A sheet folded in two leaves is called folio; if folded in 4 leaves, quarto, or 4to.; if in 8 leaves, octavo, or 8vo.; if in 12 leaves, duodecimo, or 12mo.; if in 18 leaves, 18mo.. &c.

Which are silver?

Which are Ans. By a carat is meant purity of gold indicated? the gold coin in the U.S.? What is the weight of the

QUESTIONS. What is Federal money? What is its unit? Which of the coins of the U. S. are gold? copper? What is meant by a carat? part of any quantity of gold. How is the Give an example. What is the standard of Of the silver coin? Of the copper coin? eagle? Of the dollar? Of the cent? Repeat the table of Federal Money.

What is English money? Was it ever used in this country? Repeat the table. What are the gold coins of Great Britain? The silver coins? What is the value of the English guinea? Of the English pound? What is the fineness of the gold coin of Great Britain? Of the silver coin? Repeat the table of French money.

For what is Troy weight used? What is its unit of weight? What is the standard of weight of the Troy lb. in the U. S.? Of what is it the standard? Repeat the table.

For what is Apothecaries' weight used? How are drugs bought and sold? What is the weight of the Troy lb. and oz.? Repeat the table.

For what is A voirdupois weight used? Repeat the table. How is the A voirdupois pound determined? How many grains in 1 lb. Troy? In 1 lb. Avoirdupois? In 1 oz. A voirdupois? In 1 dr.? What is the weight of the lb. Avoirdupois compared with the lb. Troy? What is the weight of the hundred weight by the laws of the U.S.? In what cases is the ton of 2240 lb., the cwt. of 112 lb., and the qr. of

28 lb. still used? What are used in other cases? chased? What is gross weight? Net weight?

How is fish pur

What is long measure sometimes called? For what is it used? Repeat the table.

Repeat the table.

For what is cloth measure used? For what is square measure used? Repeat the table. What is used in measuring land? What is a square? Draw one on the slate or black-board. What is a rectangle? Draw one. What is a square inch? Draw one. A square foot? What is the rule for finding the number of square inches, feet, &c., in For what is cubic measure used? cube? A cubic inch? A cubic foot?

a square or rectangular surface? Repeat the table. What is a How may the number of cubic

inches, feet, &c., in a solid whose surfaces are all squares or rectangles, be found?

Repeat the table.

How many

peck?

For what is dry measure used? cubic inches in a bushel? In a half For what is liquid measure used? Repeat the table. How many cubic inches in the common gallon? In the Imperial gallon of Great Britain? In a gallon of milk or malt liquors? What is said of the hogshead? Of the barrel?

Repeat the table of time. What is the exact solar year? The civil year? When does leap-year occur? How many days are there in each month?

Repeat the table for circular measure. For what is it used? What is a quadrant? A sign? Repeat the miscellaneous table. The table for books.

64. ADDITION OF COMPOUND NUMBERS.

Simple numbers are those which express things of the same kind. Compound numbers are those which express things of different kinds, or denominations; thus, 5 apples, 4 hats, are simple numbers; 5 cwt. 2 qr., 3 miles 5 furlongs 7 rods, are compound numbers.

Compound Addition is the addition of several numbers of dif

ferent denominations.

What is the sum of £5 14s. 7d. 3qr., £13 16s. 8d. 1qr., and £17 9d. 1qr.?

£

s. d. gr.

5

7 3

16

8

9 1

13

17

1440

Having placed farthings under farthings, &c., we add the column of farthings, and find the sum 5, which is equal to 1d. 1qr. over. We write the 1qr. in its place, and add the 1d. with the next column, which amounts to 25d., or 2s. 1d. Writing the 1d. in its place, we add the 2s. with the column of shillings, the sum of which is 32s., or £1 128. We then add the £1 with the column of pounds, the whole amount of which is 36. Hence we derive the

36 12 1 1

RULE FOR COMPOUND ADDITION. Write the numbers of the same denomination in a column under each other. Beginning with the lowest denomination, add each column separately, and divide the sum of each by as many of that denomination as make one of the next greater. Write the remainder underneath, and carry the quotient to the next higher

column.

