36. How many cubic inches are contained in a cube that may be inscribed in a sphere 40 inches in diameter ?

37. The dimensions of a bushel measure are 18 inches wide, and 8 inches deep; what should be the dimensions of a similar measure that would contain 4 quarts?

38. A gentleman willed of his estate to his wife, and ₫ of the remainder to his oldest son, and of the residue, which was $151.33, to his oldest daughter; how much of his estate is left to be divided among his other heirs?

39. A man bequeathed of his estate to his son, and of the remainder to his daughter, and the residue to his wife; the difference between his son and daughter's portion was $100; what did he give his wife?

40. A young man lost of his capital in speculation; he afterwards gained $ 500; his capital then was $1250; what was the sum lost?

41. From of a yard, there was sold of it; how much remained?

42. Sold a lot of shingles for $ 50, and by so doing I gained 12 per cent.; what was their value?

43. If tallow be sold at 74d. per lb., what is the value of 17cwt. 3qr. 18lb.?

44. If of a yard cost $5.00, what quantity will $ 17.50 purchase?

45. If a man travel 17rd. 10ft. in of an hour, how far will he travel in 8 hours?

46. When $11.75 are paid for 24 acres, what quantity will $100.00 purchase?

47. John Savory and Thomas Hardy traded in company; Savory put in for capital $ 1000; they gained $128.00; Hardy received for his share of the gains $70; what was his capital?

48. E. Fuller lent a certain sum of money to C. Lamson, and, at the end of 3 years, 7 months, and 20 days, he received interest and principal $ 1000; what was the sum lent?

49. Lent $88 for 18 months, and received for interest and principal $97.57; what was the per cent.?

50. When of a gallon cost $87, what cost 74 gallons?

51. When $71 are paid for 18 cost 5 yards?

yards of broadcloth, what

52. How many yards of cloth, at $4.00 per yard, must be given for 18 tons 17cwt. 3qr. of sugar at $9.50 per cwt.?

53. How much grain, at $1.25 per bushel, must be given for 98 bushels of salt, at $0.45 per bushel?

54. How many acres of land, at $37.50 per acre, must be given for 86 tons 18cwt. 3qr. 20lb. of coal, at $8.50 per ton?

55. A person, being asked the time of day, replied, that of the time passed from noon was equal to of the time to midnight. Required the time.

56. How many cubic feet of water in a pond, that contains 200 acres, and is 20 feet deep?

57. On a certain night, in the year 1842, rain fell to the depth of 3 inches in the town of Haverhill; the town contains about 20,000 square acres. Required the number of hogsheads of water fallen, supposing each hogshead to contain 100 gallons, and each gallon 282 cubic inches.

58. If the sun pass over one degree in 4 minutes, and the longitude of Boston is 71° 4' west, what will be the time at Boston, when it is 11h. 16m. A. M. at London?

59. When it is 2h. 36m. A. M. at the Cape of Good Hope, in longitude 18° 24' east, what is the time at Cape Horn, in longitude 67° 21' west?

60. Yesterday my longitude, at noon, was 16° 18′ west; to-day I perceive by my watch, which has kept correct time, that the sun is on the meridian at 11h. 36m.; what is my longitude?

61. Sound, uninterrupted, will pass 1142 feet in 1 second; how long will it be in passing from Boston to London, the distance being about 3000 miles?

62. The time which elapsed between seeing the flash of a gun, and hearing its report, was 10 seconds; what was the dis

tance?

63. If a globe of silver, 2 inches in diameter, be worth $125, what would be the value of a globe 3 inches in diameter?

64. J. Pearson has tea, which he barters with M. Swift, at

10 cents per lb. more than it costs him, against sugar, which costs Swift 15 cents per pound, but which he puts at 20 cents per pound; what was the first cost of the tea?

65. Q and Y barter; Q makes of 10 cents 12 cents; Y makes of 15 cents 19 cents; which makes the most per cent., and how much?

66. A certain individual was born in 1786, September 25, at 27 minutes past 3 o'clock, A. M.; how many minutes old will he be July 4, 1844, at 30 minutes past 5 o'clock, P. M., reckoning 365 days for a year, excepting leap years, which have 366 days each?

67. The longitude of a certain star is 3s. 14° 26′ 14′′, and the longitude of the moon at the same time is 8s. 19° 43′ 28"; how far will the moon have to move in her orbit to be in conjunction with the star?

68. From a small field containing 3A. 1R. 23p. 200ft., there were sold 1A. 2R. 37p. 30yd. 8ft.; what quantity remained?

69. What part of of an acre is § of an acre?

70. A thief was brought before a certain judge, and it was proved that he had stolen property to the value of 1£. 19s. 11d. He was sentenced either to one year's imprisonment in the county jail, or to pay 1£. 19s. 11 d. for the value of every pound he had stolen; required the amount of the fine?

