248 



SCIENCE, 



[N. S. Vol. IV. No. 87. 



hydrogen made the essence of the process 

 novel. Then Noyes devised a new method 

 of weighing hydrogen directly, and a new 

 manipulation for combining it with oxygen, 

 and carried out the process in an apparatus 

 having the advantage of great simplicity. 

 Further, since our last meeting the Smith- 

 sonian Institution has published a work 

 containing three series of determinations of 

 the value in question. 



In England, Lord Eayleigh used another 

 novel method of combining oxygen and hy- 

 drogen, in which he weighed both elements 

 in the form of gas. He also made two 

 series of determinations of the ratio of the 

 densities of the gases. Scott determined 

 the ratio of the volumes of the gases which 

 combine, in several series of experiments of 

 great accuracy. Dittmar and Henderson 

 rendered an important service by repeating, 

 with many modifications, the experiments 

 of Dumas ; with the advantage which the 

 later experimenter commonly has over the 

 earlier, they were able to secure a much 

 higher degree of precision and to eliminate 

 the sources of constant error which Dumas 

 detected too late. 



In France, Leduc repeated the experi- 

 ments of Dumas and also determined the 

 ratio of the densities of the two gases. 



In Denmark, Thomsen has applied a dif- 

 ferent process, in which the atomic weight 

 of a given metal is compared with those of 

 oxygen and of hydrogen successively. 



"We have, then, eleven series of determi- 

 nations of the atomic weight of oxygen. 

 One of these, for reasons which, so far, are 

 chiefly matter of conjecture, differs much 

 from the mean of all the others. These 

 other ten are concordant ; they differ, on 

 the average, only one part in twenty-two 

 hundred from their mean, and the greatest 

 difference from the mean is about one part 

 in a thousand. 



Since these experiments have been made 

 by different processes, by different men, un- 



der varied conditions, and since the great- 

 est difference from the mean of the whole is 

 only one part in a thousand, it is probable 

 that the mean of all differs from the truth 

 by much less than one part in a thousand. 

 The errors of our experiments are of two 

 kinds — accidental and systematic. If we 

 shoot a hundred times at a mark, about 

 half of our shots fall a little to the right 

 and about half a little to the left. These 

 are accidental errors ; accidental errors are 

 lessened as our manipulation improves, and 

 they but slightly affect our final mean. 

 Systematic errors affect all our results in 

 the same direction. Suppose we fire a hun- 

 dred shots at a target one thousand yards 

 distant, not examining the target, till the 

 shots are all fired. If, now, the sights of 

 our rifle were set for five hundred yards, 

 all our shots would strike too low. This 

 is a systematic error ; systematic errors 

 diminish as our knowledge increases. 



Accidental errors can be rendered harm- 

 less by taking the mean of numerous deter- 

 minations made by the same method. But 

 systematic errors must be detected and 

 avoided. That they have been detected 

 and avoided in any given case can never be 

 definitely known ; it can, at best, be pre- 

 sumed from the fact that experiments by 

 different methods give the same result. 



As to the atomic weight of oxygen, acci- 

 dental errors have now been fairly elimin- 

 ated, and we can make definite numerical 

 statements on this point. If each of the 

 ten sets of experiments were to be repeated, 

 with the same skill and knowledge, there is 

 not one chance in a thousand that the new 

 mean would differ from the present mean 

 by as much as one part in sixteen thousand. 

 Again, if ten new sets of experiments were 

 to be made by new methods and new ex- 

 perimenters, there is not one chance in a 

 thousand that the new mean would differ 

 from the present mean by as much as one 

 part in twenty-five hundred. 



I 



