﻿Sensitive Form of Thomson Galvanometer. 557 



for convenience that each member of the system is equivalent 

 to a circular disk whose diameter, 2 r, is equal to the length 

 of the longest magnet of the system, and whose thickness, w, 

 is such that the mass of the disk is equal to the sum of the 

 masses of the individual magnets *. Then the mass of the 

 disk will be Ar 2 w and its moment of inertia B?-hv. The mass 

 and moment of inertia of the mirror will be A'r 2 w and 

 BV 4 w respectively. 



Then, if t denote the time of single swing, M the residual 

 magnetic moment of the system, and H the strength of the 

 field in which the system swings : — 



V MH V MH 



The moment of the force required to produce unit 

 deflexion, 0, of the system is FCm ; where C is the current 

 flowing in the coils, m the individual magnetic moment of 

 one member of the system, and F a constant involving the 

 constant of the coils, the intensity of magnetization, &c; and 

 it is also equal to MH0. Therefore 



MH = F/0Cm=F'CW 2 , 



since the magnetic moment is, for the same intensity of 

 magnetization in different disks, proportional to the mass of 

 the disk, that is to wr 2 . 

 Therefore, finally, 



Hence, if t is constant, C varies as r 2 plus a constant ; that 

 is, the sensitiveness increases somewhat less rapidly than the 

 mass of the system diminishes. But if no limit is imposed 

 on the time of vibration, but only on the final degree of 

 astaticism, then MH = const., hence Cm = const., or the 

 sensitiveness varies directly as the magnetic mass. It is 

 true that the conditions of use impose the former rather than 

 the latter limit, but for an average time of single swing of 

 10 sec, which is not inconveniently long, I believe that a 

 system weighing from 40 to 60 mgs. will be found best, for 

 if very great sensitiveness is required, we can use a time of 

 swing of from three to four times this without as great 

 inconvenience as would result from the use of a system only 



* It is not of importance here to consider the most effective form or 

 arrangement of individual magnets, as we are only considering relations 

 between systems of the same form, but of varying dimensions. 



