On the opposite page, 30 cities and towns are exhibited in their respective situations, relative to each other; and the number of miles, by mail-road from town to town, is noted in figures.

11. Find the distance from Washington, through the intermediate towns, to Augusta, Me....... from Washington to Detroit....... from Washington to St. Louis....... from Washington to Natchez....... from Washington to New Orleans....... from New Orleans to Augusta, Me.

12. Suppose a citizen in each of the places on the opposite page, to start for Washington, and travel 7 miles an hour, 10 hours in each day; how long will each one be in performing his journey?

13. How long would it take you to walk from your school-room to Washington; allowing that you could walk 31⁄2 miles an hour, 7 hours in each day?

14. Two men started at the same time- one of them from New Orleans, and the other from Augusta, Me.— and travelled towards each other, with equal speed. Between what two towns, and what distance from each of these towns did they meet?

15. Mr. A. went from Portland to Baltimore, travelling 5 miles an hour, and 10 hours a day. Mr. B. performed the same journey; but started 1 day later, and travelled 7 miles an hour. Where did B. pass A.?

16. Divide $1000 among A, B, and C, giving B twice as much as A, and C twice a Quch as B.

17. Gunpowder is composed of 5 parts sulphur, 7 parts charcoal, and 38 parts nitre. How many pounds of each ingredient, in 100 pounds of powder?

18. A and B purchased a cow for $16. A paid $9 of the price, and B paid $7. They sold the cow for $21. What was each one's share of the gain?

Solution. Since A paid of the price, and B, A must have of the gain, and B.

19. C and D traded in partnership; C owned $450 of the stock in trade, and D $290. They gained $146 What was each one's share of the gain?

20. Suppose $1000 stock in trade to gain $230; what is the gain on $351 of that stock?

21. E and F purchased 245 acres of land, for $2600 E paid $1200 of the money, and F paid the remainder. How much land should each one have?

22. The national debt of England is not less than $1900 000 000. Allowing 5 per cent. interest to be paid on this sum, how many families would it support, each family spending $400 per annum?

23. If a man can dig a trench in 15 days, and a boy can dig the same trench in 18 days, in what time can they both dig it? (See example 20, Oral sec.)

24. How many days will it take 17 men to perform a piece of work, that 1 man can perform in 95 days? 25. How many days will it take 30 men to perform a piece of work, that 4 men can perform in 50 days? 26. How many days. will it take 25 men to perform a piece of work, that 6 men can perform in 40 days?

27. If 15 yards of carpeting, which is one yard wide, will cover the floor of a room, how many yards of carpeting, 3-quarters wide will cover the same floor?

Direction. Find the number of square quarters contained in 15 yards of the wider carpeting; then divide this number, by the number of square quarters contained in one yard of the narrower carpeting.

28. Suppose 3 yards of broad-cloth 5-quarters wide, to be made into a cloak; how many yards of silk 3-quarters wide, will it take to line the cloak?

29. How many yards of carpeting that is 5-quarters wide, will cover the floor of a room which is 19 feet in length, and 15 feet in width?

30. How many bricks will it take to build a wall, 1 foot thick, 5 feet high, and 24 feet long; each brick being 8 inches long, 4 inches wide, and 2 inches thick?

31. If a man can hoe of an acre of corn in a day, and a boy of an acre, how much can they both hoe in a day? In what time can they both hoe 9 acres?

32. There is a cistern, having 3 pipes; the first pipe will discharge the cistern in 4 hours, the second in 5 hours, the third in 6 hours. What part of the contents of the cistern would all the pipes together let off in 1 hour In what time would they all discharge the cistern?

33. What is the height of a steeple, whose shadow is 148 feet 4 inches, when a shadow 5 feet 4 inches long is projected from a post 6 feet 4 inches high?

34. A trader failed in business, owing $11000, and having only $5000 to divide among his creditors. How much did he pay on a debt of $95.20?

How many

35. A fox has 50 rods the start of a greyhound, but the hound runs 15 rods while the fox runs 9. rods must the hound run, to catch the fox? 36. A cubic foot of air weighs 1 ounce. pounds of air does a room contain, which is 16 feet long, 14 feet wide, and 10 feet high?

How many

37. What number must that be, which, being increased by its half, and its third, becomes 88?

38. A and B hired a pasture for $30. A turned in 3 cows, and B turned in 12 sheep. Allowing 5 sheep to be equal to 1 cow, what must each pay?

39. Suppose London has 1 500 000 inhabitants, New York 350 000, Philadelphia 220 000, New Orleans 115 000, Baltimore 110 000, and Boston 105 000; how many times greater is London, than each of the others?

When a scholar has reached this point, it will be well to consider how much more time he is likely to devote to study. If he have but a few months more to spend in school, the SUPPLEMENT will furnish for him the suitable exercises, with which to finish his course of study in arithmetic. If, however, he is likely to continue at school for several years, he may omit the Supplement, and enter immediately upon the exercises of PART THIRD.

In the preceding chapters, departments of business are not arranged under distinct heads. The arrangement is strictly arithmetical, and business examples are made incidental to the course In the Supplement, departments of business are separately presented, in distinct articles. These articles, although brief, are rendered sufficient, by the learner's previous familiarity with the operations they require.

SUPPLEMENT.

ARTICLE I.

INDICATIVE CHARACTERS OR SIGNS.

Plus,) standing between numbers, indicates that they are to be added together; thus, 3+2 is 5.

-- (Minus,) indicates that the number after it is to be subtracted from the number before it; thus, 5-2 is 3. X (Into,) indicates that one number is to be multiplied into another; thus, 4×3 is 12.

÷ (By,) indicates that the number on the left is to ve divided by the number on the right; thus, 12÷3 is 4.

=

(Equal to,) indicates that the number before it is equal to the number after it; for example, 4+2=6. 6-2-4. 5X3-15. 15÷÷3-5.

CANCELLATION OF FACTORS.

THE CANCELLATION OF FACTORS is the excluding of such factors from an operation as balance each other. Any two equal factors, one being a factor of a dividend, and the other a factor of the divisor, or, one a factor of a numerator, and the other of the denominator, may be cancelled, that is, crossed and omitted. For example, of ofis reduced to a simple fraction, as follows

Here we cancel the two threes, and multiply 1 by 1, and 4 by 2.

13 1

4 2

=

When one of two opposite factors will divide the other without a remainder, both may be cancelled, and the quotient retained in the place of the factor divided. For instance, let us find what is 3 of 3 of 19 of 4 of 20.

2

of of to a simple fraction.

When all of a term is cancelled off, the new term must be I.