32 
MR. LUBBOCK’S RESEARCHES 
+ 
{ 
27 e 2 
63 e 2 
- 3 in) } 
128(1—m) 3 16 (2— 2m + c)(2— 2m —c) 64 (2 — m) (2 — 3 m) 
27 , 9 
cos 4 t 
+ 
32 (1 - m) (2 — 2m— c) 
63 
ecos (4 t — #) + — 
[131] 
ecos (4 t + x) 
32(1 - m) (2 — 2 m + c) 
[132] [133] 
e.cos (4 t — z) — 
9 
e, cos (4 f + 2 ) 
64(1—m) (2 — 3 m)"' 64(1—m) (2 —m) ' 
[134] [135] 
+ < + 
+ + 
45 
64(1 — m) (2-2m-2c) + 32 (2-2 m — c) 2 } e ~ C ° S ^ 
[136] 
- o | e- cos (4t + 2x) 
[137] 
+ 
+ 
{- 
{- 
2 c) 32 (2 —2 m — c) a 
9 9 
32 (I - m) (2 — 2m + 2c) + 32 (2 — 2 m + c) 
189 189 
64 (1 — m) (2 — 3 m — c) 32 (2 — 2 m + c) (2 — 3 m) 
——- > e e, cos (4 t — x — 2 ) 
— 3 m) J 
9 
64 ( 1 — m) (2 — Bile) 32 (2 — 2 m + c) (2 — m) 
f_ _ 27 , 27 
L 64 (1 — m) (2 — in — 
+ {- 
[138] 
-- lee, cos (4 t + x -f z) 
— m) J 
[139] 
+ 
+ - 5 ; 
in) (2 — in — c) 32 (2 — 2 m — c) (2 — m) 
—— j e e, cc r j (4 t — :r 4- 2 ) 
[140] 
63 
+ 
63 
+ 4 + 
64 (1 — m) (2 — m + c) 32 (2 — 2 m + c) (2 — 3 m) 
153 
(4 (+,-,) 
[141] 
+ 
441 ] 0 
___ S p ~ i 
+ 
64 (1 — m) (2 — 4 m) 1 128 (2 - 3 m)°- J £, ~ C ° S 1 2 ^ 
[142] 
e°- cos (At + 2z) 
[143] 
128 (2 - my- 1 
ft (I +« 2 ) _ ft , 2h j, 1 
r 2 
h 8 s- 
= A + 2ft J_ + h ( r j-LV+ — 5c + — ^._L + h A 
r 2 r r \ r / r 3 r r r 
Developments which are required when the cube of the disturbing force is 
considered. 
Neglecting in R the terms multiplied by and by s 2 , and omitting the fac¬ 
tor m, 
R 
= - 4^{ 1 + 3COS(2X ~ 2A ' ) } 
