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。