Butifthiscauseofincompletenessbeborneinmind，socialsegregationswillbeseentoconformtothesameprincipleasallothersegregations。§169。Canthegeneraltruththusvariouslyillustratedbededuced
　　fromthepersistenceofforte，incommonwithforegoingtruths？Probably
　　theexpositionatthebeginningofthechapterwillhaveledmostreaderstoconcludethatitcanbesodeduced。Theabstractpropositionsinvolvedarethese:——First，thatlikeunits，
　　subjecttoauniformforcecapableofproducingmotionsinthem，willbe
　　movedtolikedegreesinthesamedirection。Second，thatlikeunitsifexposed
　　tounlikeforcescapableofproducingmotioninthem，willbedifferently
　　moved—movedeitherindifferentdirectionsortodifferentdegreesinthe
　　Samedirection。Third，thatunlikeunitsifactedonbyauniformforcecapable
　　ofproducingmotioninthem，willbedifferentlymoved——movedeitherin
　　differentdirectionsortodifferentdegreesinthesamedirection。Fourth，
　　thattheincidentforcesthemselvesmustbeaffectedinanalogousways:like
　　forcesfallingonlikeunitsmustbesimilarlymodifiedbytheconflict;
　　unlikeforcesfallingonlikeunitsmustbedissimilarlymodified;andlike
　　forcesfallingonunlikeunitsmustbedissimilarlymodified。Thesepropositions
　　maybereducedtoastillmoreabstractform。Theyallimplythatinthe
　　actionsandreactionsofforceandmatter，anunlikenessineitherofthe
　　factorsnecessitatesanunlikenessintheeffects，andthatintheabsenceofunlikenessineitherofthefactorstheeffectsmustbealike。Whentheyarethusgeneralized，thedependenceofthesepropositionson
　　thepersistenceofforceisobvious。Anytwoforcesthatarenotalike，are
　　forceswhichdiffereitherintheiramountsordirectionsorboth;andby
　　whatiscalledtheresolutionofforces，itmaybeprovedthatthisdifference
　　isconstitutedbythepresenceintheoneofsomeforcenotpresentinthe
　　other。Similarly，anytwounitsorportionsofmatterwhichareunlikein
　　size，form，weight，orotherattribute，canbeknownasunlikeonlythrough
　　someunlikenessintheforcestheyimpressonus;andhencethisunlikeness
　　also，isconstitutedbythepresenceintheoneofsomeforceorforcesnot
　　presentintheother。Suchbeingthecommonnatureoftheseunlikenesses，
　　whatisthecorollary？Anyunlikenessintheincidentforces，wherethethings
　　actedonarealike，mustgenerateadifferencebetweentheeffects;since，
　　otherwise，thedifferentialforceproducesnoeffect，andforceisnotpersistent。
　　Anyunlikenessinthethingsactedon，wheretheincidentforcesarealike，
　　mustgenerateadifferencebetweentheeffects;since，otherwise，thedifferential
　　forcewherebythesethingsaremadeunlike，producesnoeffect，andforce
　　isnotpersistent。While，conversely，iftheforcesactingandthethings
　　actedonarealike，theeffectsmustbealike;since，otherwise，adifferentialeffectcanbeproducedwithoutadifferentialcause，andforceisnotpersistent。Thusthesegeneraltruthsbeingnecessaryimplications。ofthepersistence
　　offorce，allthere—distributionsabovetracedoutascharacterizingEvolution
　　initsvariousphases，arealsoimplicationsofthepersistenceofforce。
　　Ifofthemixedunitsmakingupanyaggregate，thoseofthesamekindhave
　　likemotionsimpressedonthembyauniformforce，whileunitsofanother
　　kindaremovedbythisuniformforceinwaysmoreorlessunliketheways
　　inwhichthoseofthefirstkindaremoved，thetwokindsmustseparateand
　　integrate。Iftheunitsarealikeandtheforcesunlike，adivisionofthe
　　differentlyaffectedunitsisequallynecessitated。Thusthereinevitably
