194 7MNRAS.107. .274M Actually, theinvestigationofFraunhoferlinesissofascinating,richin lines isduetotheairydanceofatomsinfieryradiationSun. observational detailsandsoimportanttheoretically,thatIshallhavetorestrict When Kirchhoffini860madehisdrawingandcatalogueofthesolarspectrumf, the individualFraunhoferlinesthereisagreatvarietyofintensityprofiles. characteristic letterfromatog,indicatingthewidthin7differentgrades;and a workinwhichhelostmostofhissight,withgreatcaregavetoeachline all knowthatprogressinthisfieldisduetothecooperationofmanyscientists because withthisworkareconnectedsomanypersonalreminiscences;butwe spectrum, thefullrichnessofthatchiaroscuro.Andthencomestheorist, telescope reveals.Aspectrumlooksatfirstsightlikearatherdullsuccession similarly hehadalsoascaleforthedarknessinsideline,runningfrom1to6. all overtheworld.* deriving bythepowerofhisphantasyhowthatmusicundulatingspectral methods anddiscoveringtheinfinitevarietyofshadeshalftonesinthat of brightanddarkstripes.Butnowcomestheobserver,usinghisrefined with asharpcentralcore. to presentbeforeyousomeofthemoreimportantmomentsindevelopment myself toonepartofthesubject:photometry;eventhen,Ishallonlybeable The spectroscopistcouldnotshowyouanyofthewonderfulpictureswhich stones, eachofthemcorrespondingtothelinesonedefinitedegreedarkness. His lithographicreproductionofthesolarspectrumwasprintedwith6different In thisframeIshallgiveanaccountmoreparticularlyoftheworkdoneatUtrecht and inthereportbyRedman,M.N.,98,311,1938. either byitswidthordarknessbothofthem.Thiscelebrated It isinterestingtofindthegreenmagnesiumlineA5183asabroad,shallowband be made.Thepioneerinthisfield,asso manyothers,wasSchwarzschild field wouldbeopentoinvestigation,assoon quantitativemeasurementscould not madebefore1900.Anenormousamount ofmaterialwasavailable,avast a preliminary,ratherqualitativeestimateoftheimpressionwhichlinemakes, of ourknowledgeandageneralviewthepresentstateproblemsinvolved. at Gottingen.HisprofilesofthelinesHand K,determinedforthecentreof 1896), characterizedeachFraunhoferlinebyanumber,the“intensity”: Rowland scale,thoughbeingadmittedlyrough,provedofthegreatestuse during manyyearsuptoourday.Rowland’s collaborator,Jewell,madeinter- esting observationsonsomeprofiles.J © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Generalreferencestotheliteraturemaybefoundin Unsold, PhysikderSternatmosphären, f “UntersuchungenüberdasSonnenspectrum”,Abh. Akad. Berlin,1861. î Ap.J.,3,100,1893. Already thefirstobservationsofagoodsolarspectrumrevealed,thatamong A lectureonFraunhoferlineshasinevitablyasomewhatabstrusecharacter.. Actual measurementsconcerningtheintensity insideFraunhoferlineswere Rowland, inhisPreliminaryTableofSolarSpectrumWave-lengths(1893-* THE FRAUNHOFERLINESOFSOLARSPECTRUM {George DarwinLecture,deliveredbyProfessorM.G.J.Minnaert, on 1947May9) 194 7MNRAS.107. .274M No. 3,1947TheFraunhoferlinesoftheSolarSpectrum the Sun’sdiskandforlimb,arefirstprofilesevermeasured(1914); their precisionisstillcomparabletothatofmodernmeasurements. years nobodyfollowedthenewpathway,discoveredbyhim.Itwasonlyin the happycircumstancethatJulius,professorofexperimentalphysics,had kept atPotsdam,wasappliedtotheinvestigationofFraunhoferlinesby under theleadofOmstein,directedtheireffortstophotometrylaboratory younger generationofastronomersandphysicists.* 1927 thatthetraditionofreliablephotographicphotometry,whichhadbeen created aheliophysicaldepartmentathisinstitute.Since1920ourphysicists, the multipletrules;photometricpropertiesofphotographicplateswere spectra ;MollconstructedhismicrophotometerBurgerandDorgelodiscovered investigated; vanCittertandBurgerusedthestepreducerdeveloped heliophysical departmentfoundatonceanewfieldofactivity.AndIremember the wonderfulnewmethodstoinvestigationofFraunhoferlines.The of manymetres,wehadtorecordthedetailedprofiledarklines,notwider first stepswereverycautious.Inaspectrum,obtainedwithfocallength that ourveryfirstmicrophotometerrecordofsomesmallpartthesolarspectrum stimulating foranastrophysicisttotakepartinthatdevelopment,andapply a methodforthecorrectionofprofileinstrumentalinfluences.Itwasvery awoke atoncetheveryambitiousplanofacompletephotometricatlas.Our value. Allpossiblesourcesoferrorwereexaminedonebyone,theirinfluence than afewtenthsofmillimetre,surroundedbyfloodslight;andwewanted first periodbyvonKliiber,Unsold,Plaskett,Dunham,Righini,Woolley, and thattheresultsfromthispioneeringperiodseemedtoagreeinarather on themeasurementswereminimizedandremainingeffectsestimated. seemed almostincrediblethattheintensityprofilerecordedwouldhaveanyreal to measuretheintensityineachpointwithaprecisionoffewpercent!It unexpected andverysatisfactoryway.Whenreadingagainthepapersfromthis soon similarmeasurementsweremadeatotherinstitutesallovertheworld, hoped andourself-confidenceincreased.Itwasagreatencouragement,that Gradually, wefoundthatourresultsweremorereliablethancouldhave trouble andconcern,gettingsatisfactoryresults ! any hesitationthesesamemeasurements,which forusweresuchasourceof have bestowedallpossiblecareontheirmethod beforetheystartedmeasuring. greatly impressedbytheirfundamentalwork, whichbecamethebasisforall some precisionisstillastonishinglysmall.Imention thefirstfourBalmerlines, physicists havefollowedthegoodtraditionof classical astronomy,andthatthey modern spectrophotometricinvestigations.It maybesafelyassertedthatastro- Bruggencate, Thackeray,Allen,andatUtrechtbyMuldersHoutgast,oneis Carroll andthoseofthenextgeneration,representedbyRedman,ten stand, thatwefeltavery strongdesiretomakeavailablefortheoreticalinvestigatioa H andK,theCaresonance-line 4227,theDlinesofsodium,Sr-ion line4078, and fiveheavylinesofiron intheviolet,altogethersixteenlines.You willunder- © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The independentdevelopmentoftheUtrechtmeasurementsfwasdueto But Schwarzschild’sphotometricmethodiscumbersome,andformany The numberofFraunhoferlineswhichthe profilehasbeenstudiedwith Our rewardis,thatwenowseeournaiveyounger studentsmakingwithout * vonKliiber,Z.Phys.,44, 481, 1927. f Z.Phys.,45,610,1927. 