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Les diagrammes suivants illustrent la m6thode. 1 2 3 1 2 3 4 5 6 DEPARTMENT OF THE INTERIOR CANADA Hon. W. J I!oriiE, Minialer. \V. W. Tort, r.M.r.., Def. ily Mimsler. PUBLICATIONS Dominion Observatory OTTAWA ,P< W. F. Kino, C.M.G., LL.D., Director. Vol. I, No. 10 Orbit of b Persei BY J. B. CANNON, M.A. P CAl MT W3 POl-10 OTTAWA Government Printing Bureau 1911 ECOLt POLYTECHNIUUE BIBLIOlHECUt ECOLE POLYTECHNIOUE BiBllOTHFOiit DEPARTMENT OF THE INTERIOR CANADA II, ,s U I l!."iit. W<.,i.«/.r. W W f,„A. f MC . Ihj.nhj Minister. PUBLICATIONS A Dominion Observatory OTTAWA \V. F. Kino, C'.M.U., LL.D., Uinclor. Vol. I, No. 10 Orbit of b Persei BY (t^f J. B. CANNON, M.A. O T T A W A CioVERNMENT PRINTING HuHEAU 19 1 » 60443—1 ni;r.l'r ('I h i'i:i;-i;i m J. I). CANNON, M.A. h rn-i i (rt^l'' 1()"'7, (5 ^."O" d.','. iiia liiiiaiiird ln!r ~liiiu ili'ul.lr liiii -, III (lie second siK'CI rum lliii- appi aiiii:^,. liic line- aic im: at all 'Aril ilfUncd and ii;easures on llieui arc iinly lair a-- will \>r mtii 1i\ ilic inai^iiii iidi- i)f the fi'sidtials. Tiie lilif^ wliirli >lic)\\ ddiililiiiii arc 11 . II,,. and in (jiic case the iron liiic .'\ id |."i. 'riiirty->i\ plates dating; I'loin (hidi.er II), p.ild, \n Aiuil 'Jl. IMII. v.-ero taken in all. The lines are a'noni the a\c:a,iie I'm- this tyjie. i'.eiii'^- a ddulile .^pcciniiM and the tun conipiinciit> hcinr, -cpaiaMc in iinl\ a tew plates, the inea^iiiinii is iiiore diiliciili than it wmilij iitherwi c he. All plate> were taken with liic >in'.Jc-pri>ni .-pccini;irapli, the Icni^iji rciniired for u>in,u the three ]iri-in> hein^ ton cnat foi' a ~tar of this ina^nitiidc. Si'cd 27 plates were usim! t hiiiiifihniil for the >anie rea-iHi. althoii'^ih a liner tiiaiiicd jilate niijiht ha.xi' liccn \ ( . y ad\ ;intaj;cn\is foi' ^liewint; d(iul)liii^ of lines. 'I'he line.> measured were: — ■|\ni,i I. I IJiir.iiii. \\ uvc-I.cnulli. i:irim'iil. i Wiivi'-I.i'imtli. 1 : i ll\ilr>1 UK) lIvilriiKfii l:;|il (;;;( Iron I.' I'.i-JiWi Ilyiliii|i(Mi inn s^O Iriin iat."