The annexed diagram (Fig. 1) shows the form that calculation has led Mr.
Pictet to. The sides of the boat are two planes parallel with its axis,
and perfectly vertical. The keel (properly so called) is formed by
the joining of the two vertical planes. The surface thus formed is a
parabola whose apex is in front, the maximum ordinate behind, and the
concavity directed toward the bottom of the water. The stern is a
vertical plane intersecting at right angles the two lateral faces and
the parabolic curve, which thus terminates in a sharp edge. The prow of
the boat is connected with the apex of the parabola by a curve whose
concavity is directed upward.

[Illustration: Fig. 4.--Diagram of the variations in the power as a
function of the speed.]

When we trace the curve of the tractive stresses in a boat thus
constructed, by putting the speeds in abscisses and the tractive
stresses in ordinates, we obtain a curve (Fig. 2) which shows that the
same tractive stress applied to a boat may give it three different
speeds, M, M', and M'', only two of which, M and M'', are stable.

Experimental verifications of this study have been partially realized
(thanks to the financial aid of a number of persons who are interested
in the question) through the construction of a boat (Fig. 1) by the
Geneva Society for the Construction of Physical Instruments. The vessel
is 20.25 m. in length at the water line, has an everywhere equal width
of 3.9 m., and a length of 16 m. from the stern to the apex of the
parabola of the keel. The bottom of the boat is nearly absolutely flat.
The keel, which is 30 centimeters in width, contains the shaft of the
screw. The boiler, which is designed for running at twelve atmospheres,