THE ERRORS OF PRECISION. 



We have sufficiently explained this point and shall have 

 to come back to it when we reach the discussion of the 

 atomic weight of carbon in relation to that of oxygen. 



Precision of Weighing. 



At this point we shall now consider the accuracy of 

 weighing and the degree of certainty of the ratios calculated, 

 that is, the number of decimals that are reliable. 



First, as to the accuracy of weighing, we know that it 

 generally exceeds the accuracy of the chemical operations 

 and processes involved in changing the substance taken into 

 the final product. 



It is therefore, on the whole, to be carefully born in 

 mind, that the accuracy of weighing exceeding that of the 

 chemical processes, the accuracy of the final weights is less 

 than the accuracy of the actual weighings, and especially 

 that the ratio calculated is subject to even an uncertainty due 

 to the most accurate part of this work, namely, the weighing. 



It is of the highest importance that this subject should 

 be fully understood in order that the data of experience 

 obtained in the chemical laboratory can be taken for what 

 they really are neither less nor more accurate than the 

 actual work done. 



We therefore shall consider the points mentioned sepa- 

 rately, one at a time, with such detail as seems necessary. 



The Balance used by Dumas. 



The weighings above given are expressed in milli- 

 grammes; only in one single instance is the half milligramme 

 stated. This does not mean that this half milligramme was 

 actually weighted by a weight, but 7 milligrammes were 

 plainly insufficient and 8 milligrammes as much in excess. 



This little circumstance of the single half-milligramme 

 recorded shows that the weighings were exact to the nearest 

 milligramme, and no more. 



Dumas himself states that the ie balance used very readily 

 shows the milligramme" (Oeuvres, p. 251). He mentions 



