354: C. Barus — Contractions of Fitzgerald- Lor entz Effect. 



dh/h=-p/4, dv/v.= + /3 a /4, db/b= -/J 2 / 4 

 These in equation (3) give, apart from signs, 

 da= -/T/2, A]¥=p 2 fi;il, 

 Using the constants of the apparatus specified, 



A ^ = io~°xio-' = 1(r , cm 



10~ 2 



Hence even in the case of the above only moderately sensitive 

 pendulum about three interference rings should vanish between 

 the positions h, v, b and h f , v\ b'. 



Contractions of the pendulum itself are negligible, as these 

 merely displace the center of gravity in its own plane and are 

 otherwise not amplified. All contractions of the linear inter- 

 ferometers are compensated. Tidal forces have approximately 

 the same value in the two positions and may be allowed for. 

 Unfortunately the earth (radius r) itself contracts under the 

 same relations, to an oblate spheroid with its minor axis 



r Vl — /3 2 in the direction of motion ; and as the direction of 

 gravity will probably follow the displacement, dd, of the 

 radius in latitude 23*5°, the effect on the pendulum will be 

 neutralized. The A, v, b triangle, in other words, is a part of 

 the earth. Specifically in fig. 2, the triangle h, v, b moves 

 inward a distance s and it is easily shown that the angle 

 between p and q, the new radius vector, is da 1 = dd = # a /4. 

 Similarly the angle between two tangents is here also 

 d(f=/3 2 /4:, both being decrements. Hence since nothing 

 is changed at a' in the A', v', b' triangle, da = 2d0 = /3 2 /2, 

 agreeing with the above value. Thus the center of gravity of 

 the horizontal pendulum lies in the normal plane whose trace 

 is q and the displacement from^? to q would not be recognized. 

 Similarly if the horizontal pendulum were attached to a 

 massive vertical pendulum (rigid plumb line) the displacement 

 dd = /3 2 /4 would entirely escape detection. 



Nevertheless it has seemed to me worth while to develop a 

 method which, potentially at least, would be able to measure 

 the small displacements in question, as there are other non- 

 compensated micro-displacements of the earth's diameter, in 

 relation to which the method would be applicable. 



Brown University, Providence, R. I. 



