Athirdviewholdsthat，atleastinthecaseofcomplexideas，obliviscenceconsistsinthecrumblingintopartsandthelossofseparatecomponentsinsteadofingeneralobscuration。Theideaofresolutionintocomponentpartsrecentlyspokenofsuppliesheretheonlyexplanation。\"Theimageofacomplexobjectisdiminourmemorynotbecauseasawholewithallitspartspresentandinorderitisilluminatedbyafeeblerlightofconsciousness，butitisbecauseithasbecomeincomplete。Somepartsofitareentirelylacking。Aboveallthepreciseconnectionofthosestillextantis，ingeneral，missingandissuppliedonlybythethoughtthatsomesortofuniononceexistedbetweenthem;thelargenessofthesphereinwhich，withoutbeingabletomakeafinaldecision，wethinkthisorthatconnectionequallyprobable，determinesthedegreeofdimnesswhichwearetoascribetotheideainquestion。\"[3]
Eachoftheseopinionsreceivesacertain，butnotexclusive，supportfromtheactualinnerexperiences，orexperiencessupposedtobeactual，whichweattimeshave。Andwhatisthereason？Itisthatthesefortuitousandeasilyobtainedinnerexperiencesaremuchtoovague，superficialandcapableofvariousinterpretationstoadmitintheirentiretyofonlyasingleinterpretation，oreventoletitappearasofpreponderatingprobability。
Whocould，witheventolerableexactness，describeinitsgradualcoursethesupposedoverlayingorsinkingorcrumblingofideas？Whocansayanythingsatisfactoryabouttheinhibitionscausedbyseriesofideasofdifferentextent，oraboutthedisintegrationthatafirmcomplexofanykindsuffersbytheuseofitscomponentsinnewconnections？Everybodyhashisprivate\"explanation\"oftheseprocesses，buttheactualconditionswhicharetobeexplainedare，afterall，equallyunknowntoallofus。
Ifoneconsidersthelimitationtodirect，unaidedobservationandtothechanceoccurrenceofusefulexperiences，thereseemsbutlittleprospectofimprovementinconditions。Howwilloneforexampledeterminethedegreeofobscurationreachedatacertainpoint，orthenumberoffragmentsremaining？
Orhowcantheprobablecourseofinnerprocessesbetracedifthealmostentirelyforgottenideasreturnnomoretoconsciousness？Section27。MethodsofInvestigationofActualConditionsBythehelpofourmethodwehaveapossibilityofindirectlyapproachingtheproblemjuststatedinasmallanddefinitelylimitedsphere，and，bymeansofkeepingaloofforawhilefromanytheory，perhapsofconstructingone。
Afteradefinitetime，thehiddenbutyetexistentdispositionslaiddownbythelearningofasyllable-seriesmaybestrengthenedbyafurthermemorisationoftheseries，andtherebytheremainingfragmentsmaybeunitedagaintoawhole。Theworknecessaryforthiscomparedwiththatnecessarywhensuchdispositionsandfragmentsareabsentgivesameasureforwhathasbeenlostaswellasforwhatremains。Theinhibitionswhichidea-groupsofdifferentsortsorextentsmayoccasioninrelationtoothersmust，asaresultoftheinterpositionofwelldefinedcomplexesofideasbetweenlearningandrelearning，betrayitselfinthemoreorlessincreasedworkofrelearning。Thelooseningofabondofconnectionbysomeotheruseofitscomponentscanbeinvestigatedinasimilarmannerasfollows：
afteracertainserieshasbeenstudied，newcombinationsofthesameseriesarememorisedandthechangeintheamountofworknecessaryforrelearningtheoriginalcombinationisthenascertained。
First，Iinvestigatedthefirstmentionedoftheserelationsandputthequestion：Ifsyllableseriesofadefinitekindarelearnedbyheartandthenlefttothemselves，howwilltheprocessofforgettinggoonwhenleftmerelytotheinfluenceoftimeorthedailyeventsoflifewhichfillit？Thedeterminationofthelossessufferedwasmadeinthewaydescribed：
aftercertainintervalsoftime，theseriesmemorisedwererelearned，andthetimesnecessaryinbothcaseswerecompared。
Theinvestigationsinquestionfellintheyear1879-80andcomprised163doubletests。Eachdoubletestconsistedinlearningeightseriesof13syllableseach（withtheexceptionof38doubleteststakenfrom11-12
A。M。whichcontainedonlysixserieseach）andtheninrelearningthemafteradefinitetime。Thelearningwascontinueduntiltwoerrorlessrecitationsoftheseriesinquestionwerepossible。Therelearningwascarriedtothesamepoint;itoccurredatoneofthefollowingtimes，——namely，afteraboutonethirdofanhour，after1hour，after9hours，oneday，twodays，sixdays，or31days。
Thetimesweremeasuredfromthecompletionofthefirstsetoffirstlearnings，asaconsequenceofwhichnogreataccuracywasrequiredincaseofthelongerintervals。Theinfluenceofthelastfourintervalswastestedatthreedifferenttimesofday（p。33[endofChapterIII]）。
Somepreliminaryremarksarenecessarybeforetheresultsobtainedcanbecommunicated。
Similarexperimentalconditionsmaybetakenforgrantedinthecaseoftheseriesrelearnedafteranumberofwholedays。Atanyratethereisnowayofmeetingtheactualfluctuationsevenwhenexternalconditionsareasfaraspossiblesimilar，otherthanbyamultiplicationofthetests。
Wheretheinnerdissimilaritywaspresumablythegreatest，namelyaftertheintervalofanentiremonth，Iapproximatelydoubledthenumberoftests。
