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of it。
For this ignorance； however deplorable from other points of view； gave me a rare advantage in this case。 It was in fact extremely unlikely that my subliminal consciousness； which had never known what a cubic root was or the root of any other power； could help the horse。 I therefore took from a table a list containing several problems； all different and all equally unpleasant looking； covered up the solutions； asked Krall to leave the stable and； when alone with Zarif； copied out one of them on the black…board。 In order not to overload these pages with details which would only be a repetition of one another； I will at once say that none of the antitelepathic tests succeeded that day。 It was the end of the lesson and late in the afternoon； the horses were tired and irritable； and； whether Krall was there or not； whether the problem was elementary or difficult； they gave only absurd replies； wilfully 〃putting their foot in it；〃 as one might say with very good reason。 But； next morning； on resuming their task； when I proceeded as described above； Mohammed and Zarif； doubtless in a better temper and already more accustomed to their new examiner； gave in rapid succession correct answers to nearly every problem set them。 I am bound in fairness to say that there was no appreciable difference between these results and those which are obtained in the presence of Krall or other onlookers who； consciously or unconsciously； are already aware of the answer required。
I next thought of another and much simpler test； but one which； by virtue of its very simplicity； could not be exposed to any elaborate and farfetched suspicions。 I saw on one of the shelves in the stable a panel of cards； about the size of an octavo volume； each bearing an arabic numeral on one of its sides。 I once more asked my good friend Krall； whose courtesy is inexhaustible； to leave me alone with his pupil。 I then shuffled the cards and put three of them in a row on the spring…board in front of the horse； without looking at them myself。 There was therefore； at that moment； not a human soul on earth who knew the figures spread at the feet of my companion； this creature so full of mystery that already I no longer dare call him an animal。 Without hesitation and unasked； he rapped out correctly the number formed by the cards。 The experiment succeeded； as often as I cared to try it； with Hanschen； Mohammed and Zarif alike。 Mohammed did even more： as each figure was of a different colour； I asked him to tell me the colourof which I myself was absolutely ignorantof the first letter on the right。 With the aid of the conventional alphabet； he replied that it was blue； which proved to be the case。 Of course； I ought to have multiplied these experiments and made them more exhaustive and complicated by combining； with the aid of the cards and under the same conditions； exercises in multiplication； division and the extracting of roots。 I had not the time； but； a few days after I left； the subject was resumed and completed by Dr。 H。 Hamel。 I will sum up his report of the experiments： the doctor； alone in the stable with the home （Krall was away； travelling）； puts down on the black…board the sign ＋ and then places before and after this sign； without looking at either of them； a card marked with a figure which he does not know。 He next asks Mohammed to add up the two numbers。 Mohammed at first gives a few heedless taps with his hoof。 He is called to order and requested to be serious and to attend。 He then gives fifteen distinct taps。 The doctor next replaces the sign ＋ by X and； again without looking at them； places two cards on the blackboard and asks the horse not to add up the two figures this time； but to multiply them。 Mohammed taps out； 〃27；〃 which is right； for the black…board says； 〃9 X 3。〃 The same success follows with other multiplication sums： 9 X 2； 8 X 6。 Then the doctor takes from an envelope a problem of which he does not know the solution： fourth root of 7890481。 Mohammed replies； 〃53。〃 The doctor looks at the back of the paper： once more； the answer is perfectly correct。
16
Does this mean that every risk of telepathy is done away with？ It would perhaps be rash to make a categorical assertion。 The power and extent of telepathy are as yet； we cannot too often repeat； indefinite； indiscernible； untraceable and unlimited。 We have but quite lately discovered it； we know only that its existence can no longer be denied； but； as for all the rest； we are at much the same stage as that whereat Galvani was when he gave life to the muscles of his dead frogs with two little plates of metal which roused the jeers of the scientists of his time； but contained the germ of all the wonders； of electricity。
Nevertheless； as regards telepathy in the sense in which we understand and know it to…day； my mind is made up。 I am persuaded that it is not in this direction that we must seek for an explanation of the phenomenon； or； if we are determined to find it there； the explanation becomes complicated with so many subsidiary mysteries that it is better to accept the prodigy as it stands； in its original obscurity and simplicity。 When； for instance； I was copying out one of the grisly problems which I have mentioned； it is quite certain that my conscious intelligence could make neither head nor tail of it。 I did not so much as know what it meant or whether the exponent 3。 4。 5 called for a multiplication； a division or some other mathematical operation which I did not even try to imagine； and； rack MY memory as I may； I cannot remember any moment in my life when I knew more about it than I do now。 We should therefore have to admit that MY subliminal self is a born mathematician； quick； infallible and endowed with boundless learning。 It is possible and I feel a certain pride at the thought。 But the theory simply shifts the miracle by making it pass from the horse's soul to mine； and the miracle becomes no clearer by the transfer； which； for that matter； does not sound probable。 I need hardly add that； a fortiori； Dr。 Hamel's experiments and many others which I have not here the space to describe finally dispose of the theory。
17
Let us see how those who have interested themselves in these extraordinary manifestations have attempted to explain them。
As we go along； we will just shear through the feeble undergrowth of childish theories。 I shall not； therefore； linger over the suggestions of cheating； of manifest signs addressed to the eye or ear； of electrical installations that are supposed to control the answers； nor other idle tales of an excessively clumsy character。 To realize their inexcusable inanity we have but to spend a few minutes in the honest Elberfeld stable。
At the beginning of this essay； I mentioned the attack made by Herr Pfungst。 Herr Pfungst； the reader will remember； claims to prove that all the horse's replies are determined by imperceptible and probably unconscious movement on the part of the person putting the questions。 This interpretation； which falls to the ground； like all the others； in the face of the actual facts； would not deserve serious discussion； were it not that the Berlin psychologist's report created an immense sensation some years ago and has succeeded in intimidating the greater part of the official German scientific world to this day。 It is true that the report in question is a monument of useless pedantry； but we are none the less bound to admit that； such as it was； it annihilated poor Von Oaten； who； being no controversialist and not knowing how to proclaim the truth which was struggling for utterance； died in gloom and solitude。
To make an end of this cumbrous and puerile theory； is it necessary to emphasize again that experiments in which the animal does not see the questioner are as regularly successful as the others？ Krall； if you ask him； will stand behind the horse； will speak from the end of the room； will leave the stable altogether； and the results are just the same。 They are the same again when the tests are made in the dark or when the animal's head is covered with a close…fitting hood。 They do not vary either in the case of Berto； who is stone…blind； or when any other person whatever sets the problem in Krall's absence。 Will it be maintained that this outsider or that stranger is acquainted beforehand with the imperceptible signs that are to dictate the solution which he himself often does not know？
But what is the use of prolonging this fight against a cloud of smoke？ None of it can bear examination； and it calls for a genuine effort of the will to set one's self seriously to refute such pitiful objections。
18
On the ground thus cleared and at the portal of this unlooked…for riddle； which comes to disturb our peace in a region which we thought to be finally explored and conquered； there are only two ways； if not of explaining； at least of contemplating the phenomenon： to admit purely and simply the almost human intelligence of the horse； or to have recourse to an as yet very vague and indefinite theory which； for lack of a better designation； we will call the mediumistic or subliminal theory and of which we will strive presentlyand no doubt vainlyto dispel the grosser darkness。 But； whatever interpretation we