Extra-Sensory Perception - (02) Historical Background
The evidence reported for Extra-Sensory Perception is very varied in character, especially if we include the less experimental and more complex types of phenomena. First of all in importance is the division of this evidence into perception of mental conditions (telepathy) and of physical objects (clairvoyance). And, secondly, these may vary as to the spatial conditions concerned; i.e., the images or objects may be distant or nearby. Third, there may be a time variable as well, along with either condition mentioned—the image or objective event may be a past, present or future one. Fourth might be mentioned the wide range of experience or objective facts that seems to be perceivable extra-sensorially; feelings and emotions; various cognitive experiences, of perceptual or imaginal origin; complex purposes and attitudes or sentiments, and objective facts of almost any conceivable type. And so on; the limits of evidential variety are not known because the principles are not known and recognizable.
There is also a large group of phenomena of parapsychic nature that are not easily determined to be due to simple E.S.P. They constitute most of the naturally or spontaneously occurring parapsychic phenomena, such as veridical dreams and waking hallucinations. For one thing, they not infrequently carry the suggestion of agency of an incorporeal personality—as in apparitional monitions, for instance. And, again, there is often possible question as to whether the senses may not really be involved and the event be indeed a parapsycho-physical one, as, for example, in collective and simultaneous hallucinations of a veridical nature. For these and other reasons, these uncontrolled parapsychical occurrences are not ideal material for a study into the questions we have undertaken here to investigate, although they are often most impressive and interesting. They have served, however, to awaken attention to the problems and, indeed, to direct interest considerably beyond our present questions to the other divisions of the parapsychological field.
In the early years of the Society for Psychical Research in England there were extensive collections made of reports of spontaneous parapsychic
incidents and systematic study was made of the data obtained. Such material forms the basis of the two volumes, "Phantasms of the Living", 1 of Myers' "Human Personality", 2 and, more recently, of Osty's "Supernormal Faculties in Man" 3 and of Dr. Prince's "Human Experiences", B.S.P.R. Bulletins XIV and XX. In these and other works literally thousands of individual experiences have been examined, classified and reported. The total effect is quite impressive in emphasizing the frequency and generality of distribution of such occurrences among the population; they range in the different studies from an estimated 1 for every 4 individuals, to 1 in 7 and 1 in 10 for the other larger surveys. Some other good suggestions and impressions stand out from these huge and laborious compilations; namely: many instances have seemed to be pure telepathy and have suggested what is for some students an adequate explanation for all; many cases of apparitions of the dying coincided with actual death to a degree significantly beyond chance expectation; friendship accompanied 32% of the spontaneous "telepathic" impressions in the study reported in "Phantasms of the Living" and family relationship 53%; the occurrence of such experiences was found to be no more rare among the highly educated 4, nor even among the scientific, classes than among the general population—in fact, the estimate of frequency given by Dr. Prince, based on a questionnaire study of a Who's Who population of 10,000, is the highest we have had—1 in 4; there are other such points of interest and value. But, in spite of its considerable value, the survey method does not constitute the best approach to our particular problems and we will, therefore, have to refer the reader to the literature cited for any further interest he may have in the spontaneous occurrences. In any event, a summary of such data is impossible; a statement of cases studied, with statistical treatment of frequency and chance expectation, does not do justice either to the value of such material or to the more likely errors it is exposed to. The reports are, however, well worth reading in full, at the same time that they baffle summary statement. Most fair-minded readers of these collections would, I think, be led, as were the investigators, to regard them as genuinely evidencing a parapsychic principle of some sort. But few would agree as to what it is. Hence the need to control the phenomena, if possible, or at least to approximate them under conditions of systematic observation; and, if possible, to vary conditions so as to isolate the factors involved.
Between these spontaneous parapsychic phenomena and the results of more definitely experimental investigation of the subject, there is an
intermediate group of data which seems clearly to evidence an extrasensory mode of perception. I refer to the results of systematic observation of clairvoyance mainly in its various forms of private and professional practise: dowsing, or clairvoyance with the use of the divining-rod; "psychometry", or clairvoyance with the use of an object of fixation connected with the situation in question; crystal-gazing, card-clairvoyance, and the like. If in such practise there are given facts not known by the recognized means, as many studies claim to show is true, we have in them somewhat better material for study than in spontaneous cases, due to the fact that precautions can be taken and conditions imposed that permit systematic observation and approach to some degree of true experimentation. Much study has been done on such material, often with a more or less experimental procedure involved. The study of the divining-rod and its use in the location of desired underground substances—water, coal, oil, ores, etc.—has been pushed by Sir Wm. Barrett almost to the point of clear-cut experiment 1, and he is convinced that the dowser can, for instance, parapsychically perceive water, and locate its depth, direction and strength of flow, and often its duration. But most of the data on dowsing have been obtained by following the practitioner and observing the conditions and results. Even this method furnishes a striking array of evidence.
There have been some apparently very carefully conducted studies reported on parapsychic sensitives of the type called "psychometric mediums", who appear to be able to give knowledge, parapsychically obtained, concerning absent and unknown persons (who may be living or not) when a token or "object of contact" belonging to the person concerned is placed in their hands: Dr. Pagenstecher's report 2 of the work of Senora de Z., Prof. Oskar Fischer's study of Raphael Schermann 3, Tischner's cases in "Telepathy and Clairvoyance" 4 under the heading of (his suggested improvement of the name) "psychoscopy", and Dr. W. F. Prince's study of Mrs. King. 5 In the last named of these studies the calculation of the probability on the chance hypothesis of obtaining the results actually given yields a very impressive figure. And while I am here classifying this work among the observational, rather than among the more clearly experimental investigation, I wish to make clear at once that this is not to belittle it; for, with the sensitive concerned, it probably was the best
way to proceed (certainly so at first) and, in view of the high quality of the observation and precaution, we may give great confidence to the work. So that, in so far as the sensitive's work, carefully observed, can reveal its own nature, this is done. But to discover underlying principles and inner relations we must vary the sensitive's ways of performing. We can, perhaps, for the open-minded scientist even answer our first question (Does E.S.P. occur?) by this intermediate or systematic observational type of investigation. For that matter, many intelligent students have been convinced of the existence of another mode of perception by the spontaneous parapsychic occurrences alone. There are, however, those more sceptical minds that demand some measure of experimental manipulation and some artificial control of the phenomena in question before they venture credence. (For these people the laboratory is often too much emphasized but there are many of them.) But to answer our second question, What is the nature of E.S.P., we have to experiment and doubtless to extend our experimental technique considerably beyond its present state of development .
