is applied to Domestic Bills of Exchange? State the value of the old currencies of different sections of the Union.

When are numbers said to be PRIME TO EACH OTHER? How may we tell by inspection, whether a number is divisible by 2, 3, 4, 5, 6, 9, 10, 11, or 25? How may we determine whether a given number is a prime number? How is a number resolved into its prime factors? How do we discover all the divisors of a number? What is the rule for determining the number of divisors? How may the resólution into prime factors be applied in the reduction of fractions to their lowest terms?

What is the cause of NUMERICAL APPROXIMATIONS? Propose and explain examples in Addition and Subtraction of Circulating Decimals. In contracted multiplication and division ;-in division of circulating decimals. What is a continued fraction? Explain the mode of finding approximate values for a continued fraction? How may any square root be resolved into a continued fraction? How may the extraction of roots of the higher powers be contracted?

What is the JULIAN YEAR? Explain the distinction between the Old and New Style? What is the Dominical Letter? How is it found for any Julian Year?—for any Gregorian Year? How may we find the day of the week, corresponding to any given day of the month in any year proposed?

How may we find the AREA OF A TRIANGLE?—of a rectangle?—of a trapezoid?-of any plain surface bounded by straight lines?-of a circle?-of an ellipse?—the surface of a sphere?-of a cylinder? What is the rule for finding the solid contents of a cylinder?—of the frustrum of a cone? -of a sphere? How do we find the dimensions of a cask? -the carpenters' tonnage of a vessel ?

How do we find the SPECIFIC GRAVITY of a body ?—the distance at which objects may be seen, at sea or on level ground?-the distance of a gun or thunder cloud?—the pressure of water against a bank?

Troy

Repeat the Table of AVOIRDUPOIS WEIGHT; Weight;-Apothecaries' Measure ;-Dry Measure;-Liquid Measure;-Long Measure;-Time Measure ;-Square Measure;-Cubic Measure ;-Cloth Measure ;-Chain Measure.

MISCELLANEOUS EXAMPLES.

1. If the multiplicand is 7, and the product 2, what is the multiplier ?

2. The dividend is 1, and the quotient 8; what is the divisor?

3. The dividend is 64, and the quotient 183; what is the divisor?

4. The sum of two numbers is 7, and one of the numbers is 4.759; what is the other?

5. The difference of two numbers is 13%, and the greater number is 29.43; what is the less?

6. The sum of two numbers is 759, and their difference is 63; what are the numbers?

31

7. What number must be subtracted from 39% to leave 17,2?

25

8. What number must be added to 235 to make 47.432 ? 9. What number must be multiplied by 37, and the product divided by 7.365 to give 83 as a quotient?

10. What is the difference between and 46 of 7 T. 15 cwt. 3 qr.?

11. What is the difference between 28 miles, and 27 m. 7 fur. 39 r. 5 yd. 2 ft. 11.9 in. ?

12. Reduce of 9 m. 7 fur. 39 r. 5 yd. 2 ft., to inches. 13. If from a purse containing £35 7s. 11d., I pay to each of 15 laborers, £1 9s. 83d., how much will be left?

14. Find the sum, the difference, and the product of 874.91, and 42.

15. If 29 men can build 471⁄2 rods of wall in 94 days, how much can 15 men build in 24 days?

16. A grocer sold 17 cwt. 3 qr. 17 lb. of sugar, at 64 cents a pound, receiving in exchange 29 barrels of flour at $43 per barrel, and the balance in money. How much money did he receive?

17. From of 3 T. 17 cwt., subtract of 7 T. 3 cwt. 1 qr. 18 lb.

18. What will be the freight of 173 cwt. for 895 miles, if $7.63 be paid for carrying 11 tons, 9 miles?

13

19. How many raisins at 8 cents a pound, must be given in exchange for 163 gal. 2 qt. 3 gi. of wine, at $1.12 per gallon.?

20. Bought 16 cwt. 3 qr. 16 lb. of rice, at $4.00 per cwt. and 9 cwt. 2 qr. 5 lb. of pearl barley, at $4.37 per cwt. How much would be gained on the whole, by selling each at 4 cents a pound?

