﻿706 



Prof. S. R. Milner on 



the lines, or in other words in terms of the infinitesimal 

 rotations which are given to the set of axes as the lines are 

 traced out. Although a precisely similar method can be 

 applied to the electromagnetic field, it is not at first sight 

 clear how the axes are to be oriented at any given point 

 which may be chosen as a starting point. In the electro- 

 magnetic field the directions of the electric and magnetic 

 forces are in general neither along the same line nor at right 

 angles to each other, and there is no more justification for 

 putting the ^-axis along either of these lines than along the 

 other. It is, however, always possible to choose the axes of 

 x y and z at any point such that their directions enjoy a 

 unique symmetry with respect to e and h, in that no pre- 

 dominance is given to either over the other. To effect this 

 choose them so that the following equations are satisfied : — 



e z = 0, 7^=0, e x e y + li x liy=0. 



(i) 



This makes z perpendicular to the plane in which e and h lie 

 at the point, x and y lie in it, their directions, shown in 

 fig. 1, being such as to make the dotted rectangles equal 

 in area. 



. Fig. 1. 



Considering the field as a four-dimensional entity there is 

 the time nxis to be oriented also. This lies at right angles 

 to the hyperplane, or instantaneous space in which the axes 

 of x y and z are drawn. The consideration of the field in 

 hyperspace is greatly simplified by adopting the formal 

 representation of it introduced by Minkowski in which the 

 time axis t is replaced by an "imaginary time" axis l = ict, 

 or, taking c=l, I — it. The Minkowski world substitutes a 