20 275 194 7MNRAS.107. .274M + where Mulderswasallowedtotakethewholeseriesofspectralrecordswith the splendidequipmentthereavailable.Thespectrahaveadispersionof 276 M.G,J.MinnaertVol.107 work isdoneinasystematicway,onemaybeabletocorrectafterwards not onlythesesixteenlinesoutof20,000,butmanymore,andevenallthem, 3 mm./A.inthesecondorder,beautifuldefinition,andareliablestandardization; become atonceapparent. TheshallowhydrogenlinesandtheCö -lines in known Fraunhoferlineswererevealedoneby oneforthefirsttimeintheirtrue accumulated atUtrechtandincreasedbyinformationfromotherworkersin gradually tookshapeandseemedmorepossiblethroughtheexperience, if possible.Theplanforageneralphotometricatlasofthewholesolarspectrum to aminimum. that bothoftheseinstrumentsareadaptedtotheirparticularproblem.The Mulders andmyself,eachtakingforhisshareapartofthework.*Agreat the field.Ofcourse,insuchanundertakingitisimpossibletogivefullcare light ofthedarkroomhowgraphsappeared andhowtheprofilesofwell- the graininessofplate.TheUtrechtdevice isonlypracticalwhenthe consecutive surfaceelementsoftheplatebymeansaHartmannphotometer. deal ofthecreditisduetogeneroushelpMt.WilsonObservatory, relatively simplewaytheerrorsleft.TheplanwascarriedoutbyHoutgast, each ofthelines,asmaybedoneinindividualinvestigations.Butif plate, sothatthesamediaphragmcanbekept in use,butitreducesthegraininess whole ofouratlas.Forasimilarpurposeanentirelydifferentinstrument photographic curve,correspondingtotheplatewhichweareinvestigating. metric research,onewouldhavehadtomeasurebyeyethedensityofall their fulllengthisabout12m.Intheveryfirstperiodofspectrophoto- spectra ofmoderatedispersion;butithas the disadvantagethatitincreases curve changesquicklyalongthespectrum, as isgenerallythecaseinstellar used bythemfortheirwonderfulAtlasofStellarSpectra.Ihavetheimpression great ingenuityhasbeendevisedbyWilliamsandHiltneratMichigan;itwas in thesamecumbersomewayasweformerlydidwhendeterminedtrans- tedious measuringandreadingfromgraphsplottingpointbypoint,exactly the transmissioncurveintoanintensitycurve,isstillnowgenerallymadeby the transmissionofplateallalongspectrumissolvedbyanentirely intensity values. characteristic curveremainsthesameovera considerabledistancealongthe This wassolvedbyaddingarelativelysimpleauxiliaryapparatustotheordinary completely automaticanddirectregistrationoftheintensitycurveisnecessary.f to followsuchalengthyprocedure.Thetotallengthofthemicrophotometer automatic apparatus.However,thesecondstepinvolved,conversionof microphotometer ;adiaphragmisinserted,cutoutintheformofcharacteristic mission withtheHartmann.Inourcase,itwouldhavebeenutterlyimpossible Since theinventionofmicrophotometer,thiswholeprocessderiving records amountedto120m.Whenhandlingsuchextensivematerial,a The instrumentworksremarkablywellandhasbeeninfulloperationforthe Michigan apparatuscanbeusedwithoutcomplications evenifthecharacteristic © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Minnaert,Houtgast,Mulders, PhotometricAtlasoftheSolarSpectrum,Amsterdam, 1940. f MinnaertandHoutgast,Z. Astrophys.,15,354,1938. When turningtheleaves oftheatlas,manystrikingfeaturesspectral lines It wasarealthrilltodeveloptheintensitycurves recorded,toseeinthered 194 7MNRAS.107. .274M © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Monthly NoticesofR.A.S. Violet Rect A—Mount Wilson.B, C,D—Evershed, The FraunhoferLines oftheSolarSpectrum,M.G.J.Minnaert. Vol. 107,Plate9. 194 7MNRAS.107. .274M out howfartheirprofileshavetobecorrectedforinstrumentaldistortionand lines uptoH17,whichUnsoldalsoremarked;theycanonlybeseenonthe the infra-red^broadwingsofsodiumandmagnesiumlines,deep No. 3,1947TheFraunhoferlinesoftheSolarSpectrum277 that ourinstrumentalwidthhadbeenoverestimatedalittle,andthe effect uponthenarrowsolarlines.Fromarandomselectionofwellisolated into alinewithwidthof61mA.(inthesecondorder,À=6000A.).However, should ratherbetakenas5imA.fLetusnowconsidertheinfluenceofthis microphotometer recordsandnotbylookingattheoriginalplate.* mental curve:wefoundthatatrulymonochromaticlinewouldbebroadened broadening. Fromplatestakenforthatpurpose,wedeterminedtheinstru- iron linesintheviolet,complicatedblendsultra-violetarestriking. instrumental broadening,severalmethodsareavailable.Inourexperience,that lines, recordedintheatlas,wedrawtypicalmeanprofiles.Tocorrectthesefor van deHulst,fromacarefulanalysisoftheatmosphericoxygenlines,showed rection variessomewhat fromplateto;accordinghiscurves, thecentral in Fig.I. other andquickerprocedures.Wefindnowthecorrectedprofilesasdrawn of BurgerandvanCittertJisstillveryreliable;butdeHulst§hasdescribed Shortly afterthepublication,Muldersdescribedfaintultra-violethydrogen who carefullydeterminedwithhisinterferometer thetruecentralintensityof some weaklines.BycomparisonwiththeUtrecht atlas,hefindsthatthecor- © Royal Astronomical Society • Provided by theNASA Astrophysics Data System J! P.A.S.P.y53,200,1941. § B.A.N.y9,225,1941;and 10,79,1946*Seealso:Kremer,B.A.N.y9,229,1941. t Z.Phys.,79,722,1932and 81,428,1933. t B.A.N.10,79,1946. * Mulders,P.A.S.P.53,38, 1941. y f It isveryimportanttoexaminethenarrowerlinesofatlasandfind A valuablecheckontheseresultsisobtainedfrom measurementsbyShane¡¡, Profiles offaintFraunhoferlinesfromtheUtrechtAtlas. Fig. i. 20* 194 7MNRAS.107. .274M intensities ofthelinesconsideredshouldfallwithinrangeindicatedinour 278 M.G.J.MinnaertVol.107 diagrams byverticalbars(Fig.i). reliable way.Ifthecorrectedcentralintensityisaboutright*,otherpoints of theprofilewillbestillbetter.Itiswellknownthatinprinciple,givenan can befullyresolved.Inpracticethereareverydefinitelimits.Butapparently accurate