,illu/ration3 ,plate ,i4 ,! ,,cop]nican or ,,sol> ,,sy/em4 ,! comp>ative ,di/ances ( ! ,planets f ! ,sun ,t4 ,cond] ,sculpt4 ,,! ,,/udy ,,( ,,a/ronomy1 ,,adapt$ ,,to ,,! ,,capacities ,,( ,,y\?3 ,,9 ,,twelve ,,famili> ,,dialogues1 ,,betwe5 ,a ,,tutor ,,& ,,8 ,,pupil3 ,expla9+ ! ,g5]al ,,ph,,nom5a ( ! ,,heav5ly ,,bodies1 ! ,,!ory ( ! ,,tides1 c4 ,,illu/rat$ ,,) ,,copp]-,,plates4 ,,by ,,john ,,/$man4 ,,london3 ,,pr9t$ ,,= ,c4 ,,dilly1 ,,9 ,,! ,,p\ltry4 ,m4,,dcc4,,xcvi4 ---------------------------------------- -------------------------------- ,,errata4 ,page #bj4 l9e #h4 = he read !4 ---- #bb4 -- #f4 ---- #bc4 -- #b4 -- disk -- disc4 ---- #db4 -- la/ ---- #gi4 -- #e4 ---- #gd4 -- #f4 -- x axis -- its axis4 ---- #gh4 -- #ai4 dele ,m]cury4 ---------------------------------------- -------------------------------- ,,preface4 ,x has long be5 a matt] ( surprize to ^? :o are int]e/$ 9 ! education ( y\?1 t1 among ! num]\s publications int5d$ = _! improvem5t1 s few attempts h be5 made to facilitate ! /udy ( ,a/ronomy4 ,_m excell5t treatises h be5 writt5 on ?is important & useful sci5ce2 b if x be consid]$ t !y ab\nd ) te*nical t]ms1 un9telligible to juv5ile m9ds1 x _c be expect$ t !y %\ld d]ive any great advantage f ! p]usal ( !m4 ,to remove ^! difficulties1 ! ,au?or has endeav\r$1 :5ev] he _h occasion to use !m1 to give su* illu/rations z to leave no d\bt on ! "y /ud5t's m9d respect+ _! true mean+4 ,! subject appe>$ to him to be be/ calculat$ = dialogues1 :i* are c]ta9ly m agreeable z well z m p]spicu\s to "y p]sons1 ?an ! disc\rag+ =mality ( a treatise4 ,& x is presum$ ! language w be f\nd natural & easy4 ,9 ! ord] he has *os51 he has be5 c>eful n to introduce any ?+ new1 till ! =m] "p1 on :i* x dep5ds1 has be5 cle>ly expla9$4 ,on ! :ole1 x has be5 8 aim to r5d] x z concise & pla9 z ! nature ( ! subject w admit2 & he flatt]s himself1 t at a "t :5 ! sci5ces are s univ]sally /udi$1 ! introduction n[ (f]$ to ! public w n be unacceptable4 ---------------------------------------- -------------------------------- ,,cont5ts4 ,,dialogue ,i4 p4 #a4 ,introduction4 ,def9ition4 ,! sun & planets4 ,a globe def9$4 ,sun's di/ance & magnitude4 ,planets1 :at2 _! names1 p]iods1 & di/ances f ! sun2 _! magnitudes1 comp>$ ) ! e>?2 call$ inf]ior & sup]ior1 :y4 ,comets2 d]ivation ( ! "n4 ,sol> sy/em2 :y s call$4 ,,dialogue ,,ii4 p4 #aj4 ,diff]5t sy/ems expla9$4 ,planets appe> l />s2 !y %9e by reflection2 h[ kn[n f />s2 !y nev] tw9kle1 :y4 ,/>s %9e ) _! own native light2 _! inconceivable di/ance2 are suns1 ! c5t]s ( o!r sy/ems4 ,plurality ( worlds4 ,,dialogue ,,iii4 p4 #bj4 ,! e>? has ! appe>ance ( a /> to ,v5us4 ,remote objects appe> at equal di/ances f u4 ,our e>? is a moon to ! moon4 ,! orb ( ! moon visible soon aft] ! *ange2 h] disc & bulk comp>$ ) ! e>?2 h] mean di/ance4 ,sun's disc comp>$ ) h]s4 ,our sun a />1 if se5 f a planet ( ano!r sy/em4 ,/>s z f> f ea* o!r z ! ne>e/ is to u4 ,/>s di/+ui%$ by _! app>5t magnitude4 ,! ,milky ,way innum]able />s4 ,numb] ( />s visible at "o "t to ! nak$ eye4 ,,dialogue ,,iv4 p4 #bi4 ,/>s divid$ into con/ellations2 necess>y = asc]ta9+ ! situation ( ! planets1 & ( ! />s ) ea* o!r4 ,planets motion regul> if se5 f ! sun2 irregul> z se5 f ! e>?1 ! motion be+ sometimes direct1 sometimes retrograde2 at o!rs !y appe> /ation>y4 ,sup]ior & inf]ior conjunction1 & opposition1 :at4 ,v5us has ! diff]5t phases ( ! moon4 ,planets1 h[ di/+ui%$ f ea* o!r4 ,,dialogue ,v4 p4 #ci4 ,ecliptic1 :at4 ,incl9ation ( ! orbits ( ! planets4 ,nodes ( ! planets1 :at4 ,a plane1 :at4 ,planets move 9 unb\nd$ space4 ,m]cury & ,v5us se5 on ! sun's disc4 ,numb] ( signs 9 ! zodiac4 ,zodiac1 :at4 ,a degree1 :at4 ,names ( ! signs4 ,numb] ( degrees 9 ea* sign4 ,sun's place 9 ! ecliptic4 ,table ( signs1 _! *>act]s1 c4 ,to f9d ! sun's place 9 ! ecliptic = any day 9 ! ye>4 ,,dialogue ,,vi4 p4 #ej4 ,! orbits ( ! planets are n true circles1 b some:at elliptical4 ,p]ihelion1 aphelion1 & mean di/ance1 :at4 ,attraction1 :at4 ,laws ( attraction4 ,attraction ( gravitation1 its effects4 ,simple motion rectil9eal4 ,attractive or c5tripetal1 & projectile or c5trifugal =ces1 :at4 ,,dialogue ,,vii4 p4 #fa4 ,bodies mov+ 9 circles h a t5d5cy to fly (f4 ,planets kept 9 _! orbits by ! jo9t action ( ! c5tripetal & c5trifugal =ces2 !y describe equal areas 9 equal times4 ,orbits ( ! comets v elliptical4 ,! e>? 9 its p]ihelion 9 ,decemb]4 ,equation ( "t4 ,c5t] ( gravity1 :at2 sun & planets move r\nd x4 ,sun ! c5t] ( ! sy/em4 ,,dialogue ,,viii4 p4 #gc4 ,! e>? revolves on its axis4 ,cause ( day & night4 ,! motion ( ! e>? s uni=m z n to be p]ceiv$4 ,! app>5t motion ( ! sun caus$ by ! e>?'s motion on its axis4 ,an objection to ! e>?'s motion answ]$4 ,! sun & "s ( ! planets revolve on _! axes4 ,atmosph]e1 :at2 cause ( twilight4 ,horizon1 :at2 ! sun & moon appe> l>ge/ ne> ! horizon1 :y2 !y appe> above ! horizon :5 bel[ x2 caus$ by refraction2 prov$ by exp]im5t4 ,,dialogue ,,ix4 p4 #hg4 ,incl9ation ( ! e>?'s axis4 ,an angle1 :at4 ,! poles1 :at4 ,equ9octial1 :at4 ,e>?'s p>allelism describ$4 ,! axis ( ! e>? po9ts to ! same p>ts ( ! heav5s4 ,equator1 ecliptic1 pol> circles1 & m]idians1 expla9$4 ,diff]5ce ( "t betwe5 places ly+ "u diff]5t m]idians4 ,longitude1 :at4 ,h[ to r$uce longitude to "t1 & "t to longitude4 ,latitude1 :at4 ,,dialogue ,x4 p4 #aja4 ,! seasons4 ,v]nal & autumnal equ9oxes4 ,days & nights always equal1 if ! axis ( ! e>? 7 p]p5dicul> to ! plane ( its orbit4 ,seasons occasion$ by ! incl9ation ( ! e>?'s axis4 ,seasons cont9u$4 ,days & nights equal at all times "u ! equator4 ,! sun above ! horizon ( ! poles six mon?s2 & six mon?s bel[ !m alt]nately1 s t !y h b "o day & "o night 9 ! ye>2 ! longe/ day "u ! pol> circles is tw5ty-f\r h\rs4 ,! sun rises on diff]5t po9ts ( ! compass at diff]5t seasons ( ! ye>4 ,twilight 9 ! pol> regions ( long duration4 ,we are ne>e/ ! sun 9 w9t]1 yet x is our colde/ season1 :y4 ,! e>? divid$ into zones2 prov$ to be globul>1 b is n a true sph]e4 ,,dialogue ,,xi4 p4 #abj4 ,! moon4 ,h] diamet]1 synodical & p]iodical revolutions4 ,h] phases4 ,has always ! same side to ! e>?1 & makes a revolution on h] axis e lunation4 ,has m\nta9s & valleys1 b no seas nor atmosph]e2 yet may be inhabit$4 ,h] real & app>5t motion describ$4 ,eclipses4 ,( ! sun2 total & p>tial eclipses4 ,digit1 :at4 ,eclipse ( ! moon4 ,p5umbra1 :at4 ,c5tral & total eclipse4 ,:y we h n an eclipse at e full & *ange ( ! moon4 ,%e does n always rise ) ! sun at *ange2 nor :5 he sets at full4 ,%e is visible :5 totally eclips$4 ,,dialogue ,,xii4 p4 #acf4 ,tides4 ,occasion$ by ! attraction ( ! sun & moon1 & _! c5trifugal =ces2 exemplifi$ by an exp]im5t4 ,spr+ & neap tides4 ,tides n highe/ directly "u & opposite ! moon1 b aft] %e has pass$ ! m]idian4 ,!y are lat] & lat] e day4 ,rule = f9d+ ! proportional magnitudes ( ! planets comp>$ ) ! e>?2 or ! proportion t "o globe be>s to ano!r4 ,a cube numb]1 :at4 ,table ( roots1 squ>es1 & cubes2 an example4 ,rule = f9d+ ! mean di/ances ( ! planets f ! sun4 ,dr4 ,turn]'s rule = extract+ ! cube root2 an example to expla9 ! rule4 ,example to f9d ! mean di/ance ( ,m]cury f ! sun4 ,table ( diamet]s1 c4 ,conclusion4 ---------------------------------------- -------------------------------- ,,dialogue ,i4 ,,tutor4 ,well1 ,sir6 ,i suppose ?is e>ly visit is 9 consequ5ce ( my promise1 & y\r anxiety to become an a/ronom]4 ,,pupil4 ,x is1 ,sir4--,& z a/ronomy is a sci5ce ( :i* ,i h a v imp]fect idea1 ,i mu/ beg ( y to expla9 x to me4 ,,tutor4 ,t ,i %all d ) pleasure4 ,b y surely _c :olly =get :at ,i h =m]ly told y4 ,h[ev]1 z ,i mean to treat ! subject z if y _h no previ\s k ( x1 y w h an opportunity f :at y c recollect1 to make su* rem>ks1 & ask su* que/ions1 z may appe> mo/ mat]ial to y4 ,,pupil4 ,i ?ank y1 ,sir1 x is j :at ,i wi%4 ,,tutor4 ,by a/ronomy !n is meant a k ( ! heav5ly bodies1 ! sun1 moon1 planets1 comets1 & />s1 respect+ _! nature1 magnitudes1 di/ances1 motions1 c4 ,,pupil4 ,i fe> ,i %all f9d x a difficult /udy4 ,,tutor4 ,h pati5ce4---- 8,! wise & prud5t conqu] difficulties1 8,by d>+ to attempt !m4 ,slo? & folly 8,%iv] & %r9k at sight ( toil & dang]1 8,& make ! impossibility !y fe>40 ,,pupil4 ,?is gives me enc\ragem5t1 &1 if y w h pati5ce ) me1 ,i w endeav\r to pr(it by y\r in/ructions4----,pray1 ,sir1 :at is ! sun8 ,,tutor4 ,! sun1 ! s\rce ( light & heat1 has be5 consid]$ a globe ( fire1 r\nd :i* sev5 o!r sph]ical bodies revolve at diff]5t di/ances f him1 & 9 diff]5t p]iods ( "t1 f we/ by s\? to ea/4 ,^! are ! planets#a4 ,footnote #a3 ,f ,planeta1 rov+ or w&]+4 ,,pupil4 ,any r\nd ball is a globe1 is x n8 ,,tutor4 ,a sph]e or globe is def9$ a r\nd solid body1 e "p ( ^: surface is equally di/ant f a po9t )9 call$ its c5t]2 & a l9e drawn f "o side ?r\gh ! c5t] to ! opposite side1 is call$ its diamet]4 ,,pupil4 ,y say ! sun has be5 consid]$ a globe ( fire4 ,is he n n[ ?\ght to be s8 ,,tutor4 #b;,doctor ,h]s*ell1 f "s late obs]vations1 is ( a diff]5t op9ion4--,b :at ?9k y ( 8 magnitude8 ,footnote #b3 ,see 8 lett] read at ! ,royal ,society1 ,decemb] #ah?1 #agid4 ,,pupil4 ,i really _c conjecture4--,?is ,i "k1 t :5 ,i saw him ?r\gh ! fog ! o!r day1 he appe>$ ab\t ! size ( a common plate4 ,,tutor4 ,y mu/ n always judge by appe>ances4 ,y w f9d t !re is a mat]ial diff]5ce betwe5 8 real & app>5t magnitude1 :i* ,i ?9k y w be conv9c$ ( :5 ,i tell y1 t he is no less ?an #ie millions ( miles f our e>?4 ,,pupil4 ,n9ety-five millions ( miles6 ,y a/oni% me4 ,,tutor4 ,y w1 ,i d>e say1 be no less surpriz$ at be+ told1 t he is m ?an a million ( times z l>ge z our e>?4 ,,pupil4 ,x is almo/ incr$ible6 ,& :at are ! planets8 ,,tutor4 ,! planets are opaque1 t is d>k bodies1 :i* receive _! light f ! sun2 &1 z ,i told y1 revolve ab\t him4 ,! fir/1 or t ne>e/ ! sun1 is call$ ,m]cury1 ! next ,v5us1 !n ! ,e>?1 ,m>s1 ,jupit]1 ,saturn1 & ,georgian1 or ! ,georgium ,sidus4#c ,^! are call$ prim>y planets4 ,footnote #c3 ,_! *>act]s are1 ,sun1 ,m]c4 ,v5us1 ,e>?1 ,m>s1 ,jup4 ,saturn1 ,georgian1 4 ,,pupil4 ,are !re !n any o!rs8 ,,tutor4 ,yes4 ,!re are f\rte5 o!rs1 :i* move r\nd _! respective prim>ies z _! c5t]s1 & ) !m r\nd ! sun1 & are call$ second>ies1 satellites or moons4 ,,pupil4 ,h all ! prim>ies second>ies8 ,,tutor4 ,only f\r ( !m h moons4 ,! e>?1 ,i ne$ n tell y1 has "o2 ,jupit] has f\r2 ,saturn sev51 besides a /up5d\s r+ :i* surr\nds 8 body2 & ,georgian two4 ,,pupil4 ,9 :at "t1 & at :at di/ances1 f ! sun1 d ! planets p]=m _! p]iodical revolutions8 ,,tutor4 ,m]cury revolves ab\t ! sun 9 #hh days1 at ! di/ance ( #cf millions ( miles4 ,v5us1 at ! di/ance ( #fh millions ( miles1 completes h] revolution 9 #bbd days4 ,e>?1 on :i* we live1 at ! di/ance ( #ie millions ( miles1 p]=ms its p]iod 9 "o ye>4#d ,footnote #d3 ,! motion ( ! e>? 9 its orbit is at ! rate ( #fh ?\s& miles an h\r4 ,m>s1 at ! di/ance ( #ade millions ( miles1 9 little less ?an two ( our ye>s4 ,jupit]1 at ! di/ance ( #did millions ( miles1 9 ne> #ab ye>s4 ,saturn1 at ! di/ance ( #ijf millions ( miles1 9 ab\t #cj ye>s4 ,georgian1 discov]$ a few ye>s s9ce by ,dr4 ,h]s*ell1 p]=ms its p]iod at ! di/ance ( #ahab millions ( miles1 9 ab\t #hc ye>s4#e ,footnote #e3 ,z ! di/ances ( ! planets1 :5 m>k$ 9 miles1 are a bur!n to ! memory1 a/ronom]s (t5 express _! mean di/ances 9 a %ort] way1 by suppos+ ! di/ance ( ! e>? f ! sun to be divid$ into t5 p>ts4 ,m]cury may !n be e/imat$ at f\r ( su* p>ts f ! sun1 ,v5us at sev51 ! ,e>? at t51 ,m>s at fifte51 ,jupit] at fifty-two su* p>ts1 ,saturn at n9ety-five1 & ,georgian #aij p>ts4 ,see ,plate ,i4 ,fig4 #a4 ,^! are calculat$ by multiply+ ! respective di/ances ( ! planets by #aj1 & divid+ by #ie1 ! mean di/ance ( ! e>? f ! sun2 & may be set (f by any scale ( equal p>ts4 ,,pupil4 ,:at proportion does ! e>? be> 9 magnitude to ! o!r planets8 ,,tutor4 ,! e>? is f\rte5 times z l>ge z ,m]cury1 v little l>g] ?an ,v5us1 & ?ree times z l>ge z ,m>s4 ,b ,jupit] is m ?an f\rte5 hundr$ times z l>ge z ! e>?2 ,saturn above a ?\s& times z l>ge1 exclusive ( 8 r+2 & ,georgian eighty-two times z l>ge4 ,,pupil4 ,h y any ?+ else1 ,sir1 to rem>k conc]n+ ! planets8 ,,tutor4 ,!re are sev]al o!r ?+s ,i int5d to make y acqua9t$ )1 namely1 _! nature1 appe>ances1 motions1 c4 ,at pres5t ,i %all only say1 t ,m]cury & ,v5us are call$ #f;inf]ior planets1 _! orbits or pa?s describ$ 9 go+ r\nd ! sun1 be+ )9 t ( ! e>?2 & ! o!r f\r1 ^: orbits are )\t ! e>?'s orbit1 #gsup]ior planets4 ,footnote #f3 ,p]haps ) m propriety int]ior or inw>d4 ,footnote #g3 ,ext]ior or outw>d4 ,,pupil4 ,!re is "o ?+ m ,i wi% to "k1 if---- ,,tutor4 ,i suppose y 7 go+ to say if n too mu* tr\ble2 t is q unnecess>y1 z y well "k t :]e ,i see a desire to le>n1 tea*+ is to me a pleasure4--,:at is x8 ,,pupil4 ,t y w be s k9d z to in=m me :at ! comets are1 & if !y h any motion8 ,,tutor4 ,! k we h ( comets is v imp]fect1 z !y af=d few obs]vations on :i* to gr\nd conjecture4 ,!y are g5]ally suppos$ to be planet>y bodies1 =m+ a "p ( our sy/em3 =1 l ! planets1 !y revolve ab\t ! sun1 b 9 diff]5t directions1 & 9 extremely long elliptic curves1 be+ sometimes ne> ! sun1 at o!rs /ay+ f> beyond ! orbit ( ! out]mo/ planet2 :]eas ! orbits ( ! planets are ne>ly circul>4 ,! p]iod ( "o1 :i* appe>$ 9 #afhj1 is comput$ to be #ege ye>s4 ,,pupil4 ,:5ce d !y d]ive _! "n8 ,,tutor4 ,f ,cometa1 a hairy />1 because !y appe> ) long tails1 some:at resembl+ hair3 "s1 h[ev]1 h be5 se5 )\t ?is app5dage1 z well def9$ & r\nd z planets4 ,,pupil4 ,y say our sy/em3 :at am ,i to und]/& by x8 ,,tutor4 ,! ^w sy/em1 9 an a/ronomical s5se1 means a numb] ( bodies mov+ r\nd "o common c5t] or po9t3 &1 because ! planets & comets revolve ab\t ! sun1 x is call$ ! ,sol> ,sy/em 7,plate ,i4 fig4 #b472 & we say our sy/em1 z ! e>? is "o ( ! planets4 ,o!r sy/ems h be5 inv5t$ = solv+ ! appe>ances & motions ( ! heav5ly bodies1 a description ( :i* ,i %all leave till ,i next see y4 ---------------------------------------- -------------------------------- ,,dialogue ,,ii4 ,,pupil4 ,i am afraid1 ,sir1 ,i am come be=e y are prep>$ = me3 b ! v great pleasure ,i receiv$ ye/]day1 induc$ me to be ) y z e>ly z possible4 ,,tutor4 ,i am glad to see y1 & happy to f9d y are s well pleas$ ) y\r difficult /udy4 ,x w1 ,i assure y1 give y m exalt$ ideas ( ! ,deity ?an any t ,i "k (4 ,! ,psalmi/ 0 und\bt$ly ( ?is op9ion :5 he said1 ,! ,heav5s decl>e ! glory ( ,god1 & ! ,firmam5t %ewe? 8 h&y "w4 ,,pupil4 ,i w no long] call x a difficult1 b a pleas+ /udy1 & feel myself a%am$ at hav+ us$ ! expression4 ,i %all n[ beg y to expla9 to me ! diff]5t sy/ems4 ,,tutor4 ,! sy/em ,i h be5 describ+ to y 0 kn[n & taught by ,py?agoras1 a ,greek philosoph]1 :o fl\ri%$ ab\t #ejj ye>s be=e ,*ri/1 z he f\nd x impossible1 9 any o!r way1 to give a consi/5t acc\nt ( ! heav5ly motions4 ,?is sy/em1 h[ev]1 0 s extremely opposite to all ! prejudices ( s5se & op9ion1 t x nev] made any great progress1 nor 0 ev] widely spread 9 ! anci5t _w4 ,ptolemy1 an ,egyptian philosoph]1 :o fl\ri%$ #acj ye>s aft] ,*ri/1 suppos$ t ! e>? 