44 VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



(g) Both curves are of Type I, the equations being as follows: 

 Distribution No. 188, primaries: 



2.7363 



!,= 433.4048(1 , ^^^^ 

 Distribution No. 189, secondaries: 



""•"^ 5^0536) \^ ~ 1.4484/ 



.784 



.8726 



y = 151.m2{l + ^y'^{l--^) 



.2063 



The curves are shown graphically in fig. 8. The frequencies are 

 reduced to percentages, so that both curves have the same area in the 

 diagram. The greater skewness of the secondary distribution is very 

 evident from the diagram. 



40 



30 



20 



4> 

 •00 

 ID 



10 



li 



\2. 



4 5 6 7 8 9 



Leaf number 

 Fig, 8. — Frequency histogiams and fitted curves for variation in primary and secondary branch 

 whorls. Series I, II, and III combined. primaries; secondaries. 



It is interesting to note that the analytical results give a greater 

 range of variation for primary than for secondary branches. This is 

 what we should expect on general principles to find, because the prim.ary 

 branches are so much longer, and consequently bear so many more 

 whorls, than do the secondaries. 



Comparing the results for primary branches with those for the main 

 stem given in table 10 (p. 32) we note that (a) the variation is dis- 



