inm r 



of Secondary Electromagnetic Waves. 273 



where r is the distance to the reflector, and A is the ampli- 

 tude of the magnetic force. The magnetic component of the 

 reflected wave, supposed as above to be from a second " vibra- 

 tor," will be given by* 



as this has the same phase at the reflector as the incident 

 beam. Here + E is the maximum value of the electrifica- 

 tion induced by the incident wave on the second "vibrator," and 

 I is the equivalent distance apart of the positive and negative 

 charges, which, taken roughly, is the length in the direction of 

 the electric displacement of the reflector supposed rectangular. 

 An approximation for E may be easily obtained from the 

 value for the induced current arrived at, by assuming that the 

 magnetic force parallel to the reflector due to the induced 

 current is such as to neutralize the effect of the direct radia- 

 tion immediately behind the reflector f. If c is the amount 

 of the current per centimetre cross section in the reflector, 

 the magnetic force due thereto parallel to the reflector and 

 close up to it is 2ttc ; that is to say, it is assumed equal to the 

 force due to an infinite current- sheet of intensity c per centi- 

 metre cross section. (See Maxwell, chap, xii.) This is to be 

 put equal to the magnetic force of the direct radiation at the 



reflector A cos 27r— . Recollecting that c is in electromag- 



T 



netic units, we have for the amplitude of the total charge 

 along the edge k of the reflector, 



E=kY\ cdt = kY\ #^cos27r- dt= 



Jo Jo 2?r T 



4tt 2 



This neglects the end irregularities in the electrification. 



At any point in front of the reflector the disturbance is the 

 sum of P and P / , and we have a series of stationary waves, 

 complicated, however, by the fact that the velocity and the am- 

 plitude of one of the components are functions of the distance. 



PH-F=Bcos2tt^ +a\ 



represents the stationary waves when 



r=Hl^.^(sin^ + ^cos4.g + (0[l + (^} 



* Wiedemann's Annalen, January 1889. 



t This, as a method of evaluating the electrification, was pointed out 

 to the author by Prof. Fitzgerald. 



