No. 479] 



VARIATION IN LOTUS 



765 



observation polygon in this region except as a result of random 

 sampling. 



The fact that this distribution approaches very closely to the 

 normal type is indicated by the value obtained for the theoretical 

 range of variation when a Type 1 curve is used. It will be recalled 

 that this type of curve has the range limited in both directions, 

 while the normal curve has an infinite range. Using the values 

 of the moments given in Table 3, 1 find for the Type 1 curve: — 



Total range = 60.8794 

 Lower limit of range = -3.9252 

 Upper " " '•' = 56.9541 



It is clear that the theoretical range greatly overestimates the 

 observed. Of course the start at -4 seeds appears at first sight 

 to be an absurdity, but it must be remembered that this value is 

 subject to a considerable probable error, and that it is possible to 

 get as great an extension as this of the range of the theoretical 

 curve below zero as a result merely of random sampling. Further- 

 more it must be admitted that while the upper limit of the range 

 at 57 seeds seems very improbable, yet, for anything we know to 

 the contrary, it is not imp(xssible.^ In general it is clear from this 

 case that as the lyp(> 1 curve approaches the normal its range 

 becomes greatly cxtciidtHl. 



There is one further point regarding this material to which 

 attention should be called, namely, the bearing of the results on the 

 question of the distribution of fecundity. It is evident that the 

 number of seeds borne by a plant is the measure of its fecundity. 

 In considering data like those here presented the question at once 

 arises as to whether each different class of capsules contributes 

 its proportionate share in the total number of seeds available for 

 the propagation of a succeeding generation. A moment's con- 

 sideration shows that this cannot be the case in Xelumbium. The 

 figures given in Table 5 demonstrate this. To avoid the possibility 

 of misunderstanding, the manner in which this table is formed may 



^Since writing the above I have seen some actual -tati^tir-^ of variation 

 in seed number in the lotus in which the upper Uniit <>f Hic „h>tM-vo(l ran^e 



