1916AJ 29. .173V found bymeasuringthefractionoftotalrelative tion thatweareconsideringhereisanotherone: the lineardimensionshavebeendeterminedinanum- visual, spectroscopicandevenphotometricmeasures VOL. XXIX of thecomponents.Itisaverysimpleonetheoreti- of individualstars.Thesolutionthisproblemis two componentsopeningthusawaytofindmasses namely, thepartitionofthattotalmassamong imations tothetotalmassofsystem.Theques- ber ofbinariesandconsequentlywehavegoodapprox- or thefairlywellknownparallaxesofsomethem made tofindthemassesofbinarystars.Combining ponents ofabinary,Areferringtothebrighterone or theonethatistakenasoriginforrelative motion thatistobeattributedeachoratleastone the samedirectionasonechosenforaandC;Kis suppose motion. Considertheirabsolutepositions(eventually cally. LetuscallAandBthemassesoftwocom- time t.Thenweshallhave: measure thesepositionsfromafixedoriginandin In theserelations¡irepresentstheproper-motionof certain fixeddirection,beitinrightascension, center ofgravitythesystem,measuredalsoalong with theconditionr—Ca. the relativecoordinate,—BtoA,—atsame ponents —ifnecessarycorrectedforparallaxandr the massesmeaningthenfractionsofmass declination, orinanyotherchosendirection.Wewill corrected forparallax,)onthecelestialsphere.We call aandbtheabsolutecoordinatesoftwocom- the systemthatbelongstoeachcomponent.Wewill In recentyearsseveralsuccessfulattemptshavebeen a =¡dt~(1—A)rAKorb¡¿tAr ASTBONOMICAL JOURNAL © AmericanAstronomical Society A B=1 MASS-RATIOS INVISUALBINARYSTARS, ALBANY, N.Y.,1916,JULY15 FOUNDED BYB.A.GOULD. By G.VANBIESBROECK. NO. 694 THE Provided bytheNASAAstrophysics DataSystem requirements insuchacase. r andt.Threesufficientlydistantepochswillfulfillall two epochswefind: the requireddata.FromequationsinCfor problem aslongthereisnoproportionalitybetween we seethattherewillbenoindeterminatenessinthe tion containingthethreeunknowms:¡jl,AandK, the starstobeconsideredbecausegissufficientlywell so twounknownsonlyaretobeconsidered:AandK. Two epochs,letuscallthem1and2,willfurnishall known fromalongseriesofmeridianobservations.If different epochswededucelinearequationsofcondi- From measuresofoneorotherthecomponentsat tion nearlyparalleltotherelativedisplacementbe- a constanttermdependingontheinitialconditions. the denominatorinrelationgivingAwillbenearly in rightascensionwouldbeofnovalue,asthatcase tion relativetotheprincipalstarmeasuresin sidered thecompanionismovingprincipallyindeclina- tween thetwoepochs.Ifforinstanceattimecon- be amaximumwhenthemeasuresaremadeindirec- measurement. Therelativedisplacementr—will dition fixesthemostadvantageousdirectionfor The bestdeterminationofAwillbeobtainedwhenthe relative motion,thatentersinthedenominator,is known theformulacangivegoodresultsprovided the valuesofr.Evenwhenperiodisentirelyun- when thetwocomponentscanbemeasuredsoastogive equal tozero. denominator r—nisaslargepossible.Thatcon- directly measuredquantities,anddoesnotcontainthe declination willgivethebestpossibleresult.Measures elements oftheorbitalmotionbinaryconsidered 21} 2 The questionisfurthersimplifiedinthemajorityof We seethatthemassAisgivenasasimpleratioof M (t2él)(C2Cl) A =~ r —n 2 NO. 22 (173) 1916AJ 29. .173V this observatory,mostofthemnottakenforpar- ticular