GENERAL INTRODUCTION. 



The Mathematical Problem. 



The, theoretical or mathematical problem to be solved in 

 order to obtain the true or absolute atomic weight from the 

 varied values furnished by the chemical laboratory work, 

 has hitherto received only a formal treatment in the use of 

 the mean and its probable error. We must briefly consider 

 this formal study before we can give the outline of our own 

 general solution of the problem. 



The Mean. 



Chemists have, thus far, supposed that the mean value of 

 the individual chemical determinations is nearer the true 

 value sought for than any of the actual determinations made. 



This mean value is calculated by summing up all indi- 

 vidual values found and dividing this sum by the number of 

 determinations made. 



But what evidence do we possess proving that the average 

 of the individual measures is the true measure? Absolutely 

 none at all. 



On the contrary, every chemist will readily admit that 

 some chemical operations necessarily give values always too 

 high, while others give them always too low. The great 

 master Berzelius has already recognized this fact, and made 

 it the basis of his most admirable rule of procedure. True 

 At. Weights, p. 16. 



"Try to find that method of analysis, in which the 

 " accuracy of the result will depend to the least extent on 

 " the skill of the operating chemist; and when this method 

 " has been selected, then consider what unavoidable con- 

 " ditions are present which may cause errors in the result, 

 ff and ascertain whether they will increase or diminish the 

 " same. Thereafter make another determination, in which 

 11 exactly the opposite effects only can be produced. If the 

 " result remains the same, the determination was correct." 

 Sebelien, p. 13, quoted from Gilbert's Annalen, vol. 18, p. 

 537; 1814. 



This rule of Berzelius points to our higher and lower 

 limits, between which the time atomic weight must fall. 



