IMAGE EVALUATION TEST TARGET (MT-3) f ; L 1.0 I.I '"IIIIIM IIIIM :' 1^ III 2j0 lllll 1.8 1.25 1.4 1.6 6" ► Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 ■I . m i I i| i iMi H i p i Hym i wyinm i i i iii ii L "1 jU^ (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Un des symboles suivants apparaitra sur la dernidre image de cheque microfiche, selon le cas: le symbole —^ signifie "A SUIVRE ". le symbole V signifie "FIN". Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, (eft to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent dtre film^s d des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clichd, il est filmd A partir de i'angle sup^rieur gauche, de gauche d droite. et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagrammes suivarits illustrent la m6thode. rrata o selure, 1 d a 32X 1 2 3 1 2 3 4 5 6 1 ¥*»iwfwpsw^'- mm^: w^^ '!!' i:i.^;iii|ii'f|.i,i; ,.;i INVtISTlGATION o» ANCE OF THE SUN /!« AMD or TUB II tS WHICH DEPENB UPON IT, numtsot Oai«llVATIO»S OF MARS, MAOC DCniM THK )f ?#If ION (JF 18e«, ANR^FROM Of 8]gR SOtJRCIf i'-M'J js:^-' 1X^1 f^ ■\w,-f-»^ APPENDIX 11. INVESTIGATION KK rill DISTANCE OF THE SUN, \N1» l>K TIIK ELEMENTS WHICH DEPEND UPON 11. lUO.M IMI, OBSERVATIONS OF MARS, MADK. l)IRIN.f x ^H AI'PKNDIX II 1 N V EST Id AT I ON or Til DISTANCE OF THE SI N AM> or THE ELEMENTS WHICH DEPEND UPON IT. About ten voars since, iistroiiDiiKirs lu',i!;iui to susiu-rt tlmt Knekc's viiliic of the Sim's ilis- tiiiK'O, deduced tVoia t!io Irinisits of Veimsiiillic years ITCl and ITCi), was lar-;ely in error. Tlie different nn'tiioils available for its correction all agreed in indicating' a diininntion of between one twenty-fifth and oiie-tidrtietli ol' the whole distance. Tiie last doubt of liu! cor- rectness of the suspicion was removed by the jjublication of I'owalky's paper on the Transit of 1769. In this paper it was shown that, with our more accurate kiiowIed-;e of the positions of the observing stations, the results of this Transit agreed with those of the modern measures. The magnitude of the correction being such as seriously to alTcct rhe reduction of meridian observations of Mercury, Venus, and Mars, as well as our coniput itions of the mass of the Eartli and the parallactic equation of the Moon, it becomes important to (h^terinine it with pre- cision, even in advance of the coming transits of Venus. In siudi a determination the results of all methods which can be relied on, or the precision of which can be estimated, ought, I con- ceive, to be combined in the final result. Let us, then, glance at tiie various methods now available. 1. By Observations of TromUsof Fc«(/.s".— This method has gone into our school-books as the one superior to all others in the precision of its results. It is true that transits which occurred a centurv ago, when the art of observation was in its infancy, have furnished the solar parallax which iuis hitherto been adopted as the standard. It is also possible that, should the civilized world take due interest in the observation of the next two transits, and sliould circumstances prove favorable, the precision of either result may exceed that of any other one determination. But it is certain that our modern determinations by other methods are more [)recise than any that can be derived from the pas' transits of Venus, and opportunities which occur in but one generation of men out of four are too rare to bo implicitly relicMl on in future. 2. From Observations of 3Jars ivhen near the Earth.— Thvce methods of making these obser- vations have been employed. «. By nearly simultaneous observations of difference of declination between Mars and a neighboring star, at Observatories situated in different hemispheres of the earth, and by means of Equatorial Telescopes. For the employment of this method the United States Astronomical '^\. INVKSTKiATloN OF THK DIS !A\('K Ol" TirK SUN Kxpcditidii to Chili \v;is (H^niii/.i'il, It was a^uiii |ii(i|ii)S((l hy Captain (lilliss. in 1 Sll-J, ami til>scrvatiniiM in this way ucic niailc at l'|isala, liL'idrn, ami Wiisliiiigtoii, in tlio N'nitlicrii Iloin- is|ili('r('. and Santiaizo in the Smitlicrn. ;9. U\ similar dliscivations with a Meridian Circle, Mars liein^^ coinpaieil with ii imiMlKd- of pro-soleete(| stars. 'J'his is the inethdd pnipd.-ed l)y Winneeke, and most extensively earried out in ISC.'J. it waslirst employed in \s:',-2, hetween the Observatories of (Jroenwieh, Cambridt;;e, and Allnn 1, in liie Nmllieni Ilend-pln re, and Cape of Ciond Hope in the Snnlhern. The residt was 1)".(»'JS.* whieh il nnw appears was not oidy nearer the truth than I'lneke's value, Init was all'eeted with a prohaldc error less than tin- alisojulo error of the latter. As compared with the lirst, tiiis phin has this advanta;:e: that, comparisons lioiiijj,' mado with the same stars ni,i:ht altor iiii;lil, theic is little dan^'er of oliservations Ix'in;^' lost at oiio station for want of correspondiiiL;- ones at anolhei-; while, liv (he other, sinc(( tie.- planet must he. compared with a dilferent .-tar on eveiy iii^ht, thev will be hwl, urdess made on the same ni^'lit at both stations. 