202 HINRICHS— ATO^IIC WEIGHT OF VANADIUM. [April 21, 



accentuated, that large constant and systematic errors may exist 

 though the value found for the probable error of the mean is in- 

 significant. In Clarke's third edition (1910, pp. 93-98) the probable 

 error of the mean amounts to only one unit in the fifth decimal of 

 the analytical ratio while the constant error of that ratio amounts to 

 120 such units, according to the famous analyses of Stas and Baxter. 



To detect the constant and systematic errors we have always 

 plotted the results of the individual experimental determinations 

 as ordinates to the weight taken as abscissse. In these diagrams 

 the scale selected for the atomic weights or the ratios must be very 

 great while that for the weight taken has to be small. In my diagram 

 representing in this manner all the atomic weight determinations of 

 hydrogen made in a century (Rcziic gen. dc Chiiiiie, 1910, p. 380) 

 the unit of atomic weights is 30 meters (about 100 feet) while a 

 decagram of water produced is represented by three centimeters 

 (or a little over one inch). 



To permit this scorch for the really iniportant constant and sys- 

 tematic errors, we give the weight taken (to the decigram) in all our 

 tables. For a series of determinations, we give the total weight 

 taken for all the determinations of the series, and the mean weight 

 taken for each determination — which is obtained from the total by 

 dividing this latter by the number of determinations made. 



Table II. thus shows that 50 determinations have actually been 

 made for the determination of the atomic weight of vanadium on 

 4 grams each of the substance taken, not counting the seven pre- 

 liminary determinations on i gram of matter each. 



It is also seen at a glance that by reaction 98 the work of Roscoe 

 ought to be the most reliable, while for 270 the work of Prandtl 

 should be the best and that the work done by one chemist for 311 

 has been carried out under equally as favorable condition in regard 

 to the weight operated upon. 



By means of the reference letter specified in the last column the 

 corresponding line on the diagrams can be instantly identified. We 

 may here already remark, that the length of this line, extending to 

 the right or to the left from the vertical in the middle, marks the 

 magnitude of the departures for the elements as indicated by the 

 chemical symbol added. 



