MICHIGAN ACADEMY OF SCIENCE. 103 



SOME RESULTS OF A STUDY OF CORRELATION IN THE CRAY- 

 FISH'. 



A. B. CLAWSON. 



The problem dealt with in this paper may be stated in the following 

 way: Do morphologically homologous characters exhibit a generally 

 higher degree of correlation in their variation than non-homologous 

 characters? This question is one of considerable interest both from the 

 standpoint of comparative morphology, and also from, that of the 

 analysis of the fundamental nature of organic correlation. There is 

 available but little quantitative evidence on the question. The following 

 authors have, in the memoirs indicated, briefly discussed the matter: 



(a) Duncker, Georg. Weber Asymmetrie bei "Gelasimus Pugilator" (Latr.) Biametrika Vol. 

 II, pp. 307-320. 1902-3. 



(b) Lewenz & Whitelev, "A Second Study of the Variability and Correlation of the Hand." Biora- 

 etrika, Vol . I, pp. 345-360, 1902. 



(c) Schuster. "Variation in Epagurus prideauxi" (Heller.) Biometrika, Vol. II, pp. 191-210, 

 1902-3. 



(d"> Warren, "An Investigation on the Variability of the Human Skeleton." Pliil. Trans. B 

 1897 Vol. 189, pp. 125-227. 



(e) Yerkes, "A Study of Variation in the Fiddler Crab Gelasimus Pugilator" (Latr.) Proc. of the 

 American Academy of Arts & Sciences. Vol. 36, pp. 417-442, 1900-1. 



The joints of the legs in the crayfish are organs especially well adapted for a study of 

 this question, because we have in this case strict serial homology of individual members, 

 accompanied with a definite and considerable degree of differentiation in the different 

 legs. Furthermore the firm exoskeleton makes it possible to attain accuracy in measur- 

 ing with comparative ease and certainty. 



As material for the investigation a collection of cray fish {Camborus propinquus, Girard.) 

 belonging to the University of Michigan museum was kindly placed at our disposal by 

 the Curator, Mr. Chas. C. Adams. The individuals comprised in this collection were 

 taken July 24, 1903, without selection by Mr. J. B. Field from the River Rouge near Birm- 

 ingham, Michigan. They form a homogeneous sample of the species as it exists in that 

 locality. 



In all there were about 450 adult individuals, including both sexes, in the collection. 

 For reasons which need not be entered into here it was decided to use only males in this 

 work. Out of the 450 individuals some 325 were found to be males. Of these a certain 

 number had joints that we wished to measure either lost or undergoing regeneration. All 

 such individuals were discarded. There were left finally 283 individuals with the parts 

 chosen for measurement present in normal condition. Eleven measurements were made 

 on each individual. 



The following characters were measured: 



1. Length of the meripodite of the right great cheliped from the edge of its proximal dorsal pro- 

 cess for articulation with the ischiopodite to the distal edge of the joint on dorsal medium line. Fig. 

 I, a-b. 



2. Length of the meripodite of the first walking leg of the right side, measurements from same 

 points as in 1. 



3. Length of the meripodite of the second walking leg of the right side; measurements from the 

 same points as in 1 and 2. 



4. Length of the carpopodite of the right great cheliped from the proximal dorsal edge to the end 

 of the distal dorsal process where it articulates with the propodite. Fig. I, d-e. 



^Contributions from the Zoological Laboratory, University of Michigan, No. 98. 



Note. In a general plan of investigation of organic correlation it was proposed as one item to make 

 a thorough study of the degree of correlation existing between the different members of a group of 

 serially homologous, but differentiated organs. Tlie appendages of the crayfish seemed to be very 

 favorable objects for such a study and consequently I suggested to Mr. Clawson that he take up the 

 problem on this form. This was done in the second semester of the academic year 1903-04. The 

 present paper is the first report on a portion of the results obtained. A complete account of the re- 

 sults wUl be published later. I am responsible for the arrangement of the present paper. I am in- 

 debted to the Carnegie Institution of Washington for a grant to aid in this and other biometric work 

 now in progress. 



RAYMOND PEARL. 



