[ 575 ] 



LV. Note on a Possible Source of Error in the Use of a 

 Ballistic Galvanometer. By R. Beattie, B.Sc* 



UNLESS more than ordinary care is taken in setting up 

 a ballistic galvanometer of the movable magnet type, 

 the chances are that the magnetic axis of the needle does not 

 lie exactly in the plane of the coil. Whenever this is the 

 case, the magnetic field setup in the galvanometer during the 

 passage through it of a quantity of electricity has a component 

 along the needle's length tending to alter temporarily its 

 magnetic moment, and so tending to modify the throw — 

 causing it to be in defect of a normal throw when the needle 

 in its first swing passes through the plane of the coil, in 

 excess when it does not. I£ we admit that the change, sup- 

 posed small, in the magnetism of the needle is at each instant 

 proportional to the component of the field in the direction of 

 the needle's axis, we can readily find an expression for the 

 amount of the error which is thus introduced. For it is then 

 not difficult to show that the throw is proportional, not to the 

 quantity Q of electricity which traverses the galvanometer, 

 but to 



Q + «G0 \i 2 dt, 



where G denotes the coil constant of the galvanometer^ a 

 the induction-coefficient of the needle, 6 its (small) initial 

 angular displacement, i the instantaneous value of the current, 

 and t its duration. The percentage error is accordingly 



100 



3^j/*i M 



and it is of some little interest to inquire whether this 

 may not, on occasion, be so large that it cannot be entirely 

 disregarded. 



The value of the coefficient a. which enters into (1) is not 

 easily assigned ; it may be very large or it may be very small. 

 Since it is equal to the susceptibility of the needle corre- 

 sponding to the application and removal of a small magnetic 

 force, divided by its intensity of magnetization ; and since 

 the former of these quantities increases as the latter dimin- 

 ishes ; we see that a will be small if the needle is strongly 

 magnetized, but large if the needle has lost a good deal of its 

 magnetism. For the present purpose it will be sufficient to 

 take a as being '002, a number fairly representative of what 



* Communicated by the Author. 



