894 



KEPORT — 1898. 



case the distribution of variations (see fig. 3) is very nearly symmetrical, and in 

 an account of these crabs which I ■wrote before Professor Pearson's memoir was 

 published I treated them as symmetrical. The curve actually drawn on the 

 diagram is one constructed by Professor Pearson himself from the data given by 

 my measurements of the crabs, and it fits the observations very sensibly better 

 than the symmetrical curve. So that this dimension of a crab's carapace does 

 vary by chance, but the chance of a given deviation from the mean length is not 

 quite the same in both directions. 



Now, admitting for the moment that these differences in the length of a part 

 of the crab's carapace can affect the crab's chances of survival, you see that natural 

 selection has abundant material on which to work. The production of this regular 

 series of deviations from the mean length of the antero-lateral margin is as 

 definite a character of the crabs as the mean itself ; and in every generation a 



Fig. :^. 



150 



KH.v 



720 



73U 



74U 



770 



7SU 



790 



800 



Diagram showing the magnitude of the antero-lateral margin (in terms of carapace- 

 length) in 999 female shore-crabs from Naples. 



series of deviations from the mean is regularly produced, according to a law which 

 we can learn if we choose to learn it. 



Now suppose it became advantageous to the crabs, from some change in them- 

 selves or in their surroundings, that this part of their carapace should be as long 

 as possible. Suppose the crabs in which it was shorter had a smaller chance of 

 living, and of reproducing, than the crabs in which it was longer. 



Suppose that crabs in which this dimension is longest were as much more pro- 

 ductive than those in which it was shortest, as the most prolific marriages are more 

 fertile than the least prolific marriages among ourselves. Professor Pearson has 

 pointed out that half the children born in England are the offspring of a quarter 

 of the marriages. If we suppose the productiveness among crabs to vary as much 

 as it does among ourselves, only that in crabs the productiveness is greater, the 

 greater the length of this bit of the carapace, then half of the next generation of 



