7. A physician bought 1 pound of ipecacuanha for $ 1.80, and retailed it out in doses of 5 grains, at 124 cents each. How much did he get for it over the cost ? Ans. $ 142.20. AVOIRDUPOIS, TROY, AND APOTHECARIES' Weight Com PARED. 132. The relative value of the pound, and its subdivisions, of the several weights, in Troy grains, and in denominations of each other, is shown in the following TABLE. 1 dr. Ap. 1 lb. Av. 7000 gr. Tr. ilb. 2oz. 11pwt. 16gr. Tr. 1 lb. Tr. or Ap. 5760 13oz. 214fdr. Av. 1 oz. Tr. or Ap. 480 loz. 1175dr. Av. 1 oz. Av. 4371 18pwt. 54gr. Tr. 60 214dr. Av. 1 dr. Av. 2711 1pwt. 3'lgr. Tr. 1 pwt. Tr. 24 za dr. Av. 1 sc. Ap. 20 dr. Av. 1 gr. Tr. or Ap. . 1 dr. Av. NOTE. To change a quantity from one weight to its equivalent in another weight, reduce the given quantity to Troy grains, and then find their value in denominations of the weight required. 66 EXAMPLES. 1. Change 131b. 6oz. Avoirdupois weight to Troy weight. 2. Change 16lb. 3oz. 1pwt. 1gr. Troy weight to Avoirdupois weight. 3. Change 3lb. 8oz. 10pwt. to drams of Apothecaries' weight. Ans. 356dr. 4. Change 356 drams Apothecaries' weight to Troy weight. Ans. 3lb. 8oz. 10pwt. 5. An apothecary bought by Avoirdupois weight 2lb. 8oz. of quinine at $ 2.40 per ounce, which he retailed at 20 cents a scruple. What was his gain on the whole? 6. If I should buy by Avoirdupois weight 121b. of opium af 374 cents per ounce, and sell it by Troy weight at 40 cents per ounce, should I gain or lose by so doing? Ans. Lose $ 2. LINEAR OR LONG MEASURE. 133. Linear or Long Measure is used in measuring distances in any direction. TABLE. 66 12 Inches (in.) ft. 3 Feet 1 Yard, yde 51 Yards, or 16] Feet, 1 Rod, or Pole, rd. 40 Rods 1 Furlong, fur. 8 Furlongs, or 320 Rods, “ 1 Mile, 3 Miles 1 League, lea 69] Miles (nearly) 1 Degree on the equator, deg. oro. 360 Degrees. 1 Great Circle of the Earth. m. NOTE 1. — 12 lines make 1 inch; 4 inches, 1 hand; 6 feet, 1 fathom; 120 fathoms, 1 cable length; 7} cable-lengths, 1 mile; do of a degree of the circumference of the earth, 1 knot, or geographical mile, equal to 142 statute miles. NOTE 2. - The yard adopted by the United States government as the standard unit of linear measure is the same as the imperial yard of Great Britain, which, as compared with a pendulum vibrating seconds in the latitude of London, the pendulum moving in a vacuum, at the level of the sea, and at the temperature of 62° Fahrenheit, should bear the proportion of 36 to 3976683 inches. A metre, the unit of linear measure, as established by the French government, is equal to about 392 English inches. NOTE 3. — The English statute mile is the same as that of the United States, but that of other countries differs in value from it; as the German short mile is equal to 6857 yards, or about 31 English miles; the German long mile, to 10125 yards, or about 5$ English miles; the Prussian mile, to 8237 yards, or about 47. English miles; the Spanish common league, to 7416 yards, or about 4} English miles; the Spanish judicial league, to 4635 yards, or about 23 English miles. NOTE 4. A degree of longitude is zło of any circle of latitude. As the circles of latitude diminish in length, the degrees of longitude vary in length under different parallels of latitude. Thus, under the equator, the length of a degree of longitude is about 69 statute miles; at 25° of latitude 6216 miles; at 40° of latitude, 53 miles; at 42° of latitude, 514 miles; at 49° of latitude, 451 miles; at 60°, 3473 miles. EXAMPLES. 1. In 96deg. 56m. 7fur. 32rd. 12ft. 6in. how many inches ? 2. In 424320486 inches how many degrees? 3. How many feet in 79 miles ? 4. Required the miles in 417120 feet. 5. How many inches in 396 furlongs ? 6. Required the furlongs in 3136320 inches ? 7. How many inches from Harerhill to Boston, the distance being 30 miles ? 