2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 54 



new material accumulated that in 1897 ^ a new edition of this work, revised 

 to date, became necessary. Since then, much more has been done, with 

 great improvements in technique, especially by Richards and his col- 

 leagues at Harvard University, by Edgar F. Smith in Philadelphia, and 

 by Guye at Geneva, not to mention many other workers of high merit. 

 The assimilation of this new material, and its combination with the 

 older data, is the object of the present volume. 



At the very beginning of my work, a fundamental question confronted 

 me. Should I treat the investigations of different individuals separately, 

 or should I combine similar data together in a manner irrespective 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 composition 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 formulse employed are given in another place. Beginning 

 with the ratio between oxygen and hydrogen, each series of experiments 

 was taken by itself, its arithmetical mean was determined, and the 

 probable error of that mean was computed. Then the several means 

 were combined according to the appropriate formula, eacli one receiving 

 a weight dependent upon its probable error. The general mean thus 

 established was taken as the most probable value for the ratio, and at 

 the same time its probable error was mathematically assigned. In the 

 former editions of this work it was used to give the atomic weight of 

 oxygen referred to hydrogen as unity. In the present edition the oxygen 

 standard is assumed, and the atomic weight of hydrogen is determined. 

 This is in accordance with the decisions of the International Committee 

 on Atomic Weights; although my personal preference, on theoretical 

 grounds, is for the hydrogen standard. The subsequent computations, 

 however, are rendered simpler by assuming that = 16, and that is a 

 principal reason for my change of policy. 



Next in order came a number of elements which were best considered 

 together; namely, silver, chlorine, bromine, iodine, potassium, sodium, 

 nitrogen, sulphur and carbon. Their atomic weights, with those of 

 hydrogen and oxygen, form a fundamental group, by means of which 



' Smithsonian Miscellaneous Collections, Vol. 38, Serial No. 1075, pp. vi, 370. 



