speeds.]

The _friction_ of water against the polished surfaces of the vessel's
sides has not as yet been directly measured, but some indirect
experiments permit us to consider the resistances due thereto as small.
The entire power expended for the progress of the vessel is, then,
utilized solely in displacing certain masses of water and in giving them
a certain amount of acceleration. The masses of water set in motion
depend upon the surface submerged, and their acceleration depends upon
the speed of the vessel. Mr. Pictet has studied a form of vessel in
which the greatest part possible of the masses of water set in motion
shall be given a vertical acceleration, and the smallest part possible
a horizontal one; and this is the reason why: All those masses of water
which shall receive a vertical acceleration from the keel will tend to
move downward and produce a vertical reaction in an upward direction
applied to the very surface that gives rise to the motion. Such reaction
will have the effect of changing the level of the floating body; of
lifting it while relieving it of a weight exactly equal to the value
of the vertical thrust; and of diminishing the midship section, and,
consequently, the motive power.

[Illustration: Fig. 3.--Diagram of variations in tractive stresses and
tonnage taken as a function of the speed.]

All those masses of water which receive a horizontal acceleration from
the keel run counter, on the contrary, to the propulsive stress, and it
becomes of interest, therefore, to bring them to a minimum. The vertical
stress is limited by the weight of the boat, and, theoretically, with an
infinite degree of speed, the boat would graze the water without being
able to enter it.