NA TURE 



97 



TIIUKSDAY. MAY 31, 1894. 



MA THE MA TIC A L THEORIES 

 ELASTICITY. 



OF 



A History of ihe Elasticity and Strength of Materials. 

 Vol.11. Pai-tsI and II. By the late Isaac Todhunter, 

 D.Sc, F.R.S. Edited and completed by Karl Pearson, 

 M..^., Professor of Applied Mathematics, University 

 College, London. fCambridge : at the University 

 Press, 1S93. 



A Treatise on the Mathematical Theory of Elasticity. 

 By A. E. H. Love, M.A., Fellow and Lecturer of St. 

 John's College, Cambridge. V'ol. II. (Cambridge : at 

 the University Press, 1893.) 



Introduction to the Mathematical Theory of the Stress 

 and Strains of Elastic Solids. By Benjamin William- 

 son, D.Sc, D.C.L., F.R S., Fellow and Senior Tutor 

 of Trinity College, Dublin. (London : Longmans, 

 Green, and Co., 1894.) 



Theory of Structures and Strength of Materials. By 

 Henry T. Bovey, M.A., D.C.L., F.R.S.C, Professor of 

 Civil Engineering and Applied Mechanics, M'GiU 

 University, Montreal. (New York: John Wiley and 

 Sons. London : Kegan Paul, Trench, Trubner, and 

 Co., 1893.) 



PROFESSOR KARL PEARSON is to be congratu- 

 lated on having brought his task, after nine years' 

 hard work, to a conclusion ; and the result would sur- 

 prise Dr. Todhunter, the original projector of the treatise, 

 could he see the three large volumes, of 2200 pages and 

 iSoo articles, which have grown from the notes he made 

 for a modest history of elasticity. The labour in the 

 preparation of this history must have been enormous ; it 

 is the sort of work which is best left for a (lerman to 

 carry out ; even the cutting of the pages is sufficient to 

 give the reviewer a headache and mental indigestion. 



The assistance of Mr. C. Chree is gratefully acknow- 

 ledged in the preface, also of M. Flamant, Professor at 

 the Ecole des Fonts et Chaussdes, Paris ; and the Syndics 

 of the Cambridge University Press are thanked for their 

 financial assistance in the production of the book. 



The part relating to St. Venant's writings, which forms 

 the first half of p.irt i , vol. ii.,. was issued separately 

 some four years ago, and received notice in these columns 

 in the number for March 20, 1890. 



It is impossible within any reasonable limits to give an 

 idea of the developments which the subject has received 

 at the hands of the various mathematicians whose work 

 is cited in the pages. A mere enumeration of the principal 

 names — St. Ven mt, Rankine, Kupffer, Wertheim, 

 Zoppritz, Neumann, Kirchhoff, Clebsch, Boussinesq, 

 Thomson and Tait, &c. — and the list of chief elasticians 

 given on p. xv., will show that the subject has attracted 

 the attenti(m of the principal analysts, who seek for the 

 stimulus and directing influence of real physicial 

 problems. 



It must be allowed that the mode of attack of some 



of these problems is, by reason of their extreme difficulty, 



I alcuLited to shock the mathematical prudery of certain 



pure analysts ; and also that there is not yet complete 



NO. I 283, VOL. 50] 



accord among elasticians in the results they obtain ; 

 but then, to quote Rankine's eloquent words from his 

 " Preliminary Dissertation on the Harmony of Theory 

 and Practice in Mechanics" : " The question in Practical 

 Science is — ivhat are we to do? — a ([uestion which 

 involves the necessity for the immediate adoption of 

 some rule of working. In doubtful cases we cannot 

 allow our machines and our works of improvement to 

 wait for the advancement of science ; and if existing data 

 are insufficient to give an exact solution of the question, 

 that approximate solution must be acted upon which the 

 best data attainable show to be the most probable." 



" In Theoretical Science, the question is — What arewe 

 to think? and when a doubtful point arises for the solu- 

 tion of which either experimental data are wanting, or 

 mathematical methods are not sufficiently advanced, it is 

 the duty of philosophic minds not to dispute about the 

 probability of conflicting suppositions, but to labour for 

 the advancement of experimental inquiry and of 

 mathematics, and to await patiently the time when 

 these shall be adequate to solve the question." 



So far as concerns the analyst who despises the 

 stimulus that arises from the contemplation of the difficul 

 ties of an actual problem, the above advice in Theoretical 

 Science amounts very much to what King Paramount says 

 to the wise men of Utopia — " Go and play in the corner." 



A distinguished biologist once said to the editor of 

 the present work, that he had for many years given up 

 endeavouring to ascertain what others had done or were 

 doing in his subject. To follow the great mass of con- 

 temporary work meant to expend his time in historical 

 investigations rather than in original research (p. 488). 

 But the present volumes on the history of elasticity will 

 save this expenditure of time, and enable the investigator 

 to start where others have left off 



The curious spiral lines, crossing at 45^ the circles 

 concentric with a punched hole, called Liider's curves, and 

 shown in the frontispiece of part ii., vol. ii., are interesting 

 in confirming \V. Carus Wilson's theory, that plastic 

 yielding of an elastic metal takes place chiefly by shear- 

 ing in directions inclined at 45" to the principal tension. 

 The subject has recently been discussed in the Comptes 

 Rendus, by M. Hartman, who brings out these curves 

 more clearly by biting into the steel with acid. 



Mr. Love's vol. ii. of his treatise on the mathematical 

 theory of elasticity also completes the work, of which the 

 first volume was noticed in N.^TURE, April 6, 1893. 



A valuable historical chapter begins the volume, but 

 we are puzzled to see the authors of a well-known treatise 

 on Natural Philosophy given as Kelvin and Tait ; it 

 might as well be said that the Duke of Wellington com- 

 manded the British Forces in the Peninsula. 



We learn incidentally that the battle over the theory of 

 the curved plate is still raging, and that the rival theories 

 of Lord Rayleigh and Mr. Basset do not yet meet with 

 the author's complete acceptance ; the investigations of 

 Mr. Bryan and of the author on the wrinkling of the 

 plating of a ship, and on the collapse of boiler flues, dis- 

 cussed in chapter xxiii., will do much to bring into focus 

 the real points at issue. 



The problem of the spiral spring, with Kirchhotf's 

 kinetic analogue of the steady motion of a gyrostat, is 

 treated in an interesting manner ; what is the modifica- 



V 