'J'he (lisadvanta.i;-es are, that the residls are ailectt'd l>y the errors arishifi; from crroneoiis division ol the circle, or othi'r causes |)ecidiar to each star, and t!ial t\n* obser- vations cannot be i-epcaled on the .-ame ni;^lit. '!'he proliable mauiiitnde of the lirst error may be inferred from the results of the investi;.:;ations of Auwers on the declinations of the funda- mental stars, from whi( h it would seem that the probable erroi' ;irisin,n' frorii these causes is between two and three-tenths of a sec(Uid. it is, ther(d'ore. advisalile to compare with as many stars as jiossilile. in older to diminish the ciiaiices of error. Inaliilily to re|)eat the observa- tions will ap|>ear a less seri(Uis objection, if we rellect that, from some cause m- another, micro- metric comparisons with an Krpiatorial do not often e.xhioit the precision of meridian observations. On the whole, 1 conceive that, in a LCeiieral combination of the [jriiicipal a(;tive Observatories of th(> world, the iiiicroiuetric method woidd bi' preferable; while, if the number in either lieui- isphere is limitiMJ to one or two, the preference must ii(> ^iven to the Cin.'le observations. The ;irran,u-einents of 1862 were precisidy the reverse of this. y. By <'ill'erences of Itight Ascension between Mars and iiei;j;Iibiu'in^' stars east ami west of the Meridian, .^o far as 1 am aware, this method was first employed by the .Messrs. Bond at the Observatory of Harvard Colle-i-e, duriii'; the opposition of lS4t)-50.t The value then obtained was 8".005, with a probable error of 0".4. It was also proposed by the A,-troiiomer Ko\ al, and actually employed at the Royal Observatory, Greeiiwiidi, in I8Gl'. The result has not, 1 believe, been j)nbiished. This method has not received the attention it deserves, probiibiy from a general distrust of time observations, if employed at a station of less than forty decrees latitude, with a steady and carefully-adjusted instruumeiit, ami if care be taken to eliminate every source of constant personal error, its results mij;ht, i conceive, be received with entire coniideiiee. Among the measuies necessary to secure a reliable result may be placed the making of the observations on one side of the uieridiaL with an inverting eye-piece, that the apparent direction of motion of tiie jjlanet may be as nearly as possilije tiie same on both sides of the meridian. It is possible that observations over tiio horizontal wires of an Alto/.imuth might be pref- erable to that over the right ascension wires of an Equatorial. ;>. From tltc Observed ParaUactie Int'inalUtj of tlie Moon. — This inecpuility has the solar parallax as a factor, into which it is multiplied nearly fifteen times. Since astronomers ought to be able to detoruiine the coellicient of this inequality without a probable error of more than a tenth of a second, the solar parallax ought, it would seem, to be determined from it without a probable error exceeding 0".00T, and, therefore, with greater precision than by any other method yet employed. Unfortunately, however, the uncertainty of the observed value of the parallactic inequality still amounts to several tenths of a second, so that there is no hope of attaining this degree of precision. \. * Abtiononiische Nuchrithteu, No. 'lij'i. t Astronomical Journal, No. lOU. MMfe4«lcil li\ |jt> N'cnicr in liis soliir tallies. KikiwIhi^- tlic paialliix and mass oi' tin- Monu, wc can (•(ini|iut(' liic ili-^lamc ol' till' (H'Mtro of tlic Earth I'roiii tiic (•nniin(ni centre ol' ij;iMvit_v of the Kaith ami Mnun, amnml which tho Kivrth'rt cenfre revolves in ii lunar nnmth. Also, from ohservations of the Sun, Venus, or Mars, wo can determine the aULjle which this sanu' distani'c sul>tends when seen IVoni the Sun. A eomparison of IJMse two data j,iives the an^le wliich the I'adins of the I'larlh it>e||' suhlends, as seen rroiii tho Sun, (.r the solar parallax. This method is tlu; least precise of all, since" it jiivcs (he solar parallax as the |iro(luct oi' two factors, noitlicM' of which are determined with ;j;i> at precision. The observed value of the lunar eijuatioii must at present (h'pend on oliserveil ri;4'hl ascensions of the Sun, of whicli the probalilo error is very laij:e, and tiie uncertain factor of this element is ahoiit one-third ;^reater than unity. Therefore, snpposiii},; the mass of the Moon known, the uioi'c lo;j,ical course would seem to lie to determine the lunar inecpiality from the solar parallax. .'). Fruiii Kr/icrliiK iilid I)i hriiiiiinliii/iN ii/' tin Vi-lniihi of Llijlil, rmiiliiiinl irilli tin l:iiiiini nilur of llic All' rniliiiH III' fjiijlit. — Foueault's lieautifid experiments with the revolving- mirror art! so well known that tln'v need not he descrilied, 'I'lie theoietical olijections to this method do not seem to mo to have much toic(>, and 1 se(> no iusuperahle reason why its results should not he US reliable as thos(! of any other method. It is (piite true that in experiments so delicate^ hidden causes of constant error may defy the scrutiny of the experimentalist. It is also true that Foucalt's operations liav(> not been published with that fullness of <|etail necessary to satisfy astronomers that his results could not have been vitiated by any smdi cau>(!. I5ut, to test the reli- ableness of lii(! results, it is, 1 think, oidyjiei'essary that the determination should be repeated with apparatus a.s dilVeriuit as possible from that used by Foucault. Such a rep.'tition is a desideratum bothfor Physics and Astronomy. A desirable modi Heat ion of tho apparatus would ln', if practicable- placing tho fixed refiector at a gr(.'at distance, say ."