414 Prof. E. Edlund on the Theory 



integrals of the right-hand member of the preceding equation, 



2 r*=i # 



[H 2 + (R + r) 2 ]y 0=o (l-sin 2 esin 2 0)i 



2H 2 C$= t d(j> 



[H 2 + (E + rf]*X =0 (1 - sin 2 sin 2 </>)* 

 The elliptical integral of this will be 



9 9H 2 



[H 2 +(R + rf]i * ' [H 2 +(R + r) 2 J^H 2 +(R-r) 2 ] 



3. We will take as example H = R=10. ® will then be 



25°' 18, and the value of the formula (7) — . Multiplying 



this expression by 2~MrvAs, we have the total induction of the 

 ring equal to 0'2214 MuAs. 



If the magnet were at rest, but As in rotation as before 

 with the angular velocity v, and if the magnetism of the pe- 

 riphery were concentrated in the axis of the magnet, the 

 calculation of the magnitude of the induction would give the 

 following results : — The velocity of the element of the circuit 

 would be vR, the intensity of the magnetic pole would be 

 27rrM, and the cosine of the angle which the plane passing 

 through the direction of motion and the pole makes with the 



horizontal plane would be — — — ^r|« In virtue of formula (6) 



ylx + -tl j 



the induction would be 



27rrMi?R 2 Aa 



(R 2 + H 2 )t* 



If, as we have supposed above, H = R=10, we obtain, as 

 the value of the induction in As, 02221 MvAs, a value which 

 only differs from the former value by a little more than 0*3 

 per cent. 



Let us take some other examples. Suppose that H = and 

 R=10r. When the magnet and the element are in rotation 

 in the same direction with the same angular velocity v, 

 we obtain from formula (7) the magnitude of induction 

 = 0*630 MvAs. If the magnet is at rest and the element As 

 moves with the angular velocity v, and if we suppose the 

 magnetism concentrated in the axis of the magnet, the mag- 

 nitude of the induction will be equal to 0*628 M.v As, expres- 

 sions which differ from one another by 0*25 percent. Let us 

 suppose H = and R = 20r. The elliptical integral gives in 

 this case the value of the induction as equal to 0*3144 Mt-As. 



