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1.
cord. ft. in.
264 105 1106
146 115 1640
117 117 1194

10. SOLID MEASURE.

2. yd. ft.

in. 79 22 927 27 25 1525

3.
cord. ft. in.
216 12 1716
46 106 302

11. WINE MEASURE. 1.

2. hhd. gal. qts. pts.

T. P. hhd. gal. qts. pts.gs. 68 18 3 1

8 2 0 48 1 0 1 36 46 2 1

4 0 3 24 3 1 0 31 35 1 0

12. DRY MEASURE. 1.

2. qr. bu. pks. qts pts

ch. qr. bu. pk. qt. pt. 6 5 2 7 0

38 3 4 1 0 1 4 6 3 7 1

24 2 6 1 7 0 1 6

7 1

Application of the two preceding Rules. 1. If a man purchase a yoke of 3. A man sold a lot of land for oxen for £15 5. 8d. four cows 735 11s. 6d. and received at for £20 10s. 6d. and a horse for one time £ 195 13s. 11d. and at $26, what did they all cost ? another £61 58.; how much is Ans. $61 16s. 2d. there yet due ?

Ans. 478 12s. 7d. 2. If I buy 4 yards of silk for 1 29. one piece of shirting for 4. A man bought 624 yds. 3 21 Os. 8d. 3 handkerchiefs for | qrs. of cloth, and sold at one 9s. 3d. one yd. of cambrick for time 247 yds. at another 25 yds. 4s. 3 d. and one penknife for 3s. 2 qrs. and at another 114 yds lqr. 9d. what is the amount of the pur- | how much has he left? chase ?

Ans. 238. Ans. £2 19s. 114d. !

QUESTIONS.
1. What is the table of Federal mo 12. Of ale and beer measure ?

ney, and how are the several. 13. Of dry measure?
denominations marked ?

14. What is Compound Addition ? 2. The table of English money? 15. By what are the operations in 3. The table of Troy Weight?

the Compound Rules regulated ? 4. Of Avoirdupois Weight? 16. What is the rule for Compound 5. Of Time ?

Addition ? 6. Of circular motion ?

17. Wbat is the method of proof? 7. Of cloth measure ?

18. What is Compound Subtraction? 8. Of long measure ?

19. What is the rule for Compound 9. Of square measure ?

Subtraction ? 10. Of solid measure ?

20. What is the method of proof? 11. Qf wine measure ?

4. Reduction.

REDUCTION is the method of bringing numbers of one name or denomination into another, retaining the same value.

Reduction is of two kinds, Descending and Ascending.

Reduction Descending is when a higher denomination is to be brought into a lower, as pounds into shillings, pence and farthings, and is performed by Multiplication.

Reduction Ascending is when a lower denomination is to be brought into a higher, as farthings into perce; shillings and pounds, and is performed by Division.

1. REDUCTION DESCENDING.

d. qrs.

Rule. Multiply the highest denomination by the number which it takes of the next less to make one of that, adding the number of the second name; and so continue till you have brought it as low as the question requires.

Examples. 1. In £65 4s. 6d. 2qrs. how many farthings? £. s.

Here 65 pounds is the highest denomination. 6 5 4 6 2 Then because 20 shillings make one pound, I mul20

tiply 65 by 20, adding at the same time, the 4s. to

the product, and the sum is 1304 shillings; then 1304

because 12 pence make one shilling, I multiply the 12

shillings by 12, adding the 6d. and the sum is 15654

pence; lastly, because 4 farthings make oné pen1 5 6 54

ny, I multiply the pence by 4, adding the 2 farth4

ings, and the work is done. In this way I find that

in £65 4s. 6d. 2qrs. there are 62618 farthings. 6 2 618

2. In £1465 14s. 5d. how ma 5. In 250 Eagles how many ny farthings ? Ans. 1497092.qrs. cents ? Ans. 250000 cents.

3. In 221b. 6 oz. 10 pwt. 15 6. In 37 pistoles, at 22s. how grs. how many grains ?

many pénce and farthings ?' Ans. 129855.

Ans. 9768d. 39072 qrs. 4. In 4E. 88 4d. 6cts. 2ın. how 6. In 29 guineas, at 28s. how

many farthings? Ans. 48462 mills.*

Ans. 38976 qrs.

many mills ?

* To reduce eagles to dollars add one cipher; to dımes add 2; to cents add 3; to mills add 4. To reduce dollars to dimes add one cipher; to cents add 2; to mills add 3. To reduce dimes to cents add one cipher ; toʻmills add 2. To reduce cents to mills add one cipher.

2. REDUCTION ASCENDING.

Rule. Divide the lowest denomination by the number which it takes of that to make one of the next higher, and so continue to do till you have brought it into the denomination required.

Examples. 1. In 62618 farthings how many pounds ? 4 ) 6 2 6 18

By comparing the 'examples in Reduction De1 2 ) 1 5 6 5 4 2qrs. scending with those in Reduction Ascending, it

will be seen that they reciprocally prove each 210)1 3 014 6d. other.

£6 5

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4s. Ans. £65 4s. 6d. 2qrs.

2. In 1407092 farthings how 5. In 39072 farthings how mamany pounds ?

ny pistoles ?

Ans. 37. Ans. £1465 14s. 5d. 6. In 129855 grains how many 3. In 20465 mills how many pounds ? eagles, dollars, &c.

Ans. 221b. 6oz. 10pwt. 15grs. Ans. 2E. SO 4d. 6cts. 5 mills:

7. In 25684 cents how many 4. In 8642 mills how many eagles ? dollars?

Ans. 25E. 86 8d. 4cts. Ans. $8 6d. 4cts. 2m. 3. REDUCTION ASCENDING AND DESCENDING.

