OF THE GASEOUS AND LIQUID STATES. 413 



shews that this effect, in the case of very rare gases, is the same as if the 

 volume of the space in which the molecules are free to move had been 

 diminished by four times the sum of the volumes of the molecules themselves. 

 He then substitutes for V, the volume of the vessel in Clausius' formula, this 

 volume diminished by four times the molecular volume, and thus obtains the 

 equation 



where p is the externally applied pressure, -=j is the molecular pressure 



arising from attraction between the molecules, which varies as the square of 

 the density, or inversely as the square of the volume. The first factor is thus 

 what he considers the total effective pressure. V is the volume of the vessel, 

 and b is four times the volume of the molecules. The second factor is there- 

 fore the "effective volume" within which the molecules are free to move. 



The right-hand member expresses the kinetic energy, represented by the 

 absolute temperature, multiplied by a quantity, R, constant for each gas. 



The results obtained by M. Van der Waals by a comparison of this equa- 

 tion with the determinations of Regnault and Andrews are very striking, and 

 would almost persuade us that the equation represents the true state of the 

 case. But though this agreement would be strong evidence in favour of the 

 accuracy of an empirical formula devised to represent the experimental results, 

 the equation of M. Van der Waals, professing as it does to be derived from 

 the dynamical theory, must be subjected to a much more severe criticism. 



It appears to me that the equation does not agree with the theorem of 

 Clausius on which it is founded. 



In that theorem p is the pressure of the sides of the vessel, and V is 

 the volume of the vessel. Neither of these quantities is subject to correction. 



The assumption that the kinetic energy is determined by the temperature 

 is true for perfect gases, and we have no evidence that any other law holds 

 for gases, even near their liquefying point. 



The only source of deviation from Boyle's law is therefore to be looked 

 for in the term %Z2<(Rr), which expresses the virial. The effect of the repul- 

 sion of the molecules, causing them to act like elastic spheres, is therefore to 

 be found by calculating the virial of this repulsion. 



