20. How many cubic feet in a block of granite, 65 in. long, 42 in. wide, and 36 in. thick? 21. How many cubic feet in a load of wood, 8 ft. long, 41 ft. high, and 31 ft. wide ? 22. How many cords of wood in a pile, 46 ft. long, 16 ft. high, and 15 feet wide ? 23. How many cubic feet in a vat, 12 ft. long, 87 ft. wide, and 7} ft. deep ? 24. How many cubic feet in a bin, 12 ft. long, 9 ft. deep, and 7 ft. wide ? 25. How many cubic yards in a cellar, 18 ft. long, 12 ft. wide, and 9 ft. deep? 26. How many cubic feet in a stick of timber, 2 ft. square, and 40 ft. long? 27. How many cubic feet in a cistern 15 ft. long, 12 ft. wide, and 10 ft. deep ? 287. To reduce Cubic to Dry, or Liquid Measure. First reduce the given yards, feet, &c., to cubic inches; then divide by the number of cubic inches in a gallon, or bushel, as the case may be, and the quotient will be the answer required. (Arts. 260, 263.) 28. In 10752 cubic feet, how many bushels ? Solution. 10752 x 1728 = 18579456 cubic inches; and 18579456--2150-4=8640 bushels. 29. In 21504 cubic feet, how many bushels ? 30. In 462 cubic feet, how many wine gallons ? 31. In 1155 cubic feet and 33 inches, how many wine gallons ? 32. In 846 cubic feet, how many beer gallons ? 33. In 1128 cubic feet and 141 in., how many beer gallons ? 34. How miny bushels will a bin contain, which is 5 ft. long, 5 ft. wide, and 4 ft. deep? 35. How many bushels will a bin contain, which is 8 ft. long, 43 ft. wide, and 3$ ft. deep? QUEST.--287. How reduce cubic to dry, or liquid measure ? 36. How many bushels will a bin contain, which is 14 ft. long, 10 ft. 8 in. wide, and 6 ft. 8 in. deep ? 37. How many wine gallons in a cistern, which is 6 ft. long, 5 ft. wide, and 4 feet deep ? 38. How many barrels of water (wine meas.) will a cistern hold, which is 20 ft. long, 15 ft. wide, and 10 ft. deep? 39. The distributing reservoir of the Croton Water Works in the City of New York, is 436 ft. square and 40 feet high: how many hogsheads of water will it hold? 288. To reduce Dry, or Liquid, to Cubic Measure. First find the number of bushels, if dry measure, or gallons, if liquid measure, in the given example; then multiply by the number of cubic inches in gallon, or bushel, as the case may be, and the product will be the answer required. (Art. 263.) 40. How many cubic feet in a bin, which contains 100 bushels ? Solution. 100 X 2150 to 215040, and 215040 • 1728= 1247885, or 124 cubic feet. Ans. 41. How many cubic feet in a lime kiln, which holds 500 bushels ? 42. How many cubic feet in the hold of a ship, which contains 1000 bushels of grain ? 43. How many cubic feet in 1 hogshead, wine measure ? 44. How many cubic feet in a cistern, which holds 50 barrels of water ? 45. How many cubic feet in a vat, which contains 100 hogsheads wine measure ? 289. To reduce Liquid to Dry Measure, or Dry to Liquid Measure. First find the cubic inches in the given example ; then divide them by the number of cubic inches in a gallon, or bushel, as the case may be, and the quotient will be the answer required. 289. How reduce liquid QUEST.-288. How reduce dry, or liquid measure to cubic ? to dry measure? How, dry to li quid measure ? many bushels ? 46. In 40 gallons wine measure, how Solution.—40 X 231=9240 cu. in., and 9240 cu. in. 21504= 419 bushels. Ans. 47. In 6 hogsheads, 16 gallons, how many bushels ? 48. In 5 bushels, how many gallons wine measure ? 49. In 3200 quarts dry measure, how many hogsheads wine measure ? 290. To reduce Wine to Beer Measure, or Beer to Wine Measure. First find the number of cubic inches in the given example; then divide them by the number of cubic inches which it takes to make a gallon in the required measure. 50. In 94 wine gallons, how many beer gallons ? Solution.-94 X 231=21714 cu. in., and 21714 cu. in. - 282= 77 gallons. Ans. 51. In 1 hhd. wine measure, how many beer gallons ? 52. A tavern-keeper bought 4 hhds. of cider wine measure, and retailed it by beer measure: brw many gallons did he lose? 53. In 20 beer gallons, how many wine gallons ? 54. A grocer bought 7238 gallons of milk beer measure, and retailed it by wine measure: how many gallons did he gain ? 55. A druggist bought 10000 gallons of alcohol beer measure, and sold it by wine measure: how many gallons did he gain ? 56. A grocer bought 65 hhds. 29 gals. and 2 quarts of milk by beer measure, and sold it to his customers by wine measure: how many quarts more did he sell than he bought ? 