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