518 
ON THE DEVELOPMENT OF THE DISTURBING 
[479 
I write 
The term in question is given by Leverrier as Q-e) 2 (2) l , = e 2 .|(2), h=i and K} = A 1 , 
— & • i (— A i + Aj + Ai), which agrees. 
Similarly the term in e 4 is 
l»6j- — 54j« - 48<?>( )i — 96j 2 ( ),+ 144( ), + 144( ).} i A~i, 
= =|g ¡(96j 4 - 54j>) A-J - 48j ! - 96j s Ar< + 144A,^ + 144Ar- i |, 
and the term in question is given by Leverrier as (| e) 4 (4) 4 = e i . (4), h = i and 
IV = A\ 
= g4 iV {i (- 9f 2 + 16f 4 ) A 1 ' - i 2 Aj - 2 i 2 AJ + 3Ai + 3Ai\, 
which agrees. I have not made the comparison of any more terms. 
Leverrier’s Results expressed in terms of the Arguments, L' — ©', X' - TT, X — 0, X — IT. 
The angles which Leverrier uses in his arguments are V, X, co, vs', and t , viz. 
we have, 
V = ©' + (X' -©'), 
X = 0' + (X -©), 
•a — 0' + (IT - ©'), 
co = @' + (11 -©), 
r' = ©', 
where X, II, © are the mean longitude of the planet m, its perihelion and the mutual 
node, all in the orbit of m\ and similarly L', IT, ©' are the mean longitude of the 
planet m!, of its perihelion and of the mutual node, all in the orbit of m'. On 
substituting the foregoing values of V, X, &c., ©', as it should do, disappears, and the 
arguments are all of them linear functions of X' — ©', IT — ©', X — ©, II — © ; or, if 
we please, of X' — ©', L' — IT, X — ©, X — II, that is of the distances of each planet 
from its own perihelion and from the mutual node. It is, I think, convenient to use 
these last angular distances, and accordingly in Leverrier’s arguments, I write, 
V = ©' + (X'-© / ), 
X = ©' . 
*r' = & + (X' - ©') - (X 7 - IT), 
&>=©'. 
T = ©', 
+ (X-@), 
+ (X — ©) — (X — n),