When we turn to the more definitely experimental evidence for E.S.P., we shall see at once the advantages and the dangers of experimentally following one hypothesis without full recognition of the other possible hypotheses—perhaps the greatest danger-point in all human thought. The early experiments grew out of the need to test what appeared to be non-sensory transference of thought from mind to mind. This was early given the name of "telepathy" by Frederic Myers and it became for the English-speaking world, at least, the ruling hypothesis for all parapsychic perception. And experiments were framed to exclude sensory and rational cognition, but not any other possible parapsychic cognition. This is still true to the present day in parapsychic investigation. Experimental tests for telepathy, as I know them, invariably fail to exclude the possibilities of clairvoyance. Our own at first failed to do so.
The early experiments, then, dealt with undifferentiated E.S.P.; either telepathy or clairvoyance, or both. The fact that they were called experiments in "thought-transference" or a little later in "telepathy" merely shows the pre-experimental belief of the investigators. But, in view of the fact that the foremost need at that stage was to discriminate rather between E.S.P. in general, on the one hand, and the sensory and chance hypotheses on the other, the work was of great value. The experimental design consisted first in the choice of material rendering computation of chance expectation easy and of making possible an estimation of the anti-chance value of the deviation from chance; thus, playing cards, lotto blocks, numerals of a chosen range and the like, were used, all with known probability in guessing. Second, various conditions were obtained
for the elimination of sensory cues, such as separation by closed doors, by distance, by silence, by screening, position out of visual field, etc. Third, the range of thought-types transferable was worked at somewhat, using tastes, diagrams, pain localization, colors, melodies, etc. Fourth, the value of hypnotic trance, too, was tested. And there were other features.
On the whole the early experiments in E.S.P. were admirably conducted (with the one limitation indicated above) as one would expect from the array of highly impressive names connected with them. The experiments with the Creery sisters, for instance, were conducted by Professors William Barrett, Henry Sidgwick and Balfour Stewart, by Mrs. Henry Sidgwick, Frederic Myers, Edmund Gurney and Frank Podmore. The Guthrie experiments, mainly carried out on drawings, led to other scholars being drawn into the research, among them Oliver Lodge, then a young professor of Physics at Liverpool, whose discussion of the results seems to me a masterpiece of scientific judgment. 1 Another lengthy and fruitful series is what we may call the "Smith Series", so called because Mr. G. A. Smith was concerned in all of them as the hypnotist. He put the subjects into trance for the experiments and frequently acted as agent. In these remarkable experiments a wide variety of thought material for transference was used, and the condition of separation of agent and percipient by walls and by distance was instituted. It was found that walls and short distances (10 to 17 feet) did not prevent the transference, though the results were not so high as with agent and percipient in the same room. At longer distances the result was failure. Numbers were used for these tests and calculation of value from the anti-chance viewpoint was relatively simple.
In all this work the results were sufficiently striking to leave no doubt as to the exclusion of the hypothesis of chance. Even when the nature of the material was not such as to permit calculation of mathematical odds against the chance theory, the percentage of successes was impressive enough to discourage doubt. The explanation then was either one of E.S.P. or of some normal mode of perception, involving conscious or unconscious evasion of the conditions intended to eliminate the senses. The only seriously proposed alternate hypothesis was that of "involuntary whispering" suggested by Hansen 2 and Lehmann, psychologists, of Denmark. In 1895 they offered this explanation of the results published in the Proceedings of the S.P.R., claiming to have demonstrated in the laboratory the adequacy of their view. But after Professors Henry
[paragraph continues] Sidgwick 1 and William James 2 pointed out the inapplicability of the hypothesis to the results in question and exposed its own intrinsic errors in logic, Professor Lehmann withdrew his theory. 3 Later, 4 while insisting upon the applicability of the involuntary whispering theory to certain of the results, he went so far in the other direction as to assert that, in the experiments in which agent and percipient were separated by a door and some distance, there was evidence of another, an unknown, factor at work and he appears to have accepted telepathy as a fact under those conditions.
Not all attempts made by investigators to demonstrate " telepathy" in this early period, the 80's and 90's, however, were so strikingly successful. Prof. Charles Richet 5 of Paris in 1884 made 2,927 tests on ordinary individuals guessing card suits, and got very low results, still, however, above chance by a margin of 57. This is between 3 and 4 times the probable error, and slightly under the minimum commonly taken as a significant result. He made, however, an interesting observation—that those who were worked for long series of over 100 did not do so well. And if the shorter series (those of under 100) are taken alone, 1,833 trials give 510 successes, which is 52 above chance or over 4 times the probable error. Max Dessoir's experiments 6 with drawings for material are not nearly so striking as those of the Smith or the Guthrie series; in fact, to the ordinary judge, they seem very poor. Yet, when an adequate method of evaluation was developed by Dr. W. F. Prince (B.S.P.R. Bulletin XVI, pp. 104-114) the drawings become clearly significant. Large numbers of tests were made on ordinary citizens both in England and America with a view to getting at the commonness of the " telepathic" ability. 12,130 trials were made in America, directed by Professors J. M. Peirce and E. C. Pickering, with results only slightly over chance expectation. 17,653 were made in England and reported by Gurney; these gave 347 above chance. This is at a low rate of scoring, comparatively; but, due to the large number of trials, it is significant, with odds against the chance explanation of 20 millions to one. Yet impressive as are such figures, they are small in comparison to the odds against chance attained in only 497 of the tests made with the Creery sisters and limited to the condition that none but the investigators knew the object selected. These 497 trials give odds of septillions to one against the chance theory. 7
There is a very interesting group of experiments carried out mainly during the 80's and 90's in France by a number of eminent physicians and university professors, on a line that implies E.S.P. of some kind, as interpreted by some of the students of the parapsychic field. They have to do with hypnotization at a distance, under conditions that exclude sensory, mnemonic and rational cognition. The earliest case was reported by Esdaile, a Scotch surgeon in Calcutta. The names of Gibert, Janet, Hericourt, Dufay, and Dusart are most prominently mentioned in the later work. Frederic Myers made a study with Janet, with apparently excellent results—80% successes in 20 trials. Myers concludes that it is due to telepathy; 1 Janet acknowledges the facts but refuses to accept Myers's interpretation. He implies that he has a different view of the experiments but does not even hint to us what it is. 2 There we have to leave this most fascinating block of data, until some one else undertakes a repetition.
