by ! ,dep>tm5t ( ,ma!matics at ! ,univ]sity ( ,glasg[47 ,transcrib]'s ,note3 ,?is text is int5d$ = us]s ^: text read]s _c use ! real 7unicode_/utf-#h7 v]sion ( ! file4 ,*>act]s 9 ! ,greek alphabet are repres5t$ z foll[s3 alpha1 beta1 gamma1 etc4 ,9 ! orig9al text1 ! units h & m1 & ord9als ? & / 7 pr9t$ z sup]scripts4 ,= readability1 !y h n be5 repres5t$ z su* 9 ?is file4 ,simil>ly = ! & - signs :5 us$ to describe int]m$iate /ell> col\rs4 ,o!r sup]scripts are indicat$ by ! c>at symbol1 1 & subscripts by an und]l9e1 4 ,,lectures ,,on ,,/ell> ,,/ati/ics ,,by ,c4 ,v4 ,l4 ,,*>li] ,,sci5tia ,,publi%] ,,lund #aiba ,,hamburg #aiba ,,pr9t$ ,,by ,l,,tcke ,,wulff ,,*apt] ,i4 ,,app>5t ,,attributes ,,( ,,! ,,/>s4 #a4 ,our k ( ! />s is bas$ on _! app>5t attributes1 obta9$ f ! a/ronomical obs]vations4 ,! object ( a/ronomy is to d$uce h]efrom ! real or absolute attributes ( ! />s1 :i* are _! position 9 space1 _! movem5t1 & _! physical nature4 ,! app>5t attributes ( ! />s are /udi$ by ! aid ( _! radiation4 ,! *>act]i/ics ( ?is radiation may be describ$ 9 diff]5t ways1 accord+ z ! nature ( ! light is def9$4 7,undulatory !ory1 ,emission !ory47 ,f ! /ati/ical po9t ( view x w be conv5i5t to consid] ! radiation z consi/+ ( an emanation ( small p>ticles f ! radiat+ body 7! />74 ,^! p>ticles are *>act]iz$ by c]ta9 attributes1 :i* may diff] 9 degree f "o p>ticle to ano!r4 ,^! attributes may be1 = in/ance1 ! diamet] & =m ( ! p>ticles1 _! mode ( rotation1 c4 ,by ^! attributes ! optical & electrical prop]ties ( ! radiation are to be expla9$4 ,i %all n "h attempt any su* explanation1 b %all conf9e myself to ! prop]ty :i* ! p>ticles h ( possess+ a diff]5t mode ( deviat+ f ! rectil9e> pa? z !y pass f "o m$ium to ano!r4 ,?is deviation dep5ds 9 "s way on "o or m attributes ( ! p>ticles4 ,let u suppose t x dep5ds on a s+le attribute1 :i*1 ) a t]m9ology d]iv$ f ! undulatory !ory ( ,,huygh5s1 may be call$ ! wave-l5g? 7lambda7 ( ! p>ticle4 ,! /ati/ical *>act]i/ics ( ! radiation are !n 9 ! fir/ place3-- 7#a7 ! total numb] ( p>ticles or ! int5sity ( ! radiation2 7#b7 ! mean wave-l5g? 7lambda#j7 ( ! radiation1 also call$ 7or ne>ly id5tical )7 ! effective wave-l5g? or ! col\r2 7#c7 ! disp]sion ( ! wave-l5g?4 ,?is *>act]i/ic ( ! radiation may be det]m9$ f ! spectrum1 :i* also gives ! v>iation ( ! radiation ) lambda1 & h5ce may also det]m9e ! mean wave-l5g? ( ! radiation4 ,moreov] we may f9d f ! radiation ( a /> its app>5t place on ! sky4 ,! int5sity1 ! mean wave-l5g?1 & ! disp]sion ( ! wave-l5g? are 9 a simple mann] connect$ ) ! temp]ature 7,t7 ( ! />4 ,accord+ to ! radiation laws ( ,,/ephan & ,,wi5 we f9d1 inde$ 7comp>e ,l4 ,m4 #daa7 t ! int5sity is proportional to ! f\r? p[] ( ,t1 :]eas ! mean wave-l5g? & ! disp]sion ( ! wave-l5g? are bo? inv]sely proportional to ,t4 ,x foll[s t ) increas+ temp]ature ! mean wave-l5g? dim9i%es--! col\r *ang+ into violet--& simultane\sly ! disp]sion ( ! wave-l5g? & also ev5 ! total l5g? ( ! spectrum are r$uc$ 7decrease74 #b4 ,! app>5t position ( a /> is g5]ally d5ot$ by its "r asc5sion 7alpha7 & its decl9ation 7delta74 ,tak+ into acc\nt ! app>5t di/ribution ( ! />s 9 space1 x is1 h[ev]1 m practical to *>act]ize ! position ( a /> by its galactic longitude 7l7 & its galactic latitude 7b74 ,be=e def9+ ^! coord9ates1 :i* w be g5]ally us$ 9 ! foll[+ pages1 x %\ld be po9t$ out t we %all also g5]ally give ! coord9ates alpha & delta ( ! />s 9 a p>ticul> mann]4 ,we %all !re=e use an abridg$ notation1 s t if = in/ance alpha #ag;h #ddm4#g & delta #ce4hd1 we %all write 7alphadelta7 7#agddce74 ,if delta is negative1 = in/ance delta -#ce4hd1 we write 7alphadelta7 7#agddce71 s t ! la/ two figures are 9 italics4 ,transcrib]'s ,note3 ,9 ?is v]sion ( ! text1 ! la/ two figures are enclos$ 9 braces to repres5t ! italics4 ,?is notation has be5 introduc$ by ,,pick]+ = v>iable />s & is us$ by him ev]y:]e 9 ! ,annals ( ! ,h>v>d ,obs]vatory1 b x is also well suit$ to all />s4 ,?is notation gives1 simultane\sly1 ! *>act]i/ic num]o ( ! />s4 ,x is true t two or m />s may 9 ?is mann] obta9 ! same *>act]i/ic num]o4 ,!y are1 h[ev]1 easily di/+ui%able f ea* o!r ?r\gh o!r attributes4 ,! galactic coord9ates l & b are ref]r$ to ! ,milky ,way 7! ,galaxy7 z plane ( ref]5ce4 ,! pole ( ! ,milky ,way has accord+ to ,,h\zeau & ,,g\ld ! position 7alphadelta7 7#abdebg74 ,f ! di/ribution ( ! />s ( ! spectral type ,b ,i h 9 ,l4 ,m4 ,,ii1 #adb f\nd a some:at diff]5t position4 ,b hav+ asc]ta9$ lat] t ! real position ( ! galactic plane requires a great] numb] ( />s = an accurate det]m9ation ( its value1 ,i h pref]r$ to employ ! position us$ by ,,pick]+ 9 ! ,h>v>d catalogues1 namely 7alphadelta7 7#abdjbh71 or alpha #ab;h #djm #aij1 delta #bh1 :i* position is n[ exclusively us$ 9 ! /ell> /ati/ical inve/igations at ! ,obs]vatory ( ,lund & is also us$ 9 ^! lectures4 ,! galactic longitude 7l7 is reckon$ f ! asc5d+ node ( ! ,milky ,way on ! equator1 :i* is situat$ 9 ! con/ellation ,aquila4 ,! galactic latitude 7b7 gives ! angul> di/ance ( ! /> f ! ,galaxy4 ,on plate ,i1 at ! end ( ^! lectures1 w be f\nd a fairly detail$ diagram f :i* ! conv]sion ( alpha & delta ( a /> into l & b may be easily p]=m$4 ,all />s hav+ an app>5t magnitude bright] ?an #dm are directly drawn4 ,in/ead ( giv+ ! galactic longitude & latitude ( a /> we may cont5t ourselves ) giv+ ! galactic squ>e 9 :i* ! /> is situat$4 ,= ?is purpose we assume ! sky to be divid$ into #dh squ>es1 all hav+ ! same surface4 ,two ( ^! squ>es lie at ! nor!rn pole ( ! ,galaxy & are designat$ ,,ga#a & ,,ga#b4 ,twelve lie nor? ( ! galactic plane1 betwe5 #j & #cj galactic latitude1 & are designat$ ,,gc#a1 ,,gc#b1 4441 ,,gc#ab4 ,! correspond+ squ>es s\? ( ! galactic equator 7! plane ( ! ,galaxy7 are call$ ,,gd#a1 ,,gd#b1 4441 ,,gd#ab4 ,! two pol> squ>es at ! s\? pole are call$ ,,gf#a & ,,gf#b4 ,f9ally we h #aj ,b-squ>es1 betwe5 ! ,a- & ,c-squ>es & #aj correspond+ ,e-squ>es 9 ! s\!rn hemisph]e4 ,! di/ribution ( ! squ>es 9 ! heav5s is "h graphically repres5t$ 9 ! projection ( ,,flam/e$1 :i* has ! advantage ( giv+ areas proportional to ! correspond+ sph]ical areas1 an arrangem5t necess>y1 or at lea/ highly desirable1 = all /ell> /ati/ical rese>*es4 ,x has also ! advantage ( af=d+ a cont9u\s repres5tation ( ! :ole sky4 ,! correspond5ce betwe5 squ>es & /ell> con/ellations is se5 f plate ,,ii4 ,arrang+ ! con/ellations accord+ to _! galactic longitude we f9d nor? ( ! galactic equator 79 ! ,c-squ>es7 ! con/ellations3-- ,h]cules1 ,cygnus1 ,cepheus1 ,cassiopa1 ,auriga1 ,gem9i1 ,canis ,m9or1 ,pyxis1 ,vela1 ,c5taurus1 ,scorpius1 ,ophiu*us1 & s\? ( ?is equator 79 ! ,d-squ>es73-- ,aquila1 ,cygnus1 ,lac]ta1 ,&rom$a1 ,p]seus1 ,orion1 ,canis ,major1 ,puppis1 ,c>9a1 ,circ9us1 ,corona au/ralis1 ,sagitt>ius1 m5tion+ only "o con/ellation = ea* squ>e4 ,at ! nor? galactic pole 79 ! two ,a-squ>es7 we h3-- ,canes ,v5atici & ,coma ,b]5ices1 & at ! s\? galactic pole 79 ! two ,f-squ>es73-- ,cetus & ,sculptor4 #c4 ,*anges 9 ! position ( a />4 ,f ! positions ( a /> on two or m occasions we obta9 its app>5t motion1 also call$ ! prop] motion ( ! />4 ,we may di/+ui% betwe5 a secul> "p ( ?is motion & a p]iodical "p4 ,9 bo? cases ! motion may be ei!r a reflex ( ! motion ( ! obs]v]1 & is !n call$ p>allactic motion1 or x may be caus$ by a real motion ( ! />4 ,f ! p>allactic motion ( ! /> x is possible to d$uce its di/ance f ! sun1 or its p>allax4 ,! p]iodic p>allactic prop] motion is caus$ by ! motion ( ! e>? ar\nd ! sun1 & gives ! annual p>allax 7pi74 ,9 ord] to obta9 available annual p>allaxes ( a /> x is usually necess>y = ! /> to be ne>] to u ?an #e siriomet]s1 correspond+ to a p>allax great] ?an #j4jd4 ,m seldom we may 9 ?is mann] obta9 tru/wor?y values = a di/ance am\nt+ to #aj siriomet]s 7pi #j4jb71 or ev5 /ill great] values4 ,= su* l>ge di/ances ! secul> p>allax1 :i* is caus$ by ! progressive motion ( ! sun 9 space1 may give bett] results1 especially if ! mean di/ance ( a gr\p ( />s is simultane\sly det]m9$4 ,su* a value ( ! secul> p>allax is also call$1 by ,,kapteyn1 ! sy/ematic p>allax ( ! />s4 ,:5 we speak ( ! prop] motion ( a />1 )\t fur!r specification1 we mean always ! secul> prop] motion4 #d4 ,t]re/rial di/ances are n[1 at lea/ 9 sci5tific rese>*es1 univ]sally express$ 9 kilometres4 ,a kilometre is1 h[ev]1 an inappropriate unit = cele/ial di/ances4 ,:5 deal+ ) di/ances 9 our planet>y sy/em1 ! a/ronom]s1 s9ce ! "t ( ,,newton1 h always us$ ! mean di/ance ( ! e>? f ! sun z univ]sal unit ( di/ance4 ,reg>d+ ! di/ances 9 ! /ell> sy/em ! a/ronom]s h _h a v>y+ practice4 ,g]man a/ronom]s1 ,,seelig] & o!rs1 h long us$ a /ell> unit ( di/ance correspond+ to an annual p>allax ( #j4b1 :i* has be5 call$ a ,siriusweite4 ,to ?is "n x may be ju/ly object$ t x has no int]national use1 a great desid]atum 9 sci5ce4 ,aga9/ ! !oretical def9ition ( ?is unit x may also be said t a di/ance is suitably to be def9$ ?r\gh ano!r di/ance & n ?r\gh an angle--an angle :i* corresponds moreov]1 9 ?is case1 to ! h>monic mean di/ance ( ! /> & n to its ari?metic mean di/ance4 ,! same objection may be made to ! unit p>sec4 propos$ 9 #aiab by ,,turn]4 ,= my "p ,i h1 s9ce #aiaa1 propos$ a /ell> unit :i*1 bo? 9 "n & def9ition1 ne>ly co9cides ) ! proposition ( ,,seelig]1 & :i* w be exclusively us$ 9 ^! lectures4 ,a siriomet] is put equal to #ajf times ! planet>y unit ( di/ance1 correspond+ to a p>allax ( #j4bjfbfe 79 practice suffici5tly exactly #j4b74 ,9 popul> writ+s1 ano!r unit3 a light-ye>1 has = a v long "t be5 employ$4 ,! relation betwe5 ^! units is #a siriomet] #ae4gi light-ye>s1 #a light-ye> #j4jfcc siriomet]s4 #e4 ,9 reg>d to "t also1 ! t]re/rial units 7second1 day1 ye>7 are too small = /ell> wants4 ,z be+ consi/5t ) ! unit ( di/ance1 ,i h propos$ = ! /ell> unit ( "t a /ell> ye> 7/471 correspond+ to #ajf ye>s4 ,we ?us obta9 ! same relation betwe5 ! /ell> & ! planet>y units ( l5g? & "t1 :i* has ! advantage t a velocity ( a /> express$ 9 siriomet]s p] /ell> ye> is express$ ) ! same num]als 9 planet>y units ( l5g? p] ye>4 ,spectroscopic det]m9ations ( ! velocities1 ?r\gh ! ,,doppl]-pr9ciple1 are g5]ally express$ 9 km4 p] second4 ,! relation ) ! /ell> unit is ! foll[+3 #a km4_/sec4 #j4baaa sir4_//41 #j4baaa planet>y units p] ye>1 #a sir4_//4 #d4gcge km4_/sec4 ,?us ! velocity ( ! sun is #bj km4_/sec4 or #d4bb sir4_//4 7 #d4bb e>? di/ances f ! sun p] ye>74 ,( ! num]ical value ( ! /ell> velocity we %all h opportunity to speak 9 ! foll[+4 ,= ! pres5t x may suffice to m5tion t mo/ />s h a velocity ( ! same degree z t ( ! sun 79 ! mean some:at great]71 & t ! highe/ obs]v$ velocity ( a /> am\nts to #gb sir4_//4 7 #cdj km4_/sec474 ,9 ! next *apt] ,i give a table conta9+ ! mo/ spe$y />s4 ,! lea/ value ( ! /ell> velocity is evid5tly equal to z]o4 #f4 ,int5sity ( ! radiation4 ,?is v>ies )9 wide limits4 ,! fa9te/ /> :i* c give an impression on ! photographic plates ( ! greate/ in/rum5t ( ! ,m\nt ,wilson obs]vatory 7#ajj in* reflector7 is ne>ly #ajj million times fa9t] ?an ,sirius1 a /> :i* is itself m ?an #ajjjj million times fa9t] ?an ! sun--speak+ ( app>5t radiation4 ,! int5sity is express$ 9 magnitudes 7m74 ,! reason is p>tly t we %\ld o!rwise necess>ily h to deal ) v l>ge numb]s1 if !y 7 to be proportional to ! int5sity1 & p>tly t x is prov$ t ! human eye appreh5ds quantities ( light z proportional to m4 ,?is dep5ds ^u a g5]al law 9 psy*o-physics1 kn[n z ,,fe*n]'s law1 :i* says t *anges ( ! app>5t impression ( light are proportional n to ! *anges ( ! int5sity b to ^! *anges divid$ by ! primitive int5sity4 ,a simil> law is valid = all s5sations4 ,a conv]sation is inaudible 9 ! vic9ity ( a wat]fall4 ,an increase ( a load 9 ! h& f n9e to t5 hectograms makes no great diff]5ce 9 ! feel+1 :]eas an increase f "o to two hectograms is easily appreciable4 ,a mat* light$ 9 ! day-"t makes no increase 9 ! illum9ation1 & s on4 ,a ma!matical analysis %[s t f ! law ( ,,fe*n] x foll[s t ! impression increases 9 ari?metical progression 7#a1 #b1 #c1 #d1 4447 simultane\sly ) an increase ( ! int5sity 9 geometrical progression 7,i1 ,i#b1 ,i#c1 ,i#d1 44474 ,x is ) ! sight ! same z ) ! he>+4 ,x is well kn[n t ! numb]s ( vibrations ( ! notes ( a h>monic scale foll[ ea* o!r 9 a geometrical progression ?