of Unipolar Induction. 



411 



magnet is thus almost without importance for the induction. 

 The two theories diverge in this case in an essential manner ; 

 and this divergence is of great importance for the use of the 

 theory to explain several other natural phenomena. The fact 

 that the rotation of the magnet is without real significance in 

 the case in question may be proved more completely in the 

 following manner. 



2. Supposing that the circle hcdf(fig. 4) represents the 

 horizontal section of a vertical magnet, in which plane one of 



Fig. 4. 



the poles lies (e. g. the south pole), and that vertically beneath 

 a there is an element of the vertical circuit As ; and let us 

 suppose that the element of the circuit and the magnet are 

 both in rotation with the angular velocity v in the direction 

 of the arrow about the axis o of the magnet. Let us then 

 denote by E the distance from the element of the circuit 

 beneath a to the axis of the magnet, taking the radius oc of 

 the magnet equal to r, and supposing that the element As is at 

 a distance H vertically below the horizontal plane first men- 

 tioned. Let us further suppose a vertical plane passing through 

 the vertical element of the circuit As and the axis of the mag- 

 net, and that another vertical plane passes through the same 

 element and the point c situated on the circumference of the 

 magnet at the angular distance u from the line o m. The first 

 of these vertical planes will consequently intersect the hori- 

 zontal plane mentioned along a o and the second along a c. 

 The element of the circuit A s moves in the direction ag = vH, 



2E2 



