of floating Bodies , and the Stability of Ships. 6g 
mode of argument it is shewn, that if the original position of 
equilibrium be that of instability, when the solid by revolving 
on its axis has become situated in a second position of equi- 
librium, it will float permanently, that is with stability, in that 
second position. And in general, when a floating solid re- 
volves round a given horizontal axis, and passes through 
several positions of equilibrium, those of stability and in- 
stability are alternate, no position of either species following 
immediately a position of the same species. In order, there- 
fore, to find what position a solid will assume after it has 
overset from any situation of unstable equilibrium, it is only 
necessary to ascertain the angle of inclination from the given 
situation through which the solid must revolve on the axis of 
motion, so that the distance GZ (fig. 2.) between the two 
vertical lines which pass through the centre of gravity of the 
solid and the centre of gravity of the part immersed may be- 
come evanescent. It is necessary in the next place, to determine 
whether any position of equilibrium originally given is that of 
stability or instability. This point will be ascertained by 
having recourse to the general value which has been investi- 
gated, for expressing the distance between the two vertical 
lines GO, ST (fig. 2.) ; or GZ — ds. In the line ER 
take any point t, and through t draw qtz parallel to GO. 
As long as == ET is greater than ds = ER, the point Z, 
and the line of support QZ , will be between the axis and those 
parts of the solid which are immersed by the inclination, 
don of permanent equilibrium, and is deflected from that position through a small 
angle, the force of the fluid’s pressure causes the solid to revolve round its axis in a 
direction contrary to the inclination ; and if the equilibrium is unstable, the same force 
acts to increase the said inclination ; this latter case corresponds to that of the equi- 
librium in which the solid is situated after it has revolved through the angle A. 
