Gases and the Equation of V trial. 197 



would vary from -68 for hydrogen to '81 for argon ; but 

 Sutherland's law* 



* a TTT7T (9) 



probably represents the facts better than (6), whatever value 

 may be assigned to n. According to the theory of corre- 

 sponding states, G should be proportional to the critical 

 temperature when we pass from one gas to another. 



A similar application of the method of dimensions will 

 give interesting information respecting the virial, when the 

 lorce of repulsion is 



cf>( p ) = - /jL p-» (10) 



The virial is a definite function of N the number of mole- 

 cules, m the mass of each molecule, V the velocity of mean 

 square on which the temperature depends, {j, the force at 

 unit distance, and v the volume of the containing vessel. 

 Of these quantities the virial is of the dimensions of energy, 

 X has none, m is a mass simply, V is a velocity, v a volume, 

 while fi has the dimensions 



mass x (length)"" 1 " 1 x (time) -2 . 



Hence if we suppose that the virial varies as v~ s , we rind 

 that it must be proportional to 



a— 3«-l 



(mV 2 ) "- 1 • ^ n - J . /-<: .... (11) 

 <»r since m\' 2 represents temperature, 



n—Ss—l I - 



T "-' ■ M "-'•<' (12) 



Fur example, if *=0, 



Zpfip) x T, (13) 



whatever n may be. Hence a term in the virial equation 

 independent of volume must be proportional to temperature, 

 as in (1). Again, if s=l, 



-i 



1p4>(p> v. p-'.T- 1 (U) 



Of this we have already had examples, both the virial terms 

 in Van der Waals' equation being proportional to v~ l . The 

 first, representing the virial of collisional forces, corresponds 

 in [1-ij to /i = y~, giving proportionality to T. The second 

 i- independent of T and can be reconciled with (14) only by 



* Phil. Ma#. vol. xxxvi. p. 513 (1803). 



