. W. E. Castle 297 



homozygous for the recessive allelomorphs of these factors. If the three 

 factors were supposed to be equivalent one with another in their whitening 

 influence, the hypothesis would straightway break down in the face of 

 the experimental results. But Punnett adds to the hypothesis as follows. 

 The potency of each of the three assumed factors is supposed to be 

 different The recessive factor, p, is supposed to produce white spotting 

 of the Dutch type either in a heterozygous or in a homozygous state. 

 The recessive factor, t, by itself produces a white pattern only in a 

 homozygous state, but in association with p or with s adds to the 

 whitening effect, raising the grade of the pattern produced. 



The third assumed recessive factor, s, can by itself produce no white, 

 either as a heterozygote or as a homozygote, but when associated with p 

 or with t it adds to the whitening effect of those factors in three out of 

 six combinations shown in Punnett's Fig. 2. 



This is a rather complicated set of hypotheses to make " out of whole 

 cloth," but no objection need be raised on that score. Any hypothesis is 

 justifiable which will work. But the more secondary hypotheses are 

 required to make it work, the more will the entire scheme be open to 

 suspicion and the stronger must be the evidence that it does work, that 

 it will in reality enable us to predict results not otherwise predictable. 

 Let us see if this is true of Punnett's three-factor hypothesis. When 

 applied to the F^ generation from this cross, Punnett's scheme fits the 

 observed results fairly well. But the real test of a scheme built up on 

 so many arbitrary and independent assumptions is to apply it to other 

 crosses than that which it was apparently framed to meet, the peculiar 

 F^ distribution. If, for example, it fits a back-cross test as well as the F^ 

 test, it will gain much in acceptability. Punnett makes such an appli- 

 cation in his Table II and apparently is fairly well satisfied with the 

 result, better at any rate than with admitting "modification" under 

 any circumstances. 



But Punnett's calculated distribution differs from the actual one in 

 the following essential regards. The lower calculated group shows two 

 chief modes instead of the actual one mode. The more pronounced of 

 the two calculated modes differs widely in position from the actual 

 mode. The upper calculated group is far from symmetrical and shows 

 its chief mode on the wrong grade. 



It appears therefore that, while Punnett's three-factor h3rpothesis 

 may, with the aid of a number of carefully framed secondary hypotheses, 

 be made to fit fairly well the observed results for the F^ generation, it 

 fails to agree at all well with the observed results in the more critical 



Journ. of Gen. x 21 



