8 
MR. LUBBOCK’S RESEARCHES 
+ 9*569 1515 ee, cos (2 t + x + z) -f 9*8697180 e e t cos ( x — z) 
[13] [14] 
— 0'04S6780 ee / cos (2 1 — x + z) + 0*4139940 e e t cos (2 t + x — z) 
[15] [16] 
— 0*0479097 e ; 2 cos 2 z — 0*799 1728 e, 2 cos (2 * — 2 z) 
[17] [18] 
— 9*5709386y 2 cos2z — 9*5761 195y 2 cos (2 t — 2 y) 
[62] [63] 
where the logarithms of the coefficients are written instead of the coefficients 
themselves. 
T1 in. a-f 34 20 0 , , 38 .38 , 0 , x 20 , 0 . 
R — s — _ — cos 2 t + — - e cos x + — e cos (2 t — x) - — e cos (2 t + 2) 
‘ “ a, 3 1 137 27 77 17 ' 27 v ’ 
[0] [1] [2] [3] [4] 
“ || e , cos 2 - ^ e , cos (2 i - z) + I? e, cos (2 / + z) + e 2 cos 2 x 
[5] [6] [7] [8] 
— — e 2 cos (2 t — 2 x) — e 2 cos (2 t + 2 x) + ^ e e l cos (x + 2) 
[9] [10] [1 1] 
+ _ e e, cos (2 t — x — z) + — e e, cos (2 t + x + 2) + — e e ; cos (x + 2) 
*/ 
[12] [13] [14] 
66 lc . . . ■. 83 /Oil \ 67 0 0 
— — e e, cos (2 t — x 4- 2) — — e e t cos (2 t + x — 2) — — e,~ cos 2 2 
[15] [16] [17] 
_ “33 e? cos (2 1 — 2 2) — y 2 cos 2 y — ^ y 2 cos (2t — 2y) nearly. 
3/ 43 6J 
[18] [62] [63] 
I make use of these approximate coefficients in the following development 
solely in order that it may occupy less space. 
_68 ,, 20 
a» I 137 0 T + 27 
38 0 , 38 „ / , , . 1 . 20 o / , , . 1 
-f7 e - r ‘ -rrr> + M + » e 'W + M 
* See Phil. Trans. 1831, p. 275. 
t r 5 — = r 0 ' + r,' cos 2 t + e r./ cos x + e r 3 ' cos (2 t — x) &c. 
[0] [1] P]' [3] 
$ A = A, sin 2 1 + e sin (2 t — x) + 8cc. 
[1] [3] 
