president's address — SECTION A. 29 



Fitzgerald-Lorentz Hypothesis. — There is evidence of a varied 

 nature that the ether is stationary and not .entrained by moving 

 bodies, and further evidence that positive effects to be expected 

 from the earth's motion through that stationary ether do not exist. 

 Taken together, these statements require material bodies to con- 

 tract in length when set in motion. Stated more explicitly, the 

 Fitzgerald-Lorentz hypothesis is that a solid body of length L when 



at rest if given a velocity u contracts in the direction of motion to 

 1 " 



a length L (1 — ifi/v'^)'- or L\ 1 — /:?-, y being the velocity of light- 

 there is no change at right angles to the direction of movement- 

 The shrinkage is very small, and the orbital velocity of the earth 

 would only cause the very small change of 6 cms. in the earth's 

 diameter. 



Experimental Confirmation. — Lorentz has applied the con- 

 traction to electrons in motion, and predicted the effect of it 

 on their electro-magnetic mass. An electron which is a sphere 

 when at rest becomes an elipsoid when in motion with its short axis 

 in the direction of motion, and the axis at right angles unchanged. 

 Its author calls it a deformable electron, and has calculated its 

 transverse [mi) and longitudinal (m,) electro-magnetic mass at dif- 

 ferent velocities. They are 



1 



where m^ is the mass of the electron for very small speeds. For the 

 transverse mass we have : 



and the longitudinal mass increases even more rapidly. 



This variation of mass with velocity has been confirmed by the 

 refined experiments of Bucherer^ and Wolz^, who used /5 rays from 

 radium having velocities between '3 and -7 of that of light. 



As stated above, Einstein has laid down how length and time 

 are to be measured so that no positive effects are to be expected 

 from a convection of optical, electrical, or other apparatus relative 

 to the stationary ether. All moving bodies are subject to the 

 Fitzgerald-Lorentz contraction in the direction of motion ; and 

 Einstein shows that if clocks when in motion and at rest are synchro- 

 nised by light signals then they may be used to measure time 

 consistently with the principle of relativity. The moving clocks, 

 he shows, run slower than the stationary ones. When a clock is in 

 motion with a velocity u it beats with a period of 1/v/l — /3- 

 seconds, instead of the seconds it beats when at rest, whereB=ii/v. 



i. Ann.d. Phya. 1909. 



