On a Gravitational Problem* 91 



and the change in resistance due to twisting tends to 

 become independent of both the frequency and the radius 

 of the wire, whereas the change in self-induction tends 

 to vanish. 



For the intermediate case, in which rfl lies between the 

 limits of about 10 and 70, the formula? (36, 37) must be used, 

 provided that a satisfies the proper condition. These formulae 

 require the functions P and Q when x lies between 2 and 7. 



In a paper recently presented to the Physical Society *, 

 Mr. H. G. Savidge has given tables of these functions 

 suitable for the case in question, together with graphs of the 

 functions — j?Q, xF of (39). The formulae (36), (37) are 

 therefore rendered sufficient for practical use. 



VII. Note on a Gravitational Problem. 

 By C. V. Burton, B.Scf 



1. "VX7TTH0UT actual loss of generality, the question 

 n here considered may be stated as follows : — If the 

 action of gravity were intermittent in character, the mutual 

 attraction of any tiro bodies fluctuating between zero and twice 

 its mean value, how long could, the period of the fluctuation be 

 tvithout giving rise to observable periodic effects? At a first 

 glance we might be tempted to reply that the period could 

 only be a very small fraction of a second ; but though this 

 answer would be justified if the earth were perfectly rigid, 

 the yielding of the earth to pressure and to shearing-stress 

 completely changes the aspect of the problem, and the results 

 obtained are so different from what might have been hastily 

 assumed, that a brief indication of them may possess some 

 interest. 



2. Let us suppose that the gravitation-constant G repre- 

 sents merely the mean value of G(l-f-A^), where A is a 

 numerical constant ; so that, at any time t, the attraction 

 between masses m, m! at a distance r apart is 



G(1 + A^>0"^7>' L> . 



For the sake of simplicity the earth will now be regarded as 

 spherical and sensibly homogeneous ; and accordingly the 

 intensity of the gravitative field at any point of the surface at 

 time t will be 



<7(1-KV>9; (1) 



* Supra, p. 49. 



t Communicated by the Physical Society : read November 26, 1909. 