instrumentalcurveandprecisemeasurements,arbitrarilynarrowlines the instrumentalcurveofouratlasissufficientlynarrow,comparedtorather for allofthem.Theprofilesthusobtained,similartothosedrawnonFig.1,are the trueshapesoffaintFraunhoferlines.Theatlasissufficientforafull considerable widthofallsolarlines,tomakeareliablecorrectionpossible resolution ofallsolarlines. For apartitisdueofcoursetodiffractionbythefinitesizegrating;but the widthofthisinstrumentalcurveseemstobeproportionalwave-length, to checkthisfordifferentspectrographs. other effectsmustbecertainlyinvolvedalso.Asfaraspresentexperiencegoes,, as mightbeexpectedforadiffractionphenomenon.Itwouldimportant observed inagreatnumberoftheisolatedlinesthroughoutouratlas(Plate9A). It isofcoursenecessarytoascertainwhetherthiseffectmustbeascribedareal asymmetry intheFraunhoferlines,ortoanspectrograph^ to havecleanandsimpleexperimentalconditions.Theasymmetryshows or toinertiainthemicrophotometricapparatus. again, towardsthered,apparentlyasstronginatlas. remains, alwaystowardsthered;recordsforwardandbackwardareidentical. This provesthatinertiaofthemicrophotometerisexcluded(cf.Plate9CandD). taken bymeansofhisautocollimatingspectrograph withliquidprisms,its metry isagainpresent,tothered,andbyaboutsameamountasin grating spectrographatHale’sprivateobservatory,Pasadena.Theasym- microphotometer, withoutcylindricallensesorintensityapparatus,justinorder solar effect! Mt. Wilsonplate.Onewouldalmostsuspectthatthephenomenonisatrue asymmetry inthespectrallinesissmall,but distinctlytowardthevioletside. still morereduced(Plate9CandD). instrumental origin,whichistobefoundin thespectrograph.Letusnow dispersion isequivalenttothatoften63deg. flintglassprisms*.Herethe (Plate 9B).Inasecondseriesofplatesfrom Evershedtheasymmetryis trouble. Itmaybethat inbigspectrographstheobjectivedoes not always with therightsideof the grating.Therecordsshowthatasymmetry is compare aspectrumtakenatHale’slaboratory withtheleftsideandanother towards theredinboth cases.Itmaybethatthegratingitselfissource ofthe j8, 327,1939. Those ofAllenareappreciably lower,Ap.J.85,165, 1937- y © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The excellentagreementshowsthatsuchcorrectionscanbemadeinaquite The originoftheinstrumentalbroadeningisstillnotfullyunderstood. * Thecentralintensitiesfound agreereasonablywellwiththoseoftenBruggencate,Z. Astrophys. Another interestingproblemistheslightasymmetrytowardred, y 3. Wenowinvestigateaplateofthesamespectralregion,takenwith 2. Themicrophotometerisruninthereversedirection;asymmetry 4. Fortunately,Evershedwassokindasto send usafewveryfineplates, 1. WebeginbyrecordingaMt.WilsonplatenearA6100withanordinary 5. Fromtheserecordsitisnowclearthatthe asymmetryinouratlashasan 194 7MNRAS.107. .274M 6 absorbed intheline.Thisarea,whichwe express asanequivalentwidthf, catalogue fromourgraphs.Thisworkwasundertaken inthedifficultyearsof shape ofeachparticularline,independentanytheory. a beautifulcatalogueofequivalentwidths,which wasextensivelyused.JAfter intensity”. Theintroductionofthisconcept provedveryuseful,bothfroma from eachprofile,howeverdistortedbytheinstrument,weareabletoderive a preliminarycommunication oftheirresults,whicharebeingpublishedinB.A.N. the warbyateamofolderandyoungerUtrecht astronomers,andIcaninform is amoreprecisedefinitionofwhatwasformerly calledrathervaguelythe“line a mostvaluablecharacteristic:thearea,whichismeasureforenergy of solarlineprofileseitherbymeanstheinterferometerorprecisecorrections the publicationofouratlas,wethoughtthatit wouldbeusefultoderiveasimilar descriptive andatheoreticalpointofview. Already in1934,Allenpresented to theatlascurves.Foronlythismethodgivesinformationonindividual instrumental curveisalsoproportional toA. original determinationsfromneonlines;{b)aslightcontractionaftervande sufficient toexplaintheasymmetricline-wings;andthismodificationseems Hulst ;(¿r)theasymmetry,asderivedfromwingsofwellisolatedlines. Allen andMenzel,itproved afterwardsusefultomeasurewidthsinmicro-wave-lengths= 10“A. as establishedunlessconfirmedbyverypreciseexperiments. reasonable, consideringthedifficultiesofdetermininganinstrumentalcurve. (Dunham, Publ.Amer.astr. Soc.,7,215,1933.)Thisisthemoreso,because widthofthe considering theinfluenceofinstrumentalcurve.*Thiscurve,asitwas concentrate theraysinaperfectlysymmetricalimage.Inanycaseitisclearthat No. 3,1947TheFraunhoferlinesoftheSolarSpectrum279 indeed someasymmetry;aslightincreaseofthiswouldalreadybe determined fromneonlinesandpublishedintheintroductionofouratlas,shows of Fraunhoferlines,mentionedsometimesintheliterature,cannotbeconsidered all careshouldbegiventosuchinstrumentalimperfections.Atrueasymjnetry © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * ThissubjecthasbeenfullyinvestigatedbyMessrsBuys andOngering;Ithankthemfor X Mem.Commonw.Obs.Austr., 1,No.5,1934and2,6,1938;Ap.J.,88,125,1938. t Firstintroduced:Versi. ned. natuur-geneesk.Congres,1923.Fromtheoretical results of Apart fromsuchadetailedandalwaysdifficultanalysis,itisimportantthat It willcertainlyproveveryinterestingtoundertakeadetailedinvestigation Fig. 2finallypresentsthebestavailablemeancurve.Itembodies:{a)our It mustbepossibletoaccountfortheasymmetryofatlaslinesby 194 7MNRAS.107. .274M g8o M.G.J.MinnaertVol.107 you thattheinfra-redspectrum,recordedinfirstorder,isnowpractically ready forpublication.Thisisthepartmosturgentlyneeded,becauseithas inflexion inthegraphisduetoaFraunhoferlineorgraininessofphoto- not yetbeentreatedbyAllenandsupplementshiswork.Itiscurioushowmany and finallyblurredagainbytheinstrumentalcurveintomodelblends,thus profiles, onceforallaccuratelymeasured,andtowhichtheatlaslinesareeasily and quickermethodinmakingglassscaleswithagreatvarietyofstandard with sufficientprecisionbymeansofaplanimeter.Wefoundmuchbetter blends isagainaspecialproblem;forthispurpose,wellisolatedlinesofthe