ACTUAL ERRORS OF THE MEAN". 25 



The Seven Means are all Mean. 



Professor Mallet made seven series of determinations, 

 according to as many different chemical methods or pro- 

 cesses. 



This is the common practice of chemical science to-day, 

 and such different series are undertaken in the hope that 

 thereby the errors referred to may balance and thus disap- 

 pear from the final result, at which the mean value of the 

 means of each series is taken. 



Exactly why such seven errors should balance and mutu- 

 ally destroy one another so as to give a final mean without 

 error, is not stated. 



The means given by Professor Mallet for each of his seven 

 series, and his final mean, are as follows (according to 

 Ostwald, Zeitschrift, IV, 478; 1889) : 



Series I, from gold chloride, . . , . . Mean, 196.722 



" II, " gold bromide, 196.790 



" III, " potassium gold-chloride, . . . 196.775 



" IV, " trimethyl ammonium gold chloride, 197.225 



" V, " potassium gold cyanide, .... 196.825 



tf VI, " same to hydrogen, I 97- I 37 



" VII, " same to zinc, 196.897 



General Mean, 196.80 



While there thus is a range of almost half a unit between 

 the lowest mean 196.775 (III Series) and the highest mean 

 197.225 (IV Series), the results of each series and of each 

 individual determination are given to the third decimal. 

 It would not look like exact science if less than three deci- 

 mals were used. 



As the most probable mean of the means of the seven 

 series, Professor Mallet gives 196.80 as the atomic weight of 

 gold according to his great chemical research which has 

 been very highly honored. 



But we really do not care for the most probable mean 

 value at all. What we would like to know is the true atomic 

 weight of gold. If there is exact science, it ought to be able 

 to give us exactly that answer in one exact number. 



