[ 101 ] 



XIV. On the Theorem of the Mean Ergal, and its Application to 



the Molecular Motions of Gases. By R. Clausius. 



[Continued from p. 46.] 



§ 9. ~V\7E now turn to the second part of our investigation, 



* w namely the application of the theorem of the mean 



ergal to the molecular motions of gases. 



In the consideration of gases, we start from the hypothesis 

 that their molecules move in straight lines and only change 

 their directions through collisions with one another or striking 

 against the solid sides of the containing vessel. We will preli- 

 minarily regard the molecules as material points; that is, we 

 will neglect the circumstance that the constituents of a molecule 

 are also in motion relative to each other. 



In reference to the mean length of path of the molecules be- 

 tween two collisions, I have already* arrived at certain results, 

 some of which I will here briefly recapitulate. 



After discussing the somewhat complicated action exerted by 

 two moving molecules on approaching one another, I said that, 

 for an approximate consideration of these occurrences, in which 

 the question is only the determination of certain mean values, 

 the notion of a sphere of action may be introduced ; and this I 

 defined as a sphere described about the centre of gravity of the 

 molecule, to the surface of which sphere the centre of gravity of 

 another molecule can come before a recoil commences. 



If we picture to ourselves, as is sometimes done for the sake 

 of clearness, the molecules as elastic balls, w r hich on their sur- 

 faces meeting recoil from one another, we must conceive the 

 diameter of the balls to be as great as the radius of the sphere 

 of action just now denned. This radius I denoted by p. Further, 

 the side of the little cube obtained when the molecules are ima- 

 gined to be arranged cubically in the space which includes them 

 I designated by \, so that \ y signifies that portion of the space 

 which falls to each molecule. With the aid of these symbols I 

 constructed the following equation for the case in which only 

 one molecule was in motion and the rest were fixed, the mean 

 path-length of the moving molecule being /' : — 



V=~ (68) 



irp* 



When the other molecules are also moving, in order to deter- 

 mine the mean length of path, we need only diminish the last 

 expression in the same ratio as the absolute velocity of the mole- 

 cule considered is less than its relative velocity to the other mo- 



* Pogg. Ann. vol. cv. p. 239; Abhandlungensammlung, vol. ii. p. 260; 

 Phil. Mag. S. 4. vol. xvii. p. 81. 



