294 Prof. K. Pearson. Mathematical Contributions [Jan. 20. 

 Whence we find 



%J<r m = 0-890,051, Sy/o-j, = 0*891,209, 



and 



K = 0-5446. 



This is a very reasonable value of fraternal correlation, agreeing 

 quite well with results obtained for horse, man and dog. It is worth 

 noting that 



irfi x r hh = r »<2 Xr *A = 0-4010, 



and, therefore, either equals r xts or r vtl fairly closely : in fact, within 

 the probable error of their difference. 



Hence, it would appear highly probable that the cross-relation 

 between one brother's head length and a second brother's age is solely 

 •due to the correlation of the ages between the two brothers. 



If such a result as 



*H x r hh = r xt . 2 (?;) 



should be verified on the reduction of further data, it will enable us 

 to much simplify our formulae. 

 Thus we easily find for this case 



2-b = <r x vl - r xt f, - y = Vy\/ 1 - r y t{ 



and 



l-f*« ■ 



Or, we require to find only the uncorrected correlation (p) the growth 

 correlation (/'), and the correlation between periods of growth (r). 

 The correction to be made to the apparent correlation is then the 

 subtraction from it of 



1 - /••-' ' 



I hope shortly to ascertain whether relations like >/ above hold also 

 for other head-measurements on growing children. 



