44

DENSITY OF SOLIDS.

[21.

and the weight, after careful drying of the outside, is taken. Bottles which contain 20 or 50 grammes up to the graduation on the neck may be employed instead of the smaller one when the quantity of liquid is large.

The determination of the density of gases is the same in principle; a flask or globe is weighed when empty, again when filled with air, and a third time when the gas under trial has been substituted for atmospheric air. Gases, however, are liable to considerable changes of volume from slight variations of external circumstances; hence, in taking their density, certain precautions are necessary, which will be fully described further on (146).

(22) Density of Solids.-With solids, a different, but not less simple method is adopted, though resting on a principle by no means so obvious. This principle was one of the great discoveries of Archimedes: it may be thus explained :—When a

FIG. 5.

body is plunged beneath the surface of a liquid, it obviously displaces a volume of such liquid equal to itself, and consequently it is pressed upon or supported in the liquid, with a force exactly equal to that with which the particles of the liquid were supported, when they previously occupied its place; the solid will therefore appear to have lost weight exactly equal to that of the volume of liquid which it has displaced. The operation required for ascertaining the density consists,

therefore, in weighing the solid in air, then having, as in fig. 5, suspended it by a horsehair from the scale-pan, placing it in distilled water,* and again weighing; the difference of the two weights will be that of its own volume of water.

* In exact experiments the temperature of the water should be noted, 4° C. being that to which such comparisons are referred, though the temperature of 60° F. (15°5 C.), hitherto used in England, is practically more convenient, because more easily attained.

Loss: being the weight of an equal volume of

water

0'71 grammes.

The density of the lead is obtained from these data by the application of proportion, in the following manner :—

071: 8.20 :: 1'000 : * (=11'549), sp. gr. of lead.

The rule for obtaining the density of a solid may therefore be expressed in the following terms :-Divide the weight of the body in air by the loss which it experiences when weighed in water; the quotient is the required density. The experimental proof of the correctness of the principle-viz., that the solid loses weight equal to that of the water which it displaces, is easily given. Take a solid metallic cylinder which accurately fits, and completely fills, the cavity of a cylindrical cup; counterpoise the two when suspended in air from one extremity of the balance beam. Then withdraw the metallic cylinder, and suspend it by a hair to a hook at the bottom of the cup, which must still remain attached to the balance, and place the cylinder so suspended in distilled water; the counterpoise will now be much too heavy fill the cup with water-(add, that is, the weight of a volume of water equal to the volume of the cylinder,) and the equipoise will be restored.

Occasionally it happens that a knowledge of the density of a body in the form of a powder is required; in such a case the method of taking the density requires to be slightly modified. Suppose that it be desired to find the density of a species of sand; we may proceed as follows:-Take a bottle which contains, when full, a known weight of distilled water, 100 grammes for example; weigh into it, when empty, a quantity, e.g., 15 grammes, of sand. Supposing that the sand had not displaced any water, the bottle, when filled up with that liquid, would now weigh 115 grms. ; but on actually weighing the bottle after it has been filled up, it is found that the water and sand together weigh only 1096 grms.; the sand therefore has displaced 5'4 grms. of water. We have thus the data for calculating the density of the sand, as follows:

:

5'4: 150: 1'000 : x (= 2'777), the density of the sand.

If the substance be soluble in water, it must be weighed in air as usual; then in spirits of wine, in oil of turpentin, or in some liquid which does not dissolve it, and the density of which is known.

If the body be so light as to float in water, it must be first weighed in air, and then attached to a solid, the weight of which in water has been ascertained, and which is sufficiently heavy to keep the lighter body, when fastened to it, beneath the surface; the weight in water of the two united bodies is then determined, and the result thus obtained is deducted from the weight of the heavier

46

DENSITY-THE HYDROMETER.

[22.

solid in water: if to this remainder the weight of the light body in air be added, we are furnished with the weight of a volume of water equal to that of the lighter solid, and have the data for calculating the density by proportion, in the usual manner.

FIG. 6.

(23) The Hydrometer.-Another method of taking the density of liquids consists in the use of the instrument called the hydrometer or areometer.* The hydrometer (fig. 6) consists of a graduated stem, which is made to float vertically in the liquid, by means of a hollow ball of glass or brass counterpoised' by a duly adjusted weight attached to the lower end of the instrument. A portion of the stem of the instrument must always float above the surface of the liquid the density of which is to be determined. It is obvious, that when placed in any liquid contained in a vessel of sufficient depth, it will sink until it has displaced a volume of liquid equal to its own weight in a dense liquid it will sink to a smaller depth, in a less dense liquid it will sink to a greater extent; an additional portion of the stem being in the latter case immersed, until it has displaced a sufficient additional quantity of the liquid to compensate for the diminished density of the liquid under trial. The instrument may either be supplied with a scale graduated upon the stem by trial in liquids of known density, so as to give the result by mere inspection, or an arbitrary scale of equal parts may be used, and the values indicated may be ascertained by reference to tables constructed for the purpose. In practice, it is found convenient to employ two instruments, one of which is graduated for liquids less dense than water, the other for those which are denser; the need of an inconvenient length of stem is thus obviated.

