ASTATIC SYSTEMS. 287 



298. ACTION OF A UNIFORM FIELD ON A MAGNET. If we con- 

 sider a magnet whose moment M equals ml, situated in a uniform field 

 whose strength F makes the angle 6 with the axis of the magnet, 

 the moment of the couple produced by the action of the field is 

 equal to Yml sin 6 or FM sin 6. This is the moment of the couple 

 which would tend to turn the magnet about a straight line perpen- 

 dicular to the magnetic axis and to the force of the field. 



If the magnet is movable about a given axis, the couple of 

 rotation only depends on the projections M x and F x of the magnetic 

 moment and of the strength of the field, on a plane perpendicular to 

 the axis, for the projections on the axis are without influence. If B 1 

 is the angle of the directions of M x and of F 1? the moment of the 

 couple is equal to FjMj sin # r 



Let, generally, #, , c and a, /?, y denote respectively the cosines 

 of the angles which the directions of F and M make with three 

 rectangular axes, and let us replace these magnitudes by their pro- 

 jections on the three axes. The moment of the couple which tends 

 to turn the magnet about the axis of z is 



Z = F. Ma -F 

 We shall have, similarly, for the other axes, 



The product FM is sometimes called the moment of the action 

 of the field upon the magnet ; it is the moment of the couple which 

 would be produced if the magnet were perpendicular to the direction 

 of the field. As a particular case, if T is the intensity of the 

 terrestrial field, the product TM will be the moment of the terrestrial 

 action on the magnet. 



299. ASTATIC SYSTEMS. Take the particular case of two mag- 

 nets (Fig. 72) whose magnetic moments are OA and OA', the 



Fig. 72. 



resultant moment is the diagonal OB of the parallelogram drawn on 

 OA and OA'. If the moments OA and OA' are equal and exactly 



