of the Liquid and Gaseous States of Matter. G71 



2T C 



calories per gram at -~, which at that temperature may be 



taken equal to L\ The above value for P n is practically the 

 same as that obtained previously by equation (6), viz. 1992. 



Thus we see that K 3 or -—■ is independent of the tempe- 



1 



rature and equal to unity, or at least approximately so. 



This result throws some light on a very important point. 

 !So far we have not yet obtained any information as to 



whether the function $„( — , ft J in the expression for the 



attraction between two molecules is a function of the 

 temperature or of the distance between the molecules, or 

 of both. Referring back to the demonstrations of the 

 equations (2) and (3), containing K 2 and A x respectively, 



it will be seen that if <f>2\~~~ •> ft) * s a function of the 



temperature only, it can at once be taken outside the 

 summation and integral signs, and then appears as a factor 



of K 2 and Ax, which disappears in -t-2 or K 3 . The expression 



1 

 thus appears to be a temperature function only. This point 



will be discussed at length in a separate paper. 



A general equation of the different states of matter will 

 now be developed and some special cases of this general 

 equation considered. 



Substituting for the intrinsic pressure in equation (1) 

 from equation (2), we have 



rr /1\ W /tj /—\2 RT 



p + K 2 — ) (2 VmJ = . 



1 \vmj mv 



There is one point which has not been taken account of in 

 formulating this equation, to which attention was first drawn 

 by van der Waals. When the density of a gas is so great 

 that the diameter of the molecules is comparable with their 

 distance of separation, the diminution of the mean free path 

 of a molecule on collision owing to its finite size is appre- 

 ciable. The pressure is therefore greater than that given by 

 Boyle's law, and according to van der Waals is such as if 

 the volume of the gas were smaller than it actually is by 

 four times the space actually occupied by the molecules. For v 

 we must therefore write (u — b), where b is the space occupied 

 by the molecules. The effect produced by the molecules 

 having finite size is quite large. Thus, consider a liquid at a 

 low temperature : the pressure of its saturated vapour or 