　　arisesthedemarcatedgroupingwhichweeverywheresee。Byvirtueofthis
　　segregation，growingevermoredecidedwhilethereremainsanypossibility
　　ofincreasingit，thechangefromuniformitytomultiformityisaccompanied
　　byachangefromindistinctnessintherelationsofpartstodistinctness
　　intherelationsofparts。Aswebeforesawthatthetransformationofthe
　　homogeneousintotheheterogeneousisinferablefromthatultimatetruth
　　whichtranscendsproof;sowehereseethatfromthissametruthisinferable
　　thetransformationofanindefinitehomogeneityintoadefiniteheterogeneity。
　　Chapter22Equilibration§170。towardswhatdothesechangestend？Willtheygoonforever？
　　orwilltherebeanendtothem？Canthingsincreaseinheterogeneitythrough
　　allfuturetime？ormusttherebeadegreewhichthedifferentiationand
　　integrationofMatterandMotioncannotpass？Isitpossibleforthisuniversal
　　metamorphosistoproceedinthesamegeneralcourseindefinitely？ordoes
　　itworktowardssomeultimatestateadmittingnofurthermodificationof
　　likekind？Thelastofthesealternativeconclusionsisthattowhichwe
　　areinevitablydriven。Whetherwewatchconcreteprocesses，orwhetherwe
　　considerthequestionintheabstract，wearealiketaughtthatEvolutionhasanimpassablelimit。There—distributionsofmatterwhichgoonaroundus，areeverbeingbrought
　　toconclusionsbythedissipationofthemotionswhicheffectthem。Therolling
　　stonepartswithportionsofitsmomentumtothethingsitstrikes，andfinally
　　comestorest;asdoalso，inlikemanner，thevariousthingsithasstruck。
　　DescendingfromthecloudsandtricklingovertheEarth'ssurfacetillit
　　gathersintobrooksandrivers，water，stillrunningtowardsalowerlevel，
　　isatlastarrestedbytheresistanceofotherwaterthathasreachedthe
　　lowestlevel。Inthelakeorseathusformed，everyagitationraisedbya
　　windortheimmersionofasolidbody，propagatesitselfaroundinwaves
　　whichdiminishastheywiden，andgraduallybecomelosttoobservationin
　　motionscommunicatedtotheatmosphereandthematterontheshores。The
　　impulsegivenbyaplayertoaharp—stringistransformedthroughitsvibrations
　　intoaerialpulses;andthese，spreadingonallsides，andweakeningasthey
　　spread，soonceasetobeperceptible，andaregraduallyexpendedingenerating
　　thermalundulationsthatradiateintospace:eachaerialpulsecausingcompression
　　andevolutionofheat。Equallyinthecinderwhichfallsoutofthefire，
　　andinthevastmassofmoltenlavaejectedbyavolcano，weseethatthe
　　molecularagitationdispersesitselfbyradiation;sothatthetemperature
　　inevitablysinksatlasttothesamedegreeasthatofsurroundingbodies。
　　Theproximaterationaleoftheprocessexhibitedundertheseseveralforms，
　　liesinthefactdweltonwhentreatingoftheMultiplicationofEffects，
　　thatmotionsareeverbeingdecomposedintodivergentmotions，andthese
　　intore—divergentmotions。Therollingstonesendsoffthestonesithits
　　indirectionsdifferingmoreorlessfromitsown，andtheydothelikewith
　　thethingstheyhit。Movewaterorair，andthemovementisquicklyresolved
　　intodispersedmovements。Theheatproducedbypressureinagivendirection
　　diffusesitselfbyundulationsinalldirections。Thatistosay，thesemotions
　　undergodivisionandsubdivision，andbycontinuanceofthisprocesswithoutlimittheyare，thoughneverlost，graduallydissipated。Inallcases，then，thereisaprogresstowardequilibrium。Thatuniversal
　　co—existenceofantagonistforceswhich，aswebeforesaw，necessitatesthe
