358 



SCIENCE. 



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



ciple and by contrast with Gauss's prin- 

 ciple, of such exceptional utility in the 

 development of modern physics ; finally the 

 development of the Leibnitzian doctrine of 

 work and vis viva into the law of the con- 

 servation of energy, which more than any 

 other principle has consciously pervaded 

 the progress of the nineteenth century. 

 Clausius's theorem of the 'Virial' (1870) 

 and Jacobi's (1866) contributions should 

 be added among others. 



The potential, though contained explic- 

 itly in the writings of Lagrange (1777), 

 may well be claimed by the last century. 

 The differential equation underlying the 

 doctrine had already been given by La- 

 place in 1782, but it was subsequently to 

 be completed by Poisson (1827). Gauss 

 (1813, 1839) contributed his invaluable 

 theorems relative to the surface integrals 

 and force flux, and Stokes (1854) his 

 equally important relation of the line and 

 the surface integral. Legendre (published 

 1785) and Laplace (1782) were the first 

 to apply spherical harmonics in expansions. 

 The detailed development of volume sur- 

 face and line potential has enlisted many 

 of the ablest w^riters, among whom Chasles 

 (1837, 1839, 1842), Helmholtz (1853), C. 

 Neumann (1877, 1880), Lejeune-Dirichlet 

 (1876), Murphy (1833) and others are 

 prominent. 



The gradual growth of the doctrine of 

 the potential would have been accelerated, 

 had not science to its own loss overlooked 

 the famous essay of Green (1828) in which 

 many of the important theorems were an- 

 ticipated, and of which Green's theorem 

 and Green's function are to-day familiar 

 reminders. 



Recent dynamists incline to the . uses of 

 the methods of modern geometry and to 

 the vector calculus with continually in- 

 creasing favor. Noteworthy progress was 

 first made in this direction by Moebius 

 (1837-43, 'Statik,' 1838), but the power 



of these methods to be fully appreciated 

 required the invention of the 'Ausdehn- 

 ungslehre,' by Grassmann (1844), and of 

 'quaternions,' by Hamilton (1853). 



Finally the profound investigations of 

 Sir Robert Ball (1871, et seq., 'Treatise') 

 on the theory of screws with its immediate 

 dynamical applications, though as yet but 

 little cultivated except by the author, must 

 be reckoned among the promising heritages 

 of the twentieth century. 



On the experimental side it is possible to 

 refer only to researches" of a strikingly 

 original character like Foucault's pendu- 

 lum (1851) and Fizeau's gyrostat; or like 

 Boys's (1887, et seq.) remarkable quartz- 

 fiber torsion-balance, by which the Newton- 

 ian constant of gravitation and the mean 

 density of the earth originally determined 

 by Maskelyne (1775-78) and by Cavendish 

 (1798) were evaluated with a precision 

 probably superior to that of the other re- 

 cent measurements, the pendulum work of 

 Airy (1856) and Wilsing (1885-87), or 

 the balance methods of Jolly (1881), 

 Konig and Richarz (1884). Extensive 

 transcontinental gravitational surveys like 

 that of Mendenhall (1895) have but begun. 



HYDRODYNAMICS. 



The theory of the equilibrium of liquids 

 was well understood prior to the century 

 even in the case of rotating fluids, thanks 

 to the labors of Maclaurin (1742), Clairaut 

 (1743) and Lagrange (1788). The gen- 

 eralizations of Jacobi (1834) contributed 

 the triaxial ellipsoid of revolution and the 

 case has been extended to two rotating at- 

 tracting masses by Poincare (1885) and 

 Darwin (1887). The astonishing revela- 

 tions contained in the recent work of Poin- 

 care are particularly noteworthy. 



Unlike elastics, theoretical hydrodynam- 

 ics passed into the nineteenth century in 

 a relatively well-developed state. Both 

 types of the Eulerian equations of motion 



