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A

TREATISE

OF

MECHANICS,

THEORETICAL, PRACTICAL,

AND

DESCRIPTIVE.

BY OLINTHUS GREGORY, LL.D.

OF THE ROYAL MILITARY ACADEMY, WOOLWICH;

HONORARY MEMBER OF THE PHILOSOPHICAL SOCIETIES OF LONDON AND

NEWCASTLE-UPON-TYNE,

AND OF THE NEWCASTLE ANTIQUARIAN SOCIETY.

THE THIRD EDITION,

CORRECTED AND IMPROVED.

VOL. I.

CONTAINING

THE THEORY OF STATICS, DYNAMICS, HYDROSTATICS, HYDRO-

DYNAMICS, AND PNEUMATICS.

Philosophia mater omnium bonarum artium est.

CICERO.

Meta autem Scientiarum vera et legitima, non alia est, quam ut dotetur

vita humana novis inventis, et copiis. BACON. Nov. Org.

LONDON:

PRINTED FOR F. C. AND J. RIVINGTON; G. WILKIE; J. RICHARD-
SON; LACKINGTON AND CO.; Ģ. KEARSLEY; LONGMAN, HURST,
REES, ORME, AND BROWN; J. TAYLOR; BALDWIN, CRADOCK,
AND JOY; AND WALKER AND EDWARDS.

1815.

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TO THE RIGHT HONOURABLE

JOHN JOSHUA PROBY,

EARL OF CARYSFORT;

KNIGHT OF THE MOST ILLUSTRIOUS ORDER OF ST. PATRICK, &c. &c. &c.

MY LORD,

ALTHOUGH the promotion of the arts and sciences has been ever deemed the proper province of the great and noble, yet it has not always been the good fortune of those who employ their time and exertions in the dissemination of knowledge, to meet with a patron who is at once distinguished by his rank, his talents, and his zeal in the encouragement of useful performances. I cannot, therefore, but deem it a high honour, and a source of considerable gratification, that I am permitted to present a Treatise of Mechanics to the public, under your lordship's protection: and I have been doubly solicitous that the work which you have thus been pleased to encourage, may not be found altogether unworthy the approbation of such a patron.

When I reflect upon your lordship's eminent and accurate acquaintance with many of the subjects discussed in the following sheets, my diffidence might be justly alarmed; but I throw myself upon the candour and kindness I have so often experienced: and

though I am not vain enough to imagine that my undertaking will be found free from faults and errors, or that these can escape your notice; yet I have the satisfaction to know, notwithstanding, that whatever will stand the test of a correct and solid judgment, or may be found calculated to enlarge the stock of human knowledge, or more widely to diffuse an acquaintance with the principles of a branch of science of acknowledged utility, will not fail to receive your lordship's commendation and support.

Allow me, my lord, publicly to thank you for the numerous favours you have conferred upon me in different periods of my life, and to subscribe myself, with unfeigned respect, and the sincerest gratitude,

My lord,

Your lordship's most obliged

and most obedient Servant,

OLINTHUS G. GREGORY.

PREFACE.

IT has of late been a too prevailing opinion in this country, that

a man may become celebrated as a natural philosopher, and be very successful in the application of his knowledge to practical purposes, particularly in the construction of machinery, while he is completely unacquainted with the principles of mathematics. Among a variety of unpleasant consequences which have resulted from this erroneous opinion, may be reckoned, the rapid decline of the mathematical sciences in Britain, the dissemination of superficial and vague notions on physical topics, and the absolute necessity of having recourse to foreign publications for profound and extensive information on those subjects, which we should have supposed, had not experience convinced us to the contrary, Englishmen would have been proud to cultivate; since they were first placed upon an unshaken basis in the Principia of our own countryman, the illustrious Newton. It has been asserted by a competent judge, Dr. Robison, and it is mortifying to reflect that the assertion is true, "that while the continent has supplied us with most elaborate and useful treatises on various articles in physical astronomy, practical mechanics, hydraulics, and optics, there has not appeared in Britain half a dozen treatises worth consulting for the last forty years." We have, it is readily admitted, many popular works on mechanics, hydrostatics, &c. in which the principles are exhibited, and their application to the useful purposes in life illustrated by examples; but since their authors have scarcely ever aimed at demonstration, those who rest satisfied with the information they can gather from these treatises, can at best acquire but a kind of second-hand knowledge of unproved principles loosely floating in the mind; and must

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