Mr. H. A. Rowland on Magnetic Distribution. 363 



is 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 



\= f e-", (18) 



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 number 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 combina- 

 tion 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 



M- £ S h --\ l ~ e ~ r b \ 



47rr 2 R/l2 r .l+e-*J' ' * ' (l9 ) 



and if 7 is the weight of a unit of volume of the steel and W is 

 the weight of the magnet, we have finally 



wkeC= 7i =p \/w 