In France the Schmoll and Mabire series, 3 in Germany Schrenck-Notzing's, 4 in America the Rawson 5 experiments, and in England the Wingfield series 6 of 3,024 trials on number-guessing (with successes 10 times the chance expectation) and about half a dozen others of less importance went on to strengthen the argument for a function beyond chance, fraud and mal-observation—for a parapsychical mode of perception. As to what it was, what its relations might be to physics, to biology, to the rest of mental life, there was very little discovered. But the fact itself was amply proved over and over. (For a better and fuller review of the experimental work thus far mentioned see B.S.P.R. Bulletin XVI, by Dr. Prince.)
Curiously enough, however, the fact seems to require proof over and over—many, many times. For we find in the 20th century that Bruck, 7 a physician in Germany, Warcollier 8 in France, Coover, 9 and Estabrooks, 10 psychologists, and the famous novelist, Upton Sinclair, 11 in America (to mention only a few), have all produced fresh series of experiments primarily to answer the first question—Does it occur?—as if it were still an unsettled question. This will, I predict, be one of the more amazing facts for the future historian of science. And after reading Bruck and Warcollier and
[paragraph continues] Coover and Estabrooks and Sinclair, as well as the more numerous and more varied series that preceded, still the student who would work in the field today must set out first to prove it all over again! Scientific method and systematic observation have meant so little that we dare not lean on them heavily unless we are already prepared, by a priori mental attitude, to accept their findings.
Yet there has been some progress; if not in conviction, at least in interest. At least three University laboratories have opened up to the problems and our own becomes a fourth. Coover and Estabrooks worked in psychological laboratories, at Stanford and Harvard respectively. The third laboratory study by Brugmanns 1 at Groningen (with Professor Heymanns) is a double step forward, for it aimed to go beyond the first problem of proof and to try to find facts of natural relationships in the direction mainly of physiological measurements correlated with success in "telepathy". And the results of Brugmanns are striking also in proof-value, as well as contributing something to our knowledge of conditions. The 187 trials yielded 60 successes as against 4 for chance expectation. The conditions for exclusion of sensory perception were elaborate and appear highly satisfactory.
The Sinclair book, "Mental Radio", does the great service, first, of reaching a wider public with very good and seemingly reliable results. It is rather of the systematic observational type than the more purely experimental. But there are some good distance experiments and an interesting introspective report by the percipient, who is Mrs. Sinclair herself. The exhaustive analysis of the original materials by Dr. Prince in B.S.P.R. Bulletin XVI adds a great deal to its value, and includes the independent and confirmatory tests on Mrs. Sinclair made by Professor William McDougall.
Prof. Coover seems to have regarded his own work as negative and in many respects it was. But it seems pretty clear that he might have obtained more positive results and perhaps made considerable contribution by the very simple device of repeating the tests with those who succeeded best the first time. Even as it was, his 10,000 tests on "telepathy" (undifferentiated E.S.P.) and clairvoyance, yielded 294 successes as against chance expectation of 250 (p. equals 1/40). This deviation of 44 is over 4 times the probable error and would be generally regarded as statistically significant. Prof. Coover does not appear to have discovered this contribution which he made to the subject. But, what is much more important, the bulk of this positive deviation was contributed by a few of his 100 subjects—eight in number—who were among the highest in both
sets of the experiments—i.e., both in the pure clairvoyance tests and in the tests where both clairvoyance and telepathy were possible (loosely called "telepathy"). Of the 12 highest scorers in the " telepathy" series and the 10 highest of the clairvoyance series, 5 were the same subjects. This was indeed a doubly valuable discovery, had the investigator been aware of it. Without a doubt he would then have carried out the very experiments we have done in this laboratory fifteen years later. These results of Coover's work, if selected thus, become tremendously significant—20 times the probable error. Now, this selection is permissible, of course, only if there is valid reason to suppose individuals may differ as to their "guessing" ability, which involves the point in question—since on a chance hypothesis they should not. But it might well have suggested to Prof. Coover the need for long and careful testing of these more promising subjects—to ascertain if they differed permanently. Finding that 5 of the best subjects in either series were also best in both would suggest to any interested investigator the possibility of a good clairvoyant being also a good telepathic percipient—that, or else that in the "telepathic" series it was really the clairvoyant function that operated. This would have been a valuable "lead". While, then, Prof. Coover did not prove anything at all, perhaps, he unwittingly opened up some very interesting suggestions, which might profitably have been followed up. (Especially so in view of the generous endowment provided and the ideal laboratory and library facilities.) 1
Dr. Estabrooks took the same type of subject, the average college student, and, using playing-cards also, found some evidence of "telepathic" ability in them. His conditions were excellent for excluding sense perception. The best points of his work were (1) some evidence of a lowering of the scoring-rate with progress through a run of 20 trials, the last 10 yielding less than the first ten. And (2) the fact that one group ran considerably below chance expectation when asked to run a second series, at a longer distance than the first. These, too, are interesting leads had the investigator been able to follow them up. He explained the decline in the run as due to "fatigue" (presumably of the "telepathic" function) and the drop below chance in the special instance as perhaps due to space limitations.
Another variation of E.S.P. research is represented in the inclusion of other species in the range of "subject material". The more experimental of the animal parapsychic studies are those by the late Prof.
[paragraph continues] Bechterew, 1 eminent Russian psychologist and physiologist, on Durow's circus dogs, and of Dr. Louisa E. Rhine and myself, with the horse Lady as subject. 2 In both cases a positive conclusion of "telepathy" was announced, after the investigation. There have been other cases brought before psychologists, 3 however, and for these I will refer the reader to the review in the report on Lady.
These animal cases have an especial interest for two reasons. One is the fact that in them the conditions often approximated pure telepathy as distinguished from the telepathy-with-clairvoyance-just-as-possible type of experiment which we have been reviewing thus far. Prof. Bechterew merely thought of the object in the room or in the adjoining room with which he wanted the dog to perform—i.e., he did not otherwise single it out. Supposedly it had no other isolation than the mental choice he exercised. There was thus an inadequate basis for clairvoyance, it would appear. In the Lady experiments I looked at the blocks, with eyes screened. This is not so free from objective selection, then, as is the other case. The second point of interest is the fact that Lady, the filly, lost her ability to perceive or to be controlled extra-sensorially (at least, as far as our tests could determine) after about a year of demonstration, and came to depend upon the rather obvious movements of the trainer for guidance, movements which, of course, we had had to eliminate during the earlier production period. This loss of ability in an E.S.P. subject has had other examples, notably the several Creery sisters, and Prof. Brugmann's subject, Van Dam, and perhaps others. It will be of especial interest in connection with this report.
