1890.] 



occurring in certain Decapod Crustacea. 



453 



That the deviations from the normal value of the coefficients of Q 

 shown in the foregoing are accidents due to the small number of 

 observations upon which the curves are based is shown by the fol- 

 lowing table, in which each entry is the mean of the corresponding 

 entries of all the preceding tables : — 



Grade. 



Mean of 

 observed 

 coefficients 

 of Q. 



Normal. 



Grrade. 



Mean of 

 observed 

 coefficients 

 of Q. 



Normal. 



5° 



+ 2-55 



+ 2-44 



60° 



-0 36 



-0-38 



10 



+ 1-99 



+ 1-90 



70 



-0-78 



-0-78 



20 



+ 1'24 



+ 1-25 



75 



-1-03 



-1 -oo 



25 



+ 0-97 



+ 1-00 



80 



-131 



-1-25 



30 



+ 0-74 



+ 0-78 



90 



-1-97 



-1-90 



40 



+ 0-35 



+ 0-38 



95 



-2 -49 



-2-44 



50 



o-oo 



o-oo 









Results similar to the above have been obtained from measure- 

 ments of a larger series of organs, and parts of organs, in Pandalus 

 annulicornis (tw^o races) and Palcemon serratus (one race) ; but, at 

 present, not more than 100 individuals of each race have been 

 measured, and the curves of distribution of the magnitudes of the 

 various organs are therefore more irregular than those given for the 

 shrimp. In these cases, however, there is no constant deviation in 

 any direction from the normal curve. There seems, therefore, no 

 ■reason to doubt that an extended series of measurements w 7 ill show 

 •that the variations of these animals obey the law of error as closely 

 as do those of Crangon. I hope shortly to collect such a series of 

 measurements. 



It seems, therefore, that Mr. Gralton's prediction is fully justified ; 

 and that (1) the variations in size of the organs measured occur with 

 the frequency indicated by the law of error ; and (2) the " probable 

 error" of the same organ is different in different races of the same 

 species. 



I have attempted to apply to the organs measured the test of 

 correlation given by Mr. Gralton (' Roy. Soc. Proc.,' vol. 45, No. 274, 

 pp. 135 et 'seq.) ; and the result seems to show that the degree of 

 correlation between two organs is constant in all the races examined, 

 Mr. Galton has, in a letter to myself, predicted this result. A result 

 of this kind is, however, so important to the general theory of 

 heredity, that I prefer to postpone a discussion of it until a larger 

 body of evidence has been collected. 



