104 MOLECULAR MOTION AND ITS ENERGY 45 



which, at the pressure P = 1 metre of mercury, is filled by 

 the mass of gas used in the experiment, Eegnault's 

 formula can be more simply written 



2 



or 



pv + (A + %B)v- 1 - Bv~ 2 = 1 + A +B. 



In this form it agrees with the theoretically deduced formula 

 of van derWaals for the temperature 0, viz. 



pv + av~ l bp abv~* = B, 



if it is allowable to replace the pressure in the correction 

 term bp by the reciprocal of the volume in accordance with 

 the approximately correct Boyle's law 



for then van der Waals's formula runs 



pv + (a b)v~ l abv~ 2 = E, 



so that it is equivalent to Regnault's if the constants 

 calculated for unit of mass are related to each other 

 according to these equations : 



a - b = A + 2B, 

 ab = B, 



E = 1 + A + B. 



Under these circumstances a detailed comparison of the 

 formula with the numbers obtained directly is not necessary. 

 But it should be mentioned that from the values of A and 

 B found byEegnaultwe shall afterwards be able to calcu- 

 late 1 the numerical values of a and b, which represent the 

 magnitude of the cohesion and the extension in space of the 

 molecules. 2 



46. Pressure- and Volume-coefficients 



Van der Waals's formula is also suitable for explain- 

 ing the variation in the values of the expansion-coefficients, 



1 Van der Waals, Continutteit ; Both, Wied. Ann. xi. 1880, p. 1. 



2 See Chap. X. 



