DERIVATION AND ANALYSIS OF METHODS. 27% 
2. Transversely, as for Half Water-line —Starting with the conventional 
ydx as the vertical generating strip of the area, its moment about the x 
axis is equal to: 
ydx X 3y = gy dx; 
the moment for the entire area, M = 1 f y"de. 
Taking y as the distance of the center of gravity from the x axis, then 
(1) 
In using this formula it must be noted in particular that 
By = 39 Hye +s. Pat ae (2) 
CENTER OF BUOYANCY. 
1. Longitudinally.—The longitudinal position of the center of buoyancy 
of a vessel is obtained by taking the algebraic sum of the moments of the 
elementary volumes, Sdx, about the midship section and dividing by the 
volume. Thus 
MM _S Sdve _ sBSx (1) 
eee f Sdx szS 
Thus x, the distance from S to midship section, equals 0, s, 25, 3s, etc., 
for the different sections measuring from the midship section toward either 
end of the ship; thus for a section 8 intervals away x = 8s, etc. Putx = ms 
where 2 represents the number of intervals, then (1) becomes 
gt sans S 
ey eee 
but s inside the sign is constant, so we may take it outside the sign, and put 
Sins _ sinS 
=> = 5 2 
a Sas @) 
This gives us the value of x in terms of the sectional areas. 
