o f tame, and at the fame points o f the horiaon, and are
therefore called jfW 'f t a r s ; but he finds., that a few
others, called plands, together with the fan and moon,
are constantly changing their fituatiOn's, - each .conti-
nually riling and fetting at different, points ^of the-
horizon, and at different intervals elf time. Now the
determination o f the-fimes of-the- rifing and fetting o f
the heavenly bodies ; the finding o f their polition at any
given timer or the rime from their polition ;~ the caufes
o f the different lengths o f days and nights ; the changes
o f feafons ; and' the like, conllitute what is called the
doSrine o f thefphere.'
40. L e t pep'q reprefent the earth, h the placé o f the
fpeöator, H Z R N thé fphere o f the fixed lia r s ; and although
the fixed liars do not lie-in the concave furface
[planes, f t ;-’refpe£t to the fpljere-of the fixed1 liars, may1 -
[btrcùhfidered as coinciding. Nóvd>as the earth revolve»
daily about itsmxis, the heavenly bodies mull fueceffive-
ly rife andjftt in that time, and appear to deferibe circles
o f a fphere', o f ’which the center o f the earth is the een-1
ter, yet on account o f the immenfe dillance, even o fthe I
neared o f them, their relative fituations are not . at all
affefted by the motion o f the earth, and therefore the I
place o f a body in our fyftem may be referred to them, I
in the fame, manner as i f they were, placed as is here
ïtippofed. Slow the circle pbep'q i f the meridian o f the
fpedator at b, and let this circle be extended to the heavens
and there mark, out the circle P Z E P '^ f and it
will be the celeftiSl meridian of. the place ; whenever
therefore a; body in the heavens comes to this circle, it
is in the meridian o f the fpe&ator b ; and this circle divides
the heavens into two h’emifplieres, the eaflcrn and I
the wejlern. L e t abo be a plane touching the earth at I
the place l o f the fpeftatbr, then this plane will be his
fenfible horizon, becaufe it divides the viable- part aZo
o f the heavens, from the invifible part aN ó ; and if a
plane H R be drawn .through the center o f the earth,
parallel'to abo, it is called the rational haijregn; and as
the arc R» fubtends no fenfible 'angle at the earth, theft
* -This is not accurately true, the earth’s axis varying a little from
nutation of the earth’s axis, and was difeovered by Da, Br a d l e y .
which are' perpendicular to the earth’s axis, andi <
Iconfequehtly 'p aialk‘1 to '4 ‘ach*other.!, ’’L e t p f be the
|aXisrof*the-earth, p the north pdïe,' ~p' thçLoutH« -püle
and Iet tvqs He the equator; then ïf t fte plané o f t h e
[equator be extended up- to * -the' heavens,' it will there’
mark aOt a circle EF<!$S called Ùi&Jclijltàl equator j.
land i f pp' bfe prodücëd 'to the heavens to'; 'f ’ , 'ri>",'thefe
[points are called the pôlesfôf the èeleftialtequator ; and
[the liar neareft tojthefe is ’ eaDed'the pole ftar. Now,
I although the earth in its orbit, continually cil anges its
[place, yet as the axis’ always côhrinncK parallel to itfelf*,
the points P , P ', w ill not, fromtt-he’immenfe diftance o f
theriixed liars,jbefenfibly altered. L â a b e t h e antipoa
I des to l , then -if'the diameter in be proddded-td Z and N ,
IZ is the zeni&SJLthe fpefitafor, and N the nadir. T ip i s
we may conceive th e r e a t circles, and kny places upon
[the earth’? ferfeee, tô b( fftin ’fernd' to the heaveiisi
I Now the, latitude o f'th e place S’-uÿqh'the earth’ s fur-
fece is, mekfered by the deÿéesxôffft’H'ëare ÏI;,• but th e
[arc" Z E coutitpsÿhe fame i&ynBer'oM'egrëè6 'as the 'arC:
be, tbereforS-the arc 2 $ !ri ^hç ’he^'èïlfni.éâïiifeB |h£-
pS itu d e o f b the fpéâator ; andt'he'dejjrCf a v>f-the arc bp,
I which meafilres the diftande o f th’e fpedlator ffo'fnthepole,
I coataine'itBe fame number<sf degrees as, the,,1 arc Z P ,
I Hence, as the equator, zenith, p o k ',rind hoii/on in the-
-heavens, may be conudeVed* as correfpondiljjgl^fcoy; th e
equator, place o f !,tht IpccUtor, pole-.,' and b on/on.o f
th e earth, and the angular ftiftarrcea of- raeriqr ntferare
refpeélively equal 'tb ' thiffs f« tire -’latter; We may, fo r
our p refont purpefe, leave, out the confideraticn o f th e
earth, and only fcoiffider tKe-eqUatorflénith'; “pofes, and
I horizon o f the heavens.
