Correlation and Application of Statistics to Problems of Heredity 49 



mean of its generation and we find no incompatibility of the Ancestral Law 

 with any change of type. What we obviously must do is to study the 

 change of type or of successive means ; regression is a wholly independent 

 matter, and "the racial centre of regression " something which has no essen- 

 tial existence, biologically or statistically. 



The next point that Galton makes is that the variabilities 07VI— ii! 2 

 and (T f Jl—r- cannot be quite constant; it is not clear whether he only 

 means by this that 07 and therefore cr, the population variability, changes 

 with the course of evolution. This is very possible, though there is small 

 likelihood of its being discoverable in breeding only six generations of moths, 

 if kept under the same environment. Selection might equally well change 

 type and variability; but if the distributions of frequency were normal, the 

 type and variability would be uncorrelated, and the selection of one would not 

 necessarily affect the other. Hence I do not see why Galton says the change 

 in the Quartiles is probably connected with the value of the Median ; least 

 of all do I grasp why he should refer at this point to Macalister's curve for 

 the geometric mean. Whatever application that curve may have to variation 

 in sensations, this is the only occasion on which I have seen it suggested 

 that it has any claim to be used for bodily measurements. It might be as 

 justifiably used for physical measurements on man as for those on moths, but 

 I can hardly imagine profit coming from such an application. 



The last point made by Galton, namely that the fertility and vitality of 

 stocks widely divergent from the mediocre are likely to be affected, is a very 

 important one and is probably the reason why it is not possible to carry size 

 selection far, at any rate by rapid strides. This has been demonstrated not 

 only on the moth material at present under discussion, but by more recent 

 endeavours to modify small mammals by selecting for size. 



The reader who is interested in this matter would do well to refer at 

 least to Merrifield's first report* on the moth-breeding experiments. He will 

 then quickly understand why they failed to satisfy Galton's thirst for data ! 

 The spring and autumnal broods were really dimorphous, the males appeared 

 to be larger in one and the females in the other; the wing lengths were not 

 the same in the two. Thus the fact of two broods a year would certainly 

 not expedite matters. Further, the fertility of the largest and the smallest 

 Mas reduced below that of the mediocre, and when Merrifield took steps to 

 obtain by forcing under higher temperatures more frequent broods, not only 

 did he increase the size of his moths' wings, but the "giant" line and the 

 "dwarf" line became sterile and he had to start again from the mediocre. 

 In fact artificial means had to be used to get the moths from the pupae near 

 enough in time to breed with one another. Further, changes in environment 

 or food had to be made to hasten the larvae to the pupal stage because food 

 supplies were getting low. And all these changes appear to have been 

 associated with variations in size so that finally the irregularities were too 

 widespread for any statistical treatment of the data, or as Galton himself 



* Trans. Entomological Soc. London (Dec. 7, 1887), 1888, pp. 123-136. 

 pgiii 7 



