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200 Experimental Proof of Archimedes' Principle.

in a glass vessel of water graduated in cubic inches, will cause the water to rise equally one cubic inch, just as if another cubic inch of water had been poured into the jar. But, in this case, a simple measurement of the solid cube would suffice to show its true volume. 2. The apparent loss of weight by immersion of the solid is exactly equal to the weight of the volume of water which it displaces. This may be proved by the following experiment :

A cubic inch of brass, D, weighs in air, or is exactly counterpoised by 2014 grains. Assuming that that weight has been accurately determined, we suspend by a silk thread beneath a short scale-pan B (fig. 89), a hollow brass cube C, the cavity of which is exactly

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filled by the solid brass cube, D, which is itself suspended by a silk thread from the hollow cube c. We place in the scale-pan, A, the weights required to counterpoise B, C, D, in air. We then bring the glass vessel E, nearly filled with distilled water, below the short scale-pan B, so as to immerse the brass cube D in the water. The scale-pan B will rise immediately, as if there had been a loss of weight. This, as it has already been explained, is owing to the solid cube D being buoyed up by the pressure of the water around it. We ascertain the amount of this loss of weight by putting weights into the scale-pan B, and it will be found to be 252 grains and a fraction which need not be here considered. We now remove the weight from the scale-pan, and fill the hollow cube C with distilled

The Specific Gravity Phial.

201

water. The balance is immediately restored. We know that the capacity of the hollow cube is exactly equal to a cubic inch, and therefore we have a visible proof that a cubic inch of water-the quantity displaced by the cube D-weighs 252 grains; and dividing the known weight of the solid cube by 252 (2014 ÷ 252 8), we find that 8 is the specific gravity of the brass. What is true of a cube is true of all other forms of solids, however irregular.

335. Specific gravity of liquids.

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The specific gravity bottle or flask, as it is called, furnishes a simple and accurate method of ascertaining the relative weights of equal volumes either of liquids or small solids, and thus of determining their specific gravities. It is simply a thin glass flask (see fig. 90), provided with a finely-perforated stopper and a counterpoise. The flask is carefully manufactured so as to hold, according to its size, 250, 500, or 1000 grains of distilled water at 62° F. The perforated stopper allows of the flask being perfectly filled. The specific gravity of any liquid is therefore at once determined by its weight. Thus the 1000 grain bottle filled with concentrated sulphuric acid will require 846 grains in addition to the counterpoise; and when filled with alcohol it will weigh 204 grains less than its counterpoise. Thus the weights of its volume of these liquids are 1846 and 796 grains respectively; and their specific gravities must be 1846 and 0.796, that of water being taken as unity.

Fig. 90.

When there is but a small quantity of liquid, a 250-grain bottle must be used. Filled with benzoline at 62° F. its contents weigh 177 grains. Its specific gravity is thus 177 250, or 4 × 177 ÷ 1000 708. To get the specific gravity with the 250-grain phial, we have thus simply to multiply the weight of its contents by 4, and point off three decimal places.

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The 1000 grain bottle is most convenient for finding the specific gravity of solids in powder or in fine grains, such as platinum grains, gold-dust, diamonds, rubies, and emcralds. The following is the result of an experiment on the native platinum grains from Siberia. The weight of the water in the bottle counterpoised at 62° was 1000 grains, and the weight in air of the platinum taken for the experiment was 40 grains. The united weights therefore were 1040 grains. On introducing the grains of platinum into the bottle, they displaced a quantity of water equal to their own bulk; and the

202

Specific Gravity of Gases.

bottle with the grains thus lost weight in proportion. A sufficient time was allowed for the free escape of air adhering to the metallic grains, and the bottle was again weighed. It was found to have lost exactly 2'5 grains by the displacement of water, which represented the bulk or volume of the platinum grains. The specific gravity was therefore obtained by dividing the weight of platinum by the weight of its bulk of water: 402'5=16, the specific gravity of Siberian platinum ore.

The lightest solid known is lithium, which has a specific gravity of 0'59, a metal which is a constituent of the alkali lithia. It is even lighter than any known liquid, for benzoline, the lightest liquid, has a specific gravity of o'65, and on this the metal lithium will float like cork upon water (see Art. 329).

336. Specific gravity of air or gases.

This is ascertained by means of a glass globe or flask of known size, and furnished with a stopcock. It is first weighed when emptied by the air-pump, and afterwards when filled successively with water and with air or different gases. A comparison of the weights gives the specific gravities as already described.

