44 IDEAL AND ACTUAL GASES 101 



which may also be written 



if we introduce the number n of molecules in the volume 

 v instead of the number N contained in unit volume. 



In its new shape the formula shows itself as an applica- 

 tion of the theorem of the conservation of energy to the 

 system of n molecules, by stating that the energy of motion 

 represented by the term on the left-hand side of the equa- 

 tion finds its equivalent in the volume v being filled at 

 the pressure p. If the medium has internal cohesion, this 

 pressure is not the only equivalent, but there is another 

 pressure arising from the cohesion that must be added to p 

 in the preceding equation. 



On the other hand, the volume v of the gas which 

 occurs in the equation must be diminished if the molecules 

 occupy space ; for the molecules fly about here and there, 

 not in the whole of the space filled with the gas, but in that 

 part which is left free between them. The number of colli- 

 sions, therefore, depends only on the extension of this space 

 that is left free, and not on the whole of the volume filled. 

 The intensity, therefore, of the pressure exerted will also be 

 determined only by this smaller volume. 



The theoretical formula consequently needs correction on 

 both grounds, and we must put 



where ( denotes the pressure arising from the cohesion, and 

 b the space by which the volume v has to be diminished. 



Of the two new magnitudes introduced, the latter b is 

 made up of the sum of the volumes which are so filled by 

 the n molecules that no other molecule could force its way 

 into any one of them. Possibly the volume filled by a 

 molecule in this sense is actually determined by its own 

 extension in space ; a different assumption, however, is quite 

 possible. Physicists who believe in a luminiferous ether, 

 which is different from ponderable matter, would be dis- 

 posed to consider the volume of the ether atmospheres con- 

 densed about the atoms rather than that of the molecules. 

 The assumption of Clausius, Maxwell, and others is also 



