1916ApJ 43 . . 103R 2 interval offourmonthscoveredbytheobservations, andanyvaria- nights, withremarkablyaccordantresults,the averagedeviation light intheopticalsystemsandshade-glasseswereverycarefully siderable accuracy. made inthelastfewyears,anditsvalueisnowknownwithcon- bearing onthealbedoofearth,andtheoreticaldiscussion shown thedesirabilityofageneralrevisiondata,anddiscus- THE STELLARMAGNITUDESOFSUN,MOON, ficial starwasassumedtobeabsolutelyconstant throughoutthe 0^05, whichisallthemorenotablebecause the fightofarti- with thesame“artificialstar.”Thecorrectionsforlossof glasses, andthedirectimageofCapellaformedbyalargerobjective, of thesunformedbyasuitablecombinationlensesandshade- of thewholewillformalaterpaper. ness ofthesun,moon,andplanetsarepresentedbelow.Thedata sion ofthetheory.Theresultingconclusionsregardingbright- object ofobtainingtrustworthyvaluesfortextbookpurposes,has of asingleday’sornight’sresultfromthegeneral meanbeingonly determined. Thesunwasobservedon6days,andthestarn albedo ofthevariousmemberssolarsystem,begunwith tions initwouldtendtoincreasethedeviations. Heconcludes the typestillcalledbyhisname,andcomparedstarlikeimage serious considerationisthatbyZöllner,whousedaphotometerof that thedifferenceofmagnitudebetween sunandCapellais © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 1 2 An examinationofthedataconcerningbrightnessand a) Oftheolderdeterminations,onlyonewhichnowdeserves Several determinationsofthisfundamentalconstanthavebeen SeeMüller,DiePhotometriederGestirne(Leipzig,1897), p.316. PhotometrischeUntersuchungen (Leipzig,1865),pp.107,124-25. I. THESTELLARMAGNITUDEOESUN By HENRYNORRISRUSSELL AND PLANETS 103 1916ApJ 43 . . 103R 0 m included intheassignedprobableerror.WithHarvardmag- française pourPAvancementdeScience,Congrèsd’Angers, 1903, P-255)isinaccessible who comparedthelightofastandardelectriclamp,shiningthrough nitude ofCapella,0.21,themagnitudesunwouldbe—26.66. a bluescreen,withthatofthesunweakenedbydivergencethrough 104 HENRYNORRISRUSSELL from aglassplateatanangleof45,withVega,directlyseenby a lensofshortfocallengthbymeansLummer-Brodhunphotom- 26.87=^=0.05, theuncertaintiesofinstrumentalconstantsbeing mean distancegiveslightequalto100,000bougiesdécimalesat his lampandthepercentageofitslighttransmittedbyblue quelques centièmes.Fabryalsodeterminedthecandle-powerof eter, andlatercomparedthelightofsamestandard,reduced makes thesun26^94brighterthanVega,orofmagnitude—26.80 solution, andgivesashisresultsthatthesuninzenithat the nakedeye.Underclearskiesandforbodiesnearzenith to astellarimagebymeansofmicroscopeobjectiveandreflected the resultsobtainedondifferentdaysornightsdifferedonlyby Zöllner photometertheimageofsun,reflectedfromsurface on theHarvardscale. sons weremadebetweenVenusandvariousbrightstars.The of asmalllensatdistance152m,withVenus,whichwasnear showed thatVenus,42daysbeforeinferiorconjunction(when, sion), was486brighterthanProcyon,6^30 thanPolaris, constants ofreductionwereverycarefullydetermined.Observa- elongation andvisibleinfulldaylight.Laterauxiliarycompari- according toMüller,itwas0^66brighterthanontheformerocca- The supplementaryobservations,mademorethanayearlater, days afterinferiorconjunction,withanaveragedeviationof0^10. tions onsevendaysmadethesun22^93brighterthanVenus112 i m,whileVegainthezenithisequaltoacandleat780m.This to thewriter. of thesestars,andweights4,1,proportional tothenumberof and 3^22brighterthanSirius.Withthe Harvard magnitudes © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 2 2 z b) NextinorderoftimeisthedeterminationbyC.Fabry, c) Ceraski,observingatMoscowin1903,comparedwitha Annalesdel’ObservatoireMoscou,2dseries,5,1-30,1911. ComptesRendus,137,973and1242,1903.Themoredetailed account{Assoc, 1916ApJ 43 . . 103R pentane lampshiningthroughacellfilledwithbluesolution. in diameter,frontoftheobjective,andextra-focalimages image ofthesun,shiningthroughasmallaperture,about1mm nights ofobservation,thesun’smagnitudecomesout—26.60on using Capella,Arcturus,Vega,andSiriusasreferencestars,gave of stars,2or3mmindiameter.Thecomparisonlightwasa a shadowphotometer,thebrightnessofcenterfocal what enormousinstrumentalconstants,representingtheeffects for asingledetermination. Ten independentdeterminations,onasmanydaysandnights, work. magnitude. of thevariousmethodsweakeningsun’slight,havetobe the Harvardscale. cesses shouldallbeaffectedwitherrorsofthesamesignand for itishighlyimprobablethatfoursuchradicallydifferentpro- The probableerrorofonedetermination,assumingthemtobe determined ineverycase.TheresultsontheHarvardscaleare: are inremarkablygoodagreement,especiallywhenitisconsidered the sun’smagnitudeas—26.83,anaveragedeviationof0^19 errors ofthevariousmethodsobservationmustbeverysmall, equal weight,comesout^0^075,showingthatthesystematic also beenmade,eachbasedonaconsiderable amountofcareful his well-knownextra-focalmethod,findsamean valueof—25^83, 12-inch telescopeof135feetfocallength,compared,bymeans © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS105 1 2 2 1 d) W.H.Pickering,observinginJamaica1901,witha These fourdeterminations,madeinaltogetherdifferentways, King, comparingthesunwithPolaris,Arcturus, andCapellaby Two determinationsofthesun’sphotographic magnitudehave Ibid.,59,248. HarvardAnnals,61,56-71. Zöllner —26^66 Pickering —26.83 Fabry —26.80 Ceraski —26.60 Simple mean—26.72=^=0.04 1916ApJ 43 . . 103R magnitude ontheHarvardscale. graphic magnitudeshereadopted,is+0^79, whichdiffersfrom the value—25^93maybeadoptedfor sun’sphotographic magnitude betweenVegaandtheotherstarscanbededuced Arcturus. determination maybegivendoubleweightin taking themean,and Vega.... so approximatelyreducedtotheHarvardphotographicscale of thedifferenceshiscolor-indicesfromthatCapella,and which indicateavariationwithspectralclassabout50percent vard visualmagnitudesgivesthecolor-indicesinthirdcolumn, showing: King’s photographicmagnitudesforthelatter,givefollowing photographic magnitudebetweenthesunandstarswhich,with with anaveragedeviationofonly0^07forhis11determinations. are obtained.Theseingoodagreementandgiveameanof greater thanforKing.IfBirck’sresultsarealteredbyone-third and thesolartypeofspectrum,figuresgiveninlastcolumn directly fromBirck’sobservations,andcomparisonwiththeHar- Birck’s methodsofobservation.Thephotographicdifferencein arises fromadifferenceincolor-equationbetween-King’sand The discordancebetweentheresultsfoundfromthreestars Capella. . of themeasurementsabsorptionscreenswhichwere than thisagreementwouldindicate,onaccountoftheuncertainty The probableerrorofthemeanispresumablysomewhatlarger io6 HENRYNORRISRUSSELL to thatofPickering’svisualobservations,findsdifferencesin employed. — 26^12.Onaccountoftheuncertaintythis correction,King’s © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 1 The color-indexofthesun,resultingfrom visualandphoto- Inauguraldissertation(Göttingen,1909). Birck, workingextra-focallybyamethodessentiallysimilar Star Magnitude Difference 27.76 27.04 25-95 Birck of 1 Birck 0.00 i •7 1.02 Color-Index King 0.82 0.00 1.09 Magnitude graphic Photo- King 0.14 1.03 1-33 Uncorrected — 26.01 -26.43 -25.81 Magnitude ofSun Photographic Corrected — 26:15 — 26.01 — 26.20 1916ApJ 43 . . 103R 1 2 obtained. Theremaybeadifferenceinscale betweenthetwo making theredstarsbrighter.Ifobserved differencesare reduced tospectrumGonthisassumption,and groupedaccording small, beingapproximately0^035foreachspectralclass,Müller probable error. to magnitude,themeansgiveninlower partofTableIare Magnitude. . Fainter than4¥o brighter by0^19thanthoseofthefinalPotsdamcatalogue,and stars, whichrangeinbrightnessfromSiriustoPolaris,areall Durchmusterung. Müller’smagnitudesforhis14fundamental between thoseoftheRevisedHarvardPhotometryandPotsdam will beadoptedasthemainbasisofpresentdiscussion.The given inTableI.Therelativecolor-equationofthetwosystemsis Harvard, groupedaccordingtospectralclassandmagnitude,are defined byTableIV,p.235,ofhismemoir,andisintermediate scale ofmagnitudestowhichtheseobservationsarereferredis King’s meanvalueforstarsofClassG,+0^72,bylessthanits Die PhotometriederGestirne,1897. Brighter than4^0 about thesame.ThemeanvaluesofdifferenceMüllerminus the differencesforfainterstars,thoughmoreirregular,average tions ofthebrightnessplanetsarethoseMüller,which Number Mean M—H. Mean M—H... Mean M—H... Number Number © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS107 1 PotsdamPublications,8,PartIV,pp.197-371,1893,with someadditionsin By farthemostextensiveandhomogeneousseriesofobserva- HarvardAnnals,59,179. n. THEMAGNITUDESOFPLANETS +o¥os +o¥o4 +o¥o8 o¥ 3 3 8 3 +o¥o7 -J-o¥oi +o¥i8 TABLE I i¥9 8 6 5 +o¥o7 ■o¥o5 ■o¥o8 3^7 3 3 8 Spectral Class — -o¥i5 0.02 5^o +o¥o2 —o¥io ■o¥o8 5^5 K 8 8 3 —o¥io —o¥o6 -o¥i3 K2 toM 6¥2 8 5 +o¥o6 —o¥o6 —o¥oi AU 7¥ 26 20 2 9 1916ApJ 43 . . 103R 1 0o 0 Venus mean oppositionforMars,are: systems, butitisverysmall.Inwhatfollowswillbeassumed planet, reducedtostandarddistance.FormulaeIandIIgive brighter atthefullthanhalfphase,bothformulaewillbe of weightbeing=*=0^137withI,and=*=0^135II.Anobserva- Mars. than ontheHarvardsystem,andthatforUranus,Neptune, that thebrighterplanetsaremeasured0^06fainterbyMüller variation almostexactlylikethatofthemoon. phase-angle 6?8,gavethevalue—2.81formagnitudeof observations almostequallywell,theprobableerrorofunit angle, andreducedtomeandistancefromthesununitdis- formulae forthestellarmagnitudecorrespondingtophase- the asteroidsnocorrectionisnecessary. io8 Within therangeofphaseinwhichboththeseplanetshavebeen retained. AsMüllerpointsout,formulaIIindicatesaphase- tance fromtheearth,incaseofMercuryandVenus,to observed, theirvariationisalmostidentical.Jupitercanbe to theratherimprobableconclusionthatMercuryis21times tion byJostduringthetotalsolareclipseofMay28,1900,at observed onlyuptoabouta=12°.Withinthis regionitsbright- equally goodfromo°to47®,themaximumphaseobservable. factorily overthewiderangefrom24to156,andthatforMarsis Phase-angle i?o3?!5?57?5 9?o io?3ii?i ness variesfarlessthanthatofanythe inner planetswould. Magnitude —2.27—2.23—2.24—2.20 —2.26—2.20 Müller’s meanresultsforgroupsofabout30 observationsareas follows : 120, andwithinthisintervalthetwoformulaerepresent — 2.63and—1.94,respectively.Since,however,formulaIleads © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem o 1 Mercury canbeobservedonlybetweenphase-angles50and For thoseplanetswhichshowconspicuousphases,Müller’s The formulaforVenusrepresentstheobservationsverysatis- HeidelbergMittheilungen^No.1(1901). o II. Mag.