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



by the symmetry of the curves, may be obtained from as few 

 as 18 analyses (J) and not over 30 (K). The number of 

 analyses for H and I are about midway between those for 

 J and K. 



The curves in the above figure are about as symmetrical as 

 those shown in fig. 3, although based on very much smaller 

 numbers of analyses. That none of the curves at their ex- 

 tremities approach the abscissa axis closely is due to the latter 

 fact. For example, one analysis equals 5 per cent of 20 

 analyses so that if no more than two analyses fell in a limiting 

 group they would equal 10 per cent as plotted on the diagram. 

 The curves have not been extended to zero ordinate values in 

 order to emphasize the limiting summation groups. 



The distribution of summations of analysts H and I is dis- 

 tinctly better than for J and K. In fact H has a greater pro- 

 portion of summations in his maximum group than analyst A 

 (fig. 3) ; I has a greater proportion than B or C. The limits 

 of their summations, also, are more restricted than for either 

 A, B, or C. These facts, in connection with the small number 

 of analyses, make it practically certain that analysts H and I 

 exercised more than usual care in their work. They may have 

 made some of their analyses in duplicate as well as made special 

 redeterminations in some instances. Such a procedure means, 

 of course, that their results have more than the average chance 

 of being good. Analysts H and I, then, almost certainly could 

 not obtain such favorable results on a large amount of work. 

 It seems likely that the distribution shown by analysts J and 

 K, disregarding the constant errors, more nearly represents the 

 best that should be expected in ordinary practice with a small 

 number of analyses. 



The foregoing examples (figs. 3, 4, and 5) show some of the 

 more symmetrical distributions of analyses which have come 

 under the observation of the writer. They indicate, for the 

 most part, what may be expected in good analytic work. 



A study of the work of 43 analysts indicates the following 

 chances in favor of a more or less symmetrical distribution of 

 summations: 



1. When the number of analyses is over 35, the chances are 

 entirely in favor. 



2. When it is between 20 and 35, the chances are as 4 : 5. 



3. When it is between 15 and 20, the chances are as 2 : 3. 

 Below 15 analyses the chances are almost wholly against a 



symmetrical distribution so that this number is the minimum 

 for a test of this character. 



For distributions with a single maximum the chances are 

 about 1 : 3 that the group of maximum frequency will fall 

 outside the average group (lOO'OO-lOO^l: per cent). 



