K. Pearson 
335 
one set of segments may be looked upon as equivalent to a random sample of the 
other set and there is no class-differentiation. This method is so familiar to 
statisticians, who are using it every day to test whether a class is or is not 
differentiated from the general population, that it appears somewhat surprising 
that Mr Bateson should believe we are in the habit of detecting differentiation 
solely by an inspection of modes in seriations*. Whenever therefore there is a 
suspicion that " homologous " organs or parts, differing in (a) period of production, 
(b) regions of the organism where they are produced, (c) environmental conditions 
generall}^ are really differentiated, there is no difficulty for the trained biometri- 
cian in actually testing whether this differentiation exists, and, if so, the extent of 
it. The influence of such factors in the differentiation of homologous parts might 
be expressed in the following definition : 
If there be correlation between the means of the homologous parts produced 
and (a) the period of life at which they are produced, (b) the part of the organism 
in which they are produced, or (c) the environmental conditions under which they 
are produced, then we may call the arrays of organs produced under constant 
type conditions (a), (b) or (c) differentiated classes of homologous organs. But if 
the correlation between the mean characters of the arrays of organs and the factors 
(a), (b) or (c) be small or evanescent we term the organs undifferentiated. 
The differentiation in Nigella was recognised by the correlation between the 
segmentation and factor (6) long before the frequency diagram was reached. But 
surely one who has been through hundreds of distributions of variation in all kinds 
of types of life would recognise differentiation in the heavy line distribution of 
Diagi'am I. long before the next stage of determining the correlation was completed. 
Compare the distribution for Nigella with that for the veins in beech leaves of 
Diagram II. The variation in the latter is within the limits of random sampling 
a normal chance distribution. The former is seen at once to be heterogeneous. 
A change of environment alone suffices to emphasise the differentiation. The 
seed from the Nigella capsules was sown again in the following year, but very 
thinly, so that many capsules were produced on the side shoots : see dotted line 
in Diagram I. In this crop there was an average of 20 capsules to a plant, 
whereas 4 was about the average in the parental series. The distribution is so 
markedly bimodal that even Mr Bateson's third definition of discontinuity!" 
would exclude it from my " undifferentiated " like organs. Here the frequency 
of 6 segments is to that of 8 as 8 is to 3, but in a third sowing they were 
even as 9 to 2. Hence it follows that the number of capsules with about five 
segments or " low " capsules can be increased or diminished in relation to the 
" high " capsules by the environment of the plant. The material is therefore in my 
sense of the word heterogeneous or the like organs are differentiated, they stand in 
* The latter may be sometimes of use to suggest further examination, but this method is often a real 
danger when it is used by those ignorant of the extent of seriations which are solely due to random 
sampling. 
t See p. 330. 
