1 %[+ ! ord] 9 :i* !y 7 discov]$--e4 g41 circle #a ,c]es1 circle #dcc ,eros1 etc4 ,= ! mo/ "p !y are little m ?an *ips1 _w fragm5ts1 adrift 9 space1 & naturally x 0 ! l>g] & bright] ( !m t 7 fir/ discov]$4 ,! size ( ! fir/ f\r ( !m--,c]es1 ,pallas1 ,juno1 & ,ve/a--comp>$ ) ! size ( ! moon1 accord+ to ,pr(essor ,b>n>d1 is %[n 9 ,fig4 #ajj4 ,! great majority ( !m mu/ be mu* small] ?an ! smalle/ ( ^!1 p]haps n m ?an a score ( miles 9 diamet]4 ,a few ( ! a/]oids pres5t problems ( special int]e/1 su* z ,eros1 on acc\nt ( its close approa* to ! e>?2 ,polyhymnia1 ^: v ecc5tric orbit makes x a valuable means = det]m9+ ! mass ( ,jupit]1 etc42 b ^! are special cases & ! av]age a/]oid n[ receives scant att5tion1 al?\gh half a c5tury ago1 :5 only a few ( !m 7 kn[n1 !y 7 reg>d$ ) mu* int]e/1 & ! discov]y ( a new "o 0 an ev5t ( "s consequ5ce4 ,x 0 !n a favorite speculation t !y 7 9 fact fragm5ts ( an ill-fat$ planet :i* once fill$ ! gap betwe5 ! orbits ( ,m>s & ,jupit]1 b :i*1 by "s mis*ance1 _h be5 bl[n into pieces4 ,?is is n[ kn[n to be well-nigh impossible1 = e fragm5t :i* aft] ! explosion mov$ 9 an elliptical orbit1 z all ! a/]oids d move1 w\ld be br\ght back once 9 e revolution to ! place ( ! explosion1 & all ! a/]oid orbits mu/ !re=e int]sect at ?is place4 ,b !re is no su* common po9t ( int]section4 ,illu/ration3 ,,fig4 #ajj4--,! size ( ! fir/ f\r a/]oids4--,,b>n>d4 #aeg4 ,,life ,,on ,,! ,,planets4--,!re is a belief firmly gr\nd$ 9 ! popul> m9d1 & n )\t its advocates among pr(essional a/ronom]s1 t ! planets are inhabit$ by liv+ & intellig5t be+s1 & x seems prop] at ! close ( ?is *apt] to inquire briefly h[ f> ! facts & pr9ciples "h develop$ are consi/5t ) ?is belief1 & :at support1 if any1 !y l5d to x4 ,at ! outset we mu/ obs]ve t ! ^w life is an ela/ic t]m1 h>d to def9e 9 any satisfactory way1 & yet /&+ = some?+ :i* we "k "h ^u ! e>?4 ,x is ?is idea1 our famili> ?\gh crude k ( life1 :i* lies at ! root ( ! matt]4 ,life1 if x exi/s 9 ano!r planet1 mu/ be 9 its ess5tial "* l life ^u ! e>?1 & mu/ at lea/ possess ^? features :i* are common to all =ms ( t]re/rial life4 ,x is an abuse ( language to say t life 9 ,m>s may be utt]ly unlike life 9 ! e>?2 if x is absolutely unlike1 x is n life1 :atev] else x may be4 ,n[1 e =m ( life f\nd ^u ! e>? has = its physical basis a c]ta9 *emical comp\nd1 call$ protoplasm1 :i* c exi/ & p]petuate itself only )9 a n>r[ range ( temp]ature1 r\ghly speak+1 betwe5 #j & #ajj c5tigrade1 al?\gh ^! limits c be consid]ably ov]/epp$ = %ort p]iods ( "t4 ,moreov]1 ?is protoplasm c be active only 9 ! pres5ce ( wat]1 or wat] vapor1 & we may !re=e e/abli% z ! necess>y conditions = ! cont9u$ exi/5ce & reproduction ( life 9 any place t its temp]ature mu/ n be p]man5tly above #ajj or bel[ #j1 ,c41 & wat] mu/ be pres5t 9 t place 9 "s =m4 ,) ^! conditions be=e u x is pla9 t life c n exi/ 9 ! sun on acc\nt ( its high temp]ature4 ,x is conceivable t active & intellig5t be+s1 salam&]s1 might exi/ !re1 b !y c\ld n prop]ly be said to live4 ,9 ,jupit] & ,saturn ! same condition ( high temp]ature prevails1 & probably also 9 ,uranus & ,neptune1 s t x seems highly improbable t any ( ^! planets %\ld be ! home ( life4 ,( ! inn] planets1 ,m]cury & ! moon seem de/itute ( any consid]able atmosph]es1 & are !re=e lack+ 9 ! supply ( wat] necess>y = life1 & ! same is almo/ c]ta9ly true ( all ! a/]oids4 ,!re rema9 ,v5us1 ,m>s1 & ! satellites ( ! out] planets1 :i* latt]1 h[ev]1 we mu/ drop f consid]ation z be+ too little kn[n4 ,on ,v5us !re is an atmosph]e probably conta9+ vapor ( wat]1 & x is well )9 ! range ( possibility t liquid wat] %\ld exi/ ^u ! surface ( ?is planet & t its temp]ature %\ld fall )9 ! prescrib$ limits4 ,x w\ld1 h[ev]1 be /ra9+ our actual k to affirm t su* is ! case1 or to insi/ t if su* 7 ! case1 life w\ld necess>ily exi/ ^u ! planet4 ,on ,m>s we enc\nt] ! fundam5tal difficulty ( temp]ature already not$ 9 #aeb4 ,if 9 "s unkn[n way ! temp]ature is ma9ta9$ suffici5tly high = ! pol> caps to be real sn[1 ?aw+ & =m+ aga9 ) ! progress ( ! seasons1 ! necess>y conditions ( life w\ld seem to be fulfill$ "h & life if once introduc$ ^u ! planet might abide & fl\ri%4 ,b ( positive pro( t su* is ! case we h none4 ,on ! :ole1 our survey l5ds little enc\ragem5t to ! belief 9 planet>y life1 = aside f ! e>?1 ( all ! hundr$s ( bodies 9 ! sol> sy/em1 n "o is f\nd 9 :i* ! necess>y conditions ( life are c]ta9ly fulfill$1 & only two exi/ 9 :i* !re is a reasonable probability t ^! conditions may be satisfi$4 ,,*apt] ,,xii ,,comets ,,& ,,meteors #aeh4 ,,visitors ,,9 ,,! ,,sol> ,,sy/em4--,all ( ! objects--sun1 moon1 planets1 />s--:i* we h ?us f> _h to consid]1 are p]man5t citiz5s ( ! sky1 & we h no reason to suppose t _! pres5t appe>ance diff]s appreciably f :at x 0 #a1jjj ye>s or #aj1jjj ye>s ago4 ,b !re is ano!r class ( objects--comets1 meteors--:i* appe> unexpect$ly1 are visible = a "t1 & !n vani% & are se5 no m4 ,on acc\nt ( ?is tempor>y "* ! a/ronom]s ( anci5t & m$ival times = ! mo/ "p refus$ to reg>d !m z cele/ial bodies b class$ !m along ) cl\ds1 fogs1 ,jack-o'-lant]ns1 & fireflies1 z exhalations f ! swamps or ! volcano2 admitt+ !m to be inde$ important z h>b+]s ( evil to mank9d1 b hav+ no especial significance = ! a/ronom]4 ,! comet ( #afah ,a4 ,d4 inspir$ ! l9es-- ,eight ?+s !re be a ,comet br+s1 ,:5 x on high do? horrid range3 ,w9d1 ,fam9e1 ,plague1 & ,dea? to ,k+s1 ,w>1 ,e>?quakes1 ,floods1 & ,direful ,*ange1 :i*1 accord+ to ,:ite 7,hi/ory ( ! ,doctr9e ( ,comets71 7 to be taught 9 all s]i\sness to peasants & s*ool *ildr54 ,x 0 by sl[ degrees1 & only aft] direct measurem5ts ( p>allax _h %[n "s ( !m to be m di/ant ?an ! moon1 t ! tide ( old op9ion 0 turn$ & comets 7 transf]r$ f ! sublun>y to ! cele/ial sph]e1 & 9 m rec5t times meteors also h be5 recogniz$ z com+ to u f outside ! e>?4 ,a meteor1 or %oot+ /> z x is (t5 call$1 is "o ( ! commone/ ( ph5om5a1 & "o c h>dly wat* ! sky = an h\r on any cle> & moonless night )\t see+ sev]al ( ^? quick fla%es ( light :i* look z if "s /> _h sudd5ly left its place1 da%$ swiftly across a portion ( ! sky & !n vani%$4 ,x is ?is mislead+ appe>ance t probably is responsible = ! "n %oot+ />4 ,illu/ration3 ,,fig4 #aja4--;,donati's comet4--,,bond4 #aei4 ,,comets4--,comets are less common & mu* long]-liv$ ?an meteors1 la/+ usually = sev]al weeks1 & may be visible night aft] night = _m mon?s1 b nev] = _m ye>s1 at a "t4 ,dur+ ! la/ decade !re is no ye> 9 :i* less ?an ?ree comets h appe>$1 & #ahih is di/+ui%$ by ! discov]y ( t5 ( ^! bodies1 ! l>ge/ numb] ev] f\nd 9 "o ye>4 ,on ! av]age1 we may expect a new comet to be f\nd ab\t once 9 e t5 weeks1 b = ! mo/ "p !y are small affairs1 visible only 9 ! telescope1 & a f9e l>ge "o1 l ,donati's comet ( #aheh 7,fig4 #aja71 or ! ,great ,comet ( ,septemb]1 #ahhb1 :i* 0 visible 9 broad daylight close beside ! sun1 is a r>e spectacle1 & z /rik+ & impressive z x is r>e4 ,illu/ration3 ,,fig4 #ajb4--,"s fam\s comets4 ,note 9 ,fig4 #ajb ! great v>iety ( aspect pres5t$ by "s ( ! m fam\s comets1 :i* are "h repres5t$ ^u a v small scale4 ,fig4 #ajc is f a photograph ( "o ( ! fa9t comets ( ! ye> #ahic1 :i* appe>s "h z a r feeble /reak ( light amid ! />s :i* are scatt]$ ov] ! backgr\nd ( ! picture4 ,an app>5tly deta*$ portion ( ?is comet is %[n at ! extreme left ( ! picture1 look+ almo/ l ano!r indep5d5t comet4 ,! clean1 /raight l9e runn+ diagonally across ! picture is ! fla% ( a bright meteor t *anc$ to pass )9 ! range ( ! cam]a :ile ! comet 0 be+ photograph$4 ,a m /rik+ repres5tation ( a mod]ately bright telescopic comet is conta9$ 9 ,figs4 #ajd & #aje1 :i* pres5t two diff]5t views ( ! same comet1 %[+ a consid]able *ange 9 its appe>ance4 ,a /rik+ feature ( ,fig4 #aje is ! /> images1 :i* are "h drawn out into %ort l9es all p>allel ) ea* o!r4 ,dur+ ! exposure ( #b;h4 #bjm4 requir$ to impr9t ?is picture ^u ! photographic plate1 ! comet 0 cont9ually *ang+ its position among ! />s on acc\nt ( its orbital motion1 & ! plate 0 !re=e mov$ f "t to "t1 s z to foll[ ! comet & make its image always fall at ! same place4 ,h5ce ! plate 0 cont9ually %ift$ relative to ! />s ^: images1 drawn out into l9es1 %[ ! direction 9 :i* ! plate 0 mov$--i4 e41 ! direction 9 :i* ! comet 0 mov+ across ! sky4 ,! same effect is %[n 9 ! o!r photographs1 b less conspicu\sly ?an "h on acc\nt ( _! %ort] exposure times4 ,^! pictures all %[ t "o end ( ! comet is bright] & app>5tly m d5se ?an ! o!r1 & x is cu/om>y to call ?is bright "p ! head ( ! comet1 :ile ! bru%like app5dage t /reams away f x is call$ ! comet's tail4 ,illu/ration3 ,,fig4 #ajc4--;,brooks's comet1 ,novemb] #ac1 #ahic4 ,,b>n>d4 #afj4 ,,! ,,p>ts ,,( ,a ,,comet4--,x is n e comet t has a tail1 ?\gh all ! l>ge ones d1 & 9 ,fig4 #ajc ! deta*$ piece ( comet>y matt] at ! left ( ! picture repres5ts v well ! appe>ance ( a tailless comet1 a r l>ge b n v bright /> ( a fuzzy or hairy appe>ance4 ,! ^w comet means long-hair$ or hairy />4 ,some?+ ( ?is vagu5ess ( outl9e is f\nd 9 all comets1 ^: exact b\nd>ies are h>d to def9e1 in/ead ( be+ %>p & clean-cut l ^? ( a planet or satellite4 ,(t51 h[ev]1 !re is f\nd 9 ! head ( a comet a mu* m solid appe>+ "p1 l ! r\nd :ite ball at ! c5t] ( ,fig4 #ajf1 :i* is call$ ! nucleus ( ! comet1 & appe>s to be 9 "s sort ! c5t] f :i* its activities radiate4 ,z %[n 9 ,figs4 #ajf & #ajg1 ! nucleus is sometimes surr\nd$ by :at are call$ envelopes1 :i* h ! appe>ance ( successive wrapp+s or halos plac$ ab\t x1 & odd1 spurlike projections1 call$ jets1 are sometimes f\nd 9 connection ) ! envelopes or 9 place ( !m4 ,^! figures also %[ :at is q a common *>act]i/ic ( l>ge comets1 a d>k /reak runn+ d[n ! axis ( ! tail1 %[+ t ! tail is holl[1 a m]e %ell surr\nd+ empty space4 ,illu/ration3 ,,fig4 #ajd4--,swift's comet1 ,april #ag1 #ahib4--;,,b>n>d4 ,! am\nt ( detail %[n 9 ,figs4 #ajf & #ajg is1 h[ev]1 q exceptional1 & ! ord9>y comet is mu* m l ,fig4 #ajc or #ajd4 ,ev5 a great comet :5 x fir/ appe>s is n unlike ! deta*$ fragm5t 9 ,fig4 #ajc1 a fa9t & r\ndi% pat* ( foggy light :i* gr[s ?r\gh successive /ages to its maximum e/ate1 develop+ a tail1 nucleus1 envelopes1 etc41 only to lose !m aga9 z x %r9ks & f9ally disappe>s4 ,illu/ration3 ,,fig4 #aje4--,swift's comet1 ,april #bd1 #ahib4--;,,b>n>d4 #afa4 ,,! ,,orbits ,,( ,,comets4--,x w be rememb]$ t ,newton f\nd1 z a !oretical consequ5ce ( ! law ( gravitation1 t a body mov+ "u ! influ5ce ( ! sun's attraction might h z its orbit any "o ( ! conic sections1 ellipse1 p>abola1 or hyp]bola1 & among ! #djj & m comet orbits :i* h be5 det]m9$ e "o ( ^! orbit =ms appe>s1 b curi\sly en\gh !re is n a hyp]bola among !m :i*1 if drawn ^u pap]1 c\ld be di/+ui%$ by ! unaid$ eye f a p>abola1 & ! ellipses are all s long & n>r[1 n "o ( !m be+ s ne>ly r\nd z is ! mo/ ecc5tric planet orbit1 t a/ronom]s are accu/om$ to look ^u ! p>abola z be+ ! normal type ( comet orbit1 & to reg>d a comet ^: motion diff]s mu* f a p>abola z be+ abnormal & call+ = "s special explanation4 ,! fact t comet orbits are p>abolas1 or diff] b little f !m1 expla9s at once ! tempor>y "* & spe$y disappe>ance ( ^! bodies4 ,!y are visitors to ! sol> sy/em & visible = only a %ort "t1 because ! p>abola 9 :i* !y travel is n a clos$ curve1 & ! comet1 hav+ pass$ once along t portion ( x ne> ! e>? & ! sun1 moves (f along a pa? :i* ev] !reaft] takes x f>!r & f>!r away1 beyond ! limit ( visibility4 ,! developm5t ( ! comet dur+ ! "t x is visible1 ! gr[? & disappe>ance ( tail1 nucleus1 etc41 dep5d ^u its *ang+ di/ance f ! sun1 ! highe/ developm5t & mo/ complex /ructure be+ pres5t$ :5 x is ne>e/ to ! sun4 ,illu/ration3 ,,fig4 #ajf4--;,head ( ,coggia's comet1 ,july #ac1 #ahgd4--,,tr\velot4 ,fig4 #ajh %[s ! pa? ( ! ,great ,comet ( #ahhb dur+ ! p]iod 9 :i* x 0 se51 f ,septemb] #c1 #ahhb1 to ,may #bf1 #ahhc4 ,^! dates--,,ix1 #c1 & ,v1 #bf--;are m>k$ 9 ! figure opposite ! p>ts ( ! orbit 9 :i* ! comet /ood at ^? times4 ,simil>ly1 ! positions ( ! e>? 9 its orbit at ! beg9n+ ( ,septemb]1 ,octob]1 ,novemb]1 etc41 are m>k$ by ! ,roman num]als ,,ix1 ,x1 ,,xi1 etc4 ,! l9e ,s ,v %[s ! direction f ! sun to ! v]nal equ9ox1 & ,s is ! l9e along :i* ! plane ( ! comet's orbit int]sects ! plane ( ! e>?'s orbit--i4 e41 x is ! l9e ( nodes ( ! comet orbit4 ,s9ce ! comet approa*$ ! sun f ! s\? side ( ! ecliptic1 all ( its orbit1 save ! little segm5t :i* falls to ! left ( ,s 1 lies bel[ 7s\?7 ( ! plane ( ! e>?'s orbit1 & ! "p :i* w\ld be hidd5 if ?is plane 7 opaque is repres5t$ by a brok5 l9e4 ,illu/ration3 ,,fig4 #ajg4--;,head ( ,donati's comet1 ,septemb] #cj1 ,octob] #b1 #aheh4--;,,bond4 #afb4 ,,elem5ts ,,( ,a ,,comet',s ,,orbit4--,!re is a !orem ( geometry to ! effect t ?r\gh any ?ree po9ts n 9 ! same /raight l9e "o circle1 & only "o1 c be drawn4 ,correspond+ to ?is !re is a !orem ( cele/ial me*anics1 t ?r\gh any ?ree positions ( a comet "o conic section1 & only "o1 c be pass$ along :i* ! comet c move 9 accordance ) ! law ( gravitation4 ,?is conic section is1 ( c\rse1 its orbit1 & at ! discov]y ( a comet a/ronom]s always ha/5 to obs]ve its position 9 ! sky on diff]5t nights 9 ord] to obta9 ! ?ree positions 7"r asc5sions & decl9ations7 necess>y = det]m9+ ! p>ticul> orbit 9 :i* x moves4 ,! circle1 to :i* ref]5ce 0 made above1 is completely asc]ta9$ & def9$ :5 we "k its radius & ! position ( its c5t]4 ,a p>abola is n s simply def9$1 & five numb]s1 call$ ! elem5ts ( its orbit1 are requir$ to fix accurately a comet's pa? ar\nd ! sun4 ,two ( ^! relate to ! position ( ! l9e ( nodes & ! angle :i* ! orbit plane makes ) ! plane ( ! ecliptic2 a ?ird fixes ! direction ( ! axis ( ! orbit 9 its plane1 & ! rema9+ two1 :i* are ( m int]e/ to u1 are ! date at :i* ! comet makes its ne>e/ approa* to ! sun 7p]ihelion passage7 & its di/ance f ! sun at t date 7p]ihelion di/ance74 ,! date1 ,septemb] #ag?1 plac$ ne> ! c5t] ( ,fig4 #ajh1 is ! =m] ( ^! elem5ts1 :ile ! latt]1 :i* is too small to be accurately measur$ "h1 may be f\nd f ,fig4 #aji to be #j4hb ( ! sun's diamet]1 or1 9 t]ms ( ! e>?'s di/ance f ! sun1 #j4jjh4 ,illu/ration3 ,,fig4 #ajh4--,orbits ( ! e>? & ! ,great ,comet ( #ahhb4 ,fig4 #aji %[s on a l>ge scale ! %ape ( t "p ( ! orbit ne> ! sun & gives ! successive positions ( ! comet1 at int]vals ( #b_/aj ( a day1 on ,septemb] #af? & #ag?1 %[+ t 9 less ?an #aj h\rs--#ag4j to #ag4d--! comet swung ar\nd ! sun ?r\gh an angle ( m ?an #bdj4 ,:5 at its p]ihelion x 0 mov+ ) a velocity ( #cjj miles p] second6 ,?is v unusual velocity 0 due to ! comet's extraord9>ily close approa* to ! sun4 ,! e>?'s velocity 9 its orbit is only #ai miles p] second1 & ! velocity ( any comet at any di/ance f ! sun1 provid$ its orbit is a p>abola1 may be f\nd by divid+ ?is numb] by ! squ>e root ( half ! comet's di/ance--e4 g41 #cjj miles p] second equals #ai #j4jjda_/b4 ,illu/ration3 ,,fig4 #aji4--,motion ( ! ,great ,comet ( #ahhc 9 pass+ ar\nd ! sun4 ,mo/ ( ! visible comets h _! p]ihelion di/ances includ$ betwe5 #a_/c & #d_/c ( ! e>?'s di/ance f ! sun1 b occasionally "o is f\nd1 l ! second comet ( #ahhe1 ^: ne>e/ approa* to ! sun lies f> outside ! e>?'s orbit1 9 ?is case halfway out to ! orbit ( ,jupit]2 b su* a comet mu/ be a v l>ge "o 9 ord] to be se5 at all f ! e>?4 ,!re is1 h[ev]1 "s reason = believ+ t ! numb] ( comets :i* move ar\nd ! sun )\t ev] com+ inside ! orbit ( ,jupit]1 or ev5 t ( ,saturn1 is mu* l>g] ?an ! numb] ( ^? :i* come close en\gh to be discov]$ f ! e>?4 ,9 any case we are rem9d$ ( ,kepl]'s say+1 t comets 9 ! sky are z pl5tiful z fi%es 9 ! sea1 :i* seems to be v little exagg]at$ :5 we consid] t1 accord+ to ,kleib]1 out ( all ! comets :i* ent] ! sol> sy/em probably n m ?an #b or #c p] c5t are ev] discov]$4 ,illu/ration3 ,,fig4 #aaj4--,! ,great ,comet ( #ahdc4 #afc4 ,,dim5sions ,,( ,,comets4--,! comet ^: orbit is %[n 9 ,figs4 #ajh & #aji is ! f9e/ & l>ge/ t has appe>$ 9 rec5t ye>s4 ,its tail1 :i* at its maximum ext5t w\ld h m ?an bridg$ ! space betwe5 sun & e>? 7#ajj1jjj1jjj miles71 is made v mu* too %ort 9 ,fig4 #aji1 b :5 at its be/ 0 probably n inf]ior to t ( ! ,great ,comet ( #ahdc1 %[n 9 ,fig4 #aaj4 ,z we %all see lat]1 !re is a peculi> & special relation%ip betwe5 ^! two comets4 ,! head ( ! comet ( #ahhb 0 n especially l>ge--ab\t twice ! diamet] ( ! ball ( ,saturn--b its nucleus1 accord+ to an e/imate made by ,dr4 ,elk9 :5 x 0 v ne> p]ihelion1 0 z l>ge z ! moon4 ,! head ( ! comet %[n 9 ,fig4 #ajg 0 too l>ge to be put 9 ! space betwe5 ! e>? & ! moon1 & ! ,great ,comet ( #ahaa _h a head consid]ably l>g] ?an ! sun itself4 ,f ^! colossal sizes d[n to ! smalle/ %r$ j visible 9 ! telescope1 comets ( all dim5sions may be f\nd1 b ! small] ! comet ! less ! *ance ( its be+ discov]$1 & a comet z small z ! e>? w\ld probably g unobs]v$ unless x approa*$ v close to u4 #afd4 ,,! ,,mass ,,( ,a ,,comet4--,!re is no kn[n case 9 :i* ! mass ( a comet has ev] be5 measur$1 yet no?+ ab\t !m is m sure ?an t !y are bodies ) mass :i* is attract$ by ! sun & ! planets1 & :i* 9 its turn attracts bo? sun & planets & produces p]turbations 9 _! motion4 ,^! p]turbations are1 h[ev]1 too small to be measur$1 al?\gh ! correspond+ p]turbations 9 ! comet's motion are sometimes enorm\s1 & s9ce ^! mutual p]turbations are proportional to ! masses ( comet & planet1 we are =c$ to say t1 by comp>ison ) ev5 su* small bodies z ! moon or ,m]cury1 ! mass ( a comet is utt]ly insignificant1 c]ta9ly n z great z a t5-?\s&? "p ( ! mass ( ! e>?4 ,9 ! case ( ! ,great ,comet ( #ahhb1 if we leave its hundr$ million miles ( tail out ( acc\nt & suppose ! entire mass cond5s$ into its head1 we f9d by a little computation t ! av]age d5sity ( ! head "u ^! circum/ances mu/ h be5 less ?an #a_/aejj ( ! d5sity ( air4 ,9 ord9>y laboratory practice ?is w\ld be call$ a pretty good vacuum4 ,a /rik+ obs]vation made on ,septemb] #ag1 #ahhb1 goes to confirm ! v small d5sity ( ?is comet4 ,x is %[n 9 ,fig4 #aji t e>ly on t day ! comet cross$ ! l9e jo9+ e>? & sun1 & !re=e pass$ 9 transit ov] ! sun's disk4 ,two obs]v]s at ! ,cape ( ,good ,hope saw ! comet approa* ! sun1 & foll[$ x ) _! telescopes until ! nucleus actually rea*$ ! edge ( ! sun & disappe>$1 beh9d x z !y suppos$1 = no trace ( ! comet1 n ev5 its nucleus1 c\ld be se5 aga9/ ! sun1 al?\gh x 0 c>efully look$ =4 ,n[1 ! figure %[s t ! comet pass$ betwe5 ! e>? & sun1 & its d5se/ p>ts 7 !re=e too att5uat$ to cut (f any p]ceptible fraction ( ! sun's rays4 ,9 o!r cases />s h be5 se5 ?r\gh ! head ( a comet1 %9+ app>5tly ) undimm$ lu/]1 al?\gh 9 "s cases !y seem to h be5 slightly refract$ out ( _! true positions4 #afe4 ,,meteors4--,be=e proce$+ fur!r ) ! /udy ( comets x is well to turn aside & consid] _! humbl] relatives1 ! %oot+ />s4 ,on "s cle> ev5+1 :5 ! moon is abs5t f ! sky1 wat* ! heav5s = an h\r & c\nt ! meteors visible dur+ t "t4 ,note _! pa?s1 ! "p ( ! sky :]e !y appe> & :]e !y disappe>1 _! brightness1 & :e!r !y all move ) equal swiftness4 ,out ( su* simple obs]vations ) ! unaid$ eye !re has gr[n a l>ge & important bran* ( a/ronomical sci5ce1 "s p>ts ( :i* we %all briefly summ>ize "h4 ,a p>ticul> meteor is a local ph5om5on se5 ov] only a small "p ( ! e>?'s surface1 al?\gh occasionally a v big & bright "o may travel & be visible ov] a consid]able t]ritory4 ,su* a "o 9 ,decemb]1 #ahgf1 swept ov] ! ,unit$ ,/ates f ,kansas to ,p5nsylvania1 & 0 se5 f elev5 diff]5t ,/ates4 ,b ! ord9>y %oot+ /> is mu* less conspicu\s1 &1 z we "k f simultane\s obs]vations made at neighbor+ places1 x makes its appe>ance at a height ( "s #ge miles above ! e>?'s surface1 occupies some?+ l a second 9 mov+ ov] its pa?1 & !n disappe>s at a height ( ab\t #ej miles or m1 al?\gh occasionally a big "o comes d[n to ! v surface ( ! e>? ) =ce suffici5t to bury itself 9 ! gr\nd1 f :i* x may be dug up1 h&l$1 weigh$1 & turn$ ov] to ! *emi/ to be analyz$4 ,! pieces ?us f\nd %[ t ! big meteors1 at lea/1 are masses ( /one or m9]al2 iron is q commonly f\nd 9 !m1 z are a consid]able numb] ( o!r t]re/rial sub/ances comb9$ 9 r peculi> ways4 ,b no *emical elem5t n f\nd on ! e>? has ev] be5 discov]$ 9 a meteor4 #aff4 ,,nature ,,( ,,meteors4--,! swiftness ) :i* ! meteors sweep d[n %[s t !y mu/ come f outside ! e>?1 = ev5 half _! velocity1 if giv5 to !m by "s t]re/rial volcano or o!r explosive ag5t1 w\ld s5d !m completely away f ! e>? nev] to return4 ,we mu/ !re=e look ^u !m z s _m projectiles1 bullets1 fir$ aga9/ ! e>? f "s outside s\rce & arre/$ 9 _! motion by ! e>?'s atmosph]e1 :i* s]ves z a cu%ion to protect ! gr\nd f ! bomb>dm5t :i* w\ld o!rwise prove 9 ! highe/ degree dang]\s to bo? prop]ty & life4 ,! spe$ ( ! meteor is *eck$ by ! resi/ance :i* ! atmosph]e (f]s to its motion1 & ! en]gy repres5t$ by t spe$ is trans=m$ into heat1 :i* 9 less ?an a second raises ! meteor & ! surr\nd+ air to inc&esc5ce1 melts ! meteor ei!r :olly or 9 "p1 & usually de/roys its id5tity1 leav+ only an impalpable du/1 :i* cools (f z x settles sl[ly ?r\gh ! l[] atmosph]e to ! gr\nd4 ,! heat+ effect ( ! air's resi/ance is proportional to ! squ>e ( ! meteor's velocity1 & ev5 at su* a mod]ate spe$ z #a mile p] second ! effect ^u ! meteor is ! same z if x /ood /ill 9 a ba? ( r$-hot air4 ,n[1 ! actual velocity ( meteors ?r\gh ! air is (t5 #cj or #dj times z great z ?is1 & ! correspond+ effect ( ! air 9 rais+ its temp]ature is m ?an #a1jjj times t ( r$ heat4 ,small wond] t ! meteor is br\ght to lively inc&esc5ce & consum$ ev5 9 a fraction ( a second4 #afg4 ,,! ,,numb] ,,( ,,meteors4--,a s+le obs]v] may expect to see 9 ! ev5+ h\rs ab\t "o meteor e #aj m9utes on ! av]age1 al?\gh1 ( c\rse1 9 ?is respect mu* irregul>ity may occur4 ,lat] 9 ! night !y become m frequ5t1 & aft] #b ,a4 ,m4 !re are ab\t ?ree times z _m to be se5 z 9 ! ev5+ h\rs4 ,b no "o p]son c keep a wat* ^u ! :ole sky1 high & l[1 9 front & beh9d1 & exp]i5ce %[s t by increas+ ! numb] ( obs]v]s & assign+ to ea* a p>ticul> "p ( ! sky1 ! total numb] ( meteors c\nt$ may be increas$ ab\t five-fold4 ,s1 too1 ! obs]v]s at any "o place c keep an effective wat* ^u only ^? meteors :i* come into ! e>?'s atmosph]e )9 "s mod]ate di/ance ( _! /ation1 say #ej or #ajj miles1 & to wat* e "p ( t atmosph]e w\ld require a l>ge numb] ( /ations1 e/imat$ at some?+ m ?an #aj1jjj1 scatt]$ sy/ematically ov] ! :ole face ( ! e>?4 ,if we piece toge!r ! sev]al numb]s above consid]$1 tak+ #ad z a fair av]age ( ! h\rly numb] ( meteors to be se5 by a s+le obs]v] at all h\rs ( ! night1 we %all f9d = ! total numb] ( meteors enc\nt]$ by ! e>? 9 #bd h\rs1 #ad #e #aj1jjj #bd #af1hjj1jjj4 ,)\t lay+ too mu* /ress ^u ?is p>ticul> numb]1 we may fairly say t ! meteors pick$ up by ! e>? e day are to be reckon$ by millions1 & s9ce !y come at all seasons ( ! ye>1 we %all h to admit t ! region ?r\gh :i* ! e>? moves1 in/ead ( be+ empty space1 is really a du/ cl\d1 ea* individual p>ticle ( du/ be+ a prospective meteor4 ,on ! av]age ^! individual p>ticles are v small & v f> ap>t2 a cl\d ( silv] dimes ea* ab\t #bej miles f its ne>e/ neighbor is p]haps a fair repres5tation ( _! av]age mass & di/ance f ea* o!r1 b1 ( c\rse1 great v>iations are to be expect$ bo? 9 ! size & 9 ! frequ5cy ( ! p>ticles4 ,!re mu/ be great numb]s ( !m t are too small to make %oot+ />s visible to ! nak$ eye1 & su* are occasionally se5 d>t+ by *ance across ! field ( view ( a telescope4 #afh4 ,,! ,,zodiacal ,,light is an effect probably due to ! reflection ( sunlight f ! myriads ( ^! t9y meteors :i* occupy ! space inside ! e>?'s orbit4 ,x is a fa9t & diffuse /ream ( light1 some?+ l ! ,milky ,way1 :i* may be se5 9 ! e>ly ev5+ or morn+ /ret*+ up f ! sunrise or sunset po9t ( ! horizon along ! ecliptic & foll[+ its c\rse = _m degrees1 possibly ar\nd ! entire circumf]5ce ( ! sky4 ,x may be se5 at any season ( ! ye>1 al?\gh x %[s to ! be/ advantage 9 spr+ ev5+s & autumn morn+s4 ,look = x4 #afi4 ,,great ,,meteors4--,b !re are o!r meteors1 v]itable fireballs 9 appe>ance1 f> m conspicu\s & impos+ ?an ! ord9>y %oot+ />4 ,su* a "o explod$ ov] ! city ( ,madrid1 ,spa91 on ! morn+ ( ,febru>y #aj1 #ahif1 giv+ 9 broad sunlight a brilliant fla% :i* 0 foll[$ n9ety seconds lat] by a succession ( t]rific noises l ! dis*>ge ( a batt]y ( artill]y4 ,fig4 #aaa %[s a l>ge meteor :i* 0 se5 9 ,cali=nia 9 ! e>ly ev5+ ( ,july #bg1 #ahid1 & :i* left beh9d x a lum9\s trail or cl\d visible = m ?an half an h\r4 ,n infrequ5tly l>ge meteors are f\nd travel+ toge!r1 two or ?ree or m 9 company1 mak+ _! appe>ance simultane\sly z did ! ,cali=nia meteor ( ,octob] #bb1 #ahif1 :i* is describ$ z triple1 ! trio foll[+ "o ano!r l a tra9 ( c>s1 & ,arago cites an in/ance1 f ! ye> #ahcj1 :]e )9 a %ort space ( "t "s =ty brilliant meteors cross$ ! sky1 all mov+ 9 ! same direction ) a :i/l+ noise & display+ 9 _! flight all ! colors ( ! ra9b[4 ,! mass ( great meteors su* z ^! mu/ be measur$ 9 hundr$s if n ?