98 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



Table 51.— Weighted mean variability of successively formed primary- 

 branch whorls. 



Even with this sHght smoothing it is clear from the figures them- 

 selves that the variability is tending to become smaller in the higher 

 whorls, till we finally reach a condition of no variability at the ends of 

 the branches, or in other words, till all the frequency falls on one type 

 of whorl. These data are shown graphically in fig. 17. 



l+Z 3+4 5+6 7+8 9+10 



Whorls 



Fig. 17.— Scedastic curve for primary-branch whorls of Series I, II, and III combined. The 



abscissas give the position of the whorls, and the ordinates the ratio cnx/cy. o O^ 



observations. The fitted straight line and parabola are given by continuous lines. 



From this diagram it is at once evident that there is a clearly marked 

 and definite tendency for the variability to decrease with the successive 

 formation of whorls. Whorls formed when the branch first begins its 

 growth are more variable than those formed later. In order to give a 

 more precise idea of the rate at which this decrease in variability goes 

 on I have fitted to the observations given in fig. 17 a straight line and a 

 parabola. The fitting was very easily done by the method of moments 