purpose.Thestrikingadvantageofphotogra- gravity cannotbeassumed,longerintervalsoftime 2J 2398,.)thetimecoveredbyplateswaslarge time coveredbytheplates;inothercasestwo reasons, themostfrequentonebeingshortnessof some ofthesestarshadtobediscardedforvarious phy inthiscaseisshownespeciallybythesmallnum- present someresultsobtainedfromplatesavailableat parallax work,giveanenormousadvantageover is requiredinthemeasurementofthesequantities. image, buttheirdistancewastoosmall(suchasOA’ terminations ofrelativemassesseemedpossible.Bya observatory, anumberofstarswerefoundwherede- sonal errorsarereducedtoaminimum. servations wherepersonalandsystematicerrorsconceal superior tolongseriesofmeridianormicrometricob- ber ofyearsrequiredforobtainingdatathatarefar Masses inVisualBinarySystems/’[LickObs.Bull. “ ObservingListfortheDeterminationofRelative meridian orvisualmicrometerwork.'Aitkenbriefly were retainedasisillustratedhereafter.Thefirst enough sofarastherelativemotionisconcerned,but 235, £Scorpii,ß80)makingmeasuresontheindividual components weresufficientlybrighttoproducean chances ofvitiatingtheresultsbysystematicorper- differential way,asisdoneinparallaxwork,andthe work thedeterminationscanbemadeinapurely most ofthesmalldisplacements.Inphotographic No. 208,Vol.VII,p.7].Itistheaimofthisnoteto called attentiontothatpointwhenhepublishedhis with long-focusinstruments,suchasareusedinstellar become smallatthesametimehighestaccuracy short, butasthedifferencesC—Ci,andrn, large enoughduringthetimecoveredbytwoepochs. proved tobenecessary.Finallyfourbinarystars as insuchcasestheproper-motionofcenter more carefulconsiderationoftheobservationaldata components difficult.Insomeinstances(61Cygni, For thatpurposemeasuresofphotographsobtained will besmalliftheintervaloftimet—hisrelatively The influenceofanerrorintheassumedproper-motion 174 duced fromheliometermeasures.Fromphotographic For theparallaxweadoptedPeter’svalue0".18de- determinations Russellfound0".19.Finallyforthe 2 2 In lookingovertheplatematerialavailableatthis In declination In rightascension © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System THE ASTRONOMICALJOURNAL Principal Star + 12".81 - 5.99 Measured Displacement Companion recent yearswaslargerinrightascensionthan served manyyears.Theperiodislongandstillun- the equationsofcondition. unfinished seriesofparallax-platestakenforthisstar, declination. Butaswefoundonhandamongthe the orbitalmotionforestablishingcoefficientsin the relativemotionwasthoughttobelargeenoughin two goodplatesseparatedbyanelevenyearinterval consider thiswellknownsystem,thathasbeenob- placements ofthetwocomponentswerefound: pendence method.Thesolutionsormeasureddis- have beenusedandthemeasuresreducedbyde- this wasdonebymeansoíAGstarsreducedtothe ordinates, itisimportanttoorienttheplatecarefully: As theproper-motionofthisstarislargeinbothco- Schles. 