A. D. Darbishire. 
16 
general rule which statisticians employ is that deviations very 
seldom occur at a distance outside the Probable Error which is 
more than four times as great as that between the Probable Error 
and the mean. It should not, however, be forgotten that half the 
deviations are expected to fall outside and half inside the Probable 
Error; so that if a long series of results accord so closely with 
expectation that all of them fall inside the Probable Error there 
is ground for believing that they have been invented. The formula 
for calculating the Probable Error is as follows :— 
100 [0-67449 x \J a (1—")] 
* 
in which x is the total number of individuals (in the case of a 
Mendelian F 2 for instance); and a is the number (of recessives in 
the case under discussion), the Probable Error of whose percentage 
of the whole number is to be calculated. 
Let me give an instance 1 in which the accordance between 
observation and expectation has been tested by means of this 
formula. The experiment in which I tested the theory of ancestral 
contribution consisted of crossing a pure yellow cotyledoned Pea 
with an “extracted” green one belonging to the F 5 generation, and 
in determining the ratio of greens in the F 2 derived from this cross. 
Eight different races of yellow Peas were employed in making these 
crosses, and the proportion of greens occurring in the F 2 generations 
derived from each of these yellow- races was determined separately. 
They are given in the following Table, together with the actual 
number of yellows and of greens, the actual deviation from 25%, and 
the Probable Error in each case. The total F 2 has also been 
classified with regard to the ancestry of the green parent of the 
cross (the crosses having been made on three plants of different 
ancestry) so that the total F 2 may be sub-divided into eleven groups, 
eight being derived from classification according to the yellow 
ancestor of the cross, three according to classification by the 
green ancestor of the cross. In six of these eleven groups the 
deviation is in the plus direction, in five in the minus direction. It 
w-ill further be seen that seven of the deviations (478, 479, 481, 482, 
493, 483 and 484) fall within the Probable Error, and that the 
1 These results appeared in Proc. Roy. Soc., Vol. 81, B, p. 61, 
it SiiJ . 
