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。