2 VARIATION AND CORRELATION IN THE CRAYFISH. 



In looking about for an organism suitable for such a study, the 

 common freshwater crayfish at once occurred to one as an especially 

 favorable form. In the crayfish there is no doubt about the serial 

 homology (attaching to the term the significance which it ordinarily 

 has in comparative anatomy) of the several joints of the successive ambu- 

 latory appendages. The most anterior leg (the cheliped) is widely dif- 

 ferentiated from the more posterior walking legs, among which as a class 

 there is little differentiation. Thus we are enabled easily to compare the 

 relative variability and correlation in slightly differentiated and greatly 

 differentiated homologous parts. Further, the firm exoskeleton makes it 

 possible to take measurements with a maximum of accuracy. Finally, 

 it is possible to obtain fairly large numbers of adult individuals with 

 relative ease. 



The present paper forms one of a series in course of publication by one 

 of the authors, all of which have as their general aim the analysis of the 

 factors of variation and correlation, as a contribution toward the eventual 

 determination of the fundamental physiological (morphogenetic) laws 

 which underlie these phenomena. In different papers of the series the 

 attempt has been made to analyze by experiment and observation, sup- 

 plemented by biometrical methods, the influence of different factors on 

 the degree and nature of the variation exhibited by particular sets of 

 organs or characters. The number of factors which conceivably may 

 play a part in influencing variation is of course very great. From the very 

 complexity of the problem we are forced to the admittedly slow process 

 of making detailed and thorough studies of but few of these factors at 

 a time. The present paper deals with the influence on variation of 

 two such conceivable factors, namely, the degree of differentiation or 

 development of parts fundamentally similar in their structure, and the 

 relationship between such parts expressed in the term "homology." 

 In other papers of the series which either have appeared or will be pub- 

 lished shortly other sets of factors have been considered. The under- 

 lying ideas which have been in the mind of the writer of this paper 

 throughout the course of his work on variation are [a) that the plie- 

 nomena of continuous variation must themselves be thoroughly analyzed 

 before we can get at the laws which underlie them, and (6) that the 

 most certain way to make progress towards the desired goal is by follow- 

 ing the method of quantitative analysis. As the work has progressed, 

 the more firmly has the writer been convinced of the essential truth of 

 these ideas. 



