substance is equal to the weight of 2 of the same bulk of water. Thus the weight of a cubic foot of the substance is 2 5 of the weight of a cubic foot of water, and the specific 2 2 gravity of the substance is And is also the proportion 5 of a volume of water to the volume of an equal weight of the substance. 441. To find the specific gravity of a solid which is lighter than water we may proceed thus. Take a vessel with vertical sides, and having one side carefully marked with horizontal straight lines so that we know how much of the vessel is occupied by any liquid put into it by noting the line to which the level rises. Fill the vessel with water up to any of these lines, and note the line. Put the solid to float on the water; in consequence of this the level will rise: note the line at which the level stands. Again push the solid entirely under the surface, and note the line at which the level of the water stands. Thus we can determine the volume of the portion of the solid immersed when floating in equilibrium, and also the whole volume of the solid; the former divided by the latter gives the specific gravity of the solid. For example, suppose the side of the vessel to be marked with equidistant horizontal lines; and let the level of the water rise from its first position through 2 divisions when the solid floats; and let the level of the water rise from its first position through 4 divisions when the solid is entirely immersed. Thus the two volumes are in the proportion of 23 to 4; and the specific gravity of the 2 solid by Art. 440 is that is 5 8' 442. Or we might determine the specific gravity of a solid which floats on water in the following way. First weigh the solid. Then attach one end of a string to the solid, immerse the solid completely in water, and let the string pass under a pully at the bottom of the water, then rise vertically and have its other end attached to the arm of a balance. By this means we ascertain what is the weight of water equal in bulk to the solid, diminished by the weight of the solid itself; and by adding the known weight of the solid itself we obtain the weight of an equal bulk of water. Divide the weight of the body by the weight of an equal bulk of water, and the quotient is the specific gravity of the body. For example, suppose that a solid weighs 5 ounces; when the solid is kept completely immersed in water by a string which passes under a pully and then rises vertically, let the force which the string exerts be equal to 7 ounces: then the weight of water equal in bulk to the solid is 12 ounces, and therefore the specific gravity of the solid is 7 12 443. There is still another method for determining the specific gravity of a solid which floats on water. Attach the solid to a second so dense that both together sink in water; this body may be called the sinker. Weigh the two together both in the water and out of the water; the difference is the weight of water equal in bulk to the two solids. Also determine separately the weight of water equal in bulk to the sinker, and then by subtraction we know the weight of water equal in bulk to the first solid. Weigh this solid separately; then its specific gravity is the quotient of this weight by the weight of an equal bulk of water. For example, a piece of wood and iron together weigh 138 ounces, and in water 8 ounces; so that 130 ounces is the weight of water equal in bulk to the two. Again, the iron alone weighs 78 ounces, and in water 68 ounces, so that the weight of an equal bulk of water is 10 ounces; and the weight of water equal in bulk to the wood is therefore 120 ounces. Moreover as the wood and iron together weigh 138 ounces, and the iron alone weighs 78 ounces, the wood weighs 60 ounces. Hence finally the specific gravity of the wood is 120 that is 60 444. We have made repeated use of the important principle that when a solid is immersed in a liquid the weight is diminished by the weight of an equal bulk of the liquid, but there is one curious application of the principle to which we have not yet drawn attention. The air is a 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: 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; then the specific gravity of the liquid is 18 20' that is 9 10 447. 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 that is 185. 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 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 |