as singleandwidened,oraclosedoubletofnormallines.Theanalysis run ofthecontinuousbackground.Abnormallybroadlinesmaybeconsidered graphic plate.Thenformanystronglinesthereisdoubtconcerningtheprecise matched. Anotherveryfrequentdifficultyisthequestionwhetherasmall involved whichcanbesolvedonlybytnuchexperienceanddiscrimination. furnishing reliablestandardsforcomparison.Sotherearemanyquestions atlas werecorrected,theoreticallycompoundedintoagreatvarietyofblends^ difficulties havetobesolvedinanapparentlysosimpleundertaking.Thus the faintlines,withequivalentwidthsbelow20mA.,aredifficulttomeasure observatory forthisprogramme,weaskedhertomakeindependentmeasurements of severalseriesselecteddubiouslines.AtthesametimeIaminformed, by thecourtesyofBabcock,thataverycompletecataloguepfra-red solar spectrumhasnearlybeenfinishedattheMountWilsonObservatory. Both setsofAmericanmeasurementswillfurnishanexcellentcheckonour interpretation. catalogue andaveryusefulestimateofthepossibleerrors,duetodifferences,in Fraunhofer lines,asiftheirintensitieswereinvariableandonceforallfixed. times duringaseriesofyears.Suchfundamentalinvestigationwasmade constant, bycomparingplates,takenwiththesameinstrumentatdifferent It isabsolutelynecessarytoinvestigatewhetherthesolarspectrumreally by vanderMeer*,usingthecollectionofspectrogramstakenatUtrecht. very sensitive;itcanbeusedforplateswithoutanycalibration.Iwould His method,beingpurelydifferential,isatthesametimeverysimpleand of thesolartemperature;adifference25 deg.wouldhavebeendetected, like toseeitappliedthematerialofotherobservatories.Theresultwas:an astonishing constancyofthesolarspectrum, whichmeansalsoconstancy by comparinglinesofverydifferentexcitation potentials.Thisisfullyinline with thewell-knownconstancyofsolarradiation. Thevariationsinthefar ultra-violet, ascertainedfromgeophysicalobservations, apparentlydonotaffect violet radiationoriginatesinthechromosphere. Atthesametimethisisavery the gaseswhichabsorbFraunhoferlines, probablybecausethefarultra- happy circumstanceforallofuswhoareengaged inmeasuringintensitiesand making catalogues,becausenowwearesure thattheequivalentwidthshave fixed values;found atdifferenttimesandbyobservers canbe directly compared,and the caregiventoprecisemeasurementsisjustified. of dataaccumulated,the theoryalsoofFraunhoferlineswasdeveloped, andit © Royal Astronomical Society • Provided by theNASA Astrophysics Data System As MissFarnsworthatMountÍHoiyokekindlyofferedthehelpofher In alltheseconsiderationswehavementioned“the”equivalentwidthsof * Variatiesvan Fraunhofer-lijnen,Dissertation, Utrecht,1936;Z.Astrophys. 13,157»1937« y While themethodsofmeasurement wereimprovedandwhileahuge amount 194 7MNRAS.107. .274M / resonancecurve,oneofthesewell-knowncurveswhichourstudentshavebeen 4 No. 3,1947TheFraimhoferlinesoftheSolarSpectrum281 the theoreticalsideofsubject.Actuallybothmethodsinvestigationhave towards progress.Alreadythefirstandmostprimitiveintensitymeasurements light insidetheline,andalsoagreateremissioncoefficient,heapparentlymeans have contributedtothesolutionofthatfundamentalquestion:‘howdoes atic exposition,Ihavedescribedfirsttheobservations,andwillconsidernow has reachedatthismomentamoreorlessclassicform.Forthesakeofsystem- into heat,andreverselytheatomisagainexcitedbycollisions.Butwhen that KirchhoffandStokeseachstressedpartofthephenomenon.When continually influencedeachotherandtheirinteractionhasbeeriagreatstimulus that thereispurelythermalabsorption:theabsorbedradiationconverted a Fraunhoferlineactuallyoriginate?”Itisperhapsnotgenerallyknown the effectofselectiveabsorptionandemission,becauseitismadeatarelatively waves *,hehasinmindtheprocesswhichwenowcallselectivescattering: absorbed radiationisatoncere-emitted,withoutaninteractionofotheratoms. Kirchhoff assumesthatthesolargaseshaveagreaterabsorptioncoefficientfor plays animportantrôlebecameatonceclearwhensomemeasurementsof hold partofthefield,andthattheirrelativeimportancehasnotyetbeenentirely illustrate hisviewofthematterbyanexperiment;actuallyitwasonlyin1924that radiation ofsodium.Itisinterestingthatthesetwotheoriesevennoweach high pressureandinthepresenceofmanymolecules.Stokeswasnotableto profiles becameavailable,madebySchwarzschild,vonKliiberandatUtrecht. and isnowconsideredabetterdescriptionofthephenomena.fThatscattering Dunoyer bymeansofmodernvacuumtechniquedemonstratedthepureresonance than 30or20percentofthecontinuousbackground,whereasmanylineshave at thesametimealldifficultiesanduncertainties oftheinstrumentalcurveand recording formanyyearsinpracticalworkonelectricalcircuits.Thesesame central intensitiesofonly5percentandless.JUnsoldmadeagreatstep§ Kirchhoff’s celebratedexperimentonthereversalofsodiumlinesshows broad andhazy. lines fortheprofileofastrongFraunhoferline.Thisispractically by showingquantitativelythatscatteringdampedatomsaccountsinbroad settled. ForalongtimetheconceptionofKirchhoffgenerallyprevailed. important tomakethebulkofallfainter linesusefulfortheory,avoiding By thermalabsorptionthecoreofaFraunhoferlinecouldneverbecomedarker The modelofStokeswastakenupmuchlaterbyJulius,StewartandSchwarzschild Stokes picturesthevibratingatomsandresonatorswhichre-emitarriving it wasprovedsoonthatthemostinterestinglines hadonlyanequivalentwidth curves nowexplainalsowhyFraunhoferlinesarenotsharpandblack,but the equivalentwidths,andwhenrelation betweentheseequivalentwidths, the correctionforfiniteresolvingpower;this wasthemorenecessary,because of afewhundredthsanangstrom.Thisproblem wassolvedbymakinguseof work remainsofhistorical importance, thoughtheanomalousrefractionindensity gradients, Ap.J.y 85,165,1937;Shane, LickObs.Bull.,19,119,1941. also consideredbyhim,isnow knowntobenegligible. © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Phil.Mag.,19,196,i860. f Selectivescatteringisidentical withtheanomalousscatteringadvocatedbyJulius. His Î Thackeray,M.N.,95,293, 1935;Redman,M.N.,95,742,1935and97,552,1937; Allen, § Z.Phys.,44,793,1927. Originally onlyveryfewlinescouldbemeasured inareliableway.Itwas 194 7MNRAS.107. .274M I 282 M.G.J.MinnaertVol.107 way, butwhichweatoncerecognizedwhen,justintime,apaperofSchützwas strength whentheconcentrationofresonatorsorabsorbingatoms widths, fWefoundremarkablecurves,drawnatfirstinapurelyempirical from theveryfaintesttostrongestlines,wasfound.Themethod there isalsoabroadeningduetotheDopplereffectofthermalmotionand very insensitivetothestellarmodel,buttheygivefullinformationconcerning introduced byRussellandprovedwonderful.