Another proposition which Allen established as a rule of conduct was that between two trading towns in the same neighbourhood there must almost of necessity be correspondence. He noticed with surprise that between Stone and Coventry, according to the vouchers sent him, not a single letter had passed during a whole quarter. "I will not say it is impossible," he writes to the surveyor, "that no letters should during this time pass between such trading places, but during your stay at Stone I must in a particular manner desire you will examine whether you receive none."
A third proposition was that there could not be what, if it be not a contradiction in terms, we will call a one-sided correspondence. He regarded it as an absolute certainty, amounting almost to an axiom, that whatever number of letters a town might receive, it would send the same or nearly the same number in reply. If, therefore, as between two towns, he found from his vouchers that one was sending to the other more letters than the other sent in return, he immediately concluded that something was wrong. It is interesting to note how his views on this point were confirmed by experience. During the year 1732 the postage on letters sent from Nottingham to Newark amounted to £25, whereas on those sent from Newark to Nottingham it amounted to only £13. Surely, writes Allen, the amounts should be nearly equal. Ascertain whether this comes "from faults, errors, or a real deadness in the correspondence," and to enable him to do this the surveyor was to take the Newark office under his care for a week or a fortnight. Here Allen speaks with confidence indeed, and yet as though some doubt might exist; but a few years later there is no doubt at all. "In the Chipping Norton vouchers," he writes, "another remarkable oddness is that the letters received by that deputy appear to be double the number sent from that office, which is not only different from any other well-managed office, but 'tis out of all rules of proportion with respect to correspondence." And again, "The receipt of Chipping Norton's letters are still double the number of what Mr. Mackerness in his vouchers enters as sent from his stage. I can't conceive how 'tis possible for this difference to arise where an office is justly managed. Fully examine into the cause of it."