586 Dr. A. 0. Rankine and Dr. L. Silberstein on 



This formula for the dissipation will, however, be correct 

 only if the Osborne Reynolds criterion is satisfied. If h 

 denote the vertical dimensions of the motion and v the 

 viscosity, this criterion is that uh/v shall be greater than 

 1000. For semidiurnal motions in a viscous medium, 

 ]t 2 = vJco i so that the criterion becomes a\(ya>)* or 800. Thus 

 it is not satisfied in general, though it probably holds in 

 many places. Where it fails, the dissipation is due to 

 ordinary viscosity and not to turbulence, and is readily 

 estimated to be of order 1*2 x 10" 3 erg per sq. cm. per 

 second or 0*6 X 10 16 ergs per second in all. 



Thus friction in mid-ocean in any case is of the order of 

 10 16 ergs per second ; whereas Gr. I. Taylor finds that the 

 actual dissipation in the Irish Sea is about 3 x 10 17 ergs per 

 second, and I find that the dissipation required to account 

 for the moon's secular acceleration is about 1*4 x 10 19 ergs 

 per second. Thus the influence of tides in the open ocean 

 on the moon is insignificant in comparison with that of the 

 partly enclosed seas, and has no observable astronomical 

 effect. 



LVI. Propagation of Light in a Gravitational Field. 

 By A. O. Rankine, I).Sc n and L. Silberstein, Ph.D.* 



AS far as we know it has always been taken for granted, 

 without any experimental support, that the velocity 

 of light in a gravitational field, such as that of the earth, is 

 independent of the orientation of the light oscillations. It 

 seemed to us desirable to investigate, with as much precision 

 as possible, whether, and how far, this is true; whether, for 

 instance, the velocity of propagation c h of horizontal oscil- 

 lations is, or is not, appreciably different* from c v , the 

 velocity of propagation of vertical oscillations. Such an 

 enterprise was the more attractive as a slab of space, so to 

 speak, of considerable thickness is always readily available 

 thus promising the possibility of reaching a very high degree 

 of exactness. 



Before passing on to the description of our experiments 

 and their simple theory, it may be well to notice that 

 according to Einstein's generalized theory of relativity and 

 gravitation, we should have, rigorously, c v = c h , more 

 generally a velocity of propagation rigorously independent 

 of the direction of the light vector relatively to the lines o£ 

 force in any gravitational field. In fact, by Einstein's theory, 



* Communicated by the Authors. 



