418 wells: interpretation of mineral analyses 



This leads us to the conclusion that ''residual errors" or "dif- 

 ferences" have very little meaning by themselves. This meaning 

 can only be brought out by comparison with the magnitudes 

 involved. For example an error of 1 gram in weighing 7 grams of 

 arsenic is a very different order of error from that of 1 gram in 

 59 grams of silver. This is a general proposition but it has partic- 

 ular application in chemical operations where we are so frequently 

 concerned with the numbers of atoms involved, the atoms hav- 

 ing different weights. If we are to make equally good determina- 

 tions of atomic quantities of two substances we must keep our 

 relative errors not our absolute errors the same in the two deter- 

 minations. So far as my experience in tracing the effects of errors 

 upon the results in different chemical operations goes, I believe 

 that the best policy for the chemist to pursue is to assume a given 

 error in a measurement, carry thru the whole calculation and 

 ascertain exactly what effect the error will produce in the final 

 result. As is well known, relative errors in a magnitude are trans- 

 mitted unchanged in multiplication and division of the magnitude 

 by other magnitudes, but they are affected irregularly or may 

 practically disappear in additions and subtractions. 



The chemist well knows that in addition to "random" errors 

 there are errors that depend on the elements involved and the 

 methods used. For example, it is not difficult to determine silver 

 with accuracy; the same cannot be said of arsenic. Sulfur is 

 usually weighed as barium sulfate, a substance over seven times 

 heavier than its equivalent of sulfur, while copper is frequently 

 weighed as metal. Even if the same accidental error in milli- 

 grams is made in weighing these two substances the sulfur deter- 

 minations will turn out to be seven-fold as accurate as that of 

 the copper. Neglecting these special relations, however, it may 

 be said that errors will tend to be proportional to the magnitudes 

 involved. This relation does not hold strictly because the analyst 

 usually allows himself a little more laxity in the case of the minor 

 constituents and in these the "constant" errors attain more signif- 

 icance. This difference in the nature of the errors is of fundamental 

 importance in deciding upon methods of calculation and comparison. 



In the method employed by Van Horn and Cook one deter- 



