Fig. 405. Co-ordinates of chimpanzee’s skull, as a projection of the Cartesian co-ordinates of Fig. [404].
Let us now inscribe in our Cartesian co-ordinates the outline of a human skull (Fig. [404]), for the purpose of comparing it with the skulls of some of the higher apes. We know beforehand that the main differences between the human and the simian types depend upon the enlargement or expansion of the brain and braincase in man, and the relative diminution or enfeeblement of his jaws. Together with these changes, the “facial angle” increases from an oblique angle to nearly a right angle in man, {771} and the configuration of every constituent bone of the face and skull undergoes an alteration. We do not know to begin with, and we are not shewn by the ordinary methods of comparison, how far these various changes form part of one harmonious and congruent transformation, or whether we are to look, for instance, upon the changes undergone by the frontal, the occipital, the maxillary, and the mandibular regions as a congeries of separate modifications or independent variants. But as soon as we have marked out a number of points in the gorilla’s or chimpanzee’s skull, corresponding with those which our co-ordinate network intersected in the human skull, we find that these corresponding points may be at once linked up by smoothly curved lines of intersection, which form a new system of co-ordinates and constitute a simple “projection” of our human skull. The network
| Fig. 406. Skull of chimpanzee. | Fig. 407. Skull of baboon. |
represented in Fig. [405] constitutes such a projection of the human skull on what we may call, figuratively speaking, the “plane” of the chimpanzee; and the full diagram in Fig. [406] demonstrates the correspondence. In Fig. [407] I have shewn the similar deformation in the case of a baboon, and it is obvious that the transformation is of precisely the same order, and differs only in an increased intensity or degree of deformation.
In both dimensions, as we pass from above downwards and from behind forwards, the corresponding areas of the network are seen to increase in a gradual and approximately logarithmic order in the lower as compared with the higher type of skull; and, in short, it becomes at once manifest that the modifications of jaws, braincase, and the regions between are all portions of one continuous and integral process. It is of course easy to draw the {772} inverse diagrams, by which the Cartesian co-ordinates of the ape are transformed into curvilinear and non-equidistant co-ordinates in man.
From this comparison of the gorilla’s or chimpanzee’s with the human skull we realise that an inherent weakness underlies the anthropologist’s method of comparing skulls by reference to a small number of axes. The most important of these are the “facial” and “basicranial” axes, which include between them the “facial angle.” But it is, in the first place, evident that these axes are merely the principal axes of a system of co-ordinates, and that their restricted and isolated use neglects all that can be learned from the filling in of the rest of the co-ordinate network. And, in the second place, the “facial axis,” for instance, as ordinarily used in the anthropological comparison of one human skull with another, or of the human skull with the gorilla’s, is in all cases treated as a straight line; but our investigation has shewn that rectilinear axes only meet the case in the simplest and most closely related transformations; and that, for instance, in the anthropoid skull no rectilinear axis is homologous with a rectilinear axis in a man’s skull, but what is a straight line in the one has become a certain definite curve in the other.
Mr Heilmann tells me that he has tried, but without success, to obtain a transitional series between the human skull and some prehuman, anthropoid type, which series (as in the case of the Equidae) should be found to contain other known types in direct linear sequence. It appears impossible, however, to obtain such a series, or to pass by successive and continuous gradations through such forms as Mesopithecus, Pithecanthropus, Homo neanderthalensis, and the lower or higher races of modern man. The failure is not the fault of our method. It merely indicates that no one straight line of descent, or of consecutive transformation, exists; but on the contrary, that among human and anthropoid types, recent and extinct, we have to do with a complex problem of divergent, rather than of continuous, variation. And in like manner, easy as it is to correlate the baboon’s and chimpanzee’s skulls severally with that of man, and easy as it is to see that the chimpanzee’s skull is much nearer to the human type than is the baboon’s, it is also not difficult to perceive that the series is not, {773} strictly speaking, continuous, and that neither of our two apes lies precisely on the same direct line or sequence of deformation by which we may hypothetically connect the other with man.
As a final illustration I have drawn the outline of a dog’s skull (Fig. [408]), and inscribed it in a network comparable with the Cartesian network of the human skull in Fig. [404]. Here we attempt to bridge over a wider gulf than we have crossed in any of our former comparisons. But, nevertheless, it is obvious that our method still holds good, in spite of the fact that there are various specific differences, such as the open or closed orbit, etc., which have to be separately described and accounted for. We see that the chief essential differences in plan between the dog’s skull and the man’s lie in the fact that, relatively speaking, the