( m) 
planes of the paraboloid parallel to the planes of the parallelopipe- 
don. Hence a pair of faces is always normal to the level of the 
liquid and from a closer investigation it appears that of the com¬ 
pletely immersed edges the largei 1 will run parallel to the level of 
the liquid. The complete solution is represented in the plate in 
fig. A. In the different compartments of the cube the positions 
are indicated by (11), (21), (la), (2a), (lb) and (2b), according to the 
edges intersected by the surface of the liquid corresponding to l, a 
or b and according to their being normal: (1/), (la), (lb), or oblique: 
(2/), (2d), (2b) with respect to the surface of the liquid. 
Here follow the equations of the ci 
different regions: 
Lirved surfaces, separating the 
Surf. OCQA vl nd 0 1 C 1 D 1 A 1 
„ OCEA 
6 (1 — e) — 8 (1 — s) 8 = s*»j 2 
„ O&E^ 
6s — 8s 8 = £ 8 »j 8 
Cylind. surf. OG, OB and O x G x , O l D l 
6s (1—s) = if 
„ OH, AE 
6 (1—s) —^ 8 (1—s) 2 = 13* 
O x H 1 ,A 1 E x 
6s — 8s* =.'if 
„ GUG X ,DRB X 
6s (1 — s) if = 1 
„ HLS, ENT 
{6 (1—s) — 8 (1—s) s ] ij* = 1 
„ II X L X S, E x N x 'f 
(6s—8s 8 ) ^ = 1. 
6. Method of the remaining cases. 
We place the parallelopipedon in such a manner, that 3 edges coincide 
with the axes of coordinates. We call the edges 21, 2a, and 2b, and 
the segments which the level plane or this plane produced cuts from 
the x, y and 2-axis resp. a, v and w, which, segments are always to 
be taken positively. Finally we call the coordinates of the partial 
centre of gravity (i. e. of immersed or floating part) x,y,z, which 
quantities are thus well-known functions of u, v and w different for 
the different cases. 
As the specific weight is 
immersed or floating part ii 
relation exists: 
upposed to be given, the volume of the 
known, so that between u, v and w a 
*>*•."> = . ® 
which again turns out differently for the different cases. 
Now x, y,z is a point of the surface ( G ). The equation of surface (0) 
is therefore determined by elimination of u, v and to out of (1) a n( * 
fhe three equations expressing x, y and 2 in u, v and w. Furthermore 
it is a property of' the surface (G) that the normal in a point x, y, - 
IS perpendicular to the corresponding level plane. 
