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



of a single summation only so far as a large amount of work 

 conduces to more accordant results than a small amount. Thus 

 the difference between the probable error of the average sum- 

 mation of a chemist who has done much work and of one who 

 has done little may be as great as 200 per cent, whereas the 

 difference in the probable errors of their single summations 

 may not exceed 25 per cent. For this reason the probable 

 error of a single summation is the more valuable guide to the 

 quality of a chemist's work. 



The probable errors for single summations and the average 

 summations of 43 analysts, who have made 15 or more 

 analyses, weighted according to their relative amount of work, 

 are : 



Single summation, ifcO'SO per cent. 



Average summation, ±0-02 per cent. 



The effect of a considerable difference in the number of 

 analyses on the values of the probable errors is shown by the 

 following figures : 



1. For those chemists who have made 50 or more analyses. 

 Single summation, ±0'20 per cent ; average summation, ±0*01 

 per cent. 



2. For those chemists who have made between 15 and 50 

 analyses. Single summation, ±0*40 per cent; average sum- 

 mation, ztO'07 per cent. 



It is the opinion of the writer, based on all available data, 

 that the probable error of rfc0'30 per cent for a single summa- 

 tion furnishes a fair guide for judging a chemist's technical 

 skill, so far as it may be judged by the summation of analyses. 

 If a closer estimate of a chemist's work is desired, then the 

 values based on the amount of work done should be used. 



To give point to the foregoing general values, the probable 

 errors, and also the constant errors, for the work of those 

 chemists whose distribution curves have been presented in 

 figures 3-5 may be stated : 



Analyst No. of anals. Constant error P. e. single sum. P. e. ave. sum. 



A 



450 



— 0-02 



±0-16 



±0-01 



B 



140 



— 0-22 



•26 



•02 



C 



77 



+ 0-12 



•20 



•02 



D 



37 



— 0-08 



•24 



•04 



E 



147 



— 0-02 



•30 



•02 



F 



46 



— 0-39 



•39 



•06 



G 



50 



4-0-45 



•43 



•06 



H 



21 



o-oo 



•18 



•04 



I 



24 



+ 0-01 



•20 



•04 



J 



17 



-0-11 



•26 



•06 



K 



31 



4-0-19 



•28 



5 



