PLUCKER ON THE THEORY OF DIAMAGNETISM. 349 



length, and rotate with the Hne around the fixed point O. To 

 determine the points in the horizontal plane for which the 

 moment of inertia due to each of the single poles P and Q dis- 

 appears, we obtain immediately the two following equations in 

 polar coordinates : 



cos2</)+^— + — jcos(f)— 3 = 0, (8) 



+ — )cos(/)— 3 = (9) 



*-& 



r J 



The two curves represented by these equations are similar, 

 but extend from the point O in different directions, the first 

 towards the pole P, the second towards the pole Q. If the 

 point O lies in the middle between P and Q, the two curves 

 are equal. 



20. As the equations (8) and (9) are independent of />t, the 

 two curves in question, geometrical loci of the indifferent points, 

 remain the same, no matter how small or how great the mag- 

 netic intensity of the poles P and Q may be, or how the polarity 

 induced by these poles in the bar of iron during its rotation 

 round the point O may change in point of intensity. 



21. Instead of the polar coordinates r and <^, we will intro- 

 duce rectangular ones, a and «/, by assuming O as the origin 

 and permitting the x axis to pass through the poles P and Q. 

 Then we have 



cos <^ = - 5 r^ = c^'^ + 2/^, 



by which the first part of the equation (8) becomes the fol- 

 lowing : 



~|(^-3c)2/2 + ^(^-c)2j (10) 



The curve of indifferent points corresponding to the pole P 

 is therefore represented by the equation 



y'---^ (-) 



It is only necessary to change the value of c and the sign of x, 

 to obtain from the last equation the equation of the curve cor- 

 responding to the pole Q. 



