9i8 



THE HEREDITY OF THE BLOOD GROUPS 



However, there are four cases where an mother is stated to have given birth to 

 an AB child, but since in each case the father was either an A or a B there was either 

 an illegitimacy or an error in technique. Also in the obstetrical material cited by 

 Hirschfeld' there are seven instances in which an O mother is stated to have given 

 birth to an AB child but nothing is said as to the group of the father. It is to be noted 

 that if all of these cases are accepted as correct they would count against Hirschfeld's 

 explanation of a lethal effect of incompatibility between O mothers and AB children, 

 but at the same time they would rule out Bernstein's multiple-allelomorph theory. 

 On account of our inability to examine the original description of these cases, they 

 are not included in our table as exceptions to Bernstein's theory. Their existence, 

 however, shows how seriously further accurate work is needed. (It should also be 

 pointed out that in almost none of the recorded instances is mention made of the 

 examination of the serum as well as the cells of each individual.) 



TABLE VIII 



Differing Values of "r" in Various Races on Bernstein's Assumption 



POPXJXATION 



Investigation 



Austrians 



Laps in Sweden 



Hungarians 



Gypsies in Forro 



1,500 people (summary) 



L. and H. Hirschfeld 



Rietz 



Verzar and Weszeczky 

 Verzar and Weszeczky 

 Verzar and Weszeczky 



Frequency of Groups 



42 



51 



31.8 



18.3 



31- 



40 

 42 



39-7 

 40.8 

 38. 8 



8.0 



4 

 12.4 



27 



w o 



^ Zi 



Q 



But does not the remarkable fit of the calculations to the formula p+q+r=i 

 command acceptance of Bernstein's hypothesis? Bernstein's formula may be tested 

 by deriving from his assumptions a value of r in a manner different from his. Thus the 

 probable frequency of group B, which is genetically BR or BB, is (2qr+q-) as above. 

 Then: _ 



2qr+q^ = B , 

 2qr = B — q2 , 

 B-q^ 



r= 



2q 



Similarly, in terms of A and p, r is found to equal 



A 



Now, if we take concrete 



instances and derive p and q by the formulae of Bernstein and then derive r according 

 to both of the two new formulae which follow from Bernstein's assumptions, we find 

 in many cases a wide divergence from the value of r when it is taken as equal to y'O. 

 We find now that p+q+r does not equal i as frequently as formerly. We append a 

 few such calculations in Table VIII. 



In view of these considerations it is perhaps wiser not to accept the multiple- 



' Hirschfeld, L.: ibid., p. 420. 1926. 



