2 THE ATOMIC WEIGHTS, 



At the very beginning of m}'- work, certain fundamental questions con- 

 fronted me. Should I treat the investigations of different individuals 

 separately, or should I combine similar data together in a manner irre- 

 spective of persons ? For example, ought I, in estimating the atomic 

 weight of silver, to take Stas' work by itself, Marignac's work by itself, 

 and so on, and then average the results together; or should I rather 

 combine all series of figures relating to the composition of potassium 

 chlorate into one mean value, and all the data concerning the composi- 

 tion of silver chloride into another mean, and, finally, compute from such 

 general means the constant sought to be established ? The latter plan 

 was finally adopted ; in fact, it was rendered necessary by the method of 

 least squares, which, in a special, limited form, was chosen as the best 

 method of dealing with the problem. 



The mode of discussion and combination of results was briefly as 

 follows. The formulae 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 

 experiments 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 estab- 

 lished was taken as the most probable value for the atomic weight of 

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

 assigned. 



Next in order came a group of elements which were best discussed 

 together, namely, silver, chlorine, potassium, sodivim, bromine, and 

 iodine. For these elements there were data from many 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 nineteen 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 suggested 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 refer- 

 ence to elements whose atomic weights have been defectively ascertained 

 will receive a high probable error, and its weight, when combined with 

 other values, will be relatively low. For exam])le, an atomic weight 

 ascertained by direct comparison with hydrogen will, other things being- 

 equal, have a lower probable error than one which is referred to hydro- 

 gen through the intervention of oxygen ; and a metal whose equivalent 

 involves only the probable error of oxygen should be more exactly 



