215 
He then takes the outer surface of one of these shells to pass 
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 in- 
troduced, the proof is thereby deprived of its simple and ele- 
mentary character. Whether these criticisms on M. Chasles’ 
method are well founded or not, the author thinks that mathe- 
maticians 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 shows 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. 
On a theory of the forms of floating leaves in certain 
plants. By W. P. Hien. 
Consider the curved margin of an undivided portion of a leaf 
which floats in a stream exposed to the resistance of the cur- 
rent; suppose that the power of growth is exerted equally at 
all points of the margin, tends to push the margin normally 
outwards so as to oppose rather than co-operate with the cur- 
rent, and is just balanced at the instant considered by the other 
mechanical forces which act on the margin; and further sup- 
pose that the margin remains asa flexible curve with tangential 
tension but not submitted to either normal strains or wrench- 
ing couples. 
