8 THE ATOMIC WEIGHTS. 



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

 is as follows : 



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 : 



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

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



(9.) 



When several independent values have been calculated for an atomic 

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

 (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. 



OXYGEN. 



The ratio between oxygen and hydrogen is the foundation upon which 

 the entire system of atomic weights is sustained. Hence, the accuracy 

 of its determination has, from the beginning, been recognized as of ex- 

 treme importance. A trifling error here may become cumulative when 

 repeated through a moderate series of other ratios. But few of the 

 elements have, so far, been compared directly with th unit, hydrogen ; 

 practically all of them are referred to it through the intervention of 

 oxygen, and therefore the ratio in question requires discussion before 

 any other can be profitably considered. 



Leaving out of account the earliest researches, which now have only 

 historical value, the first determinations to be noted are those of Dulong 

 and Berzelius,* who, like some of their successors, effected the synthesis 

 of water over heated oxide of copper. The essential features of the 

 method are in all cases the same. Hydrogen gas is passed over the hot 

 oxide, and the water thus formed is collected and weighed. From this 

 weight and the loss of weight which the oxide undergoes, the exact com- 



* Thomson's Annals of Philosophy, July, 1821, p. 50. 