Another diversion in type of experiment, while we are still dealing with undifferentiated E.S.P. conditions (though they are still commonly called "telepathic"), is the condition of distance between agent and percipient. There was failure under this condition in the Smith series (except for very short distance) and success in the Sinclair tests. We have yet to review the Usher and Burt 4 tests made at a distance of from 120 to 960 miles, yielding in 60 trials with playing cards 4 successes complete and 14 right in value. This is at a very good rate of scoring but the number of trials is small for a conclusion. They did much better in the same room, getting 9 hits in 36 trials. The Miles and Ramsden 5 long-distance tests were made by having the percipient, Miss Ramsden, record daily
and send to Miss Miles her impressions of what the latter was doing at a certain hour (7 P.M.). Miss Miles then got objective records, pictures, etc., for all of her setting that she could. Out of 30 trials, 13 were regarded as successful, barring what would conceivably be accidental. This series was not very experimental, it is obvious, but most critics have been impressed by it, in spite of its difficulty of mathematical evaluation. Another similar series is reported by Mr. Wales and Miss Samuels, 1 and is likewise difficult to judge, although impressive in its totality.
The trans-Atlantic series conducted by a Paris group directed by M. Warcollier and a New York group under Prof. Gardner Murphy of Columbia I have not been able to find in print, but critics who have seen the results seem to regard it as difficult to evaluate and inconclusive, 2 as are likewise regarded the results of the two radio-broadcast experiments in "telepathy", the first conducted by Dr. Murphy, broadcasting from Chicago, and the second by Dr. Woolley, 3 from London. The sequel-series of experiments following the Woolley-broadcast that was carried out by Mr. S. G. Soal 4 was negative. So we may say, it appears, that of the reported experiments in "telepathy" with distance, the short Sinclair-Irwin series of seven drawings made at 30 miles from the agent, is perhaps the best. (See. B.S.P.R. Bulletin XVI, pp. 9-15.)
This brief sketch is far from complete, even in the mere mention of titles, so extensive has the literature become. Especially in reference to continental European work is it incomplete. The work of the Russians, Dr. Kotik 5 and Dr. Chowrin, 6 that of the French Dr. Geley on Ossowiecki, of the German, Dr. von Wasielewski 7 on Miss von B. (with whom Dr. Tischner also worked) are examples of omissions. But there is great similarity in all this work, and we have given, I think, a fair notion of the field and its advance—or lack of it.
Similarity of work in this field does not mean any extensive following of the work of others, but rather an ignoring of its conclusions and a starting all over again "to establish the fact" first of all (a phrase that is repeated so often that it becomes commonplace after 50 years of research and almost as many researches; and the same ground is covered, with many of the same difficulties that others have had and with the same general degree of success, very often). In 1932, fifty years after the Creery sisters’ investigation by the S.P.R., it publishes Mr. Soal's long research
made to prove the factuality of "telepathy"—which ended negatively. There are two points that are worthy of attention in this situation: first, our evident lack of progress in "establishing the fact" for society at large; this is obvious, and is the more remarkable in England, where the most of the work has been done. And, second, in these recent failures we have strong indication of real lack of progress in understanding "telepathy"; its requirements and functioning are still so little understood that we have these long negative series after a half-century of study.
The following general points seem to stand out as worth noting in the past contributions from these "telepathy" experiments: first, the evidence is (to one who labors through it all) overwhelmingly convincing of some extra-sensory mode of perception. That this includes the perception of mental states of a wide range of variety is also clear. That the hypnotic trance is not necessary, but is a possible "telepathic" working condition, seems also proved. Several interesting cases of loss of ability with lapse of time are recorded. Some decline of rate of success with length of the run is suggested by Richet and Estabrooks. Suggestion is made that certain drugs may help, but the only evidence is that of Brugmanns, who found improvement with alcohol (30 gms.), but only 29 trials are reported. The agent's greater tendency to fatigue and headache is referred to by several (Lodge, Guthrie, Sinclair), and the general need for passivity and serenity on the part of the percipient. Most of these points are fairly clearly indicated, if not established.
Strangely enough there has been comparatively little experimental work on the seemingly simpler phenomenon of clairvoyance. This is, perhaps, an effect of the large influence that spontaneous occurrences have had upon the course of parapsychological thinking. These more often seemed telepathic rather than clairvoyant in nature. Still it is a remarkable fact that clairvoyance has been so neglected that it has never been thought necessary to eliminate it by condition from telepathy experiments. Consequently all the phenomena of these have been possibly also clairvoyant in nature. Prof. Coover even used card-guessing in the presence of the card as a control on the telepathic series—thus allowing clairvoyance to operate but being so sure it did not function that the results were taken as chance products. (They were, however, above, by about twice the p.e.) The same loose condition has existed in all the telepathy experiments I am acquainted with; but, of course, with no danger to conclusions so far as concerns the demonstration of extra-sensory perception. While we have had this undifferentiated E.S.P. as regularly possible in the so-called "telepathic" tests, there were some where it seems unlikely that clairvoyance played much part. In Prof. Brugmann's experiment with Van Dam, he looked down through a glass-covered hole in the ceiling at
the blindfolded subject, "willing" the subject's hand to move to a certain square on a large checkered diagram before him. Here the looking was objective, of course, and there was an objective record of the choice to be "willed", also; yet the conspicuous thing was the agent's act of willing. We can conclude nothing, but in fairness I think we can say that the mental activity of the agent was probably the guiding factor, rather than his objective behavior or his record on paper. In Prof. Bechterew's tests of Durow's dogs, he sometimes did not even look at the object and we come still closer to pure telepathy conditions—perhaps close enough. But why not pure telepathy experiments by definite planning of the conditions?
Of pure clairvoyance we have had a few series of tests, rather similar to the "telepathy" data in quality and in range. Prof. Richet deserves credit for the first systematic experimentation in clairvoyance. 1 His tests made in Paris in 1888 with Leonie B. in hypnotic trance, using playing-cards sealed in opaque envelopes, were very successful. Leonie got 12 cards correct (probability of 1/52) in 15 trials and in a later series 5 in 25 (after having been transported to England and back, where a negative series was carried out). The odds against getting 12 hits in 15 trials on playing cards on chance alone is given by Richet as 1 quintillion to 1.
