H. H. Robinson — Chemical Analyses of Igneous Rocks. 257 



Art. XYII. — The Summation of Chemical Analyses of Igne- 

 ous Rocks / by H. H. Robinson. 



Theoretically the summation of a complete chemical anal- 

 ysis should be 100 per cent ; actually it rarely is that. Although 

 an analyst may take every precaution to ensure a strictly accu- 

 rate result, most of his summations will be either higher or 

 lower than the true one. Are these departures from the mean 

 value distributed in any definite and orderly manner ? It is 

 the purpose of this paper to discuss this question in general as 

 well as in individual cases, first touching briefly on some of the 

 analytical errors that may affect such a distribution, and also 

 to show how the probable errors of an analyst's summations 

 may be used as a guide to the quality of the analytical work. 



The study is based on the analyses of the Washington and 

 Washington-Roth tables,* as well as on more recent analyses. 

 Their number is 3,391. The only analyses omitted are : (1) 

 those whose summation has been recalculated to 100 per cent, 

 or by estimation of some constituent is equal to 100 per cent, 

 and (2) those whose summation is distinctly low through the 

 non-determination of some constituent. The statistical data 

 are given in Table I. The summations were tabulated, and 

 are here given, on the basis of a 0*05 per cent unit in order to 

 lessen work. 



An inspection of the table shows that there are few analyses 

 with low summation, but that the number increases in a strik- 

 ing manner from about 99 per cent to a maximum at 100"15- 

 100*19 per cent. Likewise there is a marked decrease in the 

 number of analyses from the maximum to about 101"50 per 

 cent and then a gradual decrease to the highest summations. 

 The different summations are thus distributed with consider- 

 able regularity either side of the maximum. What is the 

 probable character of this distribution % 



As a matter of pure chance it would seem probable that the 

 high and low summations should be evenly distributed either 

 side of the maximum, provided no unusual factors affect the 

 summation of the analyses. The fitted distribution or proba- 

 bility curve should be symmetrical with respect to the vertical 

 axis passing through the maximum. It is necessary, therefore, 

 to examine the factors involved before a conclusion can be 

 reached as to the most probable character of the distribution. 



It appears most likely that the errors due to the methods 

 used in the determination of the individual constituents of a 

 silicate analysis tend to balance one another, so that, given 



* Washington, H. S., Chemical Analyses of Igneous Rocks, Prof. Paper, 

 U. S. G. S., Nos. 14 and 28, 1903 and 1904. 