473 urable imagesofbothcomponents,weretherefore was foundnecessarytorecomputebetterelementsof systems -generallyonlyonecomponentcouldbemeas- mean ofthetwodates1910.2.Fivecomparisonstars Tr 2194 as toyieldtwoindependentdeterminations. measured inbothrightascensionanddeclination,so both coordinates.Thetwoplates,whichshowmeas- certain byatleastacentury.Therelativemotionin be takenfromthebestsources.Forlaststarit — sothattheellipticelementsofmotionhadto ured —atleastthetimewhenplatesweretaken star isacasewheretheperiodstillverydoubtful measures ofthecompanion.Forthreeother and wheretherelativemotionwasfoundfrom + 10".51 - 4.40 values giveninBoss’P.G.C.Thecorresponding proper-motion ofthesystemwehaveadopted displacements inthe10.897years’intervalbetween Number As afirstapplicationofthepreceedingremarkswe The followingplateshavebeenused: m hm t? Cassiopeiae£60(3.6—79) 0 43+57°17'(1900) 1915 Aug.18 1904 Sept.26 Principal Star Date + 12" - 6 Corrected forParallax ,05 ,72 hm Gr. M.T. 20 44 17 44 Companion + 10".42 - 5.69 + 0.161 +0.678 Parallax Factors In a$ -0.479 -0.839 N°- 694 1916AJ 29. .173V Xor ter ofgravityhasbutlittleinfluence. tion, sothattheuncertaintyofpositioncen- tions coveringalongertimethantheperiodofrevolu- P. G.C.andisbasedonaseriesofmeridianobserva- additional unknown.ItsvaluewastakenfromBoss’ so wellknownthatitoughtnottobeintroducedasan and lastepoch.Theproper-motionofthesystemis the motionbeingsmallindeclinationbetweenfirst of therevolutionsscrew(1R=2".665)in column "Solution,"weremadeinrightascensiononly, N°- 694 From thesedatawefind: the twoplatesaregivenatsametime: From declinationsA=0.71(Weight85)) From rightascensionsA=0.38(Weight60)> of hisP.G.C.(p.264): has beenmadebyL.Boss,asisfoundintheappendix, gives ^Á4l=0.67. discussion byT.Lewus(Mem.R.A.S.,Yol.LYX,p.18) crometrie measuresw=0.268orA0.789.later observations comparedwiththecontemporaneousmi- result. termine theparallaxwouldgiveahigherweightto larger numberofplatestakensoastoavoidorde- Astr., Yol.V)foundfromadiscussionofthemeridian agreement mustbeconsideredassatisfactory.A The measures,theresultofwhichisgiveninvalues A morethoroughdiscussionofmeridianobservations As farbackas1881L.Struve(MelangesMath,et As onlyoneplatehasbeenusedforeachepochthe B Plate No. 2534 2533 468 410 272 247 Proper motions(1910.2) © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System A B 1916 May3 1910 Apr.10 16 May3 11 Aug.19 10 July30 11 Apr.22 Date THE ASTRONOMICALJOURNAL + 12.28-10.42 - 5.69+4.46 - 6.05+4.46 12.72 -10.42 Time inDecimal Fraction ofYear 1910.274 1916.339 s r/ + 0.1392 — 0.523 11.306 16.339 11.631 10.577 0.81 fromrightascensions 0.77 fromdeclinations tions ofcondition,itwasthoughtadvisabletodeduce Publik, desAstroph.Obs.Potsdam,Vol.XX,p.146. them fromLohse’sellipticalelementsasgivenin which dependsthecoefficientsofmassinequa- unless theplateswereexceptionallygood.Thisimage Instead ofusingittofindtherelativeposition,upon was wellmeasurableononlyoneoftheearlierplates. image ofthecompanionweakanddifficulttomeasure nitudes bymeansoftherotatingsector.Thismade tude of70Ophiuchiiwasreducedbyaboutfivemag- for thepresentpurposes,Ihavetakentwoadditional shortness ofthetimecovered. pressions fororbitalandproper-motionrespectively." plates asseeninthefollowingtable: plates in1916,theearlierepochbeingmadeupoffour measured byhimcoveringtooshortanintervaloftime measured bySlocum(Aph.J.41,241).Theplates have onlyasmallinfluenceontheresultbecauseof very uncertain“owingtotheindependenceofex- whence headopts0.57,buttheresultisconsideredas assumed; apossibleerrorinthisvaluecanhowever