" Skin "-effect in Electrical Oscillatoi's. 3 



less than that amount. Chemically deposited silver failed 

 when the film was so thin as not to be opaqne to light. The 

 thickness of this film he places at less than l/i,000 mm . It was 

 probably not 1/10 of that thickness and, moreover, hardly con- 

 tinuous metal. He remarks that the action of the waves 

 scarcely penetrates farther into the wire than does the light 

 which is reflected from its surface. Similar experiments on 

 the screening effect of extremely thin metal leaf are given by 

 Lodge and others. 



A calculation of the superficial shell effective in the reflec- 

 tion of Hertzian oscillations is given by Poincare,* who finds 



the thickness at which the effect is - of its amount at the sur- 



face, 



for frequency, n = 50 X 10 6 , thickness = 0'002 cm ; 

 " " n = 500 XI 6 , thickness = 0-006 cm . 



This estimate is probably too high. 



J. J. Thomson has treated the " skin "-effect with consider- 

 able fulness. In a note appended by him to Art. 690 of the 

 third edition of Maxwellf he obtains as the resistance per unit 

 length of the conductor 



where the symbols have the meanings given above. This, 

 again, is the same as the values obtained by Kayleigh and 

 Stefan. 



We can obtain the relative current densities at different 

 depths below the surface for any given frequency in the fol- 

 lowing way. StefanJ has shown that if w be the component 

 of the current in the direction of the axis of 2, and if it does 

 not vary with s, the equation 



cho a- / d 2 w 



?) w 



dt 4:7rfjL \dx* dy* 



must be satisfied. 



When the depth to which the action penetrates is small the 

 effect of curvature of the surface may usually be neglected, in 

 which case (4) may be replaced by 



dw a- d*w . . 



( 5 ) 



dt 4717* dot? 



246 and fol. 

 I, p. 246 and fol. 

 % Sitzungsberichte der Wiener Akad. der Wiss., xcv (II), p. 91t, 1887. 



* Oscillations £lectriques, p. 246 and fol 

 f See also Recent Researches, p. 246 and fol 



