PLUCKER ON THE THEORY OF DIAMAGNETISM. 353 



Assuming the centre of rotation of the lever to be central 

 between the two poles, we find the moment of rotation due to 

 the action of both poles on the entire length of the lever to be 



This expression must be reduced to one-half, if we take only 

 one-half of the lever, or regard one of the poles only as active. 



25. The last expression is a function of R and (f>. For a given 

 position of the lever, which is determined by the value of <^, the 

 value and sign of this expression depend upon the length of 

 the lever R. When the sign is positive the lever approaches to 

 the axial position, when it is negative it recedes from this posi- 

 tion. If we regard R and </> as polar coordinates and then set 

 the last expression equal null, then the resulting equation 



represents a curve which immediately determines the motion of 

 a lever of given length in all its positions. The development of 

 this equation is easy but somewhat tedious. 



26. In 23 we have regarded the coefficient fi as constant. This 

 would really be the case if the little needles at right angles to the 

 length were permanent magnets, whose intensity is not changed 

 by the induction of the poles P and Q. If however these needles 

 are of soft iron, then the intensity of the magnetism excited in 

 them by the poles, depends upon their distance from these poles. 

 From the analogy of central forces, must we not assume that 

 for the case of magnetic saturation — a case perhaps which does 

 not exist — the intensity of the excited magnetism varies inversely 

 as the square of the distance ? 



Let K be the magnetic intensity of the pole P, and \ that of 

 two ends of the needle ; then, according to the first assumption, 

 we have 



According to the last assumption, we should have 



if we denote the intensity of the magnetism excited in the ends 

 of the iron needle by the pole P, at the unit of distance by X 

 and permit m to retain its former meaning. The natural case 



