SYMBOLS COMMON IN NAVAL ARCHI TECTURE USED IN THIS BOOK. A S.A. C.E. . a. b. Bm Bx. Bw. *A B. . B G . . Area of load water plane. Sail area in square feet. А LXB Bxd dicular. G H . = . . . . . C HA. Mid-section area. M.C. Height of transverse metacentre above base. G.Z. Stability lever. G.M. Height of transverse metacentre above centre of gravity. B.M. Height of transverse metacentre above centre of buoy ancy. L.M.C. Longitudinal metacentre above base. & Centre of gravity below L. W.L. G Centre of gravity above L. W.L. p Prismatic coefficient. Water line. Placed before dimensions indicates that these are the registered or tonnage dimensions. I. Moment of inertia of load water plane. M Metacentre and moment. M Moment to alter trim one inch at load line. 0 On drawings locates the intersection of projected water line with the elevation. Centre of gravity of sail plan, or centre of effort. ข. Ordinates or stations. Common interval or abscissa between ordinates. Resistance. Draught of water moulded (mean). d> Draught of water forward Power. Di x V 8 I.H.P. * .... Per. W (OD 2. } Per inch ; also tons per inch of immersion at L. W.L. Algebraical Signs. + Plus, addition. Positive. Semicircle. Compression. tive. Tension, Equal to. co Infinity Unequal to. Arc. > Greater than. Difference. * Not greater than. () [] {} Vincula. < Less than. C Constant. * Not less. d Differential. X By. Multiplied by s Integration. :: Multiplied by. Ratio. Isto. f Functions. : So is. As (ratio). Divided by.g Gravity. I Perpendicular to. k Coefficient. || Parallel to. n Any number. # Not parallel. a An angle. ... Because. 8 Variation. ... Therefore. A Finite difference. Angle. 0, Ø Any angles. L Right angle. 7 Ratio of circumference to di. ameter of circle. A Triangle. Parallelogram. Sum of finite quantities. Square. VSquare root. O Circumference. ♡ Cube root. Circle. nth root. p Radius. THE NAVAL CONSTRUCTOR CHAPTER I. DISPLACEMENT (D). The displacement of any floating body whether it be a ship, a barrel, a log of lumber or, as in the case of the great Philosopher who first discovered its law, the human person, is simply the amount of water forced or squeezed aside by the body immersed. The Archimedian law on which it is based may be stated as :All floating bodies on being immersed in a liquid push aside a volume of the liquid equal in weight to the weight of the body immersed. From which it will be evident that the depth to which the body will be immersed in the fluid will depend entirely on the density of the same, as for example mercury the immersion would be very little “indeed compared with salt water, and slightly less in sast water than in fresh. It is from this principle that we are enabled to arrive at the exact weight of a ship, because it is obvious that if we can determine the number of cubic feet, or volume as it is called, in the immersed body of a ship, then, knowing as we do that there are 35 cubic feet of salt water in one ton, this volume divided by 35 will equal the weight or displacement in tons of the vessel. If the vessel were of box form, this would be a simple enough matter, being merely the length by breadth by draught divided by 35, but as the immersed body is of curvilinear form, the problem resolves itself into one requiring the application of one of a number of ingenious methods of calculation, the principal ones in use being (1) The Trapezoidal Rule, (2) Simpson's Rules, and (3) Tchibysch eff's method. Simpson's First Rule. The calculation of a curvilinear area by this rule is usually defined as dividing the base into a suitable even number of ecual parts, erecting perpendicular ordinates from the base to the curve, and after measuring off the lengths of these ordinates, to the sum 1 |