THE FACTORIAL HYPOTHESIS 221 



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- 

 bihs, is entirely a matter of choice. Hence, no matter 

 whether red or w^hite 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 possibiHty 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 



