第38章

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。*<*SirDavidBrewsterhascitedwithapproval，acalculationbyM。Babinet，

totheeffectthatonthehypothesisofnebulargenesis，thematterofthe

Sun，whenitfilledtheEarth\'sorbit，musthavetaken3181yearstorotate;

andthatthereforethehypothesiscannotbetrue。ThiscalculationofM。

Babinetmaypair—offwiththatofM。Comtewho，contrariwise，madethetime

ofthisrotationagreeverynearlywiththeEarth\'speriodofrevolution

roundtheSun。ForifM。Comte\'scalculationinvolvedapetitioprincipii，

thatofM。Babinetisbasedontwoassumptionsbothofwhicharegratuitous，

andoneoftheminconsistentwiththedoctrinetobetested。Hehasevidently

proceededonthecurrentsuppositionrespectingtheSun\'sinternaldensity，

whichisnotproved，andfromwhichtherearereasonsfordissenting;and

hehasevidentlytakenforgrantedthatallpartsofthenebulousspheroid，

whenitfilledtheEarth\'sorbit，hasthesameangularvelocity;whereas

if（asisimpliedinthenebularhypothesis，rationallyunderstood）this

spheroidresultedfromtheconcentrationofwidely—diffusedmatter，theangular

velocityofitsequatorialportionwouldobviouslybefargreaterthanthatofitscentralportion。>Hypothesisaside，theprincipleofequilibrationisstillperpetually

illustratedinthoseminorchangesofstatewhichtheSolarSystemundergoes。

Eachplanet，satellite，andcomet，exhibitsatitsaphelionamomentaryequilibrium

betweenthatforcewhichurgesitfurtherawayfromitsprimary，andthat

forcewhichretardsitsretreat。Inlikemanneratperihelionaconverse

equilibriumismomentarilyestablished。Thevariationofeachorbitineccentricity，

andinthepositionofitsplane，hassimilarlyalimitatwhichtheforces

producingchangeintheonedirection，areequalledbythoseantagonizing

it;andanoppositelimitatwhichanoppositearresttakesplace。Meanwhile，

eachofthesesimpleperturbations，aswellaseachofthecomplexonesresulting

fromtheircombination，exhibits，besidesthetemporaryequilibrationat

eachofitsextremes，acertaingeneralequilibrationofcompensatingdeviations

oneithersideofameanstate。Thatthemovingequilibriumthusconstituted

tends，inthecourseofindefinitetime，tolapseintoacompleteequilibrium，

bythegradualdecreaseofplanetarymotionsandeventualintegrationof

alltheseparatemassescomposingtheSolarSystem，isabeliefsuggested

bycertainobservedcometaryretardations——abeliefentertainedbysome

ofhighauthority。Thereceivedoptionthattheappreciablediminutionin

theperiodofEncke\'scomet，impliesalossofmomentumcausedbyresistance

totheetherealmedium，commitsastronomerswhoholdit，totheconclusion

thatthissameresistancemustcausealossofplanetarymotions——aloss

which，infinitesimalthoughitmaybeinsuchperiodsaswecanmeasure，

will，ifindefinitelycontinued，bringthesemotionstoaclose。Evenshould

therebe，asSirJohnHerschelsuggests，arotationoftheetherealmedium

inthesamedirectionwiththeplanets，thisarrest，thoughimmenselypostponed，

wouldnotbeabsolutelyprevented。Suchaneventuality，however，mustin

anycasebesoinconceivablyremoteastohavenootherthanaspeculative

interestforus。Itisreferredtohere，simplyasillustratingthestill—continued

tendencytowardscompleteequilibrium，throughthestill—continueddissipationofsensiblemotion，ortransformationofitintoinsensiblemotion。ButthereisanotherspeciesofequilibrationgoingonintheSolarSystem，

withwhichthehumanraceislessremotelyconcerned。Thetacitassumption

thattheSuncancontinuetogiveoffanundiminishedamountoflightand

heatthroughallfuturetime，isnowabandoned。Involvingasitdoes，under

adisguise，theconceptionofpowerproducedoutofnothing，itisofthe

sameorderasthebeliefwhichmisleadsperpetual—motionschemers。Thespreading

recognitionofthetruththatwhateverforceismanifestedunderoneshape

mustpreviouslyhaveexistedunderanothershape，impliesrecognitionof

thetruththattheforceknowntousinsolarradiations，isthechanged

formofsomeotherforceofwhichtheSunistheseat;andthat，bytheemission

oftheseradiations，thisotherforceisbeingslowlyexhausted。Theforce

bywhichtheSun\'ssubstanceisdrawntohiscentreofgravity，istheonly

onewhichphysicallawswarrantusinconcludingtobethecorrelateofthe

forcesemanatingfromhim:theonlyassignablesourcefortheinsensible

motionsconstitutingsolarlightandheat，isthesensiblemotionwhichdisappears

duringtheconcentrationoftheSun\'smass。Webeforesawittobeacorollary

fromthenebularhypothesis，thatthereissuchaprogressingconcentration

oftheSun\'smass。Andhereremainstobeaddedthefurthercorollary，that

justasinthecaseofthesmallmembersoftheSolarSystem，theheatgenerated

byconcentration，onceescapingrapidly，hasineachleftacentralresidue

whichescapesbutslowly;sointhecaseofthatimmenselylargermassforming

theSun，theimmenselygreaterquantityofheatgeneratedandstillinprocess

ofrapiddiffusion，must，astheconcentrationapproachesitslimit，diminish

inamount，andeventuallyleavebutarelativelysmallinternalremnant。