112 CONSTANT- VOLTAGE TRANSMISSION 



where LI is the inductance of each wire due to its own 

 current, MI is the inductance for pairs consisting of the 

 centre wire and an outer wire, and M z is the average 

 inductance for pairs consisting of two outer wires. 



Then Z,i = 2 log e y + X 



and Mi = 2 log, 



For the third term it is convenient to use the following 



theorem based on Cotes's theorem 

 f\ 



in trigonometry: 



If a circle of radius a (Fig. 13) 

 be divided into m equal parts at 

 A, B, C, D, etc., then 



A B . A C . A D etc. (to m-i 

 factors) = ma' 1 * 



Thus the mean value of log t 



FIG. 13. Geometrical T 



Division of Circle. _ j O g ( a m 



The average value of M 2 is, therefore, 



Therefore L' = 98 log + - 24 log e 2 



6O log e 2 12 lOge 6 



In the above, the voltages induced in the seven wires 

 have been added together and unit current has been 



* C. E. Guye, "Comptes Rendus," Vol. CXVIII, p. 1329, 1894. 

 C. E. Guye, "L'Eclairage Electrique," Vol. Ill, p. 20, 1895. 

 E. B. Rosa, "Bulletin of the Bureau of Standards," Vol. IV, 

 No. 2, p. 335, 1907. 



