NOTE.-Medicines are bought and sold in quantities by avoirdupois weight.

1. How many grains in 2 scruples?

2. How many scruples in 5 drams? In 7 drams? 9 drams? 12 drams? 20 drams?

3. How many drams in 21 scruples? In 27 scruples? 33 scruples? 40 scruples?

4. How many drams in 5 ounces? In 8 ounces? 10 ounces? 12 ounces?

5. How many pounds in 36 ounces? In 72 ounces? 96 ounces? 120 ounces?

6. How many ounces in 5 pounds? In 8 pounds? 10 pounds? 12 pounds?

WRITTEN EXERCISES.

7. Reduce 16 lb. 113 53 29 10 gr. to grains. 8. Reduce 103 33 to grains.

9. Reduce 3563 to pounds.

10. Reduce 26484 gr. to higher denominations. 11. How many pounds in 5760 > ?

12. How many doses, of 18 gr. each, in 53 29 of tartar emetic ?

13. How many pills, of 5 gr. each, can be made from 13 23 29 of calomel?

14. How many ounces of calomel will make 480 'pills, each weighing 6 grains?

NOTE. A sheet of paper folded in 2 leaves is called 2 folio; in 4 leaves, a quarto, or 4to; in 8 leaves, an octavo, or 8vo; in 12 leaves, a duodecimo, or 12mo; in 18 leaves, an 18mo.

1. How many sheets of paper in 5 quires?

2. How many quires of paper in 4 reams? In 8 reams? 12g reams? 15 reams?

3. How many bundles of paper in 6 reams? In 12 reams? 18 reams? 32 reams?

4. How many eggs in 5 dozen? In 73 dozen 8 dozen? 12 dozen? 20 dozen?

5. How many years are 4 score years? 3 score years and 10?

WRITTEN EXERCISES.

6. How many sheets of paper in 12 reams? 7. Reduce 6 rm. 15 qu. 12 sheets to sheets.

8. What will 7200 sheets of paper cost, at $8.50 a ream?

9. How many crayons are there in 36 boxes, if each box contains one gross?

10. If a shirt require 6 buttons, how many shirts will 12 gross of buttons trim?

11. What will 44 gross of lead-pencils cost, at 75 cents a dozen?

12. A stationer bought 15 reams of letter-paper at $3.50 a ream, and sold it at 25 cents a quire. How much did he gain?

LESSON XIII.

DEFINITIONS, PRINCIPLES, AND RULES.

Art. 99. A Denominate Number is a number composed of concrete units of one or several denominations.

Art. 100. Denominate Numbers are either Simple .or Compound.

A Simple Denominate Number is composed of units of the same denomination; as, 7 quarts.

A Compound Denominate Number is composed of units of several denominations; as, 5 bu. 3 pk. 7 qt.

NOTE.-Compound Denominate Numbers are properly called Compound Numbers, since every compound number is necessarily denominate.

Art. 101. Denominate numbers express Currency, Measure, and Weight.

Currency is the circulating medium used in trade and commerce as a representative of value. Measure is the representation of extent, capacity, or amount.

Weight is a measure of the force called gravity, by which bodies are drawn toward the earth.

Art. 102. The following diagram represents the three general classes of denominate numbers, their subdivisions, and the tables included under each:

1. Of extension, 2. Surfaces: Square Measure.

Art. 103. The Reduction of a denominate number is the process of changing it from one denomination to another without altering its value.

Art. 104. Reduction is of two kinds, Reduction Descending and Reduction Ascending.

Reduction Descending is the process of changing a denominate number from a higher to a lower denomination. It is performed by multiplication.

Reduction Ascending is the process of changing a denominate number from a lower to a higher denomination. It is performed by division.

Art. 105. RULE FOR REDUCTION DESCENDING. 1. Multiply the number of the highest denomination by the number of units of the next lower which equals a unit of the higher, and to the product add the number of the lower denomination, if any.

2. Proceed in like manner with this and each successive result thus obtained, until the number is reduced to the required denomination.

NOTE. The successive denominations of the compound number should be written in their proper order, and the vacant denominations, if any, filled with ciphers.

Art. 106. RULE FOR REDUCTION ASCENDING. 1. Divide the given denominate number by the number of units of its own denomination, which equals one unit of the next higher, and place the remainder, if any, at the right.

2. Proceed in like manner with this and each successive quotient thus obtained, until the number is reduced to the required denomination.

3. The last quotient, with the several remainders annexed in proper order, will be the answer required.