ELECTRO-MAGNETISM. 



observed, that when the position of the 

 needle differs much from that oi' SN, 

 the two poles, N and S, will be at very 

 different distances from the wire, and 

 the intensity of the force being inversely 

 as the distance, the forces acting upon 

 the two poles will, in consequence, differ 

 materially. When the forces concur in 

 their rotatory effect, the result will not 

 be affected by this difference ; but when 

 they oppose each other, the increase of 

 force acting on the nearer pole, will go 

 far towards compensating for the greater 

 obliquity of its direction, and will bring 

 it more nearly to an equality with the 

 smaller force, which acts with greater 

 mechanical advantage on the distant 

 pole. This equality is actually attained 

 when the wire passes through the cir- 

 cumference of the circle ; for now the 

 force acting upon S,Jig. 19, in the direc- 



Fig. 1 9. 



tion RS, is to the force acting upon N, 

 in the direction RN, inversely as the 

 distances WS and WN ; that is, they 

 are as \VN to \YS : but as the former 

 acts by the lever C s, and the latter by 

 the lever C n, which are themselves in 

 the proportion of WS to WN, they must, 

 by the laws of statics, be exactly in 

 equilibrium. 



To place the matter in another point 

 of view, the forces RS and RX, when 

 combined together, produce, as their re- 

 sultant, the force RW, which, being 

 directed to the centre of motion C, can 

 have no tendency to produce rotation. 

 Hence it follows, that the needle, what- 

 ever be its position in the circumference, 

 will appear to be totally uninfluenced by 

 Ihe wire : the action of the latter, on both 

 poles, exactly balancing each other. 



(38.) This state of equilibrium no 

 longer remains when the wire is within 

 the circle, fig. 20. It will now be found, 

 that in no position of the needle do the 

 two forces conspire to produce the same 

 rotatory motion^and that they oppose one 

 another in every part of the circle. The 



only position in which the equilibrium is 

 stable, is that of NS, the north pole 

 being to the left, and the south pole to 

 the right of the wire ; a position which, 

 it should be observed, is exactly the re- 



verse of that which the needle assumes 

 when the wire is out of the circle, as 

 in figs. 17 and 18. When disturbed 

 from this position, and brought to n' s', 

 for example, the force urging the pole 

 n', which is nearest to the wire, becomes 

 more effective than that acting upon the 

 more distant pole s', and, therefore, 

 brings back the needle to its station. 

 But if the pole N were placed on the 

 opposite side of the wire, as at n', the 

 tangential force which carries it towards 

 the wire, is, here also, more effective 

 than that which acts upon the distant 

 pole s', and which tends to move it in 

 the contrary direction ; the needle, there- 

 fore, strikes against the wire, and being 

 unable to pass it, remains in contact 

 with it. If the. needle be carried still 

 further from the wire, however, the su- 

 periority of this force will continually 

 diminish, and cease entirely when the 

 needle is in the transverse position SN, 

 shown in fig. 21, where the two poles, S 

 and N, are equi-distant from W. Here 

 there is again an equilibrium, but it is of 



Fig. 21. 



