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The following diagrams illustrate the method: Les cartes, planches, tableaux, etc.. peuvent etre filmAs i des taux da reduction diff^rents. Lorsque la document est trop grand pour etre reproduit en un seul cliche, il est filmd A partir de Tangle sup^rieur gauche, de gauche it droite, et de haut en bas, en prenant le nombre d'images n^cessaire. Les diagrammes suivants illustrent la m^thode. 1 2 3 1 2 3 4 5 6 DEPARTMENT OF THE INTERIOR C.V.NADA Hon. W. J. lio.-HE, Minister. W. W . CoriT, CM C, [jepuly Mmuler. PUBLICATIONS Dominion Observatory ,i'« OTTAWA W. F. Kino, C.M.G., LL.D., Director. Vol. II, No. 12 Mean distance of stars whose radial velocities, proper motions and parallaxes have been determined BY REYNOLD K. VOLNG, Ph. D. D CAl MT 403 P02-12 O T T A W A CnJVEIl.VME.NT riUNTINU DuUEAD 1 'J 1 5 Lr.OlE POmECHfJIOUE BIBLIOIHEOUE I DEFARTMKNT OF IHK INTERIOR CANADA HnN. W .1. !:,„-,i,:, .\ti„,,t,r. \V, W. CuKl, CMC, l>,puly .\t,n„Ur PUBLICATIONS nr THB Dominion Observatory OTTAWA W. F. Kino, C.M.G., LL.D., Diredor. Vol. II, No. 12 Mean distance of stars whose radial velocities, proper motions and parallaxes have been determined A" V BY REYNOLD K. YOING, IMi. D, ( ) T T A U A GoVEKNMKNT PRINTING UnUEAD 1 !• I .-, SICS'J mi;a\ i)i>r.\\( i; or siaus wiiosi: kadiai. \ lii.ocnii.; i)i:ri;i{.MiM:i). i'i{(>i'i;i( ll\ \i\A \M| I) K \ill Si,, I' .1) 'I'lic tnlliiwiiin iii\(-liL;alioii \\a- iimlrriakcn id aii-\vci- die i|U(-tinn. ^^'" ''"' ""•••'II 'li-iaiKv of Ihc Mar- a> diMcrrniiicl \vnu\ \\iv\v pn.p ■■ in(,ii,,ii~ and radial vclocii ic- a^rrc will) thr mraii di>ianiT a-^ lnriii..| iimn i|,c mcd parallaxcs^.' 'I'll'- data lor llir parallaxes wnv ^di'.-ird iriars of I Ills list, radial \clocilic< were (.i)taiiicd fruiii I lie Mount WiUonr and l,ick Ol.scrvatoryl results. Tli.. proper motion^ of all tln-e -tars arc very larj^e. and indeed for the most part the stars wire .-elected for parallax incusiir.;- Miciit on this account. The excc,ssi\-e ina-init udi> of the cros- motion may 1)0 diu' I- to the proximity of the stars, 2. to the cxccssi\c speed, .'!. to exi-epiionally lartje values of the inclination of the motion to the line of si |Mt ^rniliil. ;i -iiluliiili lui llic -iih~ iniiliiiM Un^ iiiiidc Willi I h'' i"'~nli Ilitilll .\«lll|>i()ll ui' \|)('\ I )i rliiuii mn III \|H\ \ i-lnl'il \ III Sun _'70 •117 \i llli' lliiiliiijl 111' i';ii-|i ~l;ir I- CDirrrliil with llir-f \alufs, we lllnl that llir asiiaili- laillal \rliicil\ inr liir nlir iiUllillril ami ~i\l \ --r\ rli -lar> 1- l.'iL* kllnllli't IT- I'lir I'-l (il -lai- ilicluilr- liilir h l\|)r -tar-, -cv ml rrll \. lull \ -riuhi I . lull \ -liiilil (i. I liiil \ •t'liiii l\ , -cvni M. aiiil Imii- nl iinkiiuun lypc, ( ain|ilirir~ a\riai:r lailial \ cliiril ii - Inr llii- di^l riliiil inn of -Irllar l\|ii- wiiuM 111' \'.'