552 HINRICHS— TRUE ATOMIC WEIGHT OF BROMINE. [April 4. 



VIII. The Analytical Excess e. 



This is the number of units of the fifth decimal by which r 

 exceeds R; that is 



e = r — R. (2) 



Table II. gives the following results : 



TABLE IV. 

 Values of the Analytical Excess, e. 



The concordance between r (experiment) and R (absolute value) is al- 

 most perfect, ez^r — R affecting the millionths almost exclusively (in all but 

 four of the thirty cases!). 



If we were to decide by mean values, in accordance with the 

 common practice of the school, we would have to conclude that the 

 true atomic weight of bromine is 80 exactly ; for the mean analytical 

 excess is only 8 millionths above in the first and second ratios and 

 merely 2 millionths below in the third ratio. This implies a truly 

 marvelous approximation to our absolute atomic weight Br ^80 

 exactly. 



Since the third ratio is mathematically the sharpest, being near 

 unity, we might claim in truth having demonstrated with " astro- 

 nomical precision " that the atomic weight of bromine is 80 exactly. 



By means of the known value of the variation A we can readily 

 convert the value of the analytical excess into the corresponding 

 departure e in thousandths of the unit of atomic weights. 