0 fix$ 9 ! c5t]1 & t ! sun & ! re/ ( ! heav5ly bodies mov$ r\nd x 9 tw5ty-f\r h\rs1 or "o natural day1 z ?is seem$ to correspond ) ! s5sible appe>ances ( ! cle/ial motions4 ,?is sy/em 0 ma9ta9$ f ! "t ( ,ptolemy to ! revival ( le>n+ 9 ! sixte5? c5tury4 ,at l5g?1 ,cop]nicus1 a native ( ,pol&1 a bold & orig9al g5ius1 adopt$ ! ,py?agorean sy/em1 & publi%$ x to ! _w 9 ! ye> #aecj4 ,?is doctr9e _h be5 s long 9 obscurity1 t ! re/or] ( x 0 consid]$ z ! inv5tor4 ,europe1 h[ev]1 0 /ill imm]s$ 9 ignorance2 & ! g5]al ideas ( ! _w 7 n able to keep pace ) ^? ( a ref9$ philosophy4 ,?is occasion$ ,cop]nicus to h few abettors1 b _m oppon5ts4 ,ty*o ,brahe1 9 p>ticul>1 a noble ,dane1 s5sible ( ! defects ( ! ,ptolemaic sy/em1 b unwill+ to ackn[l$ge ! motion ( ! e>?1 endeav\r$1 ab\t #aehf1 to e/abli% a new sy/em ( 8 own2 b1 z ?is prov$ to be /ill m absurd ?an t ( ,ptolemy1 x 0 soon explod$1 & gave way to ! #h;,cop]nican or true ,sol> ,sy/em4 ,footnote #h3 ,see ,plate ,i4 fig4 #b4 ,,pupil4 ,i confess1 ,i %\ld h ?\ght ) ,ptolemy1 t ! e>? 0 9 ! c5t]1 & t ! sun mov$ r\nd x4 ,,tutor4 ,y mu/ at pres5t cont5t y\rself ) kn[+ t x is n s2 & x %all be my bus9ess to prove x4 ,,pupil4 ,may ,i beg ! fav\r ( ! in=mation y int5d$ respect+ ! planets8 ,,tutor4 ,i w grant x ) pleasure4 ,! planets are sph]ical bodies1 :i* appe> l />s1 b are n lum9\s2 t is1 !y h no light 9 !mselves2 ?\gh !y give u light2 = !y %9e by reflect+ ! light ( ! sun4 ,,pupil4 ,y say1 ,sir1 t !y appe> l />s2 if s1 h[ am ,i to "k !m f />s8 ,,tutor4 ,v easily3 = ! />s1 or z !y are m prop]ly call$ fix$ />s1 always keep ! same situation ) respect to ea* o!r2 :]eas ! planets1 z !y move r\nd ! sun1 mu/ be cont9ually *ang+ _! places among ! fix$ />s1 & ) "o ano!r4 ,,pupil4 ,is !re any o!r me?od ( di/+ui%+ !m besides :at y h m5tion$8 ,,tutor4 ,yes4 ,! planets nev] tw9kle l ! fix$ />s1 & are se5 e>lie/ 9 ! ev5+ & late/ 9 ! morn+4 ,,pupil4 ,h[ is ! tw9kl+ ( ! />s 9 a cle> night acc\nt$ =8 ,,tutor4 ,x arises f ! cont9ual agitation ( ! air or atmosph]e ?r\gh :i* we view !m2 ! p>ticles ( air be+ always 9 motion1 w cause a tw9kl+ 9 any di/ant lum9\s body1 :i* %9es ) a /rong light4 ,,pupil4 ,!n1 ,i suppose1 ! planets n be+ lum9\s1 is ! reason :y !y d n tw9kle4 ,,tutor4 ,mo/ c]ta9ly4 ,! feeble light ) :i* !y %9e is n suffici5t to cause su* an appe>ance4 ,,pupil4 ,h ! />s !n light 9 !mselves8 ,,tutor4 ,!y und\bt$ly %9e ) _! own native light1 or we %\ld n see ev5 ! ne>e/ ( !m3 ! di/ance be+ s imm5sely great1 t if a cannon-ball 7 to travel f x to ! sun1 ) ! same velocity ) :i* x left ! cannon1 x w\ld be m ?an #a million1 #hfh ?\s& ye>s1 be=e x rea*$ x4#i ,footnote #i3 ,! di/ance ( ,syrius is #ah1gag1ddb1fij1ebf miles4 ,a cannon-ball go+ at ! rate ( #aadc miles an h\r1 w\ld only rea* ! sun 9 ab\t #a1hfh1cjg ye>s1 #hh days4 ,adams's ,lectures1 vol4 #d4 page #dd4 ,,pupil4 ,?is is wond]ful inde$6 :at !n are !y suppos$ to be8 ,,tutor4 ,suns4 ,,pupil4 ,suns6 ! fix$ />s suns6 ,,tutor4 ,yes1 suns4 8,"o sun by day1 by night t5 ?\s& %9e40 ,& :at w increase y\r a/oni%m5t1 ea* ( !m is ! c5t] ( a sy/em ( planets1 :i* move r\nd him4#aj ,footnote #aj3 ,dr4 ,h]s*ell says1 t 9 "s clu/]s ( />s he has obs]v$1 !y appe> too close toge!r to admit any planets to revolve ab\t !m4 8,obs]ve h[ sy/em into sy/em runs40 8,:at o!r planets circle o!r suns40 ,,pupil4 ,i am almo/ lo/4--,i us$ to ?9k !y 7 design$ to give u light4 ,,tutor4 ,?is is a vulg> error4--,!y 7 d\btless creat$ = a mu* nobl] purpose1 s9ce ?\s&s ( !m are invisible to u )\t ! help ( a telescope2 & we receive m light f ! moon ?an f all ! />s toge!r4 ,,pupil4 ,h[ d y "k !y are suns8 ,is _! be+ lum9\s a pro( ( _! be+ s8 ,,tutor4 ,no4 ,b we "k t ! sun %9es ) 8 own light on all ! planets belong+ to our sy/em2 & f :at ,i h told y1 h ! greate/ reason to believe t ! />s %9e ) _! own light3 we !re=e f analogy conclude1 t !y are s _m suns convey+ light & heat to o!r worlds#aa4 ,footnote #aa3 ,dr4 ,h]s*ell ?9ks x probable t ! sun & fix$ />s may be inhabit$4 ,,pupil4 ,are !re !n o!r worlds besides ?is we live 98 ,,tutor4 ,consid]4--,has n ! e>? we inhabit a moon to enlight5 x8 ,,pupil4 ,yes1 ,sir4 ,,tutor4 ,& h ,i n told y t ,jupit]1 ,saturn1 & ,georgian1 h also moons8 ,,pupil4 ,?is ,i well rememb]4 ,,tutor4 ,= :at purpose !n d y suppose ^? orbs 7 design$8 ,,pupil4 ,inde$1 ,i _c tell4 ,,tutor4 ,y surely _c imag9e t !y 7 int5d$ = our use1 s9ce we knew no?+ ( !m till aft] ! inv5tion ( telescopes4 ,,pupil4 ,t is :at ,i ?9k no "o c suppose4 ,,tutor4 ,& d n all ! planets enjoy ! b5efit ( ! sun 9 common ) u8 ,,pupil4 ,und\bt$ly4 ,,tutor4 ,well1 !n2 ( :at use w\ld ! light & heat be :i* is convey$ to !m f ! sun2 or ! light :i* !y receive f _! moons if !re are no inhabitants8 ,,pupil4 ,i "k ( none4 ,,tutor4 ,c y !n h any d\bt ab\t _! be+ inhabit$8 ,,pupil4 ,no1 ,sir4--,b y say t ! />s are suns1 ea* ( :i* is ! c5t] ( a sy/em ( planets or worlds4 ,,tutor4 ,if y are satisfi$ t ! planets belong+ to our sy/em are inhabit$1 & t ! fix$ />s are suns1 ! c5t]s ( o!r sy/ems1 :at reasonable objection c y h to all ! planets 9 ! univ]se be+ s8 ,,pupil4 ,x is :at ,i _c compreh5d4 ,,tutor4 ,x may be s4--,b is n ! same ,almighty ,p[]1 :o does no?+ 9 va91 z capable ( mak+ t5 ?\s& worlds if he pleas$1 z well z "o8 ,,pupil4 ,i w n presume to dispute 8 p[]2 b are we n told t all mank9d desc5d$ f ,adam8 ,,tutor4 ,yes2 ,moses wrote conc]n+ ?is e>?1 he has n made u acqua9t$ ) ! inhabitants ( ! o!r planets3 = aught we "k !y might desc5d f o!r ,adams4--,to-morr[ ev5+1 ,i hope to see y aga94 ---------------------------------------- -------------------------------- ,,dialogue ,,iii4 ,,pupil4 ,i recollect1 ,sir1 y m5tion$ la/ night1 t ! planets appe> l />s4 ,our e>? is a planet2 h[ c x h ! appe>ance ( a />8 ,,tutor4 ,if y 7 on ! planet ,v5us1 ! e>? w\ld h z mu* ! appe>ance ( a /> z ,v5us has to u4 ,,pupil4 ,b ,v5us appe>s among/ ! fix$ />s4 ,,tutor4 ,yes4 ,& s w\ld ! e>? appe> f ,v5us4 ,,pupil4 ,h[ c x be8 ,,tutor4 ,because1 9 :atev] "p ( ! univ]se we are1 we appe> to be 9 ! c5t] ( a concave1 t is holl[1 sph]e1 :]e remote objects appe> at equal di/ances f u3 s t1 :e!r we are on ! planet ,v5us or on ! e>?1 9 ?is p>ticul> ! effect w be ! same4 ,,pupil4 ,!n ! light we receive f ! sun is by reflection convey$ to ! o!r planets4 ,,tutor4 ,no d\bt ( x4 ,& our e>? appe>s z a moon to ! inhabitants ( ! moon1 & und]goes ! v>i\s *anges ( t planet4 ,,pupil4 ,h y any pro( ( ?is1 ,sir8 ,,tutor4 ,no?+ c be cle>]2 =1 on a f9e ev5+1 soon aft] ! *ange ( ! moon1 :5 ! e>? appe>s ne>ly z a full moon to ! moon1 & we see a fa9t /reak ( light1 ! :ole body ( ! moon is visible to u4 ,,pupil4 ,i rememb] to h se5 x4 ,,tutor4 ,y d8--,! e>? !n w appe> !re ?irte5 times z l>ge z ! moon does to u2 ( c\rse x mu/ reflect a /rong light on ! body ( ! moon1 & x is by t light we see t "p ( ! moon :i* is turn$ f ! sun4 ,,pupil4 ,is ! e>?1 !n1 only ?irte5 times z big z ! moon8 ,,tutor4 ,9 solidity x is ab\t fifty times z l>ge2 b its disc or face is only ?irte5 times4 ,,pupil4 ,:at is ! moon's di/ance f ! e>?8 ,,tutor4 #bdj ?\s& miles1 :i* is ab\t #djj times less ?an t ( ! sun4 ,,pupil4 ,& yet %e appe>s z f> di/ant z ! sun4 ,,tutor4 ,y are n[1 ,i hope1 conv9c$ ( :at ,i said relative to di/ant objects4 ,,pupil4 ,i am1 ,sir3 & ,i suppose ! reason ( ! moon's appe>+ z l>ge z ! sun1 is because %e is s mu* ne>] to u4 ,,tutor4 ,x is s4--,=1 at a total eclipse ( ! sun1 :i* happ5s :5 ! moon is 9 a "r l9e betwe5 ! sun & ! e>?1 ! sun is obscur$ f our sight1 al?\gh 8 disc is #afj ?\s& times z l>ge z t ( ! moon4 ,9 l mann] w\ld ! moon1 :5 at full1 be hid by plac+ y\r cricket-ball 9 a l9e betwe5 y\r eye & h]1 yet1 y "k1 ! ball is n s l>ge z ! moon2 b be+ ne>] ! eye1 x is app>5tly s4 ,,pupil4 ,?is is v cle>4 ,b---- ,,tutor4 ,i conjecture y 7 go+ to ask me to expla9 ! nature ( eclipses4 ,,pupil4 ,t 0 c]ta9ly my int5tion1 ,sir4 ,,tutor4 ,!re are o!r ?+s y mu/ be made acqua9t$ ) be=e y w be able to compreh5d x1 & :i* ,i w endeav\r to make y und]/& be=e we ent] on ! subject4 ,,pupil4 ,:5ev] y please1 ,sir4 ,,tutor4 ,y h tak5 a view ( ! e>? f ! planet ,v5us4--,suppose ,i transport y to "o ( ! planets belong+ to ano!r sy/em2 :at description d y ?9k y %\ld give ( x8 ,,pupil4 ,i mu/ consid]4 ,:at ,i n[ call a /> w\ld be a sun4 ,! planets ( t sy/em ,i %\ld see z ,i n[ d ^? belong+ to ours3 our sun w\ld be a />2 & ! e>?1 ) all ! o!r planets1 w\ld be invisible4 ,,tutor4 ,v well1 ,sir4 ,c y !n f9d x difficult to conceive t all ! />s are z f> f ea* o!r 9 unb\nd$ space z our sun is f ! ne>e/ />8 ,,pupil4 ,x is h>d to conceive3 b :5 ,i consid] t :]ev] ,i am1 e remote object appe>s at an equal di/ance f me1 ! difficulty vani%es4 ,,tutor4 ,t y might =m "s idea ( ! imm5se di/ance ( ! fix$ />s1 y mu/ recollect1 ,i m5tion$ ! "t a cannon-ball w\ld be 9 rea*+ ! ne>e/ ( !m4 ,,pupil4 ,i d1 ,sir4 ,m ?an #a1hfh1jjj ye>s4 ,,tutor4 ,y h an excell5t memory4 ,i suppose !n y "k ! di/ance ( ! e>? f ! sun8 ,,pupil4 ,yes1 ,sir4 ,i wrote x d[n2 &1 x made s /rong an impression on my memory1 t ,i believe ,i %all nev] =get x4--#ie millions ( miles4 ,,tutor4 ,n[1 suppose ! e>? to be 9 t "p ( its orbit :i* is ne>e/ to ! />1 x w\ld be #ie millions ( miles ne>] to x ?an ! sun is4 ,,pupil4 ,c]ta9ly4 ,,tutor4 ,&1 9 ! opposite side ( its orbit1 z mu* f>!r f ! />4 ,,pupil4 ,)\t d\bt4 ,,tutor4 ,!n y f9d t ! e>? is #aij millions ( miles ne>] to ! /> at "o "t ( ! ye> ?an x is at ano!r2 & yet ! magnitude ( ! /> does n appe> ! lea/ alt]$1 nor is its di/ance affect$ by x4 ,,pupil4 ,a pro( ( its amaz+ di/ance4--,i 0 go+ to ask a silly "q4 ,,tutor4 ,:at is x8 p]haps n s simple z y may imag9e4 ,,pupil4 ,:e!r ! mo/ conspicu\s />s are n suppos$ to be ! ne>e/ to u8 ,,tutor4 ,und\bt$ly4--,& are call$ />s ( ! fir/ magnitude2 ! next 9 spl5dor1 />s ( ! second magnitude2 & s on to ! six? magnitude2 & ^? beyond1 :i* are n visible to ! nak$ eye1 are call$ telescopic />s4 ,,pupil4 ,! di/ance ( ! telescopic />s mu/ be great inde$1 beyond all conception4 ,,tutor4 ,y judge rightly2 & _! numb]s are beyond all computation4 ,doctor ,h]s*ell says1 he has n a d\bt b t ! broad circle 9 ! heav5s1 call$ ! ,milky ,way1 is a mo/ ext5sive /ratum ( />s1 he hav+ discov]$ 9 x _m ?\s&s4 ,besides1 "s />s appe> to him d\ble1 o!rs treble1 c4 n t !y are really s1 b are />s at diff]5t di/ances f u1 :i* appe> ne>ly 9 a "r l9e4 8,z 9 ! milky-way a %9+ :ite 8,o'erfl[s ! heav'ns ) "o cont9u$ light1 8,t n a s+le /> c %ew 8 rays1 8,:il/ jo9tly all promote ! common blaze40 ,,pupil4 ,i h he>d ( numb]+ ! />s2 b t1 ,i f9d1 is impossible4 ,,tutor4 ,if y mean t imm5se ho/ ( />s ,i h be5 describ+1 x is impossible2 b1 ?\gh 9 a cle> w9t]'s night1 )\t moon%9e1 !y seem to be innum]able1 :i* is ow+ to _! /rong sp>kl+1 & our look+ at !m 9 a confus$ mann]2 yet :5 ! :ole firmam5t is divid$ z x has be5 done by ! anci5ts1 ! numb] t c be se5 at a "t1 by ! nak$ eye1 is n above a ?\s&4 ,,pupil4 ,pray1 ,sir1 h[ did ! anci5ts divide ! firmam5t8 ,,tutor4 ,i w\ld will+ly answ] y\r "q2 b1 z ,i f9d ,i %all n h "t to give y t in=mation ,i wi%1 ,i %all po/pone x till ,i see y to-morr[ ev5+4 ---------------------------------------- -------------------------------- ,,dialogue ,,iv4 ,,tutor4 ,! anci5ts1 9 r$uc+ a/ronomy to a sci5ce1 comb9$ ! fix$ />s into con/ellations1 all[+ sev]al />s to make "o con/ellation3 &1 = ! bett] di/+ui%+ & obs]v+ !m1 !y r$uc$ ! con/ellations to ! =ms ( animals1 or to ! images ( "s kn[n ?+s1 by :i* means !y 7 enabl$ to signify to o!rs any p>ticul> /> !y meant to notice4 ,job m5tions two ( ! con/ellations1 namely1 ,orion & ,pleiades1 :i* %ews ! /udy ( a/ronomy to be v anci5t4 ,,pupil4 ,pray1 ,sir1 h[ may ,i "k !m8 ,,tutor4 ,by /udy+ ! use ( ! cle/ial globe1 on :i* !y are drawn4 ,,pupil4 ,w y be k9d en\gh to in/ruct me1 ,sir8 ,,tutor4 ,at "s future "t ,i probably may3 at pres5t y are n prep>$ = x4 ,,pupil4 ,i am satisfi$4--,h y any ?+ m to rem>k ( ! con/ellations1 ,sir8 ,,tutor4 ,yes4 ,! situation ( ! planets1 z !y are cont9ually *ang+ _! places1 c\ld n be po9t$ out )\t fir/ divid+ ! />s into con/ellations3 h5ce1 necessity 0 ! "m ( inv5tion4 ,,pupil4 ,& ,i ?9k a v +5i\s "o4--,if ,i may be all[$ a comp>ison1 ,i w suppose ! diff]5t k+doms ( ! _w on my dissect$ map1 to repres5t s _m con/ellations2 !n1 if ,i he> ( ,london1 ,i "k x is 9 ,engl&2 if ( ,p>is1 9 ,france2 ( ,lisbon1 9 ,portugal2 & s on4 ,^! ,i w\ld comp>e ) />s ( ! fir/ magnitude1 be+ ! *ief cities ( _! respective k+doms2 inf]ior cities1 />s ( ! second magnitude2 pr9cipal t[ns ( ! ?ird1 c4 ,,tutor4 ,a v apt comp>ison inde$4 ,n[ if y he> ( a travell] sett+ (f f ,london to ,dov]1 !nce to ,calais1 ,p>is1 ,b]n1 & s on to ,rome1 y "k t he mu/ g ?r\gh "p ( ,engl&1 ,fl&]s1 ,france1 ,switz]l&1 & ,italy1 pass+ _m t[ns & villages on 8 way4 ,,pupil4 ,t is v evid5t4 ,,tutor4 ,v well1 !n2 9 l mann] w\ld ! planets1 if se5 f ! sun1 be trac$ f /> to />1 f con/ellation to con/ellation1 ?r\gh _! :ole p]iods4 ,,pupil4 ,x is n possible to view !m f ! sun1 surely1 is x8 ,,tutor4 ,no1 c]ta9ly4 ,,pupil4 ,:y !n d y say if se5 f ! sun8 ,,tutor4 ,because x is !re only _! motions c appe> uni=m2 z se5 f ! e>? !y app>5tly move v irregul>ly4--,suppose y 7 9 ! c5t] ( a circul> c\rse2 &1 :il/ a horse 0 go+ r\nd1 y kept y\r eye on him3 _c y conceive t y %\ld see him run r\nd ! c\rse 9 a regul> mann]1 mov+ ! :ole "t ! same way8 ,,pupil4 ,x is n at all difficult to conceive4 ,,tutor4 ,aga94 ,imag9e y\rself plac$ at a consid]able di/ance on ! outside ( ! c\rse1 :]e y c\ld see ! horse ! :ole "t he 0 go+ r\nd1 w\ld he appe> to move z uni=mly z be=e8 ,,pupil4 ,c]ta9ly n3 on ! opposite side ( ! c\rse 8 motion w\ld be ! same z :5 ,i /ood 9 ! c5t] ( x2 :5 he 0 approa*+ me1 ,i %\ld sc>cely see him move2 9 t "p ( ! c\rse next to me he w\ld move 9 a direction contr>y to :at he did at fir/2 & aga9 :5 go+ f me1 8 motion w\ld be sc>cely visible4 ,,tutor4 ,?is ,i ?9k w give y a tol]able idea ( ! irregul> motion ( ! inf]ior planets1 z se5 f ! e>?4 ,:5 f>!