\s&s ( p\nds1 & /ories are curr5t1 al?\gh n v well au!nticat$1 ( ev5 l>g] ones1 _m tons 9 weight1 hav+ be5 f\nd p>tially buri$ 9 ! gr\nd4 ,( meteors :i* h be5 actually se5 to fall f ! sky1 ! l>ge/ s+le fragm5t recov]$ weighs ab\t #ejj p\nds1 b x is only a fragm5t ( ! orig9al meteor1 :i* mu/ h be5 mu* m massive be=e x 0 brok5 up by collision ) ! atmosph]e4 ,illu/ration3 ,,fig4 #aaa4--,! ,cali=nia meteor ( ,july #bg1 #ahid4 #agj4 ,,! ,,velocity ,,( ,,meteors4--,e meteor1 big or little1 is subject to ! law ( gravitation1 & be=e x enc\nt]s ! e>? mu/ be mov+ 9 "s k9d ( orbit hav+ ! sun at its focus1 ! p>ticul> species ( orbit--ellipse1 p>abola1 hyp]bola--dep5d+ ^u ! velocity & direction ( its motion4 ,n[1 ! direction 9 :i* a meteor is mov+ c be det]m9$ )\t s]i\s difficulty f obs]vations ( its app>5t pa? across ! sky made by two or m obs]v]s1 b ! velocity c n be s readily f\nd1 s9ce ! meteors g too fa/ = any ord9>y process ( tim+4 ,b by photograph+ "o ( !m two or ?ree times on ! same plate1 ) an int]val ( only a t5? ( a second betwe5 exposures1 ,dr4 ,elk9 has succe$$ 9 %[+1 9 a few cases1 t _! velocities v>i$ f #bj to #be miles p] second1 & mu/ h be5 consid]ably great] ?an ?is be=e ! meteors enc\nt]$ ! e>?'s atmosph]e4 ,?is is a great] velocity ?an t ( ! e>? 9 its orbit1 #ai miles p] second1 z might h be5 anticipat$1 s9ce ! m]e fact t meteors c be se5 at all 9 ! ev5+ h\rs %[s t "s ( !m at lea/ mu/ travel consid]ably fa/] ?an ! e>?1 =1 c\nt+ 9 ! direction ( ! e>?'s motion1 ! region ( sunset & ev5+ is always on ! re> side ( ! e>?1 & meteors 9 ord] to /rike ?is region mu/ ov]take x by _! swift] motion4 ,we h "h1 9 fact1 ! reason :y meteors are especially abundant 9 ! morn+ h\rs2 at ?is "t ! obs]v] is on ! front side ( ! e>? :i* cat*es swift & sl[ meteors alike1 :ile ! re> is pelt$ only by ! swift] ones :i* foll[ x4 ,a comp>ison ( ! relative numb] ( morn+ & ev5+ meteors makes x probable t ! av]age meteor moves1 relative to ! sun1 ) a velocity ( ab\t #bf miles p] second1 :i* is v approximately ! av]age velocity ( comets :5 !y are at ! e>?'s di/ance f ! sun4 ,a/ronom]s1 !re=e1 consid] meteors z well z comets to h ! p>abola & ! elongat$ ellipse z _! *>act]i/ic orbits4 #aga4 ,,meteor ,,%[]s--,,! ,,radiant4--,!re is evid5t among meteors a di/9ct t5d5cy = individuals1 to ! numb] ( hundr$s or ev5 hundr$s ( millions1 to travel toge!r 9 flocks or sw>ms1 all go+ ! same way 9 orbits almo/ exactly alike4 ,?is greg>i\s t5d5cy is made manife/ n only by ! fact t f "t to "t !re are unusually abundant meteoric displays1 b also by a /rik+ peculi>ity ( _! behavior at su* times4 ,! meteors all seem to come f a p>ticul> "p ( ! heav5s1 z if "h 7 a hole 9 ! sky ?r\gh :i* !y 7 introduc$1 & f :i* !y fl[ away 9 e direction1 ev5 ^? :i* d n visibly />t f ?is place hav+ pa?s among ! />s :i*1 if prolong$ backw>d1 w\ld pass ?r\gh x4 ,! cause ( ?is appe>ance may be und]/ood f ,fig4 #aab1 :i* repres5ts a gr\p ( meteors mov+ toge!r along p>allel pa?s t[>d an obs]v] at ,d4 ,travel+ unse5 above ! e>? until !y enc\nt] ! upp] /rata ( its atmosph]e1 !y "h become inc&esc5t & spe$ on 9 p>allel pa?s1 #a1 #b1 #c1 #d1 #e1 #f1 :i*1 z se5 by ! obs]v]1 are project$ back aga9/ ! sky into lum9\s /reaks t1 z is %[n by ! arr[heads1 b1 c1 d1 all seem to radiate f ! po9t a--i4 e41 f ! po9t 9 ! sky ^: direction f ! obs]v] is p>allel to ! pa?s ( ! meteors4 ,illu/ration3 ,,fig4 #aab4--;,explanation ( ! radiant ( a meteoric %[]4--,,d5n+4 ,su* a display is call$ a meteor %[]1 & ! po9t a is call$ its radiant4 ,note h[ ^? meteors :i* appe> ne> ! radiant all h %ort pa?s1 :ile ^? remote f x 9 ! sky h long] ones4 ,qu]y3 ,z ! night we>s on & ! />s %ift t[>d ! we/1 w ! radiant %>e 9 _! motion or w x be left beh9d8 ,w\ld ! lum9\s "p ( ! pa? ( any ( ^! meteors pass across ! radiant f "o side to ! o!r8 ,is su* a cross+ ( ! radiant possible "u any circum/ances8 ,fig4 #aac %[s h[ ! meteor pa?s are gr\p$ ar\nd ! radiant ( a /rongly m>k$ %[]4 ,select f x ! meteors :i* d n belong to ?is %[]4 ,illu/ration3 ,,fig4 #aac4--,! radiant ( a meteoric %[]1 %[+ also ! pa?s ( ?ree meteors :i* d n belong to ?is %[]4--,,d5n+4 ,_m hundr$s ( ^! radiants h be5 obs]v$ 9 ! sky1 ea* ( :i* repres5ts an orbit along :i* a gr\p ( meteors moves1 & ! relation ( "o ( ^! orbits to t ( ! e>? is %[n 9 ,fig4 #aad4 ,! orbit ( ! meteors is an ellipse ext5d+ out beyond ! orbit ( ,uranus1 b s ecc5tric t a "p ( x comes inside ! orbit ( ! e>?1 & ! figure %[s only t "p ( x :i* lies ne>e/ ! sun4 ,! ,roman num]als :i* are plac$ along ! e>?'s orbit %[ ! position ( ! e>? at ! beg9n+ ( ! t5? mon?1 elev5? mon?1 etc4 ,! meteors fl[ along _! orbit 9 a long procession1 ^: direction ( motion is indicat$ by ! arr[ heads1 & ! e>?1 com+ 9 ! opposite direction1 plunges into ?is /ream & receives ! meteor %[] :5 x rea*es ! int]section ( ! two orbits4 ,! long arr[ at ! left ( ! figure repres5ts ! direction ( motion ( ano!r meteor %[] :i* enc\nt]s ! e>? at ?is po9t4 ,illu/ration3 ,,fig4 #aad4--,! orbits ( ! e>? & ! ,novemb] meteors4 ,c y det]m9e f ! figure answ]s to ! foll[+ que/ions8 ,on :at day ( ! ye> w ! e>? meet ea* ( ^! %[]s8 ,w ! radiant po9ts ( ! %[]s lie above or bel[ ! plane ( ! e>?'s orbit8 ,w ^! meteors /rike ! front or ! re> ( ! e>?8 ,c !y be se5 9 ! ev5+ h\rs8 ,f _m ( ! radiants ye> aft] ye>1 ^u ! same day or week 9 ea* ye>1 !re comes a sw>m ( %oot+ />s1 %[+ t !re mu/ be a cont9u\s procession ( meteors mov+ along ?is orbit1 s t "s are always ready to /rike ! e>? :5ev] x rea*es ! int]section ( its orbit ) !irs4 ,su* is ! explanation ( ! %[] :i* appe>s ea* ye> 9 ! fir/ half ( ,augu/1 & ^: meteors are sometimes call$ ,p]seids1 because _! radiant lies 9 ! con/ellation ,p]seus1 & a simil> explanation holds = all ! /> %[]s :i* are repeat$ ye> aft] ye>4 #agb4 ,,! ,,leonids4--,!re is1 h[ev]1 a k9d ( /> %[]1 ( :i* ! ,leonids 7radiant 9 ,leo7 is ! mo/ conspicu\s type1 9 :i* ! %[]1 al?\gh repeat$ f ye> to ye>1 is mu* m /rik+ 9 "s ye>s ?an 9 o!rs4 ,?us1 to quote f ! hi/orian3 ,9 #ahcc ! %[] 0 well obs]v$ along ! :ole ea/]n coa/ ( ,nor? ,am]ica f ! ,gulf ( ,mexico to ,halifax4 ,! meteors 7 mo/ num]\s at ab\t #e ,a4 ,m4 on ,novemb] #ac?1 & ! ris+ sun c\ld n blot out all traces ( ! ph5om5a1 = l>ge meteors 7 se5 n[ & !n 9 full daylight4 ,)9 ! scope t ! eye c\ld conta91 m ?an tw5ty c\ld be se5 at a "t %oot+ 9 e direction4 ,n a cl\d obscur$ ! broad expanse1 & millions ( meteors sp$ _! way across 9 e po9t ( ! compass4 ,_! coruscations 7 bright1 gleam+1 & incessant1 & !y fell ?ick z ! flakes 9 ! e>ly sn[s ( ,decemb]4 ,b1 s f> z is kn[n1 none ( !m rea*$ ! gr\nd4 ,an illit]ate man on ! foll[+ day rem>k$3 ,! />s cont9u$ to fall until none 7 left4 ,i am anxi\s to see h[ ! heav5s w appe> ?is ev5+1 = ,i believe we %all see no m />s4 ,an eyewitness 9 ! ,s\!rn ,/ates ?us describes ! effect ( ?is %[] ^u ! plantation negroes3 ,upw>d ( a hundr$ lay pro/rate ^u ! gr\nd1 "s spee*less & "s ) ! bitt]e/ cries1 b ) _! h&s uprais$1 implor+ ,god to save ! _w & !m4 ,! sc5e 0 truly awful1 = nev] did ra9 fall mu* ?ick] ?an ! meteors fell t[>d ! e>?--ea/1 we/1 nor?1 & s\? x 0 ! same4 ,9 ! prec$+ ye> a simil> b feebl] %[] f ! same radiant creat$ mu* al>m 9 ,france1 & ?r\gh ! old hi/oric records its repetitions may be trac$ back at int]vals ( #cc or #cd ye>s1 al?\gh ) _m int]ruptions1 to ,octob] #ab1 #ijb1 ,o4 ,s41 :5 an imm5se numb] ( fall+ />s 7 se5 to spread !mselves ov] ! face ( ! sky l ra94 ,su* a /> %[] diff]s f ! "o repeat$ e ye> *iefly 9 ! fact t its meteors1 in/ead ( be+ drawn out into a long procession1 are ma9ly clu/]$ 9 a s+le flock :i* may be long en\gh to require two or ?ree or f\r ye>s to pass a giv5 po9t ( its orbit1 b :i* is f> f ext5d+ entirely ar\nd x1 s t meteors f ?is s\rce are abundant only 9 ^? ye>s 9 :i* ! flock is at or ne> ! int]section ( its orbit ) t ( ! e>?4 ,! fact t ! ,leonid %[] is repeat$ at int]vals ( #cc or #cd ye>s 7x appe>$ 9 #agii1 #ahcb-'cc1 #ahff-'fg7 %[s t ?is is ! p]iodic "t 9 its orbit1 :i* latt] mu/ ( c\rse be an ellipse1 & presumably a long & n>r[ "o4 ,x is ?is orbit :i* is %[n 9 ,fig4 #aad1 & ! /ud5t %\ld note 9 ?is figure t if ! meteor /ream at ! po9t :]e x cuts ?r\gh ! plane ( ! e>?'s orbit 7 ei!r ne>] to or f>!r f ! sun ?an is ! e>? !re c\ld be no %[]2 ! e>? & ! meteors w\ld pass by )\t a collision4 ,n[1 ! meteors 9 _! motion are subject to p]turbations1 p>ticul>ly by ! l>ge planets ,jupit]1 ,saturn1 & ,uranus1 :i* slightly *ange ! meteor orbit1 & x seems c]ta9 t ! *anges ?us produc$ w sometimes ?ru/ ! sw>m inside or outside ! orbit ( ! e>?1 & ?us cause a failure ( ! %[] at times :5 x is expect$4 ,! meteors 7 due at ! cross+ ( ! orbits 9 ,novemb]1 #ahii & #aijj1 &1 al?\gh a few 7 !n se51 ! %[] 0 f> f be+ a brilliant "o1 & its failure 0 d\btless caus$ by ! out] planets1 :i* swit*$ ! meteors aside f ! pa? 9 :i* !y _h be5 mov+ = a c5tury4 ,:e!r !y w be aga9 swit*$ back s z to produce future %[]s is at ! pres5t "t unc]ta94 #agc4 ,,capture ,,( ,,! ,,leonids4--,b a f> m /rik+ effect ( p]turbations is to be f\nd 9 ,fig4 #aae1 :i* %[s ! relation ( ! ,leonid orbit to ^? ( ! pr9cipal planets1 & illu/rates a curi\s *apt] 9 ! hi/ory ( ! meteor sw>m t has be5 work$ out by ma!matical analysis1 & is probably a pretty good acc\nt ( :at actually befell !m4 ,e>ly 9 ! second c5tury ( ! ,*ri/ian era ?is flock ( meteors came d[n t[>d ! sun f out] space1 mov+ along a p>abolic orbit :i* w\ld h c>ri$ x j inside ! orbit ( ,jupit]1 & !n h s5t x (f to return no m4 ,b su* 0 n to be its fate4 ,z x approa*$ ! orbit ( ,uranus1 9 ! ye> #abf ,a4 ,d41 t planet *anc$ to be v ne> at h& & p]turb$ ! motion ( ! meteors to su* an ext5t t ! "* ( _! orbit 0 completely *ang$ into ! ellipse %[n 9 ! figure1 & 9 ?is new orbit !y h mov$ f t "t to ?is1 p]man5t in/ead ( transi5t memb]s ( ! sol> sy/em4 ,! p]turbations1 h[ev]1 did n end ) ! ye> 9 :i* ! meteors 7 captur$ & annex$ to ! sol> sy/em1 b ev] s9ce t "t ,jupit]1 ,saturn1 & ,uranus h be5 pull+ toge!r ^u ! orbit1 & h gradually turn$ x ar\nd into its pres5t position z %[n 9 ! figure1 & x is *iefly ?is %ift+ ( ! orbit's position 9 ! ?\s& ye>s t h elaps$ s9ce #ijb ,a4 ,d4 t makes ! meteor %[] n[ come 9 ,novemb] in/ead ( 9 ,octob] z x did !n4 ,illu/ration3 ,,fig4 #aae4--,suppos$ capture ( ! ,novemb] meteors by ,uranus4 #agd4 ,,break+ ,,up ,a ,,meteor ,,sw>m4--,h[ closely pack$ toge!r ^! meteors 7 at ! "t ( _! annexation to ! sol> sy/em is unkn[n1 b x is c]ta9 t ev] s9ce t "t ! sun has be5 ex]t+ ^u !m a tidal influ5ce t5d+ to break up ! sw>m & di/ribute its p>ticles ar\nd ! orbit1 z ! ,p]seids are di/ribut$1 &1 giv5 suffici5t "t1 x w accompli% ?is1 b up to ! pres5t ! "w is only p>tly done4 ,a c]ta9 numb] ( ! meteors h ga9$ s mu* ov] ! sl[] mov+ ones z to h made an extra circuit ( ! orbit & ov]tak5 ! re> ( ! procession1 s t !re is a ?9 /ream ( !m ext5d+ entirely ar\nd ! orbit & furni%+ 9 e ,novemb] a ,leonid %[]2 b by f> ! l>g] "p ( ! meteors /ill cl+ toge!r1 al?\gh drawn out into a /ream or ribbon1 :i*1 ?\gh v ?91 is s long t x takes "s ?ree ye>s to pass ?r\gh ! p]ihelion ( its orbit4 ,x is only :5 ! e>? plunges ?r\gh ?is ribbon1 z x %\ld 9 #ahii1 #aijj1 #aija1 t brilliant ,leonid %[]s c be expect$4 #age4 ,,relation ,,( ,,comets ,,& ,,meteors4--,x appe>s f ! =ego+ t meteors & comets move 9 simil> orbits1 & we h n[ to pu% ! analogy a little fur!r & note t 9 "s in/ances at lea/ !y move 9 id5tically ! same orbit1 or at lea/ 9 orbits s l t an appreciable diff]5ce betwe5 !m is h>dly to be f\nd4 ,?us a comet :i* 0 discov]$ & obs]v$ e>ly 9 ! ye> #ahff1 moves 9 ! same orbit ) ! ,leonid meteors1 pass+ its p]ihelion ab\t t5 mon?s ahead ( ! ma9 body ( ! meteors4 ,if x 7 set back 9 its orbit by t5 mon?s' motion1 x w\ld be a "p ( ! meteor sw>m4 ,simil>ly1 ! ,p]seid meteors h a comet mov+ 9 _! orbit actually imm]s$ 9 ! /ream ( meteor p>ticles1 & sev]al o!r ( ! m conspicu\s /> %[]s h comets att5d+ !m4 ,p]haps ! mo/ rem>kable case ( ?is "* is t ( a %[] :i* comes 9 ! latt] "p ( ,novemb] f ! con/ellation ,&rom$a1 & :i* f its association ) ! comet call$ ,biela 7aft] ! "n ( its discov]]7 is frequ5tly ref]r$ to z ! ,bielid %[]4 ,?is comet1 an inconspicu\s "o mov+ 9 an unusually small elliptical orbit1 _h be5 obs]v$ at v>i\s times f #aggb d[n to #ahdf )\t pres5t+ any?+ rem>kable 9 its appe>ance2 b ab\t ! beg9n+ ( ! latt] ye>1 ) v little w>n+1 x broke 9 two1 & = ?ree mon?s ! pieces 7 wat*$ by a/ronom]s mov+ (f1 side by side1 some?+ m ?an half z f> ap>t z are ! e>? & moon4 ,x disappe>$1 made ! circuit ( its orbit1 & six ye>s lat] came back1 ) ! fragm5ts ne>ly t5 times z f> ap>t z be=e1 & aft] a %ort /ay ne> ! e>? once m disappe>$ 9 ! di/ance1 nev] to be se5 aga91 al?\gh ! fragm5ts %\ld h return$ to p]ihelion at lea/ half a doz5 times s9ce !n4 ,9 "o respect ! orbit ( ! comet 0 rem>kable3 x pass$ ?r\gh ! place 9 :i* ! e>? /&s on ,novemb] #bg? ( ea* ye>1 s t if ! comet 7 at t p>ticul> "p ( its orbit on any ,novemb] #bg?1 a collision betwe5 x & ! e>? w\ld be inevitable4 ,s f> z is kn[n1 no su* collision ) ! comet has ev] occurr$1 b ! ,bielid meteors :i* are /rung along its orbit d enc\nt] ! e>? on t date1 9 great] or less abundance 9 diff]5t ye>s1 & are wat*$ ) mu* int]e/ by ! a/ronom]s :o look ^u !m z ! f9al appe>ance ( ! dbris ( a worn-out comet4 #agf4 ,,p]iodic ,,comets4--,! ,biela comet is a specim5 ( ! type :i* a/ronom]s call p]iodic comets--i4 e41 ^? :i* move 9 small ellipses & h correspond+ly %ort p]iodic times1 s t !y return frequ5tly & regul>ly to p]ihelion4 ,! comets :i* accompany ! o!r meteor sw>ms--,leonids1 ,p]seids1 etc4--also belong to ?is class z d "s #cj or #dj o!rs :i* h p]iodic times less ?an a c5tury4 ,z has be5 already indicat$1 ^! deviations f ! normal p>abolic orbit call = "s special explanation1 & ! sub/ance ( t explanation is conta9$ 9 ! acc\nt ( ! ,leonid meteors & _! capture by ,uranus4 ,any comet may be ?us captur$ by ! attraction ( a planet ne> :i* x passes4 ,x is only necess>y t ! p]turb+ action ( ! planet %\ld result 9 a dim9ution ( ! comet's velocity1 = we h already le>n$ t x is ?is velocity :i* det]m9es ! "* ( ! orbit1 & any?+ less ?an ! velocity appropriate to a p>abola mu/ produce an ellipse--i4 e41 a clos$ orbit ar\nd :i* ! body w revolve "t aft] "t 9 endless succession4 ,we note 9 ,fig4 #aae t :5 ! ,leonid sw>m enc\nt]$ ,uranus x pass$ 9 front ( ! planet & _h its velocity dim9i%$ & its orbit *ang$ into an ellipse !reby4 ,x might h pass$ beh9d ,uranus1 x w\ld h pass$ beh9d _h x come a little lat]1 & ! effect w\ld !n h be5 j ! opposite4 ,its velocity w\ld h be5 increas$1 its orbit *ang$ to a hyp]bola1 & x w\ld h left ! sol> sy/em m rapidly ?an x came into x1 ?ru/ out in/ead ( held 9 by ! di/urb+ planet4 ,( su* cases we c expect no record to rema91 b ! captur$ comet is its own witness to :at has happ5$1 & be>s impr9t$ ^u its orbit ! br& ( ! planet :i* sl[$ d[n its motion4 ,?us 9 ,fig4 #aae ! *ang$ orbit ( ! meteors has its aphelion 7"p remote/ f ! sun7 q close to ! orbit ( ,uranus1 & "o ( its nodes1 mho1 ! po9t 9 :i* x cuts ?r\gh ! plane ( ! ecliptic f nor? to s\? side1 is also v ne> to ! same orbit4 ,x is ^! two m>ks1 aphelion & node1 :i* by _! position id5tify ,uranus z ! planet in/rum5tal 9 captur+ ! meteor sw>m1 & ! date ( ! capture is f\nd by work+ back ) _! respective p]iodic times to an epo* at :i* planet & comet 7 simultane\sly ne> ?is node4 ,jupit]1 by reason ( 8 great mass1 is an especially effici5t captur] ( comets1 & ,fig4 #aaf %[s 8 gr\p ( captives1 8 family ( comets z !y are sometimes call$4 ,! sev]al orbits are m>k$ ) ! names commonly giv5 to ! comets4 ,frequ5tly ?is is ! "n ( _! discov]]1 b (t5 a diff]5t sy/em is foll[$--e4 g41 ! "n #ahhf1 ,,iv1 means ! f\r? comet to pass ?r\gh p]ihelion 9 ! ye> #ahhf4 ,! o!r great planets--,saturn1 ,uranus1 ,neptune--h also _! families ( captur$ comets1 & accord+ to ,s*ulh(1 :o does n entirely agree ) ! common op9ion ab\t captur$ comets1 ! e>? has caught no less ?an n9e ( ^! bodies4 ,illu/ration3 ,,fig4 #aaf4--;,jupit]'s family ( comets4 #agg4 ,,comet ,,gr\ps4--,b !re is ano!r k9d ( comet family1 or comet gr\p z x is call$1 :i* des]ves "s notice1 & :i* is be/ exemplifi$ by ! ,great ,comet ( #ahhb & its relatives4 ,no less ?an f\r o!r comets are kn[n to be travel+ 9 sub/antially ! same orbit ) ?is "o1 ! gr\p consi/+ ( comets #affh1 ,i2 #ahdc1 ,i2 #ahhj1 ,i2 #ahhb1 ,,ii2 #ahhg1 ,i4 ,! orbit itself is n q a p>abola1 b a v elongat$ ellipse1 ^: major axis & correspond+ p]iodic "t c n be v accurately det]m9$ f ! available data1 b x c]ta9ly ext5ds f> beyond ! orbit ( ,neptune1 & requires n less ?an #ejj ye>s = ! comet to complete a revolution 9 x4 ,x 0 = a "t suppos$ t "s "o ( ! rec5t comets ( ?is gr\p ( five might be a return ( ! comet ( #affh br\ght back ahead ( "t by unkn[n p]turbations4 ,!re is /ill a possibility ( ?is1 b x is q out ( ! "q to suppose t ! la/ f\r memb]s ( ! gr\p are any?+ o!r ?an sep>ate & di/9ct comets mov+ 9 practically ! same orbit4 ,?is common orbit sugge/s a common orig9 = ! comets1 b leaves u to conjecture h[ !y became sep>at$4 ,! obs]v$ orbits ( ^! five comets pres5t "s slight discordances among !mselves1 b if we suppose ea* comet to move 9 ! av]age ( ! obs]v$ pa?s x is a simple matt] to fix _! sev]al positions at ! pres5t "t4 ,!y h all rec$$ f ! sun ne>ly on l9e t[>d ! bright /> ,sirius1 & 7 all ( !m1 at ! beg9n+ ( ! ye> #aijj1 /&+ ne>ly motionless inside ( a space n bigg] ?an ! sun & di/ant f ! sun ab\t #aej radii ( ! e>?'s orbit4 ,! great rapidity ) :i* !y swept ?r\gh t "p ( _! orbit ne> ! sun 7see #afb7 is be+ comp5sat$ by ! pres5t extreme sl[ness ( _! motions1 s t ! comets ( #affh & #ahhb1 ^: passages ?r\gh ! sol> sy/em 7 sep>at$ by an int]val ( m ?an two c5turies1 n[ /& toge!r ne> ! aphelion ( _! orbits1 sep>at$ by a di/ance only #ej p] c5t great] ?an ! diamet] ( ! moon's orbit1 & !y w cont9ue sub/antially 9 ?is position = "s two or ?ree c5turies to come4 ,! sl[ness ) :i* ^! bodies move :5 f> f ! sun is /rik+ly illu/rat$ by an equation ( cele/ial me*anics :i* = p>abolic orbits takes ! place ( ,kepl]'s ,?ird ,law--viz43 r#c _/ ,t#b #agh1 :]e ,t is ! "t1 9 ye>s1 requir$ = ! comet to move f its p]ihelion to any remote "p ( ! orbit1 ^: di/ance f ! sun is repres5t$1 9 radii ( ! e>?'s orbit1 by r4 ,if ! comet ( #affh _h mov$ 9 a p>abola in/ead ( ! ellipse suppos$ above1 h[ _m ye>s w\ld h be5 requir$ to rea* its pres5t di/ance f ! sun8 #agh4 ,,relation ,,( ,,comets ,,to ,,! ,,sol> ,,sy/em4--,! orbits ( ^! comets illu/rate a t5d5cy :i* is becom+ ev] m /rongly m>k$4 ,because comet orbits are ne>ly p>abolas1 x us$ to be assum$ t !y 7 exactly p>abolic1 & ?is c>ri$ ) x ! conclusion t comets h _! orig9 outside ! sol> sy/em4 ,x may be s1 & ?is view is 9 "s degree support$ by ! fact t ^! ne>ly p>abolic orbits ( bo? comets & meteors are tipp$ at all possible angles to ! plane ( ! ecliptic in/ead ( ly+ ne> x z d ! orbits ( ! planets2 & by ! fur!r fact t1 unlike ! planets1 ! comets %[ no m>k$ t5d5cy to move ar\nd _! orbits 9 ! direction 9 :i* ! sun rotates ^u 8 axis4 ,!re is1 9 fact1 ! utmo/ confusion among !m 9 ?is respect1 "s go+ "o way & "s ano!r4 ,! law ( ! sol> sy/em 7gravitation7 is impress$ ^u _! movem5ts1 b its ord] is n4 ,b z obs]vations gr[ m num]\s & m precise1 & comet orbits are det]m9$ ) increas+ accuracy1 !re is a /eady ga9 9 ! numb] ( elliptic orbits at ! exp5se ( ! p>abolic ones1 & if comets are ( extrane\s orig9 we mu/ admit t a v consid]able p]c5tage ( !m h _! velocities sl[$ d[n )9 ! sol> sy/em1 p]haps n s mu* by ! attraction ( ! planets z by ! resi/ance (f]$ to _! motion by meteor p>ticles & sw>ms along _! pa?s4 ,a /rik+ in/ance ( :at may befall a comet 9 ?is way is %[n 9 ,fig4 #aag1 :]e ! tail ( a comet appe>s sadly di/ort$ & brok5 by :at is presum$ to h be5 a collision ) a meteor sw>m4 ,a m fam\s case ( imp$$ motion is (f]$ by ! comet :i* be>s ! "n ( ,encke4 ,?is has a p]iodic "t less ?an t ( any o!r kn[n comet1 & at int]vals ( =ty mon?s comes back to p]ihelion1 ea* "t mov+ 9 a little small] orbit ?an be=e1 unque/ionably on acc\nt ( "s resi/ance :i* x has suff]$4 ,illu/ration3 ,,fig4 #aag4--;,brooks's comet1 ,octob] #ba1 #ahic4--;,,b>n>d4 #agi4 ,,! ,,developm5t ,,( ,a ,,comet4--,we saw 9 #agd t ! sun's action ^u a meteor sw>m t5ds to break x up into a long /ream1 & ! same t5d5cy to break up is true ( comets ^: att5uat$ sub/ance pres5ts scant resi/ance to ?is =ce4 ,accord+ to ! ma!matical analysis ( ,ro*e1 if ! comet /ood /ill ! sun's tidal =ce w\ld t5d fir/ to draw x out on l9e ) ! sun1 j z ! e>?'s tidal =ce pull$ ! moon out ( %ape 7 #db71 & !n x w\ld cause ! light] "p ( ! comet's sub/ance to fl[ away f bo? ends ( ?is long diamet]4 ,?is de/ructive action ( ! sun is n limit$ to comets & meteor /reams1 = x t5ds to te> ! e>? & moon to pieces z well2 b ! d5sities & ! result+ mutual attractions ( _! p>ts are f> too great to p]mit ?is to be accompli%$4 ,z a curiosity ( ma!matical analysis we may note t a sph]ical cl\d ( meteors1 or du/ p>ticles weigh+ a gramme ea*1 & plac$ at ! e>?'s di/ance f ! sun1 w be brok5 up & dissipat$ by ! sun's tidal action if ! av]age di/ance betwe5 ! p>ticles exce$s two y>ds4 ,n[1 ! e>? is f> m d5se ?an su* a cl\d1 ^: extreme t5uity1 h[ev]1 sugge/s :at we h already le>n$ ( ! small d5sity ( comets1 & prep>es u 9 _! case = an outfl[ ( p>ticles at bo? ends ( ! diamet] direct$ t[>d ! sun4 ,some?+ ( ?is k9d actually occurs1 = ! tail ( a comet /reams out on ! side opposite to ! sun1 & 9 g5]al po9ts away f ! sun1 z is %[n 9 ,fig4 #aji1 & ! envelopes & jets rise up t[>d ! sun2 b an inspection ( ,fig4 #ajf w %[ t ! tail & ! envelope are too unlike to be produc$ by "o & ! same set ( =ces4 ,x 0 long ago sugge/$ t ! sun possibly ex]ts ^u a comet's sub/ance a repell+ =ce 9 addition to ! attract+ =ce :i* we call gravity4 ,we ?9k naturally 9 ?is connection ( ! repell+ =ce :i* a *>ge ( electricity ex]ts ^u a simil> *>ge plac$ on a neighbor+ body1 & we note t if bo? sun & comet c>ri$ a consid]able /ore ( electricity ^u _! surfaces ?is w\ld furni% j su* a repell+ =ce z seems indicat$ by ! ph5om5a ( comets' tails2 = ! =ce ( gravity w\ld op]ate betwe5 ! sub/ance ( sun & comet1 & on ! :ole w\ld be ! controll+ =ce1 :ile ! electric *>ges w\ld produce a repulsion1 relatively feeble = ! big p>ticles & /rong = ! little ones1 s9ce an electric *>ge lies :olly on ! surface1 :ile gravity p]meates ! :ole mass ( a body1 & ! ratio ( volume 7gravity7 to surface 7electric *>ge7 increases rapidly ) increas+ size4 ,! repell+ =ce w\ld ?ru/ back t[>d ! comet ^? p>ticles :i* fl[$ out t[>d ! sun1 :ile x w\ld urge =w>d ^? :i* fl[$ away f x1 ?us produc+ ! diff]5ce 9 appe>ance betwe5 tail & envelopes1 ! latt] be+ reg>d$ f ?is /&po9t z /unt$ tails /rongly curv$ backw>d4 ,9 rec5t ye>s ! ,russian a/ronom] ,br$i*9 has made a c>eful /udy ( ! %ape & positions ( comets' tails & f9ds t !y fit ) ma!matical precision to ! !ories ( electric repulsion4 #ahj4 ,,comet ,,tails4--,accord+ to ,br$i*91 a comet's tail is =m$ by some?