1148 THE BELL SYSTEM TECHNICAL JOURXAL, SEPTEMBER 1954 



rod of radius ri and increase the latter to /'i + di\ by changing eo to ci 

 in the shell Vi < r < /'i + dri . For such a perturbation, since A\ and E^ 

 are continuous at the boundary, they suffer no change when the boundary 



moves; Er however is discontinuous and (Er),, = -(7!-'r), where fAV), and 



(Er)i are the noimal fields just outside and just inside the rod. The per- 

 turbation formula (unsealed), thus gives 



6(3 = -f (ei - 6o) I E, r + \E^\' -\-^-^\ (Er), |- )-27rr,8n , 



or, scaled, with r and /'i representing scaled radii, 



1 (ei - 1){\E,'C ^ lE^f ^ e^\{Er)if) 



6/3 = 



r 



/■i5ri 



Ei*-Hrr dr 



The formula (16) for the magnetic perturbation may now be written 



5^ = , 



Vi dvi 



L\Mo / Mo 



61-1 1 EM) \' + I EM) P + ei I {Er)i 



Inside the rod, we may write 



H-Xr,) 



di 



and then 



H. = 



•_ 2 



EAn) 



E, = jcE, 



jai Hr = jcfi 



dE, 



dr 



r 



■}- - 7 dE- 



,m'H,^j0^-E,-\- -er^ 



r or 



The integrals are readily carried out and are as follows: 



[ ' \Ht fr dr 

 Jo 



E:(rr) 



(€i ^ c (3 )[ Fiain) + + I - Ic^ei 



f \Ht*-Ht)rdr 

 J I) 



jE.\n) 



a,-' 



(ei + c /3 ) - 2ceil5 F(airi) + + — - 