4 1 . - L e t iM m JPZ'EHP'Ngfl .je,pyefeht.the-ee«-
leftial meridian to thé place o f a fpectator upon the
its paral lelifa from the attraflion of. the moon. This is called the
earth
- are in the prime vertical, or in the eaft ; hence, a body
on the fame, fide o f the equator with the fpe&ator, comes
to the- eaft after it is rifen ; a body on the contrary fide,
before it rifes ; and a body in the equator, when it rifes.
• As* this-figure may reprefent the ■ weftern hemifphere,
the fame circles ea, E L f , tm, will reprefent the- motion
o f the -heavenly bodies as they defcend.from the meridian'
earth whole zenith is Z , the fpeéfcator being fnppofed
in north latitudi ; and let the figure reprefent either the
eaftenr or. weftern hemifphere o f the heavens; we mull :
’ 1 %ure to reprefent h a lf a globe,
and allthe-lines upon it to reprefent circles-; and asi i f we
■ conceiye- the eye to. be1 vertical to the middle point O o f
the figure, all the circles which .pafs through that -point-•
will appear right lines, therefore.-the right lines W M ,
PO P ', E Q Q , HOR, mull be -’ cbnfidered as femicircles,
.HOR reprefenting .the horizon, £ 0 .^the;;equatqr, ZO N
•a vertical circle palling through, the zenith and, nadir,
perpendicular to the horizon, and this is called th.oprhpe
vertical, cutting the horizen in 0 the eaft-’ qibjsëfl: point
■ of the horizon, - aecording, as;the figure rèpre&ntsthe
-eaftern orweftertf hèmifphere. , th e fp effa ife'lè in g
tfuppsfed tb ,JBe at Z f .and ‘looking along thie »meridian
Z P R ‘tfhVards:, the north i priori’ , R muft; öè rihetnorth
point o f the'horizon, and confeqi. j i iK ' t l i t oi^nïiltc
Ipomt friwilljbettheifouth po in t; 1 andiWiéfee^poïnt .©;bt-
fefts the points H, l i , it miuft reprefent the eaft orjMst);
fyóilït Vll lIjcIc, ( ijJ c.-. drh^^vcirmê4',,tfee|r:jfitóes
p a lll‘g ^the h ^uUs ol t]iuJtpllcic..--rltr-'-ri lilt
findh cii-U; fi 4^1 m>', a?, R p 1 iTklttuttJie Lcju-l01
1 micircle / ’0 V,4{hii^et /Ule\ f i j ijhitlc'-f
in, 0 , and 1 Ju iHo^e -it J jil^ t s ;riï£.ftW't(|if-hJe3,<<je, mt, inf
SBd.'J^rï, N ijwtlii cüiprn., 01 (lunï
tajpews to'fitferibe^.feva. yt^.,snts5te -wi^^il^e -an
>an gle 'i'f^ f? ,» ï’' r7rie "Vthe'ff /ft* tin tn t j ( i;7 xHU,the
circle EO!p__ in that at gle, and ( OL •« U.reprefent t’h^
^ S g ^ S & W ’afe.aE’Qiht^eavi.iily hi i3ie'% feMeiY'ajq-pV' f *
rdlüri^-^diW^d^êrib'iejsit-her -the equatoi
acirobsipafrifel -to the equatt}r,»asaatd;pgt as til? f.wly i0’ :
an;or. -out zrf ^he’.-sqirator, i f we t uK-fü Syi-fie 1 1 e y/j
4!epi*efeat.the eaftern henfp'fpliere, § J i,
,-fent-their apparent paths as they piovejffoip' thejmerkrivfi
■ .undertfe^ib^ig^riEtthey come totbe-meridian-above
sthe horizon, andfhe,p,oints,%,(5%jr»'<aye-tl&lpqjipts}j$f
ihonzon where they fife. Npw ae, IpF. mt, arqjbifeéfed
-in ~c, 0r r,s therefore /tb,,the,part a-bope;tft,e-hp4z»n -js
"greater tliKU-n5 the pai# jario-w; EQ the pa rt -abo y,e ,is
equal to O ^ th c part bglo® ;!#n<j!frithe;p»« above is-lefs
than sm the part helo’-v ; and as Z rsprefe &tsvt]ië vplape
* f the fp.eftator, it follows, that thofe heavenly bodies -
which are on ;the fame fide o f tile equator ;u; the fpeéfa-
itor, H S he longer, above the horizon than below.,; thofe
bodies which are in the equator, are as long-.ah.oyiè . the
-hoi-ixon cas; below ; and thofe bodies, which,are on the :
■ *ppoftU£Ae*>i tke equator to -that o f the fpefta-tor, wife
