W. F. R. Weldon 
301 
Having made the measurements of all the sections, it was necessary to find 
some way of making the results, obtained from one section, comparable with those 
obtained from another. All that is known about the plane of a given section is, 
that it is one of the infinite number of planes passing approximately through the 
axis of the shell. There is no way of determining the angle between the plane of 
a section and that in which the spiral itself begins. 
In comparing sections of C. laminata, the measures of the peripheral radius 
(the only character studied) were tabulated by reference to their angular distance 
from the plane containing a columellar radius 5 ram. long. Such a method, applied 
to young and old alike, gives results which are strictly comparable, and it therefore 
gives a reliable measure of the relative variability in young and in adults ; it has 
however the great disadvantage that the absolute variability is so distorted that 
the standard deviation of peripheral radii, actually obtained, is nearly worthless as 
an indication of variability. 
For the purposes of the present enquiry, an attempt was made, within the 
limits of every successive 180°, to determine first the mean length and standard 
deviation of each of the three elements measured, considered by itself, and secondly 
the meau and standard deviation of the array of any one element, associated with a 
fixed type of one or of both the others. Thus, starting with a columellar radius of 
2 mm., in adult shells, and taking every length of this radius which occurred in 
the following half-revolution, it was found that the range of columellar radii in this 
particular half-revolution was from 2"00 to 2*49 mm. The mean and standard 
deviation of this group was determined. Taking the values of P and of p, associated 
with these values of G, the mean and s.D. of each of these was also determined ; 
then, by making the three correlation-tables between 0 and P, G and p, P and p, 
the mean value and the standard deviation of any one of the three sets of measures, 
associated with fixed type of either or both the others, could also be found. 
The mean values of the characters measuretl, as well as their standard devia- 
tions, are given for young and for adults in Table I : it will be seen that they are 
roughly identical. The degree of identity of mean character in corresponding- 
regions of the young and adult shells cannot, however, be adequately judged from 
these results. Each entry in Table I, except those in the first column, records the 
Mean or the Standard Deviation of a character, as determined for a group of cases 
in which the columellar radius varied in length between the fixed limits given in 
the first column ; but within these limits, the mean value of the columellar radius, 
and its standard deviation, are largely affected by the mean position and standard 
deviation of position of the planes in which the sections were cut. These quantities 
cannot be directly determined, and we have no right to assume without evidence 
that the mean position of the adult sections, with reference to the origin of the 
shell-spiral, was exactly the same as that of the sections of young individuals. In 
order to compare the two sets of results in a more useful way, the regression of 
pei'ipheral radius-length and that of perpendicular on the length of the columellar 
radius has been determined from the correlation tables for all the measurements 
