﻿720 Mr. A. Bramley on Radiation. 



Summary. 



When viewed in a suitable hyperplane, i. e., when suitably 

 transformed, the electric and magnetic forces at any point 

 of the general electromagnetic field can be made to coincide 

 in direction. This direction determines an electromagnetic 

 line, continuous through hyperspace, from a set of which an 

 electromagnetic tube can be constructed, Four such tubes, 

 mutually perpendicular, can be constructed containing any 

 point, and each is characterized by the constancy of the flux 

 of the quantity 



R = {(e 2 -h 2 ) 2 + 4(eh) 2 }i 



over its cross section. A complementary theorem for each 

 tube relating to the twist of its generating lines determines 

 the internal constitution of R as expressed by the ratio of 

 the magnetic to the electric force present in the compound 

 vector. R is shown to be a u five- vector/' i. e., a six-vector 

 with its two parts equal ; it is a function of position asso- 

 ciated with two absolutely orthogonal planes uniquely fixed 

 at each point of the four-dimensional field. 



The University, Sheffield, 

 29th June, 1922. 



LXIL Radiation. By Arthur Bramley. 

 To the Editors of the Philosophical Magazine. 



Gentlemen, — 



IN the following discussion we shall make use of the idea 

 that energy possesses mass, a principle which has been 

 so fruitful in explaining the behaviour of light-rays in a 

 gravitational field and which is a natural consequence of the 

 electromagnetic theory. 



If energy possesses mass, then the fundamental laws of 

 mechanics ought to apply to it. Following this idea, we 

 shall attempt to show how the laws of radiation are related 

 to the fundamental principles of mechanics and electro- 

 dynamics. 



The values of the potentials are : 



„ TT 1 3 2 U V 



H=rotU. 



