694 



SCmNGE. 



[N. S. Vol. VII. No. 177. 



M. MrD-STEM DWMETEK. 



Fia. I'l. 



ir- BASE: DIAMETER. 



Fig. 13. 



r. LEAF-WIDTH. 



Fig. 15. 



K-^PlXE-LENGTH 



Fig. 16. 



relative abundance of its forms and its 

 confluence with allied species — only for that 

 region. For the complete determination of 

 its true characteristics the species must be 

 studied throughout its entire range. This 

 can often be done approximately by the 

 study of a large collection representing the 

 various parts of that range, as is now done 

 in ordinary systematic work. However, 

 two groups found to be so isolated and di- 

 vergent as to constitute distinct species in 

 any one region where their ranges or spe- 



cific factors overlap will doubtless be found 

 to continue distinct in all parts of their 

 ranges, as the greatest confluence of such 

 groups is necessarily at points where they 

 occur together. 



This method attempts only to express in 

 mathematical terms the facts already recog- 

 nized by systematists in the discrimination 

 of species ; it attempts to determine, by im- 

 partial quantitative enumeration of indi- 

 viduals, the specific type and the limits of 

 specific variation, as well as the relative 