=—0.90+0.0284(0,—5o°)-|-o.000102(a—50) .... Mag.=—i.79+0.0149a ... .Mag.=—4.71+0.013220+0.00000042503 HENRY NORRISRUSSELL 1916ApJ 43 . . 103R 1 3 2 4 7 5 r 6 8 0^02 andtheLommel-Seeligerlaw0^03. phase-variations whichappearwhentheringisvisibleareexplicable 0^05, whereasiftheplanetbehavedlikeMarsitwouldbe0^15, The wholevariationwithintheselimitscanhardlymuchexceed by Seeliger’stheory,whichtakesaccountofthemeteoricconstitu- variation withphase,accordingtoBaldwin’sobservations.The and iflikethemoon,0^22.Lambert’slawgivesavariationof invisible thevalue+0.95,inexactagreementwithresultsof Baldwin’s directobservations.Thecorrectionforthefightof tion oftherings.Müller,applyingthistheorytohis252observa- earth abovetheirplane. rings isapproximately0^04foreverydegreeofelevationthe tions, findsforthemagnitudeatmeanoppositionwithring Pickering, from31nights’measuresin5years,obtains5.51, here, givingMüller’sobservationsdoubleweightonaccount the value5.86from93observationsin8differentyears,while a surprisingdiscordance.Thevalue5.74willbeadopted of theirgreaternumber.ForNeptune,Müllerfinds7.66as been determinedbyBarnard,themagnitudes Pickering fromtheresultsofseveralobservershavebeen agreement. the meanof138observations,Pickering7.65from66observa- the Harvardscale,from32observations—allinremarkable tions, andBaldwin7.99onthePotsdamscale,or7.64 0.030 forJuno,and0.022Vesta.The meanvalueofthis of allobservers.Theyare0.043f°Ceres,0.038forPallas, adopted. Theratesofchangeinmagnitudeperdegreephase- degree. constant for34asteroidsisfoundbyMüller tobe0^030per angle arefromMüller’ssummary,takingagainthemeanresult © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS109 4 2 1 Saturn, whentheringisinvisible,likewiseshowsnosensible For themagnitudeofUranusatmeanopposition,Müllerfinds For thefourbrightestasteroids,whosediametershave 3 PhotometriederGestirne,p.347. HarvardAnnals,46,204. Op.cit.,p.348. MonthlyNotices,69,458,1909. 8 6 s Ibid.,24,265;46,203. PhotometricderGestirne,p.378. MonthlyNotices,68,620,1908. 1 HarvardCircular,No.169,1911. 1916ApJ 43 . . 103R 3 2 Neptune +7-65Vesta6.04JupiterIV....+6.26 Uranus +5-74Juno8.95JupiterIII..+5.08 Saturn +0.89Pallas.^.84JupiterII5-6 Jupiter —2.29Ceres+7•I5-54 sent thevariationwithphaseincaseofVenus,Mars,and has derivedempiricalformulaefromhisownobservationstorepre- focal observationsappeartobetheonlypublishedmaterial.King similarly extrapolated,applyingtothelatteracorrectionof—0^12 extrapolated tozerophase,withMüller’svisualmagnitudes, satellites. known aboutthechangeofbrightnesswithphaseforanythese have beenadopted,andforTitanthemeanofresultsGuth- numerous, andhisempiricalformulaerepresenttheircoursevery therefore: on theHarvardscale,forbodiesmoreremotethanMars,are to reducefromthePotsdamHarvardscale.Itappears nick andWendell,whichdifferbyonly0^03.Nothingatallis Saturn, andderivedcolor-indicesbycomparingthesemagnitudes, first groupofobservationsonVenus,which areverydiscordant ing toSeeliger’stheorywereemployed.There isnoappearance night’s observationsequalweight,withtheresultsshownin formulae weregroupedaccordingtothephase-angle,givingeach closely, thesewereadoptedasastandardofreduction,andthe actually made.AsMüller’sobservationsaremuchthemore and photographicobservationsatthephaseswhichtheywere the writerthatitwouldbepreferabletocomparedirectlyvisual of changeinthecolor-indexwithphase,except inthecaseof differences betweenKing’sphotographicmagnitudesandthese Table II.ThemagnitudesofSaturncomputed byMülleraccord- no HENRYNORRISRUSSELL © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 2 3 1 For thephotographicmagnitudesofplanets,King’sextra- The adoptedvaluesofthestellarmagnitudeatmeanopposition, Guthnick’s magnitudesforthefourGalileansatellitesofJupiter HarvardAnnals,69,223,1914. Ibid.,59,261-64. AstronomischeNachrichten,198,251,1914. Titan +8.30 1916ApJ 43 . . 103R 2 inter se.Furtherobservationshereareevidentlydesirable;in their absencethesimplemeanofallobservationsistaken. 116.6. m. THEVARIATIONSOPMOON’SBRIGHTNESSWITHPHASE found above),thecolor-indicesoffourplanetsbecome:Venus, After correctionby0^06toreducetheHarvardvisualscale(as moon atdifferentphasesdemandconsideration.Thoughthelight- curves derivedbythevariousobserversdifferveryconsiderably, image ofthemoongivenbyhis“astrometer.”Sincetheywere which consistofdirectcomparisonsmanystarswiththereduced +0.78; Mars,+1.38;Jupiter,+0.50;Saturn,+1.12. the samemeancurve,asisshownbelow. their actuaFobservationscanallbesatisfactorilyrepresentedby Zöllners reductionoftheseobservationswas usedinderivingthe inconsistent withEuler’s“law,”whichHerschelsupposedtobe provisional curvedescribedbelow,butinthe finaldiscussionthe true, heconcludedthattheywereaffectedbysystematicerrors, and theirtruevaluewasfirstpointedoutby BondandZöllner. rections giveninthefootnotetop.175. 1847), pp.353-374- 04°6. 84.9. 75-4. 8.6, 2.6. Phase-Angle © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETSm 1 2 1 Seven seriesofobservationstherelativebrightness The earliestreliableobservationsarethoseofSirJohnHerschel, FromtheplotinTafelIVofhisPhotometrischeUntersuchungen, withthecor- ResultsofAstronomicalObservationsMadeattheCape GoodHope(London, +0.67 + ÄO +0.46 +0.52 +0.49 +0.38 Jupiter K-M Mean Venus Obs. 10 9 Deviation Average o¥5 0-33 o. 14 o. 29 o. 12 0.12 3 TABLE II I 32.7- 25.0. S'6. 4-9 • 0.6, 2.7, Phase-Angle 1 +1.34 + i¥o +1-33 + I-3 + 1.05 + 1.07 3 Saturn K-M Mean Mars Obs. 10 10 8 8 Deviation Average 0^21 0.12 o. 18 0.26 0.06 0.06 1916ApJ 43 . . 103R results dependsontheconstancyofhisstandardlampforweeks As inthecaseofhisobservationssun,accuracy blue screentomaketheartificiallightsimilarincolormoon. lamp, thelatterbeingputatsuchadistance as tosecureequality sity ofdirectmoonlightwiththatanamyl-acetate standard at atime,buttheagreementofhisresultsshowsthatinthisrespect without theinterventionofartificiallight.Theirlargenumber, Professor Pickering,oneonaccountofknowninstrumentaldefects, with apentanelampshiningthroughbluesolution.Ofthe his apparatuswassurprisinglysuccessful. 83, on64nights,addstothevalueofseries. comparisons ofmoonlightwiththeextra-focalimagesstars, eters, andwithexemplarycare.Hewasthefirsttointroducea altitude wasonly8°. the otherforaverylargebutunexplaineddiscordance. comparing directmoonlightbymeansofashadowphotometer discussion, ashavealsoasetofobservationsmadewhenthemoon’s, 26 nights’observations,thoseon2nightshavebeenrejectedby results thenobtainedhavereceivedhalf-weightinthepresent globe toobtainequahtyoftheimages.Ofhis13nightsobserva- glass globewiththatofalamp,shiningthroughsmalldiaphragm theories, comparedtheimageofmoonreflectedfromasilvered the moonwasverydifferentfromthatpredictedbyexisting values aretakenfromthenewreductionofHerscheFsobservations and reflectedinthesameway,varieddistancefrom which isdescribedinthenextsectionofthispaper. tion (inthespringofi860),3aredescribedas“hazy,”and 112 HENRYNORRISRUSSELL 3 > ThevisualobservationsofW.H.Pickeringweremadeby © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 4 3 5 2 1 1 Zöllner’s observationsweremadewithtwopolarizingphotom- King’s extensiveseriesofobservationsconsistphotographic HarvardAnnals,61,62-69. Stebbins andBrown,usingseleniumcells,comparedtheinten- 4 Ibid.,59,63-94. PhotometrischeUntersuchungen,p.102. MemoirsofÙieAmericanAcademyArtsandSciences,N.S. 8,221-266,1861. Bond, whofirstshowedthattheactualphase-variationof * AstrophysicalJournal,26,326,1907. 1916ApJ 43 . . 103R 1 mean ofalltheresultsobtainedoneachnighthasbeentaken,and magnitude fromhisassumedbrightnessofthefullmoon)were most extensiveseriessofarpublished.Theyconsistofcomparisons ness ofthemoonatequalphasesbeforeandafterfull.The into betteragreementbyapplyingcorrectionstothevaluesof had beendrawn,especiallyintheimmediateneighborhoodof with Polaris.ThenormalsgivenbyWirtzhavebeentakenasthey all nightsgiventhesameweight. observers werethefirsttocallattentiondifferenceinbright- series isentirelypermissible. zero-point correctionstoimprovetheagreementofvarious given byPickering,King,andStebbins).Itappearedatonce with aZöllnerphotometerofreducedpointimagethemoon appeared Wirtz’sreductionoftheobservationsWislicenus, of theelectricaleffecttointensityillumination.These of effect,thuseliminatingthequestionproportionahty phase-angle; thesecond,differenceof themoon’sstellar included inthediscussion,light-curvegiven inTableIIIwas full brightnessassumedbyeachobserver.Asthesevalueswere full, andthatthedifferentseriesofobservationscouldbebrought curves givenbythevariousobserversarose,notfromcontradic- observer’s results(reducedwhennecessarytodifferencesofstellar stand. adopted asdefinitive.Inthistablethefirst columngivesthe Wislicenus’ importantseriesofobservations appearedandwas determined atall,isknownwithmuchlessaccuracythantherela- of themoonandordinarystandardsstellarmagnitude,when empirical formulae,andastherelationbetweenbrightness determined independentlyineachcase,fromfreehandcurvesor compared withaprovisionallight-curve(themeanofthecurves tions intheobservations,butfromwaywhichtheircurves that muchthegreaterpartofdiscrepanciesbetweenlight- tive brightnessofthedifferentphases,applicationthese © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS113 1 In reducingtheseobservationstoacommonstandard,each After severalapproximations,duringthe course ofwhich Finally, justintimeforinclusionthepresentdiscussion,has AstronomischeNachrichten,201,289-331,1915. 114 HENRY NORRIS RUSSELL magnitude at this phase, before the full, and that of the full moon, the third, the corresponding intensity of moonlight, taking the full moon as 1000; and the fourth, the mean surface brightness of the visible portion of the moon’s disk, expressed in stellar magni- tudes and referred to the full as standard. The next three columns give similar data for the moon after the full; the following column, the mean magnitude for equal phases on both sides of the full; and that succeeding it, magnitudes computed on the empirical assump- tion that the brightness of the moon varies as the cube of its elonga- tion from the sun. The residuals in the last column show that this relation is very nearly true except within 30o of the full, where it gives too small a value. TABLE m Light-Curve of the Moon

