QUETELET ON THE SCIENCE OF MAN. 53 



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 (" Anthro- 

 pom.," p. 349), and the number of marriages of men and women at 

 different ages (" Phys. Soc," i., 272). The actual series of numbers 

 given by observation are placed beside series computed according to 

 the law of the expanded binomial, the same which is applied in the 

 theory of probabilities to such calculations as that of the proportion- 

 ate distribution of less probable events on each side of a most proba- 

 ble maximum term, the distribution of errors of observation of a sin- 

 gle object, and of accidental variations in general. It is the closeness 

 of approximation between the observed and calculated series of varia- 

 tions, computed not only as to the dimensions, but the actions of man, 

 which gives to M. Quetelet'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 im- 

 presses on the mind a conception 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 nation is not even complete without 

 its dwarfs and giants. In fact, if all the monstrously short and tall 

 men of a particular 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 accu- 

 racy how many dwarfs and giants of each size had been removed. 



M. Quetelet's investigations further prove, or tend to prove, that 

 similar laws of variation from the central type govern the distribution 

 of individuals classed according 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 symmetrical 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 bino- 

 mial of the sixth order ; the numbers are reduced as follows from the 

 table (" Anthropom.," p. 365) : 



Renal force, degrees 90 100-110 120-130 140-150 160-170 



No. of men in 64 18 14 20 15 



Binom. coeff 1 6 15 20 15 