+ l ! foll[+ process3 ,9 ! head ( ! comet itself a c]ta9 "p ( its matt] is brok5 up into f9e bits1 s+le molecules p]haps1 :i*1 z !y no long] cl+ toge!r1 may be describ$ z 9 ! condition ( vapor4 ,by ! repell5t action ( bo? sun & comet ^! molecules are ca/ out f ! head ( ! comet & /ream away 9 ! direction opposite to ! sun ) diff]5t velocities1 ! heavy ones sl[ly & ! light ones fa/]1 mu* z p>ticles ( smoke /ream away f a smoke/ack1 mak+ = ! comet a tail :i* l a trail ( smoke is compos$ ( con/antly *ang+ p>ticles4 ,! result ( ?is process is %[n 9 ,fig4 #aah1 :]e ! positions ( ! comet 9 its orbit on successive days are m>k$ by ! ,roman num]als1 & ! brok5 l9es repres5t ! pa?s ( molecules m,i1 m,,ii1 m,,iii1 etc41 expell$ f x on _! sev]al dates & travel+ !reaft] 9 orbits det]m9$ by ! comb9$ effect ( ! sun's attraction1 ! sun's repulsion1 & ! comet's repulsion4 ,! comet's attraction 7gravity7 is too small to be tak5 into acc\nt4 ,! l9e drawn upw>d f ,,vi repres5ts ! positions ( ^! molecules on ! six? day1 & %[s t all ( !m are arrang$ 9 a tail po9t+ ne>ly away f ! sun4 ,a simil> con/ruction = ! o!r dates gives ! correspond+ positions ( ! tail1 always po9t+ away f ! sun4 ,illu/ration3 ,,fig4 #aah4--;,=mation ( a comet's tail4 ,only ! lighte/ k9d ( molecules--e4 g41 hydrog5--c\ld drift away f ! comet s rapidly z is "h %[n4 ,! heavi] ones1 su* z c>bon & iron1 w\ld be repell$ z /rongly by ! electric =ces1 b !y w\ld be m /rongly pull$ back by ! gravitative =ces1 ?us produc+ a mu* sl[] sep>ation betwe5 !m & ! head ( ! comet4 ,con/ruct a figure su* z ! above1 9 :i* ! molecules %all rec$e f ! comet only "o eigh? z fa/ z 9 ,fig4 #aah1 & note :at a diff]5t position x gives to ! comet's tail4 ,in/ead ( po9t+ directly away f ! sun1 x w be b5t /rongly to "o side1 z is ! l>ge plume-%ap$ tail ( ! ,donati comet %[n 9 ,fig4 #aja4 ,b obs]ve t ?is comet has also a ne>ly /raight tail1 l ! !oretical "o ( ,fig4 #aah4 ,we h "h two di/9ct types ( comet tails1 & accord+ to ,br$i*9 !re is /ill ano!r b unusual type1 ev5 m /rongly b5t to "o side ( ! l9e jo9+ comet & sun1 & appe>+ q %ort & /ubby4 ,! exi/5ce ( ^! ?ree types1 & _! peculi>ities ( %ape & position1 are all satisfactorily acc\nt$ = by ! supposition t !y are made ( diff]5t mat]ials4 ,! relative molecul> weights ( hydrog51 "s ( ! hydroc>bons1 & iron1 are su* t tails compos$ ( ^! molecules w\ld behave j z d ! actual tails obs]v$ & classifi$ into ^! ?ree types4 ,! spectroscope %[s t ^! mat]ials--hydrog51 hydroc>bons1 & iron--are pres5t 9 comets1 & leaves little room = d\bt ( ! ess5tial s\ndness ( ,br$i*9's !ory4 #aha4 ,,dis9tegration ,,( ,,comets4--,we mu/ reg>d ! tail z wa/e matt] ca/ (f f ! comet's head1 & al?\gh ! am\nt ( ?is matt] is v small1 x mu/ 9 "s measure dim9i% ! comet's mass4 ,?is process is1 ( c\rse1 mo/ active at ! "t ( p]ihelion passage1 & if ! comet returns to p]ihelion "t aft] "t1 z ! p]iodic ones :i* move 9 elliptic orbits mu/ d1 ?is wa/e ( mat]ial may become a s]i\s matt]1 lead+ ultimately to ! comet's de/ruction4 ,x is significant 9 ?is connection t ! p]iodic comets are all small & inconspicu\s1 n "o ( !m %[+ a tail ( any consid]able dim5sions1 & x appe>s probable t !y are f> advanc$ along ! road :i*1 9 ! case ( ,biela's comet1 l$ to its dis9tegration4 ,_! fragm5ts are 9 "p /rewn ?r\gh ! sol> sy/em1 mak+ "s small fraction ( its cl\d ( cosmic du/1 & 9 "p !y h be5 c>ri$ away f ! sun & scatt]$ ?r\gh\t ! univ]se along hyp]bolic orbits impress$ ^u !m at ! "t !y left ! comet4 ,b x is n ?r\gh ! tail only t ! dis9tegrat+ process is work$ out4 ,:ile ,biela's comet is p]haps ! mo/ /rik+ in/ance 9 :i* ! head has brok5 up1 x is by no means ! only "o4 ,! ,great ,comet ( #ahhb ca/ (f a consid]able numb] ( fragm5ts :i* mov$ away z indep5d5t ?\gh small comets & o!r m rec5t comets h be5 se5 to d ! same4 ,an ev5 m /rik+ ph5om5on 0 ! gradual break+ up ( ! nucleus ( ! same comet1 #ahhb1 ,,ii1 into a half doz5 nuclei arrang$ 9 l9e l beads ^u a /r+1 & po9t+ along ! axis ( ! tail4 ,see ,fig4 #aai1 :i* %[s ! s]ies ( *anges obs]v$ 9 ! head ( ?is comet4 #ahb4 ,,comets ,,& ,,! ,,spectroscope4--,! spectrum pres5t$ by comets 0 long a puzzle1 & /ill reta9s some?+ ( t "*1 al?\gh mu* progress has be5 made t[>d an und]/&+ ( x4 ,9 g5]al x consi/s ( two q di/9ct p>ts--fir/1 a fa9t backgr\nd ( cont9u\s spectrum due to ord9>y sunlight reflect$ f ! comet2 &1 second1 sup]pos$ ^u ?is1 ?ree bright b&s l ! c>bon b& %[n at ! middle ( ,fig4 #dh1 only n s %>ply def9$4 ,^! b&s make a discont9u\s spectrum q simil> to t giv5 (f by comp\nds ( hydrog5 & c>bon1 & ( c\rse indicate t a "p ( ! comet's light orig9ates 9 ! body itself1 :i* mu/ !re=e be inc&esc5t1 or at lea/ mu/ conta9 "s inc&esc5t portions4 ,illu/ration3 ,,fig4 #aai4--,! head ( ! ,great ,comet ( #ahhb4--,,w9lock4 ,by heat+ hydroc>bons 9 our laboratories until !y become inc&esc5t1 some?+ l ! comet spectrum may be artificially produc$1 b ! be/ approximation to x is obta9$ by pass+ a disruptive electrical dis*>ge ?r\gh a tube 9 :i* fragm5ts ( meteors h be5 plac$4 ,a fla% ( lightn+ is a disruptive electrical dis*>ge ^u a gr& scale4 ,n[1 meteors & electric ph5om5a h be5 indep5d5tly br\ght to our notice 9 connection ) comets1 & ) ?is sugge/ion x is easy to frame a g5]al idea ( ! physical condition ( ^! objects--= example1 a cl\d ( meteors ( diff]5t sizes s loosely clu/]$ t ! av]age d5sity ( ! sw>m is v l[ inde$2 ! sev]al p>ticles 9 motion relative to ea* o!r1 z well z to ! sun1 & di/urb$ 9 t motion by ! sun's tidal action4 ,ea* p>ticle c>ries its own electric *>ge1 :i* may be ( high] or l[] t5sion ?an t ( its neighbor1 & is ready to leap across ! int]v5+ gap :5ev] two p>ticles approa* ea* o!r4 ,to ^! conditions add ! inductive effect ( ! sun's electric *>ge1 :i* t5ds to produce a p>ticul> & artificial di/ribution ( electricity among ! comet's p>ticles1 & we may expect to f9d an endless succession ( sp>ks1 t9y lightn+ fla%es1 spr++ f "o p>ticle to ano!r1 mo/ frequ5t & mo/ vivid :5 ! comet is ne> ! sun1 b nev] /rong en\gh to be sep>ately visible4 ,_! numb] is1 h[ev]1 great en\gh to make ! comet 9 "p self-lum9\s ) ?ree k9ds ( light--i4 e41 ! ?ree bright b&s ( its spectrum1 ^: wave l5g?s %[ 9 ! comet ! same elem5ts & comp\nds ( ! elem5ts--c>bon1 hydrog51 & oxyg5--:i* *emical analysis f9ds 9 ! fall5 meteor4 ,x is n to be suppos$ t ^! are ! only *emical elem5ts 9 ! comet1 z !y c]ta9ly are n ! only ones 9 ! meteor4 ,!y are ! easy ones to detect "u ord9>y circum/ances1 b 9 special cases1 l t ( ! ,great ,comet ( #ahhb1 ^: ne> approa* to ! sun r5d]$ its :ole sub/ance inc&esc5t1 ! spectrum gl[s ) additional bright l9es ( sodium1 iron1 etc4 #ahc4 ,,collisions4--,a "q sometimes ask$1 ,:at w\ld be ! effect ( a collision betwe5 ! e>? & a comet8 f9ds its answ] 9 ! results rea*$ 9 ! prec$+ sections4 ,!re w\ld be a /> %[]1 m or less brilliant accord+ to ! numb] & size ( ! pieces :i* made up ! comet's head4 ,if ^! 7 l ! rema9s ( ! ,biela comet1 ! %[] might ev5 be a v tame "o2 b a collision ) a great comet w\ld c]ta9ly produce a brilliant meteoric display if its head came 9 contact ) ! e>?4 ,if ! comet 7 built ( small pieces ^: individual weights did n exce$ a few ounces or p\nds1 ! e>?'s atmosph]e w\ld prove a p]fect %ield aga9/ _! attacks1 r$uc+ ! pieces to h>mless du/ be=e !y c\ld rea* ! gr\nd1 & leav+ ! e>? un9jur$ by ! enc\nt]1 al?\gh ! comet might suff] sadly f x4 ,b big /ones 9 ! comet1 meteors too massive to be consum$ 9 _! flight ?r\gh ! air1 might "w a v diff]5t effect1 & by _! bomb>dm5t play sad havoc ) p>ts ( ! e>?'s surface1 al?\gh any su* result z ! wreck+ ( ! e>?1 or ! de/ruction ( all life ^u x1 does n seem probable4 ,! #dj meteors ( #afi may /& = a collision ) a small comet4 ,consult ! ,bible 7,jo%ua x1 #aa7 = an example ( :at might happ5 ) a l>g] "o4 ,,*apt] ,,xiii ,,! ,,fix$ ,,/>s #ahd4 ,,! ,,con/ellations4--,9 ! e>li] *apt]s ! /ud5t has le>n$ to di/+ui% betwe5 w&]+ />s 7planets7 & ^? fix$ lum9>ies :i* rema9 ye> aft] ye> 9 ! same con/ellation1 %9+ = ! mo/ "p ) unv>y+ brilliancy1 & pres5t+ ! mo/ p]fect kn[n image ( immutability4 ,hom] & ,job & prehi/oric man saw ,orion & ! ,pleiades mu* z we see !m to-day1 al?\gh ! precession1 by *ang+ _! relation to ! pole ( ! heav5s1 has alt]$ _! ris+s & sett+s1 & x may be t _! lu/] has *ang$ 9 "s degree z !y grew old ) ! pass+ c5turies4 ,illu/ration3 ,,fig4 #abj4--;,illu/rat+ ! division ( ! sky into con/ellations4 ,! division ( ! sky into con/ellations dates back to ! mo/ primitive times1 long be=e ! ,*ri/ian era1 & ! crook$ & irregul> b\nd>ies ( ^! con/ellations1 %[n by ! dott$ l9es 9 ,fig4 #abj1 su* z no mod]n a/ronom] w\ld devise1 are an inh]itance f antiquity1 conf\nd$ & made worse 9 its desc5t to our day4 ,! b\nd>ies assign$ to con/ellations ne> ! s\? pole are mu* m smoo? & regul>1 s9ce ?is "p ( ! sky1 invisible to ! peoples f :om we inh]it1 0 n /udi$ & mapp$ until m mod]n times4 ,! old traditions associat$ ) ea* con/ellation a figure1 (t5 drawn f classical my?ology1 :i* 0 suppos$ to be sugge/$ by ! gr\p+ ( ! />s3 ?us ,ursa ,major is a great be>1 /alk+ across ! sky1 ) ! h&le ( ! ,dipp] = 8 tail2 ,leo is a lion2 ,cassiopeia1 a lady 9 a *air2 ,&rom$a1 a maid5 *a9$ to a rock1 etc42 b = ! mo/ "p ! resemblances are f>-fet*$ & q too fanciful to be foll[$ by ! ord9>y eye4 #ahe4 ,,! ,,numb] ,,( ,,/>s4--,z num]\s z ! />s ( heav5 is a famili> figure ( spee* = express+ ! idea ( c\ntless numb]1 b z appli$ to ! visible />s ( ! sky ! words convey q a wrong impression1 =1 "u ord9>y circum/ances1 9 a cle> sky e /> to be se5 may be c\nt$ 9 ! c\rse ( a few h\rs1 s9ce !y d n exce$ #c1jjj or #d1jjj1 ! exact numb] dep5d+ ^u atmosph]ic conditions & ! ke5ness ( ! individual eye4 ,te/ y\r own vision by c\nt+ ! />s ( ! ,pleiades4 ,six are easily se51 & y may possibly f9d z _m z t5 or twelve2 b h[ev] _m are se51 !re w be a vague impression ( m j beyond ! limit ( visibility1 & d\btless ?is impression is p>tly responsible = ! popul> exagg]ation ( ! numb] ( ! />s4 ,9 fact1 mu* m ?an half ( :at we call />light comes f />s :i* are sep>ately too small to be se51 b ^: numb] is s great z to m ?an make up = _! individual fa9tness4 ,! ,milky ,way is j su* a cl\d ( fa9t />s1 & ! /ud5t :o c obta9 access to a small telescope1 or ev5 an op]a glass1 %\ld n fail to turn x t[>d ! ,milky ,way & see = himself h[ t vague /ream ( light breaks up into %9+ po9ts1 ea* an indep5d5t />4 ,^! fa9t />s1 :i* are f\nd 9 e "p ( ! sky z well z 9 ! ,milky ,way1 are usually call$ telescopic1 9 recognition ( ! fact t !y c be se5 only 9 ! telescope1 :ile ! o!r bright] ones are kn[n z lucid />s4 #ahf4 ,,magnitudes4--,! telescopic />s %[ among !mselves an ev5 great] range ( brightness ?an d ! lucid ones1 & ! sy/em ( magnitudes 7 #i7 has accord+ly be5 ext5d$ to include !m1 ! fa9te/ /> visible 9 ! greate/ telescope ( ! pres5t "t be+ ( ! sixte5? or sev5te5? magnitude1 :ile1 z we h already le>n$1 />s on ! divid+ l9e betwe5 ! telescopic & ! lucid ones are ( ! six? magnitude4 ,to comp>e ! am\nt ( light receiv$ f ! />s ) t f ! planets1 & p>ticul>ly f ! sun & moon1 x has be5 f\nd necess>y to prolong ! scale ( magnitudes backw>d into ! negative numb]s1 & we speak ( ! sun z hav+ a /ell> magnitude repres5t$ by ! numb] -#bf4e4 ,! full moon's /ell> magnitude is -#ab1 & ! planets range f -#c 7,v5us7 to #h 7,neptune74 ,ev5 a v few ( ! />s are s bright t negative magnitudes mu/ be us$ to repres5t _! true relation to ! fa9t] ones4 ,sirius1 = example1 ! brighte/ ( ! fix$ />s1 is ( ! -#a magnitude1 & su* />s z ,arcturus & ,vega are ( ! #j magnitude4 ,! relation ( ^! magnitudes to ea* o!r has be5 s *os5 t a /> ( any "o magnitude is v approximately #b4e times z bright z "o ( ! next fa9t] magnitude1 & ?is ratio furni%es a conv5i5t me?od ( comp>+ ! am\nt ( light receiv$ f diff]5t />s4 ,?us ! brightness ( ,v5us is #b4e #b4e times t ( ,sirius4 ,! full moon is #b4ei times z bright z ,v5us1 etc42 only x %\ld be obs]v$ t ! numb] #b4e is n exactly ! value ( ! light ratio betwe5 two consecutive magnitudes4 ,/rictly ?is ratio is ! #ajja_/e #b4eaai1 s t to be entirely accurate we mu/ say t a diff]5ce ( five magnitudes gives a hundr$fold diff]5ce ( brightness4 ,9 ma!matical symbols1 if ,b repres5ts ! ratio ( brightness 7quantity ( light7 ( two />s ^: magnitudes are m & n1 !n ,b 7#ajj77m-n7_/#e ,h[ mu* bright] is an ord9>y fir/-magnitude />1 su* z ,aldeb>an or ,spica1 ?an a /> j visible to ! nak$ eye8 ,h[ _m ( ! fa9te/ />s visible 9 a great telescope w\ld be requir$ to make "o /> j visible to ! unaid$ eye8 ,h[ _m full moons mu/ be put 9 ! sky 9 ord] to give an illum9ation z bright z daylight8 ,h[ l>ge a "p ( ! visible hemisph]e w\ld !y occupy8 #ahg4 ,,classification ,,by ,,magnitudes4--,! brightness ( all ! lucid />s has be5 c>efully measur$ ) an in/rum5t 7photomet]7 design$ = t special purpose1 & ! foll[+ table %[s1 accord+ to ! ,h>v>d ,photometry1 ! numb] ( />s 9 ! :ole sky1 f pole to pole1 :i* are bright] ?an ! sev]al magnitudes nam$ 9 ! table3 ,! numb] ( />s bright] ?an magnitude #a4j is #aa #b4j #ci #c4j #adb #d4j #dfc #e4j #a1dhc #f4j #d1cbf ,x mu/ n be inf]r$ f ?is table t !re are 9 ! :ole sky only #d1cbf />s visible to ! nak$ eye4 ,! actual numb] is probably #ej or #fj p] c5t great] ?an ?is1 & ! normal human eye sees />s z fa9t z ! magnitude #f4d or #f4e1 ! discordance betwe5 ?is numb] & ! previ\s /atem5t1 t ! six? magnitude is ! limit ( ! nak$-eye vision1 hav+ be5 introduc$ 9 ! attempt to make precise & accurate a classification into magnitudes :i* 0 at fir/ only r\gh & approximate4 ,?is same /riv+ aft] accuracy leads to ! introduction ( fractional numb]s to repres5t gradations ( brightness int]m$iate betwe5 :ole magnitudes4 ,?us ( ! #b1hdc />s includ$ betwe5 ! fif? & six? magnitudes a c]ta9 proportion are said to be ( ! #e4a magnitude1 #e4b magnitude1 & s on to ! #e4i magnitude1 ev5 hundr$?s ( a magnitude be+ sometimes employ$4 ,we h f\nd ! numb] ( />s includ$ betwe5 ! fif? & six? magnitudes by subtract+ f ! la/ numb] ( ! prec$+ table ! numb] imm$iately prec$+ x1 & simil>ly we may f9d ! numb] includ$ betwe5 ea* o!r pair ( consecutive magnitudes1 z foll[s3 ,magnitude #j #a #b #c #d #e #f ,numb] ( />s #aa #bh #ajc #cba #a1jbj #b1hdc #d #cm #ab #cf #ajh #cbd #igb #b1iaf ,9 ! la/ l9e ea* numb] aft] ! fir/ is f\nd by multiply+ ! prec$+ "o by #c1 & ! approximate agreem5t ( ea* su* numb] ) t pr9t$ above x %[s t on ! :ole1 z f> z ! table goes1 ! fa9t] />s are approximately ?ree times z num]\s z ^? a magnitude bright]4 ,! magnitudes ( ! telescopic />s h n yet be5 measur$ completely1 & _! exact numb] is unkn[n2 b if we apply our pr9ciple ( a ?reefold increase = ea* successive magnitude1 we %all f9d = ! fa9t] />s--^? ( ! t5? & twelf? magnitudes--prodigi\s numb]s :i* run up into ! millions1 & ev5 ^! are probably too small1 s9ce d[n to ! n9? or t5? magnitude x is c]ta9 t ! numb] ( ! telescopic />s increases f magnitude to magnitude 9 m ?an a ?reefold ratio4 ,?is is balanc$ 9 "s degree by ! less rapid increase :i* is kn[n to exi/ 9 magnitudes /ill fa9t]2 & apply+ our =mula )\t reg>d to ^! v>iations 9 ! rate ( increase1 we obta9 z a rude approximation to ! total numb] ( />s d[n to ! fifte5? magnitude1 #hf1jjj1jjj4 ,! ,h]s*els1 fa!r & son1 actually c\nt$ ! numb] ( />s visible 9 ne>ly #h1jjj sample regions ( ! sky1 &1 inf]r+ ! "* ( ! :ole sky f ^! samples1 we f9d x to conta9 #eh1ejj1jjj />s2 b ! magnitude ( ! fa9te/ /> visible 9 _! telescope1 & includ$ 9 _! c\nt1 is r unc]ta94 ,h[ _m fir/-magnitude />s w\ld be ne$$ to give z mu* light z d ! #b1hdc />s ( magnitude #e4j to #f4j8 ,h[ _m t5?-magnitude />s are requir$ to give ! same am\nt ( light8 ,to ! mod]n man x seems natural to ascribe ! diff]5t brilliancies ( ! />s to _! diff]5t di/ances f u2 b su* 0 n ! case #b1jjj ye>s ago1 :5 ea* fix$ /> 0 commonly ?\ght to be fa/5$ to a cry/al sph]e1 :i* c>ri$ !m ) x1 all at ! same di/ance f u1 z x turn$ ab\t ! e>?4 ,9 break+ away f ?is errone\s idea & le>n+ to ?9k ( ! sky itself z only an atmosph]ic illusion ?r\gh :i* we look to />s at v diff]5t di/ances beyond1 x 0 easy to fall into ! opposite error & to ?9k ( ! />s z be+ mu* alike "o ) ano!r1 &1 l pebbles on ! bea*1 scatt]$ ?r\gh\t space ) "s r\gh degree ( uni=mity1 s t 9 e direction !re %\ld be f\nd 9 equal measure />s ne> at h& & />s f> (f1 ea* %9+ ) a lu/] proportion$ to its remot5ess4 #ahh4 ,,di/ances ,,( ,,! ,,/>s4--,n[1 9 ord] to sep>ate ! true f ! false 9 ?is la/ mode ( ?9k+ ab\t ! />s1 we ne$ "s k ( _! real di/ances f ! e>?1 & 9 seek+ x we enc\nt] :at is p]haps ! mo/ delicate & difficult problem 9 ! :ole range ( obs]vational a/ronomy4 ,z %[n 9 ,fig4 #aba1 ! pr9ciples involv$ 9 det]m9+ ^! di/ances are n fundam5tally diff]5t f ^? employ$ 9 det]m9+ ! moon's di/ance f ! e>?4 ,?us1 ! ellipse at ! left ( ! figure repres5ts ! e>?'s orbit & ! position ( ! e>? at diff]5t times ( ! ye>4 ,! direction ( ! /> ,a at ^! sev]al times is %[n by l9es drawn ?r\gh ,a & prolong$ to ! backgr\nd app>5tly furni%$ by ! sky4 ,a simil> con/ruction is made = ! /> ,b1 & x is readily se5 t ow+ to ! *ang+ position ( ! obs]v] z he moves ar\nd ! e>?'s orbit1 bo? ,a & ,b w appe> to move ^u ! backgr\nd 9 orbits %ap$ l t ( ! e>? z se5 f ! />1 b hav+ _! size dep5d5t ^u ! />'s di/ance1 ! app>5t orbit ( ,a be+ l>g] ?an t ( ,b1 because ,a is ne>] ! e>?4 ,by measur+ ! angul> di/ance betwe5 ,a & ,b at opposite seasons ( ! ye> 7e4 g41 ! angles ,a--,jan4--,b1 & ,a--,july--,b7 ! a/ronom] det]m9es f ! *ange 9 ?is angle h[ mu* l>g] is ! "o pa? ?an ! o!r1 & ?us concludes h[ mu* ne>] is ,a ?an ,b4 ,/rictly1 ! diff]5ce betwe5 ! ,janu>y & ,july angles is equal to ! diff]5ce betwe5 ! angles subt5d$ at ,a & ,b by ! diamet] ( ! e>?'s orbit1 & if ,b 7 s f> away t ! angle ,jan4--,b--,july 7 no?+ at all we %\ld get imm$iately f ! obs]vations ! angle ,jan4--,a--,july1 :i* w\ld suffice to det]m9e ! />s' di/ance4 ,suppos+ ! diamet] ( ! e>?'s orbit & ! angle at ,a to be kn[n1 c y make a graphical con/ruction t w det]m9e ! di/ance ( ,a f ! e>?8 ,illu/ration3 ,,fig4 #aba4--;,det]m9+ a />'s p>allax4 ,! angle subt5d$ at ,a by ! radius ( ! e>?'s orbit--i4 e41 #a_/b 7,jan4--,a--,july7--is call$ ! />'s p>allax1 & ?is is commonly us$ by a/ronom]s z a measure ( ! />'s di/ance in/ead ( express+ x 9 l9e> units su* z miles or radii ( ! e>?'s orbit4 ,! di/ance ( a /> is equal to ! radius ( ! e>?'s orbit divid$ by ! p>allax1 9 seconds ( arc1 & multipli$ by ! numb] #bjfbfe4 ,a weak po9t ( ?is me?od ( measur+ /ell> di/ances is t x always gives :at is call$ a relative p>allax--i4 e41 ! diff]5ce betwe5 ! p>allaxes ( ,a & ,b2 & :ile x is cu/om>y to select = ,b a /> or />s suppos$ to be mu* f>!r (f ?an ,a1 x may happ51 & sometimes does happ51 t ^! comp>ison />s z !y are call$ are z ne> or ne>] ?an ,a1 & give a negative p>allax--i4 e41 ! diff]5ce betwe5 ! angles at ,a & ,b proves to be negative1 z x mu/ :5ev] ! /> ,b is ne>] ?an ,a4 ,! fir/ really successful det]m9ations ( /ell> p>allax 7 made by ,/ruve & ,bessel a little prior to #ahdj1 & s9ce t "t ! di/ances ( p]haps #ajj />s h be5 measur$ ) "s degree ( reliability1 al?\gh ! p>allaxes !mselves are s small--nev] z great z #a''--t x is extremely difficult to avoid fall+ into error1 s9ce ev5 = ! ne>e/ /> ! problem ( its di/ance is equival5t to f9d+ ! di/ance ( an object m ?an #e miles away by look+ at x fir/ ) "o eye & !n ) ! o!r4 ,too %ort a base l9e4 #ahi4 ,,! ,,sun ,,& ,,8 ,,neighbors4--,! di/ances ( ! sun's ne>] neighbors among ! />s are %[n 9 ,fig4 #abb1 :]e ! two circles hav+ ! sun at _! c5t] repres5t di/ances f x equal respectively to #a1jjj1jjj & #b1jjj1jjj times ! di/ance betwe5 e>? & sun4 ,9 ! figure ! direction ( ea* /> f ! sun corresponds to its "r asc5sion1 z %[n by ! ,roman num]als ab\t ! out] circle2 ! true direction ( ! /> f ! sun c n1 ( c\rse1 be %[n ^u ! flat surface ( ! pap]1 b x may be f\nd by elevat+ or depress+ ! /> f ! surface ( ! pap] ?r\gh an angle1 z se5 f ! sun1 equal to its decl9ation1 z %[n 9 ! fif? column ( ! foll[+ table1 ,! ,sun's ,ne>e/ ,neighbors ---------------------------------------- ---------------------- ,no4 ,,/>4 ,magnitude4 ,r4 ,a4 ,dec4 ,p>allax4,di/ance4 ---------------------------------------- ---------------------- #a a ,c5tauri #j4g #ad4e;h4 -#fj #j4ge #j4bg #b ,ll4 #ba1ahe #f4h #aa4j #cg #j4de #j4df #c #fa ,cygni #e4j #ba4j #ch #j4dj #j4ea #d ,h]culis #c4f #af4g #ci #j4dj #j4ea #e ,sirius -#a4d #f4g -#ag #j4cg #j4ef #f ,s #b1cih #h4b #ah4g #ei #j4ce #j4eh #g ,procyon #j4e #g4f #e #j4cd #j4fj #h g ,draconis #d4h #ag4e #ee #j4cj #j4fh #i ,gr4 #cd #g4i #j4b #dc #j4bi #j4ga #aj ,lac4 #i1ceb #g4e #bc4j -#cf #j4bh #j4gd #aa s ,draconis #d4h #ai4e #fi #j4be #j4hb #ab ,a4 ,o4 #ag1dae-f #i4j #ag4f #fh #j4be #j4hb #ac ,cassiopei #c4d #j4g #eg #j4be #j4hb #ad ,altair #a4j #ai4h #i #j4ba #j4ig #ae e ,indi #e4b #ba4i -#eg #j4bj #a4jc #af ,gr4 #a1fah #f4g #aj4a #ej #j4bj #a4jc #ag #aj ,urs ,majoris #d4b #h4i #db #j4bj #a4jc #ah ,ca/or #a4e #g4e #cb #j4bj #a4jc #ai ,ll4 #ba1beh #h4e #aa4j #dd #j4bj #a4jc #bj o#b ,eridani #d4e #d4b - #h #j4ai #a4jh #ba ,a4 ,o4 #aa1fgg #i4j #aa4b #ff #j4ai #a4jh #bb ,ll4 #ah1aae #h4j #i4a #ec #j4ah #a4ad #bc ,b4 ,d4 #cf1 #c1hhc #g4a #bj4j #cf #j4ah #a4ad #bd ,gr4 #a1fah #f4e #aj4a #ej #j4ag #a4ba #be b ,cassiopei #b4c #j4a #ei #j4af #a4bh #bf #gj ,ophiu*i #d4d #ah4j #b #j4af #a4bh #bg ,s #a1eaf #f4e #aa4b #gd #j4ae #a4ch #bh ,gr4 #a1hcj #f4f #aa4h #ci #j4ae #a4ch #bi m ,cassiopei #e4d #a4j #ed #j4ad #a4dg #cj e ,eridani #d4d #c4e -#aj #j4ad #a4dg #ca i ,urs ,majoris #c4b #h4i #dh #j4ac #a4eh #cb b ,hydri #b4i #j4c -#gh #j4ac #a4eh #cc ,fomalhaut #a4j #bb4i -#cj #j4ac #a4eh #cd ,br4 #c1jgg #f4j #bc4a #eg #j4ac #a4eh #ce e ,cygni #b4e #bj4h #cc #j4ab #a4ga #cf b ,com #d4e #ac4a #bh #j4aa #a4hg #cg ps#e ,aurig #h4h #f4f #dd #j4aa #a4hg #ch p ,h]culis #c4c #ag4b #cg #j4aa #a4hg #ci ,aldeb>an #a4a #d4e #af #j4aj #b4jf #dj ,capella #j4a #e4a #df #j4aj #b4jf #da ,b4 ,d4 #ce1 #d1jjc #i4b #bj4a #ce #j4aj #b4jf #db ,gr4 #a1fdf #f4c #aj4c #di #j4aj #b4jf #dc g ,cygni #b4c #bj4c #dj #j4aj #b4jf #dd ,regulus #a4b #aj4j #ab #j4aj #b4jf #de ,vega #j4b #ah4f #ci #j4aj #b4jf ---------------------------------------- ---------------------- 9 :i* ! numb]s 9 ! fir/ column are ^? plac$ adjac5t to ! />s 9 ! diagram to id5tify !m4 ,illu/ration3 ,,fig4 #abb4--,/ell> neighbors ( ! sun4 #aij4 ,,light ,,ye>s4--,! radius ( ! inn] circle 9 ,fig4 #abb1 #a1jjj1jjj times ! e>?'s di/ance f ! sun1 is a conv5i5t unit 9 :i* to express ! /ell> di/ances1 & 9 ! prec$+ table ! di/ances ( ! />s f ! sun are express$ 9 t]ms ( ?is unit4 ,to express !m 9 miles ! numb]s 9 ! table mu/ be multipli$ by #ic1jjj1jjj1jjj1jjj4 ,! ne>e/ />1 a ,c5tauri1 is #be1jjj1jjj1jjj1jjj miles away4 ,b !re is ano!r unit 9 m common use--i4 e41 ! di/ance travel$ ov] by light 9 ! p]iod ( "o ye>4 ,we h already f\nd 7 #ada7 t x requires light #hm4 #ahs4 to come f ! sun to ! e>?1 & x is a simple matt] to f9d f ?is datum t 9 a ye> light moves ov] a space equal to #fc1cfh radii ( ! e>?'s orbit4 ,?is di/ance is call$ a light ye>1 & ! di/ance ( ! same />1 a ,c5tauri1 express$ 9 t]ms ( ?is unit1 is #d4bf ye>s--i4 e41 x takes light t long to come f ! /> to ! e>?4 ,9 ,fig4 #abb ! /ell> magnitudes ( ! />s are indicat$ by ! size ( ! dots--! bigg] ! dot ! bright] ! />--& a m]e inspection ( ! figure w s]ve to %[ t )9 a radius ( #cj light ye>s f ! sun bright />s & fa9t ones are mix$ up toge!r1 & t1 s f> z di/ance is conc]n$1 ! sun is only a memb] ( ?is sw>m ( />s1 ^: di/ances ap>t1 ea* f its ne>e/ neighbor1 are ( ! same ord] ( magnitude z ^? :i* sep>ate ! sun f ! ?ree or f\r />s ne>e/ x4 ,fig4 #abb is n to be suppos$ complete4 ,d\btless o!r />s w be f\nd ^: di/ance f ! sun is less ?an #b1jjj1jjj radii ( ! e>?'s orbit1 b x is n probable t !y w ev] suffice to m ?an d\ble or p]haps treble ! numb] "h %[n4 ,! va/ majority ( ! />s lie f> beyond ! limits ( ! figure4 #aia4 ,,prop] ,,motions4--,x is evid5t t ^! />s are too f> ap>t = _! mutual attractions to h mu* influ5ce "o ^u ano!r1 & t we h "h a case 9 :i*1 accord+ to #cd1 ea* /> is free to keep un*ang$ its /ate ( re/ or motion ) unv>y+ velocity along a /raight l9e4 ,_! v "n1 fix$ />s1 implies t !y are at re/1 & s a/ronom]s long believ$4 ,hipp>*us 7#abe ,b4 ,c47 & ,ptolemy 7#acj ,a4 ,d47 obs]v$ & record$ _m all9eations among ! />s1 9 ord] to give to future g5]ations a means ( settl+ ?is v "q ( a possible motion ( ! />s & a result+ *ange 9 _! relative positions ^u ! sky4 ,= example1 !y f\nd at ! beg9n+ ( ! ,*ri/ian era t ! f\r />s1 ,capella1 e ,p]sei1 a & b ,arietis1 /ood 9 a /raight l9e--i4 e41 ^u a great circle ( ! sky4 ,v]ify ?is by direct ref]5ce to ! sky1 & see h[ ne>ly ^! />s h kept ! same position = ne>ly tw5ty c5turies4 ,?ree ( !m may be id5tifi$ f ! /> maps1 & ! f\r?1 e ,p]sei1 is a ?ird-magnitude /> betwe5 ,capella & ! o!r two4 ,o!r all9eations giv5 by ,ptolemy are3 ,spica1 ,arcturus & b ,bootis2 ,spica1 d ,corvi & g ,corvi2 a ,libr1 ,arcturus & z ,urs ,majoris4 ,arcturus does n n[ fit v well to ^! alignm5ts1 & ne>ly two c5turies ago x1 toge!r ) ,aldeb>an & ,sirius1 0 on o!r gr\nds suspect$ to h *ang$ its place 9 ! sky s9ce ! days ( ,ptolemy4 ,?is discov]y1 long s9ce fully confirm$1 gave a great impetus to obs]v+ ) all possible accuracy ! "r asc5sions & decl9ations ( ! />s1 ) a view to f9d+ o!r cases ( :at 0 call$ prop] motion--i4 e41 a motion peculi> to ! individual /> z contra/$ ) ! *ange ( "r asc5sion & decl9ation produc$ = all />s by ! precession4 ,s9ce ! middle ( ! eighte5? c5tury !re h be5 made _m ?