344 BOTANICAL GAZETTE [NOVEMBER 
results. For this reason it is necessary to describe in some detail 
the method which was elaborated. First, for delimiting the region 
about the hole within which the hyphae were to be considered, the 
following rule was employed. Only those hyphae growing from 
spores which chanced to be located in a cylinder of medium situated 
over the hole were taken into consideration. This cylinder was 
delimited as nearly as possible by the eye, in such a way that the 
center of its base coincided with the center of the hole, its diameter 
being 3 times that of the hole. Although the holes varied consider- 
ably in diameter (8-45 u), it was found that the average was about 
16, and that, by turning the fine adjustment of the microscope a 
suitable number of revolutions, a thickness of medium would be 
traversed approximately equal to one diameter of the hole. In all 
cases the hyphae coming from spores directly over the hole, that is, 
in an inner cylinder with the hole as its base, were neglected, owing 
to the difficulty in many cases of assigning a definite direction to 
them. Thus the region in which the germ tubes were considered 
was a cylindrical zone concentric with the hole, and equal in width 
and height to one diameter of the hole. 
It is of course clear that the whole purpose of the adoption of 
this arbitrary region was to secure uniformity of conditions for 
collecting the data. For the most exact work, indeed, the portion 
of the medium chosen for examination should correspond to a hem- 
isphere whose base coincides with the base of the above described 
cylinder, and: thus has a radius equal to 1.5 times the diameter of 
the hole. However, it is practically impossible to define the out- 
line of such a hemisphere with any accuracy by focusing, and so a 
cylinder of the dimensions described was chosen as the nearest 
practical approximation. 
The next step was to determine as accurately as possible the 
direction taken by the hyphae. An imaginary straight line was 
projected from the center of the hole to the spore itself, in cases 
where the germ tube was fairly straight (fig. 1); if, however, the 
germ tube curved markedly, this method was modified slightly, as 
explained below. This line was supposed to make angles of 45° 
with two other imaginary lines intersecting one another at right 
angles at the spore. The 4 regions, of go° each, thus marked out by 
