ROBINSON'Serles T. Write,

SERIES OF MATHEMATICS.

The most Complete, Practical, and Scientific Series of Mathematical
Text-Books ever Issued in this Country.

Graded to the wants of Primary, Intermediate, Grammar, Normal,
and High Schools, Academies, and Colleges.

Progressive Table Book,

Progressive Primary Arithmetic,

First Lessons in Mental and Written Arithmetic, ·
Progressive Intellectual Arithmetic,

Rudiments of Written Arithmetic,
Progressive Practical Arithmetic,
Key to Practical Arithmetic,
Progressive Higher Arithmetic,
Key to Higher Arithmetic,

Arithmetical Examples-Mental and Written,

New Elementary Algebra,

Key to New Elementary Algebra,

New University Algebra,

Key to New University Algebra,

New Geometry and Trigonometry,

Geometry, Plane and Solid. In separate vol.,

Trigonometry, Plane and Spherical. In separate vol.,

New Analytical Geometry and Conic Sections,

New Surveying and Navigation,

New Differential and Integral Calculus,

University Astronomy-Descriptive, Theoretical, and Physical,
Key to Geometry and Trigonometry, Analytical Geometry
and Conic Sections, Surveying and Navigation,

Kiddle's New Elementary Astronomy,

Mark's First Lessons in Geometry,

Entered according to Act of Congress, in the year 1871,
BY DANIEL W. FISH, A.M.,

In the Office of the Librarian of Congress, at Washington.

THI

PREFACE.

HIS work is not intended to take the place of any other, nor to constitute a necessary part of the Series to which it belongs, nor is it adapted to the use of those just commencing the study of Arithmetic; but it has been prepared to meet a demand in graded and advanced schools for a larger number of carefully prepared and practical examples for review, drill, and test exercises, than are furnished from ordinary text-books, and is to be used in connection with any systematic class-book, or Series on the subject.

Of course it is no substitute for a systematic treatise. On the contrary, its leading aim is, to bring together promiscuously a large number of examples involving all the principles and ordinary processes of theoretical and practical arithmetic, both Mental and Written, without rules, analyses, processes, or answers.

Such a work cannot fail to be of great utility, if properly used, in thoroughly exercising the pupil's judgment; in bringing into use his knowledge of the theory and applications of numbers, previously obtained from some systematic treatise; in cultivating a habit of patient investigation and self-reliance; in testing the truth and accuracy of his own work by proof-the only true test he will have to

depend upon in all the computations in the real business transactions in after-life; in a word, in making him independent of text-books, written rules, and analyses.

Although the examples are mixed, and without gradation, yet there is a general classification of them, the work being divided into six chapters. The first chapter presents the Standards and Tables of Weights and Measures, and numerous Comparative and Miscellaneous Tables, valuable for reference; the second involves the applications of the Elementary Rules of Arithmetic, and the Properties of Numbers; the third embraces Simple, Common, and Decimal Fractions; the fourth takes in Compound and Denominate Numbers and Proportion; the fifth includes Percentage, in all its varied applications; and the sixth comprehends all other subjects properly belonging to this Science.

The examples in each chapter involve the combination and application of the principles and processes contained in the preceding ones, but not to any extent those of the following chapters. Classes, therefore, that in regular course have gone over the Simple Rules of Arithmetic only, will find in the second chapter of this book all they need in the way of supplementary examples for drill and review. Those who have finished Fractions in any regular text-book will here have in Chapter Third proper exercises for testing their knowledge and skill in this part of the science; and so they may proceed, by successive reviews, till the same searching test comes to be applied to every part of the subject.

Two editions are printed; one with answers at the close of the book for the use of teachers only; the other edition is without answers, and designed for the use of classes.

BROOKLYN, Sept., 1871.

D. W. F.

MEASURES.

CHAPTER I.

1. Measure is that by which extent, dimension, capacity, or amount is ascertained, determined according to some fixed standard.

NOTE. The process by which the extent, dimension, capacity, or amount is ascertained, is called Measuring; and consists in comparing the thing to be measured with some conventional standard.

Measures are of seven kinds:

1. Length.

2. Surface or Area.

3. Solidity or Capacity.

4. Weight, or Force of Gravity. 5. Time.

6. Angles.

7. Money or Value.

The first three kinds may be properly divided into two classes-Measures of Extension and Measures of Capacity.

MEASURES OF EXTENSION.

2. Extension has length, breadth, and thickness.
A Line has length only.

A Surface or Area has length and breadth.
A Solid has length, breadth, and thickness.

LINEAR MEASURE.

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

4. 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.