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。
　　Iftheabstractbutfamiliarconceptionsof’power，’’disposition，’
　　besubstitutedfortheconcreteideasofsavinginworkandeasierreproduction，themattercanbestatedasfollows。Asaresultofthelearningofaserieseachmemberlassatendency，alatentdisposition，todrawafteritself，atitsownreturntoconsciousness，allthemembersoftheserieswhichfollowedit。Thesetendenciesareofvaryingstrength。Theyarethestrongestforthememberswhichimmediatelyfollow。Thesetendenciesareaccordinglyingeneralmosteasilydemonstrableinconsciousness。Theserieswillreturninitsoriginalformwithouttheinterventionofotherinfluenceswhiletheforcesdirectedtotheresuscitationoftheremainingmemberscanbeexplicitlydemonstratedonlybytheintroductionofotherconditions。
　　Itisnaturallynotconceivablethatbyamerecapriceofnaturethevalidityoftheprinciplesdiscoveredshouldbelimitedexclusivelytothecharacterofthematerialinwhichtheywereobtained——i。e。，toseriesofnonsensesyllables。Theymaybeassumedtoholdinananalogouswayforeverykindofidea-seriesandforthepartsofanysuchseries。
　　Itgoeswithoutsaying，whereverrelationsexistbetweentheseparateideas，otherthanthoseoftemporalsequenceandseparationbyintermediatemembers，theseforceswillcontroltheassociativeflow，notexclusively，butwithreferencetoallthemodificationsandcomplicationsintroducedbyrelationsofvariousaffinities，connection，meaning，andthelike。
　　Atanyrate，itwillnotbedeniedthatthedoctrineofAssociationwouldgainthroughageneralvalidityoftheseresultsagenuineroundingoutand，sotosay，agreaterreasonableness。Thecustomaryformulation，"ideasbecomeassociatediftheyareexperiencedsimultaneouslyorinimmediatesuccession，"hassomethingirrationalaboutit。Iftheimmediacyofsuccessionistakenprecisely，theprinciplecontradictsthemostcommonexperiences。
　　Ifitisnottakenexactly，thenitishardtostatewhatkindofsequenceisproperlymeantAtthesametimeitisnotclearwhyasequencenotquitedirectshouldhaveanadvantagewhichsuddenlydisappearsinthecaseofasequencestillmoreindirect。Aswenowknow，thedirectnessorindirect-nessofthesequenceiswithouteffectuponthegeneralnatureofwhathappensbetweenideaswhichsucceedeachother。Inbothcasesconnectionsareformedwhichonaccountoftheircompletesimilaritycanbedesignatedonlybythecommonterm，Association。Buttheseareofdifferentstrength。Asthesuccessionofunitedideasapproachesidealimmediacytheconnectingthreadsgrowstronger，andinproportionasitdepartsfromthisideal，thesethreadsgrowweaker。Theassociationsbetweenmoredistantterms，althoughactuallypresentanddemonstrableunderproperconditionshave，nevertheless，onaccountoftheirslightstrength，practicallynosignificance。Theassociationsbetweenadjacenttermsare，onthecontrary，ofrelativelygreatimportance，andwillmaketheirinfluenceabundantlyfelt。Ofcourse，iftheserieswereleftentirelytothemselvesandiftheywerealwaysproducedinpreciselythesameorder，foreachtermtherewouldappearonlyoneassociation，therelativelystrongest——namely，thatwiththeimmediatelysucceedingterm。Butseriesofideasareneverlefttothemselves。Therichandquicklychangingorderofeventsbringsthemintothemostmanifoldrelations。
　　Theyreturnwiththeirmembersinthemostvariedcombinations。Andthen，undercertaincircumstances，thestrongeroftheselessstrongassociationsbetweenmoredistanttermsmustfindopportunitytoauthenticatetheirexistenceandtoenterintotheinnercourseofeventsinaneffectiveway。Itiseasytoseehowtheymustfavoramorerapidgrowth，aricherdifferentiation，andamany-sidedramificationoftheideaswhichcharacterisethecontrolledmentallife。Ofcoursetheyalsofavoragreatermanifoldness，andsoapparentlyagreaterarbitrarinessandirregularity，inmentalevents。
