210 Prof. L. T. More on the 



unit of matter. And they give to it the following properties : — 

 its mass is wholly electromagnetic ; the motive forces are 

 electric forces ; and the laws of mechanics are to be deduced 

 from the laws of electromagnetics. 



Professor Abraham defines the electron as a rigid sphere 

 with an electric charge distributed uniformly throughout it 

 in concentric spherical shells. This charge is a constant, and 

 its volume and surface densities are homogeneous. Neglecting 

 the obscurity which occurs when we try to imagine what the 

 sphere is, on which the electricity is distributed, and what its 

 measure is if it be not mass, we follow him in the development 

 of his equations for energy and momentum. 



The total electric or potential energy is given by the 

 equation 



U 



32ttR 

 the magnetic or kinetic energy by 



T 



8 *l-8 J 



32ttR 



loo; 



/3 ° 1 



,], 



and the electromagnetic momentum by 



, ri _2T e* Tl + ,3 2 , 1 + 8 2 1 



I G ' - t = iessv L^sr log 1—8-J3J ' 



where e is the electric charge ; 



R, the radius of the sphere ; 

 v, the velocity of the electron ; 

 V, the velocity of light ; 



Since the electromagnetic mass factor of | G | is dependent 

 on the velocity, we may separate it into two components — a 

 " longitudinal " mass due to a change in linear velocity alone, 

 and a " transverse" mass due to a change in direction only. 

 The equation of motion thus becomes 



F = (m +m')f' + (m + m")f", 



where F is any external force ; 



m , the ponderable mass ; 

 m', the longitudinal electromagnetic mass ; 

 m", the transverse electromagnetic mass ; 

 f and/", the corresponding accelerations. 



