nature of the question requires the answer to be greater or less than the third term; if greater, write the greater of the two remaining numbers for the second term, and the less for the first; but, if less, write the less for the second and the greater for the first; in either case, divide the product of the second and third terms by the first, and the quotient will be the term sought.

NOTE.-If the first and second terms are in different denominations, they should be reduced to the same before stating the question.

REMARK.-Every one who intelligently solves an example by proportion, does, in effect, solve it by analysis, but the Teacher should use much care on this point, since the scholar learns much faster when he analyzes a question than when he merely follows a rule.

Let the following examples be solved by analysis and by proportion.

Ex. 2. If a man earn $24 in 2 months how much will he earn in 9 months?

2:9:24: 4th term.

9

2)216

$108, Ans.

Since we are seeking for dollars, we make $24 the 3d term, and then, as a man will earn more in 9 months than he will in 2 months, we make 9 the 2d term and 2 the 1st. To analyze the above we say, If a man earn $24 in 2 months, then in 1 month he will earn of $24, i. e. $12; and if he earn $12 in 1 month, then in 9 months he will earn 9 times $12, i. e. $108, Ans.

3. If a staff 3 feet long casts a shadow 4 feet, what is the height of a steeple which, at the same time, casts a shadow 240 feet? Ans. 180 feet.

4. If a staff 3 feet long casts a shadow 4 feet, how long is the shadow of a steeple which is 180 feet high, at the same time?

5. If a steeple 180 feet high casts a shadow 240 feet, what is the height of a staff which, at the same time, casts a shadow 4 feet?

6. If a steeple 180 feet high casts a shadow 240 feet, what is the length of the shadow cast by a staff 3 feet high, at the same time?

7. If a locomotive run 39000 miles in 13 weeks, how far, at that rate, would it run in 52 weeks?

8. If 33 men perform a piece of work in 67 days, in how many days will 11 men perform the same?

Ans. 201.

9. If a man's salary amounts to $2700 in 3 years, what will it amount to in 11 years?

10. If a man's salary amounts to $9900 in 11 years, in how many years will it amount to $2700 ?

11. If I pay 2s. 8d. per week for pasturing 2 cows, what shall I pay for pasturing 11 cows?

12. If I pay 2s. 8d. for pasturing 2 cows, how many cows can be pastured the same time for 14s. 8d.?

13. If 13a. 2r. 6rd. of land is worth 130£. 9s. 6d., what is the value of 94a. 3r. 2rd.?

STATEMENTS BY PROPORTION.

13a. 2r. 6rd.: 94a. 3r. 2rd. :: 130£. 9s. 6d. : 4th term; or, 13.5375a.: 94.7625a. :: 130.475£. : 4th term ; or, 2166rd.: 15162rd.:: 31314d.: 4th term.

14. If 94a. 3r. 2rd. of land cost 913£. 6s. 6d., how much land may be bought for 130£. 9s. 6d. ?

15. If 13a. 2r. 6rd. of land cost 130£. 9s. 6d., how much may be bought for 913£. 6s. 6d. ?

16. If 94a. 3r. 2rd. of land cost 913£. 6s. 6d., what will 13a. 2r. 6rd. cost?

17. If 12 yds. of silk that is 2 yd. wide will make a dress, how many yds. of muslin that is 18 yd. wide will be required to line it? Ans. 6

18. If of a ship cost $1163, what is of her worth?

19. If 6 men perform a piece of work in 40 days, how long. will it take 10 men to do the same?

20. If of a barrel of flour cost $3.60, what will 14 barrels cost?

21. If of an acre of land is worth $36.40, what is the value of 15 acres at the same price?

22. If 6 men can mow 12a. 3r. 16rd. of grass in 2 days, by working 6 hours per day, how many days will it take them if they work only 4 hours per day?

23. If 2bbl. of flour are worth as much as 3 cords of wood, how many barrels of flour will pay for 45 cords of wood?

24. If 4 men can perform a piece of work in 16 days, how many men must be added to the number to perform the same in 4 days?

25. A ship's crew of 15 men is provisioned for 30 days; how many men must be discharged that the provision may last 15 days longer?

26. A bankrupt, owing $25000, has property worth $15000; how much will be received on a debt of $500?

27. A man, owning of a ship, sells of his share for $20000; what is the value of the ship?

28. Borrowed $300 for 9 months; for how long must $450 be lent to repay the favor?

29. If, when flour is worth $12 per barrel, a penny loaf weighs 4oz., what ought it to weigh when flour is worth $8 per barrel?

30. A and B hired a pasture for $45.90, in which A pastured 11 oxen and B 19; what shall each pay?

31. If 13 men perform a piece of work in 45 days, how many men must be added to perform the same in of the time?

32. How many yards of cloth of a yard wide are equal to 63 yards 14 yards wide?

33. If 10 horses eat 35 bushels of oats in 2 weeks, how many bushels will 14 horses eat in the same time?

34. If the interest on $700 is $42 in one year, what will be the interest on the same sum for 3 years?

35. How many yards of paper 2 feet in width will paper a room that is 13 feet long, 12 feet wide and 9 feet high?

36. If I pay $168 for 63 gallons of wine, how much water shall I add that I may sell it at $2 per gallon without loss?

37. A certain house was built by 30 workmen in 97 days, but, being burned, it is required to rebuild it in 30 days; how many men must be employed?

38. A garrison of 1500 men has provisions for 12 months; how long will the same provisions last if the garrison is reenforced by 300 men?

39. If a piece of land 20 rods long and 8 rods wide contain an acre, how long must it be to contain the same when it is but 2 rods wide?

40. If the earth revolves 366 times in 365 days, in what time does it revolve once? Ans. 23h. 56m.

41. A wall which was to be built 24 feet high was raised 8 feet by 6 men in 12 days; how many men must be employed to complete the wall in 12 days more?

42. A wall was completed by 12 men in 12 days; how many men would complete the same in 4 days?

43. Paid $3.50 for 7lb. of tea; what should I pay for 191b.?

44. If a man perform a journey in 6 days when the days are 12 hours long, in how many days of 8 hours each will he perform the same?

45. Lent a friend $500 for 3 months; afterwards he lent me $300. How long may I retain it to balance the favor?

46. If 9 yards of muslin that is 14 yards wide will make a dress, how many yards of lining will be required, that is but of a yard wide?

47. A cistern has a pipe that will fill it in 6 hours; how many pipes of the same size will fill it in 45 minutes?

48. A cistern has 3 pipes; the first will fill it in 3 hours, the second in 4 hours and the third in 5 hours. In what time will they together fill the cistern? Ans. 11 hours.

49. A can cut a field of grain in 8 days; A and B can cut it in 6 days. In what time can B do the same?

50. If 2 horses can draw a load of 16 tons upon a railway, how many horses will be required to draw 72 tons?