H. A. JBumstead — Lor entz-Fitz Gerald Hypothesis. 497 



The distances x, y, z are measured by standards at rest, £, 77, f, 

 by standards in motion. The distance between two points 

 (say on the a?-axis) when measured by the first is x 2 — x 1 ; when 



a* 9 — sr, 

 measured by the second, it is £„— £ = — . The length of 



the moving standards, when parallel to the axis of x are thus 

 -y/ 1 — /3 2 times the fixed standards ; when perpendicular to x, 

 they have the same length as the fixed standards. In order 

 therefore that Einstein's principle should hold, it is necessary 

 that all moving objects should suffer the Lorentz-FitzGerald 

 contraction. 



It is easy to compare the rates of the fixed and moving 

 clocks by considering two events whose difference in time as 

 measured by the fixed clocks is t 2 —i t ; as measured by amoving 

 clock whese coordinate is f, let the interval be r^ — r^ Then 



['. - '1 - v~ Oy-^JJ 



1 ' Vi-f 



But ar 2 = y/ 1 _ fi> £' — vt a and x l = ^/ 1 _ ^ g' — vt l 

 So that r 2 - r v = Vl-^ 2 ('. - *i)- 



Thus the moving clocks run slower than the fixed ones ; if a 

 clock at rest beats seconds, it must, when in motion, have a 



period of — =^=r seconds.* 



V 1 - § 2 



It is possible that the principle of relativity may come to 

 be regarded as one of the fundamental empirical laws of 

 Physics, occupying a position analogous to that of the Second 

 Law of Thermodynamics. It rests on a similar basis, in that 

 no deviations from it have been observed. Indeed the anal- 

 ogy may be made more complete by showing that the denial 

 of the principle leads to a third kind of perpetual motion, by 

 which the kinetic energy of any body might be exhausted and 

 the body be brought to rest with reference to the ether.f 

 There is however an enormous difference in the breadth of 

 the evidence on which the two principles rest. Yiolations of 

 the principle of relativity lead only to minute effects which 

 must be sought for in difficult and recondite experiments. 

 The fact remains however that, so far as our knowledge 

 extends, the principle holds ; the most reasonable course in 

 regard to it, and that which promises to be most fertile in 

 results, is to accept it provisionally and to develop its conse- 



* This relation between the time in fixed and moving systems was also 

 taken into account by Lorentz, by means of a variable which he calls local 

 time. Versnch einer Theorie, §31. 



\ Larmor in FitzGerald's Papers, p. 566. 