\gh1 = ! e>1 ! int]vals betwe5 ! notes are appreh5d$ z equal4 ,! magnitudes play ! same rle 9 relation to ! quantities ( light z d ! log>i?ms to ! correspond+ numb]s4 ,if a /> is consid]$ to h a brightness int]m$iate betwe5 two o!r />s x is n ! diff]5ce b ! ratio ( ! quantities ( light t is equal 9 ea* case4 ,! bran* ( a/ronomy 7or physics7 :i* deals ) int5sities ( radiation is call$ photometry4 ,9 ord] to det]m9e a c]ta9 scale = ! magnitudes we mu/ *oose1 9 a c]ta9 mann]1 ! z]o-po9t ( ! scale & ! scale-ratio4 ,bo? may be *os5 arbitr>ily4 ,! z]o-po9t is n[ almo/ unanim\sly *os5 by a/ronom]s 9 accordance ) t us$ by ! ,h>v>d ,obs]vatory4 ,no rigor\s def9ition ( ! ,h>v>d z]o-po9t1 z f> z ,i c see1 has yet be5 giv5 7comp>e h[ev] ,h4 ,a4 #ejc71 b consid]+ t ! ,pole-/> 7alpha ,urs ,m9oris7 is us$ at ,h>v>d z a fundam5tal /> ( comp>ison = ! bright] />s1 & t1 accord+ to ! obs]vations at ,h>v>d & ^? ( ,,h]tzsprung 7,a4 ,n4 #deah #aiaa71 ! light ( ! ,pole-/> is v ne>ly inv>iable1 we may say t ! z]o-po9t ( ! photometric scale is *os5 9 su* a mann] t = ! ,pole-/> m #b4ab4 ,if ! magnitudes are giv5 9 ano!r scale ?an ! ,h>v>d-scale 7,h4 ,s471 x is necess>y to apply ! z]o-po9t correction4 ,?is am\nts1 = ! ,potsdam catalogue1 to -#jm4#af4 ,x is fur!r necess>y to det]m9e ! scale-ratio4 ,our magnitudes = ! />s emanate f ,,ptolemy4 ,x 0 f\nd t ! scale-ratio--giv+ ! ratio ( ! light-int5sities ( two consecutive classes ( magnitudes--accord+ to ! old] values ( ! magnitudes1 0 approximately equal to #b4 ,:5 exact photometry began 7) in/rum5ts = measur+ ! magnitudes7 9 ! middle ( la/ c5tury1 ! scale-ratio 0 !re=e put equal to #b4e4 ,lat] x 0 f\nd m conv5i5t to *oose x equal to #b4eab1 ! log>i?m ( :i* numb] has ! value #j4d4 ,! magnitudes be+ !mselves log>i?ms ( a k9d1 x is evid5tly m conv5i5t to use a simple value ( ! log>i?m ( ! ratio ( int5sity ?an to use ?is ratio itself4 ,?is scale-ratio is (t5 call$ ! ,,pogson-scale 7us$ by ,,pogson 9 8 ,catalogue ( #ec kn[n v>iable />s1 ,a/r4 ,obs4 ( ! ,radcliffe ,obs]vatory1 #ahef71 & is n[ exclusively us$4 ,x foll[s f ! def9ition ( ! scale-ratio t two />s = :i* ! light int5sities are 9 ! ratio #ajj3a diff] by exactly #e magnitudes4 ,a /> ( ! #f? magnitude is #ajj times fa9t] ?an a /> ( ! fir/ magnitude1 a /> ( ! #aa? magnitude #ajjjj times1 ( ! #af? magnitude a million times1 & a /> ( ! #ba/ magnitude #ajj million times fa9t] ?an a /> ( ! fir/ magnitude4 ,! /> magnitudes are n[1 ) a c]ta9 res]vation = sy/ematic errors1 det]m9$ ) an accuracy ( #jm4#a1 & clos]4 ,evid5tly1 h[ev]1 !re w correspond to an error ( #j4a 9 ! magnitude a consid]able unc]ta9ty 9 ! light ratios1 :5 ^! diff] consid]ably f ea* o!r4 ,sun -#bfm4#fj ,full moon -#aam4#gg ,v5us - #dm4#bh ,jupit] - #bm4#ce ,m>s - #am4#gi ,m]cury - #jm4#ij ,saturn #jm4#hh ,uranus #em4#hf ,neptune #gm4#ff ,a consequ5ce ( ! def9ition ( m is t we also h to d ) negative magnitudes 7z well z ) negative log>i?ms74 ,?us1 = example1 = ,sirius m -#a4eh4 ,! magnitudes ( ! great] planets1 z well z ^? ( ! moon & ! sun1 are also negative1 z w be se5 f ! adjo9+ table1 :]e ! values are tak5 f ,die ,photometrie d] ,ge/irne by ,g4 ,m,,ll]4 ,! app>5t magnitude ( ! sun is giv5 by ,z,,lln] 7#ahfd74 ,! o!r values are all f\nd 9 ,potsdam1 & allude g5]ally to ! maximum value ( ! app>5t magnitude ( ! moon & ! planets4 ,! brighte/ /> is ,sirius1 :i* has ! magnitude m -#a4eh4 ,! magnitude ( ! fa9te/ visible /> evid5tly dep5ds on ! p5etrat+ p[] ( ! in/rum5t us$4 ,! telescope ( ,,william ,,h]s*el1 us$ by him & 8 son 9 _! />-gauges & o!r /ell> rese>*es1 all[$ ( ! disc]n+ ( />s d[n to ! #ad? magnitude4 ,! l>ge in/rum5ts ( our "t h>dly rea* mu* f>!r1 = visual obs]vations4 ,:51 h[ev]1 photographic plates are us$1 x is easily possible to get impressions ( fa9t] />s1 ev5 ) r mode/ in/rum5ts4 ,! l>ge #ajj-;in* mirror ( ! ,wilson ,obs]vatory r5d]s possible ! photographic obs]vations ( />s ( ! #bj? app>5t magnitude1 & ev5 fa9t]4 ,! obs]vations ( visual magnitudes are p]=m$ almo/ exclusively ) ! photomet] ( ,z,,lln] 9 a m or less improv$ =m4 #g4 ,absolute magnitude4 ,! app>5t magnitude ( a /> is *ang$ z ! /> *anges its di/ance f ! obs]v]1 ! int5sity increas+ indirectly z ! squ>e ( ! di/ance ( ! />4 ,9 ord] to make ! magnitudes ( ! />s comp>able ) ea* o!r x is conv5i5t to r$uce !m to _! value at a c]ta9 unit ( di/ance4 ,z su* we *oose "o siriomet]4 ,! correspond+ magnitude w be call$ ! absolute magnitude & is d5ot$ by ,m4#d ,we easily f9d f ! table giv5 9 ! prec$+ p>agraph t ! absolute magnitude ( ! sun1 accord+ to ,z,,lln]'s value ( m1 am\nts to #c4d1 ( ! moon to #ca4b4 ,= ,jupit] we f9d ,m #bd4f1 = ,v5us ,m #be4c4 ,! o!r planets h approximately ,m #cj4 ,= ! absolute magnitudes ( ^? />s = :i* x has hi!rto be5 possible to c>ry out a det]m9ation1 we f9d a value ( ,m betwe5 -#h & #ac4 ,we %all give 9 ! ?ird *apt] %ort tables ( ! absolutely brighte/ & fa9te/ />s n[ kn[n4 #h4 ,photographic magnitudes4 ,! magnitudes :i* h be5 m5tion$ 9 ! prec$+ p>agraphs all ref] to obs]vations tak5 ) ! eye1 & are call$ visual magnitudes4 ,! total int5sity ( a /> is1 h[ev]1 ess5tially dep5d5t on ! in/rum5t us$ 9 measur+ ! int5sity4 ,besides ! eye1 ! a/ronom]s use a photographic plate1 bolomet]1 a photo-electric cell1 & o!r in/rum5ts4 ,! diff]5ce 9 ! results obta9$ ) ^! in/rum5ts is due to ! circum/ance t diff]5t p>ts ( ! radiation are tak5 into acc\nt4 ,! usual photographic plates1 :i* h _! pr9cipal s5sibility 9 ! violet p>ts ( ! spectrum1 give u ! photographic magnitudes ( ! />s4 ,x is1 h[ev]1 to be rem>k$ t ^! magnitudes may v>y f "o plate to ano!r1 accord+ to ! di/ributive function ( ! plate 7comp>e ,l4 ,m4 #fg74 ,?is v>iation1 :i* has n yet be5 suffici5tly /udi$1 seems h[ev] to be r inconsid]able1 & mu/ be neglect$ 9 ! foll[+4 ,! photographic magnitude ( a /> w 9 ^! lectures be d5ot$ by m'1 correspond+ to a visual magnitude m4 ,9 practical a/ronomy use is also made ( plates :i*1 z ! result ( a c]ta9 prep>ation 79 col\r ba?s or 9 o!r ways71 h acquir$ a di/ributive function ne>ly correspond+ to t ( ! eye1 & especially h a maximum po9t at ! same wave-l5g?s4 ,su* magnitudes are call$ photo-visual 7comp>e ! memoir ( ,,p>khur/ 9 ,a4 ,j4 #cf #aiab74 ,! photographic magnitude ( a /> is g5]ally det]m9$ f measurem5ts ( ! diamet] ( ! /> on ! plate4 ,a simple ma!matical relation !n p]mits u to det]m9e m'4 ,! diamet] ( a /> image increases ) ! "t ( exposure4 ,?is increase is due 9 "p to ! diffraction ( ! telescope1 to imp]fect a*romatism or sph]ical ab]ration ( ! objective1 to irregul> gr9d+ ( ! glass1 & especially to v>iations 9 ! refraction ( ! air1 :i* produce an oscillation ( ! image ar\nd a mean position4 ,! z]o-po9t ( ! photographic magnitudes is s det]m9$ t ?is magnitude co9cides ) ! visual magnitude = su* />s z belong to ! spectral type ,a#j & h m #f4j1 accord+ to ! proposal ( ! int]national sol> conf]5ce at ,bonn1 #aiaa4 ,det]m9ations ( ! photographic or photo-visual magnitudes may n[ be c>ri$ out ) great accuracy4 ,! me?ods = ?is are _m & are well summ>is$ 9 ! ,report ( ! ,c\ncil ( ! ,r4 ,a4 ,s4 ( ! ye> #aiac4 ,! mo/ effective & f>-rea*+ me?od seems to be t propos$ by ,,s*w>zs*ild1 call$ ! half-grat+ me?od1 by :i* two exposures are tak5 ( ! same "p ( ! sky1 :ile at "o ( ! exposures a c]ta9 grat+ is us$ t r$uces ! magnitudes by a con/ant degree4 #i4 ,col\r ( ! />s4 ,! radiation ( a /> is diff]5t = diff]5t wave-l5g?s 7lambda74 ,z reg>d+ o!r mass ph5om5a we may !re=e m5tion3--7#a7 ! total radiation or int5sity 7,i71 7#b7 ! mean wave-l5g? 7lambda#j71 7#c7 ! disp]sion ( ! wave-l5g? 7sigma74 ,9 ! prec$+ p>agraphs we h treat$ ( ! total radiation ( ! />s z ?is is express$ ?r\gh _! magnitudes4 ,! mean wave-l5g? is pretty closely def9$ by ! col\r1 :]eas ! disp]sion ( ! wave-l5g? is f\nd f ! spectrum ( ! />s4 ,!re are blue 7,b71 :ite 7,w71 yell[ 7,y7 & r$ 7,r7 />s1 & int]m$iate col\rs4 ,! exact me?od is to def9e ! col\r ?r\gh ! mean wave-l5g? 7& n conv]sely7 or ! effective wave-l5g? z x is mo/ usually call$1 or f ! col\r-index4 ,we %all rev]t lat] to ?is "q4 ,!re are1 h[ev]1 a great _m direct eye-e/imates ( ! col\r ( ! />s4 ,col\r correspond+ to a giv5 spectrum4 ,sp4 ,col\r ,numb] ,b#c ,,yw- #afa ,a#j ,,yw- #ghh ,a#e ,,yw #aae ,f#e ,,yw1 ,,wy- #bie ,g#e ,,wy #baf ,k#e ,,wy1 ,y- #eeb ,m ,y1 ,y #ie ----------------------------- ,sum 444 #bbbb ,spectrum correspond+ to a giv5 col\r4 ,col\r ,sp4 ,numb] ,w1 ,w ,a#j #bha ,,yw- ,a#j #cef ,,yw ,a#e #dhb ,,yw1 ,,yw- ,f#c #baa ,,wy ,g#d #bfd ,,wy1 ,y- ,k#a #bhi ,y1 ,y ,k#d #bed ,,ry-1 ,,ry ,k#e #he -------------------------------- ,sum 444 #bbbb ,! signs & - indicate int]m$iate %ades ( col\r4 ,! prec$+ table drawn up by ,dr4 ,,malmqui/ f ! col\r obs]vations ( ,m,,ll] & ,,kempf 9 ,potsdam1 %[s ! connection betwe5 ! col\rs ( ! />s & _! spectra4 ,! ,potsdam obs]vations conta9 all />s nor? ( ! cele/ial equator hav+ an app>5t magnitude bright] ?an #gm4#e4 ,we f9d f ^! tables t !re is a well-pron\nc$ regression 9 ! correlation betwe5 ! spectra & ! col\rs ( ! />s4 ,tak+ toge!r all :ite />s we f9d ! correspond+ mean spectral type to be ,a#j1 b to ,a#j corresponds1 ^u an av]age1 ! col\r yell[-:ite4 ,! yell[ />s belong 9 ! mean to ! ,k-type1 b ! ,k-/>s h ^u an av]age a %ade ( :ite 9 ! yell[ col\r4 ,! coeffici5t ( correlation 7r7 is n easy to compute 9 ?is case1 because "o ( ! attributes1 ! col\r1 is n /rictly graduat$ 7i4e4 x is n express$ 9 numb]s def9+ ! col\r74#e ,us+ ! coeffici5t ( cont+5cy ( ,,pe>son1 x is1 h[ev]1 possible to f9d a fairly reliable value ( ! coeffici5t ( correlation1 & ,,malmqui/ has 9 ?is way f\nd r #j4he1 a r high value4 ,9 ord] to facilitate ! discussion ( ! relation betwe5 col\r & spectrum x is conv5i5t to deal "h ) ! "q ( ! spectra ( ! />s4 #aj4 ,spectra ( ! />s4 ,9 ord] to introduce ! discussion ,i fir/ give a li/ ( ! wave-l5g?s ( ! ,,frau5h(] l9es 9 ! spectrum1 & ! correspond+ *emical elem5ts4 ,,frau5h(] l9e ,elem5t lambda ,a #gei4d ,b #fhf4h ,c7alpha7 ,h 7hydrog57 #fef4c ,d#a ,na 7sodium7 #ehi4f ,d#c ,he #ehg4f ,e ,fe 7iron7 #ebg4j ,f7beta7 ,h #dhf4b 7gamma7 ,h #dcd4a ,g ,ca 7calcium7 #dcj4h h7delta7 ,h #daj4b ,h7epsilon7 ,ca7,h7 #cif4i ,k ,ca #cic4d ,! fir/ column gives ! ,,frau5h(] d5om9ation ( ea* l9e4 ,moreov] ! hydrog5 l9es alpha1 beta1 gamma1 delta1 epsilon are d5ot$4 ,! second column gives ! "n ( ! correspond+ elem5t1 to :i* ea* l9e is to be attribut$4 ,! ?ird column gives ! wave-l5g? express$ 9 million?s ( a millimet] z unit 7mumu74 ,on plate ,,iii1 :]e ! classification ( ! /ell> spectra accord+ to ! ,h>v>d sy/em is reproduc$1 w be f\nd also ! wave-l5g?s ( ! pr9cipal ,h & ,he l9es4 ,by ! visual spectrum is usually und]/ood ! "p ( ! radiation betwe5 ! ,,frau5h(] l9es ,a to ,h 7lambda #gfj to #djj mumu71 :]eas ! photographic spectrum g5]ally lies betwe5 ,f & ,k 7lambda #ejj to #djj mumu74 ,9 ! e>lie/ days ( spectroscopy ! spectra ( ! />s 7 classifi$ accord+ to _! visual spectra4 ,?is classification 0 introduc$ by ,,sec*i & 0 lat] m precisely def9$ by ,,vogel4 ,! ?ree classes ,i1 ,,ii1 ,,iii ( ,,vogel correspond approximately to ! col\r classification into :ite1 yell[1 & r$ />s4 ,photography has n[ almo/ entirely tak5 ! place ( visual obs]vations ( spectra1 s t ,,sec*i's & ,,vogel's def9itions ( ! /ell> spectra are no long] applicable4 ,! t]m9ology n[ us$ 0 introduc$ by ,,pick]+ & ,miss ,,cannon & embraces a great _m types1 ( :i* we "h describe ! pr9cipal =ms z !y are def9$ 9 ,"p4 ,,ii ( ,vol4 ,,xxviii ( ! ,annals ( ! ,h>v>d ,obs]vatory4 ,x may be rem>k$ t ,,pick]+ fir/ arrang$ ! types 9 alphabetical ord] ,a1 ,b1 ,c1 c41 suppos+ t ord] to correspond to ! temp]ature ( ! />s4 ,lat] ?is 0 f\nd to be p>tly wrong1 & 9 p>ticul> x 0 f\nd t ! ,b-/>s may be hott] ?an ^? ( type ,a4 ,! foll[+ is ! temp]ature-ord] ( ! spectra accord+ to ! op9ion ( ! ,h>v>d a/ronom]s4 ,type ,o 7,,wolf-,,rayet />s74 ,! spectra ( ^! />s consi/ ma9ly ( bright l9es4 ,!y are *>act]iz$ by ! bright b&s at wave-l5g?s #dfc mumu & #dfi mumu1 & ! l9e at #eja mumu *>act]i/ic ( gase\s nebulae is sometimes pres5t4 ,?is type embraces ma9ly />s ( relatively small app>5t brightness4 ,! brighte/ is gamma ,velorum ) m #b4bb4 ,we %all f9d t ! absolute magnitude ( ^! />s ne>ly co9cides ) t ( ! />s ( type ,b4 ,! type is gr\p$ into five subdivisions repres5t$ by ! lett]s ,oa1 ,ob1 ,oc1 ,od & ,oe4 ,^! subdivisions are condition$ by ! v>y+ int5sities ( ! bright b&s nam$ above4 ,! due sequ5ce ( ^! sub-types is = ! pres5t an op5 "q4 ,among int]e/+ />s ( ?is type is zeta ,puppis 7,od71 9 ! spectrum ( :i* ,,pick]+ discov]$ a previ\sly unkn[n s]ies ( helium l9es4 ,!y 7 at fir/ attribut$ 7by ,,rydb]g7 to hydrog5 & 7 call$ additional l9es ( hydrog54 ,type ,b 7,orion type1 ,helium />s74 ,all l9es are "h d>k4 ,besides ! hydrog5 s]ies we "h f9d ! ,he-l9es 7#cif1 #djc1 #dab1 #dad1 #ddg1 #dga1 #dic mumu74 ,to ?is type belong all ! bright />s 7beta1 gamma1 delta1 epsilon1 zeta1 eta & o!rs7 9 ,orion ) ! exception ( ,betelgeuze4 ,fur!r1 ,spica & _m o!r bright />s4 ,on plate ,,iii epsilon ,orionis is tak5 z repres5tative ( ?is type4 ,type ,a 7,sirius type7 is *>act]iz$ by ! great int5sity ( ! hydrog5 l9es 7comp>e plate ,,iii74 ,! helium l9es h vani%$4 ,o!r l9es visible b fa9tly4 ,! great] "p ( ! />s visible to ! nak$ eye are f\nd "h4 ,!re are #abea />s bright] ?an ! #f? magnitude :i* belong to ?is type4 ,sirius1 ,vega1 ,ca/or1 ,altair1 ,d5eb & o!rs are all ,a-/>s4 ,type ,f 7,calcium type74 ,! hydrog5 l9es /ill r prom95t b n s broad z 9 ! prec$+ type4 ,! two calcium l9es ,h & ,k 7#cif4i1 #cic4d mumu7 /rongly pron\nc$4 ,among ! />s ( ?is type are f\nd a great _m bright />s 7comp>e ! ?ird *apt]71 su* z ,pol>is1 ,canopus1 ,procyon4 ,type ,g 7,sun type74 ,num]\s metallic l9es toge!r ) relatively fa9t hydrog5 l9es4 ,to ?is class belong ! sun1 ,capella1 alpha ,c5tauri & o!r bright />s4 ,type ,k4 ,! hydrog5 l9es /ill fa9t]4 ,! ,k-l9e atta9s its maximum int5sity 7is n especially pron\nc$ 9 ! figure ( plate ,,iii74 ,?is is1 next to ! ,a-type1 ! mo/ num]\s type 7#aadb />s7 among ! bright />s4 ,we f9d "h gamma ,&rom$1 beta ,aquil1 ,arcturus1 alpha ,cassiopei1 ,pollux & ,aldeb>an1 :i* la/ =ms a transition to ! next type4 ,type ,m4 ,! spectrum is b&$ & belongs to ,,sec*i's ?ird type4 ,! flut+s are due to titanium oxide4 ,only #aij ( ! />s visible to ! nak$ eye belong to ?is type4 ,g5]ally !y are r fa9t1 b we "h f9d ,betelgeuze1 alpha ,h]culis1 beta ,pegasi1 alpha ,scorpii 7,ant>es7 & mo/ v>iables ( long p]iod1 :i* =m a special sub-type ,md1 *>act]iz$ by bright hydrog5 l9es toge!r ) ! flut+s4 ,type ,m has two o!r sub-types ,ma & ,mb4 ,type ,n 7,,sec*i's f\r? type74 ,b&$ spectra4 ,! flut+s are due to comp\nds ( c>bon4 ,"h are f\nd only fa9t />s4 ,! total numb] is #bda4 ,all are r$4 #bg />s hav+ ?is spectrum are v>iables ( long p]iod ( ! same type z ,md4 ,! spectral types may be summ$ up 9 ! foll[+ way3-- ,:ite />s3--,,sec*i's type ,i3--,h>v>d ,b & ,a1 ,yell[ 3-- ,,ii3-- ,f1 ,g & ,k1 ,r$ 3-- ,,iii3-- ,m1 3-- ,,iv3-- ,n4 ,! ,h>v>d a/ronom]s d n conf9e !mselves to ! types m5tion$ above1 b fill up ! int]vals betwe5 ! types ) sub-types :i* are designat$ by ! "n ( ! type foll[$ by a num]al #j1 #a1 #b1 4441 #i4 ,?us ! sub-types betwe5 ,a & ,f h ! designations ,a#j1 ,a#a1 ,a#b1 4441 ,a#i1 ,f#j1 c4 ,exceptions are made z already indicat$1 = ! extreme types ,o & ,m4 #aa4 ,spectral index4 ,x may be ga!r$ f ! above description t ! def9ition ( ! types implies _m vague mom5ts4 ,especially 9 reg>d to ! ,g-type are v diff]5t def9itions inde$ accept$1 ev5 at ,h>v>d4#f ,x is also a defect t ! def9itions d n directly give quantitative *>act]i/ics ( ! spectra4 ,none ! less x is possible to sub/itute = ! spectral classes a cont9u\s scale express+ ! spectral "* ( a />4 ,su* a scale is inde$ implicit 9 ! ,h>v>d classification ( ! spectra4 ,let u use ! t]m spectral index 7s7 to def9e a numb] express+ ! spectral "* ( a />4 ,!n we may conv5i5tly def9e ?is conception 9 ! foll[+ way4 ,let ,a#j correspond to ! spectral index s #j4j1 ,f#j to s #a4j1 ,g#j to s #b4j1 ,k#j to s #c4j ,m#j to s #d4j & ,b#j to s -#a4j4 ,fur!r1 let ,a#a1 ,a#b1 ,a#c1 c41 h ! spectral indices #j4a1 #j4b1 #j4c1 c41 & 9 l mann] ) ! o!r int]m$iate sub-classes4 ,!n x is evid5t t to all spectral classes betwe5 ,b#j & ,m !re corresponds a c]ta9 spectral index s4 ,! extreme types ,o & ,n are n "h includ$4 ,_! spectral indices may h[ev] be det]m9$1 z w be se5 lat]4 ,?\gh ! spectral indices1 def9$ 9 ?is mann]1 are directly kn[n = e spectral type1 x is nev]!less n obvi\s t ! s]ies ( spectral indices corresponds to a cont9u\s s]ies ( values ( "s attribute ( ! />s4 ,?is may be se5 to be possible f a comp>ison ) ano!r attribute :i* may be r m>k$ly graduat$1 namely ! col\r ( ! />s4 ,we %all discuss ?is po9t 9 ano!r p>agraph4 ,to obta9 a well graduat$ scale ( ! spectra x w f9ally be necess>y to *ange to "s ext5t ! def9itions ( ! spectral types1 a *ange :i*1 h[ev]1 has n yet be5 accompli%$4 #ab4 ,we h f\nd 9 #i t ! light-radiation ( a /> is describ$ by means ( ! total int5sity 7,i71 ! mean wave-l5g? 7lambda#j7 & ! disp]sion ( ! wave-l5g? 7sigmalambda74 lambda#j & sigmalambda may be d$uc$ f ! spectral obs]vations4 ,x mu/ "h be obs]v$ t ! obs]vations give1 n ! int5sities at diff]5t wave-l5g?s b1 ! values ( ^! int5sities z !y are appreh5d$ by ! in/rum5ts employ$--! eye or ! photographic plate4 ,= ! d]ivation ( ! true curve ( int5sity we mu/ "k ! di/ributive function ( ! in/rum5t 7,l4 ,m4 #fg74 ,z to ! eye1 we h reason to believe1 f ! bolometric obs]vations ( ,,langley 7#ahhh71 t ! mean wave-l5g? ( ! visual curve ( int5sity ne>ly co9cides ) t ( ! true int5sity-curve1 a conclusion easily und]/ood f ,,d>w9's pr9ciples ( evolution1 :i* dem& t ! human eye 9 ! c\rse ( "t %all be develop$ 9 su* a way t ! mean wave-l5g? ( ! visual int5sity curve does co9cide ) t ( ! true curve 7lambda #ecj mumu71 :5 ! greate/ visual en]gy is obta9$ 7,l4 ,m4 #fg74 ,z to ! disp]sion1 ?is is always great] 9 ! true int5sity-curve ?an 9 ! visual curve1 = :i*1 accord+ to #aj1 x am\nts to approximately #fj mumu4 ,we f\nd inde$ t ! visual int5sity curve is ext5d$1 approximately1 f #djj mumu to #gfj mumu1 a six? "p ( :i* int]val1 approximately1 corresponds to ! disp]sion sigma ( ! visual curve4 ,9 ! case ( ! photographic int5sity-curve ! circum/ances are diff]5t4 ,! mean wave-l5g? ( ! photographic curve is1 approximately1 #dej mumu1 ) a disp]sion ( #af mumu1 :i* is consid]ably small] ?an 9 ! visual curve4 #ac4 ,bo? ! visual & ! photographic curves ( int5sity diff] accord+ to ! temp]ature ( ! radiat+ body & are !re=e diff]5t = />s ( diff]5t spectral types4 ,"h ! mean wave-l5g? foll[s ! =mula ( ,,wi51 :i* says t ?is wave-l5g? v>ies inv]sely z ! temp]ature4 ,! total int5sity1 accord+ to ! law ( ,,/ephan1 v>ies directly z ! f\r? p[] ( ! temp]ature4 ,ev5 ! disp]sion is dep5d5t on ! v>iation ( ! temp]ature--directly z ! mean wave-l5g?1 inv]sely z ! temp]ature ( ! /> 7,l4 ,m4 #da7--s t ! mean wave-l5g?1 z well z ! disp]sion ( ! wave-l5g?1 is small] = ! hot />s ,o & ,b ?an = ! cool] ones 7,k & ,m types74 ,x is 9 ?is mann] possible to det]m9e ! temp]ature ( a /> f a det]m9ation ( its mean wave-l5g? 7lambda#j7 or f ! disp]sion 9 lambda4 ,su* det]m9ations 7f lambda#j7 h be5 made by ,,s*e9] & ,,wils+ 9 ,potsdam1 by ,,ros5b]g & o!rs1 ?\gh ^! rese>*es /ill h to be develop$ to a great] degree ( accuracy4 #ad4 ,effective wave-l5g?4 ,! mean wave-l5g? ( a spectrum1 or1 z x is (t5 call$ by ! a/ronom]s1 ! effective wave-l5g?1 is g5]ally det]m9$ 9 ! foll[+ way4 ,on acc\nt ( ! refraction 9 ! air ! image ( a /> is1 )\t ! use ( a spectroscope1 really a spectrum4 ,aft] "s "t ( exposure we get a some:at r\nd image1 ! position ( :i* is det]m9$ precisely by ! mean wave-l5g?4 ,?is me?od is especially us$ ) a s-call$ objective-grat+1 :i* consi/s ( a s]ies ( metallic ?reads1 /ret*$ p>allel to ea* o!r at equal int]vals4 ,on acc\nt ( ! diffraction ( ! light we n[ get 9 ! focal plane ( ! objective1 ) ! use ( ^! grat+s1 n only a fa9t] image ( ! /> at ! place :]e x w\ld h aris5 )\t grat+1 b also at bo? sides ( ?is image second>y images1 ! di/ances ( :i* f ! c5tral /> are c]ta9 !oretically kn[n multiples ( ! effective wave-l5g?s4 ,9 ?is simple mann] x is possible to det]m9e ! effective wave-l5g?1 & ?is be+ a tol]ably well-kn[n function ( ! spectral-index1 ! latt] c also be f\nd4 ,?is me?od 0 fir/ propos$ by ,,h]tzsprung & has be5 ext5sively us$ by ,,b]g/r&1 ,,lundm>k & ,,l9dblad at ! obs]vatory ( ,upsala & by o!rs4 #ae4 ,col\r-index4 ,we h already po9t$ out 9 #i t ! col\r may be id5tifi$ ) ! mean wave-l5g? 7lambda#j74 ,z fur!r lambda#j is closely connect$ ) ! spectral index 7s71 we may use ! spectral index to repres5t ! col\r4 ,in/ead ( s !re may also be us$ ano!r expression = ! col\r1 call$ ! col\r-index4 ,?is expression 0 fir/ introduc$ by ,,s*w>zs*ild1 & is def9$ 9 ! foll[+ way4 ,we h se5 t ! z]o-po9t ( ! photographic scale is *os5 9 su* a mann] t ! visual magnitude m & ! photographic magnitude m' co9cide = />s ( spectral index #j4j 7,a#j74 ,! photographic magnitudes are !n unequivocally det]m9$4 ,x is f\nd t _! values sy/ematically diff] f ! visual magnitudes1 s t = type ,b 7& ,o7 ! photographic magnitudes are small] ?an ! visual1 & ! contr>y = ! o!r types4 ,! diff]5ce is greate/ = ! ,m-type 7/ill great] = ! ,n-/>s1 ?\gh "h = ! pres5t only a few det]m9ations are kn[n71 = :i* />s if am\nts to ne>ly two magnitudes4 ,s mu* fa9t] is a r$ /> on a photographic plate ?an :5 obs]v$ ) ! eye4 ,! diff]5ce betwe5 ! photographic & ! visual magnitudes is call$ ! col\r-index 7c74 ,! correlation betwe5 ?is index & ! spectral-index is f\nd to be r high 7r #j4if74 ,9 ,l4 ,m4 ,,ii1 #ai ,i h d$uc$ ! foll[+ tables giv+ ! spectral-type correspond+ to a giv5 col\r-index1 & inv]sely4 ,,table #a4 ,,giv+ ,,! ,,mean ,,col\r-,,index ,,correspond+ ,,to ,a ,,giv5 ,,spectral ,,type ,,or ,,spectral ,,index4 ----------------------------------- ,spectral ,col\r-index type index ---------------------------------- ,b#j -#a4j -#j4df ,b#e -#j4e -#j4bc ,a#j #j4j #j4jj ,a#e #j4e #j4bc ,f#j #a4j #j4df ,f#e #a4e #j4fi ,g#j #b4j #j4ib ,g#e #b4e #a4ae ,k#j #c4j #a4ch ,k#e #c4e #a4fa ,m#j #d4j #a4hd ---------------------------------- ,,table #a994 ,,giv+ ,,! ,,mean ,,spectral ,,index ,,correspond+ ,,to ,a ,,giv5 ,,col\r-,,index4 ----------------------------------- ,col\r-index ,spectral index type ---------------------------------- -#j4d -#j4gj ,b#c -#j4b -#j4hj ,b#g #j4j #j4aj ,a#a #j4b #j4ej ,a#e #j4d #j4ij ,a#i #j4f #a4cj ,f#c #j4h #a4gj ,f#g #a4j #b4aj ,g#a #a4b #b4ej ,g#e #a4d #b4ij ,g#i #a4f #c4cj ,k#c #a4h #c4gj ,k#g #b4j #d4aj ,m#a ---------------------------------- ,f ea* catalogue ( visual magnitudes ( ! />s we may obta9 _! photographic magnitude ?r\gh add+ ! col\r-index4 ,?is may be consid]$ z kn[n 7tak+ into acc\nt ! high coeffici5t ( correlation betwe5 s & c7 z soon z we "k ! spectral type ( ! />4 ,we may conclude directly t ! numb] ( />s hav+ a photographic magnitude bright] ?an #f4j is consid]ably small] ?an ! numb] ( />s visually bright] ?an ?is magnitude4 ,!re are1 inde$1 #dgja />s = :i* m #f4j & #bhgd />s hav+ m' #f4j4 #af4 ,radial velocity ( ! />s4 ,f ! values ( alpha & delta at diff]5t times we obta9 ! compon5ts ( ! prop] motions ( ! />s p]p5dicul> to ! l9e ( sight4 ,! ?ird compon5t 7,w71 9 ! radial direction1 is f\nd by ! ,,doppl] pr9ciple1 ?r\gh measur+ ! displacem5t ( ! l9es 9 ! spectrum1 ?is displacem5t be+ t[>ds ! r$ or ! violet accord+ z ! /> is rec$+ f or approa*+ ! obs]v]4 ,! velocity ,w w be express$ 9 siriomet]s p] /ell> ye> 7sir4_//47 & alt]nately also 9 km4_/sec4 ,! rate ( conv]sion ( ^! units is giv5 9 #e4 #ag4 ,summ+ up ! rem>ks "h giv5 on ! app>5t attributes ( ! />s we f9d !m ref]r$ to ! foll[+ pr9cipal gr\ps3-- ,i4 ,! position ( ! />s is "h g5]ally giv5 9 galactic longitude 7l7 & latitude 7b74 ,moreov] _! equatorial coord9ates 7alpha & delta7 are giv5 9 an abridg$ notation 7alphadelta71 :]e ! fir/ f\r numb]s give ! "r asc5sion 9 h\rs & m9utes & ! la/ two numb]s give ! decl9ation 9 degrees1 ! latt] be+ pr9t$ 9 italics if ! decl9ation is negative4 ,ev5tually ! position is giv5 9 galactic squ>es1 z def9$ 9 #b4 ,,ii4 ,! app>5t motion ( ! />s w be giv5 9 radial compon5ts 7,w7 express$ 9 sir4_//4 & _! motion p]p5dicul> to ! l9e ( sight4 ,^! compon5ts w be express$ 9 "o compon5t 7u#j7 p>allel to ! galactic plane1 & "o compon5t 7v#j7 p]p5dicul> to x4 ,if ! di/ance 7r7 is kn[n we are able to conv]t ^! compon5ts into compon5ts ( ! l9e> velocity p]p5dicul> to ! l9e ( sight 7,u & ,v74 ,,iii4 ,! int5sity ( ! light ( ! />s is express$ 9 magnitudes4 ,we may di/+ui% betwe5 ! app>5t magnitude 7m7 & ! absolute magnitude 7,m71 ! latt] be+ equal to ! value ( ! app>5t magnitude suppos+ ! /> to be situat$ at a di/ance ( "o siriomet]4 ,! app>5t magnitude may be ei!r ! photographic magnitude 7m'71 obta9$ f a photographic plate1 or ! visual magnitude 7m7 obta9$ ) ! eye4 ,! diff]5ce betwe5 ^! magnitudes is call$ ! col\r-index 7c m'-m74 ,,iv4 ,! *>act]i/ics ( ! /ell> radiation are ! mean wave-l5g? 7lambda#j7 & ! disp]sion 7sigma7 9 ! wave-l5g?4 ,! mean wave-l5g? may be ei!r directly det]m9$ 7p]haps z effective wave-l5g?7 or f\nd f ! spectral type 7spectral index7 or f ! col\r-index4 ,!re are 9 all eight attributes ( ! />s :i* may be f\nd f ! obs]vations3--! sph]ical position ( ! /> 7l1 b71 its di/ance 7r71 prop] motion 7u#j & v#j71 radial velocity 7,w71 app>5t magnitude 7m or m'71 absolute magnitude 7,m71 spectral type 7,sp7 or spectral index 7s71 & col\r-index 