1; area of the midship section, for ships of 120 guns, as 812 to 1; for ships of 90 guns, as 789 to 1; for 50-gun frigates, as 77 to for corvettes, as 723 to 1; and for brigs, as 682 to 1. And the area of the after section is to the area of the midship section in the same ships respectively as 731 to 1, as 719 to 1, as ⚫698 to 1, 619 to 1, and as 526 to 1. The centre of gravity of the load-water section, in well formed bodies, is about one seventy-fifth of the length of the water-line before the middle. The position of the centre of gravity of displacement should be a definite proportion of the length of the water-line before the middle of that line; in fast sailing ships this proportion varies between 01 to 1 and 015 to 1. For further particulars, and for the formation of the shear and half-breadth plans, see Fincham's "Outline of Ship-building." The curve described by the centre of buoyancy, the metacentric The line A B is the water-line when the vessel is at rest, and R Q is the water-line when the vessel is inclined to the angle QSB=0. During the successive inclinations of the vessel from its upright position to the angle 0, the centre of gravity of immersion, or buoyancy, will describe the curve P P', which is called the metacentric involute. a T Draw P' V perpendicular to the curve P P' at P', and equal to the radius of curvature. The curve VI, traced by the successive centres of curvature as the vessel inclines from its upright position to the angle e, is called the metacentric curve by M. Bouguer, but metacentric evolute would be more appropriate. Hence, the curve VI is the evolute of which P P" is the involute. It would not be difficult to show that P' V is perpendicular to the corresponding water-line R Q. For the same vessel and displacement the curves P P' and I V are independent of the centre of gravity G of the vessel, but it is evident that the position of the centre of gravity will affect its stability, which depends upon the perpendicular from G to the line PI V. The surface, of which a Ob is a section, that touches the successive water-line planes as the vessel inclines from its upright position to the angle e, is denominated the surface of the planes of flotation, or the envelope of the water-line planes. When the vessel partakes of a rolling and pitching motion, this surface will 120 CONSTRUCTION OF MEN-OF-WAR. be touched generally by the plane of flotation R Q in a point T; and Euler has proved that this point is the centre of gravity of the plane RQ. (See Fincham's "Outline of Shipbuilding," page 164.) To find the centre of gravity of a ship by Chapman's method. Let the vessel be perfectly upright, that is, let all the weights be equally balanced on each side. Move the weights from one side of the vessel to the other in the same transverse direction, then the vessel will be inclined through an angle 0, which is measured by a quadrant fixed in the main hatchway with a plumb-line attached to its centre. (See Papers on "Naval Architecture,” vol. 3, page 218.) Multiply each weight by the distance through which it has been moved, add the products together and call the sum s. Let the volume of immersion corresponding to the angle 0. mm' = the distance between the centres of gravity of immersion and emersion. V volume of displacement. PG = the distance of the centre of gravity from the centre of gravity of displacement. Another method of finding the centre of gravity has been proposed by Mr. Barton, which consists of moving the guns aft. A third method has been proposed by Richard Abethell, Esq., Master Shipwright at Portsmouth Dockyard, by which the necessity of moving the weights on board to produce an inclination is avoided. (See Papers on "Naval Architecture," vol. 2, pages 49 and 51.) This method is as follows:-"We will suppose, by the falling of the tide in the dock, the after extremity of the keel to come first in contact with the blocks; then, as the tide continues to fall, the after-body is gradually forsaken by the water, and the fore-body further immersed; a constant equilibrium being maintained between the total weight of the ship, and the pressure of the water against the immersed part of the body, until the ship is a-ground fore and aft. At any intermediate instant the ship may be considered as a lever of the second kind, of which the fulcrum is the transverse line or point of contact of the keel and after block, and the power and weight the weight of the immersed volume and of the ship respectively; each acting in the vertical line passing through its centre of gravity. As we can, by mensuration and calculation from the draught of the ship, easily find its weight, that of the immersed volume, and the perpendicular distance of the line of pressure from the fulcrum; in the equation of the moments, the distance of the vertical line passing through the centre of gravity of the ship is the only unknown quantity, which is therefore readily determined." area of the midship section, for ships of 120 guns, as 812 to 1; for ships of 90 guns, as 789 to 1; for 50-gun frigates, as ⚫77 to 1; for corvettes, as 723 to 1; and for brigs, as 682 to 1. And the area of the after section is to the area of the midship section in the same ships respectively as 731 to 1, as 719 to 1, as ⚫698 to 1, 619 to 1, and as 526 to 1. The centre of gravity of the load-water section, in well formed bodies, is about one seventy-fifth of the length of the water-line before the middle. The position of the centre of gravity of displacement should be a definite proportion of the length of the water-line before the middle of that line; in fast sailing ships this proportion varies between 01 to 1 and ⚫015 to 1. For further particulars, and for the formation of the shear and half-breadth plans, see Fincham's "Outline of Ship-building." The curve described by the centre of buoyancy, the metacentric The line A B is the water-line when the vessel is at rest, and R Q is the water-line when the vessel is inclined to the angle QSB=0. During the successive inclinations of the vessel from its upright position to the angle 0, the centre of gravity of immersion, or buoyancy, will describe the curve P P', which is called the metacentric involute. M a Draw P' V perpendicular to the curve PP' at P', and equal to the radius of curvature. The curve VI, traced by the successive centres of curvature as the vessel inclines from its upright position to the angle e, is called the metacentric curve by M. Bouguer, but metacentric evolute would be more appropriate. Hence, the curve VI is the evolute of which P P" is the involute. It would not be difficult to show that P' V is perpendicular to the corresponding water-line R Q. For the same vessel and displacement the curves P P' and I V are independent of the centre of gravity G of the vessel, but it is evident that the position of the centre of gravity will affect its stability, which depends upon the perpendicular from G to the line P' V. The surface, of which a Ob is a section, that touches the successive water-line planes as the vessel inclines from its upright position to the angle 0, is denominated the surface of the planes of flotation, or the envelope of the water-line planes. When the vessel partakes of a rolling and pitching motion, this surface will |