556 HINRICHS— TRUE ATOMIC WEIGHT OF BROMINE. [April 4, 



Second. By the " Chemical Perturbations," representing all de- 

 terminations by a single straight line, intersecting the axis of abscis- 

 sae of weights taken. 



This also demonstrates completely that the true atomic weights 

 cannot be determined by empirical methods alone. 



In fact, the empirical methods lead really more and more away 

 from the truth by the chemists trying to secure greater concordance 

 — which can most easily be reached by limiting the range of weights 

 taken (as already shown here) and in many other ways, all leading 

 into error. We hope soon to take up this most important practical 

 subject more thoroughly. 



Third. — By the rcdnctio ad ahsurdnm, showing that the atomic 

 weight for the individual determination is de facto a function of 

 the weight taken for effecting the determination ; this result is 

 evidently absurd, because the atomic weight in its very nature is 

 independent of the amount or weight of the substance operated upon. 



In other w'ords : the individual determinations establish the line 

 of perturbation only, the intersection of which with the axis of 

 weights taken (for ^ = 0) gives the true solution for all experiments 

 represented on that line of perturbations. 



Final Conclusion. While each one of these three demonstrations, 

 taken separately, is sufficient to prove that the true atomic weight 

 of bromine is 80 exactly, they properly constitute three consecutive 

 steps in one complete demonstration which itself has been gradually 

 developed in that order above given. It may be best to repeat them 

 here as links of that chain of demonstration : 



1. The values of the analytical excess e are minute and of oppo- 

 site sign, giving a mean more or less closely approaching to zero ; 

 hence the horizontal line e^o, determined theoretically by the 

 atomic ratio R, is the locus of the true atomic w^eight. 



2. The straight line of perturbation is a second locus of the 

 same; hence the intersection of these tivo lines determines the iveight 

 for zi'hich the laboratory zi'ork is i^'itliout error. 



3. The other parts of the line of perturbation give the atomic 

 weight as function of the weight taken for the experiment, which 

 being absurd, proves that they only serve to determine the point 



