PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
281 
This repulsion may easily be taken advantage of by using it as the basis of a meter 
for alternating currents. 
If the coils consist of two circles of radii a and c (the former the greater), with their 
centres coincident and planes making an angle 9, and we send a current I sin r pt 
through the larger, there will be a couple tending to increase the angle 9. 
This has been proved experimentally by Professor Thomson : its amount proves 
to be 
_2pY^_ 
1 S 2 + f N 2 
e 4 
« 4 
sin 9 cos 9 + | 
(^j sin 9 cos 9 (YO cos 2 9 — 3) + . . . 
The positions 9=0 and 9 = tt/2 are positions of equilibrium, the former being 
unstable and the latter stable. 
By making the plane of the primary vertical and suspending the secondary inside 
so as to be capable of turning round a vertical axis by means of bifilar suspension 
with 9 = 0 as position of equilibrium, the deflection 9, when the alternating current 
is passing, will give the intensity of current. 
We might also get the intensity by suspending the secondary by a single thread 
and observing the time of a small oscillation about 9 = n/2. 
If the moment of inertia of the secondary about the vertical be mk 2 it is not difficult 
to show that the number of oscillations per second is 
277-yc 2 
2nd 3 (S 2 + 
N | 
Professor Elihu Thomson has devised other interesting experiments of which the 
followung is an example :— 
A sheet of copper is placed so as to half cover an alternating magnetic pole. Upon 
this, near the pole, is laid a hollow sphere of copper. The electromagnetic action 
produces a couple so powerful that the friction of rotation is overcome and the sphere 
is spun round. 
The mathematical analysis for this case being complicated I have evaluated the 
couples called into action in various combinations of hollow spherical and cylindrical 
shells. 
It is a known fact that in a spherical conductor no external field can give rise to 
induced currents that do not circulate in concentric spherical shells. After a 
preliminary theorem to the effect that there are no other families of surfaces which 
possess similar properties, the case has been considered of an infinitely long, thin, 
circular cylindrical shell in a field consisting of alternating currents parallel to its 
axis. 
If the electrokinetic momentum of the primary field be expanded in harmonics over 
the cylinder, it turns out that if all the terms of each harmonic have the same phase, 
MDCCCXCII.-A, 2 O 