Inthecaseofanintervalofninehoursandanintervalofonehourbetweenlearningandrelearning，thereexisted，however，anoticeablyconstantdifferenceintheexperimentalconditions。Inthelaterhoursofthedaymentalvigorandreceptivityareless。Theserieslearnedinthemorningandthenrelearnedatalaterhour，asidefromotherinfluences，requiremoreworkforrelearningthantheywouldiftherelearningweredoneatatimeofmentalvigorequaltothatoftheoriginallearning。Therefore，inordertobecomecomparable，thenumericalvaluesfoundforrelearningmustsufferadiminutionwhich，atleastinthecaseofthe8hourinterval，issoconsiderablethatitcannotbeneglected。Itmustbeascertainedhowmuchlongerittakestolearnatthetimeofday，B，serieswhichwerelearnedinasecondsatthetimeofday，A。TheactualdeterminationofthisquantitypresupposesmoreteststhanI，uptothepresent，possess。
Ifanecessarybutinexactcorrectionisappliedtothenumbersfoundfor1andfor8hours，thesebecomeevenmoreunreliablethaniflefttothemselves。
Intheeaseofthesmallestinterval，onethirdofanhour，thesamedrawbackreappears，thoughtoalessdegree;butitisprobablycompensatedforbyanothercircumstance。Theintervalasawholeissoshortthattherelearningofthefirstseriesofatestfollowedalmostimmediatelyorafteranintervalofoneortwominutesuponthelearningofthelastseriesofthesametest。Forthisreasonthewholeformedsotospeak，onecontinuoustestinwhichtherelearningoftheseriestookplaceunderincreasinglyunfavorableconditionsasregardsmentalfreshness。Butontheotherhandtherelearningaftersuchashortintervalwasdoneratherquickly。Ittookhardlyhalfofthetimerequiredforthelearning。Bythismeanstheintervalbetweenthelearningandrelearningofacertainseriesbecamegraduallysmaller。Thelaterseriesthereforehadmorefavorableconditionswithregardtothetimeinterval。Inviewofthedifficultyofmoreaccuratedeterminations，Ihavetakenitforgrantedthatthesetwosupposedcounteractinginfluencesapproximatelycompensatedeachother。Section28。ResultsInthefollowingtableIdenoteby：
Lthetimeoffirstlearningoftheseriesinseconds，justastheywerefound，thereforeincludingthetimeforthetworecitations。
WLthetimeforrelearningtheseriesalsoincludingtherecitations。
WLkthetimeofrelearningreducedwherenecessarybyacorrection。
DthedifferenceL-WLorL-WLk，asthecasemaybe——thatis，thesavingofworkinthecaseofrelearning。
Qtherelationofthissavingofworktothetimenecessaryforthefirstlearning，givenasapercent。InthecalculationofthisquotientIconsideredonlytheactuallearningtime，thetimeforrecitationhavingbeensubtracted。[4]
Thelatterwasestimatedasbeing85secondsfortworecitationsof8seriesof13syllableseach;thatwouldcorrespondtoadurationof0。41
secondsforeachsyllable（p。31[ChapterIII，Section15]）。
ThusQ=（100D）/（L-85）
FinallyA，B，Cmeanthepreviouslymentionedtimesofday，10-11A。M。，11-12A。M。，6-8P。M。
Ahastyglanceatthefiguresaboverevealsthefactthatforeachintervaloftimethesavingsinworkwhichbecomeevidentwhentheseriesisrelearnedhaveveryfluctuatingvalues。（Thissavinginworkiseachtimethemeasurefortheamountrememberedattheendoftheinterval。）Thisisespeciallythecasewiththeirabsolutevalues（D），butisalsothecasewiththerelativevalues（Q）。Theresultsaretakenfromtheearlierperiodandsufferfromseveraldisturbinginfluencestowhichmyattentionwasfirstdrawnbytheteststhemselves。
Inspiteofallirregularitiesindetail，however，theygroupthemselvesasawholewithsatisfactorycertaintyintoanharmoniouspicture。Asaproofofthistheabsoluteamountofthesavinginworkisoflessvalue。
Thelatterevidentlydependsuponthetimeofday——i。e。，uponthechangesinthetimeofthefirstlearningdependentuponit。Whenthischangeisgreatest（timeC），Dalsoisgreatest;
forthetimeB，theyarein3/4ofthecaseslargerthanforthetimeA
（aftermultiplyingby4/3）。Ontheotherhand，thevalues（Q）foundfortherelationofeachsavingofworktothetimeoriginallyspent，areapparentlyalmostindependentofthisratio。Theiraveragesareclosetogetherforallthreetimesofday，anddonotshowanycharacterofincreaseordecreaseinthelaterhours。AccordinglyIheretabulatethelatter。Section29。DiscussionofResults1。Itwillprobablybeclaimedthatthefactthatforgettingwouldbeveryrapidatthebeginningoftheprocessandveryslowattheendshouldhavebeenforeseen。However，itwouldbejustasreasonabletobesurprisedatthisinitialrapidityandlaterslownessastheycometolighthereunderthedefiniteconditionsofourexperimentforacertainindividual，andforaseriesof13syllables。Onehouraftertheendofthelearning，theforgettinghadalreadyprogressedsofarthatonehalftheamountoftheoriginalworkhadtobeexpendedbeforetheseriescouldbereproducedagain;after8hourstheworktobemadeupamountedtotwothirdsofthefirsteffort。Gradually，however，theprocessbecameslowersothatevenforratherlongperiodstheadditionallosscouldbeascertainedonlywithdifficulty。After24hoursaboutonethirdwasalwaysremembered;after6daysaboutonefourth，andafterawholemonthfullyonefifthofthefirstworkpersistedineffect。Thedecreaseofthisafter-effectinthelatterintervalsoftimeisevidentlysoslowthatitiseasytopredictthatacompletevanishingoftheeffectofthefirstmemorisationoftheseserieswould，iftheyhadbeenlefttothemselves，haveoccurredonlyafteranindefinitelylongperiodoftime。
