Ourunitsoflinearextensionarethelengthsofmassesofmatterorthe
　　spacesbetweenmarksmadeonthemasses，andweassumetheselengths，or
　　thesespacesbetweenmarks，toremainunchangedwhilethetemperatureis
　　unchanged。Fromthestandard—measurepreservedatWestminster，arederived
　　themeasuresfortrigonometricalsurveys，forgeodesy，themeasurementof
　　terrestrialarcs，andthecalculationsofastronomicaldistances，dimensions，
　　etc。，andthereforeforAstronomyatlarge。Weretheseunitsoflength，original
　　andderived，irregularlyvariable，therecouldbenocelestialdynamics，
　　noranyofthatverificationyieldedbyitoftheconstancyofthecelestial
　　massesandoftheirenergies。Hence，persistenceofthespace—occupyingspecies
　　offorcecannotbeproved，forthereasonthatitistacitlyassumedinevery
　　experimentorobservationbywhichitisproposedtoproveit。Thelikeholds
　　oftheforcedistinguishedasenergy。Theendeavourtoestablishthisby
　　measurement，takesforgrantedboththepersistenceoftheintrinsicforce
　　bywhichbodymanifestsitselfasexisting，andthepersistenceoftheextrinsic
　　forcebywhichbodyacts。Foritisfromtheseequalunitsoflinearextension，
　　throughthemediumoftheequal—armedleverorscales，thatwederiveour
　　equalunitsofweight，orgravitativeforce;andonlybymeansofthesecan
　　wemakethosequantitativecomparisonsbywhichthetruthsofexactscience
　　arereached。Throughouttheinvestigationsleadingthechemisttotheconclusion
　　thatofthecarbonwhichhasdisappearedduringcombustion，noportionhas
　　beenlost，whatishisrepeatedly—assignedproof？Thataffordedbythescales。
　　Inwhattermsistheverdictofthescalesgiven？Ingrammes——inunits
　　ofweight——inunitsofgravitativeforce。Andwhatisthetotalcontent
　　oftheverdict？Thatasmanyunitsofgravitativeforceasthecarbonexhibited
　　atfirst，itexhibitsstill。Thevalidityoftheinference，then，depends
　　entirelyupontheconstancyoftheunitsofforce。Iftheforcewithwhich
　　theportionofmetalcalledagramme—weighttendstowardstheEarth，has
　　varied，theinferencethatmatterisindestructibleisvicious。Everything
　　turnsonthetruthoftheassumptionthatthegravitationoftheweights
　　ispersistent;andofthisnoproofisassigned，orcanbeassigned。Inthe
　　reasoningsoftheastronomerthereisalikeimplication，fromwhichwemay
　　drawthelikeconclusion。Noproblemincelestialdynamicscanbesolved
　　withouttheassumptionofsomeunitofforce。Thisunitneednotbe，like
　　apoundoraton，oneofwhichwecantakedirectcognizance。Itisrequisite
　　onlythatthemutualattractionwhichsometwoofthebodiesconcernedexercise
　　atagivendistance，shallbetakenasone;sothattheotherattractions
　　withwhichtheproblemdeals，maybeexpressedintermsofthisone。Such
　　unitbeingassumed，themotionswhichtherespectivemasseswillgenerate
　　inoneanotherinagiventime，arecalculated;andcompoundingthesewith
　　themotionstheyalreadyhave，theirplacesattheendofthattimearepredicted。
　　Thepredictionisverifiedbyobservation。Fromthis，eitheroftwoinferences
　　maybedrawn。Assumingthemassestobeunchanged，theirenergiesmaybe
　　provedundiminished;orassumingtheirenergiesundiminished，themasses
　　maybeprovedunchanged。Butthevalidityofoneorotherinferencedepends
　　whollyonthetruthoftheassumptionthattheunitofforceisunchanged。
　　Letitbesupposedthatthegravitationofthetwobodiestowardseachother
　　atthegivendistancehasvaried，andtheconclusionsdrawnarenolonger
　　true。Norisitonlyintheirconcretedatathatthereasoningsofterrestrial
　　andcelestialphysicsassumethePersistenceofForce。Theequalityofaction
　　andreactionistakenforgrantedfrombeginningtoendofeitherargument;
　　andtoassertthatactionandreactionareequalandopposite，istoassert
　　thatForcepersists。Theimplicationisthattherecannotbeanisolated
　　force，butthatanyforcemanifestedimpliesanequalantecedentforcefromwhichitisderived，andagainstwhichitisareaction。Wemightindeedbecertain，evenintheabsenceofanysuchanalysisas
　　theforegoing，thattheremustexistsomeprinciplewhich，asbeingthebasis
　　ofscience，cannotbeestablishedbyscience。Allreasoned—outconclusions
　　whatevermustrestonsomepostulate。Asbeforeshown（§23），wecannot
　　goonmergingderivativetruthsinthosewidertruthsfromwhichtheyare
　　derived，withoutreachingatlastawidesttruthwhichcanbemergedinno
　　other，orderivedfromnoother。Andtherelationinwhichitstandstothe
　　truthsofscienceingeneral，showsthatthistruthtranscendingdemonstration
　　isthePersistenceofForce。Tothisanultimateanalysisbringsusdown，andonthisarationalsynthesismustbuildup。§62。Butnowwhatistheforceofwhichwepredicatepersistence？
　　Thatwhichthewordordinarilystandsforistheconsciousnessofmuscular
　　tension——thefeelingofeffortwhichwehaveeitherwhenputtingsomethinginmotionorwhenresistingapressure。Thisfeeling，however，isbutasymbol。In§18itwassaidthatthough，sinceactionandreactionareequal
　　andopposite，weareobligedtothinkofthedownwardpullofaweightas
　　equaltotheupwardpullwhichsupportsit，andthoughthethoughtofequality
　　suggestskinshipofnature，yet，aswecannotascribefeelingtotheweight，
　　weareobligedtoadmitthatForceasitexistsbeyondconsciousnesshas
　　nolikenesstoforceasweconceiveit，thoughthereisbetweenthemthe
　　kindofequivalenceimpliedbysimultaneousvariation。Theeffortofone
　　whothrowsacricketballisfollowedbythemotionoftheballthroughspace，
　　anditsmomentumisre—transformedintomuscularstraininonewhocatches
　　it。Whattheforcewaswhenitexistedintheflyingcricketballitisimpossible