　　BeforeIproceedfurther，Iwishtoaddafewwordsconcerningtheabovementioned（p。91[Section35]）derivationoftheassociationofsuccessiveideasfromtheunitaryconsciousnessofaunitarysoul。Thereisacertaindangerinbringingtogetherapresentresultwithonefoundpreviously。
　　Imentionedabove（p。47[beginningofChapterV]）thatthenumberofsyllableswhichIcanrepeatwithouterrorafterasinglereadingisaboutseven。
　　Onecan，withacertainjustification，lookuponthisnumberasameasureoftheideasofthissortwhichIcangraspinasingleunitaryconsciousact。Aswejustnowsaw，associationsareformedofnoticeablestrengthovermorethanseveninterveningmembers，thereforebetweenthebeginningandendofanine-syllableseries。Andonaccountofthesizeofthenumbersobtainedandthenatureoftheirgradation，itseemsprobablethat，evenwithalargernumberofsyllables，connectionswouldbeformedbetweentheirextremes。If，however，associationsarebuiltbetweenmemberstoofarseparatedtobeheldtogetherinasingleconsciousact，itisnolongerpossibletoexplainthepresenceofthoseassociationsonthebasisofthesimultaneouspresenceoftheunitedideasinconsciousness。
　　However，Irecognisethatthoseforwhomsuchaderivationisacherishedmatterarenotnecessarilyforcedbytheabovediscussiontoabandontheirconception。Sucharethosewhoconsidertheunitaryactsofaunitarysoulassomethingmoreoriginal，intelligible，transparentorbetterworthyofbeliefthanthesimplefactsofassociationdescribedabove，sothatthereductionofthelattertotheformerwouldbeanoteworthyachievement。
　　Oneneedsbuttosaythat，inthecaseofanunfamiliarsequenceofsyllables，onlyaboutsevencanbegraspedinoneact，butthatwithfrequentrepetitionandgraduallyincreasingfamiliaritywiththeseriesthiscapacityofconsciousnessmaybeincreased。So，forexample，aseriesof16syllables，whichhavebeenthoroughlymemorised，maybepresentinasingleconsciousact。Accordinglythis"explanation"isfreelyavailable。Thoseforwhomitwasofvalueinthecaseofassociationbysimultaneityorimmediatesuccessioncanemployitfullyaswellforourcaseofindirectsequence。Andbecauseofthemodestrequirementswhichinpsychologyaresooftenimposeduponexplanations，thisviewwilldoubtlessforalongtimeservetomakedimthevisionandsopreventthefrankrecognitionofthisasoneofthemostwonderfulofallriddles，anditwillalsoactasahindranceinthesearchforitstrueunderstanding。Section40。ReverseAssociationsOfthemanyproblemswhichspringoutoftheresultspresentedIhavebeenableforthetimebeingtoinvestigateonlyafewandthesebymeansofonlyasmallnumberofexperiments。
　　Asaresultofthefrequentrepetitionofaseries——a，b，c，d……——certainconnections——ab，ac，ad，bd，etc。——
　　areformed。Theideaa，wheneverandhoweveritreturnstoconsciousness，hascertaintendenciesofdifferentstrengthtobringalsowithittoconsciousnesstheideasb，c，d。Arenowtheseconnectionsandtendenciesreciprocal？
　　Thatis，ifatanytimecandnotaistheideabysomechancerevived，doesthishave，inadditiontothetendencytobringdandebackwithit，asimilartendencyinthereversedirectiontowardsbanda？Inotherwords：——Asaresultofthepreviouslearningofa，b，c。[sic]d，thesequencesa，b，c，a，c，e，aremoreeasilylearnedthananygroupingofequallengthofsyllablespreviouslyunknownsuchasp，q，r……Isthesamethingtrueofthesequencescba，andeca？Asaresultofmanifoldrepetitionofaseriesareassociationsalsoformedinthereverseorder？
　　Theviewsofthepsychologistsseemtobedivergentuponthispoint。
　　Onesidecallattentiontotheundoubtedfactthatinspiteofcompletemasteryof，say，theGreekalphabetapersonisnotatallinapositiontorepeatitreadilybackwardsifhehasnotspeciallystudiedandpracticeditinthisform。
　　Theothersidemakeextensiveuseofreverseassociations，asofsomethingquiteintelligible，intheirexplanationoftheoriginofvoluntaryandpurposivemovements。Accordingtothemthemovementsofthechildareatfirstinvoluntaryandaccidental。Withcertaincombinationsofthese，intenselypleasurablefeelingsresult。Inthecaseofmovementsasoffeelings，memorytracesremainwhich，byrepetitionoftheoccurrences，arealwaysmorecloselyassociatedwitheachother。Ifthisconnectionhasattainedacertainstrength，themereideaoftheagreeablefeelingleadsbackwardstotheideaofthemovementwhicharousedit;thencomestheactualmovementandwithitalsotheactualsensedfeeling。
　　TheconceptionofHerbart，whichwelearnedtoknowabove（p。94[Section35]），holdsthemiddlecoursebetweenthesetwoviews。Theideac，whichappearsinthecourseofaseries，fuseswiththeideasbanda，whichhaveprecededitandwhichareyetpresentalthoughbecomingdim。Ifcislateronreproduced，itbringsbandawithitbutdimmed，notfullyuninhibitedorclearlyconscious。Withthesuddenarousalofamemberoutofthemidstofaserieswesurveythatwhichpreceded"atonceingradedclearness";butneverdoesithappenthattheseriesrunsoffinreverseorder。Tothememberwhichspringsupinconsciousnesstheresucceedindueorderandincompleteconsciousnessthosetermswhichfolloweditintheoriginalseries。
　　ForthepurposeoftestingtheactualrelationsIcarriedoutanexperimententirelysimilartothepreviouslydescribedinvestigations。Outofgroupseachcomposedofsix16-syllableseriesarrangedbychancenewgroupswerederivedeitherthroughmerereversalofthesequenceorbythatplustheskippingofanintermediatesyllable。Thenthetwosetsofgroupswerelearnedbyheart，thederivedform24hourslaterthantheoriginal。
　　Iftheschemefortheoriginalformiswrittenasfollows：I（1）I（2）1（3）……I（15）I（16），thenthecorrespondingderivedseriesisthusdesignated：Inthecaseofmerereversalofthesyllablesequence;I（16）I（15）I（14）……I（2）I（1），[sic]
　　Inthecaseofreversalplusskippingofanintermediatesyllable，I（16）I（14）I（12）……I（4）I（2）I（15）I1（13）……I（3）I（1）。
　　ForthefirstkindofderivationIhavecarriedouttenexperiments;
　　forthesecond，onlyfour。
　　Theresultsareasfollows：
　　Inrelationtothetimeoflearningtheoriginalseriesthesavingamountsto124percent。
　　Inrelationtothetimeoflearningtheoriginalseriesthesavingamountedto~percent。
　　Asaresultofthelearningofaseriescertainconnectionsofthemembersarethereforeactuallyformedinareverseaswellasinaforwarddirection。
　　Theseconnectionsarerevealedinthisway，thatserieswhichareformedoutofmembersthusconnectedaremoreeasilylearnedthansimilarseries，whoseindividualmembersarejustasfamiliarbutwhichhavenotbeenpreviouslyconnected。Thestrengthofthepredispositionsthuscreatedwasagainadecreasingfunctionofthedistanceofthemembersfromeachotherintheoriginalseries。Itwas，however，considerablylessforthereverseconnectionsthanfortheforwardones，thedistancesbeingequal。Withanapproximatelyequalnumberofrepetitionsoftheseriesthememberimmediatelyprecedingagivenmemberwasnotmuchmorecloselyassociatedwithitthanthesecondonefollowingit;thesecondpreceding——sofarasmaybedeterminedonthebasisofthesefewresearches——scarcelyasfirmlyasthethirdfollowing。
　　Ifonecouldassumeamoregeneralvalidityforthisrelationfoundherefirstinconnectionwithsyllableseries，themutuallyopposedexperiencesjustmentionedwould，Ibelieve，becomethoroughlyintelligible。Whereaseriesconsistsofonlytwomembers——asinthecaseoftheconnectionbetweenasimpleideaofmovementandthatofanagreeablefeeling——then，bymeansoffrequentrepetitiontheendtermwillacquiresostrongatendencytocallupafteritselftheinitialtermthatthelatterwillactuallyappear。Forthebringingupofthetermfirstprecedingitistheonlythingforwhich，asaresultofthemanyrepetitions，thesecondtermhasacquiredapredisposition。But，nomatterhowmanyrepetitionstheremaybeinthecaseofalongseries，itwillneverhappenonthearousalofamiddletermthattheserieswillreappearinareverseorder。For，howevereasilytheimmediatelyprecedingtermmayconnectitselfwiththeoneforthemomentaroused，theimmediatelysucceedingtermwillappearmoreeasilybyfar，andsowillwinthevictory，providedotherinfluencesdonotintervene。
