36 2 



NATURE 



[Mar. 7, 1872 



extremely narrow-chested men of 28in., and the few ex- 

 tremely broad-chested men of 42in. These two examples 

 may represent the more symmetrical cases of distribution 

 of individuals on both sides of a central type, as worked 

 out by M. Ouetelet from various physical measurements 

 applied to large numbers of individuals. Here the ten- 

 dency to vary is approximately equal in both directions. 

 Where the tendency to vary is perceptibly different in the 

 two directions the curve loses its symmetry, as in the 

 figures representing the weights of women at different ages 

 (Anthropom. p. 349), and the number of marriages of men 

 and women at diiferent ages (Phys. Soc. i. 272). The 

 actual series of numbers given by observation are placed 

 beside series computed according to the law of the ex- 

 panded binomial, the same which is applied in the theory 

 of probabilities to such calculations as that of the pro- 

 portionate distribution of less probable events on each 

 side of a most probable maximum term, the distribution 

 of errors of observation of a single object, and of acci- 

 dental variations in general. It is the closeness of approxi- 

 mation between the observed and calculated series of 

 variations, computed not only as to the dimensions, but 

 the actions of man, which gives to M. Ouetelet's theory its 

 remarkable definiteness and precision. 



The diagram of statures here figured, which may be 

 looked upon as representing a nation measured in one 

 particular way, at once impresses on the mind a concep- 

 tion of a race-type materially differing from the vague 

 notions hitherto current. It is seen that individual men 

 of different statures are required to constitute a nation, 

 but they are required in less and less proportion as they 

 depart in excess or defect from the central type. The na- 

 tion is not even complete without its dwarfs and giants. 

 In fact, if all the monstrously short and tall men of a par- 

 ticular country were put out of sight, and the census of the 

 population taken according to stature, the national formula 

 thence deduced would enable a statistician to reckon 

 with considerable accuracy how many dwarfs and giants 

 of each size had been removed. 



M. Ouetelet's investigations further prove, or tend to 

 prove, that similar laws of variation from the central type 

 govern the distribution of individuals classed accord- 

 ing to other bodily dimensions, and also according 

 to physical qualities such as weight and strength, it 

 being borne in mind that the particular expressions with 

 their descriptive curves differ for the various qualities or 

 faculties of man, being also in some cases much less sym- 

 metrical than in others. An absolute coincidence of the 

 series of observed facts with the numerical law chosen to 

 express them would be too much to expect ; it is a great 

 deal to obtain even a rough coincidence. For instance, 

 when the strength of a number of men is estimated by a 

 dynamometer, the maximum number showed 140 to 150 

 degrees on the scale, the number of weaker and stronger 

 men being both fewer from this point, groups following 

 approximately the proportions of the coefficients of a bi- 

 nomial of the 6th order ; the numbers are reduced as 

 follows from the table (Anthropom. p. 365) : — 

 Renal force, degrees. . 90 loo-lio 120-130 140-150 1G0-170 

 No. of men in 64 ... I 8 14 20 15 



Dinom. coeff I 6 15 20 15 



Renal force, degrees I So- 190 200 

 No. of men in 64 ... 6 I 



Binom. coeff 6 i 



In the various numerical examples here given, the element 

 of age is not introduced, the ages of the individuals being 

 calculated or taken as uniform. The problem of variation 

 of numerical distribution of a population at dift'erent ages 

 is treated by M. Ouetelet in a comparatively simple case, 

 that of the stature-curve. Here a curve approximating to 

 a parabola is laid down, the ages of man from birth on- 

 ward being measured along its axis ; each double ordinate 

 of this curve forms the base on which a binomial curve is 

 erected perpendicularly, the vertices of these curves form- 

 ing a curve of mean stature, of the nature of a curve of 

 mortality (Anthropom. p. 264). How far M. Ouetelet 

 may succeed in his contemplated purpose of carrying his 

 method from the physical into the intellectual and moral 

 nature of man, it is premature to judge. 



Without entering into the more intricate and difficult 

 problems opened by this theory of central types, it is 

 evident that the bearing of its main conception on the 

 problems of anthropology and biology in general is highly 

 important. Some able anthropologists have accepted the 

 theory of the mean or central standard as a basis for the 

 comparison of races, but this line of research is still in its 

 infancy. In IVI. Ouetelet's last volume a principle is 

 worked out which serves as a bridge between the old 

 and new methods. His experience is that in a well- 

 marked population no extraordinary number of observa- 

 tions is required for the determination of the mean man. 

 In former ages, one result of the national type being so 

 preponderant in number and so easily recognisable was 

 that the bodily measurements of any man of ordinary 

 stature and proportions could be trusted to give, with 

 reasonable accuracy, the standard measures of the nation, 

 such as the foot, cubit, fathom, &c. In the same manner 

 M. Ouetelet finds a small number of selected individuals 

 sufficient for ascertaining the standard national propor- 

 tions of the human body, male and female, from year to 

 year of growth ; his tables, founded for the most part on 

 Belgian models, are given in an appendix. This method 

 is applicable to the purposes of general anthropology. Thus 

 a traveller, studying some African or American race, has to 

 select by mere inspection a moderate number of typical 

 men and women, by comparison of whose accurately ad- 

 measured proportions he may approximate very closely to a 

 central race-type.* It is not necessary to dwell on the ob- 

 vious difficulties of connecting the standard types of mixed 

 nations with the races composing them. The stature- 

 curve of England differs visibly in proportions from that 

 of Italy, the measurements of Scotch and American 

 soldiers show very different mean and extreme terms, and 

 the problems of race underlying these differences are of a 

 most complex character, the more so when the considera- 

 tion is introduced of the race-type varying within itself 

 from century to century. M. Ouetelet is naturally apt, 

 when expressing his views in an exordium or a peroration, 

 to draw a good deal on the anticipated future results of his 

 adii irable method ; but in judging of the value of his doc- 

 trine of central types, the best criterion is his actual suc- 

 cess in reducing the observed facts of nature to numerical 



* Thus General Lefroy's measurements of tliirty-three Chipewyan Indians 

 (" Journal of the Ethnological Society." vol. ii. p. 44, 1870) are sufficient to 

 determine the stature of the mean man as about 5 ft. 7 in. , the number of 

 inaividuals in this maximum, group being S. It is even possible to guess 

 from this small number of measurements the numerical law of variation in 

 the tribe, the series of groups from 5 ft. 3 in. to 5 ft. 1 1 in. being as follows :— 

 I, i\, 2;, 6,8, 4!, 4!, 3, J. 