71. My chaise having been injured by a very bad boy, I am obliged to sell it for $68.75, which is 40 per cent. less than its original value; what was the cost?

72. Charles Webster's horse is valued at $ 120, but he will not sell him for less than $134.40; what per cent. does he intend to make?

73. Three merchants, L. Emerson, E. Bailey, and S. Curtiss, engaged in a cotton speculation. Emerson advanced $3600, Bailey $4200, and Curtiss $2200. They invested their whole capital in cotton, for which they received $15000 in bills on a bank in New Orleans. These bills were sold to a Boston broker at 15 per cent. below par; what is each man's net gain?

Ans. Emerson $

Bailey $

Curtiss $

74. Bought a box made of plank, 3 inches thick. Its length on the outside is 4ft. 9in., its breadth 3ft. 7in., and its

height 2ft. 11in.

make the box, and

How many square feet did it require to how many cubic feet will it hold?

Ans. square feet, cubic feet. 75. How many bricks will it require to construct the walls of a house, 64 feet long, and 32 feet wide, and 28 feet high? The walls are to be 1ft. 4in. thick, and there are also three doors 7ft. 4in. high, and 3ft. 8in. wide; also 14 windows 3 feet wide and 6 feet high, and 16 windows 2ft. Sin. wide and 5ft. Sin. high. Each brick is to be 8 inches long, and 4 inches wide, and 2 inches thick.

76. John Brown gave to his three sons, Benjamin, Samuel, and William, $1000, to be divided in the proportion of 3, 4, and , respectively; but William, having received a fortune by his wife, resigns his share to his brothers. It is required to divide the whole sum between Benjamin and Samuel.

Ans. Benjamin $

Samuel $

77. Peter Webster rented a house for one year to Thomas Bailey, for $100; at the end of four months, Bailey rented one half of the house to John Bricket, and at the end of eight months, it was agreed by Bricket and Bailey to rent one third of the house to John Dana. What share of the rent must each pay?

Ans. Bailey $

Bricket $ and Dana $

78. I have a plank 421 feet in length, 12 inches wide, and 3 inches thick; required the side of a cubical box that can be made from it?

79. D. Small purchased a horse for 10 per cent. less than his value, and sold him for 16 per cent. more than his value, by which he gained $21.84; what did he pay for the horse?

80. Minot Thayer sold broadcloth at $4.40 per yard, and by so doing he lost 12 per cent.; whereas he ought to have gained 10 per cent.; for what should the cloth have been sold per yard?

81. A gentleman has five daughters, Emily, Jane, Betsey, Abigail, and Nancy, whose fortunes are as follows. The first two and the last two have $19,000; the first four $19,200; the last four $20,000; the first and the last three $20,500; the first three and the last $21,300. What was the fortune of each?

318

WEIGHTS, MEASURES AND MONEY.

THE tables in this work are intended to afford the learner a knowledge of the various weights, measures and moneys used in different countries, sufficient for the ordinary purposes of business and of practical arithmetic. It is here proposed to supply some items of information, such as are not found in popular works of this kind, nor, it is believed, in any compact or easily accessible form.

WEIGHTS AND MEASURES.

The use of weights and measures can be traced back to a very early period of the world. Josephus, the Hebrew historian, asserts, that they were invented by Cain, the tiller of the ground and the first builder of a city. Whatever authority is to be attached to this statement, we learn from the Book of Genesis that the cubit was employed in designating the dimensions of Noah's ark; and it is reasonable to suppose that several other measures, and a few simple weights, such as were demanded by the common intercourse and employments of mankind, were in use among the antediluvians.

In the time of Abraham, we find mention made of measures of capacity, (measures of meal) and also of money. With the latter, the patriarch bought a field of Ephron, the Hittite, for which he paid him four hundred shekels of silver. This sum was weighed out to Ephron, a circumstance plainly indicating that the value of money was then reckoned by its weight, as has been that of coins in all ages.

But though the use of weights and measures can be referred to an origin thus remote in time, we are not to suppose that they were at first employed with the accuracy and uniformity of modern times. On the contrary, as men's ideas of distance, quantity and value were, in the early stages of society, vague and indefinite, so also were their standards of comparison.

When it was first proposed to establish some measure by which small distances should be estimated, it was natural to have recourse to some parts of the human body, as the arm, the foot, the hand; and hence the origin of the cubit, the length of the arm from the elbow to the end of the longest finger; of the foot, the length of a man's foot; and of the palm or handbreadth, the width of a man's hand. The span was the distance from the end of the thumb to that of the little finger, when extended; and the fathom the space between the extrem-, ities of the outstretched arms.