Here again Galton applied his method with remarkable success. Referring to the progenitors of A and B, determining how many of each type there were in the direct pedigree of A and of B, he arrived at the same formula as before, with the simple difference that instead of expressing the probable average intensity of one character in several individuals, the prediction is given in terms of the probable number of A's and B's that would result on an average when particular A's and B's of known pedigree breed together.
The law as Galton gives it is as follows:—
"It is that the two parents contribute between them on the average one-half, or (0·5) of the total heritage of the offspring; the four grandparents, one-quarter, or (0·5)2; the eight great-grandparents, one-eighth, or (0·5)3, and so on. Then the sum of the ancestral contributions pressed by the series
{(0·5) + (0·5)2 + (0·5)3, &c.},
which, being equal to 1, accounts for the whole heritage."
In the former case where A and a are characters which can be denoted by reference to a common scale, the law assumes of course that the inheritance will be, to use Galton's term, blended, namely that the zygote resulting from the union of A with a will on the average be more like a than if A had been united with A; and conversely that an Aa zygote will on the average be more like A than an aa zygote would be.
But in the case of A's and B's, which are assumed to be mutually exclusive characters, we cannot speak of blending, but rather, to use Galton's term, of alternative inheritance.
Pearson, finding that the law whether formulated thus,
