INTRODUCTORY. LXXIX 



A curious result of this theory is found in the calcuUition as to dwarfs and giants. 

 In the o-eneral estimation, dwarfs and giants are regarded as monstrosities, anomahes 

 of the human species, but they fall into their places naturally and symmetrically, and 

 are necessary to complete the grand scale of human stature. Indeed, so little is there 

 of accidental in their exceptional stature that, in measuring the population of a country, 

 if the dwarfs and giants were purposely concealed from view, it would be possib e Irom 

 the measurements obtained not only to declare the number of each that should exist, 

 but also to assign to them their actual stature.' _ 



M Quetelet exhibits in tabulated form the results of observations made m 1^ ranee, 

 Belo-ium Italy, and the United States. In these, the figures obtained by calculation 

 approach with remarkable closeness to the actual measurements. For example, the 

 result of twenty years of observation on his part in Belgium gives the mean stature 

 of his countrymen at 1.68 metres, (6G. 14 inches,) and the number' per thousand of 

 that heioht, by actual measurement, is 138 ; by the calculus, it is 136.^ Mr. Elliott, in 

 25 878 examinations, found the mean height to be 1.73 metres, (68.20 inches,) and the 

 number of men per thousand of that height was 157 ; by the calculation, the number 



ari-ived at was 153.^ • • i 



The following tables, somewhat abridged and re-arranged from the originals, 

 conveniently exhibit the symmetrical result of the actual and of the calculated 

 observations in so me extensive records of stature and girth of chest. 



,;;^^;;^lv for tUo former, and to speak of the latter (averasO as the ' aritbmotical mea..' We prefer the ten. average 

 not on y beeauso both are truly arithmetical means, bnt hecanse the latter term carries alreaay w,th rt that v.fated 

 Zl vuLr association .'hich ;enaers it less fit for exact and philosophical nse. An ayerage njay ex.st of tire most 

 different obiects as of the hei-^hts of honses in a town or the sizes of books in a library. It may be convement to con- 

 t?rge.S n lion^f Hi 'hings averaged, bnt inyolves no conception of a na.nral and r.ccn.nizable <^^^^^^ 

 lid ferencesfrom which ought to be regarded as deyiations from a standard. The notion of a mean, on the other 

 hand does imply such a conception, standing disliuguished from an average by th>s very feature, v.z, the regular 

 ma°ch of the groups, increasing to a maximum and then again diminishing. An average g,ves ns no assurance that the 

 "ut rro .m be like the past. A mean may be reckoned on with the most implicit conhdence. All the phdosoph.cal 

 ireof statistical results depends on a due appreciation of th.s distinction, and acceptance of rts consequences."- 

 (iJdiH. KetJieit!, No. clxxxv, vol. xcii.) 



1 Jnthropomaric, p. 56. ' ^'''f' P' 287- 



3 On the military statistics of the United States of Ammca, 4to, Berlin, ISbJ, p. J4. 