There were also the experiments of Dr. Backman 2 of Sweden in the 90's, in which he put his subjects into hypnotic trance and commanded them to "visit" specified points at some distance and report what they "saw". They were able to perceive parapsychically to a degree that, if the report is acceptable, leaves little doubt of the fact of E.S.P. The exclusion of telepathy is not as clear-cut as is desirable and his results are, unfortunately, not capable of definite evaluation. There is not sufficient experimental character to such observations to enable definite conclusions to be drawn regarding the successful exclusion of such factors as infer-ability, guidance by unconsciously given indications, laxity in observation and coincidence. One does not see in the text, however, any ground for these alternative explanations.
In 1895 Mrs. Verrall 3 tested pure clairvoyance on playing-cards, in conjunction with tests of hyperaesthesia and its possible functioning in parapsychic tests. She found that, under her conditions (which deliberately permitted it), hyperaesthesia of sight and touch could function to a degree, but that there was something more, presumably clairvoyance.
Tischner reviews Kotik's work on the clairvoyance of his subject Lydia, carried out in Russia in 1908: Tischner's review is inadequate for a judgment of the original work; but he states his conviction that some of
the experiments "are beyond criticism". Tischner's own clairvoyance tests are not, as they are reported, explainable by any known alternative hypothesis. One has only the alternative of doubting the honesty or intellectual balance of the experimenter, and he quotes several witnesses in support. He used numbers of three or more digits, or words, written on slips of paper and folded up. He and the several witnesses testify to the exclusion of all trickery and, since the 78 trials gave 40 successes, the chance theory certainly does not apply. Tischner was on guard especially against "pellet switching", since the sensitive claimed to have done this earlier in his career under different circumstances. Tischner's "psychoscopic" observations ("psychometry") are likewise impressive, as described. Twenty-six witnessed experiments gave 61.5% positive results.
Miss Jephson published in 1928, the results of 6,000 tests for clairvoyant perception of suits of playing-cards, made on 240 people, yielding results that average somewhat above mean chance expectation and, with the number of trials given, pass well beyond the minimum for significance. She obtained 1832 hits on suits or 332 above chance expectation, which would be approximately 14 times the probable error. Her results in pure clairvoyance compare roughly with those of Estabrooks on "telepathy"—i.e., with both telepathy and clairvoyance possible. I quote the following figures of comparison from Miss Jephson's article:
Total color right
Total suit right
Early guesses, color right
Early guesses, suit right
[paragraph continues] It would be very doubtful then if Estabrooks or, perhaps, if any one had actually demonstrated pure telepathy, in view of these results. For, if clairvoyance is possible, it must safely be excluded before telepathy can be inferred as the operative principle. I feel particularly indebted to Miss Jephson's work in that it helped to stimulate my own interest in clairvoyance. A second report in 1931, in conjunction with Messrs. Soal and Besterman, 1 does not confirm the earlier work and its "fatigue-curve" hypothesis. (This last point is discussed later in this report.)
If the more experimental studies of clairvoyance were regarded as the only "pure clairvoyance" material, the evidence would not be at all overwhelming. I think it would be good but in need of much repetition. Even so, it is far ahead of the definitely experimental evidence for "pure telepathy", for of such there is nothing on record, to my knowledge. And, if we accept provisionally the evidence from the "telepathy" tests in which clairvoyance was not excluded, we may as well accept the evidence for
clairvoyance from "psychometry", in which telepathy (extended and generalized) is not often excluded. If we do, I am inclined again to give the odds of weight of evidence in favor of clairvoyance, especially if we include the dowsing or divination data under this heading. The long list of first class "psychometric" cases is rather impressive: Señora de Z., Dr. Prince's Mrs. King, Dr. Osty's Mme. Morel and Mlle. de Berly, Rafael Schermann, Wasielewski's Miss Von B., Tischner's Mr. H., Dr. Geley's Ossowiecki, Paschal Forthuny, to mention some of the more famous.
With practically no pure telepathy experiments and few pure clairvoyance tests, we have little or no basis of evidence for a study of relations between these two phenomena. Kotik's Lydia did both clairvoyance and telepathy (without excluding clairvoyance, so far as Tischner's review shows), and Wasielewski and Tischner's Miss Von B. did likewise. Coover's subjects did card-guessing in their barely significant way, under the same two conditions, pure clairvoyance and telepathy-plus-clairvoyance. But we cannot draw any conclusions about results from such conditions. The need for an experimental separation of the two is strikingly clear, all the more so since most students of the subject have had hypothetical views of some kind as to the relationship. In a very general way the Frenchmen, Richet, Osty and Geley, have preferred to think telepathy a special case of a general clairvoyance ("cryptesthesia", Richet's term, "metagnomy" Boirac's term). The English and American students have been slow to recognize clairvoyance, as is shown by the lack of any definite test of it in those countries until Miss Jephson's in 1928 and by their long ignoring the need for excluding it from telepathic experiments. There has been some bias against clairvoyance in Germany too, as is illustrated by Prof. Oesterreich's attempt to explain clairvoyant phenomena by telepathy—telepathy expanded to unlimited dimensions. Barrett and Myers have theories for telepathy, but not for clairvoyance. Both Myers and Mrs. Sidgwick have suggested that there are probably connections between the two. 1 Tischner and Wasielewski are of the same mind. 2
A final phase of this review concerns the various hypotheses proposed to explain E.S.P. These fall into two groups in general—physical hypotheses and non-physical. The physical hypotheses are the more numerous and popular, as well as the more elaborated. But in a general way they are all radiant or wave hypotheses, since this is the only physical principle available as yet for such theorizing. Even Ford's electron theory becomes as good a wave theory as any, since electrons are discovered to conduct themselves in the undulatory way.
A number of attempts have been made to offer hypothetical explanations for either telepathy or clairvoyance, but very few have tried to explain both at once. It is this attempt at a joint theory that gives the peculiar logical difficulty. Some find it easy to suppose brain-waves for telepathy but they seem to balk at supposing the same sort of waves to be emanating from all things clairvoyantly perceptible; and well they might! Others find it easy to suppose a "magnetic", "telluric" or "rhabdic" emanation or force to be exercised by metals, waters—substances in general; but they likewise find a large gap between these forces and the thought-images of a telepathic agent's mind.
