Permanent Magnets. 147 



Mcalc. = 22'7 +n 3-3. 

 1$ calc. = til-Ill. 

 The limiting value F =l-25 centim., 



§=•657. 



The expressions above arrived at for bars within the range 

 covered by the linear relations may be put in a more conve- 

 nient form by introducing x, the length of the cylinder, instead 

 of the number n, into the expressions. Remembering that 



mra = N, mx=l, 

 and putting 



M = M + wM / J 



where M , M / are constants, the moment of a bar of length x is 



m I u I 

 Again, putting i$ = nW, where W is a constant, 



n=fim'; (i) 



also - 47rM a3 



_ 4tt_/Mo , M^\ 



In this last put x=0, then 



^EWS' ^ 



Applying these formulae, we find for bars of length x, 

 magnetized in the same manner as A, B, C respectively, the 

 following expressions, within the linear range: — 



A. B. 0. 



M, . . 5-24^ + 5-88^ 2 , 4-51^ + 5-77^ 6-22 *? + 4-46 .z 2 . 

 % . . 28-9^, 25-30 oj, 5-483^. 



f ...™ ^+-955, ^ + -898. 



J X X ' X 



F... -758 + -851#, -746 + -955^', l-25 + '898^ 



F 



R 



•775, -762, -657. 



L2 



