March 20, 1890] 



NATURE 



459 



curved plate, to begin by neglecting the terms depending 

 on the stretching of the material, which involve the first 

 power of the thickness of the plate, in comparison with 

 the terms depending on the bending, involving the cube 

 of the thickness ; thus apparently neglecting the first 

 power compared with the third power of small quan- 

 tities. But, if we take a thin sheet of brass or iron in our 

 hands, we shall find it quite easy to bend, but apparently 

 impossible to stretch or shear in its own plane, showing 

 that the stretching stresses may be considered as non- 

 existent, by reason of requiring such large forces to pro- 

 duce them. 



Before pure mathematical treatment can make much 

 progress in Elasticity, much more experimental demon- 

 stration is required of the behaviour of pieces of metal of 

 mathematical form under given applied forces ; and such 

 experiments can be carried out in testing-machines, now 

 forming an indispensable part of a physical laboratory. 



Saint- Venant's memoir on torsion, analysed in Section 

 I., is familiar to us through its incorporation by Thomson 

 and Tait, and shows that Saint- Venant carried out, with 

 the comparatively crude methods at his disposal, valuable 

 experiments, from which much theoretical deduction has 

 been made ; the analogues of the mathematical analysis 

 in the problem of the torsion of the cylindrical beam of 

 given cross section, and of the flow of viscous liquid 

 through a pipe of the same section, or of the rotational 

 motion of a frictionless liquid filling the cylinder being 

 very striking. Prof Pearson introduces great elegance 

 and interest into the series which arise by a free use of 

 the notation of hyperbolic functions, and we think there 

 is still some interesting work for pure mathematicians in 

 the identification of those series which are expressible by 

 elliptic functions. But it certainly looks curious to find 

 in § [287] the old familiar polar co-ordinates treated as 

 mere conjugate functions, without reference to their geo- 

 metrical interpretation. 



Section II. is occupied with the analysis of Saint- 

 Venant's memoirs of 1854 to 1864, in which he attacks 

 such questions in practical elasticity as the longitudinal 

 impact of bars, illustrated by very ingenious graphic 

 diagrams, and also the conditions of stress of a cylindrical 

 shell, in equilibrium under given applied internal and 

 external pressures. This is the problem required in the 

 scientific design of modern built-up artillery ; and it is 

 noticeable that Saint- Venant's solution differs materially 

 from Lamd's, subsequently popularized by Rankine, the 

 theory employed, as far as it will go, by scientific gun- 

 designers all over the world. 



The researches in technical Elasticity of Section III. 

 arose in the annotations of Navier's " Lemons sur la 

 Resistance des Corps solides " ; the mantle of Navier 

 descended on the shoulders of Saint- Venant, and ulti- 

 mately the notes of Saint- Venant overwhelmed the original 

 text of his master Navier ; and, according to Section IV., 

 Saint-Venant has practically done the same thing with 

 Clebsch's " Elasticitat." 



Being the mathematical referee for all the difficult 

 theoretical problems arising with the extensive use of 

 the new materials iron and steel in architecture and 

 engineering, Saint-Venant was provided with a number 

 of useful problems on which to exercise his ingenuity ; 

 such as the impact of bars, the flexure of beams due to a 



falling weight or a travelling load, the critically dangerous 

 speeds of fly-wheels and piston-rods, and so on ; all 

 problems hitherto solved by practical rule of thumb, the 

 practical constructor encountering and opposing the 

 difficulties without knowing why and how they arose. 



Saint- Venant's investigations urgently need extension 

 and application to the critically dangerous conditions 

 which can arise in the stresses in artillery, when the 

 dynamical phenomena are analysed, due to the sudden 

 and periodic application of the powder pressure, and to 

 the wave-like propagation and reflection of the stresses in 

 the material. At present, we can only investigate the 

 theoretical strain set up in the material of the gun by a 

 steady hydrostatic pressure equal to the maximum pres- 

 sure of the powder, employing Lamd's formulas, and then 

 employ an arbitrary factor of safety, say 10, in the design 

 of the gun, to provide against the contingencies of the 

 dynamical phenomena we have not yet learnt how to 

 discuss. 



In the old times, before the Cambridge Mathematical 

 Tripos was reduced to its present meagre curriculum, the 

 examiner would have found the present volume very 

 useful in suggesting good ideas, capable of testing rea- 

 sonably the mathematical power of the candidates ; at 

 present, the chief class to profit by the present work are 

 the practical constructors, who will learn where to look 

 for the useful information on the narrow technical point 

 which concerns them. 



Prof Pearson has brought his onerous task one step 

 nearer to completion in this interesting volume, a monu- 

 ment of painstaking energy and enthusiasm. 



A. G. Greenhill. 



GLOBES. 



Hues' s Treatise on the Globes (1592). Edited by Clements 

 R. Markham, C.B., F.R.S. (London ; Reprinted by 

 the Hakluyt Society, 1889.) 



THE Hakluyt Society has for its object the reprinting 

 of rare or unpublished voyages and travels, and 

 few are worthier of this honour than the *' Tractatus de 

 Globis " of Robert Hues. The author of this work was 

 an intimate friend of Sir Walter Raleigh, and combined 

 book-learning with practical knowledge gained by joining 

 in some of the voyages to the New World with navigators 

 whose names have made the sixteenth century famous. 

 He strongly urged that his countrymen would have still 

 further surpassed their Spanish and Portuguese rivals 

 if they had "but taken along with them a very reasonable 

 competency and skill in geometry and astronomy." In 

 those days logarithms were unknown, and the solution of 

 the problems of nautical astronomy required advanced 

 mathematical knowledge. It was hoped that this diffi- 

 culty would be overcome by the extended use of globes, 

 which at once reduces these complex questions to approxi- 

 mate solution by inspection. After the construction of 

 the Molyneux globes, Hues's treatise came into very 

 general use, and no doubt played an important part in 

 the explorations of the succeeding century. 



It seems strange in these days, when a globe can be 

 purchased for a few shillings, to read that only three 

 centuries ago the construction of globes entailed such 

 great expense that the liberal patronage of a merchant 



