282 Mr. Atwood's Disquisition on 
to the longer axis, and therefore parallel* to a line drawn 
through all the points D, from one extremity of the vessel to 
the other ; the several lines DS are the perpendicular distances 
of these parallel lines, and are consequently all equal. In the 
next place, it is requisite to determine the magnitude of the 
line DS, according to the given conditions : whatever be the po- 
sition of the points S, if lines CH are drawn through S, in each 
of the sections, inclined at an angle to the line BA, equal to 
the given angle of the vessel's inclination, the same plane will 
pass through all the lines CH. It is required to ascertain at 
what distance DS, from the points D, the plane CH, coinciding 
with the water’s surface when the vessel is inclined, must pass, 
so as to cut off a volume on the side ASHZ>, being the volume 
Immersed, which shall be equal to the volume in the Side 
BSCr, which has emerged from the water, in consequence of 
the vessel’s inclination. 
In each section, through the middle point D, draw a line 
NDW, inclined to BA at an angle ADW, equal to the given 
angle of the vessel’s inclination ; the same plane will pass 
through the lines NDW, in all the sections. By the methods 
which have been described, let the area of the figure ADW h 
be measured in each section ; from these equidistant areas, the 
solid contents of the volume between the two planes DA-f and 
DW, and the side of the vessel intercepted, may be inferred by 
* The points D being coincident with the water’s surface, a line passing through 
them must be horizontal ; and being, by the supposition, situated in the same plane 
with the longer axis, must therefore be parallel to it. 
f Since the same plane passes through the lines DA, drawn coincident with the 
water’s surface in all the sections,- this plane may be supposed projected into the line: 
DA on the plane DOA. For similar reasons, the line DW represents the plane which 
passes through all the lines DW in all the sections*. 