2。Leastsatisfactoryintheresultsisthedifferencebetweenthethirdandfourthvalues，especiallywhentakeninconnectionwiththegreaterdifferencebetweenthefourthandfifthnumbers。Intheperiod9-24hoursthedecreaseoftheafter-effectwouldaccordinglyhavebeen21/2percent。Intheperiod24to48hoursitwouldhavebeen6。1percent;inthelater24hours，then，aboutthreetimesasmuchasintheearlier15。Suchaconditionisnotcredible，sinceinthecaseofalltheothernumbersthedecreaseintheafter-effectisgreatlyretardedbyanincreaseintime。Itdoesnotbecomecredibleevenundertheplausibleassumptionthatnightandsleep，whichformagreaterpartofthe15hoursbutasmallerpartofthe24，retardconsiderablythedecreaseintheafter-effect。
Thereforeitmustbeassumedthatoneofthesethreevaluesisgreatlyaffectedbyaccidentalinfluences。Itwouldfitinwellwiththeotherobservationstoconsiderthenumber33。7percentfortherelearningafter24hoursassomewhattoolargeandtosupposethatwithamoreaccuraterepetitionofthetestsitwouldbe1to2unitssmaller。However，itisupheldbyobservationstobestatedpresently，sothatIamindoubtaboutit。
3。Consideringthespecial，individual，anduncertaincharacterofournumericalresultsnoonewilldesireatoncetoknowwhat\"law\"isrevealedinthem。However，itisnoteworthythatallthesevenvalueswhichcoverintervalsofonethirdofanhourinlengthto31daysinlength（thusfromsinglefoldto2，000fold）maywithtolerableapproximationbeputintoarathersimplemathematicalformula。Icall：
tthetimeinminutescountingfromoneminutebeforetheen（lofthelearning，bthesavingofworkevidentinrelearning，theequivalentoftheamountrememberedfromthefirstlearningexpressedinpercentageofthetimenecessaryforthisfirstlearning，candktwoconstantstobedefinedpresentlyThenthefollowingformulamaybewritten：
b=100k/（（logt）ck）
Byusingcommonlogarithmsandwithmerelyapproximateestimates，notinvolvingexactcalculationbythemethodofleastsquares，k=1。84
c=1。25
Thentheresultsareasfollows：
Thedeviationsofthecalculatedvaluesfromtheobservedvaluessurpasstheprobablelimitsoferroronlyatthesecondandfourthvalues。WithregardtothelatterIhavealreadyexpressedtheconjecturethatthetestmighthavegivenheretoolargeavalue;thesecondsuffersfromanuncertaintyconcerningthecorrectionmade。Bythedeterminationmadefort，theformulahastheadvantagethatitisvalidforthemomentinwhichthelearningceasesandthatitgivescorrectlyb=100。Inthemomentwhentheseriescanjustberecited，therelearning，ofcourse，requiresnotime，sothatthesavingisequaltotheworkexpended。
Solvingtheformulaforkwehavek=b（logt）c/（100-b）
Thisexpression，100-bthecomplementoftheworksaved，isnothingotherthantheworkrequiredforrelearning，theequivalentoftheamountforgottenfromthefirstlearning。Callingthis，v，thefollowingsimplerelationresults：b/v=k/（logt）cToexpressitinwords：whennonsenseseriesof13syllableseachwerememorisedandrelearnedafterdifferentintervals，thequotientsoftheworksavedandtheworkrequiredwereaboutinverselyproportionaltoasmallpowerofthelogarithmofthoseintervalsoftime。Toexpressitmorebrieflyandlessaccurately：thequotientsoftheamountsretainedandtheamountsforgottenwereinverselyasthelogarithmsofthetimes。
Ofcoursethisstatementandtheformulauponwhichitrestshaveherenoothervaluethanthatofashorthandstatementoftheaboveresultswhichhavebeenfoundbutonceandunderthecircumstancesdescribed。Whethertheypossessamoregeneralsignificancesothat，underothercircumstancesorwithotherindividuals，theymightfindexpressioninotherconstantsIcannotatthepresenttimesay。Section30。ControlTestsAtanyrate，eventhoughonlyformyowncase，Icantoacertainextentgivesupporttotwoofthevaluesmentionedbytestswhichweremadeatotherperiods。
FromaperiodevenfurtherbackthanthatoftheinvestigationsabovementionedIpossessseveraltestswithseriesoftensyllables，fifteenseriescomposingonetest。Theserieswerefirstmemorisedandthen，atanaverageof18minutesafterthefirstlearning，eachserieswasrelearned。
Sixtestshadthefollowingresults：——
Whenrelearningseriesoftensyllableseach，18minutesafterthefirstmemorisation，56percentoftheworkoriginallyexpendedwasthereforesaved。Thenumberagreessatisfactorilywiththeonefoundabove（p。68
[section28]）fortherelearningofseriesofsyllablesof13syllableseachafter19minutes，58percent。Alsothefactthatthelatter，notwithstandingthelongerinterval，isstillalittlegreater，harmonisescompletely，aswillbeseen，withtheresultsofthenextchapter。Accordingtothem，shorterseries，whenmemorised，areforgottenalittlemorequicklythanlongeronce。
Fromtheperiodof1883-84，Ihaveseventests，consistingofnineseriesof12syllableseachthatwererelearned24hoursafterthefirstmemorisation。
Thefollowingresultswereobtained：
Theafter-effectofthefirstmemorisationstillnoticeableafter24
hours，washereequivalenttoasavingofworkof33。4percentofthefirstexpenditure。Thisnumberalsoagreessatisfactorilywiththeonecommunicatedabovefortherelearningofseriesof13syllableseachafter24hours（33。7percent），althoughthesetwowereobtainedatfarseparatedtime-periodsandinthecourseofwidelydifferentinvestigations。
Footnotes[1]ThisistheopinionofAristotleandisstillauthoritativeformanypeople。Lately，forinstance，Delboeufhastakenitupagain，andhasuseditasacomplementtohis\"théoriegénéraledelasensibilité。\"Inhisarticle，Lesommeiletlesrêves（Rev。Philos。IX，p。153f。），hesays：Nousvoyonsmaintenantquetoutactedesentiment，depenséeoudevolitionenvertud’uneloiuniverselleimprimeennousunetraceplusoumoinsprofonde，maisindélébile，généralementgravéesuruneinfinitédetraitsantérieurs，surchargéeplustardd’uneautreinfinité