The physicist, Sir William Crookes, perhaps the first general theorist of the field, proposed in 1897 1 the theory that telepathy might be due to high frequency vibrations of the ether generated by molecular action of the brain of the agent and received by the percipient's. He was conscious of the difficulty his theory encountered in the inverse-square law of decline of intensity with distance, but felt that our ignorance might be cloaking some principle which covers this point of difficulty. Another eminent physicist, Professor Ostwald, 2 has proposed a physical theory for telepathy, offering an energetic theory which assumes the transformation of known physiological energies into unknown forms that can be projected through time and space, received by the percipient and reconverted to known forms. But the great physicist of "energetics" had no evidence from his science to show that energies can be projected toward a goal, unless through a material channel. The energies radiate on a spherical front, so far as we know them. Sir William Barrett, another physicist, in argument against a physical theory of telepathy, 3 reminds us that the radiation theories would require, to reach 1000 feet, 1 million times the intensity of the transmitted telepathic stimulus that is required for one foot, and concludes that "it is highly improbable that telepathy is transmitted by waves radiating in every direction, like light from a candle." He quotes Myers, Mrs. Sidgwick and other eminent students as of like opinion concerning telepathy—that it is a psychical, rather than a physical, phenomenon. Myers was especially opposed to a physical, and insistent upon a psychical, theory. But of what sort of a theory a psychical one is we have very little understanding, other than the fact that it is not physical (i.e., mechanical).
Turning to the more comprehensive theories that embrace both clairvoyance and telepathy, we find three which are very wide apart in viewpoint and which will serve here to represent widely different possible
approaches. These are hypotheses suggested by Hyslop, Forel and Tischner. Hyslop's 1 hypothesis (which he suggested without advocacy) is the " spirit hypothesis" applied to telepathy and clairvoyance. The incorporeal personality is supposed in this hypothesis to be a " carrier" of the mental state or stimulus that the percipient receives, for both phases of E.S.P. It will be seen at once that this hypothesis would at best only pass the problem on to a stage of still greater complexity, since we wonder quite naturally how the "spirit carrier" obtains his "load", if not by clairvoyance and telepathy! Which is as bad as ever.
Tischner 2 invokes a theory of super-individual or collective mind, which serves as a common reservoir. He quotes E. von Hartmann as explaining telepathy through "telephonic connection with the Absolute" and aligns himself with this view. The connection is, he believes, through the "subconscious mind". This hypothesis is less definite and, perhaps, less extravagant, as some would regard it. But, in essence, it leaves us no more advanced toward explanation than Prof. Hyslop's suggested hypothesis. For we have to explain the business of "fishing" in the "reservoir" of the absolute or the collective mind quite as inevitably as if we just omitted all that, and assumed a direct contact between agent and percipient or object and clairvoyant. If we should need to bring in these other complications, "spirits", "reservoirs", etc., as inferred accessory factors in telepathy and clairvoyance, it would be fully acceptable to do so; but let us not obscure the fact that they do not explain telepathy and clairvoyance at all. They only complicate it. For all "absolutes" and "spirits" would have to perceive extra-sensorially themselves. These two theories, then, leave us as we were.
Ford's theory 3 is a hard-boiled physical one, an electron-theory. The electrons come either from the brain of the agent or from the object, and when they come off in certain complexes they convey to the brain of the percipient the stimulation which leads to perception. A given "electron-complex" can stimulate a corresponding "engram-complex" in the percipient's brain, provided the percipient has previously established such an engram-complex through experience of the perception in question. This previous set-up is essential, because there is required the existing engram-complex in the percipient's brain which through "homophonous and synchronous" vibration may be aroused by an appropriate electron-complex, and perception effected. Thus the thought of a card-figure would give off from the agent's brain the same electron-complex as would the card-figure itself, both exciting the same engram-complex.
But one need only remember that substances regularly emitting electrons—i.e., radioactive—are rare in nature. Physics is, of course, alert to this phenomenon. And, to secure intensities of the strength necessary for distance E.S.P. (a million times stronger radiation at a thousand feet than at one), there would be need for some remarkable electronic emission (indeed!), which could hardly have escaped physicists.
On the reception end of the E.S.P. phenomenon there has only been the vague inference of some hidden sense (cryptesthesia), a "sixth sense", as Prof. Richet, the leading exponent of this view, has called it. 1 The usage is not clear as to whether any reception whatever would be regarded as sensory, or whether the selective interception of a special energy pattern by a specialized and localized organ would be meant. No clarity has yet been achieved on this important end of the function of E.S.P.
For a summary of the chapter, one may say that the evidence for general E.S.P. is good but the theories are bad; and our knowledge of the phenomena needs refinement through variation and improvement of conditions. We need tests for pure telepathy and more of them for pure clairvoyance, made under conditions that enable easy evaluation of significance, provide safe exclusion of other modes of cognition, and introduce variation enough to suggest the relation of E.S.P. to other processes and lead to its natural explanation.
15:1 By Gurney, Myers, and Podmore; Soc. Psy. Res. (London), 1886.
15:2 Longmans and Co., London, 1903.
15:3 Trans. by Stanley DeBrath; E. P. Dutton, New York, 1923.
15:4 See Human Experiences, B.S.P.R. Bulletin XIV.
16:1 See the interesting contribution in The Divining-Rod, Barrett and Besterman, London. Also Chap. IV, Richet's Thirty Years of Psychical Research, Macmillan, 1923. (Trans. by Stanley DeBrath.)
16:2 A.S.P.R. Proc. Vol. XVI, New York.
16:3 Experimente mit Rafael Schermann, Urban, Berlin, 1924.
16:4 Harcourt, Brace and Co., New York, 1925.
16:5 A.S.P.R. Proc. Vol. XVIII, New York, 1924, pp. 178-244. Another great case that belongs perhaps half-way in this department of the subject but is somewhat more experimental than these is that of Prof. Gilbert Murray, as reported by Mrs. Verrall, Proc. S.P.R. 29: pp. 64-110 and by Mrs. Sidgwick, 34: pp. 212-274. Prof. Murray usually requires a "point of contact" (a hand-clasp), but not one connected with the situation in question, and his work seems to be more telepathic than clairvoyant also, though the writing and speaking by the agents are required, and we cannot, therefore, be sure of telepathy.
18:1 Proc. S.P.R. Vol. II, pp. 189-200, 1884.
