4 Prof. W. h\ K, Weldon. Certain [Mar. 3, 



Fig 1. 



arc expressed in terms of the body length, taken as 1.000. As the 

 average length of the shrimps used was rather over 50 mm., the 

 measurements, in the form in which they are recorded, are accurate 

 only to the nearest unit. The roughness of the edges of the parts 

 measured, and the fact that the animals were preserved in spirit, 

 made any attempt to attain greater accuracy exceedingly difficult. 



The variations in the length of the four organs here discussed have 

 already been shown to occur with a frequency which agrees very 

 closely with that indicated by the law of probability (cf. ' Roy. Soc. 

 Proc.,' vol. 47, p. 445). The closeness with which the distribution of 

 deviations in the samples used agreed with that indicated by a proba- 

 bility curve may be gathered from the diagrams, figs. 2 and 3, which 

 are fairly typical of the whole series. 



1. — Total Length of Carapace and Length of Post-spinous Portion. 



The relation between these two parts has been determined in five 

 races of shrimps ; of these the sample containing the greatest num- 

 ber of individuals was obtained at the laboratory of the Marine 

 Biological Association at Plymouth. 



The mean length of the carapace, in 1000 adult female shrimps 

 from Plymouth, was 249'63 thousandths of the body length; the 

 probable error of distribution about this average was 4"55. These 

 numbers will be denoted in what follows by M c and Q c respectively. 

 The mean length of the post-spinous portion (Mp 3 ) was 177*53, its 

 probable error (Q^) being 3*50. 



These numbers having been determined, the individuals were 

 sorted into groups, such that the recorded length of the carapace, c, 

 was the same in each group'. The mean length of the post-spinous 

 portion, ps, was then determined in each group. The results are 

 entered in the first two columns of Table I. Each pair of entries in 

 the table gives a datum for determining the mean deviation of ps 

 which is associated with a given value of c. If each value obtained in 

 this way be divided by the probable error of the organ to which it 

 belongs, a series of pairs of values will be obtained, from each of which 



