quadrate bone is strongly inclined downwards and forwards. The whole skull has a configuration which stands, apparently, in the strongest possible contrast to that of a more normal Ornithosaurian such as Dimorphodon. But if we inscribe the latter in Cartesian coordinates (Fig. [387], a), and refer our Pteranodon to a system of oblique co-ordinates (b), in which the two co-ordinate systems of parallel lines become each a pencil of diverging rays, we make manifest a cor­re­spon­dence which extends uniformly throughout all parts of these very different-looking skulls.

We have dealt so far, and for the most part we shall continue to deal, with our co-ordinate method as a means of comparing one known structure with another. But it is obvious, as I have said, {757} that it may also be employed for drawing hypothetical structures, on the assumption that they have varied from a known form in some definite way. And this process may be especially useful, and will be most obviously legitimate, when we apply it to the particular case of representing intermediate stages between two forms which are actually known to exist, in other words, of reconstructing the transitional stages through which the course

Fig. 388. Pelvis of Archaeopteryx.

Fig. 389. Pelvis of Apatornis.

of evolution must have successively travelled if it has brought about the change from some ancestral type to its presumed descendant. Some little time ago I sent to my friend, Mr Gerhard Heilmann of Copenhagen, a few of my own rough co-ordinate diagrams, including some in which the pelves of certain ancient and primitive birds were compared one with another. Mr Heilmann, who is both a skilled draughtsman and an able morphologist, returned me a set of diagrams which are a vast improvement on my own, {758} and which are reproduced in Figs. [388]–393. Here we have, as extreme cases, the pelvis of Archaeopteryx, the most ancient of known birds, and that of Apatornis, one of the fossil “toothed”

Fig. 390. The co-ordinate systems of Figs. [388] and 389, with three intermediate systems interpolated.