In thepresentseriesofplatesapparentmagni- The parallaxofthisbinary(tt=0".21)hasbeen In thepresentdeterminationproper-motionwas Principal StarCompanion Solution (RightAscension) M 0.685 0.327 0.458 0.326 0.371 0.687 70 OphiuchiI2272(43-58) h Displacements 18Qm +2°31'(1900) 1.871 1.873 1.124 Mean 0.79 + 12".28 - 5".69 Correction for + 0.066 + 0.048 -0.058 -0.058 -0.067 -0.074 Parallax 175 1916AJ 29. .173V r Yol. CLXY,p.158(1904)]frommeridianobservations plate isavailable. is entitledtomuchlessweightbecauseonl}oneearlier the companion: give: unit asthemeasuredquantitiesbecome: relative positionsr=psinBexpressedinthesame that ofatrailonthefirstplateused.Thecomputed is inerror,andfinds: observations showsthatoneofPrey’snormalplaces An independentdeterminationfromthemeasuresof position-angles havebeencorrectedforprecession 1821 —1894hadgiven: 176 (1908)] fromanindependentdiscussionofthemeridian ( —0°.06)from1900tothatfirstdate.Hencethe a Corrected The sixequationsofconditionfortheprincipalstar For thefivedatesconsideredwehave: Previous determinationsbyA.Prey[Astr.Nachr., Comstock [Asir.Nadir.,Yol.CLXXYIII,p.18 The directionofthemeasurementonplatesis +0.297 for 7T 0.629 0.627 0.391 0.393 0.370 From declinations0.27 From both0.20 From rightascensionsA=1—Z0.19 1910.274 153°.593".425 1910.577 152.613.505 16.339 139.734.845 11.306 150.443.693 11.631 149.553.775 © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System C Corrected + 1.057 A =0.53±0.02 for 7T 1.815 1.813 A =0.56 e (1900.0) +0.206 THE ASTRONOMICALJOURNAL /dt .607 .607 .055 .125 .156 +0.573 1.177 .177 .685 .606 .719 r/ of theP.G.C.,p.275: observations. the elaboratediscussionoflongseriesmeridian six platescoveringayearintervaloftime,the firms entirelythislastvalue.Althoughbasedononly for astaralwaysdifficulttomeasure.However,re- probable errorisassmalltheonethatresultedfrom former, e=0.36inthelatter.Yetatpresent from Aitken’sElements[Publ.LickOhs.,Yol.XII, recent setsofelements:thefirstcolumnisdeduced micrometric measuresoftwostarsinthevicinity: p. 141(1908)]comestoasimilarconclusionabout time thedifferencebetweentwosystemsissmall orbital motionindeclinationasresultingfromtwo er-motion istakenfromtheP.G.C.:N=TO".427. puting thecorrespondingsmallcorrection.Theprop- 0.Q06 ±016bySlocumandMitchell[Aph.J., the plateshavebeenmeasuredinthatdirectiononly. system ontheparallax-platesisbuiltupbybrighter Prey’s computationandfindsfromadiscussionof Vol. XXXVIII,p.23(1913)]hasbeenadoptedincom- in declinationduringthetimecoveredandconsequently p. 161,(1914)]thelastonefromAbetti’sElements arc, aregivenundera.Thelastcolumnsgivethe The reductionsareshowninthetablefollowing. differ byaboutfourmagnitudes.Theimageofthe elements arequitedifferent;e.g.,e=0.22inthe [Mem. Spelt.liai.,Vol.I,p.178(1912)].Someofthese component only.Therelativemotionhasbeenlargely cent observationsfavorAitken’sorbit. L. Bossfindsthefollowingvaluesinappendix It isseenthatthepresentphotographicresultcon- B =0.507orA—0.493fromdeclinations. About thesametimeLau[Bull.Astr.,Vol.XXV, B =0.456orA0.544fromrightascensions The parallaxofthisstarissmall.valuett= The correctedmeasures,convertedintosecondsof The brightnessofthetwocomponentsthisbinary From rightascensionsA=0.52±0.02 