MERISTIC VARIATION 71 



Botanists would say that what seem to us as radial series, 

 with the members standing on the same horizontal level, are in 

 most cases really shortened stems, bringing these parts into a 

 relation which is apparent rather than actual, as would happen if 

 we could telescope any long stem until the leaves, regularly dis- 

 posed along its length, should come to occupy the same plane. 1 



In this view of the case the petals of flowers and the branch- 

 ing of stems, as in the stooling of grain, would be examples of 

 linear series very much shortened rather than of radial series, 

 according to the strictest definition of the term. For our purposes, 

 however, this structural point may be waived, and all apparent 

 cases of radial symmetry treated as actual. 



Observations indicate and experiments show that members of 

 such series may be increased in number almost indefinitely. All 

 the members may be doubled simultaneously (as five petals 

 increased to ten), or any one member (original segment) may 

 double or even triple, or it may be entirely suppressed without 

 reference to other members of the series. 



The natural method of doubling seems to be for cell division 

 to proceed one step beyond the normal, giving rise to two instead 

 of one. If this occurs in all the members (petals), then the 

 members will all be doubled, as ten instead of five ; if only in 

 part, then only that portion will be affected, making six, seven, 

 or even eight instead of five. Thus we have clover running all 

 the way from the normal three up to as high as seven leaflets. 



Manifestly if cell division proceeds two stages beyond the 

 normal, each of the twin pair again dividing, it will result in 



1 Leaves are arranged in regular order upon the stems of plants according to 

 a system constituting the mathematical series, |, ^, f, f, etc., in which the 

 numerator indicates the number of circuits around the stem to reach a leaf 

 directly over the one with which the count was started, and the denominator the 

 number of leaves that would be passed in such a circuit. It therefore repre- 

 sents the number of members in a whorl of a shortened stem of this character. 



Corn, for example, belongs, with all other members of the grass family, to 

 the fraction | , built upon the plan of two. This number runs throughout the 

 plant, and while the number of rows of corn on the cob may vary freely from 

 eight to twenty-four, no case of an odd number of rows has ever been reported. 

 This fact tends to set some limits to even so wayward a thing as meristic varia- 

 tion, which seems never to have produced an ear of corn with an odd number of 

 rows. This seems marvelous when we consider the havoc it works with digits 

 and with even so complicated a structure as a head. 



