THE FACTORIAL HYPOTHESIS 275 
assuming the absence of the factor, the dominant 
character being considered as a ‘‘presence.”” Domi- 
nance, however, is often found to be incomplete if 
exact quantitative studies are made. In fact, char- 
acters are known to show all degrees of dominance 
and recessiveness over their alternative allelomorphs. 
Which character is to be considered dominant and 
which recessive when each allelomorph has an equal 
effect, as in the case of the red and the white Mira- 
bilis, is entirely a matter of choice. Hence,no matter 
whether red or white is presence, the present factor is 
not truly dominant. It seems reasonable, then, to 
suppose that if presence and absence is true a hybrid 
(with one presence) might approach more nearly the 
type with two absences than to the type with two 
presences. In such a case the present factor would 
actually be the recessive. Such a case is in fact 
known. In the cross of horned by hornless sheep, 
the horned condition dominates in one sex and the 
hornless in the other. Here no matter which is 
considered as a presence it must be conceded that in 
one sex or the other it is recessive. The view that 
dominance of a factor proves its presence and 
recessiveness its absence should therefore be aban- 
doned. 
A further argument against the theory of presence 
and absence is found in the evidence, already given, 
which indicates the possibility of multiple allelo- 
morphs. On the presence and absence system, only 
two kinds of -allelomorphs, the presence and the 
absence, are possible, and no character differences 
