INTRODUCTION. IX 



will be more exactly known than one which depends upon 

 the greater 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 osten- 

 sibly mathematical, it cannot be purely so. Chemical con- 

 siderations are necessarily involved at every turn. In as- 

 signing 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 worth- 

 less because of constant errors. In certain instances there 

 were grave doubts as to whether particular figures should 

 be included or rejected in the calculation of means ; there 

 having been legitimate reasons for either procedure. Prob- 

 ably many chemists would differ with me upon such points 

 of judgment. In fact, it is doubtful whether any two chem- 

 ists, working independently, 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 con- 

 clusions. 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 correc- 

 tion altogether. In a majority of instances the errors thus 

 introduced are slight ; nevertheless they exist, and interfere 

 more or less with all attempts at a theoretical consideration 

 of the results. For example, they affect seriously the in- 

 vestigation of Front's hypothesis, and at'e often great enough 

 to account for seeming exceptions to it. Such questions as 

 these will be considered in the appendix. 



Another serious source of error affecting many of the re- 



