ATOMIC WEIGHTS 5 



with reference to the entire mass of material, and would practically 

 vanish from the final means. 



Concerning this subject of constant and accidental errors, a word may 

 be said here. My own method of discussion eliminates the latter, which 

 are, in great part at least, removable by ordinary averaging; but the 

 constant errors, vicious and untractable, remain, at least partially. Still, 

 where many ratios are considered, even the systematic errors may in 

 part compensate each other, and do less harm than might be expected. 

 They have, moreover, a peculiarity which deserves some attention. 



In the discussion of instrumental observations, the systematic errors 

 are commonly constant, both as to direction and as to magnitude. They 

 are therefore independent of the accidental errors, and computation of 

 means leaves them untouched. But in the measurement of chemical 

 ratios the constant errors are most frequently due to an impurity in one 

 of the materials investigated. If different samples of a substance are 

 studied, although all may contain the same impurity, they are not likely 

 to contain it in the same amount: and so the values found for the ratio 

 will vary. In other words, such errors may be constant in direction but 

 variable in magnitude. That variation appears in the probable error 

 computed for the series of observations, diminishes its weight when com- 

 bined with other series, and so, in part, corrects itself. It is not removed 

 from the result, but it is self-mitigated. The constant errors familiar to 

 the physicist and astronomer are obviously of a different order. 



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 only 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 judgment 

 — 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 good 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. 



One possibly weak point in the method adopted, deserves to be men- 