> "^ riir aiilrrlllilll iil lIli' I W 1 1 \all|r- -Upjiiirl- llir riiiiclil~iiiii iliat till' iiiian M'liirii\ iii' llii -lar^ rinplnynl i-< mil >ircall>' in r\rc-^ 1)1 I 111' axi'Taiii'. I III' piujii I' iiiiiiiiin- ai rii:lii amili"' In iIh' >iilai' niniinn t I'uinjKirii'nts'i ami aliiiiti ilir iliMTiiun nl ,-ular nuiiinn i ninipnnrni > i were al-n I'uiiipiiiril wjili llic alii)\r Nalui's t'lir ihr -ular niuiiiin, 'I'lir pu^iliun ol' iIh' api'x a- lilM'll li\ llii^ -prrial jil'iHIp 111 >lai'- i- prclrllcil. Iirrau-r wr ihi'll ilrliiaml i)iil\' lliat the imiliun- -liall lir ai raiiilniii ainmiii I licniM-Kc-- wliicli i^ a li-;-^ raiiical a>>unipiiiin iliaii iliai ilir\ lie ai ramluni with I'c^pci'i iii a ni\rn iliicction, an a>>uin|(liiiM ur wuiilij lia\r in niakr il we hail ailuptcd any utiicr piisitioii ul' the apex. Till' iliirrtidii of llic ~ulai' imitiiin lii'tci'inini'il from this solution has vci'N lilllc \viiij;lii whrii applii'd In iln- univi'i'sc in jicncral. lull il is inicroiinii III iioir in pa>>iiiii thai il i> llic ilcdinai inn which shows ihc variiitioii fitiin the Usually accc|itc(l valiii's. N'cai'lx all llic -Iar> iwcil arc in ihc norlhci'ii licmi.-phci'c. 'riii- wa> line al>o of ihc siar- cinplovcd liy ( 'aiii|)l)cll* in hi-, lir^l Miluiion Inr ihi' -un- wa> fioni iwo hundred and eighty \ clocilic.-. Hoih -.(ilulions ;j;i\-c licA \aluc- for ihc dcclinalion of ihc apex, Whclhcr I he small dci'liiial ion- an due In ihc norihcrn pii>ilions of ihc siars or arc In lie a~crilicd In llie chance iipcr;iiion of un>yninici rical dalu is hard lo -■ii\'. The aiirccmcni would lend In -how ihal the norihcrn lienii>plierc jii\es low \aluc- for the dcclinalion nf the apex. ♦A|i J v.. I l:i. Ml. MK\>ntI.I> \M> "OMITIKI) I'MIVI.I.W nK -l\l(~ 325 'I'lic 1111:111 ill-l;il|ii' (i| llir litiili|i (it >tli:-- \Ml- fVilllMlti'il tlOlli llir fdlllMllll ' m Where ff,„ i> till iiieaii , |)iinill:i\. T„, \^ tlic iiieiiii ('(Hiipoiieiit (if |)i(i|it'r rniitidii iit lijilit aiinle< to tlie sdlitr iiiolidii. \ ,„ is llic Mieaii riulial veldcitw I'.i^^lity-llircc r' :ii'(' |idsili\c and ei>:lil\ -Idiir nenalive, and tli( ir uveraKc value is ()■■ :{;{!(. wiiiili makes w,,, cdinpiiled ()"!()(). 'I'lie mean parulla'c us (il)ser\t'd t'dr the ^ame -iar> i> 0" 07l' it ue icjeei a dd/e'i stars whose l)i()per nidtidiis are larne and uhicli were ndt rejected liy tlie cdndi'icjn tlial the rudial velocity lie und r lili\ kilnmeiro, we olitain a computed mean l)aralla\ 0" OS") as oppoxd to 0" Olid dh>er\cd. The rejection (if these stars does iidl alter the ratio of the coinputeil and niiserved parallaxes materially. Melhdds of determininji; the mean distance of the slais hased upon the data from the c componentN are still a\ailalile, and while these can not he cdiisidered as having as much weight as thd>e based on the t eompoiients, it is of interest to see how tiie\' a^ree with the results above. The first method is based upon the muiinitude of the parallactic motion. We have iletermined by a system of trials, that mean distance, such that when each star is corrected for the solar motion, the total sum of the l)dsitive 1' components is