ELECTRO-MAGNETISM. 



sent through such a wire wiil affect a 

 needle placed between its two branches 

 with twice the force that a single wire 

 would have exerted. This effect may be 

 exhibited by the following simple appa- 

 ratus, represented in Jig. f>9 ; where the 

 two cups terminating the bent wire 

 W A w B which passes above and be- 



Fig. 59. 



low a magnetic needle balanced on a 

 point, enable us to transmit through it 

 an electric current in any direction we 

 please. This current, moving in opposite 

 directions in the upper and lower hori- 

 zontal portions of the wire, will con- 

 spire, in bolh cases, to deflect it from 

 its natural position in the same direc- 

 tion, and to bring it into a position 

 nearer to a right angle to the plane of 

 the wires. 



(92.) The force with which each pole 

 is impelled in a line at right angles to 

 the plane in which the wires are situated, 

 is directly as the intensity of the cur- 

 rent, (supposing it to be equal in both 

 wires,) and directly as the length of the 

 interval between the wires, and also in- 

 versely as the square of the distance of 

 the pole from the wires. This will ap- 

 pear from the following considerations. 

 Let A and B represent the sections 

 of two wires passing perpendicularly 

 through the plane of the figure, C being 



Fig. GO. 



A. 



the middle point of the line A B, which 

 constitutes the interval between them. 

 Let the magnetic pole P be placed at 

 various distances along the line C R, 

 perpendicular to A B, and consequently 

 perpendicular to the vertical plane which 



passes through AB, and comprehends 

 the two wires. Supposing the wires to 

 be of indefinite length ; the law of ac- 

 tion is such, that the intensity of the 

 tangential force exerted on the pole P 

 by the wire A, is inversely as the dis- 

 tance A P, which we shall call a, and is 

 in the direction P Q, perpendicular to 

 A P. In like manner, the wire B exerts 

 upon the pole P, a force in the direction 

 of P S, and which, on the supposition of 

 an equal intensity in the two currents, 

 is equal to the former force. If these 

 two forces be represented by the lines 

 P Q and P S, which we shall call q and 

 s, the resultant force will be represented 

 by the diagonal P R of the parallelo- 

 gram, having P Q and P S for its sides. 

 Calling PR, r, and AB, i y we have 

 this proportion, 



: : q : r, 



that is, 



but, in different positions of P along the 

 line C R, q will vary inversely as a ; and 



therefore r will be as ; that is, the 

 a 2 



force by which the pole P is urged in 

 the direction of the line C R, by the con- 

 joined action of the two wires A and B, 

 varies, in different situations in that line, 

 inversely as the square of its distance 

 from either of the wires, and directly as 

 the length of the interval between the 

 wires. 



(93.) In order to estimate the rota- 

 tory force exerted on a needle constrained 

 to move round a fixed axis in a plane 

 perpendicular to that of the wires, as in 

 the examples above given, $$ 90, 91 ; it 

 will be necessary to resolve the force 

 above found into one acting in the di- 

 rection of the tangent to the circumfe- 

 rence of rotation ; that is, to reduce it 

 in the proportion of radius to the cosine 

 of the angle which the needle forms with 

 the plane of the wires. 



(94.) In the situation of the magnet 

 represented in fig. 59, where the wires, 

 instead of extending indefinitely in the 

 horizontal direction, enclose the magnet 

 also on the sides, the influence of the 

 lateral portions A and B require to be 

 taken into account in estimating the 

 effect produced. A little consideration 

 will satisfy us that the action of these 

 parts concur with those of the horizontal 

 portions in giving the same directive 

 tendency to the needle ; and that, in 

 fact, if we suppose the wire to be bent 



