PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
309 
(a.) The couple exerted on a shell is independent of a, i.e., of the direction of the 
axis of the electromagnet. 
(/3.) The shells have equal couples in opposite directions, the parts of the shells 
directed towards one another being driven towards the electromagnet if (f> is less than 
a right angle and driven away from it if <f> exceeds a right angle. If <f> be a right 
angle the couple vanishes. 
Fig. 32. Fig. 33. 
The Mechanical Effect of Currents set up in a Thin Spherical Shell. 
16. In obtaining the currents set up by a given field we follow Professor C. Niven : 
T, using spherical coordinates and the ordinary notation, be the current function of 
Fig. 34. 
the distribution in the shell, P the potential of imaginary matter spread over it with 
surface density <£, then 
1 d 
n =-adr^’ F = °> 
G = - 
dV 
a sin 6 d$> ’ 
H = — 
a dd 
The components of the current are 
a sin 6 d<p ’ 
u = 0, v = — 
- 
a 
