The pressure upon a perpendicular surface will of course vary with the depth. If a board one foot square be placed perpendicularly in a vessel of water, and be divided into horizontal sections, each one inch deep, then calling the pressure at the depth of one inch 1, the pressure at two inches will be 2, at three inches 3, and so on; hence the whole pressure will be equal to the sum of the series 0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12: this will amount to half the pressure which would have occurred if the board had been situated horizontally 12 inches below the surface. Now, as the centre of gravity of this surface is situated in the middle of the board, it follows that the area of the board, multiplied by the distance of its centre of gravity beneath the surface, will be equal to the pressure. From a more extended investigation it is found that this rule is general, that the pressure of a fluid against any surface, in a direction perpendicular to it, varies as the area of the surface multiplied into the depth of its centre of gravity. From this we see that the pressure against the four sides and bottom of a cubical vessel is equal to three times the weight of the contained fluid.
From this also may be calculated the pressure on dock gates, on the lower parts of ships, and large cisterns, coolers, etc. In all cases of pressure the amount, as determined above, must be multiplied by the specific gravity of the fluid employed, as it will be evident, that if two vessels of equal sizes and similar shapes be filled, one with water, and the other with mercury, that the pressure on the base of the latter will be so much greater than that on the former, as the weight of the mercury exceeds that of the water. The equal pressure in all directions causes the surface of all large bodies of water to be horizontal, and also the surfaces of any two bodies of water communicating by a tube or otherwise; hence the construction of water levels. In the annexed cut A B is a tube turned up at each end, and filled with mercury or water. Upon the surface of the fluid at c and d are small floats, carrying an upright sight, with a horizontal wire or hair across it. When the instrument is held in the hand, on looking through c its cross wire will cover that of d, because the fluid stands equally high in both legs.
If it be required to know whether any distant object be horizontal, it is only necessary to point the instrument toward it; and if the two cross wires and the object coincide, the object is in the same horizontal line. The common spirit level consists of a small tube filled with spirits of wine, except a small space, which contains a bubble of air. The tube is hermetically sealed; and when placed on a horizontal surface, the bubble will be seen in the middle of the tube. A little reflection on the nature of hydrostatic pressure will show its applicability to the purpose of ascertaining the comparative weights of bodies, or, what is commonly termed their specific gravities. If a body of any shape, either as heavy as water, or heavier than it, be plunged into a vessel filled with that liquid, it will of course displace a quantity of fluid equal to its own bulk, and if the quantity be measured, we have a ready measurement of the magnitude of the solid body that was immersed; for as the water displaced is equal in bulk to the size of the irregular solid, a measurement of the one will serve to ascertain the other. Again, if the quantity displaced be weighed, and the immersed solid weighed also, we shall have the relative weights of the two substances, or their specific gravities.
If the whole of the water displaced could be accurately collected and weighed, this method would furnish a ready mode of ascertaining the relative weights of any two bodies. Thus, if two bodies of equal weight, successively plunged into water, were to displace one and two ounces of water respectively, the relative weights of the bodies would be as 2 to I. As, however, considerable difficulty would arise in the use of this method, the following process is used with bodies heavier than water. Weigh the body in air, and also in water, observe how much of its weight it loses by immersion in the water, and then divide the weight of the body in air by the loss in water. Suppose a piece of gold to weigh 58 grains, by weighing it immersed in water it would lose 3 grains of its weight; divide the 58 grains by 3, and it will give 191/3 as the specific gravity of gold; that is, the gold would be 191/3 times heavier than an equal bulk of water. The weights of solid and liquid bodies are usually compared with that of water, one cubic foot of which contains just 1000 ounces avoirdupoise. Hence, by referring to tables of specific gravities, we obtain the real as well as the relative weights of bodies.
Thus, in the example we have given, a cubic foot of gold would weigh 1000 X 191/3 = 19,333 ounces. If the solid consist of a substance that is soluble in water, it must be covered with a coating of wax or varnish, and an allowance made for the difference produced by the coating. When the solid consists of several small pieces, a cup must be previously immersed in the water, and accurately counterpoised; the fragments may then be placed in it, and the loss of weight ascertained. If the body whose specific gravity is required be lighter than water, another heavier body must be attached to it, and the loss of weight in the compound being noticed, the loss in the heavier body must be subtracted from it, and it will give the loss of weight in the body under investigation. The specific gravity of liquids is found by filling a small bottle (which holds a definite quantity, say 1000 grains of water,) with the liquid under examination, and then weighing the quantity contained, the proportion which this bears to 1000 is the specific gravity of the liquid. Thus, if the bottle be successively filled with water, real alcohol, and nitric ether, the weight of the equal measures would be 1000, 797, and 908, which represent the specific gravities of these fluids.
This experiment shows clearly the nature of specific gravity, which it will be seen is simply obtaining the real weights of equal measures of different substances. If we could obtain a cylinder or cube of copper, and another of gold, of exactly the same dimensions, and compare their true weights with the weight of a portion of water of the same magnitude, we should at once obtain their relative or specific gravities; but as it is inconvenient to alter the shapes of bodies, and, in many cases, would be next to impossible to obtain them of precisely the same dimensions, the usual mode of weighing in water, by which we obtain the weight of a quantity of water of equal bulk with the solid, is infinitely preferable. For further information on the subject of this article see BramaH's Press, Hvdrometer, Specific Gravity, etc.