\s&s ( obs]vations ( ?is k9d1 ^: results h gone into /> *>ts & /> catalogues1 & :i* are n[ be+ supplem5t$ by a photographic survey ( ! sky t is int5d$ to record p]man5tly ^u photographic plates ! position & magnitude ( e /> 9 ! heav5s d[n to ! f\rte5? magnitude1 ) a view to ultimately det]m9+ all _! prop] motions4 ,! complete a*ievem5t ( ?is result is1 ( c\rse1 a ?+ ( ! remote future1 b suffici5t progress 9 det]m9+ ^! motions has be5 made dur+ ! pa/ c5tury & a half to %[ t ne>ly e lucid /> possesses "s prop] motion1 al?\gh 9 mo/ cases x is v small1 !re be+ less ?an #ajj kn[n />s 9 :i* x am\nts to s mu* z #a p] annum--i4 e41 a rate ( motion across ! sky :i* w\ld require ne>ly ! :ole ,*ri/ian era to alt] a />'s direction f u by s mu* z ! moon's angul> diamet]4 ,! mo/ rapid kn[n prop] motion is t ( a telescopic /> midway betwe5 ! equator & ! s\? pole1 :i* *anges its position at ! rate ( ne>ly #i p] annum1 & ! next greate/ is t ( ano!r telescopic />1 9 ! nor!rn sky1 ,no4 #bh ( ,fig4 #abb4 ,x is n until we rea* ! t5? place 9 a li/ ( l>ge prop] motions t we f9d a bright lucid />1 ,no4 #a ( ,fig4 #abb4 ,x is a significant fact t = ! mo/ "p ! />s ) l>ge prop] motions are precisely ! ones %[n 9 ,fig4 #abb1 :i* is design$ to %[ />s ne> ! e>?4 ,?is connection betwe5 ne>ness & rapidity ( prop] motions is inde$ :at we %\ld expect to f9d1 s9ce a giv5 am\nt ( real motion ( ! /> along its orbit w produce a l>g] angul> displacem5t1 prop] motion1 ! ne>] ! /> is to ! e>?1 & ?is fact has guid$ a/ronom]s 9 select+ ! />s to be obs]v$ = p>allax1 ! prop] motion be+ det]m9$ fir/ & ! p>allax aft]w>d4 #aib4 ,,! ,,pa?s ,,( ,,! ,,/>s4--,we h already se5 reason = ?9k+ t ! orbit along :i* a /> moves is practically a /raight l9e1 & f a /udy ( prop] motions1 p>ticul>ly _! directions across ! sky1 x appe>s t ^! orbits po9t 9 all possible ways--nor?1 s\?1 ea/1 & we/--s t "s ( !m are d\btless direct$ ne>ly t[>d or f ! sun2 o!rs are squ>e to ! l9e jo9+ sun & />2 :ile ! va/ majority occupy "s position int]m$iate betwe5 ^! two4 ,n[1 our relation to ^! real motions ( ! />s is well illu/rat$ 9 ,fig4 #aab1 :]e ! obs]v] f9ds 9 "s ( ! %oot+ />s a trem5d\s prop] motion across ! sky1 b sees no?+ ( _! rapid approa* to him1 :ile o!rs appe> to /& motionless1 al?\gh1 9 fact1 !y are mov+ q z rapidly z are _! fell[s4 ,! fix$ /> resembles ! %oot+ /> 9 ?is respect1 t its prop] motion is only t "p ( its real motion :i* lies at "r angles to ! l9e ( sight1 & ?is ne$s to be supplem5t$ by t o!r "p ( ! motion :i* lies p>allel to ! l9e ( sight1 9 ord] to give u any k ( ! />'s real orbit4 ,illu/ration3 ,,fig4 #abc4--,motion ( ,pol>is 9 ! l9e ( sight z det]m9$ by ! spectroscope4 ,,fro/4 #aic4 ,,motion ,,9 ,,! ,,l9e ,,( ,,sight4--,x is only )9 ! la/ #be ye>s t any?+ :atev] has be5 accompli%$ 9 det]m9+ ^! /ell> motions ( approa* or recession1 b )9 t "t mu* progress has be5 made by apply+ ! ,doppl] pr9ciple 7 #hi7 to ! /udy ( /ell> spectra1 & at ! pres5t "t ne>ly e great telescope 9 ! _w is engag$ ^u "w ( ?is k9d4 ,! %ift+ ( ! l9es ( ! spectrum t[>d ! violet or t[>d ! r$ end ( ! spectrum indicates ) c]ta9ty ! approa* or recession ( ! />1 b ?is %ift+1 :i* mu/ be det]m9$ by comp>+ ! />'s spectrum ) t ( "s artificial light %[+ correspond+ l9es1 is s small 9 am\nt t its accurate measurem5t is a matt] ( extreme difficulty1 z may be se5 f ,fig4 #abc4 ,?is cut %[s along its c5tral l9e a "p ( ! spectrum ( ,pol>is1 betwe5 wave l5g?s #d1dej & #d1fjj t5? met]s1 :ile above & bel[ are ! correspond+ p>ts ( ! spectrum ( an electric sp>k ^: light pass$ ?r\gh ! same spectroscope & 0 photograph$ ^u ! same plate ) t ( ,pol>is4 ,?is comp>ison spectrum is1 z x %\ld be1 a discont9u\s or bright-l9e "o1 :ile ! spectrum ( ! /> is a cont9u\s "o1 brok5 only by d>k gaps or l9es1 _m ( :i* h no correspond+ l9es 9 ! comp>ison spectrum4 ,b a c]ta9 numb] ( l9es 9 ! two spectra d correspond1 save t ! d>k l9e is always pu%$ a v little t[>d ! direction ( %ort] wave l5g?s1 %[+ t ?is /> is approa*+ ! e>?4 ,?is spectrum 0 photograph$ = ! express purpose ( det]m9+ ! />'s motion 9 ! l9e ( sight1 & ) x !re %\ld be comp>$ ,figs4 #abd & #abe1 :i* %[ 9 ! upp] "p ( ea* a photograph obta9$ )\t comp>ison spectra by all[+ ! />'s light to pass ?r\gh "s prisms plac$ j 9 front ( ! telescope4 ,! l[] section ( ea* figure %[s an enl>gem5t ( ! orig9al photograph1 br++ out its details 9 a way n visible to ! unaid$ eye4 ,9 ! enl>g$ spectrum ( b ,aurig a rate ( motion equal to t ( ! e>? 9 its orbit w\ld be repres5t$ by a %ift+ ( #j4jc ( a millimet] 9 ! position ( ! broad1 hazy l9es4 ,illu/ration3 ,,fig4 #abd4--,spectrum ( b ,aurig4--,,pick]+4 ,despite ! difficulty ( deal+ ) su* small quantities z ! above1 v satisfactory results are n[ obta9$1 & f !m x is kn[n t ! velocities ( />s 9 ! l9e ( sight are ( ! same ord] ( magnitude z ! velocities ( ! planets 9 _! orbits1 rang+ all ! way f #j to #fj miles p] second--m ?an #bjj1jjj miles p] h\r--:i* latt] velocity1 accord+ to ,campbell1 is ! rate at :i* m ,cassiopei is approa*+ ! sun4 ,! /ud5t %\ld n fail to note "o important diff]5ce betwe5 prop] motions & ! motions det]m9$ spectroscopically3 ! latt] are giv5 directly 9 miles p] second1 or p] h\r1 :ile ! =m] are express$ 9 angul> measure1 seconds ( arc1 & !re c be no direct comp>ison betwe5 ! two until by means ( ! kn[n di/ances ( ! />s _! prop] motions are conv]t$ f angul> into l9e> measure4 ,we are br\ght ?us to ! v he>t ( ! matt]2 p>allax1 prop] motion1 & motion 9 ! l9e ( sight are intimately relat$ quantities1 all ( :i* are ess5tial to a k ( ! real motions ( ! />s4 ,illu/ration3 ,,fig4 #abe4--,spectrum ( ,pollux4--,,pick]+4 #aid4 ,,/> ,,drift4--,an illu/ration ( h[ !y may be made to "w toge!r is furni%$ by "s ( ! />s--:i* make up ! ,great ,dipp]--b1 g1 e1 & z ,urs ,majoris1 ^: prop] motions h long be5 kn[n to po9t 9 ne>ly ! same direction across ! sky & to be ne>ly equal 9 am\nt4 ,m rec5tly x has be5 f\nd t ^! />s are all mov+ t[>d ! sun ) approximately ! same velocity--#ah miles p] second4 ,"o o!r /> ( ! ,dipp]1 d ,urs ,majoris1 %>es 9 ! common prop] motion1 b its velocity 9 ! l9e ( sight has n yet be5 det]m9$ ) ! spectroscope4 ,^! simil> motions make x probable t ! />s are really travel+ toge!r ?r\gh space along p>allel l9es2 & on ! supposition t su* is ! case x is q possible to write out a set ( equations :i* %all involve _! kn[n prop] motions & motions 9 ! l9e ( sight1 toge!r ) _! unkn[n di/ances & ! unkn[n direction & velocity ( _! real motion along _! orbits4 ,solv+ ^! equations = ! values ( ! unkn[n quantities1 x is f\nd t ! five />s probably lie 9 a plane :i* is turn$ ne>ly edgewise t[>d u1 & t 9 ?is plane !y are mov+ ab\t twice z fa/ z ! e>? moves ar\nd ! sun1 & are at a di/ance f u repres5t$ by a p>allax ( less ?an #j4jb--;i4 e41 six times z great z ! out]mo/ circle 9 ,fig4 #abb4 ,a mo/ extraord9>y sy/em ( />s :i*1 al?\gh sep>at$ f ea* o!r by di/ances z great z ! :ole bread? ( ,fig4 #abb1 yet move along 9 p>allel pa?s :i* x is difficult to reg>d z ! result ( *ance1 & = :i* x is equally difficult to frame an explanation4 ,illu/ration3 ,,fig4 #abf4--,! ,great ,dipp]1 pa/1 pres5t1 & future4 ,! />s a & ( ! ,great ,dipp] d n %>e 9 ?is motion1 & mu/ ultimately "p company ) ! o!r five1 to ! complete de/ruction ( ! ,dipp]'s %ape4 ,fig4 #abf illu/rates ?is *ange ( %ape1 ! upp] "p ( ! figure 7a7 %[+ ^! sev5 />s z !y 7 gr\p$ at a remote epo* 9 ! pa/1 :ile ! l[] section 7c7 %[s _! position = an equally remote epo* 9 ! future4 ,!re is no resemblance to a dipp] 9 ei!r ( ^! configurations1 b x %\ld be obs]v$ t 9 ea* ( !m ! />s a & keep _! relative position unalt]$1 & ! o!r five />s also keep toge!r1 ! entire *ange ( appe>ance be+ due to ! *ang+ positions ( ^! two gr\ps ) respect to ea* o!r4 ,?is ph5om5on ( gr\ps ( />s mov+ toge!r is call$ /> drift1 & q a numb] ( cases ( x are f\nd 9 diff]5t p>ts ( ! sky4 ,! ,pleiades are p]haps ! mo/ conspicu\s "o1 = "h "s sixty or m />s are f\nd travel+ toge!r along simil> pa?s4 ,repeat$ c>eful measurem5ts ( ! relative positions ( />s 9 ?is clu/] %[ t "o ( ! lucid />s & f\r or five ( ! telescopic ones d n %>e 9 ?is motion1 & !re=e are n to be consid]$ z memb]s ( ! gr\p1 b r z isolat$ />s :i*1 = a "t1 *ance to be ne>ly on l9e ) ! ,pleiades1 & probably f>!r (f1 s9ce _! prop] motions are small]4 ,to rightly appreciate ! extreme sl[ness ) :i* prop] motions alt] ! con/ellations1 ! /ud5t %\ld be> 9 m9d t ! *anges %[n 9 pass+ f "o section ( ,fig4 #abf to ! next repres5t ! effect ( ! pres5t prop] motions ( ! />s accumulat$ = a p]iod ( #bjj1jjj ye>s4 ,w ! />s cont9ue to move 9 /raight pa?s = s long a "t8 #aie4 ,,! ,,sun',s ,,way4--,ano!r & ev5 m int]e/+ application ( prop] motions & motions 9 ! l9e ( sight is ! det]m9ation f !m ( ! sun's orbit among ! />s4 ,! pr9ciple involv$ is simple en\gh4 ,if ! sun moves ) respect to ! />s & c>ries ! e>? & ! o!r planets ye> aft] ye> into new regions ( space1 our *ang+ po9t ( view mu/ displace 9 "s measure e /> 9 ! sky save ^? :i* happ5 to be exactly on ! l9e ( ! sun's motion1 & ev5 ^! w %[ its effect by _! app>5t motion ( approa* or recession along ! l9e ( sight4 ,s f> z _! own orbital motions are conc]n$1 !re is no reason to suppose t m />s move nor? ?an s\?1 or t m g ea/ ?an we/2 & :5 we f9d 9 _! prop] motions a di/9ct t5d5cy to radiate f a po9t some:]e ne> ! bright /> ,vega & to conv]ge t[>d a po9t on ! opposite side ( ! sky1 we inf] t ?is does n come f any g5]al drift ( ! />s 9 t direction1 b t x m>ks ! c\rse ( ! sun among !m4 ,t x is mov+ along a /raight l9e po9t+ t[>d ,vega1 & t at lea/ a "p ( ! velocities :i* ! spectroscope %[s 9 ! l9e ( sight1 comes f ! motion ( ! sun & e>?4 ,work+ along ^! l9es1 ,kapteyn f9ds t ! sun is mov+ ?r\gh space ) a velocity ( #aa miles p] second1 :i* is decid$ly bel[ ! av]age rate ( /ell> motion--#ai miles p] second4 #aif4 ,,di/ance ,,( ,,sirian ,,& ,,sol> ,,/>s4--,by comb9+ ?is rate ( motion ( ! sun ) ! av]age prop] motions ( ! />s ( diff]5t magnitudes1 x is possible to obta9 "s idea ( ! av]age di/ance f u ( a fir/-magnitude /> or a six?-magnitude />1 :i*1 :ile x gives no in=mation ab\t ! actual di/ance ( any p>ticul> />1 does %[ t on ! :ole ! fa9t] />s are m remote4 ,b "h a broad di/9ction mu/ be drawn4 ,by f> ! l>g] "p ( ! />s belong to "o ( two well-m>k$ classes1 call$ respectively ,sirian & sol> />s1 :i* are readily di/+ui%$ f ea* o!r by ! k9d ( spectrum !y furni%4 ,?us b ,aurig belongs to ! ,sirian class1 z does e o!r /> :i* has a spectrum l t ( ,fig4 #abd1 :ile ,pollux is a sol> /> pres5t+ 9 ,fig4 #abe a spectrum l t ( ! sun1 z d ! o!r />s ( ?is class4 ,two ?irds ( ! sun's ne> neighbors1 %[n 9 ,fig4 #abb1 h spectra ( ! sol> type1 & 9 g5]al />s ( ?is class are ne>] to u ?an are ! />s ) spectra unlike t ( ! sun4 ,! av]age di/ance ( a sol> /> ( ! fir/ magnitude is v approximately repres5t$ by ! out] circle 9 ,fig4 #abb1 #b1jjj1jjj times ! di/ance ( ! sun f ! e>?2 :ile ! correspond+ di/ance = a ,sirian /> ( ! fir/ magnitude is repres5t$ by ! numb] #d1fjj1jjj4 ,a ?ird-magnitude /> is on ! av]age twice z f> away z "o ( ! fir/ magnitude1 a fif?-magnitude /> f\r times z f> (f1 etc41 ea* additional two magnitudes d\bl+ ! av]age di/ance ( ! />s1 at lea/ d[n to ! eigh? magnitude & possibly f>!r1 al?\gh beyond ?is limit we h no c]ta9 k4 ,put 9 ano!r way1 ! nak$ eye sees _m ,sirian />s :i* may h gone out & ceas$ to %9e c5turies ago1 = ! light by :i* we n[ see !m left ^? />s be=e ! discov]y ( ,am]ica by ,columbus4 ,= ! /ud5t ( ma!matical ta/es we note t ! results ( ,kapteyn's inve/igation ( ! mean di/ances 7,d7 ( ! />s ( magnitude 7m7 may be put into two equations3 ,= ,sol> ,/>s1 ,d #bc #bm_/#b ,= ,sirian ,/>s1 ,d #eb #bm_/#b :]e ! coeffici5ts #bc & #eb are express$ 9 light ye>s4 ,h[ long a "t is requir$ = light to come f an av]age sol> /> ( ! six? magnitude8 #aig4 ,,consequ5ces ,,( ,,/ell> ,,di/ance4--,! am\nt ( light :i* comes to u f any lum9\s body v>ies inv]sely z ! squ>e ( its di/ance1 & s9ce _m ( ! />s are *ang+ _! di/ance f u q rapidly1 x mu/ be t ) ! lapse ( "t !y w gr[ bright] or fa9t] by reason ( ?is alt]$ di/ance4 ,b ! di/ances !mselves are s great t ! mo/ rapid kn[n motion 9 ! l9e ( sight w\ld require m ?an #a1jjj ye>s 7probably sev]al ?\s&7 to produce any p]ceptible *ange 9 brilliancy4 ,! law 9 accordance ) :i* ?is *ange ( brilliancy takes place is t ! di/ance mu/ be increas$ or dim9i%$ t5fold 9 ord] to produce a *ange ( five magnitudes 9 ! brightness ( ! object1 & we may apply ?is law to det]m9e ! sun's rank among ! />s4 ,if x 7 remov$ to ! di/ance ( an av]age fir/-1 or second-1 or ?ird-magnitude />1 h[ w\ld its light comp>e ) t ( ! />s8 ,! av]age di/ance ( a ?ird-magnitude /> ( ! sol> type is1 z we h se5 above1 #d1jjj1jjj times ! sun's di/ance f ! e>?1 & s9ce #d1jjj1jjj #ajf4f1 we f9d t at ?is di/ance ! sun's /ell> magnitude w\ld be alt]$ by #f4f #e magnitudes1 & w\ld !re=e be -#bf4e #cc4j #f4e--;i4 e41 ! sun if remov$ to ! av]age di/ance ( ! ?ird-magnitude />s ( its type w\ld be r$uc$ to ! v limit ( nak$-eye visibility4 ,x mu/ !re=e be relatively small & feeble z comp>$ ) ! brightness ( ! av]age />4 ,x is only its close proximity to u t makes ! sun look bright] ?an ! />s4 ,! fix$ />s may h planets circl+ ar\nd !m1 b an application ( ! same pr9ciples w %[ h[ hopeless is ! prospect ( ev] see+ !m 9 a telescope4 ,if ! sun's ne>e/ neighbor1 a ,c5tauri1 7 att5d$ by a planet l ,jupit]1 ?is planet w\ld furni% to u no m light ?an does a /> ( ! tw5ty-second magnitude--i4 e41 x w\ld be absolutely invisible1 & w\ld rema9 invisible 9 ! mo/ p[]ful telescope yet built1 ev5 ?\gh its bulk 7 increas$ to equal t ( ! sun4 ,let ! /ud5t make ! computation lead+ to ?is result1 assum+ ! /ell> magnitude ( ,jupit] to be -#a4g4 #aih4 ,,d\ble ,,/>s4--,9 ! con/ellation ,taurus1 n f> f ,aldeb>an1 is ! f\r?-magnitude /> ? ,tauri1 :i* c readily be se5 to consi/ ( two />s close toge!r4 ,! /> a ,capricorni is pla9ly d\ble1 & a %>p eye c detect t "o ( ! fa9t />s :i* ) ,vega make a small equilat]al triangle1 is also a d\ble />4 ,look = !m 9 ! sky4 ,9 ! /rict language ( a/ronomy ! t]m d\ble /> w\ld n be appli$ to ! fir/ two ( ^! objects1 s9ce x is usually re/rict$ to ^? />s ^: angul> di/ance f ea* o!r is s small t 9 ! telescope !y appe> mu* z d ! />s nam$ above to ! nak$ eye--i4 e41 _! angul> sep>ation is measur$ by a few seconds or fractions ( a s+le second1 in/ead ( ! six m9utes :i* sep>ate ! compon5t />s ( ? ,tauri or a ,capricorni4 ,!re are f\nd 9 ! sky _m ?\s&s ( ^! close d\ble />s1 ( :i* "s are only optically d\ble--i4 e41 two />s ne>ly on l9e ) ! e>? b at v diff]5t di/ances f x--:ile m ( !m are really :at !y seem1 />s ne> ea* o!r1 & 9 _m cases ne> en\gh to influ5ce ea* o!r's motion4 ,^! are call$ b9>y sy/ems1 & 9 cases ( ?is k9d ! pr9ciples ( cele/ial me*anics set =? 9 ,*apt] ,,iv hold true1 & we may expect to f9d ea* compon5t ( a d\ble /> mov+ 9 a conic section ( "s k9d1 hav+ its focus at ! common c5t] ( gravity ( ! two />s4 ,we are ?us pres5t$ ) problems ( orbital motion q simil> to ^? :i* occur 9 ! sol> sy/em1 & c>eful telescopic obs]vations are requir$ ye> aft] ye> to fix ! relative positions ( ! two />s--i4 e41 _! angul> sep>ation1 :i* x is cu/om>y to call _! di/ance1 & _! direction "o f ! o!r1 :i* is call$ position angle4 #aii4 ,,orbits ,,( ,,d\ble ,,/>s4--,! sun's ne>e/ neighbor1 a ,c5tauri1 is su* a d\ble />1 ^: position angle & di/ance h be5 measur$ by successive g5]ations ( a/ronom]s = m ?an a c5tury1 & ,fig4 #abg %[s ! result ( plott+ _! obs]vations4 ,ea* black dot t lies on or ne> ! circumf]5ce ( ! long ellipse /&s = an obs]v$ direction & di/ance ( ! fa9t] ( ! two />s f ! bright] "o1 :i* is repres5t$ by ! small circle at ! int]section ( ! l9es inside ! ellipse4 ,x appe>s f ! figure t dur+ ?is "t ! "o /> has gone completely ar\nd ! o!r1 z a planet goes ar\nd ! sun1 & ! true orbit mu/ !re=e be an ellipse hav+ "o ( its foci at ! c5t] ( gravity ( ! two />s4 ,! o!r /> moves 9 an ellipse ( precisely simil> %ape1 b probably small] size1 s9ce ! dim5sions ( ! two orbits are inv]sely proportional to ! masses ( ! two bodies1 b x is cu/om>y to neglect ?is motion ( ! l>g] /> & to give to ! small] "o an orbit ^: diamet] is equal to ! sum ( ! diamet]s ( ! two real orbits4 ,?is practice1 :i* has be5 foll[$ 9 ,fig4 #abg1 gives correctly ! relative positions ( ! two />s1 & makes "o orbit d ! "w ( two4 ,illu/ration3 ,,fig4 #abg4--,! orbit ( a ,c5tauri4--,,see4 ,9 ,fig4 #abg ! bright /> does n fall any:]e ne> ! focus ( ! ellipse m>k$ out by ! small] "o1 & f ?is we inf] t ! figure does n %[ ! true %ape ( ! orbit1 :i* is c]ta9ly di/ort$1 =e%ort5$1 by ! fact t we look obliquely d[n ^u its plane4 ,x is possible1 h[ev]1 by ma!matical analysis1 to f9d j h[ mu* & 9 :at direction t plane %\ld be turn$ 9 ord] to br+ ! focus ( ! ellipse up to ! position ( ! pr9cipal />1 & ?us give ! true %ape & size ( ! orbit4 ,see ,fig4 #abh = a case 9 :i* ! true orbit is turn$ exactly edgewise t[>d ! e>?1 & ! small />1 :i* really moves 9 an ellipse l t %[n 9 ! figure1 appe>s to oscillate to & fro along a /raight l9e drawn ?r\gh ! pr9cipal />1 z %[n at ! left ( ! figure4 ,9 ! case ( a ,c5tauri ! true orbit proves to h a major axis #dg times1 & a m9or axis #dj times1 z great z ! di/ance ( ! e>? f ! sun4 ,! orbit1 9 fact1 is int]m$iate 9 size betwe5 ! orbits ( ,uranus & ,neptune1 & ! p]iodic "t ( ! /> 9 ?is orbit is #ha ye>s1 a little less ?an ! p]iod ( ,uranus4 ,illu/ration3 ,,fig4 #abh4--;,app>5t orbit & real orbit ( ! d\ble /> #db ,com ,b]5icis4--,,see4 #bjj4 ,,masses ,,( ,,d\ble ,,/>s4--,if we apply to ?is orbit ,kepl]'s ,?ird ,law 9 ! =m giv5 x at page #agi1 we %all f9d-- a#c _/ ,t#b 7#bc4e7c _/ 7#ha7b k 7,m m71 :]e ,m & m repres5t ! masses ( ! two />s4 ,we h already se5 t k1 ! gravitation con/ant1 is equal to #a :5 ! masses are measur$ 9 t]ms ( ! sun's mass tak5 z unity1 & :5 ,t & a are express$ 9 ye>s & radii ( ! e>?'s orbit respectively1 & ) ?is value ( k we may readily f9d f ! above equation1 ,m m #b4e--;i4 e41 ! comb9$ mass ( ! two compon5ts ( a ,c5tauri is equal to r m ?an twice ! mass ( ! sun4 ,x is n e d\ble /> to :i* ?is process ( weigh+ c be appli$4 ,! major axis ( ! orbit1 a1 is f\nd f ! obs]vations 9 angul> measure1 #ce 9 ?is case1 & x is only :5 ! p>allax ( ! /> is kn[n t ?is c be conv]t$ into ! requir$ l9e> units1 radii ( ! e>?'s orbit1 by divid+ ! angul> major axis by ! p>allax2 #dg #ce #j4ge4 ,our li/ ( di/ances 7 #ahi7 conta9s f\r d\ble />s ^: p]iodic times & major axes h be5 fairly well det]m9$1 & we f9d 9 ! accompany+ table ! in=mation :i* !y give ab\t ! masses ( d\ble />s & ! size ( ! orbits 9 :i* !y move3 ---------------------------------------- ------------ ,,/>4 ,major ,m9or ,p]iodic ,mass4 axis4 axis4 "t4 ---------------------------------------- ------------ a ,c5tauri #dg #dj #ha y4 #b #gj ,ophiu*i #ef #dh #hh #c ,procyon #cd #ca #dj #c ,sirius #dc #cd #eb #d ---------------------------------------- ------------ ,! orbit ( ,uranus1 diamet] #ch1 & ,neptune1 diamet] #fj1 are ( mu* ! same size z ^! d\ble-/> orbits2 b ! planet>y orbits are ne>ly circul>1 :ile 9 e case ! d\ble />s %[ a sub/antial diff]5ce betwe5 ! long & %ort diamet]s ( _! orbits4 ,?is is a *>act]i/ic feature ( mo/ d\ble-/> orbits1 & seems to /& 9 "s relation to _! p]iodic times1 =1 on ! av]age1 ! long] ! "t requir$ by a /> to make its orbital revolution ! m ecc5tric is its orbit likely to prove4 ,ano!r elem5t ( ! orbits ( d\ble />s1 :i* /&s 9 ev5 clos] relation to ! p]iodic "t1 is ! major axis2 ! small] ! long diamet] ( ! orbit ! m rapid is ! motion & ! %ort] ! p]iodic "t1 s t a/ronom]s 9 se>* ( int]e/+ d\ble-/> orbits devote !mselves by pref]5ce to ^? />s ^: di/ance ap>t is s small t !y c b>ely be di/+ui%$ "o f ! o!r 9 ! telescope4 ,al?\gh ! half-doz5 />s conta9$ 9 ! table all h orbits ( mu* ! same size & ) mu* ! same p]iodic "t z ^? 9 :i* ,uranus & ,neptune move1 ?is is by no means true ( all ! d\ble />s1 _m ( :i* h p]iods runn+ up into ! hundr$s if n ?\s&s ( ye>s1 :ile a few complete _! orbital revolutions 9 p]iods comp>able )1 or ev5 %ort] ?an1 t ( ,jupit]4 #bja4 ,,d>k ,,/>s4--,procyon1 ! next to ! la/ /> ( ! prec$+ table1 calls = "s special m5tion1 z ! det]m9ation ( its mass & orbit /&s ^u a r diff]5t basis f t ( ! o!r />s4 ,m ?an half a c5tury ago x 0 discov]$ t its prop] motion 0 n /raight & uni=m aft] ! fa%ion ( ord9>y />s1 b pres5t$ a s]ies ( loops l ^? m>k$ out by a bright po9t on ! rim ( a swiftly runn+ bicycle :eel4 ,! hub may move /raight =w>d ) uni=m velocity1 b ! po9t ne> ! tire goes up & d[n1 &1 :ile %>+ 9 ! =w>d motion ( ! hub1 runs sometimes ahead ( x1 sometimes beh9d1 & su* seem$ to be ! motion ( ,procyon & ( ,sirius z well4 ,bessel1 :o discov]$ x1 did n hesitate to apply ! laws ( motion1 & to affirm t ?is visible *ange ( ! />'s motion po9t$ to ! pres5ce ( an unse5 companion1 :i* produc$ ^u ! motions ( ,sirius & ,procyon j su* effects z ! visible companions produce 9 ! motions ( d\ble />s4 ,a new k9d ( />1 d>k in/ead ( bright1 0 add$ to ! a/ronom]'s doma91 & its discov]] boldly sugge/$ ! possible exi/5ce ( _m m4 ,t c\ntless />s are visible is cle>ly no argum5t aga9/ ! exi/5ce ( z _m m invisible ones4 ,!re is no reason to ?9k radiance a necess>y prop]ty ( cele/ial bodies4 ,b mo/ a/ronom]s 7 incr$ul\s1 & x 0 n until #ahfb t1 9 ! te/+ ( a new & p[]ful telescope j built1 a d>k /> 0 br\ght to light & ! companion ( ,sirius actually se54 ,! visual discov]y ( ! d>k companion ( ,procyon is ( /ill m rec5t date 7,novemb]1 #ahif71 :5 x 0 detect$ ) ! great telescope ( ! ,lick ,obs]vatory4 ,?is discov]y is s rec5t t ! orbit is /ill v unc]ta91 be+ bas$ almo/ :olly ^u ! v>iations 9 ! prop] motion ( ! />1 & :ile ! p]iodic "t mu/ be v ne>ly correct1 ! mass ( ! />s & dim5sions ( ! orbit may require consid]able correction4 ,! companion ( ,sirius is ab\t t5 magnitudes & t ( ,procyon ab\t twelve magnitudes fa9t] ?an ! /> itself4 ,h[ mu* m light does ! bright /> give ?an its fa9t companion8 ,despite ! trem5d\s diff]5ce ( brightness repres5t$ by ! answ] to ?is "q1 ! mass ( ,sirius is only ab\t twice z great z t ( its companion1 & = ,procyon ! ratio does n exce$ five or six4 ,! visual discov]y ( ! companions to ,sirius & ,procyon removes !m f ! li/ ( d>k />s1 b o!rs /ill rema9 unse51 al?\gh _! exi/5ce is indicat$ by v>iable prop] motions or by v>iable orbital motion1 z 9 ! case ( z ,cancri1 :]e "o ( ! compon5ts ( a triple /> moves ar\nd ! o!r two 9 a s]ies ( loops ^: pres5ce indicates a di/urb+ body :i* has nev] yet be5 se54 #bjb4 ,,multiple ,,/>s4--,comb9ations ( ?ree1 f\r1 or m />s close to ea* o!r1 l z ,cancri1 are call$ multiple />s1 & :ile !y are f> f be+ z common z are d\ble />s1 !re is a consid]able numb] ( !m 9 ! sky1 #ajj or m z aga9/ ! m ?an #aj1jjj d\ble />s t are kn[n4 ,t _! relative motions are subject to ! law ( gravitation admits ( no s]i\s d\bt1 b ma!matical analysis breaks d[n 9 face ( ! difficulties "h pres5t$1 & no a/ronom] has ev] be5 able to det]m9e :at w be ! g5]al "* ( ! motions 9 su* a sy/em4 ,illu/ration3 ,,fig4 #abi4--;,illu/rat+ ! motion ( a spectroscopic b9>y4 #bjc4 ,,spectroscopic ,,b9>ies4--,9 ! ye> #ahij ,pr(essor ,pick]+1 ( ! ,h>v>d ,obs]vatory1 ann\nc$ ! discov]y ( a new class ( d\ble />s1 invisible z su* 9 ev5 ! mo/ p[]ful telescope1 & produc+ no p]turbations su* z h be5 consid]$ above1 b %[+ 9 _! spectrum t two or m bodies mu/ be pres5t 9 ! s\rce ( light :i* to ! eye is indi/+ui%able f a s+le />4 ,9 ,fig4 #abi we suppose ,a & ,b to be ! two compon5ts ( a d\ble />1 ea* mov+ 9 its own orbit ab\t _! common c5t] ( gravity1 ,c1 ^: di/ance f ! e>? is sev]al million times great] ?an ! di/ance betwe5 ! />s !mselves4 ,"u su* circum/ances no telescope c\ld di/+ui% betwe5 ! two />s1 :i* w\ld appe> fus$ into "o2 b ! small] ! orbit ! m rapid w\ld be _! motion 9 x1 & if ?is orbit 7 turn$ edgewise t[>d ! e>?1 z is suppos$ 9 ! figure1 :5ev] ! />s 7 9 ! relative position !re %[n1 ,a w\ld be rapidly approa*+ ! e>? by reason ( its orbital motion1 :ile ,b w\ld move away f x1 s t 9 accordance ) ! ,doppl] pr9ciple ! l9es compos+ _! respective spectra w\ld be %ift$ 9 opposite directions1 ?us produc+ a d\bl+ ( ! l9es1 ea* s+le l9e break+ up into two1 l ! d\ble-sodium l9e ,d1 only n spac$ s f> ap>t4 ,:5 ! />s h mov$ a qu>t] way r\nd _! orbit to ! po9ts ,a1 ,b1 _! velocities are turn$ at "r angles to ! l9e ( sight & ! spectrum returns to ! normal type ) s+le l9es1 only to break up aga9 :5 aft] ano!r qu>t] revolution _! velocities are aga9 p>allel ) ! l9e ( sight4 ,! int]val ( "t betwe5 consecutive d\bl+s ( ! l9es 9 ! spectrum ?us furni%es half ! "t ( a revolution 9 ! orbit4 ,! di/ance betwe5 ! compon5ts ( a d\ble l9e %[s by means ( ! ,doppl] pr9ciple h[ fa/ ! />s are travel+1 & ?is 9 connection ) ! p]iodic times fixes ! size ( ! orbit1 provid$ we assume t x is turn$ exactly edgewise to ! e>?4 ,?is assumption may n be q true1 b ev5 ?