{.OOO or 4,000 metres from the revolving mirror. When the Great 'J'ransit Ciicle was mounted at tin; Naval Ohsei-valoiy, the (pH>stion arose whether, in the reduction of observations of the Sun and I'lanets, it ,\as jiossible to eiriploy a value of tin? parallax so near the triitii that there would be little (h.nger of future investigators having to cdrrect our results on account of eri'or in tlie adopted constant of s.ilar parulhix. The most proi.dsing source of an accurate parallax seemed to be the observations of Mars, made in 18(!2on tho plan of Winneeke. 'I'hey formeil a better planned, better executed, and more extended series than was ev(M- b(d'ore available. In tin,' Southern iJeunsphere the Observatories of Williamstown. Cape of Good llopi-, and Santiagt.. .vorkeilwith remarkable suc- cess, securing, altogether, observations of Mars and comparison stars on 14.'! niiihts. In tlio Northern I-Ieii)isph(!re the Observatories of Pulkowa. I'eterslmrg, llelsingfors, \'ienna. Berlin, Leiden, Greenwich, Albiiny, and Washington, ar(> known to have co-operated. So extended ii co-operative eilbrt on the part of astronomers all over tho civilized world has not, I believe, been seen since the transit of Venus in tho last century. Throe partial discussions of these observations have appeared. 1. Winnocke, by a comparison of observations at Pulkowa and tho Cape of Good n>)[)e, on thirteen corresponding nights, found tho solar parallax S". 9(i4.* %. Mr. E J. Stone, of the Royal Observatory, Greenwich, discussed tho observations of Greenwich, the Cape, and Williamstown, deducing the parrallax 8".it43.+ 3. The corresfionding observations at Albany, Washington, and Santiago, were discussed by Mr. Ferguson in the Washington Astronomical Observations for ISO.''!, with the following results: From 12 oliHcrvations of W;isliingt()ii aiul Santiago - - - - 8".8,'M \h " " Albany S'.Gll Astrononiischc Niiclukhten, No. 14t'!). t Memoirs of ttie Royal Astioiioiiiical Society, Vol. 'X\, p. 97. 4 INVKHTKiAl'ION OK I'lli: DISTANCK <)1' TIIK «UN The nictliod !i(l(.|)t<'(l by ciicli ..!' tlii'so iiivr>ti;riit.)rs Wiis fliiil (if (•(Uiiim 'ismi (if piiirs of (•(irics|iniiiliii).'- (iliscivatloiis iiiinli'— (UK- ill ciicli licinisiilicrc. Miiiiv uliscrviif iniiK iit tlic niui Htulioii wiiiilil lie lust Wiv uiiiil iif cirii'siioiHliiij; civati(iiis at tin' dllicr. Thus, mit oi ii ^M'aiwl Intal (if iiK.ri' than ;!(»() iilir-cival ions, (inly 2<) wtic ('iii|il(iy('(l liy WiiiiHM'k(\ TiH by Stone, ami K; by Fciyiisoii. l-'ivc of tliosc used by Winn, rkc aid Stoiio bcinn- tlic Humo, tlic ^iiiii total ii.mmI iiy flic tlircc asti( incrs is only I'J'). Tlic lliicc results arc, tlicroforo, so far from liinil thai a ('oiii|il('t(' (lisciissioii is to lie dt'sircd. 'i'liis discussion I have iu-eii |MTiiiil tc(l and cnaldci! to nndci'takc by Rear- Adiniial Chark^s 11. I»avis. lat(dy Sii|.ciiiitendciit of thn Naval Obscivatoi*'. At liis re(|Uest, copies of the iin- imblishcil (.liservalions of Williainstown and the Cape \vcr(( obtiiincd from Robert .1. lOllery, es.].. and ^-ir Thomas Maclear, the directors of those Obscrvat.nies. The Observatory of Tnl- kowi, as the orijiinator of the plan, haviiif;' u jnior rijiht to the .general discussion, its consent was also obtained thronuh its (list in;;nislied director, who coiiiiminiciited the obs(jrvations ol Sawitch and Kreii^'er. made at l'etersl)iir;;' and llclsini^fors. The IdllowinL;' coiisideratiiais may lead to a method of deterininini;- the parallax of Mars from observalions, inoi'c sinipit! and ri^'orous than that of correspond in-' jmirs of obsorvatioiis: 'I'he perturbations iiitiic motions of the Earth and Mars lu'ine; perfectly known for the period which we consider, every observation of that planet will lead rigorously to an iMpiation of con- dition iiclv cell its parallax, the six elements of its orbit, and the six (dements of the Karth's (libit, 'I hiileen or more observations will, when compared with any theory, snilice, formally, to correct the elcmeiils (d that theory. But, if the observations extcMid throu(;h only a short interval, say one month, the coellicieiils ol'the corrections will be so miniitt! that no trustworthy values i\[ the corriM'tions can be deduced. We shall, in fact, lind that our e(piations will only snilice to determine a lew functions ol'the elements, and that the (dements themselves, if their values are only chosen so as to satisfy those I'unctions, may all vary widely, without ceasiiin' to satisfy our cMpiations of condition. If, now, we can lix a priori f)n the entire number of functioiKs of this kind, and- use them in litiii of the elements of the Earth and .Nbirs, our ("(juations will be practically as rigorous as il we had introduced the entire number of thirteen unknown (piantitiei-. One of