690 



SCIENCE. 



[N. S. Vol. VII. No. 17T. 



the lower jaw. Data are given on length 

 of skull, which we assume to be the chief 

 differential. Plotting these data (Fig. 8) 

 we find that they form one curve with, how- 

 ever, three maxima. The index of isolation 

 between the first and second modes is 8% ; 

 between the second and third 18%. The 

 curves from each locality overlap the ad- 

 jacent modes. The index of divergence is 

 less than 100. 



Again we have a case of three alleged 

 species of the mole Scaphanus from the ex- 

 treme northwestern part of the United 

 States. The difierentise are size of body, 

 color and length of face. ITumerical data 

 are given by True on skull length which 

 is closely correlated with the size of the 

 body. The curve (Fig. 9) gives three 

 maxima. The index of isolation between 

 the first and second maxima is 66 ; between 

 the second and third, 100. The end of the 

 constituent curves do not overlap the ad- 

 jacent modes. The indices of divergence 

 are about 170 and 130 respectively. We 

 may admit these as distinct species. 



Again the hare, Lepus p)alustris, varies in 

 different localities chiefly in the breadth of 

 the face. Miller and Bangs * from a study 

 of eight individuals concluded that there 

 were two species which they called L. palus- 

 tris and L. paludicola. Later Chapman f 

 concluded from a study of nineteen indi- 

 viduals from the same localities as those of 

 Miller and Bangs that the two forms are 

 only varieties. "Which view is correct? 

 Plotting (Fig. 10) the ratio greatest nasal 

 width, basilar length of skull, we find that 

 the index of isolation is 33, the index of 

 divergence is 70. These forms are no 

 doubt varieties. 



A case from fishes : Two species, Leu- 

 dseus balteatus and L. hydrophlox, from the 

 Columbia Eiver basin differ in the number 

 of rays in the anal fin. The mode of these 



* Proc. Biol. Soc. Wash., IX., 1894. 



fBull. Amer. Mus. Nat. Hist., VI., 341, 1894. 



two groups is different, but an overlapping 

 occurs. Are not these groups perhaps 

 varieties? (Fig. 11.) The index of isola- 

 tion is 50% ; that of divergence is 100%. 

 The case is a doubtful one. We are near 

 the limit between species and varieties. 



Additional examples from mammals, 

 birds and fishes might be given, but those 

 already considered may sufiBce to illustrate 

 the method by which a conclusion as ta 

 where the line should be drawn has been 

 reached for animals. The conclusion is 

 that when the chief differential of any two 

 groups shows an index of isolation of 50% 

 or more, or when their index of divergence 

 is 100% or more, the two groups are spe- 

 cies ; otherwise they are varieties. 



B. The Chief Differential and Specific vs. In- 

 dividual Characters. By J. W. Blankin- 

 SHip, Harvard University. 

 In the previous part of this paper a 

 method was shown for the determination 

 of the value of species by means of the iso- 

 lation and divergence indicated by the 

 chief- differential. In this will be considered 

 the determination of the chief-differential 

 itself as the most marked of the specific 

 characters, and also the mathematical dis- 

 crimination of specific and individual char- 

 acters. 



I. Determination of the Chief- differential. 



Necessarily all the specific characters are 

 considered in the determination of species, 

 but these characters are of different values 

 and their variation from one species into 

 the other is never strictly correlative, hence 

 systematists in the case of critical inter- 

 grades are compelled to separate the species 

 by a single character in order to ensure 

 uniformity in their determinations. That 

 character is taken which is most distinct in 

 the two species and exhibits correlative va- 

 riation with the other, minor, specific cha- 

 racters. That most distinctive character is 



