the Absurdity of Diamagnetic Polarity. 265 



8A^+f(I, 0)81 <0. 



But since I 2 = A 2 + B 2 + C 2 , we have, when B and C are 

 constant, 



181 = ASA. 



Hence, for all values of 8A, we have 



If the quantity — + y\)r, within {...}, be positive, A can 



only decrease ; if it be negative, A can only increase ; if it 

 be zero, A can neither increase nor decrease. We have, 

 therefore, in stable equilibrium, at every point of a " perfectly 

 soft " substance, 



IdV IdY IdY 1 , . 



Ad^ = Bdi Gdi =-I^ 1 '^ ■■•(*) 



We must now explain the meaning of the differential co- 

 efficients of V. We know that if at any external point 

 P(#, y, z), a unit positive pole be placed without disturbing 

 the magnetization of any part of the given material system, 



\a^~l^'~ C ~dz) wiH be the ma S netic forces ( X > Y > Z )> 

 parallel to the axes, exerted on the unit pole at P by the 

 given system. When the point P is within the given system, 

 we cannot place a unit pole there without disturbing the 

 system. We therefore imagine a small right circular cylinder, 

 whose axis coincides with the direction of magnetization and 

 whose ends are perpendicular to the axis, removed from about 

 the point P ; and suppose that no change is made in the 

 system beyond the removal of the contents of the cylinder. 

 If the point P is in the midst of a liquid or gas, a thin sub- 

 stance, the magnetization of which may be neglected, must 

 be used as a lining for the cylinder, so that the interior of 

 the cylinder is vacuous. Then if V be the potential at P of 

 the new system obtained by removing the contents of the 



/ Q ]Y / dV' dV / 

 cylinder from the original system, I — -=— , — -j-, -±- J 



will be the magnetic forces parallel to the axes, exerted by 

 the new system on a unit positive pole placed at P without 

 disturbing the system. But if V v was the potential at P of 

 Phil. Mag. S. 5. Yol. 32. No. 196. Sept. 1891. T 



