334 
On the Fundamental Conceptions of Biology 
of vital statistics. It must be admitted at oncej however, that in this discussion 
of evolution by discontinuous variations I have used the term not in the precise 
sense of any of the definitions discussed on p. 329, but in what appears to be 
the sense actually adopted by Mr Bateson in the body of his treatise, i.e. as a 
name for any abnormal value of a character in an individual which has not 
been linked up in continuous series with the bulk of the so-called normal popula- 
tion ; whether the abnormal character is path(jlogical or not, whether it could or 
could not be linked up if a large enough population were taken, is as a rule not 
discussed*. 
Yet it is to this vague " dififerentiant variation," represented in his book by 
apjDarently unlinked charactei' values, that Mr Bateson appeals for the basis of his 
theory of evolution. It is because I do not, according to him, recognise its exist- 
ence that my memoir on homotyposis is idle. Nay, rather because it is unrecog- 
nisable ! According to Mr Bateson it crosses and re-crosses normal variation in 
such a manner that the two cannot be distinguished. What in ray memoir 
on homotyposis I do recognise and try to avoid is a frequency distribution, the 
elements of which are not homogeneous, i.e. are not due to the same group of 
chance-causes, but are compounded of two or more series due wholly or in part to 
different groups of chance-causes "I". This is what I understand by differentiation, 
but it is something totally different from Mr Bateson's " differentiant variation," 
as illustrated in his treatise. It is, however, all that my memoir is concerned 
with, and I do not hold the tests for such differentiatioii peculiarly hard to 
apply. 
Mr Bateson takes the case of a syllid with numerous segments apparently 
undifferentiated but with marked differentiation of the segn^ents at the posterior 
and anterior ends. How, he asks, are we to consider which, if any, of these 
segments are suitable for investigating homotj'posis? Probably I should not take 
such a case for studying homotj'posis at all, for each segment may bear an organic 
relation to its neighbours ; there may well be a condition — as of fitting of adjacent 
parts — which is expressly excluded in the production of pure homotypes. But if 
Mr Bateson desires to know how I should determine whether there was differentia- 
tion of any significance between two of these segments for any chosen character, 
the biometric answer is perfectly simple. Measure the characters of these two 
particular segments in a sufficiently large population and determine whether the 
differences of the means and of the standard deviations are or are not sensible in 
comparison with the probable errors of those differences. If they are not, then 
* Of course Mr Bateson has distinctly stated that the continuity of the frequency distribution has 
nothing to do Avith his definition of discontinuity (see p. 328, above). But he certainly does not apply any 
other test than the apparent discontinuity of the frequency to the bulk of his cases, — he never applies 
any other of his own definitions. 
t E.g. n 2J-sided teetotums might stand for n chance-causes; each on a spin of the whole system 
would give results peculiar to that spin. A frequency curve based on those spins would be "homo- 
geneous"; but if in the middle of the operations, m of the n teetotums were replaced by 5-sided 
teetotums there would be differentiation iu the frequency in my sense. 
