W. F. R. Weldon 
235 
Since there are four possible combinations of each pair of characters, the 
number of possible combinations of the three pairs of characters is clearly 4^ = 64; 
and if we consider the union of male dominant with female recessive gametes to be 
the same as that of female dominant and male recessive, the number of different 
combinations is 27. Of these 27 different combinations, eight will each occur 
once, 12 will each occur twice, six will each occur four times, and one will occur 
eight times, in 64. The combinations actually deduced from the behaviour of the 
hybrids of the second genei-ation and their offspring occurred with the following 
frequencies in the 639 plants : 
TABLE III. 
Frequency of the various possible combinations of Characters in Hybrids of the 
Second Generation from Races which differed in three Characters. 
Combination 
Frequency 
Combination 
Frequency 
Combination 
Frequency 
AABBCC 
8 
AABBCc 
22 
AABBcc 
14 
AAbbCc 
17 
AABbCc 
45 
AAbbCC 
9 
aaBBCc 
25 
aaBbCc 
36 
AAbbcc 
11 
aabbCc 
20 
AaBBCc 
38 
aaBBCC 
8 
AABbCC 
15 
AabbCc 
40 
aaBBcc 
10 
AABbcc 
18 
AaBbCC 
49 
aabbCC 
10 
aaBbC'G 
19 
AaBbcc 
48 
aabbcc 
7 
aaBbcc 
24 
AaBBCC 
14 
AaBbCc 
78 
AaBBcc 
18 
AabbCC 
20 
Aabbcc 
16 
These numbers are all correlated, so that the system of results must be judged 
as a whole. Applying the method of Pearson (No. 25) the chance that a system 
will exhibit deviations as great as or greater than these from the result indicated 
by Mendel's hypothesis is about 0'95 (see Elderton, this Journal, ante, p. 161), 
or if the experiment were repeated a hundred times, we should expect to get a 
worse result about 95 times, or the odds against a result as good as this or better 
are 20 to 1. 
Mendel's statements are based upon work extending over eight years. The 
remarkable results obtained are well worth even the great amount of labour 
they must have cost, and the question at once arises, how far the laws deduced 
from them are of general application. It is almost a matter of common knowledge 
that they do not hold for all characters, even in Peas, and Mendel does not suggest 
that they do. At the same time I see no escape from the conclusion that they 
do not hold universally for the characters of Peas which Mendel so carefully 
describes. In trying to summarise the evidence on which my opinion rests, I have 
no wish to belittle the importance of Mendel's achievement. I wish simply to 
call attention to a series of facts which seem to me to suggest fruitful lines of 
enquiry. 
22—2 