delinéamentsdetoutenature。maisdontl’écritureestnéanmoinsindéfinimentsusceptibledereparaîtreviveetnetteaujour。\"
（Weseenowthatbyagenerallaweveryactoffeeling，thoughtorwillleavesamoreorlessdeepbutindelibleimpressuponourmind，thatsuchatracingisusuallygravenuponaninfinitenumberofprevioustracesandlaterisitselfoverlaidwithinnumerableothersbutneverthelessisstillcapableofvividandclearreappearance。）Itistruethatheproceeds：
\"néanmoins……ilyaquelquevéritédansl’opinionquiveutquelamémoirenonseulementsefatiguemaiss’oblitère\"
（nevertheless……thereissometruthintheopinionthatmemorynotonlybecomesfatiguedbutthatitdisappears\"），butheexplainsthisbythetheorythatonememorymighthinderanotherfromappearing。Siunsouvenirnechassepasl’autre，onpeutdumoinsprétendrequ’unsouvenirempêchel’autreetqu’ainsipourlasubstancecérébrale，chezl’individu，ilyaunmaximumdesaturation。\"（Ifonerecollectiondoesnotactuallydriveoutanother，itmayatleastbemaintainedthatonerecollectionhinderstheotherandthatthusthebrainofeachindividualissaturtated。）
ThecurioustheoryofBainandothersthateachideaislodgedinaseparateganglioncell，anhypothesisimpossiblebothpsychologicallyandphysiologically，isalsorootedtoacertainextentinAristotle’sview。
[2]Herbartandhisadherents。See，forinstance，Waitz，LeehrbuchderPsychologieSect。16
[3]Lotze，Metaphysik（1879），p。521;alsoMikrokosoms（3）I，p。231ff。
[4]AtheoreticallycorrectdeterminationoftheProbableErrorsofthedifferencesandquotientsfoundwouldbeverydifficultandtroublesome。ThedirectlyobservedvaluesLandWLwouldhavetobemadethebasisofit。Buttheordinaryrulesofthetheoryoferrorscannotheappliedtothesevalues，becausetheserulesarevalidonlyforobservationsgainedindependentlyofoneanother，whereasLandWLareinwardlyconnectedbecausetheywereobtainedfromthesameseries。
Thesourceoferror，\"difficultyoftheseries，\"doesnotvarybychance，butinthesamewayforeachpairofvalues。ThereforeItookherethelearningandrelearningoftheseriesasasingletestandtheresultingDorQ，asthecasemaybe，asitsnumericalrepresentative。FromtheindependentlycalculatedDandQ，theprobableerrorswerethencalculatedjustasfromdirectlyobservedvalues。Thatissufficientforanapproximateestimateofthereliabilityofthenumbers。
ClassicsintheHistoryofPsychology——Ebbinghaus（1885）Chapter9Memory：AContributiontoExperimentalPsychologyHermannEbbinghaus（1885）TranslatedbyHenryA。Ruger&ClaraE。Bussenius（1913）
CHAPTERIXRETENTIONASAFUNCTIONOFTHEORDEROFSUCCESSIONOFTHEMEMBERSOFTHESERIES\"HowoddaretheconnectionsOfhumanthoughtswhichjostleintheirflight。\"Section35。AssociationaccordingtoTemporalSequenceanditsExplanationIshallnowdiscussagroupofinvestigationsmadeforthepurposeoffindingouttheconditionsofassociation。Theresultsoftheseinvestigationsare，itseemstome，theoreticallyofespecialinterest。
Thenon-voluntaryre-emergenceofmentalimagesoutofthedarknessofmemoryintothelightofconsciousnesstakesplace，ashasalreadybeenmentioned，notatrandomandaccidentally，butincertainregularformsinaccordancewiththeso-calledlawsofassociation。Generalknowledgeconcerningtheselawsisasoldaspsychologyitself，butontheotherhandamorepreciseformulationofthemhasremained——characteristicallyenough——amatterofdisputeuptotheverypresent。EverynewpresentationstartsoutwithareinterpretationofthecontentsofafewlinesfromAristotle，andaccordingtotheconditionofourknowledgeitisnecessarysotodo。
Ofthese\"Laws，\"now——if，inaccordancewithusageanditistobehopedinanticipationofthefuture，theuseofsoloftyatermispermittedinconnectionwithformulaeofsovagueacharacter——oftheselaws，I
say，thereisonewhichhasneverbeendisputedordoubted。Itisusuallyformulatedasfollows：
Ideaswhichhavebeendevelopedsimultaneouslyorinimmediatesuccessioninthesamemindmutuallyreproduceeachother，anddothiswithgreatereaseinthedirectionoftheoriginalsuccessionandwithacertaintyproportionaltothefrequencywithwhichtheyweretogether。
Thisformofnon-voluntaryreproductionisoneofthebestverifiedandmostabundantlyestablishedfactsinthewholerealmofmentalevents。
Itpermeatesinseparablyeveryformofreproduction，eventheso-calledvoluntaryform。Thefunctionoftheconsciouswill，forexample，inallthenumerousreproductionsofthesyllable-serieswhichwehavecometoknow，islimitedtothegeneralpurposeofreproductionandtolayingholdofthefirstmemberoftheseries。Theremainingmembersfollowautomatically，sotospeak，andtherebyfulfillthelawthatthingswhichhaveoccurredtogetherinagivenseriesarereproducedinthesameorder。
However，themererecognitionoftheseevidentfactshasnaturallynotbeensatisfyingandtheattempthasbeenmadetopenetrateintotheinnermechanismofwhichtheyaretheresult。IfforamomentwetrytofollowupthisspeculationconcerningtheWhy，beforewehavegonemorethantwostepswearelostinobscuritiesandbumpupagainstthelimitsofourknowledgeoftheHow。
Itiscustomarytoappealfortheexplanationofthisformofassociationtothenatureofthesoul。Mentalevents，itissaid，arenotpassivehappeningsbuttheactsofasubject。Whatismorenaturalthanthatthisunitarybeingshouldbindtogetherinadefinitewaythecontentsofhisacts，themselvesalsounified？Whateverisexperiencedsimultaneouslyorinimmediatesuccessionisconceivedinoneactofconsciousnessandbythatverymeansitselementsareunitedandtheunisonisnaturallystrongerinproportiontothenumberoftimestheyareentwinedbythisbondofconsciousunity。
