94 Dr. L. Silberstein on General Relativity 



These values show that the conductivity of sea-water for all 

 frequencies as used in wireless telegraphy is very nearly 

 equal to the value of the same for steady currents to within 

 less than half a percent., the small differences obtained 

 most probably being due to a small capacity effect of parts 

 of the shunt on other parts. 



A calculation of the true direct current conductivity from 

 the resistance and the dimensions of the tube yielded the 

 value 



•0377 H" 1 per centimetre cube 

 at 12°' 5 C. corresponding to 



o-=3*77 . 10~ n electromagnetic unit. 



As the conductivity varies very much with the temperature 

 and the origin of the sample, a value of a between 1 and 

 5 . 10 -11 is therefore appropriate to form the numerical basis 

 for the theory of propagation of electromagnetic waves over 

 the surface of the sea. 



In conclusion I wish to thank Sir J. J. Thomson for his 

 valuable advice and kindness in putting at my disposal the 

 instruments of the laboratory. 



Cavendish Laboratory, 

 Cambridge. 



VII. General Relativity without the Equivalence Hypothesis. 

 By L. Silberstein, Ph.D., Lecturer in Natural Philosophy 

 at the University of Rome *. 



1. Purpose and scope of the present inquiry. 



fTTHE generalized theory of relativity as proposed by 

 J_ Einstein in 1912, and since that time repeatedly modi- 

 fied by himself and by his followers, has one very strong 

 point, the requirement of general covariance of all physical 

 laws, and one weak point, to wit, the originally so-called 

 "equivalence hypothesis" which places gravitation on an 

 entirely exceptional and privileged footing, bringing it into 

 intimate connexion with the fundamental tensor which 

 appears in the line-element of the world. I propose to 

 retain the strong point and to reject the weak one, and thus 

 to develop the° implications of the general principle of 

 relativity without the equivalence hypothesis, in fact, without 

 privileging gravitation at all. This is the purpose of the 

 * Communicated by the Author. 