　　toimagine:wehavenotermsofthoughtinwhichtorepresentit。Andit
　　isthuswithallthetransformationsofenergytakingplaceintheworld
　　around。Thoseillustrationsgivenin§66，showingthechangesofform
　　whichenergyundergoesandtheequivalencebetweensomuchofitinoneform
　　andsomuchinanother，failtoenlightenusrespectingtheenergyitself。
　　Itassumesunderthisorthatsetofconditionsthisorthatshape，andthe
　　quantityofitisnotalteredduringitstransformations。Forthatinterpretation
　　ofthingswhichisalonepossibleforusthisisallwerequiretoknow——
　　thattheforceorenergymanifested，nowinonewaynowinanother，persists
　　orremainsunchangedinamount。Butwhenweaskwhatthisenergyis，there
　　isnoanswersavethatitisthenoumenalcauseimpliedbythephenomenaleffect。HencetheforceofwhichweassertpersistenceisthatAbsoluteForce
　　weareobligedtopostulateasthenecessarycorrelateoftheforceweare
　　consciousof。BythePersistenceofForce，wereallymeanthepersistence
　　ofsomeCausewhichtranscendsourknowledgeandconception。InassertingitweassertanUnconditionedReality，withoutbeginningorend。Thus，quiteunexpectedly，wecomedownoncemoretothatultimatetruth
　　inwhich，aswesaw，ReligionandSciencecoalesce——thecontinuedexistence
　　ofanUnknowableasthenecessarycorrelativeoftheKnowable。
　　Chapter7ThePersistenceofRelationAmongForces§63。Thefirstdeductiontobedrawnfromtheultimateuniversal
　　truththatforcepersists，isthattherelationsamongforcespersist。Supposing
　　agivenmanifestationofforce，underagivenformandgivenconditions，
　　beeitherprecededbyorsucceededbysomeothermanifestation，itmust，
　　inallcaseswheretheformandconditionsarethesame，beprecededbyor
　　succeededbysuchothermanifestation。EveryantecedentmodeoftheUnknowable
　　musthaveaninvariableconnexion，quantitativeandqualitative，withthatmodeoftheUnknowablewhichwecallitsconsequent。Fortosayotherwiseistodenythepersistenceofforce。Ifinanytwo
　　casesthereisexactlikenessnotonlybetweenthoseconspicuousantecedents
　　whichwecallthecauses，butalsobetweenthoseaccompanyingantecedents
　　whichwecalltheconditions，wecannotaffirmthattheeffectswilldiffer，
　　withoutaffirmingeitherthatsomeforcehascomeintoexistenceorthat
　　someforcehasceasedtoexist。Iftheco—operativeforcesintheonecase
　　areequaltothoseintheother，eachtoeach，indistributionandamount;
　　thenitisimpossibletoconceivetheproductoftheirjointactioninthe
　　onecaseasunlikethatintheother;withoutconceivingoneormoreofthe
　　forcestohaveincreasedordiminishedinquantity;andthisisconceivingthatforceisnotpersistent。Toimpressthetruththusenunciatedunderitsmostabstractform，someillustrationswillbedesirable。§64。Lettwobullets，equalinweightsandshapes，beprojectedwith
　　equalenergies;then，inequaltimes，equaldistancesmustbetravelledby
　　them。Theassertionthatoneofthemwilldescribeanassignedspacesooner
　　thantheother，thoughtheirinitialmomentawerealikeandtheyhavebeen
　　equallyresisted（foriftheyareunequallyresistedtheantecedentsdiffer）
　　isanassertionthatequalquantitiesofforcehavenotdoneequalamounts
　　ofwork;andthiscannotbethoughtwithoutthinkingthatsomeforcehas
　　disappearedintonothingorarisenoutofnothing。Assume，furtherthatduring
　　itsnightoneofthemhasbeendrawnbytheEarthacertainnumberofinches
　　outofitsoriginallineofmovement;thentheother，whichhasmovedthe
　　samedistanceinthesametime，musthavefallenjustasfartowardsthe
　　Earth。Nootherresultcanbeimaginedwithoutimaginingthatequalattractions
　　actingforequaltimes，haveproducedunequaleffects;whichinvolvesthe
　　inconceivablepropositionthatsomeactionhasbeencreatedorannihilated。
　　Again，oneofthebulletshavingpenetratedthetargettoacertaindepth，
　　penetrationbytheotherbullettoasmallerdepth，unlesscausedbygreater
　　localdensityinthetarget，cannotbementallyrepresented。Suchamodification
　　oftheconsequentswithoutmodificationoftheantecedents，isthinkable
　　onlythroughtheimpossiblethoughtthatsomethinghasbecomenothingornothinghasbecomesomething。Itisthusnotwithsequencesonly，butalsowithsimultaneouschanges
　　andpermanentco—existences。Givenchargesofpowderalikeinquantityand
　　quality，firedfrombarrelsofthesamestructure，andpropellingbullets
　　ofequalweights，sizes，andforms，similarlyrammeddown;*anditisanecessary
　　inferencethattheconcomitantactionswhichmakeuptheexplosion，will
　　beartooneanotherlikerelationsofquantityandqualityinthetwocases。
　　Theproportionsamongthedifferentproductsofcombustionwillbeequal。
　　Theseveralamountsofenergytakenupingivingmomentumtothebullet，
　　heattothegases，andsoundontheirescape，willpreservethesameratios。
　　Thequantitiesoflightandsmokeintheonecasewillbewhattheyarein
　　theother;andthetworecoilswillbealike。Fornodifference，ofrelation
　　amongtheseconcurrentphenomenacanbeimaginedasarising，withoutimaginingitasarisingbythecreationorannihilationofenergy。Thatwhichholdsbetweenthesetwocasesmustholdamonganynumberof
　　cases;andthatwhichhereholdsbetweencomparativelysimpleantecedents
　　andconsequents，mustholdhoweverinvolvedtheantecedentsbecomeandhoweverinvolvedtheconsequentsbecome。§65。ThusUniformityofLaw，resolvableaswefinditintothepersistence
　　ofrelationsamongforces，isacorollaryfromthepersistenceofforce。
　　Thegeneralconclusionthatthereexistconstantconnexionsamongphenomena，
