Leçons sur l'application de la Mécanique... was published I think in 1863 or 1864 with notes by Saint-Venant, but I have not seen it."

Of the majority of the other memoirs falling before 1870, there exist in most cases only brief extracts in French from the introductory paragraphs. This would be sufficient to shew, without the occasional remarks for changes scattered about the pages, that the MS. is not in the form in which Dr Todhunter would finally have published it. To these considerations must be added those arising from the fact that all the memoirs and papers after 1871, including some of the most important of Saint-Venant's researches on intermolecular action, plasticity, impact and above all the Annotated Clebsch (see our Arts. 245-408), fall beyond the date to which Dr Todhunter had carried his work.

Such then are the reasons which have led to the reconstruction of this portion of the History. I have felt the heavy responsibility involved in adopting this course. But it has seemed to me that the best memorial to the first Cambridge historian of mathematics would be that the last history bearing his name should have the widest possible sphere of usefulness. That usefulness will, I am firmly convinced, be best obtained by its comprehensive character, by its attempt to be a Repertorium of elasticity rather than an Historique Abrégé of its purely mathematical side. I recognise fully with my kindly French critic of the Bulletin the importance of the latter, but its possibility will only be actual on the completion of the former. To follow, even at a distance, Wiedemann rather than Bertrand must be the editor's duty; not an easy one it must be confessed, but one requiring time and labour rather than historical talent and insight. In the words of the German proverb: wer giebt was er hat, der ist werth, dass er lebt.

For assistance in the revision of the proofs of this part I have in the first place to thank Mr C. Chree of King's College, Cambridge. His suggestions and corrections have been of extreme value to me, and his criticisms enabled me to remove many imperfections. Mr W. H. Macaulay has again lent me his aid in the discussion of mathematical and other difficulties; while I am much indebted to M. Flamant, Professeur à l'École des Ponts et Chaussées, for the generosity with which he has devoted a portion of his busy time to reading the proofs of this account of his friend and master's researches. His corrections have been of much service, especially in the French portions of the work. For the temporary index attached to this part I am, so far as the titles are concerned, personally responsible. Perhaps, only the writer of a book is in a position to prepare an efficient set of titles. I have, however, to thank Miss L. Eckenstein for the more laborious task of alphabetically arranging the titles and for a verification of the entries.

UNIVERSITY COLLEGE, LONDON,

December 29, 1888.

KARL PEARSON.

SECTION II.

Memoirs of 1854-1864, Flexure, Distribution of

Elasticity, etc.

51-105

References throughout this extract to the articles of the first volume have an
asterisk affixed, e.g. Art. 128*. Numbers without an asterisk refer to the articles
of the extract.

ERRATA. V

Art. 4 (8) dele reference to Hopkins.

Art. 171 (a) for neutral line read neutral axis.

CHAPTER X.

SAINT-VENANT, 1850-1886.

SECTION I. Torsion.

[1.] WE commence our second volume with some account of the later work of the great French elastician whom we are justified in placing beside Poisson and Cauchy. From the last memoir referred to in our first volume till June 13, 1853 we have nothing to report. A slight note, however, entitled: Divers résultats relatifs à la torsion, which was read to the Société philomathique (Bulletin, February 26, 1853, or L'Institut, no. 1002, March 16, 1853), sufficiently indicates that our author had been diligently at work during these years on his new theory of torsion. On the 13th of June, 1853, his epoch-making memoir was read to the Academy (Comptes rendus, T. xxxvI. p. 1028). The memoir was inserted in T. XIV. of the Mémoires des Savants étrangers, 185, pp. 233-560, under the title:

Mémoire sur la Torsion des Prismes, avec des considérations sur leur flexion, ainsi que sur l'équilibre intérieur des solides élastiques en général, et des formules pratiques pour le calcul de leur résistance à divers efforts s'exerçant simultanément.

We have referred to it in our first volume as the memoir on Torsion, and shall continue to do so.

The memoir was referred by the Academy to a committee consisting of Cauchy, Poncelet, Piobert and Lamé. Their report drawn up by Lamé (Comptes rendus, T. XXXVII., December 26, 1853, pp. 984-8) speaks very highly of the memoir. We cite the concluding words:

S.- V.

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