of a column of water, whose base is of the same area as that of the aperture in the vessel, and whose length is equal to the depth of the hole from the surface of the water. Hence, in vessels of large draught, the keels should possess considerable strength to enable them to oppose the upward pressure, exerted by the water in which they float.

с

126. As a consequence of the law of equal pressure, every portion of the sides of a containing vessel are exposed to pressure, corresponding to the weight of the fluid pressing against it. In the vessel of water, ACD, if a particle of fluid situated at B be pressed by the column of water above AB, it will, for reasons already stated, be at the same time pressed upwards (124) by an equal force, and this pressure will be communicated laterally to the particles lying on the same horizontal layer between BC and BD: thus every point in the sides of the vessel is pressed with the same force, as the fluid particles contained in the horizontal layer corresponding to it are. As a general rule, the pressure supported by the sides of a containing vessel is equal to the weight of a fluid column, having for its vertical height the depth of the centre of gravity of the side below the surface; and for its base, a surface equal to that of the side of the vessel.

E

B

127. The lateral pressure increases with the depth of the fluid; for in the vessel н the fluid column AC transmits its pressure (126) to the horizontal layer CD to D; and the column EF pressing upon the layer FG, has its force transmitted by FG to G; then the pressure at G must be greater than at D, because Er is longer than AC. Therefore the formula already given for calculating the pressure on the base (122) will apply to the lateral pressure; letting в represent the side instead of the base of the vessel.

F

H

CENTRE OF PRESSURE.

87

In a vessel of water of 5 feet deep, the pressure on a square inch of lateral surface, at 1 foot deep, will be =

pound.

3

=

4

5

=

= 2

When the pressure upon the base of a cubical vessel of water is known, the lateral pressure can be readily calculated, for the pressure upon any one side of a cubical vessel, filled with fluid, is one half of the pressure on the base. For the bottom sustains a pressure equal to the whole weight of the

C

B

fluid, and the pressure sustained by the side is equal to the weight of the prism ABCDEF, which is half the cube,* and therefore equal to half the pressure on the base.

From this fact follows the remarkable circumstance that the fluid, in a cubical vessel, produces a total amount of pressure three times as great as its own weight; for if this = 1, and as upon each of the four sides it produces a pressure equal to half that on the base, × 4: 2; and upon the bottom a pressure equal to its own weight, the total pressure exerted by it must be 2 + 1 = 3.

128. The point where all these pressures (121-7), in a mass of fluid, are equally balanced, is termed the centre of pressure; this would be identical with the centre of gravity

Euclid, B. ii. props. 28 and 40.

(31), if the lower layers of fluid were not compressed by the weight of those above them, on which account it is always

G

lower than this point. In a

vessel whose sides are paralle

с

f

D

B

lograms, the centre of pressure 9 is found by bisecting the horizontal sides, by the line AB, and dividing GD into three

equal portions by the lines ef; produce f to g, and the point

tube c, on pouring water into them up to the line 7, it will be found to present a level surface in both; and

EQUILIBRIUM OF SOLIDS IN FLUIDS.

89

the fluid in each will be at the same elevation; for if the water in A, instead of being at 1, was at mm, it is obvious that the layer of fluid pp would be submitted to unequal pressure, being in в pressed by the long column. lp, and in a pressed only by the shorter column mp, and consequently equilibrium could not exist (119). Therefore the particles of fluid acted upon by the strongest force will move, and attain a state of rest only when the level of the fluid is the same in both vessels. The only circumstance introducing the slightest exception to this law is capillarity (16), by which, if one of the vessels, as в, in the above figure be very narrow, the water, or other fluid, will have a tendency to rise to an higher elevation than the fluid in a.

A

B

130. The above law applies only when the communicating vessels are filled with the same fluid; for if fluids of different densities incapable of mixing, as water and mercury, be used, the elevations acquired by each will be found to be in the inverse ratio of their specific gravities. Let mercury be poured into the tube AB until the horizontal portion c becomes filled, then pour water into в, and it will be found that, to raise the mercury in a to the height of one inch, a column of water, rather more than 13.5 inches high, will be required in B; the specific gravity of mercury, as compared to water, being as 13-59 to 1.

с

131. When a solid is immersed in a fluid, it displaces a quantity of the latter equal to its own bulk, a legitimate consequence of the impenetrability of matter (2). If this quantity of fluid be lighter than the solid, the latter will sink, but if heavier, it will swim: this has been already alluded to (29). But if the fluid displaced be of the same weight as the immersed solid, the latter will remain at rest in the fluid, in whatever position it be placed; a circumstance arising from the force of gravitation acting equally upon

the solid and the fluid displaced, the quantities of matter in each being equal (27). Fishes appear to be in this state of equilibrium when immersed in their own element; and for the purpose of enabling them to preserve this state at different depths they are provided with an airbladder, by compressing or expanding which, they are enabled to acquire the same density as that of the water. At a very great depth, the air in this organ becomes considerably condensed, and on suddenly rising to the surface it expands; and it occasionally happens that this takes place with such force, that the muscular efforts of the animal are unable to control it, and the organ is ruptured, causing an extravasation of air into the surrounding tissues. The known hydrostatic toy, in which a hollow glass figure, partly filled with water, floats or sinks in a vessel of water by pressing the piece of caoutchouc with which the latter is covered, is a popular illustration of these facts.

132. The well-known hydrostatic principle that solids, immersed in fluids, displace a quantity of the latter equal to their own bulk, was first observed by Archimedes, who studied it with no less industry than success. This sage moreover discovered that a body, when immersed in a fluid, loses a portion of its weight equal to that of the displaced fluid. The most satisfactory mode of proving the correctness