28 o 
Mr. Atwood's Disquisition on 
CASE XIII. 
The longer axis of a vessel is supposed to be divided into a 
given number of equal parts, and vertical sections to pass 
through the several points of division, intersecting the axis at 
right angles : the form and magnitude of each particular sec- 
tion being given, with the common distance between them, 
the positions of the centres of gravity of the vessel, and of the 
volume displaced, and the distance of the water-section from 
the keel, being known, it is required to construct the measure 
of the vessel's stability, when it is inclined from the upright 
through a given angle. 
Let OBOAW (Tab. XV. fig. 30. ) represent any vertical section 
of a vessel ; suppose it to be the greatest or principal section : BA 
is the breadth of this section at the water-line, when the vessel 
floats upright : let CH represent the line which coincides with 
the water's surface, when the vessel is inclined from the up- 
right through the given angle ASH. From the nature of the 
conditions, it is sufficiently evident that the point S, in any in- 
dividual section, will not be determined on the same principle 
by which the position of that point was fixed according to 
the former solutions ; that is, by making the area ASH equal 
to the area BSC ; because, the volume immersed, and that 
which is caused to emerge in consequence of the vessel's in- 
clination, will not now be proportional to these areas, as 
they * are on a supposition that the vertical sections are similar 
and equal figures. But, in the present case, the vertical sections 
being different, both in form and magnitude, the water's sur~ 
* See page 210. 
