In order to demonstrate that the cephalic index does not determine the form of the cranium, Sergi makes use of a number of different geometric figures, such as a triangle, an ellipse, a trapezoid inscribed within equal rectangles, and which consequently have an equal base and equal altitude, that is, the same proportion between length and width.

It follows that skulls corresponding more or less closely in shape, trapezoidal, trigonocephalic, ellipsoidal, plagiocephalic, and hence both normal and abnormal, can be expressed by a cephalic index having the same identical figures.

But, although the cephalic index is far from being descriptive in regard to the form of the cranium, it constitutes an anthropological datum that has two advantages: 1. It depends upon measurements and is therefore accessible to those who, not being anthropologists, lack the trained eye that can distinguish with careful accuracy the true forms of the cranium in their manifold variety. Furthermore, since the measurement of maximum diameters is sure and easy and may be obtained with exactness, regardless of the thickness of the hair, it may be applied in anthropological research to all subjects. 2. The cephalic index, even if it does not give us the form, does give us a fact which has a bearing upon the form, namely, whether the cranium is long or short; in other words, it substantially represents the most real and evident difference between the different types of cranium. And since the cranium has a visibly spheroid form, that is, with smooth and rounding surfaces, and constantly adheres to this generic delineation, the fact of being longer or shorter introduces a definite differentiation into the general and accepted form, and gives a very simple and concise indication of it, that conveys the idea more clearly than a description would.

Granting the practicality of this line of research, the cephalic index may also be accepted as an index of form, so long as there is no intention of going deeply into minute differentiations for systematic purposes. Professor Sergi himself, author of the system that forms the basis of the study of cranial forms, urged me to exclude from a practical course in pedagogic anthropology the classification of forms, limiting the concept of form to that included in the cephalic index.

The cephalic index has the additional advantage of having been extensively studied and consequently of having an abundance of mean averages for comparison that are of great practical use. Furthermore, the idea it gives regarding the cranium by means of one simple figure serves to convey certain fundamental principles with great clearness.

In dealing with figures that determine an anthropological datum of such high importance, it is necessary to define its limits and its nomenclature.

Various authors have introduced their own personal classification of the cephalic index, and no small confusion in nomenclature has resulted; so much so that a need was felt of establishing a uniformity of numerical limits and of the relative terminology, in other words, of simplifying the scientific language.

Accordingly, a congress was held at Frankfort in 1885, at which the following nomenclature was established by international agreement: