ATOMIC WEIGHTS 3 



other atomic weights are determined. Direct comparisons with oxygen 

 or hydrogen are relatively few; indirect determinations with the aid of 

 silver and the halogens are many. For the elements in question there 

 were data from many experimenters. All similar figures, that is, the 

 figures for each ratio, were first reduced to a common standard, and 

 then the individual means were combined into general means. Thus all 

 the data were condensed into fifty-five ratios, from which a number 

 of values for each atomic weight could be computed. The ratios represent 

 the actual experimental work ; the atomic weights are inferential. Finally, 

 the several values for each atomic weight are treated as if they were 

 means of the usual type, and combined by the method of least squares 

 into a general mean, which is supposed to represent the most probable 

 value for each constant. The fundamental values having been deter- 

 mined, they are next applied to the calculation of what may be called 

 the secondary atomic weights, and in this work the probable error of each 

 term in each ratio is taken into accoimt. This will appear more clearly 

 evident in the subsequent actual calculations. 



But although the discussion of atomic weights is ostensibly mathe- 

 matical, it cannot be purely so. Chemical considerations are necessarily 

 involved at every turn. In assigning weights to mean values I have 

 been, for the most part, rigidly guided by mathematical rules; but in 

 some cases I have been compelled to reject altogether series of data 

 which were mathematically excellent, but chemically worthless because 

 of constant errors. In certain instances there were grave doubts as to 

 whether particular figures should be included or rejected in the calcula- 

 tion of means, there having been legitimate reasons for either procedure. 

 Probably many chemists would difi'er with me upon such points of judg- 

 ment. In fact, it is doubtful whether any two chemists, working inde- 

 pendently, would handle all the data in precisely the same way, or 

 combine them so as to produce exactly the same final results. Neither 

 would any two mathematicians follow identical rules or reach identical 

 conclusions. In calculating the atomic weight of any element those 

 values are assigned to other elements which have been determined in 

 previous chapters. Hence a variation in the order of discussion might 

 lead to slight differences in the final results. 



As a matter of course the data herein combined are of very unequal 

 value. In many series of experiments the weighings have been reduced 

 to a vacuum standard; but in other cases chemists have neglected this 

 correction altogether. In a majority of instances the errors thus intro- 

 duced are slight; nevertheless they exist, and interfere more or less with 

 all attempts at a theoretical consideration of the results.^ 



' For a discussion of these vacuum corrections see Guye and Zachariades, Compt. Rend., 149, 593. 

 The errors in reductions to a vacuum are larger than has been commonly supposed. 



