STUDIES ON MAGNETIC DISTRIBUTION 123 



lame et avec une quatrieme. Finalement les deux courbes se joignent 

 au 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 theoret- 

 ically 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 increase in the area of the rod, and should produce nearly 

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



3 



diameter in a rod of circular section. Now the quantity p = ~* is 



m 



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

 decreases as d 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 and are given by 

 the equation 



which is not dependent on the length of the rod This is exactly the 

 result found by Coulomb (Biot's Physique, vol. iii, pp. 74, 75). M. 

 Jamin has also remarked this. He states that as he increases the num- 

 ber of plates 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 combination is at its maximum." The normal magnet, 

 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 the following, supposing the weight of the 

 bar to be a fixed quantity in the first three. 



1st. The magnetic moment. 



2nd. The attractive force at the end. 



3rd. The total number of lines of magnetic force passing from the 

 bar. 



4th. The magnetic moment, the length being constant and diameter 

 variable. 



Either of these may be regarded as a measure of the power of the 

 bar, according to the view we take. The magnetic moment of a bar is 

 easily found to be 



