§ 4. If I have dwelt thus on difficulties and misconceptions, it is not that I may boast of having altogether triumphed over them. On the contrary, they have made it impossible to attain more than a fraction of what I once hoped. I began with the idea that the census might be extended to 50,000 persons; the group actually included numbers only 5705. Still, though this is certainly not a showy number, any one who is familiar with work in averages will, I think, admit that it is adequate for the purpose; and the friends who have assisted in the collection of the answers (to whom I take this opportunity of offering my grateful thanks).

I need hardly warn the reader not to confound the group of hallucinations belonging to the limited number of persons who were expressly asked the above question, with the large collection of similar experiences which has been frequently mentioned in some of the preceding chapters. That large collection includes the smaller group, and also census-eases which fell outside the twelve years' limit; but it includes also 'a far larger number of cases which were received quite irrespectively of the census need certainly not feel that their labour has been in vain. It is possible for a small group to be quite fairly representative. Thus, if 50 males were taken at random from the inhabitants of London, if the heights of their respective owners were measured, and added together, and if the total were divided by 50, the result might be taken as representing, within extremely small limits of error, the average height of adult male Londoners,* we should not get a much more correct result by taking the mean of 500, or 500,000 heights. This is the simplest sort of case. When it is a question of what proportion of the population have had a certain experience which many of them have not had, we must take a larger specimen-number, adjusting it to some extent by our rough previous knowledge.

For instance, if we want to know what proportion of the inhabitants of London have had typhoid fever, it would not be safe to take 50 of them at random, and then, if we found that 10 of these had had the illness, to argue that one-fifth of the inhabitants of London had had it. Our rough knowledge is that a great many have not had it, and that a good many have; and in such circumstances we should probably get a very appreciably more certain result by enlarging our representative group to 500.1 If, again, the experience was of extraordinary rarity, such as leprosy, the number of our specimen-group would have to be again increased; even if we took as many as 500,000 people at random, that is about one-ninth of the population, and ascertained that one of them was a leper, it would not be safe to conclude that there were nine lepers in London. Now our rough knowledge as to hallucinations would place them in this regard very much more on a par with typhoid fever than with leprosy. We realise that a great many people have not had experience of them; but we realise also that they are in no way marvellous or prodigious events.

And if a group of 5705 persons seems a somewhat arbitrary number by which to test their frequency, the view that it is too small and that 50,000 would be greatly preferable, is one that can at any rate hardly be held with consistency by advocates of the theory of chance-coincidence. For the main prop of that theory, as we have seen, is the assumption that purely subjective hallucinations are tolerably common experiences; whereas it is only of decidedly rare experiences that the frequency, in relation to the whole population, would be much more correctly estimated from the proportion of fifty thousand people that have had them than from the proportion of five thousand people that have had them. However, the adequacy of the latter number approves itself most clearly in the course of the census itself. We find as we go on that hallucinations are sufficiently uncommon to force us to take our specimen-group of persons in thousands, not in hundreds, but not so uncommon as to force us to take very many thousands: after the first thousand is reached the proportion of "yeses" to "noes" keeps pretty uniformly steady - as would, no doubt, be the case if the question asked related not to hallucinations but to typhoid fever.

As regards the sort of persons from whom the answers have been collected - if there have been any answers from persons whose deficiencies of education or intelligence rendered them unfit subjects for a simple inquiry bearing on their personal experience, they form, I may confidently say, an inappreciable fraction of the whole. Perhaps a fourth of the persons canvassed have been in the position of shopkeepers and artisans or employ is of various sorts; but the large majority have belonged to what would be known as the educated class, being relatives and friends of the various collectors. It is, no doubt, safest to assume that a certain degree of education is a pre-requisite to even the simplest form of participation in scientific work; and this condition, it will be observed, in no way detracts from the representative character of the group. A few thousand educated persons, taken at random, present an abundantly sufficient variety of types; and, indeed, for the purpose in view, the group is the more truly representative for belonging mainly to the educated class, inasmuch as it is from that class that the majority of the cases which are presented in this work as probably telepathic are also drawn.

1 In the recently issued Supplement to the Registrar-General's Reports for 1870-80, he bases his conclusions as to the proportionate deadliness of different diseases in the various occupations on batches of 500-1000 deaths.