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power, as a consequence, to the cube of such velocity.

[Illustration: Fig. 2.--Diagram of tractive stresses at different 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.

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

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