PREFACE. THIS 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, January, 1875. D. W. F. MEASURES. · CHAPTER I. . 1. A Measure is a standard unit, established by law or custom, by which quantity, as extent, dimension, capacity, amount, or value is measured or estimated. Thus, the standard unit of Measures of Extension is the yard; of Liquid Measure, the wine gallon; of Dry Measure, the Winchester bushel; of Weight, the Troy pound, etc. Hence the length of a piece of cloth is ascertained by applying the yard measure; the capacity of a cask, by the use of the gallon measure; of a bin, by the use of the bushel measure; the weight of a body, by the pound weight, etc. 2. Measures may be classified into six kinds : 1. Extension. 2. Capacity. 3. Weight. 4. Time. 5. Angles or Arcs. MEASURES OF EXTENSION. 3. Extension has length, breadth, and thickness. 4. A Line has length only. 5. A Surface or Area has length and breadth. 6. A Solid has length, breadth, and thickness. LINEAR MEASURE, 7. Linear Measure, also called Long Measure, is used in measuring lines and distances. In 8. Cloth Measure is practically out of use. measuring goods sold by the yard, the yard is divided into halves, fourths, eighths, and sixteenths. At U. S. Custom-Houses, in estimating duties, the yard is divided 11. The following are sometimes used: 3 Barley-corns, or Sizes 1 Inch. 4 Inches 33 Feet Used by shoemakers. 3 Inches 21.888 Inches = 1 Pace. = 1 Palm. 6 Points 12 Lines 1. The nautical mile (or knot) is the same as the geographical mile, and is used in measuring the speed of vessels. 2. The geographical mile is of bu or bo of the distance round the center of the earth. It is a small fraction more than 1.15 statute miles. 3. The length of a degree of latitude varies, being 68.72 miles at the equator, 68.9 to 69.05 miles in middle latitudes, and 69.30 to 69.34 miles in the polar regions. The mean or average length, 69.16, is the standard recently adopted by the U. S. Coast Survey. A degree of longitude is greatest at the equator, where it is 69.16 miles, and it gradually decreases toward the poles, where it is 0. 12. Surveyors' Linear Measure is used by land surveyors in measuring roads and boundaries of land. 1. A Gunter's Chain is the unit of measure, and is 4 rods, or 66 feet long, and consists of 100 links. 2. Engineers commonly use a chain or measuring tape, 100 feet long, each foot divided into tenths. 3. Measurements are recorded in chains and hundredths. |