Permanent Magnets. 151 



magnetic resistance, then 



P 



which accounts for IS being proportional to the length, or to 

 the thickness of the disk, the point which it seems impossible 

 to deal with by the method of induction. 



As to the focal distance, or distance between the points of 

 application of the resultants, it is easy to see that for thin 

 disks it must be nearly equal to some constant, which we may 

 call F . We can thus establish for the moments of very thin 

 disks the formula 



Moment = ^^ (S= area) ; 

 and putting for U its value, 



Moment = 5^^; 

 4:7rp 



or if a bar of length I be divided into m pieces, so that 



/ 

 os= — 

 rn? 



then the moment of one piece . . . . = — ° _ 



4:7rp m' 



and total moment of bar cut up into pieces = o \ 



4:7Tp ' 



a finite limit when m is great. 



We cannot deal accurately with the intervening distribu- 

 tions, as they require the knowledge of the value of F in order 

 to obtain the moments from the inductions. But we may 

 consider the case, which is not far from the truth, for bars 

 whose length is about half the limit of the linear range viz. 

 where we suppose F = .#, or/=l, or that the foci are at the 

 ends of the bar. It will be seen that this is very nearly true 

 for n = 3 in bar A. In this case, putting x for F, 



P'S 



Moment = -. — a?\ 



47T/0 



and for a short range the moment can be expressed approxi- 

 mately in terms of the square of the length. The true forms 

 of the expressions throughout the linear range have been given 

 above. 