Before Full After Full Mean Phase-Angle Surface Surface Mag. Light Bright- Mag. Light Bright- Obs. Comp. O.-C. ness

o o¥oo 1000 o¥oo o¥bo 1000 o¥oo o¥oo o¥i6 —o¥i6 10 o. 22 816 0.21 0.22 816 0.21 o. 22 0.34 — . 12 20 0.44 666 0.41 0.48 642 0.45 0.46 0.54 — .08 30 0.67 540 0.59 0.74 SOS 0.66 0.72 0.75 — .03 40 0.90 436 0.77 1.03 387 0. 0.96 0.97 — .01 90 So i 13 353 0. i.31 299 1. 10 1.22 1.23 — .01 92 60 1.37 283 1.06 1.58 234 i. 27 1-47 1.47 .00 70 1.65 218 1. 22 1.86 180 1-43 1.76 1.76 .00 80 1.98 161 1.40 2.17 136 1- 2.07 2.07 .00 59 90 2.35 US 1.60 2.50 100 i.75 2.42 2.41 + .01 100 2.78 77 1.82 2.86 72 1.90 2.82 2.79 + .03 no 3.22 Si 2.01 3-27 49 2.06 3-25 3-23 + .02 120 3- 31 2.26 3-74 32 2.23 3-757 3- + .01 7 74 ISO 4- 18 2.52 4.30 19 2- 4.353 4- .00 9 433 5 I40 5- 9 2.81 4.98 10 2.65 5.061 5.06 .00 4 ISO 6.09 4 315 5-89 2-95 5-99 5- 0.00 99

