142. How to Ascertain the Specific Gravity of Solids.—It results from the upward pressure of water that a body weighs less in water than in air. Take a piece of gold or any other substance, a, Fig. 90 (p. 107), and weigh it suspended as you see from one of the scales. Introduce the gold now into a cup of water, and you will find that a part of the weight must be taken from the opposite scale to preserve the balance. The weight which you take from the scale will be the weight of a quantity of water equal in bulk to the piece of gold; for the immersed body is supported with a force equal to the weight of the water it displaces (§ 137). By comparing, therefore, its weight in water with its weight in air we determine its specific gravity. Thus if a lump of gold weigh nineteen ounces, and on being weighed in water weighs eighteen, it will prove that gold is nineteen times as heavy as water. And if a lump of copper weigh nine ounces in air and eight in water, it is nine times as heavy as water. Calling water, therefore, 1, the specific gravity of gold is 19, and of copper 9. It is obvious that a body of the same specific gravity with water would weigh nothing when immersed in water, for it would be supported with an upward pressure precisely equal to its own weight, just as the same bulk of water is. A pound of water, therefore, will weigh nothing in water. The experiment can easily be tried. Weigh a glass bottle, suspended on one arm of the scale-beam, and then put a pound of water in it. On immersing it in water it will be balanced if you take out the pound weight in the opposite scale.
143. Archimedes and the Crown.—Hiero, King of Syracuse, stipulated for a crown of pure gold. But suspecting the maker of it of adulterating the gold, he called upon Archimedes to detect the imposture. He did it in this way: He procured two lumps of gold and silver of the same weight with the crown, and observed the quantity of water which each displaced. He then tried the crown, and found that it displaced less than the silver and more than the gold, and therefore concluded that it was an alloy of the two metals. All this was suggested to him by his experience in the bath, referred to in § 138.
Fig. 91
144. How to Ascertain the Specific Gravity of Liquids.—There are several modes of ascertaining the specific gravities of different liquids. The instrument called a Hydrometer furnishes the most common mode. This is used chiefly in determining the quality of spirit. The more alcohol and the less water spirit contains the less is its specific gravity. The Hydrometer consists of two bulbs of glass, A B, Fig. 91, with a slender stem, C, which is graduated. In the lower bulb are a few shot or a little mercury, to give the instrument its proper weight, and to make its centre of gravity to be in the lower part. The lighter the fluid to be tested is the lower will the instrument sink in it. This is a very accurate instrument, detecting the slightest adulteration in spirits. Dr. Arnot tells an amusing story of the detection of a Chinese trader in liquors. He had sold a quantity of liquor to the purser of a ship, averring it to be of the same quality with a sample which he had given him. The purser tried it with his Hydrometer, and found it to be of greater specific gravity than the sample. The Chinese promptly denied the fraud; but on being told the exact quantity of water which he had added, he was so much confounded that he immediately confessed his guilt, and made ample amends. When the Hydrometer was shown to him he offered a large price for what appeared to him to be a magical instrument, foreseeing that it would be of great advantage to him in his business.
In Switzerland and in the north of Italy, where the peasants bring their milk to a common dairy, and are allowed a quantity of cheese at the end of the season in proportion to the amount of milk which they have brought, a Hydrometer is used to test the quality of the milk. There is a propriety in this, not only as a safe-guard against adulteration, but because there is a difference of quality in the milk of different cows, some giving a much more watery milk than others.
145. Centre of Gravity in Floating Bodies.—The same principles which apply to the centre of gravity in bodies standing on a firm basis apply also to floating bodies. That the centre of gravity may be low in a loaded vessel the heavy part of the cargo is put underneath, and generally ballast of stone or iron is necessary for the same purpose. In large flat-boats, the base of support being extensive, there is not the same need of taking care that the centre of gravity be low. If a ship be laden in part with an article which will dissolve in water, there is much danger, if the ship should leak, that this portion of the cargo shall be dissolved and be pumped out with the bilge-water, thus altering the trim of the vessel, or removing the centre of gravity from over the middle line, and bringing it too far forward, or carrying it too far back, making the ship wholly unmanageable. Four large English ships, in part loaded with saltpetre, were supposed to be lost from this cause in 1809 off the Isle of France. The immense ice-islands, or icebergs, which float about in summer in the polar regions, by melting irregularly often change the place of their centre of gravity, and in turning over present one of the most sublime spectacles in nature. A mountain of ice, extending high in the air and deep in the sea, suddenly turns over, and produces a rolling of the ocean which is often felt at the distance of many leagues.