*Comparingthecomponents of manyotherobserversandtheorists,itispossiblenowtopicturealreadyin appearing especiallyinthefaintlines.Thecurveofgrowthforsolarlineshas the profileofspectrallines.Justastheseprofilescanbededucedfroma published onthecurvesofgrowthlaboratorylines.JCurvesare been constructedlateronthebasisofmuchmorematerialandwithconsiderably augments. RussellhadconsideredtheincreaseofRowlandintensity. of multiplets,wefindacurvegrowth,indicatinghowthelinesincreasein increased accuracybyRighini,Menzel,Allen,R.B.King,K.O.Wright,andour From ourcurves,MuldersandIwereabletoconcludethatthedampingof It wasclearthatmoresignificantdatacouldbeobtainedbyplottingtheequivalent hear theethermusicemittedbybuzzingswarm,butrefinedanalysis detail thebehaviourofatomsinradiationfieldSun. The metalsareforagreatpartionized;fewpercentofthemexcited. be foundfromthecurveofgrowth,inbothcasesbysolvinganintegralequation. blurred spectrumbycorrectingfortheinstrumentalcurve,similarlytheymay transmitted energytotheair;soithasexperienced somefriction;soitis milliards ofcorpuscules.Thesewehaveneverobservedindividually,only Fraunhofer linesisabouttentimestheclassicaldamping,andthatapartfromthis of ikm.asecond.Whenetherwavesarrive,theseatomsstartresonating; nitrogen, oxygen,whichtogetherperhapsmaybeputequalto2000particles. but thenIcannothearit;assoonperceive asound,thechordmusthave most ofthemhavingbeenejectedfromhydrogenatoms.Allaremoving atom. Weseebeforeoureyesthatthereareabout10,000hydrogenatoms original resultshavebeenmainlyconfirmed.§Fromthisworkandfromthat radiation damping:astringgivesonlypure tonewhenvibratinginavacuum, of thesewavesrevealseachmotion,adventurehappeningtoanysingle but whyaretheydampedindoingso?Thisquestionhasstimulatedextremely against onemetalatom;moreuncertainistheabundanceofhelium,carbon, quickly bythermalagitation.Moreoverthereareturbulentmotionsoftheorder Now anatomisnotidenticalwithaclassical resonator.Wecalculatedwhat damping inFraunhoferlinesisactuallytentimes theclassicalradiationdamping. interesting investigationsonatomicbehaviour. Wefirstconsideredclassical Austr., I,No.5,1934;K. O. Wright,Ap.J.,99,249,1944;Rubenstein,92, 114,i94°- damped ;soitstoneisnotpureanymore.The curveofgrowthshowedthatthe Goldberg, Ap.J.,87,81,1938; R.B.King,Ap.J.,87,40,1938;Allen,Mem.Commonw. Obs. > ïQS)93°and1,300,1930; MinnaertandSlob,Proc.Acad.Sei.Amst.,34,543,1931. General review inObservatory,57,328, 1934. Some freeelectronsshootthroughtheswarm,aboutonetothousandparticles, © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Russell,Adams,Moore,Ap.jf.,68,1,1928. § Righini,Mem.Oss.Arcetri, Fase.48,1933;Mem.Soc.astr.Ital.,7,Menzel, Baker, X Schütz,Z.Phys.,64,662, 1930. t MinnaertandvanAssenbergh,Z.Phys.,53,248,1929; MinnaertandMulders,Z.Astrophys., Let usconsideravolumeelementofthesolaratmosphere,containingsome 194 7MNRAS.107. .274M :i - oftheenergy!TheprecisetheorythiseffectwasdevelopedlaterbyLindholmJ _Nq. 3,1947TheFraunhoferlinesoftheSolarSpectrum283 . andinamoregeneralformbyvandeHulst. - arethey?Herealso,differentpossibilitieshavebeenconsidered.Itmaybe . aquantumatomwoulddo;itcouldbesometimesmore,lessdamped . absorptionbyanatomtherefollowsemissioninthesamefrequency. ^ experiencealinearStarkeffect.Intheircasethestatisticalbroadeningby -as directlyAstrophysicallyspeakingsuchprocessesarenearlyirrelevant, - andtheradiationemitted.Weknowthat theatomicenergylevelsarenot now andthen,inordertoconfusethephasecoherenceofscatteredwave- than aresonator,butfactor10couldcertainlynotbeexpected. 935; Stromgren, Z.Astrophys.,10,237, 1935;Dempster,Ap.J.,96, 295,1942. typical collision,whichquenchestheenergyofexcitedatom.Butthisis work ?*Thekindofdisturbancemostlyconsideredbythephysicistsisa But couldthiseffectoperateato*oiatm.?Andifso,howpreciselydoesit identical withwhatwecalledthermalabsorption,andwhichhavealready are familiarwiththeidea,thatspectrallinesbecomehazierbypressure. had onlytomodifythefrequencyofavibratingatomduringveryshortmoment excluded becauseofthecentralintensities.ThenWeisskopfandLenz that thequadraticStarkeffectofelectronsplaysarôle.ButStrömgren, train. Sothiswasthesolution;therecouldbedisturbanceandstillnoquenching discovered another,amuchmoresubtledisturbance.fParticlespassingalong vibration ?Areallatomsequallyeffectiveinthisrespect,andhow inverse sixthpowerofthedistance.Thisthenseemstobeultimateexplana- calculated fromatomictheory§,andtenBruggencateHoutgast||showed tion forthehazinessofFraunhoferlines:phasedisturbancesbyhydrogenatoms. from observationsthatintheSunmostimportanteffectisduetoVan der Waalsforcesofthehydrogenatoms,whichactproportionallyto A physicistwouldbeastonishedtohearthequestionputthatwayandhe different fromallotherlines,becausehydrogenatomsaretheonlyoneswhich reply :“Ofcoursenot;thereturningelectroncanfallbackjustaswellinsteps because theyaretoagreatextentbalancedbythereverseprocesses;fornearly each quantumoflight,splitintopieces,thereisanewweldeçltogether. perfectly sharp,butmaybepicturedasgroups ofnumerousnarrow-spaced and asmallamountofcontinuousradiation is pouringdownintothestrong sub-levels. Anelectron,startingfromoneof thesub-levels,mayfallbackto But owingtotheanisotropyofsolarradiation field,thebalanceisnotperfect, Stark effectofneighbouringionsisthemostefficientperturbation. Burkhardt, Z.Phys.,115,592, 1940. Fraunhofer lines,sothattheircoresbecomeless dark.