> ■ itT.'i Ilydrogui , :JU7017;t ,jCaldum , J'Jaa-S25 I J I _^___ •I. I) le V 171 t<)i;I\ nil (mi (IT- Iv.d pl'i''^ i.iili:; 2 •2m PI lil.K ATIONS IlK TIIK rMlXllMOS ai'/ liniu (..iintdl pcriastron. ami 'ln' rc-iilual- fmiii ihc <'ciii('ci,i| ciiuc I Mil I II I II K iiii^r.iiv \riiiNs ('iiMI'iPNKNT 1. C.'llUIHiVKNT II. IMuli' Pat<'. 1003 .Nov 3 Nov 111 I'.KMi .<,I.t HI. 1009 >,Tt 2. I'.HO (let. I...... JiiU.'Ui Uuy. IMia ■J. UCi, l'.'-J-{CJJ 1 J'l' i:t.'i'.)Mt I 1-'^ 7.47:i-97S MO >*.,"i.",-' 017 .V.>1 +52-5' ;Hi(i '.Hi'.i li;i V>1. Wt. OC. Vel. Wt. o*. -12 5 - 0-5 1 • 111 .". -6.31 +52-5 1 +12-5; 1 -31 4 -9.6, TAI'.I 1. Ill (111 \\\.\ nl',.~i:i;\.\l li iN,~ * i. Com ! ■IINF.N. 1. C'.iMl ONKM 11 'C 1 i Plate w Dati'. X Jllll.lU l'li:i.«c. c M Day. t VpI. Wt. (>C. 1 Vcl. Ul (i-C. I'MI) 111. .^7J.. [M (in. Ill at , 2. Hs.'.i.'i."i>n:i(i i M-.M +3.V4 l-.'i -7.(1 :i73>* (; |(W. 12 (X) j (•.■.7-7tiO 1 iWu -27f r,r,'- It) mn ]»i Xi)V. 9 72 i.ts.-, (HO ' .11.'. + 12-h 3-7!- 92 3S1U I< Xki: r, 70 '.1,111 1 T.'o .-.l-.l +41-S 2-5 + .5-3 .'tsati I'l '[ie<: « 77 iir_| 7' 1(1 114 -;mfi , 1.5 - 9-5 3.>Si-l i* :i>r. 10 .".II (iiii .■-'11 • llhD 1 +51-: 2.7 - 5-2: 'l;nri iS t07S Ills: lUKI 4113 413:1 4143 4170 4185 4195 4246 (• li (>i li II Dtttc. 1910 12 . t>f l).v. 15 Dir. Id I),..- 21 IJ.I- 30 Kill Jun. 5. Juii. 12. Jun. 10. Jun. 17. Jun. m. Jun. lU IVb. 15. K.l>. 'JO. F.l). 2.'i. IIVl, -27. Il-fl). 2S. M:tr I. Mil ■-'. Mm- li. M..r 7. M,,i s M r. Ill .Mar. li! Mnr II Mm J I M:,.. 2H Vpiil 10 \l.|il II 711 \|.i.l II 7.-, jAi.ril24 1 70 m. 00 70 70 OH Ofi no no 74 00 112 m 05 an 01 70 60 H7 45 fiS ii'.i Julian l)»y. V.l. \V I 3 ii(»,o:s.7;u) 021 O'JO 02l' tUO (rj7-."iii (i:;ci 71'. oiJ 71:1 OI'.IIWO OM-724 a>l 7(12 ()-,:, VMi ii.".i; i;ij U.S.) 1,11) mwr.io I'lii r.t.; I'll .■)l'.i I I' I,". O'.ii; II' 17 ll'K liij i(i:!j,so nil .")s:i nw. .".ij lU'.l ."lU) 110 .V))) 120 ,>I2 124 0i>8 137 M2 l:;s .■,;j'l 1 1 1 ,-,.-,(l 151 542 ; •■'■: ! I-2D7 I IIS 1124 ■:)4!» ■3; IS ■N7.S •225 Jill I ■■7 s nil, II I :U() •37!) ■JSI) 2s\t •7'.)3 Jli!) 7I.H) mil 127 •y.M •4.S!» ll.'