INFLUENCE OF SHAPE ON ISOTROPIC BODIES. 669 



By pressing a series of sheets of paper, which are then cut in 

 the form of a cylinder, the axis is magnetic with emery paper 

 and diamagnetic with paper covered with powdered bismuth. 



In like manner a bismuth cube, which has been compressed, 

 sets in such a manner that the line of pressure is axial. 



These experiments seem to show that partially, at least, the 

 phenomena of crystalline magnetism are due to inequalities of 

 pressure, resulting from molecular structure, rather than to the 

 molecules themselves. 



1230. INFLUENCE OF SHAPE ON ISOTROPIC BODIES. The 

 preceding considerations only apply when the coefficients of mag- 

 netisation have considerable values, for we must allow for induced 

 magnetisation (358), which depends on the shape of the bodies ; 

 but isotropic bodies of any shape give analogous results in certain 

 particular cases. 



Let us suppose an ellipsoid of an isotropic substance placed in 

 a uniform field, and that the coefficient of magnetism is uniform. 

 The magnetic moments parallel to the three axes are respectively 

 proportional (388) to 



and 



These three factors, which we shall denote as f, f, and f\ may 

 be considered as coefficients of mean magnetisation ; it is seen that 

 the ellipsoid behaves as a crystallised body, having for principal 

 coefficients of magnetisation the same quantities f, f, and f", and 

 all the preceding theorems are applicable. In particular, the 

 couples for the three axes are respectively proportional to the 

 differences /-/', /' -/", and /-/". 



This is also the case for a parallelopipedon of dimensions 20, 

 2#, and 2c; the couple of rotation about a line parallel to the edges 

 only depends on the difference of the mean coefficient of magnetism 

 parallel to the two systems of edges perpendicular to the first. 



This is the case of a magnet which oscillates in the terrestrial 

 field. If / and /' are the mean coefficients of longitudinal and 

 transverse magnetism, M the rigid magnetic moment of the mag- 

 net, and u its volume, the directing couple is 



* (/-/') = MH 



