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Apothecaries' weight is used by apothecaries and physi clans, in compounding medicines. The denominations are pounds, ounces, drams, scruples, and grains.
20 grains, (grs.) make 1 scruple, marked .
17. In 9. 83. 13. 29. 19 grs., how many grains.
4 quarters 20 hundred weight
16 drams, (drs.) make
175 oz. Troy pois. 1 lb. Troy
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.
18. Reduce 55799 grs. to pounds.
1 hundred weight,
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. Nat 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-perts, 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 144b. avoirdu5760 grains, and 1 lb. avoirdupois 7000 grains Troy. G
19. What will 5 cwt. 3 qrs. 17lb. of sugar come to, at 12 cents a pound.
21. A merchant would put 109 cwt. 0 qrs. 12 lb. raisins into boxes, containing 26 lb. each; how many boxes will it require?
23. In 12 tons, 15 cwt. 1 qr. 19 lb. 6 óz. 12 dr. how many drams?
25. In 28 lb. avoirdupois, how many pounds Troy?
20. How much sugar, at 124 cents a pound, may be bought for $82′625 ?
22. In 470 boxes of raisins, containing 26 lb. each, how many cwt.?
24. In 7323500 drams, how many tons?
Cloth measure is used in selling cloths and other goods, sold by the yard, or ell. The denominations are ells, yards, quarters, and nails.
27. In 573 yds. 1 qr. 1 na. How many nails?
29. In 151 ells Eng. how many yards?
Note. Consult T 34, ex. 9.
26. In 34lb. 0 oz. 6 pwt
16 grs. Troy, how many
1 nails, (na.) or 9 inches, make 1 quarter, 1 quarters, or 36 inches,
1 ell English,
28. In 9173 nails, how ma ny yards?
30. In 1883 yards, how many ells English?
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.
3 barley-corns, (bar.) make 1 inch,
1 rod, perch, or pole,
5 yards, or 16 feet, 40 rods, or 220 yards, 8 furlongs, or 320 rods, 3 miles,
60 geographical, or 694} 1 degree,
180 half of the multiplicand.
31. How many barley-corns 32. In 4755801600 barleywill reach round the globe, it corns, how many degrees? being 360 degrees?
a great circle, or circumfer ence of the earth.
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 =3 the whole number, 69, and to 264211200 half feet, which, the product add half the multi-divided by 33, gives 8000400 plicand. Thus : rods.
or, &c., we may reduce the divisor to halves, or fourths, &c., and reduce the dividend to the same; then the quo
25020 statute miles in 360 de-tient will be the true answer.
Hence, when the divisor is encumbered with a fraction,
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.
3 feet1 yard.
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.
144 square inches
12 X 12; that is,
12 inches in length and 12 inches make 1 square foot. in breadth
40 square rods,
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 = 1.44 square inches.
9 square feet 3 X 3; that is, 3 feet in length and 3 feet in breadth 30 square yards = 5 × 51, or 2721 square feet 161 × 161,
roods, or 160 square rods,
1 square yard.
( 1 square rod, perch or pole.
- 1 square mile.
Note. Gunter's chain, used in measuring land, is 4 rods 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.
37. In 17 acres 3 roods 12 38. In 776457 square feet, rods, how many square feet? how many acres? Note. In reducing rods to Note. Here we have 776457 feet, the multiplier will be square feet to be divided by 2724. To multiply by, is to 2721 Reduce the divisor to take a fourth part of the mul-fourths, that is, to the lowest tiplicand. The principle is denomination contained in it; the same as shown 34, then reduce the dividend to ex. 31. fourths, that is, to the same denomination, as shown T32, ex. 34.
39. Reduce 64 square miles o square feet?
41. There is a town 6 miles square; how many square square miles. miles in that town? how many acres?
SOLID OR CUBIC MEASURE.
Solid or cubic measure is used in measuring things that have length, breadth, and thickness; such as timber, wood, stone, bales of goods, &c. The denominations are cords, tons, yards, feet, and inches.
36. It has been shown, that a square yard contains 3 X 3 9 square feet. A cubic yard is 3 feet long, 3 feet vide, and 3 feet thick. Were it 3 feet long, 3 feet wide, nd one foot thick, it would contain 9 cubic feet; if 2 feet hick, it would contain 2 X 918 cubic feet; and, as it is 3 feet thick, it does contain 3 x 927 cubic feet. This will clearly appear from the annexed figure.
It is plain, also, that a cubic foot, that is, a solid, 12 inches in length, 12 inches in breadth, and 12 inches in thickness, will contain 12 X 12 X 12 = 1728 solid or cubic inches.
40. In 1,784,217,600 square feet, how many square miles? 42. Reduce 23040 acres to
1 yd. 3 ft. wide.