416 



ON THE ATTRACTION OF AN INDEFINITELY THIN SHELL. 



[53 



through the attracted point, and having found the attraction of this shell 

 by a method applicable to this particular case, he deduces from it the 

 attraction of the general confocal shell. Now it may be remarked on this 

 that the method of finding the attraction of the shell contiguous to the 

 attracted point does not seem free from objection, and also that it may 

 be doubted whether it is legitimate to include this limiting case under the 

 general one without a special examination. If, in order to remove these 

 objections, special considerations are introduced, the proof is thereby deprived 

 of its simple and elementary character. Whether these criticisms on M. 

 Chasles' method are well founded or not, the author thinks that mathema- 

 ticians will not be displeased to see a direct determination of the attraction 

 of a shell on an external point without the intervention of another shell 

 whose outer surface passes through that point. In order to make the paper 

 more complete, the author briefly shews how from the expression for the 

 attraction of a shell, we may pass to the expression the integral of which 

 gives the attraction of a homogeneous ellipsoid on an external point. 



