418 



Prof. E. Edlund on the Theory 



become lower for the interior layers than for the exterior ones, 

 it is evident that this will also be the case for the total effect 

 of the magnet. 



4. It has been supposed above that the element of the cir- 

 cuit at rest As was at a distance, greater or less, outside of 

 the exterior layer of the magnet in rotation ; and it has been 

 shown at the same time that the induction of this element was 

 in general very feeble. We will now suppose that the vertical 

 element of the circuit is in the axis of the magnet and in the 

 same horizontal plane as the pole. 



The distance between the elementary pole Wrdu situated at 



c and the element of the circuit As is then equal to r. The 



angle /3 is evidently a right angle, and yfr is equal to zero. In 



virtue of formula (6), the induction of the element of the 



.,-, ,, , , ■, MrvrAsdu , ., 

 magnet will consequently be equal to ^ wnen the 



magnet is in rotation with the angular velocity v ; and as this 

 expression is equal for all values of the angle u, the induction 

 of the whole layer will be equal to (3*2832 MrAs. This value 

 is the same as that we obtain when the element As is in rota- 

 tion at a distance r round a magnetic pole of which the inten- 

 sity is equal to that of the exterior of the magnet, and is 

 consequently 27r^M. 



5. It is easy to explain in an elementary way why, when 

 the element is outside of the external layer, the induction 

 becomes so feeble in comparison with that produced when the 

 element is situated in the axis of the ring. 



Let the circle dpfmg (fig. 5) 

 represent the horizontal plane in 

 which one of the poles of the ver- 

 tical magnet is situated, and let us 

 suppose that the element As at rest 

 is placed at the point a. The magnet 

 is in rotation in the direction indi- 

 cated by the arrow. An elementary 

 magnet at m moves then in the di- 

 rection mk, and the angle which this 

 direction of motion makes with the 

 line of junction between m and a 

 (the angle /3 of the formula 6) is a 

 right angle. When the elementary 

 magnet reaches g the angle in ques- 

 tion is acute, and it becomes zero at 

 d, from which point a line drawn to 

 a is a tangent to the circle. Sin 8 



