During the 17th century the custom continued of giving to the sterns a great elevation above the surface of the water, and of loading that part, as well as tho bows, with ornaments. The sterns of ships of war were, till about forty-five years since, made, at their junctions with the sides, of an angular form, or, as they were called, square; and before 1729 they had projecting galleries or balconies extending across them, and to some distance along each after-quarter of the ship. The galleries were afterwards much diminished in breadth ; but it was not till 3796 that, by the influence of Lord Spencer, who was then the first lord of the Admiralty, these, as well as the great projecting heads, were entirely omitted in the construction of ships. fu 1816 Sir Robert Seppingsf proposed to make the sterns curvilinear like the bows, but more flat ; and by the adoption of his plan there was gained consider able strength, such a form enabling the ship to resist with great effect the force of a sea in striking the stern, and that of ehot when fired against it. With respect also to the means of defence at the stem and quarters of a ship, it may be observed that the curvilinear stern has greatly tho advantage over those of all angular construction, there being in angular an interval opposite each quarter of the ship towards which none of the after-guns can be brought to bear, while such interval does not exist in the curvilinear. In a ship with a curvi linear stern, the ports may be disposed so as to allow guns to fire in any direction diverging from a centre within the ship ; and at the same time the after broadside guns may be trained so as to fire obliquely towards the fore or after part of the ship. Thus there will be afforded several intervals opposite the stern and quarters, within which the lines of fire may cross each other ; and consequently the defence will be as powerful about the stern as at any other part of the ship. It may be added that when the guns in a square stern are trained at their greatest degree of obliquity to the sides -of the ships, their muzzles will be considerably within the timbers; and consequently, in firing, some danger may exist of blowing away part of the stern or quarter. The curvilinear form is now, with slight modifications, generally adopted for ships of war ; and the only objection hitherto made to it is that the interior accommodations are thereby rather diminished.
In 1791 there was formed, in London, a Society for the Improvement of Naval Architecture; and its first steps consisted in offering prizes for the best papers which. should be written on the subject of the resistance of fluids, on designs for vessels, on the proportions of masts, &c. The association threw much light on the art of constructing ships ; and both the theory and practice of that art have been advanced by means of the school which was attached to the Naval College at Portsmouth, under the superintendence of Dr. Inman. During the year 1860, however, an Institute of Naval Architects, under the pre sidency of Sir John Pakington, was originated in London, and bids fair to bring together the ablest members of the profession in England, as also men eminent in mechanical science. The late principal of the School of Naval Architecture, the Rev. Dr. Woolley, has already given a useful paper on mathematical theory, while men like Mandalay, Scott Russell, Grantham, Fairbairn, &c. have contributed valuable assistance. (` Transactions of the Institute of Naval Architects for 1860.') In the present article it is intended to give some account of the mathematical principles of naval architecture; the mechanical con struction of ships being reserved for the articles SHIP-BUILDING and STEA3I VESSEL.
The body of a ship about its middle has nearly the form of a portion of a hollow cylinder, with its axis horizontal, and its convex surface downwards Above the surface of the water on which it floats the sides are curved, so as at the head to have, in a horizontal direction, the form of a Gothic arch more or leas acute. The breadth diminishes gradually towards the stern, which above water is either a plane surface nearly perpendicular to the ship's length, or, agreeably to the con struction introduced by Sir Robert Seppings, curved so as to have, in a horizontal section, nearly the form of a semi-ellipse. Below the surface of the water the body of the ship is curved in a horizontal direction towards the head and stern, so as to terminate at those places in angles which diminish from that surface downwards ; and thus a vertical section, taken perpendicularly to the length of the ship, at some distance from the middle towards either extremity, presents on each side the form of a curve of contrary flexure.
Experiments have shown, that when the quantity of sail is the same, the velocity of a ship is increased by increasing the ratio between its length and breadth, and both English and French constructors have one on for many years augmenting that ratio ; but this increase has its limit. The advantage of diminished breadth is accompanied by a diminution of stability, and a deficiency in .this respect may produce serious evils. It may prevent the use of the lower guns on the Ice side from the fear that the ports may be under water, and the use of the guns on the weather-side from inability to give them sufficient depression ; and by causing the keel to take an oblique position in the direction of its depth, the lateral resistance of the water being diminished, the lee-way of the ship is increased. The power of the rudder and sails to produce rotation about a vertical axis is greater in a long than in a short ship, because the rudder and sails are at greater distances from that axis, and because the impulse of the water on the rudder is more direct : yet the resistance which the water opposes to that rotation increases in a still higher ratio ; and thus the difficulty of working to windward is increased with the length of the ship. Lastly, the quantity of artillery in a ship will indirectly affect the relation between the length and breadth ; for an increase of weight above water produces a diminntion of stability by causing the centre of gravity of the ship to be more elevated, and this evil must be counter acted by increasing the breadth. In several English ships of war carrying from 46 to 120 guns, it has been found by adnaeasurement that the ratio of the breadth to tho length varied from 1 to 1 , and that it had no dependence either upon the number of guns or upon the tonnage of the ship. The greatest length which may be given to ships of war is a point still undetermined ; and the length seems to have hitherto gone on increasing in the navies of all nations. In 1786 was built the Victory, of 100 guns; this was then the greatest three-decker in the British service, and Its length was 186 feet. In 1793 the Ville de Paris, of DLO guns, and 190 feet long, was built at Chatham ; and in 1809 was built the Caledonia, of 120 guns, whose length was 205 feet, while the Hood of 91 guns and 3232 tons, launched, at Chatham, in 1859, is 238 feet long, and the Galatea frigate, launched in 1859, having 26 guns, and being of the burden of 3202 tuns, has a length of 230 feet.