Cuvier endeavoured to find the relation of the skull and the face by making an antero-posterior section of the skull, and directly measuring the surfaces of the section. He found that in the White the face represented about 0·25 of the skull, 0·30 in the Yellow, and 0·40 in the Black. These results entirely accord with those furnished by the study of prognathism.
This relative difference of the development of the face led Camper to the conception of his celebrated facial angle. Struck by seeing painters represent Negroes as Whites painted black, he studied the anatomical characters of the skull, and gave, as the proper distinction, the angle formed by two lines; the one passing from the auditory canal to the root of the nose, the other tangential to the forehead and to the nasal bone, both being represented upon a vertical projection of the model. Camper made use of his method to distinguish between the products of Greek and Roman art. He thus represented a decreasing scale from the works of art in statuary to non-adult apes. I reproduce it, not because of its real value, but on account of the importance which has been attributed to it. The following are the variations of the facial angle, according to Camper:
| Greek statues | 100° | Yellow race | 75° |
| Roman statues | 95° | Black race | 70° |
| White race | 80° | Young apes (superior type) | 65° |
Geoffroy Saint-Hilaire and Cuvier, M. Jules Cloquet and Jacquard have adopted different methods in determining the facial angle. Morton, Jacquard, and M. Broca have invented instruments for measuring it directly. M. Topinard, after having examined the several methods, gives, with justice, his opinion in favour of that of Cloquet, which places the upper extremity of the angle at the alveolar border. M. Jacquard had chosen the nasal spine, remarking at the same time that the difference between the two angles might be of service in the calculation of prognathism.
Camper, or rather those who have followed him, wished to consider the size of the facial angle as a sign of superior intellectual power. His graduated scale has evidently given rise to this false idea. Pathological facts should have sufficed to show how great was the error. The work of Jacquard has, moreover, established this fact beyond a doubt. This author has proved a difference of more than 16° in the educated White of Paris, that is to say, 6° more than the distance established by Camper as separating the Negro from the White. Jacquard, again, has proved in the French race the existence of an angle of 90°, an angle which Camper believed to belong only to the ideal representations of the human form. Now this remarkable angular superiority was by no means accompanied by an exceptional intelligence.
If we pass from the psychological to the anatomical meaning I shall have similar remarks to make. There has been much discussion as to the position of the upper extremity of the facial line, which, with the horizontal line, forms the angle of Camper. It has been thought desirable to avoid the frontal sinuses, and to seek in the facial angle indications relative to the dimensions of the encephalon, and not those of any particular bone. I think, on the contrary, that we must be content with the latter, and not go further. It is evident that the dimensions of the encephalon are independent of the position of the frontal point, and that it may be more or less extended to the right, left, or behind this point without the facial angle being affected in any manner whatever.
The exact determination of the means of the facial angle will still, however, be valuable, like all those which it is possible to calculate upon the human body, provided there is a sufficient distance between these means. But M. Topinard has shown that this difference is not more than three degrees. Without altogether renouncing the ideas of Camper, we see that science now has characters preferable to those which he discovered.
A more important angle is the anterior parietal angle, formed on both sides of the skull by two lines tangential to the most prominent point of the zygomatic arch, and to the fronto-parietal suture. By taking the most prominent point of the parietal eminences as the second extremity, we obtain the posterior parietal angle. Prichard applied the term pyramidal skulls to those in which these lines converged. I have endeavoured to measure the angle directly with an instrument of my own invention, and my first researches have led me to results which I believe to be interesting. The angle is sometimes wide, sometimes narrow, and may be altogether wanting when the two tangents are parallel. It is, then, sometimes positive, sometimes negative. The latter is the case in the fœtus and infants of all races. The negative angle is also met with in adults. This trait appears to have been very striking in Cuvier, judging from a fine portrait of the great naturalist when still young. I have found it to be -18° and -22° in two living persons, both remarkable for their intelligence. The positive maximum which I observed upon an Esquimaux cranium was +14°. I have employed this character in my course of lectures to complete the characterization of a great number of races, but have never published any details.
M. Topinard has just filled this gap in a work which confirms, and at the same time, completes all my first results. His researches, bearing solely upon skulls, have given him as limits of individual variations, 5° and +30°; as limits of the means, +2°·5 and +20°·3. He found in the New Caledonians the most pyramidal heads. Finally, he has seen in children from the age of four months to sixteen years, the angle decreasing from -24° to 0° and rise to 7°.