\gh ! orbit %\ld deviate consid]ably f ?is position1 x w /ill pres5t ! ph5om5on ( ! d\ble l9es ^: displacem5t w n[ %[ some?+ less ?an ! true velocities ( ! />s 9 _! orbits1 s9ce ! spectroscope measures only t compon5t ( ! :ole velocity :i* is direct$ t[>d ! e>?1 & x is important to note t ! real orbits & masses ( ^! spectroscopic b9>ies1 z !y are call$1 w usually be some:at l>g] ?an ^? indicat$ by ! spectroscope1 s9ce x is only 9 exceptional cases t ! orbit w be turn$ exactly edgewise to u4 ,! bright /> ,capella is an excell5t illu/ration ( ^! spectroscopic b9>ies4 ,at int]vals ( a little less ?an a mon? ! l9es ( its spectrum are alt]nately s+le & d\ble1 _! maximum sep>ation correspond+ to a velocity 9 ! l9e ( sight am\nt+ to #cg miles p] second4 ,ea* compon5t ( a d\bl$ l9e appe>s to be %ift$ an equal am\nt f ! position occupi$ by ! l9e :5 x is s+le1 ?us indicat+ equal velocities & equal masses = ! two compon5t />s ^: p]iodic "t 9 _! orbit is #ajd days4 ,f ?is p]iodic "t1 toge!r ) ! velocity ( ! />'s motion1 let ! /ud5t %[ t ! diamet] ( ! orbit--i4 e41 ! di/ance ( ! />s f ea* o!r--is approximately #ec1jjj1jjj miles1 & t _! comb9$ mass is a little less ?an t ( a ,c5tauri1 provid$ t _! orbit plane is turn$ exactly edgewise t[>d ! e>?4 ,!re are at ! pres5t "t 7#aija7 #cd spectroscopic b9>ies kn[n1 includ+ among !m su* />s z ,pol>is1 ,capella1 ,algol1 ,spica1 b ,aurig1 z ,urs ,majoris1 etc41 & _! numb] is rapidly increas+1 ab\t "o /> out ( e sev5 ^: motion 9 ! l9e ( sight is det]m9$ prov+ to be a b9>y or1 z 9 ! case ( ,pol>is1 possibly triple4 ,on acc\nt ( small] di/ance ap>t _! p]iodic times are mu* %ort] ?an ^? ( ! ord9>y d\ble />s1 & range f a few days up to sev]al mon?s--m ?an two ye>s 9 ! case ( ,pegasi1 :i* has ! longe/ kn[n p]iod ( any /> ( ?is class4 ,spectroscopic b9>ies agree ) ord9>y d\ble />s 9 hav+ masses r great] ?an t ( ! sun1 b !re is z yet no assur$ case ( a mass t5 times z great z t ( ! sun4 #bjd4 ,,v>iable ,,/>s4--,att5tion has already be5 drawn 7 #bc7 to ! fact t "s />s %9e ) a *ang+ brightness--e4 g41 ,algol1 ! mo/ fam\s ( ^! v>iable />s1 at its maximum ( brightness furni%es ?ree times z mu* light z :5 at its m9imum1 & o!r v>iable />s %[ an ev5 great] range4 ,! /> o ,ceti has be5 nam$ ,mira 7,lat91 ! wond]ful71 f its extraord9>y range ( brightness1 m ?an six-hundr$-fold4 ,= ! great] "p ( ! "t ?is /> is invisible to ! nak$ eye1 b dur+ "s ?ree mon?s 9 e ye> x bright5s up suffici5tly to be se51 ris+ q rapidly to its maximum brilliancy1 :i* is sometimes t ( a second-magnitude />1 b m frequ5tly only ?ird or ev5 f\r? magnitude1 &1 aft] %9+ = a few weeks ) ne>ly maximum brilliancy1 fall+ (f to become invisible = a "t & !n return to its maximum brightness aft] an int]val ( elev5 mon?s f ! prec$+ maximum4 ,9 #aija x %\ld rea* its greate/ brilliancy ab\t midsumm]1 & a mon? e>li] ?an ?is = ea* succe$+ ye>4 ,f9d x by means ( ! /> map1 & by comp>+ its brightness f night to night ) neighbor+ />s ( ab\t ! same magnitude see h[ x *anges ) respect to !m4 ,! int]val ( "t f maximum to maximum ( brightness--#cca4f days = ,mira--is call$ ! />'s p]iod1 & )9 its p]iod a /> regul>ly v>iable runs ?r\gh all its *anges ( brilliancy1 mu* z ! wea!r runs ?r\gh its cycle ( *anges 9 ! p]iod ( a ye>4 ,b1 z !re are wet ye>s & dry ones1 hot ye>s & cold1 s also ) v>iable />s1 _m ( !m %[ diff]5ces m or less pron\nc$ betwe5 diff]5t p]iods1 & "o su* diff]5ce has already be5 not$ 9 ! case ( ,mira2 its maximum brilliancy is diff]5t 9 diff]5t ye>s4 ,s1 too1 ! l5g? ( ! p]iod fluctuates 9 _m cases1 z does e o!r circum/ance connect$ ) x1 & pr$ictions ( :at su* a v>iable /> w d are notori\sly unreliable4 #bje4 ,,! ,,algol ,,v>iables4--,on ! o!r h&1 "s v>iable />s pres5t an almo/ p]fect regul>ity1 repeat+ _! *anges "t aft] "t ) a precision l t ( clockwork4 ,algol is "o type ( ^! regul> v>iables1 hav+ a p]iod ( #fh4haed h\rs1 dur+ six sev5?s ( :i* "t x %9es ) un*ang+ lu/] z a /> ( ! #b4c magnitude1 b dur+ ! rema9+ #i h\rs ( ea* p]iod x runs d[n to ! #c4e magnitude1 & comes back aga91 z is %[n by a curve 9 ,fig4 #acj4 ,! horizontal scale "h repres5ts h\rs1 reckon$ f ! "t ( ! />'s m9imum brightness1 & ! v]tical scale %[s /ell> magnitudes4 ,su* a diagram is call$ ! />'s light curve1 & we may read f x t at any "t betwe5 #e;h4 & #cb;h4 aft] ! "t ( m9imum ! />'s magnitude is #b4cb2 at #b;h4 aft] a m9imum ! magnitude is #b4hh1 etc4 ,:at is ! magnitude an h\r & a half be=e ! "t ( m9imum8 ,:at is ! magnitude #dc days aft] a m9imum8 ,illu/ration3 ,,fig4 #acj4--,! light curve ( ,algol4 ,! arr[s %[n 9 ,fig4 #acj are a feature n usually f\nd ) light curves1 b 9 ?is case ea* "o repres5ts a spectroscopic det]m9ation ( ! motion ( ,algol 9 ! l9e ( sight4 ,^! obs]vations ext5d$ ov] a p]iod ( m ?an two ye>s1 b !y are plott$ 9 ! figure ) ref]5ce to ! numb] ( h\rs ea* "o prec$$ or foll[$ a m9imum ( ! />'s light1 & ea* arr[ %[s n only ! direction ( ! />'s motion along ! l9e ( sight1 ! arr[s po9t+ d[n d5ot+ approa* ( ! /> t[>d ! e>?1 b also its velocity1 ea* squ>e ( ! rul+ correspond+ to #aj kilomet]s 7#f4b miles p] second74 ,! diff]5ces ( velocity %[n by adjac5t arr[s come ma9ly f errors ( obs]vation & furni% "s idea ( h[ consi/5t among !mselves su* obs]vations are1 b !re c be no d\bt t be=e m9imum ! /> is mov+ away f ! e>?1 & aft] m9imum is approa*+ x4 ,x is evid5t f ^! obs]vations t 9 ,algol we h to d ) a spectroscopic b9>y1 "o ( ^: compon5ts is a d>k /> :i*1 once 9 ea* revolution1 p>tially eclipses ! bright /> & produces ?us ! v>iations 9 its light4 ,by comb9+ ! spectroscopic obs]vations ) ! v>iations 9 ! />'s light1 ,vogel f9ds t ! bright />1 ,algol1 itself has a diamet] some:at great] ?an t ( ! sun1 b is ( l[ d5sity1 s t its mass is less ?an half t ( ! sun1 :ile ! d>k /> is a v little small] ?an ! sun & has ab\t a qu>t] ( its mass4 ,! di/ance betwe5 ! two />s1 d>k & bright1 is #c1bjj1jjj miles4 ,fig4 #abi1 :i* is drawn to scale1 %[s ! relative positions & sizes ( ^! />s z well z ! orbits 9 :i* !y move4 ,! m]e fact already not$ t close b9>y sy/ems exi/ 9 consid]able numb]s is suffici5t to make x probable t a c]ta9 proportion ( ^! />s w\ld h _! orbit planes turn$ s ne>ly edgewise t[>d ! e>? z to produce eclipses1 & correspond+ to ?is probability !re are already kn[n no less ?an #ae />s ( ! ,algol type ( eclipse v>iables1 & only a beg9n+ has be5 made 9 ! se>* = !m4 ,illu/ration3 ,,fig4 #aca4--,! light curve ( b ,lyr4 #bjf4 ,,v>iables ,,( ,,! b ,,lyr ,,type4--,9 addition to ^! !re is a c]ta9 fur!r numb] ( b9>y v>iables 9 :i* bo? compon5ts are bright & :]e ! v>iation ( brightness foll[s a v diff]5t c\rse4 ,capella w\ld be su* a v>iable if its orbit plane 7 direct$ exactly t[>d ! e>?1 & ! fact t its light is n v>iable %[s conclusively t su* is n ! position ( ! orbit4 ,fig4 #aca repres5ts ! light curve ( "o ( ! be/-kn[n v>iable sy/ems ( ?is second type1 t ( b ,lyr1 ^: p]iod is #ab days #ba4h h\rs1 & ! /ud5t %\ld read f ! curve ! magnitude ( ! /> = diff]5t times dur+ ?is int]val4 ,accord+ to ,my]s1 ?is light curve & ! spectroscopic obs]vations ( ! /> po9t to ! exi/5ce ( a b9>y /> ( v rem>kable "*1 su* z is %[n1 toge!r ) its orbit & a scale ( miles1 9 ,fig4 #acb4 ,note ! tide :i* ea* ( ^! />s raises 9 ! o!r1 ?us *ang+ _! %apes f sph]es into ellipsoids4 ,! a/oni%+ dim5sions ( ^! />s are 9 "p comp5sat$ by _! v l[ d5sity1 :i* is less ?an t ( air1 s t _! masses are respectively only #aj times & #ba times t ( ! sun6 ,b ^! dim5sions & masses p]haps require confirmation1 s9ce !y dep5d ^u spectroscopic obs]vations ( d\btful int]pretation4 ,9 ,fig4 #acb :at relative positions mu/ ! />s occupy 9 _! orbit 9 ord] t _! comb9$ light %\ld give b ,lyr its maximum brightness8 ,:at position w furni% a m9imum brightness8 ,illu/ration3 ,,fig4 #acb4--,! sy/em ( b ,lyr4--,,my]s4 #bjg4 ,,v>iables ,,( ,,long ,,& ,,%ort ,,p]iods4--,x mu/ n be suppos$ t all v>iable />s are b9>ies :i* eclipse ea* o!r4 ,by f> ! l>g] "p ( !m1 l ,mira1 are n to be acc\nt$ = 9 ?is way1 & a di/9ction :i* is pretty well m>k$ 9 ! l5g? ( _! p]iods is significant 9 ?is connection4 ,!re is a consid]able numb] ( v>iable />s ) p]iods %ort] ?an a mon?1 & !re are _m hav+ p]iods long] ?an #f mon?s1 b !re are v few hav+ p]iods long] ?an #ah mon?s1 or int]m$iate betwe5 #a mon? & #f mon?s1 s t x is q cu/om>y to divide v>iable />s into two classes--^? ( long p]iod1 #f mon?s or m1 & ^? ( %ort p]iod less ?an #f mon?s1 & t ?is di/9ction corresponds to "s real diff]5ce 9 ! />s !mselves is fur!r m>k$ by ! fact t ! long-p]iod v>iables are prevail+ly r$ 9 color1 :ile ! %ort-p]iod />s are almo/ )\t exception :ite or v pale yell[4 ,9 fact1 ! long] ! p]iod ! r$d] ! />1 al?\gh x is n to be inf]r$ t all r$ />s are v>iable2 a consid]able p]c5tage ( !m %9e ) con/ant light4 ,! eclipse explanation ( v>iability holds good only = %ort-p]iod v>iables1 & possibly n = all ( !m1 :ile = ! long-p]iod v>iables !re is no explanation :i* comm&s ! g5]al ass5t ( a/ronom]s1 al?\gh unv]ifi$ hypo!ses are pl5ty4 ,! numb] ( />s kn[n to be v>iable is ab\t #djj1 :ile a consid]able numb] ( o!rs are suspect$1 & x w\ld n be surpris+ if a l>ge fraction ( all ! />s %\ld be f\nd to fluctuate a little 9 brightness4 ,! sun's spots may suffice to make x a v>iable /> ) a p]iod ( #aa ye>s4 ,! discov]y ( new v>iables is ( frequ5t occurr5ce1 & may be expect$ to become m frequ5t :5 ! sky is sy/ematically explor$ = !m by ! +5i\s device sugge/$ by ,pick]+ & illu/rat$ 9 ,fig4 #acc4 ,a giv5 region ( ! sky--e4 g41 ! ,nor!rn ,cr[n--is photograph$ repeat$ly ^u ! same plate1 :i* is %ift$ a little at ea* new exposure1 s t ! />s %all fall at new places ^u x4 ,! f9ally develop$ plate %[s a r[ ( images correspond+ to ea* />1 & if ! />'s light is con/ant ! images 9 any giv5 r[ w all be ( ! same size1 z are mo/ ( ^? 9 ,fig4 #acc2 b a v>iable /> su* z is %[n by ! arr[head reveals its pres5ce by ! brok5 aspect ( its r[ ( dots1 a m9imum brilliancy be+ %[n by small] & a maximum by l>g] ones4 ,9 ?is p>ticul> case1 at two exposures ! /> 0 too fa9t to pr9t its image ^u ! plate4 ,illu/ration3 ,,fig4 #acc4--;,discov]y ( a v>iable /> by means ( photography4--,,pick]+4 #bjh4 ,,new ,,/>s4--,next to ! v>iable />s ( v long or v irregul> p]iod /& ! s-call$ new or tempor>y />s1 :i* appe> = ! mo/ "p sudd5ly1 & aft] a brief "t ei!r vani% altoge!r or s9k to comp>ative insignificance4 ,^! 7 =m]ly ?\ght to be v rem>kable & unusual occurr5ces--! bir? ( a new _w--& x is notewor?y t no new /> is record$ to h be5 se5 f #afgj to #ahdh ,a4 ,d41 = s9ce t "t !re h be5 no less ?an five ( !m visible to ! nak$ eye & o!rs telescopic4 ,9 s f> z ^! new />s are n ord9>y v>iables 7,mira1 fir/ se5 9 #aeif1 0 long c\nt$ z a new />71 !y are commonly suppos$ due to *ance enc\nt]s betwe5 />s or o!r cosmic bodies mov+ ) consid]able velocities along orbits :i* approa* v close to ea* o!r4 ,! actual collision ( two d>k bodies mov+ ) high velocities is cle>ly suffici5t to produce a lum9\s />--e4 g41 meteors--& ev5 ! close approa* ( two cool$-(f />s1 might result 9 tidal actions :i* w\ld r5d op5 _! cru/s & p\r out ! gl[+ matt] f )9 s z to produce tempor>ily a v great accession ( brightness4 ,! mo/ fam\s ( all new />s is t :i*1 accord+ to ,ty*o ,brahe's report1 appe>$ 9 ! ye> #aegb1 & 0 s bright :5 at its be/ z to be se5 ) ! nak$ eye 9 broad daylight4 ,x cont9u$ visible1 ?\gh ) fad+ light1 = ab\t #af mon?s1 & f9ally disappe>$ to ! nak$ eye1 al?\gh !re is "s reason to suppose t x c be id5tifi$ ) a ruddy /> ( ! elev5? magnitude 9 ! con/ellation ,cassiopeia1 ^: light /ill %[s traces ( v>iability4 ,no mod]n tempor>y /> approa*es t ( ,ty*o 9 spl5dor1 b 9 "s respects ! rec5t ones surpass x 9 int]e/1 s9ce x has be5 possible to apply ! spectroscope to ! analysis ( _! light & to f9d !reby a mu* m complex set ( conditions 9 ! /> ?an w\ld h be5 suspect$ f its light *anges alone4 ,"o ( ! mo/ extraord9>y ( new />s1 & ! mo/ brilliant "o s9ce t ( ,ty*o1 appe>$ sudd5ly 9 ! con/ellation ,p]seus 9 ,febru>y1 #aija1 & = a %ort "t equal$ ,capella 9 brightness4 ,b its light rapidly wan$1 ) p]iodic fluctuations ( brightness l ^? ( a v>iable />1 & at ! pres5t "t 7,septemb]1 #aijb7 x is lo/ to ! nak$ eye1 al?\gh 9 ! telescope x /ill %9es l a /> ( ! n9? or t5? magnitude4 ,by ! aid ( p[]ful photographic app>atus1 dur+ ! p]iod ( its wan+ brilliancy a r+ ( fa9t nebul\s matt] 0 detect$ surr\nd+ ! /> & drift+ ar\nd & away f x mu* z if a s]ies ( nebul _h be5 ?r[n (f by ! /> at ! "t ( its sudd5 outbur/ ( light4 ,b ! extraord9>y velocity ( ?is nebul> motion1 ne>ly a billion miles p] h\r1 makes su* an explanation almo/ incr$ible1 & a/ronom]s are m incl9$ to believe t ! r+ 0 m]ely a reflection ( ! />'s own light f a cl\d ( meteoric matt]1 into :i* a rapidly mov+ d>k /> plung$ &1 aft] ! fa%ion ( t]re/rial meteors1 0 rais$ to brilliant inc&esc5ce by ! collision4 ,if we assume ?is to be ! true explanation ( ^! extraord9>y ph5om5a1 x is possible to %[ f ! kn[n velocity ) :i* light travels ?r\gh space & f ! rate at :i* ! nebula spread1 t ! di/ance ( ,nova ,p]sei1 z ! new /> is call$1 corresponds to a p>allax ( ab\t "o "o-hundr$? ( a second1 a result t is1 9 sub/ance1 confirm$ by direct telescopic measurem5ts ( its p>allax4 ,ano!r mod]n tempor>y /> is ,nova ,aurig1 :i* appe>$ sudd5ly 9 ,decemb]1 #ahia1 wan$1 & 9 ! foll[+ ,april vani%$1 only to reappe> ?ree mon?s lat] = ano!r season ( r5ew$ brightness4 ,! spectra ( bo? ^! mod]n ,nov conta9 bo? d>k & bright l9es displac$ t[>d opposite ends ( ! spectrum1 & sugge/+ ! ,doppl] effect t w\ld be produc$ by two or m gl[+ bodies hav+ rapid & opposite motions 9 ! l9e ( sight4 ,b ! mo/ rec5t inve/igations ca/ discr$it on ?is explanation & leave ! spectra ( tempor>y />s /ill a subject ( debate among a/ronom]s1 ) respect bo? to ! motion !y indicate & ! intr9sic nature ( ! />s !mselves4 ,! v>y+ aspect ( ! spectra sugge/$ at "o "t ! sun's *romosph]e1 at ano!r "t ! conditions t are pres5t 9 nebul1 etc4 ,,*apt] ,,xiv ,,/>s ,,& ,,nebul #bji4 ,,/ell> ,,colors4--,we h already se5 t "o /> diff]s f ano!r 9 respect ( color z well z brightness1 & ! dilig5t /ud5t ( ! sky w n fail to obs]ve = himself h[ ! lu/] ( ,sirius & ,rigel is m ne>ly a pure :ite ?an is t ( any o!r />s 9 ! heav5s1 :ile at ! o!r end ( ! scale a ,orionis & ,aldeb>an are /rongly ruddy1 & ,ant>es pres5ts an ev5 deep] tone ( r$4 ,betwe5 ^! extremes ! light ( e /> %[s a mixture ( ! ra9b[ hues1 9 :i* a v pale yell[ is ! pr$om9ant color1 %ad+ (f1 z we h se51 to :ite at "o end ( ! scale & r$ at ! o!r4 ,!re are no gre5 />s1 or blue />s1 or violet />s1 save 9 "o exceptional class ( cases--viz41 :]e ! two compon5ts ( a d\ble /> are ( v diff]5t brightness1 x is q ! usual ?+ = !m to h diff]5t colors1 & !n1 almo/ )\t exception1 ! color ( ! fa9t] /> lies ne>] to ! violet end ( ! spectrum ?an does ! color ( ! bright "o1 & sometimes %[s a di/9ctly blue or gre5 hue4 ,a f9e type ( su* d\ble /> is b ,cygni1 9 :i* ! compon5ts are respectively yell[ & blue1 & ! yell[ /> furni%es eight times z mu* light z ! blue "o4 ,! exception :i* d\ble />s ?us make to ! g5]al rule ( /ell> colors1 yell[ & r$1 b no color ( %ort] wave l5g?1 has nev] be5 satisfactorily expla9$1 b ! rule itself pres5ts no difficulties4 ,ea* /> is an inc&esc5t body1 giv+ (f radiant en]gy ( e wave l5g? )9 ! limits ( ! visible spectrum1 &1 inde$1 f> beyond ^! limits4 ,if ?is radiant en]gy c\ld come unh9d]$ to our eyes e /> w\ld appe> :ite1 b !y are all surr\nd$ by atmosph]es--analog\s to ! *romosph]e & rev]s+ lay] ( ! sun--:i* absorb a portion ( _! radiant en]gy &1 l ! e>?'s atmosph]e1 take a heavi] toll f ! violet ?an f ! r$ end ( ! spectrum4 ,! great] ! absorption 9 ! />'s atmosph]e1 !re=e1 ! feebl] & ! ruddi] w be its light1 & correspond+ to ?is ! r$ />s are z a class fa9t] ?an ! :ite ones4 #baj4 ,,*emi/ry ,,( ,,! ,,/>s4--,! spectroscope is pre-em95tly ! in/rum5t to deal ) ?is absorption ( light 9 ! /ell> atmosph]es1 j z x deals ) t absorption 9 ! sun's atmosph]e to :i* are due ! d>k l9es ( ! sol> spectrum1 al?\gh ! fa9tness ( />light1 comp>$ ) t ( ! sun1 pres5ts a s]i\s ob/acle to its use4 ,despite ?is difficulty mo/ ( ! lucid />s & _m ( ! telescopic ones h be5 /udi$ ) ! spectroscope & f\nd to be simil> to ! sun & ! e>? z respects ! mat]ial ( :i* !y are made4 ,su* famili> *emical elem5ts z hydrog5 & iron1 c>bon1 sodium1 & calcium are scatt]$ broadca/ ?r\gh\t ! visible univ]se1 & :ile x w\ld be unw>rant$ by ! pres5t /ate ( k to say t ! />s conta9 no?+ n f\nd 9 ! e>? & ! sun1 x is evid5t t 9 a broad way _! sub/ance is l r ?an unlike t compos+ ! sol> sy/em1 & is subject to ! same physical & *emical laws :i* obta9 "h4 ,galileo & ,newton ext5d$ to ! heav5s ! t]re/rial sci5ces ( ma!matics & me*anics1 b x rema9$ to ! n9ete5? c5tury to %[ t ! physics & *emi/ry ( ! sky are l ! physics & *emi/ry ( ! e>?4 #baa4 ,,/ell> ,,spectra4--,:5 ! spectra ( great numb]s ( />s are comp>$ "o ) ano!r1 x is f\nd t !y be> "s relation to ! colors ( ! />s1 z1 inde$1 we %\ld expect1 s9ce spectrum & color are bo? produc$ by ! /ell> atmosph]es1 & x is f\nd useful to classify ^! spectra into ?ree types1 z foll[s3 ,type ,i4 ,sirian />s4--,speak+ g5]ally1 ! />s :i* are :ite or v fa9tly t+$ ) yell[1 furni% spectra l t ( ,sirius1 f :i* !y take _! "n1 or t ( b ,aurig 7,fig4 #abd71 :i* is a cont9u\s spectrum1 especially ri* 9 en]gy ( %ort wave l5g?--i4 e41 violet & ultraviolet light1 & is cross$ by a relatively small numb] ( heavy d>k l9es correspond+ to ! spectrum ( hydrog54 ,sometimes1 h[ev]1 ^! l9es are mu* fa9t] ?an is "h %[n1 & we f9d associat$ ) !m /ill o!r fa9t ones po9t+ to ! pres5ce ( o!r metallic sub/ances 9 ! />'s atmosph]e4 ,^! metallic l9es are n always pres5t1 & sometimes ev5 ! hydrog5 l9es !mselves are lack+1 b ! spectrum is always ri* 9 violet & ultraviolet light4 ,s9ce ) increas+ temp]ature a body emits a cont9ually increas+ proportion ( en]gy ( %ort wave l5g? 7 #aah71 ! ri*ness ( ^! spectra 9 su* en]gy po9ts to a v high temp]ature 9 ^! />s1 probably surpass+ 9 "s consid]able measure t ( ! sun4 ,/>s ) ?is type ( spectrum are m num]\s ?an all o!rs comb9$1 b next to !m 9 po9t ( numb]s /&s-- ,type ,,ii4 ,sol> />s4--,to ?is type ( spectrum belong ! yell[ />s1 :i* %[ spectra l t ( ! sun1 or ( ,pollux 7,fig4 #abe74 ,^! are n s ri* 9 violet light z are ^? ( ,type ,i1 b 9 complexity ( spectrum & 9 ! numb] ( _! absorption l9es !y f> surpass ! ,sirian />s4 ,!y are suppos$ to be at a l[] temp]ature ?an ! ,sirian />s1 & a mu* l>g] numb] ( *emical elem5ts seems pres5t & active 9 ! rev]s+ lay] ( _! atmosph]es4 ,! /rong resemblance :i* ^! spectra be> to t ( ! sun1 toge!r ) ! fact t mo/ ( ! sun's /ell> neighbors h spectra ( ?is type1 ju/ify u 9 rank+ bo? !m & x z memb]s ( "o class1 call$ sol> />s4 ,type ,,iii4 ,r$ />s4--,a small numb] ( />s %[ spectra comp>able ) t ( a ,h]culis 7,fig4 #acd71 9 :i* ! blue & ! violet "p ( ! spectrum is almo/ oblit]at$1 & ! rema9+ yell[ & r$ p>ts %[ n only d>k l9es1 b also num]\s broad d>k b&s1 %>p at "o edge1 & gradually fad+ out at ! o!r4 ,x is ?is selective absorption1 ext+ui%+ ! blue & leav+ ! r$ end ( ! spectrum1 :i* produces ! ruddy color ( ^! />s1 :ile ! b&s 9 _! spectra are *>act]i/ic ( *emical comb9ations1 & _! pres5ce 444 proves t at c]ta9 elevations 9 ! atmosph]es ( ^! />s ! temp]ature has sunk s l[ t *emical comb9ations c be =m$ & ma9ta9$ 7,s*e9]-,fro/74 ,"o ( ! *emical comp\nds "h indicat$ is a hydroc>bon simil> to t f\nd 9 comets4 ,9 ! :ite & yell[ />s ! temp]atures are s high t ! same *emical elem5ts1 al?\gh pres5t1 c n unite "o ) ano!r to =m comp\nd sub/ances4 ,illu/ration3 ,,fig4 #acd4--,! spectrum ( a ,h]culis4--,,esp94 ,mo/ ( ! v>iable />s are r$ & h spectra ( ! ?ird type2 b ?is does n hold true = ! eclipse v>iables l ,algol1 all ( :i* are :ite />s ) spectra ( ! fir/ type4 ,! ord9>y v>iable /> is !re=e "o ) a d5se atmosph]e ( relatively l[ temp]ature & complex /ructure1 :i* produces ! prevail+ r$ color ( ^! />s by absorb+ ! major "p ( _! radiant en]gy ( %ort wave l5g? :ile all[+ ! long]1 r$ waves to escape4 ,al?\gh _! exact nature is n und]/ood1 !re c be little d\bt t ! fluctuation 9 ! light ( ^! />s is due to processes tak+ place )9 ! /> itself1 b :e!r above or bel[ its photosph]e is /ill unc]ta94 #bab4 ,,classes ,,( ,,/>s4--,!re is no h>d-&-fa/ divid+ l9e betwe5 ^! types ( /ell> spectra1 b ! *ange f "o to ano!r is by ins5sible gradations1 l ! transition f y\? to manhood & f manhood to old age1 & along ! l9e ( transition are to be f\nd numb]less peculi>ities & v>ieties ( spectra n enum]at$ above--e4 g41 a few />s %[ n only d>k absorption l9es 9 _! spectra b bright l9es z well1 :i*1 l ^? 9 ,fig4 #dh1 po9t to ! pres5ce ( inc&esc5t vapors1 ev5 9 ! out] p>ts ( _! atmosph]es4 ,among ! lucid />s ab\t #ge p] c5t h spectra ( ! fir/ type1 #bc p] c5t are ( ! second type1 #a p] c5t ( ! ?ird type1 & ! rema9+ #a p] c5t are peculi> or ( d\btful classification4 ,among ! telescopic />s x is probable t mu* ! same di/ribution holds1 b 9 ! pres5t /ate ( k x is n prud5t to speak ) entire confid5ce ^u ?is po9t4 ,t ! great numb] ( />s ^: spectra h be5 /udi$ %\ld admit ( a classification s simple z ! above1 is an impressive fact :i*1 :5 supplem5t$ by ! fur!r fact ( a gradual transition f "o type ( spectrum to ! next1 leaves little room = d\bt t 9 ! />s we h an innum]able ?rong ( individuals belong+ to ! same species b 9 diff]5t /ages ( developm5t1 & t ! sun is only "o ( ^! individuals1 ( some?+ less ?an m$ium size & 9 a /age ( developm5t :i* is n at all peculi>1 s9ce x is %>$ by ne>ly a f\r? ( all ! />s4 #bac4 ,,/> ,,clu/]s4--,9 previ\s *apt]s we h not$ ! ,pleiades & ,prsepe z /> clu/]s visible to ! nak$ eye1 & to !m we may add ! ,hyades1 ne> ,aldeb>an1 & ! little con/ellation ,coma ,b]5ices4 ,b m impressive ?an any ( ^!1 al?\gh visible only 9 a telescope1 is ! spl5did clu/] 9 ,h]cules1 ^: appe>ance 9 a telescope ( mod]ate size is %[n 9 ,fig4 #ace1 :ile ,fig4 #acf is a photograph ( ! same clu/] tak5 ) a v l>ge reflect+ telescope4 ,?is is only a type ( _m telescopic clu/]s :i* are scatt]$ ov] ! sky1 & :i* are made up ( />s pack$ s closely toge!r z to become indi/+ui%able1 "o f ano!r1 at ! c5t] ( ! clu/]4 ,)9 an area :i* c\ld be cov]$ by a ?ird ( ! full moon's face are cr[d$ 9 ?is clu/] m ?an five ?\s& />s :i* are unque/ionably close neighbors1 b ^: app>5t ne>ness to ea* o!r is d\btless due to _! great di/ance f u4 ,x is q probable t ev5 at ! c5t] ( ?is clu/]1 :]e m ?an a ?\s& />s are includ$ )9 a radius ( #afj1 ! actual di/ances sep>at+ adjo9+ />s are mu* great] ?an t sep>at+ e>? & sun1 b f> less ?an t sep>at+ ! sun f its ne>e/ /ell> neighbor4 ,illu/ration3 ,,fig #ace4--,/> clu/] 9 ,h]cules4 ,an int]e/+ discov]y ( rec5t date1 made by ,pr(essor ,bailey 9 photograph+ /> clu/]s1 is t "s few ( !m1 :i* are especially ri* 9 />s1 conta9 an extraord9>y numb] ( v>iable />s1 mo/ly v fa9t & ( %ort p]iod4 ,two clu/]s1 "o 9 ! nor!rn & "o 9 ! s\!rn hemisph]e1 conta9 ea* m ?an a hundr$ v>iables1 & an ev5 m extraord9>y case is pres5t$ by a clu/]1 call$ ,messi] #e1 n f> f ! /> a ,s]p5tis1 :i* conta9s no less ?an sixty-?ree v>iables1 all ab\t ( ! f\rte5? magnitude1 all hav+ light p]iods :i* diff] b little f half a day1 all hav+ light curves ( ab\t ! same %ape1 & all hav+ a range ( brightness f maximum to m9imum ( ab\t "o magnitude4 ,an extraord9>y set ( co9cid5ces :i* po9ts unmi/akably to a common orig9 & cause ( v>iability4 ,illu/ration3 ,,fig4 #acf4--,/> clu/] 9 ,h]cules4--,,keel]4 ,illu/ration3 ,,fig4 #acg4--,! ,&rom$a nebula z se5 9 a v small telescope4 ,illu/ration3 ,,fig4 #ach4--,! ,&rom$a nebula & ,holmes's comet4 ,photograph$ by ,,b>n>d4 ,illu/ration3 ,,fig4 #aci4--;,a draw+ ( ! ,&rom$a nebula4 ,illu/ration3 ,,fig4 #adj4--;,a photograph ( ! ,&rom$a nebula4--,,rob]ts4 #bad4 ,,nebul4--,return+ to ,fig4 #acf1 we note t its backgr\nd has a hazy appe>ance1 & t at its c5t] ! />s c no long] be di/+ui%$1 b bl5d "o ) ano!r s z to appe> l a bright cl\d4 ,! out] "p ( ! clu/] is resolv$ into />s1 :ile 9 ! picture ! inn] portion is n s resolv$1 al?