7c74 ,( ^! ! col\r-index1 ! spectral type1 ! absolute magnitude & also 7to a c]ta9 degree7 ! radial velocity may be consid]$ z indep5d5t ( ! place ( ! obs]v] & may !re=e be consid]$ n z only app>5t b also z absolute attributes ( ! />s4 ,betwe5 ?ree ( ^! attributes 7m1 ,m & r7 a ma!matical relation exi/s s t "o ( !m is kn[n z soon z ! o!r two h be5 f\nd f obs]vations4 ,,footnotes3 ,footnote #a3 ,m$del&5 frn ,lunds ,obs]vatorium1 ,no4 #da4 ,footnote #b3 ,m$del&5 frn ,lunds ,a/ronomiska ,obs]vatorium1 ,s]ie ,,ii1 ,no4 #ad4 ,footnote #c3 ,annals ( ! ,h>v>d ,obs]vatory1 vol4 #ej4 ,footnote #d3 ,9 ord] to d$uce f ,m ! app>5t magnitude at a di/ance correspond+ to a p>allax ( #a we may subtract #cm4#dh4 ,to obta9 ! magnitude correspond+ to a p>allax ( #j4a we may add #a4eg4 ,! latt] di/ance is *os5 by "s writ]s on /ell> /ati/ics4 ,footnote #e3 ,! be/ col\r-scale ( ! latt] sort seems to be t ( ,,o/h(f4 ,footnote #f3 ,comp>e ,h4 ,a4 #ej & ,h4 ,a4 #ef & ! rem>ks 9 ,l4 ,m4 ,,ii1 #ai4 ,,*apt] ,,ii4 ,,s\rces ,,( ,,our ,,pres5t ,,k ,,( ,,! ,,/>s4 #ah4 ,9 ?is *apt] ,i %all give a %ort acc\nt ( ! publications 9 :i* ! mo/ complete in=mation on ! attributes ( ! />s may be obta9$1 ) %ort notices ( ! cont5ts & g5esis ( ^! publications4 ,x is1 h[ev]1 n my int5tion to give a hi/ory ( ^! rese>*es4 ,we %all consid] m p>ticul>ly ! que/ions relat+ to ! position ( ! />s1 _! motion1 magnitude1 & spectra4 #ai4 ,place ( ! />s4 ,dur*mu/]ungs4 ,! mo/ complete data on ! position ( ! />s are obta9$ f ! /> catalogues kn[n z ,dur*mu/]ungs4 ,!re are two su* catalogues1 :i* toge!r cov] ! :ole sky1 "o--visual--p]=m$ 9 ,bonn & call$ ! ,bonn] ,dur*mu/]ung 7,b4 ,d471 ! o!r--photographic--p]=m$ 9 ,cape ,! ,cape ,photographic ,dur*mu/]ung 7,c4 ,p4 ,d474 ,z ! fir/ ( ^! catalogues has long be5--& is to "s ext5t ev5 n[--our pr9cipal s\rce = ! /udy ( ! sky & is moreov] ! fir/ ent]prise ( ?is k9d1 ,i %all give a some:at detail$ acc\nt ( its orig9 & cont5ts1 z relat$ by ,,argel&] 9 ! introduction to ! ,b4 ,d4 ,b4 ,d4 0 plann$ & p]=m$ by ! ,sw$i%-,f9n ,,argel&] 7born 9 ,memel #agii74 ,a s*ol> ( ,,bessel he 0 fir/ call$ z director 9 bo1 !n 9 ,hls+=s1 & f !re w5t 9 #ahcf to ,bonn1 :]e 9 ! ye>s #aheb to #ahef he p]=m$ ?is great ,dur*mu/]ung4 ,z in/rum5t he us$ a ,,frau5h(] comet-seek] ) an ap]ture ( #gf mm1 a focal l5g? ( #fej mm1 & #aj times magnify+ p[]4 ,! field ( sight _h an ext5sion ( #f4 ,9 ! focus ( ! objective 0 a semicircul> piece ( ?9 glass1 ) ! edge 7 ! diamet] ( ! semicircle7 p>allel to ! circle ( decl9ation4 ,?is edge 0 %>ply gr\nd1 s t x =m$ a n>r[ d>k l9e p]ceptible at /> illum9ation4 ,p]p5dicul> to ?is diamet] 7! h\r-l9e7 7 #aj l9es1 at ea* side ( a middle l9e1 drawn at a di/ance ( #g'4 ,^! l9es 7 drawn ) black oil col\r on ! glass4 ,! obs]vations are p]=m$ by ! obs]v] ,a & 8 assi/ant ,b4 ,a is 9 a d>k room1 lies on a *air hav+ ! eye at ! ocul> & c easily look ov] #b 9 decl9ation4 ,! assi/ant sits 9 ! room bel[1 sep>at$ by a bo>d floor1 at ! ,?i$e clock4 ,f ! beg9n+ ( ! obs]vations ! decl9ation circle is fix$ at a c]ta9 decl9ation 7:ole degrees74 ,all />s pass+ ! field at a di/ance small] ?an "o degree f ! middle l9e are obs]v$4 ,h5ce ! "n ,dur*mu/]ung4 ,:5 a /> passes ! h\r l9e ! magnitude is call$ out by ,a1 & not$ by ,b toge!r ) ! "t ( ! clock4 ,simultane\sly ! decl9ation is not$ by ,a 9 ! d>kness4 ,on "s occasions #cj />s may be obs]v$ 9 a m9ute4 ,! fir/ obs]vation 0 made on ,febr4 #be1 #aheb1 ! la/ on ,m>* #bg1 #ahei4 ,9 all !re 7 #fbe obs]vation nights ) #ahda zones4 ,! total numb] ( />s 0 #cbdaih4 ,! catalogue 0 publi%$ by ,,argel&] 9 ?ree p>ts 9 ! ye>s #ahei1 #ahfa & #ahfbg & embraces all />s betwe5 ! pole & #b s\? ( ! equator bright] ?an #im4#e1 accord+ to ! scale ( ,,argel&] 78 aim 0 to regi/] all />s up to ! #i? magnitude74 ,to ?is scale we return lat]4 ,! catalogue is arrang$ 9 accordance ) ! decl9ation-degrees1 & = ea* degree accord+ to ! "r asc5sion4 ,quotations f ,b4 ,d4 h ! =m ,b4 ,d4 #bc4agd1 :i* signifies3 ,zone #bc1 /> ,no4 #agd4 ,,argel&]'s "w 0 cont9u$ = />s betwe5 delta -#b & delta -#bc by ,,s*,,nfeld1 accord+ to mu* ! same plan1 b ) a l>g] in/rum5t 7ap]ture #aei mm1 focal l5g? #aicj mm1 magnify+ p[] #bf times74 ,! obs]vations 7 made 9 ! ye>s #ahgf to #ahha & include #accfei />s4#h ,! positions 9 ,b4 ,d4 are giv5 9 t5?s ( a second 9 "r asc5sion & 9 t5?s ( a m9ute 9 decl9ation4 #bj4 ,! ,cape ,photographic ,dur*mu/]ung#i 7,c4 ,p4 ,d474 ,?is embraces ! :ole s\!rn sky f -#ah to ! s\? pole4 ,plann$ by ,,gill1 ! photographs 7 tak5 at ! ,cape ,obs]vatory ) a ,,dallmey] l5s ) #ae cm4 ap]ture & a focal-l5g? ( #ace cm4 ,plates ( #cj #cj cm4 give ! coord9ates = a surface ( #e #e squ>e degrees4 ,! photographs 7 tak5 9 ! ye>s #ahhe to #ahij4 ,! measurem5ts ( ! plates 7 made by ,,kapteyn 9 ,gron+5 ) a p>allactic measur+-app>atus specially con/ruct$ = ?is purpose1 :i* p]mits ( ! direct obta9+ ( ! "r asc5sion & ! decl9ation ( ! />s4 ,! measurem5ts 7 made 9 ! ye>s #ahhf to #ahih4 ,! catalogue 0 publi%$ 9 ?ree p>ts 9 ! ye>s #ahif to #aijj4 ,! positions h ! same accuracy z 9 ,b4 ,d4 ,! :ole numb] ( />s is #dedhge4 ,,kapteyn consid]s ! catalogue complete to at lea/ ! magnitude #im4#b4 ,9 ! two great catalogues ,b4 ,d4 & ,c4 ,p4 ,d4 we h all />s regi/]$ d[n to ! magnitude #i4j 7visually7 & a good way bel[ ?is limit4 ,probably z f> z to #ajm4 ,a ?ird great ,dur*mu/]ung has = "s "t be5 9 prep>ation at ,cordoba 9 ,arg5t9a4#aj ,x cont9ues ! s\!rn zones ( ,,s*,,nfeld & is = ! pres5t complet$ up to #fb s\!rn decl9ation4 ,all ^! ,dur*mu/]ungs are ultimately bas$ on /> catalogues ( small] ext5t & ( great precision4 ,( ^! catalogues we %all n "h speak 7,comp>e1 h[ev]1 #bc74 ,a great ,dur*mu/]ung1 t w include all />s to ! #aa? magnitude1 has = ! la/ ?irty ye>s be5 9 progress at diff]5t obs]vatories propos$ by ! congress 9 ,p>is1 #ahhh4 ,! obs]vations proce$ v irregul>ly1 & !re is little prospect ( gett+ ! "w f9i%$ 9 an appreciable "t4 #ba4 ,/> *>ts4 ,= ! pres5t we possess two great photographic /> *>ts1 embrac+ ! :ole heav53--,! ,h>v>d ,map 7,h4 ,m47 & ! ,,frankl9-,,adams ,*>ts 7,f4 ,a4 ,c474 ,! ,h>v>d ,map1 ( :i* a copy 7or m correctly two copies7 on glass has k9dly be5 plac$ at ! disposal ( ! ,lund ,obs]vatory by ,mr4 ,,pick]+1 embraces all />s d[n to ! #aa? magnitude4 ,x consi/s ( #ee plates1 ea* embrac+ m ?an #ijj squ>e degrees ( ! sky4 ,! photographs 7 tak5 ) a small l5s ( only #b4e cms4 ap]ture & ab\t #cb4e cms4 focal-l5g?4 ,! "t ( exposure 0 "o h\r4 ,^! plates h be5 c\nt$ at ! ,lund ,obs]vatory by ,hans ,,h5ie4 ,we return lat] to ^! c\nts4 ,! ,,frankl9-,,adams ,*>ts 7 made by an amateur a/ronom] ,,frankl9-,,adams1 p>tly at 8 own obs]vatory 7,m]vel ,hill7 9 ,engl&1 p>tly 9 ,cape & ,johannesburg1 ,transvaal1 9 ! ye>s #aije-aiab4 ,! photographs 7 tak5 ) a ,taylor l5s ) #be cm4 ap]ture & a focal-l5g? ( #aad cm41 :i* gives r good images on a field ( #ae #ae squ>e degrees4 ,! :ole sky is "h reproduc$ on1 9 all1 #bjf plates4 ,ea* plate 0 expos$ = #b h\rs & #bj m9utes & gives images ( ! />s d[n to ! #ag? magnitude4 ,! orig9al plates are n[ at ! obs]vatory 9 ,gre5wi*4 ,"s copies on pap] h be5 made1 ( :i* ! ,lund ,obs]vatory possesses "o4 ,x %[s />s d[n to ! #ad?-#ae? magnitudes & gives a spl5did survey ( ! :ole sky m complete1 inde$1 ?an c be obta9$1 ev5 = ! nor? sky1 by direct obs]vation ( ! heav5s ) any telescope at pres5t accessible 9 ,sw$54 ,! ,f4 ,a4 ,c4 h be5 c\nt$ by ! a/ronom]s ( ! ,lund ,obs]vatory1 s t ?us a complete c\nt ( ! numb] ( />s = ! :ole heav5 d[n to ! #ad? magnitude has be5 obta9$4 ,we %all lat] h an opportunity ( discuss+ ! results ( ^! c\nts4 ,a great /> map is plann$ 9 connection ) ! ,p>is catalogue m5tion$ 9 ! prec$+ p>agraph4 ,?is ,c>te du ,ciel 7,c4 d4 ,c47 is /ill unf9i%$1 b !re seems to be a possibility t we %all "o day see ?is "w c>ri$ to completion4 ,x w embrace />s d[n to ! #ad? magnitude & ?us does n rea* s f> z ! ,f4 ,a4 ,c41 b on ! o!r h& is c>ri$ out on a consid]ably great] scale & gives bett] images ?an ,f4 ,a4 ,c4 & w !re=e be ( a great value 9 ! future1 especially = ! /udy ( ! prop] motions ( ! />s4 #bb4 ,di/ance ( ! />s4 ,z ! det]m9ation1 f ! annual p>allax1 ( ! di/ances ( ! />s is v prec>i\s if ! di/ance exce$s #e sir4 7pi #j4jd71 x is only natural t ! catalogues ( />-di/ances %\ld be b few 9 numb]4 ,! mo/ complete catalogues are ^? ( ,,big\rdan 9 ! ,bullet9 a/ronomique ,,xxvi 7#aiji71 ( ,,kapteyn & ,,we]sma 9 ! publications ( ,gron+5 ,nr4 #bd 7#aiaj71 embrac+ #cfe />s1 & ( ,,walkey 9 ! ,j\rnal ( ! ,briti% ,a/ronomical ,association ,,xxvii 7#aiag71 embrac+ #fbe />s4 ,?r\gh ! spectroscopic me?od ( ,,adams x w be possible to enl>ge ?is numb] consid]ably1 s t ! di/ance ( all />s1 = :i* ! spectrum is well kn[n1 may be det]m9$ ) fair accuracy4 ,,adams has up to n[ publi%$ #afdf p>allax />s4 #bc4 ,prop] motions4 ,an excell5t catalogue ( ! prop] motions ( ! />s is ,,lewis ,,boss's ,prelim9>y ,g5]al ,catalogue ( #fahh />s 7#aiaj7 7,b4 ,p4 ,c474 ,x conta9s ! prop] motions ( all />s d[n to ! six? magnitude 7) few exceptions7 & moreov] "s fa9t] />s4 ,! catalogue is consid]$ by ! editor only z a prelim9>y to a great] catalogue1 :i* is to embrace "s #bejjj />s & is n[ ne>ly complet$4 #bd4 ,visual magnitudes4 ,! ,h>v>d obs]vatory has1 "u ! direction ( ,,pick]+1 made its pr9cipal aim to /udy ! magnitudes ( ! />s1 & ! hi/ory ( ?is obs]vatory is at ! same "t ! hi/ory ( ! treatm5t ( ?is problem4 ,,pick]+1 9 ! g5u9e ,am]ican mann]1 is n satisfi$ ) ! ?ree ?irds ( ! sky visible f ! ,h>v>d obs]vatory1 b has also f\nd$ a daught] obs]vatory 9 ,s\? ,am]ica1 at ,arequipa 9 ,p]u4 ,x is !re=e possible = him to publi% catalogues embrac+ ! :ole heav5 f pole to pole4 ,! la/ complete catalogue 7#aijh7 ( ! magnitudes ( ! />s is f\nd 9 ! ,annals ( ! ,h>v>d ,obs]vatory ,t4 #ej 7,h4 #ej74 ,x conta9s #iaaj />s & c be consid]$ z complete to ! magnitude #fm4#e4 ,to ?is catalogue are g5]ally ref]r$ ! magnitudes :i* h be5 adopt$ at ! ,obs]vatory ( ,lund1 & :i* are treat$ 9 ^! lectures4 ,a v important1 & 9 "o respect ev5 /ill m compreh5sive1 catalogue ( visual magnitudes is ! ,potsdam ,g5]al ,catalogue 7,p4 ,g4 ,c47 by ,m,,ll] & ,,kempf1 :i* 0 publi%$ simultane\sly ) ,h4 #ej4 ,x conta9s ! magnitude ( #adaii />s & embraces all />s on ! nor!rn hemisph]e bright] ?an #gm4#e 7accord+ to ,b4 ,d474 ,we h already se5 t ! z]o-po9t ( ,h4 #ej & ,p4 ,g4 ,c4 is some:at diff]5t & t ! magnitudes 9 ,p4 ,g4 ,c4 mu/ be increas$ by -#jm4#af if !y are to be r$uc$ to ! ,h>v>d scale4 ,! diff]5ce betwe5 ! two catalogues h[ev] is due to "s ext5t to ! col\r ( ! />s1 z has be5 %[n by ,messrs4 ,m,,ll] & ,,kempf4 #be4 ,photographic magnitudes4 ,our k ( ?is subject is /ill r incomplete4 ,! mo/ compreh5sive catalogue is ! ,act9ometrie by ,,s*w>zs*ild 7#aiab71 conta9+ ! photographic magnitudes ( all />s 9 ,b4 ,d4 d[n to ! magnitude #gm4#e betwe5 ! equator & a decl9ation ( #bj4 ,9 all1 #cebb />s4 ,! photographic magnitudes are h[ev] n r$uc$ = ! z]o-po9t 7comp>e #f74 ,^! is also a photometric photographic catalogue ( ! />s ne>e/ to ! pole 9 ,,p>khur/'s ,y]kes act9ometry 7#aiab71aa :i* conta9s all />s 9 ,b4 ,d4 bright] ?an #gm4#e betwe5 ! pole & #gc nor!rn decl9ation4 ,! total numb] ( />s is #fgb4 ,dur+ ! la/ few ye>s ! a/ronom]s ( ,h>v>d & ,m\nt ,wilson h produc$ a collection ( /&>d photographic magnitudes = fa9t />s4 ,^! />s1 :i* are call$ ! pol> sequ5ce1#ab all lie 9 ! imm$iate neighb\rhood ( ! pole4 ,! li/ is ext5d$ d[n to ! #bj? magnitude4 ,moreov] simil> /&>d photographic magnitudes are giv5 9 ,h4 ,a4 #ga1 #he & #aja4 ,a discussion ( ! col\r-index 7i4e41 ! diff]5ce betwe5 ! photographic & ! visual magnitudes7 w be f\nd 9 ,l4 ,m4 ,,ii1 #ai4 ,:5 ! visual magnitude & ! type ( spectrum are kn[n1 ! photographic magnitude may be obta9$1 ) a g5]ally suffici5t accuracy1 by add+ ! col\r-index accord+ to ! table #a 9 #ae above4 #bf4 ,/ell> spectra4 ,"h too we f9d ! ,h>v>d ,obs]vatory to be ! lead+ "o4 ,! same volume ( ! ,annals ( ! ,h>v>d ,obs]vatory 7,h4 #ej7 t conta9s ! mo/ complete catalogue ( visual magnitudes1 also gives ! spectral types = all ! />s !re includ$1 i4e41 = all />s to #fm4#e4 ,miss ,,cannon1 at ! ,h>v>d ,obs]vatory1 des]ves ! pr9cipal cr$it = ?is great "w4 ,n cont5t ) ?is result %e is n[ publi%+ a /ill great] "w embrac+ m ?an #bjjjjj />s4 ,! fir/ f\r volumes ( ?is "w are n[ publi%$ & conta9 ! fir/ twelve h\rs ( "r asc5sion1 s t half ! "w is n[ pr9t$4#ac #bg4 ,radial velocity4 ,9 ?is matt]1 aga91 we f9d ,am]ica to be ! lead+ nation1 ?