It is now nearly a year ago since we announced to our readers the researches that had been undertaken by the learned physicist, Raoul Pictet, in order to demonstrate theoretically and practically the forms that are required for a fast-sailing vessel, and since we pointed out how great an interest is connected with the question, while at the same time promising to revert to the subject at some opportune moment. We shall now keep our promise by making known a work that Mr. Pictet has just published in the _Archives Physiques et Naturelles_, of Geneva, in which he gives the first results of his labors, and which we shall analyze rapidly, neglecting in doing so the somewhat dry mathematical part of the article. For a given tonnage and identical tractive stresses, the greater or less sharpness of the fore and aft part of the keel allows boats to attain different speeds, the sharper lines corresponding to the highest speeds, but, in practice, considerably diminishing the weight of freight capable of being carried by the boat. [Illustration: FIG. 1. PICTET'S HIGH SPEED BOAT. A. Lateral View. B. Plan. C. Section of the boiler room. D. Section of the cabin.] Mr. Pictet proposed the problem to himself in a different manner, and as follows: Determine by analysis, and verify experimentally, what form of keel will allow of the quickest and most economical carriage of a given weight of merchandise on water. We know that for a given transverse or midship section, the tractive stress necessary for the progression of the ship is proportional to the _square_ of the velocity; and the motive 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.