Pedigree Moth-breeding . 27 



I have exhibited to this Society, as an example of the law of 

 variability, a row of about 100 pods of sweet peas, the produce or 

 brood of a single plant, which I had arranged edgeways, like the 

 vertical lines in fig. 1. Their outline expresses very distinctly the 

 peculiar shape of the curve of variability. 



The object of preserving the entire brood of moths is to obtain 

 careful after-measurements from which to deduce the values of 

 M and of Q in each case. When this is done we shall be able to 

 deal with each group in its entirety, and to submit it to mathe- 

 matical treatment. 



The data I have hitherto used in my inquiries were rarely 

 derived from more than three generations, but the condition of 

 statistical constancy in the peculiarities of a population, of which 

 I will again speak, enabled me to extend their scope. They 

 sufficed in this way to lead to many interesting, though perhaps 

 only approximative, results. One is that each parent contributes, 

 on the average, one quarter of the total hereditary peculiarities of 

 the child, each grandparent one-sixteenth, and so on. In other 

 words, that the two parents together contribute one-half, the four 

 grandparents a quarter, the eight great-grandparents one-eighth, 

 and so on, the whole heritage being thus accounted for. But when 

 none of the progenitors besides the two parents are known, their 

 implied peculiarities must be taken into account. They admit of 

 being calculated, and have to be allowed for in the form of an 

 increase to the hereditary contributions of the parents. It is 

 foimd that each parent should in that case be held to contribute 

 one-third ; the difference between one-third and one-quarter (or 

 one-twelfth) being the amount of the implied heritages. It is, 

 however, highly probable from other considerations that, though 

 this simple formula may be closely true for the parents, and 

 nearly true for the grandparents, it may become sensibly and 

 increasingly different for remoter progenitors. It is this that I 

 want to investigate, chiefly through inquiries into Regression. 

 Moreover, all theory concerning the cause and character of Stability 

 of Type, and of much else of high interest in any general view of 

 Heredity, must be based upon the facts of Regression, which such 

 experiments as those proposed can alone, so far as I see, be likely 

 to declare in a trustworthy way. 



The laws of simple heredity, as I made them out, involve only 

 five constants. These admit of being separately determined, and 

 they are at the same time connected by an equation that serves to 

 verify their observed values. The equation depends on the fact 

 alluded to, that successive generations of the same population 

 yield identical biological statistics, although each family, or brood, 



