l　aware　that　an　explanation　laden　to　such　an　extent　with　mysteries　explains　but　very　little　more　than　silence　does；　nevertheless；　it　is　at　least　a　silence　traversed　by　restless　murmurs；　and　sedulous　whispers　that　are　better　than　the　gloomy　and　hopeless　ignorance　to　which　we　would　have　perforce　to　resign　ourselves　if　we　did　not；　in　spite　of　all；　to　perform　the　great　duty　of　man；　which　is　to　discover　a　spark　in　the　darkness。
  It　goes　without　saying　that　objections　are　raised　from　every　side。　Among　men；　arithmetical　prodigies　are　looked　upon　as　monsters；　as　a　sort　of　extremely　rare　teratological　phenomenon。　We　can　count；　at　most；　half…a…dozen　in　a　century；　whereas；　among　horses；　the　faculty　would　appear　to　be　almost　general；　or　at　least　quite　common。　In　fact；　out　of　six　or　seven　stallions　whom　Krall　tried　to　initiate　into　the　secrets　of　mathematics；　he　found　only　two　that　appeared　to　him　too　poorly　gifted　for　him　to　waste　time　on　their　education。　These　were；　I　believe；　two　thoroughbreds　that　were　presented　to　him　by　the　Grand…duke　of　Mecklenburg　and　sent　back　by　Krall　to　their　sumptuous　stables。　In　the　four　or　five　others；　taken　at　random　as　circumstances　supplied　them；　he　met　with　aptitudes　unequal；　it　is　true；　but　easily　developed　and　giving　the　impression　that　they　exist　normally；　latent　and　inactive；　at　the　bottom　of　every　equine　soul。　From　the　mathematical　point　of　view；　is　the　horse's　subliminal　consciousness　then　superior　to　man's？　Why　not？　His　whole　subliminal　being　is　probably　superior　to　one；　of　greater　range；　younger；　fresher；　more　alive　and　less　heavy；　since　it　is　not　incessantly　attacked；　coerced　and　humiliated　by　the　intelligence　which　gnaws　at　it；　stifles　it；　cloaks　it　and　relegates　it　to　a　dark　corner　which　neither　light　nor　air　can　penetrate。　His　subliminal　consciousness　is　always　present；　always　alert；　ours　is　never　there；　is　asleep　at　the　bottom　of　a　deserted　well　and　needs　exceptional　operations；　results　and　events　before　it　can　be　drawn　from　its　slumber　and　its　unremembered　deeps。　All　this　seems　very　extraordinary；　but；　in　any　case；　we　are　here　in　the　midst　of　the　extraordinary；　and　this　outlet　is　perhaps　the　least　hazardous。　It　is　not　a　question；　we　must　remember；　of　a　cerebral　operation；　an　intellectual　performance；　but　of　a　gift　of　divination　closely　allied　to　other　gifts　of　the　same　nature　and　the　same　origin　which　are　not　the　peculiar　attribute　of　man。　No　observation；　no　experiment　enables　us；　up　to　the　present；　to　establish　a　difference　between　the　subliminal　of　human　beings　and　that　of　animals。　On　the　contrary；　the　as　yet　restricted　number　of　actual　cases　reveals　constant　and　striking　analogies　between　the　two。　In　most　of　those　arithmetical　operations；　be　it　noted；　the　subliminal　of　the　horse　behaves　exactly　like　that　of　the　medium　in　a　rate　of　trance。　The　horse　readily　reverses　the　figures　of　the　solution；　he　replies；　〃37；〃　for　instance；　instead　of　〃73；〃　which　is　a　mediumistic　phenomenon　so　well…known　and　so　frequent　that　it　has　been　styled　〃mirror…writing。〃　He　makes　mistakes　fairly　often　in　the　most　elementary　additions；　and　subtractions　and　much　less　frequently　in　the　extraction　of　the　most　complicated　roots；　which　again；　in　similar　cases；　such　as　〃xenoglossy〃　and　psychometry；　is　one　of　the　eccentricities　of　human　mediumism　and　is　explained　by　the　same　cause；　namely；　the　inopportune　intervention　of　the　ever　fallible　intelligence；　which；　by　meddling　in　the　matter；　alters　the　certainties　of　a　subliminal　which；　when　left　to　itself；　never　makes　a　mistake。　It　is；　in　fact；　quite　probable　that　the　horse；　being　really　able　to　do　the　small　sums；　no　longer　relies　solely　on　his　intuition　and；　from　that　moment；　gropes　and　flounders　about。　The　solution　hovers　between　the　intelligence　and　the　subliminal　and；　passing　from　the　one；　which　is　not　quite　sure　of　it；　to　the　other；　which　is　not　urgently　appealed　to；　comes　out　of　the　conflict　as　best　it　may。　The　case　is　the　same　with　the　psychometric　or　spiritualistic　medium　who　seeks　to　profit　by　what　he　knows　in　the　ordinary　way；　so　as　to　complete　the　visions　or　revelations　of　his　subconscious　sensibility。　He；　too；　in　this　instance；　is　nearly　always　guilty　of　flagrant　and　inexplicable　blunders。
