90 



ELECTRO-MAGNETISM. 



(291.) If a steel bar, instead of being 

 bent into the form of a horseshoe, be 

 formed into a complete ring, fig. 167, 



Fig. 167. 



and then magnetized, it exhibits no 

 magnetic properties as long as the ring 

 is entire; but when broken into any 

 number of portions, each part has two 

 poles, and possesses all the properties 

 of an ordinary magnet. This experi- 

 ment suggested the theoretical investi- 

 gation of the properties of a system of 

 small circular currents situated in planes 

 perpendicular to another circle, passing 

 through all their centres. The result of 

 the investigation of this problem led to 

 a mathematical theorem exactly con- 

 formable to observation ; a ring so con- 

 stituted, or an electro-dynamic ring, as 

 it has been called, being found, both 

 from theory and experiment, to exert no 

 action upon a voltaic conductor or mag- 

 net, at whatever distance from it, or in 

 whatever situation it may be placed. 



(292.) In viewing the application of 

 Ampere's theory to the mutual action 

 of two magnets, we might content our- 

 selves with the observations already 

 made as to the mutual action of two 

 electro- dynamic cylinders, which may 

 be taken as their representatives ; and 

 simply refer to the general principle 

 deduced from theoretical considerations, 

 251, namely, that the resultants of all 

 the actions may be reduced to forces 

 emanating from the poles, and inversely 

 proportional to the squares of the dis- 

 tances. Yet as a more popular view of 

 the actual operation of the forces derived 

 from the attraction or repulsion of cur- 

 rents in the simpler cases may be more 

 satisfactory, we shall examine a few of 

 these cases. 



(293.) It will be evident that when 

 two magnets are presented to each 

 other, with their axes in the same line, 

 it must depend upon the similarity or 

 contrariety of the directions of the cur- 

 rents at the adjacent ends, whether these 

 ends will attract or repel each other. 

 The former, it is well known, happens 



when poles of opposite denomination 

 front each other ; the latter when similar 

 poles are brought together. The mo- 

 tion of the currents in the first case may 

 be aptly illustrated by two watches laid 

 the one above the other, so that the dial 

 of the one may be in contact with the 

 back of the other, for the hands in both 

 watches will then be moving in the same 

 direction. We may obtain a represen- 

 tation of the second case, by placing 

 the watches either face to face, or back 

 to back ; for in either of these situations, 

 the motion of the hands in the two 

 watches are in opposite directions. The 

 electric currents in the former case will 

 exert a mutual attraction; and in the 

 last, a mutual repulsion. 



(294.) In estimating the attractive or 

 repulsive forces which arise in other 

 relative positions of the magnets, we 

 must take into account, not merely the 

 terminal currents, but those which exist 

 along the whole length of both magnets. 

 The general resultants of all the forces 

 thus arising may be reduced to attrac- 

 tive or repulsive forces between the 

 whole of each of the sides of one mag- 

 net, and the whole of each of the sides 

 of the other magnet. Thus, supposing 

 two magnets to be situated horizontally 

 nearly in the position to which they 

 would be brought by the influence of 

 terrestrial magnetism, the east side of 

 the one will attract the east side of the 

 other, and repel the west side ; the west 

 side will, in like manner, attract the 

 west and repel the east. Hence the 

 general tendency of all these actions is 

 to turn the magnets so as to bring 

 the two eastern sides, for example, 

 as near together as possible, and pa- 

 rallel to each other; that is, into a 

 relative position, such that the north 

 pole of each magnet shall be adjoining 

 to the south pole of the other ; and in 

 this situation the greatest amount of 

 attractive force will be exerted. 



(295.) In positions intermediate to 

 these, and especially when much in- 

 clined to each other, the estimation of 

 the resultant force in each ; individual 

 case is often difficult, from the complex 

 operation of the numerous forces that 

 are in action in a variety of directions. 

 Thus, if one of the magnets, situated 

 as just described, parallel to each 

 other, and with their dissimilar poles 

 adjacent, be moved in the line of its 

 axis till the two ends, having similar 

 poles, are brought into the same plane, 

 as shown in fig. 168, a strong repulsion 



