30 
MR. LUBBOCK’S RESEARCHES 
Again 
S d R = - i - 38 m?n^a ee t | cog ^ t — x) r b ' sin z — sin (2 t — x) X b cos z | 
mm, a-ee, f . 38 . . N 38 , ■ /r> , . 
= - L_ - 1 | + — r b ' sm (2 t - x + z) - _ r b ' sin (2 t — x — z) 
— §? X 5 sin (2 £ — x + z) — \ b sin (2 f — x — z) j, 
= - : j + ^|r 5 '->. 5 jee / sin(2i-x + z) + |r s ' + A 5 } ee, sin(2 t — x — z)| 
[ 15 ] ' [ 12 ] 
which terms are given in the development of & d R, p. 18 . 
Similarly 
8 = — ~ ~ V/^a ^ e e ; | — s ' n (2 ^ — x) r b cos z + cos (2 t — x) A 5 sin z | 
_ _ ■ 38 m t a e f _ _ i s ; n (2 t — x + z) — r b ’ sin (2 1 — x — x) 
17 a* l 
+ A 5 sin (2 t — x + z) — X 5 sin (2 t — x — z) | 
_ - | 4. | r& f _ Xs | e e t sin (2 t — x+ z) + r 5 ' + A 5 j e^sin (2 < — z — z)| 
[ 15 ] [ 12 ] 
these terms are given in the development of § P- 25 and p. 24 . 
Suppose (717) ~ L> 2 y sin ( 2t + y) 8 s ~ y s 147 sin ( 2 t — y) 
/ d R\ . 20m l a‘ 2 „ . , n * . , 0 , . 
(T 7 ) 5 5 = 27 g 8 y ~ Si47 sm (2 * + y ) sin ( 2 t ~y) 
yds/ 
= ^7"{“ ^ s h7 7 2 cos 4<+ ^Si 47 y 2 cos2 2/j 
[131] " [62] 
which terms are found in the development of ci R. 
d. 
(£)*- 
_ . 20 m m t a ^ ^ s j n (2 t + y) cos (2 < — y) 
27 a, 3 
_ mm t a 2 
« 7 ~" 
{ — «147 r 2 sin 4 ^ *147 7"-sin 2 2/j 
[131] [62] 