　　ordinarilyregardedasaninductiveconclusiononly，isreallyaconclusiondeduciblefromtheultimatedatumofconsciousness。Morethanthismaybesaid。Everyapparentinductiveproofoftheuniformity
　　oflawitselftakesforgrantedboththepersistenceofforceandthepersistence
　　ofrelationsamongforces。Forintheexactsciences，inwhichalonewemay
　　seekrelationsdefiniteenoughtoproveuniformity，anyallegeddemonstration
　　mustdependonmeasurement;andaswehavealreadyseen，measurement，whether
　　ofmatterorforce，assumesthatbotharepersistentinassumingthatthe
　　measureshavenotvaried。Whileatthesametimeeverydeterminationofthe
　　relationsamongthem——inamount，proportion，direction，orwhatnot——
　　similarlyimpliesmeasurement，thevalidityofwhichasbeforeimpliesthepersistenceofforce。Thatuniformityoflawthusfollowsinevitablyfromthepersistenceof
　　force，willbecomemoreandmoreclearasweadvance。Thenextchapterwill
　　indirectlysupplyabundantfrustrationsofit。
　　Chapter8TheTransformationandEquivalenceofForces§66。When，totheunaidedsenses，Sciencebegantoaddsupplementary
　　sensesintheshapeofmeasuringinstruments，menbegantoperceivevarious
　　phenomenawhicheyesandfingerscouldnotdistinguish。Ofknownformsof
　　force，minutermanifestationsbecameappreciable;andformsofforcebefore
　　unknownwererenderedcognizableandmeasurable。Whereforceshadapparently
　　endedinnothing，andhadbeencarelesslysupposedtohaveactuallydone
　　so，instrumentalobservationprovedthateffectshadineveryinstancebeen
　　produced:theforceshavingreappearedinnewshapes。Herehasatlength
　　arisentheinquirywhethertheforcedisplayedineachsurroundingchange，
　　doesnotintheactofexpenditureundergometamorphosisintoanequivalent
　　amountofsomeotherforceorforces。Andtothisinquiryexperimentisgiving
　　anaffirmativeanswer，whichbecomesdailymoredecisive。Séguin，
　　Mayer，Joule，Grove，andHelmholtz，aremorethanotherstobecreditedwith
　　theenunciationofthisdoctrine。Letusglanceattheevidenceonwhichitrests。Motion，whereverwecandirectlytraceitsgenesis，wefindhadpre—existed
　　assomeothermodeofforce。Ourownvoluntaryactshavealwayscertainsensations
　　ofmusculartensionastheirantecedents。When，asinlettingfallarelaxed
　　limbweareconsciousofabodilymovementrequiringnoeffort，theexplanation
　　isthattheeffortwasexertedinraisingthelimbtothepositionwhence
　　itfell。Inthiscase，asinthecaseofaninanimatebodydescendingto
　　theEarth，theforceaccumulatedbythedownwardmotionisequaltotheforce
　　previouslyexpendedintheactofelevation。Conversely，Motionthatisarrested
　　produces，underdifferentcircumstances，heat，electricity，magnetism，light。
　　Fromthewarmingofthehandsbyrubbingthemtogether，uptotheignition
　　ofarailway—brakebyintensefriction——fromthelightingofdetonating
　　powderbypercussion，uptothesettingonfireablockofwoodbyafew
　　blowsfromasteam—hammer;wehaveabundantinstancesinwhichheatarises
　　asMotionceases。Itisuniformlyfoundthattheheatgeneratedisgreat
　　inproportionastheMotionlostisgreat;andthattodiminishthearrest
　　ofmotionbydiminishingthefriction，istodiminishthequantityofheat
　　evolved。TheproductionofelectricitybyMotionisillustratedequallyin
　　theboy'sexperimentwithrubbedsealing—wax，inthecommonelectricalmachine，
　　andintheapparatusforexcitingelectricitybytheescapeofsteam。Wherever
　　thereisfrictionbetweenheterogeneousbodieselectricaldisturbanceis
　　oneoftheconsequences。MagnetismmayresultfromMotioneitherimmediately，
　　asthroughpercussiononsteel，ormediatelyasthroughelectriccurrents
　　previouslygeneratedbyMotion。Andsimilarly，Motionmaycreatelight;either
　　directly，asintheminuteincandescentfragmentsstruckoffbyviolentcollisions，
　　orindirectly，asthroughtheelectricspark。"Lastly，Motionmaybe
　　againreproducedbytheforceswhichhaveemanatedfromMotion;thus，the
　　divergenceoftheelectrometer，therevolutionoftheelectricalwheel，the
　　deflectionofthemagneticneedle，are，whenresultingfromfrictionalelectricity
　　palpablemovementsreproducedbytheintermediatemodesofforce，whichhavethemselvesbeenoriginatedbymotion。"ThatmodeofforcewhichwedistinguishedasHeat，isnowregardedas
　　molecularmotion——notmotionasdisplayedinthechangedrelationsofsensible
　　massestooneanother，butasassessedbytheunitsofwhichsuchsensible
　　massesconsist。Omittingcasesinwhichthereisstructuralrearrangement
　　ofthemolecules，heatedbodiesexpand;andexpansionisinterpretedasdue
　　tomovementsofthemoleculesinrelationtooneanother:wideroscillations。
　　Thatradiationthroughwhichanythingofhighertemperaturethanthingsaround
　　it，communicatesHeattothem，isclearlyaspeciesofmotion。Moreover，
　　theevidenceaffordedbythethermometerthatHeatthusdiffusesitself，
　　issimplyamovementcausedinthemercurialcolumn。Andthatthemolecular
　　motionwhichwecallHeat，maybetransformedintovisiblemotion，familiar
　　proofisgivenbythesteam—engine;inwhich"thepistonandallits
　　concomitantmassesofmatteraremovedbythemoleculardilatationofthe
　　vapourofwater。"WhereHeatisabsorbedwithoutapparentresult，modern
　　inquirieshavedetectedunobtrusivemodifications:asinglass，themolecular
　　stateofwhichissofarchanged，thataAlarizedrayoflightpassingthrough
　　itbecomesvisible，whichitdoesnotwhentheglassiscold;orasonpolished
　　metallicsurfaces，whicharealteredinmolecularstructurebyradiations
　　fromobjectsveryclosetothem。ThetransformationofHeatintoelectricity
　　occurswhendissimilarmetalstouchingeachotherareheatedatthepoint
