124 Mr. W. Sutherland on the 



molecules of the body reduces to that part due to action be- 

 tween the layer and the matter it encloses. Now the resultant 

 attraction of the enclosed mass on a portion of the layer whose 

 surface is unity is Kp 2 , where K is Laplace's constant and p 

 is the density of the body : hence the internal virial will have 

 the same value as if it arose from a pressure Kp 2 , which Van 

 der Waals calls the molecular pressure. According to the 

 usual method of estimating the virial pressure over a closed 

 surface, we find that the virial of the internal forces is § Kp 2 v, 

 and thus the equation of the virial becomes 



iSmV 2 = f (p + Kp*)v. 



Van der Waals then argues that the external pressure p which 

 the containing wall exerts on a mass of gas depends on the 

 number of collisions which it experiences in unit time ; and 

 he finds that, on the elastic-sphere theory of molecules, if the 

 spatial extension of all the molecules in volume V is 6 X , then 

 the number of collisions per unit time against the walls will 

 be greater than if the molecules were points with the same 



mass and moving with the same velocity in the ratio 7^—; 



and the pressure will be correspondingly increased. Hence, 

 according to Van der Waals, we must correct the previous 

 equation to the form 



i2mV 2 =f(p + Kp 2 )<>-&), 



where b represents 4Z>,. He then assumes that ^2 mY 2 is 

 always directly proportional to the temperature as measured 

 absolutely on the air-thermometer, and reduces the above to 

 his typical form 



(p + ^){v-b) = K{\ + at). 



Whatever may be the value of the reasoning by which this 

 form has been derived from the equation of the virial, there 

 is no doubt about the service which it has done in Van der 

 Waals' s hands to the cause of molecular science ; but the 

 equation as it stands has been found wanting when applied to 

 any series of experiments with a wide range of pressure and 

 temperature. 



To meet the deficiencies in it, Clausius (Wiedemann's 

 Ann. ix. 1879) constructed the form 



_ RT C 



which is evidently derived from Rankings form with two 



