102 Prof. T. Carnelley on an Algebraic Expression of 



By substituting (3) in (2) we get 



107'7=c{m^ + 3x + l)=c(m i + l) + 3xc. 

 But 



c (m 4 + l)=39; 



.-. 107*7=39 + 3^ or ac=22'90. 



By proceeding in a similar manner the following values 

 xc are obtained from the pairs of elements (all belonging 

 group 1) named : — 





on 



l K and Cu . . 



. #c=24-30 



jj 



K and Kb . . 



. ac=23-15 



n 



K and Ag . 



. arc=22-90 



;; 



K and Cs . . 



. a;c=23-40 



1) 



K and Au . 



. xc=22'56 



JJ 



Cu and Rb . 



. xc= 22-00 



J? 



Cu and Ag . 



. 0c=22-2O 



5? 



Cu and Cs . 



. ^=23-10 



JJ 



Cu and Au . 



. ^=22*22 



73 



Rb and Ag . 



. a?c= 22-40 



jj 



Rb and Cs . 



. #c = 23*65 



?j 



Rb and Au . 



. ^=22*32 



>; 



Ag and Cs . 



. . 0c=24-9O 



jj 



Ag and Au . 



. . ac=22'30 



» 



Cs and Au . 



. . 0c=21-43 





Mean= 22-85 



Or, in other words, the difference between the atomic weights 

 of any two elements in group 1 (from series I v. upwards) 

 divided by the difference between the number of the series to 

 which each element belongs, gives a constant, or 



B— A 



= constant =22-85, 



y— *• 



where x and y are the numbers of the series to which the 

 elements A and B respectively belong. That is to say, the 

 difference between successive elements of group 1 from 

 series IV. upwards is practically constant and equal to 22*85. 



Now the constant 22*85 is very nearly identical with the 

 atomic weight of sodium, which the most trustworthy deter- 

 minations have shown to be 22*99. 



If x be 3 J, then c — 



22*85 



= 6*53, or if, in place of 22*85, 



. 22*99 



we take the atomic weight of sodium, then c— Q =6*57, 



