255 LECTURE XXI. 



When a solid body floats in a- fluid, it displaces a quantity of the fluid, equal 

 to itself in weight; and every solid, which is incapable of doing this, must sink. 

 For in order that the solid may remain at rest, the pressure of the fluid below 

 it, reduced to a vertical direction, must be precisely equal to its weight; but 

 before the body was immersed, the same pressure was exerted on the portion 

 of the fluid which is now displaced, and was exactly counterbalanced by its 

 weight; consequently that weight was equal to the weight of the floating 

 body. 



Since the force, which supports the weight of a floating body, is the pres- 

 sure of the fluid immediately below it, if this pressure be removed or dimi- 

 nished, the body may remain at rest below the surface of the fluid, even when 

 it is specifically lighter. Thus a piece of very smooth wood will remain, for 

 some time, in contact with the flat bottom of a vessel of water, until the water 

 insinuates itself beneath it; and it will continue at the bottom of a vessel of 

 mercury, without any tendency to rise, since the mercury has no disposition 

 to penetrate, like water, into any minute interstices which may be capable of 

 admitting it. And, for a similar reason, if the pressure of the incumbent 

 fluid be removed from the upper surface of a solid substance, wholly immers- 

 ed in it, the solid may remain suspended, although heavier than an equal 

 bulk of the fluid. Thus, if a tube or vessel of any kind, open above and below 

 have a bottom of metal, ground so as to come into perfect contact with it, 

 without being fixed, the bottom will appear to adhere to the vessel, when it is 

 immersed to a sufficient depth in water, the vessel remaining empty. 



In order that a floating body may remain in equilibrium, it is also neces- 

 sary that its centre of gravity be in the same vertical line with the centre of 

 gravity of the fluid displaced; otherwise the weight of the solid will not be 

 completely counteracted by the pressure of the fluid. The nature of the equi- 

 librium, with respect to stability, is determined by the position of the meta- 

 centre, or centre of pressure, which may be considered as a fixed point of 

 suspension, or support, for the solid body. It is obvious that when the lower 

 surface of the body is spherical or cylindrical, the metacentre must coincide 

 with the centre of the figure, since the height of this point, as well as the 

 form of the portion of the fluid displaced, must remain invariable inallcircum- 

 :4tances, and the nature of the equilibrium will depend on the distance of the 



