494 



The Journal of Heredity 



mal, even if the cases were sufficiently 

 numerous, which they arc not. 



THE CRITICAL CASE. 



But on the other hand, when two non- 

 albino individuals have among their 

 offspring one or several albinos, we can 

 affirm, if Mendel's Law is exact, that 

 these two parents are heterozygous 

 DR; and we know that the pro])ortion 

 of recessives RR in unions between 

 heterozvgotes is 25 in 100, according 

 to the 'formula DRxDR = 25<^f DD+ 

 50% DR-f-25S;RR. In the pedigrees 

 collected by Pearson, Nettleship and 

 Usher, we shall therefore seek the cases 

 where one or more albino children have 

 been produced by normal parents; and 

 we shall see whether their numerical 

 proportion, relative to the total num- 

 ber of children born from those couples, 

 accords with Mendel's Law. 



It must be carefully noted that the 

 theoretical figure, when we proceed 

 thus, is not 25%, but a larger figure, 

 separated the more widely from 25, in 

 projjortion as the number of children 

 born to the couple is the smaller. For 

 each of the children successively born 

 to our heterozygous coui:)le, there are 

 indeed 25 chances in 100 or one chance 

 in four that he will be an albino. But 

 when the total niimber of ofTspring 

 contains no albino, the case escapes 

 our observation. If, for exam])le, the 

 phratry ' consists of but one individual, 



the only jjhratrics noted in our statis- 

 tics are those in which this unique sub- 

 ject is an albino, and the proportion is 

 therefore 100%. In phratries composed 

 of two children, there is one chance in 

 four that the eldest-born shall be an 

 albino, there is also one chance in four 

 that the second shall also be an albino, 

 and consequently there is one chance in 

 4x4, or 16, that both subjects be al- 

 binos. On the other hand, there are 

 three chances in four that the first- 

 born be not an albino, three chances in 

 four that the second shall not be an 

 albino, either, and consequently 3x3 

 chances in 4x4, or nine chances in 16, 

 that both the children be normal. But 

 as these cases escape observation, there 

 remain one phratry of two albinos in 

 two children, and six phratries of one 

 albino in two children, or eight albinos 

 in 14 children — that is, 57 in 100. Con- 

 tinuing thus we find, for phratries of 

 three, four, five, six, seven, eight, nine, 

 10, 11, 12, and 13 children, the figures of 

 43, 36, 33, 30, 28.8, 27.7, 27. 26.4, 26, 

 25.7, 25.5 (in 100) — a proportion that 

 continually approaches the proportion 

 25 ]jer 100, without ever reaching it. 



Such are the theoretical figures, cal- 

 culated according to Mendel's Law; 

 we must now compare them with the 

 figures contained in the genealogical 

 work of Pearson, Nettleshijj and Usher. 

 These figures are contained in the fol- 

 lowing table: 



* For the sake of simplicity I thus designate the ensemble of brothers and sisters borne to the 

 same parents. The English eugenists use the neologism sibship in the same sense, making use 

 of the word sibling to designate each of the individuals making up a sibship, whatever be his or 

 her sex. 



