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 1:03. 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 : Sea water 1.027 Alcohol 795 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 ounces; thus taking water for the standard, the specific 1 1/ 1000' 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 would be in equilibrium if B the space BC. This supposes that the surface AB and the orifice at Care exposed to the same pressure, as for instance that of the atmosphere, which will be explained hereafter. If the pressure at the level AB is greater than at C, the effect is the same as if the height BC were increased to the extent which would correspond to this excess of pressure; and similarly if the pressure at the level AB is less than at C the height BC must be supposed diminished to a corresponding extent. Each particle of liquid on leaving the vessel will describe a parabola by virtue of the principles of Chapter XX.; and thus by the continuous stream of particles we obtain a visible representation of the parabolic course. 466. If we suppose the hole to be in the shape of a horizontal pipe the liquid will issue in a horizontal direction, so that the particles start from the highest point of their course and afterwards continually descend. But we may if we please insert at C a short pipe inclined to the horizon upwards, and then the fluid will ascend obliquely to some height before it begins to descend. Or the short pipe may be first horizontal for a brief space, and then turn vertically upwards: in this case the liquid spouts vertically upwards, and according to theory would rise to the level of AB. 467. Although the theory on which the preceding Article depends is beyond the range of the present work, yet there is one part of the result involved in it of which the reasonableness may be rendered tolerably evident; and this process well deserves attention. The liquid at C issues with a certain velocity, namely, with that which would be acquired in falling freely down BC. Hence if we want the liquid to issue with twice this velocity we must make the hole, not at twice the depth of C below the surface, but at four times this depth: that is, we have as it were to provide four times the pressure in order to secure twice the velocity. But the apparent difficulty is soon removed. For since the velocity at the lower hole is to be double that at the higher hole, each particle issues from the lower hole with double the velocity with which it issues from the higher hole; and moreover supposing the holes to be of the same size, double the number of particles will issue in the same time from the lower hole as from the higher hole. Thus, in all, we have at the lower hole four times the effect produced which is produced at the higher hole, corresponding, as might be expected, to the circumstance that the pressure at the lower hole in equilibrium is four times that at the higher. 468. There are two cases of the motion considered in Art. 466, namely, that in which the liquid in the vessel is always maintained at the same level, and that in which it is not. In the latter case the value which theory gives for the velocity does not agree with observation when the level of the descending fluid comes near the hole. But in both cases, so long as the hole is not too near the surface of the liquid the actual velocity of the issuing liquid does not differ much from the value assigned by theory. But when the liquid is made to spout vertically upwards it does not reach the level of the liquid in the vessel; the velocity of the issuing fluid is diminished by the friction against the sides of the pipe or opening through which it escapes, and the resistance of the air also produces a sensible effect. 469. If we know the size of a hole and the velocity with which liquid is escaping through it, we can calculate the amount of liquid which will flow out in an assigned time. But in making such calculations and comparing the results with observation it is found that the theoretical estimate is too large. Some curious phenomena have been noticed in connexion with this subject. We will suppose that the hole is very small, that it is in the base of the vessel, and that the base is very thin; this special |