SCIENCE. 



[N. S. Vol. XI. No. 264. 



to the theory of structures, to the theory of 

 hydromechanics, to the elastic solid theory 

 of light, and to the theory of crystalline 

 media. 



In closing these very inadequate allusions 

 to this intensely practical and abstrusely 

 mathematical science, it is fitting that 

 attention should be called to the magnifi- 

 cent labors of the ' dean of elasticians,' M. 

 Barr6 de Saint- Venant. It was the object 

 of his life-work to make the theory of elas- 

 ticity serve the utilitarian purposes of the 

 engineer and at the same time to divest it 

 so far as possible of all empiricism. His 

 epoch-making memoir* of 1853, on the 

 torsion of prisms, is not only a classical 

 treatise from the practical point of view, 

 but one of equal interest and importance in 

 its theoretical aspects. His investigations 

 are everywhere delightfully interesting and 

 instructive to the physicist ; and many 

 parts of them are replete, as observed by 

 Kelvin and Tait,t with "astonishing the- 

 orems of pure mathematics, such as rarely 

 fall to the lot of those mathematicians who 

 confine themselves to pure analysis or geom- 

 etr}', instead of allowing themselves to be 

 led into the rich and beautiful fields of 

 mathematical truth w^hich lie in the way of 

 physical research. " More important still in 

 a didactic sense are his annotated edition 

 of ISTavier's ' Eesistance des Corps Solides,' 

 of 1864, and his annotated edition of the 

 French translation of the ' Theorie der Elas- 

 ticitat fester Korper,' of Clebsch, which 

 appeared in 1883. These monumental 

 works, whose annotations and explanatory 

 notes quite overshadow the text of the 

 original authors, must remain for a long 

 time standard sources of information as to 

 the history, theorj^ methods and results of 

 this complex subject. The luminous expo- 



* ' Miimoire sur la torsion des prismes,' etc., pnb- 

 lished in Memuires des samnts etrangeres. Tome XIV., 

 1855. 



t Natural Philo.sophy, ad ed., Part II., p. 249. 



sition, the penetrating insight into physical 

 relations, and the scientific candor in his 

 criticism of other authors, render the work 

 of Saint- Venant worthy of the highest ad- 

 miration. 



Closely allied to the theory of elasticity, 

 though historically much older, is the sci- 

 ence of hydromechanics. The latter is, in- 

 deed, included essentially in the former ; 

 and probably the great treatises of the next 

 century will merge them under the title of 

 molecular mechanics. It may seem some- 

 what singular that the mathematical theory 

 of solids should have originated so many 

 centuries later than the theory of fluids ; 

 for at first thought, tangible though flexible 

 solids would appear much more susceptible 

 of investigation than mobile liquids and in- 

 visible gases. But a little reflection leads 

 one to the conclusion that it was, in fact, 

 much easier to observe the data essential 

 to found a theory of hydromechanics than 

 it was to discover the principles which led 

 to the theory of stress and strain ; and the 

 time interval between Archimedes and Gal- 

 ileo may serve perhaps as a rough measure 

 of the relative complexity of hydrostatics 

 and the theory of flexure and torsion of 

 beams. It must not be inferred, however, 

 that the simplicity of the phenomena of 

 fluids in a state of relative rest extends to 

 the phenomena of fluids in a state of rela- 

 tive motion ; for the gap that separates 

 hydrostatics from hydrokinetics is one 

 which has not yet been fully bridged even 

 by the aid of the powerful resources of. 

 modern mathematics. 



The elements of hydrokinetics, with which 

 branch of hydromechanics this sketch is 

 alone concerned, were laid down by Euler 

 about the middle of the last century.* It 



* 'Principes g^neraux du niouvement desflui des. ' 

 Hiatoire de V Academic de Berlin, 1755. 



'DePrincipiis motus fluidorum.' Novi Commentarii 

 Academise, Scientiarum Imperialis Petropolitanse, Tomvis 

 XLV., Pars I., pro anno 1759. 



