Fig. 157.—The shaded portion represents the eccentricity of the curve, due to the presence of cretins.
Whenever a binomial curve constructed from a large number of individuals is found to be eccentric; and shows, e.g., in the case of stature, a deviation toward the low statures, it reveals (see De Helguero's curves) the presence of a heterogeneous intermixture of subjects, for example, of children among adults, or, as in the case demonstrated by De Helguero, an intermixture of pathological individuals with normal persons (Fig. 157).
The binomial curve obtained by De Helguero from the inhabitants of Piedmont included, as a matter of fact, a great number of cretins; they formed within the great normal mass of men, a little mass of individuals having a stature notably inferior to the normal.
By correcting the eccentric curve on the left of the accompanying figure, and by tracing a dotted line equal and symmetrical to the right side, we obtain a normal binomial curve; well, this curve will actually be reproduced if we subtract all the cretins from the whole mass of individuals.
The section distinguished by parallel lines represents that portion of the curve which departs from the normal toward the low statures, and is due to the cretins; it may be transformed into a small dotted binomial curve at the base, which is constructed from the statures of the cretins alone.
Accordingly, the symmetrical binomial curve gives us a mean average value in relation to a specified measurement.
What has been said regarding stature serves as an example; but it may be repeated for all the anthropometric measurements, as Viola has proved by actual experiment.
The sitting stature, the thoracic perimeter, the dimensions of an entire limb or of each and every segment of it; every particular which it has seemed worth while to take into consideration, comports itself in the same manner; and this is also true of all the measurements of the head and face.
That is to say, if we make a seriation of measurements relating to the sitting stature of an indeterminate number of individuals, we find a numerical prevalence of those corresponding to the medial measurement marked upon the axis of the abscissæ; and the number of individuals will continue to decrease with perceptible symmetry on each side of the centre, i.e., toward the higher and lower statures. If we take into consideration the significance of the sitting stature, this binomial curve relates to individuals who possess a normal physiological mass (the bust; centre of density) and to individuals who fall below or exceed that mass. We have already, in speaking of the types of stature, taken the bust under consideration in relation to the limbs, in order to judge the more or less favourable reciprocal development; but here we obtain an absolute datum of normality, independent of proportional relations to the body as a whole; in other words, there exists a physiological mass for the human body which is normal in itself. The individuals whose sitting stature corresponds to the medial measure of the binomial curve, are precisely those who have the normal development of bust.
The same thing repeats itself in the case of the thoracic perimeter, or the weight, or the length of the leg, or the cranial circumference, etc.