﻿00 Dr. W. F. G. Swarm on the 



certainly satisfy (1). Let ns imagine them expressed as 

 functions of d\ y. z, t, and let us denote them by/', g\ h', a', 

 b', c . Now let us imagine another electron moving in some 

 orbit s 2} the first being absent, and let the field of the electron 

 when expressed in terms of x,y, ~, t, be denoted by/", </', h" 9 

 a", b" ', c" . Now it is an algebraical fact that if the functions 

 /, g', 1L a\ V, c', and /", </', A", a", b", c", satisfy (1), the 

 functions / +f", ff' + ff", h' + h", a' + a", &c. also satisfy (1), 

 which means, that if the two electrons are brought into each 

 other's vicinity _, we can imagine them to describe orbits of 

 the same shape as those which they described when alone, 

 and we shall obtain a solution of the electromagnetic equa- 

 tions corresponding to this case by simply adding the fields 

 which the electrons would produce if alone. We have to 

 make no special adjustments in the fields in order to keep 

 the flux round each electron constant, because the surface 

 integral of the setherial displacement due to one electron 

 gives a zero effect when integrated round the other. This 

 solution would of course mean that the two electrons were 

 producing no action on each other. We may on this line of 

 argument imagine any number of electrons moving about in 

 the vicinity of each other, and if we add the fields corres- 

 ponding to each electron when moving in its present manner, 

 but out of the vicinity of the others, we obtain a solution 

 satisfying the electromagnetic equations, each electron 

 apparently moving independently and uninfluenced by the 

 others. A simpler example is afforded by considering two 

 electrons moving with constant velocity v along the axis of «r, 

 and separated by a fixed distance. If we simply add the 

 known fields corresponding to these two elections when 

 moving separately, we shall obtain a solution of the electro- 

 magnetic equations which will be consistent with the electrons 

 moving in the manner stated for all time, and yet we know 

 that they would not do so, they would repel each other. 



These examples suffice to show that it is not sufficient to 

 say that because a system satisfies the electromagnetic equa- 

 tions, it is a system which can actually exist. Of course, if 

 at any instant we are given, at all points, the actual field of 

 a system which really can exist, the electromagnetic equations 

 will determine for all rime the subsequent and previous history 

 of the system, for the time rates of change of /', </, h are, at 

 each instant, given in terms of the spacial derivatives of 

 a, 6, c, and an analogous remark applies to the time rates of 

 change of a. b, c. If we were to start from any actually 

 existing system of electronic motions, and try to separate an 

 electron out and cause it to move by itself in the path denoted 