18:2 Hansen, F.C.C. and Lehmann, A., Uber Unwillkürliches Flüstern, Phil. stud. 17: pp. 471-530, 1895.
19:1 Proc. S.P.R. 12: pp. 298-315, 1896-1897.
19:2 Psych. Rev. 3, pp. 198-200, 1896; 4: pp. 654-655, 1897; Science, 8: p. 956, 1898.
19:3 James: Messrs. Lehmann and Hansen on Telepathy, Science, 9: pp. 654-655, 1899. Prof. Lehmann's words are: "not yet established (bewiesen)".
19:4 Lehmann, A., Aberglaube und Zauberei, 2d Ed., Stuttgart, Enke, 1908. This statement is based on Prof. Coover's Abstract, Experiments in P.R., Stanford, 1917, pp. 33-35.
19:5 See Abstract, Gurney. E., Proc. S.P.R., 2: pp. 239-64, 1884.
19:6 Phantasms of the Living, Vol. II, pp. 642-53, 1885.
19:7 Phantasms of the Living, Vol. I, p. 25.
20:1 For a review of this work consult Myers, Human Personality, 2 vols., Vol. 1: p. 568
20:2 P. 125, Vol. 1, A History of Psychology as Autobiography, Ed. by Murchison, 1930, Clark University Press.
20:3 Proc. S.P.R. 4: pp. 324-337; 5: pp. 169-215.
20:4 Proc. S.P.R., 7: pp. 3-22. See also Dr. W. F. Prince's review and criticism, B.S.P.R., Bulletin XVI, pp. 126-128.
20:5 Proc. S.P.R., XI: pp. 2-17.
20:6 Phantasms of the Living, I, p. 34, and II, p. 653.
20:7 Scientific American, May, 1924.
20:8 La Télépathie, Paris, 1921.
20:9 Experiments in P.R., Stanford, 1917, p. 640.
20:10 B.S.P.R., Bulletin V, p. 28.
20:11 Mental Radio (Sinclair), Los Angeles, 1930, p. 239.
21:1 Compt. Rend. Off. du Premier Cong. Internat’l des Recherches Psychiques, 1932, pp. 396-408.
22:1 In the interest of completeness perhaps I should mention Dr. Troland's short study of telepathy made at Harvard in 1916-1917, including only 605 trials with a probability of ½. It has no significance whatever and was too small a series to be important. There was also the negative report of an examination by Prof. Stratton of a man who claimed telepathic powers and who invited the inquiry. (The control of another person by obscure signs, Psych. Rev. 28: pp. 301-334, 1921.) One can readily see that Prof Stratton might have been right in his conclusion of sensory following of signals, but might equally well have been wrong—in having provided conditions unfavorable for abstraction, as I can see now was the case. The "internal" field is even more important than the outer in psychological experimentation.
23:1 Bechterew, W. Zeitschrift f. Psycho-Therapie, 8: pp. 280-304, 1924.
23:2 Rhine, J. B. and Louisa E., Jour. Abn. and Soc. Psy., 23: pp. 449-466, 1929; and 24: pp. 289-292, 1929.
23:3 The Eberfeld horses were doubtless best known among these. Krall was convinced that his horses were capable of telepathy but the demonstration of it has remained too debatable for definite conviction. Krall's own report in 1927 (Ztschft f. Parapsychol. 21: pp. 150-153) entitled "Denkbüertragung Zwischen Mensch and Tier", lacks too much in completeness and detail to permit a safe judgment.
23:4 Annal. Sci. Psych., XX: pp. 14-21, and pp. 40-53, 1910.
23:5 Proc. S.P.R., XX I: pp. 60-93, 1907; XXVII: pp. 279-317, 1914.
24:1 Proc. S.P.R., XXXI: pp. 124-217, 1920.
24:2 S. G. Soal, Proc. S.P.R., XL, 1932, p. 168. Dr. W. F. Prince was very noncommittal in his review, p. 21, B.S.P.R., Bulletin VI, which I take as also an indication of the inconclusiveness of the experiment.
24:3 Proc. S.P.R., 38: pp. 1-9, 1928.
24:4 Proc. S.P.R., XL, pp. 165-362, 1932.
24:5 Die Emanation der psycho-physischen Energie. (Munich) 1908.
24:6 Expmtl. Untersuchungen auf dem Gebiete des räumlichen Hellsehens (Munich) 1909.
24:7 Telepathie and Hellsehen. (Halle) 1921.
26:1 Proc. S.P.R., VI: pp. 66-83, 1889.
26:2 Proc. S.P.R., VII: pp. 199-220; pp. 370-373.
26:3 Proc. S.P.R., XXXVIII: pp. 223-271, 1928.
27:1 Proc. S.P.R., XXXIX: pp. 375-414, 1931.
28:1 Proc. S.P.R., XXXI: p. 377, 1921.
28:2 Tischner, loc. cit., p. 206.
29:1 Proc. S.P.R., XII: p. 352, 1897.
29:2 This mention is based on Tischner's review, op. cit., p. 206.
29:3 Proc. S.P.R., XXX: pp. 251-260, 1920.
30:1 Life after Death, E. P. Dutton, New York, 1918; pp. 137-142
30:2 Op. cit., p. 211.
30:3 Jour. fur Psychol. and Neurol., 1918.
31:1 Notre Sixieme Sens, Editions Montaigne. Paris, 1928.
APPENDIX TO CHAPTER 2
Mathematics of Probability Used in Evaluation
From the beginning of the scientific period of parapsychology, the subject has had the aid of mathematical methods in its technique of evaluation. Professor Richet first introduced the mathematics of probability into this field in his treatment of the results of his earlier work on "suggestion mentale" or "telepathy", in 1884. 2 And since then the names of Edgeworth and R. A. Fisher of England and of Hawkesworth in America have appeared frequently in connection with probability estimation in the parapsychic branch of the field.
I am no mathematician and must rely upon methods already developed, when they can be found. But in this work it is fortunately possible to make experimental method conform to easy computation of significance of results and this I have done. I have been able, by adhering to the use of five simple card-figures, to keep the probability of success by pure chance at 1/5 for each trial. Where a straight run of consecutive
successes is to be evaluated for anti-chance probability, simply raising 1/5 to the power equal to the number of consecutive successes gives the value desired. This is established probability mathematics.
