the Stability of Ships. zpg 
given ordinates be multiplied into its perpendicular distance 
from the ordinate a. The terms resulting will be a x o, b x r, 
c x 2r, d x S r , &c.; let these terms be added together, and 
half the sum of the first and last term being subtracted from 
the amount, let the result be denoted by the letter C ; C r — area 
CLFK x KP will be the sum of the products arising from mul- 
tiplying each evanescent area QX into its distance QK from 
the first ordinate a. In the line KH, set off a line KI* 
= ItrcoAH • A hrough the point I, draw I T perpen- 
dicular to CH ; and, through the vessel's centre of gravity G, 
draw GZ perpendicular to IT. GZ is the measure of the ves- 
sel's stability, when it is inclined from the upright through the 
angle ASH. 
In the cases which have preceded, the vertical sections of 
vessels, or segments of vessels, are assumed as equal and similar 
figures : whereas, in reality, the form and magnitude of the 
sections are gradually changed, according as they intersect the 
longer axis at a greater or less distance from the head or stern. 
The solutions of the preceding cases, and the principles therein 
established, may be next applied to investigate the stability of 
vessels, taking into consideration the form and magnitude of 
each particular section intersecting the longer axis at right 
angles, and at equal distances; taking into account also, by 
the methods which have been described, all the sections inter- 
mediate between those which are given, that may be conceived 
to intersect the axis at a very small common interval. 
* Since the Rule i. is employed in obtaining the value of the quantity C r, accord- 
ing to this computation, the area COAH ought to be measured by the same rule ; in 
which case, the line KI will be determined nearly with the same exactness as by either 
of the Rules n. or m. 
