SPECIFIC GRAVITY. THE abfolute 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; fo 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 fame magnitude, and are proportional to their denfity. 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. PROBLEM I. To find the specific gravity of a body heavier than water. RULE. Find the weight of the body in air, and alfo in water, and their difference is the weight loft in water. Then, As the weight loft in water Is to the weight of the body in air, So is the specific gravity of water EXAMPLE EXAMPLE I. A piece of brafs weighed 3 cwt. in air, and only 2 cwt, 2 qrs. 14 lb. in water; required its fspecific gravity. A piece of fteel weighed 394 lb. in air, and 344 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 fpecific gravity of lead. Anf. 11325. PROBLEM II. To find the specific gravity of a body lighter than water. RULE. 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 mafs, 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 Is to the fpecific gravity of water, So is the weight of the light body in air To its specific gravity. EXAMPLE EXAMPLE I. A piece of afh 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 8 lb. in water; required the specific gravity of the afh. Ex. 2. A piece fir weighs 1 cwt. 2 qrs. and a piece steel being affixed which weighed 3 cwt. in air, but in water 2 cwt. qrs. 13 lb.; fuppofing the compound to weigh 1 cwt. I qr. 161 lb. in water, required the specific gravity of fir. Anf. 550. Ex. 3. Suppofe a piece cork weighs 25 lb. in air, and that a piece lead, which weighs 100 lb. in air, and 91.17 lb. in water, is fixed to it; and that the compound mafs, being immerfed in water, weighs 12 lb. required the fpecific gravity of sork. Anf. 24c. PROBLEM III. A mixture of two ingredients being given, to find the quantity of each. RULE. Find the fpecific gravity of the mixture, and of each of the ingredients, and multiply the difference of each by the other. Then fay, As the greatest product Is to each of the lefs products, So is the weight of the compound mass EXAMPLE I. Suppofe a mass of gold and filver weighs 9 lb. and that its fpecific gravity is 15618, (the specific gravity of gold is 19640, and of filver 11091) required the quantity of each ingredient. As 133518282: 446080029: 3 lb. filver nearly. Ex. 2. A mixture, whofe fpecific gravity is. 8784, is made of tin and copper, and weighs 112 lb.; the fpecific gravity of tin is. 7320, and of copper 9000; how much of each ingredient? 100 lb. copper. Anf. { 12 lb. tin. Ex. 3. A goldfmith mixes 18 ounces gold with alloy, and forms a mass of 24 ounces, whose specific gravity is 180co; the specific gravity of gold is 19637; required the fpecific gravity of the alloy. Anf. PROBLEM IV. To find the weight af a body from its magnitude, RULE. As I cubic foot Is to the content of the body, To its weight. EXAMPLE I. Required the weight of a block of marble 6 feet long, 5 broad, and 6 Inches thick. |