406 Dr. Oliver Lodge on Opacity. 



when we have to lay down continuity conditions, and, 

 according to the particular kind of aether-theory adopted so 

 will the boundary conditions differ. My present object is to 

 awaken a more general interest in the subject and to repre- 

 sent Mr. Heaviside's treatment of a simple case ; but it must 

 be understood that the continuity conditions appropriate to 

 oblique incidence have been treated by other great mathe- 

 matical physicists, notably by Drude, J. J. Thomson, and 

 Larmor, also by Lord Rayleigh, and it would greatly 

 enlarge the scope of this Address if I were to try to discusss 

 the difficult and sometimes controversial questions which 

 arise. I must be content to refer readers interested to the 

 writings of the Physicists quoted — especially I may refer to 

 J. J. Thomson's ' Recent Researches,' Arts. 352 to 409, and 

 to Larmor, Phil. Trans, 1895, vol. 186, Art, 30, and other 

 places.] 



Now apply this to an example. Take k for gold, as we 

 have done before, to be 1/2000 fi seconds per square centim. 

 and v = Sx 10 10 centim. per sec, for v is the velocity in the 



n being the index of refraction, and m the relative inductivity. Hence, 

 adding and subtracting, 



E_ 2= 2 

 E, 1-hW 

 and 



E 3 \—nm m 



E,~~ 1+nm ' 

 well-known optical expressions for the transmitted and reflected ampli- 

 tudes at perpendicular incidence, except that the possible magnetic property 

 of a transparent medium is usually overlooked. 



Treatment of a conducting boundary. — But now, if the medium on the 

 other side of the boundary is a conductor instead of a dielectric, a term 

 in one of the general equations must be modified; and, instead of 

 curl H=KjpE, Ave shall have, as the fundamental equation inside the 

 medium, 



— — _ = 4ttA;L; 

 dx 



or more generally (4ttZ;+K//)E. 



So, on the far side of a thin slice of thickness z, the magnetic intensity 

 H 2 is not equal to the intensity H^+Hg on the near side, but is less by 



f/H = 4:TrkEdx = 4:7rkE 2 z = 4nkftvzH. a ; 

 and this explains the second of the continuity equations immediately 

 following in the text. 



In a quite general case, where all the possibilities of conductivity and 



capacity &c. are introduced at once, the ratio of E/H is not pv or O/K)*? 



but is ( y g-^-u.pf{4iiTk-\-\i.p)~ 2 for waves in a general material medium, 



{g may always be put zero), or (R-j-pL)*(Q.+^S) 2 for waves guided by 

 a resisting wire through a leaky dielectric. 



The addition of dielectric capacity to conductivity in a film is there- 

 fore simple enough and results in an equation quoted in the text below. 



