344 PARTICULAR CASES. 



For a very flattened ellipsoid, which at the limit might be con- 

 founded with a very thin disc, the force in the interior is given by 

 the equations 



F=-47rI, or F= -Tr 2 ^/! -e? 2 I, 



according as the magnetisation is perpendicular or parallel to the 

 plane of the disc. 



For a very elongated ellipsoid we have, in like manner, 



F-- 3 rf, or F-v*- t (/.^-i I, 



a A \ o 



according as the magnetisation is perpendicular or parallel to the 

 major axis. 



359. CYLINDER MAGNETISED TRANSVERSELY. The case of a 

 cylinder might be deduced from that of an ellipsoid, but it can be 

 easily treated directly. If we consider an unlimited circular cylinder 

 of radius #, and density equal to unity, the mass of unit length will 

 be X = ira\ 



The external action of this cylinder, at a distance r from the axis, 



\ 2 



is equal (132) to - , which gives for the potential 



p = - 27T# 2 /. r + const. 



If the cylinder has a uniform transverse magnetisation, and if we 

 take the axis of #, parallel to the magnetisation, the external potential 

 will then be 



V= -I = 1 - = 1- 



ox r ox r 2 - 



On a point in the interior, the action of a homogeneous circular 

 cylinder reduces to that of a cylindrical core passing through the 

 point. This can be easily seen by reasoning analogous to that which 

 has been applied to the sphere (42). The action of a cylinder on 



271"?^ 



a point in the interior is therefore equal to - = 27rr, and the 

 potential becomes 



P= -7rr 2 + const. 



