284 Prof. L. INatanson on the Molecular Theory 



For the magnetic field of the refracted wave let us assume 

 B ** 6 m(*-fe+s) 3 ( 12) 



where B** is real : the application of (10), § 5, and the 

 preceding equation (9) gives 



B** = ^A*V'"(r-s) (13) 



This shows that 



B** 



-rrr^. COS 11 (s — r) = V '. . ' . . (14 Cl) 



B** 



-£** sin ?i ($-?■) = —* (14 £) 



Our discussion has thus far been confined to the case of 

 external reflexion. The general conclusion at which we 

 arrive is that, availing ourselves of the principles established 

 in £§ 1-5 of the present communication, we are led in all 

 cases to correct results, although we have taken no account 

 whatever oi the requirements of boundary conditions. It 

 should be remarked that the merit of having called attention 

 to the advantage that can thus be secured belongs entirely to 

 Mr. W. Esmarch. 



§ [), Let us imagine a plate of thickness Z and of optical 

 behaviour (v, k) different from that of the void region on 

 eacli side of it. As before, let the axis of z be measured 

 vertically upwards. The plate is supposed to be bounded by 

 two parallel planes which for distinctness of conception we 

 suppose horizontal ; let the lower plane be taken for the 

 plane z = and the upper one for the plane z = Z. Conceive 

 a series of plane waves of linearly-polarized light propagated 

 verticallv upwards through the region of negative values 

 of z : 



Ei 1) = A (1, e / '^-^+^, E^ 1} = 0, Ei~ 1} = 0. . (1) 



H a) =0j H^ = A (1 V^- a -~+ f/) , H^ = 0.. (2) 



Under the influence of the penetrating wave the molecules 

 constituting the subsbnce of the plate are thrown into 

 sympathetic vibration and may be regarded, at least very 

 approximated, as centres of diverging disturbances. Our 

 aim and object is now to specify a system of these secondary 

 wave disturbances capable of maintaining themselves steadily 

 in the plate. To effect this, let us consider in how far, for- 