^f © Royal Astronomical Society • Provided by theNASA Astrophysics Data System § E.Strömgren,Stromgren. Festschr., 1940. * AgeneralreviewisfoundinUnsold,Vjschr.astr.Ges., Lpz.78,213,1943- The otherpossibilitywascollisionaldamping.Physicistsandastronomers t Weisskopf,Z.Phys.,75, 278, 1932and77,398,1932;Lenz,Z.Phys.,80,423, 1933; J Lindholm,Ark.Mat.Astr. Fys.,28,B,No.3,1942;vandeHulst,incourseofpublication. ¡j tenBruggencateandHoutgast, Z.Astrophys.,20,149,1941. But weaskfurther.Howdoesapassingatomaccelerateorretardthe y To thehydrogenlinesthemselvesthistheorydoesnotapply.Theyare Finally thereistheimportantfundamentalquestion,whetheraftereach Also inanotherwaytherecouldbeadifference between theradiationabsorbed Woolley, M.N.,94,631,1934; Observatory,57,345,1934;Pannekoek,M.N., 95, 725, 194 7MNRAS.107. .274M 284 M.G,J.MinnaertVol.107 another one,andawave-lengthshiftisobserved.*Aspecialcaseofthisthe absent inresonancelines,becausethegroundlevelisperfectlysharp.But “interlocking”, studiedbyWoolley.Itwasassumedthatthiseffectwouldbe as unsharpjustwella*naturallywidenedlevel,fQuantummechanical Houtgast madeplausiblethataleveldisturbedbycollisionsmustbeconsidered I941 calculations madebyZwanikenunderthedirectionofmycolleagueRosenfeld the propertiesofsolargaseswasactuallyatomicphysics.Theinteraction seem toconfirmthisview,butatthesametimeshowcomplicationsinvolved. you onlyfeelwhenhaveworkedinthisfield.Theinfinitelycomplicated solar atmosphereasawhole,andwehavetoconsiderhowtheinteractionofall its volumeelementsexplainstheobservedFraunhoferspectrum.Ourstudyof the powerofmathematicsintosimple,impressiveequations.Thewhole paths oftheradiation,withalltheirturnsandbendsloops,aregraspedby all theinfinitelynumerouslayersisatypicalastrophysicalproblem.These temperature, pressure,ionizationateachlevel.JInthelastfewyearswork architecture ofastellaratmospheremaythusbestudiedindetail,withits. problems oftransferinimmenseatmosphereshaveabeautytheirown,which of Wildtandotherscientists,culminatinginthatChandrasekharhis. to thecontinuousabsorptionbynegativehydrogenions,ofwhichthereisonly collaborators, hasfurnishedamostimportantbasiccontributiontothis- on Earth,wasdiscoveredfromthestudyofsolarspectrum;calculation would perceivethatthismixturehasastrikinggreen-bluecolour.Itisdue description oftheSun.§IfIcouldshowyouasamplesolargases, time itispossibletofindthetruerelationbetweenpressureandtemperature one againstmillionsofordinaryhydrogenatoms.Thisgas,practicallyunknown in thesuccessivelayers.Andthisagainisbasisforallcalculationson of itsopticalpropertieswascarriedoutentirelybytheory.Nowforthefirst Fraunhofer lineprofiles. than itwasthoughtatfirst.Itisdifferent according totheheightwhere in theultra-violet;takingthisintoaccount, andrepeatingthecomputation, Years agoIdeterminedforthisfraction0*15.Muldersmadeamuchmore lines, isusedinraisingthetemperatureofgas.Thisblanketingeffect Froc. Acad.Sei.Amst.,34,1352,1933;Weisskopf,Z. Phys.,85,451,1933ÎObservatory56, is takenawayfromthesolarspectrumbywholeofFraunhoferlines. discovered byMilne.Foritscomputationweoughttoknowhowmuchenergy astronomers haveshownthatourenergycurve hastobechangedconsiderably D ssertation,Utrecht,1933. 302, 1933;Spitzer,M.N.,96,794,1936andAp.J. 99, 107,1944;Zanstra,M.AT.,101,273, accurate measurementandfound008.||Afew yearsagohowevertheFrench in theouterlayersofSun.Partenergy,absorbedbyFraunhofer* Dissertation, Utrecht,1942. we comenowtoacoefficiento*io.Buttheblanketing effectismorecomplicated ‘ y y © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Eddington,M.iV.,89,633,1929;Woolley,91,979, 1931and98,624,1938;Pannekoek, Having studiedourvolumeelementweproceedtotheinvestigationof f Houtgast,Variationsinthe profilesofstrongFraunhoferlinesalongaradiusthe solardisk. X Strömgren,Tablesofmodel stellarAtmospheresCopenhagen,1943. y § Ap.J.104,430,1946and 104,446,1946. There remainsanuncertaintyconcerningtheexàcttemperaturedistribution H Minnaert,Z.Phys.,45, 610, 1927;Mulders,AequivalentebreedtevanFraunhofer-lynen. y 194 7MNRAS.107. .274M the intensityinlineasasimpleintegraloverscatteringand faint linesortowingsofstronglines.Weareableexpressthedip the calculationofintensitybecomesifitisappliedtoimportantcase the spectrum.Anothersourceofuncertaintyisturbulence,whichwasshown No. 3,1947TheFraunhoferlinesoftheSolarSpectrum285: absorbing material,thecontributionofeachlayerbeingweightedbyafunction scattering orbythermalabsorption;andevenaccordingtotheirspacingalong of depthcomputedonceforall*: Fraunhofer linesoriginateandaccordingtotheirmodeofformation,eitherby weighting functioncanbemade,independentlyofassumptionsaboutthe finally lostinaluminousfogofcontinuousradiation.Thecomputationthis- scattering andselectivelyabsorbingatomsateachdepth:thehighestlayersare points arenotessential.Iwouldliketoshowyouhoweasyandstraightforward. by Plasketttomodifythegeneraltemperaturedistribution. temperature distribution,bymakinguseofthedirectobservationaldataonlimb depth r,buttheyareequivalenttointegralsofkandaoverthegasmass.. are presentedhereasapracticalhelpfortheuseofouratlasandotherwork absorption, howthefirstisgraduallygettingmore importantthemoreweproceed to seehowsmallisthedifferencebetweeneffectsofscatteringandthermal that thecurvesapparentlyarereliabletoafairlyhighdegree.Itisinteresting; have beenindependentlyderivedfromtwoorthreeofthesesetsdata;itwill same authorin1913,andthoseofRaudenbusch1937.Severalthecurves weighting curves,thuscomputedforthecentreofSun,expressedinunits express thedipofprofilerelativelyto.continuousbackground.The Kourganoff f,thiscomputationiseasyandstraightforward.Weselectwave- distinctly visible,whereasthedeeperlayersareveiledmoreand be