2$e 



Prof. L. Natanson on the Molecular Theory 



direction of the axis o£ z ; or, which is the same thing, of 

 concurrent secondary waves advancing in the direction in 

 which the incident wave traverses the plate. Using the 



us in 



symbol (Ex ) + to denote this quantity (which, 



above, we propose to call "the secondary positive electric 



effect ") we shall have by (7) : 



(Ef) + =-2.N[.^_ T) -^ ) ].» 



\{t—az) 



+ ^2ttNP_ ein( t_ hz y 



2ttNQ 



Jn(t + bz) 



(9) 



i(bc-l) i{bc+l) 



It remains to find the secondary negative electric effect 

 (Ef } )_ which arises at M under the operation of secondary 

 waves crossing the plane under consideration in the negative 

 direction of the axis o£ z. Going back again to (7) we find 



(Ef)_=27rNr 



p 6 -*V;Z Q ( 



iibc+l) i{bc-l) 



inbZ -i 



■inaZJn(t ±-az) 



2ttNP 



Sn{t—b~) 



2ttNQ 



Jn{t + bz) 



(10) 



i(bc + l) i(bc-l) 



For the actual electric field at M we obtain, l)y means of 

 (9), (10) and with the assistance of (1) and (2), an ex- 

 pression which represents several superimposed sets of 

 waves travelling in the plate along the positive and negative 

 direction of z. But if we assume (as we do throughout 

 these calculations) that the state of radiation attained by the 

 system is already thoroughly steady, we have to remember 

 that the substance of the plate is incapable of transmitting 

 electromagnetic disturbances without enfeeblement and with 

 velocity c ; to secure the inexistence of such waves the 

 " inoperative " terms in the expression for the resultant 

 secondary effect must be balanced by the field of the 

 incident wave. We therefore have the equations 



P Q 



2ttN 



and 



L«X*< 



Pe" 



■1) 

 inbZ 



bc+1 



i [be + 



Q e inbZ 

 ~bc~^l 



d =A< 



l )-ind 



=o, 



(U) 



(12) 



and the component in the direction of x of the electric field 

 at M is simply 



. *T N 1 x (P€™C- *') + Q6 fa ('+**)) . . . . (13) 



