the mass of water displaced. Similarly (120) grains is the mass of the alcohol displaced; hence Ex. 3. A piece of copper wire 4 metres long weighs 17·2 grammes in air, and 15.2 grammes in water; find the diameter of the wire. As the heaviness of air is small, the weight of the wire in air may be taken as its true weight. Mass of the water displaced is 17·2 - 15.2 grammes, i.e., 2 gms. 1 gm. of water=sq. cm. by cm. length, Ex. 4. Find what weight of lead attached to 20 lbs. of cork would be just sufficient to sink it in water. 24 lb. cork = lb. water, ... •24 •24 Similarly 24 poundals, weight of cork = poundal, weight of water, 1 poundals app. wt. of cork = poundal, real wt. of cork, 20g poundals, real weight of cork, 114-1 poundals app. wt. of lead = poundal real wt. of lead. 11.4 But the apparent weight of the lead is to be equal to the apparent weight of the cork, only in the opposite direction ; hence Ex. 5. A rectangular barge open at top is made of sheet iron a quarter of an inch thick (480 lbs. per cubic foot); it is 36 feet, long, 12 feet wide and 7 feet deep: what weight placed in the barge will just sink it? For the rectangular sides 1 square foot foot long by foot deep, = 1 cubic foot foot long by foot broad by foot deep, = Ex. 6. What depth of water is required to float an iceberg one mile square by 500 feet high? 92 M of ice M of pure water, = 1 foot3 of ice = 92 foot of pure water; but the cross-section is constant, 1 foot height of ice = 92 foot height of pure water. Similarly 1025 feet of pure water 500 × 92 1.025 = foot of sea water, feet of sea water, 1. A piece of copper weighs 31 grains in air and 271⁄2 in water. Find its specific gravity. 2. A solid, of which the volume is 1.6 cubic centimetres weighs 3'4 grammes in a fluid of specific gravity 0·85. Find the specific gravity and weight of the substance. 3. A glass ball weighs 3,000 grains, and has a specific gravity 3. What will be its apparent weight when immersed in a liquid whose specific gravity is 0.92? 4. A piece of brass, whose specific gravity is 8'4 and weight 20 grammes, is attached to one end of a string which passes over a smooth pulley, and hangs in water. What weight must be attached to the other end of the string that there may be equilibrium? 5. If a piece of wood exactly counterpoises a cubic inch of brass, what is its volume, supposing the specific gravity of the wood to be 0.9, that of the brass 8.1, and that 800 cubic inches of the air in which the weighing takes place, are as heavy as a cubic inch of water at the standard temperature? 6. A body weighs 8 oz. in air, 6·17 oz. in olive oil, and 5.948 oz. in sea water. Compare the specific gravities of olive oil and sea water. 7. A body weighs in air 80 grains, in water 56 grains, and in another liquid 46 grains. Find the specific gravity of this liquid. 8. A piece of oak having a specific gravity of 74 and a volume of 32 cubic inches floats in water. How much water will it displace? 9. If a piece of wood, weighing 120 pounds, floats in water with of its volume immersed, show what is its whole volume. 10. An inch cube of a substance of specific gravity 1.2 is immersed in a vessel containing two fluids which do not mix; the specific gravities of these fluids are 10 and 15. Find what will be the point at which the solid will rest. 11. An inch cube of ice having a specific gravity 918 is floating in water of which the specific gravity is 0.99987. Find its height above the surface of the water. 12. A body floats in water with of its volume above the surface; determine its specific gravity. How much of it will be submerged in a fluid whose specific gravity is 9? 13. Suppose that an iceberg has the form of a cube, and floats flat with a height of 30 feet above the ocean. What depth will it have under the surface? 14. The specific gravity of lead is 114, that of cork 0.24. How much lead must be attached to a piece of cork weighing 3 grammes to make it sink? 15. Find whether a piece of cork weighing 2 grammes with a piece of lead weighing 6.94 grammes attached to it, will sink or swim in water. 16. A body of 300 grammes having a specific gravity 5, has 100 grammes of another substance attached to it, and the joint weight of the two in water is 300 grammes. Find the specific gravity of the attached substance. 17. A certain body A is observed to float in water with exactly half its volume submerged; and, when attached to another B of twice its own volume, it is found to be just submerged. Find the specific gravity of A and of B. 18. Find the specific gravity of a piece of cork from the following data— 19. A cube of metal is floating in mercury sp. gr. 13′6; when a weight of 170 lbs. is placed on the top, the cube is observed to sink 3 inches. Find the size of the cube. 20. A body composed partly of iron and partly of a wood (sp. gr. 0·4) is observed to be just submerged in water. Compare the volumes of iron and of wood in the body. 21. An iron ball of 12 lbs. floats in mercury covered with water. Find the weights of the parts in the two fluids. 22. A rod of uniform section is formed partly of platinum and partly of iron. The platinum portion being 2 inches long, what will be the length of the iron portion, when the whole floats in mercury with one inch above the surface? 23. How much iron must be attached to a wooden beam 10 feet long, and 5 inches broad and thick, in order to sink it? The specific gravity of the wood is '7. 24. A raft, whose weight and specific gravity are known, floats in water. Show how to determine the greatest weight which it can support without sinking. 25. An empty balloon with its car and appendages weighs in air 1,200 lbs. If a cubic foot of air weigh 1 oz., how many cubic feet of gas of specific gravity '52 must be introduced before the balloon will begin to ascend? 26. A small vessel quite filled with distilled water weighs 530 grains; and when 26 grains of sand are thrown in, the whole weighs 546 grains. Find the specific gravity of the sand. 27. A piece of copper and a piece of silver fastened to the two ends of a string passing over a pulley, hang in equilibrium when entirely immersed in a liquid whose specific gravity is 1.15. Determine the relative volumes of the masses, the specific gravities of silver and copper being 10:47 and 8.89. SECTION XXXI.-PRESSURE. ART. 152.-Intensity of Pressure. When force acts across a surface, there are two equal and oppositely directed forces. When their directions are inwards towards one another, each is called a pressure; and when outwards from one another, each is called a tension. Either of these may be specified in terms of unit surface of application; hence the idea F per L2. It is properly called intensity of pressure, but owing to the frequency with which it occurs it is commonly called "pressure." In the British system we have poundals per square foot, lb. by weight per square foot, lb. by weight per square inch, etc. By "lb. by weight" is meant 32-187 poundals (Art. 144). In the C.G.S. system we have dyne per sq. cm., gm. by weight per sq. cm., etc. ART. 153. Height of Column of a Liquid. When a mass of liquid is at a uniform temperature, the density is very nearly uniform throughout, though the lower layers have to support the weight of |