Analysis of Heterogeneity in Some Simplest Chaeactees 223 



curves of " quantitative variations " and those that stood apart and were to be 

 characterized as " qualitative." These same data would, with proper treatment, 

 give an imposing array of constants of no value or meaning, as far as the analysis 

 of the origin and meaning of the very evident heterogeneity was concerned, and 

 having already obtained an abundance of this sort of information regarding 

 these materials, at the onset of this study I discarded entirely the method and 

 attacked the problem from the point of view of genetic composition and the 

 effects of conditions in the medium. 



I have sho^^^l in Chapter II something of the natural complexity of this 

 material, of the forms that exist in nature and of the wide range in many of its 

 attributes. I was forced into this study by the attitude of De Vries in the 

 mutation theory and the position of Johannsen in his 1903 paper, and by all of 

 the current writers at that time, who as a body held to the two categories of 

 " variation." Since that time the progress of neo-Mendelism has produced 

 many changes in the viewpoint, with closer and closer approach to the concep- 

 tion of heterogeneity conceived of in purely physical terms. It is clear that 

 De Vries thought of mutations and fluctuations as distinct, and that the latter 

 were either of germinal or somatic origin, distinguished by the fact of their 

 inheritance, and if so, capable of accumulation up to certain limits. East in 

 1911 has in common with many others limited the term "fluctuation" and 

 placed the germinal variations as follows : " A fluctuation is a non-inherited 

 variation produced upon the soma by environmental conditions, while the in- 

 herited variation, the mutation if you will, is any variation quantitative 

 or qualitative, that is germinal in character." It follows from this that any 

 diversity in the observed series that is not inherited is then the product of the 

 environment upon the organism during its ontogeny. Since it was non-visible 

 in the following generations, it follows that it was absent as a part of the 

 germinal complex, which may or may not be true, and the further assumption 

 that since it was not inherited as per test it was the product of incident external 

 conditions upon the organisms during its growth. This is characteristic reason- 

 ing from effect to cause, and then broadly applying the result as a criterion to 

 separate the kinds of heterogeneity present. 



FORM-INDEX. 



For the study of form-index I took a body-index as representing a measur- 

 able character of the entire mass, and comparable to stature, tall and short 

 in some of the neo-Mendelian operations, and roughly equivalent to the same 

 index that might be derived from inorganic masses. These animals, like other 

 organisms, are during ontogeny changeable in some of the measurements of the 

 body that shift with the state of nutrition, reproduction, and age, so that I used 

 only measurements that were free from these sources of obvious error. In 

 figure 2 I have shown the measurements taken, the distance between parallels 

 passing through the anal apex and the anterior margin of the elytron (1), the 

 same measurement between the parallels passing through the anterior and pos- 

 terior margins of the pronotum (2), and the corresponding measurement of the 

 epicranium (3) . These are not influenced by the conditions of nutrition or the 

 changes in form incident to breeding. They were added to give the length or 

 longest measure of the mass ; this was divided by the greatest breadth (4), taken 

 as the greatest distance between the lateral margins of the pronotum, and this 



