Connexion between the Atomic Weights. 105 



primitive material. " But on account of the evolution of heat 

 when a polymer is formed, there will ensue, as a physical 

 consequence, the inversion of more or less of the cooling, and 

 therefore of the polymerization." Incidentally this theory is 

 used to explain the phenomena of variable stars. 



The important point about .Mills'' work is that it may be 

 considered as indicating the existence of an upper limit for 

 atomic weights. The weak point is that the number of 

 elements below this limit may be infinite. On this latter 

 question Mendeleeff ('Principles of Chemistry/ English 

 translation, 1891 ed. p. 19) expresses himself with great 

 clearness. " The actual periodic law does not correspond 

 with a continuous change of properties, with a continuous 

 variation of atomic weights — in a word it does not express 

 an uninterrupted function." 



In conclusion, Mills uses his formulse to classify the 

 elements with some degree of success. 



Stoney (Proc. Hoy. Soc. 1888, p. 115, and Circular issued 

 to members of B. A. at Bath, 1888) plots as ordinates the 

 cube roots of the atomic weights referred to lrydrogen as 

 unit, the abscissaj beino- successive integers. " A curve 



y m =klog (mx), 

 where 



log& = 0785, 

 and 



log a =1-986, 



threads its way through the positions plotted down from the 

 observations." 



Having obtained an expression of this form, Stoney inves- 

 tigated subsequent terms which should include deviations 

 from the formula. Finally a spiral was constructed and so 

 arranged that it not only showed the periodic classification of 

 the elements, but also gave by inspection the atomic weights. 



It should be noted that according to Stoney's formula 

 elements of less atomic weight than hydrogen and also of 

 greater atomic weight than uranium may exist. Three 

 elements lighter than hydrogen and six between hydrogen 

 and lithium were predicted ; a vacant " sesqui-radius " in the 

 spiral was left, across which the transition from electro- 

 positive to electro-negative elements was abrupt. This "is 

 not arbitrarily introduced into the diagram, but has a real 

 existence in nature." This " sesqui-radius " is now occupied 

 by the new gases, and thus the prophecy of Stoney has been 

 fulfilled in a most remarkable way. 



