72 ON MAGNETISM. 



cular movement of the magnet; and the distance be- 

 tween these points is measured. In that state, the 

 time of vibration is again observed. < As the force which 

 causes the vibration is the same in both cases (namely, 

 the action of terrestrial horizontal magnetism upon the 

 magnet), the moments of inertia will be proportional to 

 the squares of the two times of vibration. But the 

 difference between the two moments of inertia is 

 merely the moment of inertia of the two brass weights, 

 each being supposed collected at its sharp supporting- 

 point, and admits of being accurately computed. Then 

 the difference of the moments of inertia of the magnet 

 in its two states being known, and their proportion 

 being known, each of them is determined accurately. 



Whichever method is used, the numerical value of 

 M is found and substituted in the expression for E, and 

 the numerical value of E is obtained. 



In the observation of deflexion described in Articles 

 25 to 29, it is evident that the comparison of the mag- 

 net-powers E and A implies that their numerical values 

 are referred to the same unit. And in the investiga- 

 tion, in the present Article, of the measure of the 

 Earth's action upon the magnet, we have used exactly 

 the same formula as in Article 21, which is founded on 

 the methods of preceding Articles, in which all are 

 referred to the same unit. It follows that the numeri- 

 cal value which we have found for E is referred to the 

 same unit : namely (see Article 29) to the magnet-power, 

 or to the magnetic action at distance 1, of the standard 

 magnet S or its equal $', which are such that, when 



