Vibrations of Light with Electrical Currents. 295 



Moreover we obtain directly from equations (A) 



dv dm __ 4ik d (d(S dy\ 

 dz dy " a 2 dt \dz dyr 

 dw du _ 4k d /dy du\ ,n\ 



a^~Tz~~a^Jt\Tx~Tzr\ U 



dy dx " a 2 dt \dy dx/' \ 



by which equations a, (S, 7 may be eliminated from the previous 

 equations (8) after they have been differentiated in reference to /. 

 In this way the following equations are obtained : — 



d (du dv 



dy\dy 

 d /dv 

 dz \dz 



d (dw 

 dx \dx 



dx 

 dw 

 dy 



du 



dz 



\ d (dw du\ _ 1 d 2 u 

 / ~dz\dx~ "dz~)~ 'a 2 W 



)d (du dv\__l d 2 v 1 677-/ 

 dx \dy dx) a 2 dt 2 a 2 



)d (dv dw\ _ 1 d 

 dy \d% dy / ~~ a 2 t 



dv 

 dx 

 dw 

 dy 



167rk du 

 ~^"dt } 

 d 2 v \67rk dv 



167rk dw 



(B) 



■iv 



dt 2 



tf 



dt 



These equations for the components of the electrical current 

 agree fully with those which I have already found for the com- 

 ponents of light up to the last member, into which the electrical 

 conductivity k enters. This member indicates an absorption 

 which will be greater the greater the electrical conductivity, and 

 which is denned by the constant h in the equations (6) if in 

 these c=a V2. 



If k is very large as regards pa, equations (7) give 



2tt 

 h=p= -, 



if X denotes the wave-length of light ; from which it follows that 

 the amplitude of a ray of light which, for instance, has passed 

 through a layer of a good conductor of electricity of the thick- 

 ness of half a wave-length, is from (6) e n times lessened, and the 

 intensity reckoned proportional to the square of the amplitude, 

 e 2n or 535 times. This will be the case with all metals ; for, 



according to Weber, the conductivity of copper is in 



magnetic measurement, taking the millimetre and the second as 



c 2 1 



units of time and length, and therefore^- x t y nn ? or 283433a 



in mechanical measurement, a magnitude which is great as com- 



pared with — a. It is clear, however, that this result can only 



