554 Sir Oliver Lodge on the 



Now in the absence of gravitation the speed of light 

 must be simply c, or in other words, 



©'+(' 



d0y i r sin Odf V 



dt I 



;ind, since 7 = 1 when there is no gravitation, it follows 

 from (1) that, for light in empty space, ds = 0. 



But the essence of generalised relativity is that the 

 interval ds, whatever it may be, is invariant and independent 

 not only of choice of coordinate axes and of steady motion, 

 but independent of gravitational and all other acceleration 

 likewise ; hence, for light, ds is still zero even when 7 is 

 not equal to 1. 



So in general the velocity of light in a gravitational field 

 can be reckoned from the equation 



7 W + w + v^~ J =r ' • • (2) 



For a ray travelling along a radius vector, rdO &c being- 

 then zero, this gives 



dr 

 V= dt^ C; 

 while for a ray inclined at angle e to a radius vector, 



- (r cos e) 2 + (v si n e) 2 = ye 2 , 



v 7 sec e 



or - = /n ■ y~: 3) 



c v(l + 7taire) 



The reciprocal of this expression is the refractive index in 

 a gravitational field, which, to a first approximation, is 



_, 2GrM t n -i -, GrM . . • li 



a— L-\ 5- radially, and l-\ r. tanoentially. 



re "' ' re ° J 



Incidentally we can see that my elaborate experiment on the influence 

 of matter on ether in its neighbourhood (Phil. Trans. A. 1893 and 1897), 

 which gave a negative result when tested between a pair of whirling- 

 disks, would have failed to give a positive result even if the whirling 

 disks had been so absurdly massive as to cause a gravitational potential 

 comparable with that existing at the surface of the sun. For, in 

 accordance with Fizeaus experiment, light is carried forward with the 

 extra speed v(l— I//* 2 ), which, since the peripheral speed v was usually 

 150 metres a second in that experiment, gives a ratio to the velocitv of 

 light 



-B™, • - =4x10 12 . 

 He- c 



The smallest ratio that could have been observed in that apparatus 

 was the hundredth of a wave-length divided by the total effective 

 journey of the light, say 22 metres, — a ratio which is 3xl0 -10 , or 

 seventy-fold lacking in what would be necessary. 



