﻿Unipolar Induction* 939 



rotation of the material bodies concerned, a principle which 

 has often been assumed almost as an axiom in treating of 

 electromagnetic phenomena. 



In the steady state E' must vanish everywhere, hence 



From this it is easily shown by integration that if <£ is the 

 electrostatic potential at any point on the cjdinders, the 

 potential at infinity being taken as zero, then 



where &/ is the angular velocity of the cylinders relative to 

 the magnet, and N is the total magnetic induction through 

 the periphery of the cylinder at the point in question. 



It is worth noting that, according to this theory, the vector 

 E' in general fails to satisfy Laplace^s Equation, even where 

 there is no volume distribution of electricity. If this were 

 not true, all effects due to electromagnetic induction would, 

 of course, be screened off by the metal case enclosing the 

 solenoid and magnet. 



The second view is taken by Lorentz, who puts 



B'-=B+irVB], 



where V is the velocity relative to the eether and B is the 

 magnetic induction. Hence in the steady state 



where co is the angular velocity of the cylinders relative to 

 the aether. We see that if the magnet were at rest while the 

 cylinders rotated, then (1) and (2) would be identical and 

 the two theories lead to the same results ; if, however, the 

 cylinders are at rest and the magnet rotates, as was the case 

 in the present experiment, then, according to (2), <f> vanishes, 

 while according to (1) it is the same as before, so that in this 

 case the two theories lead to opposite conclusions. 



Evidently N and <f> will be practically the same for both 

 cylinders, so that the charges on the inner surface of the 

 outer cylinder, and on the outer surface of that portion of 

 the inner cylinder which is enclosed by the outer, will be 

 small ; most of the electrification required by the Moving 

 Force Line Theory will be on the outer surface of I lie outer 



