Ofcoursetheatomitselfwasinnosensedisplaced，butAvogadro’slawsoonmadeitplainthattheatomhadoftenusurpedterritorythatdidnotreallybelongtoit。Inmanycasesthechemistshadsupposedthemselvesdealingwithatomsasunitswherethetrueunitwasthemolecule。Inthecaseofelementarygases，suchashydrogenandoxygen，forexample，thelawofequalnumbersofmoleculesinequalspacesmadeitclearthattheatomsdonotexistisolated，ashadbeensupposed。Sincetwovolumesofhydrogenunitewithonevolumeofoxygentoformtwovolumesofwatervapor，thesimplestmathematicsshow，inthelightofAvogadro’slaw，notonlythateachmoleculeofwatermustcontaintwohydrogenatomsapointpreviouslyindispute，butthattheoriginalmoleculesofhydrogenandoxygenmusthavebeencomposedineachcaseoftwoatoms——elsehowcouldonevolumeofoxygensupplyanatomforeverymoleculeoftwovolumesofwater？
What，then，doesthisimply？Why，thattheelementaryatomhasanavidityforotheratoms，alongingforcompanionship，an\"affinity\"——callitwhatyouwill——whichisboundtobesatisfiedifotheratomsareintheneighborhood。Placedsolelyamongatomsofitsownkind，theoxygenatomseizesonafellowoxygenatom，andinalltheirmaddancingsthesetwomatesclingtogether——possiblyrevolvingabouteachotherinminiatureplanetaryorbits。Preciselythesamethingoccursamongthehydrogenatoms。Butnowsupposethevariouspairsofoxygenatomscomenearotherpairsofhydrogenatomsunderproperconditionswhichneednotdetainushere，theneachoxygenatomlosesitsattachmentforitsfellow，andflingsitselfmadlyintothecircuitofoneofthehydrogencouplets，and——presto！——thereareonlytwomoleculesforeverythreetherewerebefore，andfreeoxygenandhydrogenhavebecomewater。Thewholeprocess，statedinchemicalphraseology，issummedupinthestatementthatunderthegivenconditionstheoxygenatomshadagreateraffinityforthehydrogenatomsthanforoneanother。
Aschemistsstudiedtheactionsofvariouskindsofatoms，inregardtotheirunionswithoneanothertoformmolecules，itgraduallydawneduponthemthatnotallelementsaresatisfiedwiththesamenumberofcompanions。Someelementsaskonlyone，andrefusetotakemore；whileotherslinkthemselves，whenoccasionoffers，withtwo，three，four，ormore。Thuswesawthatoxygenforsookasingleatomofitsownkindandlinkeditselfwithtwoatomsofhydrogen。Clearly，then，theoxygenatom，likeacreaturewithtwohands，isabletoclutchtwootheratoms。
Butwehavenoproofthatunderanycircumstancesitcouldholdmorethantwo。Itsaffinitiesseemsatisfiedwhenithastwobonds。But，ontheotherhand，theatomofnitrogenisabletoholdthreeatomsofhydrogen，anddoessointhemoleculeofammoniumNH3；whilethecarbonatomcanholdfouratomsofhydrogenortwoatomsofoxygen。
Evidently，then，oneatomisnotalwaysequivalenttoanotheratomofadifferentkindincombiningpowers。ArecognitionofthisfactbyFranklandabout1852，anditsfurtherinvestigationbyothersnotablyA。KekuleandA。S。Couper，ledtotheintroductionofthewordequivalentintochemicalterminologyinanewsense，andinparticulartoanunderstandingoftheaffinitiesor\"valency\"ofdifferentelements，whichprovedofthemostfundamentalimportance。Thusitwasshownthat，ofthefourelementsthatentermostprominentlyintoorganiccompounds，hydrogencanlinkitselfwithonlyasinglebondtoanyotherelement——ithas，sotospeak，butasinglehandwithwhichtograsp——whileoxygenhascapacityfortwobonds，nitrogenforthreepossiblyforfive，andcarbonforfour。Thewordsmonovalent，divalent，trivalent，tretrava-lent，etc。，werecoinedtoexpressthismostimportantfact，andthevariouselementscametobeknownasmonads，diads，triads，etc。Justwhydifferentelementsshoulddifferthusinvalencynooneasyetknows；itisanempiricalfactthattheydo。Andoncethenatureofanyelementhasbeendeterminedasregardsitsvalency，amostimportantinsightintothepossiblebehaviorofthatelementhasbeensecured。Thusaconsiderationofthefactthathydrogenismonovalent，whileoxygenisdivalent，makesitplainthatwemustexpecttofindnomorethanthreecompoundsofthesetwoelements——namely，H——O——writtenHObythechemist，andcalledhydroxyl；H——O——HH2O，orwater，andH——O——O——HH2O2，orhydrogenperoxide。Itwillbeobservedthatinthefirstofthesecompoundstheatomofoxygenstands，sotospeak，withoneofitshandsfree，eagerlyreachingout，therefore，foranothercompanion，andhence，inthelanguageofchemistry，forminganunstablecompound。Again，inthethirdcompound，thoughallhandsareclasped，yetonepairlinksoxygenwithoxygen；andthisalsomustbeanunstableunion，sincetheavidityofanatomforitsownkindisrelativelyweak。Thusthewell-knownpropertiesofhydrogenperoxideareexplained，itseasydecomposition，andtheeagernesswithwhichitseizesupontheelementsofothercompounds。