156 PEOCEEDINGS OF TPIE AMERICAN ACADEMY 



The one process by which the relative combining proportions of 

 oxygen and hydrogen have been hitherto directly determined is open to 

 serious criticism. In the first place, the circumstance that the weight 

 of the hydrogen is eight times smaller than that of the oxygen, and 

 that this weight has only been estimated by difference, is exceedingly 

 unfavorable to the accuracy of the process. It can easily be seen, 

 that, in order to establish a ratio like 1 to 8, the highest accuracy de- 

 mands that each term of the proportion should be known to an equal 

 degree of exactness. Thus if in a given experiment we have 8 grams 

 of oxygen uniting with 1 gram of hydrogen, it is of no avail to weigh 

 the oxygen to the tenth of a milligram, unless we can weigh the hy- 

 drogen to the same proportionate degree of accuracy. For an error 

 of eight tenths of a milligram in the weight of the oxygen, or an error 

 of nine tenths of a milligram in the weight of the water, will have no 

 more influence on the ratio we are seeking than an error of one tenth 

 of a milligram in the weight of the hydrogen. Now, in the process 

 we are discussing the weight of the water can be determined to within 

 a few tenths of a milligram ; that is, with all the accuracy with 

 which our problem requires that the larger term of the proportion 

 8 to 1 should be known. It is quite different with the weight of the 

 oxygen. This last is found by weighing the glass combustion tube 

 containing cupric oxide before and after the experiment, and between 

 the two weighings the tube is heated to a low red heat for several 

 hours while a stream of hydrogen gas is passing through it; and there 

 are several causes which may lead to the variation of these weights, 

 independent of the oxygen which has been used up in the process. 

 We shall allude to some of these causes below, but their effect would 

 be comparatively unimportant if they only led to a small error in the 

 observed weight of the oxygen. Unfortunately their effect is not thus 

 limited ; for when, in order to find the weight of the hydrogen, we 

 subtract from the weight of the water, which may be regarded rela- 

 tively as accurately known, the weight of the oxygen, which may be 

 for the causes referred to slightly erroneous, the whole error appears 

 in the weight of the hydrogen thus found, and in the opposite direc- 

 tion. If, for example, the weight of the oxygen is too large, the 

 weight of the hydrogen will be too small by exactly the same amount ; 

 and although the error may be an inconsiderable part of the weight of 

 the oxygen, it may be a very appreciable quantity in the weight of 

 the hydrogen. 



On the other hand, if a means could be devised for weighing the 

 hydrogen, leaving the oxygen to be determined by subtracting this 