/ f u _! motion is said to be direct2 :5 ne>e/ to u retrograde1 because !y appe> to be mov+ back aga92 &1 :5 approa*+1 or go+ f u1 we say !y are /ation>y2 because1 if !n obs]v$ 9 a l9e ) any p>ticul> />1 !y w cont9ue s = a consid]able "t3 n[ ^! appe>ances c\ld n happ5 if !y mov$ r\nd ! e>?4 ,,pupil4 ,no?+ c be pla9]3 = if ! e>? 7 9 ! c5t] we %\ld always see !m move ! same way4 ,,tutor4 ,:5 ! planet is ne>e/ to u1 t is 9 a l9e betwe5 u & ! sun1 we say x is 9 its inf]ior conjunction2 :5 f>!/ f u1 & ! sun is betwe5 u & ! planet1 9 its sup]ior conjunction4 ,b ! sup]ior planets h alt]nately a conjunction & an opposition4 ,,pupil4 ,a conjunction1 ,i suppose1 :5 ! sun is betwe5 ! e>? & ! planet1 & an opposition :5 ! e>? is betwe5 ! sun & ! planet2 t is1 :5 ! planet is ne>e/ to u1 & appe>s to be opposite to ! sun8 ,,tutor4 ,y are "r4--,!re=e1 :5 9 conjunction x rises & sets1 ne>ly ) ! sun2 b 9 opposition1 x rises ne>ly :5 ! sun sets1 & sets :5 he rises4 ,,pupil4 ,:y d y say ne>ly1 ,sir8 ,,tutor4 ,because x _c be exactly1 b :5 ! sun1 e>?1 & planet are 9 a "r l9e1 :i* seldom happ5s4 ,,pupil4 ,h[ d y acc\nt = ?is1 ,sir8 ,,tutor4 ,at pres5t ,i fe> y w n be able to compreh5d :at ,i wi% to expla91 z ,i mu/ use a t]m y are unacqua9t$ )4 ,! reason is1 t ! planets are v seldom 9 or ne> _! nodes at _! conjunctions or oppositions4 ,,pupil4 ,i d n inde$ und]/& :at y mean by ! ^w nodes4 ,,tutor4 ,x w be expla9$ to y 9 due "t1 & ,i %all conclude ?is ev5+ ) a few m rem>ks relative to ! appe>ance ( ! planets4 ,,pupil4 ,any ?+ y please1 ,sir4 ,,tutor4 ,y "k t ! planets1 be+ opaque bodies1 receive _! light f ! sun2 & t only t "p :i* is turn$ to ! sun c be enlight5$ by him1 :il/ ! opposite side mu/ rema9 9 d>kness4 ,,pupil4 ,?is is self-evid5t3 if ,i hold my ball to ! c&le x w h ! same effect4 ,,tutor4 ,tell me !n h[ y ?9k !y w appe> z se5 f ! e>?4 ,,pupil4 ,if1 :5 y %ew$ me ,v5us1 %e _h n appe>$ p]fectly r\nd1 ,i %\ld say t1 bo? be=e & aft] h] sup]ior conjunction ,i %\ld see h] ne>ly ) a full face2 :5 /ation>y1 only half enlight5$1 l ! moon at fir/ qu>t]2 because1 an equal portion ( ! d>k & bright p>ts w be turn$ t[>ds u2 ! bright "p w be decreas+ till h] inf]ior conjunction1 :5 ! d>k side w be turn$ t[>ds u1 & consequ5tly invisible2 ! light w !n increase2 &1 :5 %e is aga9 /ation>y1 %e w appe> l ! moon at la/ qu>t]4 ,,tutor4 ,:5 se5 ?r\gh a telescope %e has ! diff]5t appe>ances y h m5tion$2 & :5 ,i next see y ,i w %ew y t bo? ,v5us & ,m]cury may sometimes be se5 :5 9 _! inf]ior conjunctions2 ! sup]ior planets always appe> ) ne>ly a full face4 ,,pupil4 ,h[ are ! planets di/+ui%$ f ea* o!r8 ,,tutor4 ,m]cury1 f 8 vic9ity to ! sun1 is seldom se51 be+ lo/ 9 ! spl5dor ( ! sol> brightness4 ,:5 se51 he emits a v bright :ite light4 ,v5us1 kn[n by ! names ( ! morn+ & ev5+ />1 is ! brighte/1 & to appe>ance1 ! l>ge/ ( all ! planets2 h] light is ( a :ite col\r1 & s consid]able1 t 9 a dusky place %e projects a s5sible %ade4 ,%e is visible only = ?ree or f\r h\rs 9 ! morn+ or ev5+1 accord+ z %e is be=e or aft] ! sun4 ,m>s is ! lea/ bright ( all ! planets4 ,he appe>s ( a dusky r$di% hue1 & mu* l>g] at "s p]iods ?an at o!rs1 accord+ z he is ne>] to1 or f>!r f u4 ,jupit] is di/+ui%$ by 8 peculi> magnitude & light4 ,to ! nak$ eye he appe>s almo/ z l>ge z ,v5us1 b n altoge!r s bright4 ,saturn %9es b ) a pale feeble light1 less bright ?an ,jupit]1 ?\gh less ruddy ?an ,m>s4 ,! ,georgium ,sidus _c be readily p]ceiv$ )\t ! assi/ance ( a telescope4 ---------------------------------------- -------------------------------- ,,dialogue ,v4 ,,tutor4 ,be=e ,i proce$ to expla9 :at ,i promis$ y1 x is necess>y y %\ld be in=m$ t ! e>? z se5 f ! sun1 9 its p]iodical revolutions1 w describe a circle among ! />s :i* a/ronom]s call ! ecliptic1 & sometimes ! sun's annual pa?1 because ! sun1 z se5 f ! e>?1 always appe>s 9 t l9e4 ,,pupil4 ,d n all ! planets move 9 ! ecliptic8 ,,tutor4 ,no4--,on acc\nt ( ! obliquity ( _! orbits1 !y are1 9 e revolution1 "o half ( _! p]iods above ! ecliptic1 & ! o!r half bel[ x4 ,,pupil4 ,i ?9k ,i compreh5d y\r mean+2 b %all be oblig$ to y1 ,sir1 if y c make x cle>] to me4 ,,tutor4 ,i h "h a little design1 7,plate ,,ii4 ,fig4 #a47 :i* w answ] our purpose3 :]e ,s repres5ts ! sun2 ,,abcd1 ! orbit ( ! e>?2 & ,,efgh1 ! orbit ( "o ( ! inf]ior planets1 suppose ,v5us4 ,illu/ration3 ,plate ,,ii4 ,t4 ,cond] ,sculpt4 ,,pupil4 ,n[ ,i und]/& x p]fectly3 ! half ,,ehg rises above1 & ! o!r half ,,efg s9ks bel[ x1 f ! po9ts ,,eg1 :i* ,i p]ceive are 9 a l9e ) ! orbit ( ! e>?4 ,b pray1 ,sir1 h y any "n = t dott$ l9e8 ,,tutor4 ,yes1 x is call$ ! l9e ( ! nodes2 & ! po9ts ,,eg ! nodes ( ! planet3 ! latt] is call$ ! asc5d+ node1 because1 :5 ! planet is 9 ,g1 x is asc5d+ or ris+ above ! orbit ( ! e>?2 or1 :i* is ! same ?+1 above ! ecliptic3 & :5 9 ,e1 x is desc5d+ or s9k+ bel[ x1 :5ce x is call$ ! desc5d+ node4 ,b y mu/ rememb] t ! orbits ( all ! planets d n cross or int]sect ! ecliptic 9 ! same po9ts2 b t _! nodes or int]sections are at diff]5t p>ts ( x4 ,,pupil4 ,h[ c ! orbit ( ! e>? & ! ecliptic be ! same8 ,,tutor4 ,!y are v diff]5t2 b be+ 9 ! same plane1 if ! orbit ( any planet incl9es to "o x mu/ incl9e equally to ! o!r4 ,,pupil4 ,y w1 ,i fe>1 ,sir1 ?9k me v /upid3 b ,i mu/ beg ( y to in=m me :at y mean by a plane8 ,,tutor4 ,any flat surface is a plane4 ,y may !re=e suppose ! edge ( a r\nd tea-table to repres5t ! ecliptic1 & a circle )9 x1 drawn f ! c5t] ( ! table1 ! orbit ( ! e>?3 w !y n be bo? 9 ! same plane8 ,,pupil4 ,c]ta9ly4 ,,tutor4 ,y mu/ n imag9e1 :5 ,i am speak+ to y ( ! plane ( ! ecliptic1 or plane ( ! e>?'s orbit1 t x is a visible flat surface1 or1 9 speak+ ( ! orbits ( ! planets1 ,i mean solid r+s4--,no4 ,! planets p]=m _! revolutions ) ! utmo/ regul>ity1 9 unb\nd$ space2 &1 l a bird ?ro' ! air1 leave no track beh9d !m4 ,,pupil4 ,h[ !n are !y reta9$ 9 _! orbits8 ,,tutor4 ,! "q1 ,i confess1 is natural1 & is :at ,i expect$2 b ,i mu/ ( necessity po/pone x to ano!r opportunity2 & %all n[ fulfil ! promise ,i made ( %ew+ y 9 :at mann] ! inf]ior planets may be se5 :5 9 _! inf]ior conjunctions4 ,ca/ y\r eye aga9 on ! little design ,i gave y1 & consid]1 if ,v5us 7 9 h] asc5d+ node at ,g1 :5 ! e>? is at b2 or1 9 h] desc5d+ node1 at ,e1 :5 ! e>? is at a1 :at ! effect w\ld be4 ,,pupil4 ,%e w\ld be 9 a l9e ) ! sun4 ,,tutor4 ,&1 on ! sun's disc1 %e w\ld appe> a d>k r\nd spot1 pass+ ov] x4 ,^! appe>ances1 :i* are call$ transits1 happ5 v seldom3 because %e is v seldom 9 or ne> h] nodes at h] inf]ior conjunctions4 ,!re 0 "o 9 ,june #agfa1 "o 9 ,june #agfi2 & ! next w be 9 ! ye> #ahgd4 ,& z ,m]cury is se5 9 ! same mann]1 x is a pro( t _! orbits mu/ be )9 t ( ! e>?4 ,,pupil4 ,i ?ank y1 ,sir1 & %all be oblig$ to y to in=m me h[ _m con/ellations ! e>? pa/es ov] 9 e revolution8 ,,tutor4 ,twelve1 :i* correspond ) ! mon?s ( ! ye>1 & are call$ ! twelve signs ( ! zodiac4 ,,pupil4 ,:at is ! zodiac8 ,,tutor4 ,t "p ( ! heav5s :i* conta9s ! twelve signs1 & :i* y may conceive to be a zone or belt ext5d+ eight degrees on ea* side ! ecliptic1 9 :i* ! planets con/antly revolve3 s t no planet is ev] se5 m ?an eight degrees ei!r nor? or s\?1 t is above or bel[ ! ecliptic4 ,,pupil4 ,:at am ,i to und]/& by a degree8 ,,tutor4 ,all circles1 :e!r great or small1 are suppos$ to be divid$ into #cfj equal p>ts1 call$ degrees1 & ea* degree into #fj equal p>ts1 call$ m9utes3 !re=e1 if ,i speak ( a circle 9 ! heav5s1 ! circumf]5ce ( ! e>?1 or any o!r circle1 by a degree is meant ! #cfj? "p ( t circle2 & a m9ute ! #fj? "p ( a degree4 ,,pupil4 ,:at are ! names ( ! twelve signs8 ,,tutor4 ,! fir/ is call$ ,aries1 :i* y "k signifies a ,ram2 ,taurus1 ! ,bull2 ,gem9i1 ! ,tw9s2 ,canc]1 ! ,crab2 ,leo1 ! ,lion2 ,virgo1 ! ,virg92 ,libra1 ! ,balance2 ,scorpio1 ! ,scorpion2 ,sagitt>ius1 ! ,ar*]2 ,capricorn1 ! ,goat2 ,aqu>ius1 ! ,wat]-be>]2 & ,pisces1 ! ,fi%es4 ,,pupil4 ,d y wi% me to commit ^! to memory1 ,sir8 ,,tutor4 ,x is v requisite2 b z ,i "k y are fond ( v]se1 y %all he> :at ,doctor ,watts says-- ,! ,ram1 ! ,bull1 ! heav'nly ,tw9s1 ,& next ! ,crab ! ,lion %9es1 ,! ,virg91 & ! ,scales3 ,! ,scorpion1 ,ar*]1 & ,sea-goat1 ,! ,man t holds ! ,wat]-pot1 ,& ,fi% ) glitt'r+ tails4 ,,pupil4 ,i l x mu*1 z x w assi/ my memory4 ,,tutor4 ,z ! twelve signs correspond ) ! mon?s ( ! ye>1 ! e>? mu/ pass ov] ne>ly "o degree e day1 "o sign e mon?1 & 9 twelve mon?s complete a :ole circle1 or #cfj degrees2 !re=e e sign mu/ conta9 #cj degrees1 because #cj multipli$ by #ab is equal to #cfj4 ,,pupil4 ,x mu/ be s4 ,,tutor4 ,y mu/ rememb]1 t :5 ! e>? is 9 any sign1 z se5 f ! sun1 ! sun w be 9 ! opposite sign1 z se5 f ! e>?3 = in/ance1 if ! e>? be 9 ,aries1 ! sun w be 9 ,libra2 if 9 ,taurus1 ! sun w be 9 ,scorpio1 c4 !re=e1 z by ! e>?'s annual motion1 ! sun appe>s to move1 we always speak ( ! sun's1 n ! e>?'s place1 9 ! ecliptic4--,y d n seem to und]/& me8 ,,pupil4 ,n p]fectly1 ,sir4 ,,tutor4 ,take ?is orange1 & put x 9 ! middle ( ! r\nd table be=e u1 & place an apple on ! opposite side next ! w9d[3 ! orange may repres5t ! sun1 ! apple ! e>?1 & ! w9d[ ! sign ,aries4 ,n[ g r\nd ! table to ! apple2 look at ! orange1 & tell me to :at "p ( ! room ! eye w be direct$4 ,,pupil4 ,to ! "p opposite to ! w9d[1 ,sir4 ,,tutor4 ,if !n y suppose ! door1 :i* is opposite to ! w9d[1 to be ! sign ,libra1 ! sun w be 9 ,libra :5 ! e>? is 9 ,aries--w x n8 ,,pupil4 ,x is v pla94 ,,tutor4 ,i %all n[ give y a table ( ! signs1 _! *>act]s1 ! correspond+ mon?s1 & ! days ( ! mon? ! sun ent]s ea* sign1 by means ( :i*1 if y reckon a degree = a day1 y may f9d ! sun's place1 ne>ly1 = any day 9 ! ye>4 ,,pupil4 ,?is w give me mu* pleasure1 & ,i %all be happy to h x4 ,,! ,,table4 ,,nor!rn ,,signs4 ,aries1 ,taurus1 ,gem9i1 ,canc]1 ,leo1 ,virgo4 ,m>*1 ,april1 ,may1 ,june1 ,july1 ,aug4 #bj1 #bj1 #ba1 #ba1 #bc1 #bc4 ,,s\!rn ,,signs4 ,libra1 ,scorpio1 ,sagitt>ius1 ,capricorn1 ,aqua4 ,pisces4 ,sept4 ,octob]1 ,novemb]1 ,decem4 ,jan4 ,feb4 #bc1 #bc1 #ba1 #ba1 #bj1 #ah4 ,,pupil4 ,:y d y write nor!rn & s\!rn signs1 ,sir8 ,,tutor4 ,because !y are situat$ nor? & s\? ( a circle 9 ! heav5s1 call$ ! equ9octial1 :i* circle crosses ! ecliptic 9 ! po9ts ,aries & ,libra1 & ext5ds #bc-a_/b degrees on ea* side ( x2 & :i* ,i %all h occasion to m5tion to y ano!r "t4 ,,pupil4 ,:5 y ?9k prop]1 ,sir1 ,i %all be glad to h x expla9$ to me4 ,,tutor4 ,look at y\r table1 & tell me :at sign & :at degree ! sun is 9 ! #cj? ( ,m>*1 & #bj? ( ,octob]4 ,,pupil4 ,! sun ent]s ,aries ! #bj? ( ,m>*1 ( c\rse he mu/ be #aj degrees 9 t sign ! #cj?2 &1 z he does n ent] ,scorpio till ! #bc;d ( ,octob]1 he mu/ want ?ree degrees ( complet+ ! sign ,libra2 he mu/ !re=e1 on ! #bj? ( ,octob]1 be 9 #bg degrees ( ,libra4 ,,tutor4 ,v well4--,d y le>n ! table1 z y w h a f>!r use = x4 ---------------------------------------- -------------------------------- ,,dialogue ,,vi4 ,,pupil4 ,s9ce ,i 0 la/ ) y1 ,sir1 ,i h be5 ?9k+ ( :at y !n told me1 t ! planets p]=m _! revolutions 9 op5 space3 ,i h n ! lea/ idea h[ ?is c be2 if conv5i5t1 ,i %all be happy to h x expla9$4 ,,tutor4 ,x w be necess>y fir/ to in=m y1 t ! orbits or pa?s describ$ by ! revolution ( ! planets r\nd ! sun1 are n true circles 7z ,plate ,,ii4 fig4 #b47 b some:at elliptical1 t is1 long] "o way ?an ! o!r1 z fig4 #c4 ,,pupil4 ,?is is exce$+ly pla94 ,,tutor4 ,9 a circle1 ! p]iph]y or circumf]5ce is equally di/ant f a po9t )9 call$ its c5t]1 z ,a2 b an ellipsis has two po9ts call$ ! focuses or foci1 z ,b ,c4 ,9 "o ( ^!1 call$ its l[] focus1 is ! sun3 s t y see 9 e revolution ( ! planet x mu/ be ne>] to ! sun 9 "o "p ( its orbit1 ?an x is 9 ano!r4 ,,pupil4 ,i see x cle>ly4 ,,tutor4 ,n[ let ,s 7,plate ,,ii4 fig4 #d47 repres5t ! sun1 ,a ,b ,c ,d a planet 9 diff]5t p>ts ( its orbit2 :5 x is ne>e/ to ! sun1 z at ,a x is said to be 9 its p]ihelion2 :5 at ,b its aphelion2 b :5 at ,c or ,d its middle or mean di/ance1 because ! di/ance ,s ,c or ,s ,d is ! middle betwe5 ,a ,s ! lea/ & ,b ,s ! greate/ di/ance2 & half ! di/ance betwe5 ! two focuses is call$ ! ecc5tricity ( its orbit1 z ,s ,e or ,e ,f4 ,,pupil4 ,?is ,i w endeav\r to und]/&2 b ,i f9d x w take me "s "t to be p]fect$ 9 x4 ,,tutor4 ,y may /udy x at y\r leisure1 z x w n prev5t our proce$+ to ! ?+ propos$1 namely1 ! laws :i* gov]n ! motion ( ! planets1 or ,,attraction ,,( ,,gravitation4 ,,pupil4 ,by attraction ,i ?9k y mean t prop]ty 9 bodies :]eby !y h a t5d5cy to approa* ea* o!r4 ,i rememb] y told me t ! magnet ,i _h ! o!r day attract$ ! ne$le4 ,,tutor4 ,yes4 ,& y may recollect t :5 ,i took a fea!r susp5d$ by a ?read1 & put x ne> ! conductor ( ! electrical ma*9e1 x 0 /rongly attract$ by x1 & adh]$ to x z long z ! ma*9e 0 kept 9 motion4 ,,pupil4 ,i rememb] x well4 ,b :at am ,i to und]/& by attraction ( gravitation8 ,,tutor4 ,! sun1 be+ ! l>ge/ body1 attracts ! e>? & all ! o!r planets1 !y gravitate or h a t5d5cy to approa* ! sun2 ! e>? be+ l>g] ?an ! moon attracts h]1 & %e gravitates t[>ds ! e>?2 ! planets are attract$ by & gravitate t[>ds ea* o!r2 a /one :5 ?r[n f ! e>?1 by its attraction & ! gravitat+ p[] or weight ( ! /one1 is br\ght to ! e>? aga92 ! wat]s 9 ! ocean gravitate t[>ds ! c5t] ( ! e>?2 & x is by ?is p[] we /& on all p>ts ( ! e>? ) our feet po9t+ to ! c5t]4 ,,pupil4 ,?is in=mation af=ds me great pleasure4 ,,tutor4 ,hav+ m5tion$ attraction ( magnetism1 electricity1 & gravitation1 x may n be amiss to in=m y ( ano!r k9d1 call$ attraction ( cohesion4 ,,pupil4 ,any ?+ :i* t5ds to my improvem5t1 ,i %all be oblig$ to y to communicate4 ,,tutor4 ,by attraction ( cohesion is meant t prop]ty 9 bodies :i* connects or firmly unites ! diff]5t p>ticles ( matt] ( :i* ! body is compos$4 ,,pupil4 ,pray1 ,sir1 in=m me :at y mean by ! laws ( attraction8 ,,tutor4 ,y are to und]/&1 #a/4 ,t attraction decreases z ! squ>es ( ! di/ances betwe5 ! c5t]s ( ! attract+ bodies increase4 ,,pupil4 ,i mu/ beg y1 ,sir1 to expla9 to me ! mean+ ( ! squ>es ( ! di/ances4 ,,tutor4 ,any numb] multipli$ into itself is a squ>e numb]1 ?us #a is ! squ>e ( #a2 #d is ! squ>e ( #b2 #i is ! squ>e ( #c1 & s on1 because #a multipli$ into itself is #a2 #b by #b is #d2 #c by #c is #i1 c4 ,n[ suppose1 t :5 ! planet is at ,b 7,plate ,,ii4 fig4 #d47 x is twice z f> f ! sun z x is at ,a3 h[ mu* m w x be attract$ by ! sun at ,a ?an at ,b8 ,,pupil4 ,y say1 ,sir1 t ! di/ance is twice z great at ,b z at ,a8 ,,tutor4 ,i d4 ,,pupil4 ,!n z ! squ>e ( ! di/ance #b is #d1 ! decrease ( attraction at ,b1 ! planet at ,a w be attract$ ) f\r times ! =ce x w\ld be at ,b4--,am ,i "r1 ,sir8 ,,tutor4 ,p]fectly s4 ,& if ! di/ance at ,b 7 ?ree times z great z at ,a1 x w\ld be attract$ ) a =ce n9e times z great4 ,,pupil4 ,i p]ceive x mu/ be s4 ,,tutor4 ,i %all n[ give y ! #b;d law1 namely1 ,t bodies attract "o ano!r ) =ces proportionable to ! quantities ( matt] !y conta94 ,,pupil4 ,d all bodies ( ! same magnitude conta9 equal quantities ( matt]8 ,,tutor4 ,no1 c]ta9ly3 ,= a ball ( cork may be z l>ge z "o ( lead1 & yet n conta9 ! same quantity ( matt]1 because x is m por\s1 & n s compact or d5se a body z ! lead2 nei!r w a ball ( lead ( ! same magnitude z "o ( gold conta9 an equal quantity ( matt]4--,s ! sun1 ?