The manner in which this curve represents the observations of the various series is shown in Table IV, which gives, for means formed from small groups of the observations, the mean phase, the observer’s initial, the number or weight of observations com- bined into the mean, and the residual from the curve. The agree- ment of the results of the different observers is further illustrated in Table V, in which are given the mean residuals for the observa-

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1916ApJ 43 . . 103R magnitudes asgivenbyeachobserver,theaveragenumberof zero correction,describedabove,whichhasbeenappliedtothe observations combinedintoameanineachcase,andtheaverage tions nearfirstquarter,fullmoon,andlastalsothe weight. Thereisverylittleevidenceofany systematic difference between theresultsofdifferentobservers, though Kang’sphoto- of theresidualsgiveninTableIV,afterreduction tothismean graphic observationsmayperhapsindicateasmaller rangebetween the' fullandhalfmoonthantheothersdo. It seemslegitimate, ■ 49 Phase 146 124 138 139 152 118 126 134 IOI 103 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS115 98 98 83 95 82 6S 67 40 58 64 79 71 35 50 58 Obs. W W W B P K B w W K W W K B p Z H K S W K S H K Z W No. 2 3 3 3 4 Ï 4 5 3 4 3 5 6 5 7 2 7 h 2 i -f-0.06 + i¥o + .17 + .06 + .05 + .13 + .13 — .ii + .15 - .19 - .07 - .13 — .16 + .09 + .03 — .01 — .12 + .04 — .ii - .13 - .08 — .01 - .04 O.-C. 4 0.00 .00 .00 - 34' + 8 + ~ 23 - 12 - 8 + 21 — 2 4~ 28 Phase 1 3 32 32 18 14 ii 30 13 22 16 14 26 28 Observed Means 9 4 5 8 7 TABLE IV Obs. W H Z B W H K K S z K B S W P Z S P K W P B K H P p w K S No. 3 3 3 3 3 6 5 5 8 3 2 4 3 6 6 3 i 4 iè 3 5 i 5 2 2 1 5 2 4- .07 4- .11 4- .02 -f .15 — .10 -o¥o4 — .03 4- .22 — .06 — .08 — .04 — ,10 + -33 — .04 — .01 — .06 + -05 — .07 4- .06 — .l8 — 03 — .02 4- .16 — .OI — .02 — .OI O.-C. “ -03 “ 13 —0.05 0 + 34° 4- 61. + 55- + 78. + 95- 4-in. + 133- Phase 103. 125. 102. 100. 127. 139- 124. 40. 41. 60. 66. 61. 57- 93- 80. 84. 82. Obs. W H W Z w z P S K w w H K w p W W S W P K s s K No. 4- .11 4- .01 + .13 4- .02 4- .12 -o¥o5 + -05 - .04 4- .02 - 19 + .15 + *04 4- .22 4- .18 - .15 - .16 4- .42 - .14 4-0.04 - .12 O.-C. - .21 - .07 - .66 .00 ii6 HENRY NORRIS RUSSELL therefore, to combine the results of the different observers into more comprehensive normals. Unit weight was given to each individual observation by Bond, King, or Wishcenus, and weight 2 to each observation by the others, these weights being based on the average residuals given in Table V, and also on the general reliability of the

TABLE V

Mean Residuals (Algebraic) Average Zero Deviation Observer Cor- F irst Quarter Full Last Quarter rection Mag. Obs. Mag. Obs. Mag. Obs. Mag. Obs

Herschel. . +0^00 -o¥o4 7 +o¥o2 -0M04 o¥o7 2.7 Bond + .24 -}- . 08 6 - .07 5 : .14 1.9 Zöllner. . . - .06 8 + .02 : .06 4- .01 4- .04 7 7 ; 31 Pickering. + .01 — .06 3 - .05 13 + .11 8 . ii 2.>4 King — .06 + .08 40 — .06 .09 + -25 34 15 : 6-5 Stebbins.. — .02 — .01 5 - -03 8 + .04 8 . 12 2. i Wislicenus 0.00 +0.02 34 +0.01 34 — 0.02 34 0.07 4-4 methods of observation. The grouping of the observed means is shown by the spacing of Table III, and the resulting normals are given in Table VI. The residuals from the adopted light-curve are apparently accidental in character. Their average value, regardless of sign, is only =t=o¥o35.

