20 6 Mr . Atwood's Disquisition on 
cumstances. To shew that this solid will float with the axis 
inclined to the fluid's surface at a certain stated angle, depend- 
ing on the specific gravity and dimensions of the solid, he de~ 
monstrates, * that if the angle should be greater than that which 
he has assigned, the fluid's pressure will diminish it ; and that, 
if the angle should be less, the fluid's pressure will operate to 
increase it, by causing the solid to revolve round an axis which 
is parallel to the horizon. It is an evident consequence, that 
the solid cannot float quiescent with the axis inclined to the 
fluid's surface, at any angle except that which is stated. The 
force which is shewn in this proposition, to turn the solid, so 
as to alter the inclination of the axis to the horizon, is the 
same with the force of stability; the quantity or measure of 
which, Archimedes does not estimate ; nor was it necessary 
to his purpose, since the alteration of inclination required to 
establish the quiescent position, may be produced either in a 
greater or less time, without affecting his argument. It 
does not appear, that this method of determining the float- 
ing positions of bodies was afterwards extended to infer 
similar conclusions in respect to solids of any other forms, 
nor to determine any thing concerning the inclination or 
equilibrium of ships at sea, which require the demonstration, 
not only that a force exists, in given circumstances, to turn 
the vessel round an axis, but also the magnitude or precise 
measure of that force. M. Bouguer, in his treatise intitled 
“ Traite du Navire has investigated a theorem for esti- 
mating the exact measure of the stability of floating bodies. 
This theorem, in one sense, is general, not being confined to 
bodies of any particular form ; but, in respect to the angles of 
* Archimedes de iis qiue in bumido vehuntur. 
f Livr. ii. sect. 2 . chap. 8. 
