XV1 • ■ ' " I N T R O’ D
L e t ae be the -parallel defcribed by the fun -at that-
tiniej then Ra muil b | § 9$,..Br at that dillahce below
the horizrin, twilight begins ; .hence',;] 8 °-f dec.
R ^ = E H = cpfiffc ó f latitude, by art. 53. ;- therefore,
by tranfppfifion, In 11Js dt’c.izieomp. o f u i t —18?. • | B a t
i f the fun be on the o ther-lide o f the .equator at m,
then R m ± iS ° , and )S°— hecilm. ^ m = R ^ j -E H —
comp, o f lat. therefore, finds d ec .z z lS — èonip. o f
latitude. L o o k therefore into thè Nautical Almanac, and
fee on what day the fun has this declination, and yöu .
hare the time required.
- E x . L e t the latitude ‘be 520. 12' N. then its com- '
plenient is 37?. 48-'; hence, the declination is 37°. 48'
48' N . which anfwei. ts aboiltt May 19;.
and July 24,yat which times there ris-tivilight juft -all
night. Therefore from Ma y 19 . tb July 24 there will
be twilight all night. . . , ' s ï 'ft 'Af C»yi;£‘,'Vrl f t
66. T h e greateft - value; o f Jga is 230. aS ';rth ëe fore :
when aR is i'8°,!the greateff yalphrsF:^-;tf^iQ-
therefore Q f , be greater than 41 °. -2 S’, tS® Xu nniffi
always be greater than 1S0, and therefore there will be
ho twilight-when the fun is at a ; hence, wljéöjlr^ccrtn-
element o f latitude is greater than 41 °. 2&','ar-whenthë
latitude is lefs than 48?. jz 'jth s r e never canfe|^t8%ht
all.in ^ ht.tf J,
.ê ftronom ical. ‘f e rm s , I a rifing fr om d ifferent
: ^ Situa tion s o f th e Sp ecta tor y p om ih e E a r th .
' V ö 7. B y means o f th e two tropics 2nd two polar circles
alpon the earth, the whole furface j s divided iritqrtfiVC
part'd,'éaïlêd'k ó n e s that which is-inclu’ded between the
tropics, is called the torrid zone: the two parts lying
between the tropics and the polar circles, are-calle<l the
temperate zones : rthe two parts-within' the polar circles,
• are called the frigid zones. T he inhabitants, o f thefe
zónes arèdiftirigiïilhed b y the different 'direftionsmt their
lhadows arifing from the fun. T h e y ryhO live ‘betweeri
the tropics, or -in'rthb torrid zone,' have the fun vertical
to them a t nöon twicé in the y e a r ; thus, mi inhabitant
in io ° north' latitude has the -fnh vertical to him _ when
its declination is 1-0° north.'' An d, in general, this iviff
happen when the latitude ofthe inhabitant is equal to'the
declination t>£ the-ftn, and botlTóf the fame kind, that
is, both north, or both fouth. A t all other times, when
the fum cojh'édjó-" th e 1 meridian, the lhadow1 is either to
the north or the fouth o f the zenith. Thejinhabitants
o f this zotte-- are called Amphifcii, that, is, having both
kinds of meridian lhadows.
6 8 T h e y who^ffenu the temperate zones; t ~ T '
lhadows, at nobri '-always the fame wayj arid are théj-eforé
galled Helcrófcü, Anzt is, having only She; kind o f -meridian
ihadow. ' 1 ’ ! _ ‘ ffk " ‘ . J '
j -*i69I TheyriMlo live in thé frigid zones, have, when
the .days' are more than 24 hours long,, 'the fun moving
all round them, and. therefore-their lhadows are caff all
roHnd them, and hence they are called Perifdi.
jjo. The'inhabitants ó f thé earth have alfo been dif-
iinguifEied into three kinds, in refpe£t to their, relative.
tffC T' l.O N; •<
ifituations. \ T h e y who1 live at oppofite- pouiffc ofJtKe
fame parallel to the equator, are called, in. refpeftto each
Other, .Periaci. Thefe have the' fame feafons o f the
year ; but it is midnight td on.e when it is noon, or midday,.
to ihe-other. .
