488 PARTICULAR CASES. 



cylindrical coil (495) or a spherical coil with equidistant currents 

 (497). If n^ is the number of turns for unit length, we have 



o 



G = 47r^j in the first case, and in the second G = - Tm v 



O 



505. ELECTRODYNAMOMETERS. In an electrodynamometer we 

 measure directly the action exerted between two circuits, one 

 fixed and the other movable, traversed by the same or by different 

 currents. Suppose, for instance, that the magnet of a tangent 

 galvanometer is replaced by a small coil, through which a current 

 could be passed by a bifilar suspension, and which is in equilibrium 

 when the axis of the coil is in the magnetic meridian. If a current 

 I is passed through the wire on the frame of the galvanometer and 

 a current I' in the coil, the latter is displaced, and by a suitable 

 torsion a of the suspension, it is restored to its original position. 



The magnetic moment of the movable coil is proportional to I', 

 and may be represented by S* ; the couple produced by the action 

 of the frame is then GSII'. As the couple of torsion of the bifilar 

 is proportional to the sine of the angle, if T is the moment of the 



couple which corresponds to an angle of torsion equal to , 



GSII' = Tsina. 



If the two wires are traversed by the same current I, the expression 

 becomes 



GS 



Hence we might determine the strength of the current in 

 absolute measure if we knew the constants T, S, and G, or we might 

 leave these constants undetermined, and use the apparatus as an 

 instrument of comparison. This is the principle of Weber's 

 experiments. 



If we suppose that the current traverses the parallel rectangular 

 frames (492), as in Cabin's experiments, the intensity might be 

 deduced from the attractive or repulsive action exerted between the 

 two circuits. 



506. MEASUREMENT OF DISCHARGES. When the duration 

 of the current is so short that the needle has no time to undergo 

 an appreciable displacement before the current stops, it has 

 nevertheleless received an impulse or throw, and acquired a 

 certain velocity; it is impelled from its position of equilibrium, 

 and returns to it after a series of oscillations. This is the case, 