these functions, the lirst one, indeed, will be the error of declination of Mars, since this will be f;iveu by a single pair of observations. Rut, when there are a series of observa- tions, we mav takt', instead ol' the declination, the absolute distance of tlie planet from tlio l.lane of the Earth's ecpialor. This distance, or rather its error, may be developed in power.s of the time, and the coellicients of this development may be taken in lieu of the elements. That is, we \u:\\ assume that the error of tabular decdinatioii may be expressed in the form st'f Dec. , . I , , That this assumption is a safe one in the case of Mars, may be shown by takinp: the ob- st'rved tabular iirrors i;iven by Winneeke in his publication, '■ Ikobacht'ingeii des Mars um die zeit der Opposition, U^d'J," and developin;;' them in this way. Dividing- them into five series, and taking- the mean oi' each series as the error corresponding to the mean of the dates, wo have the ibllowing live tabular errors, and their products by the distaiico of Mars from the Earth: ' —- .... Unt i'. e f XA Ol.s. Aiifr. :n 4. !2H I.0(> .-, Sept. 17 .5. r>H •i. 10 11 lid .f-.. 1!) :;'. II 7 Oct. 14 4. .v. ].i>4 J 1 M :i. Wi i.7:i •> ^ ._....^ <;r AND TIIK KLKMKHTH Wllini DKI'I'.ND I'I'oN IT. 6 Dovi'lopiiiiJ,' till' lust I'dliiiim ill |)(i\V(o iicjilcctcd witlmut daiigiT of crrnr. It is to bo rciiiarlxi'd that, lii'sidcs tliosi! tiTiiis dividcil liy J in tin- i-xprrssioii for I'lror of tubular docliiiatiuii, tlicro may bo a {'oiistaiit toriii arisin;;- from constant soiircos oj error in llic inoawurod polar dirttaiiceH. I'littiiij:; J'= -Jcos Dec and «ff=oi)n'ootion of paiullax, oacli com- parison of an obsorvo(| and compiitoil docliiiatioii will ii,ivo an (Mpiatioii ol' the lorm 'J"i 'V «• ""'' /^ boin^' tlio unknown (jiiantitios to bo dotormiiu!il. S J. Tlio followiuj;- is tlio list of observations included in the (bsiaission, with tlio aiitliorit ios for tliom : NOUTIIKHN OliSKItVAIOKMES. Pull-owa. — Tliii'ly-oiie obsorvatioiis. Ho()baclituii;^("i dos Mars von l»r. A. \Viinn'cko. i/c/,su(r//or.s.— Eiglitoen observations. Beobaclitmi-'on dos Mars nnd dor Winnockosolion Vergloichsteriie. Horhst, 1802, am Roiola idiach-HrtoIsclion Moridiankroiso dor Storiiwarlo zu lIolsiiiotricas rolativas al Planeta Marte al Tiempo de su oposiciou en 18()2, voriiiradas en el Observatui'io Nacional do Santiago do Chile. Santiago, IBO."^.. This includes the entire list of those accessible observations the weight of which would be such as to sensibly afTect the concluded 'j^arallax. The entire number is as follows; In the Northern lleinisphei-" 1 "i I In the Southern Hemisphere 143 Total 2!)7 In discussing the observations, the first thiir^ to be (bine is to make thorn .-strictly com- parable with each other. This is eflected by dedti';iiig them all dinerentially from one set of comparison stars. In Winneeke's plan, each observaMon of Mars can be compared with similar observations of eight stars of comparison. An epheineris of the positicjiis of these stars being prepared, a comparison of the observed polar distance of any star with the ephenu'ris gives an apparent correction to the observation. The mean of th'^ eight corrections thus deduced from one night's work, by one observer, is considered a eorrectj.on applicable to the polar distance of Mars, observed on the same evening. If every observer observed all eight comparison stars on every night, the ado[)ted moan position of each star would be a matter of entire indill'orence. But, .since a portion of the com- ^ < 6 INVEfSTIGATlON OV TIIK IHSTANCK OF I'lIK SUN |)iiris()ii sliu-M wi-vc iVcciiiontly misled, it liccomcs iiaporlaiif that the .lilVoront stars should bo rcMluccd t(. tin- same staiulanl. Ki,-or..nsly, tliis slamlanl shouM ho, not that of al.sohito correot- noss. hilt that of each particuhu- iii>trnin(Mit as allV,i.-,l with its errors of divisions, and corrected for the constant error of the. mean of its positions of all ei-ht stars. This standard being unattainable for want of a snflicient number ol obsiMvations, we shall be obliged to use one uniform set of star t'laces, dilVering IVom absolute truth by amounts less than the accidental ernu-s of division of' our instruments. The adopted positions will be derived from the obser- vations of (Ireenwi-h, Pulkowa, Albany, and Washington. The adopted standard of dei'lination will be that of Auwers, in his paper on the corrections neces-^ary to reduce the diiVereut cata- logues to a funA coiiehided north polar distance for the same eiiocli. are given in Table I. The po>itions under the nauK^s of the Observatories are not corrected for systematic enor. The small hgures after each '-esult show the number of observatii-ns. The weights are not proportional to the numl>er of observations, but on a somewhat arbitrary scale, depending on the proiiable errors of divisions, and the discordance of individu.il observations at the several Observatorii's. In 'J'able 11 is given an ephenieris of apparent positions, computed \vith the conslanls of the American Ephemcris and Nautical Almanac. 