>4 • I'll' I •.",M) l'4O0 - S-!t, + 9-2, +rin-7\ + 51 • 9' +5!) -71 •f 51 0! + 4-t; + 24^2' +50 3 -10 + 4H^4 + 43 3 f5i»0 - 33: + 5-S, + 141 +00 2 + 31 + 2()-h + 45 3 -14 3 + 5.')-li + 45 4 -227 + .">-S • 7 +;«-5 +47-8 4;u4 + 42 I + 3-5 10+ 4 3 0-!0 2-2- 3 3 0+ I 3-2J+ » 4.«L 2-7 - 4-7 + 3-2 + •5 + 4-5 + 50 - 4-2:i- 3 0:- 3-7, ± 3^0 + 3.2 + 3-2' + 7 - 5 + 0- 2-7,- 2-7i + ('i,Mn,M- ■. r II. I s' 3! 4;- 81 7. 5 1 71) 1 - S'O • I 78-7 8: 7 H 4 7 S 8 0! 7 7 3 Ci 5 +1G8 8 - 77-3 si el ■2 -18 7 -ll'.i I) -33 -28 2 +22-7 •I" I'l.isli.Il: C ( .iiiDun. i;ini:>— _>', •2SS 1 mil \iiciN- or Ti.i: duminihn ohskhn a miiv. MKAsriM.s (IF (. ri.iisia. V.l Wt Vil. W I ■.i>\\> \,\. I w \.l \\1 ii-Ci i i;i iw 1 It !.: 1 -) 11J r.2 .'0 !_• -r -IK) liailial Vi'liirit\ ■J ^t III I I It •■Js + aaos ; + \2s i:;7J 1 ..-.r. • ()."i ■2S + 41 .S :>:,[ \rl, \\t ;j4ir> I ^ li'.l'.HI, 1 + o!l-H7| i +- 3.V5n, J IT 11 i - 34 l") - 2 (Hi •14 ■2!S + 5.-) 51) •07 ■28 + r)13 • p. - priiiiury. s - s/. \.l W V.I \\i tsCI .VJ7 • -M ::> ; l.'ilt) Tiiii -r 1701 li ItNllOO .") Sl\ " :. • m; \ taiii '•■•.{ ~ 1 ."il ■ '1. 11 i 4:i()s()>i - 1) .'jH 41>-211 - 4(i:f 4101 K'.K) 39:t3s2:. . ic IK-. : Wcichtdl nii'Mii - :t 74 4 l."i ol \ - 4M -- li 111 \: ■U't (i:. Ciirv, — ■2n — ■ Js Itailiiil \clooity - .s-y + ',1 -J ss.'ip. :is.s.'i|i. \.| \\i r>7 (,l + ii;i:,t + os-v.i \.l Ut 1 SI l.-i 1 + lil'i- Id ; + 7:i-.-.7 i: + s-jtii I '.7 :.() i; .'>7 ■ III + .-,(>■ :i7ir. ; i.",'ji; 1 J .■.7-71 s-7(. (i:, — -JS -I isc, r .".!) \rl. \\l s 7ii II.". 3007] 1. V.l \M. + 111. In 1', 7-J-4;l S-7(i ■05 •as ij i;7 12 r.'.t . 7 •_'!)() ruiiLicvrioNn iU' iiii: :">mi\iiin (Uii^KuvArniiv. Mi ASi i:i;s 111 h I'l lisi'.l— rdii/KiiH./. IsCil .">-'7 l.-,t'.)-7i;r, 1I'<1-4IMI i:!.VJ(MK. i:;!(»n:tt 4101 MK) HIHIS I'l-J.-, W.iulitiil iiirim V. \ Uailial Velocity V.-l. \\ I .■i7(ll ."■.so; - r.' In ■ rj — -'JN 17 r,7 I i,r,- I'l 1.-, I hi ■10 ••JS ;i'.w'.i - 71) 1 - :,i - in :is ; . I'l 111 r, • J- hi I v,i w f .-.:( i;i 1 ,- II v,i ' • i:; ;;i P li'.M'.t I .i'liio .;'.«■■:! \ , ' W ' ■JJ 1.' 17 ii-i •IJ •2.S + 40-2'.l ; 1 ci.-.i i;. + CM'iO - Ik-'.IN •IS ij:; ;iv IIMI .'