260 
MR. LUBBOCK’S RESEARCHES 
+ { - 1 +y}e / cos (z- 2?/)+ {- 1 + |_Je /C os (z + 2y) + 1 1 + -|| e ( cos (2 i • 
[71] [72] 
+ { ~ 3 + t} 6/C0S (2 1 + z ~ 2y ) + -|- e ' cos (2« — 2y) + e 2 cos (2x + 2y) 
[75] [77] [78] 
— ~ cos (2 1 — 2 x — 2 cos (2t + 2x — 2y) 
[79] 
[81] 
+ | 3 — y j e e, cos (a + z — 2 ?/) + | — 1 + j e e t cos (a: + z + 2 
[83] [84] 
+ | — 1 — A | e e, cos (2 * — x — z — 2 ?/) 
[85] 
+ | 3 y 1 e e ( cos (2 t + x + z — 2 y) + j 3 — ^ j e e, cos (2 t — z — 2 y) 
[87] [89] 
+ | — 1 + ~ | e e, cos (x — z + 2 y) + j 3 — A | e e ; cos (2 t — x + z — 2 ?/) 
[90] [91] 
+ | — 1 — \ } e e ‘ cos ( 2 * + x — z — 2 y) + { — -§ — y + 5 1 e* cos (2 z — 2 y) 
[93] [95] 
+ {“I “I + 5 } e / 2 cos(2z + 2 V) + {§ + |- + ^e^cos(2t-2z-2y) 
[90] [97] 
+ { T ~~ ¥ + 5 } e * C0S (2 1 + 2 * ~ 2 y) 
[99] 
3 i a 2 
Terms in i? multiplied by — y cos 4 ~ 3 
= 2 + 4 C + 4 C ' + FG e ' + ¥ Ce ' + l2“T e '-T e ' + 32 £ + 32 C ' + 
+ { - 1 + -f ~ f e, 4 j<ecosx+ {- j + j|e 2 + j- e ? } ec os (2 1 — *) 
[2] [3] 
+ {t _ re ecos ( 2< + x ) + {4 + J e * + Tq e - 2 } e - C0S2 
[4] [5] 
25 
e-e, 
■z-2y) 
[73] 
| cos 2 t 
[ 1 ] 
