W. F. R. Weldon 
119 
With probable errors of the order indicated by Tables I. and II., it is unlikely 
that any of these differences are significant. Even in the case of the last pair of 
entries the difference, although it is considerable (0 0229 mm.), is less than twice 
the probable error of the determination. 
There is therefore no evidence of change in the mean character of the peri- 
pheral spiral during growth : on the contrary, the mean value of a peripheral 
radius is seen to be the same, within the limits of error of the deterntiination, 
whether the radius be measured shortly after its formation, in young shells, or 
a long time afterwards, in the upper whorls of adult shells. 
The individuals of the two samples measured may be considered, with sufficient 
accuracy, to represent samples of two successive generations ; and the result 
obtained may be taken to show that the mean spii'al of the young generation 
is sensibly identical with that of the parental generation, and is not altered during 
growth by any process of selective destruction. That is to say, individuals of 
Glausilla laminata, taken from a very old beech-wood, in a country which the 
species is known to have inhabited at all events since pre-glacial time, are in such 
equilibrium with their surroundings that the mean character of the shell spiral 
(so far as we have studied it) is the same from genei'ation to generation, and is not 
changed during the course of a generation by any process of selective destruction. 
If the view of inheritance, formulated by Mr Galton* and generalised by 
Professor Pearson f, be true, the mean character of a race can be fixed by natural 
selection in a far shorter time than is generally supposed ; and we should be 
prepared to find local races in which the mean is sensibly stable through successive 
generations, in areas which have been inhabited even for a comparatively short 
period. It is, however, not necessary that tlie variability of such a race should be 
the same at all periods of growth. Prufessor Pearson has pointed out that if the 
law of inheritance referred to be approximately true, then a process of selection, so 
stringent that only individuals which accurately correspond to a particular type 
are allowed to breed, will fix this type as the mean of every genei'ation after it has 
operated for a small number of generations ; but even after such a selective process 
has operated for an indefinite time, the variability of young will be greater than 
that of the parental generation by an amount depending on the variability of the 
race at the time when selection began to operate. So that we may generally 
expect to find a reduction in the variability of a race during growth, long after 
selection has rendered the mean constant]:. Such selective destruction, which 
reduces the variability in every generation without changing its mean character, 
is what Professor Pearson calls " periodic selection." 
In order to discover whether periodic selection is acting upon Clausilia lami- 
nata in Gremsmlihlen or not, it is necessary to determine the variability of the 
* Galton ; Boxj. Soc. Proc. Vol. 61, p. 402. 
t Pearson ; Roij. Soc. Proc. Vol. 62, p. 400. 
X For a discussion of the residual variability here referred to, see Pearson ; Grammar of Science, 
p. 384, and Phil. Trans. 1901 (in course of publication). 