　　NomatterhowthoroughlyapersonmayhavelearnedtheGreekalphabet，hewillneverbeinaconditiontorepeatitbackwardswithoutfurthertraining。Butifhechancestosetoutpurposelytolearnitbackwards，hewillprobablyaccomplishthisinnoticeablyshortertimethanwasthecaseinthepreviouslearninginthecustomaryorder。Theobjectionisnotinpointthatapoemorspeechwhichhasbeencommittedtoheartisnotnecessarilylearnedmorequicklybackwardsthanitwasoriginallyforwards。
　　Forwiththelearninginreversedirectionthenumerousthreadsofinnerconnectiononwhichrapidlearningofmeaningfulmaterialingeneraldependswillbebroughttonothing。Section41。TheDependenceofAssociationsofIndirectSequenceupontheNumberofRepetitionsTheconnectionsetupasaresultofmanyrepetitionsbetweentheimmediatelysucceedingmembersofanidea-orsyllable-seriesisafunctionofthenumberofrepetitions。AsaresultoftheinvestigationsofChapterVI，whichwerepurposelydirectedtothediscoveryofthisrelation，anapproximateproportionality，withintolerablywidelimits，hasbeenmadeoutbetweenthenumberofrepetitionsandthestrengthoftheconnectionsestablishedbythem。Thelatterwasmeasured，preciselyasintheinvestigationsofthepresentchapter，bytheamountofworksavedinrelearningtheconnectedseriesafter24hours。
　　Ifnow，asaresultofrepetitions，connectionsarealsosetupbetweenmembersofaserieswhicharenotimmediatelysuccessive，thestrengthofthelatterisnaturallyalsoinsomewaydependentuponthenumberofrepetitions。Thequestionarisesinwhatformthedifferentdependenceoccursinthiscase。Doesaproportionalityexistherealso？Ifthenumberofrepetitionsismadegreater，willthethreadsofseparatestrength，whichbindtogetherallthemembersofaserieslearnedbyheart，increaseinstrengthinthesameproportion？Oristhenatureandrateoftheirincreaseinstrengthadifferentoneasisthecasewiththestrengthofthethreadsthemselves？Onthebasisofourpresentknowledgeneithertheonenortheotherofthesepossibilitiescanbedeclaredself-evidentTofacilitateaninsightintotheactualconditionsIhaveinstitutedafewpreliminaryexperimentsinthefollowingway。Sixaeriesof16syllableseachwereimpresseduponthememorybya16-or64-foldattentiverepetition。
　　After24hoursanequalnumberofderivedseriesofthesamelength，whichhadbeenobtainedfromthosealreadylearnedbyskippingoneintermediatesyllable，werelearnedbyhearttothefirstrepetition。Inordertomaketheinvestigationsusefulinotherways，theserieswerederivedinthiscasebyamethodsomewhatdifferentfromthatdescribedabove（p。97[Section36]）。Thelattermethoddiffersfromtheformerinthatheretheodd-numberedsyllablesoftheoriginalserieswerenotfollowedbytheeven-numberedsyllablesofthesameseries。Butalltheodd-numberedsyllablesoftwooriginalserieswereunitedtoformanew16-syllableseries。Thentheeven-numberedsyllablesofthesameoriginalserieswereunitedtoformasecondnewseries。Theschemeofthederivedserieswasthereforenot，asabove，I（1）I（3）I（5）……I（15）I（2）I（4）……I（16）II（1）II（3）II（5）……II（15）II（2）II（4）……II（16）
　　butratherI（1）I（3）I（5）……I（15）II（1）I（3）……I（15）I（2）I（4）I（6）……I（16）II（2）II（4）……II（16）
　　Theeffectofthederivationuponthelearningofthederivedseries，cannot，asitseems，beessentiallyaffectedthroughthisslightchange。
　　Here，asintheabovedescribedmethodofderivation，thesyllableswhichduringthefirstlearninghadbeenseparatedfromeachotherbyaninterveningsyllablewerelearned24hourslaterinimmediatesuccession。
　　ForeachnumberofrepetitionsusedinlearningImade8doubletests，whichgavethefollowingresults：
