Unless the student associates the notation with the concrete entities which it represents he will drop into the habit of studying symbols rather than numbers, and thus "catch the shadow rather than the substance" of a practical and fruitful knowledge of arithmetic. In this book a special effort is made to prevent the student from falling into this error, especially in the important subjects of fractions and percentage.

Definitions and rules serve many good purposes. They should not be formally committed to memory, but should be learned by associating them with the concepts which they define, or the principles on which they are based. They should be used just as a convalescent uses his crutches; that is, until the strength which he acquires by their support renders him independent of that support.

Professors T. H. Harris and R. L. IIimes, of the Louisiana State University, and Misses D. L. Bostick, F. A. Stringer, and E. Aitkens, of the New Orleans Teachers Association, have rendered valuable assistance in the preparation of this book. Mr. D. M. Raymond, President of the First National Bank of Baton Rouge, has also given much valuable information in reference to banks. To these and others the author acknowledges his indebtedness, and gives assurance that any suggestions for the further improvement of the book will be thankfully received.

BATON ROUGE, LA., July, 1902.

JAMES W. NICHOLSON.

Some numbers (integers) are most simply interpreted as counts, and others (fractions) as measures.

2. A unit is the standard by which we count or measure.

Thus:

In counting eggs by ones, one egg is the unit.

In counting pens by the dozen, a dozen pens is the unit.
In measuring a line by the yard, a linear yard is the unit.
In measuring wine by the pint, a pint of wine is the unit.

Units of the Decimal System.

3. In counting a large number of objects it is convenient to arrange them in equal groups, and when these become large to arrange them again in equal groups, and so on. The decimal system of counting, which is in common use, consists in grouping by tens, and employing each group as a unit, as follows:

4. One is the name of the primary or basic unit, and is called a unit of the first order.

5. All numbers which may be counted by ones are called integers or whole numbers. The names of the first ten integers are

one, two, three, four, five, six, seven, eight, nine, ten

6. Ten is the name of a group of ten ones, and is called a unit of the second order.

We count by tens thus:

one ten, or ten,
two tens, or twenty,

three tens, or thirty,

four tens, or forty,

five tens, or fifty,

six tens, or sixty,

seven tens, or seventy, eight tens, or eighty, nine tens, or ninety,

ten tens, or hundred.

7. Hundred is the name of a group of ten tens, and is

called a unit of the third order.

We count by hundreds as by tens, thus:

8. Thousand is the name of a group of ten hundreds, and is called a unit of the fourth order.

We count by thousands as by tens and hundreds.

9. From ten units of the fourth order is formed a ten thousand—a unit of the fifth order; and from ten units of the fifth order is formed a hundred thousand-a unit of the sixth order; and so on. That is, ten units of any order form one unit of the next higher order.

10. Names and Orders of the Units: