l6 THE ERRORS OF PRECISION. 



I have pointed out one of the most flagrant cases of the 

 multitude committed by Professor Ostwald of Leipzig under 

 the highest pretentions to scientific precision. See my 

 "True Atomic Weights," pp. 43-44; 1894. 



In the entire big book of the "Constants of Nature," 

 issued in 1897, by the Smithsonian Institution, there is not 

 half a dozen cases among the hundreds given, in which this 

 essential condition has not been violated. 



Conditions were Disregarded. 



Accordingly, practically speaking, all the calculated 

 values of the probable error of the mean values of atomic 

 weight determinations published up to-date in all scientific 

 works on atomic weights issued, have been obtained in total 

 disregard of these two fundamental conditions which are 

 pre-requisite to the application of this mode of calculation. 



In the determinations of the atomic weight of boron 

 made in the laboratory of Moissan at Paris, recommended 

 by him and his section of chemistry to the Academy of 

 Sciences for a prize which was granted in December, 1900, 

 the study of the probable error was specially accentuated ; 

 and yet neither the chemist Moissan, nor his endorsing 

 colleagues know the formula for the calculation of that 

 probable error, having omitted the coefficient %; all pre- 

 tended values given and studied (discute) and crowned by 

 the Academy are only 50 per cent too high. See Annales de 

 Chimie, etc., T. 18, p. 363; 1899, where the formula used is 

 printed as "formule connu." 



Conditions Applied by us. 



Let us apply these conditions to the calculation of the 

 probable error of the mean weight of the twenty silver 

 dollars weighed by us on April 4, 1901. See page 13. 



The number of determinations, being 20, is just passable. 



The differences are quite evenly distributed about the 

 mean, though it must be noted that the difference for the 

 lightest coin is excessive. 



