W. F. R. Weldon 
115 
and other sections may be treated in a similar way. Since all the measures in any 
section are known to be 180° apart, the position of one, relatively to the plane of 
reference, determines that of all the others. 
By the means described, the position of every radius measured, with reference 
to the standard plane, was determined : and the length of each radius, in its proper 
position, is shown in Fig. 2, where the ordinate of every dot gives the length, and 
the abscissa the distance from the standard plane, of a single radius. The whole 
number of dots in the figure should be 1949, since this was the whole number of 
radii measured in the hundred shells : but many of the measures coincide in a 
diagram of this scale, so that the actual number of dots visible is smaller. 
From these observations it was possible to determine a curve, representing 
a fairly close approximation to the law connecting change in the radius of the 
peripheral spiral with change in angular distance from the standard columellar 
radius. The determination was attempted in the following way. The observa- 
tions were first sorted into groups, such that no two observations in any group 
differed by 180° in angular distance from the standard plane; the "centroid" of 
each group, — the point whose ordinate is the mean length of all the radii in the 
group, while its abscissa is the mean angular distance of all these radii from the 
standai'd plane — was determined, and this point was considered to lie upon the 
curve required. An inspection of Fig. 8 shows that the curve I'equired is uniforndy 
convex to the base line, so that the centroid of any segment lies in reality outside 
and above it. Small portions of the curve are however so nearly straight that the 
error inti-oduced by the process adopted is not serious, at least in that portion 
of the curve which represents the upper part of the shell. 
For reasons which will presently be pointed out, I have not determined the 
probable error of the mean radius length in every group, but only in six of them. 
The mean radius length of every group, together with the probable error of the 
six groups for which it was determined, is given in the following table : 
8—2 
