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performing the operation; as the proof may render simple and clear some part or the whole of an operation that was before complicated and obscure.

The improvements in Percentage made necessary by the financial changes of the last few years are especially noticeable. The different kinds of United States' Securities, Bonds, and Treasury Notes are described, and their comparative value in commercial transactions illustrated by practical examples. The difference between Gold and Currency, and the corresponding difference in prices, exhibited in trade, are taught and illustrated, and many other things that every commercial student and business man ought to know and understand.

AUGUST, 1860.

IMPROVED EDITION.

Such changes only have been made in the present edition as were necessary to conform to law and usage, and to meet a demand from many of the best teachers of the country for a full and practical treatise on Mensuration. Hence Foreign Exchange has been so modified in the Tables and Examples as to conform to the Act of March 3, 1873, and to present usage.

Thirty-six pages of useful and practical matter on Mensuration and Measurements, have been carefully prepared and substituted at the end of the book for the lengthy treatise of the Metric System heretofore presented, and which is scarcely ever used in this country.

To avoid repetition, as well as to put in a more condensed form, the Principles and Applications of the Square and Cube roots that intervened between “Evolution” and “Series in former editions, have been embodied in these thirty-six pages, and also so much of the Metric System as is of any practical value.

It is hoped that these improvements will give new life to a book that. has already proved its merits by the large and increasing circulation it has obtained.

JULY, 1875.

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144

UNITED STATES MONEY

Notation and Numeration ......

Reduction ......

Operations....

Problems......

Ledger Accounts

Accounts and Bills..

Continued Fractions..........

145

147

147

150

153

153

161

COMPOUND NUMBERS.

Measures of Extension ......

Measures of Capacity.

Measures of Weight

Measure of Time......

Measure of Angles

Miscellaneous Tables.......

Government Standards of Measures and Weights.....

English Measures and Weights.....

French Measures and Weights..

Money and Currencies..

Reduction .......

Reduction Descending...

164

170

171

175

177

178

179

182

184

187

192

192

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