\gh 9 ! orig9al photographic plate ! individual />s c be di/+ui%$ to ! v c5t] ( ! clu/]4 ,9 _m cases1 h[ev]1 ?is is n possible1 & we h an irresolvable clu/] :i* x is cu/om>y to call a nebula 7,lat91 little cl\d74 ,! mo/ conspicu\s example ( ?is 9 ! nor!rn heav5s is ! great nebula 9 ,&rom$a 7,r4 ,a4 #j;h #cgm1 ,dec4 #da71 :i* may be se5 ) ! nak$ eye z a fa9t pat* ( foggy light4 ,look = x4 ,?is appe>s 9 an op]a glass or v small telescope n unlike ,fig4 #acg1 :i* is reproduc$ f a sket*4 ,fig4 #ach is f a photograph ( ! same object %[+ ess5tially ! same %ape z 9 ! prec$+ figure1 b br++ out m detail4 ,note ! two small nebul adjo9+ ! l>ge "o1 & at ! bottom ( ! picture an object :i* might easily be tak5 = ano!r nebula b :i* is 9 fact a tailless comet t *anc$ to be pass+ t "p ( ! sky :5 ! picture 0 tak54 ,fig4 #aci is f ano!r draw+ ( ?is nebula1 al?\gh x is h>dly to be recogniz$ z a repres5tation ( ! same ?+2 b its *>act]i/ic feature1 ! two d>k /reaks ne> ! c5t] ( ! picture1 is ju/ifi$ 9 "p by ,fig4 #adj1 :i* is f a photograph made ) a l>ge reflect+ telescope4 ,illu/ration3 ,,fig4 #ada4--,types ( nebul4 ,a comp>ison ( ^! sev]al repres5tations ( ! same ?+ w s]ve to illu/rate ! vagu5ess ( its outl9es1 & h[ mu* ! impressions to be d]iv$ f nebul dep5d ^u ! telescopes employ$ & ^u ! obs]v]'s own prepossessions4 ,! diff]5ces among ! pictures c n be due to any *ange 9 ! nebula itself1 = half a c5tury ago x 0 sket*$ mu* z %[n 9 ! late/ ( !m 7,fig4 #adj74 ,illu/ration3 ,,fig4 #adb4--,! ,trifid nebula4--,,keel]4 #bae4 ,,typical ,,nebul4--,"s ( ! fanta/ic =ms :i* nebul pres5t 9 ! telescope are %[n on a small scale 9 ,fig4 #ada1 b 9 rec5t ye>s a/ronom]s h le>n$ to place little reliance ^u draw+s su* z ^!1 :i* are n[ almo/ entirely supplant$ by photographs made ) long exposures 9 p[]ful telescopes4 ,"o ( ! mo/ exquisite ( ^! mod]n photographs is t ( ! ,trifid nebula 9 ,sagitt>ius 7,fig4 #adb74 ,note especially ! d>k lanes t give to ?is nebula its "n1 ,trifid1 & :i* run ?r\gh its brighte/ p>ts1 break+ x into seem+ly indep5d5t sections4 ,! area ( ! sky %[n 9 ?is cut is ab\t #ae p] c5t less ?an t cov]$ by ! full moon4 ,illu/ration3 ,,fig4 #adc4--;,a nebula 9 ,cygnus4--,,keel]4 ,fig4 #adc %[s a v diff]5t type ( nebula1 f\nd 9 ! con/ellation ,cygnus1 :i* appe>s made up ( filam5ts closely int]tw9$1 & /ret*es across ! sky = a di/ance consid]ably great] ?an ! moon's diamet]4 ,illu/ration3 ,,fig4 #add4--,spiral nebula 9 ,canes ,v5atici4--,,keel]4 ,a mu* small] b equally /rik+ nebula is t 9 ! con/ellation ,canes ,v5atici 7,fig4 #add71 :i* %[s a mo/ extraord9>y spiral /ructure1 z if ! />s compos+ x 7 fl[+ 9 along curv$ l9es t[>d a c5t] ( cond5sation4 ,! diamet] ( ! circul> "p ( ?is nebula1 omitt+ ! projection t[>d ! bottom ( ! picture1 is ab\t five m9utes ( arc1 a six? "p ( ! diamet] ( ! moon1 & its ?ickness is probably v small comp>$ ) its bread?1 p]haps n mu* exce$+ ! wid? ( ! spiral /reams :i* compose x4 ,note h[ ! bright />s t appe> )9 ! area ( ?is nebula fall on ! /reams ( nebul\s matt] z if !y 7 "p ( !m4 ,?is *>act]i/ic gr\p+ ( ! />s1 :i* is foll[$ 9 _m o!r nebul1 %[s t !y are really "p & p>cel ( ! nebula & n m]ely on l9e ) x4 ,fig4 #ade %[s h[ a great nebula is associat$ ) ! /> r ,ophiu*i4 ,illu/ration3 ,,fig4 #ade4--;,great nebula ab\t ! /> r ,ophiu*i4--,,b>n>d4 ,probably ! mo/ impressive ( all nebul is ! great "o 9 ,orion 7,fig4 #adf71 ^: position is %[n on ! /> map betwe5 ,rigel & z ,orionis4 ,look = x ) an op]a glass or ev5 ) ! unaid$ eye4 ,?is is sometimes call$ an amorph\s--i4 e41 %apeless--nebula1 because x pres5ts no def9ite =m :i* ! eye c grasp & little trace ( /ructure or organization4 ,x is )\t =m & void at lea/ 9 its c5tral portions1 al?\gh on its edges curv$ filam5ts may be trac$ /ream+ away f ! bright] p>ts ( ! c5tral region4 ,?is nebula1 z %[n 9 ,fig4 #adf1 cov]s an area ab\t equal to t ( ! full moon1 )\t c\nt+ z any "p ( ?is ! companion nebula %[n at "o side1 b photographs made ) suitable exposures %[ t fa9t outly+ p>ts ( ! nebula ext5d 9 curv$ l9es ov] ! l>g] "p ( ! con/ellation ,orion4 ,inde$1 ov] a l>ge "p ( ! entire sky ! backgr\nd is fa9tly cov]$ ) nebul\s light ^: bright] portions1 if ea* 7 c\nt$ z a sep>ate nebula1 w\ld c>ry ! total numb] ( su* objects well into ! hundr$s ( ?\s&s4 ,illu/ration3 ,,fig4 #adf4--,! ,orion nebula4 ,! ,pleiades 7,plate ,,iv7 pres5t a case ( a resolvable /> clu/] project$ aga9/ su* a nebul\s backgr\nd ^: v>y+ int5sity %\ld be not$ 9 ! figure4 ,a "p ( ?is nebul\s matt] is %[n 9 wisps ext5d+ f "o /> to ! next1 aft] ! fa%ion ( a bridge1 & leav+ little d\bt t ! nebula is actually a "p ( ! clu/] & n m]ely a backgr\nd = x4 ,illu/ration3 ,,! ,,pleiades 7,,aft] ,a ,,photograph7 ,fig4 #adg %[s a s]ies ( s-call$ d\ble nebul p]haps comp>able ) d\ble />s1 al?\gh ! mo/ rec5t photographic "w seems to indicate t !y are really fa9t spiral nebul 9 :i* only ! brighte/ p>ts are %[n by ! telescope4 ,accord+ to ,keel]1 ! spiral is ! prevail+ type ( nebul1 & :ile ,fig4 #add pres5ts ! mo/ p]fect example ( su* a nebula1 ! /ud5t %\ld n fail to note t ! ,&rom$a nebula 7,fig4 #adj7 %[s di/9ct traces ( a spiral /ructure1 only "h we d n see its true %ape1 ! nebula be+ turn$ ne>ly edgewise t[>d u s t its presumably circul> outl9e is =e%ort5$ into a n>r[ ellipse4 ,illu/ration3 ,,fig4 #adg4--;,d\ble nebul4 ,,h]s*el4 ,ano!r type ( nebula ( "s consequ5ce pres5ts 9 ! telescope r\nd disks l ^? ( ,uranus or ,neptune1 & ?is appe>ance has giv5 !m ! "n planet>y nebul4 ,! comet 9 ,fig4 #ach1 if small]1 w\ld repres5t fairly well ! nebul ( ?is type4 ,sometimes a planet>y nebula has a /> at its c5t]1 & sometimes x appe>s holl[1 l a smoke r+1 & is !n call$ a r+ nebula4 ,! mo/ fam\s ( ^! is 9 ! con/ellation ,lyra1 n f> f ,vega4 #baf4 ,,spectra ,,( ,,nebul4--,a /> clu/]1 l ! "o 9 ,h]cules1 %[s1 ( c\rse1 /ell> spectra1 & ev5 :5 irresolvable ! spectrum is a cont9u\s "o1 te/ify+ to ! pres5ce ( />s1 al?\gh !y /& too close toge!r to be sep>ately se54 ,b 9 a c]ta9 numb] ( nebul ! spectrum is altoge!r diff]5t1 a discont9u\s "o conta9+ only a few bright l9es1 %[+ t "h ! nebul> light comes f gl[+ gases :i* are subject to no consid]able pressure4 ,! planet>y nebul all h spectra ( ?is k9d & make up ab\t half ( all ! kn[n gase\s nebul4 ,x is wor?y ( note t a c5tury ago ,sir ,william ,h]s*el _h obs]v$ a gre5 %imm] 9 ! light ( c]ta9 nebul :i* l$ him to believe t !y 7 n ( a />ry nature1 a conclusion :i* has be5 abundantly confirm$ by ! spectroscope4 ,! gre5 %imm] is1 9 fact1 caus$ by a l9e 9 ! gre5 "p ( ! spectrum t is always pres5t & is always ! brighte/ "p ( ! spectrum ( gase\s nebul4 ,9 fa9t nebul ?is l9e con/itutes ! :ole ( _! visible spectrum1 b 9 bright] ones two or ?ree o!r & fa9t] l9es are usually associat$ ) x1 & a v bright nebula1 l t 9 ,orion1 may %[ a consid]able numb] ( extra l9es1 b = ! mo/ "p !y c n be id5tifi$ 9 ! spectrum ( any t]re/rial sub/ances4 ,an exception to ?is is f\nd 9 ! hydrog5 l9es1 :i* are well m>k$ 9 mo/ spectra ( gase\s nebul1 & !re are indications ( "o or two o!r kn[n sub/ances4 #bag4 ,,d5sity ,,( ,,nebul4--,x is kn[n f laboratory exp]im5ts t dim9i%+ ! pressure to :i* an inc&esc5t gas is subject1 dim9i%es ! numb] ( l9es conta9$ 9 its spectrum1 & we may surmise f ! v simple "* & few l9es ( ^! nebul> spectra t ! gas :i* produces !m has a v small d5sity4 ,b ?is is f> f %[+ t ! nebula itself is correspond+ly att5uat$1 = we mu/ n assume t ?is %9+ gas is all t exi/s 9 ! nebula2 s f> z telescope or cam]a are conc]n$1 !re may be associat$ ) x any am\nt ( d>k matt] :i* c n be se5 because x s5ds to u no light4 ,x is easy to ?9k 9 ?is connection ( meteoric du/ or ! /uff ( :i* comets are made1 = ^! seem to be scatt]$ broadca/ on e side ( ! sol> sy/em & may1 p]*ance1 ext5d out to ! region ( ! nebul4 ,b1 :atev] may be associat$ 9 ! nebula ) ! gl[+ gas :i* we see1 ! total am\nt ( matt]1 invisible z well z visible1 mu/ be v small1 or r its av]age d5sity mu/ be v small1 = ! space occupi$ by su* a nebula z t ( ,orion is s great t if ! av]age d5sity ( its matt] 7 equal to t ( air ! result+ mass by its attraction w\ld ex]t a s5sible effect ^u ! motion ( ! sun ?r\gh space4 ,! bright] p>ts ( ?is nebula z se5 f ! e>? subt5d an angle ( ab\t half a degree1 & :ile we "k no?+ ( its di/ance f u1 x is easy to see t ! f>!r x is away ! great] mu/ be its real dim5sions1 & t ?is increase ( bulk & mass ) increas+ di/ance w j comp5sate ! dim9i%+ int5sity ( gravity at great di/ances1 s t = a giv5 angul> diamet]--e4 g41 half a degree--! =ce ) :i* ?is nebula attracts ! sun dep5ds ^u its d5sity b n at all ^u its di/ance4 ,n[1 ! nebula mu/ attract ! sun 9 "s degree1 & mu/ t5d to move x & ! planets 9 an orbit ab\t ! attract+ c5t] s t ye> aft] ye> we %\ld see ! nebula f slightly diff]5t po9ts ( view1 & ?is *ang$ po9t ( view %\ld produce a *ange 9 ! app>5t direction ( ! nebula f u--i4 e41 a prop] motion1 ^: am\nt w\ld dep5d ^u ! attract+ =ce1 & !re=e ^u ! d5sity ( ! attract+ matt]4 ,obs]vations ( ! ,orion nebula %[ t its prop] motion is :olly inappreciable1 c]ta9ly f> less ?an half a second ( arc p] ye>1 & correspond+ to ?is am\nt ( prop] motion ! mean d5sity ( ! nebula mu/ be "s millions ( times 7#ajaj accord+ to ,rany>d7 less ?an t ( air at sea level--i4 e41 ! av]age d5sity ?r\gh\t ! nebula is comp>able ) t ( ^? upp] p>ts ( ! e>?'s atmosph]e 9 :i* meteors fir/ become visible4 #bah4 ,,motion ,,( ,,nebul4--,! extreme m9ut5ess ( _! prop] motions is a *>act]i/ic feature ( all nebul4 ,inde$1 !re is h>dly a kn[n case ( s5sible prop] motion ( "o ( ^! bodies1 al?\gh a doz5 or m ( !m %[ velocities 9 ! l9e ( sight rang+ 9 am\nt f #cj to -#dj miles p] second1 ! plus sign indicat+ an increas+ di/ance4 ,:ile a "p ( ^! velocities may be only app>5t & due to ! motion ( e>? & sun ?r\gh space1 a "p at lea/ is real motion ( ! nebul !mselves4 ,^! seem to move ?r\gh ! cele/ial spaces 9 mu* ! same way & ) ! same velocities z d ! />s1 & _! small] prop] motions across ! l9e ( sight 7angul> motions7 are an index ( _! great di/ance f u4 ,no "o has ev] succe$$ 9 measur+ ! p>allax ( a nebula or /> clu/]4 ,illu/ration3 ,,fig4 #adh4--;,a "p ( ! ,milky ,way4 ,! law ( gravitation presumably holds sway )9 ^! bodies1 & ! fact t _! sev]al p>ts & ! />s :i* are involv$ )9 !m1 al?\gh attract$ by ea* o!r1 h %[n little or no *ange ( position dur+ ! pa/ c5tury1 is fur!r evid5ce ( _! l[ d5sity & feeble attraction4 ,9 a few cases1 h[ev]1 !re seem to be 9 progress )9 a nebula *anges ( brightness1 s t :at 0 =m]ly a fa9t "p has become a bright] "o1 or vice v]sa2 b1 on ! :ole1 ev5 ^! *anges are v small4 ,illu/ration3 ,,fig4 #adi4--,! ,milky ,way ne> ? ,ophiu*i4--,,b>n>d4 #bai4 ,,! ,,milky ,,way4--,closely relat$ to nebul & /> clu/]s is ano!r feature ( ! sky1 ! galaxy or ,milky ,way1 ) ^: appe>ance to ! unaid$ eye ! /ud5t %\ld become famili> by direct /udy ( ! ?+ itself4 ,figs4 #adh & #adi are f photographs ( two small p>ts ( x1 & s]ve to br+ out ! small />s ( :i* x is compos$4 ,e /> %[n 9 ^! pictures is invisible to ! nak$ eye1 al?\gh _! comb9$ light is easily se54 ,! g5]al c\rse ( ! galaxy across ! heav5s is %[n 9 ! /> maps1 b ^! conta9 no indication ( ! weal? ( detail :i* ev5 ! nak$ eye may detect 9 x4 ,bright & fa9t p>ts1 d>k rifts :i* cut x into segm5ts1 "h & !re a hole z if ! ribbon ( light _h be5 %ot away--su* are "s ( ! features to be f\nd by att5tive exam9ation4 ,illu/ration3 ,,fig4 #aej4--,! ,milky ,way ne> b ,cygni4--,,b>n>d4 ,speak+ g5]ally1 ! c\rse ( ! ,milky ,way is a great circle completely girdl+ ! sky & hav+ its nor? pole 9 ! con/ellation ,coma ,b]5ices4 ,! wid? ( ?is /ream ( light is v diff]5t 9 diff]5t p>ts ( ! heav5s1 am\nt+ :]e x is wide/1 9 ,lyra & ,cygnus1 to some?+ m ?an #cj1 al?\gh its b\nd>ies are too vague & ill def9$ to p]mit mu* accuracy ( measurem5t4 ,obs]ve ! v bright "p betwe5 b & g ,cygni1 ne>ly opposite ,vega1 & note h[ ev5 an op]a glass w p>tially resolve ! nebul\s light into a great numb] ( />s1 :i* are "h r bright] ?an 9 o!r p>ts ( its c\rse4 ,b ! resolution into />s is only p>tial1 & !re /ill rema9s a backgr\nd ( unresolv$ %imm]4 ,fig4 #aej is a photograph ( a small "p ( ?is region 9 :i*1 al?\gh ea* fleck ( light repres5ts a sep>ate />1 ! galaxy is n completely resolv$4 ,comp>e ) ?is region1 ri* 9 />s1 ! ne>ly empty space betwe5 ! bran*es ( ! galaxy a little we/ ( ,altair4 ,ano!r hole 9 ! ,milky ,way may be f\nd a little nor? & ea/ ( a ,cygni1 & betwe5 ! extremes ( abundance & pov]ty "h not$ !re may be f\nd e gradation ( nebul\s light4 ,! ,milky ,way is n s simple 9 its /ructure z might at fir/ be ?\ght1 b a cle> & moonless night is requir$ to br+ out its details4 ,! nature ( ^! details1 ! /ructure ( ! galaxy1 its %ape & ext5t1 ! arrangem5t ( its p>ts1 & _! relation to />s & nebul 9 g5]al1 h be5 subjects ( mu* speculation by a/ronom]s & o!rs :o h s\ght to trace out 9 ?is way :at is call$ ! con/ruction ( ! heav5s4 #bbj4 ,,di/ribution ,,( ,,! ,,/>s4--,h[ f> out into space d ! />s ext5d8 ,are !y limit$ or inf9ite 9 numb]8 ,d !y =m a sy/em ( mutually relat$ p>ts1 or are !y bun*$ promiscu\sly1 ea* = itself1 )\t ref]5ce to ! o!rs8 ,"h is :at has be5 well call$ ! mo/ important problem ( /ell> a/ronomy1 ! acquisition ( well-f\nd$ ideas ab\t ! di/ribution ( ! />s4 ,:ile _m ( ! ideas ^u ?is subject :i* h be5 advanc$ by em95t a/ronom]s & :i* are /ill curr5t 9 ! books are c]ta9ly wrong1 & few ( _! speculations along ?is l9e are demon/rably true1 ! !me itself is ( su* gr&eur & p]man5t int]e/ z to dem& at lea/ a brief consid]ation4 ,b be=e proce$+ to its speculative side we ne$ to collect facts ^u :i* to build1 & ^!1 h[ev] inadequate1 are 9 ! ma9 simple & n f> to seek4 ,p>allaxes1 prop] motions1 motions 9 ! l9e ( sight1 :ile p]t95t to ! problem ( /ell> di/ribution1 are ( small avail1 s9ce !y are f> too scanty 9 numb] & relate only to limit$ classes ( />s1 usually ! v bright ones or ^? ne>e/ to ! sun4 ,almo/ ! sole available data are conta9$ 9 ! brightness ( ! />s & ! way 9 :i* !y seem scatt]$ 9 ! sky4 ,! mo/ casual survey ( ! heav5s is en\gh to %[ t ! />s are n ev5ly spr9kl$ ^u x4 ,! lucid />s are abundant 9 "s regions1 few 9 o!rs1 & ! labori\s /> gauges1 actual c\nt+ ( ! />s 9 sample regions ( ! sky1 :i* h be5 made by ! ,h]s*els1 ,celoria1 & o!rs1 suffice to %[ t ?is lack ( uni=mity 9 di/ribution is ev5 m m>k$ly true ( ! telescopic />s4 ,! rate ( increase 9 ! numb] ( />s f "o magnitude to ! next1 z %[n 9 #ahg1 is pro( ( ano!r k9d ( irregul>ity 9 _! di/ribution4 ,x is n difficult to %[1 ma!matically1 t if 9 di/ant regions ( space ! />s 7 on ! av]age z num]\s & z bright z !y are 9 ! regions ne>] to ! sun1 !n ! />s ( any p>ticul> magnitude ought to be f\r times z num]\s z ^? ( ! next bright] magnitude--e4 g41 f\r times z _m six?-magnitude />s z !re are fif?-magnitude ones4 ,b1 z we h already se5 9 #ahg1 by actual c\nt !re are only ?ree times z _m1 & f ! discrepancy betwe5 ^! numb]s1 an actual ?reefold increase in/ead ( a f\rfold "o1 we mu/ conclude t on ! :ole ! />s ne> ! sun are ei!r bigg] or bright] or m num]\s ?an 9 ! remot] dep?s ( space4 #bba4 ,,! ,,/ell> ,,sy/em4--,b ! arrangem5t ( ! />s is n altoge!r lawless & *aotic2 !re are traces ( ord] & sy/em1 & among ^! ! ,milky ,way is ! dom9ant feature4 ,telescope & photographic plate alike %[ t x is made up ( />s :i*1 al?\gh q irregul>ly scatt]$ along its c\rse1 are on ! av]age "s tw5ty times z num]\s 9 ! galaxy z at its poles1 & :i* ?9 out z we rec$e f x on ei!r side1 at fir/ rapidly & !n m sl[ly4 ,?is t5d5cy to clu/] along ! ,milky ,way is mu* m pron\nc$ among ! v fa9t telescopic />s ?an among ! bright] ones1 = ! lucid />s & ! telescopic ones d[n to ! t5? or elev5? magnitude1 :ile v pla9ly %[+ ! clu/]+ t5d5cy1 are n m ?an ?ree times z num]\s 9 ! galaxy z 9 ! con/ellations mo/ remote f x4 ,x is rem>kable z %[+ ! cond5sation ( ! brighte/ />s t "o half ( all ! />s 9 ! sky :i* are bright] ?an ! second magnitude are includ$ )9 a belt ext5d+ #ab on ei!r side ( ! c5t] l9e ( ! galaxy4 ,9 addition to ?is g5]al cond5sation ( />s t[>d ! ,milky ,way1 !re are peculi>ities 9 ! di/ribution ( c]ta9 classes ( />s :i* are wor? att5tion4 ,planet>y nebul & new />s are seldom1 if ev]1 f\nd f> f ! ,milky ,way1 & />s ) bright l9es 9 _! spectra especially affect ?is region ( ! sky4 ,/>s ) spectra ( ! fir/ type--,sirian />s--are mu* m /rongly cond5s$ t[>d ! ,milky ,way ?an are />s ( ! sol> type1 & 9 consequ5ce ( ?is ! ,milky ,way is peculi>ly ri* 9 light ( %ort wave l5g?s4 ,resolvable /> clu/]s are s mu* m num]\s 9 ! galaxy ?an else:]e1 t its c\rse across ! sky w\ld be pla9ly indicat$ by _! gr\p+ ^u a map %[+ no?+ b clu/]s ( ?is k9d4 ,on ! o!r h&1 nebul z a class %[ a di/9ct av]sion = ! galaxy1 & are f\nd mo/ abundantly 9 ^? p>ts ( ! sky f>!/ f x1 mu* z if !y repres5t$ raw mat]ial :i* 0 lack+ along ! ,milky ,way1 because already work$ up to make ! />s :i* are !re s num]\s4 #bbb4 ,,relation ,,( ,,! ,,sun ,,to ,,! ,,milky ,,way4--,! fact t ! galaxy is a great circle ( ! sky1 b only ( mod]ate wid?1 %[s t x is a widely ext5d$ & comp>atively ?9 /ratum ( />s )9 :i* ! sol> sy/em lies1 a memb] ( ! galactic sy/em1 & probably n v f> f its c5t]4 ,?is position1 h[ev]1 is n to be look$ ^u z a p]man5t "o1 s9ce ! sun's motion1 :i* lies ne>ly 9 ! plane ( ! ,milky ,way1 is ceaselessly alt]+ its relation to ! c5t] ( t sy/em1 & may ultimately c>ry u outside its limits4 ,! ,milky ,way itself is commonly ?\ght to be a r+1 or s]ies ( r+s1 l ! coils ( ! great spiral nebula 9 ,&rom$a1 & sep>at$ f u by a space f> great] ?an ! ?ickness ( ! r+ itself4 ,note 9 ,figs4 #adi & #aej h[ ! backgr\nd is made up ( bright & d>k p>ts curi\sly int]lac$1 & pres5t+ mu* ! appe>ance ( a ?9 %eet ( cl\d ?r\gh :i* we look to b>r5 space beyond4 ,:ile1 ma!matically1 ?is appe>ance c n be consid]$ z pro( t ! galaxy is 9 fact a di/ant r+1 r ?an a %eet ( />ry matt] /ret*+ cont9u\sly f ! ne>] /ell> neighbors ( ! sun into ! remote/ dep?s ( space1 nev]!less1 mo/ /ud5ts ( ! "q hold x to be su* a r+ ( />s1 :i* are relatively close toge!r :ile its c5t] is comp>atively vacant1 al?\gh ev5 "h are "s hundr$s ( ?\s&s ( />s :i* on ! :ole h a t5d5cy to clu/] ne> its plane & to cr[d toge!r a little m d5sely ?an else:]e 9 ! region :]e ! sun is plac$4 #bbc4 ,,dim5sions ,,( ,,! ,,galaxy4--,! dim5sions ( ?is /ell> sy/em are :olly unkn[n1 b !re c be no d\bt t x ext5ds f>!r 9 ! plane ( ! ,milky ,way ?an at "r angles to t plane1 = />s ( ! fifte5? & sixte5? magnitudes are common 9 ! galaxy1 & te/ify by _! feeble light to _! great di/ance f ! e>?1 :ile ne> ! poles ( ! ,milky ,way !re seem to be few />s fa9t] ?an ! twelf? magnitude4 ,h]s*el1 ) 8 telescope ( #ah in*es ap]ture1 c\ld c\nt 9 ! ,milky ,way m ?an a doz5 times z _m />s p] squ>e degree z c\ld ,celoria ) a telescope ( #d in*es ap]ture2 b ar\nd ! poles ( ! galaxy ! two telescopes %[$ practically ! same numb] ( />s1 indicat+ t "h ev5 ! small] telescope rea*$ to ! limits ( ! /ell> sy/em4 ,v rec5tly1 inde$1 ! telescope ) :i* ,fig4 #adj 0 photograph$ seems to h rea*$ ! f>!/ limit ( ! ,milky ,way1 = on a photographic plate ( "o ( its ri*e/ regions ,rob]ts f9ds x completely resolv$ into />s :i* /& out ^u a black backgr\nd ) no trace ( nebul\s light betwe5 !m4 #bbd4 ,,beyond ,,! ,,milky ,,way4--,ea* additional /ep into ! dep?s ( space br+s u into a region ( :i* less is kn[n1 & :at lies beyond ! ,milky ,way is l>gely a matt] ( conjecture4 ,we %r9k f ?9k+ x an inf9ite void1 endless empt9ess1 & our intellectual sympa?ies g out to ,lamb]t's speculation ( a univ]se fill$ ) /ell> sy/ems1 ( :i* ours1 b\nd$ by ! galaxy1 is only "o4 ,!re is1 inde$1 little direct evid5ce t o!r su* sy/ems exi/1 b ! ,&rom$a nebula is n altoge!r unlike a galaxy ) a c5tral cl\d ( />s1 & 9 ! s\!rn hemisph]e1 invisible 9 our latitudes1 are two rem>kable /ell> bodies l ! ,milky ,way 9 appe>ance1 b cut (f f all app>5t connection ) x1 mu* z we might expect to f9d indep5d5t /ell> sy/ems1 if su* !re be4 ,^! two bodies are kn[n z ! ,magellanic cl\ds1 & individually be> ! names ( ,major & ,m9or ,nubecula4 ,accord+ to ,sir ,john ,h]s*el1 ! ,nubecula ,major1 l ! ,m9or1 consi/s p>tly ( l>ge tracts & ill-def9$ pat*es ( irresolvable nebula1 & ( nebulosity 9 e /age ( resolution up to p]fectly resolv$ />s l ! ,milky ,way1 z also ( regul> & irregul> nebul 444 ( globul> clu/]s 9 e /age ( resolvability1 & ( clu/]+ gr\ps suffici5tly insulat$ & cond5s$ to come "u ! designation ( clu/]s ( />s4 ,its outl9es are vague & some:at unc]ta91 b surely include an area ( m ?an #dj squ>e degrees--i4 e41 z mu* z ! b[l ( ! ,big ,dipp]--& )9 ?is area ,h]s*el c\nt$ sev]al hundr$ nebul & clu/]s :i* f> exce$s any?+ t is to be met ) 9 any o!r region ( ! heav5s4 ,al?\gh its excessive complexity ( detail baffl$ ,h]s*el's attempts at arti/ic del9eation1 x has yield$ to ! mod]n photographic processes1 :i* %[ ! ,nubecula ,major to be an enorm\s spiral nebula made up ( subord9ate />s1 nebul1 & clu/]s1 z is ! ,milky ,way4 ,comp>$ ) ! ,&rom$a nebula1 its great] angul> ext5t sugge/s a small] di/ance1 al?\gh = ! pres5t all ef=ts at det]m9+ ! p>allax ( ei!r seem hopeless4 ,b ! spiral =m :i* is common to bo? sugge/s t ! ,milky ,way itself may be a gigantic spiral nebula ne> ^: c5t] lies ! sun1 a humble memb] ( a great clu/] ( />s :i* is r\ghly globul> 9 %ape1 b flatt5$ at ! poles ( ! galaxy & completely encircl$ by its coils4 ,h[ev] plausible su* a view may appe>1 x is = ! pres5t1 at lea/1 pure hypo!sis1 al?\gh vigor\sly advocat$ by ,ea/on1 :o bases 8 argum5t ^u ! appe>ance ( ! galaxy itself4 #bbe4 ,,absorption ,,( ,,/>light4--,we h _h abundant occasion to le>n t at lea/ )9 ! conf9es ( ! sol> sy/em meteoric matt]1 cosmic du/1 is pr(usely scatt]$1 & x appe>s n improbable t ! same is true1 al?\gh 9 small] degree1 9 ev5 ! remot] p>ts ( space4 ,9 ?is case ! light :i* comes f ! f>!r />s ov] a pa? requir+ _m c5turies to travel1 mu/ be 9 "s measure absorb$ & enfeebl$ by ! ob/acles :i* x enc\nt]s on ! way4 ,unless cele/ial space is transp>5t to an improbable degree ! remot] />s d n %[ _! true brightness2 !re is a c]ta9 limit beyond :i* no /> is able to s5d its light1 & beyond :i* ! univ]se mu/ be to u a blank4 ,a ligh?\se ?r[s into ! fog its beams only to h !m ext+ui%$ be=e a s+le mile is pass$1 & ?\gh ! cele/ial lights %9e f>!r1 a limit to _! rea* is none ! less c]ta9 if meteoric du/ exi/s outside ! sol> sy/em4 ,if !re is su* an absorption ( light 9 space1 z seems plausible1 ! univ]se may well be limitless & ! numb] ( /ell> sy/ems inf9ite1 al?\gh ! mo/ att5uat$ ( du/ cl\ds suffices to conceal f u & to %ut (f f our inve/igation all save a m9or fraction ( x & !m4 ,,*apt] ,,xv ,,gr[? ,,& ,,decay #bbf4 ,,nature ,,( ,,! ,,problem4--,to use a common figure ( spee*1 ! univ]se is alive4 ,we h f\nd x fill$ ) an activity t manife/s itself n only 9 ! motions ( ! heav5ly bodies along _! orbits1 b :i* ext5ds to _! m9ute/ p>ts1 ! molecules & atoms1 ^: vibrations furni% ! radiant en]gy giv5 (f by sun & />s4 ,"s ( ^! activities1 su* z ! motions ( ! heav5ly bodies 9 _! orbits1 seem fitt$ to be ( endless duration2 :ile o!rs1 l ! radiation ( light & heat1 are surely tempor>y1 & soon] or lat] mu/ come to an end & be replac$ by some?+ diff]5t4 ,! /udy ( ?+s z !y are ?us leads inevitably to que/ions ( :at has be5 & :at is to be4 ,a s\nd sci5ce %\ld furni% "s acc\nt ( ! univ]se ( ye/]day & to-morr[ z well z ( to-day1 & we ne$ n %r9k f su* que/ions1 al?\gh answ]s to !m mu/ be vague & 9 great measure speculative4 ,! hi/orian ( ,am]ica f9ds little difficulty ) ev5ts ( ! n9ete5? c5tury or ev5 ! eighte5?1 b ! s\rces ( in=mation ab\t ,am]ica 9 ! fifte5? c5tury are mu* less def9ite2 ! t5? c5tury pres5ts almo/ a blank1 & ! hi/ory ( ,am]ican mank9d 9 ! fir/ c5tury ( ! ,*ri/ian era is :olly unkn[n4 ,s1 z we attempt to look into ! pa/ or ! future ( ! heav5s1 we mu/ expect to f9d ! mi/s ( obscurity gr[ d5s] ) remot] p]iods until ev5 ! vague/ outl9es ( its developm5t are lo/1 & we are compell$ to say1 beyond ?is lies ! unkn[n4 ,our acc\nt ( gr[? & decay 9 ! univ]se1 !re=e1 c n aspire to cov] ! :ole duration ( ?