32 
MR. LUBBOCK’S RESEARCHES 
+ 
27 e 2 
63 e ( 2 
-3m)} 
128(1— m) 2 16(2 — 2m + c)(2 — 2 m—c) 64(2 — m) (2 — 3m) 
27 , 9 
32 (1 — m ) (2 — 2m— c) eC ° S 32 (1 — m) (2 — 2 m + c) 
[132] 
cos 4 £ 
[131] 
ecos (4 t + x) 
[133] 
+ 
63 
64 (1 — m) (2 — 3 m) 
e t cos (4 t — z) — 
9 
[134] 
64 ( 1 — m) (2 — m) 
e / cos (4 t + 2 ) 
[135] 
+ 4 + 
45 
{ 
+ + 
+ 
+ 
64 (1 — m) (2 — 2 m — 2 c) 32 (2 — 2 m — c) 
9 9 
32(1— m) (2 — 2 m + 2 c) 32(2 — 2 m + c) 
189 189 
+ 32(2-L-cr } e ' COS(4< - 21 ) 
[136] 
- 1 e 2 cos (At + 2 x) 
[137] 
{ 64(1 — m) (2 —3m — c) 32 (2 — 2 m + c) (2 — 3 m) 
9 9 
| e e, cos (4 t — x — 2 ) 
[138] 
64 (1 — ?«)(2 — m 4- c) 32 (2 — 2m + 0 ) (2 — m) 
1 e e. cos (4 t -J- x 4- 2 ) 
— m) J 
[139] 
+ {- d T(l-m) 2 ( 7 2-m-c) + 32 (2 - 2m - c) (2 - m) } e<? ' C03 (4 * ” * + s) 
[140] 
{~ 64(1 — m) (2 — m + c) + 32 (2 - 2 m + c) (2 - 3 m) } e<?/ C ° S ( 4 ^ +x-z) 
[141] 
+ 
{ 
+ { + 
+ 
64 (1 — m) (2 — m + c) 32 (2 — 2 m + c) (2 — 3 m) 
153 441 
64(1 — m) (2 — 4m) + 128 (2 — 3 m) 2 
9 
j e°~ cos (4> t — 2 z) 
[142] 
128 (2 -m) 
, e^cos (4 £ + 2z) 
[143] 
/t ( I + s 2 ) _ /t 2 /i » 1 
/i Js 5 
r 2 r r \ r / r 2 r r r 
Developments which are required when the cube of the disturbing force is 
considered. 
a 3 
Neglecting in the terms multiplied by — and by s 2 , and omitting the fac- 
tor in, 
R — ~ { ! + 3 cos (2 a — 2 A,) } 