^ 77 U I r t).-.lJ Vil, \Vi ".IS.' + 7S ',).") - I'.lls •21 — ■2.S + '.tS2 - !!)•;)« • 1 i — •"Js \,l \Vt. j ■.i7^:!J ! + .-,7 •-.2 1 . 71 .-.0 I • 7'i Hi t ,■,:; r.'i ( !,•> .-Hi 1 4 Hs^:i7 - 10 •.-)', I • Id ■2s + 48-4 iiimi 111 '' i'i:i:.~i;i. mi; \-^'i;i;s 111' h i'i;i;si:i fnntinuni. 1M,| ,VJ7 !:>i',i 7i,ii i:,.jm:!ii 1. -.1:1 -.MIS lIHl- 1(10 -t:iin(i:tl (:!■-'.")■ '.!:!!• t:tl.". 17s 11(11 V,KI 1071 'Kll lix;:i -Trill lOt:) !t7."i H'ciii-s-j.-, li'.i'.i'.p V.l \Vi \\rll!lil..l t ..1 f (il (- s:. + I'll 'II J I 111 '.i:t M f 77- 7-) 1 + CO + .".1 II (II liiian + • <.t-M\ \., _ 1 • CiK \i - ■11 CirA •L'S Hiulial Velocity + i:i-.i \r\ \\t \rl. \\1 l«l I + (M-41 1 i- 57 ■JO i t liJ 70 i \r'l VI \.l \Vl + -J'l JO I t- 47 50 1 - 11-11 ) f I'l W i 1)1 ■'.»:! + I'.tcit "iiii.". J.', liii ■ 11 ji; ij ■0) ■f .M ■ j:i is jr. I!'.! j7-.;i + 47-')'i + l.'vtiO + i.-> :!i 1011 \M. \\t mx; Vrl \Vl 71 :ii ■J^iCiO i + 'JNm'.) + s:if*7 1 :i :i - Jii 11 ■ 0.-, - -jn- til !0 1.") ■HI ■J8 (10 2 292 niii ii- \ iii's> (ii iiii'. i)ii\i:\iii\ iiii:-i.u\ A 11 iK'i . MKAsniKS or '. IM'.USKI -<■ f,/i/,w,/. 1():!1 \i'l. W 1 l.'l'.l MM 4.]!i.'. 4:i.VJ 4a40 4J:!:i 414:i 4101 7M ino ■JSti r>:n Ill's V.ld \Vci-i,tr-l iiituin \', \d Curv li!..li:il Vclorit V II If. I U'lilil I •Jitss 2<> l."> o; •2N + :i I ii):,7 . i:, i-.i \ ■ |- :.o I + :!'.l•.■,^ i ;- ivt ■•".■-' 1 + 47 |ll.-,s,, s.) (Ki I r:." + 72 Hi r.:if. - Jti:!! ■14 - .ir, •2.S - -JS !(■.'■ •.'.-, •jtiai ■ 111 ■ •'s l:; :i7 JO (l-J '.IM) :il :i'.i 'Mill + I'.'i:. — 'ji't'jj 'II :;s ; M-'.is ; 7-7:! I '.ii'iM ; 7."i I'.ii , T'. 71 I \.i \\1 Ml I I t 7ll.'.i7 1 f 70 IS I So.27, i I'.il-' i r S-J.IS — 71 71) - ■Jllll - 2.'i-ski. •_".>:< MIASIKIS I'l' !■ rilfSKI -'',ii,/iiiiir.(. iMil I UM am:, .t:ii(i Hill ;!'.i;i:i -• ■ I : 7JI) r.:< I iHill \m iii-V I nij. \ . ! W 1 \ . I W t 11.; M. ii;;", ^ \ ' W 1 \^ 1 u ■ . UK J ; + 1-97 i + 24-4S[ ;. + in- 37 1 W.iiTlil..-7'.l ■If. (\7 «:! ! + !I2-10 J lit.'. IKl -') 7'< ■II'. ■Js + \i'>s. .■1 111 ■1^ j-.' -ir i ■.J u .M HI 111: \rl W 1 :._' 1 1' I s| '.^ i: 17 ;;:i lo . s(l 77 + (1I.I-07 ^ -1:1 .