seenthattheresultingdifferences,indicatedbyverticalbars,aresmall,and (Fig. 3).TheyarebasedonAbbot’smeasurementsof1906-08,thosethe to thered. lengths wherenoinfluenceofneighbouringBalmerlinesistobefearedandwe darkening. MakinguseoftheanalysisalreadycarriedoutbyChalongeand So itisclearthattheweightingfunctionssimplyexpresshoweffectiveare all thefunctions^(r)by/c(r),anditiseasierto integrateoverrthan: illustration weassumethecalculationsof Barbier Jontheelectronpressure and temperature,usethevariationofk with wave-lengthascomputedby The discoveryoftheH~absorptionfurnishes uswiththedataneeded.Asan calculations bytheauthorare foundinB.A.N.,10,339,194b. v 1936. Aspecialcaseisstudied bytenBruggencateinNaturwiss.,33,91,1946;and moredetailed © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Unsold,Z.Astrophys.,4, 339,1932and8,225,1934;Minnaert,Z.Astrophys., 12,313,. X Barbier,Ann.Astrophys., 9, 173,1946. f ChalongeandKourganoff, Ann.Astrophys.,9,69,1946. Fortunately formanyproblemsconcerningFraunhoferlinesthesedoubtful, The integralsof—andmaybetakenforpracticalpurposesovertheopticaL For apracticalapplicationoftheseformulae,it isnecessarytodivideoncefor h J0Jo K (7 K =arÄTd Í+v(^)•a(T- K to j0J 194 7MNRAS.107. .274M 286 M.G.J.MinnaertVoL107 in unitswhichareabsoluteandthesameforallcurves.Multiplyordinates the dipoflineprofile,expressedasafractioncontinuousspectrum by o^r)and/c„(t),expressedperneutralhydrogenatom,integrate,youget Chandrasekhar. Fig.4nowshowstheweightingcurvesintheirultimateform, at thecentreofSun. ForsuchlinesasHandK,forexample,o isconstant this maybeunderstood, becausetheeffectofrapidlyincreasing general function isdirectlyameasure forthedip.Itisnowstillmoreapparent thatonly with depthandkisprobably small,sotheintegraloveroursecond weighting a smalldepthofthesolar atmospherecontributestothelineformation; and v v © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 10 I 23 X 5000 Fig. 3.—Weightingfunctions#i(t),£(t). 2 Ordinates :g Abscissae :t X85 80 194 7MNRAS.107. .274M the red,becausegeneral absorptionofH~increasessothatthedeeper layers absorption hasbeenbrought intoaccount.Theeffectofagiven number of become invisible. scattering orselectively absorbingatomsisnowclearlyseentodiminish towards more than about 15percent.Several simplifiedmodels havebeenproposed. © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The theoreticalcalculation ofprofilesislesssimplewhenthedipbecomes Fig. 4.—WeightingfunctionsÄxir),h{r). 2i , Ordinates:io~h e T P~ Abscissae: r 5000 5500 6C0Û ZQ 6500 50 Í00 7000 194 7MNRAS.107. .274M ' Themethodwasappliedto the generalcasebyMinnaertandHoutgast,Z.Astrophys., 12,96,193b. .an annulareclipsethattheFraunhoferlineslooked justthesameasincentre T .already consideredandhadgiventhegreatest troubletoastronomers.They -pictured theSunasaglowingsolidbody,surrounded byaselectivelyabsorbing 2 ► crucialpointswherethecooperationofobserversandtheoristswillbemost than before,asystematiccalculationashereexplainedwouldbeveryinteresting. . andmakeatableofthefunctions/c//c,crE,asderivedfromourpresenttheory ^8 Öne hundredyearsago this difficultywasconsideredsoinsuperablethat scientists toward thelimb,justasatmosphericlines oftheEarthdotowardsunset. the solaratmosphere,andsinceselectiveeffectsarebetterunderstoodnow modem quantitativetechnique,madebymein 1929andbyRedmanin1943.Î spectrum f:aninterestinganticipationof similar eclipseobservationswith in space.Inprinciplethemethodisremarkablysimilartoaparallaxmeasure- But nothingofthatkindhappened.Already in 1836Forbeshadnoticedduring the differencebetweenspectrumincentre andnearthelimbhadbeen atmosphere, andtheyexpectedtoseetheFraunhofer linesincreaseinstrength rv ment :weshiftthepositionofoureye,andatonceworldaroundusshows we areabletocheckwhetherhavepicturedarightourobjectanditsstructure the samelayersofSun,butliterallyspeakingfromanewpointview,and the directionofobservationrelativetosolarsurface.Actuallywelookat for thispurposethatIleftthesetheendofmylecture,inordertogivethem depth andbecomesthree-dimensional. the fullstress. initiated byPannekoek*:(i)WestartfromEddington’sequations there aretwosuchprimarilyimportantfieldsforfutureresearch,anditwas disk. Instudyingthis,weinvestigatetheinfluenceofanewvariable,whichis in anydirectionisobtainedbyawell-knowngeneralformula.Sincethediscovery necessary andwheregreatprogressinthenextyearswillhavetobemade.Ithink toward E+Id^E/dr.(3)KnowingandJateachdepth,theemergentintensity calculation isalwayspossiblewithoutrealdifficulties,accordingtothemethod measurements andonthepresentstateoftheory.Iwouldlikenowtoshow at thesurface,andintegratebyfinitesteps,proceedingtowardgreaterdepths. limb variations,theywillnotbesuffipientlyprecise.Fortunatelyadetailed This hasnotyetbeenmade. of theH~absorptionhasgivenaconsiderablymodifiedbutconsistentpicture of thesolaratmosphere.(2)WeassumeacertainvalueforandJ=i*8i7 as approximations;butformanyinvestigations,examplethecentreto If theinitialvaluehasbeenselectedright,JtendstowardE,or,moreprecisely, 0 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Pannekoek,M.N.,91,139 and519,1930;Publ.astr.Inst.Univ.Amst.