A magnetised steel bar, when tried by means of a small compass needle, is often found to exhibit, at different places in the direction of its length, a change from boreal to austral magnetism, and the contrary. These place*, are called consecutive poles.
The intensity of the force, either of attraction or repulsion, exercised by one of the poles of a magnet on any body is inversely proportional to the square of the distance of such body from that pole; and if a very small compass-needle, supported or suspended in the usual way, be brought near a magnetised bar, it must settle, between those oppo sing forces, in the direction of a tangent to some curve line passing through the two poles of the magnet. This is called the magnetic curve, and the direction of the tangent at any given point may be thus investigated :— Let N be the north and s the south pole of a magnet ; let r be any given point at.which the centre of gravity of a small euspended needle may be placed, and join r N, r s. Let the attraction of N on e be expressed by Ai and bo represented by PO; also let the repulsion exercised by a on r bo expressed by and bo represented by r e;inre the direction of s P produced. Imagine the parallelogram on to
be formed ; then, by mechanics, PQ, its diagonal,will represent the resultant of tho forces acting on a particle at r; it will therefore be the direction of the needle and of a tangent to the curve at that point. Let Lgro be represented by e; Lgrs by and let fall C D per pendicularly on r g : then by trigonomkry, is the value of P D, or the equivalent of the force represented by P 0 when reduced to the direction r Q; and 7-24 is the value of g D, or of the force P (=g of when reduced to the same direction. The sum of these, or + cos.
ITTir la the value of P Q, and represents the whole force of the magnet on the point r in the direction of that lino : hence, tr cos. cos. 0' p ql , • r se P But, by geometry, r = P Q + 2 r Q. g D whioh, by substi 1(cos. 0 cos. 0) cos. 0' becomes comes — 2 . Equating