128 Mr Glazebrook, A comparison of Maxwell's [Feb. 25, 



From these we .obtain by some simple well-known transfor- 

 mations, 



d 2 a 1 , , nns 



df = ^ a < 20 >- 



etc. 

 Thus the magnetic force is propagated as a wave with velocity 



and it can be shewn that the direction of the force is in the plane 

 of the wave. 



This is Helmholtz's result. 



According to Maxwell we have f, g, h as the components of 

 the current, so that instead of (19) we obtain 



dy d/3 d 2 ® . s 



= 4tt/ 



dy dz dxdt 



-X— - K d ( dF dn X 



dt dt\ dt dec 



■(21), 



and equations (20) become 



v=^« < 22) > 



so that the velocity of propagation of the disturbance is a / (— ™-) 



instead of 



47T/U.6 



This is the result which follows from Helmholtz's theory on 

 Maxwell's supposition as to the value of the current. 



The different expressions obtained on the two theories for the 

 velocity arise solely from the different assumptions made as to 

 what is a current in a dielectric, and are independent of the 

 value of the unknown constant k. Again, keeping to Helmholtz's 

 assumption as to the current, we have 



^X5-« 



(d?F 

 ^ e \aW + 



d 2 F d 2 £l dX) 



(23). 



dxdt dt 

 Differentiate with reference to x, y, and z and add, then 



y V = ^Tr/jbke 



d^J d( in _(dX dY dZ\ 

 dt dt \ \dx dy dz J 



.(24). 



