308 
MR. G. T. WALKER ON REPULSION AND ROTATION 
where 
"Mj 
"N, 
"Qi 
"Ri 
4' Trpo-’aa ' 3 . , . , . -j- 
— 7 7 A (— sin a + 2 cos y sin a + y ), 
4 TTVa'aa /3 . , . , . —:- 
- ,, A (cos a - 2 sin y sina + y , 
a AD ip 6 ' 7 
87r 2 <m / 4 p 2 
iP 
2 aA _ „„ ^ 
— — ( —sina + 2cosysina + y) + -^7 
2aA , . -:— x 87r 2 aa' 4 » 2 
— (COS a — 2 Sill y Sin a + y) + 
A (— sin a -f- 2 cos y' sin a + y)> 
A (cos a — 2 sin y sin a + V)- 
On multiplying up, we notice that the second terms of "Q t and "It 1 cancel, when 
multiplied respectively by "N 3 and "M 1? and we get for the couple 
ira/pcr 2aA 4nrpa-'aa' 3 K 
cPD\p' 2 A 
X [(cos a — 2 sin y sin a -f- y') (— sin a + 2 cos y sin a + y) 
— (cos a — 2 sin y sin a + y) (— sin a + 2 cos y' sin a + y')] 
or 
. 9 87r 2 p 3 c^c^ , a 3 a ,3 r . --- . ... 
A" 2 ~/ 3 L 2 srna-f-y (cos y cos a — sin y sm a) 
— 2 sin a -f- y' (cos y' cos a — sin y' sin a) 
— 4 sin a -f- y sin a + y* (cos y sin y' — cos y sin y)]. 
The expression within the bracket is 
sin 2 a + y — sin 2a -fi y' — 4 sin a -fi y sin a -(- y' sin y' — y 
or 
— 2 sin y — y [cos 2 a + y + y + 2 sin a + y sin a -j- y 7 ] 
or 
— 2 sin y — y cos y' — y. 
Hence, omitting terms of the eighth degree, the couple on the a, b shell is 
A 3 
87 r~p 2 aa'a 3 a' 3 
sin 2(f), 
where (f) is (y 7 — y), the angle subtended by the axes of the shells at the electro¬ 
magnetic filament. 
15. To this order then we have the following results 
