38 PHYSICS 



tides due to Newton (1687) and Laplace (1774), through the labors 

 of Airy, Kelvin, and Darwin. 



Finally the forbidding subject of vortex motion was gradually 

 approached more and more fully by Lagrange, Cauchy (1815, 1827), 

 Svanberg (1839), Stokes (1845); but the epoch-making integrations 

 of the differential equations, together with singularly clear-cut inter- 

 pretations of the whole subject, are due to Helmholtz (1858). Kelvin 

 (1867, 1883) soon recognized the importance of Helmholtz's work 

 and extended it, and further advance came in particular from J. J. 

 Thomson (1883) and Beltrami (1875). The conditions of stability 

 in vortex motion were considered by Kelvin (1880), Lamb (1878), 

 J. J. Thomson, and others, and the cases of one or more columnar 

 vortices, of cylindrical vortex sheets, of one or more vortex rings, 

 simple or linked, have all yielded to treatment. 



The indestructibility of vortex motion in a frictionless fluid, its 

 open structure, the occurrence of reciprocal forces, were compared 

 by Kelvin (1867) with the essential properties of the atom. Others 

 like Fitzgerald in his cobwebbed ether, and Hicks (1885) in his vortex 

 sponge, have found in the properties of vortices a clue to the pos- 

 sible structure of the ether. Yet it has not been possible to deduce 

 the principles of dynamics from the vortex hypothesis, neither is the 

 property which typifies the mass of an atom clearly discernible. 

 Kelvin invokes the corpuscular hypothesis of Lesage (1818). 



Viscosity 



The development of viscous flow is largely on the experimental 

 side, particularly for solids, where Weber (1835), Kohlrausch (1863, 

 et seq.), and others have worked out the main laws. Stokes (1845) 

 deduced the full equations for liquids. Poiseiulle's law (1847), the 

 motion of small solids in viscous liquids, of vibrating plates, and other 

 important special cases, has yielded to treatment. The coefficients 

 of viscosity defined by Poisson (1831), Maxwell (1868), Hagenbach 

 (1860), O. E. Meyer (1863), are exhaustively investigated for gases 

 and for liquids. Maxwell (1877) has given the most suggestive and 

 Boltzmann (1876) the most carefully formulated theory for solids, 

 but the investigation of absolute data has but begun. The difficulty 

 of reconciling viscous flow with Lagrange's dynamics seems first to 

 have been adjusted by Navier. 



Aeromechanics 



Aerostatics is indissolubly linked with thermodynamics. Aero- 

 dynamics has not marked out for itself any very definite line of 

 progress. Though the resistance of oblique planes has engaged the 