\gh a million ( times z big z ! e>?1 conta9s a quantity ( matt] only #bjj1jjj z great1 !re=e attracts ! e>? ) a =ce #bjj1jjj z great z ! e>? attracts him4 ,,pupil4 ,i ?9k ?is is cle>4 ,,tutor4 ,we w n[ suppose t 9 ! riv] are two boats ( equal bulk1 at ! di/ance ( tw5ty y>ds f ea* o!r1 & t a man 9 "o boat pulls a rope :i* is fa/5$ to ! o!r1 :at effect w be produc$1 or :]e d y ?9k ! boats w meet8 ,,pupil4 ,_h y n told me t bodies attract "o ano!r ) =ces :i* are proportion$ to ! quantities ( matt] !y conta91 ,i %\ld say ! boat to :i* ! rope is fa/5$ w\ld come to t 9 :i* ! man /&s3 b z ,i imag9e y mean to apply ?is to attraction1 by ! above rule1 !y w meet at a po9t :i* is half way betwe5 !m4 ,,tutor4 ,if "o boat 7 ?ree times ! bulk ( ! o!r1 h[ !n8 ,,pupil4 ,! lighte/ w\ld move ?ree times z f> z ! heavie/1 or #ae y>ds :il/ ! heavie/ mov$ only #e4 ,,tutor4 ,^u my ^w y reason philosophically4 ,9 bo? cases y are p]fectly "r4 ,,pupil4 ,z ! sun is s imm5se a body t 8 quantity ( matt] is s mu* great] ?an ! planets1 ,i am at a loss to "k :y !y are n by ! p[] ( attraction drawn to him4 ,,tutor4 ,& s !y w\ld if ! attractive p[] 7 n c\nt]act$ by ano!r ( equal =ce4 ,,pupil4 ,did y n say1 ,sir1 t ! planets are kept 9 _! orbits by attraction8 ,,tutor4 ,i did4 ,b y f9d t by attraction only ! sun w\ld draw all ! planets to himself4 ,,pupil4 ,t is evid5t4 ,b ,i wi% to "k :at ?is c\nt]act+ p[] y speak ( is8 ,,tutor4 ,i w tell y pres5tly4--,y mu/ rememb] t simple motion is naturally rectil9eal1 t is1 all bodies1 if !re 7 no?+ to prev5t !m1 w\ld move 9 /rait l9es4 ,,pupil4 ,!n z ! planet>y motion is circul>1 x _c be simple8 ,,tutor4 ,no4 ,x is a comp\nd ( ! two =ces ,i h be5 m5tion+3 ! "o is call$ ! attractive or c5tripetal =ce2 ! o!r1 ! projectile or c5trifugal =ce4 ,,pupil4 ,! =m] ,i cle>ly compreh5d1 b n ! latt]4 ,i c conceive1 t if two bodies approa* ea* o!r by attraction !y mu/ move 9 a "r l9e4 ,,tutor4 ,if y %oot a m>ble on a smoo? piece ( ice1 9 :at direction w x run8 ,,pupil4 ,/rait =w>d4 ,,tutor4 ,?is is a projectile =ce4--,c\ld y1 d y ?9k1 %oot x 9 any o!r direction8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,!n is n ?is motion also rectil9eal8 ,,pupil4 ,x is4 ,,tutor4 ,:5 y /rike a ball ) y\r cricket-bat1 or ?r[ a /one ) y\r h&1 is x n project$ or ?r[n =w>d by ! =ce ( ! bat or h&8 ,,pupil4 ,c]ta9ly4 ,,tutor4 ,& does x n move 9 a /rait l9e8 ,,pupil4 ,at fir/ x appe>s to d s2 b aft]w>ds x incl9es t[>ds & falls to ! e>?4 ,,tutor4 ,_c y acc\nt = ?is8 ,,pupil4 ,i suppose x mu/ be drawn to ! e>? by attraction4 ,,tutor4 ,y are "r4 ,! attraction ( ! e>?1 & ! resi/ance ( ! atmosph]e or air ?r\gh :i* x moves1 ret>ds its progress1 or x w\ld cont9ue mov+ 9 a /rait l9e1 ) a velocity equal to t :i* 0 at fir/ impress$ ^u x4 ,9 l mann] ! b5efic5t ,creator ( ! ,univ]se impress$ a =ce on all ! planets :i* %\ld be equal to t ( ! attractive p[] ( ! sun1 t "o might n ov]come ! o!r4 ,,pupil4 ,?is wants expla9+4 ,,tutor4 ,i w\ld will+ly gratify y1 b z ,i h mu* m to say on ! subject1 ,i fe> x w be too great a bur!n on y\r memory2 x w !re=e be bett] to po/pone x4 ,,pupil4 ,z y please1 ,sir4 ---------------------------------------- -------------------------------- ,,dialogue ,,vii4 ,,tutor4 ,hav+ at our la/ meet+ expla9$ to y ! nature ( ! attractive & projectile =ces1 ,i %all proce$ to %ew y t x is by ! jo9t action or comb9ation ( ^! two =ces t ! planets are reta9$ 9 _! orbits4 ,,pupil4 ,i am all anxiety1 z ,i wi% to be in=m$ h[1 or 9 :at mann] !y c act aga9/ ea* o!r1 to produce t effect4 ,,tutor4 ,answ] me a few que/ions1 & y w soon "k4 ,,pupil4 ,z _m z y please1 ,sir4 ,,tutor4 ,if y :irl a /one 9 a sl+1 :at w be its motion8 ,,pupil4 ,circul>4 ,,tutor4 ,is y let x sudd5ly slip out ( ! sl+1 w x cont9ue its circul> motion8 ,,pupil4 ,no1 ,sir1 b fly (f 9 a /rait l9e4 ,,tutor4 ,?is l9e y mu/ rememb] is :at ma!maticians call ! tang5t ( a circle1 z ,a a1 ,b b1 c4 7,plate ,,ii4 fig4 #e47 = all bodies mov+ 9 a circle h a natural t5d5cy to fly (f 9 t direction4 ,?us a body at ,a w t5d t[>ds a2 at ,b t[>ds b1 & s on2 b ! c5tral =ce act+ aga9/ x pres]ves its circul> motion4 ,,pupil4 ,by ! c5tral =ce "h y mean ! action ( ! h&1 d y n8 ,,tutor4 ,yes4 ,=1 z soon z ! /one is releas$ & t p[] is lo/1 x assumes its natural1 t is1 its rectil9eal motion4--,aga94 ,if y are left at lib]ty1 _c y run /rait =w>d8 ,,pupil4 ,yes1 ,sir4 ,,tutor4 ,n[1 suppose "o ( y\r companions 7 to fa/5 a rope r\nd y\r body1 & at ! ext5t ( x 7 to /& /ill & hold x tight1 ) a =ce equal to t ) :i* y run1 c\ld y1 d y ?9k1 move 9 a /rait l9e1 t is1 9 a tang5t ( a circle8 ,,pupil4 ,no1 ,sir4 ,i mu/ run 9 a circle4 ,,tutor4 ,:y8 ,,pupil4 ,because1 :il/ ! rope is ext5d$ ,i am prev5t$ runn+ 9 any o!r direction4 ,,tutor4 ,j s x is ) ! planets3 ! attractive or c5tripetal =ce ( ! sun be+ equal to t ( ! projectile or c5trifugal =ce ( ! planets1 !y are by attraction prev5t$ mov+ on 9 a /rait l9e1 &1 z x 71 drawn t[>ds ! sun2 & by ! projectile =ce f be+ ov]come by attraction4 ,!y mu/ !re=e revolve 9 circul> orbits4 ,,pupil4 ,:at ,i h s long wi%$ is n[ accompli%$4 ,i und]/& x p]fectly4 ,,tutor4 ,:at ,i h n[ expla9$ relates n only to ! prim>y planets :i* h ! sun = _! c5t] ( motion2 b1 y mu/ rememb] t ! second>y planets are gov]n$ by ! same laws1 9 revolv+ ab\t _! respective prim>ies2 =1 z by ! attractive p[] ( ! sun comb9$ ) ! projectile =ce ( ! prim>y planets !y are reta9$ 9 _! orbits2 s also ! action ( ! prim>ies ^u _! respective second>ies toge!r ) _! projectile =ce1 w pres]ve !m 9 _! orbits4 ,,pupil4 ,pray1 ,sir1 :at h y else to obs]ve8 ,,tutor4 ,h ,i n told y t ! orbits ( ! planets are n true circles1 b a little elliptical8 ,,pupil4 ,yes1 ,sir2 & ,i %all be glad to "k ! reason ( x4 ,,tutor4 ,if ! attractive p[] ( ! sun 7 uni=mly ! same 9 e "p ( _! orbits !y w\ld be true circles1 & ! planets w\ld pass ov] equal portions ( _! orbits 9 equal times2 t is1 !y w\ld move f ,b to ,c1 7,plate ,,ii4 fig4 #e47 9 ! same "t z f ,a to ,b1 c4 ,,pupil4 ,t is cle>1 b z _! orbits are elliptical1 :5 ! planets are f>!/ f ! sun1 ! velocity ) :i* !y move mu/ be less5$ z ! attraction is decreas$4 ,,tutor4 ,& !y mu/ consequ5tly pass ov] unequal p>ts ( _! orbits 9 equal portions ( "t4 ,&1 z a d\ble velocity w balance a quadruple or f\rfold p[] ( gravity or attraction1 x foll[s1 t z ! c5tripetal =ce is f\r times z great at ,a z at ,b 7,plate ,,ii4 fig4 #d47 ! c5trifugal =ce w be twice z great1 & w\ld c>ry a planet f ,a to a 9 ! same "t x w\ld f ,b to b1 & 9 its orbit f ,a to c z soon z f ,b to d1 & !reby describe ! area1 or space conta9$ betwe5 ! lett]s ,a ,s c1 9 ! same "t z ! area or space ,b ,s d4 ,= accord+ to ! laws ( ! planet>y motions1 9 _! p]iodical revolutions1 !y always describe equal areas 9 equal times4 ,,pupil4 ,! orbits ( ! comets be+ v elliptical1 ! irregul>ity ( _! motions mu/ be exce$+ly great4 ,,tutor4 ,great1 inde$6--,"o ( !m pass$ s ne> ! sun z to acquire a heat :i* ,sir ,isaac ,newton comput$ to be two ?\s& times hott] ?an r$ hot iron4#ab ,footnote #ab3 ,dr4 ,h]s*el is ( op9ion1 t bodies ne> ! sun d n acquire s great a degree ( heat z has be5 g5]ally imag9$4 ,,pupil4 ,a/oni%+6 ,if !y pass s ne> ! sun1 ! c5tripetal =ce mu/ act p[]fully on ! body ( ! comet4 ,,tutor4 ,& t =ce1 y "k1 mu/ be equall$ by ! projectile =ce2 s y f9d !y move :5 ne> ! sun ) amaz+ cel]ity4--,b :5 arriv$ at _! aphelion1 :]e ! influ5ce ( ! sun is weak1 :at a transition6 ,,pupil4 ,wond]ful1 inde$6--,_! motion is excessively sl[1 & ! sun mu/ appe> little m ?an a fix$ />4 ,surely !y _c be inhabit$1 c !y8 ,,tutor4 ,we _c speak positively2 b1 z !y diff] s mu* f ! planets1 :i* we h reason to suppose are s1 x is imag9$ !y are design$ = "s purpose unkn[n to u4 ,,pupil4 ,:5 is ! e>? 9 its p]ihelion8 ,,tutor4 ,9 ,decemb]2 & our summ] half ye> is long] ?an ! w9t] half1 by ab\t eight days4 ,,pupil4 ,i suppose ?is is occasion$ by ! inequality ( ! e>?'s annual motion4 ,,tutor4 ,x is2 & ?is inequality is ! cause ( ! diff]5ce ( "t betwe5 ! sun & a well regulat$ clock2 ! latt] keeps equal "t1 :il/ ! =m] is con/antly v>y+4 ,,pupil4 ,i h (t5 se5 9 ! almanack clock fa/1 clock sl[1 b did n "k ! mean+ ( x3 ,i imag9e x is t ! clock %\ld be s mu* fa/] or sl[] ?an ! "t by ! sun z is !re m5tion$4 ,,tutor4 ,x is3 b !re are tables calculat$ to %ew ! diff]5ce ( "t = e day 9 ! ye>2 s t if y "k ! exact times ( ! day by ! sun1 & h "o ( ^! tables1 y w see :at ! "t %\ld be by ! clock1 to a second1 :i* is n %ewn 9 a common almanack4 ,,pupil4 ,9 speak+ ( ! annual or ye>ly motion ( ! e>?1 y h no :]e m5tion$ ! cause ( ! seasons2 w x be agreeable to d x n[1 ,sir8 ,,tutor4 ,! vicissitudes ( ! seasons1 ! cause ( day & night1 c4 %all be ! subject ( future lessons3 we %all f9d suffici5t to employ u at pres5t4 ,,pupil4 ,i ?9k y told me j n[ t ! e>? is ne>e/ ! sun 9 ,decemb]2 t is our w9t]2 ?is seems a little my/]i\s4 ,,tutor4 ,x may appe> s to y n[1 by-&-by y w be ( a diff]5t op9ion4 ,i %all expla9 ?is matt] to y ) t ( ! seasons1 c4 ,,pupil4 ,i fe> ,i h int]rupt$ y4--,z y said y _h suffici5t employm5t = u1 ,i %all be glad to "k :at x is4 ,,tutor4 ,hi!rto ,i h spok5 ( ! sun's be+ fix$1 & t ! planets revolve ab\t him z a c5t]4 ,in/ead ( :i* ! sun & planets move r\nd "o common c5t]1 call$ ! c5t] ( gravity4 ,,pupil4 ,:at is ?is c5t] ( gravity8 ,,tutor4 ,h y nev] se5 a p]son raise a heavy weight by means ( a long pole or leav]1 :i* x 0 n 9 8 p[] to lift )\t x8 ,,pupil4 ,yes1 ,sir1 & x excit$ my a/oni%m5t4 ,,tutor4 ,n[1 suppose ! weight to see rais$ to be #aj ,cwt4 & ! prop on :i* ! leav] re/$ #a foot f ! body to be rais$2 & ! p]son at ! o!r end ( ! leav] #aj feet f ! prop2 ) :at weight mu/ he press to raise ! #aj ,cwt48 ,,pupil4 ,i ?9k t v easy2 =1 z he is t5 times z f> f ! prop z ! weight is1 a pressure ( #a ,cwt4 :i* is "o-t5? ( ! weight to be rais$ w d x4 ,,tutor4 ,to be sure2 & yet y say y 7 a/oni%$ :5 y saw x6 ,e ?+ we d n und]/& at fir/ appe>s difficult4--,to apply ?is to our pres5t purpose4 ,y see t a weight ( #a ,cwt4 at #aj feet f a prop1 w balance ano!r ( #aj ,cwt4 at "o foot f x4 ,n[1 in/ead ( a prop let ! two weights be nicely pois$ on a c5t]1 r\nd :i* !y may freely turn2 ! heavie/ w\ld move 9 a circle1 ^: radius1 or di/ance f ! c5t] w\ld be "o foot1 :il/ ! lighte/ w\ld move 9 "o #aj feet f ! c5t] 9 ! same "t4 ,,pupil4 ,is ! c5t] r\nd :i* !y move ! c5t] ( gravity8 ,,tutor4 ,x is2 & r\nd an imag9>y po9t z a c5t] ! sun & planets move1 always pres]v+ an equilibrium4 ,if ! e>? 7 ! only att5dant on ! sun1 z 8 quantity ( matt] is #bjj1jjj times z great z t ( ! e>?1 he w\ld revolve 9 a circle a #bjj1jjj? "p ( ! e>?'s di/ance f him1 9 ! same "t z ! e>? is mak+ "o revolution 9 its orbit1 or 9 "o ye>2 b1 z ! planets 9 _! orbits mu/ v>y 9 _! positions1 ! c5t] ( gravity _c be always at ! same di/ance f ! sun4 ,,pupil4 ,if x 71 ! balance c\ld n be pres]v$4 ,,tutor4 ,cle>ly s4 ,b y mu/ "k t ! quantity ( matt] 9 ! sun s f> exce$s t ( all ! planets toge!r1 t ev5 if !y 7 all 9 a l9e on "o side ( him he w\ld nev] be m ?an 8 own diamet] di/ant f 8 c5t] ( gravity2 !re=e1 a/ronom]s consid] ! sun z ! c5t] ( ! sy/em1 & express !mselves accord+ly4 ,,pupil4 ,z y told me ! second>y planets are gov]n$ by ! same laws z ! prim>ies1 ,i imag9e !y also ) _! prim>ies move r\nd a c5t] ( gravity4 ,,tutor4 ,!y d s4--,! e>? & moon1 ,jupit] ) 8 satellites1 ,saturn & 8 att5dants1 revolve ab\t _! respective c5t]s2 ^!1 ) ! sun & ! re/ ( ! planet>y sy/em1 make _! circuits r\nd _! c5t]2 e sy/em 9 ! univ]se is suppos$ to revolve 9 l mann]2 & all ^! toge!r to move r\nd "o common c5t]4--,h[ are we lo/ 9 contemplat+ ! omnisci5ce ( ! ,deity6 ,h[ difficult to conceive s _m millions ( bodies ( dead matt] con/antly 9 motion1 s nicely balanc$ & gov]n$ by su* un]r+ laws6--,well may we say ) ! ,psalmi/1 8,"l6 h[ manifold are ?y works1 9 wisdom ha/ ?\ made !m all40 ---------------------------------------- -------------------------------- ,,dialogue ,,viii4 ,,tutor4 ,i %all n[1 agreeably to my promise1 expla9 to y ! cause ( day & night1 & !n proce$ ) ! vicissitudes ( ! seasons4 ,,pupil4 ,t is :at ,i mu* wi% to "k2 & _h y n told me t ! e>? mov$ r\nd ! sun e ye>1 ,i %\ld h f\nd no difficulty 9 acc\nt+ = ! succession ( day & night1 s9ce ! sun appe>s to rise & set e day4 ,,tutor4 ,t is true2 b ,i ?9k ,i mu/ h conv9c$ y t s imm5se a body z ! sun _c revolve ab\t ! e>?2 z well may y suppose t 9 roa/+ a bird x is necess>y t ! fire %\ld move r\nd x4 ,,pupil4 ,t ,i ?9k w\ld be v absurd1 z x is mu* easi] = ! bird on ! spit to turn to ! fire1 ?an = ! fire to g r\nd ! bird4 ,,tutor4 ,y are c]ta9ly "r1 & if ! e>? revolve on its axis e tw5ty-f\r h\rs1 w n ! diff]5t p>ts ( x be alt]nately turn$ to ! sun1 z ! bird on ! spit is to ! fire8 ,,pupil4 ,i d n cle>ly compreh5d :at y mean by ! axis ( ! e>?2 =1 z x moves 9 op5 space & has no support1 x c h no?+ to resemble ! spit on :i* x turns4 ,,tutor4 ,c]ta9ly n4 ,by ! e>?'s axis is meant an imag9>y l9e pass+ ?r\gh its c5t]1 on :i* x is suppos$ to turn2 z y\r ball if roll$ on ! gr\nd w\ld revolve on an axis :il/ x 0 mov+ =w>d4 ,,pupil4 ,i c n[ answ] y\r "q 9 ! affirmative3 &1 z our ye> consi/s ( #cfe days1 ,i imag9e ! e>? mu/ make z _m revolutions on its axis :il/ x is go+ once r\nd ! sun4 ,,tutor4 ,und\bt$ly3 & z only "o half ( a sph]ical body c at any "t be enlight5$ by a lum9\s body1 t "p ( ! e>? only :i* is turn$ to ! sun1 c receive ! b5efit ( 8 enliv5+ rays1 :5 x w be day2 :il/ ! opposite "p w be involv$ 9 d>kness1 & x w be night4 ,,pupil4 ,i p]ceive x mu/ be s4 ,b1 if ! e>? move 9 ! mann] y describe1 ,i _c conceive h[ x is t we are n s5sible ( its motion4 ,,tutor4 ,if ! motion ( ! e>? 