August 28, 1896.] 



SCIENCE. 



249 



As to possible systematic errors, modesty 

 in statement is incumbent upon all scientific 

 men. But we bave now ten independent re- 

 sults in wbich tbe dificrence from tbe mean 

 is at most only one part in one thou- 

 sand. We may then fairly assume tbat tbe 

 systematic error of tbe mean is less tban one 

 part in one thousand. Again, we bave 

 lately been able to take one step in advance, 

 wbicb throws needed light on precisely this 

 point. It has been found possible to weigh 

 some hydrogen, to weigh the requisite oxy- 

 gen, and to weigh the water which they 

 produce. If, now, there were some unde- 

 tected systematic error in weighing either 

 one of these three substances, occasioned, 

 for instance, by some impurity remaining 

 undetected in one of them, the sum of the 

 weights of the hydrogen and oxygen would 

 differ from the weight of the water pro- 

 duced. If a pound of sugar and a pound of 

 water produce only one pound and three 

 quarters of syrup, there was a quarter of a 

 pound of sand in the sugar. ISTow it has, I 

 think, been proved that, if the sum of the 

 weights of the hydrogen and the oxygen is 

 not precisely equal to the weight of the water 

 produced, the difference is too small to be 

 detected, and cannot be more than one part 

 in twenty-five thousand. If there really 

 were a difference of this amount, and, 

 further, if this difference were due to an er- 

 ror at the precise point where it would be 

 the most mischievous, it would render the 

 atomic weight of oxygen uncertain by one 

 part in about twenty-eight hundred. 



Taking into account the presumption 

 from the concordance of the results of dif- 

 ferent experimenters and the presumption 

 from the agreement just mentioned, I think 

 we are justified in assuming that the re- 

 maining systematic error is not more than 

 one part in sixteen hundred, and that it 

 probably is not more than one part in three 

 thousand. 



If this is a reasonable assumption, the net 



results of the experiments made in Den- 

 mark, France, Great Britain and the 

 United States is that the atomic weight of 

 oxygen is between 15.87 and 15,89, and that 

 probably it is between 15.875 and 15.885. 

 By no stretch can we imagine that the 

 truth lies in the whole number 16.00, nor in 

 the even fraction 15.50. We cannot sanely 

 believe it to lie in the number 15.75, hav- 

 ing modified Front's hypothesis into the 

 new statement that all atomic weights are 

 divisible, without remainder, by one quarter 

 of the atomic weight of hydrogen. It will 

 be obvious that, if we are still resolved to 

 accept some form of the attractive illusion, 

 we must assume that the true divisor is as 

 small as one eighth of the atomic weight of 

 hydrogen, for the value 15^ is included 

 within the limits given. 



Then there is one small and well deter- 

 mined atomic weight which utterly refuses 

 to support Front's hypothesis or any modi- 

 fication yet stated by believers in the hy- 

 pothesis. Further, now that the atomic 

 weight of oxygen is well established, we 

 can compare, with hydrogen taken as unity, 

 the seven other small and well determined 

 atomic weights which have been mentioned.^ 

 We see that every value differs from an in- 

 teger ; for lithium, nitrogen and potassium 

 the difference is about one part in two 

 hundred thirty ; for sodium, sulphur and 

 chlorine, about one part in one hundred 

 eighty ; for carbon and oxygen, about one 

 part in one hundred thirty. On the average, 

 these values, which are the best determined 

 in chemistry, differ from whole numbers by 

 about one part in one hundred eighty. 

 There is less than one chance in a thousand 

 that these numbers can possibly be so much 

 in error. These are the numbers best fitted 

 to test Front's hypothesis, and their evi- 

 dence against it is decisive. 



* The values are as follows: Li=6.97, C=11.91, 

 N-=13.94, 0=15.88, Na=22.87, S=31.83, Cl=35.19, 

 K=38.84. 



