Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/109

 Rh Let the radius OP be parallel to the axis of a particular molecule in its original position.

Let SO represent on the same scale the magnetizing force X which is supposed to act from S towards 0. Then, if the molecule is acted on by the force X in the direction SO, and by a force D in a direction parallel to OP, the original direction of its axis, its axis will set itself in the direction SP, that of the resultant of X and D.

Since the axes of the molecules are originally in all directions, P may be at any point of the sphere indifferently. In Fig. 5, in which X is less than D, SP, the final position of the axis, may be in any direction whatever, but not indifferently, for more of the molecules will have their axes turned towards A than towards B. In Fig. 6, in which X is greater than D, the axes of the molecules will be all confined within the cone STT'  touching the sphere.

Hence there are two different cases according as X is less or greater than D.

Let
 * α = AOP, the original inclination of the axis of a molecule to the axis of x.
 * θ = ASP, the inclination of the axis when deflected by the force X.
 * β = 'SPO', the angle of deflexion.
 * SO = X, the magnetizing force.
 * OP = D, the force tending towards the original position.
 * SP = R, the resultant of X and D.
 * m = magnetic moment of the molecule.

Then the moment of the statical couple due to X, tending to diminish the angle θ, is and the moment of the couple due to D, tending to increase θ, is