LXXVIII INTRODUCTORY. 



M. Quetelet's examination of the labors of those who had written on the subject 

 made it evident to him that the true mode of ascertaining the typical man, if such 

 existed, was yet to be discovered. Artists had selected only such statues or living- 

 models as fulfilled their conceptions of beauty, strength, or grace ; naturalists studied 

 only individual specimens of race, and neither seemed to discern that there was sym- 

 metry in divergence and law for disagreement from the type. Allusion has already 

 been made to the artificial nature of the systems by which some one portion of the 

 body was selected as a modulus, and its remaining proportions laid down by their 

 supposed relations to this unit. The measurements taken or procured by M. Quetelet, 

 and the copious statistics obtained in the late war in the United States have almost 

 invariably confuted these supposed proportions. For example, it had been authorita- 

 tively asserted that the distance between the nipples formed exactly one-fourth part of 

 the circumference of the chest on that plane.' Mr. Gould finds the ratio of that portion 

 to the entire circumference in 2,068 white soldiers to be 0.2265 instead of 0.2500." M. 

 Quetelet's tables indicate 0.2210, (at the age of twenty -five.)^ Again, the distance between 

 the nipple? was declared to correspond to the antero-posterior diameter of the chest. 

 Quetelet's mean result for the latter (at the age of twenty-five) is 0.180 metre, and 

 for the former 0.195 metre.'' The breadth of the shoulders through the acromial 

 apophyses, according to the same authority, should be equal to half the circumference 

 of the chest. Quetelet's tables show the mean dimension of the first to be 0.39.3, but 

 of the latter 0.882, being in the ratio of 0.4455 in place of 0.5.^ In like manner, Mr 

 Gould's records of 7,904 men, all white soldiers, yield a ratio of 0.4627." 



Discarding all theories founded on arbitrary units of measurement, M. Quetelet 

 reasoned that if a typical figure or model of the human race existed, all variations 

 from it in excess or defect would be due to accidental causes ; that these divergences 

 would be found in corresponding groups ; and that by applying the theory of proba- 

 bilities to the problem, the number in each vaiying group could be approximatively 

 predicted. If men diff'ered, not from accidental causes but by reason of there being 

 no common type among them, measurements would have no determinate character or 

 numerical relation. Another consequence of this theory was that the more numerous 

 tlie observations the more efFectually would the accidental causes counteract each other, 

 and leave the general type in more predominant relief The group nearest to the 

 mean would be the most numerorfs, and the receding groups on either side would 

 diminish in number with the distance. These groups follow numerically a law which 

 can be laid down in advance, the law familiar to mathematicians as the law of the 

 co-efficients of the binomial. In the case of man, this law applies not only to his height, 

 but to the proportions of his limbs, his weight, strength, and, indeed, to all the facul- 

 ties or qualities of his body that can be reduced to figures. The typical man so 

 obtained is termed by M. Quetelet ^'I'homme inoi/en" the mean (not average) man.'' 



' BuKNT (W. IJ.) On the stature and relative proportloua of man at different epochs and in different coitntrkn. Head 

 before the British Association, Sept., 1844. See, also, HUTCHINSON, article " Thorax," Cijelopadia of anatomy and phijsioJogij ; 

 and Hammonu's Ui/giene, \>. 38. 

 - Op. cit.,j>.'26o. ' J»iWiro^;o»i(f/r!C, pp. 425, 4'2G. ^ Ibid., iibi supra. ^/M(?., pp. 4i4, 427. ^ Op. cit., yi. 2W. 



'Mean anp Average. — Tbo distinction between a mean and an average is often overlooked, or not clearly 

 comprehended. Sir John Herscbol bo clearly exhibits it that the passage is worth quoting entire. Speaking of M. 

 Quetelet's liomme moijen, he says, " Now, this result, bo it observed, is a mean as distinguished from an average. Tho 

 dist nction is one of much importance, and is very properly insisted on by M. Quetelet, who proposes to use tho word 



