252 
GENETICS: W. E. CASTLE 
Finally we may write 
p= ri4/^-^i5, (12) 
J Po ^ 2r 
where r has the same meaning as in (11), where po is the distance from 
the point P of the curve to the center M of the corresponding osculating 
conic, and where Tq is the radius of curvature at M of the locus which M 
describes when P moves along the given curve. 
'E. J. Wilczynski, Projective Diferential Geometry of Curves and Ruled Surfaces, p, 58. 
2Loc. cit., p. 59. sLoc. cit., p. 60. "Loc. cit., pp. 67-68. 
SIZE INHERITANCE IN GUINEA-PIG CROSSES 
By W. E. Castle 
BUSSEY INSTITUTION. HARVARD UNIVERSITY 
Received by the Academy, M«rch 9. 1916 
For several years my pupils and I have been engaged in studying 
the inheritance of size and weight differences among animals, these being 
characteristics of much economic importance and of peculiar theoreti- 
cal interest. Preliminary studies published in 1909 showed that size 
and weight in rabbits do not follow the Mendelian rules of dominance 
and segregation as unit-characters. But Lang subsequently suggested 
that multiple Mendelian factors may be concerned in such cases, extend- 
ing to animals a principle already recognized by Nilsson-Ehle in dealing 
with certain categories of characters in plants. Punnett and Bailey 
(1914) accept this principle in explaining weight inheritance in crosses 
of bantam fowls with those of ordinary size. They beHeve that four 
differential factors are concerned in a particular cross studied, three 
dominant factors which tend to increase size being found in the larger 
race, one such factor being found in the bantam race. By recombina- 
tion in F2 some individuals are obtained smaller than the bantam race, 
and others in F3 larger than the larger race. But there are some reasons 
for questioning the validity of this analysis which assigns very definite 
quantitative values to the several hypothetical factors, without however 
making any allowance for physiological changes of size due to non- 
genetic causes, or for possible quantitative variation in the factors them- 
selves. Moreover, let it be granted for the sake of argument that these 
four Mendelizing factors exist and that each is an independent agency 
for increasing size. On the Mendelian hypothesis there should be ob- 
tained from the cross in question individuals which lack all four of these 
factors. What, it may be asked, will their size be? Will they be with- 
