PLUCKER ON THE THEORY OF DIAMAONETISM. 351 



produce a resultant moment of rotation^ equal to the moment of 

 rotation of the first arm and acting in the same direction. 



Each of the two halves of the lever, when submitted to the 

 action of the two poles, must therefore move exactly in the same 

 manner as the whole lever. 



When the pole P recedes from the centre of suspension, the 

 dimensions of the oval OLP increase, Plate V. fig. 14. The portion 

 of the leverwhich lies within this oval and whosepoints are repelled 

 becomes greater, while the portion attracted by this pole recedes 

 further from the centre. 



To fix our attention upon a definite case, we will assume that 

 M is the end of the lever. Two conflicting forces are then active, 

 one of which seeks to place the lever in the axial position, 

 while the other forces it to the equator. (In this instance, we 

 do not take the more distant pole Gl, which acts upon the entire 

 length of the arms of the lever, and seeks to place it in the 

 equatorial position, at all into account.) When the pole P re- 

 cedes from the point O in the proportion of OL to OM, the 

 original oval passes into the one shown by a dotted line in the 

 figure, which passes through the end M of the lever and through 

 the point P', which denotes the new position of the pole, and 

 this embraces the entire arm of the lever. No point of the 

 lever arm then exists which is not forced towards the equatorial 

 position. 



23. The action of the pole P on the different points of the 

 lever increases, when these points recede from those which lie 

 upon the curve (11). For every position of the lever, we must 

 have four maxima of action, namely, a maximum of repulsion 

 between O and L, and another beyond M ; further, a maximum of 

 attraction between L and M, and a second beyond O towards K. 

 By turning the lever, we obtain as the geometric locus of these 

 maxima of attraction and repulsion an easily determined 

 curve*. For this pui'pose it is only necessary to differentiate 

 the expression 



-?^^{cos^^+(r + f)cos^-3} . . (6) 



with regard to r, and to set the differential coefficients =0. In 



* It is of course understood that these maxima are to be referred to moments 

 of rotation produced by attraction and repulsion. 



