1913-] HINRICHS— TRUE ATOMIC WEIGHT OF BROMINE. 553 



IX. The Variation of the Analytical Excess, e. 



The mere fact that the mean vakte of the excess e is very small 

 (0.2 only) is, however, not sufficient to completely establish the con- 

 clusion just drawn, as we have always accentuated; for some of the 

 individual values of the excesses might be large with opposite sign, 

 or show notable systematic variations — this they do in fact in the 

 present case. 



Hence it is necessary to study the individual values of the ana- 

 lytical excess for each laboratory determination made. They are 

 given in Table IV. of section VIII., in the last column. By simply 

 drawing (on diagram no. 750) the base line (horizontally) through 

 the point on the scale of the analytical ratios for the value of the 

 atomic ratio, J? = o.98755.7 (see VII.), we get the representation 

 of e on the diagram. This horizontal line is shown on our cut no. 

 750, which thus exhibits the exact value of the analytical excess for 

 every individual determination made. See Plate XXXIV. 



Taking this line as the new axis of abscissae for c the equation 

 of the line of perturbation will be 



^ = 0.113(75— w). (3) 



It is not necessary to discuss this equation, since it corresponds 

 exactly to that for r already considered in III. 



X. The Increment, 2. 



2 is the change in the third decimal of the atomic weight pro- 

 duced by one unit in the fifth place of the analytical ratio r. 



It will be impossible to enter here upon the complete deduction 

 of the formulas now to be presented for practical work ; for our 

 deduction we must refer to a series of papers in the Comptcs Rendns 

 from 1907 to the present and to our publications in other quarters, 

 especially including the facsimile of a general deduction which has 

 travelled between Paris and St. Louis in 1907 and again in 1908; 

 see p. 61 of my " Cinquantenaire de L'atomecanique, 1910," under 

 the title : Un Manuscrit Voyageur. All these more recent develop- 



