117 DIEECT PROPERTIES OF MOLECULES 325 



the smaller volume v b for the larger volume v = N\ 3 of 

 the whole mass consisting of N molecules. The number to 

 be subtracted has thus the meaning 



b = 4 



that is, it is equal to four times the volume actually occu- 

 pied by the whole of the molecules that are contained in 

 unit volume. 



Putting in this equation the value of the free path given 

 by the former formula i _ /o 27^7- 



which may without hesitation be here employed without 



correction, we obtain 7 T , /0 /QX 

 oL (v2/3)s-, 



so that we can calculate the molecular diameter s from the 

 known values of b and L. In this calculation we have still 

 one precaution to take; for b and L are both dependent on 

 the pressure, b being proportional to the number N and 

 therefore to the pressure, and L being inversely proportional 

 to these magnitudes. The values given in 79 and 116 for 

 the free path have reference to the pressure of one atmo- 

 sphere, while the values of b calculated by van der Waals 

 and others from his theory presuppose, at least for the 

 greatest part, the pressure of 1 metre of mercury ; to com- 

 pensate for this difference we must multiply the formula for 

 the calculation of the radius of the sphere of action by the 

 ratio of the pressures, and thus put 



where b is referred to the pressure of 1m. of mercury, and 

 p denotes the pressure in metres of mercury for which the 

 value of L, which is employed, holds good. 



From the observations made by Eegnault and 

 Cailletet on the deviations of gases from Boyle's law, 

 van der Waals 1 has calculated the following values: 



Air . ' . . . 6 = 0-0026 



Carbonic acid ... 30 



Hydrogen .... 069 



1 ContinuUeit, die. Chap. VIII. b. 41, 42, pp. 67-9. Phys. Soc. Transl. 

 pp. 400-2. F. Both, Wied. Ann. 1880, xi. p. 25. 



