350 PLUCKER ON THE THEORY OF DIAMAGNETISM. 



The equation (11) shows us immediately, that the curve re- 

 presented by it (Plate V. fig. 14), which is the geometric locus of 

 those indifferent points obtained by regarding the action of the 

 pole P alone, extends from the centre O laterally, that it is sym- 

 metrical in respect to the straight Une which unites the two poles 

 P and Q, that it has the pole P for double points, and for 

 asymptote the straight line A A, which is perpendicular to PQ, 

 and is three times as far from the centre O as the pole P. The 

 figure exhibits the course of the curve TPCPU. 



If we give the little iron bars different positions, either by 

 turning the lever or permitting it to remain fixed and moving 

 the bar along it parallel with itself, then as often as the curve is 

 crossed the moment of rotation changes its sign; if the iron 

 bar were previously attracted it will afterwards be repelled, and 

 vica versa. It is easy to convince ourselves, that w^ithin the 

 oval of the curve the moment of inertia is negative, and that 

 hence the pole here repels the iron bar. 



Let us suppose the case of a lever KN (Plate V. fig. 15) of in- 

 definite length and composed of an infinite number of infinitely 

 small needles, which are all at right angles to the length, it is 

 clear that all these needles which lie between O and L, and which 

 lie beyond M, will be repelled by the pole P ; while those which 

 lie between L and M and beyond the point O in the opposite 

 direction, will be attracted by the same pole. The manner of 

 action is indicated in the figure by little arrows. 



The way in which the second pole acts on the little needle, 

 will be determined by the second curve in exactly the same 

 manner; this curve, under the assumption that c^ = c, that is, 

 that the centre of rotation O is midway between P and Q, is 

 also shown on the figure. 



22. We will first consider only one half of the lever ON, in 

 any one of its positions. We have then two forces which 

 proceed from the pole P, and act upon the segments OE and 

 MN, as well as a third force which proceeds from Ql and acts 

 upon the whole length ON ; all three forces tend to force the 

 lever into the equatorial position. Only one force, which proceeds 

 from P and acts upon the segment LM, tends to force the lever 

 into the axial position. 



Regarding the other half of the lever, we fi^id forces which 



