I. Inlieritance in ShirJey Poppt/ 



65 



which could bo interpretod on the basi.s ot' a law of regressioii applied to the crop 

 nieans. 



Thus, whatevcr thoory of herc(lity wo apply, it must allow fur (i) absolute 

 Variation oi' the iiieaii duo to trcatnient and environrneut of the offspring crop as a 

 wholo, and (ii) sclection of parentages diffi-ring froni crop to crop. Now the.so 

 ave the very points so often misinterpreted by thosc who fall to grasp the 

 theory of regres.sion. The fir.st ditticulty is got over by remernbering that i egression 

 is not towards the parental but towanl.s the filial mean, and the .second by iioticing 

 that while both parental and filial variabilities and the correlation are changed by 

 selection of parents, the .slope of the regression line is not changed, and that the 

 slope of this line wuuld be the coefficient of parental heredity supposing the 

 j)opulation to reproduce itself stably, i.e. without change of Variation fi-ora gene- 

 ration to generation. In other words regression is summed up in : 



Probable deviatiou of individual offspring from filial mean = coefficient of 

 parental heredity x actual deviatiou of individual parent from parental mean. 



It is this " coefficient of parental heredity," equal to correlation between parent 

 and offspring multiplied by the ratio of filial to parental variability, that we must 

 find to test how far heredity in our poppies is in accordance with what we have 

 found it to be for men, horses, etc. 



Lastly we may consider seed (/3) drawn from a variety of capsules with the 

 same number of stigmata, although we have here of course no measure of the 

 original Hampden parentage. The foUowing table gives the results. 



TABLE III. 

 Weighted Capsules and Locol Offspring. Seed (ß). 



It will be Seen at once that the general results are the same, Oxford and 

 Chelsea II are the poorest of the 1900 crops ; Oxford is the most variable. But 

 Enfield II was also a poor crop, the mean having fallen back in 1901 below even 



* CLelsea II is liardlj' wortli recording with only 96 capsule.s. 40 out of the 9G capsules obtained 

 were on plants the seed of which was taken from capsules witli 7 and 8 bands, whereas at Enfield only 

 360 out of '2066 capsules came from these low band groups. It is possible that low band seeds were 

 better suited to the unfavourable Chelsea envirunment. 



Biometrika ii 9 



