IN PHYSICAL ASTRONOMY. 
289 
+3e ’ (‘ + t) - 3 ^ 1 + -f-« ! )c°s(»<+s-w) + J cos(3«( + 3s-3i5) 
j( ’ , „T”' )8 { (1 + 3 «•) r,- | a* (r„ + , s! ) } _ ,, + 2i = 0 
d A _ . _A 2A j _ J /^d_R , 
r- r ‘ r r«/ dT tU 
d £ 
-»2 
+ -|- + 2e + “^) C0S + e — tzt) + iLL cos (2nt + 2 s — 2 •nr) 
+ ^e 3 cos (3 re * + 3 s — 3 sr) 
7- = 1 + e (l - COS (n < + g - ®) + e 2 cos (2re* + 2 £ -2sr) + A e 3 cos (3 n < + 3 £ - 3 w) 
A = re| 1 -f- 2 r 0 j- t + £ 
+ | 2 | r i + -rr ( r u + r ai) | 
__ m i f (i + e "~\ anR i + e \ nR + e a ««fi ai ll « . , 
f*> l\ 2 /(re — re,) n, 11 + (2 re — re,) J J (re - «,) sm (" t “ V + £ ~ e /) 
+ | 2 |r 2 + -^-(r 12 + r 22 ) | 
m, / /, e®\ areR n 2 e 2 a n jR I 2 2 e-ara R 1C) I 1 « . 
" J U + 2) (^) + (^2^) + (3^-2re,)/ j2(^) Sin ( 2 ^- 2 ^+ £ -^ 
In the same way, by means of the Table, all the other coefficients may be 
found. 
The great inequality of Jupiter consists of the arguments 155, 174, 213, 273, 
and 312, the variable part of which is 2 w — 5 n p and arises, as is well known, 
from the introduction of the square of this quantity, which is small, by succes- 
sive integrations in the denominators of the coefficients of the sines in the ex- 
pression for the longitude, of which the above named are the arguments. 
The following are the equations which have reference to these arguments, 
and which may be found at once by Table II. 
(2«.-5re,) 2 I. 3 11 . m,a _ 0 
i? V 155 2 54 + 16 4 J ? ‘«+— 
(2re-5re,) 2 / 3 \ m t a _ „ 
& V 174 ~2 74 / r m+— -9,74-U 
(2 re — 5 re,) 2 f 3 \ m.a n 
— ^ q r 2i$ 2 7-113 j r ‘ i13 ~7j~ ? 214 — ^ 
f* 
V 
V- 
2 P 2 
