astronomy. 
ao"x fin- D X cof. A x fin. S — cof. 0 x fin. A X col. S. 
For fouth declination we mull change the figns. But, by 
Trigonometry, cof. D x cof. 5 —£ cof. S-\-D a cof. 
-S x fin. D~| 
cof. 0 x fin. A-\-S X fin. D ^ 
S — D, and cof. A X fin- 5 = -t fin. — *• fin. 
alfo fin. A x cof. S—% (in. w'-j-df-l- fin. A—S ; 
the aberration in declination — 
443 
A—S, 
lienee 
-|- i o' 
— io' 
Xf + cof 
X i 
r+ 
— io" x fin- 0 x cof. S— D ‘ 
— io" X fin- 0 X cof. S-fD J 
The two lad: terms mud have their figns changed when 
the declination is fouth. 
To find the Sun’s place when the aberration is the great- 
eft, we have in the triangle LST, fin. SL : rad :: cot. TSL 
: cot. TL ; therefore, knowing the longitude of the ftar, or 
of the point L, the longitude of T the place of the Sun is 
known. Hence we find the Sun’s longitude when the a- 
berration is greateft fubtradlive. 
To find the Aberration in Right Afccnjion. Let S be the 
true place of the ftar, abed the eiliple of aberration, apeq 
the circumfcribing circle, P the pole of the ecliptic, and 
R that of the equator, and let M SN be a conjugate dia¬ 
meter to ASB; draw FNC, DAV, perpendicular to 
ca, join V S, draw C S K, which mud be perpendicular to 
V S, and draw M G perpendicular to A B ; alfo from any 
point Q^raw Q_s\V perpendicular to ca, and QJ, sv, 
perpendicular to SV, SA, refpedtively, and s-r an ordi- 
= < 
nate to the diameter A B. Now it is manifeft, that A is 
the apparent place of the ftar when the aberration in right 
afeenfion is nothing, and M when it is greateft, becaufe a 
tangent at M is parallel to A B. By the property of the 
ellipfe, MGx ASr=ifSxcS, therefore AS ; cS or Sy :: dS 
AD AD 
: MG, hence-777- : ——:: dS : MG; but AD : d S 
19-17" 
0-83" 
3-98" 
3-98" 
fin. A —5 > 
fin.' A-\-S ) 
cof. S—D 
fin. 
fin. 
cof. S-\~D. 
VD 
SV 
Sq, therefore 
AS 
VD 
Sq : MG, that is, the 
PSR :: 20" : MG= 
the greateft aberration in right afeenfion. 
then sv is the aberra- 
__fVD 
SV : -AS 
fine of Va : the fine of ASa or cof. 
20" x cof. PSR 
li n. V a 
If the ftar be at any other point s, 
tion in right afeenfion; but sv is in a given ratio to sr, 
and sr is in a given ratio to QTT, becaufe QJ is project¬ 
ed into sr; hence sv varies as QJ the fine of Q^V, or co- 
fine of K Qjhe diflance of the Sun from that point where 
it was when the aberration was greateft. 
Now, as in the two laft figures, tan. ASD, or cot. PSR 
3 
: tan. VSa :: (AD : PD ::) fin. ftar’s lat. : rad. but tan. 
ML : MSI. :: fin. ftar’s lat. : rad. hence, as PSR—MSL, 
the tan. PSa x tan. LM is conftant, therefore LM is the 
complement of PSa; hence LM—Ka the elongation of the 
Sun from the ftar when the aberration is greateft; there¬ 
fore M is the place of the Sun at that time ; the longitude 
of which put -=.L at the time when the aberration is great¬ 
eft fubtradlive. Hence the greateft aberration in right af- 
r 2o"xco [.MSI. . . 
cenfion = --—— -. I his is the aberration at 
cof. LM 
the ftar, and therefore reduced to the equator it becomes 
20" x cof. MSL 
But, as in the laft figure but one, 
co[.MLxco(.SA( 
cof. MSL 
—-'•777-= fin. M- 
col. ML 
fin. AP._ fin. A 
tin. ME fin. L ’ 
therefore the great¬ 
eft aberration fubtraclive becomes - 
-20"X fin. A 
cof. D x fin. L ’ 
the aberration in right afeenfion at any other time 
— 20" X fin. A x cof. L — 5 
hence 
cof. D x fin. L 
— 20" x fin. A 
cof. D x fin. L 
X 
cof. L x cof. 5 + fin. L x fin. <S — 
—20" X fin. A x cot .L x cof. S—20" x fin. A X fin. S 
_ 
— (becaufe cot. L — cof. 0 X cot. A) 
—20" X fin. A Xcof.Sxcof. 0 X cot.. 4 —20"X fin ./4 X fin.S 
col. D 
—20"X cof .0 Xco f.Sx cof. A—20"Xfin. Ax fin.S 
=-;-7-. Now, 
cot. D * 
if we augment A by 90 0 , or three figns, the numerator of 
this fradtion becomes the fame as the coefficient of fin. D 
in the aberration of declination, becaufe the fin. A — cof. 
a °d cof. A — fin. A-\-t,s. But, to reduce this 
farther, we have cof. A x cof. 5 = \ cof. A-\-B -f £ cof. 
A — B, 
hence 
and fin. A x fin. S — g cof. A- 
the aberration in right 
-B— 4 cof. A+B; 
afeenfion — — 
10 " x i-j-cof.f? x cof. A —S— 10 " x 1 —cof. 0 xcof./f-j-d* 
' cof. D 
=—19-17" X cof. A —S — 0 - 83 " X cof. A-\-S X fee. D. 
As M is the place of the Sun when the aberration in 
right afeenfion is the greateft, we have cof. A EM : tan. AE 
the ftar’s right afeenfion :: rad. : tan. EM the Sun’s lon¬ 
gitude. Hence we can find the Sun’s longitude when the 
aberration is the greateft fubtradlive. From thefeexpref- 
fions for fhe aberration in right afeenfion and declination, 
M. de Lambre has computed a fet of tables, by which 
the aberration of a ftar at any time may be very readily 
found, and to which the pradfical aftronomer is referred. 
To calculate an Eclipse of the Moon. 
Being provided with a complete fet of aftronomical ta¬ 
bles, by either - of the authors recommended above, the 
firft thing to be done is to find the time of the mean oppo- 
fition, which may be obtained from the Tables of Epadts. 
The epadt for any year is the age of the Moon at the be¬ 
ginning of the year from the laft mean conjundtion, that is, 
from the time when the mean longitudes of the Sun and 
Moon 
