Page:On Faraday's Lines of Force.pdf/25

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 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 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 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^[1].

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

1. Experimental Researches (2797), (2798). See Thomson, Cambridge and Dublin Mathematical Journal, May, 1847.