262 
MR. LUBBOCK’S RESEARCHES 
+ -^e 4 cos (2 t + 4 x) — ^ L e 4 e, cos (3 x + a) 
Jo 16 
[40] [41] 
49 26 q 
- gg <? e, cos (2 * + 3 x — z) — ^e 3 e, cos (2 i — 3 a: — 2) — e 5 e, cos (3ic-x) 
[42] [43] [44] 
+ ^ e 3 ^ cos (2 ^ — 3 a; + z) + ^ e 3 e ( cos (2 t + 3 x — 2) — ^ e°- e* cos (2 x + 2 z) 
[45] [46] [47] 
+ y e 2 e i°~ cos (2 t — 2x — 2 2) — A e 5 e, 2 cos (2 x — 2 2) + y e 2 e, 2 cos (2 1 + 2x — 2 z) 
[48] [50] [52] 
— ^ ee ( 3 cos (x + 3 z) — ^^-ee, 3 cos (2 t x — 3 2) + cos (2 t + x — 3 2) 
i 0 jZ yo 
[53] [54] [55] 
-^ce; cos (x — 3 2) — e -^- cos (2 t — x + 3 2) — e e, 3 cos (2 £ + x — 3 2) 
16 32 96 
[56] [57] [58] 
- ji e ' cos 4 z + yy e 1 cos ( 2 t - 4 z) - ^e, 4 cos (2 i + 4 2) 
[59] [60] [61] 
Terms in R multiplied by y sin 2 y cos2 y y 3 or - y sin ‘ 2 ' yj 
= { 1 - y e2 + y e / 2 | cos2y + j 1 + e, 2 j cos (2 < — 2y) — 3 ecos (x - 2 j 
[62] [63] [65] 
3 3 
+ ecos (x+ 2 ^) — e cos (2 1 — x— 2 y) — ecos (2£ + x — 2y) + — e, cos (2 — 2 y) + — e, cos (2 + 2 y) 
[66] [67] [69] -[71] [72] 
+ ~ e, cos (2t — z — 2y) — y cos (2 t + 2 — 2 y) + ^ e 2 cos (2 x — 2 y) + e-cos (2 x + 2 y) 
[73] [75] [77] [78] 
— e - cos (2 1 — 2x — 2 y) — cos (2 t + 2 x — 2 y) — ee t cos (x + 2 — 2 y) 
[79] [81] [83] 
+ e c ( cos (x + 2 + 2 y) — — ee, cos (2t — x — z — 2 y) +y cos (2 < 4- x + 2 — 2 y) 
[84] [85] [87] 
