could be attained. The actual results as to the speed of the novel vessel amply justified the reliance put upon such experiments. In 1877 the French naval authorities established an experimental tank in the dockyard at Brest, and the Italian Government have formed one in the naval dockyard at Castellamare. The only experimental tank hitherto established by a private mercantile firm is that in the shipyard of Messrs Denny, Dumbarton. This establishment is on a scale of completeness not surpassed elsewhere, and is fitted with every appliance which the latest experience in such experiments shows to be advantageous. A special staff of experimentalists, forming a branch of the general scientific body, are engaged conducting experiments and accumulating data, which, besides being of service in their present daily practice, must ultimately yield fruit of a very special kind to this enterprising firm.[22] From mathematical reasoning, and by means of an extended series of experiments with models and actual ships, Mr Froude determined that for two vessels of similar form—for instance a ship and her model—the “corresponding speeds” of ship and model are to one another as the square roots of the similar dimensions, and at corresponding speeds the resistance of ship and of model are to one another as the cubes of the similar dimensions—subject to a correction concerned with skin friction necessitated by the difference in the lengths of ship and model.[23] Having obtained the resistance of a model, and from it, by an application of the above law, deduced the resistance of the full-sized vessel, the effective horse-power is found by multiplying the resistance by the speed of the vessel in feet per minute, and dividing by 33,000. From the effective horse-power an estimate of the indicated horse-power required can be made by using ratios which the one bore to the other in former ships, as obtained from a comparison of their model experiments with their measured mile trial results. The value of progressive speed trials and of experiments with models as affording convenient means whereby analysis may be made of the several sources of expenditure of power in propelling vessels can scarcely be over-estimated. From a study of the graphic records of progressive trials, and from model experiment results, Mr Froude discovered a method whereby the power expended in overcoming the frictional resistance of the engines could be determined, and estimates made of the amount of power absorbed by other elements. The method in question was communicated in full in a paper read before the Institution of Naval Architects in 1876, and has since been extensively used. Methods of analysis resulting from a simultaneous study of this subject, were also proposed by Mr Robert Mansel, a prominent Clyde shipbuilder and noted investigator, but they failed in meeting with the acceptance which was at once accorded to Mr Froude’s propositions.[24]