520 SCIENCE PROGRESS 



to the products of these expressions into the respective values 

 L, L', L" . . . , it follows that 



M M' M" 



L' 



= R (16) 



(i+a)(i-b) (i+a')(i-b') (i + a")(i - b") 



corresponding to equations (3) on p. 507 ; it is obvious that each 

 fraction is equal to R (cf. p. 507). Hence, 



RL RL' 

 M = (1 + a)(i - b)> M ' - (1 + a')(i - b') (1 5) 



an expression for M identical with that previously obtained. 



Guye adopts the value R = 22'4i2. The calculation of the 

 values of a and b depends upon a knowledge of T c and p c , the 

 critical temperature (absolute) and pressure of the gas. The 

 following equalities, connecting a, b, T c and p c , can be deduced 

 from theoretical considerations in connexion with van der Waals' 

 equation : 



_a_ T _ 8a _ 8 x 273a . . 



Hc ~ 27b" c 27bR ~ 27b(i + a)(i - b) K } 



By solving these equations, a and b may be expressed in 

 terms of T c and p c , magnitudes which can be experimentally 

 determined. The calculation involves the solution of a cubic 

 equation and the numerical values of a and b are best obtained 

 by the ingenious method given by Haentschel (11). Values of b 

 calculated in this manner agree very well with those deduced 

 from the equation 



T /T\» 



b = 0-0004496 — + o - oooooi835 I —J 



Pc re 



given by Guye and Friderich ; this equation therefore affords a 

 simple means of approximating to b for any gas. All values of 

 a and b quoted later, however, have been calculated by solving 

 the necessary cubics. 



Whilst the fundamental equation 



M = / a2 'f, aL uN C*7) 



(1 +a)(i -b) 



has the theoretical significance that attaches to a deduction from 

 van der Waals' equation, it is, like van der Waals' equation 

 itself, only approximately correct and therefore Guye has 

 modified it. The modified equations, however, can only be 

 regarded as empirical, as will be seen subsequently. 



