Anthropometry

ANTHROPOMETRY. Anthropological science aims at the establishment of man's position in nature, the discovery of the extent of human variation, the ordination of the fundamental facts concerning the growth of the individual, and the bearing on human evolution of the evidence drawn from comparisons of the existing human types with one another, or of each in turn with their pre historic precursors. Such enterprises entail both the collection and the apportionment of evidence. And when comparisons have to be made, the advantages of numerical modes of expression over those which are purely descriptive are manifest.

The measuring rod and the balance, instruments of precision, exemplify the means of collecting quantitative data, the founda tions of much of the superstructure of modern science. But in the domain of biology the very texture of living matter seems opposed to exact measurement. To this obstacle there must be added that which is set up by the unceasing metabolic mutability of protoplasm. Some there are who plead for the freedom of biological research from adverse criticism should rigid numerical methods be discarded in its prosecution. Anthropometry con stitutes one of the testing-grounds of those methods.

The history of anthropometry is retraceable far backwards in time. From the very dawn of graphic representation in the historic period, it has claimed the notice of artists. These, though they may not have collected data with scientific precision, or on a def initely systematic basis, can claim credit for attempts to interpret the various details they observed. But the scientific treatment of data representative of measurements based on a predetermined scheme, and collected systematically and consistently, is a matter of comparatively recent development. Anthropometry is still far from maturity. The measurements, the instruments of research, the methods of interpretation, all alike are subject to periodical revision, with a view to the correction of errors.

The numerical data of anthropometry are evidently susceptible to investigation statistically, although their range of distribution (in other words, their diversity) is notoriously great, as may be remarked in the variations of stature and weight among the in dividual members of an adult population.

Quetelet.

But the whole subject of anthropometrical research is influenced, if not actually governed, by the consideration that in spite of apparent irregularity the variations exhibit a distribu tion conforming to a rule termed the Law of Frequency of Error. This law "was excogitated for the use of astronomers and others who are concerned with extreme accuracy of measurement, and without the slightest idea, until the time of Quetelet (1833), that it might be applicable to human measures." The achievement has proved to include not merely anthropometric records but bio logical data of many kinds. Quetelet himself stated : "Should the type be absent, and should men differ not by reason of accidental causes but because there were no laws really applicable to them, one could measure them, as, for instance, in respect of stature, but without finding that the various individual measurements presented any particular characteristic, or any definite numerical relations.

"If,

on the contrary, all human beings have been cast in the same mould, whence they have emerged with purely accidental differences, then the groups will not be formed as above in dis orderly fashion, but their numerical values obeying the theory of probabilities will be subject to p:e-established laws so completely that the numbers representative of the several groups could be predicted in advance. For this particular instance, then, there exists a characteristic feature by means of which one realizes that the individuals are referable to the same type, and that their differences are assignable to fortuitous causes only.

"Another consequence of this theory is that the larger the number of observations the more completely do the effects of the fortuitous causes cancel each other, thus permitting of the pre dominance of the general type which they tended to mask previ ously. Thus in the human species, and having regard to individuals only, all varieties of stature are met with, at least within certain limits. Those nearest the average figure are the most numerous; those which are furthest removed from the average are the least frequent : and the several groups succeed each other in numerical sequence according to a law capable of formulation in advance. (In data found to be ordinated nearly in accord with this law, the aggregation near the median is so great that a comparatively small number of individuals will provide a sample serving to give reliable information. Beyond this number, increase in the total number does not give much greater reliability to the result.) "Now this law holds good for mankind, not merely in regard to stature in its entirety, but in respect of its several compo nents : the same applies to records of weight, to those of physical strength, and, in short, to any character that is measurable and reducible to numerical expression. . . .

"This discovery of the applicability of the law of accidental causes to human phenomena, no matter from what point of view humanity is regarded, is now a fact firmly established in science. I consider its correctness proved by the large number of instances available. . . ." Quetelet illustrated regularity in gradation by reference to the distribution of stature in adult males, selecting for this purpose data provided by no fewer than io,000 individuals. When these are ordinated according to the gradual increase of their stature, the arrangement is found to be capable of graphic representation by a curve. The curve assigned by Quetelet (and shown on p. 17 of his memoir) corresponds to that known as the curve of frequency of error (an alternative name is "normal probability curve"). It is symmetrical and unlimited in either direction.

As to the course of growth in stature from infancy to maturity Quetelet states that from the age of five years to about 15 years, the annual increments of growth are regular. This conclusion seems generally to have been accepted, and even now the sequence of records taken at intervals of a year does not serve to modify it. But the true progress of growth to maturity is not revealed un less the records are repeated more frequently. The lapse of so long as 1 2 months actually masks the important alternatives of periods of greater activity with others of relative relaxation. Quetelet himself was aware of variability in the rate of growth, and he agrees that in the development of a particular individual there present themselves almost invariably periods of arrest as well as those in which growth is more or less rapid. But Quetelet deprecated laying stress upon such varying rates of progress, and herein he failed to realize the full meaning of his data. The real significance of these alternations is that the regularity with which they succeed each other constitutes a characteristic feature of growth-changes. The realization of this detail will probably prove to have a very practical economic application.

Galton's Work.

The work of Francis Galton extends and expands that of his precursor. Galton was interested from the first in the problems of heredity. Both researchers soon realized the need for collecting reliable and suitable data on a large scale, and both turned their attention to the phenomena of human growth from infancy to maturity, and, discontented with physical measurements only, both brought physiological and intellectual manifestations within the domain of measurement.