It is thought to be unnecessary to give examples of al¥ the weights and measures. The following will be sufficient to enable the attentive scholar to make a general application of the rules. His judgment will direct him to the tables by which the several examples are reduced.

1. In £151 10s. how many 4. In 7cwt. 3qr: 10lb. how madollars ?

Ans. 8505.
ny drams?

Ans. 224768dr. 2. In 75 pistoles, at 22 shil 5. In 2549 pints how many lings, how many pounds ?

bushels ? Ans. £82 10s. Ans. 36bu. 2pk. 6qt. 1pt. 3. In 781b. 5oz. 18pwt. how 6. In 4 pieces of cloth, each many pennyweights ?

14 yards, how many nails ? Ans. 18858pwt.

Ans. 896. When it is required to take quantities of several denominations, each an equal number of times from a given quantity. Rule.-Reduce each of the quantities to the lowest denomination mentioned, and add them together for a divisor; reduce the given quantity to the same denomination for a dividend ; and the quotient will be the number sought.

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7. In £33 how many guineas, 10. A man is desirous of drawpounds, dollars and shillings, of ing off a hogshead of wine into each an equal number?

bottles containing gallons, two I guinea=28s.

quarts, quarts and pints of each 1 pound=20s.

an equal number, how many must 1 dollars 6s. 33

he have ? Ans. 33 of each and 9 1 shilling=1s. 20

pints over.

11. How many spoons, each 55 ) 660 ( 12 Ans. weighing 3oz. can be made from 55

51b. of silver? Ans. 20.

12. In 1 ton how many drams? 110

Ans. 573440dr. 110

13 In 425060 seconds how many hours ? Ans. 118h. 4m. 20s.

14. In 63360 feet how many 8. Supposing a man to be 28 miles ? years old, how many seconds has

3 ) 63360 he lived, allowing 365 days, 6h. to a year?

Ans. 883612800. 54 + 11 ) 21 120 yards. 9. Reduce one mile to barley corps.

1920 1 mile.

2
8

410) 384|0 rods.
8 furlongs.
40

8 ) 96 furlongs.

Ans. 12 miles.

320 rods.
5) *

1600
160

1760 yards.

3

15. In £231 16s. how many ducats, at 4s. 9d. each? Ans.976.

16. How many seconds. from the birth of Christ to the year 1824, allowing 3651. 5h. 48m.578. to a year. Ans. 57559853088.

17. How many inches from Montpelier to Burlington, it being 38 miles ? Ans. 2407680.

18. How many seconds are there in 8 signs, 12° 14' 26" ?

Ans. 908066. 19. In 240,000rds. how many acres ?

Ans. 1500 acres.

5280 feet.

12

63360 inches.

3

Ans. 190080 barley corns.

*To multiply by t take half the pultiplicand. The several steps in this ex. ample present at oue view the number of furlonge, rods, yards, feet, inches and barley corns in a mile.

* For 53 divide by 11 and multiply the product by 2 becausé 53=11 halves, and 11 being twice as great as 58, the true divisor, the quotient will be only half as great as it ought to be ; it must therefore be doubled.

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20. In 7248 nails how many 22. In '1008 quarts of cider ells. English ?

many tuos ?

Ans. 1. Ans. 362E E. 2qrs. 23. In 25 pistoles at 22s. how 21. In 90080 inches how ma

many pounds ? ny leagues? Ans. 1.

Ans. £27 10s. Miscellaneous Examples. 1. If a man drink a pint of rum a day, how much will he drink in a year?

Ans. 45gal. 2qt. Ipt. 2 How many barley corns will reach round the world, supposing it to be 25020 miles ?

Ans. 4755801600. 3. Divide 8:20 among 4 men so that the shares shall be to one another as 1, 2, 3, 4.

Aps. 12, 24, 36, 48. 4. How many steps of 2 feet 6 inches, must a man take in going from Burlington to Boston, it being 190 miles ? Ans. 401280.steps.

5. How many lots, each containing three quarters of an acre, are there in one square mile? Ans. 853 lots, and 40 rods over.

6. How many cubic inches in a cord of wood ? Ans. 221 184.

7. In £500 how many eagles, moidores, pistoles, crowns and dollars of each an equal number?

Ans. 76 of each, and 908 pence over. 8. If a vinter be desirous to draw off a pipe of wine into bottles containing piuts, quarts and 2 quarts, of each an equal number, how many must he have ?

Ans. 144 of each. 9. There are three fields, one containing 7 acres, another 10 acres and the other 12 acres and I rood ; how many shares of 76 rods each are contained in the whole ?

Ans. 61 shares, and 44 rods over. 10. In 172 moidores at 363. each, how many eagles, dollars and nine-pences, of each an equal number?

Ans. 92 of each, and 68 nine-pences over, 11. In 470 boxes of sugar,, each 261b. how many cwt.?

Ans. 109cwt. Oqrs. 121b. 12. If cigars cost one and a half cent each, and a person smoke 3 cigars per day, how much will it cost him for cigars during the months of January, February and March in a common year?

Ans. 405 cents, or 84 5cts. 13. In 5529600 cubic inches, how many cords of wood ?

Ans. 25 cords.

QUESTIONS. 1. What is Reduction ?

wish to take quantities of seve2. Of how many kinds is Reduction ? ral denominations, each an eqnal 3. What is Reduction Descending? number of times from a given. 4. What is Reduction Ascending?

quantity ? 5. What is the rule for Reduction 9. How many shillings in a guinea ? · Descending?

in a moidore? in a crown? in a 6. What is the rule for Reduction ducat? in a pistole ? Ascending ?

10. Which of the fundamental rules. 7. How is Reduction proved ?

are employed in Reduction ? 8. How do you proceed when you

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