　　Numberofrepetitionsemployedfortheimpressionofeachoftheoriginalseries：
　　1664Numberofsecondsrequiredforlearningthesixderivedseriesafter24
　　hours（includingtherecital）：
　　11781157
　　1216982
　　12161198
　　9501148
　　1358995
　　10191017
　　11911183
　　12301198
　　——————————————-
　　Average11701109
　　Probableerror3022Onaccountofthesmallnumberofexperimentstheresultingaveragesare，unfortunately，notveryexact;butthegeneralcharacteroftheresultswouldremainthesameevenifweconsideredthevaluefalsewithinthewholerangeoftheprobableerror。Thischaracterbecomesapparentuponcomparisonwiththevaluesgivenabove（p。56[middleofChapter6]）forlearningbyheartsix16-syllableserieswhichhadnotpreviouslybeenlearned。Thistookplacein1，270seconds。Aftertheoriginalserieshadbeenrepeated16times，thederivedserieswaslearnedwithasavingofabout100seconds;afterrepetition64times，withalikesavingof161
　　seconds。Quadruplingtherepetitionsresultedinincreasingthesavingonlyalittlemorethanhalfasmuchagain。Theincreaseinstrengthoftheassociationsreachingoveranintermediatememberwasinnowiseproportionaltothenumberofrepetitions，forthecasesstudied，notevenwithinthelimitsforwhichthiswasnoticeablythecaseforassociationsfromonemembertoitsimmediatesuccessor。Onthecontrarytheeffectoftherepetitionsinthecaseofassociationsofindirectsequencedecreasedconsiderablysoonerandmorequicklythaninthecaseofthoseofdirectsequence。
　　Thereisverycloseagreementbetweenthepairofvaluesjustfoundandthenumbergivenabove（p。99，I[Section37]）——theprocedurebeing，ashere，withouttheexclusionofknowledge——forthelearningofderivedserieswhichthedaybeforehadbeenlearnedintheiroriginalformtothepointoffirstpossiblereproduction。Thisnumber，itistrue，wasobtainedundersomewhatdifferentconditions。Inthefirstplace，notalwayswerethesamenumberofrepetitionsemployedforlearning，buteachtimeasmanyaswererequiredforthefirstpossiblereproduction——i。e。，notexactly，butontheaverage，32。Moreover，thenatureofthederivationofthesenseswassomewhatdifferent，aswasstatedabove。Butthesedifferenceshavelittleweightinthecaseofnumberswhichotherwisecouldhavelittleclaimtoexactness。Iadducethereforethisvalueforcomparison，andinadditionthenumbersgiveinChapterVIfortheinfluenceofrepetitionsontherelearningofthesameuntransformedseries。Herethenisthetable。
　　Icallattentionagaintothefactthatthenumbersgivenaboveareinpartratherinexactandthattheyweregainedunderverylimitedconditions。
　　However，itisallowabletosketchsummarilyandwithhypotheticalelaborationtheviewwhichtheseresultsmakeappeartobethemostprobableexplanationofanimportantgroupofinnerprocessesandwhichfillspleasinglyandcompletelyahithertoemptyplaceinourknowledge。
　　Withtheimprintingandinternalfixationofanidea-seriesthroughitsmanifoldrepetition，innerconnections，associations，arewovenbetweenalltheseparatemembersoftheseries。Thenatureoftheseissuchthatseriesmadeoutofmembersthusassociatedarepickedupandreproducedmoreeasily，withlessresistancetobeovercome，thansimilarseriesmadeupofmembersnotpreviouslyassociated。Theirnaturecanalsobestatedinthisway，thateachmemberoftheserieshasthedefinitetendencyonitsownreturntoconsciousnesstobringbackotherswithit。Theseconnections，ortendencies，areofdifferentstrengthfromseveraldifferentpointsofview。Forthemoredistantmembersoftheoriginalseriestheyareweakerthanforthenearer;forspecificdistancesbackwardstheyareweakerthanforthesamedistancesforward。Thestrengthofalltheconnectionsincreasesasthenumberofrepetitionsincreases。Buttheoriginallystrongerthreadsbetweenthenearermembersarestrengthenedconsiderablymorequicklythantheweakeroneswhichconnectthemoredistantterms。Themore，therefore，thenumberofrepetitionsincreases，thestronger，bothabsolutelyandrelatively，becometheconnectionsbetweenimmediatelysuccessiveterms。
