90 HENRY A. BOWLAND 



the distribution first, and then afterwards to see how the results agree 

 with experiment; in this way we can find out the defects of the theory, 

 and what changes should be made in it to adapt it to experiment. 



At present I am acquainted with two formulae giving the distribu- 

 tion of magnetism on bar magnets: the first was given by Biot, in his 

 Traite de Physique Experimentale et Mathematique, vol. iii, p. 77, and 

 was obtained by him from the analogy of the magnet to a dry electric 

 pile, or to a crystal of tourmaline electrified by heat. He compared 

 his formula with Coulomb's observations, and showed it to represent 

 the distribution with considerable accuracy. Green, in his ' Essay/ 

 has obtained a formula which gives the same distribution; but he ob- 

 tains it by a series of mathematical approximations whi^h it is almost 

 impossible to interpret physically. M. Jamin has recently used a 

 formula of the same form; but I have as yet been unable to find how 

 he obtained it. My own formulae are also quite similar to these, but 

 have the advantage of being obtained in a more simple manner than 

 Green's ; and, what is of more consequence, all the limitations are made 

 at once, after which the solution is exact; so that although they are 

 only approximate, yet we know just where they should differ from 

 experiment. 



II. 



If we take an iron bar and magnetize one end of it either by a magnet 

 or helix, we cause lines of magnetic induction s to enter that end of the 

 bar, and, after passing down it to a certain distance, to pass out into 

 the air and so round to the bar again to complete their circuit. At 

 every part of their circuit they encounter some resistance, and always 

 tend to pass in that direction where it is the least: throughout their 

 whole course they obey a law similar to Ohm's law; and the number 

 of lines passing in any direction between two points is equal to the 

 difference of magnetic potential of those points divided by the resist- 

 ance to the lines. 



The complete solution of the problem before us being impossible, let 

 us limit it by two hypotheses. First, let us assume that the permea- 

 bility of the bar is a constant quantity; and secondly, that the resist- 

 ance to the lines of induction is composed of two parts, the first being 

 that of the bar, and the second that of escaping from the bar into the 



3 For difference between lines of magnetic force and lines of magnetic induction 

 see Maxwell's 'Treatise on Electricity and Magnetism,' arts. 400, 592, and 604. 



