§ 7. Before leaving this class of experiments, I may mention an interesting development which it has lately received. In the Revue Philosophique for December, 1884, M. Ch. Richet, the well-known savant and editor of the Revue Scientifique, published a paper, entitled “La Suggestion Mentale et le Calcul des Probabilités,” in the first part of which an account is given of some experiments with cards precisely similar in plan to those above described. A card being drawn at random out of a pack, the “agent” fixed his attention on it, and the “percipient” endeavoured to name it. But M. Richet’s method contained this important novelty—that though the success, as judged by the results of any particular series of trials, seemed slight (showing that he was not experimenting with what we should consider “good subjects”), he made the trials on a sufficiently extended scale to bring out the fact that the right guesses were on the whole, though not strikingly, above the number that pure accident would account for, and that their total was considerably above that number.
This observation involves a new and striking application of the calculus of probabilities. Advantage is taken of the fact that the larger the number of trials made under conditions where success is purely accidental, the more nearly will the total number of successes attained conform to the figure which the formula of probabilities gives. For instance, if some one draws a card at random out of a full pack, and before it has been looked at by anyone present I make a guess at its suit, my chance of being right is, of course, 1 in 4. Similarly, if the process is repeated 52 times, the most probable number of successes, according to the strict calculus of probabilities, is 13; in 520 trials the most probable number of successes is 130. Now, if we consider only a short series of 52 guesses, I may be accidentally right many more times than 13 or many less times. But if the series be prolonged—if 520 guesses be allowed instead of 52—the actual number of successes will vary from the probable number within much smaller limits; and if we suppose an indefinite prolongation, the proportional divergence between the actual and the probable number will become infinitely small. This being so, it is clear that if, in a very short series of trials, we find a considerable difference between the actual number of successes and the probable number, there is no reason for regarding this difference as anything but purely accidental; but if we find a similar difference in a very long series, we are justified in surmising that some condition beyond mere accident has been at work. If cards be drawn in succession from a pack, and I guess the suit rightly in 3 out of 4 trials, I shall be foolish to be surprised; but if I guess the suit rightly in 3,000 out of 4,000 trials, I shall be equally foolish not to be surprised.
Now M. Richet continued his trials until he had obtained a considerable total; and the results were such as at any rate to suggest that accident had not ruled undisturbed—that a guiding condition had been introduced, which affected in the right direction a certain small percentage of the guesses made. That condition, if it existed, could be nothing else than the fact that, prior to the guess being made, a person in the neighbourhood of the guesser had concentrated his attention on the card drawn. Hence the results, so far as they go, make for the reality of the faculty of “mental suggestion.” The faculty, if present, was clearly only slightly developed; whence the necessity of experimenting on a very large scale before its genuine influence on the numbers could be even surmised.
Out of 2,927 trials at guessing the suit of a card, drawn at random, and steadily looked at by another person, the actual number of successes was 789; the most probable number, had pure accident ruled, was 732. The total was made up of thirty-nine series of different lengths, in which eleven persons took part, M. Richet himself being in some cases the guesser, and in others the person who looked at the card. He observed that when a large number of trials were made at one sitting, the aptitude of both persons concerned seemed to be aflected; it became harder for the “agent” to visualise, and the proportion of successes on the guesser’s part decreased. If we agree to reject from the above total all the series in which over 100 trials were consecutively made, the numbers become more striking.1 Out of 1,833 trials, he then got 510 successes, the most probable number being only 458; that is to say, the actual number exceeds the most probable number by about 1/10.
Clearly no definite conclusion could be based on such figures as the above. They at most contained a hint for more extended trials, but a hint, fortunately, which can be easily followed up. We are often asked by acquaintances what they can do to aid the progress of psychical research. These experiments suggest a most convenient answer; for they can be repeated, and a valuable contribution made to the great aggregate, by any two persons who have a pack of cards and a little perseverance.1
Up to the time that I write, we have received, in all, the results of 17 batches of trials in the guessing of suits. In 11 of the batches one person acted as agent and another as percipient throughout: the other 6 batches are the collective results of trials made by as many groups of friends. The total number of trials was 17,653, and the total number of successes was 4,760; which exceeds by 347 the number which was the most probable if chance alone acted. The probability afforded by this result for the action of a cause other than chance is ·999,999,98—or practical certainty.2 I need hardly say that there has been here no selection of results; all who undertook the trials were specially requested to send in their report, whatever the degree of success or unsuccess; and we have no reason to suppose that this direction has been ignored. It is thus an additional point of interest that in only one of the batches did the result fall below the number which was the most probable one for mere chance to give. And if we take only those batches, 10 in number, in which a couple of experimenters made as many as 1,000 trials and over, the probability of a cause other than chance which the group of results yields is estimated by one method to be ·999,999,999,96, and by another to be ·999,999,999,999,2.
To this record must be added another, not less striking, of experiments which, (though part of the same effort to obtain large collective results,) differed in form from the above, and could not, therefore, figure in the aggregate. Thus, in a set of 976 trials, carried out by Miss B. Lindsay (late of Girton College), and a group of friends, where the choice was between 6 uncoloured forms—9 specimens of each being combined in a pack from which the agent drew at random—the total of right guesses was 198, the odds against obtaining that degree of success by chance being 1,000 to 1. In another case, the choice lay between 4 things, but these were not suits, but simple colours—red, blue, green, and yellow. The percipient throughout was Mr. A. J. Shilton, of 40, Paradise Street, Birmingham; the agent (except in one small group, when Professor Poynting, of Mason College, acted) was Mr. G. T Cashmore, of Albert Road, Handsworth. Out of 505 trials, 261 were successes. The probability here afforded of a cause other than chance is considerably more than a trillion trillions to 1. And still more remarkable is the result obtained by the Misses Wingfield, of The Redings, Totteridge, in some trials where the object to be guessed was a number of two digits—i.e., one of the 90 numbers included in the series from 10 to 99—chosen at random by the agent. Out of 2,624 trials, where the most probable number of successes was