INDUCED DISCHARGES. 519 



the plane of the frame, the moment of the action of the frame on 

 the magnet for unit current is GM cos x ; if the factor G may be 

 considered as independent of the angle x, the flow of force from 

 the magnet, and which traverses the circuit, is equal to GM sin x. 



Between two different positions, x^ and ^ 2 , the variation of the 

 flow of force is then 



Qi --Q2 = MG (sin #! - sin # 2 ) . 



For a displacement of 180 from a position in which the magnet 

 is perpendicular to the frame, we shall have still 





The flow of force Q may be produced by an external current I, 

 which traverses a circuit fixed in respect of the former, and the 

 intensity of which passes from the value \ to the value I 2 . If M 

 is the coefficient of mutual induction of the two circuits, we have 





m 



The numerator is equal to MI if the phenomenon corresponds 

 to the suppression or the establishment of the inducing current ; it is 

 equal to 2 MI if the direction of the current is reversed. 



1106. DAMPING OF A MAGNET OR A FRAME. When a magnet 

 is movable in the field of a closed circuit, or when a circuit is dis- 

 placed in a magnetic field, the currents induced in the circuit tend 

 to counteract the motion ; the excess of the retardation caused by 

 closing the circuit will give a measure of its resistance. 



The problem relating to the oscillations of a magnet in the centre 

 of a frame has been investigated in 845. When the deflections are 

 very small, the resistance of the circuit is given by the expression 



A 

 (5) = * H 4 ' 



which includes the constant G of the frame on the magnet, the ratio 

 of the magnetic moment M of the magnet to the horizontal com- 

 ponent H of the external field, and the data furnished by the study 

 of oscillations for the case in which the circuit is opened or closed. 



