Atomic Laws of Thermochemistry, 21 



but this ratio has just been proved to be probably constant, 

 that is independent of R : which implies that 



(S 1 )-(S 8 )=0=(S 1 )-(S 2 ) ! 



and that/(RS) can be resolved into two factors, one depend- 

 ing on R only, and the other on S only. Let 



/(RS)=f(R)^(S), 



then the last equation becomes 



H(RS 1 )-H(RS a )" t(Si)-^(S 2 )' 



which is of course independent of R. 



Thus for the halogens, as the mean value for the ratio in 

 the last table (excluding Ag and Hg) is 2 '6, we have the 

 following fundamental equations : — 



(Cl) = (Br)=(I) (1) 



^(Cl)-f(I) = 2-6{f (Cl)-^(Br)}. ... (2) 



The third result obtained from Table V. is that the columns 

 headed CI— Br and CI— I, being the values of 



f (R){f (Cl)-^(Br)} and f (R){i/r(Cl) -^(I)} 5 



afford a clue to the law of >Jr(R). In order to deal with as 

 large numbers as possible, and so reduce the relative im- 

 portance of errors in the data, we will add the two columns 

 of differences; and since the numbers in the CI— I column are 

 on the average 2*6 times those in the CI — Br column, the 

 result of adding is to get 3*6i|r(R){i|r(Cl) — i/r(Br)}, the values 

 of which are given in the following table, arranged in order 

 of magnitude : — 









Table VI. 











417 



2 \j'&. 



38-5 



Li. 

 34-4 



Na. 

 33-4 



£Zn. 

 32-9 



|A1. 



30-7 



K. 



291 



Multiples 

 of 3-8 



41-8 

 11 



38-0 

 10 



342 

 9 



34-2 

 9 



34-2 

 9 



30-4 



8 



30-4 

 8 





£Cd. 

 23-7 



Us. 

 23'4 



iPb. 

 221 



Cu. 

 21-8 



Ag. 

 179 



iHg. 

 124 





Multiples 

 of 3-8 



22-8 

 6 



22-8 

 6 



22-8 

 6 



22-8 

 6 



19-0 

 5 



11-4 

 3 





The second row of numbers is a series of multiples of 3 # 8, 

 and a comparison of the two rows shows that the values of 

 3*6^(R){^(C1)— ^(Br)} approximately form a series of 





