1892.] 



Correlated Variations in Crangon vulgaris. 



Kow ;_;f = 0-590; a,d| f = = 0-591. . 



So that the assigned value of r fulfils all the required conditions 

 very fairly well. 



Having found a relation between the deviation of carapace lengths 

 and that of post-spinous lengths, which is constant for all magnitudes 

 of either organ in one local race, the question at once arises whether 

 this relation is not a specific character of the shrimp, which is con- 

 stant in all local races. At the beginning of the inquiry Mr. Gralton 

 suggested to me that the relation between the two organs indicated 

 by the value of r was of such a kind that r might be expected to have 

 the same value in all races of the same species, and in some cases in 

 groups of species. A determination of the relation between carapace 

 length and post-spinous length, and of other relations which are to be 

 discussed below, has abundantly confirmed Mr. Galton's prediction. 



In order to test the constancy of the relation between them, the 

 variations in total length of carapace, and in length of the post-spinous 

 portion, were measured in samples of adult female shrimps from 

 Helder (North Holland), from Southport, from Sheerness, and from 

 Eoscoff (Finistere) — that is, from four places fairly distant from 

 Plymouth, and differing from Plymouth and from each other in 

 climatic conditions, in salinity and other characters of the sea water, 

 and in nature of the sea bottom.* Each of these races was found to 

 differ from the others in the average length of the organs measured, 

 and in the probable error of distribution of each organ about its 

 average; but the relation between the two organs, as measured by the 

 value of r, was very fairly constant throughout. 



The details of each determination of r are given in Tables III — X, 

 at the end of the paper ; they are constructed on precisely the same 

 plan as that used for Tables I and II, and need not therefore be 

 further explained. The values of r deduced from all the tables are — 



In Plymouth r — 0*81 (1000 individuals examined) 



In Southport 0"85 ( 800 „ „ ), 



InRoscoff 0-80 ( 500 „ „ ) 



In Sheerness 0'85 ( 380 „ „ ) 



In Helder 0'83 ( 300 „ „ ) 



The approach to identity between these values is very striking.. 

 The differences between them are certainly large ; but they are not, 

 as it seems to me, larger than the probable error of each determination. 

 The number of individuals employed, even in the races from Plymouth 



* I am glad to express my gratitude to Dr. P. P. C. Hoek, to Professor Delage, 

 and to Messrs. W. Garstang and W. H. Shrubsole, for their kindness in procuring 

 for me these samples. 



