90 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



The diagram brings out very sharply a number of points. In the 

 first place we see that, whatever the part of the plant, first whorls con- 

 tribute proportionately very largely towards the frequencies on the low 

 leaf -numbers. As we go out towards the distal end of the branch or 

 the main stem the proportionate frequency of 9 and 10 leaved whorls 

 increases. Thus if we compare the rectangle representing 7-leaved 

 whorls with that for 10-leaved whorls we see at once that the sub- 

 divisions of the first decrease for each division of the plant as we go 

 towards the top of the diagram, while the subdivisions of the latter 

 increase. This means of course that the skewness of the distributions 

 is changing in the manner schematically indicated in the following 

 diagram: 



Small leaf-num- 

 ber per whorl 

 Proximal whorls, 



") Positive ) 

 ■ j skewness. C 



Leading 

 through var- 

 ious inter- 

 mediate stages, 



Including 



symmetry, to 



extreme. 



Positive 



r High leaf- 

 „i,«^v,^.,o ■^ number per 

 skewness. I ^j^^^l_ Tistal 



whorls. 



A and C would represent the extreme conditions of proximal and 

 distal whorls, while B would represent one of a whole series of inter- 

 mediate stages passed through as we go from A to C. It will be under- 

 stood that this diagram is purely schematic, but fairly represents the 

 essential facts very closely. The same stages as those indicated may 

 indeed be seen in plate ll, or in the correlation tables (cf . supra) on 

 which it is based, while a careful examination of the data will leave no 

 doubt in the mind of the reader that the general trend of the frequency 

 distributions in respect to skewness is fundamentally that indicated. 

 We see, then, that homologous organs on the same individual plant run 

 through the whole gamut of skewness from positive (A), through perfect 

 symmetry* to negative (C) . The phenomenon of skew variation stands 

 forth in this case, free of doubtful interpretation through selection or 

 any similar factor, clearly and definitely as a phenomenon of growth. In 



*Cf . for example the distribution for the third whorl on primary branches in Series 

 I, II, and III combined. 



