692 



SCIENCE. 



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



From the table above we may collect the 

 following data : 



tively with that of the chief-differential. 

 Any variable character in the two species 



Of these seven characters the stem-height 

 and the spike-length show no apparent dif- 

 ferentiation for the two species ; the differ- 

 entiation is slight in the mid-stem diameter, 

 but is marked in the other characters. 

 Both isolation and divergence are greatest 

 in the spike-diameter, which therefore 

 should be taken for the chief- differential. 

 The isolation being above 50 per cent. (89) 

 and the divergence above 100 per cent. 

 (137), both are undoubtedly good species- 

 Taking those characters showing marked 

 differentiation, the modes indicate the most 

 frequent form of the species, the smaller size 

 being angustifolia and the larger latifolia, and 

 hence represent the specific types of those 

 species as they occur in this region. This 

 specific type must not be confused with the 

 historical typie, which is the form of the spe- 

 cies first described and may occur at any 

 point within the normal limits of the vari- 

 ation of the species. 



II. Specific and Individual Characters. 

 In order to make the enumeration of dif- 

 ferentiae accurate it may be necessary in 

 the discrimination of species to determine 

 which characters can be regarded as spe- 

 cific and which as individual. Those cha- 

 racters are called specific which differ in 

 some respect in the two species and whose 

 difference increases or diminishes correla- 



not exhibiting such correlation is regarded 

 as individual. 



In order to determine this fact of correla- 

 tion, these same characters of Typha were 

 compared with the spike-diameter as sub- 

 ject. The average stem-height, base-diam- 

 eter, leaf-width, etc., was found of all 

 specimens having a spike-diameter of 8 

 mm., the same of 9 mm., 10 mm., and so on 

 up to 36 mm. Correlation is then shown 

 by the character having a proportional in- 

 crement or reduction in size in comparison 

 with the chief-differential, the spike-diam- 

 eter. The result is given in the table below. 



From this it appears that the correlation 

 with the spike-diameter is well-marked in 

 the case of the base-diameter, the mid-stem 

 diameter and the leaf-width. It is apparent 

 in the stem-height and spike-length, yet 

 is not so close as to give rise to two modes 

 in the table of frequency. The case of the 

 interval is peculiar. In the table of fre- 

 quency it exhibits a combined normal and 

 half Galton- curve, while in the table of 

 correlation above, there is little increase or 

 decrease in the first ten numbers (good 

 angustifolia) and the subsequent decrease is 

 probably due to intergrading. This charac- 

 ter then exhibits individual variation for 

 this species.* 



* Of the other characters of Ti/pha not here consid- 

 ered, the pollen-grains might possibly prove a better 



