Vibrations of Light with Electrical Currents. 299 



.#-axis fulfil just the very conditions which are deduced from 

 the theory of light for this element; and since the direction of 

 the axis is arbitrarily chosen, the same must hold good for all 

 elements of the surface. 



Thus, as, assuming these limiting conditions, the integrals to 

 the surface disappear, by the above calculation, from the first 

 equation (B) there results 



d /da d0\ d (dy JA^. ¥■■&*'. Ifor* «k 



dy \dy dx ) dz \dx dz) ~ a 2 dtf- « 2 dt 

 If, in accordance with the earlier notation, we put 



d* d$ .iz^^'ldQ 



dx dy dz 2 dt 



and further, on the right hand, in accordance with the general 

 theorem (5), 



the equation takes this form — 



1 dm 16tt/c dci 



2 dx dt a 1 at 



In an analogous manner the two other equations (B) give 



2 dy dt « dt 



1 d*n . , \Qirk dy 

 2dzTr* 7rW+ -a*-dF > 

 from the latter of which we obtain by the elimination of H, 



dv_dw ^A.( d £^iz) 



dz dy ~ a 2 dt \dz dy/' 

 an equation which is identical with the first equation (9) ; and 

 both the others can be formed in a corresponding manner. 

 If now, by the aid of these equations, 



do dw dw die die dv 

 dz dy dx dz dy dx 

 be eliminated from equations (B), the first of these, after inte- 

 grating in respect to t, will give 



d tda d/3\ d /dy dcc\ _ 1 du * 

 dy \dy dx / dz \dx dz) ~ 4k dt 

 which is identical with the first equation (8) ; and if here the 

 last member, in accordance with (5), be put 



1 d*« 



-4™^*-^-^ 



A. <v 



