yearjaefow?** Henoe, the different lengths bf|dly§ .and-’
nights,- a^fflthe variety o f feafons, arife,from the fun
- b e i e s on one fide o f the eqnatoi,
times on the othcV^p1j|f-from ihaGpiptid* C L 'b ein g inclined
to the equator, .o^frgnrthe a x i S l lie^earth which
coincidi'S with P P ', being inclined to the ecliptic C L ,
the path- o f the earth. y{ 1
v * -44*: A s th@jl|Mdllua ina'tes'^dhe^half of tihe earth, or
i^QfialHrqupd abdut S i t pl&pe.,* to ^hichl^^^s ■ s.eri|^|^
wh e^^ois‘>«i;the -will far
Ia8 e^h4p^io^ ■ when he is' .on ^Ithe .eqiia-
’tor," the noEth pole will.be within; the illuminated'papfe,
«^and the f©uth&pideswilhfbe; in the dark part j- and when
the fun is on the fouth fide_o£-the-equator,; the- fouth
poItTwill he 'withi®®^x illuminated part,,and thenorth
pole in. the dark part, ^p^^^ge^fun is got-to 23°J28!,
(his? greateft diftair^fibmMe\equatp^)pie^e|^d^L^
gates.the earth to 230. ra.h' ©hithe .other fide o f fehe:g@|^%
and if'two circles be deferibed aboutdfrelppMsyaththat
difta'nce$‘ that about the ‘north pole.is calk’d th e arctic
circle, and that abqutithefauth pole is- callecktlfe antarctic
circle-.C Thefe are, afibifeaMed polar*.circles. If. two
circles be. deferibed upornthe .eat^h^pai^^bto.the equator,
at the diftanceW-230.48fefrom it, they are called^
tropical circles* or the tropics.
* 45. ;Xet H ttv,.R<uit »yyfhe ifmall Hrcles parallel to
Now it k manifeft,' that a bqdyiw.hich deferihes
the circle P®-, oranycirpkiffy nearer to'P^ue^sfe^j and
fuch circles are called, circles of perpetual apparition j and
.the ftars which?defcribe them 'are called Circumpolar Aars.
T h e body which deferabes~ the circle^w^rj juftf becomes
:vihble at.. P', and then it initantly«defeends. belbw .the
horizon ; but the bodies; which arP^raarer-to P'nare
gever Suckare the phenomena of the diurnal
»Uiotions :of^ie heavenly- bodies,- when, the fpe&ator is
■ fituated any iwhere between the equator and the poles ;
-and; this is called an- oblique fpbere, becaufe all the bodies
c^ife and fet obliquely, ta. the horizon;.. 3
be ait fhe-'éqpMör^ |
ciies with janfwers„ the-
' earth,-and
confequen.tly f'O P coincides with HOR^ Hence, as the/
'Cq ilator/Ëè^ i § ^rp^dicularstp|t¥|h©rKon, ;fcKe q n p ^ |
ace, mrt% parallel to E O ^ J are ajfo -perpendicular to the I
horizon,'arid thereforejhe horizon bife&s‘7Ehem.> % T o a
fpe&ator therefore; ,at the equator, all j h e a v e n l y
'•bodies in their diuyi^lnfotiphMe?as!,J^ng|above the hoii-
zon ‘aïi'efow?; - and they rifeaïid'fet at right anglesrto it,*,
oh^hich' account,' this.is'exiled a right fphere” Hencè,.
