1909. | OF THE LIMPET PATELLA VULGATA. PHYA 
Throughout all these changes there persists a great uniformity. 
The relation that L>B>Ab>Af>H had no exceptions in the 
one thousand and three shells measured, except that occasionally 
in small shells B equalled Ab. ‘The apex is wlways nearer to the 
anterior margin than to the posterior margin. The greatest 
breadth is invariably behind the apex, and ‘usually behind the 
middle point of the shell, so that the outline of the margin is not 
an ellipse. Some results published by Malard (7) are “obtained 
upon the assumption that the outline of the shell-margin may he 
treated as an ellipse. The index of ellipticity is calculated for 
several subspecies of Patella, and also an index of height. It 
does not appear that any allowance v as made for the differences 
in the ratio of length to breadth and ob each to height, which are 
found in shells of different lengths. For a form collected at. 
Barfleur the index of ellipticity was 6908; the curve of fr equency 
was asymmetric and of Type J. Malard’ s inference that in this 
case selection was more pronounced in one divection than the 
other is quite unjustified. 
The question naturally arises, are these changes in shape 
simply due to “laws of growth,” or are they brought about 
by selection? It seems fairly certain that the changes in the 
‘atios of the various dimensions of the shell are not due to the 
action of a process of natural selection, and that for two reasons : 
first, the changes are perfectly continuous and gradual from 
stage to stage ; “second, they are exhibited by every shell without 
exception. If the changes were due in any marked degree to the 
action of natural selection, a process of differential destruction 
must have been active at all stages, and one would expect to find 
dead shells which did not exhibit in their shape the changes 
which all good-sized limpets show. But such shells ave not to be 
met with. 
It can indeed be proved directly that the changes in shape 
may take place without the action of natural selection For 
instance, 76 shells of 40-45 mm. length were collected at the 
Cloch, Gourock, and the mean breadth at a length of 40-42°5 mm. 
was calculated. The value obtained was 35°1448 mm., and his 
ratio of length to breadth was 1174. The mean breadth at + 
length of 15-17-5 mm. was also calculated from measurements of 
50 to 60 of these shells, advantage being taken of the lines of 
growth visible on the shell. (A few shells 38-40 mm. in length, 
collected at the same time as the 40-45 mm. set, were measured 
in order to make up ee number to 60.) The ratio of length to 
breadth at this length was 1:26. The ratio of length to breadth 
in 60 shells 15- 17-5 mm. in length collected at tite same place 
and time as the large shells was 1:24. Now within the group 
composed of the 60 large shells natural selection has not acted, 
for natural selection Le by elimination, and there has been no 
elimination within the group. It is true that selection may have 
been at work before the ler vgth of 15-17°5 mm. was reached, and 
that these shells may r epresent a selected sample of the population 
below 15-17°5 mm. It is true also that natural selection me ay 
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