276 SHIP CALCULATIONS; 
distance of the center of gravity of the half-girth from water-line is the same 
as that of the whole girth, and the same is true of its distance from the 
midship section; so we will deal with half-girths for the sake of simplicity. 
The moment of the half-girth 4B about water-line is evidently equal to its 
length multiplied by the distance from its center of gravity to water-line 
= AB X g:C. Every section on the body plan must be treated in this 
fashion to determine graphically its center of gravity and the distance of 
its center of gravity from water-line. It must not be overlooked that we 
are getting the moments of the area of the plating surface which is propor- 
tional to its weight, and the problem becomes similar to that where it is 
required to find the center of gravity of a plane surface bounded by a curve, 
if we only consider that the ordinates in this case are curved instead of 
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Fic. 1. 
straight. That is, the half-girths are curved ordinates of the plating surface, 
and are equivalent in lengths to the straight ordinates of the developed 
surface if it were rolled out flat from the keel. Let us represent the half- 
girths by the curved ordinates y,, y2, and ys, for the first, second, third, etc., 
sections. Let the distances g,C from the center of gravity of each half-girth 
to water-line be represented by 21, %, 2, etc., for the different sections. 
As in a plane surface, the curved element of surface = ydx, where y is 
the curved ordinate and x is the fore and aft distance. The elementary 
moment about water-line = ydx.z, and the sum of all the elementary 
moments is f ydx.g. Then evidently 
Woe 9 (x) 
