68 THE ESSEX NATURALIST
What I have done is to use this kind of mathematics to
calculate the number of chance alignments which will arise
among sites distributed at random, and then to determine
the number of actual site-alignments in three areas of Essex.
If the number of multiple-site alignments in Essex should
prove to be significantly greater than would be expected
from among the same number of sites distributed purely at
random, then it would be scientifically improper to reject
Watkins' theory out of hand, however improbable the
archaeological basis might seem.
I give the detailed calculus in an appendix and will here
seek to show that the mathematics is reliable by taking a
deliberate random scattering and demonstrating how well
the results of calculation agree with the alignments found
in that case.
I scattered fifty beans on a sheet of paper the size of a
1" O.S. Map sheet and marked the nearest part of each
bean-shadow on the paper. The results are shown below.
Table 1
Sample of random distribution of 50 spots and the align-
ments resulting by chance among them :—
Order of Calculated expectation Alignments
Alignment from theory actually found
3-spot ...... 52 ...... 54
4-spot ... ... 5 ... ... 4
5-spot ... less than 1 ... ... 0
The third column shows the number of alignments actually
found after the somewhat laborious task of checking the
1,225 separate possible alignments. If the actual results are
compared with column 2, which gives the calculated ex-
pectations, it will be seen that the theoretical basis of my
calculation is confirmed by reasonably close agreement with
experiment in this case.
Again to do Watkins justice, he has not entirely ignored
this critical aspect, and I must quote from his chapter 27,
entitled "Obscurities and Objections":—
''An objection which has partial foundation in fact is that
alignments cannot be assumed to be designed, but result