424 Dr. F. G. Donnau on the Relative Rates of 



described the method which was afterwards worked out by 

 Bunsen*. The subject was taken up by Gr. G. Schmidt t 

 in 1820; and. he deduced from his experiments the law of 

 the inverse square root of the density, i. e. the law which was 

 rediscovered by Graham. The subject was then treated in a 

 masterly fashion by de Saint- Venant and WantzelJ. They 

 obtained the equation for the adiabatic efflux of an ideal gas 

 on the assumption § that the pressure at the vena contracta is 

 equal to the external pressure ; and they likewise observed 

 that this equation leads to absurd results when the external 

 pressure becomes zero. Their experiments showed the efflux 

 to be independent of the external pressure when the latter 

 is less than about one-half the pressure in the gas-reservoir; 

 and they suggest empirical formulae for dealing with this case. 

 About this time occur the classical experimental researches of 

 Graham || . His experiments were conducted with minute 

 holes in very thin-walled partitions ; and he coined the word 

 effusion to denote the efflux in this case. It must be observed, 

 however, that so long as the apertures are not comparable with 

 molecular dimensions, the phenomenon of effusion is simply 

 that of efflux on a small scale. The important point is that 

 the diameter of the hole should be sufficiently large, when 

 compared with the thickness of the partition, to render the 

 effects due to viscosity negligibly small. Graham's experi- 

 ments established the law of the inverse square root of the 

 density If. Hydrogen, however, showed a marked deviation, 

 which was rightly attributed by Graham to the effect of 

 viscosity being more marked in this case owing to the 

 lightness of the gas. The efflux of gases was investigated by 

 Weisbach**, and by Thomson and Joule It j but the theory 

 was not advanced beyond the point to which it been carried 

 by Saint-Venant and Wantzel. In 1886 the adiabatic theory 

 of efflux was subjected to an elaborate experimental investi- 

 gation by Hirn J J, who rediscovered §§ the phenomenon 



* Gasornetrische Methoden, Braunschweig, 1857. p. 1^8 et seq. 



t Gilb. Ann. Bd. Ixvi. p. 89 (1820). 



X Journ. de I Ecole Polyt. torn. xvi. cak. 27, p. 85 (1839). 



§ Navier, " Memoires sur l'Hicoulement des Fluides Elastiques," 

 tome viii. de V Academic des Sciences, Juin 1829. 



|i Phil. Trans, iv. p. 573 (1846). 



51 Many of Graham's results show that the " law " is subject to consi^- 

 derable deviations. 



** Experimental Hydraulik, 1855, p. 184 et seq. 



ft Proc. Roy. Soc. 1856, p. 178. 



XX Ann. de Chim. et de Fhys. ser. 6, torn. vii. p. 289 (1886). 



§§ It is remarkable how often this phenomenon has been rediscovered. 

 Thus it was observed by Graham, Hirn. Napier (Engineer, 1867), Wilde 

 (Phil. Mag. 1886). 