　　ofcontact:electriccurrentsbeingsoproduced。Solid，incombustiblematter
　　putintoheatedgas，aslimeintotheOxyhydrogenflame，becomesincandescent;
　　andsoexhibitstheconversionofHeatintolight。Theproductionofmagnetism
　　byHeat，ifitcannotbeprovedtotakeplacedirectly，maybeprovedto
　　takeplaceindirectlythroughtheagencyofelectricity。Andthroughthe
　　sameagencymaybeestablishedthecorrelationofHeatandchemicalaffinity
　　——acorrelationwhichisdirectlyshownbythemarkedinfluenceHeatexercisesonchemicalcompositionanddecomposition。ThetransformationsofElectricityintoothermodesofforceareclearly
　　demonstrable。Producedbythemotionofheterogeneousbodiesincontact，
　　Electricity，throughattractionsandrepulsions，willimmediatelyreproduce
　　motioninneighbouringbodies。InthiscaseacurrentofElectricitymagnetizes
　　abarofsoftiron;andinthatcasetherotationofanequippedmagnetgenerates
　　currentsofElectricity。Hereisthecellofabatteryinwhich，fromthe
　　playofchemicalaffinities，anelectriccurrentresults;andthere，inthe
　　adjacentcell，isanelectriccurrenteffectingchemicaldecomposition。In
　　theconductingwirewewitnessthetransformationofElectricityintoheat;
　　whileinelectricsparksandinthevoltaicarcweseelightproduced。Molecular
　　arrangement，too，ischangedbyElectricity:asinstancethetransferof
　　matterfrompoletopoleofabattery;thefracturescausedbythedisruptive
　　discharge;theformationofcrystalsundertheinfluenceofelectriccurrents。
　　Andthenthat，conversely，Electricityisdirectlygeneratedbyrearrangement
　　ofthemoleculesofmatter，isshownwhenastorage—batteryoraccumulatorisused。HowfromMagnetismtheotherphysicalforcesresult，mustbenextbriefly
　　noted——briefly，becauseineachsuccessivecasetheillustrationsbecome
　　ingreatparttheobverseformsofthosebeforegiven。ThatMagnetismproduces
　　motionistheordinaryevidencewehaveofitsexistence。Inthemagneto—electric
　　machinearotatingmagnetevolveselectricity。andtheelectricitysoevolved
　　mayimmediatelyafterexhibititselfasheat，light，orchemicalaffinity。
　　Faraday'sdiscoveryoftheeffectofMagnetismonpolarizedlight，aswell
　　asthediscoverythatchangeofmagneticstateisaccompaniedbyheat，point
　　tofurtherlikeconnexions。Lastly，experimentsshowthatthemagnetization
　　ofabodyaltersitsinternalstructure;andthat，conversely，thealterationofitsinternalstructure，asbymechanicalstrain，altersitsmagneticcondition。Improbableasitseemed，itisnowprovedthatfromLightalsomayproceed
　　thelikevarietyofagencies。Raysoflightchangetheatomicarrangements
　　ofparticularcrystals。Certainmixedgases，whichdonototherwisecombine，
　　combineinthesunshine。Insomecompoundslightproducesdecomposition。
　　Sincetheinquiriesofphotographershavedrawnattentiontothesubject，
　　ithasbeenshownthat"avastnumberofsubstances，bothelementary
　　andcompound，arenotablyaffectedbythisagent，eventhoseapparentlythe
　　mostunalterableincharacter，suchasmetals。"Andwhenadaguerreotype
　　plateisconnectedwithaproperapparatus"wegetchemicalactionon
　　theplate，electricitycirculatingthroughthewires，magnetisminthecoil，heatinthehelix，andmotionintheneedles。"ThegenesisofallothermodesofforcefromChemicalAction，scarcely
　　needspointingout。Theordinaryaccompanimentofchemicalcombinationis
　　heat;andwhentheaffinitiesareintense，lightalsoisproduced。Chemical
　　changesinvolvingalterationofbulk，causemotion，bothinthecombining
　　elementsandinadjacentmassesofmatter:witnessthepropulsionofabullet
　　bytheexplosionofgunpowder。Inthegalvanicbatteryweseeelectricity
　　resultingfromchemicalcompositionanddecomposition。Whilethroughthemediumofthiselectricity，ChemicalActionproducesmagnetism。Thesefacts，thelargerpartofwhichareculledfromGrove'sworkonTheCorrelationofPhysicalForces，showthateachforceistransformable，
　　directlyorindirectly，intotheothers。IneverychangeForce（orEnergy，
　　asinthesecasesitiscalled）undergoesmetamorphosis;andfromthenew
　　formorformsitassumes，maysubsequentlyresulteitherthepreviousone
　　oranyoftherest，inendlessvarietyoforderandcombination。Itisfurther
　　nowmanifestthatthephysicalforcesstandnotsimplyinqualitativecorrelations
　　withoneanother，butalsoinquantitativecorrelations。Besidesproving
　　thatonemodeofforcemaybetransformedintoanothermode，experiments
　　showthatfromadefiniteamountofone，theamountsofothersthatarise
　　aredefinite。Ordinarilyitisdifficulttoshowthis;sinceitmostlyhappens
　　thatthetransformationofanyforceisnotintosomeoneoftherestbut
　　intoseveralofthem:theproportionsbeingdeterminedbyever—varyingconditions。
　　Butincertaincasespositiveresultshavebeenreached。Mr。Joulehasascertained
　　thatthefallof772lb。throughonefoot，willraisethetemperatureof
　　apoundofwateronedegreeofFahrenheit。Dulong，Petit，andNeumann，have
　　provedarelationinamountbetweentheaffinitiesofcombiningbodiesand
　　theheatevolvedduringtheircombination。Betweenchemicalactionandvoltaic
　　electricityaquantitativeconnexionhasbeenestablishedbyFaraday。The
　　well—determinedrelationsbetweentheamountsofheatgeneratedandofwater
　　turnedtosteam，orstillbettertheknownexpansionproducedinsteamby
　　eachadditionaldegreeofheat，maybecitedinfurtherevidence。Henceit
　　isnolongerdoubtedthatamongtheseveralformswhichforceassumes，thequantitativerelationsarefixed。###第16章§67。ThroughouttheCosmosthistruthmustinvariablyhold。Every
