This measure is employed in measuring surfaces, or that which has length and breadth, as flooring, plastering, paving, land, &c.

This measure is employed for measuring solid bodies, that is, bodies having length, breadth, and thickness; as boxes, bins, timber, stone, &c. The cord of wood contains 128 solid feet. Hence, a pile of wood 8 feet long, 4 feet high, and 4 feet thick, contains just a cord, since 8X4X4=128.

This measure is employed to measure wine, alcohol, oil, and all other liquors, except beer, ale, and milk. The gallon measure contains 231 cubic inches. A gallon of pure water, at the temperature of 41 degrees, which is nearly its greatest density, weighs 81000 pounds avoirdupois. The British Imperial gallon contains 277.274

cubic inches.

This measure is the appropriate one for measuring beer, milk, and ale, but has, for the most part, fallen into disuse, and wine measure taken its place. The beer gallon contains 282 cubic inches.

This measure is employed for measuring all kinds of grain, fruit, salt, &c. The standard of measure is the Winchester bushel, which contains 2150.4 cubic inches.

The 6 hours over 365 days in each year, amount to 24 hours, or 1 day, in 4 years. Hence, every fourth year contains 366 days. This additional day is joined to the month of February. The following lines will aid the scholar in remembering the number of days in each month.

"Thirty days hath September,
April, June, and November;
February twenty-eight alone;
All the rest have thirty-one,
Except in leap-year, then's the time
When February has twenty-nine."

This measure marks the divisions of the circle. It is employed in measuring latitude and longitude, also in measuring the motion of the heavenly bodies.

leaves, it is called

N. B.-When a sheet of paper is folded so as to produce 18

18mo.

Duodecimo, or 12mo.

Octavo, or 8vo.

Quarto, or 4to.

Folio.

§ 153. The denominations composing each of the preceding Tables agree in kind, but differ in value; the higher denominations being, in each case, produced by the repetitions of the lower denominations. The number of units required of a lower denomination to make 1 of the next higher denomination is, however, constantly varying. Hence, in operating with Compound Numbers, we have no uniform number by which we divide in reducing the lower to the higher denominations, or by which we multiply in bringing high denominations to those of lower value, but must in each case be guided entirely by the numerical relation the denomination operated upon, sustains to the other kindred denominations.

COMPOUND ADDITION.

RULE.

§ 154.-1. Write down the several numbers, placing the same denominations under each other.

2. Beginning with the lowest denomination, add each column separately; and dividing the amount of each by the number required of the denomination added to make one of the next higher denomination, write the remainder at the foot of the column, and add the quotient to the next column.

3. Continue this process through all the denominations, and write down the whole amount of the last or left-hand column.

1. What is the amount of £33 8s. 9d. 2qr.; £16 12s. 3d. 1qr; £23 13s. 11d. 3qr.; and £37 10s. 7d. 2qr.?

It will be observed that pounds are written under pounds, shillings under shillings, pence under pence, and farthings under farthings.

H

We first add the farthings, and obtain 8 as the amount= 2d. and no remainder. We therefore write a cipher under farthings, and add the 2 pence into the column of pence, and find the amount to be 32d. 2s. 8d. We therefore write the 8d. at the foot of the column, and add the 2s. into the column of shillings, and find the amount to be 45s.=£2 5s.; and writing down the 5s. we add the £2 into the column of pounds, and find the amount of that column to be £111, and there being no denomination higher than pounds, we write down the whole amount, viz., £111. The answer to the sum is therefore, £111 5s. 8d. Oqr. (Table I.)

154. In compound addition how are the numbers to be written? With what denomination do we begin to add? How add? By what do you divide the amount of each column? Where do you write the remainder? To what add the quotient? What is written down at the left-hand column ?

We prove an operation in Compound Addition in the same manner as in Simple Addition. (§ 32.)

2. What is the amount of £13 17s. 11d. 1qr.; £22 14s. 9d. 1gr.; £37 18s. 6d. 3qr.; and £46 13s. 7d. 2qr.? Ans. £121 4s. 10d. 3qr. 3. What is the amount of £75 19s. 11d. 3qr.; £63 17s. 5d. 1qr.; £41 12s. 3d. 3gr.; and £11 15s. 8d. 3qr.? Ans. £193 5s. 5d. 2qr. 4. What is the amount of £105 1s. 2d. 3qr.; £218 11s. 5d. 2qr.; £199 17s. 9d. 2qr.; and £77 18s. 3d. 3qr.? Ans. £601 8s. 9d. 2qr. 5. What is the amount of £1 11s. 9d. 1qr. ; £7 7s. 7d. 3qr.; £17 13s. 9d. 3qr.; and £21 14s. 6d. 1gr.? Ans. £48 7s. 9d. Oqr.

6. A silversmith bought of A, 3 lb. 9 oz. 14 pwt. 16 gr. of silver; of B, 9 lb. 11 oz. 17 pwt. 18 gr.; of C, 1 lb. 8 oz. 19 pwt. 21 gr.; and of D, 3 lb. 7 oz. 12 pwt. 16 gr. How much silver did he buy? (Table II.)

Ans. 19 lb. 2 oz. 4 pwt. 23 gr. 7. What is the amount of 16 83 33 19 8 gr.; 883 13 29 5 gr.; 9 10 3 33 73 19 1 gr.? (Table III.)

43 29 ; and 21

Ans. 56 73 13 09 14 gr. 8. What is the amount of 15 cwt. 3 qr. 24 lb. 8 oz. 13 dr.; 21 cwt. 1 qr. 16 lb. 13 oz. 6 dr.; 37 cwt. 2 qr. 12 lb. 3 oz. 15 dr.; and 27 cwt. 1 qr. 17 lb. 13 oz. 9 dr.? (Table IV.) Ans. 102 cwt. 1 qr. 21 lb. 7 oz. 11 dr. 9. What is the amount of 12 yd. 3 qr. 3 na.; 17 yd. 1 qr. 2 na.; 81 yd. 3 qr. 3 na.; and 5 yd. 2 qr. 1 na. ? (Table V.) Ans. 117 yd. 3 qr. 1 na. 10. What is the amount of 16 m. 5 fur. 27 rd. 3 yd. 2 ft. 9 in. 1 b. c.; 12 m. 7 fur. 31 rd. 4 yd. 1 ft. 10 in. 2 b. c. ; 21 m. 3 fur. 12 rd. 1 yd. 1 ft. 11 in. 2 b. c.; and 25 m. 2 fur. 15 rd. 4 yd. 2 ft. 3 in. 1 b. c.? (Table VI.)

Ans. 76 m. 3 fur. 7 rd. 3 yd 2 ft. 11 in. 11. What is the amount of 16 hhd. 41 gal. 1 qt 1 pt.; 21 hhd. 17 gal. 3 qt. ; 63 hhd. 2 qt. 1 pt. ; 36 hhd. 45 gal. 1 pt.? (Table X.) Ans. 137 hhd. 41 gal. 3 qt. 1 pt.

How do we prove simple addition?