108 VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



ble; primary-branch whorls are more variable; a maximum of variability 

 is reached in secondary-branch whorls as a class; and in tertiary and 

 quaternary whorls the variability tends to decline. It is obvious that 

 the variation shown by any composite group of whorls will depend on 

 two factors: (a) the real variability of the whorls in a given position, 

 and (6) the mixing of whorls of differentiated types (i. e., whorls which 

 occur at different positions) . Now, in the case of main-stem whorls as a 

 class the effects of both a and b are at the minimum as a result respectively 

 of the operation of our second and first growth laws. In primary-branch 

 whorls the effect of the factor b is greater than in the main stem, but 

 since many primary branches are very long the influence of the law of 

 diminishing variability comes in through a to keep down the variation ex- 

 hibited by the group as a whole. When we come to secondary-branch 

 whorls this lowering of the variation through the presence of long 

 branches with many whorls of low variability no longer occurs, because 

 there are few or no long branches. Finally, the drop in the variability 

 shown by tertiary-branch whorls as a class is clearly due to the fact 

 that owing to the extreme shortness of these branches factor b contrib- 

 utes very little to the sum total, but instead we have the expression 

 practically of a alone. 



In following sections of the paper the operation of the law of dimin- 

 ishing variability in other phenomena than whorl production will be dis- 

 cussed. A discussion of its theoretical bearings and interpretation will 

 also be undertaken later in the paper. It need only be pointed out here 

 that it is merely a special case of a much more general biological law 

 applying to other phenomena besides those of growth. Jennings ( :05) in a 

 recent paper has enunciated what is essentially the same law in the field 

 of behavior in the following terms : ' 'The resolution of one physiological 

 state into another becomes easier and more rapid after it has taken 

 place one or more times." 