　　change，orgroupofchanges，goingoninit，mustbeduetoforcesaffiliable
　　onthelikeorunlikeforcespreviouslyexisting;whilefromtheforcesexhibited
　　insuchchangeorchangesmustbederivedothersmoreorlesstransformed。
　　Andbesidesrecognizingthisnecessarylinkingoftheforcesatanytime
　　manifestedwiththoseprecedingandsucceedingthem，wemustrecognizethe
　　amountsoftheseforcesasnecessarilyproducingsuchandsuchquantitiesofresults，andasnecessarilylimitedtothosequantities。ThatunificationofknowledgewhichisthebusinessofPhilosophy，is
　　butlittlefurtheredbytheestablishmentofthistruthunderitsgeneral
　　form。Wemusttraceitoutunderitsleadingspecialforms。Changes，and
　　theaccompanyingtransformationsofforces，areeverywhereinprogress，from
　　themovementsofstarstothecurrentsofcommodities;andtocomprehend
　　thegreatfactthatforces，unceasinglymetamorphosed，arenowhereincreased
　　ordecreased，itisrequisitetocontemplatethechangesofallkindsgoing
　　onthatwemaylearnwhencearisetheforcestheyandwhatbecomesofthese
　　forces。Ofcourseifanswerableatall，thesequestionscanbeansweredonly
　　intheestablishrudestway。Themostwecanhopeistoestablishaqualitative
　　correlationthatisindefinitelyquantitative——quantitativetotheextentofimplyingsomethinglikeadueproportionbetweencausesandeffects。Letus，then，considertheseveralclassesofphenomenawhichtheseveralconcretesciencesdealwith。§68。TheantecedentsofthoseforceswhichourSolarSystemdisplays，
　　belongtoapastofwhichwecanneverhaveanythingbutinferentialknowledge。
　　ManyandstrongasarethereasonsforbelievingtheNebularHypothesis，
　　wecannotyetregarditasmorethananhypothesis。If，however，weassume
　　thatthematterofourSolarSystemwasoncediffusedandhadirregularities
　　ofshapeanddensitysuchasexistingnebulaedisplay，orresultedfromthe
　　coalescencesofmovingnebulousmasses，wehave，inthemomentaofitsparts，originalandacquiredforcesadequatetoproducethemotionsnowgoingon。Variousstagesintheformationofspiralnebulaeimplythatrotation
　　inmanycasesresultsfromconcentration:whetheralways，thereisnoproof;
　　forlargenebulaearetoodiffused，smallonestoodense，andothersare
　　seentoomuchedgeways，toyieldevidence。Butintheabsenceofadverse
　　pre—arrangementsomerotationmaysafelybeinferred。Sofarastheevidence
　　carriesus，weperceivesomequantitativerelationbetweenthemotionsgenerated
　　andthegravitativeforcesexpendedingeneratingthem。IntheSolarSystem
　　theoutermostplanets，formedfromthatmatterwhichhastravelledtheshortest
　　distancetowardsthecommoncentreofgravity，havethesmallestvelocities。
　　Doubtlessthisisexplicableontheteleologicalhypothesis，sinceitis
　　aconditiontoequilibrium。Butwithoutinsistingthatthisisbesidethe
　　question，itwillsufficetopointoutthatthelikecannotbesaidofthe
　　planetaryrotations。Nosuchfinalcausecanbeassignedfortherapidaxial
　　movementofJupiterandSaturn，ortheslowaxialmovementofMars。If，however，
　　welookforthenaturalantecedentsofthesegyrationswhichallplanets
　　exhibit，thenebularhypothesisfurnishesthem;andtheybearmanifestquantitative
　　relationstotheratesofmotions。Fortheplanetsthatturnontheiraxes
　　withextremerapidityarethosehavinglargeorbits——thoseofwhichthe
　　once—diffusedcomponents，probablyformedintobroadrings，movedtotheir
　　centresofaggregationinimmensespaces，andsoacquiredhighvelocities。
　　Whileconversely;theplanetswhichrotatewithrelativelysmallvelocities，arethoseformedoutofsmallnebulousrings。"Butwhat，"itmaybeasked，"hasinsuchcasebecomeof
　　allthatmotionwhichendedintheaggregationofthisdiffusedmatterinto
　　solidbodies？"Theansweristhatithasbeenradiatedintheformof
　　heatandlight;andthisanswertheevidence，sofarasitgoes，confirms。
　　GeologistsandphysicistsagreeinconcludingthattheheatoftheEarth's
　　interiorisbutaremnantoftheheatwhichoncemademoltenthewholemass。
　　ThemountainoussurfacesoftheMoonandofVenus，indicating，astheydo，
　　crustswhichhave，likeourown，beencorrugatedbycontraction，implythat
　　thesebodies，too，haveundergonerefrigeration。LastlywehaveintheSun
　　astill—continuedproductionoftheheatandlightwhichresultfromthe
　　arrestofdiffusedmattermovingtowardsacommoncentreofgravity。Here
　　also，asbefore，aquantitativerelationistraceable。Mars，theEarth，Venus，
　　andMercury，whichseverallycontaincomparativelysmallamountsofmatter
　　whosecentripetalmotionhasbeendestroyed，havealreadylostnearlyall
　　theproducedheat;whilethegreatplanets，JupiterandSaturn，implyby
　　theirlowspecificgravity，aswellasbytheperturbationsoftheirsurfaces，
　　thattheystillretainmuchheat。AndthentheSun，athousandtimesasgreat
　　inmassasthelargestplanet，andhavingtogiveoffanenormouslygreater
　　quantityofheatandlightduetothatlossofmolarmotionwhichconcentrationentails，isstillradiatingwithgreatintensity。§69。Thoseforceswhichhavewroughtthesurfaceofourplanetinto
　　itspresentshape，aretraceabletotheprimordialsourcejustassigned。
　　Geologicchangesareeitherdirectorindirectresultsoftheunexpended
　　heatcausedbynebularcondensation。Theyarecommonlydividedintoigneousandaqueous——headsunderwhichwemaymostconvenientlyconsiderthem。Allthosedisturbancesknownasearthquakes，allthoseelevationsand
　　subsidenceswhichtheyseverallyproduce，allthoseaccumulatedeffectsof
　　manysuchelevationsandsubsidencesexhibitedinocean—basins，islands，
　　continents，table—lands，mountain—chains，andallthoseformationswhich