337. As the volume of gases is more affected by heat than that of liquids and solids, it is necessary that their temperature should be accurately observed; and that the gases or vapours compared should be at the same temperature, or, if they differ in this respect, an allowance should be made according to certain known rules, so as to have both volumes at the same degree of the thermometer. Formerly air was taken as the standard or unit of density; and 100 cubic inches of it weigh, at mean temperature and pressure, 31 grains. It is found that 100 cubic inches of carbonic acid (or carbonic anhydride), under similar conditions, weigh 47′08 grains. Hence 47'08 31, or 1'520, is the specific gravity of carbonic acid. The lightest of all gases, hydrogen, is now generally adopted as the standard or unit of specific gravity; and as 100 cubic inches of hydrogen weigh only 2'14 grains, then 47'082'14, or 22, is the specific gravity of carbonic acid on the hydrogen scale.

338. Suppose we have to find the specific gravity of a solid lighter than water, such as cork. The cork is attached to a mass of metal or glass heavy enough to sink it, and already balanced in water for the purpose; and the buoyant effect of the cork, that is, the weight of its volume of water, is ascertained as before.

339. Suppose the solid is soluble in water-as a crystal of any

Nicholson's Hydrometer.

203

salt. It may be protected during the operation of weighing in water, by previously dipping it in melted wax, so as to leave a thin covering on it; or it may be weighed in some liquid which does not dissolve it, allowance being made for the difference between the weight of such liquid and of water.

340. Suppose the solid in the form of powder. If insoluble in water-such as gold dust-it may be weighed in a glass cup previously balanced in water, but the specific gravity bottle serves better for this purpose (see fig. 90); and if soluble in water, it must be weighed in some other liquid, and a corresponding allowance made for the specific gravity of the liquid selected for the experiment.

341. Hydrometers.

A less delicate, though practically a more ready method of ascertaining specific gravities is by means of the contrivance called a hydrometer, or areometer. This dispenses with the use of the balance, which is a delicate instrument both to handle and to keep. Hydrometers have various forms according to the use to which they are to be put.

a

d

342. Nicholson's Hydrometer is that represented in fig. 91. It consists of a light glass balloon or hollow ball, a, bearing a light scale-pan, b, on a fine stalk, and carrying another cup, c, beneath. There is a mark on the stem to which the instrument sinks in pure water, when a certain weight (such as 1000 grains) is placed in the upper scale, b. This may be used to find the density of a solid, a small piece of brass, in this way. Put the brass into b, and add weights, say 40 grains, to sink the instrument to the mark d. We know thus that the brass weighs 960 grains. Next put the brass in the lower scale, c, leaving the 40 grains in the upper: the brass is buoyed up by the weight of its volume of water, and we must put say 120 grains more in the upper scale to counterbalance this. So 960 grains is the weight of the brass in air, and 120 grains is the weight of its volume of water; hence 960 divided by 120, that is 8, is the density of brass compared with water.

Fig. 91.

In using it for the specific gravity of liquids, the lower scale may be dispensed with, or retained merely to load the instrument and keep it upright. If it take, in addition to the weight of the hydro

204

Different Uses of the Hydrometer.

meter itself (2000 grains), 1000 grains to sink it to the mark in water, it will take different weights to sink it in other liquids. In sulphuric acid it will take 3400 grains; that is to say, 5400 grains is the weight of a volume of this liquid which weighs but 3000 grains in the case of water. Hence 5400 divided by 3000, that is, 18, is the specific gravity of the acid.

343. The most common uses of hydrometers are to indicate the specific gravity, and from that the strength or quality, of the distilled spirits brought to market, or of milk, or of saline mixtures. In these cases the special names alcoholometer, saccharometer, lactometer, saiimeter, are often employed.

They are of various forms, but their general nature is the same in all. The instrument consists of a glass tube, loaded at the bottom with a little mercury to keep it upright, and graduated or marked with divisions, so that the specific gravity of any liquid may be read off at once from the depth to which the instrument sinks in it. In liquids lighter than water, the readings will obviously run up from the limit or water-mark; and in heavier ones, will run down. An ivory scale fixed to one kind of alcoholometer is marked P. S., for proof spirit, and the degrees above and below proof are indicated in figures by the exact level at which the instrument floats.

There are generally printed tables accompanying each instrument, telling the exact nature of its indications, and the allowances to be made for temperature and atmospheric pressure.

For ordinary commercial purposes, these are convenient and sufficiently precise; but they are by no means absolutely correct.

344. An old and ready method cf finding the specific gravities of liquids was to have a set of small glass bulbs or beads of known weights, so that, when thrown into any liquid, those heavier than it will sink, those which are lighter will swim, while the one which iust floats will mark its specific gravity. The bulbs are numbered once for all by the maker, so that the specific gravity is known at once by the figures upon them.

345. The following table shows the specific gravities of some common substances, referred to water as a standard :—

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