7 irregul> x w\ld be p]ceptible2 b z x meets ) no ob/ruction ! motion mu/ be s uni=m z n to be p]ceiv$4 ,,pupil4 ,_h ,i recollect$ ?is1 ,i ne$ n h giv5 y ?is tr\ble4--,b ,i am cont9ually meet+ ) fre% difficulties4 ,,tutor4 ,y h only to m5tion :at !y are1 & ,i %all take a pleasure 9 remov+ !m4 ,,pupil4 ,i ?ank y1 ,sir2 & %all be oblig$ to y to in=m me1 h[ ! motion ( ! e>? c cause ! sun to appe> to move8 ,,tutor4 ,:5 9 a c>riage :i* w5t smoo?ly on ! road1 or 9 a boat ^: motion 0 sc>cely p]ceptible on ! wat]1 did y nev] fix y\r att5tion on ! objects y pass$8 ,,pupil4 ,yes1 (t51 ,sir4 ,,tutor4 ,& _h y n kn[n t y really mov$1 & t ! trees1 c4 7 immoveable 9 ! gr\nd1 :at !n w\ld h be5 y\r op9ion8 ,,pupil4 ,t ! trees1 c4 mov$ 9 a direction contr>y to t 9 :i* ,i 0 mov+4 ,,tutor4 ,is n ?is suffici5t to conv9ce y t ! app>5t motion ( ! sun may be occasion$ by ! revolution ( ! e>? on its axis8 ,,pupil4 ,x is3--,b if s l>ge a body z ! e>? make a revolution on its axis 9 #bd h\rs1 x mu/ move ) great velocity4 ,,tutor4 ,x does s2 & ! inhabitants ( ,london by ?is motion are c>ri$ at ! rate ( #efj miles an h\r#ac4 ,footnote #ac3 ,! h\rly motion "u ! equator is #ijj miles4 ,,pupil4 ,:at an a/oni%+ rapidity6 ,,tutor4 ,n[1 ! sun ) ! re/ ( ! heav5ly bodies mu/ move r\nd ! e>?1 or ! e>? mu/ revolve on its axis 9 #bd h\rs1 to cause t appe>ance4 ,,pupil4 ,t is pla94 ,,tutor4 ,well !n1 great z y may suppose ! velocity ( ! e>? on its axis to be1 if ! sun move r\nd ! e>? 8 h\rly motion w be ne>ly #be millions ( miles2 & beyond conception w\ld be t ( ! fix$ />s4 ,:i* n[ d y ?9k is mo/ probable1 t ! sun & />s %\ld move r\nd ! e>?1 or t !y1 by ! simple motion ( ! e>?1 %\ld appe> to be 9 motion8 ,,pupil4 ,! latt]1 to be sure1 ,sir4--,i h "o difficulty rema9+1 :i* is ?is2 if a l>k rise f a field ne> ,london & rema9 9 ! air a qu>t] ( an h\r1 if ! e>? move at ! rate ( #efj miles an h\r1 x w g #adj miles :il/ ! l>k is susp5d$1 & yet x cont9ues ov] ! field1--h[ c ?is be8 ,,tutor4 ,?is objection to ! motion ( ! e>? has be5 made by ^? :o 7 old] & :o ?\ght !mselves wis] too ?an y\rself4 ,!y ei!r did n "k or did n consid]1 t ! atmosph]e :i* surr\nds ! e>? is a "p ( itself1 & gravitates t[>ds x1 & !re=e p>takes ( ! e>?'s motion & c>ries ! l>k along ) x4 ,besides1 z ! ,sun1 ,v5us1 ,m>s1 & ,jupit] are kn[n to revolve on _! axes1 we h reason to suppose t ! o!r planets1 toge!r ) ! e>?1 mu/ h ! same motion#ad4 ,footnote #ad3 ,dr4 ,h]s*ell says t sev]al ( ! fix$ />s revolve on _! axes4 ,,pupil4 ,h[ is x kn[n t !y d revolve on _! axes2 & 9 :at "t d !y p]=m _! revolutions8 ,,tutor4 ,by ! assi/ance ( telescopes d>k spots h be5 se5 on ! disc ( ! sun1 by ! motion ( :i* x is f\nd t he revolves on 8 axis 9 #be-a_/d days2 ,v5us p]=ms h] diurnal revolution 9 ab\t #bc ho4 #ba m942 ,m>s goes r\nd 8 axis 9 #bd ho4 #ci m942 & ,jupit] 9 #i ho4 #ef m942 z to ! re/1 no spot or any fix$ po9t has be5 discov]$ to asc]ta9 ! l5g? ( _! day2 ,m]cury be+ too ne> ! sun1 & ,saturn & ! ,georgium ,sidus too remote = our obs]vations4 ,,pupil4 ,i c no long] d\bt ( ! e>?'s motion3 &1 if x w n be improp]1 a description ( ! atmosph]e w give me pleasure4 ,,tutor4 ,t ,i c h no objection to4 ,! atmosph]e is a ?91 invisible fluid1 mo/ d5se or heavy ne> ! e>?1 b gr[s gradually r>] or light] ! high] we asc5d1 s mu* s1 t at ! tops ( "s high m\nta9s x is difficult to brea!4 ,x s]ves n only to susp5d ! cl\ds1 furni% u ) w9d & ra91 & answ] ! common purposes ( brea?+1 b is also ! cause ( ! morn+ & ev5+ twilight1 & ( all ! glory & brightness ( ! firmam5t4 ,,pupil4 ,h[1 pray8 ,,tutor4 ,if !re 7 no atmosph]e1 ! sun w\ld yield no light b :5 our eyes 7 direct$ t[>ds him2 & ! heav5s w\ld appe> d>k & z full ( />s z on a d>k w9t]'s night2 b ! atmosph]e be+ /rongly illum9at$ by ! sun1 reflects ! light back ^u u1 & makes ! :ole heav5s to %9e s /rongly1 t ! fa9t light ( ! />s is obscur$1 & !y are r5d]$ invisible4 ,,pupil4 ,i f9d !n ! atmosph]e is ( m use ?an ,i imag9$4 ,b h[ is x ! cause ( ! twilight8 ,,tutor4 ,! atmosph]e is ab\t #de miles above ! surface ( ! e>?1 !re=e ! sun's rays fall+ ^u ! high] p>ts ( x be=e ris+1 by reflection causes a fa9t light1 :i* increases till he appe>s above ! horizon2 & 9 ! ev5+ x decreases aft] he sets1 till he is #ah degrees bel[ ! horizon1 :]e ! morn+ twilight beg9s1 & ! ev5+ twilight ends4 ,,pupil4 ,by ! horizon1 ,i ?9k y mean t di/ant b\nd>y ( our sight :]e ! heav5s & ! e>? seem to jo9 all ar\nd u1 z x appe>s f an em95ce4 ,,tutor4 ,! v same4 ',tis t imag9>y circle :i* int]cepts f our view ! sun1 moon1 & />s ea* night2 & :51 by ! rotation ( ! e>?1 !y appe> to desc5d bel[ x1 we say !y are set2 z on ! contr>y1 ea* morn+1 :5 !y appe> above x1 we say !y rise4 8,to f9d ! spaci\s l9e1 ca/ r\nd ?9e eyes1 8,& :]e ! e>?'s high surface jo9s ! skies1 8,:]e />s fir/ set1 & fir/ beg9 to %9e1 8,!re draw ! fancy'd image ( ?is l9e40 ,,pupil4 ,a v pleas+ description1 inde$4 ,,tutor4 ,y w rememb] t ?is is call$ ! rational horizon2 b t :i* respects l& & wat] is call$ ! s5sible horizon4 ,! =m] divides ! heav5s into two equal p>ts1 & is #ij degrees di/ant f a po9t directly ov] our heads1 call$ ! z5i?1 & ! opposite po9t ( ! heav5s directly "u our feet1 call$ ! nadir4--,b ,i mu/ resume ! subject ( ! atmosph]e4 ,,pupil4 ,_h ,i n ?\ght y _h f9i%$ y\r description ( ! atmosph]e1 ,i %\ld n h presum$ to int]rupt y4 ,,tutor4 ,:at ,i h told y respect+ ! horizon is necess>y = y to be acqua9t$ )2 !re=e1 ! susp5sion is immat]ial4--,y mu/1 ,i make no d\bt1 h obs]v$ ! sun & moon at ris+ & sett+ to appe> l>g] ?an :5 high] above ! horizon4 ,,pupil4 ,i h1 frequ5tly1 ,sir4 ,,tutor4 ,& _c y tell ! reason ( x8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,! reason is ?is3 ,9 view+ !m1 :5 ne> ! horizon1 y see !m ?r\gh a ?ick] m$ium ?an :5 !y are high]1 t is1 y see !m ?r\gh a great] quantity ( ! atmosph]e2 & y n only see !m l>g]1 b really above ! horizon :il/ !y are actually bel[ x4 ,,pupil4 ,h[ d y acc\nt = ?is1 ,sir8 ,,tutor4 ,light1 l mat]ial bodies1 if x meet ) no ob/ruction1 w move 9 "r l9es2 n[1 ! rays ( ! sun 9 com+ to ! e>? mu/ pass ?r\gh a great quantity ( ! atmosph]e1 :i* be+ a fluid1 refracts or b5ds ! rays ( light1 by :i* refraction x is t we are fav\r$ ) ! sight ( ! sun #c-a_/d m9utes e morn+ be=e he rises above ! horizon1 & e ev5+ aft] he s9ks bel[ x1 :i* 9 "o ye> am\nts to m ?an #dj h\rs4 ,?is refraction is greate/ ne> ! horizon1 & ends 9 ! z5i?4 ,,pupil4 ,pray1 ,sir1 c y make ?is cle>] by an exp]im5t8 ,,tutor4 ,i h j ?\ght ( "o4 ,take a bason fill$ ) wat]1 & a /rait /ick or piece ( wire2 put x p]p5dicul>ly into ! wat]1 t is1 t x lean nei!r way1 & !re w be no refraction2 incl9e x a little t[>ds ! edge ( ! bason & x w appe> a little b5t at ! surface ( ! wat]2 incl9e x /ill m1 & ! refraction w be great]4 ,,pupil4 ,i h (t5 se5 ?is appe>ance :5 ,i h put my /ick into wat]1 b did n be=e "k ! cause4 ,,tutor4 ,y may try "o m exp]im5t4 ,p\r ! wat] out ( ! bason1 & set ! bason on ! floor2 put a gu9ea into x1 & let x repres5t ! sun4--,:y d y smile8 ,,pupil4 ,because ,i h n ! sun's repres5tative to try ! exp]im5t )4 ,,tutor4 ,well1 well1 put a %ill+ into ! bason & call x ! moon1 & x w answ] ! same purpose3--,walk backw>d till y j lose sight ( x1 !n ! "r l9e f y\r eye cont9u$ ov] ! edge ( ! bason mu/ pass beyond ! money at ! bottom ( x4 ,,pupil4 ,t is evid5t4 ,,tutor4 ,keep y\r position1 & desire "s fri5d to p\r ! wat] g5tly into ! bason s z n to remove ! money1 & y w cle>ly di/+ui% x4 ,n[1 if y call ! edge ( ! bason ! horizon1 ! wat] ! atmosph]e1 & ! %ill+ ! moon1 is x n cle> t y w see x above ! horizon1 :5 x is really bel[ x8 ,,pupil4 ,i ?9k s1 ,sir4 ,,tutor4 ,well1 try ! exp]im5t1 & let me "k ! result :5 ,i next see y4 ---------------------------------------- -------------------------------- ,,dialogue ,,ix4 ,,tutor4 ,i presume1 ,sir1 y h made ! exp]im5t ,i recomm5d$ to y4 ,,pupil4 ,i h1 ,sir2 & am s well conv9c$ ( :at y told me1 t no?+ f>!r ne$ be said on ! subject4 ,,tutor4 ,z t is ! case1 ,i %all proce$4--,i d>e say y d n =get :at ! plane ( ! ecliptic is4 ,,pupil4 ,i d n1 ,sir2 b h a p]fect recollection ( x4 ,,tutor4 ,n[1 rememb]1 t ! axis ( ! e>? is n upright or p]p5dicul> to ! plane ( ! ecliptic1 b incl9es to1 or leans t[>ds x1 #bc-a_/b degrees1 & makes an angle ) x ( #ff-a_/b degrees4 ,,pupil4 ,an angle signifies a corn]2 b t _c be ! mean+ "h4 ,,tutor4 ,t is :at is g5]ally und]/ood by an angle3 b1 9 geometry1 x means ! meet+ ( any two l9es :i* incl9e to "o ano!r1 9 a c]ta9 po9t4 ,n[1 if y conceive ! axis ( ! e>? to be "o l9e1 & ! plane ( ! ecliptic ! o!r1 ! po9t :]e !y meet or cross ea* o!r w =m an angle4 ,,pupil4 ,i ?9k ,i und]/& x2 b h[ c x conta9 #bc-a_/b or #ff-a_/b degrees8 ,,tutor4 ,y "k :at a degree is4 ,,pupil4 ,if ,i rememb] "r x is ! #cfj? "p ( a circle4 ,,tutor4 ,x is s3 & ! measure ( an angle is an arc or "p ( ! circumf]5ce ( a circle1 ^: angul> po9t is ! c5t]3 & s _m #cfj? p>ts z any arc conta9s1 s _m degrees ! measure ( ! angle is said to be2 ?us1 ,z ,c ,p 7,plate ,,iii4 fig4 #a47 makes an angle ( #bc-a_/b degrees1 because ! arc ,z ,p conta9s #bc-a_/b #cfj? p>ts ( ! :ole circle4 ,!n if ,a ,b repres5t ! plane ( ! ecliptic1 & ,n ,c ,s ! axis ( ! e>?1 z ,d ,n conta9s ! same numb] ( degrees z ,z ,p1 w n its incl9ation f a p]p5dicul> be #bc-a_/b degrees8 ,illu/ration3 ,plate ,,iii4 ,t4 ,cond] ,sculpt4 ,,pupil4 ,no?+ c be pla9]4 ,,tutor4 ,= ! same reason1 z ,p ,b conta9s #ff-a_/b p>ts ( ! :ole circle1 ! axis ( ! e>? makes an angle ( #ff-a_/b degrees ) ! plane ( ! ecliptic4 ,&1 if y add #bc-a_/b to #ff-a_/b ! sum w be #ij1 :i* is ! measure ,z ,b1 or ! f\r? "p ( ! circle1 & makes :at is call$ a "r angle1 at ! po9t or c5t] ,c4 ,,pupil4 ,x is v cle>3--b :at d ! o!r lett]s ref] to8 ,,tutor4 ,! extremities ( ! e>?'s axis are call$ ! poles1 ,n ! nor?1 & ,s ! s\? pole1 & ,p ! nor?-pole />1 to :i*1 & to ! opposite "p ( ! heav5s1 ! axis always po9ts4 ,^! extremities 9 ! heav5s appe> motionless1 :il/ all o!r p>ts seem 9 a cont9ual /ate ( revolution3 ! circle ( motion appe>s to increase ) ! di/ance f ! app>5tly motionless po9ts to t circle 9 ! heav5s :i* is at an equal di/ance betwe5 !m1 call$ ! equ9octial1 repres5t$ by ! lett]s ,q2 & is ! same ,i promis$ "s "t ago to expla9 to y4 ,,pupil4 ,i recollect x3 & z ! l9e ,a ,b repres5ts ! plane ( ! ecliptic1 ,i suppose ! l9e ,q is ! plane ( ! equ9octial1 :i* ,i see crosses x z y !n told me4 ,,tutor4 ,y are "r3 & x makes an angle ) x ( #bc-a_/b degrees4 ,x is call$ ! equ9octial1 because :5 ! sun appe>s !re1 t is1 9 ,aries or ,libra1 ! days & nights are equal 9 all p>ts ( ! _w1 :i* ,i %all %ew y 9 due "t2 & %all n[ expla9 to y :at ,i h j m5tion$1 t ! axis ( ! e>? always po9ts to ! same p>ts ( ! heav5s4 ,i am appreh5sive y w ?9k x /range t ?is %\ld be ! case1 & ! axis keep p>allel to itself4 ,,pupil4 ,:at am ,i to und]/& by ! axis be+ p>allel to itself8 ,,tutor4 ,two l9es are said to be p>allel :5 !y d n incl9e to b keep at equal di/ances f ea* o!r2 s t if !y 7 inf9itely cont9u$1 !y w\ld nev] meet4 ,n[1 if y c conceive a l9e drawn p>allel to ! e>?'s axis 9 any "p ( its orbit1 x w be p>allel to x 9 e o!r "p ( x4 ,a little draw+ ,i h by me1 7,plate ,,iii4 fig #b47 :]e ! e>? is repres5t$ 9 f\r diff]5t p>ts ( its orbit1 ,i ?9k w make ?is pla9 to y4 ,,pupil4 ,i compreh5d y\r mean+ cle>ly4 ,b1 z ! orbit ( ! e>? is #aij millions ( miles 9 diamet]1 ,i h n ! lea/ conception h[ x c incl9e to ! same po9ts4 ,_h y n told me to ! contr>y1 ,i %\ld h ?\ght x mu/ move r\nd !m 9 e revolution ( ! e>? ab\t ! sun4 ,,tutor4 ,t su* a motion w\ld be p]ceptible is evid5t1 if ! fix$ />s 7 ne> ! e>?2 b1 comp>$ ) _! di/ance1 #aij millions ( miles is b a m]e po9t3 !re=e1 ! axis always incl9es to ! same po9ts ( ! heav5s4 ,,pupil4 ,?is is a great] pro( ( ! inconceivable di/ance ( ! />s ?an :at y m5tion$ be=e1 & ,i ?\ght t v a/oni%+3 ,wond]s on wond]s con/antly arise1 ,:5e'er we view ! e>?1 or sea1 or skies4 ,,tutor4 ,x is v true4 ,& ! m we se>*1 ! m we h cause to admire ! works ( ! ,almighty4 ,,pupil4 ,pray1 ,sir1 :at is ! next ?+ y propose8 ,,tutor4 ,to make y acqua9t$ ) ! o!r circles y see 9 ! figure 7,plate ,,iii4 fig4 #a47 z x is v necess>y y %\ld "k !m4 ,,pupil4 ,w y be k9d en\gh to tell me _! names1 ,sir1 & ,i w endeav\r to rememb] !m8 ,,tutor4 ,t l9e :i* divides ! globe into two equal p>ts1 call$ ! nor!rn & s\!rn hemisph]es1 :i* answ]s to ! equ9octial 9 ! heav5s1 & is equally di/ant f ! two poles1 is call$ ! equator2 ! o!r :i* crosses x1 z ,i be=e told y1 is ! ecliptic2 ! small] circle1 nor? ( ! equator1 is ! tropic ( ,canc]2 t s\? ( x1 ! tropic ( ,capricorn2 ! circles next ! poles are call$ ! pol> circles2 or t next ! nor? pole1 ! arctic circle1 & t next ! s\? pole1 ! ant>ctic circle2 ea* ( :i* is #bc-a_/b degrees di/ant f its respective pole1 z are ! tropics f ! equator4 ,,pupil4 ,y h n m5tion$ ! l9es :i* cross ! o!r circles1 & t]m9ate 9 ! poles2 :at are !y call$8 ,,tutor4 ,!y are call$ m]idians1 because :5 any ( !m1 z ! e>? revolves on its axis1 is opposite to ! sun1 x is mid-day or noon along t l9e4 ,tw5ty-f\r ( ^! l9es are usually drawn on ! globe to correspond ) ! tw5ty-f\r h\rs ( ! day2 b y are n to suppose !re are no m ?an tw5ty-f\r2 = e place t lies ev] s little ea/ or we/ ( ano!r place has a diff]5t m]idian4--,to make ?is cle>] to y1 we w suppose ! upp] #ab 7,plate ,,iii4 fig4 #a47 to be opposite ! sun1 x w ( c\rse be noon along t l9e2 ! next m]idian m>k$ #a1 be+ #ae degrees ea/1 w h pass$ ! m]idian #a h\r1 consequ5tly x w !re be "o 9 ! aft]noon1 & s on1 accord+ to ! ord] ( ! figures1 till y come to ! l[] #ab1 :i* be+ ! "p ( ! e>? turn$ directly f ! sun1 x w be midnight on t m]idian2 on ! next m]idian1 z y proce$ r\nd1 x w be "o 9 ! morn+1 ! next two1 & s on till y arrive at ! upp] twelve1 :]e y set (f4 ,s y see !re mu/ be a cont9ual succession ( day & night4 ,?is diff]5ce ( "t betwe5 places ly+ "u diff]5t m]idians is :at is call$ longitude4 ,,pupil4 ,i ?9k ,i h he>d ( a ,mr4 ,h>rison1 :o made a "t-keep] = det]m9+ ! longitude4 ,%all ,i trespass at all if ,i beg a little f>!r in=mation on ?is subject8 ,,tutor4 ,x is my wi% at all times to satisfy y\r curiosity1 :5 ,i c d x ) propriety4 ,i %all !re=e comply ) y\r reque/4--,mr4 ,h>rison's "t-keep]1 & ^? made s9ce by o!r arti/s1 are s con/ruct$1 t ! heat & cold ( diff]5t climates w n affect !m2 =1 all metals are m or less exp&$ by heat1 & contract$ by cold2 = :i* reason x is1 t a clock or wat* made 9 ! usual way w n keep equal "t4 ,n[1 all t is requir$ ( ^! "t-keep]s to asc]ta9 ! longitude is ?is3 ,suppose a capta9 ( a vessel sail+ f ,london to ! ,we/ ,indies1 we w say ,k+/on1 9 ,jamaica4 ,on 8 passage ?i!r he makes an obs]vation1 & f9ds ! sun on ! m]idian1 or t x is twelve o'clock 9 t situation1 :5 by 8 "t-keep] x is two 9 ! aft]noon 9 ,london1 :5ce he concludes he is #cj degrees we/ ( ,london4 ,,pupil4 ,i mu/ beg y to expla9 ?is to me1 z ,i d n und]/& :y two h\rs ( "t %\ld be equal to #cj degrees ( longitude4 ,,tutor4 ,y mu/ consid]1 t z ! e>? makes a complete revolution on its axis 9 #bd h\rs1 x mu/ pass ov] #cfj degrees 9 t "t3 n[1 if y divide #cfj by #bd1 ! quoti5t #ae1 w be ! numb] ( degrees pass$ ov] 9 "o h\r2 #cj degrees w be equal to two h\rs1 c4 ,! diff]5ce ( "t betwe5 ,london & 8 situation is two h\rs1 consequ5tly ! diff]5ce ( longitude mu/ be #cj degrees3 &1 x mu/ be we/1 because ! sun _h pass$ ! m]idian ( ,london2 =1 z ! e>? revolves f we/ by s\? to ea/1 "o place :i* lies ea/ ( ano!r mu/ come fir/ to ! m]idian or opposite to ! sun4 ,!re=e1 :5 longitude is reckon$ f ,london1 if ! place lie ea/ ( t m]idian ! "t w be be=e2 if we/1 aft] ,london4 ,,pupil4 ,i see x cle>ly2 & z #fj m9utes make an h\r1 if ,i divide x by #ae1 ! quoti5t #d w be ! m9utes answ]+ to "o degree4 ,,tutor4 ,y are "r3 & = ! same reason1 #d seconds ( "t are equal to "o m9ute ( longitude1 :i* y "k is ! #fj? "p ( a degree4--,our capta9 :5 arriv$ at ,k+/on1 f9ds ! diff]5ce ( "t betwe5 x & ,london #e ho4 #f m94 #cb sec4 ,c y tell me ! longitude ( ,k+/on8 ,,pupil4 ,if ,i br+ ! h\rs & m9utes to m9utes1 & divide by #d1 ! quoti5t ,i ?9k w be degrees1 w x n8 ,,tutor4 ,x w3 & ! seconds ( "t divid$ by #d1 w be m9utes ( longitude4 ,n[ try if y c d x4 ,,pupil4 ,five h\rs #f m9utes1 multipli$ by #fj w be #cjf m9utes1 ?is divid$ by #d1 w give #gf degrees & #b ov]1 :i* #b is half a degree1 or #cj m9utes3 & #cb seconds ( "t divid$ by #d1 w be #h m9utes ( longitude1 ! sum ( :i* is #gf degrees #ch m9utes = ! longitude ( ,k+/on4 ,,tutor4 ,v well4--,i h j n[ ?