　　aredistinguishedasvolcanic，geologistsnowregardasmodificationsof
　　theEarth'scrustcausedbytheactionsandreactionsofitsinterior。Even
　　supposingthatvolcaniceruptions，extrusionsofigneousrock，andupheaved
　　mountain—chains，couldbeotherwisesatisfactorilyaccountedfor，itwould
　　beimpossibleotherwisetoaccountforthosewide—spreadelevationsanddepressions
　　whencecontinentsandoceansresult。Suchphenomenaasthefusionoragglutination
　　ofsedimentarydeposits，thewarmingofsprings，thesublimationofmetals
　　intothefissureswherewefindthemasores，mayberegardedaspositive
　　resultsoftheresiduaryheatoftheEarth'sinterior;whilefracturesof
　　strataandalterationsoflevelareitsnegativeresults，sincetheyensue
　　onitsescape。Theoriginalcauseofalltheseeffectsisstill，however，
　　asithasbeenfromthefirst，thegravitatingmovementoftheEarth'smatter
　　towardstheEarth'scentre;seeingthattothisisdueboththeeternalheatitselfandthecollapsewhichtakesplaceasitisradiatedintospace。Tothequestion——Underwhatformspreviouslyexistedtheforcewhich
　　worksoutthegeologicalchangesclassedasaqueous，theanswerislessobvious。
　　Theeffectsofrain，ofrivers，ofwinds，ofwaves，ofmarinecurrents，do
　　notmanifestlyproceedfromonegeneralsource。Analysis，nevertheless，proves
　　thattheyhaveacommongenesis。Ifweask，——Whencecomesthepowerof
　　theriver—current，bearingsedimentdowntothesea？thereplyis，——The
　　gravitationofwaterthroughoutthetractwhichthisriverdrains。Ifwe
　　ask，——Howcamethewatertobedispersedoverthistract？thereplyis，
　　——Itfellintheshapeofrain。Ifweask，——Howcametheraintobein
　　thatpositionwhenceitfell？thereplyis，——Thevapourfromwhichitwas
　　condensedwasdriftedtherebythewinds。Ifweask，——Howcamethisvapour
　　tobeatthatheight？thereplyis，——Itwasraisedbyevaporation。And
　　ifweask，——Whatforcethusraisedit？thereplyis，——TheSun'sheat。
　　JustthatamountofgravitativeforcewhichtheSun'sheatovercameinraising
　　themoleculesofwater，isgivenoutagaininthefallofthosemolecules
　　tothesamelevel。Hencethedenudationseffectedbyrainandrivers，during
　　thedescentofthiscondensedvapourtothelevelofthesea，areindirectly
　　duetotheradiatedenergyoftheSun。Similarlywiththewindsthattransport
　　thevapourshitherandthither。Consequentasatmosphericcurrentsareon
　　differencesoftemperature（eithergeneral，asbetweentheequatorialand
　　polarregions，orspecialasbetweentractsoftheEarth'ssurfacehaving
　　unlikephysicalcharacters）allsuchcurrentsareduetothatsourcefrom
　　whichtheirregularlydistributedheatproceeds。Andifthewindsthusoriginate，
　　sotoodothewavesraisedbythemonthesea'ssurface。Whenceitfollows
　　thatwhateverchangeswavesproduce——thewearingawayofcliffs，thebreaking
　　downofrocksintoshingle，sand，andmud——arealsotraceabletothesolar
　　raysastheirprimarycause。Thesamemaybesaidofocean—currents。Generated
　　asthelargeronesarebytheexcessofheatwhichtheoceanintropical
　　climatesacquiresfromtheSun;anddeterminedasthesmalleronesarein
　　partbylocalshapesofland;itfollowsthatthedistributionofsediment
　　andothergeologicalprocesseswhichthesemarinecurrentseffect，areaffiliable
　　upontheenergytheSunradiates。Theonlyaqueousagencyotherwiseoriginating
　　isthatofthetides——anagencywhich，equallywiththeothers，istraceable
　　tounexpendedcelestialmotion。Butmakingallowanceforthechangesthis
　　works，weconcludethattheslowwearingdownofcontinentsandgradualfilling
　　upofseas，effectedbyrain，rivers，winds，waves，andocean—streams，aretheindirecteffectsofsolarheat。Thusweseethatwhilethegeologicalchangesclassedasigneous，arise
　　fromthestill—progressingmotionoftheEarth'ssubstancetoitscentre
　　ofgravity;theantagonisticchangesclassedasaqueous，arisefromthestill—progressingmotionoftheSun'ssubstancetowardsitscentreofgravity。§70。Thattheforcesexhibitedinvitalactions，vegetalandanimal，
　　aresimilarlyderived，isanobviousdeductionfromthefactsoforganic
　　chemistry。Letusnotefirstthephysiologicalgeneralizations;andthenthegeneralizationswhichtheynecessitate。Plant—lifeisalldirectlyorindirectlydependentontheheatandlight
　　oftheSun—directlydependentintheimmensemajorityofplants，andindirectly
　　dependentinplantswhich，asthefungi，flourishinthedark:sincethese，
　　growingattheexpenseofdecayingorganicmatter，mediatelydrawtheirforces
　　fromthesameoriginalsource。Eachplantowesthecarbonandhydrogenof
　　whichitmainlyconsists，tothecarbondioxideandwatercontainedinthe
　　surroundingairandearth。Thesemust，however，bedecomposedbeforetheir
　　carbonandhydrogencanbeassimilated。Toovercometheaffinitieswhich
　　holdtheirelementstogetherrequirestheexpenditureofenergy;andthis
　　energyissuppliedbytheSun。When，underfitconditions，plantsareexposed
　　tothesolarrays，theygiveoffoxygenandaccumulatecarbonandhydrogen。
　　Indarknessthisprocessceases。Itceases，too，whenthequantitiesoflight
　　andheatreceivedaregreatlyreduced，asinwinter。Conversely，itisactive
　　whenthelightandheataregreat，asinsummer。Andthelikerelationis
　　seeninthefactthatwhileplant—lifeisluxuriantinthetropics，itdiminishes
　　intemperateregions，anddisappearsasweapproachthepoles。Thustheirresistible
　　inferenceisthattheforcesbywhichplantsgrowandcarryontheirfunctions，areforceswhichpreviouslyexistedassolarradiations。Thatinthemain，theprocessesofanimallifeareoppositetothoseof
　　vegetallifeisatruthlongcurrentamongmenofscience。Chemicallyconsidered，
