The Cephalic Index
Retzius was the first to take the cranium under consideration as a basis for a classification of the human races; and he attempted to determine a concept of its form by means of a numerical formula expressing the relation between the length and width of the cranium (cephalic index). Thus he distinguished the races into brachycephalics, or those having a short head; and dolichocephalics, or those having a long head. Following Retzius, who may be regarded as the founder of craniology, Broca adopted, completed and expanded this method, deriving from the cranium, or rather from the particular character given by the cephalic index, a key, as it were, suited to unlocking the intricate mysteries of hybridism among the human races. Consequently the cephalic index was not confined, as regards its importance, within the same limits as all the other indexes, but was raised by the French school, warmly seconded by Italian anthropologists, to the dignity of a fundamental determinant of the ethnic type, as definitely as, for example, the vertebral column serves as basis for a classification including all species of vertebrates.
The Germans refused to accept the cephalic index as determining the classification of races; but while seeking to prove themselves independent of it, they continued to regard the form of the cranium as a basis of classification (Rütimeyer, von Höller, and to-day Virchow), but without ever having identified, as Sergi has now done, existing forms as normal types of race.
The cephalic index is obtained by the well-known formula expressing the relation between the maximum transverse diameter of the skull (see "Technique") and the maximum longitudinal diameter reduced to 100, and is expressed as follows: Ci = 100×d/D (the cephalic index is equal to a hundred times the lesser diameter divided by the greater; in the present case the lesser diameter is the transverse).
This proportion between linear measurements cannot properly sum up the form of the cranium. We can, for example, conceive of a microcephalic cranium having a normal cephalic index, since the relation between the two maximum diameters necessary for deducing the index, does not tell us, for example, either the dimension of the cranium or the form of the forehead.
If, for instance, we should imagine a photograph of a cranium enlarged a hundred diameters, the reciprocal relations between the length and the width would still remain unchanged.
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:
- CEPHALIC INDEX.—Nomenclature established at Frankfort
- Dolichocephalia = 75 and below
- Mesaticephalia = from 75.1 to 79.9
- Brachycephalia = from 80 to 85
- Hyperbrachycephalia = 85.1 and above.
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.
But if we wish to adopt the nomenclature of Frankfort, it is necessary to keep in mind two figures denoting limits, 75 (inclusive) for dolichocephaly, and 80 (inclusive) for brachycephaly.
| 75 | dolichocephalics | |
| mesaticephalics | ||
| 80 | brachycephalics | |
| 85 | ultra |
These constitute, as it were, two centres, beyond which, on this side and on that, we may picture to ourselves the individual variations drawn up in martial line. In this case, the space between 75 and 80, in other words, the limits of mesaticephaly, may be interpreted as due to oscillations between dolicho- and brachycephaly according to the laws of variability, which is analogous to what takes place in the case of oscillations in the opposite direction (70-75 dolichocephaly; 80-85 brachycephaly). From this point of view, these two numbers, 75 and 80, constitute median centres of two different types.
But according to Broca and his school—and this view is accepted by many anthropologists—mesaticephaly should be regarded as constituting a fusion of the two other types, the brachy- and dolichocephalic, whence it follows that mesaticephalics would be hybrids. Other authorities, on the contrary, exaggerating the conception of the fixity of the cephalic index in a given race, admit the existence of mesaticephalic races.
Fig. 73. Map of the Cephalic Index in Italy.
But it has been observed that the greater number of mesaticephalics are to be found in regions where dolichocephaly prevails; in certain districts of Africa, as for example, in Somaliland, not a single brachycephalic exists, yet none the less the mesaticephalics are numerous. Accordingly, mesaticephaly may be classed with dolichocephaly and regarded as one of its variations, while it seems to be independent of brachycephaly. Therefore the nomenclature of Retzius may for many good reasons be chosen and adopted in our schools. In conclusion, we shall regard the brachycephalics and dolichocephalics as the two fundamental types; and shall adopt the figure 80, included among the brachycephalics, as the limit of separation. The different grades of dolicho- or brachycephaly are to be determined by mean averages, and the oscillations due to individual variations, by series.
Hence it is important to determine the mean average and the oscillation of the cephalic index for the different races; and this is of interest to us as educators, in order to establish the limits of normality.
The practical method of studying the cephalic index is according to geographical distribution.
Here are a few general data of the cephalic index relative to its distribution:
The most dolichocephalic of all peoples are found in Melanesia, Australia, India and Africa. In the Fiji Islands the mean cephalic index is 67; in the Caroline Archipelago it is 69; in various regions of India, 71; that of the Hottentots, 74; of the Bantus, 73. Belonging to the dolichocephalics or mesaticephalics are the populations of the extreme south of Europe (Mediterranean race) and at the extreme north (English, Scotch). On the contrary, the races of western Europe and of central Asia are brachycephalic (Celts, Mongols). The most brachycephalic of all these peoples are met with in the Transcaucasus; their mean average is 88.7. There also exists a notable brachycephalic type in France (Savoyards, 86.9; inhabitants of the upper Loire, 87.4); also in Dalmatia, 80, while the Lapps of Scandinavia are also ultrabrachycephalic, 87.4.
