211 
the Stability of Ships . 
same vessel differently laden, the stability will be measured 
by the weight of the vessel and the line G Z jointly. The 
weight of any vessel (including the lading) is equal to the 
weight of water displaced by it ; which will be obtained by 
measuring the solid contents of the^ displaced volume, and 
from knowing the weight of a given portion of sea water, such 
as a cubic foot, which weighs 64 pounds avoirdupois. The 
vessel's weight being thus obtained, the determination of the 
stability, whatever be its form or inclination from the upright, 
requires only that the line G Z shall be known, or the pro- 
portion which it bears to some given line, for instance, the 
line B A, shall be ascertained. 
A general method of constructing this line is demonstrated 
in the Phil. Trans, for the year 1 796, but is there principally 
applied to the floating position of bodies ; its use in inves- 
tigating the stability of vessels is incidentally mentioned, and 
in general terms, rather than as being itself a subject of dis- 
quisition. This theorem is founded on supposing the centres 
of gravity of the several volumes BOA, GOFH, ASH, BSC, 
(fig. 1.) to be given in position ; an assumption allowable in 
demonstrating a general theorem : but, in applying it to the 
stability of particular vessels, it becomes necessary that the 
positions of these points should be absolutely found, and the 
results combined with the other conditions, to infer the mea- 
sure of stability ; a determination which, in some cases, is 
attended with much difficulty, and in others, is not prac- 
ticable by any direct methods ; an instance, amongst manv 
that might be mentioned, in which the particular application 
is more difficult than the general demonstration of propo- 
sitions. The following constructions and investigations are 
E e 2 
