On the other hand, to obtain a fair estimate of the total number of recognised apparitions of living persons which had actually occurred, in order to compare these with the number of death-coincidences, the number of the former reported was raised, by making the correction for forgetfulness, to 1300 (v. Report, pp. 63-5, and p. 247 for details of the calculations). The final result was thus about 30 death-coincidences out of 1300 cases, or a proportion of about 1 in 43.

Since the average annual death-rate in England and Wales is 19.15 per 1000, (according to the Registrar-General's Report for 1890), the probability that any one person taken at random will die on a given day is 19.15 in 365,000, or about 1 in 19,000. This may be taken as the general probability that he will die on the day on which his apparition is seen and recognised, supposing that there is no causal connection between the apparition and the death. In other words, out of every 19,000 apparitions of living persons there should be by chance one death-coincidence.

But the actual proportion found, viz., 1 in 43, is equal to about 440 in 19,000, or 440 times the most probable number. Or, looking at the matter another way, we should require 30 x 19,000, or 570,000 apparitions to produce by chance 30 cases of death-coincidences. Of these apparitions, we may assume that about one-quarter, or 142,500, would be remembered. We should therefore expect to have to collect 142,500 cases, instead of 350, in order to obtain by chance 30 death-coincidences.

This is the case if we take, as we have done, death-coincidences to mean an apparition occurring within twelve hours of the death of the person seen. But the great majority of the coincidences are believed by the percipients to be closer than this, and the improbability of the apparition occurring by chance within an hour of the death is of course twelve times as great as that of its occurring within twelve hours of it.

This statistical result is of course worthless, unless the coincidences themselves are well authenticated. It is impossible to summarise the evidence for them, which would no doubt be estimated differently by different persons; but a large number of the best-evidenced cases are printed in the Report, and supposing that only a few of these are correctly reported, the proportion remains far too large to be attributed to chance.

The explanation of chance coincidence being thus put out of court, the opponent of a telepathic or other supernormal explanation must maintain one of three other hypotheses. (1) He may assert that the coincidences have been exaggerated to a much greater extent than the Committee allowed for; which argument can only be met by reference to the evidence - given fully in the Report - for the various cases. (2) He may suppose that they were specially sought after by the collectors and illegitimately introduced into the collection to a much larger extent in proportion to non-coincidental cases than was allowed for. Our reply would be that in twenty-six of the total number of death-coincidences, the collectors reported that they did not know of the case beforehand, and therefore could not have selected it to include. Sixteen of these cases are printed in the Report, so that the evidence for them can be studied. (3) Admitting that death-coincidences really exist, and are too frequent to be attributed to chance, it may be argued that the causal connection between hallucination and death is not telepathic, but consists in a condition favourable to hallucination being produced in the percipient in some normal way by the circumstances of the case; for instance, by anxiety about the dying person.

There is some evidence in the Report that mental tension, anxiety, or other emotional causes are to some extent favourable to hallucinations, and if a hallucination occurs, its form is likely to be determined by whatever subject the percipient is thinking of. But such a cause could only produce a death-coincidence if the percipient were aware of the dying person's condition, and in many of the cases reported (ten of which are printed in the Report), the percipient had not even heard of the dying person's illness. It was therefore impossible that anxiety should have caused the hallucination in those cases, and even in cases where some degree of anxiety existed, the closeness of the coincidence is inadequately accounted for by it.

The remainder of the Report treats of hallucinations coinciding with other events than deaths, collective hallucinations, premonitions, and what are called " local apparitions " - that is, those seen repeatedly in certain localities - and phantasms of the dead.

I must add that while this argument from statistics and percentages, capable as it is at once of accurate estimation and of indefinite extension, constitutes technically the strongest support of the thesis of causal connection between deaths and apparitions, it is yet by no means the only support, nor even the most practically convincing. Those deaths and those apparitions are not mere simple momentary facts, - as though we were dealing with two clocks which struck simultaneously. Each is a complex occurrence, and the correspondence is often much more than a mere coincidence of time alone. Sometimes, indeed, the alleged coincidence is so detailed and intimate that, if the evidence for a single case is fully believed, that case is enough to carry conviction.

The man, therefore, - he is common enough - who believes in one single case where he happens to know the people concerned, and yet discredits all other cases, is not quite so absurd as he seems; he does but exaggerate a mental attitude in itself easily explicable. One strong disintegrating shock has broken down his lifelong presumptions with more force than pages of unanswerable but dimly realised statistics.

And I admit that for myself the actual colloquy with trusted persons fresh from these experiences has brought home their reality to me with much more vividness than the study of equally good cases collected by my colleagues. I mention this because I think that students of these matters should spare no pains to get at cases first-hand, - should themselves talk with percipients; and should thus realise how deep and lasting a mark these incidents leave behind them.