72 VARIATION 



quadrupling that member of the series. If, however, only one of 

 this pair should divide again, we should then have one plus two, 

 or three, new parts in place of the one that was normal. Again, 

 if all four should start and one abort, it would likewise result 

 in three developed members instead of four that should have 

 appeared. 



All these various processes may take place, but whatever the 

 final result, and whatever number ultimately develops, the method 

 is that of doubling through cell division, giving rise naturally to 

 even numbers. Odd numbers are explainable, however, by sup- 

 posing that one of a pair continues the process one step farther 

 than its twin, or else that one of the members fails to develop. 

 In these ways an original member of a radial series may at any 

 time develop into two, three, four, or more ; and if all the mem- 

 bers take part, a true doubling results. 



Meristic variation and cell division. In the last analysis, there- 

 fore, variation in the number of members in a radial series is 

 reducible to questions of cell division. Indeed, we may go further 

 and note that all cases of meristic deviation arise in this manner ; 

 that the preservation of the normal number of multiple parts 

 depends upon successful cell division up to a certain (normal) 

 point and its abrupt cessation at that point ; and that all sorts of 

 abnormalities may arise through excessive multiplication, through 

 abortion, or through some other disturbance of the process of 

 cell division. 



This view of the case helps to explain why it is that meristic 

 variations in radial series are among the easiest to explain of all 

 variations which may present themselves to the breeder. 



Considerations of this character make clear the futility and 

 shortsightedness of appealing to reversion or atavism to explain 

 what may be a mere incident in cell division, an incident, more- 

 over, .that may never have occurred in phylogeny, may not be 

 even common in ontogeny, and is therefore not to unduly im- 

 press the observer. 1 



1 These terms will be frequently used in the text. Phylogeny refers to the 

 development of the species, ontogeny to the development of the individual. 

 The latter is supposed in a general way to repeat the steps of the former, though 

 with this view of the matter important gaps are of frequent occurrence. 



