920 
are found to produce two further new 
comb types, walnut in the F, and single in 
the F, generations. The whole result 
harmonizes with the assumption that we 
have here two allelomorphic pairs—rose 
present and absent and pea present and 
absent—the absence in each case resulting 
in single comb. 
The real discovery here is that two birds 
visibly differing in the one feature of comb 
character do not produce monohybrid off- 
spring, as in the case of the green and yel- 
low peas, but show on breeding that the 
qualities pea and rose comb belong to sep- 
arate allelomorphic pairs. This permits of 
four kinds of gametes and sixteen different 
combinations in the F, generation. That 
is, the result resembles that of a dihybrid 
rather than a monohybrid combination. 
It is really a case of the assumption of 
two factors as responsible for a single unit 
character. And the use of the presence 
and absence hypothesis perhaps tends to 
obscure the real facts. Single comb is 
superficially at least just as positive a 
character as pea or rose comb. Single 
comb is found to occur in the absence of 
either pea or rose comb. If the absence 
had not happened to have the same result 
in both cases—if, for example, absence of 
pea comb had meant no comb, then the 
eross would have had a still different re- 
sult. Stated in plain terms, the experi- 
ment shows that in applying Mendel’s 
principles to a wider and wider range of 
experimental material we find it necessary 
to provide for a much greater degree of 
variability in our results than was antici- 
pated. The pre-Mendelian dogma of the 
breaking-up of the F’, generation is to this 
degree vindicated. 
This adoption of the presence and ab- 
sence hypothesis and of additional factors 
is probably an entirely correct method of 
procedure as far as it goes, and allows 
SCIENCE 
[N.S. Vou. XXXV. No. 911 
much more fully for the real variability 
which we find in heredity. 
That the increase of diversity with added 
pairs of differentiating characters in the 
parents should follow just this Mendelian 
law is, of course, only necessary on the as- 
sumption of fixed unit characters. It is a 
question whether it is sufficiently obvious 
that we need just twelve more groups in 
which to place our phenomena when we 
pass from the results of crossing parents 
with one visible difference to those with 
two visible differences. Perhaps some 
other number of groups would really 
classify the results of such a cross just as 
well as sixteen. 
It is to be remembered that the biometri- 
cian dealing with symbols can proceed 
with perfect certainty that his results will 
be mathematically correct without troub- 
ling himself in the least as to whether his 
series of symbols corresponds to any reali- 
ties. Handling a series of the combina- 
tions of numbers or letters from one to ten 
is very elementary mathematics, but to 
hold in mind and be able to visualize from 
day to day with certainty of a constant re- 
sult ten related colors and their combina- 
tions in a bed of snap-dragons is, as can be 
shown by appropriate tests, a matter of ex- 
pert training and considerable uncertainty. 
When we realize further that unit char- 
acters are not conceived as hard and fast 
categories, but as each having an allowed 
range of fluctuating variability, we can see 
that the chances of mistake in estimating 
the sixty-four classes of offspring which 
might come from a pair of parents differ- 
ing in three characters are very great. It 
is a matter of difficulty for the student of 
the problem and it is almost impossible for 
any one who reads of such results to pass 
any critical judgment on their probable 
accuracy. 
Formally the 
presence and absence 
