310 INI' VI. INI- 



it within the inner surface of tlic shell 6' = 0, 

 use the attraction must vanish when r = 0. 



For any point without the outer surface of tin- shell 

 C = J/, because f..r point- at an indefinitely great di 

 the resultant at tract i<n of the shell must be the same as if the 

 re condensed at its centre of gravity; . 



Thus i he reijiiiivd results are obta: 



241. A j>]J nation to an indefinite cylinder. Consider next 



a hollow indefinite cylinder composed of homogeneous shells, 

 : nsity beint: a function of the distance from the ;1 

 vlinder which we take for the axis of ~. Its action upon 

 any particle will be directed towards the point win re the axis 

 is cut by a perpendicular plane passing through the attracted 

 particle. Take this point of tli r origin: let r ' 



distance from the attracted particle ; the attraction will depend 

 only on r, and its value will be 



dV 



But for the points which are not part of the mass of the 

 cylinder, we have, by Art. 238, observing that V is inde- 

 pendent of c, 



IdV 

 whence /, +-^r 



Multiplying by r, we have 

 d 



f , c 



therefore , = , 



C being some constant. 



observe, as in the case of a hollow sphere, that the 

 points exterior to the cylindrical shell and those in the interior 

 Deing separated by those of the shell, for which the circum- 