　　Tothesamedegreethemoreexclusiveanddominantbecomesthetendencyofeachtermatitsownreturnintoconsciousnesstodrawafteritselfthattermwhichhadalwaysimmediatelyfolloweditduringtherepetitions。Section42。IndirectStrengtheningofAssociationsIconcludewiththementionofanoteworthyfactwhichappearedincidentallyinconnectionwiththeinvestigationsmentionedintheprecedingparagraphs。
　　Onaccountoftheuncertaintyofthenumericalresultswhichcomeintoconsideration，Icancallattentiontoitonlywithgreatreserve。Icannot，how-ever，passitbyaltogetherbecauseitisprobableinitself，andbecause，withfurtherconfirmation，itwillthrowacharacteristiclightoninnerprocesseswhichareactuallypresentbutwhichremainunconscious。Itwillalsorevealtherelativeindependenceoftheseprocessesfromconsciousaccompaniments，asIhaveshownabove（§24）。
　　Thederivationofthetransformedseriesinthecaseofthelastmentionedinvestigationswasaccomplished，ashasbeenstated，inthefollowingway。
　　Outoftwo16-syllableseriesselectedbychance，firstalltheodd-numberedsyllableswerecombinedtoformanewseriesandthenalltheeven-numberedtoformasecondserieswhichfollowedinimmediatesuccession。Inthecaseofagroupconsistingofsixseriesofthissort，therefore，thederivedseriesIIcontainednothingbutsyllableswhichinthefirstprocessofmemorisinghadfollowedimmediatelyuponthecorrespondingmembersofseriesI。ThederivedseriesIVboreasimilarrelationtoseriesIII，andseriesVItoseriesV。Thefollowingphenomenonappeared，whichisthepeculiarrelationtowhichIwishtocallattention。LesstimewasrequiredforlearningbyheartseriesII，IV，VIontheaveragethanforseriesI，III，V，althoughinalltheothergroupsofseries，whetheroriginalorderived，theconversewasthecase。
　　Iadducesomenumericaldatainevidenceofthisrelation。
　　Fromalltheexperimentswithsixseriesof16syllableswhichwerelearnedtothepointofthefirstrecital，tenimmediatelysuccessiveexperimentsarechosenbychancefortwodifferenttime-periods。ThetimesforcommittingtomemoryseriesI，III，Varecombinedincalculation，asarealsothoseforseriesII，IV，VI。
　　ThesumofseriesII，IVandVI，foundbyaveragingthetenexperiments，ishereinbothcases，ascanreadilybeseen，considerablygreaterthanthesumofseriesI，III，V。Thedifferencesare，tobesure，ofverydifferentamountsfortheseparateexperiments，andinonecasetheyhaveapronouncednegativevalue;butthesefluctuationsarerepresentedinthelargeprobableerrorofthedifferencesoftheaverages;and，inspiteofthesizeoftheseerrors，thepositivecharacterofthedifferencesmaybeconsideredasfairlycertain。
　　Inallotherinvestigatedcasesthefollowingresultappears：therearelargefluctuationsofthedifferencesintheindividualexperiments，butacombinationoftheseveralexperimentsshowsadecisivepredominanceforseriesII，IV，VIalthoughthesurplusissmallerthaninthecaseofthetwoexperimentsinquestion。Thusinthecaseofitearliertestsinwhichserieswerelearnedbyheartwhichhadbeenderivedbyskippingoneintermediatesyllableandwhichhadbeenlearnedthedaybeforeintheoriginalformtheresultswere（p。99，I[Section37]）：
　　Sumofseries（II，IV，VI）minusSumofseries（I，III，V）=33（P。E。m=23）~
　　Withsixlatertestsofthesamesort（p。103，I[Section37]）：
　　Sumof（II，IV，VI）minusSumof（I，III，V）=42（P。E。m=
　　29）。
　　Withtenexperimentswithserieswhichhadbeenrepeatedthedaybefore16timeseach（p。55[beginningofChapter6]）：
　　Sumof（II，IV，VI）minusSumof（I，III，V）=17（P。E。m=21），etc。
