Onthebasisofthishypothesis,theexplanationofthefactthatthenumbersofthefirstgroupcomeoutsomewhattoolargeisthat,inthecourseoftheexperiment,theexistenceofasavinginworkinthecaseofthederivedserieswasanticipated,andforthisreasonthelearningoftheseriestookplaceinvoluntarilywithasomewhatgreaterconcentrationofattention。
Ontheotherhand,itmaybethat,inconsequenceoftheexcludedknowledge,therehasbeenatworkinthecaseofthenumbersofthesecondgroupadisturbingelementwhichhasmadethemsmaller。Here,tobesure,duringthelearningofthederivedseriesaverylivelycuriositydevelopedconcerningthecategoryoftransformationtowhichtheserieswhichhadjustbeenlearnedbelonged。Thatthismusthavehadadistracting,andthereforeretarding,influenceisprobablenotonlyinitselfbutalsothroughtheresultobtainedfromtheseriesderivedbypermutationofsyllables。Itwastobeexpectedthattheidentityofthesyllables,aswellasoftheinitialandendterms,wouldmakeitselffeltinthiscasebyasavingofwork,howeversmallthatsavingmightbe。Thelattereffectappears,itistrue,intheexperimentsofthefirstgroup。Withthoseofthesecondgroup,however,thereisnoticeable,insteadofthissavingofwork,aslightadditionalexpenditureoftime。This,ifitisnotmerelyaccidental,canscarcelybeexplainedotherwisethanthroughthedistractingcuriositymentioned。
Itispossiblethatbothinfluenceswereatworksimultaneouslysothatthefirstexperimentsgaveresultswhichweresomewhattoohigh;andthesecond,resultsthatweresomewhattoolow。Itisallowable,underthishypothesis,toputthetwosetsoffigurestogethersothatthecontrastingerrorsmaycompensateeachother。Inthiswaytherewasfinallyobtainedoutofthe85doubleteststhefollowingtable。Section39。DiscussionofResultsIntheforegoingtableanespecialinterest,itseemstome,isconnectedwiththelast,andalsowiththenexttothelast,rowofnumbers。Whentherewascompleteidentityofallthesyllablesandtheinitialandendtermswereleftintheirplaces,theaveragesavingoftimefor17testsdealingwiththelearningofthederivedserieswassoslightthatitwashardlytobedetermined。Itfellwithinhalfofitsprobableerror。Thesyllableswere,therefore,inthemselves,outsideoftheirconnection,sofamiliartomethattheydidnotbecomenoticeablymorefamiliarafterbeingrepeated32times。Onthecontrarywhenarelatedserieswasrepeatedthesamenumberoftimes,eachsyllablebecamesofirmlyboundtothesyllablewhichfollowed8placesbeyondthat24hourslatertheinfluenceofthisconnectioncouldbedeterminedinnodoubtfulfashion。Itattainsavalue6timestheprobableerror。Itsexistence,therefore,mustbeconsideredtobefullyprovedalthoughnaturallywecannotbesosurethatitssizeisexactlywhatitwasfoundtobeintheexperiments。Althoughitsabsolutevalueissmall,yetitsinfluenceamountstoonetenthofthatoftheconnectionwhichbindseverymembertoitsimmediatesuccessor。Itissosignificant,andatthesametimethedecreaseintheafter-effectofconnectionswhichwereformedover2,3,7interveningmembersissogradualaone,thattheassertioncanbemade,amthesegroundsalone,thateventhetermswhichstandstillfurtherfromoneanothermayhavebeenboundtoeachothersubconsciouslybythreadsofnoticeablestrengthatthetimeofthelearningoftheseries。
Iwillsummarisetheresultssofargiveninatheoreticalgeneralisation。
Asaresultoftherepetitionofthesyllable-seriescertainconnectionsareestablishedbetweeneachmemberandallthosethatfollowit。Theseconnectionsarerevealedbythefactthatthesyllable-pairssoboundtogetherarerecalledtomindmoreeasilyandwiththeovercomingoflessfrictionthansimilarpairswhichhavenotbeenpreviouslyunited。Thestrengthoftheconnection,andthereforetheamountofworkwhichiseventuallysaved,isadecreasingfunctionofthetimeorofthenumberoftheinterveningmemberswhichseparatedthesyllablesinquestionfromoneanotherintheoriginalseries。Itisamaximumforimmediatelysuccessivemembers。Theprecisecharacterofthefunctionisunknownexceptthatitdecreasesatfirstquicklyandthengraduallyveryslowlywiththeincreasingdistanceoftheterms。