NOVEMBEK 30, 1906.] 



SCIENCE. 



705 



TABLE III. PROBABLE EBRORS IN EACH OF THE SCIENCES, THE MEN OF SCIENCE BEING DIVIDED INTO 



SIX GROUPS. 



CRUDE PROBABLE ERRORS. 



M 



II. 

 III. 

 IV. 



V. 



PROBABLE ERRORS CORRECTED FOR THE RANGE. 



M 



II. 

 III. 

 IV. 



V. 



THE SAME REDUCED TO A COMMON STANDARD FOR THE THOUSAND MEN OF SCIENCE. 



In the middle part of the table the probable 

 errors have been adjusted to the ranges cov- 

 ered by each group, and in the lower part these 

 figures have been reduced to a common stand- 

 ard of a thousand, so that the results for the 

 different sciences may be comparable. 



If the range of ability is the same in each 

 science and if the difficulty of assigning the 

 order in each science is the same, then the 

 figures in the lower third of the table should 

 tend to be the same in the different sciences. 

 As the averages include from 2 to 35 cases, 

 they are subject to a probable error which 

 varies considerably. Thus, to take, for ex- 

 ample, an intermediate case — the botanists — 

 the probable errors of the six entries in the 

 upper part of the table are: 0.25, 0.33, 0.18, 

 0.28, 0.22, 0.25. They thus seem to be de- 

 termined with considerable validity. When 

 the probable errors are adjusted for the ranges, 

 a considerable ' chance ' variation is intro- 

 duced. If the figures were broken up into 



groups of different sizes, the results would be 

 different. The figures in the last three groups 

 of each of the sciences seem scarcely to be 

 significant of real differences in the sciences, 

 though they to a certain extent measure the 

 actually existing conditions. 



The figures in the table give the validity 

 with which the positions are determined, and 

 at the same time measure the relative differ- 

 ences between the men in the several groups. 

 Thus the first tenth of the chemists have on 

 the average their positions determined rela- 

 tively to other chemists with a probable error 

 of two places and the last fifth with a probable 

 error of 25 places. In relation to the first 

 hundred scientific men, a chemist in this 

 group has his position determined on the 

 average (apart from the error due to the in- 

 terpolation) with a probable error of 11 places, 

 whereas in relation to the last 200 scientific 

 men, the place is determined with a probable 

 error of 145 places. 



