On the Dynamics of the Electron. 77 



electron, — the authors of many of these theories have not 

 been able to rid themselves o£ the preconceived ideas of 

 classical mechanics. I shall, in the first place, explain my 

 own method, point out the characteristic features of my 

 theory, and then compare it with other theories. 



The equations of motion of a material particle are derived 

 from Newton's Second Law of Motion — rate of change of 

 momentum is proportional to the force applied. Combining 

 this principle with the principle of constancy of mass during 

 motion, we obtain 



m 



d?x 



alt 2 



X, 



dt 2 



d 2 * 



= Y, 



d 2 Z 



d 2 z 

 m df 2=Z ' 



wi-7-s are known as the com- 

 at 2 



The terms m^j , mjf, 



ponents of the "Effective Force," and the law may be 

 expressed by saying that the u Effective Force " is equiva- 

 lent to the " Impressed Force." 



In the case of the Electron, we hold to the axiom that the 

 " Effective force is equivalent to the Impressed force." No 

 prima facie reason can be given for the introduction of this 

 hypothesis, just as in the case of the motion of material 

 bodies. It is to be justified by its success in dealing with 

 the problem at hand. 



The Impressed force on the electron can be easily calcu- 

 lated with the aid of Lorentz's Theorem of ponderomotive 

 force. If (X, Y, Z) be the components of the electric field, 

 (L, M, N) be the components of the magnetic field at any 

 point, and p be the density of electricity, the components of 

 the force per unit volume at the point are 



/s=.p[x+l(> 2 N-* s M)] 

 /^[Y+i^L-^N)] 



/^[Z + ^M-^L)] 



(»!, v 2 , v 3 ) being the components of the velocity with which 

 the charge moves. 



