Vibrations of Light with Electrical Currents. 289 



power, c a constant, and 

 v= CCCdx J dy'dz' 



(x — x l ) [u ! {x — x ! ) + v'{y — y') +w'(z— z') ] , 



y= JJJ ^^^ (y _^ ) y (g ,^ +p f (y ,, y r )+w > (g .. jg >)] > 

 W= f f P*** d £ — (z-z') [u'(x-x ! ) +v\y-y')+w'(z-z')-} i 



in which u\ v' f w 1 are the components of the density of the cur- 

 rent in the point x* y' z' } e f the density of the free electricity 

 in this point, e 7 the density upon the element of surface ds' f and 

 r the distance of the points x y z and x' y' z 1 . . 



These formulae express that the components of the electromo- 

 tive force in x y z. which according to Ohm's law are T » -r> -r, 

 9 ' ° k k k 



are a sum of two components of electromotive force, — one arising 

 from the inducing action of free electricity, the other from the 

 inducing action of the variable intensities of the current in all 

 the elements of the body. 



Kirchhoff has further expressed the relations between the com- 

 ponents of the current and the free electricity by the two equa- 

 tions 



du dv dw _ 1 de 

 dx + fy~ ] ~dz~~~~~2dt i 



1 de 



cos \ + V COS fl + W COS v= — p ~r» _, 



(2) 



in which X, fju, and v are the angles which the normal to the sur- 

 face, directed inward, makes with the coordinate axes. 



It is at once obvious that the equations (1), which are deduced 

 in a purely empirical manner, are not necessarily the exact ex- 

 pression of the actual law ; and it will always be permissible to 

 add several members, or to give the equations another form, 

 always provided these changes acquire no perceptible influence 

 on the results which are established by experiment. We shall 

 begin by considering the two members on the right side of the 

 equations as the first members of a series. 



By the equation 