be a fsorter time .above the horizonethan below. A lfo ,
the bodies deferibihg ae, tpEj mt, rife at b, 0, s ; that
is, a body whit-hris -on- the fame fidé. bf the equator with
the fpefta-tor, rifes at b, from the eaft point 0 towards
the north point i ï ' o f the horizon,;“a~body which is in
the equator; rifes at 0 in; th.e eaft; and Jthofe.bodies
which areo» theqppfftte fide;of the .equator,ip.thefpec-
riuor, rife at , from the tail point 0 towards the fouth ,
point H. When the. bodies come to 0 , tl or n, they
above the horizon to the meridian below. Hence,
a body is at -its gneateft altitude when it is upon the
meridian ; and at equal altitudes at equal diftances on
each fide o f the meridian, i f the body have hot changed
its declination! Now as all the fixed fla r t conftantly
retain their fame . fituations, each muft always rife and
fet at the fame point o f the horizon, and continue for
the fame length o f time above the hhrizon ; -in thefe
bodies, therefore, there will be no variety o f appearance.
But the fun, moon, and planets arc continually changing
■ the-ir fituatiori, and are fometimes on one fide.of the
equator and. fometimes dnithe other. We will therefore
next deferibe the phenomena attending thefe bodies. .
J 43, The femicircle COL reprefents one 'half o f the
■ ecliptic, or one half o f the fun’ s apparent yearly motion*.;
and let C be the firft point o f capricorn, and L the fitft
point o f cancer.: I f we therefore fuppofe thofun to be
at any point p, on the contrary fide o f the equator to
that iofitiie .fpefltktoiiafei M a t (day; b y the. diurnal nota-
tion o f the earth, be, appears to deferibe the circle input
' r e t ; when he is at m, it is midnight; when fee comes to s,
■ he rifes ; 'and -when he.comes to f, it is noon ; and from
noon to midnight he will deferibe the path Isrttpm in the
, weftern hemilpbere. iNo.w as ms is. greater than st, the fun
-will.be'longer- below-the horizon titan above, and there-
.fore the nights.will.be longer than the days ; and the
ifunurifes at s -from the' eaft towards the fouth, and fets
•;as. fee febm the .weft towards. theftauth. W b.en-the fun
is in the equator at 0, his diurnal motion is then-
and as IpO^OE, he is as long below as above the horizon,
and the days and nights are equal'; -and he rifes in
the eaft at 0 , and fets in the weft. When the fun is at
an} punt 4, ton the fin ! fide-of the vquator with the
fpeftator, on that day lie defcribea, b y his diurnal motion,
the circle abcdqe, arid as akin lefs tliari- be, he &
qqngdv"imovc t\|> uorizqn |th?n bt-loir it; and '.rise^days
are longer th S ^® e 'm » t s ;‘A9<Sn.e rifes a f l from the
eaft.^toiM^tfs^fiie nOTth,. from the weft towards'the
north. ' It- is manifeft therefore, that the
length o f the days incrcafes from the time the fun leaves
C, the firft point o f capricorn till he comes to Pi, the
firft point of cancer ; in I then they gradually decreafe
again from the time the fun leaves L till-he comes to C .
I?„ar, eqpidiftatlt Jrotpr, aS^., then will bezants,
and wheijijreeTun is at equal diftances
from' .the equator, and“on'opposite fides, the length o f
idfethe- day at oneppio-ri’ equal to yfevlength o f A e
night at the ptbef, ap^^ie feAg> 9? the night .atjfhe
former is equal to the length pt the day .jt'thjS ^Sitter
time, f i t every-place therefore, .the few, in A e -coitrfe
o f a year, is ha lf a year ■ above the—horizon and lialf a
V L c 2 year