684 



SCIENCE 



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



nois also show larger gains than Harvard. 

 While Yale has more scientific men in the 

 thousand than the Johns Hopkins, and Stan- 

 ford than California, the order of the insti- 

 tutions is in each case reversed when the 

 effective strengths are calculated. The fig- 

 ures on the table appear to be significant and 

 important, and it would be well if they could 

 be brought to the attention of those respon- 

 sible for the conduct of the institutions to 

 which they relate. 



Assuming the validity of the method of 

 weighting used or, at all events, its relative 

 validity for purposes of comparison, consid- 

 erable reliance may be placed on the figures 

 given in the table. The probable error of a 

 man assigned a weight of one is greater owing 

 to the break at the bottom of the thousand, 

 and this is the largest factor in the probable 

 error of the total. Men just coming within 

 the thousand and men just falling below it 

 are of almost equal merit, yet the former are 

 counted and the latter are not. Still the prob- 

 able error of a man assigned the weight of 

 one is less than 0.5. When the errors are 

 algebraically added the probable error of the 

 sum increases as the square root of the num- 

 ber, and we may assume the probable errors 

 of the figures given in the table to be not 

 greater than one half of their square root. 

 Thus in the case of Harvard, we may assume 

 that the chances are even that its real 

 strength is between 142 and 152 and its real 

 gain between 14.3 and 18.3. 



The scientific strength of an institution 

 does not necessarily measure its total strength. 

 Common observation would lead us to believe 

 that the Jolins Hopkins and Cornell are rela- 

 tively stronger in the natural and exact sci- 

 ences than Harvard and Yale. We may per- 

 haps assume that the relative strength of a 

 university in different departments tends to 

 be proportional to the number of research de- 

 grees conferred. Data concerning these the 

 writer has each year collected and analyzed." 

 Chicago has in the past thirteen years con- 

 ferred exactly half its doctorates of philosophy 



" Cf. for the last report Science, N. S., 32 : 

 231-238, August 19, 1910. 



in the exact and natural sciences. The per- 

 centages for the other universities which con- 

 fer most of these degrees are: Cornell, 63; 

 Johns Hopkins, 5Y; Yale and Pennsylvania, 

 43 ; Harvard and Columbia, 39. On this 

 basis, the total strength of these universities, 

 the unit as before being a man in the lower 

 part of the thousand scientific men, is: 



Harvard 374.4 



Columbia 203.2 



Chicago 188.2 



Yale 140.7 



Johns Hopkins 111.1 



Cornell 91.9 



Pennsylvania 56.7 



These figures represent with tolerable ac- 

 curacy the strength of each institution, so far 

 as the subjects leading to the doctorate of 

 philosophy are concerned. They do not, how- 

 ever, give adequate recognition to the pro- 

 fessional schools, schools of law being prac- 

 tically ignored. Harvard has the strongest 

 schools of law and medicine and has a school 

 of theology, so its primacy would not be af- 

 fected if these were fully accounted for. In 

 its strength Harvard is nearly double Co- 

 lumbia and Chicago, which come close to- 

 gether. Each of these universities has nearly 

 double the strength of the Johns Hopkins, 

 which again has double the strength of 

 Pennsylvania. 



The figures at hand enable us to measure 

 the strength of the scientific departments of 

 the different universities. They are given in 

 Table XH. for the ten strongest departments 

 in each of the twelve sciences, together with 

 the gain or loss within the period of four 

 years. The institutions are arranged in the 

 order of strength of the department, but when 

 this is less than four the figures are omitted 

 to avoid giving possible information as to the 

 standing of individuals. The probable errors 

 of the figures given in the table are somewhat 

 less than one half their square root. Thus the 

 strength of the department of mathematics at 

 Chicago is equivalent to 16.8 men on the lower 

 part of the list, and the chances are even that 

 this figure is correct within two places. The 



