128 L. Page — Energy of a Moving Electron. 



the path A A' tends to he deflected along the dotted line by 

 the magnetic field. To prevent this deflection a force K a 

 must be applied. Since K a is perpendicular to the direction 

 of motion, it will do no work. Similarly with K b . However, 

 the resultant of K a and K b and of all similar pairs of forces 

 will obviously have the same direction as the motion of the 

 center of the shell and will not be zero. While the resultant 

 force at any instant should equal the rate of change of momen- 

 tum, it is necessary, even in ordinary . dynamics, to consider 



Fig. 2. 



the component forces in finding the work done by a system of 

 forces acting on a deform able body. 



Summary. 



The energy of a moving electron has been calculated by 

 finding the work done in constructing the electron out of 

 charged shells which are shrunk down from infinite size to the 

 surface of the electron, maintaining throughout the process 

 the same velocity as the electron. The work done in contract- 

 ing these shells, or the potential energy of the electron, is 

 found to be equal to the electric energy of its field. The 

 work done in maintaining the velocity of the contracting shells 

 against the retardation of the field, or the kinetic energy of 

 the electron, is found to be equal to the magnetic energy of 

 the field, but to differ from the expression for the kinetic 

 energy peculiar to Einstein's relativity dynamics. 



The resultant force which must be applied to each contract- 

 ing shell to maintain its velocity is found to be equal to the 

 product of the velocity by the rate of change of the mutual 

 mass of shell and electron,' as would be expected from the gen- 

 eralized force equation. 



Sloane Physical Laboratory of Yale University, 

 New Haven, Conn., April, 1915. 



