PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
321 
So, too, we shall have instead of 
'B = — 
21 ab 
2K a 
and 
'B =-— f — sin a + 2 cos y sin a — y], 
aa* , 
-■# - E 
(denoting by suffix Q that we have an electromagnet, not a current). 
Also 
Therefore, 
and similarly, 
and 
j,, 127 rpa'^a'b' j 
AV 3 
T7i/ 12 ir'pa a j-r p . i o / /”| 
h, =-K — sm a + 2 cos y sin a — y , 
' A jp “ 
9 /y/y / 2 
' D = - ,D', 
y\ / _ 12y?7rff o’ T 7 - p i o ' / /“| 
l) =- - — K [cos a + 2 sm y sm a — y J. 
But the couple tending to increase cf> on the a, b shell is, by (xiv.), 
^ (>\E - ' B'D). 
or 
or 
f ( AE' + 2 '^D'), 
w 
ftirpcfia' 2 2K« 12p7ra /2 cr / „ , . 
+ ( “' r,y) ’ 
where 
y* (a, y, y') = [cos a + 2 sin y sin a — y] [— sin a ffi 2 cos y' sin a — y'] 
-f 2 [— sin a + 2 cos y sin a — y] [cos a + 2 sin y' sin a — y'] 
= — 3 sin a cos a + sin a — y [4 cos a cos y — 2 sin a sin y] 
+ sin a — y' [2 cos a cos y — 4 sin a sin y] 
+ 2 sin a — y sin a — y' [2 sin y cos y + 4 cos y sin y'] 
= — f sin 2 a -j- sin a — y [cos a — y + 3 cos a + y] 
-f- sin a — y [3 COS a -f- y' — cos a — y'] 
+ [cos y — y' — COS 2 a — y — y'] [3 sill y + y' + sin y' — y]. 
MDCCCXCII.—A, 2 T 
