INTRODUCTION. 5 



That all methods of averaging are open to objections, I am of course 

 perfectly aware. I also know the doubts which attach to all questions 

 of probable error, and to all combinations of data which depend upon 

 them. I have, however, preferred to face these objections and to recog- 

 nize these doubts rather than to adopt any arbitrary scheme which per- 

 mits of a loose selection of data. After all, the use of probable error as 

 a means of weighting is but a means of weighting, and perhaps more 

 justifiable than any other method of attaining the same result. When 

 observations are weighted empirically that is, by individual judg- 

 ment far greater dangers arise. Almost unconsciously, the work of a 

 famous man is given greater weight than that of some obscure chemist, 

 although the latter may ultimately prove to be the best. But the prob- 

 able error of a series of measurements is not affected by the glamor of 

 great names; and the weight which it assigns to the observations is at 

 least as safe as any other. In the long run, I believe it assigns weight 

 more accurately, and therefore I have trusted to its indications, not as 

 if it were a mathematical fetish, but regarding it as a safe guide, even 

 though sometimes fallible. 



In Meyer and Seubert's recalculation, weights are assigned in quite a 

 novel manner. In each series of experiments the maximum and mini- 

 mum results are given, but instead of the mean there is a value deduced 

 from the sum of the weighings that is, each experiment is weighted 

 proportionally to the mass of the material handled in it. For this 

 method I am unable to find any complete justification. Of course, the 

 errors due to the operations of weighing become proportionally smaller 

 as the quantity of material increases, but these errors, with modern 

 apparatus, are relatively unimportant. The real errors in atomic weight 

 determinations are much larger than these, and due to different causes. 

 Hence an experiment upon ten grammes of material may be a little better 

 than one made upon five grammes, but it is by no means necessarily 

 twice as good. The ordinary mean of a series of observations, with its 

 measure of concordance, the probable error, is a better value than one 

 obtained in the manner just described. If only errors of weighing were 

 to be considered, Meyer and Seubert's summation method would be 

 valid, but in the presence of other and greater errors it seems to have 

 but little real pertinency to the problem at hand. 



In addition to the usual periodicals, the following works have been 

 freely used by me in the preparation of this volume: 



BERZELIUS, J. J. Lehrbuch der Chemie. 5 Auflage. Dritter Band. 

 SS. 1147-1231. 1845. 



VAN GEUNS, W. A. J. Prceve eener Geschiedenis van de ^Equivalent- 

 getallen der Scheikundige Grondstoffen en van hare Soortelijke 

 Gewigten in Gasvorm, voornamelijk in Betrekking tot de vier 

 Grondstoffen der Bewerktuigde Natuur. Amsterdam, 1853. 



