APPENDIX II. 477 



while their oxides contain an increasing quantity of oxygen 



Ag 2 CdA InA SiifcO, Sb 2 a Te 2 9 1,0, 



But to connect by a. curve the summits of the ordinates expressing any 

 of these properties would involve the rejection of Dalton's law of multiple 

 proportions. Not only are there no intermediate elements between silver, 

 which gives AgCl, and cadmium, which gives CdCl 2 , but, according to the 

 very essence of the periodic law, there can be none ; in fact a uniform curve 

 would be inapplicable in such a case, as it would lead us to expect elements 

 possessed of special properties at any point of the curve. The periods of the 

 /elements have thus a character very different from those which are so simply 

 represented by geometers. They correspond to points, to numbers, to sudden 

 changes of the masses, and not to a continuous evolution. In these sudden 

 -changes destitute of intermediate steps or positions, in the absence of 

 elements intermediate between-, say, silver and cadmium, or aluminium 

 and silicon, we must recognise a, problem to which no direct application 

 of the analysis of the infinitely small can be made. Therefore, neither the 

 trigonometrical functions proposed by Ridberg and Flavitzky, nor the pen. 

 dulum-oscillations suggested by Crookes, nor the cubical curves of the Bev, 

 Mr. Haughton, which have been proposed for expressing the periodic law, 

 from the nature of the case, can represent the periods of the chemical 

 elements. If geometrical analysis is to be applied to this subject, it will re 

 quire to be modified in a special manner. It must find the means of repre- 

 senting in a special way, not only such long periods as that comprising 



K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br, 



but short periods like the following : 



Na Mg Ai Si P 8 Cl. 



In the theory of numbers only do we find problems analogous to ours, 

 and two attempts at expressing the atomic weights of the elements by alge- 

 braic formulae seem to be deserving of attention, although neither of them 

 can be considered as a complete theory, nor as promising finally to solve the 

 problem of the periodic law. The attempt of E. J. Mills (1886) does not 

 even aspire to attain this end. He considers that all' atomic weights can be 

 expressed by a logarithmic function, 



15(71-0-9375'), 



in which the variables n and t are whole numbers. Thus, for oxygen, n = 2, 

 and t = 1, whence its atomic weight is = 15'94 ; in the case of chlorine, 

 bromine, and iodine, n has .respective values of 8, 6, and 9, whilst t = 7, 6, 

 and ; in the case of potassium, rubidium, and caesium, n = 4, 6, and 9, and 

 t = 14, 18, and 20. 



Another attempt was made in 1888 by B. N. Tchitche"rra. Its author 

 places the problem of the periodic law in the first rank, but as yet he has 

 investigated the alkali "metals only Tchitche'rin first noticed the simple 