　　vegetallifeischieflyaprocessofde—oxidation，andanimallifechiefly
　　aprocessofoxidation;chieflywemustsay，becauseinsofarasplants
　　areexpendersofforceforthepurposesoforganization，theyareoxidizers;
　　andanimals，insomeoftheirminorprocesses，areprobablyde—oxidizers。
　　Butwiththisqualification，thegeneraltruthisthatwhiletheplant，decomposing
　　carbondioxideandwaterandliberatingoxygen，buildsupthedetainedcarbon
　　andhydrogen（alongwithalittlenitrogenandsmallquantitiesofother
　　elements）intostem，branches，leaves，andseeds;theanimal，consumingthese
　　branches，leaves，andseeds，andabsorbingoxygen，re—composescarbondioxide
　　andwater，formingalsocertainnitrogenouscompoundsinminoramounts。And
　　whilethedecompositioneffectedbytheplantisattheexpenseofenergies
　　emanatingfromtheSun，there—compositioneffectedbytheanimalisatthe
　　profitoftheseenergies，whichareliberatedduringthecombinationofsuch
　　elements。Thusthemovements，internalandexternal，oftheanimal，arere—appearances
　　innewformsofapowerabsorbedbytheplantundertheshapeoflightand
　　heat。Justasthesolarforcesexpendedinraisingvapourfromthesea's
　　surface，aregivenoutagaininthefallofrainandriverstothesamelevel，
　　andintheaccompanyingtransferofsolidmatters;so，thesolarforcesthat
　　intheplantraisedcertainchemicalelementstoaconditionofunstable
　　equilibrium，aregivenoutagainttheactionsoftheanimalduringthefalloftheseelementstoaconditionofstableequilibrium。Besidesthustracingaqualitativecorrelationbetweenthesetwogreat
　　ordersoforganicactivity，aswellasbetweenbothofthemandinorganic
　　activities，wemayrudelytraceaquantitativecorrelation。Wherevegetal
　　lifeisabundant，weusuallyfindabundantanimallife;andasweadvance
　　fromtorridtotemperateandfrigidclimates，thetwodecreasetogether。
　　Speakinggenerally，theanimalsofeachclassreachlargersizesinregionswherevegetationisluxuriant，thaninthosewhereitissparse。Certainfactsofdevelopmentinbothplantsandanimals，illustratestill
　　moredirectlythetruthweareconsidering。Inpursuanceofasuggestion
　　madebyMr。（afterwardsSirWilliam）Grove，Dr。Carpenterpointedoutthat
　　aconnexionbetweenphysicalandvitalforcesisexhibitedduringincubation。
　　Thetransformationoftheunorganizedcontentsofaneggintotheorganized
　　chick，isaquestionofheat:withholdheatandtheprocessdoesnotcommence;
　　supplyheatanditgoesonwhilethetemperatureismaintained，butceases
　　whentheeggisallowedtocool。Thedevelopmentalchangescanbecompleted
　　onlybykeepingthetemperaturewithtolerableconstancyatadefiniteheight
　　foradefinitetime;thatis——onlybysupplyingadefinitequantityof
　　heat。Thoughtheproclivitiesofthemoleculesdeterminethetypicalstructure
　　assumed，yettheenergysuppliedbythethermalundulationsgivesthemthe
　　powerofarrangingthemselvesintothatstructure。Inthemetamorphosesof
　　insectswemaydiscernparallelfacts。Thehatchingoftheireggsisdetermined
　　bytemperature，asisalsotheevolutionofthepupaintotheimago;and
　　bothareacceleratedorretardedaccordingasheatisartificiallysupplied
　　orwithheld。Itwillsufficejusttoadd，thatthegerminationofplantspresentslikerelationsofcauseandeffect，aseveryseasonshows。Thusthenthevariouschangesexhibitedbytheorganiccreation，whether
　　consideredasawhole，orinitstwogreatdivisions，orinitsindividualmembers，conform，sofaraswecanascertain，tothegeneralprinciple。§71。Evenafterallthathasbeensaidintheforegoingpartofthis
　　work，manywillbealarmedbytheassertionthattheforceswhichwedistinguish
　　asmental，comewithinthesamegeneralization。Yetthereisnoalternative
　　buttomakethisassertion:thefactswhichjustify，orratherwhichnecessitate，
　　itbeingabundantandconspicuous。Atthesametimetheyareextremelyinvolved。
　　Theessentialcorrelationsoccurinorganswhicharemostlyinvisible，and
　　betweenforcesorenergiesquiteotherthanthosewhichareapparent。Letusfirsttakeasuperficialviewoftheevidence。Themodesofconsciousnesscalledpressure，motion，sound，light，heat，
　　areeffectsproducedinusbyagencieswhichasotherwiseexpended，crush
　　orfracturepiecesofmatter，generatevibrationsinsurroundingobjects，
　　causechemicalcombinations，andreducesubstancesfromasolidtoaliquid
　　form。Henceifweregardthechangesofrelativeposition，ofaggregation，
　　orofchemicalunion，thusarising，asbeingtransformedmanifestationsof
　　certainenergies;so，too，mustweregardthesensationswhichsuchenergies
　　produceinus。Anyhesitationtoadmitthismustdisappearonremembering
　　thatthelastcorrelations，likethefirst，arenotqualitativeonlybut
　　quantitative。Massesofmatterwhich，byscalesordynamometer，areshown
　　todiffergreatlyinweight，differasgreatlyinthefeelingsofpressure
　　theyproduceonourbodies。Inarrestingmovingobjects，thestrainsweare
　　consciousofareproportionatetothemomentaofsuchobjectsasotherwise
　　measured。Theimpressionsofsoundsgiventousbyvibratingstrings，bells，
　　orcolumnsofair，arefoundtovaryinstrengthwiththeamountofforce
　　applied。Fluidsorsolidsprovedtobemarkedlycontrastedintemperature
　　bythedifferentdegreesofexpansiontheyproduceinthemercurialcolumn，
　　produceinuscorrespondinglydifferentdegreesofthesensationofheat。
　　Andunlikeintensitiesinourimpressionsoflight，answertounlikeeffectsasmeasuredbyphotometers。Besidesthecorrelationandequivalencebetweenexternalphysicalforces
　　andthementalforcesgeneratedbythemundertheformofsensations，there