From declinationsA=0.58±0.03 M From StarCA=0.69±0.18 From StaraA=0.63^Q.12 r Cygni,A.G.C.13(3.8-74) hm 21 ll+37°37'(1900) N°' 694 1916AJ 29. .173V 0 N' 694 A are: the motionofcentergravity.Hisresultsfor nearer tothetruthweadoptasafinalvalue: tively, withthepurposeoffindingmass-ratioand tained byO.Struve(1851)andComstock,(1903) plates : peatedly, forthirty-fiveandsixty-oneyears,respec- given inbothcases: interesting discussionofthemeasurestwodistant Hadley finds{Pop.Astr.13.325) assumptions. Thesameweightwasgiventoallthe companions CandDthathavebeenmeasuredre- Plate No. From declinationsA=1—k0.832=±=0.359 From adiscussionofthemeasuresCstar,ob- From rightascensionsA=1—k0.570=±=0.450 A preliminarysolutionfromthefirsteightplateshad The mass-ratiohasbeencomputedunderboth In thepaperofAbetti,citedabove,wefindan Considering thatAitken’selementsseemtobe From Aitken'sElementsAbetti’s 1324 1323 157 134 A =0.52±0.030.55 Plate No. 2573 797 794 268 259 793 299 112 39 1909 Oct.30 1913 July24 1913 July24 1909 Nov.13 © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System 1916 June4 1907 Oct.12 Date 09 Sept.18 12 June23 12 June22 12 June22 10 Sept.9 10 June25 10 June18 A =0.56=±=0.04 Date A =0,53 THE ASTRONOMICALJOURNAL Solution Correctionforttg -0 .564 -0 .550 -3 .448 -3".475 in Declination + 1.083 +0.398 +0.394 +0.398 +0.078 + 0.056 + 0.022 -0.092 -0.418 Solution Right Ascension +0".048 + 0.060 -0 .066 -0 .066 Correction - .002 - .002 - .002 - .002 - .001 - .002 - .002 - .001 -0.001 for 7T possible totakeadvantageofthatcircumstance. interval oftimeissmallenoughforconsideringgasa time —nineorevenfiveyearsvaluesofdecidedly so thatonlythebrightestcomponentappearson higher accuracyareobtainedinthepresentcase.The vantage ofthelattermethod.Inamuchshorter photographic determinations,illustratewellthead- two consideredepochs,thefollowingplateshavebeen measures coveringalongintervaloftime,itisnot known quantity,whileinthediscussionofmicrometric From declinations0.19=±=0.400.47=±=0.29 From rightascensions0.47=±=0.390.51=±=0.28 parallax discussion.Theorbitalmotionbeingalmost epoch twoearlyplatesthathavenotbeenusedinthe that intervalistooshortforproducingameasurable system (theperiodislessthantwenty-sevenyears) than twoyears.Howeverfastthemotionof plates thattheyhaveusedcoveranintervalofless p. 243(1915)]havediscussedtheseforparallax,butthe plates. SlocumandMitchell[Aph./.,Yol.LXI, magnitude betweenthetwocomponentsisverylarge, measured inbothcoordinates: as largeinrightascensiondeclinationbetweenthe displacement. Therefore,wehavetakenasafirst These probableerrors,comparedwiththoseofthe This isanotherbinarystarwherethedifferenceof -0 .032 -3 .113 -3 .113 Correction 0".000 +0.033 +0.067 + 0.070 + 0.190 +0.500 -0.253 -0.886 -0.253 -0.253 for ß M 85 Pegasi=ß733(5.8-110) hm 23 57+26°33'(1900) +3".887 +3 .857 -0 .638 -0 .588 Solution Correctionforirg a resulting + 0".216 in seconds 0 .520 .381 .370 .240 .381 .293 .322 .259 Declination ,/ From C1) 0 .850 -0 .046 -0 .046 -0 .000 -0".012 0.200 .605 .605 .444 .605 .464 .443 .378 Orbital Motionr I II 0 .913 0".194 +3 .680 + 0.038 +3 .680 .606 .606 .446 .377 .606 .465 .444 0".000 177 1916AJ 29. .173V a so astorepresentwellpossibletheverydiscord- elements : ble