3. Reduce 5 lb. 7 oz. 12 pwt. 9 gr. to grains.

4. Reduce 32457 grains to pounds.

5. Reduce 41760 grains to pounds.

Ans. 7 lb. 3 oz.

6. A miner had 14 lb. 10 oz. 18 pwt. of gold dust. What was it worth at $.75 a pwt.?

Ans. $2683.50.

7. How many spoons, each weighing 2 oz. 15 pwt., can be made from 5 lb. 6 oz. of silver?

Ans. 24.

8. A goldsmith manufactured 1 lb. 1 pwt. 16 gr. of gold into rings, each weighing 4 pwt. 20 gr.; he sold the rings for $1.25 apiece. What did he receive for them? Ans. $62.50.

AVOIRDUPOIS WEIGHT.

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

The long or gross ton, hundred-weight, and quarter were formerly in com. mon use; but they are now seldom used except in estimating English goods at the U. S. custom-houses, and in freighting and wholesaling coal at the mines.

The following denominations are also in use:

100 Pounds of Grain or Flour

make 1 Cental.

APOTHECARIES' MEASURES.

188. Apothecaries' Weight is used by apothecaries and physicians in weighing medicines for prescriptions, but medicines are bought and sold by avoirdupois weight.

Apothecaries' Liquid Measure is used in compounding and measuring liquid medicines.

189. The Metric System of weights and measures originated in France in 1795, and its use is legalized in the United States. It is in general use by scientific men throughout the world.

It is a decimal system in which the various denominations are decimal multiples and submultiples of a unit. The following comparison of our ordinary decimal notation and the metric notation shows them to be the same:

The units of the different measures are: long measure, meter; land or square measure, are and square meter; wood or cubic measure, stere and cubic meter; weight, gram; capacity, liter. By adding the prefixes given in the table of notation to these words all the metric tables are formed.

1. The fundamental unit of the metric system is the meter, from which all the other units have been derived.

2. The principal point of superiority of the metric tables is their decimal scale. By means of the decimal point several denominations may be written together as one number, as in ordinary notation, and a change to higher or lower denominations is effected by simply moving the decimal point to the left or right. 3. One disadvantage in the use of the metric system lies in the fact that with us the other denominations are in such common use that it would require a careful study and comparison of the two systems, on the part of the people at large, to make the use of the metric system practicable. Again, some of the units while well adapted to the social and industrial conditions of France and other European countries, would not be convenient for use here. For instance, the are, the unit of land measure, is of an acre. While this suits the peasant farms of France very well it would be absurdly small for a farm in the United States.

4. The metric system is now used in France, Netherlands, Spain, Italy, Greece, Austria, Germany, Norway, Sweden, Switzerland, Portugal, Mexico, Brazil, Venezuela, Argentine Republic, Haiti, and other states; and to some extent in Great Britain, United States, India, Canada, and Chile.

METRIC WEIGHT.

190. The gram is the unit of weight; it is legal at 15.432 Troy grains. It is equal to the weight of a cube of distilled water, the edge of which is

a meter.

10 Milligrams (mg.)
10 Centigrams (cg.)
10 Decigrams (dg.)
10 Grams (G.)
10 Dekagrams (Dg.)
10 Hektograms (Hg.)
10 Kilograms (Kg.)
10 Myriagrams (Mg.)

TABLE.
=1 Centigram =

of

.15432 gr. Troy.

10 Quintals, or 1000 kilograms=1 Tonneau

=2204.62125 " 66

The weights commonly used are the gram, kilogram, and tonneau. The gram is used in mixing medicines, in weighing the precious metals, and in all cases where great exactness is required. The kilogram- or, as it is commonly called, the "kilo" is the usual weight for groceries and coarse articles generally; it is very nearly 2 pounds Av. The tonneau is used for weighing hay and other heavy articles; it is about 204 lb. more than our ton.

3. Reduce 3 T. 14 cwt. 74 lb. 12 oz. to ounces.

4. Reduce 119596 ounces to tons.

5. A tobacconist bought 3 T. 15 cwt. 20 lb. of tobacco, at 22 cents a pound. What did it cost him? Ans. $1654.40. 6. What will 115 kilograms of hay cost, at $10 per ton? 7. I paid $360 for 2 tons of cheese, and retailed it for 30 cents a kilogram. What was my whole gain?

8. If a person buys 10 T. 6 cwt. 3 qr. 14 lb. of English iron, by the long ton weight, at 6 cents a pound, and sells the same at $130 per short ton, what will he gain? Ans. $115.85.

9. Change 20 lb. 8 oz. 12 pwt. troy weight to avoirdupois weight. Ans. 17 lb. 10. I 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. What did I gain? Ans. $17.831.

11. From 25.8 g. take 326 cg. How much remains ? 12. A dealer bought 15 tons of coal, and sold at one time 5.32 T., at another 3.045 T., and at another 4.125 T. How much had he left?

MEASURES OF EXTENSION.

191. Extension has one or more of the 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.

STANDARD OF EXTENSION.

192. The United States standard unit of measures of extension, whether linear, superficial, or solid, is the yard of 3 feet, or 36 inches, and is the same as the imperial standard yard of Great Britain.