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



lopment of Faraday's idea of the analogy between a magnet and 

 a voltaic battery immersed in water. I shall throughout speak 

 of the conduction of, and resistance to, lines of magnetic force, 

 and shall otherwise treat them as similar to lines of conducted 

 electricity or heat, it now being well established from the re- 

 searches of Professor Maxwell and others that this method gives 

 exactly the same results as the other method of considering the 

 action to take place at a distance. 



In arranging this paper I have thought best to give the theory 

 of 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 dis- 

 tribution 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 elec- 

 trified by heat. He compared his formula with Coulomb's ob- 

 servations, and showed it to represent the distribution with con- 

 siderable accuracy. Green, in his ' Essay/ has obtained a for- 

 mula which gives the same distribution ; but he obtains it by a 

 series of mathematical approximations which it is almost impos- 

 sible 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*" to enter 

 that end of the bar, and, after passing down it to a certain dis- 

 tance, to pass out into the air and so round to the bar again to 

 complete their circuit. At every part of their circuit they en- 

 counter some resistance, and always tend to pass in that direc- 

 tion where it is the least : throughout their whole course they 

 obey a law similar to Ohm's law; and the number of lines pass- 

 ing in any direction between two points is equal to the difference 



* 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. 



