362 Mr. H. A. Rowland on Magnetic Distribution. 



magnets and steel magnets, and found that the formula? re- 

 present it in a general way, we may now use them for solving 

 a few questions that we desire to solve, though only in an 

 approximate manner. 



VI. 



M. Jamin, in his recent experiments on magnetic distribu- 

 tion, has obtained some very interesting results, although I 

 have ^shown his method to be very defective. In his experi- 

 ments on iron bars magnetized at one end, he finds the formula 

 € rl to apply to long ones as I have done. Now it might be 

 argued that as the two methods apparently give the same re- 

 sult, they must be equally correct. But let us assume that 

 the attraction of his piece of soft iron F varied as some un- 

 known power n of the surface-density 8. Then we find 



F = Ce w,L , 

 which shows that the attractive force or any power of that force 

 can be represented by a logarithmic curve, though not by the 

 same one. Hence the error introduced by M. Jamin's method 

 is insidious and not easily detected, though it is none the 

 less hurtful and misleading, but rather the more so. 



However, his results with respect to what he calls the nor- 

 mal magnet* are to some extent independent of these errors ; 

 and we may now consider them. 



Thus, in explaining the effect of placing hardened steel plates 

 on one another, he says, " Quand on superpose deux lames 

 aimantees pareilles, les courbes qui representent les valeurs de F 

 [the attractive force on the piece of soft iron] s'elevent, parce 

 que le magnetisme quitte les faces que Pon met en contact pour 

 se refugier sur les parties exterieures. En meme temps, les 

 deux courbes se rapprochent Pune de P autre et du milieu de 

 l'aimant. Cet effet augmente avec une troisieme lame et avec 

 une quatrieme. Finalement les deux courbes se joignent an 

 milieu." 



In applying the formula to this case of a compound magnet, 

 we have only to remark that when the bars lie closely toge- 

 ther they are theoretically the same as a solid magnet of the 

 same section, but are practically found to be stronger, because 

 thin bars can be tempered more uniformly hard than thick ones. 

 The addition of the bars to each other is similar, then, to an in- 

 crease in the area of the rod, and should produce nearly the 

 same effect on a rod of rectangular section as the increase of 



rd 

 diameter in a rod of circular section. Now the quantity ja = — 



* " On the Theory of the Normal Magnets," Comptes Rendus, March 31, 

 1873 ; translated in Phil. Mag. June 1873. 



