Forced Vibrations of Electromagnetic Systems. 443 



curl of e are infinitely close together, and therefore cancel, 

 not having any conductance between them to produce a dis- 

 continuity in the magnetic force. 



But if the tube have infinite conductance, we produce com- 

 plete independence between the internal and external fields, 

 except in the quite unessential particular that the two surfaces 

 of curl e are of opposite kind and time together. Equations 

 (317), (318) reduce to 



(in) E=-fe, F = -^,, K=-L*L' € pe. .(329) 



O i a 6 U Q a b O Q a 



-p__ J o r — l/Go r -p_ 1 Ji r — ,?/Grir 



"Oa — y^da ^ J 0o — y(x 0a 



(outH Y . (330) 



I H= _ 1 Jlr-yGlr 



L S Joa—yQoa 



Observe that (329) is the same as (328). The external 

 solution (330) requires y to be stated. When y = i, for a 

 boundless dielectric, the realization is immediate. 



57. s = 0. Vanishing of E all over, and of F and H also 

 internally. — This is a singularity of quite a different kind. 

 "When n = mv, we make 5 = 0. Of course there is just one 

 solution with a given wave-length along z : a great frequency 

 with small wave-length, and conversely. 



E vanishes all over, that is both inside and outside the 

 tube containing e, provided s/y is zero. The internal H and 

 therefore also F vanish. Thus within the tube is no dis- 

 turbance, and outside, (317) (318) reduce to 



(out) H = -4ttK£, F=- a -4 7 rK/^ (33n 



* ' r en r dz v 



Observe that H and F do not fluctuate or alternate along 

 r, but that H has the same distribution (out from the tube) as 

 if e were steady and did not vary along z. 



A special case is m = 0. Then also n=Q, or e is steady and 

 independent of z, F vanishes, and the first of (331) ex- 

 presses the steady state. 



Without this restriction, the current in the tube is Ke per 

 unit surface, owing to the vanishing of the opposing longi- 

 tudinal E of the field. This property was, by inadvertence, 

 attributed b} r me in a former paper* to a wire instead of a 



* " On Resistance and Conductance Operators," Phil. Mag. Dec. 1887, 

 p. 492, Ex./ 