-.1 V.l, ' Wt 7S 111 111 111 ■ I'l I t- 71 -.-S 1 Vrl. ' \Vl + 41.>1! J + H:i.7S: > h r,i.3i' 1 + t)l.J7: 1 . .;.-, -.1 ( + aiiiH J ,vi :ir, s • 1'.-' '.'1 i f It 01 ; i t I'.s 711 •.-.4 -'.IS - .'II 11 - .5m:> — ■ J^ - -'JS -.- 17 ^ . MA _".»1 IM HI. II \llii\- III illl. |)MMIMii\ iill-l.H\ \liiUV. .MI:ASI'I!I;S of h IMCHSKI— Condw/rr/. 41UJ X \ d. \\: -iM-.i .v.': ''■J M-1 '. 4:il^i-7W'> 4- ^^ ii'i ; 14SI MX) -+- liii:. 1 4:i4(i i'.:il ~ 77. M) 1 411)1 ^■'ll :ii,»:t:t ^:- ..; h; '. Wiiulin.l \ . i:i ::. \.. ;;i Ciirv. — -L'^ Radiul Vclocit\ • iJ i 4-.'4ll \ , I W I \ . I. W I ,- j.'i ii-v ; r 17 ll> 1 f V.> M , I'l s'J i:. '.ij ■Jl V.I W I Vrl \\t. V,'l. \\t Vcl. \Vl. (ilMtn nl li i i:l(>KI. 295 The ('l.Mi-\:iti(.ii.- were (■(iiiiliiiird into foiirirrn iiroups :iiiil till' n-uliiiiy; iinrnial \>h<- u-nl in ..l.taiiiin-. I>v ni.aii^ nf Dr. KiniiV y;r:ipliic nicllHHl, IHi liiiiinary clcniciii^ fdi' llir niiiil. 'I'lic ikhiiuiI iiiiicc- with mean vclin'itics, iiiraii 'ihar^i'^, wciiilii- iiinl n'-i.lnaU I'lmn linal i-iir\r aiv ^ivrii hchiw. \|'|;M il. I'LACKS. 1 Jiilwii 1>.-. 1 I'llMM' Vflority. Wc-i(tht. l:.-,M.hl:,l. 1 j 1 J un.oir. Ji:! ■MA +21-7 1 « -2 21 lixi-iiati •.V.Kt +:«! r. J ( 1 04 3 (iii'i Ji t •(VS2 + is-:i J + l(Mi 4 OtislC,'.) ■MO + 4!)l 1 :. -4C.» 5 07:1 lil'.l .'il-.l +.W-7 2 -0 10 6 Otitl -.'M 1 11 JO + .-,.-,1 1 -o:i7 7 07> .vet 1 i:ir +32-.-. 2 +3-41 S ul^ •<:t^ 1 I',i7 + 43-.-. 1 +0-77 M (H'll -'so 1 :;i.' + 1 ".»■.•< 2 -;!'.)3 1(1 lUMHil in'.rn + til) i:. + 1-W 11 ois 7:ii» 1 472 — S-!l ■•1 +:i--,2 12 017172 -100 -27:( l-.'i -0-83 i:i OKo ok; •232 -12 () ■.) -3-81 11 (>v2 7sO •318 + 41 1-5 I •f211 I'iii- piTliiuiuaiy clciiiciits ohtaiiifil were: — P =]-.")_>7:L' (lays r =••-'•■. oi =ir)(f K =■^:^:) km. 7 =21-U'_' km. T =2,iis,',),-)t;ii.") J. n. Ti) grt a closer apiiroximafum tf) tlio truo values of the olomonts a le^t-sqiiaros solution was applied. P was assumed as deiermined hut (. w. K. 7 and T wrw used in the solution. 2'.H) PrBl.lr.\TH>Ns UK lllK DOMINION ollsKKV \ I o|( V. I >lwii vaiioii f'(iiia(i(>ii> wi'H' foiihtil as follows: WciRht. ii7_' 1- w:> ' ■:','.»