　　universalityofrhythm，andwhich，aswebeforesaw，necessitatesthedecomposition
　　ofeveryforceintodivergentforces，atthesametimenecessitatestheultimate
　　establishmentofabalance。Everymotion，beingmotionunderresistance，
　　iscontinuallysufferingdeductions;andtheseunceasingdeductionsfinallyresultinthecessationofthemotion。Thegeneraltruththusfrustratedunderitssimplestaspect，wemustnow
　　lookatunderthosemorecomplexaspectsitusuallypresentsthroughoutNature。
　　Innearlyallcases，themotionofanaggregateiscompound;andtheequilibration
　　ofeachofitscomponents，beingcarriedonindependently，doesnotaffect
　　therest。Theship'sbellthathasceasedtovibrate，stillcontinuesthose
　　verticalandlateraloscillationscausedbytheocean—swell。Thewaterof
　　asmoothstreamonwhosesurfacehavediedawaytheundulationscausedby
　　arisingfish，movesasfastasbeforetowardsthesea。Thearrestedbullet
　　travelswithundiminishedspeedroundtheEarth'saxis。Andweretherotation
　　oftheEarthdestroyed，therewouldnotbeimpliedanydiminutionofthe
　　Earth'smovementwithrespecttotheSunandotherexternalbodies。Sothat
　　ineverycase，whatweregardasequilibrationisadisappearanceofsome
　　oneormoreofthemanymovementsabodypossesses，whileitsothermovements
　　continueasbefore。Thatthisprocessmaybedulyrealizedandthestate
　　ofthingstowardswhichittendsfullyunderstood，itwillbewellhereto
　　citeacaseinwhichwemaywatchthissuccessiveequilibrationofcombined
　　movementsmorecompletelythanwecandointhoseaboveinstanced。Ourend
　　willbestbeservednotbythemostimposingbutbythemostfamiliarexample。
　　Letustakethatofaspinningtop。Whenthestringwhichhasbeenwrapped
　　roundatop'saxisisviolentlydrawnoff，andthetopfallsontothetable，
　　itusuallyhappensthatbesidestherapidrotationtwoothermovementsare
　　giventoit。Aslighthorizontalmomentum，unavoidablyimpressedonitwhen
　　leavingthehandle，carriesit。awaybodilyfromtheplaceonwhichitdrops;
　　andinconsequenceofitsaxisbeingmoreorlessinclined，itfallsinto
　　acertainoscillation，describedbytheexpressivethoughinelegantword
　　"wabbling。"Thesetwosubordinatemotions，variableintheirproportions
　　toeachotherandtothechiefmotion，arecommonlysoonbroughttoaclose
　　byseparateprocessesofequilibrium。Themomentumwhichcarriesthetop
　　bodilyalongthetable，resistedsomewhatbytheairbutmainlybytheirregularities
　　ofthesurface，shortlydisappears;andthetopthereaftercontinuestospin
　　ononespot。Meanwhile，inconsequenceofthatoppositionwhichtheaxial
　　momentumofarotatingbodymakestoanychangeintheplaneofrotation，
　　（sobeautifullyexhibitedbythegyroscope，）the"wabbling"diminishes，
　　andliketheotherisquicklyended。Theseminormotionshavingbeendissipated，
　　therotatorymotion，interferedwithonlybyatmosphericresistanceandthe
　　frictionofthepivot，continuessometimewithsuchuniformitythatthe
　　topappearsstationary:therebeingthustemporaryestablishedacondition
　　whichtheFrenchmathematicianshavetermedequilibriummobile。Itistrue
　　thatwhenthevelocityofrotationsinksbelowacertainpoint，newmotions
　　commenceandincreasetillthetopfalls;butthesearemerelyincidental
　　toacaseinwhichthecentreofgravityisabovethepointofsupport。Were
　　thetop，havinganaxisofsteel，tobesuspendedfromasurfaceadequately
　　magnetized，themovingequilibriumwouldcontinueuntilthetopbecamemotionless，
　　withoutanyfurtherchangeofattitude。Nowthefactswhichitbehovesus
