The proof of this proposition--the proof, that is, of the operation in certain cases of some distant cause external to the percipient's organism--lies in a numerical comparison of those hallucinations which coincide with an external event--_e.g._, the death of the person seen--and those which do not. For when the relative frequency of hallucinations has been ascertained the probability of chance coincidence in such cases can be exactly calculated. And should it appear that coincidental hallucinations are more frequent than chance would allow, it is certain that some other cause has to be sought for. And here we are met at the outset by a serious difficulty. It would appear from the results of the census just described that hallucinations even of a vivid and interesting character tend very quickly to be forgotten. Thus, to take only the cases of _realistic_ apparitions resembling a living person, we find 157 cases recorded as occurring during the last ten years, and only 166 as occurring more than ten years ago; although, as the average age of our informants is about 40, we might have anticipated that the latter number would be about three times as great as the former.[104] But the discrepancy becomes still more striking if the figures are examined in detail. The subjoined table gives the number of apparitions resembling the human form recorded for each of the last ten years:-- ---------------------------+------+---------+---+---+---+---+---+---+- No. of Years Ago-- |1 and | b'tw'n--|2-3|3-4|4-5|5-6|6-7|7-8| |under | 1 and 2 | | | | | | | ---------------------------+------+---------+---+---+---+---+---+---+- Realistic } Living | 35 | 19 | 15| 13| 15| 13| 17| 12| Human } Dead | 12 | 10 | 7| 1| 7| 6| 6| 2| Apparitions } Unrecognised | 17 | 16 | 12| 17| 17| 13| 11| 10| +------+---------+---+---+---+---+---+---+- | 64 | 45 | 34| 31| 39| 32| 34| 24| ---------------------------+------+---------+---+---+---+---+---+---+- ---+----+------ 8-9|9-10|Total. | | ---+----+------ 8| 10 | 157 8| 3 | 62 5| 8 | 126 ---+----+------ 21| 21 | 345 ---+----+------