Il appartenait à cette noble race d'esprits tout à la fois force, ornement et

consolation de notre espèce, qui, ensemble ou isolés, laissent après eux, dans l'histoire, une traînée lumineuse, à laquelle s'allument sans cesse de nouvelles intelligences, pour former un courant toujours plus vaste de vraie et haute civilisation.

PREFACE1.

THE portion of the second volume of the History of Elasticity now published as an extract is devoted solely to the later researches of Saint-Venant. It may appear to the reader that an undue amount of space has been allotted to this one scientist, but it must be remembered that these researches extend over a period of thirty-five years, and in a certain sense contain in themselves the history of elasticity during those years. Their importance arises not only from what they themselves contribute to our subject, but from the fact that so much of the important work of the last three decades has been suggested by or has followed the lines of Saint-Venant's papers. The contributions of such elasticians as Kirchhoff and Clebsch, as Boussinesq and Lévy to both elasticity and plasticity frequently take their starting point from an idea of Saint-Venant's, while a host of minor memoirs help to fill up the gaps in his work. Thus our Chapter X. may be taken as the frame, the stoutness and solidity of which will enable us the more readily to build up the remainder of our history. By explaining the ideas, definitions and methods of the modern science of elasticity, it allows of a more succinct and orderly account of the contemporary work.

1 This preface as well as the index refer only to the present extract.

S.-V.

b

This use of Saint-Venant's researches as a basis for our treatment of the innumerable memoirs of the last thirty and more years is, however, far from the sole purpose which I hope may be served by the fulness of Chapter X. and by its separate publication at the present time. There are two special reasons the importance of which only gradually dawned upon me as I worked through the papers of Saint-Venant and those of some of his more immediate disciples. The first of these reasons is the want of an English text-book on elasticity, which deals with that portion of the subject which is of most interest and value to physical and technical students. The light which elasticity can throw on atomic and molecular problems, its value as a key to the inmost recesses of Nature's laboratory, -is well brought out in much of Saint-Venant's work; while on the other hand we find questions of impact, of plasticity, of combined strain and absolute strength dealt with in a manner which, if sometimes not final, is always suggestive. We live in an age when the physicist awaits with not unreasonable excitement for greater revelations than even those of the past two years about the ether and its atomic offspring; but we live also in an age, when the engineer is making huge practical experiments in elasticity, and when true theory is becoming an absolute necessity for him, if his experiments are to be of practical as well as of theoretical value. Small ripples of ill feeling such as spread from the recent meeting of the British Association through the scientific and technical journals cannot hinder the strong current which is carrying the practical engineer rapidly forward into theoretical elasticity, and which must in the end compel the most hardened of mathematical elasticians to leave that transcendental island where all elasticity is 'perfect,' and every load impossible, for the more imperfect but possible region of technical problems. It is this conviction of the pressing

want of an introduction to elasticity, which should supply the needs of physical and technical students, together with the essentially modern character of Saint-Venant's researches, which has led me to believe that a full account of those researches would form, at any rate for the present, the most luminous and suggestive guide possible for such students. This part of the second volume may be looked upon as an endeavour to fill for the time being this defect in our scientific literature.

But the second reason for its publication weighed with me almost as much. The more I studied Saint-Venant's work, the more new directions it seemed to me to open up for original investigation of the most valuable kind. It suggested innumerable unsolved problems in atomic physics, in impact, in plasticity and in a variety of other branches of elasticity, which do not seem beyond solution, and the solution of which if obtained would be of extreme importance. I felt convinced that a study of SaintVenant's researches would be a most valuable directive to the several young scientists, whose recent memoirs shew their interest in elasticity as well as their mathematical capacity. Many of the problems raised by Saint-Venant's suggestive memoirs were quite beyond my powers of analysis, and I recognised that the most useful task I could undertake, was by a careful account of the memoirs themselves to lead the more competent on to their solution. Judging by the time it has taken me to study and analyse these memoirs, I am justified, perhaps, in thinking that this account of them will at least save labour for other workers in the same field; the difficulty nowa-days is not so much to do original work, as to find out within the space of an ordinary life-time what is 'original' work-not only what is not done, but what wants doing. This extract, then, from Volume II. may be a helpful, if it cannot be a thorough

guide in this direction, till the years have given time for the completion of the whole History.

The responsibility, however, for the space and the manner in which Saint-Venant's researches have been dealt with rests entirely with the editor. Hence any disproportion, any possibly crude opinions, any erroneous criticism in this part of the work must be attributed to him and not to the author. The articles in this part due to the late Dr Todhunter are only three or four in number and these refer to the less important memoirs. They are marked as in Volume I. by the omission of square brackets round the article number, e.g. 101, 102, 103. This editorial preponderance requires some explanation, which will be found partly in a consideration of Dr Todhunter's original plan, partly in the dates of Saint-Venant's memoirs. As I have pointed out in the preface to Volume I. the original plan of this work was a first volume devoted to 'Theory' and a second to 'History.' Thus it arose that the important memoirs on Torsion and on Flexure were incorporated in the 'Theory' volume, and the manner in which they appear in that text book does not allow of their transfer to the 'History.' Large parts of these memoirs were at the same time omitted as having little mathematical interest, for example the entire discussions of the "fail-limit" formula and of combined strain: see Arts. 5, 52-60, etc. of this Part. Further the memoirs on Impact (written before 1870) were dismissed as falling outside the limits which Dr Todhunter had set to his work. Thus he wrote of the memoirs on transverse impact, that they form “ an interesting investigation of a mechanical problem, but it does not belong to our subject." The large section I have devoted to the Leçons de Navier would also not have formed part of the original plan. The only reference to this work which occurs in Dr Todhunter's MS. is the following: "The third edition of Navier's