860 



SCIENCE. 



[N. S. Vol. VII. Ko. 182; 



At a recent meeting of the- Regents of the 

 University of Nebraska, Dr. Frederic E. Clem- 

 ents was promoted from the position of as- 

 sistant to that of instructor in botany. The 

 following were elected fellows for the collegiate 

 year 1898-9 : In mathematics, C. C. Engberg 

 and Alta Johnson ; in chemistry, Mariel C. 

 Gere, Benton Dales and Howard C. Parmelee ; 

 in pedagogy, William R. Hart ; in zoology, 

 Albert B. Lewis and Charles C. Morison ; in 

 geology, Cassius A. Fisher ; in physics, Samuel 

 R. Cook ; in electrical engineering, Charles H. 

 True, and in botany, Albert T. Bell and Cora 

 P. Smith. 



Miss Agnes Mary Claypolb, instructor in 

 Wellesley College, has been appointed assist- 

 ant in the department of histology and com- 

 parative physiology in Cornell University. 



De. Sophus Lie, professor of mathematics in 

 the University of Leipzig, has angenommen 

 accepted a call to the University of Christiania. 



De. Gisevintjs has been appointed associate 

 professor of agriculture in the University of 

 Konigsberg ; and Dr. Richard Wachsmuth, of 

 Gottingen, has been called to a professorship of 

 physics in the University of Rostock. 



DISCUSSION AND CORRESPONDENCE. 



' A PEECISB CBITERION OF SPECIES. ' 



The papers by Professor C. B. Davenport and 

 J. W. Blankinship, suggesting the determina- 

 tion of species by means of statistical methods, 

 are welcome signs that the appreciation of the 

 value of these methods is rapidly increasing 

 among biologists. Heretofore they have been 

 applied most extensively by anthropologists ; 

 consequently the inherent difBculties have be- 

 come familiar to them, and their experiences 

 will be useful to biologists who pursue these 

 methods. 



Statistical data are generally represented in 

 the form of curves ; and experience show that 

 most curves, if the number of cases is suffi- 

 ciently large, approximately conform to the 

 probability curve. When the number of cases 

 is small the curves tend to become more and 

 more irregular, and the question arises : How 



large must the number of cases be in order to- 

 be significant, that is to say, in order to justify 

 us in assuming that the few selected individuals 

 represent a curve which deviates from the 

 probability curve? All the curves given by 

 Professor Davenport and Professor^ Blankinship 

 in their paper are based on material not suffi- 

 ciently extensive to compel us to assume that 

 the distribution differs from the law of proba- 

 bility. For example, the data contained in 

 Fig. 9, which is one of the best of Professor 

 Davenport's examples, are not of such a char- 

 acter that we must necessarily assume a curve 

 deviating from the normal probability curve. 

 If a thousand individuals had been measured 

 instead of forty- six only, irregularities of the 

 curve would probably disappear. The same is 

 true of Professor Blankinship's measurements. 

 The secondary maximum in his best table (No. 

 VI., Fig. 17) is so uncertain that, until further 

 data are forthcoming, we must assume that 

 with an increased number of measurements the 

 secondary maximum will disappear entirely. 



Furthermore, it must be considered that under 

 certain conditions the distribution of measure- 

 ments cannot conform to the probability curve. 

 Such is the case in conditions like those exem- 

 plified in Table VII. of Professor Blankinship's 

 paper. Here the greatest relative frequency is 

 that of the value zero. Smaller values are not 

 possible ; consequently all the variations must be 

 on the positive side. The same is true wherever 

 the measured value is very near zero. In these 

 cases the distribution must be a symmetrical. 



But granted the supposition that curves exist 

 which have more than one maximum, the ques- 

 tion arises whether we are justified in assuming 

 that the two maxima represent two species in- 

 habiting the same area. First of all, it must be 

 mentioned that, assuming equal frequency and 

 equal variability of the two species, two maxima 

 will occur only when the distance between the 

 two types is greater than the standard devia- 

 tion of either type. When the difference is less, 

 the result is apparently an increased variability. 

 When two maxima exist, the biological problem 

 resolves itself into a mathematical analysis of 

 the given curve. Owing to the impossibility of 

 obtaining sufficiently extensive material, and 

 to the consequent inaccuracies of the results of 



