270 SHIP CALCULATIONS; 
Equation (5) is used altogether in making actual ship calculations for 
the reason that A is already known from Table IV, areas being always 
calculated before moments; so we have to find only the numerator to 
determine x. 
If, however, we have to find the center of gravity of a water-line as a 
separate problem, the following is preferred, being simpler 
_ szny 
ai Sy (6) 
Example—The corrected semi-ordinates of the load water-plane of 
a vessel 368 feet long, commencing aft, are 9.2, 22.3, 29.5, 33-6, 35-7, 36.1, 
34.5, 29.2, 21.2, 11.5, 1.0 feet respectively. Find the distance of center of 
gravity from the middle ordinate. 
TABLE VI.—To FIND THE DISTANCE OF THE CENTER OF GRAVITY OF THE 
Loap WATER-LINE FROM THE MIDDLE SECTION. 
SST eal 
Number of 
Lengths of intervals from| Product for 
4 ordinates. middle moments. 
Number of ordinate Ordinate 
from forward. , 
y n ny 
NCEE SERS Or ISSA recon ota HS Ho (4) 0.5 5 2.5 
Fictieh Cidtoo GOD 00010. 010.00 bts0.0 0 11.5 4 46.0 
Joncas entree aor Sicichee ere aoRE ond esc 21.2 3 63.6 
Aacsonadgeacoog0onnsgaDod 29.2 2 58.4 
ARDS oie cn Ie aI een xO ac 34-5 I 34.5 
buco nob e sono taoee eo 36.1 (0) 205.0 
Loo OMG ncaa sede 35-7 I 35-7 
Leech atarcHern Urs wick oRrosd & exe 33.6 2 67.2 
Olstayaicke ns peud & spanatiorniys eieuerepenenees 29.5 3 88.5 
fol peda erat one ae RISO 22.3 4 89.2 
DT si Bees ee eats ts eta aor (4) 4.6 5 23.0 
—303.0 
2y=258.7 
zZny= — 98.6 
S= 36.8 
siny = —98.6 X 36.8 
sany _ — 98.6 X 36.8 
zy 258.7 
x= = — 14.03 ft. 
