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: xp yq zr. 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.
(5) What conclusions are recommended by "all these facts and factors"? "Truly, the results are meager. We are probably justified in saying that, anatomically, the brains of negroid races are somewhat less developed than those of Europeans." But it is held that "a little reflection shows the comparative insignificance of the distinction.... The most that can be said is that the European series will show more very large brains than the negroid, and the negroid series more very small brains than the Europeans." Precisely! And it is just this excess of "very large brains," or at least of its general correlate, very large minds, that has the profoundest "significance" for civilization, for all that is great and glorious in history and in humanity. Not only must we, in accordance with the law of Deviation from the Average, interpret this excess of "very large brains" as implying a higher general level, but the meaning and value of these exceptions are incalculable. [ [18] ] Who can estimate the import of the one brain in a million, when it is the brain of Moses or Mohammed, of Aristotle or Archimedes, of Vergil or Galilei, of Leibnitz or Voltaire, of Darwin or Washington? Such brains are the foci of the orbits of history; such men blaze out the pathways for the feet of their kind. Without them we wander round and round, lost in the erroneous wood. The race that can produce such "very large brains" is the race of advancement and culture; they shine like stars in the firmament of history, and the multitudes steer their courses thereby. It is these exceptions that mark out the line between progress and stagnation, between civilization and barbarism; a race that is deficient in such exceptions is a race already condemned.
It is altogether vain to interpose that this acknowledged anatomical defect is, after all, only slight. The difference between the brains of a fish-monger and of a Socrates may be only slight—an ounce or so in the scale, a line or so in depth of convolution; yet it corresponds to the interval between mediety and the vertex of genius. Such differences are vanishingly small, or inexpressibly great, according to the origin of reckoning. And herewith we uncover the fallacy that lies so snugly hidden away in the phrase "comparative insignificance." Undoubtedly! If we reckon from the amœba, the witling seems scarcely distinguishable from the wit; but if we reckon from the average of humanity, they start asunder like the poles. The summits of the Himalayas are only some four or five miles above the valley of the Ganges; estimated from the centre of the earth, this difference is little more than one-thousandth of the whole—a difference hardly appreciable to the eye, even when armed with a microscope; and yet it means the difference between the impenetrable jungle and the inaccessible minarets of the roof of the world. The difference between some "Rafael" and some imitation may be very slight and escape the uncritical eye, and yet make out the distinction between a masterpiece and a daub. Illustrations abound. It is a multitude of trifles that constitutes perfection; but perfection is not a trifle. That the recognized and constated superiority of the European brain is slight, by no means implies that the "mental expression" of this superiority may not be illimitably grand.
Since the question of brain-weights is extremely important, it does not seem fair to the reader to furnish him only vague, general statements. Accordingly, we here submit something more definite, even though it appear like a long parenthesis inserted in the body of our discourse.
From the autopsies of 405 Whites, Blacks, and intermediates, made by Surgeon Ira Russell, the following conclusions have been drawn by Dr. Sanford B. Hunt, surgeon of United States Volunteers in the Civil War: "(1) The standard weight of the negro brain is over five ounces less than that of the white. (2) Slight intermixture of white blood diminishes the negro brain from its normal standard, but when the infusion of white blood amounts to one-half (mulatto), it determines a positive increase in the negro brain, which, in the quadroon, is only three ounces below the white standard. (3) The percentage of exceptionally small brains is largest among negroes having but a small proportion of white blood." Of these 405, there were 141 Blacks, and only twenty-four Whites; the others were mixed. We may omit these latter, and may substitute the results of 278 other autopsies of Whites, and form this table:
| Average | Max. | Min. | 60 oz. | 55-60 | 50-55 | 45-50 | 40-45 | 35-40 | 35 | |
| 141 B. | 46.96 | 56 | 35¾ | 0 | 5 | 42 | 51 | 38 | 3 | — |
| 24 W. | 52.06 | 64 | 44½ | 1 | 4 | 11 | 7 | — | — | — |
| 278 W. | 49.05 | 65 | 34 | 7 | 28 | 99 | 97 | 39 | 7 | 1 |
Here we observe: Dr. Hunt's (1) does not seem warranted; the number (24) of White brains weighed seems too small. But the weights of the 278 Whites show that the smaller weight of the Negro brain is a fact. More extensive observation shows that the Black average is about four ounces below the White. The absence of very large brains among the Blacks comes out most distinctly. There were no Black brains weighing over fifty-six ounces, only five weighing so much as fifty-five; whereas, eight White brains weighed over sixty ounces, and forty weighed over fifty-five. Likewise of the twenty-four Whites, only one fell under forty-five ounces, but forty-one of the 141 Blacks; also, only forty-seven of the 278 Whites; it is plain, then, that large brains predominate among the Whites and small ones among the Blacks.
This, however, is not nearly all the evidence on this question. In the course of an elaborate article in the Philosophical Transactions for 1868, pp. 505 sqq., Dr. J. Barnard Davis makes this remark: "As a general conclusion, without analyzing the results of Tiedemann's gaugings of negro skulls, it may be unhesitatingly asserted that the brain-weight of negroes is positively below that of Europeans" (p. 522). "The general mean of our African races, as deduced from 113 skulls, 53 of men and 60 of women, a tolerably equal proportion, is 43.89 ounces, or 1244 grams. This is 3.23 ounces, or ninety-one grams, less than our European general mean" (p. 523). He also finds the mean internal capacity of 393 European skulls to be 92.3 cubic inches, and 113 African skulls to be 86.9 cubic inches—a defect of nearly 7 per cent. Morton found the average capacity of 62 native African skulls to be 83 cubic inches, and of 12 Afro-American skulls to be 82 cubic inches.
More recently (1880), Dr. Bischoff has published at Bonn a very thorough work on "Das Hirngewicht des Menschen," in which the present subject is handled minutely and very temperately. We translate some of his remarkably sane and judicial conclusions: "From all of this it follows that we are by no means justified in affirming outright the proposition that brain-weight and spiritual capacity and achievement keep equal pace and that a large and heavy brain of itself betokens a man highly endowed in both respects, a small and light brain a man niggardly equipped. But just as little justified would be the conclusions that size and weight of brain stand in no connection with spiritual gifts and accomplishments. Rather must we be convinced that both factors, brain-weight and spiritual capacity and achievement, are magnitudes too complex for their parallelism to appear to be proved so simply, although the same (parallelism) is none the less present" (p. 142).