THE ERRORS OF PRECISION. 



But the fine analytical balances in actual use in our labor- 

 atories permit, by the so-called method of oscillations, to 

 calculate the weight to the hundredth of the milligramme. 



Yea, the weighings of Morley are stated to the thousandth 

 of the milligramme, and those of Ramsay and Aston 

 before referred to are stated to the ten-thousandth of the 

 milligramme. 



To the uniniated it may appear as prima-facie evident, 

 that the apparent weighings being 



of Berzelius to the centigramme or 2nd ; 



of Dumas to the milligramme or 3rd ; 



of the present to the tenth mgr. or 4th ; 



of E. F. Smith to the hundredth mgr. or 5th; 

 of Morley to the thousandth mgr. or 6th ; 



of Ramsay to the ten thousandth mgr. or 7th 

 decimal of the gramme, the work of Ramsay was one hundred 

 thousand times as accurate as that of Berzelius. 



Let us see about the facts ; for we can not afford to take 

 sham accuracy for the truth. 



Weighing the Weighers. 



Now both Berzelius, in 1826, and Ramsay and Aston, in 

 1893, determined the amount of water of crystallization in 

 borax. 



Berzelius in three determinations found 47.10 per cent; 

 that is, his analytical ratio was 0.4710 being the amount per 

 unit of weight. 



Ramsay and Aston found a mean ratio of 0.471677. 

 Apparently they determined this ratio to the millionth, while 

 Berzelius reached the hundred thousandth only. 



But when we examine the seven individual determina- 

 tions made by Ramsey, we find they run all the way from 

 0.471099 as the lowest to 0.472026 as the highest. See 1. c., 

 Journal Chem. Soc. 



But the variation thus actually affects the third decimal, 

 which being uncertain, all the rest from the fourth to the 

 sixth are well, good for nothing as experimental data. 



