Fig. 30. 



MAGNETISM. 19 



given the position of the magnet M, 

 (/#. 31,) and of its two poles N and S, 



Fig. 31. 



turning on a horizontal axis in a line 

 with the magnet, is limited in its motion 

 to a vertical plane perpendicular to its 

 position of equilibrium. In this case it 

 will have no tendency to assume any one 

 position in preference to another, in 

 this plane. 



3. Magnetic Curves. 



(80.) In order still further to genera- 

 lize our views, let us conceive the needle to 

 be exceedingly short when compared with 

 the length and distance of the magnet ; 

 and we shall then arrive at still more 

 simple conclusions with regard to its po- 

 sitions of equilibrium in the magnetic 

 plane. The two poles of the needle may, 

 with regard to the action of the magnet, 

 be considered as coincident ; the inten- 

 sities of the actions of any one of the 

 poles of the magnet upon them are so 

 nearly equal that their differences may 

 be regarded as infinitely small. The at- 

 traction of the magnet for this minute 

 needle, an attraction which, as we have 

 seen, depends upon their difference, 

 must accordingly be inappreciable. But 

 the directive force, on the contrary, de- 

 pending on the sum of these actions, 

 must be very effective ; and it is to the 

 operations of the latter of these forces 

 only that we need direct our inquiries. 



(8 1 .) The problem to be solved is this : 



and also the place of the centre C of the 

 needle, which is supposed to be at liberty to 

 revolve only in the magnetic plane, to find 

 the direction C T, at which the rotatory 

 force resulting from the action of the 

 north pole N of the magnet on the two 

 poles of the needle in the direction C N, 

 exactly balances that resulting from the 

 action of the south pole S of the magnet 

 on these poles, in the direction C S, each 

 force having an intensity reciprocally 

 proportional to the squares of these re- 

 spective lines. 



It may be mathematically demon- 

 strated * that if such be the law of the 

 magnetic forces, the direction of the 

 needle is that of the tangent of a pecu- 

 liar curve of an oval shape, which 

 has been denominated the magnetic 

 curve. Every magnet having two poles 

 N and S (fg. 3'2) has a system 



* Demonstrations of this and of the other fun- 

 damental properties of the magnetic curves are 

 given in the Journal of the Royal Institution, for 

 Feb. 1831, by the author of this Treatise. 



Fig. 32. 



C2 



