SCIENCE 



in the ten groups of eight votes each received, 

 respectively, 4, 4, 2, 1, 4, 7, 4, 3, 2, and 2 votes. 

 The probable error is 0.363, and for the group 

 of eighty votes it is 3.63. The position on the 

 curve assigned by eacli of the small groups can 

 also be found and a probable eiTor calculated 

 from these ten positions. 



The proijjable eurors based on 80 votes (as a 

 rule for each fifth individual) are indicated by 

 the broken vertical line on the curve and when 

 referred to the order of merit toy the broken 

 horizontal lines. The probable errors of the 

 votes of the fire psychologists last in the fifty 

 ai'e, respectively, 3.4, 2.8, 2.8, 3.1 and 3.6, an 

 average of 3.14. The curve from No. X to 

 No. C is nearly a straight line, the vote de- 

 creasing from 79 for No. X to 3 for No. C. 

 Consequently the probable error of t)he vote 

 when referred to the order is increased by 

 about one sixth. The probaible error of posi- 

 tion at the bottom of the group of fifty is 3.6 ; 

 there are thus only three or four for whom 

 there would be as much as one chance in four 

 of being dropped from the list if the arrange- 

 ment were made by an indefinitely large elec- 

 torate of the same character. 



In the first study of the psychologists, the 

 probable error at the lower end of the fifty 

 was 10.7, that is, there were 10 or 11 for whom 

 there was one chance in four thalt they should 

 not be included on the list. There were then 

 ten arrangements in order of merit; now there 

 are eighty votes. The probable error decreases 

 as the square root of the number of observa- 

 tions, and the probable errors in ifche two cases, 

 other things being equal, should be about as 

 3 : 1, which is in fac't almost exactly the case. 

 The probable error of a single vote for the 

 psychologists low in the group of fifty at the 

 present time is thus the same as by order of 

 merit in the group of 1903. 



In the first study, however, we were con- 

 cerned with the upper quartile, and we are 

 now concerned with the upper decile of the 

 group of American psychologists. If we as- 

 sume distributions in accordance with the curve 

 of error, the men who now stand at the bottom 

 of the fifty in the present selection will be as 

 able as those who stood about twenty in the 



first arrangement. An examination of the rela- 

 tive positions of the individuals who are in 

 each of the two arrangements indicates that 

 this tends to be the case. The probable error 

 at the bottom of the fifty selected by votes 

 should be in the neighborhood of those who 

 stood about twenty in the first arrangements. 

 This would make a single vote one half as 

 valid (the ratio of the probable errors in the 

 first arrangement for those near the bottom of 

 the fourth hundred and in the tenth hundred 

 of the thousand being 64 : 125) as a single 

 judgment of order of merit. The figures given 

 should, however, be regarded as indications of 

 method rather than as exact determinations, 

 Eor they are subject to various errors. 



The average position of the survivors of the 

 first group of psychologists in the arrangement 

 of 1903 was (after deaths have been eliminated) 

 4; it is now for the same individuals 14.8. 

 Those in the four following groups of ten have 

 dropped, respectively, from 11.5 to 18.1; 20 to 

 27.4; 29.5 to 59.2, and 39.5 to 64.9. This 

 drop in position is on the average less than 

 would be expected if the 10,000 scientific men 

 of to-day are as able and have as good oppor- 

 tunity as the 4,000 scientific men of 1903. The 

 inference is that as the total number increases 

 the proportion of men of distinction decreases. 

 This may be due to the fact that men of si>ecial 

 ability find their level apart from the size of 

 the group or because the scientific career 

 attracts less able men or gives them less oppor- 

 tunity than formerly. Both factors are prob- 

 ably present; it is apparent that the situation 

 deserves further investigation. In the pre- 

 vious study it was shown thait in the increased 

 competition of a five-year period, those between 

 40 and 44 years of age remained on the average 

 about stationary; those below 40 gained; those 

 above 44 lost, the loss being in direct propor- 

 tion to the age. 



As the work of the men becomes more im- 

 portant, the differences between the indi- 

 viduals as measured by the probable error of 

 position become greater, the distribution cor- 

 responding in a general way to the upper end 

 of the curve of error. In the case of the votes 

 there are complications, for the votes for dif- 



