EQUATION AND THE NATURE OF COHESION. 18 



a. Calculation of a assuming that b c = V c j2.03. 



While this relationship is only an approximation, and probably 

 does not hold everywhere, I have computed what the value of 

 a would be were it generally true. The results are given in 

 column 2 of Table 2. (P c + a/F c 2 ) {V c — b c ) = HT: hence a = 

 2.03 RT e F J I.Q& — P C V C 2 . The critical data used in the calculation, 

 unless otherwise stated, are those of S. Young. A comparison of 

 the results in column 2 with the values of a computed from 

 the gravitational attraction and the number of valences given in 

 column 8 shows the truly remarkable agreement between them in 

 the case of all complex substances clown to and including the 

 triatomic gases. Nitrogen and the diatomic gases give, on this 

 assumption, somewhat lower values of a than are computed from 

 the gravitation, but I think it probable, from the evidence to be 

 stated presently, that this is due to the fact that in these gases 

 b ( . is nearer V c /1.9. 1 might add for purposes of comparison, that 

 van Laar's calculation of a makes b c in complex substances 

 about V c /2.1 and in the diatomic gases about V j%.h. The asso- 

 ciating substances, methyl and ethyl alcohol and acetic acid and 

 water, diverge from the values calculated from weight and valence 

 as was to be expected. The divergence of iodobenzene and brom- 

 benzene may be due to the critical data not being quite right, 



b. Calculation of a from the formula: a = 6.5 P C V 2 . 



The second method of computing a from van der Waals' 

 equation seems to me the most simple and reasonable of all the 

 methods proposed, and that it is correct for at least all the complex 

 substances, and probably for the simple diatomic gases also, is shown 

 by the fact that the values thus computed are, on the whole, 

 supported by the computations from the surface tension and the 

 latent heat. The assumption made here is that in all non associating 

 substances with compressible molecules at the critical temperature 

 the ratio of the internal to the external pressure is either exactly, 

 or very nearly a -constant. This assumption appears to me to be 

 entirely probable and I shall in a moment adduce evidence of its 

 truth. There is something which all substances have in common at the 

 critical temperature. That something might be the relation of the 

 volume occupied by the molecules to the total volume, but it appears 

 more probable to me that it would be that the energy is divided 



