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。*