eciual to the sum of the ni'gative. The mean parallax that will accomi)lish the result is ()"-H)'). a value almost in exact agreement with the value found from tiie t convponents. Reject in>; the same dozen stars as before would yield thi' value 0" (192. When the c comixineiits liave been corrected on the basis of this mean distance, the corrected values may be treateil as the r components to yield a third value for the mean distance of the stars. v,,. = 4-738 X :<2<; ri 111,11 \llu\-. n\ nil. |)MMi\!ii\ m'.-i;k\ \lnin . \\ here I , i- niiw ilir iiiraii \;iliii' of the (•(irrrctcd r componoiit-;. l''n)iii this il;it:i i!h' \:iliit' d" i:;:; ua- ulilaiiiiMi (ir 0" O'.ts il' twrl\i >la:> wrrv (, muted. The rollci Icd loull- air >ii(i\\Il in llif taltlc l>rl(i\v: I'riirii H'lT .-tars i'rnlii l.'t.'i -Iar>- <)ll.-Klt\ Kl». (I 07.' >(■ IK'.') r I '(.inlMin.iil.- I'arillaillc i I '..iiiliniiriil.- TIlUllUIl 11' IIM'i O ' Os.'i II" III.-, II ll'ij II" i:',.i u ' (I'. Is \\'li:il rlTccl -lidiilil llic |ilniiniiirii(Hi ill ~lai >1 1'caiiillili lia\r nil the r,.>illt.' ill iil'ili'i' 111 asrri'I;,iii il' llii- wii'r |ii'('-rlil. lln' .~lal'> wcl'i' tested hiitli iVniii llieir railial \elrrilie- ami inim ilieir |ii'ii|ier mnlinus. I'nr the lailial vrlurilie-. llir I'liail \alile lul' ~lai- williill -i\l\ (li'm'cr~ ol' llir NTTt ires (if preferential iiuitin i \\a~ 17 ti Ivilcmei ir~ a- nppci-ed 111 I:Mi in Iiii.' rcniainiiiji pari nl ti. >k.N . 'In H'-l ilir iniiprr iiiDiiiins, "arli star was riirrci'ted tor ilic ^ular '■iiinpniirnt mi ilir !ia-is uf the uhscfved parallax. Tlie -tal's were llieii diviiii'il iiitu I w ii iiriiiip-. i-e wilhili -i\l>- ilet;ri','S ol the \erte\ ami lliii-i' niil-iilr ilii- I'l'iiiiiii. 1 1' ilii' -tar- arc iiinviiiii murf lapiilK aliiiiii I III' lim' jniniiiii iIh' vertices, the pi'o|ici' luotioiis sliuiild lii' Hicalc-l at riiilii aimic- In ilil- line Tlic axcraiic values in the Iwn rc.iiioiis were ()■■ .')M ami II". '(77. 'i'lie imtlKnl i- dntilitless cnide anil the refiiniis rallier lame Iml we wmild lia\c e\peeleil llie .-tar streaming to luive shown innfe llian these ininiliel~ imlieale. I.el u- ennsider hnV,e\er what I he iTfeel nl >Urh a pi'el elelllial llinlinil WiMlId he nil the re-l|ll~. {'he di reel inn- nl' this lilnlinll a-!J.i\e|l li> Kapleui all- ili^ihl a-eell-inll . '. 1 1 ami _'7 I I )ee|iiial il 111 • I •! and - hi ' a lii,, whieh i- mil \ ei \ iar Imin I he ape\ nf the -iiii'- w a>- il-eii in this -iillltinli. The T riinipnlient- nl pl'npel' llinlinn -hnillil lint lie l.llieh atteeted, wiiile the railial \elneilies sIkhiIiI lie ilieieasid. anil we unillil e\pecl llitll llie applii'.iliin 111 the I'niniiila Ml'.\--1 i;i;i) \M) iiiMI'l I I.I) I'M! AI.I-.W i)K >1 AK HMilil t:i\c iiMP -iiKiH iiiiliii iIkiii lull lai'iic a \:iliir fur ilii' iikmm |i;ir,'ill;r\ III t ii'iiliiiji llic cnricricil i coinpiMJli I > liv llic >miih' luiiniila 7r,„- 1-,HS r tlic rlTiri will (jcpniil Mil the di-l ril ml i(iii i>\' the >i:ir-. If iicaiiv all ilir »l:il> were tdUliil near llic \clticcs. I ,„ would iir iiHTra.