These tables are given for reference, and not to be committed to memory. It may be well, however, to keep in mind that a meter is 39.37 in.; a square meter is (39.37)2 = 1550 sq. in.; a cubic meter is (39.37)3 = 61,025 cu. in.; a liter is 1.0567 liquid qts.; and .908 dry qts.; and that a gram is 15.432 grs.; as by these equivalents all measures expressed in one system may be converted into measures of the other. In solving the following examples the student will take his equivalents from the table, taking three places of decimals, or four when the first decimal figure is zero, and add one to the last decimal figure when the next is 5 or more. (1) Reduce 25.55kg to avoir- (2) Reduce 5 sq. yds. 6 sq. ft. dupois weight. 108 sq. in. to square 18. Find in acres, etc., the area of a field if its length be 100m and breadth 75m. 19. Determine the number of cubic meters in a box 2 yds. long, 3 ft. wide, 21 ft. deep. 20. Determine the number of cubic yards in a box 2m long, 75cm wide, 50cm deep. 21. If a man walk 75m a minute, what is his rate in miles per hour? 22. If cast-iron weigh 7.1138 per cubic centimeter, how many pounds does a cubic foot weigh? 23. How many steps 2 ft. 6 in. long will a man take in walking a kilometer? 24. Find the value of a carboy (17 qts.) of sulphuric acid, of 1.841 specific gravity, at 24 cents a pound. 25. Find the value of a carboy (171) of nitric acid, of 1.451 specific gravity, at 15 cents a pound. 26. Find the weight in pounds and in kilograms of 311 gals. of the best alcohol, specific gravity .792. 27. If the specific gravity of sea-water be 1.026, and that of olive-oil be .915, what will be the weight of a hektoliter of each in pounds and in kilograms? 28. Find the weight in pounds and in kilograms of the air, specific gravity .00129206, in a room 7m by 5m, and 3.5m high. 29. Find the weight in pounds and in kilograms of the air, specific gravity .00129206, in a room 23 ft. long, 16 ft. wide, and 10 ft. high. 30. If a balloon weigh 218, and contain 10,0001 of hydrogen gas, specific gravity .00008929, what is its lifting force in kilograms and in pounds when the air has a specific gravity of .00129206? NOTE. The lifting force = the weight of 10,0001 of air diminished by the weight of the hydrogen and balloon. 31. If a pile of wood be 1.2m wide, 7m long, and 2m high, how much is it worth, at $4.50 a cord? 32. How many miles will be travelled in 1 hr. 28 min. 21 sec., at the rate of 50km an hour? 33. Find the time of travelling 31 mi. 180 yds. at 1 min. kilometer. 25 sec. per 34. What is the weight of 12 cu. yds. 16 cu. ft. 720 cu. in. of earth of which a cubic meter weighs 1 t. 17 cwt.? 35. Find the weight in grams of a liter of mercury, of which a cubic inch weighs .4925 of a pound avoirdupois. 36. How many yards of cloth, at $3.12 a meter, should be given in exchange for 15m at $2.75 a yard? 37. If a wine merchant buy 3h of wine for 1600 francs, at what rate, United States money, does he pay a gallon, reckoning 25 francs equal to $4.85? 38. A mill-wheel is turned by a stream of water running at the rate of a yard per second in a channel 5 ft. wide and 9 in. deep. Determine the weight of water in metric tons, supplied in 12 hrs., if a cubic foot of water weigh 1000 oz. CHAPTER XV. PROPORTION. 323. The relative magnitude of two numbers is called their ratio, and is expressed by the fraction which the first is of the second. 324. The terms of this fraction are called the terms of the ratio; the numerator is called the antecedent; the denominator is called the consequent. Thus, the ratio of 2 to 3 is expressed by, of which the numerator 2 is the antecedent, and the denominator 3 is the consequent. 325. The ratio is often written, 2:3. 326. If both terms of a ratio be multiplied or divided by the same number, the ratio is not altered. = Thus, if both terms of the ratio 2:3 be multiplied by 4, the resulting ratio is 8:12, and the ratio 8:12 is equal to the ratio 2:3; for, 1. Again, if the ratio 21: 33 be multiplied by 6, the resulting ratio is 15: 20, and the ratio 21:31 is equal to 15:20; for, Since reduced to its lowest terms, the simplest expression for the ratio of 21:31 is 3:4. 2 34 = 20 327. If the numerator and denominator of a fraction be interchanged, the fraction is said to be inverted; likewise, if the antecedent and consequent of a ratio be interchanged, the resulting ratio is called the inverse of the given ratio. Thus, if the fraction & be inverted the resulting fraction is ; and the inverse of the ratio 3:4 is 4:3. |