　　heretoobservearethese。First，thatthevariousmotionswhichanaggregate
　　possessesareseparatelyequilibrated:thosewhicharesmallest，orwhich
　　meetwiththegreatestresistance，orboth，disappearingfirst;andleaving
　　atlastthatwhichisgreatest，ormeetswithleastresistance，orboth。
　　Second，thatwhentheaggregatehasamovementofitspartswithrespect
　　toeachotherwhichencountersbutlittleexternalresistance，thereisapt
　　tobeestablishedamovingequilibrium。Third，thatthismovingequilibriumeventuallylapsesintocompleteequilibrium。Fullytocomprehendtheprocessofequilibration，isnoteasy;sincewe
　　havesimultaneouslytocontemplatevariousphasesofit。Thebestcourse
　　willbetoglanceseparatelyatwhatwemayconvenientlyregardasitsfour
　　differentorders。Thefirstorderincludesthecomparativelysimplemotions，
　　asthoseofprojectiles，whicharenotprolongedenoughtoexhibittheir
　　rhythmicalcharacter，butwhich，beingquicklydividedandsubdividedinto
　　motionscommunicatedtootherportionsofmatter，arepresentlydissipated
　　intherhythmofetherealundulations。Inthesecondorder，comprehending
　　variouskindsofordinaryvibrationoroscillation，theimpliedenergyis
　　usedupingeneratingatensionwhich，havingbecomeequaltoitormomentarily
　　equilibratedwithit，thereuponproducesamotionintheoppositedirection，
　　thatissubsequentlyequilibratedinlikemanner:thuscausingavisible
　　rhythmwhichispresentlylostininvisiblerhythms。Thethirdorderofequilibration，
　　nothithertonoticed，obtainsinthoseaggregateswhichcontinuallyreceive
　　asmuchenergyastheyexpend。Thesteam—engine（andespeciallythatkind
　　whichfeedsitsownfurnaceandboiler）suppliesanexample。Heretheenergy
　　frommomenttomomentdissipatedinovercomingtheresistanceofthemachinery
　　driven，isfrommomenttomomentre—placedfromthefuel;andthebalance
　　ofthetwoismaintainedbyaraisingorloweringoftheexpenditureaccording
　　tothevariationofthesupply:eachincreaseordecreaseinthequantity
　　ofsteam，resultinginariseorfalloftheengine'smovement，suchasbrings
　　ittoabalancewiththeincreasedordecreasedresistance。This，whichwe
　　mayfitlycallthedependentmovingequilibrium，shouldbespecifynoted;
　　sinceitisonethatweshallcommonlymeetwiththroughoutvariousphases
　　ofEvolution。Theequilibriumtobedistinguishedasofthefourthorder，
　　istheindependentorperfectmovingequilibrium。Thisweseeillustrated
　　intherhythmicalmotionsoftheSolarSystem，which，beingresistedonly
　　byamediumofinappreciabledensity，undergonosensiblediminutioninsuchperiodsoftimeaswecanmeasure。Somethinghasstilltobeadded。Thereadermustnotetwoleadingtruths
　　broughtoutbytheforegoingexposition:theoneconcerningtheultimate，
　　orratherthepenultimate，stateofmotionwhichtheprocessesdescribed
　　tendtobringabout;theotherconcerningtheconcomitantdistributionof
　　matter。Thispenultimatestateofmotionisthemovingequilibrium，which
　　tendstoariseinanaggregatehavingcompoundmotions，asatransitional
　　stateonthewaytowardscompleteequilibrium。ThroughoutEvolutionofall
　　kindsthereisacontinualapproximationto，andmoreorlesscompletemaintenance
　　of，thismovingequilibrium。AsintheSolarSystemtherehasbeenestablished
　　anindependentmovingequilibrium——anequilibriumsuchthattherelative
　　motionsofitsmembersarecontinuallysocounterbalancedbyoppositemotions，
　　thatthemeanstateoftheaggregatenevervaries;soisit，thoughina
　　lessdistinctmanner，witheachformofdependentmovingequilibrium。The