The hydrometer is, with suitable precautions, capable of affording very accurate results. A particular form of the instru

*The term hydrometer means water or liquid measurer, from "dwp, water, and μέτρον, a measure; areometer is derived from ἀραιὸs, rare, and μέτρον. Tables of Baumé's and Twaddell's hydrometers will be found in the Appendix to this volume. Baumé's scale for liquids denser than water is obtained by placing the instrument in distilled water, in which it should sink till the tube is nearly covered. An aqueous solution of sodic chloride, containing 15 per cent. of the dry salt, is then prepared, and the height at which the instrument stands in this solution is marked on the stem; the interval between that and the level for distilled water is divided into 15 equal parts (points), and the remainder of the stem is graduated into degrees of equal value. The strongest oil of vitriol of commerce marks usually about 66° of such an instrument.

25.]

VARIETIES OF MOLECULAR ACTION.

47

ment, known as Sikes's hydrometer, is employed by the Excise for determining the strength of spirituous liquors. The ordinary glass instruments, however, only furnish approximations to the truth, which are quickly obtained, and for the common purposes of the arts are sufficiently exact.

(24) Correction for Weighings taken in Air.—The apparent weight of every substance in the atmosphere (that is, the attraction with which it appears to be drawn to the earth), is always a little less than its actual weight, because the air presses upon and supports the body with the same force with which it would support a portion of air of the same volume as the body itself. The weight of this displaced portion of air may be easily ascertained, if the density of the body be known for from the observed weight of the body, we can calculate directly the weight of an equal volume of water, and 16 of this weight will give the weight of a corresponding volume of air at 15°5 C. and 760mm. barometric pressure, or at o° C. under the same pressure. This weight must be added to that actually found; at the same time a similar and opposite correction will be required for the metallic weights used in the experiment, because they will also appear to be lighter than they really are; and an amount of weight greater than the true one will be required to effect the counterpoise. If, therefore, the weights have the same density as the body counterpoised, the two corrections will neutralize each other; but if, as in weighing gases, there is a great difference between them, the correction will be one of importance. The true weight sought will be thus obtained :-Add to the weight of the body in air, the weight of the volume of air which it has displaced, and deduct from this the weight of the volume of air displaced by the weights employed.

The correctness of the foregoing observations admits of an easy experimental illustration. If a light body, such as a piece of cork, be suspended in air from one end of a scale-beam, and be counterpoised at the other end by a metallic weight, then on placing the apparatus under the receiver of the air-pump, and exhausting the air, the cork will gradually acquire the preponderance; but on again admitting the air, the equilibrium will be restored.

CHAPTER III.

ON SOME VARIETIES OF MOLECULAR ACTION.

I. Elasticity.-II. Cohesion.-III. Adhesion.—IV. Crystallization.

(25) BESIDES gravity, which operates through distances so vast that the mind is lost in the attempt to estimate and explore them, other forms of attraction exist; but they are exerted only through distances so minute, as to be inappreciable to our unaided senses: and yet, upon the exertion of these attractions, the form, and even the chemical properties of bodies depend.

The first of these actions is known as cohesion; it acts between the particles of matter which are similar in kind. The degree of intensity with which this attraction is exerted in each

48

ELASTICITY-MECHANICAL PROPERTIES OF GASES. [25.

particular case determines whether the body be solid, liquid, or gaseous.

The second of these actions is that of adhesion; it is exerted between portions of matter dissimilar in kind, and unites them, as in the case of the intervention of cements, into one consistent whole.

The third, and to the chemist the most important, is that known as chemical attraction, which causes the union of dissimilar particles of matter of invisible minuteness, rearranges these particles in new forms, and produces a compound body endowed with new properties.

Reacting against all these molecular attractions, is the repulsion of heat, which may be raised high enough to overcome them all, and which in a modified form, when balanced against these attractions, produces that equipoise in distance between the constituent particles of material objects in general, which is designated as elasticity.

Attractions which thus act at these minute distances only, are termed molecular actions, in contradistinction to those which, like gravity, act upon the mass, and operate through great distances.

§ I. ELASTICITY-MECHANICAL PROPERTIES OF GASES.

(26) By elasticity we understand the resistance that a body offers to compression or to extension, and the property which it possesses of regaining its form or volume when the pressure or tension is withdrawn.

The law which regulates elasticity, in perfectly elastic bodies, may be expressed by the statement that the strain (elongation or compression) produced by the application of an external stress is proportional to the stress. Most ordinary solid bodies are sensibly perfect in elasticity when the stress applied does not exceed a certain limit. For example, a bow, or a spring bent to a certain extent with a tension of 10 lb., will be bent to double that extent with a tension of 20 lb.

All solids have limits to their elasticity, and there are very few which are perfectly elastic, even within those limits; that is to say, there are few solids which recover their form perfectly after having been stretched or compressed; if compressed beyond a certain point, they either set,' and alter their shape, as is the case with lead; or they break, as is the case with glass. The elasticity of glass and steel is, within the bounds of their cohesion, almost perfect: that of caoutchouc, on the contrary, is imperfect; for, by frequent stretching, it becomes permanently elongated.

When a rod is stretched within the limits of its elasticity, the extension is proportional to the tension applied: a tension produced by a weight of 2 kilos. will produce an extension double of that produced by 1 kilo. For equal weights,