Propagation of Light in a Gravitational Held, 589 



seemed of great interest to investigate this matter experi- 

 mentally. 



Consider two stations distant L apart on the same level. 

 Let light rectilinearly polarized at 45° to the vertical be 

 projected from the sending station. Then the phase dif- 

 ference e of the vertical and horizontal components at the 

 observing station will be given by 



eT = L(-l-A), 



where T is the period of the light in question ; or if \ = cT 

 be the normal wave-length and c v and Ch differ but little 

 .from c, 



L c v — c h /7 . 



£ =X-—c- (7) ' 



At the receiving station, therefore, we shall have elliptically 

 polarized light, the principal axes of the ellipse making an 

 angle of 45° with the vertical, and the coefficient of ellipticity, 

 or ratio of minor to major axis being given by 



h /l— cos 27re , ON 



K—~=\/~ — — - — lb) 



a V 1 + cos lire 



gle this can be 

 . /2ttV v* 



«r(-T-J =' 



If 27T6 is a small angle this can be written 



7T€. 



Thus by (7) 



G v — C h K.X 



(9) 



C 7rL 



This formula enables us to evaluate the difference of the 

 two velocities, if any, by measuring the ellipticity /c, the 

 wave-length X and the distance L being known. Owing to 

 the ease with which L can be made very great in comparison 

 with X, an exceptionally high degree of precision can be 

 attained even if it be difficult to measure small ellipticities k. 



Let us now pass to the description of the experiments. 

 For measuring optical ellipticity it is natural to turn first to 

 the Babinet compensator, although it did not appear likely that 

 the produced effect, if any, would be sufficiently great to be 

 detected by means of this instrument. Preliminary experi- 

 ments quickly established this view. Light, originally plane 

 polarized at 45° to the vertical by means of a nicol, was 

 examined at various distances up to 40 metres with a Babinet 

 compensator, and no shift of the bands was observable. It 

 was estimated that a shift of , perhaps, one-twentieth of a band 

 could be detected with certainty, and these observations 



