Oscillations in Straight Wires and Solenoids. 275 



cylinder of radius a the charge per unit length induced on 

 the surface is 



(K— 1) TTO 2 drv _ {K-l) TT 2 a*v (1 ^ 



4tt ' u l ' cU 2 u 2 h 2 ' ' { ' 



When this charge is added to the charge e on the wire, 

 equation (8) becomes 



i>o=2 



(*-S=£5S.).*(£) 



or 



2 / 1 (K-l)^ , in 



ue ° = {T7-r + ~v r°- ' • - ' (ll) 



With this correction for the specific inductive capacity of 

 the cylinder, u 2 G becomes 



u'C=— 1 ^-+ (K ~ 7 1 2 )?rV • ■ • • (12) 

 2 log 4: 



Since A=^ — and q=^-, the values of C corresponding to 

 q I 



the values of q are obtained by the formula 



u 2 C n =— oiH J-/2 — . . . . (13) 



2 log, * 



'Thus the correction for the specific inductive capacity 

 increases as the wave-length of the oscillations diminishes. 



The wave-lengths of the normal modes of oscillation 

 are obtained from the following values of p, p being 

 :2tt X (frequency) : 



Pi = i ■ ,ci7i > P* = 



2tt 3 



/v'SCV r W$( 



3. ZVS0 3 



the value of C being given by equation (13). 



Since C increases with the frequency, the ratio of the 

 frequency of the nth. oscillation to that of the first is less 

 than n. 



