ASTATIC CIRCUITS. 



473 



currents. Figures 115, 116, and 117 give examples of currents 

 which realise these conditions. 



If the two surfaces S and S' were not equal, the action of the 

 field would be proportional to their difference S - S'. 



H- S' 



Fig. 115- 



B 



Fig. 1 1 6. 



Fig. 117. 



490. ROTATION OF A CURRENT UNDER THE ACTION OF THE 

 EARTH. A portion of a current not closed, and movable about 

 an axis, takes in general a continuous rotatory motion under the 

 influence of terrestrial magnetism. 



We observe, in the first place, that in a uniform magnetic field, 

 like the terrestrial field, we may always replace a current by its 

 projection on three rectangular planes ; this amounts, in fact, to 

 replacing the strength of the field by its three rectangular 

 components. 



Consider any given current movable about an axis and determine 

 its projections on three planes, one perpendicular to its axis of 

 rotation, the two others passing through this axis, and such that 

 one of them is parallel to the direction of the field ; let S, S', and S" 

 be these three projections. The projection S" perpendicular to the 

 field will not produce any action. The action on the projection S' 

 will be purely directive ; the circuit of the current will be carried 

 along in such a manner that the surface S" is a maximum, and 

 presents its negative face to the force ; in our hemisphere the current 

 must be descending in the part turned towards the east. There 

 remains to be considered the projection S on the plane perpendicular 

 to the axis. If it is closed, and of a fixed shape, it undergoes no 

 action ; if part of it is movable, the component of the field parallel 

 to the axis will have a constant moment relatively to this axis, and 

 will produce a continuous rotation. 



