Self-induction and Resistance of Straight Conductors. 381 

 If we put 



%=^ 1 + R'* (26) 



we obtain the values of /*/ and W by writing in (23) and (24) 

 throughout c n — p 2 a ll9 c 22 — p 2 a 22 , c 13 — p 2 a 12 , ... for c n , c 22 , 

 c 12 , . . • respectively. 



A simpler case, which may be worth special mention, arises 

 when all the coefficients b 12} b 1B , . . . vanish. We have 

 then 



,/_„ r?a s? (ci2-fau) 2 (c 22 -2fa 22 ) , 



» 7*^ U * {c 22 -fa 22 f+p% 2 > - ' (20 



^=5 U + S , fa2 I^ 2 ] 2 ^ 2 .... (28) 

 (c 22 -^ 2 a 22 ) 2 +y^ 22 2 . v ; 



This case, when there are two degrees of freedom, is con- 

 sidered in my book on the e Theory of Sound,' § 117. 



If all the frictional coefficients b 22 , # 33 , . . . disappear, 



we have -o, , /nnx 



Bf = b n , ....... (29) 



and 



^-A^ ^y ( 3 °) 



o 22 jj a 22 



Whenever, during its increase, p approaches and passes 

 through one of the values proper to the free vibrations of the 

 system supposed to be vibrating under the condition that 

 tyi is constrained by a suitable force S P 1 to remain zero, // 



rises to -co and passes through to + c© . 



LI I. On the Self -induction and Resistance of Straight Conduc- 

 tors. By Lord Rayleigh, Sec. R.S., D.C.L* 



IN connection with the experimental results of Professor 

 Hughes f, I have recently been led to examine more 

 minutely the chapter in Maxwell's i Electricity and Mag- 

 netism ' (vol. ii. ch. xiii.) in which the author calculates the 

 self-induction of cylindrical conductors of finite section. The 

 problems being virtually in two dimensions, the results give 

 the ratio L : /, where L is the coefficient of self-induction, and 

 I the length considered. And since both these quantities are 

 linear, the ratio is purely numerical. In some details the 

 formulae, as given by Maxwell, require correction, and in 

 some directions the method used by him may usefully be 



* Communicated by the Author. 



t Inaugural Address to the Society of Telegraph Engineers, January 

 1886. 



