vii.] DISCUSSION OF THE DATA OF STATURE. 127 



four independent values of b, which are respectively 

 I'Ol, I'Ol, 1'20, and 1'08 ; the mean of these is T07. 



Second Method ; from the mean value of Fraternal 

 Kegression : We may look on the Population as com- 

 posed of a system of Fraternities. Call their respective 

 true centres (see last paragraph) (MF^, (MF 2 ), &c. 

 These will be distributed about P with an as yet un- 

 known Prob. Deviation, that we will call c. The 

 individual members of each Fraternity will of course 

 be distributed from their own (MF) with a Q equal to b. 

 Then (l-7}~ = c- + W (l) 



Let P + (F M ) be the stature of any individual, and 

 let P + (MF n ) be that of the M of his Fraternity, 

 then Problem 4 (page 69) shows us that : 



/T\TT7 \ 2 



the most probable value of -^ - is ^/ , 2 2 (2) 



This is also the value of Fraternal E egression, and 

 therefore equal to f. Substituting in (2), and replacing 

 c by the value given by (l), we obtain b = 0*9 8 

 inch. 



Third Method ; by the Variability in the value of 

 individual cases of Fraternal Eegression : The figures 

 in each line of Table 13 are found to have a Q equal to 

 1*24 inch, and they are the results of two independent 

 systems of variation. First, the several (MF) values (see 

 last paragraph) are dispersed from the M of all of 

 them with a Q that we will call v. Secondly the 



