PLUCKER ON THE THEORY OP DIAMAGNETISM. 345 



netic axes are all at right angles to the axis of the crystal, then 

 the pole of the magnet which assumes the place of the earth's 

 pole in the former experiment, will drive the prism of tourmaline 

 into the equatorial position. 



13. But, from the assumption just made, it would also follow 

 that the same end of the tourmaline prism must always set itself 

 at the same side of the axial line. In single crystals, indeed, 

 when the force of the magnet is not too great, this deportment 

 is actually observed ; with tourmaline and most other crystals, 

 however, no such action is exhibited. Let us therefore imagine 

 the little permanent magnets superseded by such, which, on 

 passing the equator, change their polarity ; that is to say, by 

 little bars, which, as in the case of soft iron, become magnetic 

 by induction, without the magnetism thus excited being retained 

 by the coercive force of the bars. 



14. We will now submit to calculation those results which we 

 have just derived from general considerations. 



Let the plane of the figure be that which passes through the 

 two poles, P and Q, of the electro-magnets (Plate V. fig. 13). 

 Let AB be a little bar of soft iron, attached by its centre to the 

 lever CC, which can rotate freely round the point O. From 

 the assumption that P is the north and Q the south pole of the 

 magnet, the bar of soft iron obtains a south Pole at A and a 

 north pole at B. We will in the first place calculate the mo- 

 ment of inertia of the point A, in so far as it is produced by the 

 attraction of the pole P. 



Let r be the radius of the circle described by the points A and 

 B during the rotation of the lever, c the distance of the pole P 

 from the centre of rotation O, </> the angle enclosed between the 

 lever CC and the line which unites the poles P and Q, and 

 finally, let a be the angle enclosed between the lever CC and 

 the line OA. Then we have 



OA =OB=r, OP =c, 

 COP=<^, COA=COB = a. 



We will unite the points A and P by a straight line AP ; let 

 the length of this line be 8, We then obtain for the attraction 

 of A by P the expression 



/^ 



where fju denotes the attraction for the unit of distance. Re- 

 SCIEN. MEM.— Nat. Phil. Vol. I. Part IV. 2 B 



