191 1.] HINRICHS— ATO^IIC WEIGHT OF VANADIUM. 215 



The preliminary analysis, represented in the line A at the top 

 of Fig. I, gave not only the greatest departure for \'a, but also for 

 O, in the only determination made by Berzelius. When Roscoe, 

 forty years after, made a series of four determinations the result 

 entered at E in our figure (both i and 2) he cut the departure from 

 1062 to 195 for A'a and from 263 to 47 for oxygen. If this determi- 

 nation were repeated with the benefit of all the progress made in 

 laboratory work, the resulting mark would undoubtedly find its 

 place much nearer the zero departure on the line (mainly dotted) 

 on our figure ( i ) . 



Let us also look at the results obtained by the use of reaction 

 270, best seen on Fig. 2, lines G. H, I, K, L, O, P. Of these lines, 

 G is the most distant, representing the largest departures : it marks 

 the one determination made by the old master in 183 1. Then we 

 meet, in going toward the center of perfection or zero departure, the 

 lines H, I and K bearing the mark of Roscoe and only about half as 

 far from the zero as the line G of 1831. The total number of deter- 

 minations made by Roscoe in 1868 was 8, represented by line I; 6 

 of these eight were "done by Analyst A" and are represented by 

 line H ; the other two were " done by Analyst B " and are represented 

 by line K. Finally we have three series ( I., II. and III., repre- 

 sented by lines L, P and O, respectively) made by Prandtl quite 

 recently ; of these, the last two series come quite close to the center, 

 the departure for Va being 14 only for the mean of the two series 

 (see Table V.). Since on our diagram the departures for O, CI 

 and Ag are set off as abscissae to that of Va taken as ordinate, the 

 gradual diminution of all the departures is strikingly shozvn iu the 

 lines for these elements conz'erging to the point of zero departure. 

 At the same time we here have the positive evidence that Prandtl 

 has produced two very concordant series (his II. and III.) with a 

 very small departure (mean 14 for A'a and O) and one series (his 

 first, I.) represented by line L for which the departure is 62, that 

 is more than four times as large. 



Now we may consider the results obtained by the reduction test, 

 reaction No. 98, represented on our Fig. i by the lines B, C and F. 

 Here we meet that one exception before referred to ; for the greatest 

 departure (lineB) of Berzelius is but slightly diminished by Prandtl's 



