﻿500 Prof. E. V. Huntington on a New 



Further, the quantity 



_AB 



where AB = the distance over which the aviator passes in 

 the time-interval T', may be called the self-measured velocity 

 of the aeroplane with respect to the platform S, since the 

 time interval T' is measured, not by two clocks on the 

 platform S, but by the single clock on the aeroplane. 



The relation between the quantities u and n is as follows : 



If 



u = the observed velocity of the aeroplane 



and 

 then 



n — its self-measured velocity, 



where r = the observed rate of the clock on the aeroplane. 



Dopplerh Principle. 



11. Suppose an aviator is flying in a straight line away from a given 

 station A, and let light-signals, sent out from A at intervals of T seconds 

 as measured by the clock at A, overtake the aviator at intervals of 

 T seconds as measured by the clock on the aeroplane. Then we readily 

 find that 



T' = — — , or T' = J3-, 



•1-Z 1-1 



u c c 



where w=the observed velocity of the aviator, w = his self-measured 

 velocity, and r — ihe observed rate of bis clock. 



This equation reduces to the common form when r = l } and to the 

 form given by Einstein when r= sjl — (u/c) 2 . 



In all this discussion we have supposed that the platform S 

 is at rest in the aether. Wajiow turn to the consideration 

 of the case of a platform in motion through the aether. 



11. System in Uniform Motion through the .ZEther. 



12. We consider a platform S' moving with respect to our 

 stationary platform S with a constant observed velocity v in 

 a straight line, and we proceed to show that the observers on 

 the moving platform S', having established a central clock at 

 0', can lay out a permanent system of coordinates on S 7 by 



