EXPERIMENTS ON ETHER-DRIFT 33 



A further attempt at measuring any deformation caused by- 

 motion through the ether was the result of a suggestion of 

 Prof. Trouton some years ago. It is being carried out by 

 him and the writer, but is now so near completion that, in all 

 probability, the results will have been published by the time 

 this article appears. It will, therefore, not be amiss to include 

 a short description of it. The principle underlying the investi- 

 gation is a very simple one, and in no way suggests the 

 extraordinary difficulties attending the practical measurement. 

 It is well known that the electrical resistance of a wire can be 

 measured with great accuracy, and, provided such resistance 

 depends upon the direction of ether-drift, its measurements 

 should be a suitable means of testing the question. For sim- 

 plicity, imagine a straight wire of resistance R, length /, and 

 cross-sectional area A, occupying a position with its length 

 perpendicular to the drift of the ether. If p be its specific 

 resistance, we have — 



Now suppose the wire turned through a right angle. Upon 

 the contraction hypothesis, the length will now be reduced by 



an amount | / (yj , or, writing /3 2 for ( y ) > the length is reduced 



by | / y# 2 . One diameter of the wire will remain perpendicular 

 to the drift, and will therefore be unaltered by the rotation ; the 

 other, originally parallel to the drift, will now be perpendicular 

 to it and therefore an increase in the ratio (1 + \ (3 2 ) : 1 is to be 

 expected. This will increase the area A by an amount \ A ft 2 . 

 Now if the specific resistance of the wire does not depend on 

 the motion through the ether, the new resistance (R 1 ) of the wire 

 will be 



R1 - p^rrm - R ( J - n* 



neglecting powers of /3 higher than the second. That is to say, 

 the resistance of the wire parallel to the drift is to be expected 

 to be less than when perpendicular in the ratio (1 — /3 2 ) : 1. If, 

 then, so small a difference of resistance can be detected, a m ans 

 is thus afforded of testing for the Fitzgerald-Lorentz shrin age, 

 and, consequently, for the magnitude and direction of ether-drift. 

 For this investigation, the method in use is the Wheatstone 

 bridge method for the comparison of resistances. Four coils of 



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