TABLE VI Normal Magnitudes

Phase Magnitude O.-C. Weight Phase Magnitude O.-C. Weight

— 142 5^32 +o¥oi 8è + o¥o7 —o¥o4 14 — I2Ó. 4.07 — .06 17 + 12, o. 28 + .01 18^ — IOO. 2.80 + .02 18 + 23 0.52 - .04 15 — 80. 2.02 + .04 20J + 29 0.75 + .04 19 - 65. I.40 — . II 18 + 38 0.97 .00 18 - 55- I.29 + .04 18 + 57 1- + -04 17 54 - 42. O.95 .OO 22 + 62. 1.65 4- .01 17 - 32. O.74 + .02 19 + 83. 2.20 - .07 17 - 18. O.4I 4- .01 17 + 100. 2- + .09 19 95 — ii, 0.22 — .02 17 + 119. 3- + .02 12 71 O.O9 — 0.02 I7è + 138. 4.76 - O.06 7

Tables III and IV are illustrated graphically in Fig. 1. It is clear that the transition from increase to decrease of brightness in

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1916ApJ 43 . . 103R © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 0 passing throughthefullisalmostabrupt.Thevisualstellarmag- nitude ofthemoonatanyphasemaybereaddirectlyfromthis figure. necessarily uncertain,buttheassumptionthatmoon’slight of about135.Extensionthecurvetowardnewmoonis Table IIIareprobablywithin0^05ofthetruthuptophase-angles continues tovarynearlyasthecubeofelongationfrom stellar magnitude;thelower,thoseofactualintensitymoonlight. the bestdeterminedofphotometricdata,andvaluesgivenin points out,isimmediatelyexplainedbythe greater extentofthe sun isprobablyasgoodaguideany.Accordingtothistable, known, fromtheroughcharacteroflunarsurface, which,except dark mariaintheeasternhalfofvisibledisk. Thegreatdiffer- larities.' at thefull,islargelydarkenedbyshadows ofitsownirregu- ence betweenthelightoffullandhalfphases arises,asiswell ence ofthebrightnessatoppositequadratures, asStebbins quarter, and10.otimesasbrightthelastquarter.Thediffer- the fullmoonis8.7timesasbrighthalfatfirst STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS117 The variationofthemoon’sbrightnesswithphaseisnowamong Fig. i.—Light-curveofthemoon.Theuppercurveshowsvariationsin Phase-Angle 40 80 o 60 100 20

Light 1916ApJ 43 . . 103R 2 PP- 353-372. made, consistedessentiallyofalongstaffwhichcouldbepointed of aandßCentaurigivingtheirdifference magnitudewithan lens wasmadeequalinbrightnesstothe star, viewedwithout lens ofshortfocallength,intowhichthemoon’slightwasreflected moonlight withphase;butnogeneralreductionofthemeasures, average residualof=*=0^06fromthemean. ably accurateresults,asZöllnerhasshown, 9nights’measures optical aid.Thissimplemethodofobservation yieldedremark- based onmodemphotometricmagnitudesofthecomparisonstars, most extensiveanddirectcomparisonsoftherelativebrightness made attheCapeofGoodHopein1836,consist165comparisons, be discussedinhistoricalorder. slider fromtheeye,starlikeimageofmoonproducedby at anystar,onwhichwasmountedamovableslider,carrying no seriouslabor)hasbeencarriedoutbythewriter,anditsresults ness ofthemoontothatthisstar,andBondZöllnerhave his comparisonswithaCentaurivalueoftheratiobright- through aright-angledprism.Byvaryingthedistanceof are brieflypresentedhere. appears evertohavebeenmade.Suchareduction(whichinvolved derived fromhisobservationsdataconcerningthevariationsof appearance ofWislicenus’workin1915.Herschelderivedfrom of themoonandstarswhichhadeverbeenpublishedbefore on 19nights,ofareducedimagethemoonwithbrighter minations oftheabsolutebrightnessmeanfullmoonare stars, andweremadeprimarilywiththeintentionofdetermining decidedly uncertain.Thevariousseriesofobservationswillhere extraordinarily discordant,andthisimportantconstantisstill regard totherelativebrightnessofmoon’sphases,theirdeter- the relativebrightnessofthesestars.Theyform,however, ii8 HENRYNORRISRUSSELL © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 2 1 ResultsofAstronomicalObservationsMadeattheCape of GoodHope(1847), Herschel’s “astrometer,”withwhichtheseobservationswere While theresultsofdifferentobserversagreecloselywith PhotometrischeUntersuchungen,p.176. a) HerscheVsobservations—newreduction.—Theseobservations, IV. THESTELLARMAGNITUDEOFFULLMOON 1916ApJ 43 . . 103R 0 1 f mean distance,andthentofullmoon.Herschel gives,foreach nights onwhichfiveormorestarswereobserved being smaller thanusual,themeanvalueofthis quantity forthe14 was atanaltitudeofonly16,areexcludedfromthemean.The Revised HarvardPhotometry.TheobservationsofaLyrae,which The moon’sdeclinationwas—17°,whichexplains whytheextinc- average deviationoftheobservationsfromtheirmeanisrather tion wasusuallysmallerforitthanthestars. Mean (excluding ß Corvi a Pavonis 7 Centauri ß Centauri a Lyrae a Bootis manner describedbyBirck,andbasedonthePotsdamextinction a Triang.Aust.. a Aquilae were usuallysmall,astheobservationsmadeathighaltitudes). a Centauri table, whichmadetheirdeterminationveryrapid. inches wasderivedbytheequation magnitude mofthisimageasseenatthestandarddistance100 Table VII.Themagnitudesofthestarsaretakenfrom These correctionsweretakenfromanomogrampreparedinthe and correctionswereappliedfortheatmosphericextinction(which image appearedequaltoastarofmagnitudemtheapparent a Lyrae) © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS119 Inauguraldissertation(Göttingen,1909),p.54. The resultsthusobtainedforeachnightmust bereducedto The detailsofthereductionsforatypicalnightaregivenin From eachmeasureddistanced(ininches)atwhichthemoon’s Star Reduction ofHerschel’sSeriesK 131.0 107.3 94.0 38.7 33-3 80.7 61.5 55-0 Si-7 m=m'+io+5 logd Observa- tion TABLE VII 0.89 0.86 o. 12 o. 24 0.06 2.38 2.84 2.12 1.88 Moon 0.02 0.01 0.01 Extinction .01 .05 • 05 • 05 .01 • 05 .01 0.07 0.04 Star 0.02 • 03 .07 •os .19 .02 •59 . l6 2.29 2.09 2.17 2.00 2.45 2.28 2.24 2.28 2.35 2.46 (-0.29) Residual + .06 + .16 +0.17 =*=0.10 — .01 — -05 — .OI — .20 — .12 120 HENRY NORRIS RUSSELL night, the theoretical brightness of the moon according to Euler’s law, computed by the formula 1000A2 . w M (ïëx^sm-e (i) where A is the moon’s apparent semi-diameter, including the augmentation, R the earth’s radius vector, 933''5 the moon’s mean semi-diameter, and e its elongation from the sun. If the last factor be omitted, this gives the correction to mean distance.

