- 1892.] Conflict Between Organisms. 923 
A GEOMETRICAL REPRESENTATION OF THE REL- 
ATIVE INTENSITY OF THE CONFLICT BETWEEN 
ORGANISMS. 
By Jonn A. RYDER. 
For our present purpose an organism may be thought of as 
a geometrical point in space. If such a point or organism is 
surrounded upon all sides by a homogeneous medium, such as 
air or water, it may be thought of as similarly related to the 
six faces of an enveloping or circumscribed cube, provided, the 
point or organism be placed at the point where the four diago- 
nals bisect each other that pass through the cube from one to 
the other of its four pairs of trihedral angles or corners. The 
point or organism may be thought of as if placed at o in 
the diagram (fig. 1); 
the diagonals, which 
ers | determine its posi- 
@ g tion in such an ideal 
E y or imaginary cubic 
poo 4 
i x . . 
ba = portion of space, will 
h ee LNA | be, ab, od, of and gh. 
P x . may cota The relations of the 
Be ie fe ay Al Fo point o would be 
; 4 equally well deter- 
7 ; mined by the three 
axes, x, Y, z, joining 
the centres each to 
Fic. 1. each of the three 
pairs of faces of any such ideal enveloping cube. We may 
suppose further that the point or organism at o, if it moves 
from place to place, simply alters the position in space of the 
ideal enveloping cube of which it is always conceived to be the 
central point. 
The possible number of ways of approach from every point 
on the surface of such a cubical fragment of space to the point 
x 
E 
