the Stability of Ships . <24 7 
But, until the demonstrations of the Cases vi. and vii. are 
shewn to be erroneous, and reasons are produced in support of 
M. Bouguer's propositions, which he has delivered without 
any demonstration, it may be allowable to suppose that his opi- 
nions are, in these particular instances, ill founded. 
The same principles are extended by M. Bouguer * to ex- 
press a general value of the distance between the metacentre, 
and the centre of the immersed part of the ship, when inclined to 
any angle : this distance he affirms to be flV— ; -f* in 
which expression y and v are the parts of the total ordinate of 
the water-section, (when the vessel is inclined,) at the distance 
x, measured on the longer axis from the initial point ; the pro- 
portion of y and v being determined by a line drawn parallel 
to the axis through the centre of gravity of the section ; and p 
is put for the volume immersed. 
When the centre of gravity is situated in the line QX, (fig. 16.) 
and the angle of inclination very small, the point of intersec- 
tion of the lines CH, c h, will bisect the ordinate CH : in this 
case the vessel floats permanently with the line QX vertical, and 
consequently with the line WE, or plane of the masts, inclined 
to the horizon at the angle ASH. But the line QX, consist- 
ently with the preceding observations, cannot be applied to 
measure the stability or security from oversetting of a ship, 
when the centre of gravity is placed in the line WE ; that is, 
in the plane of masts which divides the vessel into two parts 
perfectly similar and equal; the only situation which the centre 
of gravity can occupy, according to any mode of construction 
hitherto practised. 
* Traite du Navire, p. 273. 
t No demonstration is given by M. Bouguer of this proposition. 
