704 



SCIENCE. 



[N. S. Vol. XXIV. No. 622. 



grades and probable errors of the twenty men 

 of science who were assigned positions at the 

 head of each of the twelve sciences. All the 

 anthropologists are thus included in the table, 

 but only two fifths of the astronomers, one 

 fifth of the geologists, etc. In cases in which 

 an individual stands relatively higher in an- 

 other science a star is attached. 



It will be observed that the grades are, as 

 a rule, lower than the positions. As has been 

 stated, the distribution of the judgments or 

 errors in the upper part of the list is ' skewed ' 

 in a negative direction, so that the average 

 judgment is lower than the median judgment. 

 Further down the list this tendency disap- 

 pears, and towards the bottom, not given in 

 the table except for the anatomists and an- 

 thropologists, the ' skew ' is in the opposite 

 direction. Chauvenet's criterion has been ap- 

 plied; it causes but an insignificant difference 

 in the order, and for statistical purposes the 

 extra calculations involved were superfluous. 

 As has been explained, however, the incidence 

 of a divergent judgment, which might be due 

 to ignorance or prejudice, might be unjust to 

 an individual. The probable errors have been 

 obtained by taking them directly proportional 

 to the average deviation and assuming that 

 there were always ten judgments. In the 

 comparatively few cases where there were less 

 than ten judgments the probable errors of the 

 average are too small, but the differences are 

 not significant. In the measurement of sci- 

 entific merit, we are concerned not with the 

 probable error of the average, but with the 

 average probable error, which does not depend 

 on the number of cases. Figures for both 

 might be given, but they are so nearly alike 

 and so lacking in significance that it is not 

 worth while. 



As the table shows, there are in astronomy, 

 pathology and psychology men who are placed 

 distinctly at the head. In the other sciences 

 those who stand first have grades varying from 

 1.6 to 3.6. In most cases the differences in 

 grade are less than the probable errors, or not 

 much larger, and the position is not deter- 

 mined to a single place, though it is deter- 

 mined with a theoretically high degree of 

 validity within a very few places. Various 



groupings occur, which seem to represent the 

 existing conditions of the sciences. Thus 

 there are breaks of two or more units after 

 chemists 4 and 8; physicist 2; zoologists 4 

 and 6 ; geologists 2, 5 and 7 ; botanist 8 ; mathe- 

 maticians 3, 6 and 8; pathologists 1, 4, 6 and 

 9 ; psychologist 1 ; physiologists 7 and 9 ; anat- 

 omists 2 and 9, and anthropologist 5. On the 

 other hand, there are cases in which consecu- 

 tive numbers are bracketed or practically 

 bracketed. Thus mathematicians 4, 5 and 6 

 have a grade of 5.7. These various groupings 

 appear to be about what the probable errors 

 would lead us to expect. 



The probable errors tend to increase as we 

 go down the lists, but with considerable ir- 

 regu-larity. This irregularity is in part due 

 to normal variability where the number of 

 observations is small and the average devia- 

 tions are relatively large, but the larger de- 

 partures are usually significant, it being 

 easier to assign a position to some men of 

 science than to others. Thus, for example, 

 it is not easy to compare a man who has made 

 one or two important discoveries with a man 

 who has accomplished a large mass of useful 

 work. 



The tendency of the probable errors to in- 

 crease is, however, significant. It is easier to 

 assign the order at the top of the list, and the 

 difficulty increases as we go downward. This 

 subjective fact is measured by the probable 

 errors. It is in part due to less knowledge 

 of those whose work is less important. I 

 know of no way to eliminate this factor or to 

 measure its influence. But the main factor 

 is the real differences between the men, and 

 these are assumed to be inversely as the prob- 

 able errors and directly as the differences in 

 grade. 



In table III. are given all the probable 

 errors averaged in six groups for each of the 

 sciences. In the flrst and second groups are 

 included one tenth of those in each science, 

 and in the remaining groups one fifth. That 

 is, the probable errors are divided into five 

 equal groups, but the first group is divided 

 into two subgroups, in view of the fact that 

 the probable errors of the first tenth are dis- 

 tinctly smaller than those of the second tenth. 



