49 PARTICULAR CASES. 



If the deflections are small enough, we may simply take 

 i /HK H /~K~ 



= cV^ eW^' 



= 



It appears thus that the angle of throw 6 is proportional to 

 the quantity of electricity which flows during the discharge, and 

 this law of proportionality will be sufficient for all comparative 

 experiments. 



To determine m in absolute value we must know the constant 

 G of the galvanometer, and the quantities which come under 

 the root. 



It may be observed that if the needle is left to itself under 

 the influence of terrestrial magnetism, the time T of infinitely 

 small oscillations is 



from which follows 



HT 



m = - . 



g 7T 



As a matter of fact, the true angle of throw is diminished 

 by the resistance of the medium, and by the induction currents 

 which the motion of the needle produces in the wire. But if 

 the oscillations do not diminish very rapidly, this effect is allowed 

 for by adding to the angle 0, a quarter of the excess of this 

 deflection over the deflection produced on the same side by the 

 succeeding oscillation. We shall have, finally, 



m = 