　　Onaccountofthelargenessoftheprobableerrorasingleoneofthelastgivenfigureswouldhavelittlesignificance。Bymeansoftheircorrespondenceastothenatureofthedifferencetheygaininprobability，andthephenomenonbecomesquiteintelligibleinlightoftheresultsofSection18。There，andwithespecialdearnessinthecaseof16-syllableseries，itwasshownthatthelearningoftheindividualseriesoccurredintheformoffairlyregularoscillations。Thesewereofsuchasortthatarelativelyslowlylearnedseriesfollowedonelearnedrelativelymorequicklyandviceversa（p。43[endofChapter4]，Fig。3）。Sinceinthecaseofeachexperimentthefirstserieswaslearnedontheaveragethemostquicklyandthesecondthemostslowly，bythecombinationofseriesI，III，VtheaverageminimaareunitedandofseriesII，IV，VItheaveragemaxima。Thedifference，S（II，IV，VI）minus（I，III，V）is，therefore，ingeneralpositive。
　　Accordinglyitmustbesurprisingthatinthecaseofboththegroupsoftestsmentionedintheprecedingparagraphs，thisdifferenceisonthecontraryofanegativesign。
　　Thefluctuationsofthenumbersfortheseparateexperimentsarealsointhiscaseverygreat。However，itisevidentonthefirstglanceandwithoutfurthercomparisonthatastrongdisplacementofthedifferencestothenegativesidehastakenplace。Thisfactisalsoexpressedbytheaverages。Incontrastwithpreviousresults，theseriesII，IV，VIwerelearnedinsomewhatshortertimethanseriesI，III，V。
　　Thatthisexceptionrestsonmerechanceispossiblebutnotveryprobable。
　　Theprobableerrors，althoughlarge，arenotlargeenoughtoindicatethis。
　　Iwouldsoonerfearthatitwasacaseofdisturbanceoftheresultsthroughtheoft-mentionedsourceoferror，anticipationoftheoutcome（p。27ff。[ChapterIII]andp。101[Section37]）。DuringtheprogressoftheexperimentIbelievedwithincreasingcertaintythatIcouldforeseethesmallerexpenditureoftimeforthelearningofseriesII，IV，VI，anditwasonlybecauseIthoughtsomethingofthissortthatIchangedthemethodofderivationofthetransformedseries。Icannot，therefore，excludethepossibilitythat，merelyonthebasisofthishiddenpresuppositionandinamanneraltogetherunrevealedtoconsciousness，agreaterconcentrationofattentionwaspresentinlearningseriesII，IV，VIthaninlearningseriesI，III，V。However，thisassumptionisnottobetakenpositivelyasthecorrectone。Theassumptionthatthewholeofthedifferencefoundistobetracedbacktotheinfluenceofthissourceoferrorwouldinvolvetheascriptionofaprettylargefunctiontoaninvoluntaryandcompletelyunconsciousaccommodationofattentionduetoasecretexpectation。
　　Thereremains，accordingly，acertainprobabilityforthethirdpossibility，namely，thatthecontrastingcharacteroftheaveragedifferenceshasinpartatleastanobjectivebasis，thatthemorerapidlearningofthederivedseries，II，IV，VI，wasinpartduetotheirmannerofderivation。
　　Theproperwayinwhichtothinkofthiscausationwouldbecomedearonlybytheintroductionofphysiologicalconceptionswhichmustfirstbeconstructedoratleastremodelled。Ifuseismadeofthelanguageofpsychology，then，asinthecaseofallunconsciousprocesses，expressioncanbeonlyfigurativeandinexact。
　　Asaresultofthelearningbyheartofaseriesintheoriginalformtheseparatesyllables，wemustsay，retainfairlystrongtendenciesupontheirownreturntoconsciousnesstobringafterthemthesyllableswhichimmediatelysucceededthem。If，therefore，thesyllables1，3，5，etc。，returntoconsciousness，thesyllables2，4，6，etc。，haveatendencyalsotoappear。Thistendencyisnotstrongenoughtobringaboutasaconsciouslyperceivableeventtheactualappearanceof2，4，6。Thelatterareinevidenceonlyinacertaininnerconditionofexcitability;somethingtakesplaceinthemwhichwouldnothaveoccurredif1，3，5hadnotbeenrepeated。
　　Theybehavelikeaforgottennamewhichoneattemptstorecollect。
　　Thisisnotconsciouslypresent;onthecontrary，itisbeingsought。Inacertainway，however，itisundeniablypresent。Itisonthewaytoconsciousness，asonemightsay。Forifideasofallsortswerecalledupwhichstoodinconnectionwiththeearlierexperiencedname，apersoncouldusuallytellwhethertheyagreedwiththeonenowsoughtforbutnotyetfound，ornot。Asaresultofthefrequentrepetitionofthesyllables1，3，5
