10 



Prof. W. F. K. Weldon. Certain 



[Mar. 3, 



and Southport, is too small to allow of a satisfactory determination of 

 the second decimal place. The reader, who cares to do so, may satisfy 

 himself of this by taking 0*80 or 0*82 as values of r in the Plymouth 

 tables, when he will find the agreement between calculated and 

 observed values of the associated organ tc be only slightly less close 

 than in the existing table. 



It may, therefore, be fairly said that the values of r obtained by 

 examining five races of shrimps are not inconsistent with the exist- 

 ence of a constant value in all the races examined — a value lying 

 somewhere between 0*80 and 0'85. 



So that if the deviation of total carapace length from its average be 

 expressed in terms of its probable error, and if the deviation of the 

 post-spinous portion be in the same way expressed in terms of its prob- 

 able error, then, when either organ differs from its average by any 

 constant amount, the mean deviation of the other will be a constant 

 fraction of that amount, the fraction being between 0'80 and 0'85. 



A similar approximation to constancy has been found to exist in 

 the relation between three other pairs of organs, determined in the 

 samples from Plymouth and from Southport. These organs are so 

 largely independent that the probable error of the determination is 

 much greater than before ; and accordingly the irregularities in the 

 results are much greater than in the previous case. The mean values 

 ■of r are as follows : — 





Carapace length 



Carapace length 



Telson and 





and tergum vi. 



and telson. 



tergum vi. 



Plymouth .... 



0-09 



0-18 



-0-11 



Southport .... 



0-06 



0-14 



-0-09 



These values are found from the tables at the end of the paper, 

 from which it will be evident that the determination is much less 

 reliable than that first discussed. 



So far, we have only investigated the mean deviation of each organ 

 which is associated with a known constant deviation of another organ. 

 But since a fixed deviation of one organ does not as a rule involve a 

 fixed deviation of the second, it becomes necessary to inquire how the 

 values of this second organ are distributed about their mean. Mr. 

 Galton points out that the deviations of each dependent organ are 

 distributed about their mean with a probable error of Q r 2 . So 

 that in Plymouth, for example, those post-spinous carapace lengths 

 which are associated with any fixed total carapace length sho uld be dis- 

 tributed about their mean, with a probable error of Q ps — (0"81) 2 

 or 35 0*34, or 2*03 nearly. In the same way, the values of total 



