Mr. Atwood's Propositions , &c. 47 
which the solid is supported, acts upward, in' the direction of a 
vertical line (usually called the line of support), which passes 
through the centre of gravity of the part immersed : unless, 
therefore, these two lines are coincident, so that the two cen- 
tres of gravity shall be in the same vertical line, it is evident 
that the solid thus impelled, must revolve on an axis until it 
finds a position in which the equilibrium of floating will be 
permanent. 
From these observations it appears, that to ascertain the 
positions in which a solid body floats permanently on the sur- 
face of a fluid, it is requisite that the specific gravity of the 
floating body should be known, in order to fix the propor- 
tion of the part immersed to the whole : secondly, it is neces- 
sary to determine, by geometrical or analytical methods, in 
what positions the solid can be placed on the surface of the 
fluid, so that the centre of gravity of the floating body, and 
that of the part immersed, may be situated in the same verti- 
cal line, while a given proportion of the whole volume is 
immersed under the fluid’s surface. 
These particulars having been determined, evidently re- 
duce the statement of the problem into a narrow compass; 
but they are not alone sufficient to limit it : for although it 
has been shewn that a body cannot float permanently on a 
fluid unless the two centres of gravity, that have been men- 
tioned, are situated in the same vertical line, it does not follow 
that, whenever those centres of gravity are so situated, the 
solid will float permanently in that position : * consistently 
* Admitting any proposition to be true, the converse of the proposition may be 
either true generally, or with exceptions. To distinguish the cases in which it is true 
from those in which it fails, requires a separate demonstration or investigation,. 
