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ee Bal 
339 
and weighted and balanced till its descending force shall be 
equal to a power represented by half the specific gravity of the 
fluid,—it will lie on the surface of the fluid without any part 
being immersed; but if any of the fluid be afterwards with- 
drawn, the solid figure, or float, will descend in exact pro- 
portion to the quantity withdrawn, volume for volume, re- 
placing by its own bulk the abstracted fluid, provided the 
quantity of fluid removed does not exceed the float in volume ; 
and the float will again ascend in proportion as the abstracted 
fluid is restored. The float, so described, by its ascent and 
descent during the removal and replacement of the fluid, will 
maintain the surface level of the fluid at the original points. 
To consider the foregoing proposition, let us suppose, in 
Fig. 1, mw a cistern of water, of which the surface level is 
Fig. 1. 
the line mn; let asc be a sector of a semicylinder of any 
breadth, and the side ac perpendicular to the surface level 
mn. (Our remarks on the present occasion will be confined 
to the semicylinder, as that figure is the most suitable for 
our purpose.) Let pv be the axis of the semi-cylindrical float, 
