*A Arrangement and Formation of the Series. [CHAP. II. 



each direction, and if we continue to accumulate our mea 

 sures it will be found that they tend to lie continuously 

 between these extremes ; that is to say, that under those 

 circumstances no intermediate height will be found to be 

 permanently unrepresented in such a collection of measure 

 ments. Now suppose these heights to be marshalled in the 

 order of their magnitude. What we always find is some 

 thing of the following kind; about the middle point be 

 tween the extremes, a large number of the results will be 

 found crowded together: a little on each side of this point 

 there will still be an excess, but not to so great an extent ; 

 and so on, in some diminishing scale of proportion, until as 

 we get towards the extreme results the numbers thin off and 

 become relatively exceedingly small. 



The point to which attention is here directed is not the 

 mere fact that the numbers thus tend to diminish from the 

 middle in each direction, but, as will be more fully explained 

 directly, the law according to which this progressive diminu 

 tion takes place. The word law is here used in its mathe 

 matical sense, to express the formula connecting together the 

 two elements in question, namely, the height itself, and the 

 relative number that are found of that height. We shall 

 have to enquire whether one of these elements is a function 

 of the other, and, if so, what function. 



2. After what was said in the last chapter, it need 

 hardly be insisted upon that the interest and significance of 

 such investigations as these are almost entirely dependent 

 upon the statistics being very extensive. In one or other of 

 Quetelet s works on Social Physics 1 will be found a selection 

 of measurements of almost every element which the physical 

 frame of man can furnish : his height, his weight, the mus 

 cular power of various limbs, the dimensions of almost every 

 1 Essai de Physique Sociale, 1869. Anthropometrie, 1870. 



