Analysis of Heterogeneity in Some Simplest Charactees 215 



duced in the location; likewise if (PHI) is absent no general localization 

 of color occurs, a diffuse distribution with no specific spots resulting, while Sp 

 is necessary to the series to give specific form to the area in question. 



It is easy to show by present methods that there are four necessary active agen- 

 cies at work in the production of this series of spots, and while it is not known 

 what the nature of the agent is that produces the action in any instance, the 

 accuracy of operation and the certainty of the result leaves not the slightest 

 doubt that these agents are at work in the production of the spots in question. 



I have tried repeatedly to obtain, from the study of the spots in the larvae of 

 these organisms, evidence that there were various categories of " variation " in 

 the differences shown, but I find myself unable to decide which differences are 

 quantitative or qualitative, which in line or multifarious, imless I ignore obvious 

 mistreatment of the data and use unproven assumptions as true. The larvae 

 afford numerous simplest color characters, and can with adequate tests show in 

 L. decemlineata or any other species that the character presents differences in 

 quantity, arrangement, relations in space, quality and specificity of manifesta- 

 tion ; in short, it presents the array of attributes, qualities, and conditions that 

 any resultant of interacting substances and forces do, and these are heterogene- 

 ous in their manifestations. 



In the effort to understand the meaning of heterogeneity in the characters of 

 organisms, using these beetles as materials for study, I have made such use of 

 these simplest color-characters in the effort to understand the significance of the 

 characters themselves and the nature of their production and significance of their 

 differences. There has been the problem to satisfy myself concerning the two 

 categories of " variation," as defined by De Vries, to discover if the distinctions 

 made are valid, because if so they are fundamental for further investigations of 

 evolution problems. Thanks to neo-Mendelism, the nature of characters has 

 received a searching study and analysis as never before, and while incompleteness 

 is apparent in neo-Mendelian work, it has shown clearly that there are in the 

 production of the characters of organisms agents, carriers of nothing in partic- 

 ular but the properties of their own substance and capacity of action, but which, 

 when present in the mechanical system of the organism, produce the concrete 

 product and interactions in exact and predictable results. 



I have tried to give the De Vriesian criterions with regard to the diversity in 

 organisms an adequate and fair test in this material in its color, as well as in 

 other characters, as illustrative of a great series of " organic characters." If it 

 be assumed that pigment is the character, which is contrary to fact, and if it be 

 further assumed that the amount of it present represented the homogeneous 

 result in the population of uniform causes, which is also contrary to fact and if 

 it be further assumed that the measurement of the area of pigmented surface is 

 an accurate measurement of the amount present, which is also contrary to fact, 

 one is ready to begin the routine statistical study of the character and arrive at 

 "exact mathematical proofs" and demonstrate some "fundamental facts of 

 biology." De Vries took at their advertised face value the supposed accurate 

 results of the biometricians, and therein lies a serious defect in his treatment 

 of the problems of the origin and meaning of " variation " in organisms. No 

 statistician has taken care to determine that his measured material is homo- 

 geneous, or that his measured " characters " are single characters or dimensions 



