98 Prof. T. Carnelley on an Algebraic Expression of 



Faraday Lecture of this year (Cheni. Soc. Journ. lv. p. 642) 

 as haying been made by Tchitcherin in 1888, seeks to ex- 

 press the relations between the atomic volumes of the alkaline 

 metals by the formula A(2 — 0*00535 An), where A=the 

 atomic weight and n=S for Li and JSa, 4 for K, 3 for lib, 

 and 2 for Cs. 



In a paper read at the Aberdeen Meeting of the British 

 Association in 1885 (Ghem. News, nos. 1375-1378, 1886), I 

 proposed for the chemical elements the general formula 

 A n B 2 n+(2-x), in which n is the series and x the group to 

 which the element belongs ; A=12 and B= — 2. 



Since that time, and for thirteen years previously, I have 

 made frequent attempts to find a simple numerical expression 

 for the Periodic Law, but so far without marked success. 

 Early in the past summer, however, I obtained an expression 

 which, though only approximate, may still be found of con- 

 siderable interest. According to this 



i a 



A=c(m + v x ) or r =c > 



m + v x 



in which A = atomic weight, c = constant, m = a member of 

 an arithmetical progression depending on the series* to 

 which the element belongs, v = the maximum valency or the 

 number of the group* of which the element is a member. 



After numerous trials it has been found that the best 

 results are obtained when x=2, and 



m=0; 2i; 5; 8£; 12; 15J; 19; 22^; 26; 29J; and 33 

 for 

 Series n.; III.; IV.; v.; VI.; VII.; vni.; ix.; x.; XI.; and XII. 



So that 



A 

 ^=0. 



m+ V v 



It will be observed that m is a member of an arithmetical 

 series in which the common difference is 3 J, except in the 

 first two cases, where it is only 2J. 



In the following Table are given the values of c calculated 

 from the above equation. The atomic weights employed and 

 given in Column I. are taken from Clarke's ( Recalculation 

 of the Atomic Weights ' (1882), corrections being made when 

 rendered necessary by more exact determinations published 

 since Clarke's work. The atomic weights are given to the 

 first place of decimals only. 



* These terms are employed in the sense in which Mendeljeff uses 

 them in his Natural Classification of the Elements. 



