dimension, / will certainly be larger than all other cords to be 
drawn, and therefore we shall have stability for all specific weights 
between 0 and 4 , so also between 4 and 1 . Hence we know that 
the ratio to be found cannot be larger than 1 . If in fig. 1 q,=ES, 
we can choose l still smaller, without endangering the stability, if 
only the extremity of q , lies between G and S. Such a reduction* 
would have to be possible in order to allow further reduction of the 
minimum ratio to be found for all specific weights for all convex 
sections. 
Let us take a circle for the convex base of the cylinder. The 
loci of the centres of gravity of the cut-off segments are circles 
concentric with the given 'circle, i. o. w. in order to retain the 
notation of the preceding figure, we have j > 3 = RG. 
If now / — p = 2 X the radius of the normal section then for 
8 ~ i we * iave = = = RG, therefore l : p cannot be reduced 
here without leading to ^ < Vt — RG. So we find here the right 
circle cylinder for s — b to be a limiting case, and we have given 
the proof that the minimum ratio to be found is unity. 
3. In what follows we shall communicate the results of an 
investigation into the stable positions of homogeneous rectangular 
parallelepipeda. In the main we shall restrict ourselves to the 
communication of the method and of the obtained results, for the 
deduction of which we refer to our dissertation shortly to appear 1 * * 4 5 ). 
rof. Korteweo investigated the positions completely when the 
parallelepipedon is long enough to float with its axis parallel to the 
sur ace of the liquid. (Nieuw Archief voor wiskunde. Second Series, 
eighth Volume, 1907, pages 1—25): Archives Nderl. (Ser. 2), Vol. 
XII, p. 362 —388. 
The following < 
imaginable if for convenience we suppose 
1 case: hour points lie above the liquid whilst the level section 
is a parallelogram or rectangle. 
“ case: One vertex lies above the liquid. 
d rf case: Two vertices lie above the liquid. The level section is 
a trapezium, sometimes a rectangle. 
4 tl case: Three vertices lie above the liquid. The level section is 
a pentagon. 
5 th case: Four vertices lie above the liquid.- The level section is a 
hexagon. 
T hese diffe rent cases are represented in the sketch below. 
1} HaS a PP eare d since the Dutch paper was published. 
