18 THE TRUE VALUE OF a OF VAN DER WAALS' 



the ratio of the internal to the total internal and external pressure 

 is indeed a constant for all these diverse substances, ranging from 

 inorganic substances, such as SnCl±, with five atoms in the molecule,, 

 to complex substances like octane with 20 atoms, and embracing 

 a variety of different kinds of organic compounds. The ratio of 

 the total pressure to the internal is 1.158. From this we can 

 find the ratio of the internal to the external pressure. We have 



— i# 9 - -= 1.15 s . llKN(M-:/ J r =0.158r///-, 2 . BENCEfl=6.33P c r2 

 a/Pf 



,Tt will be noticed that an error of 0.1 / o in the ratio Lj(L — E) 

 becomes an error of 1 °/ o in the ratio of ajP c P c 2 . And inasmuch 

 as the Biot formula gives too high a calculated value of P close 

 to the critical temperature and this has the result of making Lj{L — E) 

 a little too high and so a/P c P c 2 a, little too low 1 have increased 

 the value 6.33 to 6.5 in my calculations. This gives a value of 

 a more nearly that calculated from the surface tension and in 

 other ways and is I believe more correct. The mean value from the 

 determinations by SC was also higher than 6.33 and was actually 

 6.63. 6.5 is jusl about the mean of these two values. Moreover, 

 if we take' >S' as 3.75, when h r is just V c j l l, then 6.5 -f~ 1 beco- 

 mes 7.5 and this is just twice 3.75. 



The relation between some of these values has been pointed out 

 by Dieterici ] ). Among the twenty five substances of which the 

 ratio of the internal to the external pressure has just been computed 

 there is no example of a tiiatomic or a diatomic gas. Hut I shall 

 show in a moment that the triatomic gases, at least, probably also 

 have this same ratio. Before taking this up, however, 'I will point 

 out that if the derivation of the ratio of the internal to the external 

 critical pressure which 1 have made does not seem sufficient, exactly 

 the same result is secured from Dieterici's equation 2 ) and that of 

 Grompton 3 ). 



CromptoN observed that the total heat of vaporization or L was very 

 nearly equal to 2 RI'LnJ^djD). In place of 2 we will substitute what 

 is in reality, I believe, its real value of V c j{V c — b c ). Hence we have: 

 V={V e j{V c —b c ))BTLn e {dlD). And for the internal latent heat, 

 L — E, we have according to Dieterici : L — E= C'RTLn v {dlJ)). 



Dividing one by the other we obtain 



L^i:~ C"PTZn e (d/D ~ {V—b^C' 



(3) 



i) Dieterici: Wied. Annalen d. Physik, 12, 111 (1903). 



-) Dieterici: Annalen .1. physik, 25, 569 (1908); 11», 14 1 (1903). 



:; ) Cuompton: Proc. Chemica] Society, 17, No. 23~>, 1901. 