41 (iO ; 120 j 2(1 ' HO ■ Sit 4:5 l,!il;iii(lc 47:i74 LiiliMidc 'Jt!l . I'isciiiiii . . I.mI.'iikIi' (iTO . Ccti . . . . I'isi'iuni . . l.iihmde I'init. I'isciniii . . Ccti . . . . (Vti . . . . (Vti . . . . I'isciuni . . I'isciuiii . . (*cti . . . . I,;il!in(lc'i<;i4 . I'isciuiii . . I'isciuiii . . Liilaiidc ;W!18 . I'isciinii . . TAIil.K 1. i c > O S r. < — ;} l!t 4.5.1 u 4.i.l •1 4:!.4 8 " - .'i,") l.'j.d (i ;(.-.s f< I7.!t 1,-, i.'i.S ;! '_ - 1 10 yit.4 (i ;;i.o 7 ;n.!i r, • yi'.'J H _ - 4 5 4r)..'> M 4t!.8 5 48.:? oo 4.-).l lit — 1 1.") 47.0 11 47.0 :i 44.7 10 48.1 7 '_ r- r^ ;■)!• V2.1 c \->A o 14.8 (i 11.7 ;i _ ^ 4 :il Vi.7 ■.' 14.0 ,') 14.8 III . , _ - (i 4!> 5^.8 Ml .5! (.7 It (;i.8 1,-, .W..-) IS — 1 .••).•! 40.(1 17 .•i!».5 H .18.7 :ii 40.!l ai J - :i7 ;w.7 ic ;u.!t ir. 'MA -M ;W.t) a.'i - 1 n; 14.-J a \r,.2 8 1().8 10 . _ - 4 .').-) '^.•^ J 4 (1.8 .'> •t.l Ift (i.O ir, _ _ •) .>{ il.Q 11 V>.'2 8 14.0 11 11.0 1 1 — 1 10 •Jl.(i 10 '21.8 1 1!>.7 II ' '."i.S fi — 1 (1 ()■».:{ B ()'->..'-. 4 .');i.7 ti ( ;•>.(; a - 5 '2"> .')1.(! ifi .'SI. It 7 'M) li) r^o.-i 8 _ - 4 .(T I.Vi in Kl.'i i:i 18.4 1", 14.8 Hi - i .-n* 4*i.O 10 v.u 7 4.'5.0 in 41. 'J i:t - _ ') ;{0 KU! 10 17.7 " i 1!M! ir. l(i.:i 1.-. !^w" "Cm 44.15 4:{.'21 '2! •.:{'> l:{.'24 Ki.Oli 4(1.75 4( ;.:?'> 5!).8!t •.i'.ir,:] 25.00 44.(i4 53.48 47.(17 ao.7(; !.:!'* 7.50 4:1.45 1(1.80 42.08 \. AND TII,K KLKMKNTS WlllCir DKI'KND UPON IT. TABLK II. Ep/u'iiirn's (if (lie appaidd Xorlh PaJar (Ustiuurx /or (rcaisit over (lie )ii/ IVas/iiiKflnn. s. Mr n J.X I'll, ST SKKMK -0 I'is. II I'is. r I'is. 4:!29-. ; 1 Date. .5 I'is. •Jii C'fli. ••' 211.(1(1 ,5:t. IS H 5S :!(• :i:i. ss 1 1 . "^7 5s. i:( 211. 7C> 42. .59 l-'.s:i .52.(12 17 44 Sci)t. '.1 ;!'J. c.) II. 17 57. 21^ 25. 7 1 4 1 . 55 17.-*:! 51. 12 1(1 ."l.'» l'.> ;ii.77 111.74 5(1. 7(t 24.91 41'. 7:! 17. (17 5(1. 15 15 94 29 ai.MC, m. ,55 .5(1. :i7 24. ;!;! III. It; 1(1. 55 5(1.(15 15 54 SECOND i^EKI KS. -9 I'is. I.ul. 2(114. ," I Datr. Liil. (17(1. 15 Ccti, 11(1 I'is. 1 20 Ccti. 4:iCi'ii. is. ^, ^, 1 1 H ^, ,, ^, Sipt. 19 44.4:5 17. (Mi M. 47 11. (iC. 2(1.(14 .52. 79 :!:i..5(i 4(1 / 5 29 4:». H(i Ki.Sli 17.^^0 Id. ;>ii 19.(111 .52.(1(1 :i:t. lid Id 111 Oct. 9 4:i. 54 Ki.Sli 17. :!s 9. 97 19.4(1 .52.(11 ;i;!. ;t(i ;!9 -1 TiiiKi) sKini:."^. Dat.'. iLal. 2fil. : 44 Pis. Lai. C70. 15 Ccti. 2(! C.ti. Hi Pis. ,"'9 Pis. 4:! Ci'ti. Oct. 9 i:!.52 59. 7:5 4:t. 54 Kl. K! .5(1. 29 2:5. 99 19.40 .52.(11 19 i:{..5H .59. 78 4:5 4:5 17.04 5(1. 44 2:5. sf, 19.41 .52. 92 29 1:5.88 t)U. 08 4:1. 50 17.47 5(1. 74 2:5. 92 19.(14 2(1 Ceti. 5:5. 42 FOI JKTII Si: Liil. 1170. {IKS. Lai. 1299. 20 Ceti. Date. L. 437:54. Lal.atil. 44 Pi.s. 29 Cell. Oct. 19 15. If) 1:5.58 .59. 78 4:5. 4:! 17.82 10.89 .5(1. 44 1(1.45 W 1.5. (i2 1:5.82 (10.01 1 4:i. 5(1 17.95 ll.:tl .5(1. 74 1(1.7(1 Nov. ti 16.21 14.22 ti0.40 I 4:1.74 i 18. 19 11.92 57.21 17.20 The observations being till reduced according to one iiiiit'orin .system, no details need lie given except tor tliose cases in wliich a mode of observation dilVerent from that WinneeUe lias adopted, or in wliich some of the elements of reduction are doubtful or imjierfect. GiiKi:.N\vicii. Only a small number of the comparison stars, seldom more than four, were observed on an\' one evening. Tvloreover, the same stars were frecinently sel(M"t(.'d night after night, so that the positions of Mars depend mainly on less than half the entire list of stars. Tin; doiilile wire system was not used, but the single wire was placed alternately tangent to the two limbs of the planet. P^'oru the discordance of the measured diameter.-, this method would appear inncli leas accurate than that of double wires. 8 IWKSTKJATION OV TIIK DISTANCK OK I'lIK SUN A i,i;a\v. Ilcrc!, also, ii siiiulc wire was placiM) nltiM-Miitcly taiiu'i'iit to tlio two liint)s of tlio pliUiot, several contacts witli each liinli lieiiiu- iiiaile. As tlie fixeil wire was used in tlioso !iieasnrcs, and lliere wa> nut time to read tlie mici:isco|)es lur all the contacts, tlie leatlinj^fs were rol'erred to tiie n)icidsc(i|ies liy an a|i|iaratiis invented !iv Mitciiell, called a Declinometer. Tiiirf appa- ratus is descrilieil in tin' puMication.- el tlie Dudley Ohservatoiy, and the mode of usiiiu; it in tiic present ease, as well as an aiistract of the oiiservations, maybe found in tiie volume of Washington ()liservatinii> for Is(!;>. Owiii;:; to the irren'iilarity of this nietiiod. I have hesitated til admit its results. IJiii alter a carcinl scrutiny of the observations, and a piM'sonal i-xamina- tiiin of tlie apparatus, 1 am iinalile to see liow any sourci' of constant error conld have cri'pt in, and have therefore admitled them with a small wci ,;ht. WASIlINCTiiN. During; the first series (until September 21) the stiir observations were irregular, two of the observers |dacin:^' the star ima,:;c between the wires, and tlio third usiiijj,- wire 1 exi'hisively. The employment 111 the foriiier system for a limited number of the obs(>rvations does not seem lut when the same wire is used for all the ci)m[)arisou star^, and the mean of the two wires for Mars, any error in the ado|)te(l distance of the wires will all'ei't all tiie oiiscrvat i|iecliv(dy ; ii, and d^ the declinations of another star, deduceil on the same dates with wires 2 and 1. Then, it h be the correction to the adopted distance of wires_ we shall hav(^ — ■ .;=i(D|-D, + 'J'riie (bslaiicc for Se|itiinber 14.00 Adopted distanci' in imlilislied reductions 11.02 J'-rror of pulilislicd reductions 0.02 The correction on account of ermneous half distaiioe, being imly a liundredth of a second, has been iiegU'cti'd. WlI.I.IAMSTOWX. It is not stated by Mr. Kllery whether a single wire or a pair of wires was used. The North I'olar Distances, as forwarded in nninuscript, were not corrected for errors of divisii>n. They were, however, aceompaiiiod by u table, giving the errors of iliviuion for every AND TIIK KLHMENT.S WMICII DKI'KN'I) IU'()\ 11'. !» (lojrroo of zeiiitli distaiioo. Uiifortniiiitcly, it was nut stati'il (Mtlicr in wliat ijircctioii tlin /.