42 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



are shown in table 19. In this ' 'difference table' ' the differences are taken 

 as positive when the primary-branch constant is the greater and nega- 

 tive when the constant for the secondaries is the greater. The absolute 

 differences are taken as percentages of the primary-branch constant, in 

 each case, to obtain the relative differences. 



Table 19. — Difference table comparing secondary with primary -branch whorls. 



Totals for series. 



Series. 



n! 

 m{ 



IV { 



VI j 



Diflferences. 



Absolute 

 Relative 

 Absolute 

 Relative 

 Absolute 

 Relative 

 Absolute 

 Relative 

 Absolute 

 Relative 

 Absolute 

 Relative 



difference . 

 difference.. 



difference 

 difference.. 



difference 

 difference.. 



difference 

 difference.. 



difference 

 difference.. 



difference 

 difference 



per cent, 

 per cent. 



per cent, 

 per cent. 



per cent, 

 per cent. 



Between means 

 (unit = 1 leaf). 



0.658±0.074: 



7.67 



.540± .066 



6.21 

 .330± .084 



3.83 

 .392± .037 



4.36 



.367± .114 



4.48 



- .038± .086 



.43 



Between 



coefflcients of 



variation. 



-0.655±0.663 



4.7 

 -1.823± .573 



13.2 

 -2.191± .725 



16.5 

 - .867± .303 



7.7 



-2.556dt:1.055 



15.1 



.490± .706 



3.2 



We see that generally the differences are positive in the "mean" 

 column and negative in the two variability columns, thus indicating 

 what was pointed out above, that whorls on secondary branches have 

 fewer leaves to the whorl and tend to be more variable than those on 

 primary branches. In respect to variation in leaf-number, then, the 

 secondary branches stand in much the same relation to the primaries as 

 the latter do to the main stem. In one case. Series VI, the order of the 

 differences is reversed, the mean being higher and the variability lower 

 for the secondary-branch whorls than for the primary, but no special 

 stress can be laid on this apparent exception to the rule, because the 

 differences are altogether insignificant in comparison with their proba- 

 ble errors. The differences between the means are, with this single 

 exception, significant in comparison with their probable errors. In the 

 variability columns the individual differences when taken singly are in 

 most cases not certainly significant. Due weight must, however, be 

 given to the fact that all tend in the same direction (except of course Series 

 VI) . I think we may safely conclude that, in general, whorls on sec- 

 ondary branches are as a class more variable in respect to leaf -number 

 than are whorls on primary branches. 



We may now consider analytically the variation in primary and sec- 

 ondary branch whorls, in comparison with each other and with whorls 

 on the main stem. As in other cases I have used the combined distri- 



