might all, for example, represent different types of beauty. Beauty is neither a simple nor a constant thing; it is attainable through a variety of combinations, just as the number 500 can be got by adding or multiplying together a great variety of numerical arrangements. Two long numerical formulae might both simplify out to 500, but half the length of one truncated and put end on to the truncated end of the other, might give a very different result. It is quite conceivable that you might select and wed together all the most beautiful people in the world and find that in nine cases out of ten you had simply produced mediocre offspring or offspring below mediocrity. Out of the remaining tenth a great majority would be beautiful simply by “taking after” one or other parent, simply through the predominance, the _prepotency,_ of one parent over the other, a thing that might have happened equally well if the other parent was plain. The first sort of beauty (in my three formulae) wedding the third sort of beauty, might simply result in a rather ugly excess of F, and again the first sort might result from a combination of a, b, c, d, e, _F_, etc., and _A_, b, c, d, e, f, etc., neither of which arrangements, very conceivably, may be beautiful at all when it is taken alone. In this respect, at any rate, personal value and reproductive value may be two entirely different things. Now what the elements of personal aspect really are, what these elements a, b, c, d, e, f, etc., may be, we do not know with any sort of exactness. Possibly height, weight, presence of dark pigment in the hair, whiteness of skin, presence of hair upon the body, are simple elements in inheritance that will follow Galton’s arithmetical treatment of heredity with some exactness. But we are not even sure of that. The height of one particular person may be due to an exceptional length of leg and neck, of another to an abnormal length of the vertebral bodies of the backbone; the former may have a rather less than ordinary backbone, the latter a stunted type of limb, and an intermarriage may just as conceivably (so far as our present knowledge goes) give the backbone of the first and the legs of the second as it may a very tall person.