(Miitli distance was coiinteil, or wlictluM' tiui coiTccf ion was to lie a|(|ilii'il to tin- ciri'lc irailinLT, wliicli iniji'iit increase toward tin; north, or tiic polar distance, wliicli increased tuw.ard the soutli. In this dilliculty, recourse was had to tin' paper ol .Mr. .'^tone, who inin'ht ii' snppo-^cd a<'i|nainlci| with the facts, and who [xibiishi-d a siniii ir talilc foi' every 10 . It Wiis foiiinl tliat he comili'd the /.enitii distance toward tiic norlh, and apphed i lie correction-; in the suae direction. To ascertain whether tiie corrections thus applied were real, thi; corrections t > the adopt(M| |)hiees of the stars were deduced frcan all the Williamsldwn eli>ervations, without applynii;' n-rois of division, and then the coi'rections were corrected for errors (d division, in order to sec whether they were thus diminished. The ri'sults W(!re: Scrii'S. Slim of c'oni'ctioiis luu'oncclcil Sum of cont'clidiis corn'i'tcil . Siiiii i>( s((iiiii'cs iiiK'orrci'tuil Sum of sciuiires convctcd - II. III. IV. Sum. — •,'. '.1 ;!.? :!. '.I i:!.7 . i 1. 1 •■>. .'> l.s •2. '.I K.-.i . ; 1.-^;! 'i. II ■J. :'.:( l.'.H ■■'. •') a.-J7 0. '.»."> li.Tl) 1.:!: :!. •-; The imi)rovemeiit is so well marked, tl.e pruliaMe error liein-' re liie d from O"..'!!) to ()".'J1, that the correctness of the assumption can haidly lie doiiiited. The errors of division havt; therefore been thus applied. SANTI.\f;o. The observations appear to have been carefidly made throIl^•hollt. Tlnsy do not, howevi^r, imjiress one with a hii;'h sense of the cxcelleiici' of the .Meridian Circle, or, at least, of the pre- cision with wdiieh its microscopes can be read. There is also a weak point in one of the im- portant elements of reduction, .namely, the inclination of the declination wires. Thei'e ■•ivc. two of these wires, one fixed, the other movable by a micrometer screw. In the .Mars obser- vations, the latter was set over or under tiie fixed wire, at a distance somewhat less than the diameter of Mars, and the observations were then made in strict accordance with Winm^cke's pro.uramme. The oidy information respecting the inclination of the wires is in the following- words: "En el campo de vision del anteojo del Circulo Meridiano esta esteiidido iin hijo (ijo paralelo al camino que recorra una estrelhi ecuatorial. * * * Por iin, es de ailvertir ipie el hilo movil no es e.xactamenta paralelo al hilo fijo. Kstando el anteojo dirijido al Xorte, la estremidad occidental del hilo movil queda encima del hilo iijo. i la inclination de los ihjs hilas ascienda a 0°T'." From this it is deducible that the correction to the observed north [lolar distance, on account of inclination of movable wire, is negative when the observation is made before meri- dian passage, and positive afterward, and that the amount of the correction is as follows: lutt'ival from mcridiau. Condition. .V. " 10 0.31 '^0 0.61 .•{0 O.U-i 40 1 .-.'2 50 i.oli 00 1.84 70 2.14 10 INVKSTKiATION OF THE DISTANCK OF THE SUN Kitlicr tlii! clock tiiiif (if transit or the vertical wire hoiii^ p:ivoii for all extra meridian oliservatioiis. tlio polar ilistaiices ohscrviul with the movalile wire were eorreeted for inclina- tion accorilin;; to the aliove talile. It was noon seen tliat the efTect of this correction was to prodnci; Iar>-e discordances in the resnlts for i)olar |)oint deduced from tin; several stars, and tills ell'ecf was so niiiforin and well inarkeil as to leavi^ little doulit that the correction had no existence in lact. it was then foniid that some correspondence had passed lietween the Superintendent of tlie Naval < >l)servator\- and Mr. Moesta on this very suliject, in 18(U, the ellect of which was to tiirow darkness on the nature ol' the incdinatiou correction of the Santia^-o Circle during this critical |)eriiid. 1 next attempt! d to determine the inclination from observations of the same star, made on dilVerenl siiles of thi' meriilian. To ellect this, a tal)l(> was drawn n\>, showinj^ the hour angles of .Mars and I'ach of tin' ei;j;hl stars, for each of the Santia<;-o observations. It was found that I'he same star was nearly always ohx'rved with ^reat re^'ularitv on the same sidi- of the meridian, it was not |iossiiile. therefore, to determine the imdination of wires. The foll(;wiii^^ plan was adopted: In each determination of the polar point, the inclination of the mean of the wires was included as an uid than three classes with respect to excellence. The multi- pliers are assigned by tiie following considerations: 1. The nu'an error ol an observation at any one Observatory, as deduced from discordance of results for pohir jioints derived from the several stars observed on anyone evening, *J. The number of stars on which the polar point depends. The omission of several stars does not. however, seriously diminish the multiplier, unless the same stars are missed night after night, so that tli(> final result of the W(uk with any one instrument will depend on too few stars. .'