254 Mr. L. A. Pars on 



must certainly hold if we are to maintain a principle of 

 relativity: but our object at present is to show that the 

 transformation follows inevitably from far more slender 

 assumptions. The invariance of Maxwell's Equations is 

 then easily verified, and the method thus affords valuable 

 evidence in support of the theory. 



We first assume that the electromagnetic components in 

 B's system, E. r ', Ey', E z ', H/, Hy', H z ', are linear (functions- 

 of E x , Ey, E z , H z , Hy, H z , the corresponding components in 

 A's system. But this admits of considerable simplification. 

 The hypothesis that the space is isotropic leads to the con- 

 clusion that the equations of transformation must remain 

 unchanged in form when we change the signs of Ey, E z ,. 

 H y , H z and of the corresponding accented components, but 

 not of E XJ H z : for this can be effected by turning the 

 trihedrals of reference through two right angles about 

 the common axis of x. Again, the equations do not change 

 if we change Ey, E z , H y , H z into E z , — Ey, H z , — H y , effected 

 by a rotation through one right angle. By means of these 

 conditions the equations of transformation are reduced to the 

 forms : 



Ej/ ■=■«!! Ex 4-auHj. , . 



H x ' = a 41 E z -Y a. A/ Jl x -i 



( E y = # 22 Ey + a n E z + a 25 Hy + a 26 H z 

 E z ' — — a 23 E y + a 22 E z — « 26 H^ + u 25 H z 

 H y ' = a 52 Ey + a 5 3 E z + a 55 Hy + a 56 H z 



,H«' = — a 53 Ey + a 52 E z — « 56 Hy -I- «; ?5 H z . 



But E/ cannot depend on H x , so the first of equations (10) 

 reduces to E x / = a(n)E x , whence as before E X ' = E X . And 

 similarly H r ' = H z . 



The equations (11) are most simply treated by means of 

 the substitution 



Ey + zE*=P 



(11) 



H y + zH, = Q, 



Ey, E 2 , Hy, H z being real. For with this substitution the 

 equations reduce to 



P' = a(i*)P + £(u)Q 



Q'= 7 (tt)P + 8(u)Q; 



