46 THE ERRORS OF PRECISION. 



In the case of the water of crystallization, the third 

 decimal in the analytical ratio of Ramsay and Aston varied 

 from i to 2. Hence only four decimals should have been 

 recorded, instead of six. 



Or to avoid misunderstanding, the tenth of per cent of 

 water of crystallization running from one to two, only one 

 decimal more ought to have been given, the hundredth of a 

 per cent as decidedly uncertain. 



A Fine Probable Error. 



I cannot help adding, as a fine commentary to the above, 

 the " probable error " calculated by Clarke, our government 

 chief chemist, in his <e Constants of Nature," published by 

 our Smithsonian Institution in 1897. 



On page 172 the probable error of this result is given as 

 0.0086 per cent, or let us plain chemists put it at 0.009 P er 

 cent or 0.00009 per unit (our ratio). 



How easily our government chemist, by a little mechani- 

 cal calculation converts experimental results uncertain in 

 the third decimal to fine work with a probable error less 

 than a unit in the fourth place! 



No wonder that even students in our universities are 

 making atomic weight determinations. Their balances and 

 weights are finer than those Berzelius used and they can also 

 calculate the "probable error" of their result, something 

 that Berzelius did not do. 



And as A. Cornu of Paris (Nov. 16, 1894), wrote me in a 



letter very commendatory of my "True Atomic Weights," 



ti the extension of the method of the least squares has 



" unfortunately persuaded many people that syste- 



11 matic errors do not exist any more!" 



We have given evidence of the existence and great mag- 

 nitude of just such errors. 



IX. MINUTE CHEMICAL ERRORS. 



Having critically considered the common process of 

 reduction of the experimental work of atomic weight deter- 

 minations, we may next point out the leading chemical 

 features of this work. 



