May 20, 1R98.1 



SCIENCE. 



689 



be given. One of the two groups indicated 

 may have many fewer individuals than the 

 other. Very good ; this is an important 

 fact which tlie curve should be left to show. 



To sum up : The general method of at- 

 taining a precise criterion of species, as op- 

 posed to varieties, is to measure the chief 

 differential of the groups, plot the curve of 

 measurements showing the relative number 

 of cases in each class of measurements and 

 determine the index of isolation, or, if more 

 convenient, the index of divergence. If 

 either of these indices is less than a certain 

 number we have varieties; if above that 

 number, species. 



2. Determination of the Line between Species 

 and Varieties. The question now remains : 

 What is this number below which we have 

 varieties, above which species ? To deter- 

 mine it we must, as we have said, have re- 

 course to the usage of systematists. 



Let us consider first a clear case : Fig. 7 

 is formed from measurements of two species 

 of jumping mouse, Zapus hudsonius and Zapus 

 insignis. 80 individuals of each species, 

 from New Brunswick, New Hampshire, 

 Massachusetts and New York, were meas- 

 ured by Mr. G. S. Miller, * from whose 

 work the data are taken. The two species 

 occur in the same localities. Zapus insignis 

 differs from Z. hudsonius (1) in having longer 

 ears, (2) in being paler and more fulvous, 

 and (3) in being larger. Numerical data are 

 given on characters (1) and (3) only. These 

 show the length of ears to be the chief dif- 

 ferential. Plotting the length of ears, dis- 

 regarding the very slight sexual differences, 

 we see that there is an absence of inter- 

 grades. The index of divergence is 200 ; 

 that is, the distance between the modes is 

 twice the average distance of the ends of 

 the broader curve from the mode. 



Secondly, we have in Figure 8 a curve of 



* G. S. Miller, Jr. A Jumping Mouse, Zapus in- 

 signis, Miller, new to the United States. Proc. Biol. 

 Soo. Washington., VIII., 1-8, 1893. 



three undoubted varieties. The curve is 

 based on measurements of 130 individuals 

 of Scalops aquations, the Eastern mole, from 

 data furnished by True. * The moles were 



' Figs. 7, 8, 9, 10, 11. 



collected from (1) the Atlantic and Gulf 

 Slope, (2) the Mississippi Valley as far 

 south as Louisiana, (3) Texas and Okla- 

 homa. In different parts of its range the 

 species shows differences in length of skull 

 and in the form of the coronoid- process of 



* F. W. True, A Revision of the American Moles. 

 Proo. U. S. Nat. Mus., XIX., 1-112. 



