H. B. Robinson — Chemical Analyses of Igneous Rocks. 275 



A small probable error for a single summation means that 

 the summations as a whole fall within narrow limits and that 

 a large proportion are in the group of maximum frequency, 

 whereas a large probable error indicates the opposite. As a 

 general rule a small constant error is associated with a small 

 probable error for a single summation. A large constant error 

 is almost always associated with large probable errors for both 

 a single and also the average summation, as shown by analysts 

 F and G and to a less extent by B and K. When particularly 

 large it is an almost sure mark of inferior analytic skill. In 

 but one case out of ten, which have come under observation, 

 has a large constant error been accompanied by small probable 

 errors. 



Referring to the probable errors for single summations, all 

 are below the average value of ±0*30 per cent except those of 

 analysts F and G, and one (E) which is on the average. 

 Probable errors of ±0 - 18-0"26 per cent are not uncommon for 

 chemists who have made less than 30 analyses, thus comparing 

 well with the value of this error for analysts A, B, and C who 

 have done much work. For this reason the single value of 

 =t0'30 per cent has been adopted rather than the two values 

 of ±0*20 and ±0*40 per cent, depending upon a large or small 

 number of analyses. 



As already stated, the size of the probable error for the 

 average summations depends on the number of analyses. It 

 must be judged accordingly. Thus the error of ±0 - 02 per 

 cent for B and C is about equal to the value of dbO'01 per cent 

 for A. Likewise the error of ±0'04 per cent for analysts D, 

 H,and I should be considered of equal value to the smaller 

 errors for A, B, and C. 



It may be said in conclusion, then, that a probable error for 

 a single summation much less than ±0*30 per cent in connec- 

 tion with a probable error for the average summation of 

 d=0*01-0 - 03 per cent, when the number of analyses is large, or of 

 ±0'04:-0-0Q per cent when it is small (less than 50), indicates 

 good technical skill on the part of the chemist. On the other 

 hand, if the probable error for a single summation is much 

 over ±0*30 per cent and the error for the average summation 

 is in excess of the upper limits just given, then a lack of tech- 

 nical skill is indicated. 



Peabody Museum, New Haven, Conn. 



Am. Jour. Sci.— Fourth Series, Vol. XLI, No. 243.— March, 1916. 

 20 