On very general lines, it may be said that the dolichocephalics are the Eurafrican races (including the Mediterranean race, with which the first civilisations are associated: Egyptian, Greek and Roman) who migrated from the Mediterranean basin into Europe; and the brachycephalics are the Eurasian races, who on the contrary migrated from continental Asia across western Europe (the Aryans).
As far as regards Italy, its population is by no means evenly constituted. The median index given by Livi for Italy, deduced from observation of more than 29,000 subjects is 80; in regard to regional distribution, the results are shown in the following table:
| Piedmont | 85.9 |
| Emilia | 85.2 |
| Venctia | 85.0 |
| Lombardy | 84.4 |
| Umbria | 84.1 |
| Marches | 84.0 |
| Liguria | 82.3 |
| Tuscany | 82.3 |
| Campania | 82.1 |
| Abruzzo and Molise | 81.9 |
| Latium | 81.0 |
| Basilicata | 80.8 |
| Apulia | 79.8 |
| Sicily | 79.6 |
| Calabria | 78.4 |
| Sardinia | 77.5 |
Let us remember that if the cephalic index were measured directly from the cranium, the result would be one or two units less, hence the mean average of the cranial index would be about 78.
The accompanying map represents still more clearly the geographical distribution. The results show that in Piedmont, in Emilia, and in Northern Italy in general the inhabitants are more brachycephalic; while in the south and more especially in the island possessions we find the more dolichocephalic part of the population. The highest degree of dolichocephaly is found in Sardinia.
But if, instead of the cartographic summary herewith reproduced, we could examine the exhaustive one with which Livi has illustrated his great work on Anthropometry, we should discover that the distribution does not follow the great regional lines; but that as a matter of fact certain human groups exist, isolated like little islands, which have a cephalic index in marked contrast to that of the remaining population of the same region.
Thus, for example, at Lucca, in the midst of a brachycephalic population, there is a pronouncedly dolichocephalic group; and in the midst of the dolichocephalic population of Abruzzo and the neighbouring provinces, there exists at Chieti a strongly brachycephalic group. Besides these and similar groups contrasting with the regional type, there exist a multiplicity of differences, from one successive boundary line to another, so that the limits of the cephalic index may be determined with great minuteness in the various regions.
Livi's large charts lend themselves with great clearness to this sort of analytical study, which would be found to be very profitable to teachers.
It is also quite instructive to compare the different charts representing various anthropological data of ethnical importance; such, for example, as that of the distribution of stature and that of the distribution of pigmentation. These data are regarded by anthropologists as attributes of race. Well, in these three charts it is evident at the first glance that there is a notable resemblance in distribution, so much so than an eye untrained to observation would be likely to confuse them. The cephalic index, the stature, the colour of the skin are consequently of almost uniform distribution. Corresponding to the most pronounced brachycephaly, we have the tallest stature and the fairest complexion; corresponding to the most pronounced dolichocephaly, we find instead the lowest stature and the most brunette types. Such an accumulative coincidence, in certain communities, of characteristics, in contrast to those that are found combined in certain other communities, reveal the existence in Italy of two different races. One of these races seems to have descended from over the Alps; the other, to have landed on the shores of the Mediterranean. The first belong to the Eurasians; the second to the Eurafricans.
In my work upon the population of Latium, the mean cephalic index obtained by me is 78. The distribution according to the localities studied affords the mean averages noted in the following table, in which I have also recorded the maximums and minimums, and the percentage of brachycephalic and dolichocephalic individuals who contributed to the given means:
CEPHALIC INDEX AMONG THE PEOPLE OF LATIUM
(According To Montessori)
| Provinces | Mean cephalic index | Minimum | Maximum | Dolichocephalics, per cent. | Brachycephalics, per cent. |
|---|---|---|---|---|---|
| Rome | 78 | 73 | 89 | 63 | 37 |
| Castelli Romani | 76 | 70 | 79 | 100 | — |
| Tivoli | 80 | 76 | 87 | 59 | 41 |
| Velletri | 79.5 | 75 | 86 | 50 | 50 |
| Frosinone | 80.7 | 75 | 87 | 43 | 57 |
| Civitavecchia | 78.5 | 78 | 80 | 65 | 35 |
| Bracciano | 77 | 75 | 80 | 65 | 35 |
| Orte | 83.6 | 75 | 90 | 11 | 89 |
| Acquapendente | 79.4 | 76 | 81 | 60 | 40 |
The results show a preponderance of brachycephalics or of dolichocephalics in the places where the mean cephalic index is respectively highest for brachycephaly (Orte) or for dolichocephaly (Castelli Romani). Furthermore, the extreme maximum and minimum figures are found to be included in these groups (90 at Orte and 70 at Castelli).
