PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
327 
Now we had (xv.) 
v H« H ab 
A =-- cos y = — — 
P" P 
Thus, distinguishing coefficients arising from the magnet by a suffix ( / ) as distinct 
from the magnetic pole, we have 
' A = — Ka 
Ka 
1 36 3 \ . , . 3 be 
-- -J- —r sin a + —r cos a 
p 3 P 5 / p 5 
= — — [ sin a' + 3 cos y sin a + y] 
So too from 'B = Hac/p 3 (xv.) 
Ka 
We had also 
' B = — [ — cos a + 3 sin y sin a' y 1 . 
'p 6 
v 2 aa ' 2 67 rpa'a' H a!V . . , 
= -^T • -+ higher powers, 
'E = 
act' 2 (iTTpa'cr' H a'c 
* Af 
,'3 ‘ 
Hence 
p, _ T7 1 2irj)(m ^<j p . / 1 q / 7 . /“i 
, D = K ^ 3 ^ / 3 - [- sm « + 3 cos y sin a + y ] . . . 
\E = K -~v, — [— cos a' + 3 sin y sin a' + y'] . . . 
Thus the couple 
where 
# A'jp 
_ ('a' E — ' /B \D), 
Aj 
P>Trpa 2 cr K% 67 rpaa^cr' .. , , 
= ^r*7 r '^A>^ /(a r,y) ’ 
/(a', y, y') = — [— sin a' + 3 cos y sin a' -{- y] [— cos a' -j- 3 sin y' sin a' -f- y'] 
— [ — cos a' + 3 sin y sin a' + 7] [ — 2 sin a + 6 cos y sin a' + y] 
= — £ {(sin a' + 3 sin a + 2y) (cos a' — 3 cos a' -f 2y') 
+ (cos a' — 3 cos a' + 2y) (sin a' + 3 sin a' + 2y')}. 
On multiplying and continuing the practice of replacing products by sines and 
cosines of sums or differences, we get 
= — f [sin 2 cl + 3 (sin 2y + sin 2 y) + (sin 2 a' + y' — sin 2a' + y) 
— 3 sin 2 (y — y) — 9 sin 2 a' + 2y + 2y']. 
