VIII INTRODUCTION. 



The mode of discussion and combination of results was 

 briefly as follows. The formulEe employed are given in 

 another chapter. I began with the ratio between oxygen 

 and hydrogen ; in other words, with the atomic weight of 

 oxygen referred to hydrogen as unity. Each series of ex- 

 periments was taken by itself, its arithmetical mean was 

 found, and the probable error of that mean was computed. 

 Then the several means were combined according to the 

 appropriate formula, each receiving a weight dependent 

 upon its probable error. The general mean thus established 

 was taken as the most probable value for the atomic weight 

 of oxygen, and, at the same time, its probable error was 

 mathematically asssigned. 



Next in order came a group of elements which were best 

 discussed together, namely, silver, chlorine, potassium, so- 

 dium, bromine, iodine, and sulphur. For these elements 

 there were data from thirteen experimenters. All similar 

 figures were first reduced to common standards, and then 

 the means of individual series were combined into general 

 means. Thus all the data were condensed into twenty 

 ratios, from which several independent values for the atomic 

 weight of each element could be computed. The probable 

 errors of these values, however, all involved the probable 

 error of the atomic weight of oxygen, and were, therefore, 

 higher than they would have been had the latter element 

 not entered into consideration. Here, then, we have sug- 

 gested a chief peculiarity of this whole revision. The 

 atomic weight of each element involves the probable errors 

 of all the other elements to which it is directly or indirectly 

 referred. Accordingly, an atomic weight determined by 

 reference to elements whose atomic weights have been defec- 

 tively ascertained will receive a high probable error, and its 

 weight, when combined with other values, will be relatively 

 low. For example, an atomic weiglit ascertained by direct 

 comparison with hydrogen will, other things being equal, 

 have a lower probable error than one which is referred to 

 hydrogen through the intervention of oxygen ; and a metal 

 wdiose equivalent involves only the probable error of oxygen 