measuresupto1915,Ihavededucedthefollowing elements willgiveafairlygoodvalueoftherelative servations nearperiastron.Roughastheyare,these towards thepositivesideinlasttenyears, tion isstillopen,butasthevelocitiesindicateachange binary [Aph.J.,Yol.XXV,p.59(1907)].Theques- would beexpectedinastarofthistype.Thisinduced discussion, themajor-axisbeingadjustedafterwards material onlypositionangleshavebeenusedinthe elements availableneedrevision.Usingalltheavaila- tion anglehaschangedbyabout580degreessincethe the fourthquadrant. him tosuspectthebrighterstarofbeingaspectroscopic by ProfessorFrostshowlargerdiscordancesthan to belargelyinerrorbecausethestarisalwaysa difficult object. are stillveryuncertain,duemainlytothelackofob- discovery byBurnhamin1878,someoftheelements ascending nodeofthevisualorbitmustbeplacedin ant distances. as couldbeexpectedatpresent.Althoughtheposi- measures ofthisimportantstararescarceandliable elements ifthesearesufficientlywellknown.The crometric measures,ortobecomputedfromtheelliptic the totalorbitalmotioniseithertobetakenfrommi- find: means ofthetwoearlierandlaterplates,we motion wastakenfromBoss’P.G.C.Takingthe Astrographic Catalogue.Theparallaxtt=O".084was with therectangularcoordinatesfromOxford adopted fromthepaperreferredto.Theproper- equator for1900.0whichwasfoundbycomparison 178 On accountofthecharacterobservational The elementsrepresentalltheobservationsaswell Recent observationshaveshownthatthebest Measures oftheradialvelocityatthisobservatory The companionnotbeingmeasurableontheplates The platesweremeasuredinthedirectionof Displacement —0.313 1913.563 -3.736 1909.849 —3".423 P =26.70years T =1909.88 a =O'hSl e =0.390 © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System Right Ascension THE ASTRONOMICALJOURNAL ( =+13°.483) n 0 -281.2 co =98.6 1 =52.8 Declination +0 .360 +4 .245 +3".885 vestigated severaltimes: Not., Vol.LXVI,p.425,(1906)]anddeduce: found that that fromadiscussionofmeridianobservations,itwas The mass-ratioofthissystemhasalreadybeenin- the secondvaluewefindresultingvalue: detail thediscussionofmeridianobservations[Monthly Comstock [Aph.J.,Vol.XVII,p.220(1903)]deduces: by anappreciablequantity,sothatthefirstvalue periastron, whentheangularmotionisveryrapid first epochcorrespondsverynearlytothetimeof deserves thelesserweight.Givingdoubleweightto probably duetothedefectsinadoptedorbit.The astron passagewillchangespeciallytherightascension (over 50°ayear).Aslighterrorinthetimeofperi- Relative change 1913.563 1909.849 We findforthetwoepochs: motion duringthefouryearscoveredbyplates. About thesametimeBowyerandFurnergivein From measuresofthepositionadistantstarC, From declinationsA=0.3695 From rightascensionsA=0.396>j_nqq In Mem.R.A.Soc.,Vol.LVI,p.21,Lewisstates A largepartoftheuncertaintythesefiguresis From declinations I romrightascensionsA=t—r—,0.29 Hence thevalueofmassprincipalstar: A =0.20(Lewis)0.25(Ferner) From declinationsA=0.24 From rightascensionsA=0.15 118° 53 33° 35' A =0.36 A0,39 44131 0 .695+0.609-0.336 0".303 -f0".168+0".253 0.589 , °--n ^ AscensionDeclination 0.589-0.360 = 0.441 -fO .441-0.589 In Right N°- 694 1916AJ 29. .173V M 0 kind. large distancesthereis,ofcourse,nolimitationthat the distanceissmall,forinstance,lessthanl".For