668 TRANS. ST. LOUIS ACAD. SCIENCE. 



CONCIiUSION. 



Whether the conclusion, stated on p. 66^], that saturation-val- 

 ence is an equicrescent rotary function of atomic weight, is the 

 expression of a natural law, or of a mere coincidence, I leave for 

 others to decide. 



If it is only a chance coincidence, we must acknowledge it to 

 be a remarkable one. A coincidence which unites not less than 

 fifty chemical elements by so simple a relation between valence 

 and atomic weight as y = ax-^b^ must be entitled to some con- 

 sideration. 



Mendelejeft' has shown that ^^ the chemical properties of the 

 elements are a periodic function of their atomic weights T 



This statement, while it is true enough, is too indefinite to he 

 called the statement of a laiv^ since a law must be capable of some 

 quantitative mathematical expression. 



Mendelejefl^'s statement is so ingeniously framed as to link to- 

 gether in a qualitative expression all or nearly all chemical facts, 

 without alluding to any one of the individual laws embraced in 

 his generalization. The manner in which he predicted the dis- 

 covery of gallium and scandium, by the periodic recurrence of cer- 

 tain chemical and j^hysical properties corresponding to periodic 

 numerical relations between the atomic weights of known ele- 

 ments, shows conclusively that many of these unknown laws have 

 the common factor, atomic weight. 



There is room for as many of these laws as there are different 

 properties recognizable in matter. 



In the graphical representation, explained above, for the law of 

 valence we find a remarkable expression of the -'periodic func- 

 tion." 



Prout's hypothesis is merely the expression of a single fact em- 

 braced in the law. 



The changes in the atomic weights required by this law are 

 such as would generally favor the law of Avogadro and that of 

 Dulong and Petit, and would make the atomic volume curves of 

 Meyer more i-egular. 



These changes would aftect few, if any, of those elements whose 

 atomic weights have been established with tolerable certainty. 



The full expression of the law would require the existence of 

 105 elements whose atomic weights lie between i and 240. 