TABLE VIII

Correction to Aver- Image Date Stars age De- Phase- of Full Wt. Resid- viation Angle Mean Full Moon ual Distance Moon 1836 March 28. . 17 o¥i7 2.12 “5° -0^05 -A4 0^93 +0^22 N 30- • 17 . 16 1.56 -25 + .01 -0.57 i .00 + .29 3i- • 4 . 12 0.93 -13 + .04 —o. 29 0.68 - -03 April i. . 5 .08 0. — i + .06 —0.01 0.50 - . 21 45 3- • 13 . ii 1.19 + 28 + .10 —0.69 0.60 - . ii 4. . 12 •iS i .61 +41 + .09 — 1.07 0.63 - .08 7- • 5 . 16 2.71 +82 + .08 -2.23 0.56 - -15 26. . 13 •13 2.06 “59 - .03 -1-35 0.68 - -03 27. . 19 . 12 1.73 -46 + .01 -1.03 o. 71 .00 June 29. . 5 .17 i .00 + 13 + .11 —0.30 0.81 + .10 July 22.. 8 . 10 2.29 “75 + .03 -i.81 0-51 - . 20 24. . 8 • 14 1.58 -47 + .09 — 1.06 0.61 - . 10 26. . 13 . 16 1. 10 -19 + .10 —0.42 0.78 + .07 Aug. 22. . 3 . 22 152 -So + .08 -113 0.47 - .24 23. . 5 .19 1 *35 -37 + -io -0.83 0.62 - .09 Nov. 19. . 12 . ii 1-53 -38 .00 -0.85 0.68 - .03 25- • 1 1.77 +31 + .07 -0.77 1.07 + .36 Dec. 17. . 3 .04 1.85 “57 — . ii — 1.30 0.44 - .27 26. . 2 0.03 1.56 +44 +0.14 -I-I3 0.57 —o. 14 Weighted mean o. 71

Table VIII gives the results obtained from Herschel’s 19 nights of observation. The first column gives the date; the second, the number of stars compared with the moon; the third, the average deviation of the individual determinations of the moon’s brightness from the mean; the fourth, the mean stellar magnitude of the moon’s image at 100 inches distance; the fifth, the phase-angle, negative before the full; the sixth, the correction to mean distance; the seventh, the correction to full moon; the eighth, the deduced

