Inhepublishedamemoironquestionsoftheorderandrepetitionthatareatthebaseofthestudyofthesymmetryofcrystals.Thiswasfollowedinthesameyearbyamoregeneraltreatmentofthesamesubject.Anotherarticleonsymmetryanditsrepetitionsappearedin.Inthatyearhepublished,too,averyimportanttheoreticalworkontheformationofcrystals,andthecapillaryconstantsofthedifferentfaces.
ThisrapidsuccessionofinvestigationsshowshowcompletelyengrossedPierreCuriewasinthesubjectofthephysicsofcrystals.Bothhistheoreticalandhisexperimentalresearchinthisdomaingroupeditselfaroundaverygeneralprinciple,theprincipleofsymmetry,thathehadarrivedatstepbystep,andwhichheonlydefinitelyenunciatedinmemoirspublishedbetweentheyearsand.
Thefollowingistheform,alreadyclassic,inwhichhemadehisannouncement:
"Whencertaincausesproducecertaineffects,theelementsofsymmetryinthecausesoughttoreappearintheeffectsproduced.
"Whencertaineffectsrevealacertaindissymmetry,thisdissymmetryshouldbeapparentinthecauseswhichhavegiventhembirth.
"Theconverseofthesetwostatementsdoesnothold,atleastpractically;thatistosay,theeffectsproducedcanbemoresymmetricalthantheircauses."
Thecapitalimportanceofthisstatement,perfectinitssimplicity,liesinthefactthattheelementsofsymmetrywhichitintroducesarerelatedtoallthephenomenaofphysicswithoutexception.
Guidedbyanexhaustivestudyofthegroupsofsymmetrywhichmightexistinnature,PierreCurieshowedhowoneshouldusethisrevelationincharacteratoncegeometricandphysical,inordertoforeseewhetheraparticularphenomenoncanreproduceitself,orwhetheritsreproductionisimpossibleunderthegivenconditions.Atthebeginningofacertainmemoir,heinsistsintheseterms:
"Ithinkitisnecessarytointroduceintophysicstheideasofsymmetryfamiliartocrystallographers."
Hisworkinthisfieldisfundamental,andeventhoughhewasledawayfromitlaterbyotherinvestigations,healwaysretainedapassionateinterestinthephysicsofcrystals,aswellasinprojectsoffurtherresearchinthisdomain.
TheprincipleofsymmetrytowhichPierreCuriehadsoeagerlydevotedhimselfisoneofthesmallnumberofgreatprincipleswhichdominatethestudyofthephenomenaofphysics,andwhich,havingtheirrootinideasderivedbyexperiment,yetlittlebylittledetachthemselvesandassumeaformmoreandmoregeneralandmoreandmoreperfect.Itisinthiswaythattheideaoftheequivalenceofheatandofwork,addedtotheearliernotionoftheequivalenceofkineticandpotentialenergies,broughtabouttheestablishmentoftheprincipleoftheconservationofenergywhoseapplicationisentirelygeneral.InthesamewaythelawoftheconservationofmassgrewoutoftheexperimentsofLavoisier,whichbelongtothefoundationsofchemistry.Recentlyanadmirablesynthesishasmadeitpossibleforustoattainastillhigherdegreeofgeneralizationthroughtheunionofthesetwoprinciples,forithasbeenprovedthatthemassofabodyisproportionaltoitsinternalenergy.ThestudyofelectricalphenomenaledLippmanntoannouncethegenerallawoftheconservationofelectricity.TheprincipleofCarnot,bornofconsiderationsonthefunctioningofthermalmachines,hasacquiredalsosogeneralasignificance,thatitmadepossibletheforeseeingofthemostprobablecharacterofspontaneousevolutionforallmaterialsystems.
Theprincipleofsymmetryfurnishesanexampleofananalogousevolution.Tobeginwith,observationofNaturewasabletosuggesttheideaofsymmetry;thoughsuchobservationsrevealonlyimperfectlyanyregulardispositionsintheaspectsofanimalsandplants.Theregularitybecomesverymuchmoreperfectinthecaseofcrystallizedminerals.WemayconsiderthatNaturefurnishesustheideaofaplaneofsymmetryandofanaxisofsymmetry.Anobjectpossessesaplaneofsymmetry,oraplaneofreflection,ifthisplanedividestheobjectintotwoparts,ofwhicheachonemaybethoughtofastheimageoftheotherreflectedintheplaneasinamirror.Itisthis,approximately,thatoccursintheexternalappearanceofmanandofnumerousanimals.Anobjectpossessesanaxisofsymmetryoftheordern,ifitpreservesthesameappearanceafterarotationonthisaxisofthenthpartofarevolution.Thusaregularfloweroffourpetalshasanaxisofsymmetryoftheorderfour,oraquarternaryaxis.Crystalslikethoseofrocksaltorofalumpossessmanyplanesofsymmetryandmanyaxesofsymmetryofdifferentorders.
Geometryteachesustostudytheelementsofsymmetryofalimitedfiguresuch,forinstance,asapolyhedron;andtodiscovertherelationsbetweenitspartswhichpermitustoreunitedifferentsymmetriesingroups.Theknowledgeofthesegroupsisofthegreatestusefulnessinestablishingarationalclassificationofcrystalformsinasmallnumberofsystemseachofwhichisderivedfromasimplegeometricform.Thustheregularoctahedron,belongstothesamesystemasthecube,forinthecaseofeachthegroupformedbytheaxesandtheplanesofsymmetryisthesame.