{. The notes of the observers with lespect to the ((uality of the images. The precision of the oliservations, however, appears to be much less ailected by this cause than n)ight bo sup- posed. The greatest extremes of ilescri|)tion occur in the Cape observations. Here it is found that the mean discordance on six good nights is ()".37; while, on six nights noted .is very bad, or deplorably bad, it is 0".35. Here, at least, the elfects of the cause in ijuestion would appear to be entirely masked by those of other causes. 4. The number of observers. There being always a possibility of personal difTerences in the measures, greater weiglit should be given to a series made by several than to a similar series made by one observer. 4 AND THK Kl.KMKNTS WHICH DKl'KND IH'ON IT. 1 1 Tliu first c()nsi2 The adopted multiplier is supposed to carry the mean error of each ecpiatioii to i.hout ()."'.). The next eoluimi gives the comi)Uted parallax in polar i(i !». Wr"M) !». K'.ls'.tU it. D'.IOlO '.». '.l'.MII-.i ; ;). '.uc.i.'.i; i !). '.mr.n ' '.I. It'.CJlH ' it. m. R. — 7 :!8 30 (» -f -21 28 a 47 2:$ 1 43 21 2 1 11> 43 .-.I ."i() 18 7 It 3n 3 « cc O in rf. — .3i.-i;i(> I .0011(10 + .014UO 1 .o;f2!»l 1 .07177 •o,-^i-r> I , y.-'o.'.o .2Hitl(» ' . 2'.tH-,>7 Next, we have the polar distances of Mars given by the ejdiemeris. In the adopter! method of discussion it is essential that the differences between tlie ephemeris and the actual position of the planet should vary regularly during each period of twenty days. To insure this, heli- ocentric ephemerides of the Karth and Mars were computed by Mr. Charles Thirion, aid at the Naval Observatory, for every other day during the parallax observations, using Le Verricn-'s tables. In the ephemeris of tlie Earth the planetary [)erturbations were smoothed off by dif- ferences, while the lunar perturbation, instead of being taken from the tables, was rigorously computed from the co-ordinates of the Moon. In the Mars ephemeris the perturbations of each separate planet were mainly developed in powers of the time, to reduce the accidental errors in the last place of decimals, produced by adding so many terms. Com])aring these positions with those of Winneeke's ephemeris, the variations of the dif- ferences from the desired law were found to be altogether insignificant, seldom amounting to 0''.02 in longitude, and still less in latitude. I still feared that, as Winnecke used but seven decimals in computing his geocentric plans, the imperfections of the last decimal might have affected his declinations. Differencing his two-day ephemeris, the accidental errors were found not to exceed, on the average, 0".02, so that their influence would be altogether insensible. His ephemeris was therefore adopted as a basis. From the right ascension ol)servatioiis made at Pulkowa, it appeared that the tabular heliocentric longitude of the plan<>t was too great by about 2". 40. I if IJ INVKSl KiAl'KJN OF TIIK IJISTANCI': OK TIIH SUN' (|;IV: Sii|i|iii-iii--, ilii'i-.^rni-c, iImI ilir lii>li,'iist IS, +:.'.;!•>; :>\ :i.&^ ; ScittcmlMT 7. 2.U-2 ; ]7, .•{.!;'.: 27, :i2l; Oftohcr 7, ;; k; : 17, :.'.(»;! : :i7, 2.(')0; ■Novcinbor (i, +:i.2.s. 'I'lioo ((inectidiis liciiii:- iiitiTiniliitoil to cvcM-y duy, ainl applidl to WiiiiKvke'.s K|ili(>iii('iis, lavc tlic I'Mlldwiiii;- ('|ili(Mni'ris oi' the llicorctical iiortli jmlar ilistaiirrs dI' Mar.s at transit the iiii'iuiiaii dl' l*iilkc)\\a : I Dill.'. .•Viic Sr,,t •.'II Vii ','1 •Jli :iii :il I •I ;t I Id II I -J i:! It 1.". i<; 111 •^1 S(, si; -i; -I) Mi Ml M'l sr. ^^li si; SI) sr. -li -1) Ml S(l Mi ;• 1-, II ,"i:;, I l:!, I 11' Ml III, r.T 111, .-)l 10 i:! Ill I '.I •,'ii •■>'.) :!:! :!7 ■11 !."> r.i II'.' 11 .■•I •J'.l lit .'>li 7. -J .'-t i:!. :i7 111. ■111. I. :!7. ••-'7. :!.'. r>i. '.'1. II. 'ill, H7, 2 :v.). •■i'.K II. 1.'.. HI 47. il'.l iili :m mi I'.") II I'm ',»•.' Il'.l ',•:( i •.';! ] 71 1 I-.' ' K! ; :!ii 17 •1.1 I •Jl> II--' ■IS HI ;••,' I'.i '.II I I I ; II II l> 1—0 + 11 II 11 II ; I ! I :ii (14 •M. :!'.'. ■-'4. '.I. .'.4. v!:i. ,.^ .■i:i! li'.i. '.'4. it. 4. lit. :i;i. ■17. I. 14. 17 sj :!ii I I 41.4- .■>4. ;!i. 4-.'. ;!. lilt! Its. 4.->. :,(\. II. I. 11. 41 III •-'li IIS 47 :r. 7:t 4(1 .->:! HI 57 4-,' 47 (i'J Kt II :i7 + I.-..II- I.".. Ill I.'.. I.'. I.".. 1.'. I.'.. i;i 1.'.. !•.' I."i. 111! 14.1111 I4.s:! 14.71 I4..'i- 14. lit I4.:tl 14. I- 14. 1 Hi i:i. itii 11!. (17 lit. 41! i:!. IS I -J. it:! I-', (ill \2.2:> ll.s-j 111. :!it 111. ss III. li" !).7:t !». 117 7. Iili (1. S.") (1. il."> ,\ 1,". 4. "-'I II '*.*^ •J. -'I! i.:!ii + (i. :!ii o I, 1, I, I, —It, +", I I 1 1 I 1 o 'J, o •J t> o ') ') >) +4 K i'i !- It. .'.