> - ■ •_•>" r -'tlVd - ■ (iS."i * TV-.' _ Ml T.'iS - .■.71 . CiOJ (■ •l>:i 1 ■ l.-JI J ■ li."lj - it:\ f 1'.'.". - ."..'(■. + •117 - '.KIS - ■ MiM -1 I7:i _ ■ :;71 - r,7l ■t (ll'i ;i.- "^ ■(i.;7 u itrc .(■ -6-> .'/ = 5A- z = A'Sc It r _ A'mSV ~(l --- ( 117(1 i- Mi T •Jhi - I7n - .its - .^71 -I lIKi - I l»7ti -. .Sis + K'^i + 1 + 1 1,111 171 :i:.ii I'.Mi IVC! 1 "I li7J 117 :tt7 070 :«iii Wis s:!l • :; :i.-,() 1 -ti-7;H» •JO -I illO ■JO +:t'.i.'iii 1 .'■ OmIUI •-•0 -0 .VHI 10 - 1 :!so •JO -•-• if-f) 1 -I ins(> J II -r.ii.vi l-"i -!I'.I7I) ■ .'l -I sio 1 'l +.-i:ilft -."l -0.-J7II !•.■- Xoniial ciiiiatioiis rc.-ulliim I'roin tlii'S(< oh-crvatioti ('(lualidii^ were as fdlidW ~; 20.,- .11)10/, ; ■ is:k - i-7s(w/ ^ i-::^' - -i-i-r^'.c, o + 7-sr)2// - :ismz - is.h Id-. ",»;!•: " :i--J(IO'' : :! lo-o;5('w/ - !> lii:w . .'j-Tl't-H) i.'is/ '- •ti7t;=() 5(Hi;- i- 2;;-US2=() i.ViTr - _Mins .1) bc:- •^(ilviiiLi till 'I' ciiuaiiiili- till' '.aim- t'nr (lie ciiiii ermu- were I'miinl tn 67 =+ 1 -Jn km. 5A'=- 1 •'.»■_'.-) km. gr = - •(Ci.S 57'=+ ().(ils ,lay 'I'll! -.aliii' iif Ipir was greatly rciliiccl l"'mu' Imi'iiilit ilowii fnmi 241 til ]2s. I)i-ai:r('(Miii'iil ticiw'cii rm'.iputnl and i)ii 11 1 — It /' 1 I i • iiij + •.•|7'.i i -^77 j - ^Ji.i ! ) 1 '.Mil 1 (1 I • iiii^ - If.t + -IMt - Mit - 1 • I'.HI ■JO 1 • .'iii.! - liOT + TMi - -417 -1 700 2 II 1 1-7 111 - AMV, + ■•.'«•-• - ••-'•js + 4 730 1 .■ 1 . M:! - SI7 - l.Vf + 0:17 +0 SW .' 11 I • 7^7 - .-.70 - •.I.Mi + I'iti +0-460 1 1 r i.Jl + liM - (Htl + -iJiS -.iiM J II 1 -f ■ Ui? + tiW - Mil + r.'.i.". -OWH) 1 II 1 + (MKl + 11U -lUV, + 1 11:. +:)r.KO J II 1 - 1(11 + • »!.■>:! -1 (Hm -, 1 -.V-' -J O.V) 1 1 - WD - MH - .S.M -f-i 1177 ~:i 270 -.t -1-17.') - •07ii -(- ():is - l'j:i + 1 .-.(iO IS - TWi + Hll -( 711 - Hiia +:iss«o ■ r, - .fli:i +ioaB I + bll - ■S76 -2aoo 1-5 1 'ri•")•'.(■ - •.■)■_'.')=() s-iif.// - :!:5:v.'- - -L'lri/^ + •()()■'.' ~ M7i=() ID- Cm.".: - -J ■',»::'.(' f :M72'' - •-'•(io;i = () Id- l.">7'/ - '.MiiiT/' -f -0^:5=0 The Milutiiiii of llic.