276 Mr. 0. Heaviside on the 



we get from (22) by treating s 2 r as a small quantity and using 

 (26); remembering also the extension from a solid to a hollow 

 wire. 



By more complex reasoning we may similarly put the right 

 member of (54) in terms of C without the neglect of F 2 , and 

 arrive at (22) itself, in a form similar to (55) or (56). But 

 we may get it from (22) at once by a proper arrangement of 

 the terms, and introducing e. It becomes 



,= (B,» + B,»^+B M f+^^)0. . (57) 



Here R/ and R 2 " are a s before, whilst R 01 " and R 02 " are 

 similar expressions for the dielectric, on the assumption that 

 H = at r = % or at r = a 2 respectively ; thus, 



-r //_ , P2S2 J (g 2 q 2 ) — (Ji/K 1 )(g 2 a 1 )K (g 2 q 2 ) 

 * 01 ~ + 2t™ 2 J, ... - Kj . . . ' 



r> //_ p 2 s 2 J (s 2 a 1 ) — ( J 1 /K 1 )(g 2 a 2 )K Q (g 2 a 1 ) 



** 2 "" " 2ira x J x . . . - K x . . . ' 



R 03 ,f has a different structure, being given by 



-d 11 _ P2S2 J (g2«i) — ( J Q / K o)(^2^2)K (g 2 a 1 ) 



*™ - ~ 27TG, J, . .. - Kj.. .' 



In these take s 2 r small ; they will become 



01 C\;ft9 — 



f>2 



7r(« 2 2 — «! 2 ) ' 



that is, if p 2 be imagined to be resistivity, the steady flow 

 resistance per unit length of the dielectric tube (fully, p 2 is 

 the reciprocal of k 2 + c 2 p/4:7r) ; and, with k 2 = 0, 



E 0S "=--21og-=L^+^, 



if S is the electrostatic capacity per unit length, such that 

 L S=/L6 2 c 2 . Then (57) reduces to 



e=(L p + my®p + 'R l n + BJ')Q, . . . (58) 



which is really the same as (56). For, by continuity, or by 

 the second of (11), 



— =27ra 1 7 1 = 2ira l p(7= SpV, . . . (59) 



dz 



if cr is the time-integral of the radial current at r = a x , or, in 

 other words, the electrification surface-density there, when the 

 conductors are non-dielectric. (There is equal —a at the 



