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CHURCH ALINEMENTS AROUND ANDOVER

By Michael Behrend

The basic fact to be faced … is whether these mark-points or “monuments” (mounds or standing stones, or some other structure evolving from them on the same site), were designedly placed in line by man, or whether such alignment can be accidental.

Alfred Watkins

The question of how many accidental alinements can be expected among randomly placed points – a problem that has been exercising a number of mathematicians recently – is one which Watkins did face, and which he believed he had answered. He refers to it briefly in at least three books, The Old Straight Track (1925), The Ley Hunter’s Manual (1927), and Archaic Tracks Round Cambridge (19291932). In 1931 he published in the Antiquarian Association Journal a more detailed account, which was reprinted in the Journal of Geomancy, Vol. 2 No. 3. Here he tries to show, by reference to the 1-inch map of the Andover district (Ordnance Survey 3rd Series, Sheet 283) that alinements of four or more churches are more numerous than chance would allow. He had used the same example six years before, in The Old Straight Track, so presumably he thought it was fairly convincing.

Recently I have used a computer to search for all alinements of churches on the Andover map, in order to check Watkins’s findings. Before giving the results it is necessary to describe the methods that Watkins used.

If a mathematical model represents each site by a point, then an absolutely precise alinement has a probability of zero. So one has to start by specifying what kind of approximate alinement is allowed. There are various possibilities, but the criterion implied by Watkins in his paper of 1931 is as follows. Three points ACB are alined in that order provided that angle CAB or angle CBA (or both) is less than 0.25°. In general the points A, B, C, D, … form an alinement with end-points A and B provided that each of ACB, ADB, … is an alinement in the above sense. Using this definition, Watkins makes a rough calculation of the probability that 3 or 4 randomly placed points are in alinement. For 3 points he gets 1 in 240 (earlier, in The Ley Hunter’s Manual, he had said 1 in 720) and for 4 points he gets 1 in 43,200. The true figures will depend on the shape of the region concerned; but for a 3:2 rectangle such as the Andover map (18 × 12 inches) the probabilities are 1 in 140 for 3 points and 1 in 16,500 for 4 points. So Watkins’s admittedly rough and ready calculations give some idea of how many alinements to expect. But at heart he was a practical man, and when it came to assessing the results of his Andover survey he dropped his calculations and fell back on his method of counting alinements among X’s drawn at random on a sheet of paper. A pity, because by pushing his argument a step further he would have seen that something was going wrong with his random X method.

“I first tested (writes Watkins) how far the actual sites on the above map fell into alignment. I found 30 cases of three churches in line, seven cases of four in line; and one case of five. Then to test how much of this was accidental coincidence: on a blank sheet I marked (haphazard all over the sheet as before), 51 X’s. In these I found 33 cases of three in alignment, and only one case of four. Repeated tests with numbers up to 100 points on a sheet gave similar results, the number of three-point alignments increasing greatly with more points, but four-point alignments remaining very scarce.” And in Archaic Tracks Round Cambridge he says that “only one or two” 4-pointers were discoverable on a large sheet with 100 random points. However, it’s not hard to work out that from 100 points one can pick out nearly 4,000,000 sets of four; so that even if, as Watkins stated, only about 1 in 40,000 yields an alinement, there ought to be about 100 4-pointers on the sheet. If Watkins found “only one or two” he obviously wasn’t looking, hard enough, as he could have worked out himself. With 51 points on a sheet, his theory still predicts about six {111} 4-pointers. Only when the number of points is small do theory and experiment agree: on average, says Watkins, 9 points suffice to give one 3-pointer, which is about right.

The simplest explanation of this discrepancy is that as the number of points grows to several dozen, the task of finding all the alinements becomes much more arduous than Watkins suspected. In fact without modern computing facilities it’s hard to see how anyone could succeed in a reasonable length of time. Even on the actual map, where it was in his interest to find alinements, he found only a fraction of those present, as we shall see. Why he found fewer still among the random X’s is not clear, but there must have been a temptation (perhaps unconscious) not to look so hard there as on the map.

Now to summarize the alinements found on the 1-inch Andover map. Watkins chose this particular sheet (No. 233) because it was reproduced in O. G. S. Crawford’s “Andover District”, a monograph which “contains special information invaluable to ley-hunters”. (Watkins will have got no thanks from Crawford for this recommendation!) The map, according to Watkins, “contains 51 churches, practically all ancient ones”. Actually there are 55 churches, of which 10 are Victorian with no record, as far as I can find, of any previous church on the site. I included these modern churches, since they could always be ignored where necessary, and threw in 3 more churches from the modern 1-inch map (7th Series, Sheets 167 & 168), plus the former church at Ecchinswell which is not on either map but which, according to Crawford, was built on a pagan site. The grid reference for the centre of each church was estimated as accurately as possible from the 6-inch map, and an IBM 370 computer was told to print out all 3-point alinements, using the Watkins criterion with an angle of 0.50°.

We are really interested in alinements correct to 0.25° (I used a larger angle for possible future reference), and it turns out that the number of alinements on the map is just about equal to the expected number of accidental alinements. It makes no difference to this conclusion whether the Victorian churches are included or not.

The three 5-pointers are:

Amport – Monxton – Andover – Laverstoke (new) – Laverstoke (old)
S. Tidworth (new) – S. Tidworth (old) – Vernham Dean – Linkenholt – E. Woodhay
Tidcombe – Linkenholt – Faccombe – Burghclere (old) – Sydmonton

Of the 27 4-pointers, 13 are included in a 5-pointer and 14 are independent.

The third 5-pointer is the one mentioned in The Old Straight Track as being “convenient to verify”; the churches “align precisely”, says Watkins. Two years ago Chris Hutton Squire annoyed ley-hunters by stating in Undercurrents 16 that the line was inaccurate. In truth, the churches aline according to Watkins’s criterion but not Hutton Squire’s. Which criterion you adopt is a matter of choice, though the ley-width implied by accepting Watkins, viz. 65 metres, is bigger than many people would allow. In any case it was not a good example for him to choose, since Faccombe church was built only in 1866, to replace the medieval church a mile away at Netherton.

Our conclusion must be that Watkins was mistaken: there is no evidence that the alinements of churches in the Andover district are anything but accidental. Varying the critical angle makes no difference – in fact when it is increased to 0.50° the number of alinements falls below the chance level, e.g. 9 5-pointers versus an expected number of 22.8. This shortfall is ironical but probably not statistically significant.