sure resulting depends on the area of the bellows-boards, multiplied by the vertical height of the tube.

Theoretically, therefore, it appears that a quantity of water, however small, can be made to lift a weight however great-a principle sometimes spoken of as the HYDROSTATIC PARADOX.

But liquids exert a pressure against the sides, as well as upon the bases of the containing vessel-the force of that pressure depending on the height. The law for estimating such pressure is, "the horizontal force exerted against all the sides of a vessel is found by multiplying the sum of the areas of all the sides into a height equal to half that at which the liquid stands."

When bodies are sunk in a liquid, the liquid exerts a pressure which depends conjointly on the surface of the solid and the depth to which its centre is sunk. Thus, if into a deep vessel of water we plunge a bladder, to

Fig. 55.

the neck of which a tube is tied, the bladder and part of the tube being filled with coloured water, it will be seen, as the bladder is sunk, that the coloured water rises in the tube.

A pressure exerted against one portion of a liquid is instantly communicated throughout the whole mass, each particle transmitting the same pressure to those around. A striking illustration of this is seen when a Prince Rupert's drop is broken in a glass of water, the glass being instantly burst to pieces. Bramah's press, or the hydrostatic press, is an illustration of the principle developed in this lecture-that every particle of a fluid transmits the pressure it receives, in all directions, to those around. It consists of a small metallic forcing-pump, a, Fig. 55, in which a piston, s, is worked by a lever, c b d. This little pump communicates with a strong cylindrical reservoir, A, in which a water-tight piston, S, moves, having a stout flat head, P, between which and a similar plate, R, supported in a frame, the substance to be compressed, W, is placed. The cylinder, A, and the forcing-pump, with the tube communicating between them, are filled with water, the quantity of which can be increased by working the lever, d. Now it is obvious that any force, impressed upon the surface of the water in the small tube, a, will, upon the principles just described, be transmitted to that in A, and the piston, S, will be pushed up with a force which is proportional to its area, compared with that of the piston of the little cylinder, a. If its area is one thousand times that of the little one, it will rise with a force one thousand times as great as that with which the little one descends-the motive force applied at d, moreover, has the advantage of the leverage, in proportion as c d is greater than c b. On these principles it may be shown that a man can, without difficulty, exert a compressing force of a million of pounds by the aid of such a machine of comparatively small dimensions.

CHAPTER XI.

SPECIFIC GRAVITY.

Definition of the term-The Standards of Comparison-Method for Solids -Case when the Body is Lighter than Water-Method for Liquids by the Thousand-Grain Bottle-Effects of Temperature-Standards of Temperature-Other Methods for Liquids-Method for Gases-Effects of Temperature and Pressure-The Hydrometer or Arëometer.

BY the specific gravity of bodies we mean the proportion subsisting between absolute weights of the same volume. Thus, if we take the same volume of water and copper, one cubic inch of each, for example, we shall find that the copper weighs 8.6 times as much as the water: and the same holds good for any other quantity, as ten cubic inches or one cubic foot. When of the same volume the copper is always 8.6 times the weight of the water.

Specific gravity is, therefore; a relative affair. We must have some substance with which others may be compared. The standard which has been selected for solids and liquids is water; that for gases and vapours, atmospheric air.

When we speak of the specific gravity of a substance which is of the liquid or solid kind, we mean to express its weight compared with the weight of an equal volume of water. Thus, the specific gravity of mercury is 13.5; that is to say, a given volume of it would weigh 13.5 times as much as an equal volume of water.*

A TABLE OF THE MEAN SPECIFIC GRAVITIES OF VARIOUS BODIES, AT A TEMPERATURE OF 60° FAHRENHEIT.

Brande's "Dictionary of Science, Literature, and Art," 1842, p. 529.

Apparently the simplest way for the determination of specific gravities of solids, would be to form samples of a uniform volume; as, for instance, one cubic inch. Their absolute weight, as determined by the balance, would be their specific gravities.

But, in practice, so many difficulties would be encountered in such a process, that its results would not furnish us with accurate information, whereas the principles of hydrostatics furnish us with far more accurate means for resolving such problems.

To determine the specific gravity of a solid body, it is to be weighed first in air and then in water. * In the latter instance it will weigh less than in the former, because it displaces a quantity of the water equal to its own volume, and this deficit in weight is the weight of the water so displaced. The weight in air and the loss in water being thus determined, to find the specific gravity, "Divide the weight in air by the loss in water, and the quotient is the specific gravity."

"If the body be lighter than water, there must be affixed to it some substance sufficiently heavy to sink it, the weight of which, and also its loss of weight in water, are previously known. Deduct this weight from the loss of the bodies when immersed together, and divide the absolute weight of the light body by the remainder; the quotient gives the specific gravity."

For the determination of the specific gravity of liquids several methods

*To find the specific gravity of bodies.

1. If it be a solid body, heavier than water, weigh it exactly, first in air and then in water, or some fluid whose specific gravity you know; and let the absolute weight of the body A, the weight of the body in water, &c. B, the specific gravity of

=

=

A

A-B

C, the

2. For a solid body, lighter than water. Take any piece of metal, and tie it to a piece of the light body, so that the compound may sink in water; and putting A, C, D, as in No. 1, and E= weight of the metal in water, F weight of the compound in water. the specific gravity of the light body.

Then, D

AC

A+E-F

=

3. For a fluid. Take a solid body of known specific gravity, which will sink in the

A-B

fluid, and putting the same letters as in No. 1; then will C- D, the specific gravity

of the fluid.

