196 HINRICHS— ATOMIC WEIGHT OF VANADIUM. [Apm 21, 



in our necessary calculati(3ns, because the departures are small 

 quantities ; hence, all calculations, even involving the most complex 

 mathematical functions, are reduced to the simple rule of three and 

 carried out by proportional parts. The importance will soon be 

 recognized by the practice of the method. 



The actual laboratory z^'ork consists essentially in the deter- 

 mination of tii'o weights which we denote by p and q and which rep- 

 resent chemically pure compounds of the formula P and respec- 

 tively. The necessary condition is that the weight p has been com- 

 pletely changed into q according to the exact formulae P and Q by 

 means of a suitable chcuiical reaction. Of such reactions we have 

 tabulated and examined over three hundred that have been actually 

 used for atomic weight determinations. We designate each such 

 reaction by a number for ready reference. This number is simply 

 marking their place in our table above referred to ; it is arbitrary 

 but a practical necessity. We have already above referred to the 

 remarkable chemical reaction, recently applied in the Harrison Labo- 

 ratory of the University of Pennsylvania as reaction no. 311. 



Substituting the absolute atomic weights a for the chemical sym- 

 bols in the formulae of the two compounds P and 0, we can readily 

 calculate the value of the quotient P/Q which we call the atomic 

 ratio R and calculate the same to five decimals, the limit of precision 

 today. On the following pages, giving the data for the chemical 

 reactions that have been used for the determination of the atomic 

 weight of vanadium there will be found examples of these and of 

 all other processes, to which we request the reader to turn as new 

 operations are defined. 



On the other hand, the weights actually taken in the laboratory 

 and designated by the letters p and q will give the analytical ratio r 

 which w^e calculate also to five decimal places. The analytical ratios 

 determined by the different experiments with the same two com- 

 pounds P and will give hardly any identical values of r ; we notice 

 their extreme values, that is the maximum and the minimum in any 

 given series of determinations made in the same manner with the 

 identical material. The differance between the greatest and the 

 least value of the analytical ratios of a series is the range of that 

 series. This characterizes the concordance of the different deter- 



