ELLIPSOID OF INDUCTION. 667 



If we call an ellipsoid of induction the ellipsoid referred to the 

 three principal axes, and the equation of which is 



the inverse squares of the axes of the ellipsoid being respectively 

 equal to k, /', and k". 



If the body turns about the x axis, the couple of rotation is 

 proportional to k' - k" that is to say, to the difference of the 

 inverse squares of the principal sections of the ellipsoid of induc- 

 tion, by the plane perpendicular to the axis of rotation. 



This is a general property. If the body rotates about any given 

 direction, the couple is proportional to the difference of the inverse 

 squares of the axes of the ellipse obtained by cutting the ellipsoid 

 of induction by a diametral plane perpendicular to the axis of 

 rotation. In particular, if this axis is perpendicular m to one of 

 the cyclical planes of the ellipsoid, the curve of intersection is 

 circular and the equilibrium neutral. 



The corresponding directions are situate in the plane xz of the 

 extreme magnetisations, and satisfy the conditions 



the angle A, which they make with the least axis of magnetisation, 

 is given by equation 



The coefficients k, k', and k" play then the same part as the squares 

 of the velocities of propagation of plane waves in double refracting 

 media with two axes, and all the theorems established in optics have 

 their analogues in the phenomena of magnetisation. 



We may, by analogy, in crystallised bodies distinguish between 

 magnetic uniaxial and biaxial crystals. 



In like manner magnetic uniaxial bodies will be considered as 

 positive or negative, according as the coefficient of magnetisation in 

 the direction of the axis of symmetry is of greater or less value 

 than in the perpendicular direction. From what has been said 

 above, bismuth is negative and Iceland spar positive. 



Magnetic biaxial crystals, finally, are positive or negative ac- 

 cording as the angle A of the magnetic axes with the direction of 



