W. F. R. Weldon 233 
which are given. From what has been said concerning yellow and green coty- 
ledons, it is evident that the chance of getting a dominant character in a plant of 
the second hybrid generation is the chance that one or other of three combinations, 
out of four which are all possible and equally probable, occurred during the fusion 
of the gametes which gave rise to the plant. The chance that a given plant of the 
second hybrid generation will present dominant charactei's is therefore |; and the 
records may be treated as attempts to verify this experimentally. Now if a series 
of n things be observed, and the chance that any one of them has a particular 
character is f, the "probable error" of the expectation that |n of the things 
observed will show this character is well kuown to be 0 67449 V?i x | x |; so that if 
a number of such series are observed, in half of them the frequency with which 
the desired character occurs will lie between the lim its In ± 0-67449 V» x | x i 
and in half of them it will lie outside these limits. In each of Mendel's records 
of a second hybrid generation the probable error has been calculated, and the 
result is shown in the following table : 
TABLE I. 
Individuals with Dominant Characters in the Second Hybrid Generation. 
Characters Crossed 
Individuals of 
SecondHybrid 
Generation 
Number of 
Dominant 
Individuals 
Dominant 
Individuals 
on Mendel's 
Theory 
Probable 
Error of 
Theory 
Deviation of 
Observation 
from Theory 
1. (Shape of Seeds) 
7324 
5474 
5493 
+ 24-995 
-19 
2. (Colour of Cotyledons) ... 
8023 
6022 
6017-25 
+ 26-160 
+ 4-75 
3. (Colour of Seed Coatsl... 
929 
705 
696-75 
+ 8-902 
+ 8-25 
4. (Shape of Pod) ... 
1181 
882 
885-75 
+ 10-0.37 
- 3-75 
5. (Colour of Pod) 
580 
428 
435 
+ 7-034 
- 7 
6. (Distribution of Flowers) 
858 
651 
643-5 
+ 8-555 
+ 7-5 
7. (Height of Plant) 
1064 
787 
798 
+ 9-527 
-11 
Here are seven determinations of a frequency which is said to obey the law of 
Chance. Only one determination has a deviation from the hypothetical frequency 
greater than the probable error of the determination, and one has a deviation 
sensibly equal to the probable error ; so that a discrepancy between the hypothesis 
and the observations which is equal to or greater than the probable error occurs 
twice out of seven times, and deviations much greater than the probable error do 
not occur at all. These results then accord so remarkably with Mendel's summary 
of them that if they were repeated a second time, under similar conditions and on a 
similar scale, the chance that the agreement between observation and hypothesis 
would be worse than that actually obtained is about 16 to 1. 
The accuracy with which the theory fits the results obtained in the third 
hybrid generation may be tested in the same way. The plants of the second 
generation, which exhibit recessive characters, ought to produce offspring which 
Biometrika i 22 