+s1 b mu/ be limit$ 9 its scope to c]ta9 *apt]s ^: epo*s lie ne> to ! "t 9 :i* we live1 & ev5 = ^! we ne$ to be> con/antly 9 m9d ! logical bases ( su* an inquiry & ! limitations :i* !y impose ^u u4 #bbg4 ,,logical ,,bases ,,& ,,limitations4--,! fir/ ( ^! bases is3 ,an adequate k ( ! pres5t univ]se4 ,our only hope ( read+ ! pa/ & future lies 9 an und]/&+ ( ! pres5t2 n necess>ily a complete k ( x1 b "o :i* is s\nd s f> z x goes4 ,our position is l t ( a detective :o is call$ ^u to unravel a my/]y or crime1 & :o mu/ comm5ce ) ! traces t h be5 left beh9d 9 its commission4 ,! foot pr9t1 ! blood /a91 ! brok5 glass mu/ be exam9$ & comp>$1 & fa%ion$ into a !ory ( h[ !y came to be2 & z a wrong und]/&+ ( ^! elem5ts is sure to vitiate ! !ories bas$ ^u !m1 s a false sci5ce ( ! univ]se z x n[ is1 w surely give a false acc\nt ( :at x has be52 :ile a correct b incomplete k ( ! pres5t does n :olly b> an und]/&+ ( ! pa/1 b only puts u 9 ! position ( ! detective :o correctly und]/&s :at he sees b fails to take note ( o!r facts :i* might greatly aid him4 ,! second basis ( our inquiry is3 ,! assum$ p]man5ce ( natural laws4 ,! law ( gravitation c]ta9ly held true a c5tury ago z well z a ye> ago1 & = aught we "k to ! contr>y x may h be5 a law ( ! univ]se = untold millions ( ye>s2 b t x has prevail$ = s long a "t is a pure assumption1 al?\gh a necess>y "o = our purpose4 ,s ) ^? o!r laws ( ma!matics & me*anics & physics & *emi/ry to :i* we mu/ appeal2 if !re 0 ev] a "t or place 9 :i* !y did n hold true1 t "t & place lie beyond ! scope ( our inquiry1 & are 9 ! doma9 inaccessible to sci5tific rese>*4 ,x is = ?is reason t sci5ce kn[s no?+ & c "k no?+ ( a creation or an end ( ! univ]se1 b consid]s only its ord]ly developm5t )9 limit$ p]iods ( "t4 ,:at k9d ( a pa/ univ]se w\ld1 "u ! op]ation ( kn[n laws1 develop into ! pres5t "o1 is ! "q ) :i* we h to deal1 & ( x we may say ) ,helmholtz3 ,f ! /&po9t ( sci5ce ?is is no idle speculation b an inquiry conc]n+ ! limitations ( its me?ods & ! scope ( its kn[n laws4 ,to f]ret out ! processes by :i* ! heav5ly bodies h be5 br\ght to _! pres5t condition we seek fir/ ( all = l9es ( developm5t n[ 9 progress :i* t5d to *ange ! exi/+ ord] ( ?+s into some?+ diff]5t1 &1 hav+ f\nd ^!1 to trace _! effects into bo? pa/ & future4 ,any =ce1 h[ev] small1 or any process1 h[ev] sl[1 may produce great results if x works always & ceaselessly 9 ! same direction1 & x is 9 ^! processes1 ^: tr5d is nev] rev]s$1 t we f9d a p>tial clew to bo? pa/ & future4 #bbh4 ,,! ,,sun',s ,,developm5t4--,! fir/ ( ^! to claim our att5tion is ! %r9k+ ( ! sun's diamet] :i*1 z we h se5 9 ,*apt] ,x1 is ! means by :i* ! sol> output ( radiant en]gy is ma9ta9$ f ye> to ye>4 ,its am\nt1 only a few feet p] annum1 is f> too small to be measur$ ) any telescope2 b x is cumulative1 work+ c5tury aft] c5tury 9 ! same direction1 &1 giv5 "t en\gh1 x w produce 9 ! future1 & mu/ h produc$ 9 ! pa/1 enorm\s trans=mations 9 ! sun's bulk & equally significant *anges 9 its physical condition4 ,?us1 z we attempt to trace ! sun's hi/ory into ! pa/1 ! f>!r back we g ! great] %all we expect to f9d its diamet] & ! great] ! space 7volume7 ?r\gh :i* its molecules are spread4 ,by reason ( ?is expansion its d5sity mu/ h be5 less !n ?an n[1 & by go+ f> en\gh back we may ev5 rea* a "t at :i* ! d5sity 0 comp>able ) :at we f9d 9 ! nebul ( to-day4 ,if our ideas ( ! sun's pres5t me*anism are s\nd1 !n1 z a necess>y consequ5ce ( ^!1 its pa/ c>e] mu/ h be5 a process ( cond5sation 9 :i* its compon5t p>ticles 7 ye> by ye> pack$ clos] toge!r by _! own attraction = ea* o!r4 ,z we h se5 9 #abf1 ?is cond5sation necess>ily develop$ heat1 a "p ( :i* 0 radiat$ away z fa/ z produc$1 :ile ! rema9d] 0 /or$ up1 & s]v$ to raise ! temp]ature ( ! sun to :at we f9d x n[4 ,at ! pres5t "t ?is temp]ature is a *ief ob/acle to fur!r %r9kage1 & s p[]fully opposes ! gravitative =ces z to ma9ta9 ne>ly an equilibrium ) !m1 ?us caus+ a v sl[ rate ( fur!r cond5sation4 ,b x is n probable t ?is 0 always s4 ,9 ! e>ly /ages ( ! sun's hi/ory1 :5 ! temp]ature 0 l[1 contraction ( its bulk mu/ h be5 m rapid1 & attempts h be5 made by ! ma!maticians to measure its rate ( progress & to det]m9e h[ long a "t has be5 consum$ 9 ! developm5t ( ! pres5t sun f a primitive nebul\s condition 9 :i* x fill$ a space ( great] diamet] ?an ,neptune's orbit4 ,( c\rse1 num]ical precision is n to be expect$ 9 results ( ?is k9d1 b1 f a consid]ation ( ! greate/ am\nt ( heat t c\ld be furni%$ by ! %r9kage ( a mass equal to t ( ! sun1 x seems t ! p]iod ( ?is developm5t is to be measur$ 9 t5s ( millions or possibly hundr$s ( millions ( ye>s1 b almo/ c]ta9ly does n rea* a ?\s& millions4 #bbi4 ,,! ,,sun',s ,,future4--,! future duration ( ! sun z a s\rce ( radiant en]gy is surely to be measur$ 9 f> small] numb]s ?an ^!4 ,its c>e] z a disp5s] ( light & heat is mu* m ?an half sp5t1 = ! %r9kage results 9 an ev]-increas+ d5sity1 :i* makes its gase\s sub/ance approximate m & m t[>d ! behavior ( a liquid or solid1 & we recall t ^! =ms ( matt] c n by any fur!r cond5sation re/ore ! heat ^: loss ?r\gh radiation caus$ !m to contract4 ,!y may cont9ue to %r9k1 b _! temp]ature mu/ fall1 & :5 ! sun's sub/ance becomes too d5se to obey ! laws ( gase\s matt] its surface mu/ cool rapidly z a consequ5ce ( ! radiation into surr\nd+ space1 & mu/ congeal into a cru/ :i*1 al?\gh at fir/ inc&esc5t1 w spe$ily become d>k & opaque1 cutt+ (f ! light ( ! c5tral portions1 save z x may be r5t f "t to "t by volcanic outbur/s ( ! /ill inc&esc5t mass b5ea?4 ,b su* outbur/s c be ( %ort duration only1 & its f9al condition mu/ be t ( a d>k body1 l ! e>? or moon1 no long] available z a s\rce ( radiant en]gy4 ,ev5 be=e ! =mation ( a solid cru/ x is q possible t ! output ( light & heat may be s]i\sly dim9i%$ by ! =mation ( d5se vapors completely en%r\d+ x1 z is n[ ! case ) ,jupit] & ,saturn4 ,x is believ$ t ^! planets 7 =m]ly inc&esc5t1 & at ! pres5t "t are 9 a /ate ( developm5t ?r\gh :i* ! e>? has pass$ & t[>d :i* ! sun is mov+4 ,accord+ to ,newcomb1 ! future dur+ :i* ! sun c cont9ue to furni% light & heat at its pres5t rate is n likely to exce$ #aj1jjj1jjj ye>s4 ,?is idea ( ! sun z a develop+ body ^: pres5t /ate is only tempor>y1 furni%es a clew to "s ( ! vex+ problems ( sol> physics4 ,?us ! sun-spot p]iod1 ! di/ribution ( ! spots 9 latitude1 & ! peculi> law ( rotation ( ! sun 9 diff]5t latitudes1 may be1 & v probably are1 results n ( any?+ n[ op]at+ b5ea? its photosph]e1 b ( some?+ :i* happ5$ to x 9 ! remote pa/--e4 g41 an unsymmetrical %r9kage or possibly a collision ) "s o!r body4 ,at sea ! waves cont9ue to toss long aft] ! /orm :i* produc$ !m has disappe>$1 &1 accord+ to ! ma!matical rese>*es ( ,wils+1 a pr(\nd agitation ( ! sun's mass might well require t5s ( ?\s&s1 or ev5 hundr$s ( ?\s&s ( ye>s to subside1 & dur+ ?is "t its effects w\ld be visible1 l ! waves1 z ph5om5a = :i* ! actual condition ( ?+s furni%es no app>5t cause4 #bcj4 ,,! ,,nebul> ,,hypo!sis4--,! !ory ( ! sun's progressive contraction z a necess>y result ( its radiation ( en]gy is comp>atively mod]n1 b m ?an a c5tury ago philosophic /ud5ts ( ,nature _h be5 l$ 9 q a diff]5t way to ! belief t 9 ! e>li] /ages ( its c>e] ! sun mu/ h be5 an enorm\sly ext5d$ body ^: out] portions rea*$ ev5 beyond ! orbit ( ! remote/ planet4 ,laplace1 ^: speculations ^u ?is subject h _h a dom9ant influ5ce dur+ ! n9ete5? c5tury1 has left1 9 a popul> treatise ^u a/ronomy1 an admirable /atem5t ( ! ph5om5a ( planet>y motion1 :i* sugge/ & lead up to ! nebul> !ory ( ! sun's developm5t1 & 9 pres5t+ ?is !ory we %all foll[ sub/antially 8 l9e ( ?\ght1 b ) "s fre$om ( translation & _m omissions4 ,he says3 ,to trace out ! primitive s\rce ( ! planet>y movem5ts1 we h ! foll[+ five ph5om5a3 7#a7 ,^! movem5ts all take place 9 ! same direction & ne>ly 9 ! same plane4 7#b7 ,! movem5ts ( ! satellites are 9 ! same direction z ^? ( ! planets4 7#c7 ,! rotations ( ! planets & ! sun are 9 ! same direction z ! orbital motions & ne>ly 9 ! same plane4 7#d7 ,planets & satellites alike h ne>ly circul> orbits4 7#e7 ,! orbits ( comets are :olly unlike ^! by reason ( _! great ecc5tricities & incl9ations to ! ecliptic4 ,t ^! co9cid5ces %\ld be purely ! result ( *ance seem$ to ,laplace incr$ible1 &1 seek+ a cause = !m1 he cont9ues3 ,:atev] its nature may be1 s9ce x has produc$ or controll$ ! motions ( ! planets1 x mu/ h rea*$ out to all ^! bodies1 &1 9 view ( ! prodigi\s di/ances :i* sep>ate !m1 ! cause c h be5 no?+ else ?an a fluid ( great ext5t :i* mu/ h envelop$ ! sun l an atmosph]e4 ,a consid]ation ( ! planet>y motions leads u to ?9k t 444 ! sun's atmosph]e =m]ly ext5d$ f> beyond ! orbits ( all ! planets & has %runk by degrees to its pres5t dim5sions4 ,?is is n v diff]5t f ! idea develop$ 9 #bbh f a consid]ation ( ! sun's radiant en]gy2 b 9 ,laplace's day ! possibility ( g5]at+ ! sun's heat by contraction ( its bulk 0 unkn[n1 & he 0 compell$ to assume a v high temp]ature = ! primitive nebul\s sun1 :ile we n[ "k t ?is is unnecess>y4 ,:e!r ! primitive nebula 0 hot or cold ! %r9kage w\ld take place 9 mu* ! same way1 & w\ld f9ally result 9 a /> or sun ( v high temp]ature1 b its developm5t w\ld be sl[] if x 7 hot 9 ! beg9n+ ?an if x 7 cold4 ,b aga9 ,laplace3 ,h[ did ! sun's atmosph]e det]m9e ! rotations & revolutions ( planets & satellites8 ,if ^! bodies _h be5 deeply imm]s$ 9 ?is atmosph]e its resi/ance to _! motion w\ld h made !m fall into ! sun1 & we may !re=e conjecture t ! planets 7 =m$1 "o by "o1 at ! out] limits ( ! sol> atmosph]e by ! cond5sation ( zones ( vapor :i* 7 ca/ (f 9 ! plane ( ! sun's equator4 ,"h he proce$s to %[ by an appeal to dynamical pr9ciples t some?+ ( ?is k9d mu/ happ51 & t ! matt] sl\gh$ (f by ! nebula 9 ! =m ( a r+1 p]haps comp>able to ! r+s ( ,saturn or ! a/]oid zone1 w\ld ultimately cond5se into a planet1 :i* 9 its turn might %r9k & ca/ (f r+s to produce satellites4 ,illu/ration3 ,,pi]re ,,simon ,,laplace 7#agdi-ahbg74 ,planets & satellites w\ld !n all h simil> motions1 z not$ at ! beg9n+ ( ?is section1 s9ce 9 e case ?is motion is an inh]itance f a common s\rce1 ! rotation ( ! primitive nebula ab\t its own axis4 ,all ! bodies :i* circle ar\nd a planet hav+ be5 ?us =m$ f r+s :i* its atmosph]e successively ab&on$ z rotation became m & m rapid1 ?is rotation %\ld take place 9 less "t ?an is requir$ = ! orbital revolution ( any ( ! bodies :i* h be5 ca/ (f1 & ?is holds true = ! sun z comp>$ ) ! planets4 #bca4 ,,objections ,,to ,,! ,,nebul> ,,hypo!sis4--,9 ,laplace's "t ?is sl[] rate ( motion 0 also suppos$ to hold true = ,saturn's r+s z comp>$ ) ! rotation ( ,saturn itself1 b1 z we h se5 9 ,*apt] ,,xi1 ?is r+ is made up ( a great numb] ( indep5d5t p>ticles :i* move at diff]5t rates ( spe$1 & comp>+1 ?r\gh ,kepl]'s ,?ird ,law1 ! motion ( ! inn] edge ( ! r+ ) ! kn[n p]iodic "t ( ! satellites1 we may f9d t ^! p>ticles mu/ rotate ab\t ,saturn m rapidly ?an ! planet turns ^u its axis4 ,simil>ly ! inn] satellite ( ,m>s completes its revolution 9 ab\t "o ?ird ( a ,m>tian day1 & we f9d 9 cases l ?is gr\nds = objection to ! nebul> !ory4 ,comp>e also ,laplace's argum5t ) ! peculi> rotations ( ,uranus1 ,neptune1 & _! satellites 7,*apt] ,,xi74 ,d ^! =tify or weak5 8 case8 ,despite ^! objections & o!rs equally s]i\s t h be5 rais$1 ! nebul> !ory agrees ) ! facts ( ,nature at s _m po9ts t a/ronom]s ^u ! :ole are /rongly incl9$ to accept its major outl9es z be+ at lea/ an approximation to ! c\rse ( developm5t actually foll[$ by ! sol> sy/em2 b at "s po9ts--e4 g41 ! =mation ( planets & satellites ?r\gh ! ca/+ (f ( nebul\s r+s--! objections are s _m & /rong z to call = revision & possibly s]i\s modification ( ! !ory4 ,"o propos$ modification1 mu* discuss$ 9 rec5t ye>s1 consi/s 9 sub/itut+ = ! primitive gase\s nebula imag9$ by ,laplace1 a v diffuse cl\d ( meteoric matt] :i* 9 ! c\rse ( its developm5t w\ld become trans=m$ into ! gase\s /ate by ris+ temp]ature4 ,f ?is po9t ( view mu* ( ! meteoric du/ /ill scatt]$ ?r\gh\t ! sol> sy/em may be only ! fragm5ts left ov] 9 fa%ion+ ! sun & planets4 ,*amb]l9 & ,m\lton1 :o h rec5tly giv5 mu* att5tion to ?is subject1 9 diss5t+ f "s ( ,laplace's views1 consid] t ! primitive nebul\s condition mu/ h be5 "o 9 :i* ! matt] ( ! sy/em 0 s br\ght toge!r z to give l[ mass1 high mom5tum1 & irregul> di/ribution to ! out] "p1 & high mass1 l[ mom5tum1 & sph]icity to ! c5tral "p1 & !y sugge/ a possible oblique collision ( a small nebula ) ! out] p>ts ( a l>ge "o4 #bcb4 ,,bode',s ,,law4--,we %\ld n leave ! !ory ( ,laplace )\t not+ ! light x ca/s ^u "o po9t o!rwise obscure--! mean+ ( ,bode's law 7 #acd74 ,?is law1 /at$ 9 ma!matical =m1 makes a geometrical s]ies1 & simil> geometrical s]ies apply to ! di/ances ( ! satellites ( ,jupit] & ,saturn f ^! planets4 ,n[1 ,ro*e has %[n by ! application ( physical laws to ! %r9kage ( a gase\s body t its radius at any "t may be express$ by means ( a c]ta9 ma!matical =mula v simil> to ,bode's law1 save t x involves ! am\nt ( "t t has elaps$ s9ce ! beg9n+ ( ! %r9k+ process4 ,by comp>+ ?is =mula ) ! "o correspond+ to ,bode's law he rea*es ! conclusion t ! peculi> spac+ ( ! planets express$ by t law means t !y 7 =m$ at successive equal int]vals ( "t--i4 e41 t ,m>s is z mu* old] ?an ! e>? z ! e>? is old] ?an ,v5us1 etc4 ,! failure ( ,bode's law 9 ! case ( ,neptune w\ld !n imply t ! int]val ( "t betwe5 ! =mation ( ,neptune & ,uranus 0 %ort] ?an t :i* has prevail$ = ! o!r planets4 ,b too mu* /ress %\ld n be plac$ ^u ?is conclusion4 ,s long z ! mann] 9 :i* ! planets came into be+ cont9ues an op5 "q1 conclusions ab\t _! "t ( bir? mu/ rema9 ( d\btful validity4 #bcc4 ,,tidal ,,friction ,,betwe5 ,,e>? ,,& ,,moon4--,an important addition to !ories ( developm5t )9 ! sol> sy/em has be5 work$ out by ,pr(4 ,g4 ,h4 ,d>w91 :o1 />t+ ) c]ta9 v simple assumptions z to ! pres5t condition ( ?+s 9 e>? & moon1 d]ives f ^!1 by a /rict process ( ma!matical reason+1 f>-rea*+ conclusions ( great int]e/ & importance4 ,! key to ^! conclusions lies 9 recognition ( ! fact t ?r\gh ! influ5ce ( ! tides 7 #db7 !re is n[ 9 progress & has be5 9 progress = a v long "t1 a gradual transf] ( motion 7mom5t ( mom5tum7 f ! e>? to ! moon4 ,! e>?'s motion ( rotation is be+ sl[ly de/roy$ by ! friction ( ! tides1 z ! motion ( a bicycle is de/roy$ by ! friction ( a brake1 &1 9 consequ5ce ( ?is sl[+ d[n1 ! moon is pu%$ f>!r & f>!r away f ! e>?1 s t x n[ moves 9 a l>g] orbit ?an x _h "s millions ( ye>s ago4 ,fig4 #bd has be5 us$ to illu/rate ! action ( ! moon 9 rais+ tides ^u ! e>?1 b 9 accordance ) ! ?ird law ( motion 7 #cf7 ?is action mu/ be accompani$ by an equal & contr>y reaction ^: nature may readily be se5 f ! same figure4 ,! moon moves ab\t its orbit f we/ to ea/ & ! e>? rotates ab\t its axis 9 ! same direction1 z %[n by ! curv$ arr[ 9 ! figure4 ,! tidal wave1 ,i1 !re=e po9ts a little 9 advance ( ! moon's position 9 its orbit & by its attraction mu/ t5d to pull ! moon ahead 9 its orbital motion a little fa/] ?an x w\ld move if ! :ole sub/ance ( ! e>? 7 plac$ inside ! sph]e repres5t$ by ! brok5 circle 9 ! figure4 ,x is true t ! tidal wave at ,i pulls back & t5ds to neutralize ! effect ( ! wave at ,i1 b on ! :ole ! tidal wave ne>] ! moon has ! /rong] influ5ce1 & ! moon on ! :ole moves a v little fa/]1 & by virtue ( ?is add$ impetus draws cont9ually a little f>!r away f ! e>? ?an x w\ld if !re 7 no tides4 #bcd4 ,,consequ5ces ,,( ,,tidal ,,friction ,,^u ,,! ,,e>?4--,?is process ( mov+ ! moon away f ! e>? is a cumulative "o1 go+ on c5tury aft] c5tury1 & ) ref]5ce to x ! moon's orbit mu/ be describ$ n z a circle or ellipse1 or any o!r curve :i* returns into itself1 b z a spiral1 l ! balance spr+ ( a wat*1 ea* ( ^: coils is a little l>g] ?an ! prec$+ "o1 al?\gh ?is excess is1 to be sure1 v small1 because ! tides !mselves are small & ! tidal influ5ce feeble :5 comp>$ ) ! :ole attraction ( ! e>? = ! moon4 ,b1 giv5 "t en\gh1 ev5 ?is small =ce may accompli% great results1 & some?+ l #ajj1jjj1jjj ye>s ( pa/ opportunity w\ld h suffic$ = ! tidal =ces to move ! moon f close proximity ) ! e>? out to its pres5t position4 ,= millions ( ye>s to come1 if moon & e>? endure s long1 ! di/ance betwe5 !m mu/ g on increas+1 al?\gh at an ev] sl[] rate1 s9ce ! f>!r away ! moon goes ! small] w be ! tides & ! sl[] ! work+ out ( _! results4 ,on ! o!r h&1 :5 ! moon 0 ne>] ! e>? ?an n[1 tidal influ5ces mu/ h be5 great] & _! effects m rapidly produc$ ?an at ! pres5t "t1 p>ticul>ly if1 z seems probable1 at "s pa/ epo* ! e>? 0 hot & pla/ic l ,jupit] & ,saturn4 ,!n1 in/ead ( tides 9 ! wat] ( ! sea1 su* z we n[ h1 ! :ole sub/ance ( ! e>? w\ld respond to ! moon's attraction 9 bodily tides ( semi-fluid matt] n only high]1 b ) great] int]nal friction ( _! molecules "o ^u ano!r1 & correspond+ly great] effect 9 *eck+ ! e>?'s rotation4 ,b1 :e!r ! tide be a bodily "o or conf9$ to ! wat]s ( ! sea1 s long z ! moon causes x to fl[ !re w be a c]ta9 am\nt ( friction :i* w affect ! e>? mu* z a brake affects a revolv+ :eel1 sl[+ d[n its motion1 & produc+ ?us a long] day z well z a long] mon? on acc\nt ( ! moon's increas$ di/ance4 ,sl[+ d[n ! e>?'s rotation is ! direct action ( ! moon ^u ! e>?4 ,pu%+ ! moon away is ! =m 9 :i* ! e>?'s equal & contr>y reaction manife/s itself4 #bce4 ,,consequ5ces ,,( ,,tidal ,,friction ,,^u ,,! ,,moon4--,:5 ! moon 0 pla/ic ! e>? mu/ h rais$ 9 x a bodily tide manifold great] ?an ! lun> tides ^u ! e>?1 &1 z we h se5 9 ,*apt] ,,ix1 ?is tide has long s9ce worn out ! great] "p ( ! moon's rotation & br\ght our satellite to ! condition 9 :i* x pres5ts always ! same face t[>d ! e>?4 ,^! two processes1 sl[+ d[n ! rotation & pu%+ away ! di/urb+ body1 are insep>able--"o requires ! o!r2 & x is wor? not+ 9 ?is connection t :5 = any reason ! tide ceases to fl[1 & ! tidal wave takes up a p]man5t position1 z x has 9 ! moon 7 #ii71 its "w is end$1 = :5 !re is no motion ( ! wave !re c be no friction to fur!r r$uce ! rate ( rotation ( ! "o body1 & no reaction to t friction to pu% away ! o!r4 ,b ?is p]man5t & /ation>y tidal wave 9 ! moon1 or else:]e1 means t ! satellite pres5ts always ! same face t[>d its planet1 mov+ once ab\t its orbit 9 ! "t requir$ = "o revolution ^u its axis1 & ! tide rais$ by ! moon ^u ! e>? t5ds to produce "h ! result long s9ce a*iev$ 9 our satellite1 to make our day & mon? ( equal l5g?1 & to make ! e>? turn always ! same side t[>d ! moon4 ,b ! moon's tidal =ce is small comp>$ ) t ( ! e>?1 & has a va/ly great] mom5tum to ov]come1 s t its "w ^u ! e>? is n yet complete4 ,accord+ to ,?omson & ,tait1 ! moon mu/ be pu%$ (f ano!r hundr$ ?\s& miles1 & ! day l5g!n$ out by tidal influ5ce to sev5 ( our pres5t weeks be=e ! day & ! lun> mon? are made ( equal l5g?1 & ! moon !reby p]man5tly hidd5 f "o hemisph]e ( ! e>?4 #bcf4 ,,! ,,e>?-,,moon ,,sy/em4--,retrac+ into ! pa/ ! c\rse ( developm5t ( ! e>? & moon1 x is possible to rea* back by means ( ! ma!matical !ory ( tidal friction to a "t at :i* ^! bodies 7 mu* ne>] to ea* o!r ?an n[1 b x has n be5 f\nd possible to trace out ! mode ( _! sep>ation f "o body into two1 z is suppos$ 9 ! nebul> !ory4 ,9 ! e>lie/ "p ( _! hi/ory accessible to ma!matical analysis !y are di/9ct bodies at "s consid]able di/ance f ea* o!r1 ) ! e>? rotat+ ab\t an axis m ne>ly p]p5dicul> to ! moon's orbit & to ! ecliptic ?an is n[ ! case4 ,/>t+ f su* a condition1 ! lun> tides1 accord+ to ,d>w91 h be5 in/rum5tal 9 tipp+ ! e>?'s rotation axis into its pres5t oblique position1 & 9 det]m9+ ! ecc5tricity ( ! moon's orbit & its position ) respect to ! ecliptic z well z ! pres5t l5g? ( day & mon?4 #ccg4 ,,tidal ,,friction ,,^u ,,! ,,planets4--,! satellites ( ! out] planets are equally subject to influ5ces ( ?is k9d1 & !re appe>s to be indep5d5t evid5ce t "s ( !m1 at lea/1 turn always ! same face t[>d _! respective planets1 indicat+ t ! "w ( tidal friction has "h be5 accompli%$4 ,we saw 9 ,*apt] ,,xi t x is at pres5t an op5 "q :e!r ! inn] planets1 ,v5us & ,m]cury1 d n always turn ! same face t[>d ! sun1 _! day & ye> be+ ( equal l5g?4 ,9 addition to ! direct obs]vational evid5ce ^u ?is po9t1 ,s*iap>elli has s\ght to %[ by an appeal to tidal !ory t su* is probably ! case1 at lea/ = ,m]cury1 s9ce ! tidal =ces :i* t5d to br+ ab\t ?is result 9 t planet are ab\t z great z ! =ces :i* h c]ta9ly produc$ x 9 ! case ( ! moon & ,saturn's satellite1 ,japetus4 ,! same l9e ( reason+ w\ld %[ t e satellite 9 ! sol> sy/em1 save possibly ! newly discov]$ n9? satellite ( ,saturn1 mu/1 z a consequ5ce ( tidal friction1 turn always ! same face t[>d its planet4 #bch4 ,,! ,,sol> ,,tide4--,! sun also raises tides 9 ! e>?1 & _! influ5ce mu/ be simil> 9 "* to t ( ! lun> tides1 *eck+ ! rotation ( ! e>? & ?ru/+ e>? & sun ap>t1 al?\gh quantitatively ^! effects are small comp>$ ) ^? ( ! moon4 ,!y mu/1 h[ev]1 cont9ue s long z ! sol> tide la/s1 possibly until ! day & ye> are made ( equal l5g?--i4 e41 !y may cont9ue long aft] ! lun> tidal influ5ce has ceas$ to pu% e>? & moon ap>t4 ,%\ld ?is be ! case1 a curi\s inv]se effect w be produc$4 ,! day be+ !n long] ?an ! mon?1 ! moon w aga9 raise a tide 9 ! e>? :i* w run ar\nd x f we/ to ea/1 opposite to ! c\rse ( ! pres5t tide1 ?us t5d+ to accel]ate ! e>?'s rotation1 & by its reaction to br+ ! moon back t[>d ! e>? aga91 & ultimately to fall ^u x4 ,we may note t an effect ( ?is k9d mu/ be 9 progress n[ betwe5 ,m>s & its inn] satellite1 ,phobos1 ^: "t ( orbital revolution is only "o ?ird ( a ,m>tian day4 ,x seems probable t ?is satellite is 9 ! la/ /ages ( its exi/5ce z an indep5d5t body1 & mu/ ultimately fall into ,m>s4 #bci4 ,,ro*e',s ,,limit4--,9 look+ =w>d to su* a cata/rophe1 h[ev]1 due reg>d mu/ be paid to a dynamical pr9ciple ( a diff]5t "*4 ,! moon c nev] be precipitat$ ^u ! e>? entire1 s9ce be=e x rea*es u x w h be5 torn asund] by ! excess ( ! e>?'s attraction = ! ne> side ( its satellite ov] t :i* x ex]ts ^u ! f> side4 ,z ! result ( ,ro*e's ma!matical analysis we are able to assign a limit+ di/ance betwe5 any planet & its satellite )9 :i* ! satellite1 if x turns always ! same face t[>d ! planet1 c n come )\t be+ brok5 into fragm5ts4 ,if we repres5t ! radius ( ! planet by r1 & ! quoti5t obta9$ by divid+ ! d5sity ( ! planet by ! d5sity ( ! satellite by q1 !n ,ro*e's limit #b4dd r q#a_/c4 ,?us 9 ! case ( e>? & moon we f9d f ! d5sities giv5 9 #ie1 q #a4fe1 & ) r #c1ifc miles we obta9 #aa1djj miles z ! ne>e/ approa* :i* ! moon c\ld make to ! e>? )\t be+ brok5 up by ! diff]5ce ( ! e>?'s attractions = its opposite sides4 ,we mu/ obs]ve1 h[ev]1 t ,ro*e's limit takes no acc\nt ( molecul> =ces1 ! adhesion ( "o molecule to ano!r1 by virtue ( :i* a /ick or /one resi/s fracture1 b is conc]n$ only ) ! gravitative =ces by :i* ! molecules are attract$ t[>d ! moon's c5t] & t[>d ! e>?4 ,)9 a /one or rock ( mod]ate size ^! gravitative =ces are insignificant1 & cohesion is ! *ief factor 9 pres]v+ its integrity1 b 9 a l>ge body l ! moon1 ! case is j rev]s$1 cohesion plays a small "p & gravitation a l>ge "o 9 hold+ ! body toge!r4 ,we may conclude1 !re=e1 t at a prop] di/ance ^! =ces are capable ( break+ up ! moon1 or any o!r l>ge body1 into fragm5ts ( a size su* t molecul> cohesion in/ead ( gravitation is ! *ief ag5t 9 pres]v+ !m f fur!r dis9tegration4 #bdj4 ,,saturn',s ,,r+s4--,saturn's r+s are ( peculi> int]e/ 9 ?is connection4 ,! out] edge ( ! r+ sy/em lies j inside ( ,ro*e's limit = ?is planet1 & we h already se5 t ! r+s are compos$ ( small fragm5ts indep5d5t ( ea* o!r4 ,:atev] may h be5 ! process by :i* ! n9e satellites ( ,saturn came into exi/5ce1 we h 9 ,ro*e's limit ! explanation :y ! mat]ial ( ! r+ 0 n work$ up into satellites2 ! =ces ex]t$ by ,saturn w\ld te> into pieces any consid]able satellite ?us =m$ & equally w\ld prev5t ! =mation ( "o f raw mat]ial4 ,saturn's r+s pres5t ! only case )9 ! sol> sy/em :]e matt] is kn[n to be revolv+ ab\t a planet at a di/ance less ?an ,ro*e's limit1 & x is an int]e/+ "q :e!r ^! r+s c rema9 z a p]man5t "p ( ! planet's sy/em or are only a tempor>y feature4 ,! draw+s ( ,saturn made two c5turies ago agree among !mselves 9 repres5t+ ! r+s z l>g] ?an !y n[ appe>1 & !re is "s reason to suppose t z a consequ5ce ( mutual di/urbances--collisions--_! mom5tum is be+ sl[ly wa/$ s t ultimately !y mu/ be precipitat$ into ! planet4 ,b ! direct evid5ce ( su* a progress t c be drawn f pres5t data is too scanty to ju/ify positive conclusions 9 ! matt]4 ,on ! o!r h&1 ,nolan sugge/s t 9 ! out] p>ts ( ! r+ small satellites might be =m$ ^: tidal influ5ce ^u ,saturn w\ld suffice to pu% !m away f ! r+ beyond ,ro*e's limit1 & t ! v small inn] satellites ( ,saturn may h be5 ?us =m$ at ! exp5se ( ! r+4 ,! inn] satellite ( ,m>s is v close to ,ro*e's limit = t planet1 &1 z we h se5 above1 mu/ be approa*+ /ill ne>] to ! dang] l9e4 #bda4 ,,! ,,moon',s ,,developm5t4--,! f9e s]ies ( photographs ( ! moon obta9$ )9 ! la/ few ye>s at ,p>is1 h be5 us$ by ! a/ronom]s ( t obs]vatory = a m9ute /udy ( ! lun> =mations1 mu* z geologi/s /udy ! surface ( ! e>? to det]m9e some?