RICHARDS. — INTERNATIONAL ATOMIC WEIGHTS. 175 



Let us consider a concrete example, — the case of nitrogen. Few 

 would be willing to contend that the last figure in the number 14.04 is 

 certain. For the sake of argument, let us assume that the value of this 

 atomic weight may really be as low as 14.034 or as high as 14.046. 

 According, then, to the rule which has just been adopted by the Inter- 

 national Committee, this figure 4 should be omitted, and nitrogen should 

 be called 14.0. Such an omission causes an error far greater than the 

 uncertainty which leads to the dropping of the figure. The uncertainty 

 named above is only 0.04 per cent, but the minimum error in the value 

 14.0 is 0.24 per cent, if the lower value given above is supposed to be the 

 lowest possible. Clearly one must either record uncertain figures, or 

 else omit figures which have a real significance. The dropping of a 

 decimal place at once reduces tenfold the ability of a number to express 

 slight changes of value ; but numerical results may have any degree of 

 accuracy, and cannot be classed strictly into classes separated by gaps so 

 wide. For this reason it is a well-known practice in scientific calcula- 

 tion to retain during the calculation one uncertain figure, while a final 

 result is sometimes relieved of this uncertain figure. According to this 

 rule, the table of atomic weights should always give an uncertain figure 

 in each value ; for atomic weights are simply data for further calculation. 

 If this is done, the user has all the truth, and may reject as much of it as 

 his occasion permits. Such a table of atomic weights seems to me to be 

 the best, because it is capable of fulfilling all uses. 



Quite another point of view should be adopted in making a table solely 

 for common use. Here we are concerned not with the number of cer- 

 tainly ascertained figures which may have been determined by Stas, but 

 rather with those figures which will have an influence upon the work in 

 hand. Usually the error in such a value is important not on account of 

 its absolute magnitude, but rather on account of its relation to the value 

 itself. In short, the percentage error is that which ought to be considered 

 in constructing a table of atomic weights for common use. A majority 

 of chemists would probibly decide that a table in which the values were 

 within 0.1 per cent of their true values would serve all ordinary purposes. 

 Most common methods are not able to attain as great a degree of accu- 

 racy even as this, but the admission of a wider range of inaccuracy in 

 a table of atomic weights might by summation cause an appreciable 

 error. Silver might be called 108.0, chlorine 35.5, bromine 80.0, iodine 

 126.9, potassium 39.2, sulphur 32.1, and lead 207.0, without seriously 

 affecting the results of most quantitative work, and indeed every one 

 frequently uses such approximate values. Even in this approximate 



