104 H. A. Rowland — Studies on Magnetic Distribution. 



plates on one another, lie sajs : " 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 magn^tisme quitte les faces que Ton 

 met en contact pour refugier sur les parties exterieures. En 

 meme temps, les deux courbes se rapprochent I'une de I'autre 

 et du milieu de I'aimant. Get effet augmente avec une troi- 

 si^me lame et avec une quatrieme. Finalement les deux cour- 

 bes se joignent en milieu." 



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

 we have only to remark that when the bars lie closely together, 

 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 to an increase 

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

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

 in a rod of circular section. Now the quantity p=-^ is nearly 

 constant in these rods for the same quality of steel, whence r 

 decreases as c? increases; and this in equation (17) shows that 

 as the diameter is increased, the length being constant, the 

 curves become less and less steep until they finally become 

 straight lines. This is exactly the meaning of M. Jamin's 

 remark. 



Where the ratio of the diameter to the length is small, the 

 curves of distribution are apparently separated from each other, 



=4^^R^'" 



which is not dependent on the length of the rod. This is ex- 

 actly the result found by Coulomb (Biot's Physique, vol. iii, pp. 

 74, 75.) M. Jamin has also remarked this. As he increases the 

 number of plates, he states that the curves approach each other 

 and finally unite; this he calls the "normal magnet;" and he 

 supposes it to be the magnet of greatest power in proportion 

 to its weight. '' From this moment," says he, " the combina- 

 tion is at its maximum." The normal niagnet as thus defined 

 is very indefinite, as M. Jamin himself admits. 



By our equations we can find the condition for a maximum, 

 and can give the greatest values to tbe following, supposing 

 the weight of the bar to be a fixed quantity in the drst three. 



1st The magnetic moment. 



2d. The attractive force at the end. 



3d. The total number of lines of magnetic force passing from 

 the bar. 



