432 Dr. T. J. I'a. Bromwich on the 



the length on the right-hand side of equation (1) is found 

 to be approximately 1*47 kilometres. 



Accordingly, if we suppose that the units are chosen so 

 that the two fundamental constants <y and c are both ex- 

 pressed by unity, it follows that the mass of the sun is equal 

 to about 1*47 kilometres — an apparently mystical result. 



This calculation is given, in substance, in Prof. A. S. 

 Eddington's Report on Relativity *, but it seems to have 

 escaped notice to some extent. 



I am, Gentlemen, 



St. John's College, Your obedient Servant, 



Cambridge. T. J. I'A. BrOMWICH, 



June 20th, 1921. Praelector in Mathematics. 



XLVIII. The Problem of Random Flights. By T. J. I'a. 

 Bromwich, Sc.D., F.R.S., Fellow and Prcelector in 



Mathematics, St. John's College, Cambridge f . 



STUDENTS of the late Lord Rayleigh's papers will 

 recollect that he occupied himself with the above topic 

 on more than one occasion, and one of his last papers % 

 stimulated my interest in the subject. I have already 

 published a short note § dealing with the extension of 

 Bernoulli's theorem which is required in the earlier part 

 of the investigation, and I had hoped to have communicated 

 to Lord Rayleigh a method (suggested by the use of 

 Heaviside's operators) for shortening the algebra required 

 in the later part. Unfortunately our correspondence was 

 terminated by Lord Rayleigh's fatal illness, and I have been 

 delayed so far from publishing my account, which will be 

 found below. 



1. The problem of Random Flights in three 

 dimensions. 



For various reasons the discussion of the problem in three 

 dimensions is easier than in two dimensions, just as the 

 problem of wave-propagation in two dimensions is the more 

 difficult. 



* See the footnote on p. 27 ; it may be useful, perhaps, to point out 

 that a more exact form of equation (1) is really 

 y(S + E)/c 2 = 47r'V/(cT) 2 , 



where 2a is the major-axis of the earth's orbit and E is the earth's mass. 

 t Communicated bv the Author, 

 t Phil. Mag. (6) vol. xxxvii. p. 321 (1919). 

 § Phil. Mag. (6) vol. xxxviii. p. 231 (1919). 



