IS. H. Robinson — Chemical Analyses of Igneous Rocks. 26 7 



Proportion of 

 Limits Proposed by analyses in 



§§'15-100-50 Hillebrand* 55 



99-75-100-75 Hillebrandf 66 



99-50-100*75 Washington^ 76 



Hillebrand says : " Given the purest obtainable reagents, an 

 ample supply of platinum, facilities for working, and a reason- 

 ably clean laboratory, there is little excuse for the failure on 

 the part of a competent chemist to reach a summation within 

 the limits 99-75-100-50 per cent."§ Washington states : " If, 

 therefore, the analysis of a rock is satisfactorily complete, there 

 is no excuse . . . for a summation that does not fall within the 

 somewhat liberal limits here assigned."! Interpreted in the 

 light of these statements the figures in the last column of the 

 above table are a striking commentary on the quality of a 

 large proportion of the analyses of igneous rocks. Dr. Hille- 

 brand's narrower limits are presumably based on his own 

 experience; 90 per cent of his summations fall within them. 

 For the work of the chemists of the U. S. Geological Survey, 

 exclusive of Dr. Hillebrand, the proportion is 77 per cent. 

 For all chemists, exclusive of those of the Geological Survey, 

 the proportion is less than 50 per cent. These limits of 

 99-75-100-50 per cent, therefore, might well be considered too 

 narrow ; yet the writer prefers them because they furnish an 

 additional stimulus to good work. And, indeed, they are of 

 little value, and may be actually harmful, except when looked 

 at in that way. 



Having considered the general problem, the distribution of 

 the summations of individual analysts may now be taken up. 

 From a practical standpoint — improvement in analytic skill — 

 such examples are most interesting. 



As already stated, an analyst may have, in addition to the 

 ever-present residual errors, a constant personal error which 

 causes his average summation to be either above or below the 

 general average. The following examples (fig. 3) show the 

 effect of such errors in compai-isou with a normal curve. In 

 this figure, and those following, the coordinate points are con- 

 nected simply by straight lines, as sufficient for purposes of 

 illustration. The number of analyses in each summation 

 group is expressed as a percentage of the total number in 

 each case so that the results for different analysts may be com- 

 parable. 



*Bull. U. S. G. S., No. 148. 1897, p. 62. 



+ Bull. U. S. G. S., No. 422; 1910, p. 28. 



% Prof. Paper, U. S. G. S., No. 14, 1903, p. 34. 



§Bull. U. S. G. S., No. 422, 1910, p. 28. 



|| Idem, p. 36. 