EXAMPLES.

1. Add £7 18s. 5d. 3qr.; £6 12s. 3d. 1qr.; £25 15s. 3qr. 2. A merchant sold 2 T. 15 cwt. 3 qr. 16 lb. of hemp to one man, 5 T. 17 cwt. 18 lb. to another, and 10 T. 3 qr. to a third. How much did he sell?

3. Add 3 lb. 10 oz. 5 dwt. 17 gr.; 15 lb. 14 dwt. 5 gr.; 3 lb. 8 oz. 16 gr.; 4 lb. 3 dwt.; and 16 lb. 8 oz. 22 gr.

4. What is the sum of 6 m. 3 fur. 32 rd. 5 yd. 1 ft. 3 in.; 18 m. 7 fur. 27 rd. 2 ft.; 3 fur. 1 ft. 5 in.; and 16 m. 37 rd. 4 ft.?

5. Add 4 yd. 3 qr. 2 na.; 16 yd. 3 qr. 3 na.; 12 yd. 2 na.; and 3 qr. 3 na.

6. Add 616 A. 2 R. 37 sq. rd. 20 sq. yd. 17 sq. in.; 3 sq. m. 15 A. 1 R. 30 sq. rd. 4 sq. ft.; 17 A. 39 sq. rd. 95 sq. in.; and 25 sq. yd. 4 sq. ft. 142 sq. in.

7. Add 41 cords 7 C. ft.; 35 cords 3 C. ft.; 19 cords 6 C. ft.; 27 cords 5 C. ft.

8. Add 34 cu. yd. 18 cu. ft. 1016 cu. in.; 100 cu. yd. 25 cu. ft. 1654 cu. in.; and 5 cu. yd. 21 cu. ft.

9. Add 7 bu. 3 pk. 5 qt.; 8 bu. 7 qt.; 53 bu. 2 pk.; and 16 bu. 7 qt.

10. Add 456 gal. 3 qt. 2 gi.; 1120 gal. 1 pt.; 10 gal. 3 gi.; and 15 gal. 1 qt. 1 pt.

11. Add 4 y. 41 d. 7 h.; 15 y. 68 d. 15 h. 38 sec.; 18 y. 258 d. 23 h. 28 min.; 6 y. 360 d. 9 h.; and 1 yr. 317 d. 19 h. 31 min. 17 sec.

12. Add 346° 15′ 48′′; 58° 3′ 45′′; 35° 58'; and 76° 15′ 45".

After writing the subtrahend under the minuend, placing numbers of the same denomination under each other, begin with the lowest, and subtract 13 gr. from 18 gr., and write the remainder, 5 gr., under the column of grains. As you cannot take 17 dwt. from 15 dwt., add 1 oz., or 20 dwt., to 15 dwt., making 35 dwt., from which subtract 17 dwt.. and write the remainder, 18 dwt. Then, as you added 1 oz. to the minuend, you must also add the same to the subtrahend, as in simple subtraction. As you cannot subtract 7 oz. from 3 oz., add 1 lb., or 12 oz., to the 3 oz., making 15 oz.; 7 oz. from 15 oz. leaves 8 oz. Add 1 lb. to the subtrahend also, and subtract 48 lb. from 56 lb., and write the remainder, 8 lb. Hence the following

RULE FOR COMPound SubtractiON. Write the numbers as in compound addition, placing the less under the greater. Beginning at the lowest denomination, subtract each number in the lower line from the number above it, and write the remainder underneath. When any number in the upper line is less than the number below it, add to it one of the next higher denomination. Then subtract, and add one to the next higher denomination in the lower line.

EXAMPLES.

