100 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



way as we have those for Series I, II, and III, we get the results shown 

 in fig. 18. The zigzag Hne gives the weighted means of the successive 

 pairs of observations given in table 49. 



As before, I have fitted a straight line and a parabola to the data. 

 In order to have an odd number of points for the fitting of the constants, 

 the curves were calculated from the first 11 observations {I = 5) neglect- 

 ing the twelfth. Apart from the practical reason, this procedure was 

 theoretically justifiable because of the small number of whorls on which 

 this last observation is based. The equations to the curves are: 



StraightHne, y = 0.6347 1 1 - 0.3292 (|) [ 



Parabola, y = 0.6347 ] 1.0701 - 0.3292 [fj - 0.2102 (|) 



Again we see that the general trend of the curve is downwards as 

 we pass to the whorls farther out on the branches. The slope of the 



curve is somewhat more 

 rapid than in the case of 

 Series I, II, and III, but 

 the diif erence in this re- 

 spect is not great. We 

 must conclude that here 

 as in the former case the 

 variability decreases with 

 successive whorl forma- 

 tion. 



We may next consider 

 Series V and VI. Here it 

 will be recalled that we are 

 dealing not solely with 

 primary-branch whorls, 

 but with all the whorls 

 borne on branches on the 

 plant as a whole. Fur- 

 thermore, for reasons set 

 forth above (p. 58), we 

 have considered only the 

 first 10 whorls. Dealing with Series V in the same way that we have 

 with the other series (i. e., combining successive whorls in pairs and 

 taking the weighted mean for each pair) we have the result shown in 

 fig. 19. 



\+z 



3+4- 



7+8 



3+10 



5+6 

 Whorls 



Fig. 19.— Scedastic curve for whorls on branches. Series V. 

 Weighted means of successive pairs. Significance of lines 

 as in fig. 17. 



