The application of this formula would necessitate some rather complicated calculations, which it would be inconvenient to have to repeat for a large number of subjects.
But there are tables of calculations already compiled, which are due to Livi, and which are given, together with other tables, in Livi's own work, Anthropometry (Hoepli). These are numerical tables, to be read in the same manner as tables of logarithms. At the top, in a horizontal direction, the stature is given in centimetres, while in the vertical column the weight is given in kilograms. The calculation of all the ponderal indices has been worked out, in relation to every possible stature and weight. If we look up the ponderal index corresponding to the figures already cited in illustration (see p. ([182])), we find that for the adult the Pi = 23.6, and for the child the Pi = 27.4; i.e., considered relatively the child weighs more in the given case. This is the true and accurate technical method of finding the relative proportion between weight and stature.
Accordingly, we have now learned to take all the measurements relative to the form, to calculate from them the more important indices (or proportions), such as the index of stature, the index of life, and the ponderal index. We have also learned to understand and to consult the tables of anthropological calculations.
The Cranium
The Head and Cranium.—Let us bear in mind the fact that the word head is used in speaking of a living person, and cranium, of a skeleton.
The science which makes a study of the cranium is called craniology. The cranium and the head may be studied either by observing the external form—cranioscopy or cephaloscopy; or else by taking measurements—craniometry or cephalometry. Craniology makes use equally of cranioscopy and of craniometry: in fact, if cranioscopy alone were used, certain anomalies might escape attention, because we can recognise them only by measuring the head; and conversely, if we confined ourselves to craniometric researches, we might miss certain anomalies of form, which we become aware of only by attentively observing the cranium. Frequently craniometry serves to verify cranioscopy. For example, a cranium may appear to the eye too large or too small, but certainly if we measure the cranial circumference with a tape-measure we shall have an accurate decision of a case which may well be a simple optical illusion. Indeed, we all know how easy it is to give an erroneous judgment, relying only on our senses; for the personal equation enters very largely into judgments of this sort. For instance, a person of low stature easily judges that other men are tall, and vice versa. To the eye of the Italian or the Frenchman, the hair of young English girls is a pale blond; to the Scandinavians of the North it is a warm blond. If two men possessed of different æsthetic tastes and in different frames of mind wish to describe one and the same garden they will give two widely different descriptions which will reveal far more of their individual impressions and moods than of the actual characteristics of the garden described. It is easy to understand how important it is in scientific descriptions to exclude completely the influence of the observer's personality. In the cranioscopic study of a cranium, for instance, the precise characteristics of that cranium are what must be found and nothing else whatever, no matter who the student is nor in what part of the world he is working. But in order to achieve this result it is not enough to take observations; it is also necessary to know how to observe, and in observing to follow a scientific method.
Cranioscopy.—Cranioscopic methods require that the skull shall be observed from several sides. Blumenbach, who studied crania by observing them from the vertex, divided them into ovoid, rhomboid, etc., while Camper, on the other hand, studying them in profile, classified them as flat, elongated, etc., and the conclusions of the two scientists were irreconcilable.
Fig. 146.—Facial norm.