Interpreting this theoretical tabulation, Galton (6) wrote: It will be seen that more than half of each million is contained in the two mediocre classes _a_ and A; the four mediocre classes _a_, _b_, A, B, contain more than four fifths, and the six mediocre classes more than nineteen twentieths of the entire population. Thus, the rarity of commanding ability and the vast abundance of mediocrity is no accident, but follows of necessity from the very nature of these things. On decscending the scale, we find by the time we have reached _f_ that we are already among the idiots and imbeciles. We have seen that there are 400 idiots and imbeciles to any million of persons living in this country; but that 30 per cent of their number appear to be light cases, to whom the name of idiot is inappropriate. There will remain 280 true idiots and imbeciles to every million of our population. This ratio coincides very closely with the requirements of class _f_. No doubt a certain proportion of them are idiots owing to some fortuitous cause . . . but the proportion of accidental idiots cannot be very large. Hence we arrive at the undeniable but unexpected conclusion that eminently gifted men are raised as much above mediocrity as idiots are depressed below it; a fact that is calculated to enlarge considerably our ideas of the enormous difference of intellectual gifts between man and man. MISCELLANEOUS OBSERVATIONS TENDING TO DEFINE CHARACTERISTICS OF GENIUS In addition to the formulation of the rather definite concepts of genius which have been discussed, there are to be found in the literature of this topic a large number of general observations ascribing certain characteristics to persons of genius. There are also many remarks as to the conditions of living, of education, of genetics, and so forth, which are alleged to foster or to hinder the development of genius. Many of these observations and remarks emanate from others than professed psychologists, some of the most interesting coming from litterateurs and philosophers. One of the most penetrating discussions of genius by a litterateur is that of Shaw (15) in his Preface to _Saint Joan_. Shaw regards Saint Joan as a young genius, and in introducing his readers to this point of view he says: Let us be clear about the meaning of the terms. A genius is a person who, seeing farther and probing deeper than other people, has a different set of ethical values from theirs, and has energy enough to give effect to this extra vision and its valuations in whatever manner best suits his or her specific talents. Here is brought out the tendency to heterodoxy which characterizes genius and is the source of much of its difficulty. Shaw dwells upon these difficulties in saying: