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A TREATISE

ON THE

MATHEMATICAL THEORY

OF

ELASTICITY.

SlonDon: C. J. CLAY And SONS,

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CAMBRIDGE UNIVERSITY PRESS WAREHOUSE,

AVE MARIA LANE.

CamtriiBt: DEIGHTON, BELL AND CO.

%tif}is: F. A. BEOCKHAUS.

jUtfa Borli: MACMILLAN AND CO.

A TEEATISE

ON THE

MATHEMATICAL THEOKY

OF

ELASTICITY

BY

A. E. H. LOVE, M.A.

FELLOW AND LECTURER OP ST JOHN'S COLLEGE, CAMBRIDGE

VOLUME I.

CAMBRIDGE:
AT THE UNIVERSITY PRESS.

1892
[All Rights reserved.]

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Cambrfoge:

PRINTED BY C. J. CLAY, M.A. AND SONS, AT THE UNIVERSITY PRESS.

PKEFACE.

fT^HE present treatise is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity. He has unfortunately found himself unable to proceed with it, and I have therefore been obliged to take upon myself the whole of the work and the whole of the responsibility. I wish to acknowledge at the outset the debt that I owe to him as a teacher of the subject, as well as my obligation for many valuable suggestions chiefly with reference to the scope and plan of the work, and to express my regret that other engagements have prevented him from sharing more actively in its production.

The division of the subject adopted is that originally made by Clebsch in his classical treatise, where a clear distinction is drawn between exact solutions for bodies all whose dimensions are finite and approximate solutions for bodies some of whose dimensions can be regarded as infinitesimal. The present volume contains the general mathematical theory of the elastic properties of the first class of bodies, and I propose to treat the second class in another volume. At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof. Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest.

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