44 IDEAL AND ACTUAL GASES 103 



tude inversely proportional to the square of the volume 

 containing the gas. 1 



Hence van der Waals's corrected formula for Boyle's 

 law becomes 



av~ 2 )(v - b), 



wherein a and b are constants independent of the pressure 

 and volume ; and if, as before, we express the molecular 

 speed by the temperature, 



(p + av~ 2 )(v - b) = E(l + a&), 



where E is a constant, and a, S denote, as before, the co- 

 efficient of expansion of gases and the temperature. Only 

 by comparison with experiment can it be determined whether 

 a and b depend on the temperature ; van derWaals finds 

 that it is tolerably sufficient to assume them both to be 

 independent of the temperature, as well as B and a. 



45. Comparison with Begnault's Observations 



The theoretical formula obtained agrees nearly exactly 

 in form with the formula of interpolation by which 

 Kegnault represented the results of his observations; for 

 . this has the form 2 



= I A(m l) + B(m - I) 2 , 

 m 



wherein m denotes the ratio of two values of the volume 

 reduced to the same temperature, say C., or 



m = V/v, 

 r that of the corresponding values of the pressure, 3 or 



r=p/P, 



while A and B are constant coefficients. If, as in 

 Eegnault's memoir, that volume F is taken as unity 



1 Hitter has proceeded by this method in determining the cohesion of 

 gases in a memoir (M6m. de la Soc. de Phys. de Geneve, xi. 1846, p. 99), with 

 which I have become acquainted only through the notice of it by von 

 Morozowicz in the Fortschritte der Physik, ii. 1846, p. 89. 



2 Mem. de I'Acad. de Paris, xxi. p. 421. 



3 See Table of Errors at the end of vol. xxvi. of the Memoires. 



