﻿and some Applications to Physical Measurements. 489 

 The forms of both curves indicate a relation of the type 



K 2 



dL = constant x 



K 2 + B' 



the term B varying for different sizes of specimen, being 

 relatively less important the greater the whole conductivity 

 of the specimen, as shown in curve (b). A similar type of 

 dependence was calculated by Mr. Kapitza, of the Cavendish 

 Laboratory, for the case of a thin spherical shell. 



For solid cylinders, the dependence of the frequency 

 change on other characteristics of the specimens was 

 examined, but it is hoped to give a complete account of the 

 results together with further tests on different forms of 

 specimens, in a subsequent paper. 



The Application of the Method to the Determination 

 of the Magnetic Susceptibilities of certain Salts. 



The general principle of the method has been given in 

 the previous paper *. It has since been applied to the 

 determination of the magnetic susceptibilities of many salts, 

 the results obtained being given below. In addition it seems 

 desirable to indicate more carefully the nature and magnitude 

 of the corrections to be applied. 



Considering the insertion of a magnetic substance in the 

 form of a cylinder of cross section A' and length I', the 

 volume susceptibility of which is K v , within the coil L of 

 Set 1, the cross section and length of which are A and I 

 respectively, thus causing the frequency, n, of the oscillations 

 to alter by an amount dn, we find, subject to the corrections 

 to be given below, 



^ 1 dn AZ Lx + L 2 

 v== 27r'~n~'A r l"~^ 2 ~' 



In all the experiments for determining ~K V , the heterodyne 

 note was obtained by beats between the first overtone of the 

 oscillations in Set 1 and the fundamental oscillation of 

 Set 2 ? as already mentioned on pages 483, 484 supra. In this 

 case, if X is the frequency of the oscillations in Set 2, and a 

 change of p beats per second is observed on inserting the 

 specimen, N = 2n, and p = 2dn. We thus obtain 



1 p Al V+- L 2 .. . 



Ky ~LV'N-AT- ET" ' ' " .' [ } 



* Belz, loc. cit. 