7 1 . T h e y whollive under, the fame meridian and in
oppofite parallels,fMi is,', in two parallels to the equal
tor, and equidiftant from it,; are called Anitcci. Thefe’
have day and night at. the fame, time, b,ut different feafons,
it being fummer. w ith one when it is winter with
■ the otlier. : -: ; A
-- 72» T h e y who live undewoppofite meridians, arid- op-
pofite parallels, are .called Antipodes. T h e fe have their
days and bights, and alfo their feafons, oppofite, that is,
it is day with one.when it is night with the other, and-
fummer with one when.it is winter with the other. (
1 “o f in d the- R ig h t J fc en fto n a nd -.Detlirmtioh. o f
• th e Heavenly -B’o'diesi
I l f lH v 'T i i ’?' ffluridali m7 b f , U’r.fti oromy is tq .dctu mine
rthe places, o f the, fixed .ftars, in order to find, b y a re-
ference to them as fixed‘pBje£tsV'the placesvo f the o ther
bodies at any given’- times, by.wl^eh -meansyotBEan Aa ce
out their patbt^in^hefbeav|ns|Ji T im jogtionS o f the
“ fixed ftars are: .found from obfervation, b y finding their
" r igtif afeenfions and-decliiiations, for it is manifeil, that
i f we know the right afCenfion Am, arid declination ms,
we. know the point s (fee figs'.page, viii).. Now the
deefination is found'thus. ;■ Find the latitude o f the place
b y the yifd. ob^ th-a^ iSfs lk’afid ,tMen>ws||no'iJiEfi the
1 omplementsof latitu le-(fee the; laff figure). B y 1 the
aftronomieal quadrant, deferibed in it 17; find the
true meridian altit'udi A /M tl le body ; theh‘ tht difference
between E H and. He 1 Ee, tht declination n/quiitd.
74. T o find t l i right afeenjum o f a. 'body. A s the
earth'...revolves., uniformly about its axis1, rthe apparent
daily motion o f all tlr e«hp%j?lp^od'ies^.an fi n g from
this mb'tibhbf the |nh.fljbe uniform ; Vand as this
; motion Jis •paralMbto., the: ;equatp_r, thc;dnterval ojfthe ■
times in whiehmny two liars pafs, o.v.eulhe meridian, is
in proportion to the correfponding arc of the equator
which paffes over-the^^idiahlih thefame interval. Now
let a clock -bc: adjrdtedbf o -gp 24 hours. in the time; the
earth makes a rotat-ion,about its axis; then it defcrib.es
about its axis an angle' o f 1.5°'every hour; and every
point of the equator, aj d air tile c i.rcles ■ h <:h are p 1 alls I
tq-it, defenbe jy^rfi'an hour; andali®Mi ftars appear to
revolve at the fame rate ; fo that if twblifars fb'p'ul'd differ
45. w-in.i'ight alcentidn, onc. o f tliem- .woukl pafs over
the meridian an hour-.after the'.other. And, in'general,'
i f you take the interval ofyfhe times in which any two
ftars pafs the,rj$rid$sn, and convert that intciTval of-tithe
into degrees, at the rate of 150 for an hour, you will’
have the dmerenee or tne rignt,a|cenfions o f tliofe two
'. ftars ; if therefore you know the1 right afeehtion o f one
, o f the ftars, you .y i l f know-the right afeenfion p'fhthe
other. Thus,- bydkn'oiying.' the right’ afeenfion 'of -one
liar, and comparing all the other heavenly bodies 'with'
I N T R ; : 0 D
'it, ypuw ilt g e t ’their righljafcenfionsr b'Fqb;.£he method ’
'W one 'ftar, ,
the reader t'd i'fn. V in c e’ s Complete' Sjlfte™. •of. AJlrandmy.
T h body meridian is
knownf b y its paffagé’1 'over the' middle.: perpendicular
wire o'f-the tranTit 'i'telefco.pc,'’as defcribed' in art. 1.8. •,
T h e right afeenfion'is reckoned -both'by time and b y ,
degrees ;! thus-,: we fay a ftar has 15°, 30°, 450. &c.
right1 afcenfioii, or its right acenfion is 1 hour 2 hours,
>'» ! * Kj !.
1 73. But a more ready’and practical method o f finding ;
itbi? right afccnfiotvp'f 'a body, is- thiis : ' f,ct a clock be
'adjnfted to go 24 'hours in the fifflfe in- which the earth
revolves about its S s K l Iwhich time.all the fixed ftars
appeari to ‘ have! made one revolution; and a élq dipt has
bdlaffed.Wfai'd tb'be^djtaftêd'tö^ffirüaf'rt'iniê.t'd^id^^tv
'plóiqt we bégm tortedioxt tble'right-afGenlion y
fffry'i'ftk'f-efmësi.cittéhe'ififeridfan^ 'théPdlöck'ipkildl-ftiow
the apparent « g ilt afcChtmb'.öf .the êitftaprovideivft was
róbjeft to; n.ó éribi; b'ecanfe it would then-Ihow,-a£,any
time, how'ffarifhè'firft point rif ai leswas from the meri-
dianV reckoning 15P■ for- every hour. Bu t -as .every d o c k ,
■ ^Iffufcjfelife'efrfvwlJnfeftibteablf at- aliy time ttstffcjkas'’
te¥A'R1T<^i&, tlffi,':weJmuftj Wheri a S a r , 'wh'ofóbppatêht
fight', 'afeérifiori 'is 'knowrif paffes the meridian,' compete
ïtSrtigKtSafcfeiffiórii-iv itb the light afccnlïón;lhpwn teethe
hrid^ïhevdiffèrénceaw ill (hbw»lth’e rterro'rf bfi'rihe J
clock. For iriftaiice; let the apparentrtight afeenfion b f “
'aldciïaran hé 4b. f f f yo"v when i t paffes Over the merithen
dibbl&(lki^at,thatii;i^#t6»l^' feft
b y thus coritinually Gonipafing -ithè' clock} w ith ' ftars
whofè right afeenfions are knownj-yoii 'wilhalways have •
thé error o f the dock-; and you will alfo:fee at what
■ VateJif'grim^W^Mii; called the irate i f its. going, , The
e rforio f'tilé ”M^^;~|fn‘d.thc'rafe ofrité gqingvbemg thus .
