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, furnishes steam to a two cylinder engine, which may be run at will, either the two cylinders separately, or as a _compound_ engine. The bronze screw is 1.3 m. in diameter, and has a pitch of 2.5 m. The vessel has two rudders, one in front for slight speeds, and the other at the stern. At rest, the total displacement is 52,300 kilogrammes. This weight far exceeds what was first expected, by reason of the superthickness given the iron plates of the vertical sides, of the supplementary cross bracing, and of the superposition of the netting necessary to resist the flexion of the whole. On another hand, the tractive stress of the screw, which should reach about 4,000 kilogrammes, has never been able to exceed 1,800, because of the numerous imperfections in the engine. It became necessary, therefore, to steady the vessel by having her towed by the _Winkelried_, which was chartered for such a purpose, to the General Navigation Company. It became possible to thus carry on observations on speeds up to 27 kilometers per hour. Fig. 3 shows how the tractive stress varies with each speed in a theoretic case (dotted curve) in which the stress is proportional to the square of the speed, in Madame Rothschild's boat, the _Gitana_ (curve E), and in the Pictet high speed vessel (curve B). The _Gitana_ was tried with speeds varying between 0 and 4 kilometers. The corresponding tractive stresses have been reduced to the same transverse section as in the Pictet model in order to render the observations comparable. At slight speeds, and up to 19.5 kilometers per hour, the _Gitana_, which is the sharper, runs easier and requires a slighter tractive stress. At such a speed there is an equality; but, beyond this, the Pictet boat presents the greater advantages, and, at a speed of 27 kilometers, requires a stress about half less than does the _Gitana_. Such results explain themselves when we reflect that at these great speeds the _Gitana_ sinks to such a degree that the afterside planks are at the level of the water, while the Pictet model rises simultaneously fore and aft, thus considerably diminishing the submerged section.