672 



SCIENCE 



[N. S. Vol. XXXII. No. 828 



SPECIAL ARTICLES 



A FURTHER STATISTICAL STUDY OF AMERICAN MEN 



OF SCIENCE 



n 



In addition to the 269 men added to the 

 thousand, whose origin, education, distribu- 

 tion, ages and standing have been considered, 

 there were 731 men on the list of 1903 who 

 retained places on the list of 1910. Some of 

 them maintained about the same places as 

 before, some improved their positions and 

 some dropped down to lower places on the 

 list. The number of places that each indi- 

 vidual moved up or down is known. A gain 

 or loss of a hundred places at the bottom of 

 the list would not be significant, as the prob- 

 able error of the change would be about 100 

 X \/2- A gain of a hundred places at the 

 top of the list, where the probable error is 

 under twenty places, would represent a certain 

 and important advance in the estimation in 

 which the work of the individual is held. The 

 value of gains or losses in difEerent points in 

 the series is inversely as the probable error 

 corrected by the range, and it is thus possible 

 to represent the gains or losses of individuals 

 wherever they occur in comparable figures. 

 If a gain of one place in the last five hundred 

 is taken as the unit, a gain of one place in the 

 upper hundreds would be approximately as 

 follows: V. = 1.5; IV. = 2; III. = 3; II. = 6, 

 and I. = 10. Dividing further the first hun- 

 dred, a gain in the lower fifty equals 8, and 

 gains in the two upper twenty-fives, respect- 

 ively, equal 10 and 14. On such a scale the 

 gain or loss of each individual has been as- 

 signed. It is a truly dramatic figure express- 

 ing with almost brutal conciseness the efforts, 

 the successes and the failures of seven years 

 of a man's life. 



The gains and losses of those on the list of 

 1903, apart from the 68 who died or removed 

 from the country, are shown in the accom- 

 panying curve (Fig. 1). 



It is a tolerably symmetric surface of dis- 

 tribution, in view of the limited number of 

 cases and the complicated conditions. 357 



men improved their positions and 575 lost 

 ground, of which latter 201 dropped out of the 

 thousand. The average loss was 113 places, 

 these being places in the lower five hundred, 

 equal to one tenth as many places in the first 

 hundred. Apart from this average change in 

 one direction, or constant error, there was an 

 average change of position, or variable error, 

 which referred to the age groups in 305 places. 



This variable error is due to two factors — ^the 

 chance error of arrangement (say 141) and 

 the real change in the position of the men — 

 and is equal to the square root of the sum of 

 their squares. The real variable error is con- 

 sequently 270. Men on the list thus lost on 

 the average 113 places, and from this average 

 there was a loss or gain of position, which on 

 the average amounted to 270 places. 



The removals from the list would tend to 

 give higher positions to those remaining on it. 

 If the 68 removals were equally distributed 

 over the list, they would allow on the average 

 an advance of 34 places to each man, or, 

 weighting the places, an advance of 73 places 

 of the value of those in the lower five hundred. 

 Instead of such an advance, there was an 

 average loss of 113 places and consequently a 

 total average loss of 186 places. With a gross 

 variable error of 305 places there might be 

 expected to be dropped from the list about 155 

 men, apart from any negative constant error, 

 or any positive advance due to the deaths. 



In a stationary scientific population it 

 might be reasonable to assume that the losses 

 by death would be filled by those below the 

 thousand and that those in the thousand would 

 maintain the same or an improved average 