Galton's outlook on the variability exhibited by the individuals of a human society is well expressed in his Herbert Spencer lec ture where he likens such variability to Proteus in the old fable, in that it can be "seized, securely bound and utilized." As com ment on the accuracy of the application of the law of frequency to the particular example of human stature he observed that "the statistical variations of stature are extremely regular, so much so that their general conformity with the results of calculations based on the abstract law of frequency of error is an accepted fact by anthropologists." (British Association for the Advancement of Science. Report 1885. Presidential Address Section H. p. 1209.) Nevertheless not all human measurements give such close approxi mation to theory as those of stature do. The theory seemed, in fact, to be limited in its range, and Galton propounded a means of bringing some of the aberrant instances within the scope of the latter. He subjected all parts of his data and methods to a keen scrutiny. His most important and more particularly personal contributions can be summed up in the words "regression" and "correlation." Regression is a feature of populations and has reference to the fact that, on the whole, the (adult) offspring must be more mediocre than their parents. Galton illustrated re gression by reference to the stature of the (adult) offspring com pared with that of the parents, and succeeded in measuring the amount of regression. At first he was concerned to compare the stature of a generation of parents with that of the succeeding offspring. Subsequently he extended the scope of the investiga tion, and published the results of studies in which the offspring were compared (inter se).

Galton discovered that the amount of regression was remark ably constant in certain instances. Taking stature as the test and comparing the "mid-filial" deviation from the average with the "mid-parental" deviation, he found that the former was on the average two-thirds of the latter. And two-thirds consequently represents the ratio of "filial regression." Three important points emerge here. In the first place, the ratio, measuring the deviation of offspring as compared with that of parent, might be used as a test of evolution, or at least of progress. For if it were repeated in successive generations, and found to vary, the inference of progress would be quite reason able.

In the second place, this discovery marks a stage in the con struction of a theory of ancestral contributions in heredity, and the evidence of the stature was considered to indicate the sim ilarity of the successive contributions to a series in which the terms were each ancestor making a contribution how ever small. This is one of the aspects of anthropology in which the work of Galton stands confronted with that of Mendel, since in the light of Mendelian research certain ancestors may contribute nothing at all. (There is, in fact, on p. 135 of Natural Inheritance, a remarkable instance of inheritance, which is possibly an example of the operation of Mendelian laws.) The third point arises in connection with the extension of the comparisons in which evidence of regression might be manifest. At first the term was used to denote the relative degree of ab normality of parent and offspring. But in the guise of correlation the term acquired a much wider significance and the extensions constitute what is perhaps the most conspicuous landmark in Galton's life-work. In the words of Karl Pearson "Galton created the subject of Correlation," and again, "Galton, starting from the organic relationship between parent and offspring . . . passed to the idea of a coefficient measuring the correlation of all pairs of organs, and thence to the organic relationship of all sorts of fac tors." The importance of the achievement is unquestioned, even though there be reservation of opinion as to the precise formulae to be employed. And the practical side of the study of correlation in human measures may be illustrated as follows. There is very general agreement as to the influence of such factors as (r ) Heredity and (2) Environment on the final constitution of the individual. As to the relative magnitude of the parts played by these factors, no opinion is possible until shares are assigned in just, i.e., in real proportion. But again, no division of responsi bility can be satisfactory until expressions of number and quantity are available for use. And the index of correlation (even if its probable error has to be appended) sums up in itself the process of attempted measurement. Finally the progress of evolution itself may ultimately prove capable of expression in terms of a particular coefficient of correlation.

Karl Pearson.

The pages of Biometrika edited by Prof. Karl Pearson, constitute a massive literary memorial of Galton. In an early study (1897), before the appearance of Biometrika, Prof. Pearson investigated the variability of the two sexes in respect of their skulls, demonstrated the application of scientific methods of measuring the degree of variability manifested in different series of skulls, and brought under consideration skulls of both sexes from all parts of the world, and of prehistoric antiquity as well as of modern date. He assumed that variations constitute the raw material of the process of evolution. He found that although he was unable to point to a measure of variation really significant of progressive evolution, nevertheless the coefficient of variation employed in his research indicated little or no excess of variability in either sex over the other. His data point to a greater variability of the races of modern times, so that their structural details are still providing opportunities for further modifications should the process of evolution lay them under contribution. The contributions to Biometrika include the refine ment of measures of variability and of degrees of correlation, and tests applicable to curves representing the distribution of meas ured characters, such as provide a means of gauging the signifi cance of two or more peaks of frequency on a given curve. Where the curve in question represents the distribution of some par ticular character (such as stature) in a population, the tendency to infer the co-existence of as many distinct "elements" in the population as there are distinct peaks on the curve, is strong and reasonable, but justifiable only if confirmed by an appropriate test. The admixture of elements, whether "racial," or other is not the only possible explanation of the occurrence. The alter natives include the possibilities (a) that the total number of records available is inadequate, (b) that individuals of the two sexes are mingled in the same group, and (c) that individuals of different ages are aggregated therein. These evidently demand close scrutiny.

With the progress of statistical research the instruments will be improved or even replaced, and the existing methods will be regarded as no longer adequate. Already the very premises of Prof. Pearson, regarding the extent to which statistical methods are strictly applicable to the elucidation of biological data, have been called in question.