Previous to this, the most widely varied classifications were in use, and the leading authorities had all introduced into the literature of the subject their own personal classifications. Here are some of the more important:
It remains to determine the extreme limits of oscillation of the index, both in relation to the normal mean and in relation to the fluctuations of this important ethnic datum in a given population.
Topinard, as we have seen, gives as his mean figures for the extreme normal limits among the human races 64 and 90.
Deniker gives, as his mean averages for the human races, the following figures: For dolichocephaly, 69.4 (natives of the Caroline Islands; Australia); For brachycephaly, 88.7 (the Ayssori of the Transcaucasus; Asia).[37] But we know that a mean is obtained from figures either greater or smaller than the mean itself, so that the limits of individual variation must exceed that of the given figures.
Accordingly the oscillation of the normal cephalic indices may be given as ranging from 70 to 90.
In regard to abnormalities (extreme human limits of the cephalic index) the authorities give 58 for dolichocephaly (scaphocephaly) and 100 for brachycephaly (in which case the cranium is round and known as trochocephalic; it is met with among the insane).
Between oscillations of such extremely wide range in the normal cephalic index, the number chosen as a medial figure to serve the purpose of dividing the dolichocephalics from the brachycephalics is that of 80, which is included within the division of brachycephaly. In spite of the nomenclature established at Frankfort, there is a distinct scholastic advantage, because of the greater simplicity of memorising and fixing the idea, in reverting to the nomenclature of Retzius, who classes as brachycephalics all crania from 80 upward, and as dolichocephalics all those below 80. It is certainly strange to class all crania from 80 to 90 without distinction as brachycephalics, and then to alter the name and call a cranium with an index of 79.9 a dolichocephalic. It has been found that there is always a slight difference between the index taken from measurements of the cranium and that obtained from measurements of the head. According to Broca, it is necessary to subtract two units from the cephalic index taken from a living person, in order to obtain that of the cranium; thus, for example, if the cephalic index (taken from life) is 80, the cranial index (taken from the skeleton) would be 78. Such differences are due to the disposition of the soft tissues. Consequently, even according to the simple subdivision of Retzius, a person who was brachycephalic during life, would become dolichocephalic after he was dead.
But this is what always happens in biology, whenever we try to establish definite limits. Life undergoes an insensible transition through successive limits and forms, and this fact constitutes the grave difficulties and the apparent confusion of biological systems. In determining degrees of difference, it is necessary to have recourse constantly to special methods, which teach us to recognise general properties and to use them as a basis in dividing living creatures into separate groups (see in the section on Method, "Mean measurements and formation of series in relation to individual variations").
Hence, for mnemonic purposes, we need remember only the single number, 80.