292 



Mr R. F. Gwyther, On the solution of the [May 25, 



polarised wave the disturbance would be in the direction of 

 the magnetic force. To make this agree with Maxwell's expres- 

 sions for the energies we must give a special value to v, thus 



kinetic energy = ^ {a 2 + /3* + y 2 }, 



1 n 



putting - 2 = — , we get 



kinetic energy 



2z/ 

 8ttV 



^ 



ir + f + h 2 }; 





•(21), 



which agree with Maxwell's expressions for the Electro-kinetic and 

 Electro-static energies. 



And these have been shewn to be equal. 



From the formulas from which this was proved it is seen that 

 the name potential energy is not quite applicable to the electro- 

 static energy, and that the whole energy must consist of the sum 

 of the two energies. 



Lastly, from the equations 



df d?% dr, d 2 % d£ d*% 



dt ' dxdt dt ' dydt dt ' dzdt 



— _ P M— P _1__ P 



~ dac m + dy xv + dz xz ' 

 etc., 



omitting, on the ground that ours is one of the simpler cases 

 of electro-magnetic action, the fact that each side vanishes in- 

 dependently, we get 



d% (dj; d%\ dr) /dr; d^ 

 dt \dz dx) dt \dx dyj 



~ dx r ™ 2 \{dt + {dt) + {dt) 



+ dy xy+ dz r ™ 



etc., 

 or 4nr (vy — <d/3) 



= -^ { a 2 -i(a 2 + ^ + 7 2 )} + |(«/3) + | ; ( .,,. 



dx 

 etc. 



dz 



.(22), 



