364 
MR. LUBBOCK’S RESEARCHES 
*26 
= !( 
1 J " 4' S ; 
) ( e ~ r 32 + e “ r 2l) + Y 
|r 5 2 + r 7 r 6 + 7-,r l8 
+ r, 
. r l 9 } 
1 + 4 e 4 
) (e 2 r 30 + e 4 r 34 ) + -| 
{^17^1 + r 5 r 6} 
1 + i“) 
| (e 2 r 33 +e 2 r 31 ) + J- 
| r I7 r l + r 7 r i} 
1 + 4 e, ) 
1 r s + -g- T 0 
*«=4 0 + 4* 
h 
+ iV' 
■ + i £ *: 
l r ” + F 6 r ' 
*“=4 (' + 4 c! . 
) r " 
‘-4 £ 4 
*-=40 + 4' 
^ r l3 
, + 4^ 
) ^4 T 27 = -| 
( i + 4 £S )’" 
^28 = 
, + 40 
) r ‘ 7 t30== ~2 
( I + 4 £S ) f “ 
*31 = 
1 + 4 £S ) 
| r l7 *33 = -f 
0+4 £ t'» 
f 34 — ■ 
3_ 
8 
s ) 
19 
t 35 - 0 
t 36 = 0 
r, 7 = 0 
=H 1 + 4") r “ + re - '» = 4 0 + 4 “) r “ + re 
*--40 + 4 eS ) r »+ r6 r < '*' = 40 + 4 £! ) r “ + n 
'<*=4( , + 4 e *) r ” + r6 r * '*»=40 + 4 £S ) + re r ’ 
'**=40 + 4 c, ) r “ + ^ 
'*«=40 + 4 £, ) r “ + re 
'*tf 40 + 4 £, )’'” + ts 
*»= 40 + 4 e ‘) r " 
Let R„ be the coefficient corresponding to the w th argument in the develop¬ 
ment of a R -f a 5 R, m R' n the coefficient corresponding to the w th argument in 
the development of abdR with its sign changed, Phil. Trans. 1832, p. 161, 
so that, for example, when the square of the disturbing force is neglected, 
Ri — — - re then 
1 4 (A a ( 3 
(2 — 2 m) 
r , {l + 3 e* (I + 4)} = (2—2 m)*— 1 < 
— {{ 2 ^ + 1 } R ‘ + 2=k, R '' 
