78 MOLECULAR MOTION AND ITS ENERGY 37 



byThos. Graham, for which also the name diffusion has 

 been used, thus giving rise to mistakes. 



The theory of this process has been already developed 

 by Daniel Bernoulli, 1 and its exactness has been con- 

 firmed by the experiments of Graham 2 and Bun sen. 3 



Bernoulli rests his theory on a proof of the proposition 

 that Torricelli's theorem is not only applicable to the 

 efflux of liquids, but may be extended also to gases. From 

 this it at once follows that the speed of efflux is proportional 

 to the square root of the pressure. Since, according to the 

 kinetic theory, the pressure varies as the square of the mean 

 speed, the signification of Torricelli's theorem on the 

 kinetic hypothesis is that the speed of efflux of a gas is 

 proportional to the mean molecular speed of its molecules. 



We should have been able to arrive directly at this con- 

 clusion from the assumptions of the theory of gases, even 

 without employing Torricelli's theorem; for it is clear 

 that one of the to-and-fro moving particles which reaches 

 the orifice can issue through it with no other speed than 

 that which it possessed before. The speed of efflux thus 

 originates directly from the speed of the molecular motion, 

 and the mean speed of the issuing particles must therefore 

 be simply proportional to the mean molecular speed. 



Here again, therefore, appears the same ratio which we 

 noted in the investigation on the speed of sound. The speed 

 of efflux, equally with the speed of propagation of sound, 

 is proportional to the mean molecular speed. The reason 

 for this simple relation between effusion and the motion of 

 sound is not far to seek. In both processes we are con- 

 cerned with the propagation of differences of pressure. In 

 the motion of sound periodical alternations of condensation 

 and rarefaction of the air are transmitted ; in efflux the 

 pressure goes from the compression vessel into outer space. 

 The difference consists only in this, that in the case of 



1 Hydrodynamica, Argentorati 1738, sect. 10, 34, p. 224. 



2 Trans. Roy. Soc. Edin. xii. 1834, p. 222 ; Phil. Mag. ii. 1833, p. 175 ; 

 Pogg. Ann. xxviii. 1833, p. 331 ; Phil. Trans. 1846, p. 573 ; 1863, p. 385. 



3 Gasometrische Methoden, Braunschweig 1857, pp. 128, &c. ; 2nd ed. 1877, 

 pp. 185, &c. 



