344 Dr. Lodge on the Rotation of the Plane of Polarization 

 very respectably with the frequency as calculated from 



3 X 10^° 



W(H) 



Returning now to the magneto-optic effect of the Leyden- 

 jar discharge, I make out its theory to be as follows : — 

 The current at any instant during the discharge is 



C=^e-'^'smpt (1) 



where m= ^^and where m^ + p^ = err-* 

 2L ^ SL 



The difference of magnetic potential between the two ends of 

 a rod of length I surrounded by a very long solenoid of n^ 

 turns of wire on unit length of it is 



4:7r/jbCnil. 

 The Verdet constant for carbon disulphide, or the rotation of 

 the plane of polarization per unit difference of magnetic 

 potential is, according to the determination of Lord Rayleigh, 

 "04202 minute for a temperature of 18° Centigrade, and 

 for sodium light. Calling this k, we have the rotation 

 effected by the current 



e = ^7rkn^lfiG (2) 



In the case of the heavy glass experiment a helix longer than 

 the stalk of glass is employed ; but in the case of the long 

 tube of GSg and four helices there will be some correction 

 necessary for the ends of the helices. This correction is, how- 

 ever, well understood, and there is no special need to intro- 

 duce it at present. 



Now the total amplitude of the light falling upon the 

 analyser being a (this amplitude being all stopped if the 

 analyser is set to darkness, and all transmitted if it be turned 

 90°), the component amplitude which will at any instant get 

 through the analyser set to darkness, when the plane of 

 polarization has been rotated through an angle 0, is 



a sin 6 ; 

 and the amount of light which gets through during the time 

 T during which an impression is capable of being accumu- 

 lated on the retina, i. e. before it has begun to die away as 

 fast as it is produced, is 



1 \a sin eydt. 



