TRANSIENT ELECTROMOTIVE FORCES. 525 



The conditions of the experiment appear then more simple than 

 in the case of rotation about a vertical axis. But the effects of 

 self-induction introduce a fresh complication. The change in the 

 direction of the current does not really take place in the horizontal 

 plane, and the effective component should be multiplied by the 

 cosine of the angle of the two planes, the determination of which 

 angle presents certain difficulties. The great advantage of the 

 former method, in which the induced currents only give a hori- 

 zontal component, is thus lost. 



1110. TRANSIENT ELECTROMOTIVE FORCES. If the rotating 

 coil is open, the only effect of the induction of the field is to 

 establish a difference of potential between the ends of the wire. 

 As the capacity of this wire is very small if it is not connected 

 with the condensers, the current is always very feeble, and the 

 term relative to the coefficient of self-induction may be neglected. 

 In this case the difference of potential at the ends of the wire 

 is constantly equal to the electromotive force wHS cos x of the 

 field (1107), and it acquires its maximum value when the frame 

 is in the plane of the meridian. 



Comparing this electromotive force, by a method of opposition, 

 with the difference of potential of two points separated by a re- 

 sistance R, on a circuit which is traversed by a constant current I, 

 we shall have 



wHS cos* 

 (10) R = - 



The same is the case if a magnet be rotated about the centre 

 of a stationary frame, the circuit of which is open. The difference 

 of potential at the two ends of the wire wGM cos^c might also 

 be determined at each instant by an opposition method, which will 

 give the equation 



wGM cosx 

 (n) R = - 



In both cases the constant elctromotive force RI should be 

 opposed for a very short time, by an instantaneous contact, to 

 the variable electromotive force of induction. It is important to 

 observe that we do not introduce either the resistance of the cir- 

 cuit or the resistance of the points of contact, which is necessarily 

 variable. 