+ ab\t ! mann] 9 :i* x 0 =m$4 ,_! conclusions are1 9 g5]al1 t at "s pa/ "t ! moon 0 a hot & fluid body :i*1 z x cool$ & cond5s$1 =m$ a solid cru/ ^: fur!r %r9kage compress$ ! liquid nucleus & l$ to a long s]ies ( fractures 9 ! cru/ & outbur/s ( liquid matt]1 ^: late/ & feeble/ /ages produc$ ! lun> crat]s1 :ile traces ( ! e>li] ones1 connect$ ) a g5]al settl+ ( ! cru/1 al?\gh ne>ly oblit]at$1 are /ill pres]v$ 9 c]ta9 l>ge b vague features ( ! lun> topography1 su* z ! di/ribution ( ! seas1 etc4 ,!y f9d also 9 c]ta9 m>k+s ( ! surface :at !y consid] conv9c+ evid5ce ( ! exi/5ce 9 pa/ times ( a lun> atmosph]e4 ,b ?is seems d\btful1 s9ce ! =ce ( gravity at ! moon's surface is s small t an atmosph]e simil> to t ( ! e>?1 ev5 ?\gh plac$ ^u ! moon1 c\ld n p]man5tly endure1 b w\ld be lo/ by ! gradual escape ( its molecules into ! surr\nd+ space4 ,! molecules ( a gas are q indep5d5t "o ( ano!r1 & are 9 a /ate ( ceaseless agitation1 ea* "o d>t+ to & fro1 collid+ ) its neighbors or ) :atev] else opposes its =w>d motion1 & travel+ ) velocities :i*1 on ! av]age1 am\nt to a good _m hundr$s ( feet p] second1 al?\gh 9 ! case ( any individual molecule !y may be mu* less or mu* great] ?an ! av]age value1 an occasional molecule hav+ possibly a velocity sev]al times z great z ! av]age4 ,9 ! upp] regions ( our own atmosph]e1 if "o ( ^! swiftly mov+ p>ticles ( oxyg5 or nitrog5 7 head$ away f ! e>? ) a velocity ( sev5 miles p] second1 ! :ole attractive p[] ( ! e>? w\ld be insuffici5t to *eck its motion1 & x w\ld !re=e1 unless /opp$ by "s collision1 escape f ! e>? & return no m4 ,b1 s9ce ?is velocity ( sev5 miles p] second is m ?an ?irty times z great z ! av]age velocity ( ! molecules ( air1 x mu/ be v seldom inde$ t "o is f\nd to move s swiftly1 & ! loss ( ! e>?'s atmosph]e by leakage ( ?is sort is insignificant4 ,b ^u ! moon1 or any o!r body :]e ! =ce ( gravity is small1 conditions are q diff]5t1 & 9 our satellite a velocity ( little m ?an "o mile p] second w\ld suffice to c>ry a molecule away f ! out] limits ( its atmosph]e4 ,?is velocity1 only five times ! av]age1 w\ld be frequ5tly atta9$1 p>ticul>ly 9 =m] times :5 ! moon's temp]ature 0 high1 = !n ! av]age velocity ( all ! molecules w\ld be consid]ably increas$1 & ! am\nt ( leakage might become1 & probably w\ld become1 a s]i\s matt]1 /eadily deplet+ ! moon's atmosph]e & lead+ f9ally to its pres5t /ate ( exhau/ion4 ,x is possible t ! moon may at "o "t h _h an atmosph]e1 b if s x c\ld h be5 only a tempor>y possession1 & ! same l9e ( reason+ may be appli$ to ! a/]oids & to mo/ ( ! satellites ( ! sol> sy/em1 & also1 ?\gh 9 less degree1 to ! small] planets1 ,m]cury & ,m>s4 #bdb4 ,,/ell> ,,developm5t4--,we h already consid]$ 9 ?is *apt] ! l9e ( developm5t foll[$ by "o />1 ! sun1 & treat+ ?is z a typical case1 x is commonly believ$ t ! life hi/ory ( a />1 9 s f> z x lies )9 our rea*1 beg9s ) a condition 9 :i* its matt] is widely diffus$1 & presumably at a l[ temp]ature4 ,contract+ 9 bulk "u ! influ5ce ( its own gravitative =ces1 ! />'s temp]ature rises to a maximum1 & !n falls (f 9 lat] /ages until ! body ceases to %9e & passes ov] to ! li/ ( d>k />s ^: exi/5ce c only be detect$ 9 exceptional cases1 su* z are not$ 9 ,*apt] ,,xiii4 ,! mo/ sy/ematic developm5t ( ?is idea is due to ,locky]1 :o looks ^u all ! cele/ial bodies--sun1 moon & planets1 />s1 nebul1 & comets--z be+ only collections ( meteoric matt] 9 diff]5t /ages ( developm5t1 & :o has s\ght by means ( _! spectra to classify ^! bodies & to det]m9e _! /age ( advancem5t4 ,:ile ! fundam5tal ideas involv$ 9 ?is meteoritic hypo!sis are n s]i\sly controv]t$1 ! detail$ application ( its pr9ciples is op5 to m "q1 & = ! mo/ "p ^? a/ronom]s :o hold t 9 ! pres5t /ate ( k /ell> spectra furni% a key to a />'s age or degree ( advancem5t d n v5ture beyond broad g5]al /atem5ts4 ,illu/ration3 ,,fig4 #aea4--,types ( /ell> spectra sub/antially accord+ to ,,sec*i4 #bdc4 ,,/ell> ,,spectra4--,?us ! types ( /ell> spectra %[n 9 ,fig4 #aea are suppos$ to illu/rate successive /ages 9 ! developm5t ( an av]age />4 ,type ,i corresponds to ! p]iod 9 :i* its temp]ature is ne> ! maximum2 ,type ,,ii belongs to a lat] /age 9 :i* ! temp]ature has comm5c$ to fall2 & ,type ,,iii to ! p]iod imm$iately prec$+ ext9ction4 ,:ile human life1 or ev5 ! duration ( ! human race1 is too %ort to p]mit a s+le /> to be foll[$ ?r\gh all ! /ages ( its c>e]1 an adequate picture ( t developm5t might be obta9$ by exam9+ _m />s1 ea* at a diff]5t /age ( progress1 &1 foll[+ ?is idea1 num]\s subdivisions ( ! types ( /ell> spectra %[n 9 ,fig4 #aea h be5 propos$ 9 ord] to repres5t ) m detail ! process ( /ell> gr[? & decay2 b = ! mo/ "p ^! subdivisions & _! int]pretation are accept$ by a/ronom]s ) mu* res]ve4 ,x is significant t !re are comp>atively few />s ) spectra ( ,type ,,iii1 = ?is is :at we %\ld expect to f9d if ! developm5t ( a /> ?r\gh ! la/ /ages ( its visible c>e] occupi$ b a small fraction ( its total life4 ,f ! same po9t ( view ! great numb] ( />s ) spectra ( ! fir/ type w\ld po9t to a long duration ( ?is /age ( life4 ,! p]iod 9 :i* ! sun belongs1 repres5t$ by ,type ,,ii1 probably has a duration int]m$iate betwe5 ! o!rs4 ,s9ce mo/ ( ! v>iable />s1 save ^? ( ! ,algol class1 h spectra ( ! ?ird type1 we conclude t v>iability1 ) its associat$ ruddy color & great atmosph]ic absorption ( light1 is a sign ( old age & approa*+ ext9ction4 ,! ,algol or eclipse v>iables1 on ! o!r h&1 hav+ spectra ( ! fir/ type1 are comp>atively "y />s1 &1 z we %all see a little lat]1 ! %ortness ( _! light p]iods 9 "s measure confirms ?is conclusion drawn f _! spectra4 ,we h not$ 9 #aif t ! sun's ne> neighbors are prevail+ly />s ) spectra ( ! second type1 :ile ! ,milky ,way is ma9ly compos$ ( fir/-type />s1 & f ?is we may n[ conclude t 9 our p>ticul> "p ( ! entire cele/ial space ! />s are1 z a rule1 some:at fur!r develop$ ?an is ! case else:]e4 #bdd4 ,,d\ble ,,/>s4--,! d\ble />s pres5t special problems ( developm5t gr[+ out ( ! effects ( tidal friction1 :i* mu/ op]ate 9 !m mu* z x does betwe5 e>? & moon1 t5d+ /eadily to increase ! di/ance betwe5 ! compon5ts ( su* a />4 ,s1 too1 9 su* a sy/em z is %[n 9 ,fig4 #acb1 gravity mu/ t5d to make ea* compon5t ( ! d\ble /> %r9k to small] dim5sions1 & ?is %r9kage mu/ result 9 fa/] rotation & increas$ tidal friction1 :i* 9 turn mu/ pu% ! compon5ts ap>t1 s t 9 view ( ! small d5sity & close proximity ( ^? p>ticul> />s we may fairly reg>d a /> l b ,lyr z 9 ! e>ly /ages ( its c>e] & de/9$ ) increas+ age to lose its v>iability ( light1 s9ce ! eclipses :i* n[ take place mu/ cease ) increas+ di/ance betwe5 ! compon5ts unless ! orbit is turn$ exactly edgewise t[>d ! e>?4 ,close proximity & ! result+ %ortness ( p]iodic "t 9 a d\ble /> seem1 !re=e1 to be evid5ce ( its y\?1 & s9ce ?is %ortness ( p]iodic "t is *>act]i/ic ( bo? ,algol v>iables & spectroscopic b9>ies z a class1 we may set !m d[n z be+1 ^u ! :ole1 />s 9 ! e>ly /ages ( _! c>e]4 ,on ! o!r h&1 x is g5]ally true t ! l>g] ! orbit1 & ! great] ! p]iodic "t 9 ! orbit1 ! f>!r is ! /> advanc$ 9 its developm5t4 ,9 8 !ory ( tidal friction1 ,d>w9 has po9t$ out t :5ev] ! p]iodic "t 9 ! orbit is m ?an twice z long z ! "t requir$ = rotation ab\t ! axis1 ! effect ( ! tides is to increase ! ecc5tricity ( ! orbit1 &1 foll[+ ?is indication1 ,see has urg$ t ) increas+ di/ance betwe5 ! compon5ts ( a d\ble /> _! orbits ab\t ! common c5t] ( gravity mu/ gr[ m & m ecc5tric1 s t we h 9 ! %ape ( su* orbits a new index ( /ell> developm5t2 ! m ecc5tric ! orbit1 ! f>!r advanc$ are ! />s4 ,x is important to note 9 ?is connection t among ! d\ble />s ^: orbits h be5 comput$ !re seems to run a g5]al rule--! l>g] ! orbit ! great] is its ecc5tricity--a relation :i* mu/ hold true if tidal friction op]ates z above suppos$1 & :i*1 be+ f\nd to hold true1 confirms 9 "s degree ! crit]ia ( /ell> age :i* are furni%$ by ! !ory ( tidal friction4 #bde4 ,,nebul4--,! nebul> hypo!sis ( ,laplace has incl9$ a/ronom]s to look ^u nebul 9 g5]al z mat]ial de/9$ to be work$ up into />s1 b :i* is n[ 9 a v crude & undevelop$ /age4 ,_! great bulk & small d5sity seem also to indicate t gravitation has n yet produc$ 9 !m results at all comp>able ) :at we see 9 sun & />s4 ,b ev5 among nebul !re are to be f\nd v diff]5t /ages ( developm5t4 ,! irregul> nebula1 %apeless & void l t ( ,orion2 ! spiral1 r+1 & planet>y nebul & ! /> clu/]1 cle>ly diff] 9 am\nt ( progress t[>d _! f9al goal4 ,b x is by no means sure t ^! sev]al types are diff]5t /ages 9 "o l9e ( developm5t2 = example1 ! primitive nebula :i* gr[s into a spiral may nev] become a r+ or planet>y nebula1 & vice v]sa4 ,s too !re is no reason to suppose t a /> clu/] w ev] break up into isolat$ />s su* z ^? ^: relation to ea* o!r is %[n 9 ,fig4 #abb4 #bdf4 ,,classification4--,consid]+ ! heav5ly bodies ) respect to _! /age ( developm5t1 & arrang+ !m 9 due ord]1 we %\ld probably f9d l[e/ d[n 9 ! scale ( progress ! irregul> nebul ( *aotic appe>ance su* z t repres5t$ 9 ,fig4 #adf4 ,above ^! 9 po9t ( developm5t /& ! spiral1 r+1 & planet>y nebul1 al?\gh ! exact sequ5ce 9 :i* !y %\ld be arrang$ rema9s a matt] ( d\bt4 ,/ill high] up 9 ! scale are /> clu/]s ^: individual memb]s1 z well z isolat$ />s1 are to be classifi$ by means ( _! spectra1 z %[n 9 ,fig4 #aea1 :]e ! ord] ( developm5t ( ea* /> is probably f ,type ,i1 ?r\gh ,,ii1 into ,,iii & beyond1 to ext9ction ( its light & ! cutt+ (f ( mo/ ( its radiant en]gy4 ,jupit] & ,saturn are to be reg>d$ z />s :i* h rec5tly ent]$ ?is d>k /age4 ,! e>? is fur!r develop$ ?an ^!1 b x is n s f> along z are ,m>s & ,m]cury2 :ile ! moon is to be look$ ^u z ! mo/ advanc$ heav5ly body accessible to our rese>*1 hav+ rea*$ a /ate ( decrepitude :i* may almo/ be call$ dea?--a /age typical ( t t[>d :i* all ! o!rs are mov+4 ,meteors & comets are to be reg>d$ z fragm5ts ( cele/ial matt]1 *ips1 too small to a*ieve by !mselves mu* progress along ! normal l9es ( developm5t1 b de/9$ soon] or lat]1 by collision ) "s l>g] body1 to %>e !nce=? 9 its =tunes4 #bdg4 ,,/ability ,,( ,,! ,,univ]se4--,x 0 consid]$ a great a*ievem5t 9 ! ma!matical a/ronomy ( a c5tury ago :5 ,laplace %[$ t ! mutual attractions ( sun & planets might inde$ produce endless p]turbations 9 ! motions & positions ( ^! bodies1 b c\ld nev] br+ ab\t collisions among !m or greatly alt] _! exi/+ orbits4 ,b 9 ! pro( ( ?is great !orem two influ5ces 7 neglect$1 ei!r ( :i* is fatal to its validity4 ,"o ( ^!--tidal friction--z we h already se51 t5ds to wreck ! sy/ems ( satellites1 & ! same effect mu/ be produc$ ^u ! planets by any o!r influ5ce :i* t5ds to imp$e _! orbital motion4 ,x is ! in]tia ( ! planet 9 its =w>d movem5t t balances ! sun's attraction1 & any dim9ution ( ! planet's velocity w give ?is attraction ! upp] h& & mu/ ultimately precipitate ! planet into ! sun4 ,! meteoric matt] ) :i* ! e>? comes ceaselessly into collision mu/ h j ?is influ5ce1 al?\gh its effects are v small1 & some?+ ( ! same k9d may come f ! m$ium :i* transmits radiant en]gy ?r\gh ! int]/ell> spaces4 ,x seems incr$ible t ! lum9if]\s e!r1 :i* is suppos$ to p]vade all space1 %\ld pres5t absolutely no resi/ance to ! motion ( />s & planets ru%+ ?r\gh x ) velocities :i* 9 _m cases exce$ #ej1jjj miles p] h\r4 ,if !re is a resi/ance to ?is motion1 h[ev] small1 we may ext5d to ! :ole visible univ]se ! words ( ,?omson & ,tait1 :o say 9 _! great ,treatise on ,natural ,philosophy1 ,we h no data 9 ! pres5t /ate ( sci5ce = e/imat+ ! relative importance ( tidal friction & ( ! resi/ance ( ! resi/+ m$ium ?r\gh :i* ! e>? & moon move2 b1 :atev] x may be1 !re c be b "o ultimate result = su* a sy/em z t ( ! sun & planets1 if cont9u+ long en\gh "u exi/+ laws & n di/urb$ by meet+ ) o!r mov+ masses 9 space4 ,t result is ! fall+ toge!r ( all into "o mass1 :i*1 al?\gh rotat+ = a "t1 mu/ 9 ! end come to re/ relatively to ! surr\nd+ m$ium4 ,comp>e ) ?is ! words ( a great poet :o 9 ,! ,tempe/ puts into ! m\? ( ,prosp]o ! l9es3 ,! cl\d-capp'd t[]s1 ! gorge\s palaces1 ,! solemn temples1 ! great globe itself1 ,yea1 all :i* x inh]it1 %all dissolve2 ,&1 l ?is insub/antial pageant fad$1 ,leave n a rack beh9d4 #bdh4 ,,! ,,future4--,9 spite ( /atem5ts l ^!1 x lies beyond ! scope ( sci5tific rese>* to affirm t ! visible ord] ( ?+s w ev] come to naught1 & ! outcome ( pres5t t5d5cies1 z sket*$ above1 may be pr(\ndly modifi$ 9 ages to come1 by influ5ces ( :i* we are n[ ignorant4 ,we h already not$ t ! f>!r our speculation ext5ds into ei!r pa/ or future1 ! m insecure are its conclusions1 & ! remot] consequ5ces ( pres5t laws are to be accept$ ) a correspond+ res]ve4 ,b ! "o great fact :i* /&s out cle> 9 ?is connection is t ( *ange4 ,! old concept ( a univ]se creat$ 9 f9i%$ =m & de/9$ s to abide until its f9al dissolution1 has pass$ away f sci5tific ?\ght & is replac$ by ! idea ( sl[ developm5t4 ,a univ]se :i* is ev] becom+ some?+ else & is nev] f9i%$1 z %ad[$ =? by ,goe! 9 ! l9es3 ,?us "w ,i at ! ro>+ loom ( ,"t1 ,& weave = ,deity a liv+ robe sublime4 ,,app5dix ,,! ,,greek ,,alphabet ,! ,greek lett]s are s mu* us$ by a/ronom]s 9 connection ) ! names ( ! />s1 & = o!r purposes1 t ! ,greek alphabet is pr9t$ bel[--n necess>ily to be le>n$1 b = conv5i5t ref]5ce3 ,greek4 ,"n4 ,engli%4 ,a a ,alpha a ,b b ,beta b ,g g ,gamma g ,d d ,delta d ,e e or e ,epsilon 7e ,z z ,zeta z ,eta e ,? ? or ? ,!ta ? ,i i ,iota i ,k k ,kappa k ,l l ,lambda l ,m m ,mu m ,n n ,nu n ,x x ,xi x ,o o ,omicron 7o ,p p ,pi p ,r r ,rho r ,s s or s ,sigma s ,t t ,tau t ,y y ,upsilon u ,ph ph ,phi ph ,* * ,*i * ,ps ps ,psi ps ,omega o ,,popul> ,,lit]ature ,,( ,,a/ronomy ,! foll[+ brief bibliography1 :ile mak+ no pret5se at complet5ess1 may s]ve z a useful guide to supplem5t>y read+3 ,g5]al ,treatises ,,"y4 ,g5]al ,a/ronomy4 ,an admirable g5]al survey ( ! entire field4 ,,newcomb4 ,popul> ,a/ronomy4 ,! second edition ( a ,g]man translation ( ?is "w by ,engelmann & ,vogel is especially valuable4 ,,ball4 ,/ory ( ! ,heav5s4 ,some:at easi] read+ ?an ei!r ( ! prec$+4 ,,*amb]s4 ,descriptive ,a/ronomy4 ,an elaborate b elem5t>y "w 9 ?ree volumes4 ,,langley4 ,! ,new ,a/ronomy4 ,treats ma9ly ( ! physical condition ( ! cele/ial bodies4 ,,proctor & ,,rany>d4 ,old & ,new ,a/ronomy4 ,special ,treatises ,,proctor4 ,! ,moon4 ,a g5]al treatm5t ( ! subject4 ,,nasmy? & ,,c>p5t]4 ,! ,moon4 ,an admirably illu/rat$ b exp5sive "w deal+ ma9ly ) ! topography & physical conditions ( ! moon4 ,!re is a *eap] & v good edition 9 ,g]man4 ,,"y4 ,! ,sun4 ,int]national ,sci5tific ,s]ies4 ,! mo/ rec5t & au?oritative treatise on ?is subject4 ,,proctor4 ,o!r ,worlds ?an ,ours4 ,an acc\nt ( planets1 comets1 etc4 ,,newton4 ,meteor4 ,encyclopdia ,britannica4 ,,airy4 ,gravitation4 ,a non-ma!matical exposition ( ! laws ( planet>y motion4 ,,/okes4 ,on ,light z a ,means ( ,inve/igation4 ,burnett ,lectures4 ,,ii4 ,! basis ( spectrum analysis4 ,,s*ell54 ,spectrum ,analysis4 ,,?omson 7,sir ,w41 ,"l ,,kelv971 ,popul> ,lectures1 etc4 ,lectures on ! ,tides1 ,! ,sun's ,heat1 etc4 ,,ball4 ,"t & ,tide4 ,an exposition ( ! rese>*es ( ,g4 ,h4 ,d>w9 ^u tidal friction4 ,,gore4 ,! ,visible ,univ]se4 ,deals ) a class ( problems inadequately treat$ 9 mo/ popul> a/ronomies4 ,,d>w94 ,! ,tides4 ,an admirable elem5t>y exposition4 ,,cl]ke4 ,! ,sy/em ( ! ,/>s4 ,/ell> a/ronomy4 ,,newcomb4 ,*apt]s on ! ,/>s1 9 ,popul> ,sci5ce ,mon?ly = #aijj4 ,,cl]ke4 ,hi/ory ( ,a/ronomy dur+ ! ,n9ete5? ,c5tury4 ,an admirable "w4 ,,wolf4 ,ges*i*te d] ,a/ronomie4 ,mn*51 #ahgg4 ,an excell5t ,g]man "w4 ,a ,,li/ ,,( ,,/>s ,,= ,,"t ,,obs]vations ,see #bj4 ---------------------------------------- ------------------------ ,,"n4 ,magnitude4 ,"r ,asc5sion4 ,decl9ation4 ---------------------------------------- ------------------------ h4 m4 b ,ceti #b #j #ch4f - #ah4e ,ceti #c #a #c4f - #aj4g a ,ceti #c #b #eg4a #c4g g ,eridani #c #c #ec4d - #ac4h ,aldeb>an #a #d #cj4b #af4c ,rigel #j #e #i4g - #h4c k ,orionis #b #e #dc4j - #i4g b ,canis ,majoris #b #f #ah4c - #ag4i ,sirius -#a #f #dj4g - #af4f ,procyon #j #g #cd4a #e4e a ,hydr #b #i #bb4g - #h4b ,regulus #a #aj #c4j #ab4e n ,hydr #c #aj #dd4g - #ae4g e ,corvi #c #ab #e4j - #bb4a g ,corvi #c #ab #aj4g - #ag4j ,spica #a #ac #ai4i - #aj4f z ,virg9is #c #ac #bi4f - #j4a a ,libr #c #ad #de4c - #ae4f b ,libr #c #ae #aa4f - #i4j ,ant>es #a #af #bc4c - #bf4b a ,ophiu*i #b #ag #cj4c #ab4f e ,sagitt>ii #b #ah #ag4e - #cd4d d ,aquil #c #ai #bj4e #b4i ,altair #a #ai #de4i #h4f b ,aqu>ii #c #ba #bf4c - #f4j a ,aqu>ii #c #bb #j4f - #j4h ,fomalhaut #a #bb #eb4a - #cj4b ---------------------------------------- ------------------------ ,,index ,! ref]5ces are to section numb]s4 ,absorption ( />light1 #bbe4 ,absorption spectra1 #hg4 ,accel]at+ =ce1 #ce4 ,adju/m5t ( obs]vations1 #b4 ,alb$o ( moon1 #ig4 ( ,v5us1 #adh4 ,algol1 #bje4 ,altitudes1 #d1 #ba4 ,&rom$a nebula1 #bad4 ,angles1 measurem5t (1 #b4 ,angul> diamet]1 #g4 ,annul> eclipse1 #fd4 ,a/]oids1 #aef4 ,atmosph]e ( ! e>?1 #di4 ( ! moon1 #ajc4 ( ,jupit]1 #aci4 ( ,m>s1 #aec4 ,aurora1 #ea4 ,azimu?1 #e1 #ba4 ,biela's comet1 #aha4 ,bode's law1 #acd1 #bcb4 ,br$i*9's !ory ( comet tails1 #ahj4 ,cal5d>1 ,o4 ,s4 & ,n4 ,s41 #fa4 ,capture ( comets & meteors1 #agf4 ,canals ( ,m>s1 #aed4 ,cele/ial me*anics1 #cb4 ,*anges ^u ! moon1 #ajh4 ,*emical con/itution ( sun1 #aaf4 ( />s1 #baj4 ,*romosph]e1 ! sun's1 #abd4 ,*ronology1 #ei4 ,classification ( />s1 #bab4 ,clocks & wat*es1 #gd4 sid]eal clock1 #ab4 ,collisions ) comets1 #ahc4 ,colors ( />s1 #bji4 ,comets1 g5]al *>act]i/ics1 #aeh-afd4 developm5t (1 #agi1 #aha4 gr\ps1 #agg4 orbits1 #afa4 p]iodic1 #agf4 spectra1 #ahb4 tails1 #ahj4 ,comets & meteors1 relation (1 #age4 ,conic sections1 #ch4 ,con/ellations1 #ahd4 ,corona1 ! sun's1 #abc4 ,crat]s1 lun>1 #aje4 ,d>k />s1 #bja4 ,day1 #eb1 #fb4 ,decl9ation1 #ba4 ,developm5t ( comet1 #agi4 ( moon1 #bda4 ( nebul1 #bde4 ( />s1 #bdb1 #bdd4 ( sun1 #bbh4 ( univ]se1 #bbf4 ,di/ribution ( />s & nebul1 #bbj4 ,diurnal motion1 #aj1 #ae4 ,doppl] pr9ciple1 #hi4 ,d\ble nebul1 #bae4 ,d\ble />s1 #aih4 developm5t (1 #bdd4 ,driv+ clock1 #hj4 ,e>?1 atmosph]e1 #dh4 mass1 #de4 size & %ape1 #dd4 w>m+ ( ! e>?1 #dg4 ,eclipses1 nature (1 #fc4 annul> eclipse1 #fd4 eclipse limits1 #fh4 eclipse maps1 #gj1 #ga4 numb] (1 9 a ye>1 #fi4 p>tial eclipse1 #fd4 pr$iction (1 #gj1 #ga4 recurr5ce (1 #gb4 %ad[ cone1 #fd1 #ff4 total eclipse1 #fd4 uses (1 #gc4 ,eclipses ( ,jupit]'s satellites1 #ada4 ,eclipse !ory ( v>iable />s1 #bje4 ,ecliptic1 #bf4 obliquity (1 #be4 ,ellipse1 #cc4 ,epo*s = planet>y motion1 #cj4 ,en]gy1 radiant1 #ge4 cond5sation (1 #gf4 ,epicycle1 #cb4 ,equation ( "t1 #ec4 ,equator1 #af1 #ba4 ,equatorial m\nt+1 #hj4 ,equ9oxes1 #be4 ,e!r1 #ge4 ,ev5+ />1 #ca4 ,facul1 #abb4 ,fall+ bodies1 law (1 #ce4 ,f9d+ ! />s1 #ad4 ,fraunh(] l9es1 #hg4 ,galaxy1 #bai4 ,geography ( ! sky1 #af4 ,graphical repres5tation1 #f4 ,grat+1 diffraction1 #hd4 ,gravitation1 law (1 #cg4 ,h>ve/ moon1 #ic4 ,heat ( ! sun1 #aah1 #abf4 ,helmholtz1 contraction !ory ( ! sun1 #abf1 #bbh4 ,horizon1 #d1 #ba4 ,h\r angle1 #ba4 ,h\r circle1 #ba4 ,hyp]bola1 #ch4 ,japetus1 satellite ( ,saturn1 #ade4 ,jupit]1 #acf4 atmosph]e1 #aci4 belts1 #acg4 invisible f fix$ />s1 #aig4 orbit (1 #bi4 physical condition1 #aci4 rotation & flatt5+1 #ach4 satellites1 #adj4 surface m>k+s1 #acg4 ,kepl]'s laws1 #cc1 #aaa4 ,latitude1 det]m9ation (1 #ah4 ,leap ye>1 #fa4 ,l5ses1 #gg4 ,leonid meteor %[]1 #agb4 p]turbations (1 #agd4 ,librations ( moon1 #ih4 ,life ^u ! planets1 #aeg4 ,light curves1 #bje4 ,light1 nature (1 #ge4 ,light ye>1 #aij4 ,limits ( eclipses1 #fh4 ,longitude1 #ef4 det]m9ation (1 #eh4 ,lunation1 #fj4 ,magnify+ p[] ( telescope1 #gi4 ,magnitude1 /ell>1 #i1 #ahf4 ,m>s1 atmosph]e1 temp]ature1 #aej4 canals1 #aed4 orbit1 #cj4 pol> caps1 #aeb4 rotation1 #aea4 satellites1 #aee4 surface m>k+s1 #aej4 ,mass1 det]m9ation (1 #cg4 ( comets1 #afd4 ( d\ble />s1 #bjj4 ( moon1 #id4 ( planets1 #dj1 #acc4 ,measurem5ts1 accurate1 #a4 ,m]cury1 #adi4 motion ( its p]ihelion1 #dc4 orbit (1 #cj4 ,m]idian1 #ai1 #ba4 ,meteors1 nature (1 #afe1 #afi4 numb] (1 #afg4 velocity1 #agj4 ,meteors & comets1 relation (1 #age4 ,meteor %[]s1 radiant1 #aga4 ,leonids1 capture (1 #agb1 #agc4 p]turbations1 #agd4 ,milky ,way1 #bai4 ,mira1 o ,ceti1 #bjd4 ,mirrors1 #gg4 ,mon?1 #fj4 ,moon1 #ia4 alb$o1 #ig4 atmosph]e1 #ajc4 *anges 91 #ajh4 d5sity1 surface gravity1 #ie4 developm5t (1 #bda4 h>ve/ moon1 #ic4 influ5ce ^u ! e>?1 #aji1 #bcc4 librations1 #ih4 map (1 #aja4 mass & size1 #id4 motion1 #bd1 #ib4 m\nta9s & crat]s1 #ajd4 phases1 #ia1 #ib4 physical condition1 #ajj1 #ajg4 ,mon?1 #fj4 ,morn+ />1 #ca4 ,motion 9 l9e ( sight1 #hi1 #aic4 ,multiple />s1 #bjb4 ,names ( />s1 #h4 ,nebul1 #bad4 d5sity1 #bag4 developm5t (1 #bde4 motion1 #bah4 spectra1 #baf4 types & classes (1 #bae4 ,nebul> hypo!sis1 #bcj4 objections to1 #bca4 ,neptune1 #adf4 discov]y (1 #da4 ,newton's laws ( motion1 #cd4 law ( gravitation1 #cg1 #dc4 ,nodes1 #ci4 relation to eclipses1 #fg1 #ga4 ,nucleus1 ( comet1 #afj4 ,objective1 ( telescope1 #gh4 ,obliquity ( ecliptic1 #be4 ,obs]vations1 ( />s1 #aj4 ,occultation ( />s1 #ajc4 ,orbits1 ( comets1 #afa4 ( d\ble />s1 #aii4 ( moon1 #ib4 ( planets1 #bh4 ,orion nebula1 #bae4 ,p>abola1 #ce1 #ch1 #afa4 ,p>abolic velocity1 #ch4 ,p>allax1 #aad1 #ahh4 ,p5umbra1 #fd1 #aba4 ,p]ihelion1 #ch4 ,p]iodic comets1 #agf4 ,p]sonal equation1 #hb4 ,p]turbations1 #ci4 ( meteors1 #agd4 ,phases1 ( ! moon1 #ia1 #ib4 ,photography1 #ha4 ( />s1 #ac4 ,photosph]e1 ( sun1 #aba4 ,planets1 #bf1 #acc4 di/ances f ! sun1 #acd4 h[ to f9d1 #bi4 mass1 d5sity1 size1 #acc4 motion (1 #bg1 #ch4 p]iodic times (1 #cj4 ,planet>y nebul1 #bae4 ,pleiades1 #af1 #bae4 ,plumb-l9e app>atus1 #aa1 #ah4 ,poles1 #ba4 ,precession1 #df4 ,prisms1 #hd4 ,problem ( ?ree bodies1 #ci4 ,prom95ces1 sol>1 #abe4 ,prop] motions1 #aia4 ,protractor1 #b4 ,ptolemaic sy/em1 #cb4 ,radiant en]gy1 #ge4 ,radiant1 ( meteor %[]1 #aga4 ,radius victor1 #cc4 ,ref]5ce l9es & circles1 #ag4 ,refraction1 #ej4 ,"r asc5sion1 #af1 #bj1 #ba4 ,ro*e's limit1 #bci4 ,rotation1 ( e>?1 #ee4 ( ,m>s1 #aea4 ( moon1 #ii4 ( ,jupit]1 #ach4 ( ,saturn1 #add4 ( sun1 #abj1 #acb4 ,s>os1 #gb4 ,satellites1 ( ,jupit]1 #acf1 #adj4 ( ,m>s1 #aee4 ( ,saturn1 #ade4 ,saturn1 #adb4 ball (1 #add4 orbit1 #bi4 r+s1 #adb4 rotation1 #add4 satellites1 #ade4 ,seasons1 on ! e>?1 #dg4 on ,m>s1 #aea4 ,%ad[ cone1 #fd1 #ff4 ,sid]eal "t1 #bj1 #ed4 ,%oot+ />s1 #aeh4 7,see ,meteor47 ,spectroscope1 #hd4 ,spectroscopic b9>ies1 #bjc4 ,spectrum1 #hd1 #hg4 ( comets1 #ahb4 ( nebul1 #baf4 ( />s1 #baa4 types (1 #hh4 ,spectrum analysis1 #he4 ,spiral nebul1 #bae4 ,/&>d "t1 #eg4 ,/>s1 #h1 #ahd4 classes (1 #bab4 clu/]s1 #bac4 colors1 #bji4 d>k />s1 #bja4 developm5t (1 #bdb4 di/ances f ! sun1 #ahh1 #aif4 di/ribution (1 #bbj4 d\ble />s1 #aih1 #bjc4 drift1 #aid4 magnitudes1 #i1 #aif4 numb] (1 #ahe4 spectra1 #baa4 tempor>y1 #bjh4 v>iable1 #bjd4 ,/>light1 absorption (1 #bbe4 ,/> maps1 con/ruction (1 #bc4 ,/ell> sy/em1 ext5t (1 #bbc4 ,sun's app>5t motion1 #be4 real motion1 #aie4 ,sun1 #aaj4 *emical composition1 #aaf4 *romosph]e1 #abd4 corona1 #abc4 di/ance f ! e>?1 #aaa4 facul1 #aai1 #abb4 gase\s con/itution1 #abg4 heat (1 #aag4 me*anism (1 #abf4 physical prop]ties1 #aae-abj4 prom95ces1 #abe4 rotation1 #abj1 #acb4 surface (1 #aai4 temp]ature1 #aah4 ,sun spots1 #aai1 #aba4 p]iod1 #abi1 #aca4 zones1 #acj4 ,telescopes1 #gh4 equatorial m\nt+ =1 #hj4 magnify+ p[] (1 #gi4 ,temp]ature ( ,jupit]1 #aci4 ( ,m>s1 #aeb4 ( ,m]cury1 #adi4 ( moon1 #ajg4 ( sun1 #aah4 ,tempor>y />s1 #bjh4 ,t]m9ator1 #ia4 ,t5? met]1 #ge4 ,tidal friction1 #bcc-bch4 ,tides1 #db4 ,"t1 sid]eal1 #bj1 #ed4 sol>1 #eb4 det]m9ation (1 #bj4 equation (1 #ec4 /&>d1 #eg4 ,triangulation1 #c4 ,trifid nebula1 #bae4 ,twilight1 #ea4 ,tw9kl+1 ( />s1 #dh4 ,univ]se1 developm5t (1 #bbf4 /ability (1 #bdg4 ,uranus1 #adf4 ,v>iable />s1 #bjd4 ,velocity1 its relation to orbital motion1 #ch4 ,v5us1 #adh4 orbit (1 #cj4 ,v]nal equ9ox1 #ba1 #be4 ,v]tical circle1 #ba4 ,wave front1 #gf4 ,wave l5g?s1 #ge1 #hf4 ,ye>1 #be4 leap ye>1 #fa4 sid]eal ye>1 #ei4 tropical ye>1 #fj4 ,z5i?1 #ba4 ,zodiac1 #bf4 ,zodiacal light1 #afh4 ,,! ,,end