

Damping of Galvanometer Needles. 565 



2. N may not be constant. — This may occur in three ways : — 

 i. The factor introduced by the air resistance may not be 

 constant, the air resistance being possibly not pro- 

 portional to the first power of the velocity. 

 ii. For the same reason it is possible that the factor 

 introduced by the viscosity of the suspension may not 

 be constant, 

 iii. The factor introduced by the eddy-current damping 

 may not be constant. There are three causes which 

 may make this factor vary. 



In the first place, since the E.M.F. induced by the 

 swinging needle is proportional to the first power of its 

 velocity and to its strength, the damping effect of the eddy- 

 currents will be proportional to the square of the strength of 

 the swinging needle ; and it is quite possible that altering the 

 strength of the controlling field may alter the strength of the 

 needle. 



Secondly, if the galvanometer coils have a self-induction 

 such that the reactance is not negligible, at the periods used, 

 when compared with the resistance, the eddy-currents set up 

 will not only lag behind the induced E.M.F., but will be to a 

 certain extent choked out. And as these effects will be 

 greater at the fast periods, the damping will be diminished at 

 these periods, thus causing the ratio t/X to increase as the period 

 decreases. 



Thirdly, it is possible that the eddy-currents will produce 

 a rise in temperature sufficient to appreciably affect the 

 resistance of the galvanometer coils. This will diminish the 

 eddy-currents most at the short periods, thus producing an 

 effect similar to that due to .self-induction, namely an increase 

 of t/X as the period decreases. 



To find out if possible which of the above was the true 

 cause of the discrepancy between theory and experiment, it 

 was decided to make some experiments in which the ratio t/X 

 was first determined for various strengths of controlling field 

 for a needle swinging in a system in which the eddy-current 

 damping was reduced to a minimum, if not entirely eliminated: 

 and secondly for the same system but with considerable eddy- 

 current damping introduced. In this way it would be possible 

 to discover whether the effect was due to the eddy-currents 

 or not. 



Some preliminary trials showed that, to obtain satisfactory 

 observations with vibrations of long period, it would be 

 necessary to perform the experiments at night when there 

 was comparative freedom from the disturbances due to 

 traffic, since, although the galvanometer was placed on a stone 



