H. H. Robinson — Chemical Analyses of Igneous Bocks. 273 



It also appears that the same chances hold for the occur- 

 rence of distributions with double maxima. 



It would be possible to determine with considerable accuracy 

 from the work of Dr. W. F. Hillebrand, because of its magni- 

 tude, what the chances are in favor of various types of 

 symmetry. The results, however, would apply only to the 

 work of analysts whose skill equals that of Dr. Hillebrand. 

 The number of such analysts is, unfortunately, too small to 

 compensate for the labor involved in the calculation of results. 

 For example, from a study of the work of analysts in general 

 the chances appear about 1 : 3 for the occurrence of double 

 maxima, whereas on the basis of Dr. Hillebrand's work they 

 are about 1 : 15. The discrepancy is due in part, certainly, to 

 the lower grade work of a considerable number of the chemists 

 whose analyses were studied. 



There is, presumably, a fairly close relationship between the 

 amount of work a chemist does and his technical skill. No 

 doubt there are many analysts whose skill, and reputation, 

 would improve noticeably with increased work. It is unfor- 

 tunate that silicate rock analysis is so time-consuming that it 

 has become customary to depend on single determinations of 

 constituents for a final result. This custom works out most 

 unfavorably with those chemists who make but a few analyses. 

 It would redound to their credit, and be an excellent thing for 

 petrology, if these analysts did all their work in duplicate. 

 Mineral analyses commonly have been made in duplicate 

 because of the importance of an accurate result for establish- 

 ing a formula. It is by no means impossible that increased 

 knowledge of rock composition, derived from physico-chemical 

 study, eventually will call for duplicate determinations in rock 

 analysis. At least it will call for work of greater accuracy 

 than much that has been done in the past or is, indeed, being 

 done at present. 



The probable error of his single summations, and to a less 

 extent that of his average summation, indicates with consider- 

 able accuracy the technical skill of the chemist..* It is not a 

 complete measure because there are possible errors which do 

 not affect the summation, a very persistent one being the 

 incomplete separation of magnesia and alumina. The number 

 of a chemist's analyses has a marked effect on the probable 

 error of his average summation because the calculation involves 

 the quantity JST X N — 1. The number affects the probable error 



*It will be recalled that the formula for the probable error of an arith- 

 metical mean is E a = - 6745i/ — LHJ , whereas for a single measurement 



y N(N - 1) 



E = A/ , where r = residual error and N the number of measurements- 



r N — 1 



