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fluid and possesses the property of buoyancy which all liquids have. Hence any body in air loses weight equal to that of an equal bulk of air. Thus if we put any body into one scale of a balance and a counterpoise into the other, we must not in general take the counterpoise as representing the exact weight of the body. The fact is that the true weight of the counterpoise, diminished by the weight of an equal bulk of air, is equal to the true weight of the body diminished by the weight of an equal bulk of air. If the body and the counterpoise have the same volume the true weight of the counterpoise is exactly equal to the true weight of the body; but if not, the true weight of the counterpoise is less or greater than the true weight of the body according as the volume of the counterpoise is less or greater than that of the body. The correction thus required to the weight of a body when estimated in the usual way is too small to be of importance in ordinary matters, though it must be regarded in scientific investigations.

445. The specific gravities of some substances have been given in Art. 403; the following are selected from an elaborate Table in Dr Young's Lectures which extends to four places of decimals:

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The specific gravities of the woods must be taken as average values, for the results will vary according to the character of particular specimens.

XXXVII. SPECIFIC GRAVITY OF LIQUIDS.

446. One of the most obvious methods of finding the specific gravity of a liquid is by actually determining the weight of an assigned volume of it. Let a flask be provided with a stopper which accurately fits it, and weigh the flask and stopper. Also fill it with water and weigh it again. Then by subtraction we know the weight of water

which would exactly fill the flask. We are now prepared to find the specific gravity of any liquid whatever. For fill the flask with the liquid and weigh it; subtract the weight of the flask, and the remainder is the weight of the liquid which would exactly fill the flask. Divide this by the weight of the water which would exactly fill the flask, and the quotient is the specific gravity of the liquid. For example, suppose that the water which would exactly fill the flask is found to weigh 20 ounces, and that the liquid which would exactly fill the flask is found to weigh 18 ounces; the specific gravity of the liquid is

18

20'

that is

9 10*

then

447. Or we may determine the specific gravity of a liquid by immersing the same solid successively in the liquid and in water. The weight lost in the first case is the weight of the liquid equal in bulk to the solid, and the weight lost in the second case is the weight of water equal in bulk to the solid: divide the former by the latter, and the quotient is the specific gravity of the liquid. For example, a piece of glass when immersed in sulphuric acid is observed to lose 185 grains of its weight, and when immersed in water is observed to lose 100 grains of its weight: hence

the specific gravity of sulphuric acid is

185

100'

that is 1'85.

448. Or we might determine the specific gravity of a liquid by floating the same solid successively on the liquid and on water. The volume immersed in the first case is the volume of the liquid equal in weight to the solid, and the volume immersed in the second case is the volume of water equal in weight to the solid; divide the latter by the former and the quotient is the specific gravity of the liquid; see Art. 440. For example, a solid floats on oil and the volume immersed is found to be 25 cubic inches; and when it floats on water the volume immersed is found to be 23 cubic inches: hence the specific gravity of the oil

is

23

25

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449. Liquids are readily combined so as to form a new liquid, and when the specific gravities of the components

are known we can determine the specific gravity of the mixture formed of assigned quantities of them, assuming that the volume of the mixture is equal to the sum of the volumes of the components. For example, suppose that a pint of water is mixed with a pint of alcohol of which the specific gravity is 8, and we want to know the specific gravity of the compound. We may if we please work with cubic feet instead of pints, and our language will then become more simple.

A cubic foot of water weighs 1000 ounces;

a cubic foot of alcohol weighs 800 ounces. Hence the two cubic feet of the mixture weigh 1800 ounces, therefore one cubic foot of the mixture weighs 900 ounces,

and therefore the specific gravity of the mixture is

that is 9.

900

1000'

In practice however it is often found that the volume of a mixture of fluids is not equal to the sum of the volumes of the components: see Art. 439.

450. All the spirits which are used in the arts and in ordinary life consist of mixtures of alcohol and some other substances, of which water is the principal. It is often important to know what proportion the alcohol is of the whole in a certain mixture; or in ordinary language to know the strength of the spirit. The more water is mixed with the alcohol the greater the specific gravity of the mixture becomes. When the mixture has about the same specific gravity as oil it is called proof spirit, so that all spirit which will float on oil is said to be above proof. Thus the process of finding the specific gravity of a liquid becomes one of practical interest, and various instruments are used for the purpose called Hydrometers. They all depend on the principle that when a body floats on a liquid it displaces a quantity of the liquid equal in weight to its

own.

451. The common Hydrometer. AB is a hollow cylindrical stem; C and D are two hollow spheres, which have their centres so situated that the axis of AB if produced would pass through them. D is loaded with lead, so that the centre of gravity of the whole instrument

A

Q

P

may be below the centre of gravity of the fluid displaced when the instrument floats with the cylindrical stem vertical and upwards. When the hydrometer floats in water suppose that the surface of the water meets the stem AB at P; and when it floats in the liquid which we are examining suppose that the surface of the liquid meets the stem AB at Q. Then the specific gravity of the liquid is the proportion which the volume of the part of the instrument below P bears to the part of the instrument below Q; see Art. 440. The volume of the part below P is the volume of the whole instrument diminished by the volume of the stem from P upwards; and the volume of the part below is the volume of the whole instrument diminished by the volume of the stem from Q upwards: thus these volumes may be readily determined.

B

с

D

B

452. Sikes's Hydrometer. This instrument differs from the preceding in two respects; the stem AB is a very thin flat bar, and there is a series of weights capable of being attached to the part of the stem below the large sphere. These weights are in the form of round discs with notches cut in them by which they can ride on the stem. The weights are of such magnitude that if the instrument would float in a liquid with the whole of its stem above the surface the addition of one weight would sink it nearly to A. By the use of the weights the instrument is in fact capable of being converted into a series of hydrometers. So long as we keep the same number of weights attached below C, the mode of obtaining from the instrument the specific gravity of a liquid is the same as in the preceding Article. But if we have to use more or fewer of the weights when the instrument floats on a liquid than when it floats on water the matter is not quite so simple. This hydrometer is

D

employed by the excise officers under the authority of government to determine the specific gravity of spirits, with the view of fixing the amount of duty to be paid; it is accompanied with a Table properly calculated which gives the specific gravity of a liquid as soon as the number of weights attached to the stem is known and the depth to which the stem sinks has been observed.

453. Nicholson's Hydrometer. C is a hollow cylinder or ball; A is a dish supported by a slender wire B, the direction of which is the same as the axis of C. From the lower extremity of C a heavy dish D is suspended. The weights of the various parts of the instrument are so adjusted that when 1000 grains are placed in the dish A, the instrument will sink in water to a point marked on the stem B near the middle of it. Therefore the weight of so much water as would be equal in volume to the instrument below the marked point is equal to 1000 grains together with the weight of the in

A

Ο

B

strument. Now put the hydrometer in the liquid which is to be examined, and by increasing or decreasing the weight in the dish A make the instrument sink again to the marked point. Thus we know the weight of so much of the liquid as is equal in volume to the instrument below the marked point. Divide this weight by the corresponding weight in the case of water, and the quotient is the specific gravity of the liquid.

454. Nicholson's Hydrometer may also be used for finding the specific gravities of solids. Place the solid, reduced to a convenient size, in the dish A, and let additional weights be placed in the dish until the instrument will sink in water to the marked point. Then the weight of the solid together with the additional weights which have been used must amount to 1000 grains, and so the weight of the solid is known. Next remove the solid from A, place it in D, and as before add weights in A until the instrument will sink to the marked point. Then the weight of the solid in water, together with the weights in A,

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