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1916ApJ 43 . . 103R 2 1 2 lens tobesimilartheprism,totallossbyreflectionat inch ontherectangularfaces.*Aslenswas only0.12inchin sions oftheprism,butfromhisfigureastrometer,which probably aboutaninch.Now,accordingto Vogel, thetransmis- from HerscheFsdata.Theprismwasofcrownglass(byFraun- be addedtheinstrumentallosses.Thelattercanestimated by socarefulanobserverrepresentstheresultofaccuratemeasure- lens andprism.Herschelstatesthatthefocallengthof is notlarge,inviewofthecharacterobservations. four surfaceswouldbe0^22.Herscheldoesnotgivethedimen- face atperpendicularincidenceshouldbe0^055.Assumingthe By Fresnel’sformula,thelossoflightbyreflectionfromsur- hofer, andoffineworkmanship)refractiveindex1.571. ratio (ido):(o.2253),orby13.24magnitudes,towhichmust ments. Thiswouldmakethemoonbrighterthanitsimagein this wasdetermined,butitisprobablethatprecisestatement was 0.2253inch.Hegivesnodetailsregardingthewayinwhich of magnitudeo.71=«=0.03ontheHarvardscale.Tofindmag- have thereforebeenassignedwhichareroughlyproportionaltothe diameter, thewholethicknessofglasstraversed bythelightwas nitude ofthemoonitself,itisnecessarytocorrectforinfluence full moon,asseeninhisastrometeratadistanceof100inches,was one nightinthesamedirection,isevidentlypresent.Weights sion oflightthrough100mmordinary crown glassis0.85 appears tobedrawnscale,itwouldseem havebeenaboutone of thesmalllens,andforlosslightinpassingthrough weight assigned,andthetenth,residualfromfinalmean. magnitude oftheimagemeanfullmoon;ninth, the unitofweight,computedfromresiduals,is=*=0^17,which square rootofthenumberobservations.Theprobableerror a Bootis,ßCentauri,andLyrae,forreasonsgivenbyHerschel. excluded fromthesecalculations,andalsooneobservationeachof The observationsofthevariablestarsaOrionisand77Arguswere © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS121 2 1 Herschel’s observationsthusindicatethattheimageofmean Some sortof“nighterror,”affectingalltheobservations AstrophysicalJournal,5,80,1897. Preston,TheoryofLight,pp.346-347. 1916ApJ 43 . . 103R 2 1 series ofcomparisons,onewithVenusandJupiter, theotherwith is probablyduetodifferencesinthemethodsofreduction,and at adjustabledistances,exactlyasintheobservations onthemoon, silvered glassglobe,werecomparedwiththose ofastandardlamp value oftheratiotoabout110,000.Theoutstandingdifference Harvard scale. moon resultingfromhisobservationsistherefore—12.79onthe may thereforebeestimatedat0^04,andthewholeinstrumental his numericalresultmustbedoubledtogivethevalueofformer. mean fullmoonandthebrightnessofatallphases, loss as0^26.Thevalueofthestellarmagnitudemeanfull the sun.Infirst,imagesofplanets, reflectedfroma The introductionofthesetwocorrectionswouldraiseHerscheFs and HerscheFsnumericalcalculationsbearthisout.Thereseems, But, accordingtoequation(1),Mis1000forthemeanfullmoon, have beenover50,000.Secondly,Herschelexpresslystates,in the estimatesofinstrumentallosses. which, accordingtoEuler’sformula,isjusthalfasgreat,andthat quantity calledIfinhisoriginalmemoir,anddefinedbyequation the footnoteinwhichheexplainshismethodofreduction,that reduced hisobservationstofullphasebymeansofEuler’sformula, for thevisualrays.ThelossbyabsorptioninHerschehsapparatus at thetimeofobservation,thatmeanfullmoonbeingunity.” which givesfartoosmallacorrection.Theobservationsnearfull, crepancy is,however,easilyexplained.Inthefirstplace,Herschel star alone,deducedtheverydifferentratioof27,400.Thedis- a Centauri.Herschelhimself,fromhiscomparisonswiththis to biswork,Herschelinadvertentlyconfusedthebrightnessof therefore, noescapefromtheconclusionthat,inthislateraddition and ifthetruecorrectionsforphasehadbeenapplied,thiswould taken separately,accordingtohisstatements,givearatioof45,000, 122 HENRYNORRISRUSSELL (1) above,is“500timestheactualilluminatingpowerofmoon and oftenonthesamenights.Fromobservations on6nights © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 1 MemoirsoftheAmericanAcademyArtsandSciences,N.S., 8,250,1861. OutlinesofAstronomy(NewYork,ed.1876),p.595. b) Bond’sobservations.—Theseconsistoftwoindependent This makesthemoon12^85,or138,000timesbrighterthan 1916ApJ 43 . . 103R 2 he concludesthatVenus,atphase-angle68?8,andreducedto similar method.Thelightofthesun,reflected fromasilvered same standard.Theaverageresidualforanightwas±0^14 mean distancefromthesunandunitearth,was case. more thanathousandtimesfainterinthesecondcase moon. Thesamereflectingglobewasusedinobservingthemoon he statesthatthelampwasdecidedlyredincomparisonwith his lampsimilarincolortothatofthemoonorplanets,and nitude comesout—12.09fromthecoróparisonswithVenus,and Harvard scale,are—3.71and—2.29;sothatthemoon’smag- Hence Bond’sobservationsmakethemeanfullmoon8^38brighter with thelight-curveofTableIII,thiswouldbe0^24brighterstill. of themeanfullmooniso¥o6brighterthanlampatonefoot, Venus and=«=o¥i2forJupiter.Bond’sassumedvaluethelight nights’ observations(rejectingonenightforgoodcause)hecon- S^oS fainterthanhislampatadistanceofonefoot,andfrom4 globe, wasagainreflectedinasecond,and comparedwiththe first. ThePurkinjeeffectwouldthereforecomeintoplaytoa and theplanets,imageoflampappearedtoeye Müller’s magnitudesfortheplanetsatthesetimes,reducedto and thezerocorrectiongiveninTableVmeansthat,ifreducedanew reflection ofa“Bengolafight”inthelatter, andthemoonwas high degree,andwouldoperatetomakethelampappearrelatively weight. Bonddidnotemployabluescreentomakethelightof than Venus,andg^&ibrighterJupiteratthegivenphases. cludes thatJupiteratmeanoppositionwas9^51fainterthanthe weakness ofthemethod,severelycriticizedby Zöllner,istheuncer- subsequently observedinexactlythesame way.Theobvious faint atthelowerintensity,andhencetomakemeasureddiffer- appears fromcomparisonwithotherobservationstobeactuallythe tainty whetherthelightofthesefireworkscould beconsideredas ence inmagnitudebetweenthemoonandplanetstoosmall,as — 12.10fromthosewithJupiter. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS123 1 12 Bond’s comparisonsofthemoonandsunweremadebyavery In spiteoftheagreementtwo,thisresultdeserveslittle Ibid.,p.287,1861.PhotometrischeUntersuchungen, p.116. 1916ApJ 43 . . 103R fc]i on 2 0 facture wereusedthroughout,andafreshoneburnedforeach value, deducedfromtheobservations,is==o!i2;butitmay the sunis471,000times,ori4¥i8,brighterthanmeanfull deviation of^o^iS.FromthesecomparisonsBondconcludesthat ratio ofsunlighttoBengolalight=*=o¥2o,andthesixmoon can, however,bederivedfromthefactthatfiveobservations comparison.” Someideaofthemagnitudeerrorsinvolved 0^03 accordingtoBond’scurve,and0^15byTableIII,sothatthe moon. Thecorrectiontofullmoonfromtheobservedphaseis months) makethedifferenceinmagnitudebetweenstarand was comparedwithanartificialstar,andthisagainCapella of thesun,ontwodays,showanaveragedeviationfrommean even roughlyconstant,if“thoseofthesamesizeandmanu- makes thatofthefullmoon—12.66.Theprobableerrorthis difference ofmagnitude,onthesystempresentpaper,is removing thepentanelamp,withbluescreenas usedinthemeasures when reducedwiththelight-curvehereadopted,givefordiffer- the meanfullmoon12^39whenreducedwithZöllner’sformula. of moonlight,tosuchadistancethatitappeared ofthesamebright- and themoon’smagnitude—12.17Harvardscale. Applying thezerocorrectionfoundabove,thisbecomes12^38 really beconsiderablygreater. ness asArcturus(whichseemednearlyofthe same color).Obser- In thosemadebyhis“secondmethod”apointimageofthemoon 14.06, which,withthevalueofsun’smagnitudealreadyfound, 124 HENRYNORRISRUSSELL which havealreadybeendescribed,werereferred tothestarsby standard lamp,withapolarizingphotometerofdifferenttype. vations wereunfortunatelymadeononly 4 nights,andtheir ii onthestar(separatedbyanaverageintervalofsomethree Ten days’observationsonthesun,and6nights’moon, (all ononenight,whenitsphasewasy?6andaltitude24)a ence ofmagnitude14^45,andforthemoon—12.27. (using adifferentopticaltrain).Eightnightsonthemoonand © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 3 1 c) Zöllnersobservations.—-Thesefallagainintotwogroups. d) TheobservationsofW.H.Pickering.—These observations, By his“firstmethod”themoonandsunwerecomparedwitha HarvardAnnals,61,63-68. PhotometrischeUntersitchungen,pp.90-115,124. 1916ApJ 43 . . 