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



method, it has established incidentally one general fact of great 

 practical importance, namely that all the atomic weights are approx- 

 imations to certain whole or half numbers, if the atomic weight of 

 oxygen is taken at 16 exactly. 



Consequently we may say that the entire mathematical problem 

 will require only the exact determination of the value of this small 

 departure (which we now represent by the Greek letter epsilon c). 



Every mathematician knows that all relations, even the most 

 complex, are thereby reduced to simple proportions. Hence all our 

 calculations can be carried out by proportional parts, if the neces- 

 sary relations have first been deduced either by geometry or by 

 development into series. We have used both methods. After over- 

 coming these difificulties we have systematized the work by simple 

 analytical processes, retaining however the general geometrical, 

 method for the presentation of the data of experiment and the results 

 of calculation, as exemplified above and in our numerous diagrams 

 of which reductions by photography are printed. 



It seems best, at this point, to state the degree of precision 

 aimed at: the third decimal (thousandths) of the atomic weight and 

 the fifth decimal (hundred thousandths) of the ratios (atomic R 

 and analytic r). If at any time we feel authorized to go beyond this 

 general limit, the higher decimals are given as decimals to the above, 

 in order to conform to definitions given and to avoid confusion. 



VI. The Departure, e. 



The true atomic weight of bromine is known to be some value 

 quite near the number 80; all chemists admit this as an established 

 fact. Hence zve limit our zvork to the cietcnnination of the precise 

 small number of thousandths of the unit, our departure e. 



Accordingly we say : the exact atomic weight of bromine is 

 80 -f- e. We then perform all analytical operations with this sum 

 instead of using the one symbol Br. Thus many terms will cancel 

 and others will drop out as minute quantities of too high an order 

 to be of influence on the result: facts and processes familiar to all 

 those versed in mathematical work. In this way we finallv obtain 

 readily workable formute. (See p. 61 of our " Cinquantenaire," 