\ght ( ano!r me?od ( r$uc+ "t to longitude1 & longitude to "t1 :i* y may probably f9d easi]4 ,h[ev]1 :5 y are 9 possession ( bo?1 y may use :i* y please4 ,,pupil4 ,t :i* is easie/ mu/1 ,i ?9k1 be be/4 ,,tutor4 ,i w give x y1 & let me h y\r op9ion ( x4 ,to r$uce "t to longitude4 ,multiply ! h\rs1 m9utes1 & seconds ( "t by #ae1 or r by ! factors z !y are call$1 namely #c & #e1 c>ry+ "o = e #fj 9 ! m9utes & seconds1 & sett+ d[n ! rema9d]1 ?us3 ho4 m94 sec4 #e #f #cb diff]5ce ( #c "t4 #ae #ai #cf #e ,degrees #gf #ch #j longitude4 ,divide ! degrees & m9utes ( longitude by #e & #c & ! quoti5t w be ! diff]5ce ( "t4 ,,pupil4 ,i give ?is ! pref]5ce4 ,,tutor4 ,z longitude is seldom m5tion$ )\t be+ accompani$ ) latitude1 t y may n be ignorant ( its mean+ :5 y meet ) x1 ,i %all j tell y t x is ! di/ance ( any place f ! equator1 reckon$ 9 degrees & m9utes on ! m]idian1 & is ei!r nor? or s\? z ! place lies nor? or s\? ( ! equator4 ,! latitude ( any place is equal to ! elevation ( ! pole above ! horizon4 ,! latitude ( ! heav5ly bodies is reckon$ f ! ecliptic1 & t]m9ates 9 ! arctic & ant>ctic circles3 & _! longitude beg9s at ! po9t ,aries4 ,,pupil4 ,:at is ! measure ( a degree8 ,,tutor4 ,a degree ( latitude is #fj geographical1 or #fi-a_/b ,engli% miles3 & a degree ( longitude on ! equator is equal to x1 because ! equator z well z ! m]idians divides ! globe into two equal p>ts4 ,b a degree ( longitude decreases z y approa* ! poles3 = at ! poles ! m]idians meet 9 a po9t1 consequ5tly a degree !re c h no dim5sion4 ,to-morr[ ,i w %ew y ! cause ( ! seasons4 ---------------------------------------- -------------------------------- ,,dialogue ,x4 ,,pupil4 ,i ?9k1 ,sir1 :5 y left me la/ night y told me our next bus9ess w\ld be to expla9 ! nature ( ! seasons8 ,,tutor4 ,i did s1 & am p]suad$ y w f9d no great difficulty 9 compreh5d+ x4--,ca/ y\r eye on ! little draw+ ,i gave y1 7,plate ,,iii4 fig4 #b47 :]e ! e>? is repres5t$ z situat$ at ! f\r qu>t]s ( ! ye>1 namely1 ,spr+1 ,summ]1 ,autumn1 & ,w9t]4--,b be=e we proce$ to an explanation x w be necess>y to rem>k1 t1 9 ! little s*eme ! eye is suppos$ to be elevat$ above ! plane ( ! e>?'s orbit1 & t we see x v obliquely4 ,! orbit by ?is means appe>s v elliptical2 &1 ! enlight5$ hemisph]e1 or t half ( ! e>? :i* is turn$ to ! sun 9 ! spr+1 & ! d>k5$ hemisph]e1 or t turn$ f him 9 ! autumn1 are !re repres5t$4 ,,pupil4 ,?is ,i und]/&4 ,,tutor4 ,well !n1 we w beg9 ) ! spr+4--,9 ?is situation ( ! e>? ! equator is exactly oppos$ to ! sun3 &1 z he always enlight5s a hemisph]e1 or half ( its surface1 8 rays w rea* to bo? ! poles3 :5ce1 f ! diurnal revolution ( ! e>?1 ! day & night are equal all ov] ! globe4 ,,pupil4 ,?is ,i rememb] y told me happ5$ :5 ! sun 0 9 ,aries & ,libra4 ,! sun is n[ ent]+ ,aries3 &1 z we are 9 ! rays ( ! sun "o half ( ! diurnal revolution1 & 9 ! %ad[ ( ! e>?1 or d>k1 ! o!r half1 ! day & night mu/ be equal4 ,,tutor4 ,c]ta9ly4 ,& z ! sun ent]s ,aries 9 ! equ9octial1 x is !n call$ ! ,v]nal1 t is1 ,spr+ ,equ9ox4 ,:5 ! sun ent]s ! opposite sign ,libra1 ! same effects are produc$1 & x is !n call$ ! ,autumnal ,equ9ox4 ,,pupil4 ,y h pass$ on f ,spr+ to ,autumn4 ,,tutor4 ,i h s4--,we w n[ return1 & trace ! e>? 9 its orbit f spr+ to summ]4--,y h already se5 t ! nor? & s\? poles are bo? enlight5$1 & t ! day & night are equal at ! equ9oxes4 ,if ! axis ( ! e>? 7 p]p5dicul> to ! plane ( ! e>?'s orbit1 ?is w\ld con/antly be ! case1 & we %\ld h no div]sity ( seasons3 =1 ! sun be+ ov] ! equator1 ! poles mu/ be p]petually enlight5$1 & ( c\rse we %\ld h equal day & night at all times ( ! ye>4 ,,pupil4 ,t is pla94 ,i suppose !n t x is to ! incl9ation ( ! e>?'s axis we are indebt$ = ! increase & decrease ( days4 ,,tutor4 ,x is occasion$ by ! incl9ation ( ! e>?'s axis & its pres]v+ its p>allelism1 :i* ,i expla9$ to y la/ ev5+4--,z ! sun is n[ 9 ! fir/ po9t ( ,aries1 ! e>? y "k mu/ be 9 ! beg9n+ ( ,libra1 x be+ ! opposite sign4--,n[ fix y\r att5tion on ! s*eme1 & imag9e ! e>? to be advanc+ 9 its orbit ?r\gh ,libra1 ,scorpio1 & ,sagitt>ius3 & at ! fir/ degree ( ,capricorn give me y\r op9ion ( ! e>?'s position4 ,,pupil4 ,! nor? pole is turn$ to ! sun1 ! s\? pole f him1 & ! tropic ( ,canc] is opposite to him4 ,,tutor4 ,h[ _m degrees are ! tropics f ! equator1 or1 9 o!r words1 :at is ! incl9ation ( ! e>?'s axis8 ,,pupil4 ,tw5ty-?ree degrees & a half4 ,,tutor4 ,& s f> are ! rays ( ! sun ca/ beyond ! nor? pole1 & fall %ort ( ! s\? pole3 s t ! :ole ( ! arctic circle is enlight5$1 & ! ant>ctic circle involv$ 9 d>kness4 ,,pupil4 ,:at conclusion am ,i to draw f ?is8 ,,tutor4 ,t 9 ! nor!rn half ( ! globe x is ! longe/ day1 or summ]1 & 9 ! s\!rn half ! %orte/1 or w9t]1 :il/ "u ! equator ! days & nights are equal4 ,,pupil4 ,i us$ to ?9k t :5 x 0 w9t] or summ] "h x 0 s 9 e "p ( ! _w4 ,,tutor4 ,y n[ f9d y\r mi/ake4 ,= z ! e>? is mak+ its progress f ,libra1 ! nor? pole is approa*+ ! sun1 & ! s\? pole rec$+ f him3 consequ5tly ! l5g? ( ! day is increas+ 9 ! nor!rn hemisph]e & decreas+ 9 ! s\!rn4--,! sun has n[ be5 ?ree mon?s above ! horizon ( ! nor? pole1 & ! same "t bel[ t ( ! s\? pole1 & 9 ?ree mon?s m1 :5 ! e>? arrives at ,aries1 ! sc5e w be rev]s$3 ! sun w be ov] ! equator1 bo? poles w be aga9 enlight5$1 & ! day & night w be equal 9 e "p ( ! globe4 ,! sun w n[ be ris+ to ! s\? & sett+ to ! nor? pole4 ,?is is our ,autumn4 ,,pupil4 ,& z ! e>? is advanc+ t[>ds w9t]1 ! s\? pole w be turn+ to ! sun1 & ! nor? pole f him1 :5ce ,i conclude t :5 ! e>? is 9 ,canc] x mu/ be summ]1 s\? ( ! equator1 :5 x is our w9t]4 ,,tutor4 ,mo/ assur$ly4 ,= y see t ! sun is ov] ! tropic ( ,capricorn1 :i* y "k is z mu* s\? ( ! equator z ! tropic ( ,canc] is nor? ( x1 :]e ! sun 0 9 our summ]4 ,! ant>ctic circle is n[ enlight5$1 & ! arctic obscur$ 9 %ade2 b1 "u ! equator !re is nei!r increase nor decrease1 ! days & nights be+ ea* twelve h\rs4 ,,pupil4 ,x is n[ our w9t]1 ! sun has be5 ?ree mon?s above ! horizon ( ! s\? pole1 & w cont9ue s till ! v]nal equ9ox1 :5 he w aga9 rise to ! nor? pole1 & s on 9 regul> succession4 ,,tutor4 ,x mu/ be pla9 !n to y t !re c be b "o day & "o night at ea* ( ! poles1 reckon+ ! "t ! sun is above or bel[ _! respective horizons2 "u ! arctic & ant>ctic circles1 ! longe/ day is tw5ty-f\r h\rs1 & 9 ! %orte/ ! sun is j visible 9 ! horizon at noon4 ,! longe/ day decreases 9 l5g? ! ne>] we approa* ! equator1 :]e ,i be=e obs]v$ !re is no v>iation1 because ! circle b\nd+ light & d>kness1 9 e position ( ! e>?1 divides ! equator into two equal p>ts2 &1 x mu/ be obs]v$1 t ! longe/ day & longe/ night are equal to ea* o!r 9 e "p ( ! globe4 ,,pupil4 ,if ! longe/ day "u ! arctic circle be j tw5ty-f\r h\rs1 ! sun mu/ rise 9 ! nor?4 ,,tutor4 ,he does s1 makes a complete circle & sets 9 ! #aenor? aga94 ,f ! arctic circle to ! equator1 he rises nor? ( ! ea/ & sets nor? ( ! we/3 at ! equator he rises due ea/ & sets due we/1 !nce s\?w>d to ! ant>ctic circle1 he rises s\? ( ! ea/1 & sets s\? ( ! we/3 & "u ! ant>ctic circle1 z ,i obs]v$ j n[1 he is visible 9 ! horizon 9 ! s\? at noon4 ,footnote #ae3 ,"h x mu/ be obs]v$ t !re w be a little v>iation f sun-ris+ to sun-sett+1 z ! e>? is advanc+ 9 its orbit4 ,,pupil4 ,we usually say1 ! sun rises 9 ! ea/ & sets 9 ! we/4 ,,tutor4 ,at ! equ9oxes x mu/ be s 9 all p>ts ( ! globe1 ! poles except$3 9 e o!r situation1 except "u ! equator1 !re is a cont9ual *ange4 ,:at ,i h n[ told y1 respect+ ! nor!rn hemisph]e1 w be rev]s$ at our %orte/ day3 t is1 9 ! nor!rn hemisph]e ! sun w rise s\? ( ! ea/ & set s\? ( ! we/2 &1 9 ! s\!rn hemisph]e ! contr>y1 ! sun w be 9 ! horizon1 at noon1 "u ! arctic circle1 & ! day w be tw5ty-f\r h\rs "u ! ant>ctic circle4 ,,pupil4 ,pray ,sir1 are ! regions )9 ! pol> circles inhabit$8 ,if !y are1 _! situation1 9 w9t]1 mu/1 ,i ?9k1 be dreadful4 ,,tutor4 ,x is =eign to my pres5t purpose to speak ( ! inhabitants ( ! e>?1 z t m prop]ly belongs to ,geography4 ,?us mu* h[ev] ,i %all tell y1 t1 al?\gh x mu/ be v cold & dre>y1 !y are n s long depriv$ ( light z y may imag9e2 =1 ev5 "u ! poles1 :5 ! sun is hidd5 f !m1 !y are b a %ort "t 9 total d>kness1 =1 y mu/ recollect1 t ! twilight cont9ues till ! sun is eighte5 degrees bel[ ! horizon2 & ! sun's greate/ depression1 y "k1 c be b tw5ty ?ree degrees & a half1 equal to ! incl9ation ( ! e>?'s axis4 ,besides ?is1 ! moon is above ! horizon ( ! poles a =tnight toge!r2 be+ half h] p]iod nor?1 & ! o!r half s\?1 ( ! equator2 &1 z ! moon at full is 9 ! sign opposite to ! sun1 ! tropical full moons mu/ be tw5ty-f\r h\rs above ! horizon at ! pol> circles4 ,,pupil4 ,?is description is v pleas+1 z ,i _h no idea ( _! be+ fav\r$ ) s mu* light 9 ! abs5ce ( ! sun3 &1 ,i f9d1 z ! sun is long] above ! horizon 9 summ] ?an 9 w9t]1 ! moon1 on ! contr>y1 cont9ues long] ) u 9 w9t]1 :5 we mo/ ne$ h] assi/ance1 ?an %e does 9 summ]4 ,,tutor4 ,z y seem to und]/& :at ,i h be5 expla9+1 ,i %all %ew y1 t ! reason :y x is hotte/ :5 we are f>!/ f ! sun is1 t 9 w9t] :5 we are ne>e/ to him ! days are %ort]1 8 rays sail v obliquely on u1 & are m disp]s$ ?an !y are 9 summ]1 :5 he n only rema9s long] above ! horizon1 b be+ high]1 8 rays fall m direct on u1 by :i* means ! e>? becomes s mu* heat$ t x has n "t 9 ! %ort nights to get cold aga94--,:5 ! e>? is ne>e/ ! sun x is summ] 9 ! s\!rn hemisph]e1 !re=e x is reasonable to suppose t ! heat !re mu/ f> exce$ ours 9 ! same latitude2 b to c\nt]act ?is _! summ] is %ort] by eight days ?an ours3 & x is well kn[n t x is mu* cold] ne> ! poles 9 ! s\!rn ?an 9 ! nor!rn hemisph]e3 b ?is is acc\nt$ = f !re be+ m l& to reta9 ! heat 9 ! latt] ?an 9 ! =m]4 ,,pupil4 ,my d\bts on ?is head be+ n[ remov$1 ,i mu/ beg y to give me su* o!r in=mation z y may ?9k prop]4 ,,tutor4 ,z !re are diff]5t degrees ( heat & cold1 ! e>? has be5 divid$ into five zones1 namely1 "o torrid1 two temp]ate1 & two frigid zones4 ,,pupil4 ,h[ are !y di/+ui%$8 ,,tutor4 ,! torrid zone is all t space surr\nd+ ! globe conta9$ betwe5 ! tropics1 hav+ ! equator runn+ ?r\gh ! middle ( x4 ,x is s call$ on acc\nt ( its excessive heat1 =1 twice e ye> ! sun is v]tical to ! inhabitants1 t is1 he %9es directly on _! heads1 & ca/s no %ad[1 b "u _! feet1 at noon4 ,,pupil4 ,we f9d x sometimes extremely hot "h 9 our summ]2 surely1 9 ! torrid zone x mu/ be almo/ insupportable8 ,,tutor4 ,!y are inur$ to x f _! infancy4--,b we are dep>t+ f our subject4--,! temp]ate zones are compreh5d$ betwe5 ! tropics & pol> circles1 t betwe5 ! tropic ( ,canc] & ! arctic circle is call$ ! nor? temp]ate zone1 & t betwe5 ! tropic ( ,capricorn & ! ant>ctic circle ! s\? temp]ate zone4 ,,pupil4 ,i suppose !y are call$ temp]ate because ! heat is n s int5se z 9 ! torrid zone8 ,,tutor4 ,true4 ,nei!r is ! cold s sev]e z 9 ! frigid zones1 :i* are ^? regions compriz$ )9 ! pol> circles1 & are d5om9at$ nor? & s\?1 z !y are contigu\s to ! nor? or s\? poles4 ,,pupil4 ,:y are !y call$ frigid8 ,,tutor4 ,!y are call$ frigid or froz5 zones1 because ne> ! poles !re are p]petual fields ( ice1 ! heat ( ! sun1 ev5 9 summ]1 be+ insuffici5t to dissolve x4--,n[ try if y c tell me ! bread? ( ea* zone 9 degrees4 ,,pupil4 ,! torrid zone be+ tw5ty-?ree degrees & a half on ea* side ! equator mu/ be =ty-sev5 degrees1 :i* mu/ also be ! bread? ( ! frigid zones1 z ! pol> circles are di/ant tw5ty-?ree degrees & a half f ! poles1 :i* are _! c5t]s4 ,&1 z f ! equator to ei!r pole is n9ety degrees1 f ! equator to ! tropics tw5ty-?ree & a half1 & f ! pol> circle to ! pole tw5ty-?ree & a half1 if ! sum ( ^!1 t is1 =ty-sev51 be tak5 f n9ety1 ! rema9d]1 =ty-?ree1 w be ! bread? ( ea* ( ! temp]ate zones4 ,,tutor4 ,v well4 ,,pupil4 ,f :at y h told me ,i h no d\bt b t ! e>? is globul>1 b ,i h no pro( ( x3 ,i mu/ !re=e beg y\r assi/ance4 ,,tutor4 ,t x _c be an ext5d$ plane1 z "s h imag9$1 is v evid5t2 =1 if x 71 ! angle made ) t plane & ! nor? pole /> w\ld be always equal1 = reasons ,i h be=e giv5 y3 nei!r c x be cyl9drical1 t is l a g>d5 roll]1 z o!rs h suppos$4--,if a p]son travel nor?w>d ! pole /> becomes m elevat$1 & if he c\ld p5etrate to ! nor? pole ( ! e>? ! /> w\ld be 9 ! z5i?1 or directly ov] 8 head3 on ! contr>y1 if he travel s\?w>d1 x is m & m depress$ till he arrives at ! equator1 :]e ! /> is 9 ! horizon2 z he proce$s x disappe>s1 & o!r />s rise to 8 view1 invisible to u4 ,"h !n y see x mu/ be circul> nor?w>d & s\?w>d4 ,,pupil4 ,i am conv9c$ x mu/ be s4 ,,tutor4 ,& x is z c]ta9 t x is s ea/ & we/3 =1 navigators h (t5 sail$ r\nd x /e]+ ! same c\rse3 t is1 if !y sail an ea/]ly or we/]ly c\rse at sett+ (f1 by cont9u+ ! same c\rse !y w return to ! port :5ce !y dep>t$4 ,?is y "k !y c\ld n d if x 7 n r\nd1 any m ?an an insect c\ld1 by cross+ a r\nd table1 arrive at ! place x set out f2 b1 by go+ r\nd ! edge x w\ld be /ill go+ =w>d & come aga9 to ! po9t x _h left4 ,,pupil4 ,x is v evid5t4 ,,tutor4 ,aga94 ,9 e direction1 if a %ip be se5 at a di/ance1 ! fir/ ?