﻿492 Mr. M. H. Belz on the Heterodyne Beat Method 



thus justified in completely neglecting the effects of de- 

 magnetization. 



(ii.) The effect of the end correction term and the position 



of the specimen. 

 In a long coil there is an appreciable length over which 

 the magnetic force is constant and given by H = '4ww 1 i, n x 

 being the number of turns per unit length. At the ends the 

 force falls to half value, and this diminution in H is 

 responsible for the correction term K in Nagaoka's formula 

 L = 47r 2 aV6.K. 



When this correction is small and so can be neglected, the 

 expression (ii.) becomes exact. In the present case, the value 

 of K was equal to 0*9873 and the error involved in neglecting 

 this end correction is about 1*3 per cent. We can allow for 

 the correction in the following way : 



The short specimen (about 8 cm. as compared with the length 

 of the coil, 36*70 cm.) was suspended in approximately the 

 centre of the coil, which can thus be supposed to consist of 

 three coils in series, one in the centre of length equal to that 

 of the specimen and without end correction, and two approxi- 

 mately equal coils on either side, to the open ends of which 

 the correction is to be applied. Let V be the length of the 

 specimen, I the length of the coil, then the total self- 

 inductance is L = CZK, while the self-inductance of the coil 

 of length V is L = CZ', where C = 47r 2 a 2 n 1 2 . The area of 

 cross section of the coil being A, that of the specimen A', 

 the self-inductance of this portion is altered to L ' where 



L / =L (H-47rK t ,A7A), 



so that the whole change in inductance of the coil, dJj, is 

 given bv 



JL = L 47tK„A7A, 



= L AirK v A'l'l(AlK), 

 and thus the expression (ii.) in the corrected form becomes 



T ^ 1 p K . volume of coil Li + L 2 .... x 



j£ = m J_ t . t , . (in.) 



2-7T "JST 'volume of specimen ' L 2 



Experimental Errors. 

 The accuracy of the estimations depends almost entirely 

 on the determinations of the change in the number of beats 

 per second tmd of the frequencies. The counting was done 

 by means of a stop-watch guaranteed to read tenths of a 

 second. The heterodyne note was adjusted by means of the 

 fine movement on the condenser of Set 2 so that a reasonable 



