﻿■88 Dr. W. F. G. Swann on the 



We know that these represent the field of an electron of 

 strength e, moving along the axis of x with velocity v. 

 Suppose, however, that we did not know this ; we should 

 find by direct differentiation that these functions satisfied (1), 

 and we should find that 



K + ^l + ^L 



~dx ^ B~ r _ '.; 



was zero at all points in space, except where the relation 

 a = vt, ?/ = z = held, in which case it would become infinite, 

 tellingus that there was an electron moving along the axis 

 of x with velocity v *. It is easy to see how the same line of 

 argument applies to more complicated systems. By trans- 

 forming the electromagnetic equations to moving axes, Sir 

 Joseph Larmor shows (' Mther and Matter,' Chapter xi.J,, 

 that if /i,#!, /*!, a l9 &>, c 1? expressed as functions of ai u y u z^ t u 

 represent the spontaneous changes of an electromagnetic 

 system S referred to axes at rest in the pettier, the same 

 functions of 



will represent 



ewjV«V, g- £^c, h+ -^b, e'»a, b + 4*rh, c- irrfy 



where /, g, A, a, b, c are the setherial displacement and 

 magnetic vectors for another electromagnetic system S ]? and 

 a/, ?/', z\ t 1 are referred to axes moving in the x direction 

 with velocity r. By an electromagnetic system, we mean a 

 system which satisfies the electromagnetic scheme at all points 

 in space, except at the singularities. 



If corresponding points and times in the two systems above 

 are related by the equations 



Oi, yi, ^) = (eVV, y\ z'), t^e-i'H'-e^v^, 



the absolute correspondence of the singularities in the two 



* It seems to me, that it is easier to take the condition/, g, or h eqnal 

 to infinity as the criterion for the determination of the position of a. 



singularity,, rather than the condition that ~ + ~- - + *~ shall not be 



di- by ds 

 zero, for /, g, h must each become infinite at a singularity, and they 

 cannot become infinite elsewhere. The criterion f=oo immediately leads 

 to the determination of the motion of the singularity in the example 

 quoted above, and moreover it immediately leads to the absolute 

 correspondence ci" the singularities in the two systems S and S u to any 

 order of vC, 