+s obs]v$ are ! top-ma/ & rigg+1 :il/ ! hull or body ( ! %ip is hidd5 beh9d ! convexity1 t is r\ndness ( ! wat]1 j z y w\ld see a man com+ ov] a hill1 y w\ld fir/ see 8 head1 he w\ld be ris+ m & m to y\r view till he arriv$ at ! top1 :]e he w\ld be full 9 sight4 ,,pupil4 ,i am at a loss to acc\nt = ! convexity ( ! wat]4 ,h[ c its surface be r\nd8 ,,tutor4 ,h y nev] obs]v$ ! drops ( wat] fall+ f ! eaves ( a h\se8 ,,pupil4 ,(t51 ,sir4 ,,tutor4 ,( :at %ape 7 !y8 ,,pupil4 ,globul>4--,b :at is ! cause ( _! be+ s8 ,,tutor4 ,attraction4--,= z e p>ticle ( wat] :i* composes ! drop t5ds to ! same c5t]1 e "p ( ! surface mu/ be equidi/ant f ! c5t]1 x mu/ !re=e be sph]ical4 ,9 l mann] if y sep>ate quicksilv]1 ea* portion w =m itself into a globe4 ,,pupil4 ,all ?is is v cle>4 ,&1 = ! same reason1 ! wat] 9 ! ocean mu/ be convex2 =1 ,i rememb] y told me t x gravitat$ t[>ds ! c5t] ( ! e>?4 ,,tutor4 ,once m4--,i ?9k y mu/ h se5 an eclipse ( ! moon4 ,,pupil4 ,i h1 ,sir4 ,,tutor4 ,( :at figure 0 ! d>k5$ "p8 ,,pupil4 ,circul>4 ,,tutor4 ,take ?is ball1 & hold x be=e ! c&le betwe5 y\r f+] & ?umb1 s t ! %ad[ may be ?r[n on ! wall1 & 9 all positions y w f9d x circul>4 ,,pupil4 ,x is s4 ,,tutor4 ,apply ?is cr[n piece 9 ! same mann]1 ) ! flat side to ! c&le4 ,,pupil4 ,x is a circle4 ,,tutor4 ,turn x a little obliquely4 ,,pupil4 ,x is n[ an ellipsis4 ,,tutor4 ,n[ turn ! edge to ! c&le4 ,,pupil4 ,! %ad[ is a /rait l9e4 ,,tutor4 ,y n[ see t no o!r body ?an t ( a globe c 9 all positions ca/ a circul> %ad[4 ,,pupil4 ,i d1 ,sir4 ,,tutor4 ,! d>kness on ! disc ( ! moon at ! "t ( an eclipse is ! %ad[ ( ! e>?1 :i* 9 all situations is circul>2 ! e>?1 !re=e1 :i* ca/s ! %ad[1 mu/ be a globe4 ,,pupil4 ,x mu/ be s4--,b---- ,,tutor4 ,! e>? is m\nta9\s4--,x is s3 b rememb] t ! highe/ m\nta9 be>s no great] proportion to ! bulk ( ! e>? ?an ! small irregul>ities on ! peel ( an orange be>s to t fruit3 t objection !re=e is soon remov$4 ,& yet x is n a true sph]e4 ,,pupil4 ,:at !n8 ,,tutor4 ,a sph]oid1 t is1 x is a little flatt5$ at ! poles1 & is 9 %ape n unlike an orange or a turnip4 ,?is y w n be surpriz$ at :5 ,i tell y t ! equatorial p>ts are ab\t f\r ?\s& miles f ! c5t] ( motion4 ,,pupil4 ,i suppose !n y inf] t z ! c5trifugal =ce is great] ! f>!r x is remov$ f ! c5t]1 t ! p>ts ne> ! poles h a t5d5cy to fly (f t[>ds ! equator4 ,,tutor4 ,i d4 ,& z we h f9i%$ ?is "p ( our subject1 ,i %all take leave ( y4 ---------------------------------------- -------------------------------- ,,dialogue ,,xi4 ,,tutor4 ,i n[ propose giv+ y a description ( ! moon1 & ,i d\bt n x w af=d y "s degree ( pleasure4 ,,pupil4 ,inde$ x w1 z ,i "k little m ?an t %e is a second>y planet or satellite1 revolv+ r\nd ! e>?1 & ) x r\nd ! sun4 ,,tutor4 ,y "k h] mean di/ance f ! e>?4 ,,pupil4 ,i did n recollect t3 #bdj ?\s& miles4 ,,tutor4 ,"r4 ,h] diamet] is ab\t #bafa miles1 & h] bulk ab\t a fiftie? "p ( ! e>?'s4 ,h] axis is almo/ p]p5dicul> to ! plane ( ! ecliptic1 consequ5tly %e c h no div]sity ( seasons4 ,,pupil4 ,:at is h] p]iod8 ,,tutor4 ,! "t %e takes to revolve f "o po9t ( ! heav5s to ! same aga9 is call$ h] sid]ial or p]iodical revolution1 & is p]=m$ 9 #bg days1 #g h\rs1 #dc m9utes2 b synodical revolution1 or ! "t tak5 up to revolve f ! sun to ! same app>5t situation ) respect to ! sun aga91 or f *ange to *ange1 is #bi days1 #ab h\rs1 & #dd m9utes4 ,,pupil4 ,i d n cle>ly compreh5d x4 ,,tutor4 ,if ! e>? _h no annual motion1 ! p]iod ( ! moon w\ld be uni=mly #bg days1 #g h\rs1 #dc m9utes2 b y are to consid] t :il/ ! moon is revolv+ r\nd ! e>?1 ! e>? is advanc+ 9 its orbit1 & ( c\rse %e mu/ be s mu* long] 9 complet+ h] synodical revolution z ! diff]5ce ( "t betwe5 t & h] sid]ial revolution4 ,?is ,i w make cle> to y 9 a few m9utes4--,:at is ! situation ( ! h\r-h& & m9ute-h& ( a wat* at twelve o'clock8 ,,pupil4 ,!y w be 9 conjunction4 ,,tutor4 ,& w !y be 9 conjunction at "o8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,yet ! m9ute-h& has made a complete revolution3 b be=e !y c be 9 conjunction aga9 ! m9ute-h& mu/ move =w>d till x ov]takes ! h\r-h&4 ,,pupil4 ,i n[ und]/& x1 & mu/ beg y to expla9 to me ! diff]5t phases ( ! moon4 ,,tutor4 ,take ?is ivory ball1 & susp5d x by ! /r+ ) y\r h& betwe5 y\r eye & ! c&le4 ,let ! c&le repres5t ! sun1 ! ball ! moon1 & y\r head ! e>?4 ,9 ?is situation1 z ! c&le enlight5s only "o half ( ! ball1 ! "p turn$ f y w be enlight5$1 & ! "p turn$ to y w be d>k4 ,?is w be a repres5tation ( ! moon at *ange1 & z no "p ( h] enlight5$ hemisph]e is turn$ to ! e>?1 %e c reflect no light ^u x1 & consequ5tly is invisible to u4 ,%e n[ rises & sets ne>ly ) ! sun4--,turn y\rself a little to ! left1 & y w obs]ve a /reak ( light l :at is call$ ! new moon4 ,,pupil4 ,i see x cle>ly4 ,,tutor4 ,move r\nd "o qu>t]4 ,,pupil4 ,"o half ( ! side next me is n[ enlight5$4 ,,tutor4 ,y may conceive x to be ! moon at fir/ qu>t]4--,g on1 & y w see ! light increase till ! ball is opposite to ! c&le1 :5 ! side next y w be :olly illum9$1 & w give y a j idea ( ! moon at full1 :i* n[ rises ab\t ! "t ( sun-sett+1 be+ opposite to ! sun3 &1 ! f>!r %e advances 9 h] orbit ! lat] %e rises4 ,,pupil4 ,x is pla9 x mu/ be s4 ,%e rises ) ! sun at *ange1 be+ !n 9 conjunction3 & z %e revolves 9 h] orbit ! same way z ! e>? does on its axis1 ! e>? w h f>!r to revolve ea* day be=e x c see ! moon4 ,at ! full %e is 9 opposition1 & ( c\rse rises :5 ! sun sets3 & s cont9ues to rise lat] & lat]1 till ! *ange aga94 ,,tutor4 ,y imag9e t ! moon rises exactly ) ! sun :5 %e is at *ange2 & :5 he sets1 at full4 ,i w pres5tly conv9ce y ( y\r mi/ake2 & w\ld h y n[ proce$ ) y\r ball4 ,place x aga9 opposite to ! c&le1 & z y turn r\nd y w f9d ! light gradually decrease z x be=e increas$1 t ! side t 0 be=e enlight5$ is n[ d>k1 & ! d>k side light4 ,:5 y h gone ?ree qu>t]s r\nd1 "o half ( ! side next y w be enlight5$1 & w resemble ! moon at la/ qu>t]4 ,z y g on ! d>k5$ "p w increase1 till y arrive at ! place y set (f f1 :]e ! light is q obscur$4 ,,pupil4 ,i h n[ complet$ ! circuit1 & am mu* delight$ ) x1 z by ?is simple contrivance ,i c p]ceive ! v>i\s *anges ( ! moon1 & t ! we/]n side is enlight5$ f ! *ange to ! full1 & ! ea/]n side f ! full to ! *ange4 ,,tutor4 ,i f9d !n x has fully answ]$ ! purpose int5d$4 ,,pupil4 ,inde$ x has4 ,b if y w give me leave ,i w use ! ball aga94 ,,tutor4 ,by all means4 ,,pupil4 ,i p]ceive1 z ,i move r\nd1 t ! same side ( ! ball is turn$ t[>ds me :il/ e "p is turn$ to ! c&le4 ,is x s ) ! moon8 ,,tutor4 ,x is3 & z e "p ( ! moon is turn$ to ! sun1 %e makes "o revolution on h] axis :il/ %e makes "o 9 h] orbit4 ,,pupil4 ,?is is v s+ul>4 ,if ! same side ( ! moon be always turn$ to ! e>?1 ! opposite side ( c\rse c nev] see x4 ,,tutor4 ,& !y mu/ likewise be depriv$ ( ! e>? z a moon4 ,,pupil4 ,true4 ,b h[ is x kn[n t ! same side ( ! moon is always oppos$ to ! e>?8 ,,tutor4 ,! moon1 l our e>?1 consi/s ( m\nta9s & valleys1 :i*1 :5 se5 ?r\gh a good telescope1 are v beautiful4 ,! m\nta9\s p>ts appe> z lucid spots & bright /reaks ( light3 & z ! same spots1 c4 are con/antly turn$ to ! e>?1 %e mu/ keep ! same side to ! e>?4 ,,pupil4 ,x is v cle>4 ,are !re no seas8 ,,tutor4 ,x 0 =m]ly imag9$ t ! d>k p>ts 7 seas1 b lat] obs]vations prove t !y are holl[ places or cav]ns1 :i* d n reflect ! light ( ! sun4 ,besides1 if !re 7 seas !re w\ld consequ5tly be exhalations1 & if exhalations1 cl\ds & vap\rs1 & an atmosph]e to support !m4 ,t !re are no cl\ds is evid5t1 because :5 our atmosph]e is cle>1 & ! moon above our horizon 9 ! night-"t1 all h] p>ts appe> con/antly ) ! same cle>1 s]5e1 & calm aspect4 ,,pupil4 ,has ! moon !n no atmosph]e8 ,,tutor4 ,if %e has x is imp]ceptible to u3 =1 :5 %e approa*es any />1 we _c discov] ) our be/ telescopes any *ange ( col\r or dim9ution ( lu/re 9 ! /> till ! in/ant x is lo/ beh9d h]3 :5ce x is cle>1 t %e c h no su* gross m$ium z our atmosph]e to surr\nd h]4 ,,pupil4 ,may we n !n d\bt :e!r %e be inhabit$ or n1 z )\t air we _c brea!8 ,,tutor4 ,! same ,almighty ,be+ :o creat$ u & gave u air to brea!1 may h provid$ a diff]5t way = _! exi/5ce4 ,x does n hold good t1 because we c\ld n live !re1 %e is n inhabit$4 ,fi% w live a consid]able "t 9 wat] "u an exhau/$ receiv]3 &1 ,i h he>d ( a toad be+ f\nd 9 a block ( m>ble4 ,y\r d\bt !re=e1 ,i ?9k1 ought n to be admitt$4 ,,pupil4 ,i am satisfi$4 ,& mu/ n[ beg to be in=m$ h[ ,i may obs]ve ! moon's motion4 ,,tutor4 ,h] real motion r\nd ! e>?1 may be easily kn[n by rem>k+ :5 %e is ne> any p>ticul> />4 ,?us1 suppose y see h] we/1 t is to ! "r ( x1 %e w be approa*+1 !n 9 conjunction )1 & aft]w>ds pass x t[>ds ! ea/4 ,h] app>5t motion is t ( ris+ & sett+1 :i* is occasion$ by ! rotation ( ! e>? on its axis4 ,,pupil4 ,i rememb] n long s9ce1 :5 y %ew$ me ,jupit]1 t ! moon 0 we/ ( him3 ! next ev5+ ,i saw h] almo/ appe> to t\* him1 & soon aft] at a great di/ance f him ea/]ly4 ,i n[ see t h] real motion is f we/ by s\? to ea/1 & h] app>5t motion f ea/ by s\? to we/4 ,,tutor4 ,if y h no objection1 ,i w n[ expla9 ! cause ( eclipses4 ,,pupil4 ,s f> f x1 t x w give me ! greate/ pleasure4 ,,tutor4 ,take y\r ivory ball1 susp5d x z be=e1 9 a "r l9e betwe5 y\r eye & ! c&le4--,c y see ! c&le8 ,,pupil4 ,no1 ,sir4 ,,tutor4 ,= :at reason4 ,,pupil4 ,because ! ball prev5ts ! light com+ to me4 ,,tutor4 ,?is !n repres5ts an eclipse ( ! sun1 :i* c nev] happ5 b :5 ! moon is betwe5 ! sun & ! e>?1 :i* mu/ be at ! *ange3 =1 z light passes 9 a "r l9e1 ! sun is hidd5 to t "p ( ! e>? :i* is "u ! moon1 & !re=e he mu/ be eclips$4 ,if ! :ole ( ! sun be obscur$ by ! body ( ! moon1 ! eclipse is total3 if only a "p be d>k5$1 x is a p>tial eclipse2 & s _m twelf? p>ts ( ! sun's diamet]1 z ! moon cov]s1 s _m digits are said to be eclips$4 ,,pupil4 ,may n ! ^w digit be appli$ to ! moon z well z ! sun8 ,,tutor4 ,x may3 = x means a twelf? "p ( ! diamet] ( ei!r ! sun1 or ! moon4 ,,pupil4 ,z y h n[ %ewn me ! cause ( an eclipse ( ! sun1 ,i am anxi\s to h t ( ! moon expla9$4 ,,tutor4 ,we mu/ aga9 h rec\rse to y\r little ball4--,turn y\rself r\nd till x is opposite to ! c&le 9 a l9e ) y\r head1 & y w see t no light c be ?r[n on x f ! c&le1 because y\r head is betwe5 !m4 ,9 l mann] ! rays ( ! sun are prev5t$ fall+ on ! moon1 by ! int]position ( ! e>?3 %e mu/ !re=e be eclips$4 ,,pupil4 ,i see x cle>ly4 ,& z an eclipse ( ! sun happ5s :5 ! moon is at *ange1 t ( ! moon mu/ be :5 %e is at full2 =1 x is !n only ! e>?'s %ad[ c fall on ! moon1 ! e>? be+ at no o!r "t betwe5 ! sun & h]4 ,,tutor4 ,! diamet] ( ! %ad[ is ab\t ?ree times t ( ! moon1 & consequ5tly ! moon mu/ be totally eclips$ :il/ %e cont9ues 9 x4 ,on ! contr>y1 ! %ad[ ( ! moon at an eclipse ( ! sun1 cov]s s small a "p ( ! e>?'s surface1 t ! sun is totally or c5trally eclips$ to b a small "p ( x2 & its duration is v %ort4 ,b a fa9t or p>tial %ad[ surr\nds ?is d>k5$ %ade1 9 :i* ! sun is m or less eclips$1 z ! place is ne>] to or f>!r f its c5t]2 ?is p>tial %ad[ is call$ ! p5umbra4 ,i h prep>$ = y a little draw+1 repres5t+ an eclipse bo? ( ! sun & moon1 :i* ,i ?9k w enable y bett] to und]/& :at ,i h be5 expla9+4 7,plate ,,iv4 ,fig4 #a & #b47 ,9 ! =m]1 p4 p4 is ! p5umbra4 ,illu/ration3 ,plate ,,iv4 ,t4 ,cond] ,sculpt4 ,,pupil4 ,9 :at does a c5tral diff] f a total eclipse8 ,,tutor4 ,an eclipse ( ! sun may be c5tral1 & n total2 =1 ^? :o are "u ! po9t ( ! d>k %ad[1 w see ! edge ( ! sun l a f9e lum9\s r+1 all ar\nd ! d>k body ( ! moon :5 ! sun is eclips$ at ! moon's greate/ di/ance f ! e>?2 b :5 %e is ne>e/ ! e>? at an eclipse ( ! sun1 ! eclipse is total4 ,:5 ! p5umbra fir/ t\*es ! e>?1 ! g5]al eclipse beg9s2 :5 x leaves ! e>?1 ! g5]al eclipse ends4 ,an eclipse ( ! moon always beg9s on ! moon's ea/]n side1 & goes (f on h] we/]n side2 b an eclipse ( ! sun beg9s on ! sun's we/]n side1 & goes (f on 8 ea/]n side4 ,:5 ! moon is eclips$ 9 ei!r ( h] nodes1 ! eclipse is bo? c5tral & total4 ,,pupil4 ,pray1 :at is ! reason we h n an eclipse at e full & *ange ( ! moon8 ,,tutor4 ,= ! same reason t ,m]cury & ,v5us are n se5 to pass ov] %e sun's disc at e inf]ior conjunction4 ,,pupil4 ,is ! orbit ( ! moon !n incl9$ to ! plane ( ! ecliptic8 ,,tutor4 ,x is3 & no eclipse ( ! sun c happ5 b :5 ! moon is )9 #ag degrees ( ei!r ( h] nodes3 nei!r c !re be "o ( ! moon1 unless %e be )9 #ab degrees4 ,at all o!r new moons %e passe? ei!r above or bel[ ! sun1 z se5 f ! e>?3 & at all o!r full moons above or bel[ ! e>?'s %ad[1 accord+ z %e is nor? or s\? ( ! ecliptic4 ,y n[ see t ! moon mu/ sometimes rise be=e & sometimes aft] ! sun at *ange1 & be=e or aft] he sets at full4 ,,pupil4 ,i d1 ,sir1 & am mu* oblig$ to y = ?is pleas+ acc\nt ( ! moon1 & ( eclipses3 & if y h any ?+ f>!r to obs]ve1 x w af=d me additional pleasure4 ,,tutor4 ,y may1 at "s "t or o!r1 h an opportunity ( see+ a total eclipse ( ! moon2 x w !re=e be necess>y to prep>e y = a phnom5on :i* o!rwise y might be mu* surpriz$ at1 & t is1 t aft] ! moon is imm]s$ 9 ! e>?'s %ad[1 %e is /ill visible4 ,,pupil4 ,?is is a phnom5on t ,i am n able to acc\nt =2 =1 ! moon be+ an opaque body1 %e _c %9e by h] own light#af1 & ! rays ( ! sun are prev5t$ fall+ on h] by ! int]position ( ! e>?1 %e _c !re=e %9e by reflection4 ,footnote #af3 ,dr4 ,h]s*ell supposes ! moon & ! re/ ( ! planets may h "s inh]5t light3 ! side ( ! planet ,v5us1 turn$ f ! sun1 hav+ be5 se51 z we see ! moon soon aft] ! *ange4 ,,tutor4 ,x is by reflection t we see h]2 = ! rays ( ! sun :i* fall ^u our atmosph]e are refract$ or b5t into ! e>?'s %ad[1 & s fall+ ^u ! moon are reflect$ back to u4 ,if we _h no atmosph]e1 %e w\ld be totally d>k1 & ( c\rse invisible to u4 ,,pupil4 ,:at is h] appe>ance8 ,,tutor4 ,x is t ( a dusky col\r1 some:at l t>ni%$ copp]4--,i h "o ?+ m to rem>k be=e we quit ?is subject1 :i* is1 t ! moon's nodes h a retrograde or backw>d motion1 9 a direction contr>y to ! e>?'s annual motion1 & g ?r\gh all ! signs & degrees ( ! ecliptic 9 little less ?an n9ete5 ye>s1 :5 !re w be a regul> p]iod ( eclipses1 or return ( ! same eclipses = _m ages4 ,,pupil4 ,pray1 ,sir1 :at d y propose = our next subject8 ,,tutor4 ,! ebb+ & fl[+ ( ! sea1 or cause ( ! tides4 ---------------------------------------- -------------------------------- ,,dialogue ,,xii4 ,,tutor4 ,9 ord] to expla9 ! cause ( ! tides1 ,i h s9ce ,i saw y la/ prep>$ a little draw+ = y1 7,plate ,,iv4 fig4 #c47 :]e ,s repres5ts ! sun1 ,m ! moon at *ange1 ,e ! c5t] ( ! e>?1 & ,a ,b ,c ,d its surface1 cov]$ ) wat]4 ,x is obvi\s1 f ! pr9ciples ( gravitation1 t if ! e>? 