NEW DlAMAGNETIC ATTACHMENT TO THE LANTERN 79 



When the vibrating body is very small the first two terms will suffice: 

 hence we have 



M= i a 



in which I is the length of the bar. If d is the density of the body 

 (weight of a unit of volume), I = ^ and n becomes 



in which, however, it is to be noted that ^ .7 is essentially negative 



and so the sign of the term containing it will be positive in the actual 

 development. 



This equation is independent of the dimensions of the body, and 

 hence we conclude that when the body is small and very long as com- 

 pared with its other dimensions, the number of vibrations which it will 

 make in a given field is dependent merely on its coefficient of magneti- 

 zation and on its density; a result first given by Sir Wm. Thomson, in 

 the paper referred to. I have given it once more and put it in its 

 present form merely to call attention to the facility with which can 

 be obtained from it when we have measured R in different parts of the 

 field by known methods. This could be done by means of a rotating 

 coil as used by Verdet, or by my magnetic proof plane which I will 

 soon describe, combined with my method of using the earth inductor. 

 This will give the best method that I know of for obtaining K for 

 diamagnetic or weak paramagnetic substances. 



Troy, January 15, 1875. 



