inhepublishedamemoironquesionsofheorderandrepeiionhaareahebaseofhesudyofhesymmeryofcrysalshiswasfollowedinhesameyearbyamoregeneralreamenofhesamesubjecanoheraricleonsymmeryandisrepeiionsappearedininhayearhepublished,oo,averyimporanheoreicalworkonheformaionofcrysals,andhecapilryconsansofhedifferenfaces

hisrapidsuccessionofinvesigaionsshowshowcompleelyengrossedpierrecuriewasinhesubjecofhephysicsofcrysalsbohhisheoreicalandhisexperimenalresearchinhisdomaingroupediselfaroundaverygeneralprinciple,heprincipleofsymmery,hahehadarrivedasepbysep,andwhichheonlydefinielyenunciaedinmemoirspublishedbeweenheyearsand

hefollowingisheform,alreadycssic,inwhichhemadehisa

ouncemen:

whenceraincausesproduceceraineffecs,heelemensofsymmeryinhecausesoughoreappearinheeffecsproduced

whenceraineffecsrevealaceraindissymmery,hisdissymmeryshouldbeappareninhecauseswhichhavegivenhembirh

heconverseofhesewosaemensdoesnohold,aleaspracically;haisosay,heeffecsproducedcanbemoresymmericalhanheircauses

hecapialimporanceofhissaemen,perfecinissimpliciy,liesinhefachaheelemensofsymmerywhichiinroducesarereedoallhephenomenaofphysicswihouexcepion

guidedbyanexhausivesudyofhegroupsofsymmerywhichmighexisinnaure,pierrecurieshowedhowoneshouldusehisreveionincharaceraoncegeomericandphysical,inorderoforeseewheheraparicurphenomenoncanreproduceiself,orwheherisreproducionisimpossibleunderhegivencondiionsahebegi

ingofacerainmemoir,heinsissinheseerms:

ihinkiisnecessaryoinroduceinophysicsheideasofsymmeryfamiliarocrysallographers

hisworkinhisfieldisfundamenal,andevenhoughhewasledawayfromierbyoherinvesigaions,healwaysreainedapassionaeineresinhephysicsofcrysals,aswellasinprojecsoffurherresearchinhisdomain

heprincipleofsymmeryowhichpierrecuriehadsoeagerlydevoedhimselfisoneofhesmallnumberofgreaprincipleswhichdominaehesudyofhephenomenaofphysics,andwhich,havingheirrooinideasderivedbyexperimen,yelilebyliledeachhemselvesandassumeaformmoreandmoregeneralandmoreandmoreperfeciisinhiswayhaheideaofheequivalenceofheaandofwork,addedoheearliernoionofheequivalenceofkiicandpoenialenergies,broughabouheesablishmenofheprincipleofheconservaionofenergywhoseapplicaionisenirelygeneralinhesamewayhewofheconservaionofmassgrewouofheexperimensofvoisier,whichbelongohefoundaionsofchemisryrecenlyanadmirablesynhesishasmadeipossibleforusoaainasillhigherdegreeofgeneralizaionhroughheunionofhesewoprinciples,forihasbeenprovedhahemassofabodyisproporionaloisinernalenergyhesudyofelecricalphenomenaledlippma

oa

ouncehegeneralwofheconservaionofelecriciyheprincipleofcarno,bornofconsideraionsonhefuncioningofhermalmachines,hasacquiredalsosogeneralasignificance,haimadepossibleheforeseeingofhemosprobablecharacerofsponaneousevoluionforallmaerialsysems

heprincipleofsymmeryfurnishesanexampleofananalogousevoluionobeginwih,observaionofnaurewasableosuggesheideaofsymmery;houghsuchobservaionsrevealonlyimperfeclyanyregurdisposiionsinheaspecsofanimalsandpnshereguriybecomesverymuchmoreperfecinhecaseofcrysallizedmineralswemayconsiderhanaurefurnishesusheideaofapneofsymmeryandofanaxisofsymmeryanobjecpossessesapneofsymmery,orapneofreflecion,ifhispnedividesheobjecinowopars,ofwhicheachonemaybehoughofasheimageofheoherreflecedinhepneasinamirroriishis,approximaely,haoccursinheexernalappearanceofmanandofnumerousanimalsanobjecpossessesanaxisofsymmeryofheordern,ifipreserveshesameappearanceaferaroaiononhisaxisofhenhparofarevoluionhusaregurfloweroffourpealshasanaxisofsymmeryofheorderfour,oraquarernaryaxiscrysalslikehoseofrocksalorofalumpossessmanypnesofsymmeryandmanyaxesofsymmeryofdifferenorders

geomeryeachesusosudyheelemensofsymmeryofalimiedfiguresuch,forinsance,asapolyhedron;andodiscoverhereionsbeweenisparswhichpermiusoreuniedifferensymmeriesingroupsheknowledgeofhesegroupsisofhegreaesusefulnessinesablishingaraionalcssificaionofcrysalformsinasmallnumberofsysemseachofwhichisderivedfromasimplegeomericformhusheregurocahedron,belongsohesamesysemashecube,forinhecaseofeachhegroupformedbyheaxesandhepnesofsymmeryishesame