8 THE ESSEX NATURALIST
intercalated between the larger ones converging from the cir-
cumference of the cap towards the stipe. Between each
longer and its neighbouring shorter gill a still shorter one may
be inserted and so on. Buller points out that there tends to be
a series of gills of decreasing size expressed by x, x, 2x, 4x . . .
where x is the number of long gills.
Diameter of stipe in mm. (x)
Fig. 4. The (x)s represent diameters of pileus averaged against diameter
of stipe: 1166 determinations. The straight line would be obtained if stipe
width were proportional to pileus width. The curve is obtained if the cube of
the pileus diameter varies as the square of the stipe width. After Bond (1952).
If we consider two adjacent long gills in the region near the
stipe we may, perhaps, suppose that their distance apart is the
minimum consistent with efficient spore discharge. As we fol-
low them outwards towards the edge of the cap their distance
apart increases. However, it is not safe to intercalate a shorter
gill until the distance apart of the long gills is double the neces-
sary minimum and only then if the gill has a negligible thick-
ness (Fig. 5 Sector A: note that the safe distance between the
gills is here taken as 1 unit). We see then that as a method
of partitioning the under surface of the pileus radial gills are
rather inefficient because so much space is wasted by this
necessity to reach double the safe interval before inserting a