2. From £15 18s. 6d. 2qr. subtract £8 15s. 7d. 1qr.

3. From 11 T. 15 cwt. 3 qr. 12 lb. 11 oz. 15 dr. subtract 5 T. 3 qr. 15 lb. 14 oz. 6 dr.

4. From 10 m. 3 fur. 6 rd. 5 yd. 2 ft. subtract 5 fur. 10 rd. 5 yd. 9 in.

5. From 1056 gal. 3 qt. 1 pt. subtract 623 gal. 3 qt. 1 pt. 3 gi.

6. Subtract 8 bu. 3 pk. 5 qt. from 15 bu. 3 pk. 3 qt. 1 pt. 7. Subtract 3 fur. 9 rd. 5 yd. 2 ft. from 5 fur. 10 rd. O yd. 1 ft.

NOTE. In this example two rods instead of one must be added to the yards.

8. Subtract 3 A. 2 R. 15 sq. rd. 30 sq. yd. 5 sq. ft. 84 sq.

in. from 5 A. 1 R. 100 sq. in.

9. From 16 d. 17 h. 18 m. 19 sec. subtract 2 d. 23 h. 25 m.

35 sec.

10. Subtract 1840 yr. 6 mo. 15 d. from 1848 yr. 3 mo. 23 d.

11. From 540 ch. 15 bu. 2 pk. 1 qt. O pt. subtract 158 ch. 20 bu. 3 pk. 3 qt. 1 pt.

12. From 4 S. 15° 45′ 15" subtract 8 S. 17° 25′ 38′′.

NOTE. 12 signs may be added to the minuend if it is less than the subtrahend.

66. MULTIPLICATION OF COMPOUND NUMBERS.

6 5

487

1. How much will 7 watches cost, at £6 5s. 8d. apiece? Beginning with the lowest denomination, 7 times 8d. £ S. d. are 56d. 4s. 8d. Write the 8d. and carry the 4s. to be added to the next product. 7 times 5s. are 35s., and : £1 19s. Write the 19s. and carry the £1 to the next product. 7 times £6 are £42, and £1 43 19 8 are £43. Hence the following

4s. are 39s.

RULE FOR COMPOUND MULTIPLICATION. Beginning with the lowest denomination, multiply each denomination in order, and divide and carry as in compound addition.

NOTE. If the multiplier is a composite number, multiply first by one factor, and then by the other. (28.)

EXAMPLES.

2. Multiply 31 bu. 3 pk. 5 qt. by 8. 6 bu. 3 pk. 0 qt. 1 pt. by 5.

3. Multiply 208 gal. 3 qt. 0 pt. 3 gi. by 3; by 9; by 18. 4. Multiply 56 lb. 8 oz. 18 dwt. 17 gr. by 4; by 16; by 24. 5. Multiply 2 yr. 175 d. 6 h. 19 min. 25 sec. by 3; by 15; by 21. Call 365 days: 1 = year.

6. Multiply 45 m. 7 fur. 29 rd. 3 yd. by 8; by 12; by 16.

67. DIVISION OF COMPOUND NUMBERS.

1. Divide 14 bu. 3 pk. 6 qt. of beans equally among 5 men.

qt. pl.

bu. pk. qt. pl. 5) 14 3 6

2

3 7 1

Dividing 14 bu. by 5, the quotient is 2 bu., and 4 bu. remaining. We set down the 2 bu., and to the remainder, 4 bu., or 16 pecks, we add the 3 pecks in the dividend. Dividing the amount, 19 pecks, by 5, the quotient is 3 pecks, and 4 pecks over. Write down the 3 pecks, and to the remainder, 4 pecks, or 32 quarts, we add the 6 quarts in the dividend, making 38 quarts. Dividing this by 5, the quotient is 7 quarts, and 3 quarts remaining. Reducing the remainder to pints, and dividing by 5, we have 11⁄2 pt. for the quotient. From this example we derive the following

RULE FOR COMPOUND DIVISION. Beginning with the highest, divide each denomination separately. When there is a remainder, reduce it to the next lower denomination, to which add the number (if any) of that denomination in the dividend, and divide the sum as before. If the divisor is more than 12, perform the work by long division, and write the quotient to the right of the dividend.