INTRODUCTION. 6 



known than one which depends upon the errors of silver and chlorine. 

 These points will appear more clearly evident in the subsequent actual 

 discussions. 



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 mathematicall}^ 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 differ 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 

 w^Quld an}' 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 most 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. 



Necessaril}^ this work omits many details relative to experimental 

 methods, and particulars as to the arrangement of special forms of apjja- 

 ratus. For such details original memoirs must be consulted. Their in- 

 clusion here would have rendered the work unwarrantably bulk}^ There 

 is such a thing as over-ex haustiveness of treatment, which is equally 

 objectionable with under-thoroughness. 



Of course, none of the results reached in this revision can be consid- 

 ered as final. Every one of them is liable to repeated corrections. To 

 my mind the real value of the work, great or little, lies in another direc- 

 tion. The data have been brought together and reduced to common 

 standards, and for each series of figures the probable error has been de- 

 termined. Thus far, however much my methods of combination may 

 be criticised, I feel that my labors Avill have been useful. The ground is 

 cleared, in a measure, for future experimenters; it is possible to see more 

 distinctl}^ what remains to be done ; some clues are furnished as to the 

 relative merits of different series of results. 



On the mathematical side my method of recalculation has obvious 

 deficiencies. It is special, rather than general, and at some future time, 

 when a sufficiently large mass of evidence has accumulated, it must 



