INTRODUCTION. 7 



them, in some way, it is determined that each definite kind of differ- 

 entiated whorl shall occur among all whorls in a particular proportion. 

 What are these constant factors and according to what laws do they 

 operate? This is our problem. 



We have, then, by analysis of the gross frequency distribution for 

 the plant as a whole, to investigate the biological laws which lead to 

 the production in this particular organism of the characteristic distribu- 

 tion observed. In biometrical terminology our problem is one of intra- 

 individual variability. 



Specifically it seemed very desirable to study in detail such questions 

 as the following: 



(1) The relation between the form of a given part and position in the 

 organism as a whole. Does the number of leaves in a given whorl of a 

 Ceratophyllum plant bear any definite relation to the position of that 

 whorl? Such a relationship between position and differentiation has 

 been found in a number of cases. (Cf . Pearson ( :05) , illustrations A and 

 D; also Shull (:05) and Tammes (:03), for example.) 



(2) The relation of such a positional differentiation to the variation 

 and correlation of the differentiated parts. Does the variation exhibited 

 among all the whorls occupying the same position on Ceratophyllum 

 plants bear any definite relation to the position on the plant? 



(3) The effect of environmental influences on positional differen- 

 tiation. 



(4) The effect of environmental influences on the growth of the 

 organism as a whole. 



(5) The relationship between intra-individual, intra-racial, and inter- 

 racial variation and correlation. 



These statements will suffice to indicate the general standpoint from 

 which the work was done, and consequently it will not be necessary to 

 enumerate further at this point the specific questions investigated. 



Ceratophyllum is in many respects a very favorable form for the 

 study of such problems as those outlined. It usually occurs in great 

 abundance wherever it is found at all, and, being a widely distributed 

 plant, can easily be obtained from a variety of habitats. Furthermore, 

 the individual plant attains to a large size, which is very important for 

 work on intra-individual variability. The plant is comparatively simple 

 in structure and presents characters easily capable of quantitative deter- 

 mination. It would, in fact, be almost ideal for an investigation of this 

 kind were it not for the fact that, as will be shown later in the paper, 

 the differences produced in the form of the plant by different environ- 

 ments are not very marked. Ceratophyllum appears to be a much less 

 plastic form than many of the land plants. 



