356 



SCIENCE. 



[N. S. Vol. XXII. No. 560. 



of Betti (1872), applied by Cerruti (1882) 

 to solids with a plane boundary— problems 

 to which Lame and Clapeyron (1828) and 

 Boussinesq (1879-85) contributed by other 

 methods; the case of the strained sphere 

 studied by Lame (1854) and others; Kirch- 

 hoff 's flexed plate (1850) ; Rayleigh's treat- 

 ment of the oscillations of systems of finite 

 freedom (1873) ; the thermo-elastic equa- 

 tions of Duhamel (1838), of F. Neumann 

 (1841), of Kelvin (1878) ; Kelvin's analogy 

 of the torsion of prisms with the supposed 

 rotation of an incompressible fluid within 

 (1878) ; his splendid investigations (1863) 

 of the dynamics of elastic spheroids and the 

 geophysical applications to which they were 

 put. 



Finally, the battle royal of the molecular 

 school following Navier, Poisson, Cauchy 

 and championed by de St. Venant, with 

 the disciples of Green headed by Kelvin 

 and Kirchhotf— the struggle of the fifteen 

 constants with the twenty-one constants, in 

 other words— seems to have temporarily 

 subsided with a victory for the latter 

 through the researches of Voigt (1887-89). 



CRYSTALLOGRAPHY, 



Theoretical crystallography, approached 

 by Steno (1669), but formally founded by 

 Haiiy (1781, 'Traite,' 1801), has limited 

 its development during the century to sys- 

 tematic classifications of form. Thus the 

 thirty-two type sets of Hessel (1830) and 

 of Bravais (1850) have expanded into the 

 more extensive point series involving 230 

 types due to Jordan .(1868), Sohncke 

 (1876), Federow (1890) and Schoenfliess 

 (1891). Physical theories of crystalline 

 form have scarcely been unfolded. 



CAPILLARITY. 



Capillarity antedated the century in 

 little more than the provisional, though 

 brilliant, treatment due to Clairaut (1743). 

 The thpcry arose in almost its present state 



of perfection in the great memoir of La- 

 place (1805), one of the most beautiful 

 examples of the Newton-Boscovichian 

 (1758) molecular dynamics. Capillary 

 pressure was here shown to vary with the 

 principal radii of curvature of the exposed 

 surface, in an equation involving two con- 

 stants, one dependent on the liquid only, 

 the other doubly specific for the bodies in 

 contact. Integrations for special condi- 

 tions include the cases of tubes, plates, 

 drops, contact angle, and similar instances. 

 Gauss (1829), dissatisfied with Laplace's 

 method, virtually reproduced the whole 

 theory from a new basis, avoiding molecu- 

 lar forces in favor of Lagrangian displace- 

 ments, while Poisson (1831) obtained La- 

 place's equations by actually accentuating 

 the molecular hypothesis; but his demon- 

 stration has since been discredited. Young 

 in 1805 explained capillary phenomena by 

 postulating a constant surface tension, a 

 method which has since been popularized 

 'dj Maxwell ('Heat,' 1872). 



With these magnificent theories pro- 

 pounded for guidance at the very threshold 

 of the century, one is prepared to antici- 

 pate the wealth of experimental and of de- 

 tailed theoretical research which has been 

 devoted to capillarity. Among these the 

 fascinating monograph of Plateau (1873), 

 in which the consequences of theory are 

 tested by the behavior both of liquid lamel- 

 lae and by suspended masses, Savart's 

 (1833), and particularly Rayleigh's, re- 

 searches with jets (1879-83), Kelvin's rip- 

 ples (1871), may be cited as typical. Of 

 peculiar importance, quite apart from its 

 meteorological b'^'.aring, is Kelvin's deduc- 

 tion (1870) of the interdependence of sur- 

 face tension and vapor pressure when vary- 

 ing with the curvature of a droplet. 



DIFFUSION. 



Diffusion was formally introduced into 

 physics by Graham (1850). Fick (1855), 



