160 



Prof. Karl Pearson. 



Equation (xx) becomes 



a'- 1-56851 a + 0*5 = 

 or, a = 0-445057. 



Hence y = 0-019594, P = 0-341279. 



This effectually shows us that for this case y cannot be taken equal 

 to (3, or the reversion series started from the parents, 

 Further, we reach from Equation (xi) : 



Pn = 0-30124(J)'^ + 0•698761(0•286336)'^ 



Such a value again demonstrates that in this case the ancestral correla- 

 tion differs totally in form from what might be deduced from the 

 theory of blended inheritance, i.e., it shows us how we must distinguish 

 between a law of regression and a law of reversion. 



Putting n = 3, we have ps = 0-0541 for the calculated value of the 

 great grandparental correlation. This may be, I think, considered in 

 satisfactory agreement with the observed value 0*0404. Had we deter- 

 mined our 8 and c by the method of least squares, so as to satisfy the 

 three relations 



Pi = J(l - c) + c8, p, = l(l-c) + c8-\ PS = -^-(1 - c) + c8o 



as closely as possible, we should have got, of course, still more accord- 

 ant results. 



We can now put down our general conclusions : 



63'256 per cent, of Basset Hounds take after tlieir parents (50) 



3-488 ,, revert to grandparents (25) 



3'105 ,, great grandparents (12*25) 



2-764 „ „ „ great^ „ (6*25) 



2-460 „ „ „ great' „ (3*125) 



2-190 „ „ „ great^ „ (1*5625) 



1-949 „ „ „ great' „ (0-78125) 



1-735 „ „ „ greaf^ „ (0-390625) 



14*053 per cent, of Basset Hounds revert to still higher ancestry 

 (0*390625). Now the divergence here from Mr. Galton's original 

 statement of the law is most significant ; I have put in brackets the 

 percentages deduced from that statement. In our case we have a 

 comparatively small reversion to each generation of ancestry, but the 

 percentage, 1*7, is still sensible in the case of the 8th ascending genera- 

 tion. In Mr. Galton's case we have very substantial reversions to 

 grandparents and great grandparents, but the rate of diminution in- 

 stead of being the loss of about 1/9 at each stage is 1/2 ! As a result, 

 the reversion to the 8th ascending generation is less than 0*4. It can- 



