294 PROCEEDINGS OF THE AMERICAN ACADEMY 



If the oxygen is taken as 15.96, copper becomes 63.44. With 

 oxygen 15.87, the value sinks to 63.09. 



The mathematical discussion of these results is omitted, because 

 it gives an exaggerated notion of the accuracy of the final average. 

 The real probable error of this average is much more dependent upon 

 the chemical purity of the electrolytic copper than upon the mere 

 mechanical or experimental error with which alone the theory of 

 least squares is competent to deal. 



It is apparent that any one of the methods, thoroughly investigated, 

 would have long ago afforded a fairly accurate knowledge of the atomic 

 weight. Too much cannot be said against the multiplication of incom- 

 plete or carelessly obtained data ; for such data carry with them not 

 only uncertainty and confusion in the present, but also additional 

 labor for a reviser in the future. 



In the present investigation every reaction was assumed to involve 

 some constant error, and every substance was assumed to contain some 

 constant impurity, until a proof of the contrary was obtained. The 

 research consisted, in fact, of a succession of mutual checks. The 

 attempt was made to adopt precautions of a consistent order of refine- 

 ment ; and the still remaining causes of possible error have been care- 

 fully pointed out in the description. The not inconsidei'able outlay of 

 time, thought, and labor has been more than repaid by a conviction 

 of the definiteness of the combining proportions which four years ago 

 would have seemed to the writer impossible. 



