Manchester Memoirs, Vol. It. (1907), No. (►. 11 



one side, and for Bismuth and Ytterbium on the other. 

 Most of these discrepancies are, however, to be found in 

 the groups having even numbers, shown in dotted lines 

 on the diagram, it being more especially their upper ends 

 which are out of line. It will also be noticed that with 

 the exception of the II. group in which the Calcium point 

 bulges to the left, all the other even groups bulge to the 

 right, in such a way as to make it appear probable that a 

 very close agreement would be obtained if two formulas 

 were used, one for the odd, the other for the even numbers 

 of groups. The formula for the even groups would then 

 have to contain an additional term of the form 



3.sin(N.7-5°-45°). 

 There is, however, no justification for this complication, 

 yet this difficulty of harmonising the atomic weights 

 suggests the possibility that Mendeleeff's grouping is 

 not satisfactory, and that perhaps a more simple 

 relationship than that indicated by the formula might 

 be found by comparison not of the atomic weights but 

 of the molecular weights. At any rate, if two molecules 

 of Sodium naturally replace one of Magnesium and two- 

 thirds of Aluminium, etc., why then should not there be a 

 relationship between the atomic weights divided by the 

 greatest valency of the elements, and why should not 

 each element appear several times either as a simple atom 

 or as a cluster of atoms ? A table constructed on this 

 principle has a very confusing appearance, but although 

 no attempt has been made to enquire into this departure, 

 it must not be overlooked that it is perhaps the only 

 system in which a suitable place can be found for Hydrogen. 

 In the present arrangement the Hydrogen position is the 

 one for which N is minus one. It falls in line with the 

 Chlorine group, but to suggest that on account of the 

 negative value of N the chemical properties should be 



