364 
MR. LUBBOCK’S RESEARCHES 
r.7 = 
3 
2 
(-4-: 
)(e°- 
*1S = 
3 
o + i-: 
) (e 2 
*19 = 
4' 
(‘ + 4 
I (e 2 ' 
*20 = 
4 1 
( 1+ 4‘ s ) 
| r 8 - 
too = 
4 1 
)r w - 
*2 4 = 
4 1 
(- 4 ^: 
j r i9 
*26 = 
4' 
) r ‘ 4 
tor) — — 
4 ( 
h 
*32 — - 
l-i 
*35 — 
0 
*38 = 
4( 
1+ 4 es ) 
r °o ' 
*40 = 
4< 
;-+h 
I»m- 
*42 = 
4< 
4 + 4 ea ) 
| r 24 ■ 
‘““IC + 4 '*)’•»+ r 6 '■ 
t “=4( i + H r " 
'"=4( i + l- e ’b 
= 4 (* + 1 ea ) r '> 
tj » = 4 (* + 4 e *) r “ 
r>,=: 4 (* + 4 e ") 
t 36 = o 
-fO+T-) 
-tO + t-) 
c "=4( i + 4‘ ! )’'" 
= o 
16 
16 r ® 
'« = 4(‘ + T e, ) r “ + Te 
t “=4( l+ 4 e, ) r “ + re' 
'»=y( 1 + H r * + r- 
r " = 4( 1+ 4 e2 ) r » + re r > 
v * , = 4 (' + i e ‘) r " + T6 r ’ 
>-4( 1 + T') , ' + f.'' 
*«=4( , + 4“)4 
Let R„ be the coefficient corresponding to the w th argument in the develop- 
ment of a R + a 5 R, m R' n the coefficient corresponding to the n th argument in 
the development of ahdR with its sign changed, Phil. Trans. 1832, p. 161, 
so that, for example, when the square of the disturbing force is neglected, 
R] — — — - ~z then 
1 4 u, a , 3 
{ l+3e, ( l + 4)} = 
(2— 2m) 2 
(2—2 m) 2 — 1 
(2 — 2 ro)»— I { { 2 — 2 to + 1 } R ‘ + 2 — 2 m fi| } 
{ 1 _|- r ,} = 1 -«!_2{{± + 1 } Ki+ ^ E ,-} 