not interferewiththeimageofprincipalstarwhen from theslownessofmotion,wehaveadopted fifteen years).Besidesthislimitoftimeresulting yield measurablequantitiesbythephotographicmeth- od afterarelativelyshortintervaloftime(tenor limited tostarswherethemotionisfastenough which itisunsafetoassumethatthecompaniondoes cessful determinationofmass-ratio.Thelistwas stars whereconditionsseemtobefavorableforasuc- the determinationofAwillbeabout6%:avery 1.5 asthelimitofdifferencemagnitude,inside small amount,consideringthenatureofproblem and theresultsobtainedsofarinthisdirection. ered bytheplatesisonlyO".50,probableerrorof tion weseethatiftherelativemotionintimecov- probable errorofabout0".03fromoneplate.Analo- found repeatedlybyearlierinvestigators. ments. Notconsideringtheinfluenceofproper-mo- gous resultshavebeenfoundwithotherlargeinstru- son starsconsideredasafixedbackground,with positions; i.e.,referredtoanumberoffaintcompari- taken withthe40-inchtelescopegivesemi-absolute by Schlesingeritcanbeconsideredthattheplates small massofthebrightercomponent,thathadbeen no otherinstanceinwhichithasbeenpossibleto equal it ishereassumedthatthetwomassesaresensibly is verygreat,asinthepresentinstance.Accordingly, ponent, especiallywhenthediscrepancyinbrightness the greatermass,whilestrongnaturalinference must beinfavorofgreatermassforthebrightercom- bility thatthefaintercomponentofabinarystarhas brighter componenthasthesmallermass.“Thereis demonstrate withastrongpreponderanceofproba- But heacceptsreluctantlytheconclusionthat p. 278): same authorsgive: N' 694 We havecollectedinthefollowinglistanumberof As aresultoftheparallax-campaignstartedhere The photographicresultunquestionablyconfirmsthe The morerecentdiscussionbyL.Bossgave(P.G.C., From adiscussionofthemeasuresCstar From declinationsA=0.16±0.20 From rightascensionsA=0.49±0.16 From declinationsA=0.29 From rightascensionsA=0.26 © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System THE ASTRONOMICALJOURNAL 7 r/ uncertain atthepresenttime. on theparallaxprograms. then givethenecessarydata. four orfiveyearstherightascensiondirectionwould interval oftimeoughttobeaboutfifteenyears. requires onlyacoupleofyears,thiscangohandin hand withthedeterminationofparallax. results canbeobtainedfrommeridianobservations. 1919 thedeclinationcouldnolongerbeused;after But asanindependentphotographicdetermination val isallthatneeded. be settled,butverylikelyatenorfifteenyearsinter- of thetwocoordinatesismostfavorable.Assoon so thatitisalmostimpossibletopredictnowwhichone as thecompanionisagainmeasurablequestionwill years. right ascensionandindeclination.Ifmeasured motion, butforyearsthecompanionhasbeeninvisible, as thelowernecessarylimitisreachedinaboutseven obliquely, thedisplacementof0.5thatweconsider in acentury.”Bymeansofphotographythedeter- mination couldbemadeaftersometenyearsbothin ures, begunnow,willyieldagoodvalueform'/mwith- parallax programofoneormoreobservatories.After dozen stars. a decadeorsomaterialwillbeavailableforaboutthree tions willofcoursehavetobechangedaftersomejmars. tion ofmeasurementgoodresultsaretobeexpected. With veryfewexceptionsthestarsarealreadyon In someofthemorerapidlymovingstarstheseindica- of aboutO".50,bothinrightascensionanddeclination. This showsafterwhatlapseoftimeandindirec- quired forobtainingaminimumorbitaldisplacement The twolastcolumnsgivethenumberofyearsre- follows : laxes, Aug.