^44 Mr. Atwood’s Disquisition on 
radius of curvature of the curve EQ at the point Q. Also, EW is 
perpendicular to the water’s surface AB, when the vessel floats 
upright ; and XQ is perpendicular to the water’s surface, when 
the vessel is inclined through the angle ASH. When the vessel 
floats upright, the stability is measured by the sine of inclina- 
tion and the line GW jointly ; and therefore the angle of in- 
clination being given, will be measured by the line GW, and 
will depend in some ratio or proportion on the line EW, when 
GE remains the same, or when G is made to coincide with E. 
The question is, whether the stability, when the vessel is 
inclined to the angle ASH, will depend in a similar degree on 
the line QX ? Respecting the supposed analogy it may be re- 
marked, that one condition absolutely necessary to establish it 
is wanting ; namely, the centre of gravity G ought to be situ- 
ated in the line XQ ; but it is considerably distant from that 
line, being placed in the vertical axis of the vessel WGE. This 
material difference in the conditions corresponding to the two 
cases, is sufficient to destroy all inference from analogy, even 
if arguments of this kind could be admitted, in geometrical 
subjects, to supply the place of demonstration. It is not diffi- 
cult to shew geometrically, in what position and circumstances 
of the vessel the line XQ will be the correct measure of its 
stability. Suppose that, by any alteration in the distribution of 
the ballast or lading, the centre of gravity should be removed 
from the line WGE to the line XGQ, the vessel will float per- 
manently with the line XQ perpendicular to the horizon, and 
the mast WE will be inclined to it at the angle = ASH. 
Since XQ is the radius of curvature of the curve EQ at the 
point Q, and is also perpendicular to CH, the point X will be 
the true position of the metacentre, corresponding to the float- 