Whenever，now，byanychanceonepartonlyofsucharelatedcomplexisrevived，whatelsecanitdothantoattracttoitselftheremainingparts？
Butthisconceptiondoesnotexplainasmuchasitwasintendedtodo。
Fortheremainingpartsofthecomplexarenotmerelydrawnforthbuttheyrespondtothepullinanaltogetherdefinitedirection。Ifthepartialcontentsareunitedsimplybythefactoftheirmembershipinasingleconsciousactandaccordinglyallinasimilarfashion，howdoesitcomeaboutthatasequenceofpartialcontentsreturnsinpreciselythesameorderandnotinanychancecombination？Inordertomakethisintelligible，onecanproceedintwoways。
Inthefirstplaceitcanbesaidthattheconnectionofthethingspresentsimultaneouslyinasingleconsciousactismadefromeachmembertoitsimmediatesuccessorbutnottomembersfurtherdistant。Thisconnectionisinsomewayinhibitedbythepresenceofintermediatemembers，butnotbytheinterpositionofpauses，providedthatthebeginningandendofthepausecanbegraspedinoneactofconsciousness。Therebyreturnismadetothefacts，buttheadvantagewhichthewholeplausibleappealtotheunitaryactofconsciousnessofferedissilentlyabandoned。For，howevermuchcontentiontheremaybeoverthenumberofideaswhichasingleconsciousactmaycomprehend，itisquitecertainthat，ifnotalways，atleastinmostcases，weincludemorethantwomembersofaseriesinanyoneconsciousact。Ifuseismadeofonefeatureoftheexplanation，thecharacteristicofunity，asawelcomefactor，theotherside，themanifoldnessofthemembers，mustbereckonedwith，andtherightofrepresentationmustnotbedenieditonassumedbutunstatablegrounds。Otherwise，wehaveonlysaid，——anditispossiblethatwewillhavetobecontentwiththat——
thatitissobecausetherearereasonsforitsbeingso。
Thereis，consequently，thetemptationtousethissecondformofstatement。
Theideaswhichareconceivedinoneactofconsciousnessare，itistrue，allboundtogether，butnotinthesameway。Thestrengthoftheunionis，rather，adecreasingfunctionofthetimeorofthenumberofinterveningmembers。Itisthereforesmallerinproportionastheintervalwhichseparatestheindividualmembersisgreater。Leta，b，c，dbeaserieswhichhasbeenpresentedinasingleconsciousact，thentheconnectionofawithbisstrongerthanthatofawiththelaterc;andthelatteragainisstrongerthanthatwithd。Ifaisinanywayreproduced，itbringswithitbandcandd，butb，whichisboundtoitmoreclosely，mustarisemoreeasilyandquicklythanc，whichiscloselyboundtob，etc。Theseriesmustthereforereappearinconsciousnessinitsoriginalformalthoughallthemembersofitareconnectedwitheachother。
SuchaviewasthishasbeenlogicallyworkedoutbyHerbart。Heseesthebasisoftheconnectionofimmediatelysuccessiveideasnotdirectlyintheunityoftheconsciousact，butinsomethingsimilar：opposedideaswhichareforcedtogetherinaunitarymindcanbeconnectedonlybypartialmutualinhibitionfollowedbyfusionofwhatremains。Yetthis，forourpurpose，isnotessential。Heproceedsasfollows：
\"Letaseries，a，b，c，d……begiveninperception，thena，fromtheveryfirstmomentoftheperceptionandduringitscontinuance，issubjectedtoinhibitionbyotherideaspresentinconsciousness。
Whilea，alreadypartiallywithdrawnfromfullconsciousness，ismoreandmoreinhibited，bcomesup。Thelatter，atfirstuninhibited，fuseswiththeretiringa。cfollowsand，itselfuninhibited，isunitedwiththefastdimmingbandthestillmoreobscureda。
Inasimilarfashiondfollowsandunitesitselfinvaryingdegreeswitha，b，andc。Thusthereoriginatesforeachoftheseideasalawaccordingtowhich，afterthewholeserieshasbeenforcedoutofconsciousnessforsometune，initsownwayonitsrenewedappearanceeachideastrugglestocallupeveryotherideaofthesameseries。Supposethataarisesfirst，itismorecloselyconnectedwithb，lesswithc，stilllesswithd，etc。But，takeninthereverseorderb，c，andd，allinanuninhibitedcondition，arefusedwithwhatremainsofa。Consequentlyaseekstobringthemcompletelybacktotheformofanuninhibitedidea;butitseffectisquickestandstrongestuponb，sloweroncandstillslowerond，etc。（wherebycloserinspectionshowsthatbsinksagainwhilecisstillrising，andthatinthesamewaycsinkswhiledrises，etc。）。Inshort，theseriesrunsoffasitwasoriginallygiven。Ifwesuppose，onthecontrary，thatcwastheoneinitiallyreproduced，thenitseffectondandthesucceedingmembersissimilartothatrevealedbya——i。e。，theseriesc，d，……runsoffgraduallyinconformitywithitsorder。banda，however，experienceanaltogetherdifferentinfluence。Withtheirseparateconsciousresidues，theuninhibitedchadfused;itseffectuponaandbwasthereforewithoutlossofpowerandwithoutdelay，butthiseffectwaslimitedtobringingbacktheconsciousresiduesofaandbboundupwithit，onlyapartofbandastillsmallerpartofabeingrecalledtoconsciousness。This，then，iswhathappensiftheprocessofrecallbeginsanywhereatthemiddleofaknownseries。
Thatwhichprecededthepointofrecallrisesatonceingradeddegreesofclearness。Thatwhichfollowed，onthecontrary，runsoffintheorderoftheoriginalseries。Theseries，however，neverrunsbackwards，ananagramisneverformedoutofawellunderstoodwordwithoutvoluntaryeffort。\"[1]
