in relation to Pressure, Volume, and Temperature. 399 

 ^ 1-00646 -s 



■tl= m > 



lo I (6) 



a = 0-00874, f V ' 



6=0-0023. J 



This equation, extraordinarily simple in form, gives pressure- 

 curves corresponding well with those constructed by Andrews 

 and supplemented by J. Thomson, and exhibiting likewise the 

 characteristic difference between the forms which belong to 

 temperatures above and below 31°. 



As to the more precise numerical accordance of the values 

 of p calculated from this equation with those observed by An- 

 drews, Van der Waals himself made the remark that with 

 volumes less than 0*0046 the value of p can no longer be 

 regarded as constant, but must become less as the volume 

 decreases. But by what function of the volume one has to 

 represent b he had not yet succeeded in discovering*. 



In addition to these there are other deviations, which could 

 only reveal themselves later ; for after the publication of Van 

 der Waals's work the stock of observations suitable for com- 

 parison with the calculated values received a great and impor- 

 tant enrichment, as Andrews continued his investigation, and 

 published in 1876 three new series of observations for the 

 temperatures 6° # 5, 64°, and 100°f , which far surpass those pre- 

 viously published in extent and possess an enhanced degree of 

 exactness. On comparison with these experiments, the equa- 

 tion set up by Van der Waals is found not to agree with expe- 

 rience, and cannot be brought into accordance even by alter- 

 ing the values attributed to the constants, but needs for that 

 purpose a more essential modification. 



The principal reason of these deviations appears to me to be 

 the following. Yan der Waals assumed it as self-evident that 

 the mutual attraction of the molecules is independent of the 

 temperature, and therefore can only be a function of the 

 volume. According to that, when a gas is heated at constant 

 volume the molecular attraction must remain unaltered. This 

 would doubtless be true if the motion of the molecules of a gas 

 at a lower temperature differed from that at a higher tempe- 

 rature only by the different quantity of the mean vis viva of 

 the motion, but in all other respects took place in precisely 

 the same manner, the paths of all the molecules and the ratios 

 of the velocities in the different stages of a path remaining the 

 same. I also believe that such an assumption respecting the 



* Op. cit. pp. 78 & 52. 



t Phil. Trans. 1876, p. 421. 



