ELECTRO-MAGNETISM 



that point, are equal. It will also be 

 convenient to analyze the actions of 

 each circular current into those exerted 

 in planes at right angles to each other, 

 a mode of viewing them which, being 

 analogous to the artifice of the re- 

 solution of forces constantly resorted 

 to in dynamics, will make no dif- 

 ference in the results. Conceive, then, 

 that the currents, instead of moving 

 in the circumference of a circle, tra- 

 verse the four sides of a square, and 

 that the cylinder is represented by a 

 square prism. S N, fig, 140, is in- 

 tended to convey the idea of a prism, 

 so constituted, the surface of which is 



Fig. 140. 



occupied by electric currents circulating 

 round each of the laminae, into which it 

 may be divided by planes perpendicular 

 to its axis, the direction of the currents 

 being marked in the two sides which 

 come into view, by the arrows. On the 

 sides opposite to them, and which are 

 not seen, the currents are, of course, 

 moving in the contrary directions. 



(239.) Let us now examine the effects 

 of currents in each side upon a straight 

 conductor, whose direction is at right 

 angles to the axis, and which is placed 

 in various positions with regard to the 

 prism. 



Let P Q R S, fig. 141, be the upper 

 surface of this prism, its axis being 

 horizontal ; let W be the section of a 

 vertical conducting wire, of indefinite 



length, perpendicular to the plane of the 

 figure ; and let the current be moving in 

 this wire in the same direction as those 

 currents which traverse the adjacent ver- 

 tical side of the prism, of which the upper 

 edge is P Q. We shall suppose, for exam- 

 ple, that the currents are ascending in the 

 wire, and also in the side adjacent to it, 

 whence they traverse the upper side 

 from P Q towards R S (as denoted by 

 the arrows), descending again on the 

 side opposite to W, and of which the 



edge is R S, and returning on the lower 

 side in a direction from R S towards 

 PQ. 



Since the currents are passing in op- 

 posite directions in the upper and lower 

 surfaces of the prism, their effects on W 

 (as far as any horizontal motion is con- 

 cerned) are completely neutralized ; and 

 we need, therefore, only examine the ac- 

 tions of the vertical surfaces PQ and RS. 

 Let RW and S W be the sections of two 

 vertical planes, drawn from W to R and 

 to S, cutting P Q in U and V respectively. 

 It follows from the proposition above 

 referred to that the actions of the cur- 

 rents in that portion of the surface P Q, 

 adjacent to W, which is included be- 

 tween U and V, are exactly balanced 

 by the currents in the whole of the sur- 

 face R S, opposite to it, and which run 

 in contrary directions. The resulting 

 action, therefore, will be determined 

 only by the currents in the remaining 

 portions of the surface P Q, situated 

 between P and U on the one side, and 

 between V and Q on the other, both of 

 which attract the current in W: the 

 former in the direction of W u, the lat- 

 ter in the direction W v. These two 

 forces combine in giving a resultant in 

 the direction W r, indicating an attrac- 

 tion towards the centre of the prism. 



(240.) In proportion as the situation 

 of the vertical conductor is taken nearer 

 to either of the extremities of the prism, 

 such as Q S, for instance, the portion 

 P U of the side P Q, intercepted between 

 the plane RW and the extremity P, 

 increases in extent, while the portion 

 VQ diminishes. Consequently the forces 

 arising from the attractions of the former 

 portion are proportionally increased, and 

 those from the latter diminished, and the 

 resulting force gradually becomes more 

 inclined towards P. 



(241.) When W is situated in the 

 plane of the side Q S, as in fig. 142, the 

 force arising from the currents adjoining 



W 



Fig. 142. 



TJ>" 



to Q vanishes entirely, and the action 

 upon the wire depends solely upon the 

 currents in the remoter division of the 

 side PQ, namely, that comprehended 

 between P and U. The resultant force 

 will therefore be directed towards these 



