(3) With respect to "complexity of structure," which is supposed to condition or to indicate mental development, there is declared to be a "lack of any definite and certain knowledge as to the fundamental facts." This, also, seems true. Quantitative information is wanting, but qualitative is at hand. We have no definite and certain knowledge as to the significance of the gyri and sulci in the brain; but this does not invalidate the general proposition that relates them _in some way_ with mental power. The brain of a Helmholtz would almost certainly be deeply carved; the brain of an imbecile would almost certainly be uncommonly smooth. Between these extremes there lie relations infinite in variety and impossible to grade, so crossed and intercrossed are they with other elements. Nevertheless, the two opposite poles remain fixed, and the general indications of convolutions and of smoothness, other things being equal, cannot be mistaken. (4) As to skull capacity, there are many difficulties in the way, and "the value of this evidence has come to be regarded as less than it was once considered to be, but still to a certain extent significant. In a general way it may be said to bear out the observations on the actual brains." We do not see how it could well be expected to do much more. Here, then, are three indicia--weight of brain, complexity of its structure, capacity of skull--each related directly, though indeterminately, to power of mind. If we call them _x_, _y_, _z_, then we may say, with some approach to truth, that mental strength depends upon their product, each taken with an unknown exponent, thus: _x^p y^q z^r_. This expression, to be sure, is not adequate; there are yet other factors, it may be many, as the post-pubertal extension of structural elements, and therewith of physiological connections, which we have no means of measuring or observing. But the real significance of these three is not, indeed cannot be, doubted. Thus, Manouvrier determined the skull capacity of thirty-two distinguished men to average 1663 cc., or 103 cc. above the general mean of 1560 cc.--an excess of nearly 7 per cent. Again, the mean weight of brain of thirty-four such men reached 1533 grammes--an excess of 163 over the average (1370), or almost exactly 12 per cent. No amount of reasonable allowance can rob these results of their import. It is no answer to say that the cranial capacity of forty-one murderers averaged 1593 cc., or 33 cc. (about two per cent.) above the mean. We see no reason why a murderer might not have more than ordinary intelligence, though many be degenerates; it is not at all unlikely that his central nervous system or some part of it should be highly developed. Unless we err widely, not a few of the greatest characters of history have been great criminals.