It will thus be seen that model experiments had been made by investigators long before the time of the late Dr. William Froude, of Torquay. It was not, however, until this gentleman took the subject of resistance of vessels in hand that designers were enabled to render the results from model trials accurately applicable to vessels of full size. This was principally due to his enunciation and verification by experiment of what is now known as the "law of comparison," or the law by which one is enabled to refer accurately the resistance of a model to one of larger size, or to that of a full sized vessel. In effect, the law is this - for vessels of the same proportional dimensions, or, as designers say, of the same lines, there are speeds appropriate to these vessels, which vary as the square roots of the ratio of their dimensions, and at these appropriate speeds the resistances will vary as the cubes of these dimensions. The fundament upon which the law is based has recently been shown to have found expression in the works of F. Reech, a distinguished French scientist who wrote early in the century.

There are no valid grounds for supposing that the discovery of Reech was familiar to Froude; but even were this so, it is abundantly evident that, although never claimed by himself, there are the best of grounds for claiming the law of comparison, as now established, to be an independent discovery of Froude's.

Dr. Froude began his investigations with ships' models at the experimental tank at Torquay about 1872, carrying it on uninterruptedly until his death in 1879. Since his decease, the work of investigation has been carried on by his son, Mr. R. E. Froude, who ably assisted his father, and originated much of the existing apparatus. At the beginning of 1886, the whole experimental appliances and effects were removed from Torquay to Haslar, near Portsmouth, where a large tank and more commodious offices have been constructed, with a view to entering more extensively upon the work of experimental investigation. The dimensions of the old tank were 280 ft. in length, 36 ft. in width, and 10 ft. in depth. The new one is about 400 ft. long, 20 ft. wide, and 9 ft. deep. The new establishment is more commodious and better equipped than the old, and although the experiments are taken over a greater length, the operators are enabled to turn out results with as great dispatch as in the Torquay tank. The adjacency of the new tank to the dockyard at Portsmouth enables the Admiralty authorities to make fuller and more frequent use of it than formerly.

Since the value of the work carried on for the British government has become appreciated, several experimental establishments of a similar character have been instituted in other countries. The Dutch government in 1874 formed one at Amsterdam which, up till his death in 1883, was under the superintendence of Dr. Tideman, whose labors in this direction were second only to those of the late Dr. Froude. In 1877 the French naval authorities established an experimental tank in the dockyard at Brest, and the Italian government have just completed one on an elaborate scale in the naval dockyard at Spezia. The Spezia tank, which is 500 ft. in length by about 22 ft. in breadth, is fully equipped with all the special and highly ingenious instruments and appliances which the scientific skill of the late Dr. Froude brought into existence, and have been since his day improved upon by his son, Mr. R. E. Froude, and other experts.

Through the courtesy of our own Admiralty and of Messrs. Denny, of Dumbarton, the Italians have been permitted to avail themselves of the latest improvements which experience has suggested, and the construction of the special machinery and apparatus required has been executed by firms in this country having previous experience in this connection - Messrs. Kelso & Co., of Commerce Street, Glasgow; and Mr. Robert W. Munro, of London.

Having briefly traced the origin and development of the system of model experiment, it may now be of interest to describe the modus operandi of such experiments, and explain the way in which they are made applicable to actual ships. The models with which experiments are made in those establishments conducted on the lines instituted by Mr. Froude are made of paraffin wax, a material well adapted for the purpose, being easily worked, impervious to water, and yielding a fine smooth surface. Moreover, when done with, the models may be remelted for further use and all parings utilized. They are produced in the following manner: A mould is formed in clay by means of cross sections made somewhat larger than is actually required, this allowance being made to admit of the cutting and paring afterward required to bring the model to the correct point. Into this mould a core is placed, consisting of a light wooden framework covered with calico and coated with a thick solution of clay to make it impervious to the melted paraffin. This latter substance is run into the space between the core and the mould and allowed to cool. This space, forming the thickness of the model, is usually from ¾ in. for a model of 10 ft. long to 1¼ in. and 1½ in. for one of 16 ft. and 18 ft. long.

