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THE absolute gravity of a body is the force with which it tends downwards, and is always proportional to the density of the body, without any regard to its magnitude ; so that a pound of cork is as heavy as a pound of gold. But the specific gravity of bodies are their relative weights under the same magnitude, and are proportional to their density. Thus a cubic foot of lead is heavier than a cubic foot of fir ; for lead, being more dense than fir, contains a greater quantity of matter.
A cubic foot of water weighs 1000 ounces averdupois.--The specific gravities of bodies, their magnitudes, and their weights, may be found, each from the others, by the following problems.
To find the specific gravity of a body heavier than water.
Find the weight of the body in air, and also in water, and their difference is the weight lost in water. Then,
As the weight lost in water
A piece of brass weighed 3 cwt. in air, and only 2 cwt, 2. qrs. 14 lb. in water ; required its specific gravity.
A piece of steel weighed 39: lb. in air, and 341 lb when weighed in water ; what is the specific gravity of steel ?
Anf. 7850. Ex. 3. A bar of lead weighed 15 cwt. in air, but only 13 cwt 2 qrs. 19 lb. 10 oz. in water; required the specific gravity of lead.
To find the specific gravity of a body lighter than water.
Affix to it a piece of lead, iron, or any other body heavier than water, so that they may fink together; then weigh the heavier body, and the compound mass, each in water and out of water ; fubtract the difference of the one from the difference of the other; then say,
As the last remainder
A piece of ash weighs 20 lb. in air, to which is affixed a piece of copper, which weighs 15 lb. in air, and 13 lb. in water; this compound weighs 81 lb. in water ; required the specific gravity of the ash.
Ex. 2. A piece fir weighs i cwt. 2 qrs. and a piece steel being assixed which weighed 3 cwt. in air, but in water 2 cwt. 2 qrs. 1375 lb. ; supposing the compound to weigh i ewt. I qr. 16.4 lb. in water, required the specific gravity of fir.
Ex. 3. Suppose a piece cork weighs 25 lb. in air, and that piece lead, which weighs 100 lb. in air, and 91.17 lb. in water, is fixed to it; and that the compound mass, being immersed in water, weighs 12 lb. required the specific gravity of Gork.
A mixture of two ingredients being given, to find the quantity of
Find the specific gravity of the mixture, and of each of the ingredients, and multiply the difference of each by the other Then say,
As the greatest product
Suppose a mass of gold and silver weighs 9 lb. and that its specific gravity is 15018, (the specific gravity of gold is 19640, and of filver 11091) required the quantity of each ingredient.
As 133518282 : 44608002 ::9 : 3 lb. filver nearly.
133518282 : 83910280 :: 9 : 6 lb.gole.