254 Dr. R. H. Jude on the Application of the 



Then instead of repeating the Rontgen events at intervals of 

 a day, ]H them be repeated at intervals of N m days. Thereby 

 the period of the Fourier's series becomes K^T; and the 

 radiation of the Rontgen experiment, repeated at these longer 

 intervals, is represented by the coexistence of series of pen- 

 dulous terms of which the periods are 



N m T, and its integer submultiples. 



If n be changed into n -f 1 or m into m + 1, these series 

 will include new terms. 



The limit of this process, when n and m are increased 

 without limit, is that the series can contain terms with 

 periodic times of any period, whether commensurable or in- 

 commensurable with T. 



And that it then represents the Rontgen event isolated — 

 i. e. without any repetition. 



I am, Gentlemen, with thanks, 



Yours faithfully, 



G. Johnstone Stoney. 



8 Upper Hornsey Rise, N 

 July 11, 1898. 



XXII. Note on the Application of the Gamma Function to an 

 Electrostatic Problem. By R. H. Jude, M.A., D.Sc* 



/HLERK-MAXWELL in his larger work on Electricity 

 v^ deals with the distribution of electricity on a pair of 

 freely charged spheres in contact, and denoting their potential 

 by V, their radii by a and b, and their respective charges by 

 Q a and Q$, establishes the relation 



Q« ^*=* a% ( . 



V %*i s{a + b){s(a + b)-a\' ' * * ' W 



with a similar expression for Qa. 



Except in the simple case where a and b are equal, the 

 summation indicated by (1) cannot be effected by ordinary 

 algebraic methods. But by means of the Gamma Function a 

 very neat result may be obtained which, so far as I am aware, 

 has not hitherto been noticed. Thus : — 

 — If n denote any quantity which is not negative, we have by 

 a well-known theorem 



Coininunicated by the Author. 



