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(1.) The present paper endeavours to deal with a problem upon which I have long been occupied, adopting the widest basis compatible with the time and means at my disposal. In the first place, I have often been impressed with the small reduction in variability which can be produced by selection. The offspring of a single parent while diverging in character, possibly very widely from the average character of the race, will still have a variability in that character only slightly reduced, say at most 10 per cent, below the racial variability. Even if we select the ancestry for an indefinite number of generations, the offspring will have a variability upwards of 89 per cent, of that of the original race. Now this capacity in the parent for pro­ducing variable offspring must be in some manner related to the degree of resemblance in those offspring. We have thus the two fundamental divisions of our subject: (i.) What is the ratio of individual to racial variability ?. (ii.) How is the variability in the individual related to inheritance within the race ?. I must endeavour to explain my meaning a little more fully and clearly. The individual puts forth a number of like organs, corpuscles in the blood, petals of the flower, leaves of the trees, scales on the wing. These may or may not be divided up into differentiated groups. Special forms of leaves occur in the neighbourhood of the fruit; florets may be differentiated according to their position on the flower, scales according to their position on the wing; there may be two or more classes of blood-corpuscles.

philosophical transactions of the royal society of london. series a, containing papers of a mathematical or physical character

VIII. Mathematical contributions to the theory evolution. —IX. On principle of homotyposis and its relation, the variability of the individual, and to that of the race. Part I. —Homotyposis in the vegetable Kingdom