afeertained, i f the tirn'e o f the:tranfit?pf any .body hc | j
Terved, and the error o f'ifffè d o ck - be-iapplied,,,yon will-
havé the right afffènfion o f the .büfl.y. ^ J '
r .• s I 1 ~ 1 t v y ‘ , 3 .
•afeenfion 2fw, o f :any heavenlykhody t / an ifrom thefe .
; find^thei latitude ns ,
'and I.Vu' Uingirudc An- (fee'fig'..5,page : S')'; :andut is rna- ,
nifeft, that if.we' know thefe two qiiaiititica,i,ive-. .Ilia 11 j
■ alfo-know the-place r Pf- the'bodyr;;:and'icisfreqinently '
move ufefui to make ufe o f the latitude an d longitude, ,
tlian :it is- the' declination and sight doenfioir, fo r finding' J
the place o f a body §S fit list: utceffary ■ .;thëiiefore,i.Vfuch ■
cafes, to. Compute tlm latitude-' and longitude from the
■ right 'afeenfjon arid'dedinatipm; fomthe.methoiliof.domg j
U C X I O N . • . . aviy
which-, we refer the reader to the above-mentioned
work. .» 1
77. Being thus .able , to find the fituation. o f a body in
the heavens, we can every day determine the place o f
all the heavenly bodies . which have any' motions, and
thus jve, find out the paths which they deferibe, anib
howfaft they move. ; 'd:
But,He Equation of Time, ;
. 78. The b e lt. meafure o f time which we Have,.is a
clock fegrilatedl b y the vibration o f a pendulum. But
with whatever accuracy i clock may be made, i f muft
be' fiib je& tb gorirregnlarly, partly from th e . imperfection,
o f the workmanftiip, and partly from the expanfion
and contfaftion o f the mriterials by heat. and cold, by
which’ the length o f the pendulum, and. confequently
file, time o f a vibration, will;yary> A s no 'clock therefore
can be depended upon for keeping time accurately, it fo'
!.neceffaiy .tliat; we Ihould be ablc'at any time tp afeertaib
•kow much it is tob fail or too flow, and at what rate it
gains'orjlofesf' '■ F|bf 'this ’prirpofeljit. muff he compared
with fome motion which is ■ uniform, or o f which, if it
be' iiot uniform,*yqu. Cati findi the 'variation. The mo-
'yonsilqf'Hhe heavenly bodies' htave,.thevefore'beerr|cohfi-
dered.'as rnqft proper!for this ' purpofe. Now as the
- earth'ercyqlyes uniformly about; 'its aids, the ' apparent
diurnaf mo'tibh of all the heavenly bodies' about the axis
muft be uniform. I f a clbcK tlierefore' be.’adjiufted £0 go
'24-no.urs from the jpaffage o f any fixed ftar ovet'^theliney
; ridiari till it 'returns fo it' againy its rate df'going may be
: .del erminedj b y comparing, it with the' tranfit of'-any
‘’fix'fid1ffif*iaSid bhfervirig. whether the 'interyal continues
i‘tplbe 24 .hour’s ; i f ni^t', the difference Ihows how much
-it gains or’lofes in. that-time: ' A clock thus’ adjufted is
ffaid; to beiadjijfteTtb1 Jf&ea/.fime ; and all; Ihe- fidereal
’"days art eqpju.' But .ill pfilie. Jmat days are not equal,
that is, the unervifls Spin; the fun’ s leaving the meridian
ffll'it rCtiirns to it,'arc:uof ’all.cqiiaI, fo that i f a clock he
'adjjtfteJ to g ° 24 hjqurs'iii'.bne interval, another interval
'24 hours,; anil thus
lil^fjin' and tfieVelbek' will tiot'agree,'that is, the .clock
-will not:, doritmlie !tii .fttow'' 12 when the fuit comes to the
meriSanf.,&jjj?“Jo *, , M H i | '
’ 79m;F o f le t P rdprefeht ij^cjp'blfekbf'fheyetfih,1 viewy«
its eqt®ir,!qM' 'fri^q|eihe y eafth-to revolve about its
’axis, in the oalcr'qf. the.letters *ii'7wyi--; and let T D L E
!fie:t;he celeftial equator,jand; T C L the ecliptic,-rn v.'hick
:tlie fun ;
rot,, u