10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 54 



Given a proportion, A : B : : C : a;, the probable error of the fourth term 

 is as follows : 



/f^9^V +(C&)« + (Bc)2 



This formula is used in nearly every atomic weight calculation, and 

 is, therefore, exceptionally important. Rarely a more complicated case 

 arises in a proportion of this kind : 



A : B : : C + X : D + a; 



In this proportion the unknown quantity occurs in two terms. Its 

 probable error is found by this expression, and is commonly large: 



(9.) ,=^(^__^^(B=«= + A'^5^)+---^^_ 



B»c2 + AW 



When several independent values have been calculated for an atomic 

 weight they are treated like means, and combined according to formulge 

 (2) and (3). Each final result is, therefore, to be regarded as the general 

 or weighted mean of all trustworthy determinations. This method of 

 combination is not theoretically perfect, but it seems to be the one most 

 available in practice. 



