1890.] Variations occurring in certain Decapod Crustacea, 445 



ficial strata are not magnetic, regions of high vertical force comparable 

 in size with small counties, and ridge lines or loci of attraction as 

 long and almost as clearly defined as the rivers. Their course is 

 closely connected with the geology of the districts through which 

 they run. 



II. " The Variations occurring in certain Decapod Crustacea. — 

 I. Crangon vulgaris." By W. F. R. WeldoN, M.A., Fellow 

 of St. John's College, Cambridge, and Lecturer on Inverte- 

 brate Morphology in the University. Communicated by 

 Professor M. Foster, Sec. R.S. Received March 20, 1890. 



It is well known that two sets of animals, belonging to the same 

 species, but living in different places, exhibit differences from one 

 another by which they can, in many cases, be easily distinguished. 

 But it is at the same time equally certain that the forces determin- 

 ing the differences between local races of the same species do not so 

 act as to produce the same effect upon all individuals of the same 

 race : for I am aware of no case in which the individuals composing 

 any race of animals — however small and isolated the area in which 

 they live, however uniform the conditions which obtain throughout 

 that area — have been shown to resemble one another exactly in any 

 character. 



Since the adjustment of a local race to the average proper to it is 

 not complete, the question arises, whether it is not possible to deter- 

 mine the degree of accuracy with which this adjustment is effected, 

 and the law which governs the occurrence of deviations from the 

 average. The object of this paper is to give an account of certain 

 observations made at the laboratory of the Marine Biological Associa- 

 tion at Plymouth, in order to determine, first, the average length of 

 three or four organs which admitted of accurate measurement, and, 

 secondly, the frequency with which the average length and every 

 deviation from it occurred in one or two local races of Crangon 

 vulgaris. 



In making this investigation, I have had the great privilege of 

 being constantly advised and helped, in every possible way, by 

 Mr. Gralton. My ignorance of statistical methods was so great that, 

 without Mr. Galton's constant help, given by letter at the expenditure 

 of a very great amount of time and trouble, this paper would never 

 have been written. I am glad to take this opportunity of expressing 

 my gratitude for his generous conduct. I have also to thank 

 Dr. Donald MacAlister for explaining to me many points connected 

 with the law of error, and for helping me in various ways. 



2 L 2 



