INDEX CORRELATIONS. 45 



that of the propodite of leg i is not the same on the average in large 

 crayfish that it is in small. On the contrary, the proportion of these 

 two joints relative to each other, changes in a definite and orderly man- 

 ner as we pass from small to large individuals. By taking the indices 

 formed by the lengths of other joints of the legs we should reach the 

 same conclusion from them, the numerical values of the coefficients differ- 

 ing, of course, in each different case. 



An essential part of Driesch's vitalistic argument appears to depend 

 on the assumption that the proportionality of the parts in a differentiated 

 system is independent of the size of the system. As a result of quan- 

 titative studies of the proportionality of various parts and characters of 

 the body it has been shown that the proportions and absolute size are not 

 independent, but instead are correlated to a sensible degree in the follow- 

 ing organisms: Chilomonas and Paramecium (Pearl 1906 and 1907); 

 the crayfish (the present paper) ; in the aphid Hyalopterus trirhodus 

 (Warren 1902) ; and in the case of various proportions of the human skull 

 by Fawcett (1902) and Macdonell (1904). The writer has in hand unpub- 

 lished data showing the same thing for several other organisms. It is 

 not our purpose to enter here upon a theoretical discussion of Driesch's 

 "first proof," as the writer's position has already been set forth elsewhere 

 (loc. cit. ). Our present aim is merely to give in detail the additional 

 evidence afforded by this study of the crayfish on the point made in the 

 earlier paper. Putting all the evidence together, it would appear that 

 the assumption that proportionality is independent of absolute size in the 

 organism is not substantiated when an exact quantitative study of the 

 facts is made. Only by such quantitative study can it be determined 

 with any degree of precision whether or not there is a definite association 

 between two varying phenomena. 