57. A liquor dealer bought 120 pipes of wine which his clerk retailed by beer measure : how many gallons more did he buy than he sold ? 291. Since the earth revolves on its axis 1° in 4 minutes, or l' in 4 seconds of time, (Art. 268,) it is evident that longitude may be reduced to time. That is, multiplying degrees of longitude by 4 reduces them to minutes of time, multiplying minutes of longitude by 4 reduces them to seconds of time, &e. QUEST ---290. How reduce wine to beer measure? How beer to wine measure ? By reversing this process it is evident that time may be reduced to longitude. Thus, dividing seconds of time by 4, will reduce them to minutes of longitude; dividing minutes of time by 4, will reduce them to degrees, &c. Hence, 292. To find the difference of time between two places from the difference of their longitude. Reduce the difference of longitude to minutes ; multiply them by 4, and the product will be the difference of time in seconds, which may be reduced to hours and minutes. OBs. When the difference of longitude consists of degrees only, we may multiply them by 4, and the product will be the answer in minutes. 58. The difference of longitude between New York and Cincinnati is 10° 26': what is the difference in their time? Solution.—10° and 26'=626'; (Art. 281 ;) now 626'X4= 2504 seconds of time; and 2504 sec. = 60=41 min. 44 sec. Ans. 59. The difference of longitude between Albany and Boston is 2° 9': what is the difference in their time? 60. The difference of longitude between Albany and Detroit is GO 45': what is the difference in their time? 61. The difference of longitude between New Haven and New Orleans is 17° 10': what is the difference in their time? 62. The difference of longitude between Charleston, S. C. and Mobile is 8° 27' : what is the difference in their time? 63. The difference of longitude between New York and Canton is 187° 3': what is the difference in their time? 293. To find the difference of longitude between two places from the difference in their time. Reduce the given difference of time to seconds ; divide them by 4, and the quotient will be the difference of longitude in minutes, which may be reduced to degrees. (Art. 281.) Obs. When there are no seconds in the difference of time, we may divide the minutes by 4, and the quotient will be the answer in degrees. QUEST.-292. How find the difference of time between two places from their differonce of longitude ? 293. How find the difference of longitude from the difference of time ? 64. A ship sailed from Boston to Liverpool; on the fourth day the master took an observation of the sun at noon, and found by his chronometer that it was 1 hr. 5 min. and 40 sec. earlier than the Boston time: how many degrees east of Boston was the ship? Solution.—1 hr. 5 m. 40 sec.=3940 sec., (Art. 281,) and 3940 sec. ;4=985'. The ship had therefore sailed 985' east, which is equal to 16° 25'. Ans. 65. The difference of time between Albany and Buffalo is 19 minutes : what is the difference of their longitude ? 66. The difference of time between Richmond and New Orleans is 51 min. 4 sec.: what is the difference of their longitude ? 67. The difference of time between Boston and Cincinnati is 53 min. 32 sec. : what is the difference of their longitude ? COMPOUND NUMBERS REDUCED TO FRACTIONS. 294. That one concrete number may properly be said to be a part of another, the two numbers must necessarily express objects of the same kind, or objects which can be reduced to the same kind or denomination. Thus, 1 penny is to of a pound, but 1 penny cannot properly be said to be a part of a foot, or of a year ; for, feet and years cannot be reduced to pence. So, 1 orange is § of 5 oranges; but 1 orange cannot be said to be } of 5 apples, or 5 pumpkins; for apples and pumpkins cannot be reduced to oranges. Ex. 1. Reduce 2s. 7d. to the fraction of a pound. Analysis.-The object in this example is to find what part of 1 pound, 2s. 7d. is equal to. To ascertain this, we must reduce both the given numbers to the same denomination, viz: pence. Now 2s. 7d.=31d., and £1=240d. (Art. 281. I.) The question, therefore, resolves itself into this: what part of 240 is 31 ? The answer is nato; consequently 2s. 7d. (31d.) is nad of a pound. Hence, QUEST.-294. When can one concrete number be said to be a part of another ? |