-c (M|iiati(iii< ^a^(■ llir sitiuhI cnnvrlKins — 57 = — •():! km. o/v - + ■:{! km. 5« =+0°-U() 57' =+()-()0;!."') (lay The new valuc> In:- l!ir el. •UK III.- .iiav^' sati>l'ai't.iry coiiiparison liclwcen computcil ami ol.scrvalioii n-.-idiial.s ami a H'loml Idwcriii.^; of li>rr fnmi 12s to VH>. 2i»8 I'l nM' AiiiiNs OK nil-: i>ci\ii\iiin iiii--i.i:\ vium . Till piciiialilc irrur ui ;i iinrmal placi' nf ui ij;hi iiiiii> \\a- cumimiIi d ami IiiuimI to lie '2''), while tliat of n plate of average v.ciiclit \\a» ■ :i '.I. Till- iniilialilc errors of llie cleinelit^ were al-o i uiii|ii|lr.l, aini an ^i\eii Ixlow al'li'T the tiiial \alues of eacli. Till' folldwim: lalilr j;ives a suiiMnar\ of llie values of iln crimiits |iii liiiiinar> . Iii-l mi nrinl and liiial: I'tlll'ltl Pn*liiiiinHry. 1 ii>t i_'i>rtTi-hil. llll.'ll. /• iwr:u (la.vH I .•■■.'-:« .Itiyx I .v.»7:« .Ittj-n , ■ri •JIJ •« ± ()()21 (l) l.TO' ISO" N.'l l.'il" 75 ± rt» K 4:1 • 5 km. 41 '.7.'> km. 41 SO km. ± 01)7 y 'Jl trj km '.•;ir.' km. ■j:r(lf> km. ± 57 r J. Ils,ii;,il 1 1:, .1 |i Ml s.'rMi itu J. 1) •J,ll>,!I.Vi lIKi J I). ± (»■(« . (>iil\' --ix |ilat(s >li(,\\ril lim ■- iiiia.-iiraMr. Xo atlnnpl \\a- iiiaile to uel elements iinlepciid. iil l\ of liir |ii-iinary. the llilllilicl- III' |ilati- liiil 111 illt; ro!i-.iclereil silliieii'Mt lor lli.al. 'I'lie \al;ies ol -y ami T liiialU aei-i|iteil lur ihc |iiiiiiai'> wile lakeii tor llir srcoeilai'N", Ui! taki II 1^11' + u anil Ilie l\ 'Aas olilaiiiril ly irial urapliirally. Those ^i\('n |iiiitialil\- ~ui! ihe ,~i\ iil isciN at iiiii~ a- will as any The eli .iients are: /',= !•. -..'7:;-' ila.N- e,= •■J_' w, = !')ol -T") A", = 1 .'i-' • :. km. 7_ = 2:!(l'l km. 7', = -J.ll^..t."iii- Ifi'i .F. I). a^ sin / :;{,()|.s.i)lin km. The relaiiiiii exi-iiiiL; lieiuceii ihi iiia-~i's of tlie two iiodies is iiiven hy .1/ .• M - A', .• I< - \'>-2r, : |_' ,,r ;;ii : 1 The liiiure ui\cs the |\mi (■ur\i-. The douMe i-ili-les are the ohserv;. 'ion.s on seenndarv eiiiii|ii,iiinl and the lliple eirrles ale l.ick oliser\ itiolis. I)iiiiiininii ' tli,-er\ atoty. ( )tta\va. .!imi . I'.lll. Illll ,11 Ml h I'lll^KI. 209