Accordingtothisconception，therefore，theassociativethreads，whichholdtogetherarememberedseries，arespunnotmerelybetweeneachmemberanditsimmediatesuccessor，butbeyondinterveningmemberstoeverymemberwhichstandstoitinanyclosetemporalrelation。Thestrengthofthethreadsvarieswiththedistanceofthemembers，buteventheweakerofthemmustbeconsideredasrelativelyofconsiderablesignificance。
Theacceptanceorrejectionofthisconceptionisclearlyofgreatimportanceforourviewoftheinnerconnectionofmentalevents，oftherichnessandcomplexityoftheirgroupingsandorganisation。Butitisclearlyquiteidletocontendaboutthematterifobservationislimitedtoconsciousmentallife，totheregistrationofthatwhichwhirlsaroundbychanceonthesurfaceoftheseaoflife。
For，accordingtothehypothesis，thethreadswhichconnectonemembertoitsimmediatesuccessoralthoughnottheonlyonespun，are，however，strongerthantheothers。Consequently，theyare，ingeneral，asfarasappearancesinconsciousnessareconcerned，theimportantones，andsotheonlyonestobeobserved。
Ontheotherhand，themethodswhichlieatthebasisoftheresearchesalreadydescribedpermitthediscoveryofconnectionsofevenlessstrength。
Thisisdonebyartificiallystrengtheningtheseconnectionsuntiltheyreachadefiniteanduniformlevelofreproducibility。Ihave，therefore，carriedonaccordingtothismethodaratherlargenumberofresearchestotestexperimentallyinthefieldofthesyllable-seriesthequestionatissue，andtotraceaneventualdependenceofthestrengthoftheassociationuponthesequenceofthemembersoftheseriesappearinginsuccessioninconsciousness。Section36。MethodsofInvestigationofActualBehaviorResearcheswereagaincarriedoutwithsixseriesof16syllableseach。
ForgreaterclearnesstheseriesaredesignatedwithRomannumbersandtheseparatesyllableswithArabic。Asyllablegroupofthefollowingformconstituted，then，eachtimethematerialforresearch：I（1）I（2）I（3）……I（15）I（16）
II（1）II（2）II（3）……II（15）II（16）……
VI（1）……VI（15）VI（16）IfIlearnsuchagroup，eachseriesbyitself，sothatitcanberepeatedwithouterror，and24hourslaterrepeatitinthesamesequenceandtothesamepointofmastery，thenthelatterrepetitionispossibleinabouttwothirdsofthetimenecessaryforthefirst。[2]Theresultingsavinginworkofonethirdclearlymeasuresthestrengthoftheassociationformedduringthefirstlearningbetweenonememberanditsimmediatesuccessor。
Letussupposenowthattheseriesarenotrepeatedinpreciselythesameorderinwhichtheywerelearned。ThesyllableslearnedintheorderI（1）I（2）I（3）……I（15）I（16）mayforexampleberepeatedintheorderI（1）I（3）1（5）……I（15）I（2）I（4）I（6）……I（16），andtheremainingserieswithasimilartransformation。Therewillfirstbe，accordingly，asetcomposedofallthesyllablesoriginallyintheoddplacesandthenasetofthoseoriginallyintheevenplaces，thesecondsetimmediatelyfollowingthefirst。Thenew16-syllableseries，thusresulting，isthenlearnedbyheart。Whatwillhappen？Everymemberofthetransformedserieswas，intheoriginalseries，separatedfromitspresentimmediateneighborbyaninterveningmemberwiththeexceptionofthemiddletermwherethereisabreak。Iftheseinterveningmembersareactualobstructionstotheassociativeconnection，thenthetransformedseriesareasgoodasentirelyunknown。Inspiteoftheformerlearningoftheseriesintheoriginalsequence，nosavinginworkshouldbeexpectedintherepetitionofthetransformedseries。Ifontheotherhandinthefirstlearningthreadsofassociationarespunnotmerelyfromeachmembertoitsimmediatesuccessorbutalsooverinterveningmemberstomoredistantsyllables，therewouldexist，alreadyformed，certainpredispositionsforthenewseries。Thesyllablesnowinsuccessionhavealreadybeenboundtogethersecretlywiththreadsofacertainstrength。Inthelearningofsuchaseriesitwillberevealedthatnoticeablylessworkisrequiredthanforthelearningofanaltogethernewseries。Thework，however，willbegreaterthaninrelearningagivenseriesinunchangedorder。Inthiscase，again，thesavinginworkwillconstituteameasureofthestrengthoftheassociationsexistingbetweentwomembersseparatedbyathird。Iffromtheoriginalarrangementofthesyllablesnewseriesareformedbytheomissionof2，3，ormoreinterveningmembers，analogousconsiderationsresult。Thederivedserieswilleitherbelearnedwithoutanynoticeablesavingofwork，oracertainsavingofworkwillresult，andthiswillbeproportionallylessasthenumberofinterveningtermsincreases。
OnthebasisoftheseconsiderationsIundertookthefollowingexperiment。
Iconstructedsixseriesof16syllableseachwiththelatterarrangedbychance。Outofeachgroupanewonewasthenconstructedalsocomposedofsixseriesof16syllableseach。Thesenewgroupsweresoformedthattheiradjacentsyllableshadbeenseparatedintheoriginalseriesbyeither1，or2，or3，or7interveningsyllables。
Iftheseparatesyllablesaredesignatedbythepositionswhichtheyheldintheoriginalarrangement，thefollowingschemeresults：I（1）I（2）I（3）……I（15）
I（16）
II（1）II（2）II（3）……II（15）
II（16）……
VI（1）VI（2）VI（3）……VI（15）VI（16）Byusingthesameschemethederivedgroupsappearasfollows：BySkipping1SyllableI（1）I（3）I（5）……I（15）I（2）I（4）I（6）……
I（16）II（1）II（3）II（5）……II（15）II（2）II（4）II（6）……
II（16）……VI（1）VI（3）……VI（15）VI（2）VI（4）……VI（16）BySkipping2SyllablesI（1）I（4）I（7）I（10）I（13）I（16）I（2）I（5）I（8）I（11）I（14）I（3）
I（6）I（9）I（12）I（15）II（1）II（4）I（7）……II（16）II（2）II（5）……
II（14）II（3）II（6）……II（15）……VI（1）VI（4）……VI（16）VI（2）VI（5）……VI（14）
