140 PHYSICS OF THE ELECTRON 



ternal ether; if we seek, then, what is, in the case of uniform trans- 

 lation, the form that the electron would spontaneously take in order 

 to satisfy the condition of zero variation, we find precisely the oblate 

 ellipsoidal form assumed by Lorentz, with this difference, that the 

 equatorial diameter increases with the velocity instead of remaining 

 constant, as Lorentz considers it; this constancy implies a diminution 

 of the volume as the velocity increases. The equations which express 

 in this case the variation of the longitudinal and transverse mass 

 with the velocity are different from those of Abraham and Lorentz, 

 although giving always an indefinite increase of the two masses as 

 the velocity approaches that of light. 



TTb 



The equations thus obtained for the ratio of the transverse mass 



ra Q 



m, the only one so far accessible to experiment, to the mass m for 



v 

 very small velocities, as a function of the ratio /?=7 7 . of the velocity 



of the electron to that of light are: 

 (1) Invariable spherical electron, 



3 



(Equatorial diameter constant - - = (1 /? 2 ) 

 m o 

 W) _ I/ 



Volume constant - = (1 /? 2 ) 



tn ' 



m 



(28) Comparison. The researches of Kaufmann are not yet exact 

 enough to determine which of these equations represents most nearly 

 the experimental variation of the ratio ; with the velocity. In 



order to make the comparison, I have used a process similar to that 

 of Kaufmann, who eliminated the two electric and magnetic fields used 

 to deviate the /? rays, seeking to obtain the best concordance pos- 

 sible between the experimental variation of ^ and the theoretical 

 variation calculated on the hypothesis that the mass is entirely 

 electromagnetic. 



In order to make this elimination, I draw the two experimental and 

 theoretical curves representing ^ as a function of /?, on logarithmic 

 coordinates, and seek for what relative positions of the curves we ob- 

 tain the best correspondence. The results are given for the three 

 theoretical equations and the same series of experimental values. 

 The experimental points corresponding to four different series are 

 given by Kaufmann, and we see that they correspond equally well 

 with the three theoretical curves. 



