Inthestudyofthephysicalpropertiesofcrystallinematteritisnecessarytotakeaccountofthesymmetryofsuchmatter.Thisis,ingeneral,anisotropic;thatistosay,ithasnotthesamepropertiesinalldirections.Ontheotherhand,mediasuchasglassorwaterareisotropic,havingequivalentpropertiesinalldirections.Itwasthestudyofopticswhichfirstshowedthatthepropagationoflightinacrystalisdependentupontheelementsofsymmetryinthatcrystal.Thesamethingistruefortheconductionofheatorelectricity,formagnetization,forpolarization,etc.
ItwasinreflectingupontherelationsbetweencauseandeffectthatgovernthesephenomenathatPierreCuriewasledtocompleteandextendtheideaofsymmetry,byconsideringitasaconditionofspacecharacteristicofthemediuminwhichagivenphenomenonoccurs.Todefinethisconditionitisnecessarytoconsidernotonlytheconstitutionofthemediumbutalsoitsconditionofmovementandthephysicalagentstowhichitissubordinated.Thusarightcircularcylinderpossessesaplaneofsymmetryperpendiculartoitsaxisinitsposition,andaninfinityofplanesofsymmetrypassthroughitsaxis.Ifthesamecylinderisinrotationonitsaxis,thefirstplaneofsymmetrypersists,butalltheothersaresuppressed.Furthermore,ifanelectriccurrenttraversesthecylinderlengthwise,noplaneofsymmetryremains.
Ineveryphenomenontheelementsofsymmetrycompatiblewithitsexistencemaybedetermined.Certainelementscancoexistwithcertainphenomena,buttheyarenotnecessarytothem.Thatwhichisnecessaryisthatcertainonesamongtheseelementsshallnotexist.Itisdissymmetrythatcreatesthephenomenon.Whenseveralphenomenaaresuperposedinthesamesystem,thedissymmetriesareaddedtogether."WorksofPierreCurie,"page.
ItwasfromtheaboveconsiderationsthatPierreCurieannouncedthegenerallawwhosetext,alreadycited,attainsthehighestdegreeofgeneralization.Thesynthesisthusobtainedseemscomplete,andallthatwasfurtherneededwastodeducefromitallthedevelopmentsofwhichitadmits.
Forthisitisconvenienttodefinetheparticularsymmetryofeachphenomenonandtointroduceaclassificationwhichmakescleartheprincipalgroupsofsymmetry.Mass,electriccharge,temperature,havethesamesymmetry,ofatypecalledscalar,thatofthesphere.Acurrentofwaterandarectilinealelectriccurrenthavethesymmetryofanarrow,ofthetypepolarvector.Thesymmetryofanuprightcircularcylinderisofthetypetensor.Allofthephysicsofcrystalscanbeexpressedinaforminwhichtheparticularphenomenainquestionarenotspecified,butinwhichareexaminedonlythegeometricalandanalyticalrelationsbetweenthetypesofquantitieswherecertainonesareconsideredascausesandtheotheraseffects.
Thus,thestudyofelectricalpolarizationbytheapplicationofanelectricfieldbecomestheexaminationoftherelationbetweentwosystemsofvectors,andthewritingoutofasystemoflinearequationshavingcoefficients.Thesamesystemofequationsholdsfortherelationbetweenanelectricfieldandanelectriccurrentincrystallineconductors;orforthatbetweenthetemperaturegradientandtheheatcurrent,exceptthatthemeaningofthecoefficientsmustbechanged.Similarly,astudyofthegeneralrelationsbetweenavectorandasystemoftensorscanrevealallthecharacteristicsofpiezo-electricphenomena.Andalltherichvarietyofthephenomenaofelasticitydependsontherelationbetweentwosetsoftensorswhichrequire,inprinciple,coefficients.
Theforegoingbriefexpositionrevealsthehighphilosophicimportoftheseconceptionsofsymmetrywhichtouchallnaturalphenomena,andwhoseprofoundsignificancePierreCuriesoclearlysetforth.ItisinterestinginthisconnectiontorecalltherelationwhichPasteursawbetweenthesesameconceptionsandthemanifestationsoflife."Theuniverse,"hesaid,"isadissymmetricwhole.Iamledtobelievethatlife,asitisrevealedtous,mustbeafunctionofthedissymmetryoftheuniverse,oroftheconsequencesthatitinvolves."
AshisorganizationofhisworkintheSchoolprogressed,PierreCuriecouldbegintodreamofgoingforwardagainwithhisexperimentalresearch.Hecoulddoso,however,onlyundermostprecariousconditions,forhehadnotevenalaboratoryforhispersonalwork,noraroomofanykindentirelyathisdisposition.Besides,hepossessednofundstosupporthisinvestigations.ItwasonlyafterhehadbeenseveralyearsattheSchoolthatheobtained,thankstotheinfluenceofSchutzenberger,asmallannualsubventionforhiswork.Uptothattimethematerialsnecessaryforhimwereprovided,thankstothekindnessofhissuperiors,totheextentpossible,bydrawinguponaverylimitedgeneralfundoftheteachinglaboratory.Asforaplacetoworkin,hehadtocontenthimselfwithverylittle.Hesetupcertainofhisexperimentsintheroomsofhispupilswhenthesewerenotinuse.Butmorefrequentlyheworkedinanoutsidecorridorrunningbetweenastairwayandalaboratory.Itwastherethatheconducted,inparticular,hislongresearchonmagnetism.