at the equator the days and nights" are each* ..always 12
i^u^Sikng^J .There; w ill howev.èïf b^ variety'..©f|
feafons; as the fun will reeede to £ and. C, 23°. 28' on
each hderö£vli|^^,e6ïato]?i When |§|||furi
equator, he, will be veilical to the. fp"e£ta*tor at no©n%;
foi'_one ha lf o f thé year he w ill come to in? meridian to
the north</df■ :the zenith, ahd'-the .other3half o f* th&-
year, to the fouth o f the-zenith.. /
■ '47. I f the £pe&afór‘be a|^£h|^hY/, ,thèh^ P:' co'incidë»\
with Z , -mé ^ P # ^ o p f i f f i p ^ f h ; ‘^Zi\^>vdpnfequently
PO^ conc ide s with .pfOP. the circles tm,
parallel-to 'the?ëqhatpp; .‘are alfo ‘parallel"'t’o.t;he horizon,;
- trhereforeJds^^b.^ylipJHdih rhM ïup|^h|d&fêrib'es a circle
phralMhto" tte hofizofeji ^ali'the^^fecedi ftarsf.v^RiHfiare ,at
tany time-.^aböve' ithe “horizon, mult continue-' above'the
■ horiédnjfan^tb^fë which, are below,
low ;• ■'and.the'^e(^ator-alwa^rs fees the* fame face of the
heavens, Jjecaufe none ©£ the'bddies^ by. theif'-'diurnal*
-motion, can either- rife or fet. This is called a parallel
fphere, Beeaufe the diurnal»motion_of all' thefheavenly
bodies- ilf'paraüel'ïto$he horizon. But as the fun de-
4ft^$es ' ;^ ^ ^ ^ ^ ^ 4and the part
^ 0 ?T8'hever brought above the horizon, by the diurnal,
'ihotiou,. and the- part OP is never carried'below, the fun
imift bh h a lf a year below the horizon, and' half a year
above, fo that there is half a year day, and-half a year
night.
• - 481. A ll thofe things will -be very evident by,means-,
of a celeilial • globe. - Place the axis obhquely^.tö the
* This irnot accurately true, becaufe the fun’ s moti'on in the ecliptic is,not uniform^ on which account he is not exa£Uy as long on one
fide of theequator as on the other; th'e fummerhalf year,;or the time from the fun’s leaving thefirftpoirit of aries tiU he comes to the fivft
■ point of libra,;is about *8 days longer than the winter half year.
horizon,
horizon, and you will fee that all the circles parallel to
,the ?uag ^ 4l and the
mp*i e you elevate Lire pole, 01 the nearer yo'u biing^^h^''
fpe.<SaJ§-ftp/th.e p ^ p g h ^ g r e . a t - e ^ t h e difference
' o f thpfe’par.ts - 'that is/'as'^he fpedtator approaches the
pole, th e 'k ^ i^ ^ ihereafed^ aiid»||]|'at,'.
o f Gh^nighls decreafed,'' whenNitn^fun is on the
-/hmf fide ot the equator as the fpe^La'tK^and'theJength
> oi| the- ;4^ys,;Vf^:fe/d^'cif afed, anji^thatfoQ
I f yopj;bring
parallels to.tjijp equatpi/au& cut into^two equal part^^M
that- there is always equal day .aqA,‘night to fp e d la to r
jat/'the,* equator. I f ypiujh;i'iiiigt the pple- fcO the zenith,'or-
• i f the jfpe<p^hi|bi|£4rf
.. ;aboufe^
h o iizon'ai^ th e other half below, fo that the fun will
be half aiyear above th^bprizon^, and half,a year.below/
xp t i h .u s - K i p p | | | l i { f h a f t r a v e l from;.‘the4|qua1:^r-
fto,. thp fengthCof the
, day■ wilLinxf-eafe from 12 hours fp ^ iia lf^ y fir^
the tother half o f the
. increafe from ViXhopra to half a. year.t\ /
- - 49.- The greater degree o f heat in fum-mer than ip
winter, arjfes from .three caufes.;
cr time ah'oye the horizon in fummer than ip wintefi\ <-.2.
T h e fun fifing higher above the horizon in fummer thaa
in winter, -'more rays will fa ll. upo^^tlfg.ea^th in the
$hah;i a j h p latter feafon.'/ 3. The higher the
fun i^ abpve the horizon, the greater is the force o f the
rays. . Moreover, the parts which are heated, retain their|
heat for .fome tipoe, wM h^w h h the^additional heat;ap4
quiffidy ak.e if continue to increafe after the middle| o f
the fummer; -and this is the'reafon why July is generally
hotter'than, June-. ^And’^ ^ th e fank pizlfpff, :w|e frequently
find-it' hotter a f 2^ o^dock in the afternoon than
i t is? at noon. Tikewife,--bodies retain their cold for
fome time, and thus it happens, that January is'generally
colder - than D ecember..
