DERIVATION AND ANALYSIS OF METHODS. 
EXAMPLE. 
TABLE VIII.—VERTICAL POSITION OF CENTER OF BOUYANCY BY FouR 
275 
MeEtuHops. STEAM [uG oF TaBLEs I To V. 
Dy from A from 
pvnphers of water- | ‘Table III, n ndy Table III, nA 
kee column 5. column 6. 
ei tects sssicv nis: tees love's (4) 41.1 fo) @) 0.0 Gr 753h7, (4) 0.0 
te vatetalataitslais aievelst/eherer 74.8 I 74.8 1371.8 1371.8 
BRPRERN ach chor ie, aigisel Nieves s 65.7 2 131.4 | 1204.9 2409.8 
Po kao Cant POReCrO EDIE Big 51.6 3 154.8 946.3 2838.9 
ts ota Oa Bee (x) 12.9 4 @) 51.6 (4) 236.6 (4) 946.4 
Dy =246.1 z (n=Zy) =412.6 ZA =4513.3 |2(nA)=7566.9 
w = 2 feet. wa (nZy) _2 X412.6 we (WA) _2 X7566.9 
zzy 246.1 ZA 4513-3 
S =9.17 feet Paes 2=3.35 
Vs= 9027 cubic feet. 2sw'd (nZy) _8X9.17X412.6 wz (nA) _4X7566.9 
V 9027 9027 
2=3.35 2=3.-35 
CENTER OF GRAVITY OF BOTTOM PLATING. 
The weight of this plating being proportional to the volume occupied, 
evidently its center of gravity coincides with the center of form. Also 
since both sides are symmetrical, the center of gravity falls at a point in the 
diametral plane which divides the vessel into two symmetrical halves. This 
point is determined as shown on Fig. 1, page 276. 
Fig. 1 shows a single half section of the ship, and AB is the half-girth. 
Divide the half-girth into four equal parts at b, c, and d. The center of 
gravity of each of these parts is nearly at its center. Join the centers of 
the two upper parts, and those of the two lower ones, and bisect each joining 
line in gi and go. The points gi: and ge represent the combined center of 
gravity of the two lower parts and the two upper parts respectively. Join 
gi and g2 and bisect in gs. The point gs represents the center of gravity of 
the four parts of the half-girth AB. 
If we draw g:G parallel to water-line, G will be the center of gravity of 
the whole girth of the section, the two sides being symmetrical. Thus the 