\gh1 ?is "t1 x is n ! ,h>v>d or ! ,m\nt ,wilson b ! ,lick ,obs]vatory to :i* we h to give ! hon\r4 ,! em95t director ( ?is obs]vatory1 ,w4 ,w4 ,,campbell1 has 9 a high degree develop$ ! accuracy 9 ! det]m9ation ( radial velocities & has moreov] c>ri$ out su* det]m9ations 9 a l>ge scale4 ,! ,bullet9 ,no4 #bbi 7#aiac7 ( ! ,lick ,obs]vatory conta9s ! radial velocity ( #iae />s4 ,at ! obs]vatory ( ,lund1 :]e z f> z possible c>d catalogues ( ! attributes ( ! />s are collect$1 ,,gyll5b]g has made a catalogue ( ?is k9d = ! radial velocities4 ,! total numb] ( />s 9 ?is catalogue n[ am\nts to #afdj4ad #bh4 ,f9ally ,i %all briefly m5tion "s compreh5sive works on m special que/ions reg>d+ ! /ell> sy/em4 ,on v>iable />s !re is publi%$ e ye> by ,,h>twig 9 ! ,vi]teljahrs*rift d] a/ronomis*5 ,gesells*aft a catalogue ( all kn[n v>iable />s ) ne$ful in=mation ab\t _! m9ima c4 ,?is is ! complete/ & mo/ reliable ( su* catalogues1 & is always up to date4 ,a complete hi/orical catalogue ( ! v>iables is giv5 9 ,ges*i*te und ,lit]atur des ,li*twe*sels d] bis ,ende #aiae als si*] v]nd]li* an]kannt5 ,/]ne neb/ e9em ,katalog d] ,elem5te ihres ,li*twe*sels von ,g4 ,m,,ll] und ,e4 ,,h>twig4 ,leipzig #aiah1 #aibj4 ,on nebulae we h ! excell5t catalogues ( ,,drey]1 ! ,new ,g5]al ,catalogue 7,n4 ,g4 ,c47 ( #ahij 9 ! ,memoirs ( ! ,a/ronomical ,society vol4 #di1 ! ,index catalogues 7,i4 ,c47 9 ! same memoirs1 vols4 #ea & #ei 7#ahie & #aijh74 ,^! catalogues conta9 all toge!r #acbbf objects4 ,reg>d+ o!r special attributes ,i ref] 9 ! fir/ place to ! important ,annals ( ! ,h>v>d ,obs]vatory4 ,o!r ref]5ces w be giv5 9 ! foll[+1 z ne$ arises4 ,,footnotes3 ,footnote #g3 ,bonn] ,/]nv]zei*nis 9 d5 ,a/ronomis*5 ,beoba*tung5 auf d] ,/]nw>te zu ,bonn1 ,dritt] bis ,fnft] ,b&4 ,bonn #ahei-fb4 ,footnote #h3 ,bonn] ,dur*mu/]ung1 ,vi]te ,sektion4 ,a*t] ,b& d] ,a/ronomis*5 ,beoba*tung5 zu ,bonn1 #ahhf4 ,footnote #i3 ,! ,cape ,photographic ,dur*mu/]ung by ,,david ,,gill & ,j4 ,c4 ,,kapteyn1 ,annals ( ! ,cape ,obs]vatory1 vol4 ,,iii-,v 7#ahif-aijj74 ,footnote #aj3 ,cordoba ,dur*mu/]ung by ,j4 ,,?ome4 ,results ( ! ,national ,arg5t9e ,obs]vatory1 vol4 #af1 #ag1 #ah1 #ba 7#ahid-aiad74 ,footnote #aa3 ,aph4 ,j41 vol4 #cf4 ,footnote #ab3 ,h4 ,a41 vol4 #ga4 ,footnote #ac3 ,h4 ,a41 vol4 #ia1 #ib1 #ic1 #id4 ,footnote #ad3 ,a catalogue ( radial velocities has ?is ye> be5 publi%$ by ,j4 ,,v\te1 embrac+ #bjga />s4 ,fir/ catalogue ( radial velocities1 by ,j4 ,,v\te4 ,weltevr$51 #aibj4 ,,*apt] ,,iii4 ,,"s ,,gr\ps ,,( ,,kn[n ,,/>s4 #bi4 ,! numb] ( cases 9 :i* all ! eight attributes ( ! />s discuss$ 9 ! fir/ *apt] are well kn[n = "o /> is v small1 & c]ta9ly does n exce$ "o hundr$4 ,^! cases ref] pr9cipally to su* />s z are *>act]iz$ ei!r by great brilliancy or by a great prop] motion4 ,! pr9cipal reason :y ^! />s are bett] kn[n ?an o!rs is t !y lie r ne> our sol> sy/em4 ,be=e pass+ on to consid] ! />s f m g5]al /ati/ical po9ts ( view1 x may !re=e be ( int]e/ fir/ to make ourselves famili> ) ^! well-kn[n />s1 /rongly emphasiz+1 h[ev]1 ! exceptional "* ( ^! />s1 & c>efully avoid+ any g5]alization f ! attributes we %all "h f9d4 #cj4 ,! app>5tly brighte/ />s4 ,we beg9 ) ^! objects s well kn[n to e lov] ( ! /ell> sky4 ,! foll[+ table conta9s all />s ! app>5t visual magnitude ( :i* is bright] ?an #am4#e4 ,! fir/ column gives ! curr5t numb]1 ! second ! "n1 ! ?ird ! equatorial designation 7alphadelta74 ,x %\ld be rememb]$ t ! fir/ f\r figures give ! h\r & m9utes 9 "r asc5sion1 ! la/ two ! decl9ation1 italics %[+ negative decl9ation4 ,! f\r? column gives ! galactic squ>e1 ! fif? & six? columns ! galactic longitude & latitude4 ,! sev5? & eigh? columns give ! annual p>allax & ! correspond+ di/ance express$ 9 siriomet]s4 ,! n9? column gives ! prop] motion 7mu71 ! t5? ! radial velocity ,w express$ 9 sir4_//4 7,to get km4_/sec4 we may multiply by #d4gcge74 ,! elev5? column gives ! app>5t visual magnitude1 ! twelf? column ! absolute magnitude 7,m71 comput$ f m ) ! help ( r4 ,! #ac? column gives ! type ( spectrum 7,sp71 & ! la/ column ! photographic magnitude 7m'74 ,! diff]5ce betwe5 m' & m gives ! col\r-index 7c74 ,,table #b4 ,,! ,,app>5tly ,,brighte/ ,,/>s4 ,transcrib]'s ,note3 ,to cons]ve space 7ad7 is us$ 9 place ( 7alphadelta74 ---------------------------------------- --------------------------- #a #b #c #d #e #f #g #h ---------------------------------------- --------------------------- ,position ,di/ance ,"n ---------------------------------------- ---- 7ad7 ,squ>e l b pi r ---------------------------------------- --------------------------- sir4 #a,sirius 7#jfdjaf7 ,,gd#g #aie - #h #j4hgf #j4e #b;,canopus 7#jfbaeb7 ,,gd#h #bbi -#bd #j4jjg #bi4e #c,vega 7#ahccch7 ,,gc#b #cj #ag #j4jid #b4b #d;,capella 7#jejide7 ,,gc#e #aca #e #j4jff #c4a #e;,arcturus 7#adaaai7 ,,ga#b #cdd #fh #j4jge #b4g #f;alpha ,c5tauri 7#adcbfj7 ,,gd#aj #bhd - #b #j4gei #j4c #g,rigel 7#jejijh7 ,,gd#f #agf -#bd #j4jjg #bi4e #h,procyon 7#jgcdje7 ,,gc#g #ahb #ad #j4cbd #j4f #i;,a*]n> 7#jacdeg7 ,,ge#h #bef -#ei #j4jea #d4j #aj;beta ,c5tauri 7#acefei7 ,,gc#aj #bhj #b #j4jcg #e4f #aa;,altair 7#aidejh7 ,,gd#a #ae -#aj #j4bch #j4i #ab;,betelgeuze 7#jedijg7 ,,gd#f #afh - #h #j4jcj #f4i #ac;,aldeb>an 7#jdcjaf7 ,,gd#e #adi -#ai #j4jgh #b4h #ad,pollux 7#jgcibh7 ,,gc#f #afj #be #j4jfd #c4b #ae,spica 7#acaiaj7 ,,gb#h #bhf #ea 44 44 #af;,ant>es 7#afbcbf7 ,,gc#aa #cbj #ad #j4jbi #g4a #ag;,fomalhaut 7#bbebcj7 ,,ge#aj #cdh -#ff #j4ach #a4e #ah;,d5eb 7#bjchdd7 ,,gc#b #ea #a 44 44 #ai,regulus 7#ajjcab7 ,,gb#f #aif #ej #j4jcc #f4c #bj;beta ,crucis 7#abdaei7 ,,gc#aj #bgj #c #j4jjh #be4h ---------------------------------------- --------------------------- sir4 ,mean 44 44 44 #bc4ej4acd #g4c ---------------------------------------- --------------------------- ---------------------------------------- ------------------------- #a #b #i #aj #aa #ab #ac #ad ---------------------------------------- ------------------------- ,motion ,magnitude ,spectrum ,"n ---------------------------------------- -- mu ,w m ,m ,sp m' ---------------------------------------- ------------------------- sir4_//4 m' #a,sirius #a4cb - #a4ef -#am4#eh -#jm4#c ,a -#a4eh #b;,canopus #j4jb #d4ci -#j4hf -#h4b ,f -#j4dj #c,vega #j4ce - #b4ia #j4ad -#a4f ,a #j4ad #d;,capella #j4dd #f4ch #j4ba -#b4h ,g #a4ac #e;,arcturus #b4bh - #j4hb #j4bd -#a4i ,k #a4fb #f;alpha ,c5tauri #c4fh - #d4fi #j4cc #c4b ,g #a4be #g,rigel #j4jj #d4gg #j4cd -#g4j ,b#hp #j4be #h,procyon #a4bd - #j4gd #j4dh #a4e ,f#e #a4ag #i;,a*]n> #j4ji 44 #j4fj -#b4d ,b#e #j4hg #aj;beta ,c5tauri #j4jd #b4ec #j4hf -#b4i ,b#a #j4de #aa;,altair #j4ff - #f4ig #j4hi #a4b ,a#e #a4ab #ab;,betelgeuze #j4jc #d4dc #j4ib -#c4c ,ma #b4gf #ac;,aldeb>an #j4bj #aa4fc #a4jf -#a4b ,k#e #b4fg #ad,pollux #j4jg #j4hb #a4ba -#a4c ,k #b4ei #ae,spica #j4jf #j4cd #a4ba 44 ,b#b #j4hd #af;,ant>es #j4jc - #j4fc #a4bb -#c4j ,map #c4jf #ag;,fomalhaut #j4cg #a4da #a4bi #j4d ,a#c #a4dc #ah;,d5eb #j4jj - #j4hd #a4cc 44 ,a#b #a4db #ai,regulus #j4be 44 #a4cd -#b4g ,b#h #a4be #bj;beta ,crucis #j4jf #b4gd #a4ej -#e4f ,b#a #a4ji ---------------------------------------- ------------------------- m' ,mean #j4ef #c4bf #jm4#fd -#bm4#a ,f#a #a4ac ---------------------------------------- ------------------------- ,! values ( 7alphadelta71 m1 ,sp are tak5 f ,h4 #ej4 ,! values ( l1 b are comput$ f 7alphadelta7 ) ! help ( tables 9 prep>ation at ! ,lund ,obs]vatory1 or f ! orig9al to plate ,i at ! end1 all[+ ! conv]sion ( ! equatorial coord9ates into galactic ones4 ,! values ( pi are g5]ally tak5 f ! table ( ,,kapteyn & ,,we]sma m5tion$ 9 ! previ\s *apt]4 ,! values ( mu are obta9$ f ,b4 ,p4 ,c41 ^? ( ! radial velocity 7,w7 f ! c>d catalogue 9 ,lund already describ$4 ,!re are 9 all1 9 ! sky1 #bj />s hav+ an app>5t magnitude bright] ?an #am4#e4 ,! brighte/ ( !m is ,sirius1 :i*1 ow+ to its brilliancy & position1 is visible to ! :ole civiliz$ _w4 ,x has a spectrum ( ! type ,a#j & h5ce a col\r-index ne>ly equal to #j4j 7obs]vations 9 ,h>v>d give c #j4jf74 ,its app>5t magnitude is -#am4#f1 ne>ly ! same z t ( ,m>s 9 8 opposition4 ,its absolute magnitude is -#jm4#c1 i4e41 fa9t] ?an ! app>5t magnitude1 f :i* we may conclude t x has a di/ance f u small] ?an "o siriomet]4 ,we f9d1 inde$1 f ! eigh? column t r #j4e sir4 ,! prop] motion ( ,sirius is #a4cb p] ye>1 :i* is r l>ge b /ill n among ! l>ge/ prop] motions z w be se5 bel[4 ,f ! #aa? column we f9d t ,sirius is mov+ t[>ds u ) a velocity ( #a4f sir4_//4 7 #g4f km4_/sec471 a r small velocity4 ,! ?ird column %[s t its "r asc5sion is #f;h #djm & its decl9ation -#af4 ,x lies 9 ! squ>e ,,gd#g & its galactic coord9ates are se5 9 ! #e? & #f? columns4 ,! next brighte/ /> is ,canopus or alpha ,c>9 at ! s\? sky4 ,if we might place absolute confid5ce 9 ! value ( ,m 7 -#h4b7 9 ! #ab? column ?is /> w\ld be1 9 reality1 a mu* m impos+ app>ition ?an ,sirius itself4 ,rememb]+ t ! app>5t magnitude ( ! moon1 accord+ to #f1 am\nts to -#aa4f1 we %\ld f9d t ,canopus1 if plac$ at a di/ance f u equal to t ( ,sirius 7r #j4e sir471 w\ld %9e ) a lu/re equal to no less ?an a qu>t] ( t ( ! moon4 ,x is n altoge!r a/oni%+ t a fanciful a/ronom] %\ld h ?\ght ,canopus to be actually ! c5tral /> 9 ! :ole /ell> sy/em4 ,we f9d1 h[ev]1 f column #h t its suppos$ di/ance is n less t #cj sir4 ,we h already po9t$ out t di/ances great] ?an #d sir41 :5 comput$ f annual p>allaxes1 mu/ g5]ally be consid]$ z r unc]ta94 ,z ! value ( ,m is intimately dep5d5t on t ( r we mu/ consid] speculations bas$ on ?is value to be v vague4 ,ano!r reason = a d\bt ab\t a great value = ! real lum9osity ( ?is /> is f\nd f its type ( spectrum :i*1 accord+ to ! la/ column1 is ,f#j1 a type :i*1 z w be se51 is seldom f\nd among giant />s4 ,a bett] support = a l>ge di/ance c\ld on ! o!r h& be f\nd f ! small prop] motion ( ?is />4 ,sirius & ,canopus are ! only />s 9 ! sky hav+ a negative value ( ! app>5t visual magnitude4 ,space w n p]mit u to g ?r\gh ?is li/ /> = />4 ,we may be satisfi$ ) "s g5]al rem>ks4 ,9 ! f\r? column is ! galactic squ>e4 ,we call to m9d t all ^! squ>es h ! same area1 & t !re is !re=e ! same probability a priori ( f9d+ a /> 9 "o ( ! squ>es z 9 ano!r4 ,! squ>es ,,gc & ,,gd lie along ! galactic equator 7! ,milky ,way74 ,we f9d n[ f column #d t ( ! #bj />s "h consid]$ !re are no less ?an #ae 9 ! galactic equator squ>es & only #e outside1 in/ead ( #aj 9 ! galactic squ>es & #aj outside1 z w\ld h be5 expect$4 ,! numb] ( objects is1 inde$1 too small to all[ u to draw any cosmological conclusions f ?is di/ribution1 b we %all f9d 9 ! foll[+ _m simil> in/ances reg>d+ objects t are pr9cipally accumulat$ along ! ,milky ,way & are scanty at ! galactic poles4 ,we %all f9d t 9 ^! cases we may g5]ally conclude f su* a p>tition t we !n h to d ) objects situat$ f> f ! sun1 :ile objects t are uni=mly di/ribut$ on ! sky lie relatively ne> u4 ,x is easy to und]/& t ?is conclusion is a consequ5ce ( ! supposition1 confirm$ by all /> c\nts1 t ! /ell> sy/em ext5ds mu* f>!r into space along ! ,milky ,way ?an 9 ! direction ( its poles4 ,if we c\ld p]mit ourselves to draw conclusions f ! small mat]ial "h "u consid]ation1 we %\ld h5ce h reason to believe t ! bright />s lie relatively f> f u4 ,9 o!r words we %\ld conclude t ! bright />s seem to be bright to u n because ( _! proximity b because ( _! l>ge intr9sic lum9osity4 ,column #h really t5ds 9 ?is direction4 ,c]ta9ly ! di/ances are n 9 ?is case colossal1 b !y are nev]!less suffici5t to %[1 9 "s degree1 ?is unev5 p>tition ( ! bright />s on ! sky4 ,! mean di/ance ( ^! />s is z l>ge z #g4e sir4 ,only alpha ,c5tauri1 ,sirius1 ,procyon & ,altair lie at a di/ance small] ?an "o siriomet]4 ,( ! o!r />s !re are two t lie z f> z #cj siriomet]s f our sy/em4 ,^! are ! two giants ,canopus & ,rigel4 ,ev5 if1 z has already be5 said1 ! di/ances ( ^! />s may be consid]$ z r unc]ta91 we mu/ reg>d !m z be+ r l>ge4 ,z column #h %[s t ^! />s are r f> f u1 s we f9d f column #ab1 t _! absolute lum9osity is r l>ge4 ,! mean absolute magnitude is1 inde$1 -#bm4#a4 ,we %all f9d t only ! greate/ & mo/ lum9\s />s 9 ! /ell> sy/em h a negative value ( ! absolute magnitude4 ,! mean value ( ! prop] motions ( ! bright />s am\nts to #j4ef p] ye> & may be consid]$ z r great4 ,we %all1 inde$1 f9d t ! mean prop] motion ( ! />s d[n to ! #f? magnitude sc>cely am\nts to a t5? "p ( ?is value4 ,on ! o!r h& we f9d f ! table t ! high value ( ?is mean is *iefly due to ! influ5ce ( f\r ( ! />s :i* h a l>ge prop] motion1 namely ,sirius1 ,arcturus1 alpha ,c5tauri & ,procyon4 ,! o!r />s h a prop] motion small] ?an #a p] ye> & = half ! numb] ( />s ! prop] motion am\nts to approximately #j4je1 indicat+ _! relatively great