168 Dr. L. Silberstein on the recent Eclipse Results 



answer is: On experience. For, clearly, we cannot deduce 

 a relation, which is essentially electro-mechanical, from me- 

 chanical principles alone, or from electromagnetism alone. 

 Nor can we imitate the usual dispersion theory (which makes 

 use of both kinds of principles), for we are interested in 

 those portions of the aether in which there are no atoms and 

 no electrons. 



In short, as was announced in section 3, let us write down 

 the required relation by utilizing the observational result 

 obtained by the Eclipse Expedition. In other words, let us 

 see what that relation must be like in order to give the 

 observed effect. 



■ Now, if we disregard the small discrepancies (which may 

 he either due to accidental errors or, perhaps, due to a 

 superposed slight ordinary refraction), the observed total 

 deflexions of the rays passing near the Sun are represented 

 by Einstein's formula (quite apart from his theory) 



r c 2 



where r is the minimum distance of the (undeflected) ray 

 from the Sun's centre, and it can easily be shown that such 

 will be the case* if the refractive index n = c/c' at an}^ 

 distance r>R from the Sun's centre be determined by 



n 2 = 1 -+ -rr , 



cr 



or, denoting the potential by 12, and generalizing to any 

 distribution of gravitational matter, 



n>=l+f. ...... (9) 



[This, in fact, is the formula which would follow at once 

 from Einstein's approximate line-element 



20 90 



ds* = W(l - ~) - (dx* + df + dz 2 ) (1 + ==), 



for a "static "field.] 



In order to obtain the required relation, that is to say the 

 assumption to be made on the optical behaviour of the con- 

 densed aether, it is enough to combine equation (9) with 

 our last equation (8), which gives 



if. 



dlogS (10) 



* Approximately, that is, for small Ad, and consequently for 

 refractive index but little differing from unity. 



