George McMullan and Karl Pearson 
383 
II. 3 (P. P. I. 2) one brother and one sister (P. P. I. 3 and 4), but was unable to find 
any real evidence as to their condition. McMullan's informants provide no less 
than three brothers and one sister, II. 1, 5 and 6 and II. 2 respectively, all stated 
to be normal. But no evidence is forthcoming as to their names, place of origin, 
residence or descendants. Ann J. (II. 3) is reported to have been a servant in 
a farmhouse at N., and the legend suggests that her mother was possibly of the 
saine class as some of her more recent descendants, which have included tramps, 
wandering labourers and paupers. It seems almost impossible therefore to trace 
any of this t/.-family now ; some years ago Pearson made, without result, inquiries 
of residents and medical men in the neighbourhood of N., both as to the family 
and as to the existence of any similar deformity in the district. No stress ought 
to be laid on the numbers in Generation II., they are probably nut exact. Of 
Francis S., II. 4 (P. P. I. 1), we know nothing beyond his name and the fact that 
he could not write it. There is no evidence whatever to suppose him in any way 
of the same stock as II. 3*. It is clear that II. 3 could not, in Mendelian language, 
have been either a pure recessive (RR) or a jmre dominant (DD). In the former 
case she would have had no affected children, in the latter case all affected children. 
She must be looked upon as an impure dominant (DR). Thus every norma! in the 
pedigree must be looked upon as an (RR), and consequently since every mate is 
a normal, all the affected can only be (DR)'s. 
In Generation III., we have at least nine children born to Ann J. (Mrs S.), 
perhaps there may have been one or two more who died young and without 
possibility of any record of deformity surviving. Of these nine, four were affected, 
three are known to have been normal, one is reported normal (III. 9), and the 
nature of the other (III. 13) is certainly unknown. This gives a quite reasonable 
Mendelian 50%. 
In Generations IV. and V., where we know the individuals much more 
accurately, there are eight matings of affected (DR) with normal (RR). Of these 
that of IV. 9 and 10 contributes nothing as there have been only two early mis- 
carriages. The remaining seven matings have so far produced 41 offspring, of 
whom 28 have been affected, nearly two-thirds. The ratio is thus nearly 2 : 1 and 
not 1 :1. The odds against such an excess as 28 to 13 are about 100 to 1, and 
they tell very heavily against any simple Mendelian theory applying to this 
deformity. 
Thus far the normal members of the stock when mated with outside normals 
have bred only normals. This is no convincing argument for Mendelian theory, 
because in no case has an intra-stirp normal been mated either with another intra- 
stirp normal or with an abnormal. Both such matings would have to be considered 
before we could assume that an intra-stirp normal is as free from taint as an extra- 
stirp normal. Further the fact that three out of the seven matings have given 
nothing but deformed offspring is most remarkable and almost impossible on any 
purely Mendelian theory. If III. 3, IV. 15 and IV. 21 had been pure dominants, 
* IV. 3 distinctly states that there was no consanguinity. 
49—2 
