386 Lord Rayleigh on the Self-induction 



Under these circumstances we have 



L = V|_, v+( , 2 _ c2)21og _^_ ) 



+ (r 2 + e 2 ) 2 log A/(r ' + c2) }, . (11) 



in which r is written for the radius of the common surface. 

 If c is small in comparison with r, (11) becomes 



J- 3r 2 l 1+ 10r 2+ ---/' • • • {U) 



showing that when the sectional areas are given, the self- 

 induction diminishes without limit as the radius (V) increases. 

 If b denote the thickness of the walls, we have ultimately 



c 2 = 2br, 

 and 



ht ™ 



If the material composing the conductors be soft iron, the 

 self-induction will be several hundred times greater than in 

 the case of copper or other non-magnetic metal. 



I now pass on to § 689, in which Maxwell solves a problem 

 of the second class, relative to the self-induction of a cylin- 

 drical conductor, regard being had to the disturbance from 

 uniformity in the distribution of the current over the section, 

 due to induction. I will introduce the permeability yet, which 

 in this question Maxwell treats as unity. His equations (14). 

 (15), thus become 



/»C=-( 



dT 2 a y cPT 



dt ' 1 2 .2 2 dtf 



nu n fju n d n T 

 + l 2 .2 2 ...n 2 1F + 



•> 



An a w dT u 2 fi 2 d 2 T 

 AC-S=T + «/*^ + w ^---- 



dt ' 1 2 .2 2 dt 2 



d^T 

 l 2 .2 2 ...n 2 dt n 



+•••+ ,. n r 2 -^ + 



■> 



where a, equal to / / R, represents the conductivity (for steady 

 currents) of unit of length of the wire. 

 If $(x) denotes the function 



x 2 x n 



1 +*+;^FgS ; H-- . .,* y, ;2> - ^ + . . . , . (14) 



