ASTRONOMY, 
P A, and draw T (^perpendicular to A G C E, as before, 
and draw Qjq parallel to ABC, and tqr perpendicular 
to AGCE; let A e be alfo perpendicular to aged. Now, 
as the pofition of the equator and the apparent place of 
the ftar are altered in the time between the two obferva- 
tions, let m be the point where a fecondary from the ap¬ 
parent place of the (far to the equator at the firft obferva- 
tion would cut it, and v the place at the fecond obferva- 
tion, and draw vw perpendicular to AGCE; then A m 
is the apparent right afeenfion of the (far at the firft ob- 
fervation; and av at the fecond. Alfo the Sun mud be at 
t when it has the fame declination tq at the fecond obfer- 
vation as it had at the firft, and confequently qv is the ap¬ 
parent difference of right afeenfions of the Sun at t and 
ftar, which difference is found by obfervation in the fame 
manner as the difference at T was before found, when the 
equator was fixed. Alfo, as Q^q — C c = A a, and the 
angle q QR — c C Qjzr A ae, we have Q^r — ae — A ax 
cof. A ae. Now, if we put M for the mean right afeen¬ 
fion of the ftar ar the beginning of the year, and 5 for the 
fum of all the corrections due at the time of the firft ob¬ 
fervation, and s for the fum due at the fecond ; then, from 
what we have already explained, Mfi-S=Am, M-\-s—av; 
hence, if we take the former from the latter, fuppofing s 
to be greater than S, we have s — S=av — •Am—ae-\-ev— 
Aw—wmfm lying beyond w) ; but ev—Aw, hence s—S 
—ae — torn, confequently wm—ae —5— 5 . Now qv , or rw , 
is known, hence we know rm ; and, as Or is known, Qm 
will be known; and, as we alfo know Lin, we get the va¬ 
lue of QL, with which we proceed, as before, to get the 
ftar’s right afeenfion ; which having thus determined of 
one, the right afeenfion of all the heavenly bodies may 
from thence be found. 
The praftical method of finding the right afeenfion of a 
body from that of a fixed ftar, by a clock adjufted to fide- 
rial time, is this: Let the clock begin its motion from 
oh. o', o". at the inftant the firft point of Aries is on the 
meridian ; then, w hen any ftar comes to the meridian, the 
clock would (hew the apparent right afeenfion of the ftar, 
the right afeenfion being eftimated in time at the rate of 
fifteen degrees an hour, provided the clock was fubjeCl to 
no error, becaufe it would then (hew at any time how far 
the firft point of Aries was from the meridian. But, as 
the clock is neceffarily liable to err, we mu ft be able at any 
time to afeertain what its error is, that is, what is the dif¬ 
ference between the right afeepfion (hewn by the clock 
and the right afeenfion of that point of the equator which 
is at that time on the meridian. To do this, we muff, 
when a ftar, whofe apparent right afeenfion is known, pa(- 
fes the meridian, compare its apparent right afeenfion with 
the right afeenfion (hewn by the clock, and the difference 
will (hew the error of the clock. Forinftance, let Aldeba- 
ran be 4I1. 23',. 50". at the time when its tranfit over the 
meridian is obferved by the clock, and fuppofe the time 
(hewn by the clock to be 4I1. 23'. 52". then there is an er¬ 
ror of 2" in the clock, it giving the right afeenfion of the 
ftar 2" more than it ought. If the clock be compared 
with feveral ftars, and the mean error taken, we (hall have, 
more accurately, the error at the mean time of all the ob- 
fervations. Thefe obfervations being repeated every day, 
we (hall get the rate of the clock’s going, i.e. how faft it 
gains or lofes. Its error, and rate of going, being thus a(- 
certained, if the time of the tranfit of any body be obfer¬ 
ved, and the error of the clock at the time be applied, we 
(ball have the right afeenfion of the body. This is the 
method by which the right afeenfion of the Sun, Moon, 
and planets, are regularly fouild in obfervatorics. 
