Entered according to Act of Congress, in the year 1849,


In the Clerk's Office of the District Court of the United States for the Southern District of New York.





THE leading aim of the author, in preparing the present treatise, has been to produce a work of a more practical nature, and better adapted to the business of life, than any similar work hitherto offered to the public. Though the work is designed to be useful to all classes, embracing a greater variety of topics, and occupying a wider range than most treatises on mensuration, yet it is more particularly designed to meet the wants of the mechanical community, and of those whose professions involve construction, measurement, and the use of the sliding, or carpenter's rule.

As the work is strictly practical, very little matter of an abstruse nature has been introduced, and the algebraical formulas on which some of the rules are founded, have been omitted.

Though the author believes the present treatise contains more original matter than almost any other volume on a similar subject, yet he would cheerfully acknowledge his indebtedness to Bell's excellent treatise on Practical Mathematics, to Nicholson's British Mechanics, to Brande's Encyclopedia of Science, and to several other good works, from which he has borrowed a portion of his materials.

It is hoped that the work will meet with a favorable reception from the public, and that, while it answers the purpose of a good practical treatise, it will serve to inspire those into whose hands it may come, with a desire to acquire a thorough knowledge of the principles on which the more abstruse rules in this volume are founded; by which means they may be pre

pared, not only to improve and abbreviate known rules, but to deduce new ones for themselves.

Great pains have been taken to render the work accurate, concise, and easy to be understood; and, though it is far from being voluminous, it will, it is believed, be found to contain all the most useful and essential principles of that important branch of analysis, the mensuration of superficies and solids, the general principles involved in mechanics, and the construction of machinery, together with other matters of practical importance.

The carpenter's sliding rule is fully explained, and is applied to the mensuration of all regular superficies and solids, to finding the weight of bodies, to levelling, and to many other purposes.

The machinist, the carpenter, the lumberman, the millwright, the shipwright, the gauger, the cooper, the painter, and the engineer, will each find the work to be admirably adapted to supply his wants in the every-day business of life; and the student will find, in this volume, many things calculated to amuse and instruct.

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