( 3 M ) 
For s<ii the same figures can serve if we but exchange the 
immersed part for the floating one; in which case, however stability 
and equilibrium remain unchanged. 
4. Following Prof. Korteweg’s paper we shall make use of a 
graphic representation which will now however have to be a repre¬ 
sentation in three dimensions. Let us represent the lengths of the 
edges of the parallelepipedon by /, a and 6, where l^> a^> b, 
a b 
then the positions of equilibrium will be determined by — — ^ 
and s (the specific weight of the solid with respect to the liquid on 
which it floats). 
Let us now take a rectangular system of coordinates, in which 
§> and e are taken as coordinates, then each point in this system 
will denote a parallelepipedon of definite form and at the same time 
the value of s. As now §, and e are situated only between 0 and L 
we shall be able to represent the whole solution in the cube. This 
cube will be divided into compartments and to each of those compart¬ 
ments correspond one or more positions of equilibium. We have not 
succeeded in a complete division of that cube on account of the 
great analytical difficulties connected with it. What we found is 
summed up in the following. 
5. First Case. 
The surface (<?) is an elliptic paraboloid in whose axis lies the 
centre of gravity of the parallelopipedon; the normals determining 
^e positions of equilibrium lie therefore exclusively in the principal 
