Modulus of Fineness.— Lines 11 and 12 enable us to compare the different forms; and by running our eye along line 12 we are enabled to trace the effect of the successive changes in the form of water line, in bringing down the metacenter, and reducing the stability of the ship, thus giving what has been sometimes called the modulus of fineness of water line. STABILITY CALCULATION, USING THE The following tables will show the application of the above rule to the calculation of the stability levers GZ from the body plan reproduced, noting that the integrator used was metrically divided, and the original drawing was to a scale of to the foot or full size with ten Tchiby scheff ordinates. The center of gravity was assumed at 24 feet above base. The coefficients are therefore as follows, the length of vessel being 600 feet : For displacements (tons), For levers (feet), and, or, Displacement in tons = Levers in feet = 1701.5 × sum of differences of area readings. 18.9 × sum of differences of moment readings Sum of differences of area readings Displacements (D) = 1701.5 × I ) I respective to II taken up = 18.9 X lines. The angles calculated were 15o, 30°, 45°, 60°, 75°, and 90°, and the results as tabulated used to plot off the Stability Cross Curves shown from which the Stability Curves at various displacements were taken, the correction being calculated for the new locii of the center of gravity where G is the assumed position below S then GZ SZ+SG sin 0, and when above S then GZSZ-SG sin 0. So that taking the ordinates from the cross curves at the displacement dealt with SG being now known, we can determine the exact values of GZ for any angle. 45° 30° 15° Calculation of GZ Levers for Stability Cross Curves, Using the Integrator and Tchibyscheff's Rule. 9668 2002 3 1779 2111 M 4511 5,290 5097 +.586 +.586 3.560 5097 5.113 8,700 4931-.166 +.420 1.550 5169 7.224 12,280 4974.195 +225 .590 3 5519 2107 2 7874 2355 7874 5,640 0549 +.687 +.687 3.930 0549 5.103 8,680 0820 +.271 +.958 3.550 1056 7.210 12,250 1411 +355 +1.313 2.950 1647 9.565 16,300 1999 +352 +1.665 3,260 2235 L.W.L. 0365 2491 12.056 20,400 2463 +.228 +1.893 2.970 0365 L.W.L. 2423 12.058 2699 1.896 Check 90° 75° 60° INCLINA TION. Calculation of GZ Levers for Stability Cross Curves, Using the Integrator and Tchibyscheff's Rule. 4 3 2 6676 1844 6.054 10,300 2448 +.370 +1.093 3.42 0689 2090 10.067 17,130 3503 +.101 +1.440 2.70 3740 ENCES OF READINGS. ᏀᏃ SUM OF DIFFER- STABIL ITY LEVERS. |