30 
MR. LUBBOCK’S RESEARCHES 
Again 
2d R — " ' ^ eC> { cos (2 t — x) r s ' sin z — sin (2 £ — x) X 5 cos z | 
mm, a 2 ee, f . 38 , ■ /f> , . . 38 , . , . 
= ^ ( j + yy^sm (2*-x + z)-_ r b ' sin (2 t — x — z ) 
~ if S ^ n ( 2 t ~ x + 2 ) — yy A 5 sin (2 £ — x — z) j. 
~ m ” l g° { + y|{ r s' — A 5 |ee / sin(2^-^ + z) + || jr 5 ' + X 5 1 ee, sin (2 t 
[15] 
which terms are given in the development of & d R, p. 18. 
Similarly 
j/d R\ 2.2.38 m, a- f ") 
o J = y y y - e e ; | — sin (2 £ — x) r b cos z + cos (2 t — x) X 5 sin z j> 
— — — 1 — ee ( r 5 ' sin (2 t — x + z) — ry sin (2 < — x — x) 
+ X 5 sin (2 t — x + z) — X 5 sin (2 £ — x — z) j> 
= 2 ™‘ s — | + H |»V - * 5 } ee ; sin (2 it — x+ z) + ?§ |r 5 ' + A 5 jee,sin (2 < 
[15] 
these terms are given in the development of & p. 25 and p. 24. 
o /d R\ 20 m, a 2 . /0 . . 
Suppose = ■ 27 a V y sin ( 2 * + y) 2s = y s I47 sin(2*-j/) 
/ d R\ r 20 m,a- „ . . . * . , 0 . 
dTj 5 = 2 7 V ' r ' Sl47 Sm (2 1 + S') sin (2 * ~ 
y) 
= 1it{~ T 7 s ^ cos4t+ ^ s >«r 2cos2 ^} 
[131] [62] 
which terms are found in the development of h R. 
, /d R\ j, 2.20mm, a 2 „ . , , 
d ‘ \"dl) Js = “ 27 a 3 y 2 s 147 sin (2 < + y) cos (2t — y) 
mm.a’ 2 t 20 „ .... 20 „ • 0 ] 
= __l_|--s 147y 2 sin4i+ —s w y*sin2y j 
[131] [62] 
— x — z) 
[ 12 ] 
— x — z) 
[ 12 ] 
