EXAMPLES. 1. Find the distance PI in the Albion, whose tonnage is 4267 tons, and half ordinates of the water-line section are 3.5, 16.25, 23.20, 26.8, 28.45, 29.3, 29.65, 29.9, 29.95, 30, 30, 29.8, 29.6, 29.2, 28.8, 28.15, 27.05, 25.6, 23.25, 18.25, 4.6, and common interval 10 feet. 2. Find the distance PI in the Rodney, whose tonnage is 4267 tons, and whose half ordinates at the water-line section are 7.25, 17.8, 22.6, 25.1, 25.9, 26.45, 26.8, 26.95, 27, 27, 27, 27, 27, 26.9, 26.7, 26.5, 26.1, 25.65, 24.85, 23.7, 21.5, 17.35, 5, and common interval 10 feet. 3. Find the metacentre in a vessel whose displacement is 16397 cubic feet, and whose half ordinates at the water-line section are 3.95, 8.85, 12.2, 14.05, 15.05, 15.6, 15.8, 15.8, 15.7, 15.65, 15.35, 14.9, 14.2, 13.15, 11.1, 7.1, 1.15, and common interval 6 feet. 4. Find the metacentre of a vessel whose displacement is 15034 cubic feet, and whose half ordinates at the water-line section are 2.2, 6.35, 9.7, 12.2, 13.85, 14.8, 15.5, 15.7, 15.85, 15.6, 15.35, 14.8, 14.05, 12.85, 10.8, 7.15, 2.65, and common interval 6 feet. 5. Find the metacentre of a vessel whose displacement is 148914 cubic feet, and whose half ordinates at the water-line section are 6.9, 16.8, 21.8, 24.5, 25.78, 26.35, 26.75, 27, 27, 27, 27, 27, 27, 27, 27, 26.95, 26.7. 26.3, 26.05, 25.5, 24.6, 23.45, 21.35, 17.85, 8.1, and common interval 8 feet 4 inches. If the water-line section be a parallelogram, whose length and breadth are 7 and b, then B = If the water-line section be a circle, whose radius is r, then If the water-line section be an ellipse, whose semiaxes are a If the water-line section be a parabola, whose abscissa and corresponding ordinate are x and y, then B = 2x y3 MISCELLANEOUS FORMULE. Cycloid. The area of the cycloid is three times the area of the generating circle. Catenary. The area A D B A = CD. A B—t (A D B — A B) Involute of a Circle.-Let A P be the arc of the involute, and O the centre of the circle. The area included, by the radius O A, A P, and OP the cube of the string unwound, divided by three times the diameter of the circle. Spiral of Archimedes.-Let R the radius vector where the angle is 2 π, and r any other radius vector. 3π (a2 — b2)2 8 ab Evolute of an Ellipse.-The whole area = where a and b are the semi-axes of the ellipse. To find the volume of a parallelopiped. "A parallelopiped is a solid figure contained by six quadrilateral figures, whereof every opposite two are parallel."-Euclid XI., Def. A. Rule.-Multiply the area of the plane AE by the perpendicular distance between the parallel planes A E A and B D. B When a body, such as a ship for instance, floats in water it displaces a certain quantity of water. The quantity of water thus displaced is equal in weight to the floating body. Hence, to find the displacement of a ship, it is only necessary to find the cubic feet of water, the weight of which is equal to the weight of the ship; this is done by dividing the weight of the ship in pounds by the weight of a cubic foot of water in pounds, and the quotient will be the displacement in cubic feet. The weight Put = 30.75 X 2.25 X 1.5 X 58 37 6057.711 lbs. the displacement in cubic feet. .. 62 × x = the weight of water displaced. |