510 Messrs Stratton and Compton, On Accident in Heredity, 



Now the offspring of a cross true D xD will be 



dominant : recessive = p^ + ^pq + Zq^ : q^, 



i-©- ^-7 — \^ No of the offspring will be D's. 

 {p + '2.qf ^ *= 



The offspring of a cross true D x R will be 



dominant : recessive = p + q : q, 



i.e. — — ^ of the offsprmff will be D's. 

 p-{-^ ^ ^ 



The offspring of true R x R will be all R's. 



The proportion of D's to R's in the offspring of the apparent 



D X D crosses will be 



( j9^ + ^pq + 3^^) (1 - 0)2 + 2r (p + 5) (1 - 6') 6* : g^ (1 - df 



+ 2rq{l-d)e + r^e\ 

 or say X : Y. 



These offspring will have a constant proportion transformed, 

 and we shall have an apparent distribution of the offspring in 

 the ratio 



x{i-e)+7e _D 



Y(l-e) + Xd~ R '^ ^• 



In a similar way we can obtain the ratio of the true i)'s to 

 true R's resulting from the apparent D x R crosses. They are 

 (p^ + 4^pq + Sq^){l - 0)6 + r{p + q)(l -20 + 26') -.q^il- 6)6 



+ rq (1 - 2(9 + 26') + r' (1 - 6) 6, 

 or say X' : Y'. 



The proportion of apparent Z)'s to R's in these offspring 

 will be 



X'{\-6)+Y'6 _D' 



Y'{\-6) + X'6 R' ^ ^' 



The remaining equation comes from the offspring of the 

 apparent R x R crosses, which give D's to R's, in the ratio 

 {p' + ^pq + ^') 6' +2r(p + q)(l-6)6: q'6' + 2rq (1-6)6 



+ r' (1 - 6)\ 

 or say X" : Y" . 



The apparent offspring will be in the ratio 

 X''{\^6)+Y"6 _J)" 

 Y"(\-6) + X"6~ R" ^''''• 



Statistical examination of families will give in any particular 

 case the values of the right-hand side of equations (2), (3), (4) 

 and (5). It remains to determine the ratios p:q:r, and the 

 value of 6. 



