278 Mr. Atwood’s Disquisition on 
upright. Through the point E, draw EV parallel and equal to 
KL : and, in EV, take ET to EV as the area ASH h is to the 
area representing the entire volume displaced : through G, 
draw GU parallel to CH ; and, through T, draw TZ perpendi- 
cular to GU, intersecting the line GU in the point Z. GZ is 
the measure of the vessel’s stability. 
sid Method. 
Let BOA (fig. 29. ) be the given vertical section of a vessel, in- 
tersected by the water’s surface BA when floating upright. G is 
the vessel’s centre of gravity : E is the centre of gravity of the vo- 
lume displaced in the upright position. Let the area BOA be mea- 
sured by either of the three Rules, suppose Rule 1.; and through D, 
the bisecting points of BA, draw NDM inclined to the line BA 
in the angle ADM, equal to the given inclination of the vessel 
from the upright. Let the area NOAM be measured, by erecting 
equidistant ordinates on the line MN. If the area, so found, is 
equal to the area BOA, the area DBN will be equal to the area 
ADM. But, if they are unequal, let the difference be represented 
by E,and from D, toward the largest of the areas, suppose ADM, 
set off DS— NM xs t,ADM ; and ’ throu g h s - draw CSH P a “ 
rallel to NM. The area ASH/j will approximate to equality 
with the area BSCc ; and, consequently, when the vessel is in- 
clined through the given angle ASH, it will be intersected by 
the water’s surface in the line CH. On the line HC, let the 
equidistant ordinates a, h , c, d, &c. be erected perpendicular to 
CH ; and let the common internal between the ordinates be 
— - r. Let the measure of the area CLFK be obtained, and let 
m be the centre of gravity of this area : through the point m, 
draw fflP perpendicular to CH : let each of the successive 
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