The weight of the instrument is first accurately determined in air by means of an ordinary balance. Let us suppose that its weight

is 618 grains, and that the liquid whose specific gravity is to be determined, is olive oil. The hydrometer is placed in water, and the pan loaded with weights until the liquid is level with the mark on the stem. Suppose it has been necessary to add 93 grains for this purpose; these 93 grains, together with the 618 which the instrument weighs, make 711 grains, which represents the weight of water displaced by the instrument (96). The hydrometer is then removed, wiped dry, and immersed in the olive oil. Let us suppose that now only 31 grains need be added to sink the hydrometer to the mark. These, together with the 618 grains which the instrument weighs, in all 649, represent the weight of the displaced oil. We thus learn that equal volumes of oil and water weigh respectively 649 and 711. Hence we obtain the specific gravity of the latter as compared with the former by dividing 649 by 711. The quotient is o'91, which teaches us that if a certain volume of water weighs 100 grammes, the same volume of oil weighs 91 grammes. Neither Fahrenheit's nor Nicholson's hydrometers give such accurate results as the hydrostatic balance.

Specific gravity flask. This has been already described. In determining the specific gravity of a liquid, the flask is first weighed,

-103]

Tables of Specific Gravities.

93

empty, and then, successively, full of water and of the given liquid. If the weight of the flask be subtracted from the two weights thus obtained, the result represents the weights of equal volumes of the liquid, and of water, from which the specific gravity is obtained by division.

103. Use of tables of specific gravities.—Tables of specific gravity admit of numerous applications. In mineralogy the specific gravity of a mineral is often a highly distinctive character. Jewellers also use them. By means of tables of specific gravities the weight of a body may be calculated when its volume is known, and conversely the volume when its weight is known.

A knowledge of the specific gravity of a body furnishes also a simple means of calculating its volume when its weight is known, and conversely its weight when its volume is known.

With a view to explaining the last-mentioned use of these tables, it will be well to explain the connection existing between the British units of length, capacity, and weight. It will be sufficient for this purpose to define that which exists between the yard, gallon, and pound avoirdupois, since other measures stand to these in wellknown relations. The yard, consisting of 36 inches, may be regarded as the primary unit. Though it is essentially an arbitrary standard, it is determined by this--that the simple pendulum which

makes one oscillation in a second, at London on the sea level, is 39′1375 inches long. The gallon contains 277 274 cubic inches. A gallon of distilled water at the standard temperature weighs 10 lbs. avoirdupois or 70,000 grains troy; or which comes to the same thing, one cubic inch of water weighs 252·5 grains.

On the French system the meter is the primary unit, and is so chosen that 10,000,000 meters are the length of a quadrant of the meridian from either pole to the equator. The meter contains 10 decimeters, or 100 centimeters, or 1,000 millimeters, its length equals 10936 yard. The unit of the measure of capacity is the litre or cubic decimeter. The unit of weight is the

gramme, which is the weight of a cubic centimeter of distilled water at 4° C. The kilogramme contains 1,000 grammes, or is the weight of a decimeter of distilled water at 4° C. The gramme equals 15·443 grains.

Suppose it is required to calculate the weight of a cubic foot of coal. A cubic foot contains 1,728 cubic inches; the weight of a cubic foot of water would therefore be 1,728 times 252·5 grains, this being the weight of one cubic inch of water. The product of this multiplication divided by 7,000 grains (the number contained in a pound avoirdupois) gives 62.3 pounds as the weight of a cubic foot of water; and as we learn, from the tables, that coal is 1.32 times as heavy as water, the weight of a cubic foot of coal will be 1.32 times 62.3 or 83.16 pounds.

104. Hydrometers with variable volume.—The hydrometers of Nicholson and Fahrenheit are called hydrometers of constant volume, but variable weight, because they are always immersed to the same extent, but carry different weights. There are also hydrometers of variable volume but of constant weight. These instruments, known under the different names of acidometer, alcoholometer, lactometer, and saccharometer, are not used to determine the specific gravity of the liquids, but to show whether the acids, alcohols, solutions of sugar, etc., are more or less concentrated.

