﻿204 Mr. A. Kussell on the Dead Points of a 



In this equation ~2b0 represents the damping torque due to 

 air friction, //, the magnetic moment of the needle, H the 

 strength of the controlling field, G the coefficient* of the 

 galvanometer, that is, the strength of the field at the magnetic 

 poles of the needle due to unit current in the galvanometer 

 coil, and i the instantaneous value of the alternating current 

 flowing in the coil. Following Rayleigh, we have assumed 

 that the magnetism of the needle is made up of a constant 

 part and a part which is proportional to the applied magnetic 

 force. If we suppose that the eddy currents in the needle are 

 negligible, the torque produced by the variable component 

 of its magnetism is easily shown to be equal to <yi 2 sin cos 0, 

 where y is a constant. 



As the frequency of the alternating current is very high 

 compared with the free period of the galvanomeler-needle, 

 and the amplitude of the forced vibration is generally very 

 small, we see that the apparent position of equilibrium of the 

 spot of light is given by 



jjlH sin (0 — 0q) = 7A 2 sin cos 0, 



v here A is the effective value of the alternating current. 

 When 6 and O are small we have 



(e-e 9 )ie= y A?i(jA). 



The author has verified this equation experimentally, and 

 finds that for a given value of A the expression (0—0 o )/0 is 

 practically constant. If, however, A be varied between wide 

 limits, the agreement between this formula and experiment 

 is not so satisfactory. 



If we assume that the deflexion of moving coil galvano- 

 meters by alternating currents is due to the eddy currents in 

 the magnets, we find that 



(0,-*)/*=*A», 



where k is a constant. For a given value of A the author 

 found experimentally that (0q—0)J0 was practically constant, 

 but when A was varied this ratio was only approximately 

 constant. 



The Neutral Position of the Needle for Steady Currents. 

 Since the moment of the applied forces acting on the 

 needle is measured by MP#, we get, as in (1), 



~Mk 2 = [iGi cos + 7 i 2 sin cos - fiK sin (0 - <9 ) 

 — retarding torque due to air friction 

 + torque due to eddy currents in the needle. 

 * Maxwell, •' Electricity and Magnetism/ vol. ii. § 748. 



