I9II.] 



HINRICHS— ATOMIC WEIGHT OF VANADIUM. 



207 



IV. The Analytical Excess. 



The analytical excess c is only comparable in work carried out 

 according to the same chemical reaction by dilTerent chemists. This 

 condition has determined the form of Table YV., in which the capital 

 letter marks the line on our final diagram representing the work, 

 while the numbers below the letter represent: the first, the number 

 of determinations made, the second giving the analytical excess 

 obtained. This excess will naturally be found the greatest for all 

 preliminary (or pioneer) work such as that done by Berzelius in his 

 single trials of reactions (a), (&), (c). 



This table makes it very apparent that each succeeding chemist 

 benefited by the work and experience of his predecessor. This 

 show^s best under reaction 270 where Berzelius (i determination) 

 gives the excess 140, Roscoe (8 determinations) only 76 and Prandtl 

 (15 determinations) brings it down to an average of 28 only. 



For Reaction 98 this relation holds good for the work of Berze- 

 lius and Roscoe only, while that of Prandtl, done as recently as 

 1909, reaches almost the excess of Berzelius single first trial of 

 eighty years ago, although Prandtl used the mean weight of 2.5 

 grams while Berzelius had onl\- half a gram for his work. 



TABLE IV. 

 The Resulting Analytical Excess. 



