VARIABILITY OF SUCCESSIVELY FORMED WHORLS. 105 



I have fitted to the observations the following curves: 

 Straight line y = 0.7903 1 1 - 0.6428(^) [ 



Parabola y = 0.7903 ] 1.1096 - 0.6428(1^) - 0.3289(^) [ 



where ^ — 4. 



There can be no doubt that the main-stem whorls show the same 

 decrease in variability which we have observed in the other divisions of 

 the plant. Indeed, the results for the main stem are more regular than 

 for any other of the groups considered. This is of course due to the 

 fact that we have a much larger range of position (1 to 80) and so get 

 a smoothing eif ect by taking the whorls in groups of 10. In this case 

 it is clear that the parabola gives a somewhat better graduation than 

 does the straight line, but the gain is mainly in the representation 

 of the first and last observations, on neither of which can much weight 

 be laid. 



The difficulty with reference to the first observation is that so many 

 of the proximal main-stem whorls were mutilated and could not be 

 counted, thus giving disproportionate weight to the others (cf. p. 83). 

 This would of course operate to lower the variability for that group. 

 The last observation is based on too few whorls to be significant. 



So far it has been shown that when the variability of the whorls 

 situated in a definite position on an axial division is measured by taking 

 the ratio of the standard deviation of such whorls to the standard 

 deviation of all whorls on the same axial division, the degree of varia- 

 bility decreases as the distance of the whorl from the proximal end of 

 the branch (or main stem) increases. Now, this measure of variation, 

 consisting as it does of the ratio of two standard deviations, gives no 

 idea of the degree of variability in proportion to the size of the thing 

 varying. It has been shown in a preceding section that the mean 

 leaf -number changes in a very regular and definite way in successive 

 whorls, the direction of this change being an increase in the mean with 

 every increase in the distance of the whorl from a fixed point on the 

 axis. 



Since the means thus increase with successive whorl formation, 

 while, as we have seen, the absolute variability decreases, clearly there 

 must be a still more marked decrease in the relative variability in pro- 

 portion to the size. 



If we take the percentage of the standard deviation to the mean 

 (coefficient of variation) for each array corresponding to a definite posi- 