105. Beaumé's hydrometer. This, which was the first of these instruments, may serve as a type of them. It consists of a glass tube, AB (fig. 84), loaded at its lower end with mercury, and with a bulb blown in the middle. The stem, the external diameter of which is as regular as possible, is hollow, and the scale is marked upon it.

The graduation of the instrument differs according as the liquid, for which it is to be used, is heavier or lighter than water. In the first case it is so constructed, that it sinks in water nearly to the

-106]

Gay-Lussac's Alcoholometer.

A

95

top of the stem, to a point A, which is marked zero. A solution of fifteen parts of salt in eighty-five parts of water is made, and the instrument immersed in it. It sinks to a certain point on the stem, B, which is marked 15; the distance between A and B is divided into 15 equal parts, and the graduation continued to the bottom of the stem. Sometimes the graduation is on a piece of paper in the interior of the stem.

The hydrometer thus graduated only serves for liquids of a greater specific gravity than water, such as acids and saline solutions. For liquids lighter than water a different plan must be adopted. Beaumé took for zero the point to which the apparatus sank in a solution of 10 parts of salt in 90 of water, and for 10° he took the level in distilled water. This distance he divided

B

Fig. 84.

into 10°, and continued the division to the top of the scale.

The graduation of these hydrometers is entirely arbitrary, and they give neither the densities of the liquids, nor the quantities dissolved. But they are very useful in making mixtures or solutions in given proportions; the results they give being sufficiently near in the majority of cases. For instance, it is found that a well-made syrup marks 35° on Beaumé's hydrometer, from which a manufacturer can readily judge whether a syrup which is being evaporated has reached the proper degree of concentration.

106. Gay-Lussac's alcoholometer. The spirits of wine and brandy, in daily use, are a mixture of pure alcohol and water. The more alcohol they contain the stronger they are; the more water they contain so much the weaker are they. Hence it is important to have a simple means of exactly determining the quantity of water contained in spirituous liquors. This is effected by means of GayLussac's alcoholometer, which has the same shape as Beaume's, and only differs in the graduation. This is effected as follows :— Mixtures of absolute alcohol and distilled water are made, containing 5, 10, 20, 30, etc., per cent. of the former. The alcoholometer is so constructed that when placed in pure distilled water, the bottom of its stem is level with the water, and this point is zero. It is next placed in absolute alcohol, which marks 100°, and then successively in mixtures of different strengths, containing 10, 20,

30, etc., per cent. The divisions thus obtained are not exactly equal, but their difference is not great, and they are subdivided into

ten divisions, each of which marks one per cent. of absolute alcohol in a liquid. Thus a brandy in which the alcoholometer stood at 48, would contain 48 per cent. of absolute alcohol, and the rest would be water.

All these determinations are made at 15° C., and for that temperature only are the indications correct. For, other things being the same, if the temperature rises the liquid expands, and the alcoholometer will sink, and the contrary, if the temperature falls. To obviate this error GayLussac constructed a table which for each percentage of alcohol gives the reading of the instrument for each degree of temperature from 0° up to 30°. When the exact analysis of an alcoholic mixture is to be made, the temperature Fig. 85. of the liquid is first determined, and then the point to which the alcoholometer sinks in it. The number in the table corresponding to these data indicates the percentage of alcohol. From its giving the percentage of alcohol, this is often called the centesimal alcoholometer.

107. Lactometer. - The lactometer is a hydrometer like Beaumé's, specially graduated for the purpose of ascertaining the quality of milk (fig. 86). This is accomplished in the following manner :-The instrument is immersed in a vessel containing pure milk, and the point to which it sinks is marked zero on a paper strip affixed to the stem. Mixtures are then made of of milk and of water; of and, and so on to of water. The lac

Fig. 86.

10

of milk and

10

tometer is successively immersed in

these, and sinks to different depths; the point at which it stops in each case is marked by a number on the stem, and thus indicates a milk of a particular strength, that is, one containing a certain quantity of admixed water.

The lactometer is, however, no infallible test for the adulteration of milk; for the density of natural milk is subject to variation, and an apparent fraud may really be due to a bad natural quality of milk.