20 VARIATION AND CORRELATION IN THE CRAYFISH. 



altogether insignificant in bringing about our observed results. There 

 are several reasons for this opinion. In the first place, as has been stated 

 above (p. 3), before the measuring was begun the material was very 

 carefully examined and in every case where there was the slightest evidence 

 that regeneration in any of the appendages measured was going on, the 

 specimen was put aside and not included in the measuring. This would 

 at once exclude all but those in which regeneration was very nearly com- 

 plete, and that there should have been any considerable portion of the 

 sample in which the right chela was in such an advanced stage of regen- 

 eration as to be indistinguishable from the normal under careful examina- 

 tion, is very unlikely. Furthermore the facts that (i) each of the three 

 joints studied is more variable in leg i than in either of the two other 

 legs, and (ii) that the propodite of leg i is much more variable than 

 either the meripodite or carpopodite of that leg when taken together, 

 seem to us very difficult if not impossible of explanation on the assump- 

 tion that the observed degree of variation in leg i is in any considerable 

 part the result of the inclusion of non-homogeneous regenerating material. 

 The matter may be looked at in another way. It might be assumed, 

 with a fair degree of probability, that in any random sample whatever of 

 adult crayfish taken from their natural habitat there would be a definite, 

 perhaps even considerable, proportion of individuals which had regene- 

 rated at some previous time one or both of the great chelae. If, then, it 

 be further assumed that there is a tendency for a regenerated structure to 

 be formed with less quantitative precision — that is, in the aggregate with 

 greater variation — than when it is originally formed in the normal on- 

 togeny, we have at once an explanation for the greater observed variation 

 of leg I as compared with legs ii and iii. The chief difficulty with this 

 hypothesis is that we are in absolute ignorance as to the validity of the 

 second assumption. No systematic biometrical study of the relative vari- 

 ability of original and regenerated structures has ever been made, though 

 the field to be opened up by such work is a most promising one. It leads 

 at once to the general problem of the relative precision with which dif- 

 ferent morphogenetic processes operate. I have discussed this problem 

 in some detail for the normal ontogeny* and have been able to demon- 

 strate for one form, at least, that parts successively produced tend to 

 become less variable with each successive formation. If the same law 

 should hold true for regenerated structures as for successive formations 



*Cf. Pearl, Pepper, and Hagle, 1907. 