21. If 63 yd. of broadcloth cost $255, at what price. must it be sold per yd. in order to gain $25.50?

22. A hogshead of sugar at $7.00 per cwt. cost $43.75. What did it weigh?

23. How much shalloon that is yd. wide will line 14ğ yards of cloth that is 14 yd. wide?

24. What is the price of 16 boxes of raisins, each holding 93 lb. at 94 cents per lb. ?

25. How much money that is 9 per cent. below par, will pay a debt of $187.50?

26. If 9 men mow 10 acres of grass in a day, how much will 11 men mow in 2 days.

27. In what time will $150 gain $6.37 at 6 per cent. simple interest?

28. When molasses is 314 cents a gallon, how many hogsheads, each holding 97 gal. 3 qt. can I buy for $366.504 ?

29. What will be the price of 7 bales of sheeting, each bale containing 9 pieces, and each piece measuring 30 yd., if 26 yd. cost. $2.92 ?

30. Bought 39 bushels of potatoes for $12.87. At what price per bushel must they be sold, in order to gain 15 per cent.?

31. What is the interest of $9431 for 3 yr. 7 mo. 13 dy. at 7 per cent.?

32. How much may a man spend per day, whose income is $500 a year, after deducting per cent. for taxes?

33. If 16 gallons of cider can be bought for $2.75, how much may be bought for $634 ?

34. How many pieces of merino that is worth $ per yd. can be bought for $71.25, there being 28 yards in a piece?

35. Bought 7 hogsheads of sugar at $6.75 per cwt. To what did it amount, the gross weight being 6 cwt. 3 qr. 19 lb., tare 25 lb., per hogshead?

36. What will be the price of 13 bags of cotton, each weighing 5 cwt. 1 qr. 11 lb., at 11 cents per lb. ?

37. If of of 5 yd. of cloth cost $105, what will 17.63 yards cost?

38. At £1 11s. per yd. what will be the price of 3 qr. 3 na. of cloth?

39. A. lent B. $685 for 3 to receive in return, to use 7

months; what sum ought A. months?

40. How much coffee at 84 cents a pound, should be given in exchange for of 2 cwt, 2 qr. 16 lb. of tea, at 75 cents a pound?

11

41. If $63.87 will purchase 33 cwt. of butter, how much must I give for 7 cwt. 1 qr. 131⁄2 lb.?

42. A bankrupt can pay but 633 per cent. of his debts. How much will be received by a creditor for $765.62 ?

43. If of 5 of a ship be sold for $2150, what is the value of of of the remainder ?

44. What is the value of 87 barrels of oil, each containing 857 gal., at 94 cents per pint?

45. If a laborer receives $1.50 for every working day, how much can he spend each year, and save $125 ?

46. When taxes on all real and personal property are rated at 3 mills on every dollar, what must be paid by a man who is worth $7650, and who pays for 3 polls at $1.50 each?

47. How much hay will 63 horses eat in 21 weeks, if 193 cwt. will keep 4 horses 6 weeks?

48. A garrison of 500 men has provisions for 6 weeks, but finding that they will be obliged to remain 15 weeks

without an additional supply, how many men must be sent away, that the provisions may not be exhausted?

49. What part of 17A. 3R. 29r. are 11A. 2R.?

50. Reduce 168, 14.7, 13, 54, and 2, to a common de

nominator.

51. If a staff 3 ft. 3 in. high cast a shadow of 2 ft. 7 in., how long a shadow will be cast by a steeple that is 59g yds. high?

52. Bought 38 pieces of Denims, each piece containing 29 yd., for $162.50. At what price must I sell 16 yd. in order to gain 17 per cent. on the prime cost?

53. How much cotton, at 16 cents a pound, can be bought for $512}?

54. A grocer bought 7 cwt. 3 qr. 13 lb. of coffee for $70.48. What per cent. did he gain by selling the whole at 8 cents a pound?

55. Sold 39 cwt. 2 qr. 17 lb. of coffee, for $7.50 per cwt., thereby losing $37.50. What did it cost per pound? 56. What is the value of an estate, if of of it is worth $2897 ?

57. A man can perform a journey of 263 miles in 9 days, by travelling 7 hours a day. In what time can he perform a journey of 571 miles, by travelling 6 hours a day?

58. At what price per yd. must I sell 765 yd. of calico, in order to gain $15.30, the prime cost being $101.25 ?

59. In what time will $487.50 at 5 per cent., gain the same interest as $943.25, in 7 months at 6 per cent. ?

60. If 15 men in 21 days mow 301 acres of grass, how much will 84 men mow in 7 days?

61. How much indigo at $1.75 per pound, can be bought for £15 9s., when exchange is 9 per cent. above par?

62. In what time will $638 gain $95, at 4 per cent. per annum ?

63. The estate of a bankrupt is but $7350, and his debts amount to $28495. How much can he pay on a debt of $1763.25?

64. Two pieces of cloth, each containing 31 yd., cost