182 Prof. Thomson on the Theory of Magnetic Induction 



cipal axis, and the inductive capacities with reference to all these 

 principal axes are equal. 



7. If the inductive capacities with reference to three principal 

 axes through any point of a substance be equal, every line through 

 the substance is a principal axis, and the inductive capacities 

 with reference to all directions are equal ; or the substance is 

 destitute of magnecrystallic properties. 



8. A spherical portion of any homogeneous substance, sup- 

 ported in a uniform magnetic field in such a manner that it can 

 tm'n freely in any manner round its centre which is immoveable, 

 cannot be in equilibrium unless a principal axis be in the direc- 

 tion of the lines of force. If the three principal inductive capa- 

 cities be unequal, the body will be in stable equilibrium with 

 the principal axis of greatest inductive capacity, or in unstable 

 equilibriimi with either of the two other principal axes, in the di- 

 rection of the lines of force. If the two less principal inductive 

 capacities be equal to one another, the body will be in stable* 

 equilibrium with the principal axis of greatest inductive capacity 

 in the direction of the lines of force, or in unstable equilibrium 

 with the same axis pei'pendicular to the lines of force. If the 

 two greater principal inductive capacities be equal to one another, 

 the body will be in stable t equilibrium with the plane of the coitc- 

 sponding principal axes parallel to the lines of force, or in unstable 

 equilibrium with that plane perpendicidar to the lines of force. 



9. If a spherical portion, of volume a, of a substance of which 

 the three principal inductive capacities are A, B and C, be held in 

 a imiform magnetic field where the intensity of the force in abso- 

 lute measure is F, with the three principal axes of induction in- 

 clined to the direction of the force at angles of which the cosines are 

 respectively I, m, n, it will receive a state of magnetization which 

 is the resultant of three states of uniform magnetization ; one of 

 intensity A.F/, in the direction of the first principal axis; a second 

 of intensity B . Ym, in the direction of the second principal axis ; 

 and a third, of intensity C . Fm, in the direction of the third prin- 

 cipal axis ; and it will expenence a tm'ning action, of which the 

 mechanical definition is a couple, of which the moment is 



o-.F2.{mV(B-C)2 + n2/2(C-A)2 + ftM2(A_B)2}*, 



in a plane of which the direction cosines | with reference to the 



* In one respect the equilibrium might be said to be neutral rather than 

 stable, since every position into which the body may be tm-ned round the 

 stable axis is a position of equilibrium. 



t In two respects the equilibrium might be said to be neutral ; since every 

 position into which the body may be turned round the direction of the lines 

 of force is a position of equilibrium, and every position into which it may 

 be turned in the plane of the stable principal axes is a position of equilibrium. 



X Or the cosines of the incUnations of a perpendicular to the plane, to 

 the three axes. 