-cd while r',,, would irinaiii atinui llic >aiiic. II on the oilier hand ino-t ot' the -lai- wcrc niidwax hctwccii ihc vertices, then i '„ would 1)" increased and I ,., leinain consiani. A --yninietricai distrihiition slmuld leaxc the rc-ults oi' the application ol' ihi> I'oriiiiila cnlillcd to as much wciiihl as the \alue from till' T coniponents. As rejiards the adjusted \aluc which reino\cs llie parallactic et't'cct, it depcnils directly upon the \('!ocit>' ol' the sini adojitcd. The hi^hci' the \el(icit\- of tiic ~un ciio~eii, the >inallci' will lie the \alue of the parallax. Il' v.c had u-e(l a \clocity of the .-iiii alxmt twenty-live kilonietre~ per second, the ohseiAcd and computed values of the mean parallax from this source Wdulti ha\i' lieeii in aiireeincnt . The parallactic method of dclcrminiiiii the mean distance of a lii'oiip of slar> is apjilicalilc without a knowlediic of the I'adial velocities and so could have hecn applied to a mucii lariicr numher of stars. This solution lias heen practicall\ carried out hy Lewis Ii(, ss.* 1 rom ."y.V.t -lars with iiican projici' motion over '.\\"'.) per centiirv he deterniineil the parallactic motion and ass"niinf: the parallaxes to he correct. re\(rsed the prohlcm to detcrniinc the speed of the sun. It is vcvy interestinii that the velocity obtained was 2\ '^ kiloniel ro: a value which i- undoiihtedlv too hitih. hut which is ahiiosi in exact atifeement with the speed tha.t would have to lie assumc(l for the present list of stars lo .iiake the ol)serv(>d ami computed mean parallaxes ajiree. ' V'lrn,|..inl."ir.liMinial. Vnl. .'il,''l|s. .^.0y^'r.:::]^. iiiliLli. ' -■f -j^''- ;',2s I'l HI H \ I lii\> "!■ II': ' iMlNlii^ c)H-i,H\ \ MUa , (Ulicr r\|)l;inatii)n- "l' the (lirt'civiicr licUvrcn llic oU-ciMd iiini ,,„iipulr,l |.,inillax(> ^iisii!,.-! thciii-clv.-. I'Ik' rir>l i> Hial in clinn^uiii -lar- \si!li lartir |irii|»T niiili(in> we have scIim'KmI slar> wIkim' mean aiiillc "I ■mcliiialiun In tlic line (if >iiilil i- larger iliaii ilic law nl' raiuloiii iiiniinti '.soi.ld iii.,l^i, it li iliK i- tiiic Ihr prc-cni iv-iili- woulil lir cxplaiiHMl, Tlic npnaliiiii i)f ilii> factor would atTrct ivlation- coiiiici'linn parallax and pnnxT motions in general, for -ucli ivlation> arc derived from stais with lartie proper motion-. Anothei- explanation mi^ilit lie that tliesK-Uar system as a whole is rolaliiin. a phenomenon whieh would alTeet the proper motions and not the radial velocities. However this latter explanation .-eems \ cry impi-ohalile, •!- the major pari of aii>- rotational clTcct in proper molioiir- nniM lie eliminated l-y solutions for the po-ilion of the vernal e(|uiiiox. There remain- the pos-iliili'y that the .-tars em|)lo\ed contain an unuMial mimlier of iiejiative parallax.-. Dominion ' »l>-cr\atory, ( )tlawa. ,Iui\, llU."). t^OLf POL YTFCh'NiQUF OF MONTntA ll!!llllini!lllil!!llllllflll!lllllillillllllllii III! 3 133M DDOblMftl t ■(•;-; j- :^ ^" -■^