  Many　other　similarities　will　be　found　to　exist；　notably　the　way　in　which　the　lessons　vary。　Nothing　is　more　uncertain　and　capricious　than　manifestations　of　human　mediumism。　Whether　it　be　a　question　of　automatic　writing；　psychometry；　materializations　or　anything　else；　we　meet　with　series　of　sittings　that　yield　none　but　absurd　results。　Then；　suddenly；　for　reasons　as　yet　obscurethe　state　of　the　weather；　the　presence　of　this　or　that　witness；　or　I　know　not　whatthe　most　undeniable　and　bewildering　manifestations　occur　one　after　the　other。　The　case　is　precisely　the　same　with　the　horses：　their　queer　fancies；　their　unaccountable　and　disconcerting　freaks　drive　poor　Krall　to　despair。　He　never　opens　the　door　of　that　uncertain　stable；　on　important　days；　without　a　sinking　at　the　heart。　Let　the　beard　or　the　frown　of　some　learned　professor　fail　to　please　the　horses：　they　will；　forthwith；　take　an　unholy　delight　in　giving　the　most　irrelevant　answer　to　the　most　elementary　question；　for　hours　and　even　days　on　end。
  Other　common　features　are　the　strongly…marked　personality　of　the　mediumistic　〃raps〃　and　the　communications　known　as　〃deferred　telepathic　communications；〃　that　is　to　say；　those　in　which　the　answer　is　obtained　at　the　end　of　a　sitting　to　a　question　put　at　the　beginning　and　forgotten　by　all　those　present。　What　at　first　sight　seems　one　of　the　strongest　objections　urged　against　the　mediumism　of　the　horse　even　tends　to　confirm　it。　If　the　reply　comes　from　the　horse's　subconsciousness；　it　has　been　asked；　how　is　it　that　it　should　be　necessary　first　to　teach　him　the　elements　of　language；　mathematics　and　so　forth；　and　that　Berto；　for　instance；　is　incapable　of　solving　the　same　problems　as　Mohammed？　This　objection　has　been　very　ably　refuted　by　M。　de　Vesme；　who　writes：
  〃To　produce　automatic　writing；　a　medium　must　have　learnt　to　write；　before　Victorien　Sardou　or　Mlle　Helene　Schmidt　could　produce　their　mediumistic　drawings　and　paintings；　they　had　to　possess　an　elementary　knowledge　of　drawing　and　painting；　Tartini　would　never　have　composed　The　Devil's　Sonata　in　a　dream；　if　he　had　not　known　music；　and　so　forth。　Unconscious　cerebration；　however　wonderful；　can　only　take　effect　upon　elements　already　acquired　in　some　way　or　another。　The　subconscious　cerebration　of　a　man　blind　from　birth　will　not　make　him　see　colours。〃
  Here；　then；　in　this　comparison　which　might　easily　be　extended；　are　several　fairly　well…　defined　features　of　resemblance。　We　receive　a　vivid　impression　of　the　same　habits；　the　same　contradictions；　and　the　same　eccentricities；　and　we　once　more　recognize　the　strange　and　majestic　shadow　of　our　unknown　guest。
  33
  One　great　objection　remains；　based　upon　the　very　nature　of　the　phenomenon；　upon　the　really　inseparable　distance　that　separates　the　whole　life　of　the　horse　from　the　abstract　and　impenetrable　life　of　numbers。　How　can　his　subliminal　consciousness　interest　itself　for　a　moment　in　signs　that　represent　nothing　to　him；　have　no　relation　to　his　organism　and　will　never　touch　his　existence？　But　in　the　first　place；　it　is　just　the　same　with　the　child　or　the　illiterate　calculator。　He　is　not　interested　either　in　the　figures　which　he　lets　loose。　He　is　completely　ignorant　of　the　consequences　of　the　problems　which　he　solves。　He　juggles　with　digits　which　have　hardly　any　more　meaning　to　him　than　to　the　horse。　He　is　incapable　of　accounting　for　what　he　does；　and　his　subconsciousness　also　　acts　in　a　sort　of　indifferent　and　remote　dream。　It　is　true　that；　in　his　case；　we　can　appeal　to　heredity　and　to　memory；　but　is　this　difference　enough　to　settle　the　difficulty　and　definitely　to　separate　the　two　phenomena？　To　appeal　to　heredity　is　still　to　appeal　to　the　subliminal；　and　it　is　not　at　all　certain　that　the　latter　is　limited　by　the　interest　of　the　organism　sheltering　it。　It　appears；　on　the　contrary；　in　many　circumstances；　to　spread　and　extend　far　beyond　that　organism　in　which　it　is　domiciled；　one　would　say；　accidentally　and　provisionally。　It　likes　to　show；　apparently；　that　it　is　in　relation　with　all　that　exists。　It　declares　itself；　as　often　as　possible；　universal　and　impersonal。　It　has　but　a　very　indifferent　care；　as　we　have　seen　in　the　matter　of　apparitions　and　premonitions；　for　the　happiness　and　even　the　safety　of　its　host　and　protector。　It　prophesies　to　its　companion　of　a　lifetime　events　which　he　cannot　avoid　or　which　do　not　concern　him。　It　makes　him　see　beforehand；　for　instance；　all　the　circumstances　of　the　death　of　a　stranger　whom　he　will　only　hear　of　after　the　event；　when　this　event　is　irrevocable。　It　brings　a　crowd　of　barren　presentiments　and　conjures　up　veridical　hallucinations　that　are　wholly　alien　and　idle。　With　psychometric；　typtological　or　materializing　mediums；　it　practises　art　for　art's　sake；　mocks　at　space　and　time；　passes　through　personalities；　sees　through　solid　bodies；　brings　into　communication　thoughts　and　motions　worlds　apart；　reads　souls　and　lives　by　the　light　of　a　flower；　a　rag　of　a　scrap　of　paper；　and　all　this　for　nothing；　to　amuse　itself；　to　astonish　us；　because　it　adores　the　superfluous；　the　in