﻿Motion of the Lorentz Electron. 51 



ordinary mechanics and older electrodynamics so often 

 alluded to by present-day investigators of theories of the 

 atom, be after all due to neglect of proper precautions and 

 to unjustifiable usage of confessedly imperfect analytical 

 expressions as much as to defects in the fundamental prin- 

 ciples of the electron theory ? 



2. The equation of energy may be derived from the equa- 

 tion of motion by multiplying it scalarly by the velocitv v; 

 after a few simple algebraic transformations it is obtained in 

 the following form*: 



T-Q + R=rvP), (4) 



where f 1 l 



T= ^l^HP)"T ' ■ " * (5) 



2ce*(vv) 



**~ ^2_,^2J ( b ) 



rt ~ 3 \(c*-v 2 ) 2+ (c 2 -v 2 )*)' 



(V 



Here T denotes the kinetic energy of the electron and is 

 given by (5) in the usual form; (vF) gives the rate of 

 working of the mechanical force ; the remaining terms in 

 (4) are derived from the radiation pressure. Of these R is 

 essentially positive and denotes the irreversible rate of loss 

 of energy due to radiation ; the expression (7) is the well- 

 known one due to Lienard. On the other hand, Q repre- 

 sents a reversible rate of loss of energy ; hence — Q must be 

 regarded as work stored in the electron in virtue of its 

 acceleration, so that we may speak of it as acceleration 

 energy. Its existence is a direct consequence of a mechanical 

 theory of the aether f . 



3. In order to simplify the equations as much as possible 

 it is convenient to introduce a new system of units ; we shall 

 choose the 



new unit of length = 2e 2 /3c 2 m~ 1*83 . 10~ 13 cm., 

 ,, „ time = 2e 2 /3t ,3 m = 6*l . 10~ 24 sec, 



., „ velocity :=c*= 3 . 10 10 cm. /sec. 



„ force =3c 4 m 2 /2e 2 =4*3.10 6 dyne J 

 55 energy = c 2 «4 = 7-SS . 10~ 7 erg. 



The numerical values given in the last column have been 



* K R. pp. 17(>, 177. 

 t E, R. v. 0. 

 * E 2 



