36 PHYSICS 



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 Ausdehnungs- 

 lehre, 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 pendulum (1851) 

 and Fizeau's gyrostat; or like Boys's (1887, et seq.) remarkable 

 quartz-fibre torsion-balance, by which the Newtonian constant 

 of gravitation and the mean density of the earth originally deter- 

 mined by Maskelyne (1775-78) and by Cavendish (1798) were evalu- 

 ated with a precision probably superior to that of the other recent 

 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 generalizations of Jacobi (1834) contributed the triaxial ellip- 

 soid of revolution, and the case has been extended to two rotating 

 attracting masses by Poincare (1885) and Darwin (1887). The 

 astonishing revelations contained in the recent work of Poincare 

 are particularly noteworthy. 



Unlike elastics, theoretical hydrodynamics passed into the nine- 

 teenth century in a relatively well-developed state. Both types of 

 the Eulerian equations of motion (1755, 1759) had left the hands 

 of Lagrange (1788) in their present form. In relatively recent times 

 H. Weber (1868) transformed them in a way combining certain 

 advantages of both, and another transformation was undertaken 

 by Clebsch (1859). Hankel (1861) modified the equation of con- 

 tinuity, and Svanberg and Edlund (1847) the surface conditions. 



Helmholtz in his epoch-making paper of 1858 divided the subject 

 into those classes of motion (flow in tubes, streams, jets, waves) 

 for which a velocity potential exists and the vortex motions for 

 which it does not exist. This classification was carried even into 

 higher orders of motion by Craig and by Rowland (1881). For cases 

 with a velocity potential, much progress has been made during 



