116 SOREN HANSEN 
to calculate the numerical proportion of sound and diseased in the fa- 
mily, since we know nothing about the many families in which the 
disease does not appear, though the genetic antecedents for it are pre- 
sent: it is also of subordinate importance that the families are but rarely 
so large, that we can expect any frequent realisation of more compli- 
cated genetic formulae. When the usual number of children is three, 
four or five, it is not easy to show that an inherited disease occurs 
on an average in one of sixteen in a family. Using a very large material 
RtpIn (1916) with the mathematical assistance of WEINBERG has en- 
deavoured to find the numerical proportions of Dementia præcox, but 
the result is not encouraging. The only thing certain is, that the dis- 
ease occurs so rarely in families, that it must of necessity be poly- 
hybrid, but how many factors have to be presupposed, and whether 
they are recessive or dominant, cannot be solved in this way. ~ As 
already noted, all knowledge is wanting of the families in which the 
disease does not appear though the basis has been present in the ante- 
cedents. By direct study of the single families, however, it can easily 
be seen, that at least one of the factors, which cause the disease, must 
be recessive, as it is undoubtedly handed down as a recessive 
character. It only exceptionally appears in two successive generations 
and is not known to have been observed in three. We have an in- 
teresting case in the royal family of Hanover, which can be referred 
back to the insane Duke William the Pious, of Brunswick-Liineburg, 
who suffered without any doubt from Dementia præcox. How the dis- 
ease showed itself in a number of his successors, can scarcely be de- 
termined, but in the Danish King Christian VII it may certainly be 
considered to have arisen from the peculiar connection between his pa- 
rents, a homozygotic connection with respect to a recessive factor. The 
father, namely, the Danish King Frederik V was descended from Duke 
William the Pious through the latter’s granddaughter, Queen Sophie 
Amalie who married Frederik V’s great-great-grandfather, Frederik III, 
and the mother, the English Princess Louise, was a granddaughter of 
George I, who was a great-grandson of the Duke (THACKERAY, 1860). 
Royal paternity is perhaps not always quite trustworthy, and the 
genetic analysis can scarcely be considered as worked out according to 
pure principles, but we have this in favour of the correctness of the 
final result, that King Christian VII’s sister, Princess Sophie Magdalene, 
who married the Swedish King Gustaf III, whose mother, King Adolf 
Fredrik’s Queen Ulrika, was a granddaughter of George I, likewise had 
an insane son, the Swedish King Gustaf IV Adolf. Such cases are by 