It should be noted that at Castelli Romani the mean average is mesaticephalic (76), notwithstanding the absence of brachycephalics; this average is based on figures showing an extremely pronounced dolichocephaly (ranging to 70!). The groups at Castelli and at Orte also showed characteristics in respect to stature (see page ([111])); at Orte the mean stature is 1.61 m., with a maximum of 1.70 m. (very tall statures for women), and at Castelli the mean stature is 1.47 m., with a minimum of 1.42 m. (low statures).
Similarly, in regard to pigmentation, I found at Orte a prevalence of blonds, and at Castelli of brunettes. Hence the conclusion may be drawn that at Castelli and at Orte there exist groups of human beings who are of almost pure race, in the midst of a population in which racial types have become attenuated or hidden; but in centres like these we still find persistent testimony as to the ethnic factors that combined to form the people of Latium: the one, a blond, tall, brachycephalic race; the other, dark, small, and dolichocephalic.
The Cephalic Index at Different Ages of Life.—Another quality that renders the cephalic index of great importance is that it remains constant in the course of growth, since the two maximum diameters, the antero-posterior and the transverse, increase at very nearly the same rate, excepting during the earliest years, at which time the length of the cranium increases slightly more than the width. According to some authorities it is in the second year, according to others it is in the fourth or seventh, that the cephalic index becomes constant (Binet, Deniker, Pearson, Fawcette, Ammon, Johannson, and Westermarck).
The following table is one that I have drawn up on the basis of Quétélet's figures:
CEPHALIC INDEX
| Age | Males | Females | Age | Males | Females |
|---|---|---|---|---|---|
| At birth | 83 | 83 | 11 years | 80 | 79 |
| 1 year | 80 | 80 | 12 years | 80 | 79 |
| 2 years | 80 | 80 | 13 years | 80 | 79 |
| 3 years | 80 | 80 | 14 years | 80 | 79 |
| 4 years | 79 | 79 | 15 years | 80 | 79 |
| 5 years | 79 | 79 | 16 years | 80 | 79 |
| 6 years | 79 | 79 | 17 years | 80 | 79 |
| 7 years | 79 | 79 | 18 years | 80 | 79 |
| 8 years | 79 | 79 | 19 years | 80 | 79 |
| 9 years | 80 | 79 | 20 years | 80 | 79 |
| 10 years | 80 | 79 | —- | — | — |
Since it has been observed that the cranium in the course of its growth may assume forms, amounting even to apparent malformations (due chiefly to "bumps," either symmetrical or asymmetrical), which disappear during the evolution of the individual, the cephalic index, for the very reason that it does not represent a faithful description of the form, gives us precious aid in judging the cranium of the child, because it accurately determines the proportions between length and breadth which are destined to persist even in the adult, and hence serve to give, even in infancy, a sure indication of the ethnic type to which the child belongs.
Per cent.
- Negro Children
- Children born in Syria
- Children born in Russia
- Children born in Germany
- Children born in Ireland
- White Children born in America
- Children born in Italy
Fig. 74.
We owe to Dr. Ales Hrdlicka the extremely important graphic chart, which I will proceed to summarise, of the cephalic indices of children of various races: the central dotted line corresponds to the index 80: consequently the brachycephalics are indicated on the right, and the dolichocephalics on the left (Fig. 74).
In the case of Italy, the graphic line extends between the two extreme figures of 70 and 90, which are precisely the extreme limits that we have already noted for individual adults, in the case of the women of Latium: moreover, the curve is perceptibly symmetrical, although the brachycephalics are in the majority; a fact already established by Livi's mean averages. One might say that this curve was a graphic representation of Livi's two-colour method in his map of the cephalic index: one-half of Italy is brachycephalic and the other half is dolichocephalic; but since brachycephaly prevails in the northern half, a wider extent of territory is occupied by brachycephalics.
In America, where emigration brings every variety of humanity, the curve is even more symmetrical, and rests on a broader basis, representing widely separated extremes. Ireland also shows a very perceptible symmetry, the population being a mixture of Celts (brachycephalics) and of Scotch (northern blond dolichocephalics).
In Germany there is a prevalence of brachycephalics; we are here approaching the eastern regions from which the Eurasian race came through emigration. Here the Slavs and Celts (brachycephalics who immigrated into Europe at various epochs) are intermingled with a notable percentage of dolichocephalics (Teutons).
But in Russia, a region still further east, and similarly in Syria, we find an almost pure race: the curves lie wholly within the field of brachycephaly.
On the contrary, the dark-skinned children given in the last chart, and belonging to African races and tribes of American Indians, are all of them dolichocephalic.
According to Binet and other writers, the cephalic index and the cranial volume are the two anthropological data on which the criterion of normality of children's heads must be based.
When we observe a child's head which is apparently malformed, we cannot call it abnormal; it is not abnormal unless it has a volume notably too small (submicrocephaly, microcephaly) or too large (rickets, hydrocephaly); and a cephalic index exceeding the normal limits, in other words, exaggerated (scaphocephaly, trochocephaly, pathological brachycephaly occurring in hydrocephalics).