288 
Proceedings of the Royal Society of Edinburgh. [Sess. 
uniform source on one side of a straight line, and therefore may be 
ax- 
represented by y = ae~k ' 
To obtain the form of distribution the ground on both terraces was 
lined with parallel lengths of string two feet apart for a distance of fifteen 
yards, and the number of plants in each rectangular space counted. The 
numbers are given in this table : — 
Number of Plants. 
Distance. 
Upper Terrace. 
Lower Terrace, j 
■ 
0- 2 feet 
140 
1 
201 
2- 4 
47 
157 
4- 8 „ 
39 
99 
8-10 „ 
24 
50 
10-19. „ 
17 
22 
12-14 „ 
10 
20 
14-16 „ 
9 
16 
16-18 „ 
5 
4 
18-20 „ 
7 
12 
20-22 „ 
3 
6 
22-24 „ 
4 
3 
24-26 „ 
3 
3 
26-28 „ 
1 
3 
28-30 „ 
3 
4 
30-32 „ 
1 
32-34 „ 
1 
Total 
312 
605 
The equation of the theoretical curves are : — 
X 
Higher terrace y = 1 27e ~ 2-458‘ 
X 
Lower „ y = 24>8e~2 7 ^' 
The two areas show a practically identical distribution, with the excep- 
tion that the seed spreads to twice the extent on the lower than on the 
higher terrace. The nature of the fit is shown on the diagram, and as the 
soil of the locality is all forced, clay coming to the surface in patches, and 
drainage being very irregular, it is as good as might be expected, 
r 
Conclusions. 
(1) The general principles which underlie both epidemic distribution in 
space and time and random migration are identical. 
(2) Both can be deduced almost directly from the laws of chance through 
assumptions which have considerable a priori probability. 
