48 



VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



The constants for the quaternary-branch whorls of Series V are given 

 in table 24, together with their differences when compared with tertiary- 

 branch whorls. 



Table 24. — Constants for variation in whorls on quaternary branches. Series V. 



We see that the mean number of leaves in the quaternary-branch 

 whorls is less than in those on tertiaries. The difference, however, is 

 small, being of the same order as its probable error. The quaternary- 

 branch whorls are also slightly the less variable. In the case of the 

 standard deviations the difference is nearly twice its probable error. 

 We may conclude, provisionally at least, that the same kind of change 

 occurs in the mean when we pass from tertiary to quaternary branches 

 as when we pass from secondaries to tertiaries. The differences between 

 the constants for whorls on these higher-order branches in any case 

 would probably be small in absolute amount, for reasons which will 

 appear as we go on. 



THE RELATIVE SIZE OF THE DIFFERENT DIVISIONS OF THE PLANT 

 AND THE VARIATION IN THIS CHARACTER. 



It will readily be admitted that if we are to get any light on the 

 question of the factors which produce the characteristic frequency dis- 

 tributions of variation for the whorls of a particular division of the 

 plant, by a study of the laws of growth and differentiation of the whorls 

 themselves, it will be necessary to know in addition something about 

 what proportions of the total whorls on a plant fall within particular 

 divisions, and to what extent these proportions are constant for different 

 plants. Also, it is desirable to have definite information regarding the 

 average length of the different axial divisions of the plant and the 

 variation in this character. It is with these matters that the present 

 section has to do. 



Taking first the question of the proportion of the total number of 

 whorls found on different parts of the plants, we have the results set 

 forth in table 25. The figures in the vertical columns give the percent- 

 ages which whorls borne on the specified part of the plant are of the 

 total. 



