3. In 16 lb. 11 oz. 7 dr. 2 sc. 19 gr., how many grains? 4. Reduce 47 lb 63 43 to scruples. Ans. 13692 sc. 5. How many pounds of medicine would a physician use in one year, or 365 days, if he averaged daily 5 prescriptions of 20 grains each? Ans. 6 lb. 4319.

III. AVOIRDUPOIS WEIGHT.

187. Avoirdupois Weight is used for all the ordinary purposes of weighing.

SCALE-ascending, 16, 16, 100, 20; descending, 20, 100, 16, 16. NOTE. The long or gross ton, hundred weight, and quarter were formerly in common use; but they are now seldom used except in estimating English goods at the U. S. custom-houses, and in freighting and wholesaling coal from the Pennsylvania mines.

SCALE — ascending, 28, 4, 20; descending, 20, 4, 28.

The following denominations are also in use.

56 pounds make 1 firkin of butter.

1 quintal of dried salt fish.

66

1 cask of raisins.

Define avoirdupois weight. Repeat the table. Give the scale. The long ton table. What other denominations are in use? What is the value of each?

3. Reduce 3 T. 14 cwt. 74 lb. 12 oz. 15 dr. to drams.

4. Reduce 1913551 drams to tons.

5. A tobacconist bought 3 T. 15 cwt. 20 lb. of tobacco, at 22 cents a pound; how much did it cost him? Ans. $1654.40. 6. How much will 115 pounds of hay cost, at $10 per ton? 7. A grocer bought 10 barrels of sugar, each weighing 2 cwt. 17 lb., at 6 cents a pound; 5 barrels, each weighing 3 cwt. 6 lb., at 74 cents a pound; he sold the whole at an average price of 8 cents a pound; how much was his whole gain? Ans. $51.05.

8. Paid $360 for 2 tons of cheese, and retailed it for 12 cents a pound; how much was my whole gain? Ans. $140. 9. If a person buy 10 T. 6 cwt. 3 qr. 14 lb. of English iron, by the long ton weight, at 6 cents a pound, and sell the same at $130 per short ton, how much will he gain? Ans. $115.85. 10. A farmer sold 2 loads of corn, weighing 2352 lbs. each, at $.90 per bu.; what did he receive? Ans. $75.60.

11. How many pounds in 300 barrels of flour? 12. A grocer bought 3 barrels of salt at $1.25 per barrel, and retailed it at of a cent per pound? what did he gain? Ans. $2.55.

STANDARD OF WEIGHT.

188. In the year 1834 the U. S. government adopted a uniform standard of weights and measures, for the use of the custom houses, and the other branches of business connected with the general government. Most of the States which have adopted any standards have taken those of the general government.

189. The United States standard unit of weight is the Troy pound of the mint, which is the same as the imperial standard pound of Great Britain, and is determined as follows: A cubic inch of distilled water in a vacuum, weighed by brass weights, also in a vacuum, at a temperature of 62° Fahrenheit's thermometer, is equal to 252.724 grains, of which the standard Troy pound contains 5760.

190. The U. S. Avoirdupois pound is determined from the standard Troy pound, and contains 7000 Troy grains. Hence, the Troy pound is $788144 of an avoirdupois pound. But the Troy ounce contains 5760 =480 grains, and the avoirdupois ounce 70go= 437.5 grains; and an ounce Troy is 480—437.5= 42.5 grains greater than an ounce avoirdupois. The pound, ounce, and grain, Apothecaries' weight, are the same as the like denominations in Troy weight, the only difference in the two tables being in the divisions of the ounce.

1. An apothecary bought 5 lb. 10 oz. of rhubarb, by avoirdupois weight, at 50 cents an ounce, and retailed it at 12 cents a dram apothecaries' weight; how much did he gain? Ans. $33.75.

2. Change 424 drams apothecaries' weight to Troy weight. Ans. 4 lb. 5 oz.

3. Change 20 lb. 8 oz. 12 pwt. Troy weight to avoirdupois weight. Ans. 17 lb.

4. Bought by avoirdupois weight 20 lb. of opium, at 40 cents an ounce, and sold the same by Troy weight at 50 cents an ounce; how much was gained or lost? Ans. $17.831.

What is the U. S. standard of weight? How obtained? How is the avoirdupois pound determined? How is the apothecaries' pound determined? What are the values of the denominations of Troy, avoirdupois, and apothecaries' weight?

MEASURES OF EXTENSION.

192. Extension has three dimensions- length, breadth, and thickness.

A Line has only one dimension -length.

A Surface or Area has two dimensions-length and breadth. A Solid or Body has three dimensions-length, breadth, and thickness.

I. LONG MEASURE.

193. Long Measure, also called Linear Measure, is used in measuring lines or distances.

SCALE-ascending, 12, 3, 5, 40, 8; descending, 8, 40, of, 3, 12.

The following denominations are also in use:

used by shoemakers in measuring

3 barleycorns make 1 inch, the length of the foot.

1 hand,

used in measuring the height of horses directly over the fore feet. 1 fathom, used in measuring depths at sea.

1 geographic mile, { used in measuring dis

1 league.

tances at sea.

of latitude on a meridian or of

1 degree longitude on the equator.

the circumference of the earth.

How many dimensions has extension? Define a line. Surface or A solid or body. Define long measure. What are the denominations? The value of each. What other denominations are used?

area.

NOTES. 1. For the purpose of measuring cloth and other goods sold by the yard, the yard is divided into halves, fourths, eighths, and sixteenths. The old table of cloth measure is practically obsolete.

60

2. The geographic mile is of or 100 of the distance round the center of the earth. It is a small fraction more than 1.15 statute miles.

3. The length of a degree of latitude varies, being 68.72 miles at the equator, 68.9 to 69.05 miles in middle latitudes, and 69.30 to 69.34 miles in the polar regions. The mean or average length is as stated in the table. A degree of longitude is greatest at the equator, where it is 69.16 miles, and it gradually decreases toward the poles, where it is 0.

3. The diameter of the earth being 7912 miles, how many inches is it?

Ans. 501304320 inches.

4. In 168474 feet how many miles?

5. In 31 mi. 7 fur. 10 rd. 3 yd., how many feet?

6. If the greatest depth of the Atlantic telegraphic cable from Newfoundland to Ireland be 2500 fathoms, how many miles is it?

Ans. 2 mi. 6 fur. 29 rd. 14 ft.