A

"The Principles of Mechanics," by WILLIAM EMERSON, with Notes by G. A. SMEATON.

may be resorted to. One of the most simple is by the thousand-grain bottle. This consists of a light glass flask, the stopper of which is also of glass, with a fine perforation through it. When the bottle is filled with distilled water, and the stopper inserted in its place, any excess of liquid is forced through the perforation, and the bottle, on being weighed, should be found to contain one thousand grains of the liquid exactly.

If any other liquid be in like manner placed in this bottle, by merely ascertaining its weight we at once determine its specific gravity. Thus, if it be filled with oil of vitriol or muriatic acid, it will be found to hold 1,845 grains of the former, and 1,210 of the latter. These numbers, therefore, represent the specific gravities of the bodies respectively.

This instrument enables us to illustrate, in a very satisfactory manner, the effect of temperature on specific gravity. It has been said that the thousandgrain bottle is so called from its containing precisely one thousand grains of water; but very superficial consideration satisfies us that this can only be the case at a particular temperature. Suppose the bottle is of such dimensions that at 60° Fahrenheit it contains exactly one thousand grains; if we raise its temperature to 70° Fahrenheit, the water will expand, or if we lower it to 50 Fahrenheit it will contract, exactly as if it were a liquid in a thermometer. It is, therefore, very clear that temperature must always enter into these considerations, and that before we can express the relation of weight between any substance, whether solid or liquid, and that of an equal volume of water, we must specify at what particular temperature the experiment was made. For many purposes 60° Fahrenheit is selected, and for others 39° Fahrenheit, which is the temperature of the maximum density of water.

There is a second method by which the specific gravity of fluids may be known. It is to weigh a given solid (as a mass of glass) in the fluids to be tried, and determine the loss of weight in each case. Inasmuch as the solid displaces its own volume of the different liquids, the losses it experiences when thus weighed will be proportional to the specific gravities. The following rule, therefore, applies: "Divide the loss of weight in the different liquids by the loss of weight in water, and the quotients will give the specific gravities of the liquids under trial.”

For the determination of the specific gravities of gases a plan analogous in principle to that of the thousand-grain bottle is resorted to. A light glass flask, exhausted of air, is attached by means of the stop-cocks to the jar, containing the gas to be tried. This gas been passed through a drying-tube by means of a bent pipe into the jar over mercury. On opening the stopcock the gas flows in, and its weight may then be determined by the balance.

From the greater dilation of gases by heat, all that has just been said in relation to the effect of temperature on specific gravity applies here stlll more strongly. It is to be recollected that this form of bodies is, compared with atmospheric air, taken as the standard.

For gases another disturbing agency beside temperature intervenes—it is pressure. Atmospheric pressure is incessantly varying, and the densities of gases vary with it. It is not alone the thermometer, but also the barometer, which must be consulted, and the temperature and pressure both specified. Besides, great care must be taken, in transferring the gas from the jars in which it is contained, that it is not subjected to any accidental pressures in

the apparatus itself, and that the flask in which it is weighed is not touched by the hands, or submitted to any other warming or cooling influences. [The determination of the specific gravity of gaseous substances is an operation of much greater delicacy. From the extreme lightness of gases, it would be inconvenient to compare them with an equal bulk of water, and, therefore, atmospheric air is taken as the standard of comparison. The first step of the process is to ascertain the weight of a given volume of air. This is done by weighing a very light glass flask, furnished with a stop-cock, while full of air; and then weighing it a second time, after the air has been withdrawn by means of the air-pump. The difference between the two weights gives the information required. According to the observation of Prout, 100 cubic inches of pure and dry atmospheric air, at the temperature of 60°, and when the barometer stands at 30 inches, weigh 31.0117 grains. By a similar method the weight of any other gas may be determined, and its specific gravity be inferred accordingly. For instance, suppose 100 cubic inches of oxygen gas are found to weigh 34.109 grains, its specific gravity will be thus deduced; as 31.0117: 34-109: 1 (the specific gravity of air): 1-1025, the specific gravity of oxygen.-" Turner's Chemistry" edited by Baron Liebig.]

For the determination of the densities of liquids there is still another method, often more convenient than the former, and very commonly resorted to; it is by the aid of instruments which pass under the name of Hydrometers or Aërometers.

The principle on which these act is, that when a body floats upon water, the quantity of fluid displaced is equal in volume to the volume of the part of the body immersed, and in weight to the weight of the whole body.

Thus, a piece of cork floating on the surface of quicksilver, water, and alcohol, sinks in them to very different depths: in the quicksilver but little, in the water more, and in the alcohol still deeper; but, in every instance, the weight of the quantity of the liquid displaced is equal to that of the cork. It is plain, therefore, that to determine the specific gravity of a liquid, we have only to determine the depth to which a floating body will be immersed in it. The hydrometer fulfils these conditions. It consists of a cylindrical cavity of glass, A, Fig. 56, on the lower part of which a spherical bulb, B, is blown, the latter being filled with a suitable quantity of small shot or quicksilver. From the cylindrical portion, A, a tube, C, rises, in the interior of which is a paper scale bearing the divisions. The whole weight of the instrument is such that it floats in the liquid to be tried; and if that liquid is to be compared with water, and is lighter than water, the zero of the divided scale is toward the lower end of the paper; but if the liquid be heavier than water the zero is toward the top of the scale. Tables are usually constructed, so that, by their aid, when the point at which the hydrometer floats in a given liquid is determined in any experiment, the specific gravity is expressed opposite that number in the table.

Fig. 56.

Fig. 57.