The oldest method of approximating to the horse-power required to propel a proposed vessel at a given speed is to compare the new ship with ships already built by the use of formulæ known as “co-efficients of performance” deduced from the results of their speed trials. Two such co-efficients have been deduced from Admiralty practice, the one involving displacement, the other area of mid-section, with speed as the variable in both cases. Another method which has been largely used, consists in first determining the ratio of the indicated horse-power to the amount of “wetted surface,” or immersed portion of the vessel’s skin, in the exemplar ship, and then estimating from this ratio the probable value of the corresponding ratio for the proposed ship at her assigned speed. Inasmuch as these methods of procedure do not take account of the _forms_ of the hulls, and consequently of that factor in the total resistance due to _wave-making_, they cannot be used with any degree of confidence, or without large corrections, except in connection with vessels whose speeds are moderate in proportion to their dimensions: those in fact in which the resistance varies nearly as the square of the speed. A further method, somewhat resembling the one based upon the relation between indicated horse-power and the “wetted surface,” was proposed by the late Prof. Rankine, but has never been extensively employed. Apart from the unreliable nature of the results which an application of it gives—except for certain speeds—it is open to several serious objections in practice. A method of analysis and prediction, meeting with considerable acceptance from shipbuilders on the Clyde and elsewhere, has been introduced within recent years by Mr A. C. Kirk, of Messrs R. Napier & Sons.[20] The method consists in reducing all vessels to a definite and simple form, such as readily admits of comparison being made between their immersed surface, length of entrance and angle of entrance and their indicated horse-power, and from this judging of the form and proportions best suited to a given speed or power in proposed vessels. The form in question consists of a block model, having a rectangular midship section, parallel middle body, and wedge-shaped ends; its length being proportioned to that of the ship, its depth to the mean draught of water, its girth of mid-section to the girth of immersed mid-section of the ship, and the surface of its sides, bottom and ends, to the immersed surface of the ship. By finding from one or more exemplar ships—the selection of which is obviously governed by the conditions of analysis—the rate of indicated horse-power required per unit of wetted surface at the speed assigned for the proposed vessel, the appropriate rate for the latter may easily be determined.