ELECTRO-MAGNETISM. 



influence of a single circular current 

 C D, Jig. 126, on a straight terminated 

 current A B, perpendicular to the plane 

 of the circle, is to induce in it a ten- 

 dency to revolve with a motion parallel 

 to itself, round the line drawn from the 

 centre of the circle perpendicularly to 

 its plane, it is evident that the addition 

 of similar circles, placed in succession 

 exactly below the first, (supposing the 

 axis vertical, as in the figure,) uill tend 

 to increase this force of revolution. The 

 effect of each additional circle, it is true, 

 is less than the preceding, not only be- 

 cause its distance is greater, but also 

 because its action is more oblique, and 

 because the difference between the ac- 

 tions of the nearer and more remote 

 portions of the circle continually di- 

 minishes as the angle between the 

 lines drawn from the several points in 

 the straight conductor, and the centres 

 of the respective circles, increases, which 

 is the case as they are further removed 

 from the extremity of the straight con- 

 ductor. From all these considerations, 

 the force by which the current A B,Jfg. 

 139, is urged to revolve round the axis, 



Fig. 139. 

 AA 



X, in consequence of the action of the 

 lowermost circle G H, is plainly less 

 than that exerted by the circle F /, and 

 still less than that exerted by C D. 



(236.) On the other hand, if we add 

 in succession a number of circular cur- 

 rents above C D, they will conspire with 

 the lower circles in their effect of pro- 

 ducing: a tendency to revolution in the 

 straight conductor; but each will do 

 this only by its action on that part of 

 the conductor that is above its own 

 plane ; for its operation in any portion 



situated below that plane is to produce 

 a revolution in the contrary direction. 

 So that the action exerted upon any 

 elementary portion of a vertical current, 

 at E, for example, is, as far as it depends 

 upon the circles above that which is 

 nearest to it, exactly balanced by an 

 equal number of circles below it ; that 

 is, the circles lying between C and e are 

 counterbalanced by those lying between 

 e and F, the whole of that portion of 

 the cylinder between C and F being 

 neutralized ; and the only portion that 

 is active being that which lies beyond 

 F, that is, between F and G. 'This 

 active part of the cylinder becomes 

 smaller in proportion as the element is 

 situated nearer to the plane which di- 

 vides the cylinder into two equal parts ; 

 and at this point the action is reduced 

 to nothing: on the contrary, it increases 

 as the element comes nearer to either 

 extremity of the cylinder, where it is the 

 greatest of all. These extremities may 

 accordingly be considered as the active 

 poles of the cylinder, round which the 

 revolution of the conductor is made: 

 the resultant of all the forces called into 

 action by every part of the cylinder has 

 the direction of the tangent of the circle 

 of revolution ; that is to say, is at right 

 angles to the line joining the straight 

 conductor and the pole. 



(237.) It is hardly necessary to re- 

 mark that the action in this, as in 

 every other instance, is reciprocal be- 

 tween the straight conductor and elec- 

 tro-dynamic cylinder; so that if the 

 conductor be fixed and the cylinder 

 moveable, the latter will revolve round 

 the former ; or, if restricted to a motion 

 round its own axis, it will perform a 

 rotatory movement round that axis. 



(238.) The same tendency to revolu- 

 tion about the poles of an electro-dynamic 

 cylinder, arising from a force of a tan- 

 gential kind, apparently emanating from 

 these poles, is observed to take "place, 

 whatever be the angle of inclination 

 between the straight conductor and the 

 axis of the cylinder. In order to ex- 

 plain this curious fact, the application 

 of which is of considerable importance 

 in a theoretical point of view, we must 

 avail ourselves of the principle enun- 

 ciated above ( 198), namely, that the 

 electro-dynamic action of currents that 

 occupy in a similar manner two different 

 surfaces, subtending the same angular 

 extent, and lying in the same direction 

 with reference to any point, on an ele- 

 mentary portion of current situated at 