7 at re/ ! wat] 9 ! ocean w\ld be truly sph]ical1 if its figure 7 n alt]$ by ! action ( "s o!r p[]4 ,b1 daily exp]i5ce proves t x is cont9ually agitat$4 ,,pupil4 ,:at is ! cause ( ?is agitation8 ,,tutor4 ,! attraction ( ! sun & moon1 p>ticul>ly ! latt]3 =1 z %e is s mu* ne>] ! e>? ?an ! sun1 %e attracts ) a mu* great] =ce ?an he does1 & consequ5tly raises ! wat] mu* high]1 :i*1 be+ a fluid1 loses z x 7 its gravitat+ p[]1 & yields to _! sup]ior =ce4 ,,pupil4 ,:at proportion does ! attractive p[] ( ! sun be> to t ( ! moon8 ,,tutor4 ,z ?ree to t54 ,s :5 ! moon is at *ange1 ! sun & moon be+ 9 conjunction1 or on ! same side ( ! e>?1 ! action ( bo? bodies is on ! surface ( ! wat]1 ! moon rais+ x t5 p>ts1#ag & ! sun ?ree1 ! sum ( :i* is ?irte5 p>ts1 repres5t$ by ,b b4 ,n[ x is evid5t1 t if ?irte5 p>ts be add$ by ! attractive p[] ( ^? bodies1 ! same numb] ( p>ts mu/ be drawn (f f "s o!r "p1 z ,a a1 ,c c4 ,x w n[ be high-wat] "u ! moon at b1 & its opposite side d1 & l[-wat] at a & c4 ,footnote #ag3 ,by "p "h ,i d n mean any specific measure4 ,,pupil4 ,t ! attraction ( ! sun & moon mu/ occasion a swell+ ( ! wat]s on ! side next !m1 ,i c readily conceive1 & t ?is swell mu/ cause a fall+ (f at ! sides3 b t ! tide %\ld rise z high on ! side opposite to ! sun & moon1 9 a direction contr>y to _! attraction1 is :at ,i am n able to acc\nt =4 ,,tutor4 ,?is difficulty w be remov$ :5 y consid] t all bodies mov+ 9 circles h a con/ant t5d5cy to fly (f f _! c5t]s4 ,n[1 z ! e>? & moon move r\nd _! c5t] ( gravity1 t "p ( ! e>? :i* is at any "t opposite to ! moon w h a great] c5trifugal =ce ?an ! side next h]1 & at ! e>?'s c5t] ! c5trifugal =ce exactly balances ! attractive =ce3 !re=e1 z mu* wat] is ?r[n (f by ! c5trifugal =ce on ! side opposite to ! moon1 z is rais$ on ! side next h] by h] attraction4 ,h5ce1 x is pla91 t at ,d1 fig4 #c1 ! c5trifugal =ce mu/ be great] ?an at ! c5t] ,e1 & at ,e ?an ,b1 because ! "p ,d is f>!r f ! c5t] ( motion ?an ! "p ,b4 ,on ! contr>y1 ! "p ,b be+ ne>] ! moon ?an ! c5t] ,e1 ! attract+ p[] mu/ !re be /ronge/1 & weake/ at ,d4 ,&1 z ! two oppos+ p[]s balance ea* o!r at ! e>?'s c5t]1 ! tides w rise z high on t side f ! moon1 by ! excess ( ! c5trifugal =ce1 z !y rise on ! side next h] by ! excess ( h] attraction4 ,,pupil4 ,9 ?is explanation y h m5tion$ no?+ ( ! sun4 ,,tutor4 ,f :at ,i h already said x mu/ be pla9 to y t if !re 7 no moon ! sun by 8 attraction w\ld raise a small tide on ! side next him2 &1 x is z evid5t t ! tides opposite w\ld be rais$ z high by ! c5trifugal =ce3 = ! sun & e>?1 z well z ! e>? & moon1 move r\nd _! c5t] ( gravity4 ,?is may be exemplifi$ by an easy exp]im5t4 ,take a flexible hoop1 suppose ( ?9 brass1 tie a /r+ to x & :irl x r\nd y\r head1 & x w assume an elliptical %ape2 ! tightness ( ! /r+ draw+ out ! side next to y\r h&1 & ! c5trifugal =ce ?r[+ (f ! o!r4 ,,pupil4 ,?is ,i cle>ly compreh5d4 ,,tutor4 ,i %all n[ ref] y to ! next figure1 7fig4 #d47 :]e ,f repres5ts ! moon at full3 ! sun & moon are 9 opposition1 & yet ! tide is z high on ea* side z 9 ! =m] case4 ,i wi% y to %ew me ! cause4 ,,pupil4 ,i w use my endeav\r to d x1 ,sir4 ,,tutor4 ,!n ,i d\bt n y w accompli% x4 ,,pupil4 ,:5 ! moon is at full1 t5 p>ts ( wat] are rais$ f t side ( ! e>? next h]1 by h] attraction2 &1 z ! side :i* is next h] is opposite to ! sun1 ?ree p>ts mu/ be ?r[n (f by 8 c5trifugal =ce1 ! sum ( :i* w be ?irte5 p>ts next ! moon4--,f ! side opposite to ! moon1 & "u ! sun1 t5 p>ts are ?r[n (f by h] c5trifugal =ce1 & ?ree rais$ by 8 attraction1 mak+ ?irte51 ! same z be=e4 ,,tutor4 ,i c\ld n h done x bett]4 ,^! are call$ ,spr+ ,tides4 ,b :5 ! moon is 9 h] qu>t]s1 ! action ( ! sun & moon are 9 opposition to ea* o!r2 t is1 !y act 9 contr>y directions 7see fig4 #e47 ,! moon ( h]self w\ld raise ! wat] t5 p>ts "u h]1 & ?r[ (f t5 p>ts by h] c5trifugal =ce on ! opposite side2 b1 ! sun be+ !n 9 a l9e ) ! l[-wat]1 8 action keeps ! tides f fall+ s l[ !re1 & consequ5tly f ris+ s high "u & opposite to h]4 ,8 p[]1 !re=e1 on ! l[-wat] be+ ?ree p>ts1 leaves only sev5 p>ts = ! high wat]1 "u & oppose ! moon4 ,^! are call$ ,neap ,tides4 ,,pupil4 ,?is is v pla94 ,,tutor4 ,y w\ld naturally suppose t ! tides ought to be highe/ directly "u & opposite to ! moon3 t is1 :5 ! moon is due nor? & s\?4 ,b we f9d1 t 9 op5 seas1 :]e ! wat] fl[s freely1 ! moon is g5]ally pa/ ! nor? & s\? m]idian :5 x is high-wat]4 ,=1 if ! moon's attraction 7 to cease :5 %e 0 pa/ ! m]idian1 ! motion ( asc5t communicat$ to ! wat] be=e t "t w\ld make x cont9ue to rise = "s "t aft]3 z ! heat ( ! day is great] at ?ree o'clock 9 ! aft]noon ?an x is at twelve2 & x is hott] 9 ,july & ,augu/ ?an 9 ,june1 :5 ! sun is highe/ & ! days are longe/4 ,,pupil4 ,^! are conv9c+ reasons4 ,&1 pray :at "t aft] ! moon has pass$ ! m]idian1 is x high-wat]8 ,,tutor4 ,if ! e>? 7 entirely cov]$ ) wat]1 s t ! tides might regul>ly foll[ ! moon1 %e w\ld always be ?ree h\rs pa/ ! m]idian ( any giv5 place :5 ! tide 0 at ! highe/ at t place4 ,b1 z ! e>? is n cov]$ ) wat]1 ! tides d n always answ] to ! same di/ance ( ! moon f ! m]idian at ! same places1 because ! regul> c\rse ( ! tides is mu* int]rupt$ by ! diff]5t capes & corn]s ( ! l& runn+ out into ! oceans & seas 9 diff]5t directions1 & also by _! runn+ ?r\gh %oals & *annels4 ,b1 at :atev] di/ance ! moon is f ! m]idian on any giv5 day1 at any place1 :5 ! tide is at its height !re1 x w be s aga9 ! next day1 mu* ab\t ! "t :5 ! moon is at ! l di/ance f ! m]idian aga94 ,,pupil4 ,are n ! tides lat] e day ?an !y 7 ! prec$+ day8 ,,tutor4 ,yes2 & ! reason is obvi\s3 =1 :il/ ! e>? is revolv+ on its axis 9 tw5ty-f\r h\rs1 ! moon w be advanc+ 9 h] orbit2 !re=e ! e>? mu/ turn z mu* m ?an r\nd its axis be=e ! same place :i* 0 "u h] c come to ! same place aga9 ) respect to h]1 z %e has advanc$ 9 h] orbit dur+ t int]val ( "t1 :i* is #ej m9utes4 ,?is be+ divid$ by #d1 gives #ab-a_/b m9utes2 s t x w be #f h\rs #ab-a_/b m9utes f high to l[-wat]1 & ! same "t f l[ to high-wat]3 or #ab h\rs #be m9utes f high-wat] to high-wat] aga94 ,,pupil4 ,?is ,i und]/& p]fectly well4 ,,tutor4 ,i h n[ f9i%$ my description ( ! tides1 & hav+ a little "t to sp>e1 if y wi% to "k h[ to f9d ! proportionate magnitude ( ! planets ) t ( ! e>?1 & to calculate _! di/ances f ! sun1 ,i w employ x t way4 ,,pupil4 ,at our fir/ conf]5ce ,i rememb] y %ew$ me ! proportion t ! o!r planets be> to ! e>?1 ) _! p]iods & di/ances f ! sun2 b to h x 9 my p[] to make ! calculations myself1 w c]ta9ly give me great pleasure4 ,,tutor4 ,to f9d :at proportion any planet be>s to ! e>?2 or1 t "o globe be>s to ano!r1 y mu/ obs]ve t1 all sph]es or globes are 9 proportion to "o ano!r z ! cubes ( _! diamet]s4 ,s t y h no?+ m to d ?an to cube ! diamet] ( ea*1 & divide ! greate/ by ! lea/ numb]1 & ! quoti5t w %ew y ! proportion t "o be>s to ! o!r4 ,,pupil4 ,! op]ation appe>s v simple2 b1 z ,i d n "k :at a cube numb] is1 ,i _c p]=m x4 ,,tutor4 ,y _c =get :at a squ>e numb] is4 ,,pupil4 ,! product ( any numb] multipli$ into itself is a squ>e numb]1 z #d is ! squ>e ( #b4 ,,tutor4 ,any squ>e numb] multipli$ by its root1 or fir/ p[]1 w be a cube numb]4 ,?us #d multipli$ by #b w be #h1 :i* is ! cube ( #b2 #i is ! squ>e or second p[]1 & #bg ! cube or ?ird p[] ( #c1 c4 ,?is y w p]haps bett] und]/& by ,a ,,table ,,( ,roots4 #a4 #b4 #c4 #d4 #e4 #f4 #g4 #h4 #i4 ,squ>es4 #a4 #d4 #i4 #af4 #be4 #cf4 #di4 #fd4 #ha4 ,cubes4 #a4 #h4 #bg4 #fd4 #abe4 #baf4 #cdc4 #eab4 #gbi4 ,,pupil4 ,i d1 ,sir2 & am n[ prep>$ = an example4 ,,tutor4 ,! diamet] ( ! sun is #hiceeb miles1 ( ! e>? #gibj miles2 h[ mu* does ! sun exce$ ! e>? 9 magnitude8 ,,pupil4 ,! cube ( #hicebb1 ! sun's diamet]1 is #gaccgadibbfjhgbfdh2 & ( #gibj1 ! e>?'s1 #difgicjhhjjj4 ,& #gaccgadibbfjhgbfdh divid$ by #difgicjhhjjj is equal to #adceieb1 & s _m times is ! bulk ( ! sun great] ?an t ( ! e>?4 ,,tutor4 ,?is "o example may suffice1 z ,i int5d by & by to give y a table ( diamet]s1 c42 y may !n calculate ! re/ at y\r leisure4 ,,pupil4 ,i %all n[1 ,sir1 be glad to h ! o!r expla9$4 ,,tutor4 ,! p]iods ( ! planets1 or ! times !y take to complete _! revolutions 9 _! orbits1 are exactly kn[n2 & ! mean di/ance ( ! e>? f ! sun has be5 also asc]ta9$4 ,"h1 !n1 we h ! p]iods ( all1 & ! mean di/ance ( "o1 to f9d ! di/ances ( ! re/2 :i* may be f\nd by att5d+ to ! foll[+ proportion3 ,z ! squ>e ( ! p]iod ( any "o planet1 ,is to ! cube ( its mean di/ance f ! sun2 ,s is ! squ>e ( ! p]iod ( any o!r planet1 ,to ! cube ( its mean di/ance4 ,! cube root ( ?is quoti5t w be ! di/ance s\ght4 ,,pupil4 ,"h aga9 ,i f9d myself at a loss1 z ,i h n le>nt to extract ! cube root4 ,,tutor4 ,i w give y #ah;,doctor ,turn]'s rule1 :i* ,i ?9k w answ] y\r purpose4 ,footnote #ah3 ,"y ,geometrician's ,companion4 8,fir/1 hav+ set d[n ! giv5 numb]1 or resolv5d1 make a dot ov] ! unit figure1 & s on ov] e ?ird figure 7t[>ds ! left h& 9 :ole numb]s1 b t[>ds ! "r h& 9 decimals72 & s _m dots z !re are1 s _m figures w be 9 ! root4 ,next1 seek ! ne>e/ cube to ! fir/ p]iod2 place its root 9 ! quoti5t1 & its cube set "u ! fir/ p]iod4 ,subtract x !refrom2 & to ! rema9d] br+ d[n "o figure only ( ! next p]iod1 :i* w be a divid5d4 ,!n1 squ>e ! figure put 9 ! quoti5t1 & multiply x by #c1 = a divisor4 ,seek h[ (t5 ?is divisor may be _h 9 ! divid5d1 & set ! figure 9 ! quoti5t1 :i* w be ! second place 9 ! root4 ,n[1 cube ! figures 9 ! root1 & subtract x f ! two fir/ p]iods ( ! resolv5d2 & to ! rema9d] br+ d[n ! fir/ figure ( ! next p]iod1 = a new divid5d4 ,squ>e ! figures 9 ! quoti5t1 & multiply x by #c1 = a new divisor2 !n proce$ 9 all respects z be=e1 till ! :ole is f9i%$40 ,! foll[+ example w1 ,i tru/1 make x cle> to y4 ,,example4 ,x is requir$ to f9d ! cube root ( #aefbe4 4 4 #aefbe 7#be #h #ab7 #gf #aefbe 44444 ,po9t e ?ird figure1 & ! fir/ p]iod w be #ae2 ! ne>e/ cube to :i*1 9 ! table ,i gave y j n[1 y w f9d to be #h1 & its root #b2 ! #h y mu/ place "u ! #ae1 & ! #b 9 ! quoti5t3 take #h f #ae & #g w rema91 to :i* br+ d[n #f1 ! fir/ figure ( ! next p]iod1 & y h #gf = a divid5d4 ,! figure put 9 ! quoti5t is #b1 ! squ>e ( :i* is #d1 :i* multipli$ by #c is #ab1 = a divisor4 ,n[ #ab 9 #gf w be #e times2 cube #be1 & y w h #aefbe1 :i*1 subtract f ! resolv5d1 & no?+ w rema92 :i* %ews t ! resolv5d is a cube numb]1 & #be its root4 ,,pupil4 ,y say #ab 9 #gf is #e times2 ,i %\ld h said #f times4 ,,tutor4 ,9 common division x w\ld be s2 b z ! cube ( #bf w\ld be great] ?an ! resolv5d f :i* y are to subtract x1 x c g b #e times4 ,,pupil4 ,n[1 ,sir1 ,i ?9k ,i h a suffici5t k ( ! rule to solve a problem4 ,,tutor4 ,! e>?'s p]iod is #cfe days1 & its mean di/ance f ! sun #ie millions ( miles2 ! p]iod ( ,m]cury is #hh days--:at is 8 mean di/ance8 ,,pupil4 ,z ! di/ance ( ! e>? is giv51 ,i mu/ make ! squ>e ( #cfe ! fir/ t]m1 ! cube ( #ie ! second1 & ! squ>e ( #hh ! ?ird t]m ( ! proportion4 ,,tutor4 ,c]ta9ly4--,take y\r slate1 or a piece ( pap]1 prep>e y\r numb]s1 & make y\r proportion4 ,,pupil4 ,i f9d ! squ>e ( #cfe #accbbe2 ( #hh #ggdd2 & ! cube ( #ie #hegcge4 ,!n #accbbe 3 #hegcge 33 #ggdd to a f\r? t]m4 ,i n[ multiply ! second & ?ird t]ms toge!r1 & divide ! product by ! fir/1 ! quoti5t #dihcf is ! cube ( ! mean di/ance ( ,m]cury f ! sun 9 millions ( miles1 & ! f\r? t]m s\ght4 ,,tutor4 ,s f> y are "r4 ,n[ extract ! root4 4 4 #dihcf 7#cf #c #cf #bg #c #cf #bg7 #bbh ,sq4 ( #c #i #baf #dffef ,mul4 by #c #ajh #cahj ,divisor #bg #abif #cf #gggf #chhh ,cube ( #cf #dffef ,,pupil4 ,! root ,i f9d to be #cf1 :i* is ! mean di/ance ( ,m]cury f ! sun1 9 millions ( miles4 ,,tutor4 ,y n[ see1 t al?\gh #bg 9 #bbh w g #h times1 yet "h x w g b #f times2 &1 z !re is a rema9d]1 x %ews y t ! resolv5d is n a cube numb]4 ,,pupil4 ,i see x cle>ly4 ,,tutor4 ,y n[ seem p]fect 9 ! rule2 ,i %all !re=e n tr\ble y ) any m examples1 b %all give y ! table ,i promis$ y4 ,,table4 ,names ,diamet]s1 ,magnitude1 ,p]iods1 ,mean ,di/ance ( ! 9 ,engli% comp>$ 9 f ! ,sun1 ,,planets4 ,miles4 ) ! ,e>?4,ye>s & ,days4 9 ,mil4 ( ,miles4 ,sun ,a#hicebb #adceieb ---- ---- ,m]cury #cbfa #a_/ad #j ---- #hh #cf ,v5us #gfii #e_/di #j ---- #bbd #fh ,e>? #gibj #a #a or #cfe #ie ,moon #bafa #a_/di ---- ---- ,m>s #ecab #a_/c #a & #cbb #ade ,jupit] #ijbee #adgi #aa ---- #cad #did ,saturn #hjjab #ajca #bi ---- #afg #ijf ,georgian #cdbag #hb #hc ---- #aba #ahab ,footnote ,a3 ,! ,diamet]s 7 tak5 f ,adams's ,lectures1 ,vol4 ,,iv4 p4 #ci4 ,,pupil4 ,i %all take ! fir/ opportunity ( calculat+ ! re/1 9 :i* ,i am c]ta9 ,i %all h great satisfaction4 99 99 99 99 99 ,,tutor4 ,i h n[ conduct$ y ?r\gh ! elem5t>y p>ts ( a/ronomy1 h giv5 y a g5]al view ( ! sy/em ( ! _w1 & prep>$ y to pursue ! /udy ) pr(it & pleasure4--,9 y\r future rese>*es1 ! m accurate y are1 ! m y w discov] ( regul>ity1 symmetry1 & ord] 9 ! con/itution ( ! frame ( nature4 8,hail1 ,sov'reign ,goodness6 all-productive ,m9d6 8,on all ?y works ?yself inscrib'd we f9d2 8,h[ v>i\s all1 h[ v>i\sly end['d1 8,h[ great _! numb]1 & ea* "p h[ good6 8,h[ p]fect !n mu/ ! ,great ,p>5t %9e1 8,:o1 ) "o act ( en]gy div9e1 8,laid ! va/ plan1 & f9i%'d ! design60 ,,! ,,end4 ---------------------------------------- -------------------------------- ,directions to ! ,bookb9d]4 ,plate ,i4 to face ! ,title4 -------- ,,ii4 ---- page #dj4 -------- ,,iii4 ---- ---- #hh4 -------- ,,iv4 ---- ---- #aca4 ---------------------------------------- -------------------------------- ,transcrib]'s note3 ,all in/ances ( #8disk' *ang$ to #8disc' ,errata1 in/ance ( #8disk' on page #gi add$1 8---- #gi4 -- #e4 0 ,page #aa1 #8,ye>s' *ang$ to #8ye>s1' 8#acj ye>s aft] ,*ri/0 ,page #bj1 #8h e' *ang$ to #8!1' 8w\ld h z mu* ! appe>ance0 ,page #bd1 #8cannon ball' *ang$ to #8cannon-ball1' 8! "t a cannon-ball w\ld0 ,page #fc1 comma *ang$ to full /op aft] #8,,tutor1' 8,,tutor4 ,:y80 ,page #fe1 #8a' *ang$ to #8a1' 8c>ry a planet f ,a to a0 ,page #gd1 #8itaxis' *ang$ to #8its axis1' 8if ! e>? revolve on its axis e0 ,page #gh1 #8,m]cury' /ruck aft] #8,sun1' 8,sun1 ,v5us1 ,m>s1 & ,jupit] are kn[n to revolve on _! axes0 ,page #ic1 #8canc]' *ang$ to #8,canc]1' 8is ! tropic ( canc]2 t0 ,page #ic1 #8capricorn' *ang$ to #8,capricorn1' 8! tropic ( capricorn0 ,page #aae1 #8o!s' *ang$ to #8o!r1' 8& o!r />s rise to 80 ,page #aae1 #8bnt' *ang$ to #8b1' 8out f2 b1 by go+ r\nd0 ,page #aaf1 #8x's' *ang$ to #8its1' 8,h[ c its surface be r\nd0 ,page #abh1 full /op ins]t$ aft] #8eclipses1' 8expla9 ! cause ( eclipses40