26 VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



size and to its position. This is perhaps the most important point of 

 all, and it is one which is usually overlooked in criticisms of Type I 

 curves in regard to the estimation of the range. 



On the whole, I think we may conclude that the curves give good 

 fits and lead to entirely reasonable values for the physical constants. 



A point of interest brought out by these curves is the very close 

 similarity between the results for the combined Carp Lake plants, which 

 may be considered representative of the local race, and the single plant. 

 The curves are of very similar form, and the values of the constants 

 are of the same order. 



SUMMARY. 



In this section the general facts regarding variation in the number 

 of leaves to the whorl in Ceratophyllum have been brought out. It has 

 been shown (1) that the observed range of variation in this character 

 is from 3 leaves to 12 leaves, inclusive; (2) that the average number 

 of leaves to the whorl is about 8.7, with a standard deviation of about 

 1.2 leaves, leading to a coefficient of variability of about 14 per cent; 

 (3) that the variation is markedly skew in the negative direction, the 

 modal whorl having a higher number of leaves (about 9.3) than the 

 mean whorl; (4) that there are but comparatively small differences in 

 respect to this character between series collected at different times 

 and places; (5) that we reach essentially the same conclusions with 

 reference to these general facts of variation, whether we take a single 

 large plant or a number of plants from the same locality. 



We have seen in this section, in a birdseye view, the facts presented 

 by the plants when we study the individual as a whole, taking into 

 account every whorl on the plant. The attempt may now be made to 

 analyze these facts. 