103R ±1 1 average deviationfromthemeanwas==o!24,sothatprobable relative brightnessofthelampandmeanfullmoon(reducing error ofthedeterminationrelativebrightnessstar and lampfromthemeanoffouris=*=0^12,whilethat becomes —12.51onapplyingthezerocorrection. ering findsthatthemagnitudeoflatteris—12.50,which the 24comparisonsbymeansofTableIII)isonly=*=0^024.Pick- standard candle(seebelow)theratiooftwoisfoundtobe of themeanfullmoonareasfollows: already stated,themeanresultsofeachobserverformagnitude 428,000, correspondingtoadifferenceofmagnitude14.08. is probablygreater,assomeofthedeterminationsmaybeaffected puted fromtheresiduals.Theactualuncertaintyofthisresult general meanis—12.55,withaprobableerrorof=±0.07,ascom- by systematicerrors. ness by14.17magnitudes,or465,000times,withanuncertaintyof moon, itappearsthatthesunexceedsmeanfullmooninbright- If Bond’sdeterminationisgivenhalftheweightofothers, fully 10percent. making thefinalvalue—11^37.Thismakes thecolor-indexof his definitivesystemofmagnitudes,andafurther oneof—0^24 he originallygave,requiresacorrectionof+0^07 toreduceit by King’slongseriesofobservations.Thevalue —11^20,which moonlight +1^18,aboutthatofastar Class Ko,and0^39 for thedifferencebetweenhislight-curveand thatofTableIII, greater thanthatofthesun.Atfirstglance itmightbedoubted © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS125 1 /) Thephotographicmagnitudeofthemooniswelldetermined é) Frómthecomparisonsofsunlightandmoonlightwith Rejecting Bond’scomparisonswiththeplanets,forreasons From thevaluesherefoundformagnitudesofsunand Ibid.,59,153- Zöllner Herschel Pickering Bond Comparison withcandle Residual 1916ApJ 43 . . 103R 1 3 photometric observationsofWilsingandScheinerprovedthather graphic thaninthevisualregion,andhenceacolor-indexabout indicates areflectingpowerabout20percentlessinthephoto- whether themoonisreallyasredthis;butspectro- bright andadarkregion,showedsensiblythesamebehaviorfor summarized byMüller,musthavebeensystematicallyinerror, 0^25 greaterthanthatofthesun,infairagreementwithresults both, therelativereflectingpowerincreasingfromo.6iatX4480 surface isstronglycolored.Theirmeasurements,madeona be theveryrecentonebyKimball,atMountWeather,Virginia. made thesuninzenithequalto100,000meter-candles.Much to 0.64atX5130,0.875840,and1.006380.This 126 HENRYNORRISRUSSELL it ispossibleonmanydaystoextrapolatethezenith(air-mass With aphotometerofprecision,andcarefullytestedstandards for theirresultsareallmuchtoolow.Thefirstapproximately of thephotometricmeasures. surface bythecombinedlightofsunandsky,also of light,hemeasuredtheintensityilluminationof’ahorizontal the mostextensiveandpreciseseriesofobservationsappearsto albedo, itmayappropriatelybediscussedhere. unity) anddeterminethetransmissionoflightbyatmosphere sky whendirectsunlightwascutoff,andthusdeducedtheintensity on eachday.Iftheresultsaregroupedaccording tothebrightness of normalilluminationbythelatteroveralargerangezenith correct valueappearstohavebeenFabry’s,alreadyquoted,which 1909. of thelightskywhensunwashidden, thatis,according to thehazinessofweather,following meanvaluesare distances onmanydays. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 2 1 a) Sunlightandterrestrialstandards.—Theoldercomparisons, Though thisquantityisnotdirectlyrelatedtothequestionof From thedatagivenforvariousair-massesinhisTableIV, 3 MonthlyWeatherReview,43,650,1914. PhotometriederGestirne,pp.309-312. PublikationendesastrophysikalischenObservatoriumszu Potsdam, 20,No.61, V. THESTELLARMAGNITUDEOFSTANDARDCANDLE 1916ApJ 43 . . 103R 1 which unitsKimballusesthroughout: obtained, theintensityoflightbeinggiveninfoot-candles, of astronomicalphotometry,itisprobablydesirabletotakeonly off seriouslyinhazyweather.Forcomparisonwithotherresults reducing themtothezenithwithmeantransmission0.766 light atnoonlessthan1200foot-candles)canalsobeemployedby in thetable.Observationsonsevenmorecleardays(withsky the observationsmadeinfairlyclearweather,firstthreegroups for theintensityofsunlightfromzenith,9600foot-candles, found forthethreegroupsabove. vidual determinationsof=±=5.4percent.AccordingtoKimball’s pheric transmissionfoundabove,thesunoutsideouratmosphere brighter thanastandardcandleat1mdistance.Withtheatmos- statements, theprobableerrorofmean,includingsystematic or 103,000meter-candles,withanaveragedeviationfortheindi- errors, shouldnotexceed5percent. photometer, thelightofmoonwiththat ofanamyl-acetate would be0^29brighter,anditslightequalto134,500meter-candles. best determinationoftheintensitymoonlightcomparedwith in thezenith0.269=1=0.014Hefner-meter-candles. Thelight- lamp shiningthroughpale-blueglass,andthis withaHefnerlamp. artificial standardsisthatbyGraff,whocompared, withaWeber Observations on5nightsgaveforthelightof themeanfullmoon curve usedinreducingtheobservations,all of whichweremade STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS127 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 As mightbeexpected,thebrightnessofdirectsunlightfalls The meanofthe22days’observationsinclearweathergives, This determinationmakesthezenithsun12.53magnitudes b) Moonlightandstandardcandle.—Thelatestprobablythe AstronomischeNachrichten,198,14,1914. Days Light ofSky 2400 IO35 1420 UBS 880 Zenith Sun 9550 9750 9550 6700 8650 Transmission Atmospheric o. 780 0.782 0.677 0.736 0.67s 1916ApJ 43 . . 103R 1 o from themean,forreasonsstated. much lowerthanthatofanyotherobserver, itmaybeexcluded mission ofthescreenhigher,thanwouldhave beenfoundhadthe for thebrightnessofstandardcandle.As theresultisactually to heoutsidethedangerousregion,andso givetoolowavalue observations beenmadewithilluminationof sufficientintensity measured brightnessoftheunscreenedlamplower,andtrans- phenomenon istobefeared.Itwouldoperatemakethe night andisnecessarilyoflittleweight,becausethesmallnumber Vega. tions weremade—thatofmoonlight—wassolowthatthePurkinje tion ofthescreenshadowphotometerwithwhichobserva- of comparisons,andespeciallysincetheintensityillumina- with thelamp,andwithoutbluescreen,onbutasingle mission coefficientdeterminedfromcomparisonsofmoonlight measurements. Thismakesthemeter-candlei4¥40brighterthan of magnitude—13.60ontheHarvardscale,dependsatrans- of hisscreenfromthemeanalargenumberlaboratory available directcomparison,ashedeterminedthetransmission mined. Fabry’sresult,that,abougiedécimaleatdistanceof magnitudes brighterthanthemeanfullmoon. moonlight tothemeter-candleappearsthereforebeverywell states thatthemeanofaconsiderablenumberolderdetermina- 780 mwouldappearasbrightVega,appearstobethebest transmission ofthebluescreenswhicharenecessarycanbedeter- difference incolor,anddependupontheaccuracywithwhich tory standardsoflightwiththestarsarecomplicatedbygreat normal candle,or0.267Hefnerat1m.Theratioof with thatofTableIIInocorrectionisrequired.Graffalso candle onthisscale,andtheinternationalmeter-candleas1.55 standard candle,fullmoonlightmaybetakenas0.241meter- determined. SincetheHefnercandleisequaltoo.90international tions, mostofwhicharesatisfactorilyaccordant,is0.251English within 24ofthefull,tolatterphasewassonearlyidentical 128 HENRYNORRISRUSSELL © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 2 1 2 HarvardAnnals,61,69,1908. ComptesRendus,137,1242,1903. W. H.Pickering’sresult,thatastandardcandleat1mis c) Standardcandleandstarlight.-—Directcomparisonsoflabora- 1916ApJ 43 . . 103R magnitude ofthestandardcandleatadistance1m. probable errorofabout^o^os. With theweightsassigned,meanis—14.18,withanapparent mile. Anactualstandardcandle,oftheordinaryvarieties,if magnitude 0.82atadistanceof1km,and1.85 lamp was14timesfainterphotographicallythanvisually.Other was therefore+2^87,sothat,comparedwithstarsofClassA,the illumination, wasofonecandle-power,wouldappeartobestellar standards oflightmight,however,haveverydifferentcolor-indices. electric lamp,suppliedbytheBureauofStandards,wasmagni- indicate thatthedifferencewouldprobablyexceedhalfamagnitude. mination oftherelativebrightnessfullmoonandstars, light, appeartohavebeenmadeinthepastfiftyyears.Mostof urgently desirable.Nodirectvisualmeasurementsoftheratio fainter, onaccountofthePurkinjeeffect.Pickering’smeasures removed tothesedistances,wouldundoubtedlyappearmuch as thatofthestars,andintensitywhich,measuredunderhigh tude —12.06atadistanceof1m.Thecolor-indexthislamp vations byastronomerswhosemainattention wasdirected of sunlighttomoonlight,andbutonethatmoonlightstar- of light,bytrustworthyvisualandphoto-visualmethods,are and thedirectcomparisonofstarsterrestrialstandards attention ofacompetentobserverforconsiderable time. elsewhere. Adeterminationofthesefundamental photometric the existingdeterminationsarederivedfrom incidentalobser- constants withmodernprecisionwouldwell repay theundivided STELLAR MAGNITUDESOFSUN,MOON,ANDPLANETS129 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1 1 Photographically, E.S.Kinghasfoundthatastandard2-candle The otherdeterminationsgivethefollowingvaluesforstellar It followsfromtheforegoingthatalightofsamemeancolor It isevidentfromtheforegoingsummarythatprecisedeter- Ibid.,59,275. Princeton UniversityObservatory Fabry (Vega) Kimball (sun) Graff andothers(moon). January 20,1916 Weight 3 2 i