ON FARADAY'S LINES OF FORCE. 179 



conduct the lines of force better, 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 poten- 

 tial 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 resistance is greater or less than 

 that of the first medium. The amount of this increase or diminution 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 surrounding medium, there is a force tend- 

 ing 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 para- 

 magnetic 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 



* Experimental Kesearches (2797), (2798). See Thomson, Cambridge and Dublin Matiiemntical 

 Journal, May, 1847. 



232 