VI（3）VI（6）……VI（15）Byskipping3syllablesI（1）I（5）I（9）I（13）I（2）I（6）I（10）I（14）I（3）I（7）I（11）I（15）
I（4）I（8）I（12）I（16）II（1）II（5）……II（2）II（6）……II（3）II（7）……II（4）II（8）……II（16）……VI（1）VI（5）……VI（2）VII（6）……VI（3）VI（7）……VI（4）II（8）……VI（16）BySkipping7SyllablesI（1）I（9）II（1）II（9）III（1）III（9）IV（1）IV（9）V（1）V（9）VI（1）
VI（9）I（2）I（10）II（2）II（10）III（2）III（10）IV（2）IV（10）V（2）V（10）VI（2）VI（10）I（3）I（11）
II（3）II（11）III（3）III（11）IV（3）IV（11）……V（7）V（15）I（8）I（16）II（8）II（16）III（8）III（16）IV（8）IV（16）
V（8）V（16）VI（8）VI（16）
Asaglanceatthisschemewillshow，notalltheneighboringsyllablesofthederivedserieswereoriginallyseparatedbythenumberofsyllablesdesignated。Insomeplacesinordertoagainobtainseriesof16syllables1
greaterjumpsweremade;butinnocasewastheintervalless。Suchplacesare，forexample，intheseriesinwhichtwosyllablesareskipped，thetransitionsfromI（16）toI（2）andfromI（14）toI（3）。Intheseriesinwhich7intermediateswerejumped，therearesevenplaceswheretherewasnopreviousconnectionbetweensuccessivesyllablessincethesyllablesinquestioncamefromdifferentseriesandthedifferentseries，ashasbeenoftenmentioned，werelearnedindependently。Thefollowingisgiveninillustration：I（9）II（1），II（9）III（1），etc。Thenumberofthesebreaksvarieswiththedifferentkindsofderivation，butineachcaseisthesameasthenumberofskippedsyllables。Onaccountofthisdifference，thederivedseriessufferfromaninequalityinherentinthenatureoftheexperiment。
Inthecourseoftheexperimenttheskippingofmorethan7syllableswasshowntobedesirable，butIrefrainedfromcarryingthatout。Theinvestigationswiththesix16-syllableserieswerecarriedquitefar;
andifserieshadbeenconstructedusinggreaterintervals，thebreaksabovementionedwouldhavehadtoomuchdominance。Thederivedseriesthencontainedeverfewersyllable-sequencesforwhichanassociationwaspossibleonthebasisofthelearningoftheoriginalarrangement;theywereeverthusmoreincomparable。
Theinvestigationswerecarriedonasfollows：——Eachtimethesixserieswerelearnedintheoriginalorderandthen24hourslaterinthederivedandthetimesrequiredwerecompared。Onaccountofthelimitationoftheseriestothosedescribedabovetheresultsare，undercertaincircumstances，opentoaseriousobjection。Letitbesupposedthattheresultisthatthederivedseriesareactuallylearnedwithacertainsavingoftime，thenthissavingisnotnecessarilyduetothesupposedcause，anassociationbetweensyllablesnotimmediatelyadjacent。Theargumentmight，rather，runasfollows。Thesyllableswhicharefirstlearnedinoneorderandafter24hoursinanotherareinbothcasesthesamesyllables。Bymeansofthefirstlearningtheyareimpressednotmerelyintheirdefiniteorderbutalsopurelyasindividualsyllables;withrepetitiontheybecometosomeextentfamiliar，atleastmorefamiliarthanothersyllables，whichhadnotbeenlearnedjustbefore。Moreoverthenewserieshaveinpartthesameinitialandfinalmembersastheold。Therefore，iftheyarelearnedinsomewhatlesstimethanthefirstseriesrequired，itisnottobewonderedat。Thebasisofthisdoesnotnecessarilylieintheartificialandsystematicchangeofthearrangement，butitpossiblyrestsmerelyontheidentityofthesyllables。Ifthesewererepeatedontheseconddayinanewarrangementmadeentirelybychancetheywouldprobablyshowequallyasavinginwork。
InconsiderationofthisobjectionandforthecontroloftheremainingresultsIhaveintroducedafurther，thefifth，kindofderivedseries。
Theinitialandfinalsyllablesoftheoriginalserieswereleftintheirplaces。Theremaining84syllables，intermediates，wereshakenuptogetherandthen，afterchancedrawing，wereemployedintheconstructionofnewseriesbetweentheoriginalinitialandfinalseries。Asaresultofthelearningoftheoriginalandderivedseriestheremustinthiscanalsoberevealedhowmuchofthesavinginworkistobeascribedmerelytotheidentityofthesyllablemassesandtotheidentityoftheinitialandfinalmembersoftheseparateseries。Section37。Results。AssociationsofIndirectSequenceForeachgroupoforiginalandderivedseries11doubletestswereinstituted，55thereforeinall。Theseweredistributedirregularlyoverabout9months。
Theresultswereasfollows：
Tosummarizetheresults：Thenewseries-formedbyskipping1，2，3and7intermediatememberswerelearnedwithanaveragesavingof152，94，78and42seconds。Inthecaseoftheconstructionofanewseriesthroughamerepermutationofthesyllables，therewasanaveragesavingof12seconds。
Inordertodeterminethesignificanceofthesefigures，itisnecessarytocomparethemwiththesavinginworkinmycaseintherelearningofanunchangedseriesafter24hours。Thisamountedtoaboutonethirdofthetimenecessaryforthefirstlearninginthecaseof16-syllableseries，thereforeabout420seconds。
Thisnumbermeasuresthestrengthoftheconnectionexistingbetweeneachmemberanditsimmediatesequent，thereforethemaximaleffectofassociationundertheconditionsestablished。Ifthisistakenasunity，thenthestrengthoftheconnectionofeachmemberwiththesecondfollowingisagenerousthirdandwiththethirdfollowingisascantfourth。
Thenatureoftheresultsobtainedconfirm——formyselfandthecasesinvestigated——thesecondconceptiongivenaboveandexplainedbymeansofaquotationfromHerbart。Withrepetitionofthesyllableseriesnotonlyaretheindividualtermsassociatedwiththeirimmediatesequentsbutconnectionsarealsoestablishedbetweeneachtermandseveralofthosewhichfollowitbeyondinterveningmembers。Tostateitbriefly，thereseemstobeanassociationnotmerelyindirectbutalsoinindirectsuccession。
