8 Prof. J. J. Thomson. On the Effect produced by [May 2, 



K 



= V- e'^+PQE maJ '(ma). 

 The rate of production of heat in the wire is 



K 



= £- EW{ J ' 2 (ma) + J 2(ma) } e 2t (™*+^>. 



Hence the ratio of the heat generated in the wire to <n 2 /7ra 2 , the 

 heat which would be generated if the current were uniformly 

 distributed, 



_ 1^2 {J O ' 2 (^ft)+J O 2 (>Q0} 



_ 4 n a — — . 



J "(mo) 



Since when na is large J (ma) = (e na \ ^ ( 2i7rna)(\ + )- — Y this ratio 



\ 8na/ 



— \na. 



The rate at which heat is generated in the outer conductor is 



g_ e W™+2>t)JJ I 2wrl 2 (m'r)dr, 

 h 



t_ L 2 7T&2{ I '2( m '&) + I 2( m '6) 

 a 



By equations (7) and (8) we have 



LI (m'&) _ a m 2 — n 2 pin J '(ma) I (m'6) 

 EJ (ma) b /in m 2 — ri 2 J (ma) I '(m'6)' 



so that 7rL6I '(m'6)e^ 2 +^) = L'Ufz^L f> V . 



m 2 — 7&' 2 



_ ^ approximately. 



Thas the heat generated in the outer conductor 



since is small, I '(m'b) is large compared with I (m'6), and w' 2 is 

 approximately 



4 TTfJLipjc'. 