　　appearstobeacorrelationandequivalencebetweensensationsandthose
　　physicalforceswhich，intheshapeofbodilyactions，resultfromthem。
　　Inadditiontotheexcitementsofsecretingorgans，sometimestraceable，
　　therearisecontractionsoftheinvoluntarymuscles。Sensationsincrease
　　theactionoftheheart，andrecentexperimentsimplythatthemuscularfibres
　　ofthearteriesareatthesametimecontracted。Therespiratorymuscles，
　　tooarestimulated。Therateofbreathingisvisiblyandaudiblyaugmented
　　bothbypleasurableandpainfulexcitementsofthenerves，ifthesereach
　　anyintensity。Whenthequantityofsensationisgreat，itgeneratescontractions
　　ofthevoluntarymuscles，aswellasoftheinvoluntaryones。Violentpains
　　causeviolentstruggles。Thestartthatfollowsaloudsound，thewryface
　　producedbyanextremelydisagreeabletaste，thejerkwithwhichthehand
　　orfootissnatchedoutofveryhotwaterexemplifythegenesisofmotions
　　byfeelings;andinthesecasesitismanifestthatthequantityofbodily。
　　actionisproportionatetothequantityofsensation。evenwherepridecauses
　　suppressionofthescreamsandgroansexpressiveofgreatpain（alsoindirect
　　resultsofmuscularcontraction），wemaystillseeintheclenchingofthe
　　hands，theknittingofthebrows，andthesettingoftheteeth，thatthe
　　bodilyactionsexcitedareasgreat，thoughlessobtrusiveintheirresults。
　　Ifwetakeemotionsinsteadofsensations，wefindthecorrelationandequivalence
　　similarlysuggested。emotionsofmoderateintensity，likesensationsofmoderate
　　intensity，generatelittlebeyondexcitementoftheheartandvascularsystem，
　　joinedsometimeswithincreasedactionofglandularorgans。Butastheemotions
　　riseinstrength，themusclesoftheface，body，andlimbs，begintomove。
　　Ofexamplesmaybementionedthefrowns，dilatednostrils，andstampings
　　ofanger;thecontractedbrows，andwrunghands，ofgrief;thelaughsand
　　leapsofjoy;thefranticstrugglesofterrorordespair。Passingovercases
　　inwhichextremeagitationcausesfainting，weseethatwhateverbethekind
　　ofemotion，thereisamanifestrelationbetweenitsamount，andtheamount
　　ofmuscularactioninduced，fromthefidgettinessofimpatienceuptothe
　　almostconvulsivemovementsaccompanyinggreatmentalagony。Totheseseveral
　　ordersofevidencemustbejoinedthefurtherorder，thatbetweenfeelings
　　andthosevoluntarymotionswhichresultfromthem，therecomesthesensation
　　ofmusculartension，standinginmanifestcorrelationwithboth——acorrelation
　　thatisdistinctlyquantitative:thesenseofstrainvarying，otherthingsequal，directlyasthequantityofmomentumgenerated。§71a。Butnow，revertingtothecautionwhichprecededthesetwo
　　paragraphs，wehavetonote，first，thatthefactsdonotprovetransformation
　　offeelingintomotionbutonlyacertainconstantratiobetweenfeeling
　　andmotion;andthenwehavefurthertonotethatwhatseemsadirectquantitative
　　correlationisillusory。Forexample，ticklingisfollowedbyalmostuncontrollable
　　movementsofthelimbs;butobviouslythereisnoproportionbetweenthe
　　amountofforceappliedtothesurfaceandtheamountoffeelingortheamount
　　ofmotion:ratherthereisaninverseproportion，forwhilearoughtouch
　　doesnotproducetheeffectagentleonedoes。Evenwhenitisrecognized
　　thatthefeelingisnotthecorrelateoftheexternaltouchingactionbut
　　ofadisturbanceincertainterminaltactilestructures，itstillremains
　　demonstrablethatthereisnonecessaryrelationbetweentheamountofsuch
　　disturbanceandtheamountoffeelingproduced;forundersomeconditions
　　muscularmotionresultswithouttheintercalationofanyfeeling。Whenthe
　　spinalcordhasbeensoinjuredastocutoffallnervouscommunicationbetween
　　thelowerpartofthebodyandthebrain，ticklingthesoleofthefootproduces
　　convulsionofthelegmoreviolentthanitwoulddowereitaccompaniedby
　　sensation:thereisareflextransmissionofthestimulusandgenesisof
　　motionwithoutpassagethroughconsciousness。Casesofanotherclassshow
　　thatbetweencentralfeelingsoremotionsandthemuscularmovementsthey
　　initiatetherearenofixedratios:instancethesenseofeffortfeltin
　　makingasmallmovementbyonewhoisexhausted，ortheinabilityofanpatient
　　toraisealimbfromthebedhoweverstrongthedesiretodoit。Sothat
　　neitherthefeelingsperipherallyinitiatednorthosecentrallyinitiated，
　　thoughtheyarecorrelatedwithmotions，arequantitativelycorrelated。Even
　　stillmoremanifestbecomesthelackofdirectrelation，eitherqualitative
　　orquantitative，betweenouterstimuliandinnerfeelings，orbetweensuch
　　innerfeelingsandmuscularmotions，whenwecontemplatethecomplexkinds
　　ofmentalprocesses。Theemotionsandactionsofamanwhohasbeeninsulted
　　areclearlynotequivalentsofthesensationsproducedbythewordsinhis
　　earsforthesamewordsotherwisearranged，wouldnothavecausedthem。The
　　thingsaidbearstothementalactionitexcites，muchthesamerelation
　　thatthepullingofatriggerbearstothesubsequentexplosion——doesnot
　　producethepowerbutmerelyliberatesit。Whence，then，arisesthisimmenseamountofnervousenergywhichawhisperoraglancemaycallforth？Evidentlyweshallgoutterlywrongiftheproblemofthetransformation
　　andequivalenceofforcesisdealtwithasthoughanorganismweresimple
　　andpassiveinsteadofbeingcomplexandactive。Inthelivingbodythere
　　arealreadygoingonmultitudinoustransformationsofenergyveryvarious
　　intheirnatures，andbetweenanyphysicalactionfillingonitandanymotion
　　whichfollows，thereareintercalatednumerouschangesofkindandquantity。