DAMPING. 225 



or 



X' R A R' 



- + . 



r' R + R'r R + R' T O 



Equation (20), as we shall afterwards see, is one of those which 

 may be used to determine the resistance R as a function of the 

 experimental data ; it gives, in fact, to the same degree of ap- 

 proximation,* 



G 2 M TT 2 ^ 



(20)' R = - + 2Le. 



2 HT;( e -e ) 



If we replace - e by its value, we may write 



846. In most of the ordinary galvanometers the coil has of 

 itself a considerable resistance, so that the damping, due to induced 

 currents in the wire, is always very weak. 



Since Gambey's discovery! on the damping of magnets by metal 

 plates, it is usual to place above or around the needle a very thick 

 mass of copper, which is therefore a good conductor. This arrange- 

 ment may be advantageously applied to all instruments such as 

 tangent galvanometers, where the frame produces no appreciable 

 damping in consequence of its distance from the needle. In order 

 that the ratio of the magnetic moment to the moment of inertia 

 of the movable system shall be as great as possible, and in order 

 to avoid any accessory pieces, Weber J used as needle a small circular 

 mirror, magnetised along one diameter, and oscillating in the middle 

 of a cavity arranged in the centre of a very thick copper sphere. 

 This sphere, which forms a conducting screen between the magnet 

 and the coil, almost nullifies the damping due to the coil, even when 

 this is very near the needle. 



* E. DORN. Wied. Ann., Vol. xxn., p. 265. 1884. 

 + ARAGO. Ann. de Chim. et de Phys. [2], Vol. xxvin., p. 325. 1824. 

 % W. WEBER. Electrodyn. Maasbestimmungen, Vol. l. y p< 17. 1846. 

 VOL. II. Q 



