Every body immersed in a liquid is submitted to the action of two forces: gravity which tends to lower it, and the buoyancy of the liquid which tends to raise it with a force equal to the weight of the liquid displaced. The weight of the body is either totally or partially overcome by its buoyancy, by which it is concluded that a body immersed in a liquid loses a part of its weight equal to the weight of the displaced liquid.
This principle, which isthe basis of the theory of immersed and floating bodies, is called the principle of Archimedes, after the discoverer. It may be shown experimentally by means ofthe hydrostatic balance(Fig. 92). This is an ordinary balance, each pan of which is provided with a hook; the beam being raised, a hollow brass cylinder is suspended from one of the pans, and below this a solid cylinder whose volume is exactly equal to the capacity of the first cylinder; lastly, an equipoise is placed in the other pan. If now the hollow cylinder be filled with water, the equilibrium is disturbed; but if at the same time the beam is lowered so that the solid cylinder becomes immersed in a vessel of water placed beneath it, the equilibrium will be restored. By being immersed in water the solid cylinder loses a portion of its weight equal to that of the water in the hollow cylinder. Now, as the capacity of the hollow cylinder is exactly equal to the volume of the solid cylinder the principle which has been before laid down is proved.
Fig. 92.
Fig. 92.
Minerals, if suspected of containing spaces, should be coarsely pulverized, and then the second method may be conveniently applied to determine their density—thus prepared, a higher result will be obtained, and even metals when pulverized were found to give a greater specific gravity than when this is determined from samples in their ordinary state. Very fine powders may also be examined by the method in use for ascertaining the specific gravity of fluids, viz.: by comparing the weight of a measured quantity with that of the same quantity of water.
A glass vessel called a specific gravity bottle is commonly employed, which is furnished with a slender neck, upon which is a mark indicating the height reached by 1,000 grains of water. The substance to be examined is introduced till it reaches the same mark, and, the weight of the bottle being known, only one weighing is required to obtain the result.
The specific gravity of fluids is also taken by the instrument called a hydrometer or alcometer. Such instruments are much used for ascertaining the specific gravity of spirituous and other liquors, as an indication of their strength.If the solid body to be tested is lighter than water, it must be attached to some heavy substance to cause it to sink.Its specific gravity is then calculated by dividing its weight in the air by the sum of the weights of the attached body both in air and in water, first subtracting from this sum the weight of the two bodies together in the water.
Bodies soluble in water may be weighed in some other fluid, as alcohol, ether, olive oil, &c., and their proportional weight to that of this fluid being thus ascertained, their density compared with that of water is readily calculated or they may be enveloped in wax or other suitable substance to protect them, and then treated by the method just given for substances lighter than water. Gaseous bodies are weighed in a thin glass flask or other vessel made for the purpose, and provided with a stop-cock. The vessel is exhausted of air before the introduction of the gas.
Rule for finding the Specific Gravity of a Solid Body.
Weigh the solid in air and then in pure water.
The difference is the weight of water displaced, whose specific gravity is 1.000.
Then, as the difference of weight is to 1·000, so is the weight in air to the specific gravity; or divide the weight of the body in air by the difference between the weights in air and in water.
Example.
A lump of glass is found to weigh in air 577 grains; it is then suspended by a horse hair from the bottom of the scale pan, and immersed in a vessel of pure water, when it is found to weigh 399.4 grains. What is its specific gravity?
577.0Then, as 177.6 : 1 :: 577.0 : sp. gravity.399.41————177·6 the difference177·6)577·0(3·248, Ans.532·8——–44203552——–86807104——–1576014208——–1552
Fig. 93.
Fig. 93.
Note.—The above figures are introduced to show more vividly the comparison betweenbulk and weight, the size of the different substances, of course, being merely approximate. A study of the Table of Specific Gravities to be found in the next page is worthy of the time and attention.
Note.—The above figures are introduced to show more vividly the comparison betweenbulk and weight, the size of the different substances, of course, being merely approximate. A study of the Table of Specific Gravities to be found in the next page is worthy of the time and attention.