500 H. A. Bumstead — Lorentz-Fitz Gerald Hypothesis. 



In order for these periods to be equal we must have 



w 9 = (1 - ft) m x 



which is the same relation as that between the longitudinal and 

 transverse masses of Lorentz's electron. That the variation 

 with the velocity of m 1 or m 2 for ordinary matter is also the 

 same as for Lorentz's electron may be shown in many ways ; 

 the following simple example will suffice for the purpose. 



Consider an elastic rod with its length perpendicular to the 

 motion of the earth and making longitudinal vibrations. If its 

 period of vibration is T we shall have 



Toe 



|/X 



where m i is the transverse mass of any particle and /c is the 

 coefficient of stretching of the rod. We must also have, by 

 Einstein's transformation, 



' T 



T - — 



Vi - p 



where T is the period of the rod when at rest.* 



The constant k depends on the intermolecular forces in the 

 direction of the length of the rod, that is perpendicular to the 

 earth's motion ; and these must vary with the velocity in the 

 same manner as electrical forces. If we have two point. charges 

 moving through the ether in a direction perpendicular to the 

 line joining them, the force between them is 



. E = E Vl-f 



where E is the force when they are at rest.f Thus we have 



K = k vr^? 



and 



i/ - -^— = i/ m ? l - 



whence 



It follows therefore from our hypothesis not only that all mass 

 is electromagnetic but also that it varies with the speed in the 

 specific manner of Lorentz's electron. 



* If this relation did not hold for any time-keeper, the velocity of light 

 measured in a moving system would be different from that measured in a 

 system at rest, and thus the principle of relativity would be violated. 



•f See below, p. 503. 