The right afeenfion of the heavenly bodies being afeer- 
tained, the next thing to be explained is, the method of 
finding their declinations. Take the apparent altitude of 
the body, when it paffes the meridian, by an aftronomical 
quadrant; corredt it for parallax and refraction, and for 
the error of the line of collimation of the inftrument, if 
neceflary, and you get the true meridian altitude, the dif¬ 
ference between which and the altitude of the equator 
(which is equal to the complement of the latitude, pre- 
vioufly determined) is the declination required. 
To find the latitude and longitude from the right afeen¬ 
fion and declination, or the converfe, we have the follow¬ 
ing admirable rules, given by Dr. Maikelyne. 
Given the Right Afeenfion and Declination of a Heavenly Bo¬ 
dy, and the Obliquity of the Ecliptic ; to find its Latitude and 
Longitude. 1. The fine of AR. -f- cotang. decl. —10, — 
Cotang, of arc A, which call north or fouth, according as 
the declination is north or fouth. 2. Call the obliquity of 
the ecliptic fouth in the fix firft figns of AR, and north in 
the fix laft. Let the fum of arc A and obi. eclip. accord¬ 
ing to their titles, = arc B with its proper title. 3. The 
arith. confp. of cof. arc A -f- cof. arc B + tan AR. —10, 
= tan. of the longitude , of the fame kind as AR. unlefs 
arc B be more than ninety degrees, in which cafe, the 
quantity found of the fame kind as AR. muft be fubtrafl. 
ed from twelve figns, or 360 degrees. 4. The fine of lon¬ 
gitude + tan. arc B —10, zz tan. of the required latitude, 
of the fame title as arc B. If the longitude come out 
near o°, or near 180°, for the fine of long, in the laft ope¬ 
ration, fubftitute tan. long. + cof. long. —10, or the laft 
operation will be, tan. long. -J- cof. long. -J- tan. arc B —« 
20, zztan. lat. The tan. Ton. is already given. 
Given the Latitude and Longitude of an Heavenly Body, and 
the Obliquity of the Ecliptic ; to find its Right Afeenfion and 
Declination. 1. Sine long. cot. lat. —10 zz cot. arc A, 
which call north or fouth , according as the lat. is north or 
fouth. 2. Call the obliquity of the ecliptic north in the 
firft femicircle of longitude, and fouth in the fecond. Let 
the fum of arc A and obi. eclip. according to their titles, 
— arc B with its proper title. 3. The arith. comp, of cof. 
arc A cof. arc B -j- tang. long. —10, zz tan. of right 
afeenfion, of the fame kind as the longitude, unlefs arc B 
be more than 90 0 , in which cafe, the laft quantity found 
of the fame kind as the longitude, muft be fubtracled 
from twelve figns, or 360 degrees. 4. The fine AR. -f- 
tan. arc B —10, zz tan. of the required declination, of the 
fame title as the arc B. If AR. come out near o°, or 
near 180 degrees, for the fine AR. in the laft operation, 
fubftitute tan. AR. cof. AR. —10, or the laft operation 
will be, tan. AR. cof. AR. tan. arc B — 20, zz tan. 
declination. The tan. AR. is already given. 
Demonfiration. Lets be the body, pC the ecliptic, 
pQ^the equator, sr, sn, perpendicular to pC, pQ^ 
Then rad. : fin. p» :: cot.sn : cot. s' P'72, hence log. fin. 
Y'nfi- log. cot. sn —10, zzlog. cot. sfn arc A. Hence, 
s 7"nTOjT C s pr arc B. Alfo, 
-r 
cof. jp« : rad. :: tan. sp : tan. sp 
rad. : cof. spr :: tan. sp : tan. r p 
.•. cof.sptf : cof. j Y'r :: tan.ay': tan. rp — 
cof. syv X tan- «P , . r . . 
----; hence, ar. co. log. cof. sp«+ log. 
cof sXn 0 D 
cof. spr-f log. tan. sp—xo, zz log. tan. rp the longi¬ 
tude. And rad. : fin. rp :: tan. rps tan. sr; hence log. 
fin. rP-f- tan. rfs —10, =z log. tan. sr the latitude,. 
And, 
