18 



MAGNETISM. 



Fig. 28, 



the repulsive ; the former will therefore 

 prevail, and the needle will have a ten- 

 dency to move towards the magnet in 

 the direction of the line connecting their 

 centres. 



(75.) A similar process of reasoning, 

 derived from the same principles, will 

 enable us to determine the resultants 

 of the forces which act upon the needle 

 when its centre is situated in different 

 directions relatively to the axis of the 

 magnet : and consequently what will be 

 its. movements, and what its final posi- 

 tion of equilibrium. In oblique posi- 

 the repulsions of N for n, and of S for s. tions, indeed, the process of investiga- 

 They respectively impel the poles n s of tion becomes more complicated, for it is 

 the needle in the directions denoted by necessary to take into consideration the 

 the small arrows parallel to the lines in 

 which these forces act. Those which 



act. 



act upon the remote pole of the needle s, 

 compose a resultant having the direction 

 of the upper horizontal arrow R, at 

 right angles to the length of the needle, 

 which is also the radius of its revolution. 

 Those forces which act upon the oppo- 

 site pole n, compose another resultant 

 force in the opposite direction, expressed 

 by the lower horizontal arrow r. Now 

 these two resultant forces having oppo- 

 site directions, and acting at the opposite 

 ends of the needle which turns upon its 

 centre, conspire in producing a rotation in 

 the same direction with relation to that 

 centre ; and will tend to bring the needle 

 into the position shown in fig. 29, in 



Fig. 29. 



which its direction is parallel to that of 



the magnet, but in which its poles are 



reversed when compared with those of 



the magnet ; that is, the north pole of to the magnetic position that the case 



the needle being on the side of the south will admit of. It will therefore be situ- 



different intensities of each of the four 

 forces concerned, with reference not only 

 to the respective distances of the poles of 

 the needle from those of the magnet, but 

 also to their respective directions in the 

 plane of rotation. 



(76.) If the plane of rotation, to which 

 the movements of the needle is limited, 

 be one which does not pass through the 

 poles of the magnet, the complication of 

 the problem becomes still greater. There 

 are, however, three general results at 

 which we may arrive, which tend very 

 much to simplify the resolution of ques- 

 tions relating to this subject. 



(77.) The first is, that if we suppose 

 the needle to be at perfect liberty to 

 move on its centre in all directions, the 

 position of equilibrium at which it will 

 arrive by the conjoint action of all the 

 forces which impel it, will always be si- 

 tuated in the plane which includes the 

 poles of the magnet and the centre of 

 the needle. This plane may be called, 

 for the sake of distinctness, the magnetic 

 plane ; and the position assumed by the 

 needle in this plane may be called its 

 magnetic position. 



(78.) Secondly, when the movements 

 of the needle are limited to any particu- 

 cular plane, its position of equilibrium is 

 that which makes the nearest approach 



pole of the magnet, and its south pole on 

 the side of the north pole of the magnet. 

 This relative situation has been called 

 by some authors the subcontrary posi- 

 tion. 



(74.) Here also it may be remarked, 

 that in consequence of the greater prox- 

 imity of the poles of the different deno- 

 minations, compared with that of the 

 poles of the same name, the sum of 

 the attractive forces exceeds that of 



ated in a plane passing through the mag- 

 netic position, and at right angles to the 

 plane of revolution. 



(79.) Thirdly, if the plane of revolu- 

 tion be perpendicular to the magnetic 

 position, the needle will be in a state of 

 equilibrium with regard to the forces 

 exerted upon it by the magnet, in all 

 positions. Such a plane may be called 

 the plane of neutrality. An example of 

 this is shown in/^.30, where the needle, 



