ON HYDaOSTATlCS. 265 



third of the height only from the bottom. For the pressure at each point 

 may be represented by a line equal in length to its depth below the surface, 

 and a series of such lines may be supposed to constitute a triangle, of which 

 the centre of gravity will indicate the place of the centre of pressure of the 

 surface ; and the height of the cerftre of gravity will always be one third of 

 that of the triangle. It is easily inferred, from this representation, that the 

 whole pressure on the side of a vessel, or on a bank, of a given length, is pro- 

 portional to the square of the depth, below the water, to which it extends. 

 (Plate XIX. Fig. 245.) 



The magnitude of the whole pressure on a concave or convex surface may 

 also be determined by the position of its centre of gravity ; but such a de- 

 termination is of no practical utility, since the portions of the forces, which 

 act in different directions, must always destroy each other. Thus, the per- 

 pendicular pressure on the whole internal surface of a sphere filled 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 spe- 

 cific gravities; for it is obvious that the greater density of the one will pre- 

 cisely 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 con- 

 siderations are necessary for the determination of the equilibrium of fluids and 

 solids with each other; and in the first place the properties of floating bodies 

 require to be investigated, 



VOL. I. M m - 



