long-felt want, a want that has been intensified in late years by the establishment of Agricultural Colleges and Experiment Stations where the course of study consists largely of chemical analyses. In all the problems under this head the given per cents of constituents are taken from analyses made at one or the other of the Stations of the Louisiana State University and Agricultural and Mechanical College.

Special attention is called to the rational treatment of Arithmetical Signs. The theory of combining numbers connected by the signs X and ÷, as presented in this book, is original with the author, who feels confident that it has never before appeared in any Arithmetic. From a want of knowledge of this theory, numbers so connected are differently combined by different authors, and erroneous results appear in many text-books that are extensively used.

The Appendix, to be used at the discretion of the teacher, in addition to Short Methods and Miscellaneous Tables and Problems, contains a fair presentation of Circulating Decimals, Foreign Exchange, Arithmetical and Geometrical Progressions, Annuities, Building Associations, and Horner's excellent method of extracting roots.

If the problems in this book are thought to be more numerous than is always necessary, the teacher may select such as will best meet the individual wants of the pupils.

In conclusion, the author acknowledges his obligations and returns his thanks to the many persons whose printed works or verbal suggestions have assisted him in the preparation of this book, and respectfully solicits any suggestions for its further improvement.

BATON ROUGE, LA., June, 1889.

J. W. N.

ARITHMETIC.

CHAPTER I.

INTEGERS.

PRELIMINARY DEFINITIONS.

Art. 1. A unit is a single thing.

(1) One, one day, one apple, one ten, are units.

2. Units are like when they are the same, and unlike when

they are of different kinds.

(1) One dollar and one dollar are like units.

(2) One day and one gallon are unlike units.

3. A number is a unit or a collection of like units.

(1) Six, five men, ten balls, four days, are numbers.

4. The unit of a number is one of the units of which the number is formed.

(1) The unit of six is one; of twelve days, one day; of thirtyfour pounds, one pound.

5. Like numbers are those which have like units, and unlike numbers are those which have unlike units.

(1) Two days and ten days are like numbers.

(2) Three days and five boys are unlike numbers.

6. An abstract number is one that is not applied to a particular object, and a concrete number is one that is applied to some object.

(1) Nine, six, two, etc., are abstract numbers.

(2) Nine pens, six miles, etc., are concrete numbers.

An abstract number expresses how many times one quantity is contained in another, and a concrete number expresses how much one quantity is in terms of another.

7. An integer, or whole number, is a number that is composed of whole or entire units, and a fraction, or fractional number, is a number that is composed of equal parts of a whole or entire unit.

(1) Six, ten pints, five days, etc,, are integers.

(2) Two-thirds of a pint, three-fourths of a bushel, etc., are fractions.

8. Arithmetic is the science and art of numbers.

9. Science is classified knowledge.

10. Art is the practical application of science.

11. Principles are the primary truths of science.

12. A theorem is a truth to be proved.

13. A problem is a construction or question to be solved. 14. An example is a problem or theorem used to illustrate a principle or process.

15. A rule is a general description of a process.

16. A formula is the expression, by symbols, of a rule or principle.

17. In arithmetic, exercises are problems or theorems. In written exercises the successive steps of the work are to be written; and in mental or oral exercises the work is not to be written.

18. Parallel problems are those involving the same principles, and which are solved in a similar manner.

NOTE. In this treatise, the exercises often embrace parallel problems, in which case such as are designed for oral work are designated in their numbers by a different style of type; and are generally intended to illustrate the principles involved in the succeeding problems.