310 REPORT— 1871. 



On the Measurement of Man and his Faculties. By Samuel Beown, F.S.S. 



The science of probability, wliich in the course of 200 years has been perfected 

 by the great mathematicians of England, Germany, and especially of France, and 

 has rendered such serrice in astronomical researches, is still in its infancy as regards 

 its application to the problems of political and social economy, which directly 

 concern the growth of civilization, and the physical, moral, and intellectual pro- 

 gress of man. James Bernoulli by its aid proposed to investigate questions of in- 

 terest in morals and in economic science ; but his work was not published till 1713, 

 eight years after his death, and in the meantime his nephew, Nicholas Bernoulli, in 

 an essay in 1709, had treated of such questions as the number of persons living- 

 after a certain number of years out of a given number born, of the period of time 

 at the end of which an absent man of whom no tidings have been heard may be 

 considered to be dead, of the value of an annuity on human life, of marine insu- 

 rance, the probability of testimony, and of the innocence of an accused person. Not 

 to mention the extension of the science in the wi-itings of Condorcet, Laplace, and 

 Poisson to the questions of decisions of legal tribunals, of elections, of the relative 

 force of opinions in the minority of voters, the credibility of history ; the Census, 

 tables of mortality, marriage, and insurances, to illusions and mental phenomena, 

 we find in recent years the greatest impulse given to scientific methods of collect- 

 ing and comparing statistics has been by M. Quetelet, the Director of the Ilo3'al 

 Observatory at Bruxelles, President of the Central Statistical Commission of Bel- 

 gium, and the Perpetual Secretary of the Academy of Sciences. He was one of 

 the early founders of this Section at the Meeting at Cambridge in 1833, and was 

 the originator of the International Statistical Congresses which have been the 

 means of eiFecting such vast improvements in the collection, publication, and com- 

 parison of Government Statistics in every country in Europe. 



In the application of scientific methods of observation to study the physical and 

 moral qualities of man, an essential part of the inquiiy is as to his growth, and 

 the relative proportion of the various parts of the body at different ages until his 

 complete matm-ity. The last work of M. Quetelet, entitled " Anthi'opom^trie, ou 

 mesui-es des difierentes facult^s de I'homme," recently published, comprises the re- 

 sidts of many years of observations, in which, by the assistance of scientific friends, 

 artists and medical men, he has succeeded in collecting sufficient and trustworthy 

 facts to trace the law of gi-owth in every portion of the himian body at all periods 

 of life. 



The methods formerly employed to ascertain the true proportions which consti- 

 tute the typical man were not satisfactory. Natm-alists did not sufficiently study 

 the averages to discover the laws of their agreement or divergence on certain 

 points ; artists selected such types of beauty or strength as suited their special pur- 

 pose. But if some model of the human race existed the proportions of which 

 were so fixed that any deviations from it in excess or defect could only arise from 

 accidental causes, the observations recorded may be divided into groups at equal 

 intervals, and according to the theory of probability the specific number which 

 ought to be found in each group may be predicted beforehand, with a very near 

 approach to accuracy. The gi-eater the number of observations the more certainly 

 will the observed number in each group agree with the number calculated by the 

 theory. The group which approaches nearest to the mean will be the most nume- 

 rous, and the other gi-oups will be found to contain numbers, as they differ from 

 the mean in excess or defect, in exact proportion to the coefficients of the terms 

 of the binomial theorem. In accordance with this law dwarfs and giants cease to 

 be casual monstrosities. If out of a sufficient number of observations, taken in any 

 country, of the number of people measured at regular gradations of h eighty the 

 dwarfs and giants had been pm-posely excluded, we ought by means of this law 

 to be able to predict nearly not only the numbers which had been omitted, but 

 their relative statures as compared with the rest of the people. 



A remarkable confii-mation of this law was given by Mr. E. B. Elliott in the 

 measurement of the height of 25,878 volunteers to the United States Army during 

 the Civil War. The intervals of height were taken at every 25 millimetres. At 

 the mean height, 1-75 metre, the number found by measurement was 4054, or 157 