　　stateofthingsexhibitedinthecyclesofterrestrialchanges，inthebalanced
　　functionsoforganicbodiesthathavereachedtheiradultforms，andinthe
　　actingandre—actingprocessesoffully—developedsocieties，issimilarly
　　onecharacterizedbycompensatingoscillations。Theinvolvedcombination
　　ofrhythmsseenineachofthesecases，hasanaverageconditionwhichremains
　　practicallyconstantduringthedeviationsevertakingplaceonopposite
　　sidesofit。Andthefactwhichwehaveheretoobserveisthat，asacorollary
　　fromthegenerallawofequilibrium，everyevolvingaggregatemustgoon
　　changinguntilamovingequilibriumisestablished;since，aswehaveseen，
　　anexcessofforcewhichtheaggregatepossessesinanydirection，musteventually
　　beexpendedinovercomingresistancestochangeinthatdirection:leaving
　　behindonlythosemovementswhichcompensateoneanother，andsoformamoving
　　equilibrium。Respectingthestructuralstatesimultaneouslyreached，itmust
　　obviouslybeonepresentinganarrangementofforcesthatcounterbalance
　　alltheforcestowhichtheaggregateissubject。Solongasthereremains
　　aresidualforceinanydirection——beitexcessofaforceexercisedby
　　theaggregateonitsenvironment，orofaforceexercisedbyitsenvironment
　　ontheaggregate，equilibriumdoesnotexist;andthereforethere—distribution
　　ofmattermustcontinue。Whenceitfollowsthatthelimitofheterogeneity
　　towardswhicheveryaggregateprogresses，istheformationofasmanyspecializations
　　andcombinationsofparts，astherearespecializedandcombinedforcestobemet。§171。Thosesuccessivelychangedformswhich，ifthenebularhypothesis
　　begranted，musthavearisenduringtheevolutionoftheSolarSystem，were
　　somanytransitionalkindsofmovingequilibrium，severallygivingplace
　　tomoreenduringkinds。Thustheassumptionofanoblatespheroidalfigure
　　bycondensingnebulousmatter，wastheassumptionofatemporaryandpartial
　　movingequilibriumamongthecomponentparts——amovingequilibriumthat
　　musthavegrownmoresettledaslocalconflictingmovementsweredissipated。
　　Intheformationanddetachmentofthenebulousringswhich，accordingto
　　thishypothesis，fromtimetotimetookplace，wehaveinstancesofprogressive
　　equilibrationseverallyendingintheestablishmentofacompletemoving
　　equilibrium。Forthegenesisofeachsuchringimpliesabalancingofthat
　　attractiveforcewhichthewholespheroidexercisesonitsequatorialportion，
　　bythatcentrifugalforcewhichtheequatorialportionhasacquiredduring
　　previousconcentration。Solongasthesetwoforcesarenotequal，theequatorial
　　portionfollowsthecontractingmass;butassoonasthesecondforcehas
　　increaseduptoanequalitywiththefirst，theequatorialportioncanfollow
　　nofurtherandremainsbehind。While，however，theresultingring，regarded
　　asawhole，hasreachedastateofmovingequilibrium，itspartsarenot
　　balancedwithrespecttooneanother。Aswebeforesaw（§150）theprobabilities
　　againstthemaintenanceofanannularformbynebulousmatteraregreat:
　　fromtheinstabilityofthehomogeneous，itisinferablethatnebulousmatter
　　sodistributedwillbreakupintoportions，andeventuallyconcentrateinto
　　asinglemass。Thatistosay，theringwillprogresstowardsamovingequilibrium
　　ofamorecompletekind，duringthedissipationofthatmotionwhichmaintained
　　itsparticlesinadiffusedform;leavingatlengthaplanetarybodyattended
　　perhapsbyagroupofminorbodiessimilarlyproduced，constitutingamovingequilibriumthatisallbutperfect。*