vii.] DISCUSSION OF THE DATA OF STATURE. 125 



The value of the M of a small Fraternity may be 

 much affected by the addition or subtraction even of 

 a single member, it may therefore be called the apparent 

 M, to be distinguished from the true M, from which its 

 members would be found to be dispersed, if there had 

 been many more of them. The apparent M approxi- 

 mates towards the true 1VI as the Fraternity increases 

 in size, though at a much slower rate. We have now 

 somehow to get at this true JVI. For distinction and 

 for brevity let us call the apparent M of any small 

 Fraternity (MF'), and that of the corresponding true 

 M (MF). Then (MF) may be deduced from (MF 7 ) as 

 follows : — 



We will begin by allowing ourselves for the moment 

 to imagine the existence of an exceedingly large Frater- 

 nity, far more numerous than is physiologically possible, 

 and to suppose that its members vary among themselves 

 just as widely, neither more nor less so, than in the 

 small Fraternities of real life. The (MF 7 ) of our large 

 ideal Fraternity will therefore be identical with its (MF), 

 and its Q will be the same as b. Next, take at random 

 out of this huge ideal Fraternity a large number of small 

 samples, each consisting of the same number, n, of 

 brothers, and call the apparent Mid- values in the several 

 samples, (MF'j), (MF' 2 ), &c. It can easily be shown 

 that (MF'j), (MF 7 2 ), &c, will be so distributed about the 

 common centre of (MF), that the Prob. Deviation of 

 any one of them from it, that is to say, the Q of their 

 system will = b x -^. If n=l, then the Prob. Devia- 

 tion becomes b, as it should. If n = 2, the Prob. 



