May 20, 1898.] 



SCIENCE. 



Table of Coeeelation. 



693 



A normal curve of variation extends an 

 equal distance on each side of its mode, and 

 hence in a dimorphic curve composed of 

 two such normals the continued extension 

 of the interior curves below the point of 

 confluence may be determined approxi- 

 mately by reference to the exterior halves. 

 In the curve of the spike- diameter (Fig. 

 17) this overlapping portion of the curves 

 of latifolia and angustifolia (19-23 mm.) rep- 

 resents the region of intergrades bebween . 



diSerential than any of those measured, but their 

 extremely short duration (about two weelvs in the 

 year) and their microscopic size do not render them 

 generally available for systematic work. From my 

 observation of Typha in this region, I do not think 

 the color of the spike or shape of the stigmas are re- 

 liable as differentials between these two species, and 

 the floral bracts are doubtfully absent in latifolia, be- 

 coming gradually larger through the intergrades to 

 typical angustifolia. 



those two species. Also, the minimum of the 

 sinus (21 mm.), where occur the fewest in- 

 tergrades between the two species, is the 

 point where systematists would naturally 

 separate them. 



It has now been shown that confluent 

 species can be separated by a fixed amount 

 of isolation and divergence, as indicated by 

 their most distinctive character — the chief- 

 difierential, which, can be determined 

 mathematically by the measurement of all 

 the specific characters ; and finally, a 

 method has been indicated whereby specific 

 and individual characters may be distin- 

 guished by correlation. 



It should be remembered that the meas- 

 urement of individuals of a species, selected 

 impartially after a fixed method throughout 

 a given region, gives the characteristics of 

 that species — its type and variation, the 



