DERIVATION AND ANALYSIS OF METHODS. 281 
This form, using volume and water-line ordinates, is the more usually 
employed, and is preferable. 
The other form, to calculate directly from the ordinates, is obtained 
thus 
Since V = 2swrzy 
ie 
BM = S35 (4) 
EXAMPLE. A 
Given the following ordinates of half the load water-line, 0.4, 3.4, 6.8, 
9.0, 10.2, 10.4, 10.4, 10.2, 9.8, 8.2, 7.2 feet, which are those of the steam tug 
of Table IV, Column 11. Find J and BM by formule (7) and (8) using 
the values of V and 22y as already found in those tables. (See Table X). 
SUMMATION OF FORMUL. 
A =2sxy (1) 
S=2wrzy (2) 
V =sztS =wzA = 2swrDy (3) 
_ 28° 2ny 
ae 
Center of gravity of water-line, x 
gravity Ae (4) 
Say 
2 
Center of gravity of half water-line, y = oe (5) 
STS) 
Tees 
SSP 
Fh V 
Center of buoyancy (longitudinally), 
yancy (long y), x cs) (6) 
Sly 
_ 258° wz (nZy) 
V 
