Febbuaey 23, 1900.] 



SCIENCE. 



285 



a series of ten observations of the barome- 

 ter at different hours of the day will follow 

 the law of the diurnal tide. 



But, secondly : Facts do not agree with 

 the proposition. The accidental errors of 

 the most precise experiments yet made are 

 so much greater than any systematic varia- 

 tions, that nothing but accidental varia- 

 tions can be detected. To prove this, let 

 us consider Stas' synthesis of silver nitrate 

 from pure silver. This is one of the most 

 important determinations ever made ; Hin- 

 richs has discussed it twice in his volume ; 

 he asserts that the ratio of silver nitrate 

 to silver found in each analysis depends 

 on the weight of silver taken, and twice 

 draws curves to show this. I assert, on the 

 contrary, that the errors, which average 

 only 1 part in 40,000, are purely accidental, 

 and that they follow no law. This can be 

 proved by proving that the ratios obtained 

 depend on any other qu^antities selected by 

 accident just as much as they depend on the 

 weights of silver taken. Hinrichs plots the 

 resiilts of the ten determinations, using for 

 abscissas the weights of silver taken, and 

 so obtains tolerable curves. I plotted the 

 same ten observations, using for abscissas 

 not the weights of silver taken but ten num- 

 bers selected by sortes Virgilianm, and get 

 curves quite as tolerable as before ; and this 

 I did with ten different sets of abscissas, all 

 selected by pure accident. Now, quantities 

 which depend on any one of eleven sets of 

 abscissas, ten of which are selected by ac- 

 cident, are themselves accidental in their 

 variations, and the variations follow no law. 

 So far as the facts are examined, they give 

 no evidence in favor of Hinrichs' proposi- 

 tion ; we have seen that theory is equally 

 chary of her support, and we may safely 

 dismiss the suspicion that any source of 

 systematic error can be detected in deducing 

 atomic weights from the means of good 

 experiments. 



Within the limits of convenience, it is 



well to vary the amount of substance taken 

 in analytical determinations. This has been 

 a frequent practice in the finest investiga- 

 tions. But that this practice derives any 

 support from the so-called ' limit method ' 

 cannot be conceded. 



This criticism, this attempt at a theory, 

 then, removes no obstacles and reveals no 

 threatening pitfalls. If we desire a firmer 

 foundation for our system of atomic weights 

 we must simply enlarge the experimental 

 basis of our knowledge. 



If it is only by further experiment that 

 we can make surer of the atomic weight of 

 oxygen, we are to consider what kind of ex- 

 periments is most desirable. It is chiefly 

 for the sake of eliciting discussion on this 

 point that the subject of this address has 

 been chosen. 



Our present value for the ratio between 

 oxygen and hydrogen rests on one single 

 chemical combination, and upon two proc- 

 esses for determination. The first is, the 

 synthesis of water from its components. 

 The second is, the determination of the 

 densities of the gases and of their volumet- 

 ric ratio. Let us consider these in order. 



What synthetic experiments should be 

 repeated? We are met by the fact that 

 a complete synthesis, in which hydrogen 

 and oxygen and water are all three weighed, 

 can be made with errors only about one- 

 fourth as large as the errors in any of the 

 syntheses where only two substances are 

 weighed out of the three concerned. Other 

 things being equal, then, this process is by 

 far the most promising. But, so far it has 

 been carried out adequately by only one ex- 

 perimenter. Conditions were varied some- 

 what, it is true, but by no means so much 

 as they would be varied if the same person 

 repeated the experiments after an interval 

 of years ; by no means so much as if others 

 were to undertake such complete syntheses. 

 Lately, Keiser has devised a process which 

 varies in many particulars from that already 



