Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/44

 Rh Since the direction of h3 is arbitrary, we must have

The force R is a repulsion, tending to increase r; Hl and H2 act on the second magnet in the directions of the axes of the first and second magnet respectively.

This analysis of the forces acting between two small magnets was first given in terms of the Quaternion Analysis by Professor Tait in the ''Quarterly Math. Journ.'' for Jan. 1860. See also his work on Quaternions, Art. 414.

Particular Positions.

388.] (1) If λ1 and λ2 are each equal to 1, that is, if the axes of the magnets are in one straight line and in the same direction, μ12 = 1, and the force between the magnets is a repulsion

The negative sign indicates that the force is an attraction.

(2) If λ1 and λ2 are zero, and μ12 unity, the axes of the magnets are parallel to each other and perpendicular to r, and the force is a repulsion

In neither of these cases is there any couple.

(3) If

The force on the second magnet will be $$ \frac{3 m_1 m_3}{r^4} $$ in the direction of its axis, and the couple will be $$ \frac{2 m_1 m_2}{r^4} $$, tending to turn it parallel to the first magnet. This is equivalent to a single force $$ \frac{3 m_1 m_2}{r^4} $$ acting parallel to the direction of the axis of the second magnet, and cutting r at a point two-thirds of its length from m2.

Fig. 1.

Thus in the figure (1) two magnets are made to float on water, m2