50. -The orbits o f all-the.planets, and o f thesm'oob,
are inclined to the equator,"aiid therefore their motions
amongft the fixed ftars muft be in cifcl'es'inclined to the
equator : hence, fimilar phaeijomena to thofe or tHe fun ‘
will refpeftive revokitions.
A l t the..different'•appearances muft therefore!f.aM§
place in the moon; in the epurfe o f a, monthr f t is' evident
alfo] that thefe Variations ' limit be greater or-lefs,,
as the orbits ar;e morff^pr lefs inclined/to the equator^
-henpey. they muff be greater" in the moon than in the
;,:| u h | j i 3 f h | h ^ i n g mbre incdmed>to the equa-
■ tor than the § 1 « . ' j
j ó f the bch^ens above
the horizon, is equal to the<‘latitude o f the/ place.. For
,£h£v are|iZ^. (^g/2d. page x^Js the meafure o f the lati-
o f the -place Hut PJEr=zZR, each being 90°; take*
' /is /co'njp^m^tq i'ooth,' and* MZen P R -
Hence,, P Z is th'é®^p.^^^®f latitude. ]
52. If: there were a ftar exaótly in'/h^ppintP , then
by taking ils/altitude P i? a^ove the horizon' by a quadrant,;
andfQ(^tó:ipg it* for refraólion, you would get
the Xatfthte place ; but as there i%»not .a ftar in
that; p l a ( S M e | l « | ^ m a y / ^ ,foun>d'''by obferving the-
great eft and leaft altitude ó f a circumpolar ftar, apiily-
ing tfliè^orreólipn for refraótion, and half the fum wilt
be the altitude of. the pole. For if y x be the circle de- .
feribed by a qhcnmpO'ïar ftar,- then as Px n.Py, .we have
P & + f y , , and. add
. ^ t h e f ^ .and we have xR -f ;
2 P R , therefore ^ p '& ^ f P ) ,— P R the latitude/ tJ I>'
53. The angle which tM’^qji%pr'^makes with the
horizon^is equal-to the complement^ o f the, latitude oF
;S^g^cp|/'FOr H F is - the meafure o f the'angle H Ö E .;;
and as is the complement o f and"
is the'latitude. / j
54. Heh.ce, % ef latitude-of a place may be found*thus*.
L e t (%..p%e"xiv) be the ecliptic, and then when the
fun comes to <? it is at its greate'ft north declination, at which,
time the^da4] ^ ;and' at t its fouth declinatio'n-
|| thé greateft, at which time a^ ^ io r te ft’;-,
/alfo;- >^is the mciidian altitude o f the fun/on^eilong*-
' eft'day, and t:H, is 'uM?^||d|a^yd^^ Jhe ;'TOfteft.
day. /Npw,5a g ® czlEf, we have eBL— ËH'-^-
ïPL—.EH— Ê f^ E H - - E e ; add thefe /Equations toge-
E È , l tjxe^efpre, | C {9 ‘k
tH ) — E H the complement o f the latitude. 1? T he pdih-
plement o f latitude is, therefore equal to half'th^Tum so%]
the true meridian 'p| the fun On the longefff
and fhórt^eft days. *//’
1 ^5. H a lf the d ifferen t ©F the meridian' ,altitudesvó f
the fun on the lbngeft and'ihprt'eft days, is equal to* thé
inclination o f the equator'to the ’ecliptic. ' For the dif-
tween ejff and is' e^ and the half pf-^ is He?,
which 1 EOe, th e ' inclihatiori o f the.
'equator to*:theS,éeli;§biel //.?'
# The complement of an arc, or angle,, is whet it wants of 99° 5 and thzfupplemint is what an arc, or-angle, .wants-of 186^# Alfo, co ai*
titsde means the complement of. the altitude,.and' the fame for'other ^nantities..