(1915)].Theobservatoriesaredesignatedas Society, Reportofthecommitteeonstellarparal- the parallaxprogram[Public,ofAmericanAsir. components andtheobservatorieswherestarison and theirpositionforIfiOO)themagnitudesof 7. aUrs.Maj.Thedirectionofthemotionisvery 6. Y1306.Thisstaroughttobeplacedatonce 5. €Hydrce.Ifthedeterminationwasstartedin 4. RCancri.Incaseofthe—^—~Csystem, 3. Sirius.Theapparentorbitissolargethatgood 2. ß552.Thisstarhasshownconsiderableorbital 1. aFornacis.Aitken(Log.cit.)writes:“meas- The successivecolumnsgivethenamesofstars A AlleghenySSproul M McCormickYYerkes D DearbornWMountWilson A A-B 179 1916AJ 29. .173V 180 Mass-Ratios inVisualBinaryStars,byG.VanBiesbroeck. Published bytheDudleyObservatory,Albany,N.Y.,U.S.A.,towhichall Communicationsshouldbeaddressed.Price,sb.OOthevolume. Press ofThos.P.Nichols&SonCo.,Lynn,Mass.Closed,July13,1916. Yerkes Observatory,WilliamsBay,Wis.,June,1916. Btjknham 12701 12755 12196 11761 11214 11743 10846 G. C. 2007 2134 2109 1612 1036 4120 2383 2154 4187 3596 4714 4771 4477 4923 7034 6566 5652 7649 7563 7259 6641 5734 7783 7717 8933 7929 7878 9605 8372 8340 8099 426 Editor, BenjaminBoss,Albany,N.Y.;AssociateEditors:E.Barnard, ErnestW.Brown,F.R.MoultonandS.Woodward. © AmericanAstronomical Society•ProvidedbytheNASAAstrophysicsData System ß 513 £ 483 40 Eridani r; Cassiopeice 02' 79 a Fornacis a Cor.Bor. ß 552 02 82 2 1306 ß 208 Procyon Sirius f Cancri 2 1785 2 2107 X Ophiuchi y Bootis e Hydræ Castor 2 3002 jjL Droxonis 25 Can.Venat. u Cygni ß 416 y Herculis 85 Pegasi Kruger 60 ß 648 a Urs.Maj. Tr Cephei Ç Aquarii <5 Cygni T Cygni 99 Herculis 70 Ophiuchi 26 Draconis % Bootis a Centauri £ Urs.Maj. Star List ofStarsforMass-RatioDeterminations 0 THE ASTRONOMICALJOURNALN’694 w 23 23 22 21 15 14 14 13 13 11 10 22 21 16 16 17 16 16 17 19 18 18 18 17 9 0 44.5 47.6 55.8 59.1 41.8 15.6 11.8 42.8 35.3 29.8 18.5 47.9 35.8 34.5 45.6 34.1 48.9 59.1 40.8 38.5 27.1 21.7 42.6 34.2 58.2 25.4 25.0 54.2 11.9 14.2 13.8 11.8 8.9 7.9 3.8 4.2 3.8 2.3 5.5 1.7 1925.0 +57 25 + 7033 + 3918 + 1621 + 1332 + 1453 -29 17 + 5 +32 - 746 + 1757 + 6726 + 642 -16 37 + 343 +37 38 + 1925 + 2721 + 3641 + 31 + 62 + 3144 + 29 + 5434 + 2847 -22 24 +30 33 + 231 + 581 + 2641 + 74 + 57 +32 48 + 6156 + 2824 +44 57 -60 32 +37 43 -34 54 - 024 CONTENTS. 25 57 20 59 3 9 -2.0- 9.0 5.0-5.5-5.7 Magnitude 4.0- 7.6 3.9- 6.9 5.0- 7.5 7.0- 9.0 7.0- 8.8 9.1- 10.8 8.0- 9.5 7.0- 1.0 0.2-12 2.7- 3.7 6.0- 9.0 3.8- 5.5 4.7- 4.0- 4.9 5.0- 8.2 4.0- 6.7- 0.0- 7.2- 5.0- 4.9- 5.9 4.3- 6.3 2.8- 5.7- 1.7- 1 1. 4.6- 7.5 5.0- 6.5- 9.0-12.0 4.3- 4.5 6.0- 5.8-11.0 3.8- 7.5 2.8- 7.9 5.5- 9.5 5.4- 1 0.1 6.2- 7.3 5.2- 1 0.5 6.5 6.1 6.8 7.3 6.6 7.5 7.0 8.0 5.1 8.0 1.5 A, M,S,Y A, S S, Y A, S s’y” A, M,S,Y A, D,M,Y S M, Y M S,Y A, M,S,Y Y A, S,W,Y A S A, Y A, S A, S A, AI,S, S, Y A, M A, M,S. Observatories S A, S M. SY A, S A, S A, M,S A, AI,S,Y A, D,S,Y A, M,Y A, S,Y A, S A, D,S,Y D S, Y M, S,Y ? ; ; S, Y Y Y In a5 10? 10 15 10 15 10 10 15 12 15 12 10 10 12 4 8 2 4 5 5 5 9 5 6 6 Time 10 15? 15 10 10 10 10 15 15 15 10 12 12 15 5 3 4 6 4 2 1 2 5 8 3 6 Notes