360 



SCIENCE. 



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



Finally the forbidding subject of vor- 

 tex 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 interpretations of the 

 whole subject are due to Helmholtz (1858). 

 Kelvin (1867, 1883) soon i^ecogTiized the 

 importance of Helmholtz 's work and ex- 

 tended 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 treat- 

 ment. 



The indestructibility of vortex motion in 

 a frictionless fluid, its open structure, the 

 occurrence of reciprocal forces, were com- 

 pared by Kelvin (1867) with the essential 

 properties of the atom. Others like Fitz- 

 gerald 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. Kel- 

 vin invokes the corpuscular hypothesis of 

 Lesage (1818). 



VISCOSITY. 



The development of viscous flow is 

 largely on the experimental side, partic- 

 ularly 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), Max- 

 well (1868), Hagenbach (1860), 0. E. 

 Meyer (1863), are exhaustively investi- 

 gated for gases and for liquids. Maxwell 

 (1877) has given the most suggestive and 

 Boltzmann (1876) the most carefully for- 

 mulated theory for solids, but the investi- 

 gation 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. Aerodynamics has not 

 marked out for itself any very definite line 

 of progress. Though the resistance of 

 oblique planes has engaged the attention 

 of Rayleigh, it is chiefly on the experi- 

 mental side that the subject has been en- 

 riched, as, for instance, by the labors of 

 Langley (1891) and Lilienthal. Langley 

 (1897) has, indeed, constructed a steam pro- 

 pelled aeroplane which flew successfully; 

 but man himself has not yet flown. 



Moreover, the meteorological applications 

 of aerodynamics contained in the profound 

 researches of Guldberg and Molru (1877), 

 Ferrel (1877), Oberbeck (1882, 1886), 

 Helmholtz (1888, 1889) and others, as well 

 as in such investigations as Sprung 's 

 (1880) on the inertia path, are as yet rather 

 qualitative in their bearing on the actual 

 motions of the atmosphere. The marked 

 progress of meteorology is on the observa- 

 tional side. 



ACOUSTICS. 



Early in the century the velocity of 

 sound given in a famous equation of New- 

 ton was corrected to agree with observation 

 by Laplace (1816). 



The great problems in acoustics are ad- 

 dressed in part to the elastician, in part to 

 the physiologist. In the former case the 

 work of E-ayleigh ( 1877 ) has described the 

 present stage of development, interpreting 



