484 A. P. Mathews 



of hydrogen gas is somewhat lower than the figures indicate. 

 In the series methane, ethylene, pentane, hexane, heptane and 

 octane the residual valence is, respectively, 0.15, 0.9, 4.6, 5.42, 

 6.89, 9.05. In other words, the residual valence increases 

 with the number of carbon atoms as Armstrong has already 

 inferred it should do. If 0.15 be considered as the average 

 amount of residual valence of a carbon atom when united 

 with hydrogen and if the amount of residual valence increases 

 proportional to the square of the number of carbon atoms, we 

 should have R. Val. = n 2 0.15, n being the number of carbon 

 atoms. By this formula the number of residual valences 

 in the series mentioned should be, respectively, 0.6 for ethylene, 

 3.75 for pentane, 5.40 for hexane, 7.35 for heptane, and 9.60 

 for octane. These values are not very different from those 

 actually found. This relationship does not hold for the 

 esters. 



Another fact may be noticed, namely, that the differences 

 between the total number of valences in the various groups of 

 esters is very nearly the theoretical number. Thus between 

 methyl formate and methyl acetate a difference of six valences 

 is required. 5.40 was the difference found. If we take the 

 average of the total number of valences found in the two 

 esters of the formula C 3 H 6 O 2 it is 23.95. This is 5.75 valences 

 more than methyl formate has and is almost exactly six 

 less than the next higher homologues of the formula C 4 H 8 O2, 

 of which the average number of valences found was 29.91. 

 This in its turn is again 5.79 (required 6) valences less than 

 the average of the next higher group of the formula C 5 Hi O2. 

 Theoretically, there should be a difference of 32 valences be- 

 tween the molecule of hydrogen and a molecule of the formula 

 C5Hi O2, whereas the method actually shows a difference of 

 33.62. It is certainly reasonable to suppose that this, differ- 

 ence from the theoretical is to be ascribed to the larger amount 

 of residual valence possessed on the average by a molecule 

 of the ester as compared with hydrogen. 



In the case of the chlorine compounds I have assumed 

 that the valence of chlorine is three. The reason for this is 



