﻿510 Prof. E. V. Huntington on a New 



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30. Definition. The absolute rate of a clock is its "observed 

 rate " (§ 10) taken with respect to a platform S which is at 

 rest in the aether. 



Now there are two assumptions which we can make in 

 regard to the behaviour of clocks in motion through the aether. 



If we assume that the absolute rate of a clock is not altered by 

 transportation throuali the cetlier, then a clock P which agreed 

 with clock A at the beginning of its journey from A to B will 

 continue to agree absolutely with clock A, and hence, by 

 Theorem 3, will not agree with the clock at B unless the 

 platform is at rest in the aether. Therefore by this experi- 

 ment the observers could detect the motion of the platform 

 through the aether, by noting the disagreement between the 

 transported clock and the clock at B. 



31. If, on the other hand, we make the following assump- 

 tion concerning the rate of a moving clock, then this 

 possibility will be removed, and the Principle of Relativity 

 will again be satisfied : 



Assumption B. The "absolute rate" of a clock which is 

 moving through the cether with a constant velocity v is less than 

 the absolute rate of the same clock when at rest, in the ratio 



32. If this assumption is true, we have the following 

 theorem, in which 8' is any platform moving with con- 

 stant velocity through the aether, and on which a system 

 of coordinates has been laid out by the method of light- 

 signals : 



Theorem 9. If assumption B is true, the u observed rate " 

 of a clock which is moving over a platform S' with observed 

 velocity u' is less than the observed rate of the same clock when 

 at rest with respect to that platform — the ratio of the rates 

 being 



'VT-(u f ic) 2 ; 



and this result is entirely independent of the constant velocity v 

 with which the platform is moving through the aether. 



This theorem 9 is another characteristic proposition of the 

 Theory of Relativity. 



33. It should be noticed that Assumptions A and B are 

 not required for the proof of the transformation equations in 

 Theorem 1; they are required only if we wish to preserve 

 the Principle of Relativity — that is, if we wish to make it 

 impossible for the observers on our system S' to detect their 



