ALIGNMENTS OF ANCIENT SITES IN ESSEX 69
from accidental coincidence. Without fully probing the laws
of probability which govern this, I give one actual test . . .
the Andover Map (Sheet 283), which contains 51 churches,
and there are on it no less than 8 separate instances of 4
churches falling in a straight line ... To test that this might
be accidental, I took a similar-sized sheet of paper and
marked 51 crosses in haphazard distribution over it. Only
one instance could be found on this of four points
aligning ..." (The Old Straight Track, p.203.)
I have calculated, from those laws of probability which
he did not probe, the chances of finding alignments in the
case quoted by Watkins, on the assumption that the spots
and map-sheet sizes are similar to those of Essex, and I find
the results shown in Table 2.
Table 2
Watkins' investigation of Random Distribution.
Order of .. Calculated by me Pound by Watkins
... . for Random from Andover from his Random
Alignment 
 Distribution Map (283) Distil. J est
3-spot ... 96 ... 38 ... 31
4-spot ... 11 ... 8 ... 1
5-spot ... 1 ... 1 ... 0
It seems to me from the large discrepancy between the
calculated values and the number of alignments found by
Watkins on the map, that he had not fully tested all the
1,275 straight lines joining pairs of 51 sites : perhaps he had
not understood the magnitude of a complete check in this
case. Moreover, his discovery of only one-eleventh of the
4-spot alignments which one might expect to find among
51 crosses distributed at random, seems to me to point in
the same direction, unless his criterion of alignment is
inconceivably strict.
It may be objected that one or two tests of random
arrangements are inconclusive, and I agree; the statistical
value of the probable error diminishes with the square root
of the number of tests. But I have made many tests with
widely-different measures of number and size of spots, and
I can assure you that I have found no result which differs
more than 50 per cent from the calculated value, except