Mb maxwell, ON FARADAY'S LINES OF FORCE. 45 



and diamagnetic bodies worse, than the surrounding medium. By referring to (23) and (26), 

 and supposing sources to represent north magnetic matter, and sinks south magnetic matter, 

 then if a paramagnetic body be in the neighbourhood of a north pole, the lines of force on 

 entering it will produce south magnetic matter, and on leaving it they will produce an equal 

 amount of north magnetic matter. Since the quantities of magnetic matter on the whole are 

 equal, but the southern matter is nearest to the north pole, the result will be attraction. If 

 on the other hand the body be diamagnetic, or a worse conductor of lines of force than the 

 surrounding medium, there will be an imaginary distribution of northern magnetic matter 

 where the lines pass into the worse conductor, and of southern where they pass out, so that on 

 the whole there will be repulsion. 



We may obtain a more general law from the consideration that the potential of the whole 

 system is proportional to the amount of work done by the fluid in overcoming resistance. The 

 introduction of a second medium increases or diminishes the work done according as the resist- 

 ance is greater or less than that of the first medium. The amount of this increase or diminu- 

 tion will vary as the square of the velocity of the fluid. 



Now, by the theory of potentials, the moving force in any direction is measured by the 

 rate of decrease of the potential of the system in passing along that direction, therefore when 

 k', the resistance within the second medium, is greater than k, the resistance in the sur- 

 rounding medium, there is a force tending from places where the resultant force v is greater to 

 where it is less, so that a diamagnetic body moves from greater to less values of the resultant 

 force *. 



In paramagnetic bodies k' is less than k, so that the force is now from points of less to 

 points of greater resultant magnetic force. Since these results depend only on the relative values 

 of k and k', it is evident that by changing the surrounding medium, the behaviour of a body 

 may be changed from paramagnetic to diamagnetic at pleasure. 



It is evident that we should obtain the same mathematical results if we had supposed that 

 the magnetic force had a power of exciting a polarity in bodies which is in the same direction 

 as the lines in paramagnetic bodies, and in the reverse direction in diamagnetic bodies -j*. In 

 fact we have not as yet come to any facts which would lead us to choose any one out of 

 these three theories, that of lines of force, that of imaginary magnetic matter, and that of 

 induced polarity. As the theory of lines of force admits of the most precise, and at the same 

 time least theoretic statement, we shall allow it to stand for the present. 



Tlieory of Magnecrystallic Induction. 



The theory of Faraday J with respect to the behaviour of crystals in the magnetic field 

 may be thus stated. In certain crystals and other substances the lines of magnetic force are 



" Experimental Researches (2797), (2798). See Thom- 

 son, Cambridge and Dublin Mathematical Journal, May, 

 1847. 



t Exp. Res. (2429), (3320). See Weber, PoggendorfF, 

 Ixxxvii. p. 145. Prof. TyndaU, Phil, Trans. 1856, p. 237. 

 i Exp. Res. (2836), &c. 



