580 



AMERICAN MEN OF SCIENCE 



which the work of the individual is held. The 

 value of gains or losses in different 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. l. 



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 

 position, while only so many would be dropped 

 from the thousand as are accounted for by the 

 variable error. In an increasing scientific 

 population, however, the standard of the thou- 

 sand would become higher. If there were an 

 increase of ten per cent, in the number of 

 scientific men in the course of seven years, 

 then there should be 110 of the same rank as 

 the first hundred in the thousand of 1903 and 

 1,100 of the same rank as the thousand. A 

 man in the lower part of the list who main- 

 tained his absolute position would lose nearly 

 a hundred places in relative position, and, 

 apart from the variable error of position, 91 

 of those in the thousand would drop to the 

 eleventh hundred. As a matter of fact the 

 average loss in position was 113 places, and 

 the number dropped from the list was 46 in 

 excess of those accounted for by the variable 

 error. According to this argument, the in- 

 crease in the number of scientific men of 

 standing in seven years would be from 5 to 

 11 per cent., or about one half the increase of 



