ALIGNMENTS OF ANCIENT SITES IN ESSEX 67 such as Merk-stones, Mark's Ley, Stock, Cross Leys, etc., lies along these lines." (The Old Straight Track, p. 194.) Apart from the convenient etceteras, if this correspondent from Chelmsford really did write Mark's Ley for, pre- sumably, Mark's Tey, then we see to what lengths self-deception can be carried. Watkins' opponents, when they deigned to speak at all, contented themselves by saying that the theory was archaeologically preposterous and by asking whether, after all, it was not to be expected that one would find four or five ancient sites more or less in a straight line in an area of twenty or thirty miles square. These controversial arguments and their appeal to emotion seemed to me inconclusive; therefore I have recently subjected the alleged facts to scrutiny of a kind which does not seek to support or to disprove the archaeological con- clusions, but only to investigate whether the alleged alignments, or some of them at least, are likely to be deliberate and purposeful, or whether they would arise by chance among large numbers of sites distributed at random, without human intention that the sites should be so aligned. As I have chosen Essex as the field for my enquiry, I believe you may be more interested in my conclusions : I am well aware that this choice may seem not entirely fair to a theory originally developed from sites in the West Country, but we have Watkins' repeated assertion that he had abundant confirmation from London and East Anglia, as well as from other parts of England, so there is no real injustice in my choice of Essex. I will first describe the critical apparatus and then deal with the results. There is a peculiar branch of mathematics dealing with the laws of chance; as many of you know, it is possible to calculate, for example, how often three "heads" should turn up among four pennies tossed in a group. The mathe- maticians are quite clear about this, and if they found that a batch of Mint pennies gave consistently different results from that predicted, they would have no hesitation in ascribing the difference to conscious human intervention.