of Unipolar Induction. 415 



If, on the contrary, the magnet is at rest and the magnetism 

 is concentrated in the axis of the magnet, the value of the 

 induction when As has the angular velocity v will be 0*3142 

 Mr As ; and these two values are almost identical. 



Let us put H = 2r and R = 5?\ When the magnet and the 

 element of the circuit are in common rotation, we obtain from 

 formula (7) the value of induction = 1*002 MwAs; and when 

 the element of the circuit only is in rotation we obtain 1*004 

 MvAs. The difference is therefore about 0*2 per cent. 



For the case where the magnet is at rest and the element 

 alone is in rotation, we have supposed in our calculation that 

 all the magnetism of the ring is concentrated in the axis of 

 the magnet. In this manner, of course, a sufficiently exact 

 result is obtained only if the element As is at a sufficient dis- 

 tance from the surface of the magnet, as was the case in the 

 preceding examples. But we must not forget that all the 

 magnetism of the magnet is not found upon its surface ; but 

 that the subjacent layers, of which the distance from the axis 

 is only a fraction of r, are also magnetic, although their dis- 

 tance from As is greater than that of the superficial layer. 

 The mode of calculation employed, which may of course also 

 be applied to the subjacent layers, consequently gives a more 

 exact result for the magnet as a whole than for the superficial 

 layers. 



4. Let us now suppose the element As situated at the sur- 

 face of the magnet so that r = R : and let us further suppose 

 that H also is equal to r. When the element is in rotation 

 with the same angular velocity and in the same direction as 

 the magnet, we obtain, by employing formula (7), 1*926 MvAs 

 for the value of the induction. 



Let us suppose, finally, that the element As is situated within 

 the magnetic ring at the distance \t from the axis of the 

 magnet ; that the magnet and the element are in rotation in 

 the same direction with the same angular velocity ; and that 

 H=?\ 



In conformity with formula (7) the induction will now be 

 1*038 MvAs. 



§6. 



The old theory supposes that a magnet in rotation about its 

 axis produces an induction in an element of circuit at rest and 

 at a distance the same as if the magnet were at rest, but the 

 element rotated in the opposite direction but with an equal 

 angular velocity. We will now examine if this result con- 

 forms to the requirements of the mechanical theory of heat. 



1. Suppose the vertical element of the circuit at rest and 