^No. 4,1935. X Minnaert,B.A.N.,6,151, 1931;Redman,M.N..103,173,1943. f Phil.Trans.,126,453,1836. In theveryfirstperiodofsolarresearch,afterFraunhoferbutbeforeKirchhoff, The firstcrucialpointisthevariationofFraunhoferlinesoverSun’s I havetriedtogiveyouabird’seyeviewonthedevelopmentofprofile M. G.J.Minnaert dr E, Vol. 107 194 7MNRAS.107. .274M variation; inthefirstplaceforhydrogen lines,whichhavesuchaspecific investigations arebeingmadenowatourobservatory onthecentretolimb increasing distancesfromthecentre. importance; andsecondlyforthefaintlines, wherethetheoryisremarkably .a systematicwayalloverthedisk,andnotonlyatextremelimb;hecould ■considered byHoutgast.Heshowedthatvariationsintheprofilesoccur calculations havebeenmadeinanover-simplifiedway,andthattherecentdeter- -No. 3,1947TheFraunhoferlinesoftheSolarSpectrum289 and ionsovertheconsecutivelayers,butalso thevariationwithdepthof simple. Ourobserversalwayscomparethe profiles onatleastsixpoints, ‘derive thestratificationofsolaratmosphere :thedistributionofitsatoms damping andthethermal absorption.Theconceptionofa“reversing layer” .solar atmosphere.AtUtrecht,HoutgastandIhavefollowedamoredeductive .absorption andscattering,onthewave-length,partofFraunhofer •question wassolvedatthatmomentinaverysoundway—byforgettingaboutit; 595> 194°;Evans,M.N.,100, 156,1940,and101,21,1941. only accountforthembyassumingnon-coherent scattering.Severalother new assumptionswhichhavebeentried,thereisthenon-coherentscattering solar atmospherehavenotyetbeenincluded.Amongthemostinteresting ^depend onthepositionofselectivelayer,ratiobetweenthermal •decreases becauseofthesmallereffectivedepthatsametimethatitincreases and Dissertation,Utrecht,1942. of scatteredlightatright-anglestothedirectionvision.Theresultwill minations oftheH~absorptionandtheirconsequencesforstructure must supplementeachother. •direct observationsandtoderivebystepwiseinductionthepropertiesof the classicmodelofsolaratmosphere.Butwemustadmitthatmost the centretolimbvariationshavebeenquantitativelyexplainedonbasisof not lookforothermodelsequallyacceptable.Itisevidentthatbothmethods great effectonthecalculatedsolarmodel.Thedangerofdeductivemethod is thatonegetsamoreorlesssatisfactoryagreementwithcertainmodel,anddoes Both methodshavetheiradvantagesandtheir.danger.Intheuseof and absorbinginterest.PlasketttheOxfordastronomershavedonevery line whichisstudied.Allsuchdifferentpossibilitiesmakethisasubjectofgreat should beintheescapingradiation,tryingtogetaclosefitobservations.! important workinthisfield.*Theyhavetriedtotakeasastarting-pointthe we looklessdeepintothephotosphere;ifselectivegasismixedallthrough inductive method,smallerrorsofmeasurementmayhaveanunexpectedly the continuouslyabsorbingandemittingmaterial,effectivepathoflight are notsosimpleaswasthoughtintheearly’fifties.AtlimbofSun method, makingmodelsoftheatmosphere,calculatinghowlineprofiles followed afewyearslater. so overwhelmingwastheevidenceofKirchhoffandBunsen’sdiscoveries,which were abouttorejectthewholeideaofsolaroriginFraunhoferlines!The because ofthegreaterinclination.Moreover,thereisanimportantcontribution © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Plaskett,M.N.y91,870,1931, and101,3,1941;M.G.Adam,M.N.,98,112,1937, and100, t MinnaertandHoutgast,Z. Astrophys.,12,81,1936;Houtgast,Z.16, 43,1938, From thecombinedeffortsofworkersin thisfieldwemustbeableto It isremarkablethatuptonowtherenotasinglewell-studiedcaseinwhich It issincetheworkofSchwarzschildthatwehaveunderstoodthings 194 7MNRAS.107. .274M 290 M.G.J.MinnaertVol.107 up to0-5,whenlookingatthelimb. up toopticaldepthsofabout2,whenlookingatthecentreSun,andonly element. Uptonowwehaveworkedmoreorlessstatistically,butinfuture has definitelydisappeared.Weseetheintegratedeffectofselectivegases the P-Dlinesofmagnesium,whichthenfoundabeautifulexplanationbyUnsöld. closely, istheindividualcomparisonbetweenseveralspectrallinesofan become clearthatthesecontributionsfromsolarspectroscopyhaveonly been discoveredintheSunortheyhavefoundtheretheirfirstextensive than withtheelementarymultipletrules.Allentriedtofindline a detailedstudywillbenecessary.GénardandIhavemademeasurementson the concentrationfromfaintlines,whicharehardlyinfluencedbydamping. to whichitbelongs.Thisispossible.Foreachelement,wecandetermine will betoreduceagreatdiversityofapparently incoherentfactsintological be ofthegreatestimportanceforphysicsandastrophysics.Itwillhave table ofatomictransitionprobabilities,basedontheFraunhoferlines,data and titaniumlinesintheSunarebetteragreementwithlaboratoryintensities their predictedintensities.AllenandK.O.Wrightshowedthattheiron possible afterwearemoreorlessabletodiscern thefactors,determiningline of experimentalphysics,andontheoreticalcalculations.Suchatablewould was publishedandthatweareworkingoutnowourintensitycatalogue. and shouldbereplacedbyassigningtoeachlinetheindividualcurveofgrowth. Righini, whenworkingatUtrecht,comparedtheindividualsodiumlinesto Allen, M.N.,96,144,1936, and 100,4,1940;K.O.Wright,Ap.J.,99,249,1944. profiles. a beautifulandfruitfulfieldofinvestigation.Itisoftensaidthatweusethe astronomers herepresentthatthespectrophotometryofFraunhoferlinesis related totheUtrechtinvestigations,willhaveconvincedevennon-specialist To thesefaintlineswecompareeachofthestrongerlines,andarethenableto will remainforeverunknown,examplethecomposition ofthecelestialbodies consequences ofafewfundamentalphysicallaws, theultimateresultforastronomy applications. TheInternationalAstronomicalUnionintendstopublisha coherent scattering,thevanderWaals’forces,existenceofH~~,theyallhave Indeed, thecurveofgrowth,dampingbyphasedisturbances,non- stars ascosmiclaboratorieswherematterisfoundinconditionsunknownonEarth. separated. variations oftheStarkeffectinsolarironspectrum.* of oursciencewerememberasentence Auguste ComtefinhisCoursde proper being:therelativeabundancesof severalelements.Inthisstage derive theirindividualdampingconstants.Inthiswaybothfactorsmaybe or ofhumanprogress. Philosophie Positiveof1835:“Therearequestions whichforthehumanmind © Royal Astronomical Society • Provided by theNASA Astrophysics Data System t Coursdephilosophiepositive, 2,8,Paris,1835. * MinnaertandGénard,Z. Astrophys., 10,377,1935;Righini,Z. 344, 1935; The secondcrucialpointwhereobservationandtheoryoughttocooperate With respecttoourknowledgeoftheSun, mainobjectofallourwork The useofameancurvegrowthistoocrudemethodforsuchresearches, It isespeciallyinviewofthiswholeprogrammeresearchthatouratlas Once againweseethat no oneshouldtrytorestrictthegrandsweepof science I hopethatthisaperçu,limitedtoessentialproblemswhichalmostallare