§ 7. In the above estimates, I have allowed to the so-called coincidence the rather wide limit of 12 hours. But in most of the actual cases it has been much closer than this; and it will be worth while to show how a single case of very close coincidence may legitimately strengthen the argument. First, it must be unreservedly admitted that a single case, if it stood alone and no similar one had ever been heard of, would have no cogency whatever as evidence of the operation of anything beyond chance. The most extraordinary coincidence, as above remarked, may yet be totally insignificant. The d priori improbability that the tallest man of the century will be born during a transit of Venus is enormous; but such a conjunction of events, if it happened, might be at once and with moral certainty ascribed to accident; and with equal certainty might it be predicted that such a conjunction would never recur. And without resorting to imaginary examples, we often encounter conjunctions and coincidences which would have appeared, before they happened, to be extremely improbable, but the happening of which is none the less clearly accidental.

The odds are very great against two of the foremost men in a century being born on the same day; yet this happened in the case of Darwin and Lincoln, and no one imagines that one birth depended on the other. "Extraordinary coincidences" are, in fact, quite ordinary things; and only when previous experience has given us ground for suspecting (however faintly) that the conjunction in time or special combination is due to some positive causal link, can we connect the d priori improbability of a new case with an d posteriori argument that cases of that type are not due to chance.1 Now the result of § 6 may be summarised as follows. The census leads us to infer that, during the years 1874-85, out of 300,000 inhabitants of this country taken at random, 23x300.000/5705 or 1209 have had a recognised visual hallucination, representing a living person, which did not coincide with the death of that person. And during the same period, out of the same number of persons (supposing our inquiries really to have extended to so wide a circle), at least 21 have had a recognised visual hallucination which did coincide - in the sense of falling within 12 hours of - the death of the person seen.

That is, our of 12094 + 21 or 1230 hallucinations, 21, or 1 in 59, have fallen within 12 hours of the death of the person seen. Now let us apply this conclusion to case 28 (p. 152). When Mr. S. had his visual hallucination representing his friend, he would have been justified in regarding the probability that his friend would prove to have died within 12 hours of the vision as 1 in 59; whereas, if there was no ground at all for surmising that a causal connection may exist between deaths and apparitions, he would only have been justified in regarding the probability of his friend's dying on that day as about 1 in 20,440 - estimated from the death-rate which tables of mortality give for men of his friend's age (48 years). But it will be observed that the death and the apparition, for aught we know, were absolutely simultaneous, and at any rate were within a quarter of an hour of one another. Since, however, the death may have occurred 12 minutes before or 12 minutes after the apparition, we must take into account the double period; or, to allow for difference of clocks, let us say half an hour.

Now, on the supposition that telepathy is a reality in the world, closeness of coincidence rather increases than otherwise the probability that the death and the apparition in any particular case are causally connected; whereas the probability of a death accidentally falling in a particular half-hour is, of course, 48 times less than that of its falling on a particular day. Thus the a priori probability that the death, if unconnected with the apparition, would fall in the particular half-hour in which the apparition fell, was 1 in 981,120; and in considering the question of connection, it is this extremely small degree of probability which has to be contrasted with the 1 in 59 which we have taken as about the true a priori probability that this particular half-hour would prove to be that of the death.

1 In a general way, coincidences where previous experience affords some ground for suspecting (however faintly) a cause other than chance are distinguished from coincidences where no such ground exists by this fact - that the latter sort of cases, if a priori highly improbable, are not mentioned or described until after they have happened. From the mere fact that they do not belong to any known or surmised type, they do not enter into anyone's head: no one suggests, without any sort of grounds, that a particular thing will happen to some one at a particular time, or predicts any particular highly improbable coincidence, and then afterwards finds this thing or this coincidence actually occurring. Now it will scarcely be contended that the coincidence of an apparition with the death of the person seen is a combination of events which has never entered anyone's head; for it has entered the heads even of those who deny that it has ever occurred, or who ascribe its occurrence to accident. But the idea has of course had much more than this negative sort of existence; there has been a good deal of positive belief that such combinations occur, and that their "occurrence implies a causal connection between the death and the apparition.