8 THE TRUE VALUE OE a OF VAN DEE WAALS' 



gave good agreements. Br and I were provisionally also taken as 

 monovalent, but 1 have since found that elemental bromine is at 

 least trivalent, and I do not doubt that when we have accurate 

 critical data iodine will be found, often at least, to be more 

 than monovalent. Tin was tetravalent as it is supposed to be. I 

 was not content, however, to base the law I had discovered, 

 which appeared to me to be of fundamental importance, on these 

 26 substances, but T tried to compute a for all the substances 

 of which 1 could find some, or all, of the critical data. For 45 

 other substances of fair complexity, in many of which I had to 

 calculate' the critical density or the critical temperature, I found 

 the same mean value of the constant when a was divided by 

 the product of the molecular weight and valence raised to the 

 2/3ds power. There were some wide deviations, due to the uncer- 

 tainty of the critical data, but the mean constant was the same, 

 and the majority of substances gave a constant not deviating more 

 than 2 — 3 / o from the mean. I calculated, also, the critical data 

 from the surface tension measurements of other substances, and 

 found again good agreement, altho the calculations involved many 

 assumptions. I found chlorine compounds nearly everywhere in 

 agreement, were chlorine always trivalent. Only in a few cases was 

 a better agreement secured if one or more atoms of chlorine were 

 monovalent, but 1 did not doubt that this was but an appearance 

 and was due to the inaccuracy of the critical data. Sulphur was 

 found everywhere to be hexavalent except in S0 2 where it was 

 tetravalent. Sulphur is generally supposed to be tetravalent, divalent 

 or hexavalent. I found no divalent sulphur except possibly in car- 

 bonyl sulfide. Nitrogen had the valence numbers usually attributed 

 to it. The main difficulty was when I attempted to find the value 

 of a for the simple gases H 2 , N 2 . 2 , CO, C0 2 and CII 4 . The 

 value of a was very uncertain. The critical data of nearly all 

 were very imperfectly known, but fortunately this uncertainty has 

 now been removed for all but Ii 2 . I knew of no way of computing 

 a for these gases except by using van der Waals' equation and 

 making certain assumptions which might, or might not, be true, 

 but I found some empirical ways of computing from the latent 

 heat and surface tension of the liquified gases. Among other methods 

 I assumed that b c , the volume of the molecules at the critical tem- 

 perature, was always 2<5 , b being the minimum volume at absolute 

 zero. In this I was following the fact that in many substances b c 

 was known to be about V c /2, V often being nearly 4 V„, and a 

 suggestion by van der Waals that the volume of the molecules 



