C 46 3 
V. The Construction and Analysis of geometrical Propositions , 
determining the Positions assumed by homogeneal Bodies 
which float freely, and at rest, on a Fluid’s Surface ; also de- 
termining the Stability of Ships, and of other floating Bodies. 
By George Atwood, Esq. F. R. S. 
Read February 18, 1796. 
To investigate the positions assumed by homogeneal bodies 
which float freely, and at rest, on a fluid's surface, it is neces- 
sary, in the first place, to form a just conception of the several 
principles on which those positions depend. 
The proportion of the immersed part to the whole magni- 
tude of a floating body * will always be obtained, from having 
given the specific gravity of the solid in respect to that of the 
fluid ; since it is a known law of hydrostatics, that the im- 
mersed part of the solid is to the whole magnitude, in the 
proportion of those specific gravities. But a solid may be 
immersed in a fluid numberless different ways, so that the part 
immersed shall be to the whole magnitude in the given pro- 
portion of the specific gravities, and yet the solid shall not 
rest permanently in any of these positions. The reasons are 
obvious. The floating body is impelled downward by its 
weight, acting in the direction of a vertical line, which passes 
through the centre of gravity ; the pressure of the fluid, by 
* In these pages the floating bodies are always understood to be homogeneal, un- 
less the contrary be mentioned. 