di/ance4 ,t ! absolute velocity ( ^! />s is1 inde$1 r small may be f\nd f column #aj1 giv+ _! radial velocity1 :i* 9 ! mean am\nts to only ?ree siriomet]s p] /ell> ye>4 ,f ! discussion bel[ ( ! radial velocities ( ! />s we %all f9d t ?is is a r small figure4 ,?is fact is intimately b\nd up ) ! g5]al law 9 /ati/ical me*anics1 to :i* we return lat]1 t />s ) l>ge masses g5]ally h a small velocity4 ,we ?us f9d 9 ! radial velocities fre% evid5ce1 indep5d5t ( ! di/ance1 t ^! bright />s are giants among ! />s 9 our /ell> sy/em4 ,we f9d all ! pr9cipal spectral types repres5t$ among ! bright />s4 ,to ! helium />s 7,b7 belong ,rigel1 ,a*]n>1 beta ,c5tauri1 ,spica1 ,regulus & beta ,crucis4 ,to ! ,sirius type 7,a7 belong ,sirius1 ,vega1 ,altair1 ,fomalhaut & ,d5eb4 ,to ! ,calcium type 7,f7 ,canopus & ,procyon4 ,to ! sun type 7,g7 ,capella & alpha ,c5tauri4 ,to ! ,k-type belong ,arcturus1 ,aldeb>an & ,pollux & to ! ,m-type ! two r$ />s ,betelgeuze & ,ant>es4 ,us+ ! spectral indices z an expression = ! spectral types we f9d t ! mean spectral index ( ^! />s is #a4a correspond+ to ! spectral type ,f#a4 #ca4 ,/>s ) ! greate/ prop] motion4 ,9 table #c ,i h collect$ ! />s hav+ a prop] motion great] ?an #c p] ye>4 ,! designations are ! same z 9 ! prec$+ table1 except t ! names ( ! />s are "h tak5 f diff]5t catalogues4 ,9 ! a/ronomical lit]ature ( ! la/ c5tury we f9d ! /> #ahcj ,groombridge design$ z t :i* possesses ! greate/ kn[n prop] motion4 ,x is n[ di/anc$ by two o!r />s ,c4 ,p4 ,d4 #e;h4#bdc discov]$ 9 ! ye> #ahig by ,,kapteyn & ,,innes on ! plates tak5 = ! ,cape ,photographic ,dur*mu/]ung1 & ,,b>n>d's /> 9 ,ophiu*us1 discov]$ #aiaf4 ,! la/-m5tion$ />1 :i* possesses ! greate/ prop] motion n[ kn[n1 is v fa9t1 be+ only ( ! #aj? magnitude1 & lies at a di/ance ( #j4dj sir4 f our sun & is h5ce1 z w be f\nd f table #e ! ?ird ne>e/ /> = :i* we "k ! di/ance4 ,its l9e> velocity is also v great1 z we f9d f column #aj1 & am\nts to #ai sir4_//4 7 #ij km4_/sec47 9 ! direction t[>ds ! sun4 ,! absolute magnitude ( ?is /> is #aam4#g & x is1 ) ! exception ( "o o!r1 ! v fa9te/ /> n[ kn[n4 ,its spectral type is ,mb1 a fact wor? fix+ 9 our memory1 z diff]5t reasons fav\r ! belief t x is precisely ! ,m-type t conta9s ! v fa9te/ />s4 ,its app>5t velocity 7i4e41 ! prop] motion7 is s great t ! /> 9 #ajjj ye>s moves #c1 or z mu* z #f times ! diamet] ( ! moon4 ,= ?is />1 z well z = its ne>e/ neighb\rs 9 ! table1 obs]vations diff]+ only by a ye> are suffici5t = an approximate det]m9ation ( ! value ( ! prop] motion1 = :i* 9 o!r cases _m t5s ( ye>s are requir$4 ,reg>d+ ! di/ribution ( ^! />s 9 ! sky we f9d t1 unlike ! brighte/ />s1 !y are n conc5trat$ along ! ,milky ,way4 ,on ! contr>y we f9d only #f 9 ! galactic equator squ>es & #ab 9 ! o!r squ>es4 ,we %all n build up any conclusion on ?is irregul>ity 9 ! di/ribution1 b support$ by ! g5]al !sis ( ! prec$+ p>agraph we conclude only t ^! />s mu/ be relatively ne> u4 ,?is foll[s1 inde$1 directly f column #h1 z n less ?an elev5 ( ^! />s lie )9 "o siriomet] f our sun4 ,_! mean di/ance is #j4hg sir4 ,,table #c4 ,,/>s ,,) ,,! ,,greate/ ,,prop] ,,motion4 ,transcrib]'s ,note3 ,to cons]ve space 7ad7 is us$ 9 place ( 7alphadelta74 ---------------------------------------- --------------------------- #a #b #c #d #e #f #g #h ---------------------------------------- --------------------------- ,position ,di/ance ,"n ---------------------------------------- ---- 7ad7 ,squ>e l b pi r ---------------------------------------- --------------------------- sir4 #a;,b>n>ds /> 7#agebjd7 ,,gc#ab #ceh #ab #j4eae #j4dj #b;,c4 ,z4 #e;h4#bdc 7#jejgdd7 ,,ge#g #bah -#ce #j4cai #j4fe #c;,groom4 #ahcj 7#aadgch7 ,,ga#a #ace #ge #j4ajb #b4jb #d,lac4 #iceb 7#bbeicf7 ,,ge#aj #ccc -#ff #j4bib #j4ga #e;,c4 ,g4 ,a4 #cbdaf 7#bceicg7 ,,gf#b #cjh -#ge #j4bcj #j4hi #ffa ,cygni 7#bajbch7 ,,gd#b #ej - #g #j4caa #j4ff #g,lal4 #baahe 7#ajegcf7 ,,gb#e #aec #ff #j4djc #j4ea #h;epsilon ,indi 7#baeeeg7 ,,ge#i #cjd -#dg #j4bhd #j4gc #i,lal4 #babeh 7#aajjdd7 ,,gb#d #ace #fd #j4bjc #a4jb #aj,o#b ,eridani 7#jdajjg7 ,,ge#e #afh -#cf #j4agd #a4ai #aa,proxima ,c5tauri 7#adbbfb7 ,,gd#aj #bha - #b #j4ghj #j4bf #ab,oe4 ,a4 #adcbj 7#aejdae7 ,,gb#i #cad #ce #j4jce #e4ij #acmu ,cassiopei 7#jajaed7 ,,gd#d #ic - #h #j4aab #a4hd #ad;alpha ,c5tauri 7#adcbfj7 ,,gd#aj #bhd - #b #j4gei #j4bg #ae,lac4 #hgfj 7#baaaci7 ,,ge#aj #ccb -#dd #j4bdh #j4hc #af,lac4 #ajfj 7#jcaedc7 ,,ge#g #baf -#ee #j4afb #a4bg #ag,oe4 ,a4 #aafgg 7#aaadff7 ,,gb#h #ajc #ej #j4aih #a4jd #ah,van ,maan5s /> 7#jjdcjd7 ,,gd#h #ib -#eh #j4bdf #j4hd ---------------------------------------- --------------------------- sir4 ,mean 44 44 #da #j4bih #j4hg ---------------------------------------- --------------------------- ---------------------------------------- ------------------------- #a #b #i #aj #aa #ab #ac #ad ---------------------------------------- ------------------------- ,motion ,magnitude ,spectrum ,"n ---------------------------------------- -- mu ,w m ,m ,sp m' ---------------------------------------- ------------------------- sir4_//4 m' #a;,b>n>ds /> #aj4bi -#ai #im4#g #aam4#g,mb #aa4e #b;,c4 ,z4 #e;h4#bdc #h4ge #ea #i4b #aj4a ,k#b #aj4f #c;,groom4 #ahcj #g4jf -#bj #f4e #e4j ,g#e #g4f #d,lac4 #iceb #f4ij #b #g4e #h4b ,k #h4i #e;,c4 ,g4 ,a4 #cbdaf #f4aa #e #h4b #h4e ,g #i4a #ffa ,cygni #e4bg -#ac #e4f #f4e ,k#e #g4b #g,lal4 #baahe #d4gg -#ah #g4f #i4a ,mb #h4i #h;epsilon ,indi #d4gj -#h #d4g #e4d ,k#e #f4c #i,lal4 #babeh #d4dg #ad #h4e #h4e ,ma #aj4c #aj,o#b ,eridani #d4aa -#i #d4g #d4c ,g#e #e4h #aa,proxima ,c5tauri #c4he 44 #aa4j #ac4i 44 #ac4e #ab,oe4 ,a4 #adcbj #c4ge #fa #i4j #e4a ,g#j #i4i #acmu ,cassiopei #c4gc -#ba #e4g #d4d ,g#c #f4h #ad;alpha ,c5tauri #c4fh -#e #j4c #c4b ,g #a4b #ae,lac4 #hgfj #c4ec #c #f4f #g4j ,g #g4e #af,lac4 #ajfj #c4je #ah #e4f #e4a ,g#e #f4g #ag,oe4 ,a4 #aafgg #c4jc 44 #i4b #i4a ,ma #aa4j #ah,van ,maan5s /> #c4ja 44 #ab4c #ab4g ,f#j #ab4i ---------------------------------------- ------------------------- sir4_//4 m' ,mean #e4jj #ag4h #gm4#c #gm4#f;,g#h #h4g ---------------------------------------- ------------------------- ,t ! great prop] motion does n dep5d alone on ! proximity ( ^! />s is se5 f column #aj1 giv+ ! radial velocities4 ,= "s ( ! />s 7#d7 ! radial velocity is = ! pres5t unkn[n1 b ! o!rs h1 ) few exceptions1 a r great velocity am\nt+ 9 ! mean to #ah sir4_//4 7 #he km4_/sec471 if no reg>d is tak5 to ! sign1 a value ne>ly five times z great z ! absolute velocity ( ! sun4 ,z ?is is only ! compon5t along ! l9e ( sight1 ! absolute velocity is /ill great]1 approximately equal to ! compon5t velocity multipli$ by squ>e root#b4 ,we conclude t ! great prop] motions dep5d p>tly on ! proximity1 p>tly on ! great l9e> velocities ( ! />s4 ,t bo? ^! attributes "h really coop]ate may be se5 f ! absolute magnitudes 7,m74 ,! app>5t & ! absolute magnitudes are = ^! />s ne>ly equal1 ! means = bo? be5 approximately #gm4 ,?is is a consequ5ce ( ! fact t ! mean di/ance ( ^! />s is equal to "o siriomet]1 at :i* di/ance m & ,m1 inde$1 d co9cide4 ,we f9d t ^! />s h a small lum9osity & may be consid]$ z dw>f />s4 ,accord+ to ! g5]al law ( /ati/ical me*anics already m5tion$ small bodies ^u an av]age h a great absolute velocity1 z we h1 inde$1 already f\nd f ! obs]v$ radial velocities ( ^! />s4 ,z to ! spectral type1 ! />s ) great prop] motions are all yell[ or r$ />s4 ,! mean spectral index is #b4h1 correspond+ to ! type ,g#h4 ,if ! />s ( diff]5t types are put toge!r we get ! table ,type ,numb] ,mean value ( ,m ,g #h #e4c ,k #d #g4e ,m #d #i4f ,we conclude t1 at lea/ = ^! />s1 ! mean value ( ! absolute magnitude increases ) ! spectral index4 ,?is conclusion1 h[ev]1 is n g5]ally valid4 #cb4 ,/>s ) ! greate/ radial velocities4 ,!re are "s k9ds ( nebulae = :i* v l>ge values ( ! radial velocities h be5 f\nd4 ,) ^! we %all n = ! pres5t deal1 b %all conf9e ourselves to ! />s4 ,! greate/ radial velocity hi!rto f\nd is possess$ by ! /> 7#jdjhbb7 ( ! eigh? magnitude 9 ! con/ellation ,p]seus1 :i* retires f u ) a velocity ( #gb sir4_//4 or #cda km4_/sec4 ,! ne>e/ velocity is t ( ! /> 7#jajcfa7 :i* approa*es u ) approximately ! same velocity4 ,! foll[+ table conta9s all />s ) a radial velocity great] ?an #bj sir4_//4 7 #id4h km4_/sec474 ,x is bas$ on ! catalogue ( ,,v\te m5tion$ above4 ,reg>d+ _! di/ribution 9 ! sky we f9d #aa 9 ! galactic equator squ>es & #g outside4 ,a l>ge radial velocity seems !re=e to be a galactic ph5om5on & to be correlat$ to a great di/ance f u4 ,( ! #ah />s 9 consid]ation !re is only "o at a di/ance small] ?an "o siriomet] & #b at a di/ance small] ?an #d siriomet]s4 ,among ! ne>] ones we f9d ! /> 7#jejgdd71 id5tical ) ,c4 ,p4 ,d4 #e;h4#bdc1 :i* 0 ! second /> ) great prop] motion4 ,^! />s h simultane\sly ! greate/ prop] motion & v great l9e> velocity4 ,g5]ally we f9d f column #i t ^! />s ) l>ge radial velocity possess also a l>ge prop] motion4 ,! mean value ( ! prop] motions am\nts to #a4cd1 a v high value4 ,9 ! table we f9d no /> ) great app>5t lum9osity4 ,! brighte/ is ! #aj? /> 9 ! table :i* has ! magnitude #e4a4 ,! mean app>5t magnitude is #g4g4 ,z to ! absolute magnitude 7,m7 we see t mo/ ( ^! spe$y />s1 z well z ! />s ) great prop] motions 9 table #c1 h a r great positive magnitude & ?us are absolutely fa9t />s1 ?\gh !y p]haps may n be directly consid]$ z dw>f />s4 ,_! mean absolute magnitude is #c4j4 ,reg>d+ ! spectrum we f9d t ^! />s g5]ally belong to ! yell[ or r$ types 7,g1 ,k1 ,m71 b !re are #f ,f-/>s &1 curi\sly en\gh1 two ,a-/>s4 ,aft] ! designation ( _! type 7,a#b & ,a#c7 is ! lett] p 7 peculi>71 indicat+ t ! spectrum 9 "s respect diff]s f ! usual appe>ance ( ! spectrum ( ?is type4 ,9 ! pres5t case ! peculi>ity consi/s 9 ! fact t a l9e ( ! wave-l5g? #ddh4a1 :i* emanates f magnesium & :i* we may f9d on plate ,,iii 9 ! spectrum ( ,sirius1 does n occur 9 ! spectrum ( ^! />s1 ?\gh ! spectrum has o!rwise ! same appe>ance z 9 ! case ( ! ,sirius />s4 ,!re is reason to suppose t ! abs5ce ( ?is l9e indicates a l[ p[] ( radiation 7l[ temp]ature7 9 ^! />s 7comp>e ,,adams74 ,,table #d4 ,,/>s ,,) ,,! ,,greate/ ,,radial ,,velocity4 ,transcrib]'s ,note3 ,to cons]ve space 7ad7 is us$ 9 place ( 7alphadelta74 ---------------------------------------- --------------------------- #a #b #c #d #e #f #g #h ---------------------------------------- --------------------------- ,position ,di/ance ,"n ---------------------------------------- ---- 7ad7 ,squ>e l b pi r ---------------------------------------- --------------------------- sir4 #a;,a4 ,g4 ,b]l9 #acff 7#jdjhbb7 ,,gd#e #ada -#bj #j4jjg #cj4h #b,lal4 #aiff 7#jajcfa7 ,,gd#d #ic - #b #j4jaf #ab4i #c;,a4 ,oe4 #adcbj 7#aejdae7 ,,gb#i #cad #ce #j4jce #e4i #d;,c4 ,z4 #e;h4#bdc 7#jejgdd7 ,,ge#g #bah -#ce #j4cai #j4f #e,lal4 #aebij 7#jgdgcj7 ,,gc#f #aeh #bf #j4jbc #i4j #fec ,cassiop4 7#jaeefc7 ,,gc#d #ih #b 44 44 #g;,a4 ,g4 ,b]l9 #ahff 7#jeegai7 ,,gd#f #aei - #b #j4jba #i4h #h,w ,lyr 7#ahaacf7 ,,gc#b #ca #ba 44 44 #i;,boss #aeaa 7#jeeibf7 ,,gd#g #bjj -#bj #j4jab #ag4j #ajomega ,pavonis 7#ahdifj7 ,,gd#aa #cjd -#bd 44 44 #aa;,a4 ,oe4 #bjdeb 7#bjagba7 ,,ge#aj #cea -#ca #j4jae #ac4e #ab,lal4 #bhfjg 7#aecgaj7 ,,gb#aj #cbe #cd #j4jcc #f4b #ac;,a4 ,g4 ,leid5 #egcd 7#afaacb7 ,,gb#a #ba #de #j4jjb #hi4b #ad,lal4 #cgabj 7#aibicb7 ,,gc#b #cc #f #j4jej #d4a #ae,lal4 #bgbgd 7#adedba7 ,,gb#i #cjh #cd #j4jac #af4b #af,lal4 #egfa 7#jcjbbe7 ,,gd#e #abf -#bh #j4jci #e4a #ag,w4 ,b4 #ag;h4#eag 7#agbijf7 ,,gc#ab #ceh #bj #j4jad #ad4a #ah,lal4 #bciie 7#abdgag7 ,,gb#h #bga #df #j4jab #ag4j ---------------------------------------- --------------------------- sir4 ,mean 44 44 #bc4ij4jda #af4g ---------------------------------------- --------------------------- ---------------------------------------- ------------------------- #a #b #i #aj #aa #ab #ac #ad ---------------------------------------- ------------------------- ,motion ,magnitude ,spectrum ,"n ---------------------------------------- -- mu ,w m ,m ,sp m' ---------------------------------------- ------------------------- sir4_//4 m' #a;,a4 ,g4 ,b]l9 #acff #j4ed #gb #hm4#i #am4#d ,f#j #i4d #b,lal4 #aiff #j4fd -#fi #g4i #b4c ,f#c #h4e #c;,a4 ,oe4 #adcbj #c4ge #fa #i4j #e4a ,g#j #i4i #d;,c4 ,z4 #e;h4#bdc #h4ge #ea #i4b #aj4a ,k#b #aj4f #e,lal4 #aebij #a4if -#ea #h4b #c4d ,g#j #i4a #fec ,cassiop4 #j4ja -#dd #e4f 44 ,b#h #e4e #g;,a4 ,g4 ,b]l9 #ahff #j4gf -#dj #i4j #d4j ,f#j #i4i #h,w ,lyr 44 -#ci v>4 44 ,md v>4 #i;,boss #aeaa #j4aj #ci #e4b -#a4j ,g#e #f4d #ajomega ,pavonis #j4ad #ch #e4a 44 ,k #f4e #aa;,a4 ,oe4 #bjdeb #a4ah -#ch #h4a #b4d ,g#hp #i4d #ab,lal4 #bhfjg #a4ah -#cf #g4c #c4c ,a#bp #g4d #ac;,a4 ,g4 ,leid5 #egcd #j4jd -#ce #h4c -#a4e ,k#d #i4i #ad,lal4 #cgabj #j4eb -#cd #f4f #c4e ,g#b #g4f #ae,lal4 #bgbgd #j4gi #cd #h4c #b4b ,f#d #h4i #af,lal4 #egfa #j4hf -#cb #h4j #d4d ,a#cp #h4a #ag,w4 ,b4 #ag;h4#eag #j4fc -#ca #h4f #b4h ,f#a #i4a #ah,lal4 #bciie #j4hh #cj #h4b #b4j ,f#c #h4h ---------------------------------------- ------------------------- sir4_//4 m' ,mean #a4cd #af4g #gm4#g #cm4#j ,f#i #h4e ---------------------------------------- ------------------------- #cc4 ,! ne>e/ />s4 ,! /> alpha 9 ,c5taurus 0 long consid]$ z ! ne>e/ ( all />s4 ,x has a p>allax ( #j4ge1 correspond+ to a di/ance ( #j4bg siriomet]s 7 #d4bf light ye>s74 ,?is di/ance is obta9$ f ! annual p>allax ) great accuracy1 & ! result is moreov] confirm$ 9 ano!r way 7f ! /udy ( ! orbit ( ! companion ( alpha ,c5tauri74 ,9 ! ye> #aiaf ,,innes discov]$ at ! obs]vatory ( ,johannesburg 9 ! ,transvaal a /> ( ! #aj? magnitude1 :i* seems to foll[ alpha ,c5tauri 9 its pa? 9 ! heav5s1 & :i*1 9 any case1 lies at ! same di/ance f ! e>?1 or some:at ne>]4 ,x is n possible at pres5t to decide ) accuracy :e!r ,proxima ,c5tauri--z ! /> is call$ by ,,innes--or alpha ,c5tauri is our ne>e/ neighb\r4 ,!n comes ,,b>n>d's /> 7#agebjd71 ^: l>ge prop] motion we h already m5tion$4 ,z ,no4 #e we f9d ,sirius1 z ,no4 #h ,procyon1 z ,no4 #ba ,altair4 ,! o!rs are ( ! ?ird magnitude or fa9t]4 ,no4 #aj--fa ,cygni--is especially int]e/+1 be+ ! fir/ /> = :i* ! a/ronom]s1 aft] long & pa9ful endeav\rs 9 va91 h succe$$ 9 det]m9+ ! di/ance ) ! help ( ! annual p>allax 7,,bessel #ahda74 ,f column #d we f9d t ! di/ribution ( ^! />s on ! sky is tol]ably uni=m1 z might h be5 pr$ict$4 ,all ^! />s h a l>ge prop] motion1 ?is be+ 9 ! mean #c4db p] ye>4 ,?is 0 a priori to be expect$ f _! great proximity4 ,! radial velocity is1 num]ically1 great] ?an c\ld h be5 suppos$4 ,?is fact is probably associat$ ) ! g5]ally small mass ( ^! />s4 ,_! app>5t magnitude is ^u an av]age #f4c4 ,! brighte/ ( ! ne> />s is ,sirius 7m -#a4f71 ! fa9te/ ,proxima ,c5tauri 7m #aa74 ,?r\gh ! sy/ematic rese>*es ( ! a/ronom]s we may be sure t no bright />s exi/ at a di/ance small] ?an "o siriomet]1 = :i* ! di/ance is n already kn[n & well det]m9$4 ,! foll[+ table conta9s )\t d\bt--we may call !m briefly all ne> />s--all />s )9 "o siriomet] f u ) an app>5t magnitude bright] ?an #fm 7! table has #h su* />s71 & probably also all ne> />s bright] ?an #gm 7#aj />s71 or ev5 all bright] ?an ! eigh? magnitude 7! table has #ac su* />s & two ne> ! limit74 ,reg>d+ ! />s ( ! eigh? magnitude or fa9t] no sy/ematic inve/igations ( ! annual p>allax h be5 made & among ^! />s we may get f "t to "t a new /> belong+ to ! siriomet] sph]e 9 ! neighb\rhood ( ! sun4 ,to det]m9e ! total numb] ( />s )9 ?is sph]e is "o ( ! fundam5tal problems 9 /ell> /ati/ics1 & to ?is "q ,i %all return imm$iately4 ,,table #e4 ,,! ,,ne>e/ ,,/>s4 ,transcrib]'s ,note3 ,to cons]ve space 7ad7 is us$ 9 place ( 7alphadelta74 ---------------------------------------- ---------------------------- #a #b #c #d #e #f #g #h ---------------------------------------- ---------------------------- ,position ,di/ance ,"n ---------------------------------------- ---- 7ad7 ,squ>e l b pi r ---------------------------------------- ---------------------------- sir4 #a,proxima ,c5tauri 7#adbbfb7 ,,gd#aj #bha - #b #j4ghj #j4bf #b;alpha ,c5tauri 7#adcbfj7 ,,gd#aj #bhd - #b #j4gei #j4bg #c;,b>n>ds p4 m4 /> 7#agebjd7 ,,gc#ab #ceh #ab #j4eae #j4dj #d,lal4 #baahe 7#ajegcf7 ,,gb#e #aec #ff #j4djc #j4ea #e,sirius 7#jfdjaf7 ,,gd#g #aie - #h #j4cgf #j4ee #f 44 7#aaaceg7 ,,gc#f #aeh #c #j4ccg #j4fj #gtau ,ceti 7#jaciaf7 ,,gf#a #add -#gd #j4ccd #j4fb #h,procyon 7#jgcdje7 ,,gc#g #ahb #ad #j4cbd #j4fd #i;,c4 ,z4 #e;h4#bdc 7#jejgdd7 ,,ge#g #bah -#ce #j4cai #j4fe #ajfa ,cygni 7#bajbch7 ,,gd#b #ej - #g #j4caa #j4ff #aa,lal4 #bfdha 7#adbeae7 ,,gb#i #abd -#dj #j4caa #j4ff #ab;epsilon ,eridani 7#jcbhji7 ,,ge#e #aec -#db #j4bie #j4gj #ac,lac4 #iceb 7#bbeicf7 ,,ge#aj #ccc -#ff #j4bib #j4ga #ad,pos4 ,m$4 #bafd 7#ahdaei7 ,,gc#b #ef #bd #j4bib #j4ga #ae;epsilon ,indi 7#baeeeg7 ,,ge#i #cjd -#dg #j4bhd #j4gc #af;,groom4 #cd 7#jjabdc7 ,,gd#c #hd -#bj #j4bha #j4gc #ag,oe4 ,a4 #agdae 7#agcgfh7 ,,gc#h #fe #cb #j4bfh #j4gg #ah,krg] #fj 7#bbbdeg7 ,,gc#c #gb #j #j4bef #j4ha #ai,lac4 #hgfj 7#baaaci7 ,,ge#aj #ccb -#dd #j4bdh #j4hh #bjvan ,maan5s p4 m4 />7#jjdcjd7 ,,ge#c #ib -#eh #j4bdf #j4hd #ba;,altair 7#aidejh7 ,,gd#a #ae -#aj #j4bch #j4hg #bb;,c4 ,g4 ,a4 #cbdaf 7#bceicg7 ,,gf#b #cjh -#ge #j4bcj #j4hi #bc;,bradley #aehd 7#aabicb7 ,,gc#f #beb #bh #j4baf #j4ie ---------------------------------------- ---------------------------- sir4 ,mean 44 44 44 #cj4hj4cdd #j4fg ---------------------------------------- ---------------------------- ---------------------------------------- --------------------------- #a #b #i #aj #aa #ab #ac #ad ---------------------------------------- --------------------------- ,motion ,magnitude ,spectrum ,"n ---------------------------------------- -- mu ,w m ,m ,sp m' ---------------------------------------- --------------------------- sir4_//4 m' #a,proxima ,c5tauri #c4he 44 #aam4#j #acm4#i 44 #ac4e #b;alpha ,c5tauri #c4fh - #e #j4cc #c4b ,g #a4be #c;,b>n>ds p4 m4 /> #aj4bi -#ai #i4g #aa4g ,mb #aa4e #d,lal4 #baahe #d4gg -#ah #g4f #i4a ,mb #h4i #e,sirius #a4cb - #b -#a4eh - #j4c ,a -#a4eh #f 44 #b4gb 44 44 44 44 #ab4e #gtau ,ceti #a4ib - #c #c4f #d4f ,k#j #d4f #h,procyon #a4bd - #a #j4dh #a4e ,f#e #j4ij #i;,c4 ,z4 #e;h4#bdc #h4ge #ea #i4b #aj4a ,k#b #aj4f #ajfa ,cygni #e4bg -#ac #e4f #f4e ,k#e #g4b #aa,lal4 #bfdha #j4dg 44 #g4h #h4g ,g#e #h4i #ab;epsilon ,eridani #j4ig #c #c4h #d4f ,k#j #d4h #ac,lac4 #iceb #f4ij #b #g4e #h4b ,k #h4i #ad,pos4 ,m$4 #bafd #b4bh 44 #h4i #i4f ,k #aj4c #ae;epsilon ,indi #d4gj - #h #d4g #e4d ,k#e #f4c #af;,groom4 #cd #b4hi #a #h4a #h4h ,ma #i4e #ag,oe4 ,a4 #agdae #a4cj 44 #i4a #i4g ,k #aj4e #ah,krg] #fj #j4id 44 #i4b #i4f ,k#e #aj4h #ai,lac4 #hgfj #c4ec #c #f4f #g4j ,g #g4e #bjvan ,maan5s p4 m4 /> #c4ja 44 #ab4c #ab4g ,f#j #ab4i #ba;,altair #j4ff - #g #j4i #a4b ,a#e #a4ab #bb;,c4 ,g4 ,a4 #cbdaf #f4aa #e #h4b #h4e ,g #i4a #bc;,bradley #aehd #a4jf - #e #f4a #f4b ,g #f4i ---------------------------------------- --------------------------- sir4_//4 m' ,mean #c4db #i4a #fm4#c #gm4#c ,g#f #g4e ---------------------------------------- --------------------------- ,! mean absolute magnitude ( ! ne> />s is di/ribut$ 9 ! foll[+ way3-- ,m #j #a #c #d #e #f #g #h #i #aj #aa #ab #ac ,numb] #a #b #a #b #a #b #a #d #d #a #a #a #a4 ,:at is ! absolute magnitude ( ! ne> />s t are n conta9$ 9 table8 ,evid5tly !y mu/ pr9cipally be fa9t />s4 ,we may g fur!r & answ] t all />s ) an absolute magnitude bright] ?an #fm mu/ be conta9$ 9 ?is li/4 ,= if ,m is equal to #f or bright]1 m mu/ be bright] ?an #fm1 if ! /> is ne>] ?an "o siriomet]4 ,b we h assum$ t all />s app>5tly bright] ?an #fm are kn[n & are conta9$ 9 ! li/4 ,h5ce also all />s absolutely bright] ?an #fm mu/ be f\nd 9 table #e4 ,we conclude t ! numb] ( />s hav+ an absolute magnitude bright] ?an #fm am\nts to #h4 ,if1 f9ally1 ! spectral type ( ! ne> />s is consid]$1 we f9d f ! la/ column ( ! table t ^! />s are di/ribut$ 9 ! foll[+ way3-- ,spectral type ,b ,a ,f ,g ,k ,m ,numb] #j #b #b #e #i #c4 ,= two ( ! />s ! spectrum is = ! pres5t unkn[n4 ,we f9d t ! numb] ( />s increases ) ! spectral index4 ,! unkn[n />s 9 ! siriomet] sph]e belong probably1 9 ! ma91 to ! r$ types4 ,if we n[ seek to =m a conception ( ! total numb] 9 ?is sph]e we may proce$ 9 diff]5t ways4 ,,edd+ton1 9 8 ,/ell> movem5ts1 to :i* ,i ref] ! read]1 has us$ ! prop] motions z a scale ( calculation1 & has f\nd t we may expect to f9d 9 all #cb />s 9 ?is sph]e1 conf9+ ourselves to />s app>5tly bright] ?an ! magnitude #im4#e4 ,?is makes #h />s p] cub4 sir4 ,we may attack ! problem 9 o!r ways4 ,a v r\gh me?od :i*1 h[ev]1 is n )\t importance1 is ! foll[+4 ,let u suppose t ! ,galaxy 9 ! direction ( ! ,milky ,way has an ext5sion ( #ajjj siriomet]s & 9 ! direction ( ! poles ( ! ,milky ,way an ext5sion ( #ej sir4 ,we h lat] to return to ! full] discussion ( ?is ext5sion4 ,= ! pres5t x is suffici5t to assume ^! values4 ,! :ole sy/em ( ! ,galaxy !n has a volume ( #bjj million cubic siriomet]s4 ,suppose fur!r t ! total numb] ( />s 9 ! ,galaxy w\ld am\nt to #ajjj millions1 a value to :i* we %all also return 9 a foll[+ *apt]4 ,!n we conclude t ! av]age numb] ( />s p] cubic siriomet] w\ld am\nt to #e4 ,?is supposes t ! d5sity ( ! />s 9 ea* "p ( ! ,galaxy is ! same4 ,b ! sun lies r ne> ! c5tre ( ! sy/em1 :]e ! d5sity is 7consid]ably7 great] ?an ! av]age d5sity4 ,a calculation1 :i* w be f\nd 9 ! ma!matical "p ( ^! lectures1 %[s t ! d5sity 9 ! c5tre am\nts to approximately #af times ! av]age d5sity1 giv+ #hj />s p] cubic siriomet] 9 ! neighb\rhood ( ! sun 7& ( ! c5tre74 ,a sph]e hav+ a radius ( "o siriomet] has a volume ( #d cubic siriomet]s1 s t we obta9 9 ?is way #cbj />s 9 all1 )9 a sph]e ) a radius ( "o siriomet]4 ,= diff]5t reasons x is probable t ?is numb] is r too great ?an too small1 & we may p]haps e/imate ! total numb] to be some?+ l #bjj />s1 ( :i* m ?an a t5? is n[ kn[n to ! a/ronom]s4 ,we may also arrive at an evaluation ( ?is numb] by proce$+ f ! numb] ( />s ( diff]5t app>5t or absolute magnitudes4 ,?is latt] way is ! mo/ simple4 ,we %all f9d 9 a lat] p>agraph t ! absolute magnitudes :i* are n[ kn[n diff] betwe5 -#h & #ac4 ,b f ma!matical /ati/ics x is prov$ t ! total range ( a /ati/ical s]ies am\nts ^u an av]age to approximately #f times ! disp]sion ( ! s]ies4 ,h5ce we conclude t ! disp]sion 7sigma7 ( ! absolute magnitudes ( ! />s has approximately ! value #c 7we %\ld obta9 sigma #ac #h 3 #f #c4e1 b = l>ge numb]s ( individuals ! total range may am\nt to m ?an #f sigma74 ,z1 fur!r1 ! numb] ( />s p] cubic siriomet] ) an absolute magnitude bright] ?an #f is kn[n 7we h obta9$ #h 3 #d #b />s p] cubic siriomet] bright] ?an #fm71 we get a relation betwe5 ! total numb] ( />s p] cubic siriomet] 7,d#j7 & ! mean absolute magnitude 7,m#j7 ( ! />s1 s t ,d#j c be obta9$1 z soon z ,m#j is kn[n4 ,! computation ( ,m#j is r difficult1 & is discuss$ 9 a foll[+ *apt]4 ,suppos+1 = ! mom5t1 ,m#j #aj we get = ,d#j ! value #bb1 correspond+ to a numb] ( #ij />s )9 a di/ance ( "o siriomet] f ! sun4 ,we %\ld !n "k a fif? "p ( ^! />s4 #cd4 ,p>allax />s4 ,9 #bb ,i h paid att5tion to ! n[ available catalogues ( />s ) kn[n annual p>allax4 ,! mo/ ext5sive ( ^! catalogues is t ( ,,walkey1 conta9+ measur$ p>allaxes ( #fbe />s4 ,= a great _m ( ^! />s ! value ( ! p>allax measur$ mu/ h[ev] be consid]$ z r unc]ta91 & ,i h po9t$ out t only = su* />s z h a p>allax great] ?an #j4jd 7or a di/ance small] ?an #e siriomet]s7 may ! measur$ p>allax be consid]$ z reliable1 z lea/ g5]ally speak+4 ,! effective numb] ( p>allax />s is !re=e ess5tially r$uc$4 ,indirectly x is nev]!less possible to get a relatively l>ge catalogue ( p>allax />s ) ! help ( ! +5i\s spectroscopic me?od ( ,,adams1 :i* p]mits u to det]m9e ! absolute magnitude1 & !re=e also ! di/ance1 ( ev5 f>!r />s ?r\gh an exam9ation ( ! relative int5sity ( c]ta9 l9es 9 ! /ell> spectra4 ,x may be t ! me?od is n yet z firmly bas$ z x %\ld be1#ae b !re is e reason to believe t ! c\rse tak5 is ! "r "o & t ! catalogue publi%$ by ,,adams ( #ejj p>allax />s 9 ,contrib4 f ,m\nt ,wilson1 #adb1 already gives a m complete mat]ial ?an ! catalogues ( directly measur$ p>allaxes4 ,i give "h a %ort resum ( ! attributes ( ! p>allax />s 9 ?is catalogue4 ,! catalogue ( ,,adams embraces />s ( ! spectral types ,f1 ,g1 ,k & ,m4 ,9 ord] to complete ?is mat]ial by p>allaxes ( blue />s ,i add f ! catalogue ( ,,walkey ^? />s 9 8 catalogue t belong to ! spectral types ,b & ,a1 conf9+ myself to />s = :i* ! p>allax may be consid]$ z r reliable4 ,!re are 9 all #fa su* />s1 s t a sum ( #efa />s ) kn[n di/ance is to be discuss$4 ,= all ^! />s we "k m & ,m & = ! great "p ( !m also ! prop] motion mu4 ,we c !re=e = ea* spectral type compute ! mean values & ! disp]sion ( ^! attributes4 ,we ?us get ! foll[+ table1 9 :i* ,i conf9e myself to ! mean values ( ! attributes4 ,,table #f4 ,,mean ,,values ,,( m1 ,m ,,& ,,! ,,prop] ,,motions 7mu7 ,,( ,,p>allax ,,/>s ,,( ,,diff]5t ,,spectral ,,types4 ------------------------------- ,sp4,numb] m ,m mu ------------------------------- ,b #ae #b4jc -#a4fg #j4je ,a #df #c4dj #j4fd #j4ba ,f #abe #e4fj #b4aj #j4dj ,g #agi #e4gg #a4fh #j4ea ,k #ahd #f4ag #b4ca #j4ec ,m #db #f4jb #b4cj #j4hb ------------------------------- ,we %all lat] consid] all p>allax />s tak5 toge!r4 ,we f9d f table #f t ! app>5t magnitude1 z well z ! absolute magnitude1 is approximately ! same = all yell[ & r$ />s & ev5 = ! />s ( type ,f1 ! app>5t magnitude be+ approximately equal to #fm & ! absolute magnitude equal to #bm4 ,= type ,b we f9d ! mean value ( ,m to be -#am4#g & = type ,a we f9d ,m #jm4#f4 ,! prop] motion also v>ies 9 ! same way1 be+ = ,f1 ,g1 ,k1 ,m approximately #j4e & = ,b & ,a #j4a4 ,z to ! mean values ( ,m & mu we _c draw di/9ct conclusions f ?is mat]ial1 because ! p>allax />s are select$ 9 a c]ta9 way :i* ess5tially influ5ces ^! mean values1 z w be m fully discuss$ bel[4 ,! mo/ int]e/+ conclusion to be drawn f ! p>allax />s is obta9$ f _! di/ribution ov] diff]5t values ( ,m4 ,9 ! memoir ref]r$ to1 ,,adams has obta9$ ! foll[+ table 7some:at diff]5tly arrang$ f ! table ( ,,adams71#af :i* gives ! numb] ( p>allax />s = diff]5t values ( ! absolute magnitude = diff]5t spectral types4 ,a glance at ?is table is suffici5t to indicate a s+ul> & well pron\nc$ prop]ty 9 ^! frequ5cy di/ributions4 ,we f9d1 inde$1 t 9 ! types ,g1 ,k & ,m ! frequ5cy curves are evid5tly resolvable into two simple curves ( di/ribution4 ,9 all ^! types we may di/+ui% betwe5 a bright gr\p & a fa9t gr\p4 ,) a t]m9ology propos$ by ,,h]tzsprung ! =m] gr\p is said to consi/ ( giant />s1 ! latt] gr\p ( dw>f />s4 ,ev5 9 ! />s ( type ,f ?is division may be sugge/$4 ,?is di/9ction is /ill m pron\nc$ 9 ! graphical repres5tation giv5 9 figures 7plate ,,iv74 ,,table #g4 ,,di/ribution ,,( ,,! ,,p>allax ,,/>s ,,( ,,diff]5t ,,spectral ,,types ,,ov] ,,diff]5t ,,absolute ,,magnitudes4 ---------------------------------------- --------- ,m ,b ,a ,f ,g ,k ,m ,all ---------------------------------------- - - #d 44 44 44 44 44 #a 44 - #c 44 44 44 44 44 44 44 - #b #a #d #a #g 44 #b #ae - #a #b #g #g #bh #ae #d #fc - #j #c #aj #f #cb #dj #aj #ia #j #a #aa #f #g #ad #aa #ej #a #a #c #bj #i #d #a #ch #b 44 #e #dh #bf 44 #a #hj #c 44 #a #cb #cf #b 44 #ga #d 44 #a #e #be #be 44 #ef #e 44 #a 44 #f #be 44 #cb #f 44 #b 44 #c #aj 44 #ae #g 44 #a 44 44 #ad 44 #ae #h 44 44 44 44 #c #g #aj #i 44 44 44 44 #b #d #f #aj 44 44 44 44 44 44 44 #aa 44 44 44 44 44 #a #a ---------------------------------------- - ,total #h #df #abe #agi #aed #db #eed ---------------------------------------- --------- ,9 ! di/ribution ( all ! p>allax />s we once m f9d a simil> bip>tition ( ! />s4 ,argu+ f ^! /ati/ics "s a/ronom]s h put =w>d ! !ory t ! />s 9 space are divid$ into two classes1 :i* are n 9 reality closely relat$4 ,! "o class consi/s ( int5sely lum9\s />s & ! o!r ( feeble />s1 ) little or no transition betwe5 ! two classes4 ,if ! p>allax />s are arrang$ accord+ to _! app>5t prop] motion1 or ev5 accord+ to _! absolute prop] motion1 a simil> bip>tition is reveal$ 9 _! frequ5cy di/ribution4 ,nev]!less ! bip>tition ( ! />s into two su* di/9ct classes mu/ be consid]$ z vague & d\btful4 ,su* an app>5t bip>tition is1 inde$1 necess>y 9 all /ati/ics z soon z individuals are select$ f a giv5 population 9 su* a mann] z ! p>allax />s are select$ f ! />s 9 space4 ,let u consid] ?ree attributes1 say ,a1 ,b & ,c1 ( ! individuals ( a population & suppose t ! attribute ,c is positively correlat$ to ! attributes ,a & ,b1 s t to great or small values ( ,a or ,b correspond respectively great or small values ( ,c4 ,n[ if ! individuals 9 ! population are /ati/ically select$ 9 su* a way t we *oose out individuals hav+ great values ( ! attributes ,a & small values ( ! attribute ,b1 !n we get a /ati/ical s]ies reg>d+ ! attribute ,c1 :i* consi/s ( two seem+ly di/9ct normal frequ5cy di/ributions4 ,x is 9 l mann]1 h[ev]1 t ! p>allax />s are select$4 ,! reason = ?is selection is ! foll[+4 ,! annual p>allax c only be det]m9$ = ne> />s1 ne>] ?an1 say1 #e siriomet]s4 ,! direct pick+ out ( ^! />s is n possible4 ,! a/ronom]s h !re=e attack$ ! problem 9 ! foll[+ way4 ,! ne> />s mu/1 on acc\nt ( _! proximity1 be relatively bright] ?an o!r />s & secondly possess great] prop] motions ?an ^?4 ,!re=e p>allax obs]vations are ess5tially limit$ to 7#a7 bright />s1 7#b7 />s ) great prop] motions4 ,h5ce ! select$ attributes ( ! />s are m & mu4 ,b m & mu are bo? positively correlat$ to ,m4 ,by ! selection ( />s ) small m & great mu we get a s]ies ( />s :i* reg>d+ ! attribute ,m seem to be divid$ into two di/9ct classes4 ,! di/ribution ( ! p>allax />s gives u no reason to believe t ! />s ( ! types ,k & ,m are divid$ into ! two suppos$ classes4 ,!re is on ! :ole no reason to suppose ! exi/5ce at all ( classes ( giant & dw>f />s1 n any m ?an a classification ( ?is k9d c be made reg>d+ ! height ( ! m5 9 a population4 ,:at may be /ati/ically conclud$ f ! di/ribution ( ! absolute magnitudes ( ! p>allax />s is only t ! disp]sion 9 ,m is increas$ at ! transition f blue to yell[ or r$ />s4 ,! fill+ up ( ! gap betwe5 ! dw>fs & ! giants w probably be p]=m$ accord+ z our k ( ! di/ance ( ! />s is ext5d$1 :]e1 h[ev]1 n ! annual p>allax b o!r me?ods ( measur+ ! di/ance mu/ be employ$4 ,,table #h4 ,,! ,,absolutely ,,fa9te/ ,,/>s4 ,transcrib]'s ,note3 ,to cons]ve space 7ad7 is us$ 9 place ( 7alphadelta74 ---------------------------------------- --------------------------- #a #b #c #d #e #f #g #h ---------------------------------------- --------------------------- ,position ,di/ance ,"n ---------------------------------------- ---- 7ad7 ,squ>e l b pi r ---------------------------------------- --------------------------- sir4 #a,proxima ,c5tauri 7#adbbfb7 ,,gd#aj #bha - #b #j4ghj #j4bf #bvan ,maan5s /> 7#jjdcjd7 ,,ge#h #ib -#eh #j4bdf #j4hd #c;,b>n>ds /> 7#agebjd7 ,,gc#ab #ceh #ab #j4eae #j4dj #dag ,lyr ,c 7#aijccb7 ,,gc#b #ca #aj #j4abh #a4fj #e;,c4 ,z4 #e;h4#bdc 7#jejgdd7 ,,ge#g #bah -#ce #j4cai #j4fe #f;,gron4 #ai ,,viii #bcd 7#afahci7 ,,gb#a #bi #dd #j4afb #a4bg #g,oe4 ,a4 #agdae 7#agcgfh7 ,,gb#h #fe #cb #j4bfh #j4gg #h;,gron4 #ai ,,vii #bj 7#afbadh7 ,,gb#b #da #dc #j4acc #a4ee #i,pos4 ,m$4 #bafd 7#ahdaei7 ,,gc#b #ef #bd #j4bib #j4ga #aj,krg] #fj 7#bbbdeg7 ,,gc#h #gb #j #j4bef #j4ha #aa;,b4 ,d4 #efecb 7#jbabef7 ,,gd#h #ajc - #d #j4aie #a4jf #ab;,b4 ,d4 #eeeha 7#jbacef7 ,,gd#h #ajc - #d #j4ahe #a4ab #ac;,gron4 #ai ,,viii #dh 7#afjdch7 ,,gb#a #bg #df #j4jia #b4bg #ad,lal4 #baahe 7#ajegcf7 ,,gb#e #aec #ff #j4djc #j4ea #ae,oe4 ,a4 #aafgg 7#aaadff7 ,,gb#c #ajc #ej #j4aih #a4jd #af,walkey #fec 7#aeecei7 ,,gb#b #eg #de #j4age #a4ah #ag,y]kes p>allax /> 7#jbabdc7 ,,gd#h #ajg -#af #j4jde #d4eh #ah;,b4 ,d4 #efecg 7#jbabef7 ,,gd#h #ajc - #d #j4age #a4ah #ai;,gron4 #ai ,,vi #bff 7#jfbjhd7 ,,gc#c #ig #bg #j4jga #b4hj ---------------------------------------- --------------------------- sir4 ,mean 44 44 44 #bg4ej4bdd #j4ii ---------------------------------------- --------------------------- ---------------------------------------- ------------------------- #a #b #i #aj #aa #ab #ac #ad ---------------------------------------- ------------------------- ,motion ,magnitude ,spectrum ,"n ---------------------------------------- -- mu ,w m ,m ,sp m' ---------------------------------------- ------------------------- sir4_//4 m' #a,proxima ,c5tauri #c4he 44 #aam4#j #acm4#i 44 #ac4e #bvan ,maan5s /> #c4ja 44 #ab4c #ab4g ,f#j #ab4ie #c;,b>n>ds /> #aj4bi -#ai #i4g #aa4g ,mb #h4i #dag ,lyr ,c #a4ge 44 #aa4c #aj4c 44 #ab4e #e;,c4 ,z4 #e;h4#bdc #h4ge #ea #i4b #aj4a ,k#b #aj4fh #f;,gron4 #ai ,,viii #bcd #j4ab 44 #aj4c #i4h 44 44 #g,oe4 ,a4 #agdae #a4cj 44 #i4a #i4g ,k #aj4e #h;,gron4 #ai ,,vii #bj #a4bb 44 #aj4e #i4f 44 44#j #i,pos4 ,m$4 #bafd #b4bh 44 #h4i #i4f ,k #aj4c #aj,krg] #fj #j4id 44 #i4b #i4f ,k#e #aj4h #aa;,b4 ,d4 #efecb 44 44 #i4e #i4d 44 44 #ab;,b4 ,d4 #eeeha 44 44 #i4d #i4b ,g#e #aj4b #ac;,gron4 #ai ,,viii #dh #j4ab 44 #aa4a #i4c 44 44 #ad,lal4 #baahe #d4gg -#ah #g4f #i4a ,mb #h4i #ae,oe4 ,a4 #aafgg #c4jc 44 #i4b #i4a ,ma #aa4j #af,walkey #fec 44 44 #i4e #i4a 44 44 #ag,y]kes p>allax /> 44 44 #ab4d #i4a 44 44 #ah;,b4 ,d4 #efecg 44 44 #i4d #i4j 44 44 #ai;,gron4 #ai ,,vi #bff #j4ji 44 #aa4c #i4j 44 44 ---------------------------------------- ------------------------- sir4_//4 m' ,mean #b4if #bi4c #ajm4#j #im4#i ,k#a #aj4i ---------------------------------------- ------------------------- ,reg>d+ ! absolute brightness ( ! />s we may draw "s conclusions ( int]e/4 ,we f9d f table #g t ! absolute magnitude ( ! p>allax />s v>ies betwe5 -#d & #aa1 ! extreme />s be+ ( type ,m4 ,! absolutely brighte/ />s h a r great di/ance f u & _! absolute magnitude is badly det]m9$4 ,! brighte/ /> 9 ! table is ,ant>es ) ,m -#d4f1 :i* value is bas$ on ! p>allax #j4jad f\nd by ,,adams4 ,s small a p>allax value is ( little reliability :5 x is directly comput$ f annual p>allax obs]vations1 b is m tru/wor?y :5 d]iv$ ) ! spectroscopic me?od ( ,,adams4 ,x is probable f a discussion ( ! ,b-/>s1 to :i* we return 9 a lat] *apt]1 t ! absolutely brighte/ />s h a magnitude ( ! ord] -#em or -#fm4 ,if ! p>allaxes small] ?an #j4ja 7 tak5 into acc\nt we %\ld f9d t ,canopus w\ld repres5t ! absolutely brighte/ />1 hav+ ,m -#h4ag1 & next to x we %\ld f9d ,,rigel1 hav+ ,m -#f4ig1 b bo? ^! values are bas$ on an annual p>allax equal to #j4jjg1 :i* is too small to all[ ( an e/imation ( ! real value ( ! absolute magnitude4 ,if on ! contr>y ! absolutely fa9te/ />s be consid]$1 ! p>allax />s give m tru/wor?y results4 ,"h we h only to d ) ne> />s = :i* ! annual p>allax is well det]m9$4 ,9 table #h ,i give a li/ ( ^? p>allax />s t h an absolute magnitude great] ?an #im4 ,!re are 9 all #ai su* />s4 ,! fa9te/ ( all kn[n />s is ,,innes' /> ,proxima ,c5tauri ) ,m #ac4i4 ,! ?ird /> is ,,b>n>d's /> ) ,m #aa4g1 bo? be+1 toge!r ) alpha ,c5tauri1 also ! ne>e/ ( all kn[n />s4 ,! mean di/ance ( all ! fa9t />s is #a4j sir4 ,!re is no reason to believe t ! limit ( ! absolute magnitude ( ! fa9t />s is f\nd f ^! fa9t p>allax />s3--,c]ta9ly !re are _m />s 9 space ) ,m #acm & ! mean value ( ,m1 = all />s 9 ! ,galaxy1 is probably n f> f ! absolute value ( ! fa9t p>allax />s 9 ?is table4 ,?is problem w be discuss$ 9 a lat] "p ( ^! lectures4 ,,footnotes3 ,footnote #ae3 ,comp>e ,,adams' memoirs 9 ! ,contributions f ,m\nt ,wilson4 ,footnote #af3 ,! fir/ l9e gives ! />s ( an absolute magnitude betwe5 -#d4i & -#d4j1 ! second ^? betwe5 -#c4i & -#c4j1 c4 ,! />s ( type ,b & ,a are f ,,walkey's catalogue4 ,illu/ration3 ,,plate ,i4 ,,conv]sion ,,( ,,equatorial ,,coord9ates ,,into ,,galactic ,,coord9ates4 ,illu/ration3 ,,plate ,,ii4 ,squ>es & ,con/ellations4 ,illu/ration3 ,,plate ,,iii4 ,! ,h>v>d ,classification ( ,/ell> ,spectra4 ,illu/ration3 ,plate ,,iv4 ,di/ribution ( ! p>allax />s ov] diff]5t absolute magnitudes4 ,,sci5tia ,,publi%] ,k4 ,g4 ,,malmqui/3 ,a /udy ( ! />s ( spectral type ,a4 ,l4 ,m4 ,,ii1 #bb4 ,price3 #f ,kr4 ,c4 ,v4 ,l4 ,,*>li]3 ,vorlesung5 b] die ,grundzge d] ma!matis*5 ,/ati/ik4 ,price3 #aj ,kr4 ,f4 ,,ess*]3 b] die ,/]bli*keit 9 ,s*w$54 #ahhf-aiad4 ,e9e ,/abilitts- und ,korrelationsunt]su*ung4 ,l4 ,m4 ,,ii1 #bc4 ,price3 #f ,kr4 ,b4 ,f,,nge3 ,on ! di/ances & lum9osities ( />s ( spectral type ,g z d]iv$ f _! prop] motions4 ,l4 ,m4 ,,ii1 #be4 ,price3 #e ,kr4 ,c4 ,v4 ,l4 ,,*>li]3 ,introduction to ,/ell> ,/ati/ics4 ,price3 #d ,kr4 ,,nils ,h4 ,,rasmuson3 ,a ,rese>* on mov+ clu/]s4 ,l4 ,m4 ,,ii1 #bf4 ,price3 #e ,kr4 ,,sigfrid ,,raab3 ,a ,rese>* on op5 clu/]s4 ,l4 ,m4 ,,ii1 #bh4 ,price3 #h ,kr4 ,,c>l ,,wirtz3 ,fl*5helligkeit5 von #eff ,nebelfleck5 und ,/]nhauf54 ,na* photometris*5 ,beoba*tung5 am #di cm-,refraktor d] ,univ]sitts-,/]nw>te ,/raburg 7,elsa7 #aiaa-aiaf4 ,l4 ,m4 ,,ii1 #bi4 ,price3 #e ,kr4 ,c4 ,v4 ,l4 ,,*>li]3 ,/>gauges by ,william ,h]s*el 7,h7 & ,john ,h]s*el 7h74 ,l4 ,m4 ,,ii1 #cj4 ,price3 #e ,kr4 ,,pr9t$ ,,by ,l,,tcke ,,wulff1 ,,hamburg 99 99 99 99 99 ,transcrib]'s ,note3 ,! foll[+ corrections h be5 made to ! orig9al text4 ,page #d3 ,t]re/ial di/ances *ang$ to ,t]re/rial di/ances ,page #i3 we mu/ *ose1 *ang$ to we mu/ *oose1 ,page #ab3 acromasie *ang$ to a*romatism ,page #ae3 inp>ticul> *ang$ to 9 p>ticul> suppos+1 t *ang$ to suppos+ t ,page #af3 #cic4d mm *ang$ to #cic4d mumu ,page #bj3 = :i* />s if *ang$ to = :i* />s x ,page #bb3 spha]ical *ang$ to sph]ical ,page #bc3 pr9cipal sc\rce *ang$ to pr9cipal s\rce ,page #be3 l5se ) #ae cm *ang$ to l5s ) #ae cm ,page #bg3 ,?r\gh ! spectroscopie me?od *ang$ to ,?r\gh ! spectroscopic me?od made to its pr9cipal *ang$ to made its pr9cipal am]ican mann] *ang$ to ,am]ican mann] ,page #ce3 _m t5?s ( a ye> *ang$ to _m t5s ( ye>s ,page #ch3 same appe>5ce *ang$ to same appe>ance ,page #dg3 r$ /e>s *ang$ to r$ />s disp]sion 9 ,m *ang$ to disp]sion 9 ,m ,page #di3 small] ! *ang$ to small] ?an