NOVEMBEE 4, 1910] 



SCIENCE 



635 



contemporary as might be was also wanted 

 for some further studies of the conditions of 

 heredity and environment which are favorable 

 to scientific productivity. 



The methods used to select the group of a 

 thousand leading men of science were sub- 

 stantially the same as before and need not be 

 redeseribed in detail. The scientific men were 

 distributed among twelve sciences as previ- 

 ously. It was intended that the number in 

 each science should be proportional to the 

 total number of investigators in that science, 

 and it was as nearly so as is needful for the 

 purpose in view. The distribution was as fol- 

 lows: Chemistry, 175; physics, 150; zoology, 

 150 ; botany, 100 ; geology, 100 ; .mathematics, 

 80; pathology, 60; astronomy, 50; psychology, 

 50; physiology, 40; anatomy, 25; anthropol- 

 ogy, 20. 



In each science twice as many names were 

 selected and written on slips with the ad- 

 dresses and positions. The ten men of science 

 who stood at the head of the list in each sci- 

 ence in the previous arrangement were asked 

 to arrange the names in that science in the 

 order of merit. The memorandum of instruc- 

 tions read : " It is obvious that such an order 

 can be only approximate, and for the objects in 

 view an approximation is all that is needed. 

 The judgments are possible, because they are 

 as a matter of fact made in elections to a so- 

 ciety of limited membership, in filling chairs 

 at a university, etc. By merit is under- 

 stood contributions to the advancement of 

 science, primarily by research, but teaching, 

 administration, editing, the compilation of 

 text-books, etc., should be considered. The 

 different factors that make a man efficient in 

 advancing science must be roughly balanced." 



There were thus at hand in each science tgn 

 arrangements of those known to have done 

 research work in the order of the value of 

 their work, as estimated by those having ex- 

 pert knowledge. The ten positions assigned 

 to each individual were then averaged, and 

 the workers in each science were arranged in 

 order. The lists for the twelve sciences were 

 interpolated to form a combined list of a 

 thousand scientific men. A second group in 



each science and a second group of a thousand 

 scientific men were in like manner obtained. 

 This was not done before, and the second 

 thousand has less validity than the first thou- 

 sand. It has, however, a certain interest for 

 purposes of comparison. 



The average of ten judgments is not neces- 

 sarily more correct than any one of these 

 judgments; the conditions are similar to ob- 

 servations in the exact sciences. One good 

 observation may have more validity than the 

 average of a number of observations made 

 under less favorable conditions. But if ten 

 scientific men concerning whosS competence 

 it is not possible to discriminate in advance 

 make a judgment, we may take the average as 

 the most probable value. If we had but a 

 single judgment we should not know its valid- 

 ity, but with ten judgments the probable error 

 can be calculated. These probable errors tell 

 us not only the limits within which the place 

 of an individual in the series is likely to be 

 correct, but also measure the differences be- 

 tween the individuals. 



This method of converting a qualitative 

 series into a series of quantitative diiierences 

 may be illustrated by the case in which it was 

 used by the writer for the first time.^ Some 

 two hundred shades of gray were made, giving 

 approximately equal differences in illumina- 

 tion between white and black. In such a 

 series the grays toward the white end ap- 

 pear more alike than those toward the black 

 end, and two adjacent grays are indistinguish- 

 able. Psychologically it is a qualitative series. 

 If now the grays are arranged in the order of 

 brightness a number of times by the same or 

 different observers and the average position 

 in the series of each gray is determined, the 

 mean variation is inversely proportional to the 

 psychological differences between the grays. 

 There is thus determined the quantitative 

 differences in the perception and its relation 

 to the physical differences between the lights. 

 The same methods have been used in the Co- 



' " The Time of Perception as a Measure of 

 Differences in Intensity," Philos. Stttdien, 19: 

 fi.3-68, 1902. 



