ioo Mr. Atwood's Propositions determining the Positions 
always continue of the same value, and therefore y of CQ = y 
of WX or CG = W g; consequently g is the centre of gravity 
of the part immersed after the inclination. And since the 
abscissa or portion of the diameter intercepted between the 
lowest point and surface of the fluid must always be of the 
same magnitude while the specific gravity remains the same ; 
and by the construction Wx is made equal to the abscissa CO ; 
it follows, that when the solid has been so inclined, that the 
lowest point shall coincide with W, CG = wg, and conse- 
quently wg is always less than wV ; if therefore a line g% is 
drawn through the centre of gravity g perpendicular to the 
horizon, the point of intersection % with the horizontal line 
RU will be between the points F and U ; and the pressure 
of the fluid acting in the direction of the line gz will cause an 
angular motion in the solid,* which elevates the point D and 
depresses the point A, or, in other words, will counteract the 
inclination of the solid, by which it is deflected from its position 
of equilibrium. By the same method of argument it is shewn, 
that if the solid is inclined on the contrary direction, a force is 
created by the position of the centre of gravity of the part 
immersed, which restores the solid to its former situation, as 
found by the construction ; which therefore places the solid 
in a position of equilibrium which is permanent. 
The several conditions by which this construction is limited 
will be more easily deduced from analytical investigation, than 
from having recourse to geometrical constructions. 
To represent in general terms the angle CNO, at which 
the axis of the solid is inclined to the horizon, let BE = a; 
aHF or the parameter =p ; also let the specific gravity of 
the solid be to that of the fluid as n to 1 ; consequently 
* Page 63. 
