•468 . MR ROBERT WORTHINGTON. 



the organ A. But it should be noticed that the regression of 

 B on A is not the same as that of A on B : 



I.e., — IS not equal to — • 



The coefficient of regression for two correlated organs is shown 

 to be 



0-2 



S(a7/) 

 where r = — — • 



Hence, if m.^, m.^, are the means for A and B — so that x = A — m-^, 

 and 2/,„=B— ??i2 — we can write the 'regression formula' in the 

 form 



B — m., = -— r( A — ??i, ) 



Practical. 



From the general principles of the Mathematical Theory we 

 now pass on to note those applications of the method which 

 deal with measurements depending directly or indirectly on the 

 bony skeleton. We have already mentioned two practical 

 applications : 



(1) The dissection of the frequency curve for the ' Eow- 



Graves ' skulls. 



(2) The fitting of Bavarian skulls with a curve of Type IV. 



We will take the others in order of publication. 



''Regression, Heredity, and Panmioda." — (1) In order to 

 investigate the nature of direct and cross inheritance, assortative 

 mating, etc., statistics of stature are dealt with. The particular 

 measurements used are Mr Galton's data for about two hundred 

 families. The data contain records of the heights of two 

 generations of men and women. The means, standard devia- 

 tions, and their probable errors are tabulated for the following 

 groups: — males, husbands, sons, fathers in general, fathers of 

 sons, fathers of daughters : — females, wives, daughters, mothers 

 in general, mothers of sons, mothers of daughters. Coefficients 



