U. H. Robinson — Chemical Analyses of Igneous Rocks. 269 



curve thus would lie between these two groups and the curve 

 would be flatter topped than those of A and B. Disregarding 

 this fact, it may be noted that 46'8 per cent of C's summations 

 lie below his actual group of maximum frequency, whereas 

 19"5 per cent are above. It will be observed that both B and 

 C, whose groups of maximum frequency are, respectively, 

 below and above the average group of 100'00-100 - 24 per cent, 

 have the larger proportion of summations on the side of their 

 maximum group which is toward the general average of 

 100-13 per cent. 



The three curves of fig. 3 are based on a sufficiently large 

 number of analyses in each case to make them fairly reliable. 

 There is no great choice between the curves as to form, 

 although that of A is evidently better than those of B and C. 

 The work of these three analysts has been chosen for illustra- 

 tion because it typifies certain general features which may be 

 stated as follows : 



1. When the group of maximum frequency, on the basis of 

 the 0*25 per cent unit, coincides with the average group 

 (100-00-100*24 per cent), then (1) the number of analyses in 

 the groups above and below that of maximum frequency will 

 be equal, or (2) commonly a greater proportion will lie either 

 above or below as the case may be. That is to say, most 

 analysts have a slightly asymmetrical distribution of summa- 

 tionsabout the maximum which indicates the existence of a " per- 

 sonal equation." In general, however, the number of analyses 

 on opposite sides of the maximum group should be equal. 

 This is approximately true for the work of those analysts, 

 fourteen in number, who fall in this category, the figures being 

 32*3 per cent above and 31 # 5 per cent below. 



2. When the group of maximum frequency lies below the 

 common maximum group then a larger proportion of summa- 

 tions will lie above the group of maximum frequency. Six 

 out of eight analysts whose maximum group is below the aver- 

 age maximum group show this feature. For the eight analysts 

 taken together 40*9 per cent of their summations are above 

 and 21*8 per cent are below their group of maximum frequency. 



3. When the group of maximum frequency lies above the 

 average group then a larger proportion of summations will lie 

 below the group of maximum frequency. This feature is 

 shown by all the analysts, nine in number, who fall in this 

 category. The proportion of summations are 50*2 per cent 

 below and 18'9 per cent above their group of maximum 

 frequency. 



The foregoing characteristics may be taken as guides for 

 testing the normality of the distribution of an analyst's sum- 

 mations. The explanation of the relations noted under (2) and 



