1913-] HINRICHS— TRUE ATOMIC WEIGHT OF BROMINE. 547 



Each full black circle represents the determination identified by 

 the same numeral used by Mr. Weber. 



The single determinations for less than 60 (no. 7) and for more 

 than 80 grammes (no. 5) of bromine give the mean d of compara- 

 tively little importance. 



The eight determinations made with between 60 and 80 grammes 

 of bromine fall in two well-detined groups of four determinations 

 each and give the equally important two mean values marked 

 A (i, 3; 2, 10) and B (4, 8; 6, 9) of which C is the final mean.*' 



But it is clear that this mean C cannot be considered to be the 

 true mean value of the ratio r because it is nothing more than the 

 mean of eighth determinations which Mr. Weber made with the 

 eighth weights of bromine which he "happened to take." For as a 

 matter of fact, the eight determinations do not give some constant 

 value from which the individual determinations differ by small 

 deviations ecjually distributed as to amount and sign. On the con- 

 trary, the eight determinations form a well-defined straight line 

 A-B, inclined to the axis. Accordingly, it is this straight line A-B 

 itself which represents the eight determinations made by Mr. Weber. 

 Only in case the line A-B were parallel to the axis of weights taken 

 (horizontal in the drawing) and if, at the same time, all deviations 

 were small, could the point C be taken as a legitimate mean. 



It is readily seen that the line AB is the geometrical representa- 

 tion of the equation 



^=57-7 — 0.1 1 3«', (i) 



where r is expressed in units of the fifth place of decimals and w 

 in grammes of bromine taken. That is : r is not a constant, but 

 varies according to the form k — cznf, where k and c are constants, 

 We may express the strange fact revealed in the above by say- 

 ing that the result of the experiment depends on the choice of the 

 weights taken by the chemist, so much so that " we can tell as soon 

 as the weight has been taken and before the experiment has been 



*' It may be noted that of the two isolated determinations 7 and 5, the first 

 (7) is made with the smallest weight of bromine and therefore shows the 

 greatest deviation, while the last (5) made with the greatest weight of 

 bromine falls distinctly close to the line AB. 



