Dr. Oliver Lodge on Opacity. 407 



dielectric not in the conductor ; then take a film whose 

 thickness z is one twenty-fifth of a wave-length of the 

 incident light ; and the ratio of the transmitted to the 

 incident amplitude comes out 



1/9 T, 1000 ] 



irvz 200 



Some measurements made by W. Wien at Berlin in 1888 

 (Wied. Ann. vol. xxxv.), with a bunsen-burner as source of 

 radiation, give as the actual proportion of the transmitted 

 to the long-wave incident light, for gold whose thickness is 

 10 -5 centim., '0033 or 1/300 ; while for gold one quarter as 

 thick the proportion was 0'4 (see Appendix II. page 414). 



He tried also two intermediate thicknesses, and though 

 approximately the opacity increases with the square of the 

 thickness, it really seems to increase more rapidly : as no 

 doubt it ought, as the boundaries separate. However, for 

 a thickness X/25 I suppose we may assume that about l/3rd 

 of the light would be transmitted, whereas the film-theory 



Simple treatment of the E.M. theory of light. — It is tempting to show 

 bow rapidly the two fundamental electromagnetic equations, in Mr. Heavi- 

 side's form, lead to the electromagnetic theory of light, if we attend 

 specially to the direction normal to the plane of the two perpendicular 

 vectors E and H, to the direction along say x, so that v = id/dx and 

 v 2 = -d-jdx 2 . 



In an insulating medium the equations are 



curlH = KE and -curlE=^H; 

 now curl=Vv = Vj since Sv = in this case, so 



V 2 H=KvE=KcurlE= -E>H; 

 or, in ordinary form, 



<£H_ K . dm 



dx 2 ** dt 2 * 

 and there are the waves. 



If this is not rigorous, there is no difficulty in finding it done properly 

 in other places. I believe it to be desirable to realize things simply as 

 well. 



In a conducting medium the fundamental equations are, one of them, 



curl H = K E + 4tt&E = (Kp + ink) E, 



while the other remains unchanged; unless we like to introduce the non- 

 existent auxiliary g, which would make it 



-VvE=(<7+^)H, 

 and would cover wires too. 



So - v 2 H= (4tt&+I^)(#+^)H, 



the general wave equation. In all these equations p stands for djdt ; but, 

 for the special case of simply harmonic disturbance of frequency pl'2ir, of 

 course ip can be substituted. 



