20 



MAGNETISM. 



netic curves related to the line joining 

 these poles, and which may be called its 

 axis. The general form and disposition of 

 these curves, according to their different 

 distances from the magnet, is shown in 

 the figure. 



(82.) The magnetic curves have the 

 following remarkable property ; namely, 

 that the difference of the cosines of the 

 angles, which lines, drawn from any 

 point in the curve to the two poles, 

 make with the axis, taken on the same 

 side, is constant. Thus, in the curve 

 S C C' C" N, fig. 33, the sum of the 



Fig. 33. 



cosines of the angles C N X and C S X, 

 is equal to the sum of the cosines of the 

 angles C' N X and C' S X. When, how- 

 ever, the angle C" S X exceeds a right 

 angle, its cosine being negative, it will 

 be the sum (instead of the difference) 

 of the cosines of the polar angles 

 C" N S, C" S N, that is constant. When 

 the angle C'" N X is also obtuse, both 

 the cosines being negative, it is again 

 their difference that is constant. 



(83.) If two radii of equal length, N n, 

 S s,fig.34, be made to revolve in the same 



Fig. 34. 







J\: 



N and S, while their other extremities, 

 n and s, are kept continually in such a 

 relative position as that a line drawn 

 through them shall always be perpen- 

 dicular to the axis N X, then the line, 

 constituted by the successive points of 

 intersection C, C' of the radii, will be 

 a magnetic curve*. 



(84.) The most expeditious method 

 of delineating a great number of mag- 

 netic curves related to the same base, 

 in order to obtain a general view of the 

 entire system of these curves, is to de- 

 scribe from each pole, N, S (fig. 35), as 

 a centre, the equal circles or semi-circles, 

 A A, B B, with as large a radius as the 

 paper will conveniently admit of; and, 

 dividing the axis, produced till it meets 

 both circles, into any number of equal 

 parts, to mark off, on the circumferences 

 of both the circles, the points where they 

 are cut by perpendiculars from these 

 points of division ; then, drawing radii 

 from the centre of each circle to the 

 divisions of its respective circumference, 

 the mutual intersections of these radii 

 will form different series of points indi- 

 cating the course of the magnetic curves 

 which pass through them. In the pre- 

 sent case these curves are composed of 

 a succession of diagonals of the lozenge- 

 shaped interstices formed by the inter- 

 secting radii, as is shown in the upper 

 half of fig. 35. 



(85.) The forms and disposition of 

 these curves are elegantly illustrated by 

 the lines in which iron-filings arrange 

 themselves when acted upon by a power- 

 ful magnet. In order to exhibit them, 

 we need only place a sheet of paper or 

 pasteboard immediately over a straight 

 magnetic bar laid flat upon a table, and 

 scatter lightly some very fine iron-filings 

 over the pasteboard ; which is best done 

 by shaking them through a gauze bag. 

 If we then tap gently upon the paper, 

 so as to throw them into a slight agita- 

 tion, they will arrange themselves with 

 great regularity in lines, which exactly 

 follow the course of the magnetic curves, 

 extending from one pole of the magnet 

 to the other. These minute fragments 

 of iron, being rendered magnetic by in- 

 duction, have their dissimilar poles 

 fronting each other, and therefore at- 

 tract one another, and adhere together 



* The author of this Treatise has constructed a 

 system of rulers by which magnetic curves may be 

 mechanically delineated, founded on the principle 

 stated in the text. The description of this instru- 



j- j- , ., . ment is contained in the paper above referred to in 



direction rounfl their respective centres the journal of the Boyai institution. 



