( 384 ) 
homogeneous solid with those of (lie immersed parts themselves); 
the normals out of the centre of gravity of the whole solid to this 
surface (G) then indicate possible positions of equilibrium. For homo¬ 
geneous solids the only requirement for stability is that the chosen 
normal corresponds to a minimal distance of the centre of gravity to 
the surface (6r), i.e. that this distance is smaller than the smaller of 
the two principal radii of curvature of the surface (G) at the foot 
of the normal. For non-homogeneous solids the centre of gravity 
must moreover lie on the concave side of the surface (G), which 
condition is fulfilled of itself for homogeneous solids. 
It is worth mentioning, that the surface (G) is convex in all points, 
that for homogeneous solids the surface (G) may be determined for 
the floating as well as for the immersed part, whilst we must still 
bear in mind the following property: If the position of a floating 
body is given and if we determine the maximum and the minimum 
of the moments of inertia of the section of the surface of the liquid 
with the body with respect to lines through the centre of gravity 
of that section, then there exist the relations: 
where p x , p a are the principal radii of curvature of the surface (G) 
in the determined point, whilst V is the volume of the immersed part 
and T x and T a are the maximum and the minimum moments. 
2. We commence with the solution of a question put by Huygens 
(GEuvres completes, XI, p. 121 and 122) after the minimal ratio of 
the length of a right cylinder to the greatest dimension of its base, 
supposed to be everywhere convex, in order that the cylinder be 
able to float stably on any heavier liquid in such a way that its 
generatrices take a horizontal direction, if only the stability be assured 
with respect to displacements, where that direction is retained. 
Let in fig. 1 the curve PLQ be the base everywhere convex of 
^e right cylinder. For a definite specific weight 
~ with respect to the liquid (which we suppose < £) 
ve have to introduce planes cutting base as well 
s upperplane and thus to determine the surface ( G)- 
In this case where the generatrices are supposed 
parallel to the surface of the liquid we can deter¬ 
mine the position of the corresponding principal 
'I centres of curvature of the surface {G) without 
U O knowing the surface ( G ). We then apply but the 
Fig l. last mentioned property of$l. If the centres found 
