503 



SHIP. 



SHIP. 



510 



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 Xaval College at 

 Portsmouth, under the superintendence of Dr. luinan. 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, 

 aa 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 Maudslay, Scott 

 Russell, Grantham, Fairbairn, &c. have contributed valuable assistance. 

 (' Transactions of the Institute of Naval Architects for I860.') 



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-BUILDINO and 

 STEAM 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 less 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 

 gome 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 

 gone 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 lee- 

 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 obUque 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 hi 

 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 diminution 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 admeasurement 



that the ratio of the breadth to the length varied from to 



3-93 



, and that it had no dependence either upon the number of guns 



3'61 



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 188 feet. In 

 1793 the Ville de Paris, of 110 gurus, 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 1659, having 26 guns, and being of the burden of 3202 

 tons, has a length of 280 feet. 



In the Vernon, and other ships which were built according to the de- 

 signs of the late Sir William Symonds, the form of a transverse section 

 passing vertically through the hull differs from that which had been 

 before given to ships, in exhibiting an increase of breadth above the 

 plane of floatation (a horizontal plane pawing through the ship when 

 she floats upright, and coinciding with the surface of the water). This 

 construction produces, without any diminution of velocity, an increase 



of stability not only when the ship is afloat, but also when, on lying 

 aground, she is subject to the force of waves against her side. It may 

 however be said to be attended by the disadvantages of too great 

 stability ; that is, it may cause the ship to be considerably strained, 

 and the masts to be carried away by a sudden impulse of the wind. 



The lateral action of the wind against the sails, and of the waves of 

 the sea against the hull of a ship, are the causes that the plane passing 

 through its masts is made to decline from the vertical position which 

 it has when the ship is at rest ; and the ship is then prevented from 

 being overturned only by the reaction of the water against the bottom 

 and sides. The momentum of this reaction is that which is called the 

 stability of the ship. The axis of the rotation has been placed by 

 different writers in different situations, but both Bouguer and Euler 

 have proved that, if the ship has not at the same time a pitching 

 motion, it should be considered as a horizontal line passing through the 

 centre of gravity of the ship. In order to find approximatively the 

 dependence of a ship's stability on its length and breadth, let it be 

 supposed that the ship is a homogeneous solid in the form of a prism 

 or segment of a cylinder having its axis in a horizontal position ; and, 

 the vessel being supposed to float upright, let ABC (Jig. 1) be a 

 transverse section through the immersed part in a vertical plane 



Fig. I. 



\ 



passing through G and ;/, which are respectively the centres of gravity 

 of the whole solid and of that part (A B) coinciding with the surface of 

 the water : let also A' B' c' be the position of the same section when the 

 vessel is inclined. Now, while the weight of the ship remains the 

 same, the volume of the immersed part is the same whether the ship 

 be upright or inclined, and the volume raised above the water by the 

 inclination on one side is equal to the volume depressed below it on the 

 other ; therefore the area M c' x may be considered as equal to A c B, 

 and A' D M to B' D N. Next let p and ? be the centres of gravity of the 

 trilateral spaces last mentioned; then, by mechanics, the centre of 

 gravity of UDB'C" will be at some point, as r in ;> g produced, the 

 displacement of </ by the inclination being supposed to be very small ; 

 and the centre of gravity of M c' N (the section immersed when the 

 solid is inclined) will be at some point H in q r : also 



: A'DM : : pr : gr, and 

 no's (=A'B'C') : B'DN ( = A'DM) : : gr :rn. 



Therefore, p r and q r are cut proportionally in g and H ; and g n is 

 parallel to p q. Consequently 



pr :gr: : pq :gu, 

 or ABO : A'DM : : pq : ga; 



and if the inclination of the ship is very small, <j n may be considered 

 as parallel to AB. Draw the vertical line BS, and OK parallel to AB ; 

 then </H = GK. 



The area ABC may represent the volume (v) of the displacement, or 

 of the immersed part of the ship ; and the area A'D M, the volume 

 raised above or depressed below A D in consequence of the incliuatii m. 

 This trilinear space being supposed to be very small, it may be con- 

 sidered as a triangle right-angled at M : and if the length and half- 

 breadth of the solid be represented by I and b respectively, we have 

 JA'M.M for the representation of the elevated .or depressed volume. 

 But A'M varies with l> ; therefore, such volume varies with l.b-. Again, 

 by mechanics, the distance of the centre of gravity of each of those 

 volumes from a horizontal line passing through D, in a direction paral- 



lel to the axis of the solid, is equal to Z.l> ; therefore, the line pq = -b, 



or pq varies with 6. Then substituting, in the last proportion above, 

 v for ABC, l.b 1 for A'DM, and 6 tor pq; also putting OK for gu, we find 



that OK varies with -I ; or v.OK c /.6 s . Now the force of the water 

 v 



to prevent the ship from being overturned taking place, by hydrosta- 

 tics, in the vertical line HS passing through H, and being represented 

 by v ; also the ship being supposed to turn about a longitudinal axis 

 passing through o, we have V.GK for the momentum of the ship's 



