4: Chant — Experimental Investigation into the 



This is Fourier's well known equation of diffusion, which 

 Lord Kelvin* has shown to be applicable to the motion of a 

 viscous fluid, as of closed electric currents within a homoge- 

 neous conductor, of heat, of substances in solution, of electric 

 potential in the conductor of a submarine cable ; and, indeed, 

 to every case of diffusion in which the substance concerned is in 

 the same condition at all points of any one plane parallel to a 

 given plane. 



Suppose, now, the periodic current at the surface to be 

 represented by 



w = I s\n pt (6) 



We have to solve (5) subject to the conditions, 



w = I sin pt, when x = (7) 



w = " t = (8) 



The solution is 

 w= ^=l\ sin ptf e~ ^ cos j-— 2 d/3— cos ptf e~^ sin ^— dp 1 (9) 



wherein # 2 = <j/4it\x. 



As £ increases the condition of affairs approaches a " per- 

 manent" state, and then (9) reduces tof 



io = le~ x *< <r sin hi?£— a; a/ — — 1 (10) 



At the surface, i. e. when x=0 s the maximum value of the 

 current is I. It becomes - of this value at a depth 



m=/IlZ-=^/T (11) 



r 2tthp l7rf fin 



This depth J. J. Thomson;}: and Poincare§ take as the thick- 

 ness of the "skin." The. difference in phase between the cur- 

 rent at the surface and that at this depth is easily obtained 

 from (10), and is 



1 (radian) = 57*3° 



For high frequencies this thickness becomes exceedingly 

 small, and an object of the present investigation was to see if 

 an oscillator behaved differently when the metal constituting 



* Report of British Assoc, 1888, p. 571. 



f See Byerly's Fourier's Series and Spherical Harmonics, Art. 51. 



X Recent Researches, pp. 260, 281. § Oscillations Electriques, p. 252. 



