ALIGNMENTS OF ANCIENT SITES IN ESSEX 73
due to chance, and in general the number of such alignments
is not significantly greater than would be expected from
among chance arrangements of sites.
But the rare residue of six, seven or more sites in align-
ment have great odds against their being due to chance, and
it may be that a thorough investigation of these "long leys"
in the field would be worth undertaking. The discovery of
a hitherto entirely unknown antiquity on one of these
alignments, still more the successful prediction that an
intersection of two or more alignments should result in such
a discovery, would be noteworthy triumphs for Watkins"
theory and could hardly be neglected by archaeologists.
Even so, there is a small but calculable chance of such
occurrences in a purely random distribution of sites. In the
cases I have considered earlier, the chance of an additional
site appearing on one of the alignments is about one to five
against, and at one of the existing intersections, one to
twenty against. I have no evidence for any significant
discovery of this kind in Essex.
As of most investigations to prove or disprove a carefully
elaborated theory, the result is neither a clear assent nor
dissent, and the likelihood, in my submission, is that there
may be some substance in Watkins' Theory of the Old
Straight Track, but not nearly as much as the enthusiasm
of the originator led him to believe. His work has this
merit : it has provoked much thought and has called atten-
tion to a possibility which, if not effective in the sense in
which its originator believed, may nevertheless prove fruitful
in other fields of archaeological research.
Although I cannot leave you with a decisive judgment on
The Old Straight Track, I hope to have shown that very few
rectilinear alignments of ancient sites in Essex are either
purposeful or archaeologically significant.
APPENDIX
THE PROBABILITY OF RANDOM RECTILINEAR ALIGNMENT
In this appendix, I give the essential steps in the calcula-
tion without formal statement of all the mathematics
involved.
The problem is to calculate the chance that three, four or
more spots of a given diameter s, out of a total number n