Experiments with Alternating Currents, 



247 



coil is capable of explanation by means of a mechanical 

 analogy. 



In the figure, A represents a disk capable of rotation about 

 a vertical axis ; M a heavy body 

 which is capable of rotation about 

 a vertical axis XY; Oa disk cap- 

 able of rotation about an axis 

 (variable in position) joining M 

 to XY; B a disk similar to A. 

 The disks A, B, and C are supposed 

 to be of inappreciable mass. If A 

 and B (corresponding to currents) 

 rotate with equal velocities in oppo- 

 site directions, the disk C will rotate, 

 but M (corresponding to induction) 

 will remain stationary. If, now, 

 B be suddenly stopped, as M, owing to its inertia, must 

 instantaneously remain at rest, C will be instantaneously 

 stopped also, and likewise A. If the motive power of A be 

 kept continuously applied, it will immediately begin to rotate, 

 and gradually increase in velocity from zero to its maximum 

 speed. 



The cause of the production of the spark is also capable of 

 mathematical treatment. 



For simplicity, let it be assumed that the E.M.F. between 

 the ends of each coil is kept constant and equal to E. 



Let i l be the current in coil (1). 



L = coefficient of self-induction of each coil. 

 M = coefficient of mutual induction. 



Considering coil (1) 



d%i ™di 2 



E=^! + L^-M^- 2 

 1 dt dt 



Considering coil (2), 



E = i> 2 + L^-M^. 

 dt dt 



S2 



(1) 



(2) 



