37 MAGNETIC INDUCTION. 



388. ELLIPSOID. CYLINDER. For an ellipsoid magnetised 

 uniformly in any given direction, the components of the internal 

 force parallel to the axes are equal respectively to - AL, - BM, and 

 - CN (356). 



In a uniform field in which the force < makes with the axes 

 angles whose cosines are A, A', A", the components of the magneti- 

 sation will be 



These equations presuppose that the magnetisation is so weak 

 that we may admit the effects produced in different directions to 

 be superposed. 



If one of the axes of the ellipsoid is parallel to the direction of 

 the field the axis of x for instance we have 



and however great may be the value of k, the magnetisation will be 

 uniform. 



By the results indicated in (357) we might apply this expression 

 to several different cases. 



For an unlimited cylinder, perpendicular to the direction of the 

 field (358), we shall have 



I- 



389. BARLOW'S PROBLEM. The case of a dielectric layer com- 

 prised between the surfaces of two concentric spheres, and placed in 

 a uniform field (166) corresponds to that of a magnetic layer of the 

 same form placed in the same conditions. This question is known 

 as Barlow's problem. 



