ON HYDROSTATICS. 201 



with a fluid, is three times as great as the weight of the fluid ; but the 

 force tending to burst the sphere, in the circumference of any vertical 

 circle, is only three fourths of that weight. 



If two fluids are of different specific gravities, that is, if equal bulks of 

 them have different weights, their opposite pressures will counterbalance 

 each other, when their heights above the common surface are inversely as 

 their specific gravities ; for it is obvious that the greater density of the one 

 will precisely compensate for its deficiency in height. Thus, a column of 

 mercury, standing at the height of 30 inches in a tube, will support the 

 pressure of a column of water, in another branch of the tube, exactly 34 

 feet high : since the weight of 30 cubic inches of mercury is equal to that 

 of 408 cubic inches of water. (Plate XIX. Fig. 246.) 



We have hitherto considered the properties of fluids in contact with 

 solids which are immoveable, and of invariable form ; but it often happens 

 that they act on substances which are moveable ; and they are sometimes 

 contained in vessels of which the form is susceptible of variation ; in these 

 cases, other considerations are necessary for the determination of the equi- 

 librium of fluids and solids with each other ; and in the first place the 

 properties of floating bodies require to be investigated. 



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 

 diminished, 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 w r ill 

 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 contimie 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 inter- 

 stices 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 immersed 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 

 equilibrium, with respect to stability, is determined by the position of the 



