262 H. H. Robinson — Chemical Analyses of Igneous Rod's. 



examples will suffice : (1) 9 analyses of similar rocks showing 

 summations from 99*86 to 100*54 per cent; (2) 7 analyses, 

 99-59-101-00; (3) 5 analyses, 99-49-101-05; (4) 8 analyses, 

 99-86-101-16; (5) 7 analyses, 99-35-100-77; (6) 20 analyses, 

 99-58-100-72 ; (7) 21 analyses, 98-85-101-68. The range in 

 the last example is 2 - 83 per cent and for this analyst's entire 

 work on rocks of almost identical composition it is 3 - 96 per 

 cent. This, of course, is an extreme example. Commonly 

 the range of an analyst's summations will fall inside of 2 per 

 cent. In general, as shown by the analyses used in this study, 

 the range is from 97 to 103*5 per cent, or 3 per cent and more 

 either side of the general average of 100-13 per cent. 



The individual analyst's errors are generally of two kinds. 

 There is commonly a constant error represented by the differ- 

 ence between the analyst's average summation and the gen- 

 eral average. There are always accidental (residual) errors 

 represented by the differences between an analyst's single 

 summations and his own average summation. The constant 

 error is of small size compared with the accidental errors. 

 In two-thirds of the above cases it is less than 0*2 per cent and 

 the largest is 0*53 per cent. The accidental errors may be as 

 large as 2 per cent either side of the average, although the 

 great majority range from 0'5 to 0*75 per cent. 



The chances appear even that the constant error may be 

 either plus or minus. Thus out of 43 analysts all of whom 

 have made over 15 analyses, 21 have a plus error averaging 

 0*21 per cent, 20 have a minus error averaging 0*17 per cent, 

 and 2 have no error. The chances are even that the acci- 

 dental errors will be either plus or minus in so far as they rep- 

 resent errors which lie in analytic methods. The accidental 

 errors due to other causes, such as the incomplete washing or 

 collection of precipitates, may be either plus or minus, appar- 

 ently with equal chance. It thus appears that the errors 

 which affect the summation of analyses for the most part are 

 evenly distributed and consequently the probability curve for 

 summations will be symmetrical. And it would seem the most 

 probable assumption that this relation holds generally true. 



However, whether summations in general are evenly dis- 

 tributed or not will depend on whether the proper unit of 

 measure is employed. Analytic results are expressed to the 

 hundredth place of decimals — not to mention the thousandth 

 place. But a unit of measure (difference) of 0-01 per cent is 

 of no significance. A difference of - 05 per cent, the unit of 

 Table 1, is below significant size. "What then is the unit of 

 most significant size ? The requirements are that it shall show 

 a maximum of the same value as the general average (100*13) 

 and shall result in an even distribution of summations either 

 side of the maximum. 



