7* PRESSURE AND ENERGY 365 



we obtain by this method also the known relation ( 16) 



If we had taken the molecules to be not all of the same kind, 

 but had assumed that two or more kinds of molecules m ly m%, 

 . . . were mixed together, then we should have obtained, both for 

 the transmitted momentum and for the kinetic energy, formulae 

 of the same form as those just found, but of greater generality. 

 The equations would then have contained summations with respect 

 to all the different molecules m it m 2 , . . . Instead of the last 

 formula, therefore, we should have obtained, as is obvious without 

 calculation, the equation 



which has the same meaning as that in 17, and thus proves 

 Dal ton's law for the pressure of mixed gases. The hypothesis 

 of rectilinear molecular motion therefore is also sufficient by itself 

 for the theoretical proof of Dalton's law. 



8*. Kinetic Pressure of Liquefied Substances 



It is, perhaps, not even absolutely necessary for the molecular 

 motions to be rectilinear. For B o 1 1 z ma n n 1 has Attempted with 

 good results to extend the foregoing considerations to bodies which 

 are in the liquid state, and therefore to substances whose molecules 

 move, not in straight, but in curved paths. 



The case is that of substances which are mixed in very great 

 dilution with a liquid ; we can imagine, therefore, either a very 

 dilute solution of a solid body, or a liquid which has absorbed 

 small quantities of a gas or contains a small quantity of another 

 liquid. The molecules of the alien body that has been added 

 spread themselves throughout the liquid, and therefore become so 

 widely separated from each other that the forces of cohesion no 

 longer come into play. If we further assume that the liquid also 

 exerts no force on the alien molecules, or that the forces it exerts 

 mutually annul each other, the molecules of the added substance then 

 appear to be quite free from all external forces but that of gravity. 

 They would then move in straight paths just as molecules of gas 

 if they were not hindered by the molecules of the liquid and forced 



1 Zeitschr. fur phys. Chem. vi. 1890, p. 474 ; vii. 1891, p. 88. 



