Action of a Galvanic Coil on an external small Magnet. 351 



sists of. But it is evident that the motion of the current 

 parallel to the axis of the conductor has no effect in determining 

 the angular position of the magnet, inasmuch as it cuts the plane 

 in which the magnet is compelled to move at right angles. 

 Also the small secondary motions generated by the reaction of 

 the atoms against the portion of the current which flows in the 

 interior of the conductor, if they should be of sensible amount, 

 would have no tendency to cause vibrations of the magnet, 

 because the aggregate directive effects of those on the opposite 

 sides of the plane of vibration would be just equal and opposite. 

 It remains only to consider the effect of the circular motions 

 about the conductor in planes perpendicular to the plane of its axis. 

 45. Now these motions will have a directive effect on the 

 magnet in two ways, which will require separate considerations. 

 First, the angular position of the magnet will be determined in 

 part, and in a direct manner, by the circular motions about the 

 two opposite points of intersection of the axis of the conductor 

 by the transverse plane passing through the centres of the mag- 

 net and of that axis. If A and B be these points and P be the 

 given point, these motions, being in the same direction about 

 the axis of the conductor, will be in opposite directions about 

 the points A and B, and, according to the law stated in art. 43, 

 will vary inversely as the squares of the distances AP and BP. 

 Hence it is easy to calculate the sums of the resolved parts of 

 the velocities in two rectangular directions, one parallel to the 

 before-mentioned axis through the centre of the conductor, which 

 will be supposed to be the axis of z, and the other parallel to 

 the intersection of the plane of the circular axis by the plane 

 through the axis of z and the point P. If we suppose the latter 

 plane to be coincident with the plane zx, the resolved velocities 

 will be parallel to the direction of the axes of z and x. Hence 

 if z be the distance OC of the centre C of the circular axis from 

 the origin of coordinates, and if p and q be the coordinates of 

 P parallel to the axes of z and on, and a be the radius of the cir- 

 cular axis, then, the two above-mentioned velocities being ex- 

 pressed by 



" 'and 



and the sums of their resolved parts in the directions of the axes 

 being X and Z, it will be found that 



X = a ^P~ z ) Kp-z) 



((*-*)*+ ta-r*)*) 1 ((*-*)*+ te+a) 2 / 



z = Mg— fl ) , Mg+«) 



C(J>-T*)»+ fa-*)*)! ((*-*)•+ (* + «)•)*■ 