Thestrengthoftheseconnectionsdecreaseswiththenumberoftheinterveningnumbers;withasmallnumberitwas，aswillbeadmitted，ofsurprisingandunanticipatedmagnitude。
Noevidencehasbeensecured，however，establishingthefacilitationoftheprocessofrelearningaseriesbymeansoftheidentityofthesyllablesandtheidentityoftheinitialandfinalterms。Section38ExperimentswithExclusionofKnowledgeIhavehithertonotstatedtheprobableerrorsoftheresults，inordertodiscusstheirreliabilitymorefullyatthistime。
WhenIstartedupontheexperimentIhadnodecidedopinioninfavorofthefinalresults。Ididnotfindfacilitationofthelearningofthederivedseriesessentiallymoreplausiblethantheopposite。Asthenumbersmoreandmorebespoketheexistenceofsuchfacilitation，itdawneduponmethatthiswasthecorrectandnaturalthing。Afterwhathasbeensaidabove（p。27ff[middleofchapterIII]）onemightthinkthatinthecaseoftheremainingexperiments，thisideahaspossiblyfavoredamoreattentiveandthereforequickerlearningofthederivedseries，andsohas，atleast，decidedlystrengthenedtheresultingsavinginwork，evenifithasnotcauseditaltogether。
Forthethreelargestofthenumbersfound，——consequently，forthefacilitationoftheworkwhichtookplaceinthecaseoftheomissionof1，2，and3interveningsyllables——thisobjectionisofslightsignificance。
Fortheseareproportionatelysolargethatitwouldbeattributingtoomuchtoaninvoluntaryheighteningofastateofattention，voluntarilyconcentratedwithoutthistotheutmost，ifanactualinfluenceisascribedtoithere。Moreover，thegradationofthenumbers，decisivelyissuingastheydofromthedistributionoftheindividualvaluesandrunningparallelwiththenumberofskippedintermediateterms，isinconceivableonanysuchhypothesisasthis。Forthesupposedgreaterconcentrationoftheattentioncouldclearlyworkonlyingeneral。Howcoulditpossiblybringaboutsoregularagradationofnumbersinthecaseoftestswhichwereseparatedfromeachotherbyweeksandmonths？
Theobjectionpresentedabovecouldrenderdoubtfulonlythefourthresult，theproportionallyslightsavinginthelearningofseriesformedfromotherseriesbyskippingsevenintermediateterms。
Clearlyinthiscasetheexactdeterminationofthedifferenceisofespecialinterestbecauseofthesignificantsizeoftheintervaloverwhichanassociationtookplace。
Inthecaseofthepresentinvestigationsthereexiststhepossibilityofsoarrangingthemthatknowledgeconcerningtheoutcomeofthegraduallyaccumulatingresultsisexcludedandsothatconsequentlythedisturbinginfluenceofsecretviewsanddesiresdisappears。Ihaveaccordinglyinstitutedafurthergroupof30doubletestsinthefollowingwayasacontroloftheaboveresults，andespeciallyoftheleastcertainofthem。
Onthefrontsideofapagewerewrittensixsyllableseriesselectedbychanceandonthereversesideofthesamesheetsixseriesformedfromthembyoneofthemethodsofderivationdescribedabove（p。97[Section36]）。Foreachofthefivetransformations6sheetswereprepared。Thefrontsandbacksofthesecouldbeeasilydistinguishedbutnotthesheetsthemselves。Thethirtysheetswereshuffledtogetherandthenlaidasideuntilanymemoryastotheoccurrenceoftheseparatesyllablesindefinitetransformationscouldbeconsideredaseffaced。Thenthefrontside，and24hourslater，thereversesideofagivensheetwerelearnedbyheart。Thetimesnecessaryforlearningtheseparateserieswerenoted，buttheywerenotassembledandfurtherelaborateduntilall30sheetshadbeencompleted。Followingarethenumbers。
Byderivationofthetransformedseriesbyskipping1，2，3，7intermediatesyllables，thederivedserieswerethereforelearnedwithanaveragesavingof110，79，6440seconds。Onthecontrarywithderivationoftheseriesbypermutationofthesyllablesthelearningrequiredanaverageincreaseinexpenditureof5seconds。
Takenasawhole，theselastresultsexactlyconfirm，ascanbeseen，theresultthatwasobtainedatthebeginning。Thenumberoftheseexperimentswasproportionallysmalland，duringthecourseofeachexperiment，therewascompleteexclusionofknowledgeastoresults。Inspiteofthesefactsandalthoughthenumbers，consideredindividually，seemtobedistributedwithoutregardtolaw，theirgrouping，whentakenasawhole，isseentobeinconformitytoasimplelaw。Thefeweraretheinterveningmemberswhichseparatetwosyllablesofaserieswhichhasbeenlearnedbyheart，thelessistheresistanceofferedbytheseseparatedsyllablestotheirbeinglearnedinaneworder。And，inthesameway，thefeweraretheseinterveningterms，thestrongerarethebondswhich，asaresultofthelearningoftheoriginalseries，connectthetwosyllablesacrosstheinterveningmembers。
Inadditiontoagreeingintheirgeneralcourse，thenumbersforbothgroupsofexperimentsalsoagreeinthefollowingrespect。Thedifferencebetweenthefirstandsecondnumbershasthegreatestvalue，andthatbetweenthesecondandthirdhastheleastvalue。Ontheotherhand，itissurprisingthat，withrespecttotheirabsolutesize，thenumbersofthesecondgrouparethroughoutsmallerthanthoseofthefirst。Twocausesmaybebroughtforwardinexplanationofthisbehavior，which，consideringtheconformityofthenumbers，canscarcelybeaccidental。Itmaybethathereisactuallyrevealedthatinfluenceofexpectationwhichhasalreadybeenmentioned。