the Absurdity of Diamagnetic Polarity. 275 



magnetism and gravitation arising from the fixed bodies 

 X, Y, Z ...-., it can easily be shown that no state of equi- 

 librium of the body P can be stable unless it be in material 

 contact with one or more of the fixed bodies. This proposition 

 is proved in Duhem's L'aimantation per influence. When P 

 is in material contact with one or more of the fixed bodies, 

 its equilibrium may, of course, be stable. The most useful 

 case to consider is the following : — 



Imagine a small bar of bismuth B, suspended from two 

 small balloons by threads, as in the figure, and suppose that 

 the mass of the system is slightly less than the mass of the 

 air which it displaces 

 when unmagnetized and 

 near the ground. Then, 

 if the system be set free, 

 it will ascend in the air, 

 and, of course, a state 

 of stable equilibrium 

 will be attained when it 

 has risen high enough, 

 if the weather be calm. B 



We may, however, ob- 

 tain a state of stable equilibrium in a more convenient way. 

 For if a permanent strong steel magnet M be fixed some 

 distance from the ground, just over the bar B, the system of 

 the bismuth and balloons, when let go, will ascend until the 

 motion is checked by the increased density and pressure of 

 the air about M, and will ultimately take up a state of stable 

 equilibrium suspended in the air at a moderate distance from 

 the ground. 



The problem just given was, we believe, first considered by 

 Sir W. Thomson, to whom it was suggested by the story of 

 the coffin of Mahomet. 



II. We will next consider the thermal phenomena due to the 

 motion of a soft body B in presence of a permanent magnet 

 M. For simplicity, let M be held at rest and suppose its 

 magnetism " rigid." Also let B be homogeneous, and let our 

 magnetized system consist merely of the two bodies B and M, 

 situated in a vacuum. Then if the temperature, in every 

 state of equilibrium, is uniform and equal to 6, and if no heat 

 can be absorbed or given out except at the temperature 0, we 

 shall have, in any small reversible operation, 



&Q = d8<j>. 



Now the formula for the entropy is 



<£ = </> o +j7<I,0)^ (2) 



