1904.] serve to Test various Theories of Inheritance. 



Accordingly, we have : 



0, 2*2 = a-/(l-2 /0/c 2), 



C/, ?x 2 = 0"c 2 (1 - P/c 2 ), 



269 



a; 

 a; 



whence we have the following table : — 



Table of "2 x /<r c . 



C J 



c 2 (l + 2p /c 2), 



37. 



0-3. 



0-4. 



0-5. 







0-91 



-82 



0-71 







0-95 



-96 



0-87 







1 -oo 



1 -oo 



1 -oo 



z«f 



1 -09 



1-15 



1-22 



Now parental correlations in my experience of extensive masses of 

 good data are rarely as low as 03, generally over 04, or nearer even 

 0*5. But even with 0'3 we see that there ought to be about 20 per 

 cent, increase in the standard deviation of an array as we pass from 

 the mean father to a father with a deviation equal to twice the 

 paternal deviation, i.e., to an array which will be given with at least 

 a moderate number of cases in any parental correlation table. As we 

 approach a parental correlation of 0*4 — 0*5, this increase of the 

 standard deviation amounts to 40 — 72 per cent., and should be still 

 more conspicuous. We conclude, therefore, that if the parents are 

 respectively dominant in two separate groups of offspring, then when 

 we plot the standard deviations of the arraj^s of offspring to the 

 deviations of the parent from the mean, we ought to get a very 

 sensibly hyperbolic curve. Or, if we plot the squares of the one to 

 those of the other, we ought to get a sloping straight line of very 

 sensible slope, 0*1 — - 25 about, instead of the horizontal line of the 

 " Ancestral Law," 



If we suppose the same conditions to apply to a bi-parental array, 

 i.e., m\ = r>h, %i = ^2 = J °"cj = °"c 2 = o" C5 fty = f*im = 0, we find that 

 (x) reduces to 



= -c 2 {(W 



rif + r 2m 2 

 1 - r m f 



+ 



2 r if 



Or, using (ii) and (iii), which give p/ ( 



J?V, p,ac = ir-2 



■,--)}. 



1—2 ffi c Pmc 

 1-Pm/ 2 



1 - Pmf °y 



(xiii). 



