﻿Effective Adjustment of an induction-coil, 13 



determined from the known values of k 2 , L b L 2 i, and L 2 2 , 

 since 



r\ _ ^21. L x /2 T (i , 



-^12 -^21 



With regard to the ratio L 21 /L 12 , this differs from unity 

 because the current in the secondary coil during the oscilla- 

 tions is not uniformly distributed, but is greatest at the 

 central winding and nearly zero at the ends. If all the 

 windings of the secondary had equal inductive effects on 

 the primary, when reckoned per unit current, and if the 

 current in a turn of the secondary at a distance z from the 



TTZ 



central winding were proportional to cos-^, where h is 



the length of the secondary coil, it is easily seen that L 21 /L 12 

 would be equal to 7r/2. In the actual case, however, the in- 

 ductive effect of the secondary windings (per unit current) 

 diminishes from the centre towards each end. This was 

 tested by ballistic galvanometer experiments in which the 

 mutual inductance of the primary and a single turn of wire, 

 wound on the secondary (or primary) in various positions, 

 was compared with its value for the central position. From 

 the results of these measurements it was found that this 

 mutual inductance could be represented approximately by 

 the expression a — bz 2 — cz l *. Consequently L 12 is propor- 

 tional to 



'+A/2 



(a — bz 2 — cz*) cos ~ dz, 



•A/2 '* 



while L 2i is proportional to 



i +h/2 



(a-bz'-cz^dz, 



■h/2 



since the current in the primary coil is uniformly distributed. 

 The value of L 21 /L 12 is thereby reduced from 7r/2, and 

 becomes in the present case '95 tt/2. 



Another correction is necessary if, as in the present 

 experiments, the secondary terminals are connected to a 

 capacity which is not negligible in comparison with that of 

 the coil. In this case the secondary current is not quite 

 zero at the ends of the coil, but should be represented as pro- 



TTZ 



portional to cosyy-, where li' is greater than //. The value 



* The dimensions of the coils are : — primary, length 90 em., mean 

 diameter 6 # 9 cm.; secondary, length (between the terminals) 51 cm., 

 diameter (outside) 24 cm. 



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