102 Prof. F. W. Clarke on the Results obtained 



from = 15-892 to = 16-024. The mean of all is 15*9607, 

 with a probable error of ±'007. Erdmann and Marchand 

 give eight results, which average = 15*9733 ±'0113. The 

 general mean from both investigations is 



O = 15*9642±*006. 



The density of hydrogen, referred to air as unity, was deter- 

 mined by Regnault in three experiments. The mean was 

 •069263 ; ±'000019. For oxygen four determinations were 

 made by Regnault, and one of them was rejected. The three 

 remaining figures give a density of 1*105633; ±'000008. 

 The ratio between these two density-estimations gives an 

 atomic weight of = 15*9628; ±'0044. Combining this 

 with the value found from the synthesis of water, we get a 

 general mean of 



= 15*9633 ; ±'0035. 



This is the most probable value which can be deduced from 

 the published data, and it forms the corner-stone upon which 

 our entire system of atomic weights must rest. I need not 

 discuss here the methods employed in the calculation of pro- 

 bable errors; for they are given in all treatises upon least 

 squares. Suffice it to say, that I assign no arbitrary weights 

 to the values under examination ; each series of experiments 

 receives the weight to which the probable error of its mean 

 entitles it. 



Having found a value for oxygen, I next discussed in a 

 group the atomic weights of the elements chlorine, bromine, 

 iodine, silver, potassium, sodium, and sulphur. The data to 

 be considered were determined by Berzelius, Penny, Pelouze, 

 Marignac, Maumene, Gerhardt, Millon, Struve, Svanberg and 

 Struve, Turner, Dumas, Cooke, and Stas, and represented 

 twenty distinct ratios. For example, one of the most impor- 

 tant ratios was that between potassium-chloride and potassium- 

 chlorate, for which there were nine series of determinations. 

 The mean of each series was calculated, together with its 

 probable error ; and then all nine means were combined into 

 one general mean. Thus all the available data were reduced 

 to the twenty compact ratios above referred to. Two of these 

 may be cited, to illustrate the methods of calculation. 



1. Percentage of O in K CI 3 , 39-154; ±'0004. 



2. Ag : KC1 : : 100 - 69*1032 ; ±*0002. 



From the first of these ratios the molecular weight of KC1 

 is easily calculated by the usual proportion 39*154 : 60*846 : : 



3 : X- 



Using the value for oxygen previously found, ^, or KC1, 



became 74*4217 ; and as the probable errors are known for 



