284 



SCIENCE. 



[N. S. Vol. XI. No. 269. 



criticism depends on tlie knowledge and the 

 acuteness of the critic. Dr. Hinrichs pub- 

 lished, some five j^ears ago, a criticism of 

 all determinations and computations of 

 atomic weights since Dumas. As is well 

 known, he is a most strenuous and insistent 

 supporter of Prout's hypothesis. Looking 

 hastily through the volume, there was 

 found, towards the end, evidence that its 

 author was one of those who, some thirty 

 years ago, discerned that which, in the 

 hands of MendeleefE became the periodic 

 law. It seemed possible that one who had 

 early seen some indications of this law 

 might, perhaps, also have discerned, even 

 if obscureljr, some principle relating to 

 atomic weights. I therefore once spent 

 some time and pains in carefully reading 

 the book, and considered at length those 

 passages, which, if any, contained valid 

 criticism of the views which are generally 

 accepted. 



Hinrichs believes that the mean of a 

 series of determinations of an atomic weight 

 cannot give the true value sought. This 

 proposition he deduces from a mathematical 

 discussion. He believes that as larger and 

 larger quantities are taken in our analytical 

 operations, the results differ regularly from 

 ideal accuracy ; sometimes the difference 

 continually increases as the quantity taken 

 increases ; sometimes the difference in- 

 creases to a maximum and then decreases 

 again. The proper computation of an 

 atomic weight then, according to Hinrichs, 

 consists not in taking the mean of different 

 observations, made with different weight of 

 materials, but in determining the limit to- 

 wards which the series converges as the 

 weight taken decreases. A good illustration 

 is given : we cannot determine the weight 

 of a new coin by weighing any number of 

 old coins ; every coin is worn and therefore 

 light, and the mean weight of any num- 

 ber whatever is therefore necessarily below 

 the mean weight of new coins. But if we 



weigh old coins and note the date of each, 

 we may take the mean weights for each 

 year separately. If we examine coins 

 enough, these means when plotted as the 

 ordinates with the years as the abscissas, 

 will give us a " fairly regular curve, lowest 

 for the oldest coins, gradually rising to- 

 wards a limit which they would not quite 

 reach. This higher limit would evidently 

 be the mean weight of the new coin. ' ' 



This is an intelligible proposition. It 

 seemed to me worth while to examine it, for 

 to this proposition one of the most enthusias- 

 tic and most active supporters of Prout's 

 hypothesis, a man not lacking in shrewdness 

 or ability or learning, has entrusted the de- 

 fense of his favorite belief. 



He asserts that an atomic weight as de- 

 termined by experiment is variable, that it 

 depends on the amount of substance taken 

 for the analysis or other operation, and that 

 it varies in a continuous and regular man- 

 ner. His proposition is, that an atomic 

 weight as determined by experiment is a 

 function of the weight of substance taken. 

 Is there any evidence in favor of it ? 



I answer, first : Theory does not afford 

 any evidence for it. Hinrichs deduces this 

 proposition from theory by a discussion 

 which is mathematical in form. Whether 

 the proof is sound need not be considered, 

 for his theory does not attempt to show the 

 order of magnitude of the regular and con- 

 tinuous variations which are affirmed to de- 

 pend on the weight of substance taken, and 

 to show whether they can be separated from 

 the irregular and discontinuous errors due 

 to accident. We are sure that accidental 

 errors exist ; we may concede for argument, 

 that regular and continuous variations also 

 exist ; but this is far from implying that the 

 actual errors in a given set of experiments 

 will be largely or even perceptibly of the 

 latter kind. Theory shows that there is a 

 diurnal tide in the atmosphere ; but theory 

 does not show that the differences noted in 