8. Required the miles in 1900800 inches. CLOTH MEASURE. na. 66 66 yd. na. qr. = 13 134. Cloth Measure is used in measuring cloth, ribbons, lace, and other articles sold by the yard or ell. TABLE. 24 Inches (in.) make 1 Nail, 4 Nails 1 Quarter of a yard, qr. 4 Quarters 1 Yard, 3 Quarters 1 Ell Flemish, E. F. 5 Quarters 1 Ell English, E. E. in. 24 1 9 4 E. F. 27 12 1 yd. 36 16 1} 1 E. E. 45 20 5 11 1 NOTE 1. - The Ell French is 6 quarters; the Ell Scotch, 4qr. i in. NOTE 2. Cloth measure is a species of linear measure, and the yard and inch are the same in both. EXAMPLES. 1. In 17yd. 3qr. 2na, how many nails? 2. In 286 nails how many yards ? 3. In 365yd. lqr. 3na. how many nails ? 4. In 5847 nails how many yards ? 5. In 71 E. E. 4qr. how many nails ? 6. In 1436 nails how many ells English ? 7. What cost 47vd. 3qr. of silk velvet at $ 1.25 per quarter ? 8. A merchant bought a roll of cloth containing 31 E. E. and paid for it at the rate of $ 3 per yard. What did it cost him ? Ans. $ 117. ft. 66 SURFACE OR SQUARE MEASURE. 135. Square Measure is used in measuring surfaces of all kinds. TABLE. 144 Square inches (sq. in ) make 1 Square foot, 9 Square feet 1 Square yard, yd. 30 Square yards 1 Square rod or pole, p. 40 Square rods 1 Rood, R. 4 Roods 1 Acre, A. 640 Acres 1 Square mile, S. M. in. ft. 144 1 yd. 1596 9 1 p. 1 R. 1568160 10890 1210 40 1 A. 6272640 43560 4840 160 4 1 S.M. 4014489600 27878400 = 3097600 · 102400 2560 : 640 =1 NOTE. — A square is a figure bounded by four equal lines, perpendicular to each other. When the four lines are each 1 foot in length, the space enclosed is 1 square foot ; when 1 yard in length, 1 square yard; when 1 rod in length, 1 square rod; and so for any other dimension. 3ft. lyd. In this diagram the large square repreSquare foot. sents a square yard, and each of the smaller squares within it represents one square foot. Now, since there are three rows of small squares, and three square feet in each row, there will be 3 sq. ft. X 3 = 9 sq. ft. in the large square. But the large square is 3ft. in length and 3ft. in breadth; hence, To find the contents of a square, multiply the numbers denoting its length and breadth together. EXAMPLES. 1. In 57A. 3R. 27p. 21yd. 8ft. 57in. how many square inches ? 2. In 363331893 square inches how many acres ? square feet ? 5. How many square rods in 365 square miles ? 6. How many square miles in 37376000 square rods ? 7. How many acres in 12345678 square inches ? Ans. 1A. 3R. 34p. 27yd. 4ft. 54in. 3ft. = lyd. 8. Bought 39 A. 2R. 16p. of land for $ 3.75 per square wud and sold the same for $ 0.25 per square foot. What did I gain by my bargain ? Ans. $ 407,484.00. SURVEYORS' MEASURE. 136. This measure is used by surveyors in measuring land, roads, &c. NOTE 1. Gunter's chain, in length 4 poles, or 66 feet, and divided into 100 links, is that mostly used in ordinary land surveys; but in locating roads, and like public works, an engineer's chain is usually 100 feet in length, containing 120 links, each 10 inches long. NOTE 2. A section of government lands is 1 square mile, or 640 acres. An acre, as a square piece of land, will measure on each side about 209 feet or 70 paces. 625 square links make 1 square rod or pole; 16 square rods make 1 square chain, and 10 square chains make 1 acre. NOTE 3. — A rod or pole is sometimes called a perch, and each of the names given to this measure is expressive of the instrument by which it was formerly measured. EXAMPLES. 1. How many links in 46m. 3fur. 5ch. 251. ? many miles ? 5. The extent of a certain farm is found, by survey, to be 1377 square chains (Note 2). How many acres does it contain ? Ans. 137A. 2R. 32p. 6. What will be the cost of a field measuring 2,126,250 square links, at $ 80 per acre ? Ans. $ 1701.00. |