6 NILS ODHNER, NORTHERN AND ARCTIC INVERTEBRATES. V. PROSOBRANCHIA. 1 DIOTOCARDIA. 
tricets. On the horizontal or X-axis, the absolute height of the shell (taken verti- 
cally from the spire to the lowest part of the base) has been marked; its breadth 
or diameter (taken perpendicularly to the height), as well as the height of aperture, 
has been marked on the vertical or Y-axis. A specimen may, for example, have a 
height of 13, a diameter of 16.3 and an aperture height of 7.5 mm (see Fig. 1). The 
number 13 is then found on the horizontal or X-axis, the number 16.3 is to be marked 
vertically over 13 (by following the Y-axis), and the number 7.5 is to be marked in 
the same manner vertically over 13. The points thus obtained consequently show, 
that a specimen of the height 13 has a diameter of 16.8 and an aperture height of 
7.5 mm. By measuring more specimens of the height 13 it will be found that some 
have a diameter of 16.2, others 15.5 or 15 mm etc., and that the aperture height is 
in the respective cases 8.2, 7 and 7.2 mm. All these numbers are to be marked verti- 
cally over 13. The points thus obtained show that a specimen of the height 13 may 
have a diameter of 16.32—15 mm and an aperture height of 8.2—7 mm. When a very 
great number of specimens with the height 13 has been measured, all the points thus 
obtained mark the general extent of variation of diameter and aperture height in 
specimens of 13 mm in height. When the same process is performed with specimens 
of other heights, it is obvious that the points mark the extent of variation of dia- 
meter and aperture height within all these classes. By connecting the extreme points, 
which represent the extreme values, a curve is obtained, which marks the limits of 
variation of the characters under consideration. Such limits are represented by the 
lines in the diagrams. They have been constructed on the bases of a relatively small 
number of specimens and have therefore only an approximate value. They mark the 
boundaries of: distinct zones, which indicate the extent of variation of respective 
characters; thus the upper zone in Figs. 1--3 shows the extent of variation of the 
shell diameter, the lower one that of the aperture height. 
Comparing these curves with one another, the following results may be estab- 
lished: — The largest specimens are from Spitzbergen, the next in order being the 
Greenland specimens, then those from Iceland and, lastly, the Norwegian ones. The 
first-named districts, moreover, show a different position both absolute and relative 
of the variation zones, falling higher in the coordinate system than the zones of 
Iceland and Norway; consequently the species has, in general, a greater breadth and 
a higher aperture in Spitzbergen and Greenland. But the specimens from Iceland 
and Norway fall within the lower part of the zones of Greenland and Spitzbergen, 
which proves that the latter forms occur in all the districts mentioned. This fact 
is most plainly evident in respect to Spitzbergen, where the zones are narrower; the 
values of some, which are higher, fall above the limits for the majority of specimens. 
These latter accord with the Norwegian form; they seem to be rarer at Spitzbergen 
than at Greenland. 
The broader form, with a wider aperture, which is responsible for the high parts 
of the zones, is the variety umbilicalis. This form also occurs on the Norwegian 
coast, as is evident from curve 3, where some specimens fall above the highest limit; 
they are however very sparse. 
