Prof. E. Edlund on Unipolar Induction. 295 



pression conformable to the requirements of the mechanical 

 theory of heat. 



We will now treat another case of induction, sn (fig. 2) 

 represents a powerful magnet, the south pole of which is in s, 

 and the north pole in n ; and abed is a circular metal plate 

 having its centre in the prolongation of the geometrical axis 

 of the magnet, and its plane perpendicular to the same axis. 

 If the plate be set in rotation about the axis so, the electric 

 fluid will be carried in the direction of the rotation, and the 

 velocity of an electric molecule will be proportional to its dis- 

 tance from the centre o. Now let us imagine a plane con- 

 taining the axis of the magnet and an electric element dz 

 situated in m, at the distance r from the centre of the plate. 

 Then let the right lines mq and mt be drawn in this plane, 

 respectively perpendicular to the lines sm and nm. The line 

 mq is then perpendicular to the plane which passes through 

 the south pole and the tangent of the orbit of the element dz ; 

 and the line mt is perpendicular to the plane passing through 

 the same tangent and the north pole. The plate being in ro- 

 tation in the direction indicated by the arrows, the electric 

 element is urged by the south pole towards q, and by the north 

 pole towards t. Let I be the distance between the poles, p the 

 distance from the north pole to the centre of the plate, r the 

 distance from this last to the point m, and M the force of the 

 poles ; further, let k be a constant, and v the velocity of rota- 

 tion of the plate : the force with which the element dz is urged 

 by the south pole towards the periphery of the plate (or, which 

 comes to the same, the component of the action of the same 

 pole upon dz along the plane of the plate) will be given by 

 kMvr(l+p)dz 

 [(l+p) 2 + rrf 



and the force with which the north pole tends to direct the 

 same element towards its centre will be expressed by 



kM.vrpdz 



{p 2 + x 2 f 

 By equating these two expressions we shall obtain the value 

 of r for which the two forces make equilibrium. We get this 

 value from the equation 



<>2=(l+p)?p%+(l+p)ipi. 



The circle whose radius has this value may be called the neuter 

 circle. If, for example, we take Z= 10 and p = 5 centims., we 

 get r = 12*7 centims. The electric molecules situated between 

 the neuter circle and the periphery of the plate are directed by 



