tion.) Proceed in the same brought it to the denomination manner with each succeeding required. denomination, until you have brought it to the denomination required.

EXAMPLES FOR PRACTICE.

3. Reduce 32£. 15 s. 8 d.) to farthings.

5. In 29 guineas, at 28 s. each, how many farthings? 7. Reduce $163, at 6 s. each, to pence?

9. In 15 guineas, how many pounds?

4. Reduce 3142 farthings to pounds.

6. In 38976 farthings, how many guineas?

8. Reduce 11736 pence tc

dollais.

10. Reduce 21£. to guin

eas.

Note. We cannot reduce guineas directly to pounds, but we may reduce the guineas to shillings, and then the shillings to pounds.

TROY WEIGHT.

*

By Troy weight are weighed gold, silver, jewels, and all iquors. The denominations are pounds, ounces, pennyweights, and grains.

24 grains (grs.) make 1 pennyweight, marked pwt. 20 pennyweights

12 ounces

TABLE.

1 ounce,

1 pound,

OZ.

lb.

11. Bought a silver tank- 12. Paid $44'28 for a silard, weighing 3 lb. 5 oz., pay- ver tankard, at the rate of ng at the rate of $1'08 an $1'08 an ounce; what did it ounce; what did it cost?

weigh?

13. Reduce 210 lb. 8 oz. 14. In 50572 pwt. how 12 pwt. to pennyweights. many pounds? 15. In 7 lb. 11 oz. 9 grs. of silver, how

grains ?

3pwt.

16. Reduce 45681 grains many to pounds.

*The fineness of gold is tried by fire, and is reckoned in carats, by which is understood the 24th part of any quantity; if it lose nening in the trial, it is said to be 24 carats fine; if it lose 2 carats, it is then 22 carats fine, which is the standard for gold,

Silver which abides the fire without loss is said te re 12 ounces fine. The standard for silver coin is 11 oz. 2 pwts. of fine svet, and 18 pwts. of copper melted together

APOTHECARIES' WEIGHT.

Apothecaries' weight* is used by apothecaries and physicians, in compounding medicines. The denominations are pounds, ounces, drams, scruples, and grains.

TABLE.

20 grains, (grs.) make 1 scruple, marked

Э.

3 scruples

8 drams

3.

3.

lb.

18. Reduce 55799 grs. to

pounds.

AVOIRDUPOIS WEIGHT.†

By avoirdupois weight are weighed all things of a coarse and drossy nature, as tea, sugar, bread, flour, tallow, hay, leather, medicines, (in buying and selling,) and all kinds of metals, except gold and silver. The denominations are tons, hundreds, quarters, pounds, ounces, and drams.

Note 1. In this kind of weight, the words gross and net are used. Gross is the weight of the goods, together with the box, bale, bag, cask, &c., which contains them. Net weight is the weight of the goods only, after deducting the weight of the box, bale, bag, or cask, &c., and all other allowances.

Note 2. A hundred weight, it will be perceived, is 112 lb. Merchants at the present time, in our principal sea-ports, buy and sell by the 100 pounds.

* The pound and ounce apothecaries' weight, and the pound and ounce Troy, are the same, only differently divided, and subdivided.

=

192 oz. avoirdupois, and 175 lb. Troy 144 lb. avoirdu5760 grains, and 1 lb. avoirdupois = 7000 grains Troy.

G

19. What will 5 cwt. 3 qrs. 20. How much sugar, at 17 lb. of sugar come to, at 124 cents a pound, may be 124 cents a pound. bought for $82'625?

21. A merchant would put 109 cwt. 0 qrs. 12lb. of raisins into boxes, containing 26 lb. each; how many boxes will it require ?

22. In 470 boxes of raisins, containing 26 lb. each, how many cwt.?

23. In 12 tons, 15 cwt. 24. In 7323500 drams, how 1 qr. 19lb. 6 oz. 12 dr. how many tons?

many drams?

25. In 28 lb. avoirdupois,

how many pounds Troy?

26. In 34lb. 0 oz. 6 pwt. 16 grs. Troy, how many pounds avoirdupois ?

CLOTH MEASURE.

Cloth measure is used in selling cloths and other goods, sold by the yard, or ell. The denominations are ells, yards, quarters, and nails.

TABLE.

1 nails, (na.) or 9 inches, make 1 quarter, marked

1 quarters, or 36 inches,

3 quarters,

5 quarters,

1 yard,

qr. yd.

1 ell Flemish,

E. FI.

6 quarters,

Long measure is used in measuring distances, or other things, where length is considered without regard to breadth. The denominations are degrees, leagues, miles, furlongs, rods, yards, feet, inches, and barley-corns.

31. How many barley-corns | 32. In 4755801600 barleywill reach round the globe, it corns, how many degrees? being 360 degrees?

Note: To multiply by 2, is Note. The barley-corns beto take the multiplicand 2 ing divided by 3, and that times; to multiply by 1, is to quotient by 12, we have take the multiplicand 1 time; 132105600 feet, which are to to multiply by, is to take the be reduced to rods. We canmultiplicand half a time, that not easily divide by 16 on is, the half of it. Therefore, account of the fraction ; but to reduce 360 degrees to stat- 16 feet 33 half feet, in 1 ute miles, we multiply first by rod; and 132105600 feet the whole number, 69, and to 264211200 half feet, which, the product add half the multi- divided by 33, gives 8006400 plicand. Thus : rods.

360

691

3240

2160

Hence, when the divisor is encumbered with a fraction, or, &c., we may reduce the divisor to halves, or fourths,

180 half of the multiplicand. &c., and reduce the dividend

to the same; then the quo

25020 statute miles in 360 de-tient will be the true answer.

grees.

33. How many inches from 34. In 30539520 inches, Boston to the city of Wash- how many miles? ington, it being 482 miles?

35. How many times will a 36. If a wheel, 16 feet 6 wheel, 16 feet and 6 inches inches in circumference, turn in circumference, turn round round 12800 times in going in the distance from Boston to from Boston to Providence, Providence, it being 40 miles ? what is the distance?

LAND OR SQUARE MEASURE.

Square measure is used in measuring land, and any other thing, where length and breadth are considered. The denominations are miles, acres, roods, perches, yards, feet and inches.

¶ 35. 3 feet in length make a yard in long measure; but it requires 3 feet in length and 3 feet in breadth to make a yard in square measure; 3 feet in length and one foot wide make 3 square feet; 3 feet in length and 2 feet wide make 2 times 3, that is, 6 square feet; 3 feet in length and 3 feet wide make 3 times 3, that is, 9 square feet. This will clearly appear from the annexed figure.

3 feet 1 yard.

3 feet = 1 yard.

It is plain, also, that a square foot, that is, a square 12 inches in length and 12 inches in breadth, must contain 12 × 12 = 144 square inches.

144

TABLE.

square inches 12 X 12; that is,

12 inches in length and 12 inches make 1 square foot.

Note. Gunter's chain, used in measuring land, is 4 rodst in length. It consists of 100 links, each link being 7 inches in length; 25 links make 1 rod, long measure, and 625 square links make 1 square rod.