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



sions perpendicular to the motion remaining the same. If m 1 

 and m 2 are its longitudinal and transverse masses, and m the 

 mass for infinitesimal velocities, we shall have 



m> — m, 



m„ = m, 



(i-F)i 



V 1-/3 2 



where, for brevity, /3 has been put for ^. With this electron 



Lorentz has shown that no optical or electrical effects of motion 

 through the ether can be detected. 



The subject has been approached from a different stand- 

 point, and treated in a very interesting and instructive manner 

 by Einstein.* His fundamental postulate amounts to a denial 

 that it is possible to observe any effects of uniform con- 

 vection through the ether in which all the bodies concerned 

 (including the observer) take part. This he calls the Principle 

 of Relativity ; the significance of the name is that only relative 

 motion of one portion of matter with respect to another, or 

 of one electrical charge with respect to another, can produce 

 any observable effect ; uniform motion, relative to the ether 

 alone, becomes as impotent, if not as meaningless, as absolute 

 motion. 



Einstein considers two sets of coordinate axes, one at rest in 

 the ether (a?, y, s), while the other moves with the constant 

 velocity v in the x direction (f, 77, f). He defines carefully 

 the meaning of " time " (t in the fixed system, t in the moving 

 system) by means of clocks distributed at various points, some 

 at rest with the fixed axes, and some moving with the moving 

 axes. The clocks are supposed to be synchronized by light 

 signals. By kinematic considerations he shows that, in order 

 for the principle of relativity to hold, we must have, 



£ = 



VT~- 



? 



(X- 



-vt) 





1 = 



y 











£ = 



2 













1 





(*- 



V 



' V 7 ' 



x) 











V 1- 



P' 



V 



where, as before, (3 = — - • 



V 



* Ann. d. Phys., xvii, p. 891, 1905. 



