416 



Dr. T. J. I'a. Bromwich : Examples of 



But on reference to § 3 below, equations (38) -(40), it 

 will be seen that 



F(0) 



= N f 



where N , 

 expansion 



A(0)~~ w 7« J A'(«)~ 

 N A are the two coefficients 



Ni 



defined by the 



po.) 



N +N!/) + Njp 3 + 



used in equation (3) of § 1 above. 



Thus we find the supplementary rule * : 



To obtain the conditions for the time -integral to be zero } the 

 algebraic condition (found as in the last statement) need vanish 

 only so far as the constant term and the coefficient of p. 



To illustrate^ let us consider the simple example (due to 

 Rimington f) in which one arm of the balance contains an. 

 inductance and the opposite arm is shunted with a condenser. 



The resistance operators are easily seen to be 



Z x = L lP + R x , Z 2 = R 2 , Z 3 = R 3 , 



1 T , R 4 + Kp- 4 (R 4 -r 4 ) 



~\ r it 4 — ?* 4 — z — —- y? , 



-+K P i + Hpn 



where r 4 denotes the resistance of the part of R 4 which| is 

 shunted by the condenser K. Then the algebraic condition 

 for a complete balance is 



or 



(L lP + RJ {R 4 + % 4 (R,-r 4 ) | = R 2 R 3 (1 + KprJ. (32) 



* Heaviside, ' Electrical Papers/ vol. ii. p. 260. 

 t Phil. Mag. vol. xxiv, 5th ser. July 1887. 



