H. H. Robinson — Chemical Analyses of Igneous Mocks. 259 



magnesia, potash, and soda. An examination of the best 

 methods used in rock analysis, such as are given by Hille- 

 brand," shows that the probable character of the errors in the 

 determination of individual oxides is as follows : 



SiO, 



— 



MgO 



+ 



H 2 



± 



Al a O, 



— 



CaO 



± 



Ti0 2 



— 



Fe 2 3 



+ 



Na„0 



± 



PA 



-U 



FeO 



— 



K,0 



± 



MnO 



+ 



On account of the customary practice of determining A1 2 3 

 by difference, the errors for Fe„0 3 , Ti0 2 , and P 2 5 have to be 

 considered as a single error the value of which is plus. If, 

 then, the errors as a whole are of about the same size, it is evi- 

 dent that they will tend to balance because the chances for 

 plus and minus errors are equal. 



The errors which result from analytic methods alone rarely 

 neutralize one another in individual analyses. They do so 

 only in an average based on a large number of analyses. The 

 size of the unbalanced errors, however, can not well be large 

 because present-day methods of silicate rock analysis are rea- 

 sonably accurate. !No doubt such errors were more pronounced 

 in the older analytic work due to less accurate methods, less well 

 developed technic, and to poorer reagents. 



It may be concluded, then, that errors due to methods should 

 bring about a slight dispersion of individual summations on 

 either side of the general average and that this distribution 

 should be symmetrical because there is an even chance for plus 

 and minus errors. 



There is not a complete balancing of all the errors affecting 

 a summation. As is well known, analyses commonly add up to 

 more rather than less than 100 per cent. For example, 61 per 

 cent of all the analyses used in this study have summations 

 above 100 per cent. The actual average summation for all the 

 analyses is 100"13 per cent. There is thus a small constant 

 plus error due not to unbalanced errors in methods but to 

 different sources such as impurities derived from reagents or 

 from glass and porcelain vessels and to dust. This error was 

 slightly greater (0*2 per cent) in older analytic work and in the 

 future it may well be smaller than at present. It seems hardly 

 possible, however, that it will ever be entirely eliminated. 



The conclusion that errors in methods tend to offset one 

 another presumably holds only for analytic work of the better 

 quality. In poor work there may be unbalanced errors. One 

 such error is found in the determination of magnesia. To 

 illustrate this analyses with more than 20 per cent of magnesia 



*Hillebrand, W. F., The Analysis of Silicate and Carbonate Eocks, TJ. S. 

 Geol. Survey Bull. 422, 1910. 



Am. Jour. Sci. — Fourth Series, Vol. XLI, No. 243. — March, 1916. 

 19 



