272 SHIP CALCULATIONS; 
If, however, as is usually the case in ship calculations, we have already 
found the value of V, we have from (2) 
LSS 
x= V (3) 
It is in this form that it is used in standard ship calculations, for we 
will have already found V, as in Table III or V. 
Equation (2) is the simplest form if the values of S are known. 
Suppose that we have only the values of the ordinates and desire to 
find x directly from them by the shortest method; we have from (2) 
ihe sans 
Te eee 
But S = 2wZy as found in a previous example. 
Therefore 
_ sxn(wry), 
x ae =.) ? 
=) 225) 
w is constant, therefore we place it outside the sign, and cancel it from 
numerator and denominator. 
Thus 
sa(nz 
= S&(n2y) ; (4) 
DDy 
which gives the result directly from the ordinates. 
‘Either (2), (3), (4), or (5), may be used to obtain the same results, and 
let us assemble them in proper form as follows: 
x _ Sans from sectional areas. (2) 
a) LS) 
2 
=> = ms from sectional areas and volume. (3) 
t= sz(nzy) directly from the ordinates. (4) 
i zzy 
2 
a r= aoe) from ordinates and volume. (5) 
(5) is evident from (4) since V = 2sw=Zy. 
In any given problem, if we have the ordinates, they are treated as in 
Table I for the values of Zy, and from them the value of x is found as above. 