When cold, the model is floated out of the mould by water pressure and placed bottom upward on the bed of a shaping machine, an ingenious piece of mechanism devised by the late Dr. Froude, to aid in reducing the rough casting to the accurate form. The bed of this machine, which travels automatically while the machine is in operation, can be raised or lowered to any desired level by adjusting screws. A plan of water lines of the vessel to be modeled is placed on a tablet geared to the machine, the travel of which is a function of the travel of the bed containing the model. With a pointer, which is connected by a system of levers to the cutting tools, the operator traces out the water lines upon the plan as the machine and its bed are in motion, with the result that corresponding lines are cut upon the model. The cutting tools are swiftly revolving knives which work on vertical spindles moved in a lateral direction (brought near or removed from each other), according to the varying breadth of the water lines throughout the length of the model, as traced out by the operator's pointer. In this way a series of longitudinal incisions are made on the model at different levels corresponding to the water lines of the vessel.

The model is now taken from the bed of the machine and the superfluous material or projection between the incisions is removed by means of a spokeshave or other sharp hand tool, and the whole surface brought to the correct form, and made fair and smooth.

To test accuracy of form, the weight of model is carefully taken, and the displacement at the intended trial draught accurately determined from the plan of lines. The difference between the weight of model and the displacement at the draught intended is then put into the bottom of the model in the form of small bags of shot, and by unique and very delicately constructed instruments for ascertaining the correct draught, the smallest error can at once be detected and allowed for. The models vary in size from about one-tenth to one-thirtieth of the size of the actual ship. A model of the largest size can be produced and its resistance determined at a number of speeds in about two days or so. The mode of procedure in arranging the model for the resistance experiment, after the model is afloat in the tank at the correct draught and trim, consists in attaching to it a skillfully devised dynamometric apparatus secured to a lightly constructed carriage. This carriage traverses a railway which extends the whole length of the tank about 15 in. or 18 in. above the water. The floating model is carefully guided in its passage through the water by a delicate device, keeping it from deviating either to the right or left, but at the same time allowing a free vertical and horizontal motion.

The carriage with the model attached is propelled by means of an endless steel wire rope, passing at each end of the tank around a drum, driven by a small stationary engine, fitted with a very sensitive governor, capable of being so adjusted that any required speed may be given to the carriage and model. The resistance which the model encounters in its passage through the water is communicated to a spiral spring, and the extension this spring undergoes is a measure of the model's resistance. The amount of the extension is recorded on a revolving cylinder to a much enlarged scale through the medium of levers or bell cranks supported by steel knife edges resting on rocking pieces. On the same cylinder are registered "time" and "distance" diagrams, by means of which a correct measure of the speed is obtained. The time diagram is recorded by means of a clock attached to an electric circuit, making contact every half second, and actuating a pen which forms an indent in what would otherwise be a straight line on the paper.

The distance pen, by a similar arrangement, traces another line on the cylinder in which are indents corresponding to fixed distances of travel along the tank, the indents being caused by small projections which strike a trigger at the bottom of the carriage as it passes, and make electric contact. From these time and distance diagrams accurate account can be taken of the speed at which the model and its supporting carriage have been driven. Thus on the same cylinder is recorded graphically the speed and resistance of the model. The carriage may be driven at any assigned speed by adjusting the governor of the driving engine already alluded to, but the record of the speed by means of the time and distance diagrams is more definite. When the resistances of the model have been obtained at several speeds, varying in some cases from 50 to 1,000 feet per minute, the speeds are set off in suitable units along a base line, and for every speed at which resistance is measured, the resistance is set off to scale as an ordinate value at those speeds. A line passing through these spots forms the "curve of resistance," from which the resistance experienced by the model at the given trial speeds or any intermediate speed can be ascertained.

The resistance being known, the power required to overcome resistance and drive the actual ship at any given speed is easily deduced by applying the rule before described as the law of comparison. - The Steamship.