　　previouslyconnectedwiththesyllables2，4，6，thelatterwereplacedinasimilarslightlypronouncedconditionofexcitation，lyingbetweenconsciousappearanceontheonesideandsimplenon-appearanceontheother。
　　Andthisexcitationhas，asitnowappearsfromourtests，aresultaltogethersimilartothatofactualreturntoconsciousness。Innerconnectionsareestablishedbetweensuccessivelyandinternallyarousedsyllablesjustasbetweensyllablessuccessivelyraisedtoconsciousness，exceptthattheformerarenaturallyoflessstrength。Secretthreadsarespunwhichbindtogethertheseries2，4，6，notyetarousedtoconsciousness，andpreparethewayforitsconsciousappearance。Suchthreadsexistedalreadyingreaterstrengthasaresultofthelearningoftheoriginalseries;
　　thepresenteffectisthatofstrengtheningsomewhatconnectionsalreadymade。Andthatisnothingelsethanwhatwasfoundabove：iftwosyllable-combinations——1，3，5……and2，4，6……——arefrequentlyassociatedinconsciousness（thelearningoftheoriginalseries）thenthesubsequentlearningofthesecondcombination（derivedseriesII，IV，VI）soonafterthelearningofthefirst（derivedseriesI，III，V）hasconsiderablylessresistancetoovercomethanthelatter。Acertainstrengtheningofassociationstakesplace，notonlydirectly，throughconsciousrepetitionoftheassociatedmembers，butalsoindirectlythroughtheconsciousrepetitionofothermemberswithwhichthefirsthadbeenfrequentlyconnected。
　　Thiswayofviewingthematterisaconsequenceoftheassumption（whichbecamenecessaryabove，p。109[Section39]）oftheformationofassociativeconnectionsovermoreinterveningmembersthancouldbecomprehendedinoneclearlyconsciousact。Theseconnectionswouldbeveryfruitfulintheexplanationofmanysurprisingphenomenaofmemoryandrecollection，butonaccountoftheuncertaintyoftheirexperientialbasisIrefrainforthepresentfrompursuingthemfurther。
　　Footnotes[1]Herbart，Lehrb。z。Psychol。，Sect。29。Asimilar"pleasing"view，ashecallsit，wasdevelopedbyLotze，Metaphysik（1879）
　　p。527，withthemodificationthatheattemptstoeliminatethenotionofvaryingstrengthoftheideas，whichviewherejects。Inaccordancewiththeviewmentionedfirstabove，heseestherealreasonforafaithfulreproductionofaseriesofideasinthefactthatassociationismadeonlyfromonelinktothefollowinglink。Accordingly，heteaches，inhisLecturesonPsychology（p。22），"Anytwoideas，regardlessofcontent，areassociatedwhentheyareproducedeithersimultaneouslyorinimmediatesuccession——i。e。，withoutaninterveninglink。Anduponthiscanbebasedwithoutfurtherartificethespecialeasewithwhichwereproduceaseriesofideasintheirproperorderbutnotoutofthatorder。By"furtherartifice"heseemstomeanHerbart’sattemptatanarrangement[2]Ihaveomittedtopresentafewtestswithseriesof16syllableseachfromwhichthisnumberwasobtained，becausetheresultsofthesixthchaptersufficientlycoverthispoint。There（p。55[beginningofChapterVI]），wesawthatsixseriesof16syllableseach，eachseriesbeingrepeated32times，couldbememorisedafter24hoursinanaverageof863seconds。32repetitionsare，onanaverage，justnecessarytobringaboutthefirstpossiblereproductionofseriesof16syllableseach。Consideringthecloseproportionwhichexistsbetweenthenumberofrepetitionsonagivendayandthesavingofworkonthenext，itcannotmuchmatterwhethertheserieswererepeated，each32times，orwerememorisedeachtothefirstpossiblereproduction。Sincethelatterrequiresabout1，270seconds，theworkofrepetitiononthefollowingdayamounts，asstatedabove，toabouttwothirdsofthistime。Therelativesavingwhen16-syllableseriesarerelearnedafter24hours，is，therefore，scarcelydifferentfromthatfoundforseriesof12and13syllables（chaptersVIIandVIII），whileitgraduallyincreasesforstillgreaterlengthofseries。