Q P A 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 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 C Ꭰ 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, must amount to 1000 grains, and so the weight of the solid in water is known. Thus we know the weight of the solid, and also its weight in water; and therefore, by subtraction, we find the weight lost in water: divide the weight of the solid by this, and the quotient is the specific gravity of the solid. Of course any other weight might be adopted throughout instead of the 1000 grains which we have taken for simplicity. 455. "The wire which supports the dish A in this instrument is so thin, that an inch of it displaces only the tenth part of a grain of water. The accuracy of its results depending therefore on the coincidence of the mark on the wire with the surface, which can always be ascertained to a very small fraction of an inch, will come within the limit of a very minute fraction of a grain. Specific gravities may thus be obtained correctly to within a hundred thousandth part of their whole value, or to five places of decimals." 456. The hydrometer might be usefully employed to detect adulteration in various liquids which are used in ordinary life. For instance, the specific gravity of milk is greater than that of water, being about 103. By mixing water with milk the specific gravity is made less than that of milk, and the greater is the proportion of water used the more is the specific gravity diminished. Thus a very accurate hydrometer would enable us to find the proportion of water to milk in a mixture of the two. 457. A gallon is such a measure of volume as will just hold ten pounds Avoirdupois of pure water. Hence if we multiply the specific gravity of a liquid by 10 we obtain the weight in pounds of a gallon of it. 458. The following are the specific gravities of some liquids : XXXVIII. SPECIFIC GRAVITY OF GASES. 459. We have still to consider the specific gravity of gases, and we will give a Chapter to the subject here, although we shall have to allude to various matters which will be more fully explained in some subsequent Chapters, treating on Pneumatics. 460. Let us confine our attention first to one of the gaseous bodies, namely common air, which surrounds us altogether and which we continually breathe. Now although air may at first seem to have no weight, yet it really has; and we shall see hereafter that this gives rise to many important results. Here we need only say that if a flask be filled with air it will weigh more than when empty, shewing that the air has weight. 461. A very remarkable property of gaseous bodies is that they may be compressed to almost any extent. Thus air being put into a strong vessel we may compress it into half or a quarter of its original bulk. Moreover if we keep air in a vessel under a certain amount of pressure it will expand by the application of heat and contract by the withdrawal of heat. Again, the weight of an assigned volume of air or of any gas will depend to some extent on the quantity of watery vapour which is mixed with the air or gas. Instruments called hygrometers are constructed to shew the amount of this vapour. It follows from what has been said, that in speaking of the specific gravity of any gaseous body there are many circumstances which must be regarded in order to fix the exact condition of the body. 462. We may now state the facts with respect to air with sufficient accuracy for our purpose. Let the temperature be that of the freezing point of water; let the air be dry, that is free from watery vapour; let the air be in what we may call its natural state of pressure, namely, the state at which it is at the level of the sea on an ordinary day. Then it is found that a cubic foot of air will weigh nearly 1 ounces; thus taking water for the standard, the specific 1% gravity of air is that is 0013. Or we may say that water is about 768 times as heavy, bulk for bulk, as air in the state just explained. A more accurate statement is the following: 100 cubic inches of air at the temperature of 60 degrees of Fahrenheit's thermometer, and under a pressure denoted by 30 inches in the height of the barometer, weigh 31'0117 grains. 463. The specific gravities of gases are usually referred to common air as the standard; they may be referred to water if necessary by means of the facts stated in the preceding Article. The subject however is not sufficiently elementary to be pursued here; indeed the various gases are not things with which we are so familiar as we are with solids and liquids: the gases require the aid of chemistry to make them known to us. The following Table gives the ratio of the specific gravities of some of these bodies to the specific gravity of air at the same temperature and under the same pressure. 464. The subject of the motion of liquids is one of great difficulty, and though theory and experiment have been much employed on it the knowledge gained up to the present time is far from complete. We shall consider only some simple cases. 465. Velocity of issuing liquid. If a small hole be made in the side of a vessel which is full of liquid the liquid will escape with a certain velocity. The forces which produce the motion are the weight of the liquid itself and the pressure of the surrounding liquid; these T. P. 13 |