Dynamics of the Electron. 87 



Taking the theorem as it is, the total effective force on the 

 sether has been obtained by integrating / over the whole 

 space perpendicular to the axis of motion of the electron, the 

 space being bounded on the inside by the surface of the 

 electron. The " Effective force " on the electron has been 

 taken to be equal and opposite to this force. 



I may be allowed to point out here that this procedure by 

 by no means confers substantiality upon the sether. It is a 

 fictitious creation, introduced for the sake of arriving at 

 a result which, from its very nature, can be attempted only 

 by indirect means. 



It is remarkable that none of the quantities \ X^O, &c. 



vanish in this case, as in the other theories. The " Effective " 

 force on an electron, instead of simply being the rate of change 

 of " Momentum" becomes the sum total of the time-rate of 



change of the quantity I -jrj- d£l plus the space-rates of 



changes of the quantities I -^- fd£l, X-^-^dQ,, ... 



These latter quantities involve "velocity" in the second 



^j- l d£l involves " velocity " in the first order, 



so that when the velocity is a small fraction of the velocity 

 of light, the theorem approximates to Newton's Second Law of 

 Motion. 



The rest-mass calculated on this basis is equivalent to 



2 e 2 



-x 2 , and as such coincides with the value obtained by 



Sir J. J. Thomson for slow-moving electrons, and with that 

 obtained by Lorentz and Einstein. The variation of mass 

 with velocity is determined by the Principle of Relativity 

 as in the theories of Lorentz and Einstein. 



In conclusion, I wish to express my thanks to my friend 

 and colleague Mr. Satyendra Nath Basu, M.Sc, for much 

 help and useful criticism. 



Calcutta University College of Science, 

 Physical Dept., July 10, 1917. 