When, however, scattered successes are to be evaluated for anti-chance significance, the first step is to find the normal chance expectation. This is simply the number of trials (n) multiplied by the probability for success per trial (p), or np. With 1000 trials on 5-suit cards this would be 200. If more or fewer successes are obtained, the difference or deviation is found by subtraction. If 300 successes are given, there is then a positive deviation from np (or chance expectation) of 100. This can be evaluated in terms of percentages, if one merely desires to compare scoring-rates. It may be expressed as percentage of the number of trials (n), or of chance expectation (np) or, of course, as fractions of these. Here we would have a positive deviation that is 10% of n or 50% of np.
But in order to get a more general evaluation—i.e., one that gives a value that measures the rate of scoring in conjunction with the number of trials at which such a rate holds—it is necessary to measure the deviation in relation to a standardized unit of probable deviation. The arbitrary unit I shall use here is the Probable Error (p.e.) which, in this situation, is that deviation from the mean (chance) expectation at which the odds are even (1:1) as to whether pure chance alone is operating or not. The deviation is then divided by the p.e., and the value D/p.e. or critical ratio is found. This is something of a more nearly absolute estimate of the anti-chance value of a given deviation than are percentage figures. Taking the data from Table LII of Gavett's "Statistical Method", 1 I shall cite the odds against chance for the smaller values of D/p.e. (Deviation divided by the probable error.)
Odds against a chance-theory.
1 to 1
4.6 to 1
22 to 1
142 to 1
1,300 to 1
20,000 to 1
[paragraph continues] And adding higher figures adapted from R. A. Fisher's Table II, "Statistical Methods for Research Workers", 2 I get approximately,
100,000 to 1
nearly 1,000,000 to 1
over 100,000,000 to 1
[paragraph continues] Note the rapid rise of these figures for each unit of D/p.e. It is customary to accept a value of 4 as a significant D/p.e. This implies odds of 142 to 1 against a mere chance explanation.
In this report I shall use X to indicate D/p.e., which will be given for nearly every set of data reported (and all are reported). X, then, for any particular lot of data, is its "anti-chance index".
Now these values of X for particular groups of results have a progressive effect upon the mind. That is, if there are three groups, each with an X-value of 6, we can agree that these are more impressive than only one group with an X-value of 6. How much more? And how determine this? I have searched in vain for authority on this point, and have finally attempted a solution which I submit here and use in this report. It is tentatively offered and may be later rejected for a better method, if such is pointed out to me. I have made certain that this method errs, if it errs at all, on the safe side. And it is not at all necessary to any major issue of this report to use it. The reasons for using it are: first, there is needed an easy way of summating the "anti-chance" significance of many groups of results, instead of pooling them all together and getting the value of X after each addition through the report. But, second and more important, in such pooling together the results made by the high scorers are merged with perhaps a greater number of the poor scorers, so losing the greater contribution they made in the general assumption of equal distribution over the whole lot. A short series of 1000 trials by a good subject may well reach a higher figure for X than a poor scorer (only a little above mean expectation) over a series of 10,000 trials. For some purposes it is proper to pool these but for others it is proper to summate their joint effect against the chance-hypothesis by another method which gives proper weight to the scoring rates for each group. And, third, there is the reason that I have in some cases to deal with negative deviations, under conditions in which I tried to secure low results and succeeded. These, too, have their statistical significance and add, quite as well as the positive deviations, to the general weight of the conclusions. But if these were to be pooled with the totals, they would of course only detract from the total value. (Even this, however, would not at all destroy any of our conclusions, because of the large margin of safety.)
One may see the propriety of combining these values of X by remembering that each such value has a corresponding value (See Normal Probability Tables) representing the probability that the deviation it represents was due to chance alone; for example, for X = 3, this is 1/22; for X = 4, 1/142; for X = 6, 1/20,000. Now, three such values of X (for results given under conditions that permit generalization) can be combined by multiplying the three probability fractions and thus the total odds against chance be computed. (This is simple for low values but the needs of this report take in large values of X as well as small; and I have not found tables for the probabilities for large values of X.) Now, with the smaller
probability fraction thus arrived at one may obtain an equivalent value of X from the normal probability tables, if they extend that far. Working thus within the range of the tables available, it was found that the product of the probability fractions for a series of X-values came out roughly equal to the probability fraction for the square root of the sum of the squares of the X-values concerned. In each case, however, there was a lower X-value obtained by the formula Xn = √X2A + X2B + X2C than by the multiplication of the probability fractions. This is safe at least, if not exact.
I then reasoned in the following way for the deduction of a verifying procedure (for justifying the formula): each X is an independent value; it may represent a large number of trials with small deviation-rate or a shorter series with a higher rate, and vice versa. If we can find a way of checking the formula for combined values of X, it must hold for X's derived from large and small deviation rates, or large and small numbers of trials. That is, like the probability fraction which it represents, it is independently manipulable.
Now it appeared possible to check this formula's reliability in the following way: assuming equally distributed deviation-rates over a large number of trials, determine the X for the group as a whole (Xn); then divide the group into various subdivisions, large and small, and for each calculate the X-values; apply the formula to these to find Xn by this method in order to test it. I did so and found that it worked closely, yielding an Xn equal within a unit to that computed the other way, from the group as a whole. 1 If larger X-values can thus be calculated from smaller in this case (as was demonstrated) and if X-values are independently usable values (as they logically have to be), the method must stand as checked, to the extent of accuracy claimed, which is all that is needed for this work.
The formula has, therefore, been used in this report and is in any case safe from exaggerative effect on the general results. And it will, I hope, serve at the same time to raise the problem for those readers who may be on better terms with the "Queen of the Sciences".
31:2 Richet, Charles, La Suggestion Mentale et le calcul des Probabilités. Rev. Phil., 1884. For a full review in English see Gurney, Proc. S.P.R., II: pp. 239-256, 1884.
32:1 McGraw-Hill, New York, 1925, p. 180.
32:2 3rd Ed., Oliver and Boyd, London, 1930.
34:1 There is a similar practical check of the formula in Table XLIII, in the final chapter, in which the X-value is given for the results reported in the various chapters. That value for the results reported in Chapter 8 is almost the same for both ways of computing the X-value (81.9 for the formula. and 82.1 for the computation based on the pooling together of all the results). Now, here the evenness of distribution of scoring-rates for the five major subjects makes the pooling together do no violence to the resulting values. They would not have checked had the individual differences been great. Then the formula would have given the more correct value, as it does for the other chapters represented in Table XLIII.