INTRODUCTION. 3 



Having made clear the general problems with which this investigation 

 has to do it will not be necessary to state here the specific subsidiary 

 questions which we have attempted to answer. Instead these questions 

 will be stated in the body of the paper in direct connection with the data 

 bearing upon them.* 



MATERIAL. 



As material for this study a collection of crayfish belonging to the 

 Zoological Museum of the University of Michigan was used. We have 

 to thank Mr. C. C. Adams for kindly placing the material at our dis- 

 posal. The collection included about 450 adult individuals of both 

 sexes, all clearly belonging to the same species. The specimens were 

 collected from the River Rouge, near Birmingham, Michigan, on July 

 24, 1903, by Mr. J. B. Field, and were by him presented to the Univer- 

 sity Museum. They may be considered to form a homogeneous sample of 

 the crayfish population of that locality. The specimens belonged to the 

 species Carnbarus propinquus Girard. We have, then, a homogeneous 

 sample of material belonging to the same species, all the individuals of 

 which have probably been exposed to reasonably the same set of environ- 

 mental factors during their development. In the collection males were 

 about twice as numerous as females. We had at first intended to study 

 the variation in both sexes, but on account of the relatively small number 

 of the females, as well as for other reasons which need not be entered 

 into, it was decided to confine the attention to the males. All specimens 

 were discarded in which any one of the joints of the legs which were 

 chosen for measurement was either lost or undergoing regeneration. 

 There remained 283 normal males available for measurement. All these 

 males measured belonged to the so-called "Form I." It was apart from 

 the purpose of the present study to consider the relation of the dimorphism 

 of the males in the genus Carnbarus to variation, and hence only one form 

 was used in the investigation. This dimorphism has been discussed by 

 Hagen (1870), Faxon (1884), Harris (1901), and others. 



* At this point I wish to acknowledge my great indebtedness to the Carnegie Insti- 

 tution of Washington for grants, during the tenure of which this work was done. It is 

 impossible to make any adequate statement of the value of this aid in my biometric 

 work. Under the best of conditions research in this field is very laborious and time- 

 consuming, and without adequate material facilities to lighten the burden of compu- 

 tation, and uninterrupted time for work, it is practically impossible to carry through 

 any extensive plan of biometrical work in any reasonable length of time. It should be 

 stated that I am alone responsible for the actual writing of this paper. R. P. 