() +'i. •JllltH 'jifJ7r. i.'ii).-)(; Ill4:i (i,'>7-.'it llll.'l.")!) ii-j;!.')ii ^;l77 1 7:!i-.'7 .')itl4ii ;!.-.'.itr. ;t,-s,-,i; 1 17 1 II ill •jMI|-i .VJKili , (i74.VJ 7.-'(ir)i s7li:{ 'j:.'iii(! ll(Mi:!S (t.>4(j I(i:{s4 14:w;i I7it-,'l •J II 177 ',*:mi-j '..'114 IS •,'S(i.-,!t :tiiii4!) IWIlll :);!ii.vj ;i,vjiii» :t(>i4i) :!74iir) lisiTl :!S7r>ii liiM.'i'.) ;!ii;iii.s :i!)4()G Date .Sipt. Oct, •Jit liii I !) ."•'■^ Ill ss 11 SS 1'.' ss Ill S-l 14 S-; l.-> ,«.•* 1(1 -11 17 ■-11 |s ■■^11 li) Si» '.ill Sit iJI Sll 2-i Sil 'j:? Sll '.24 s-l li.-) Sil a() sit !•/ rti» as Hi» •i'J Sll ;tii S8 :{| ss 1 ss •.> ss :i ss 4 ss f '■J i ^ ~ zZ i *i -9 1. ,1) ■t- ^ ■:^ -5 x •; Z "' s "2 i t zi 7i ,»_, ^ ™ "5 ■j: ^ to < ~ ^ 1 ,-..-,, Ill +4 7. 5(1 - 1.51 -\- .:iit;ins li •-'. 7--' 4 (1.115 '.'.41 .liitiii^j III ^, 4 t 4 It.lil :t. '^s . :!M175 14 !•-'. II 1 1 1. :;i! 4. 17 . :!.-oM) IS fj. 77 1! .511. lit 5. 115 . :!7:^2ii o.> .-.Itil :! 51. 14 5. H7 . lilhiS-J •-'li II. Ill :t 45. ','7 (1.(14 . :!5^J70 •-'It 4.-.. :!7 ;i 1!^. (in 7.47 . :!:;ii7 1 :!:! •J I. nit :i :!l. Ill S.'J4 .:!■-' 1(1 1 :!ii .".. ill 1! \>o [)■> s. Hil .:iii7:i:! 411 IS.IIS ;', 1:1 ii't it. 711 . 12-7(14 41! iW.til :! 4. 17 lU. 41 . •J(1.5-J'J 4(1 ;i(). is •> 5:!. 74 11.10 . 'jmnio 4'J •2\). !l-i •^ ■K'.lll 11.77 .•.2ii'j:t :>•> !•-'..->(; '2 :(ii..-7 I'-'. 4:i . 178110 :>\ 41!. 41! •J IS. 11 1'-'. it-' .141'.2ll ."i7 i.s7 o 5. ■!() i:!..57 •J. Iiiis51 .Ml 7.1!:! I 51. -it 14.011 12. 04S71I 11 ."lit. --'-i 1 :i7. Sll 14.. 57 1.!I!Io;m o :!7. If-' 1 ■,':i. -s.i 15. ii:{ I.H-.'O-JS 4 It.-,'.') 1 S. -Jll 1.5.45 i.s:!:!7s r» S. 4.') II :>•>. 75 15. SI \.ri-i-i-i (i l.'-'lt ft :iii.iii 1(1. '-'I 1.5(1714 (i US. 1 1 II :2(i. 7ii 1(1.411 l.:{l,5il7 (i .">S, SI +0 4.'JI 1(1, 7'J O.lWl'iS 7 :i. II--' —II I-J.5I Kl.lM 1.0'.l7'-'() (i all. ,")i II •■211. 4-J 17. (i:i l.4().S()4 li '.21.1111 II 411.45 17. (Ill l.ddllitD 5 :!4.(14 1 :i.54 17. i:i l.so:ilt5 4 :!i. Ill 1 'Ji 1.117 17.08 1.1(0(171 W ill. 41! 1 ;!7. 75 Ki.llS l.lHtltl'v' 1 IW. (IS 1 54. 7:i iC). 8;i 12. 051)1)8 5!) 37.1I.5 12 ]j.5i; 10.(15 'i. 11 ill 12 .'i7 '2(i. :!!» ^ '^8. '.21 J(!..5(i 2. 1708S 54 OS. 16 'i 44. 77 l(!.4l a. '2 Kiss .->•.' i:!.4i :» I.IS — KJ.ai '>*.1.'5<1I 4!) I'j. ^':i — u 17. ;«i -fl2. '.211533 4.-) 54. S4 From flu- abovi? I'plu'iiuM'is tlu^ positions in tlu> sixth colninii were coiii[mtefl by interpo- lation, using th{> aihipti'd h)nj;itU(1('s of the Oltservatorie.s already given. V AND T1[E KLKMENTS WHICH Dl I'EM) IJi'ON 11'. 13 I\ t'ormitif^ tlio equations of (MiiKlition, tlw oliscrviitions ,ir(^ dividtMl into livi' sciics. Tlio first two scrios coniprisc tlio ohsi'ivations iiiiidc uitli tlio first ^r()ii|i of Wiinu'ilju's coiii|iiirisoii stills, iuid tlio next three tliose iiiade witli tlie tiirec t'oilowiii^ groups. Ill roriiiiii^ tlie e(|Uiitioiis of coiidilioii, tiie errors of tlic iiortli polar (listaiice of tlie oplioin- eris proved to lie so inimite that the simple error of ^'■(>oeeiif rii' declination was introduced into tlio iMjiiations instead of tiio tM'ror of ihe liiu'ar co-ordinato ;.■, which it was intended to use. The three uiiknowii ciuanlities in the ecpiations aie a> follows: M, the error of north polar distance at the middle d itu of i-acli series. /9, the change of a in ton days, siqiposcd constant tliroup;hont oacli series. -', the error of the Sun's mean equatorial hori/.ontal parallax dividend Iiy O.S'.t. The (general form of the equations of condition is 0=p|«+/,,H«:!^-;p:-+J.N.IM,.} where P=: measure of precision, (column 4 ) /=:tiino in days from the middle of each s 'lies. ;;' = planet's apparent pjeocentric zenith distance south. J.zr planet's distance from the earth. J.N.P.D. = the coinpute 14 INVK8TIGATION OF THK 1)1.STAN(;H OF TME SUN Comparison of }sorlli Pnhir iliilitinex of Mara ilvrirn] frmn ohsirrution with those giriii hij the Hphemeris, iind J'Jtjitations of condition iiirm hij t/ir lonijiiirison, FIRST SKK'IFS. . I 1 T.i "?-= »• " J = - ii K 2- ^ ^ 2 . « Dale. • )lisciv!itiirv. •_ i. 1 CC.I tri< list K(|Uati(iiis lit' coiiilitiiiii <;ivi'ii l.y till' 1 fZ ^ 3^ a 2 s. •♦- i. tH iihsci vatii.ii.H. !i g- " S -3 HI 'I a V &£. i '^ 0, dS i.-^t;->, Autj. -.'1 (•,i|)i- .... 1 :!ii. ■'•,' :i + 10.71 47.11.-. ()=:;!ni —X-.M, -:t.'-'T' + 1'.':! S;illliufr(P r.(i. I! 1 + 10. Ii 7. 17 1 —1.1 —1.1 +ii.:i Alliiiijy I(i. 17 1 — ii.:!;t .-..7'^ 1 —I.I +1.1 +".7 •!•> Williiiiiistinvii M.".'-^ ki 4- 11.7:1 :i. Oil .) — ','. 1 — '.'. ;! +o.:i ('.•l|ir .'iT. It-J \\ + 10. -1 H. iir. fi -;t. x-i +0.7 Slllllijl!.'!) •Ji.:{ + 111.7 :io. iio .1 —','.0 —-,'.1 •> '> y;t WilliiMliSldWIl •-'•J. 7.-. •> + II. >l :!;!. ■-7 *> — I.i» —','.4 —1.4 I'lilNowa . ; 1. (in ii — 1.".. '-'1 lii. .-.1 Ti —','.7 +4.(1 +0.4 CmIm' . . •: :u. 10 ;i + 10. Ill 4.-.. 0.-. :! — ','. 7 — ;!, :! +'M SiMiliafrii 1 1.4 -j- lo. -^ 11.7.-. .* — l.H —•.'.•,' — 0. It v'l Williiunsdiwii -!.W.\ •> + ll.il.'. lit. -^0 — 1.7 —'.'.4 +0. (1 (.'il|IC' i -Jl.'.*- ;i + n.oi :i(i. ','ii il — '-'. 4 — :!. :( +0. i> SiiMtiii(;o r..-.. X 1 + 10.il (1. 7.-. 1 —O.H —1.1 + 0.(1 All.any i.'i. s-j 1 — 11.71 .'». 7.-. 1 — 0. -1 +1.',' +1.(1 •j:> W'iUianisliiw 11 7. 10 •J + 1-,'. 0.". •Ji 1. ^-. .> — 1..-. —-'.4 +:!. 4 ('ajic iil.'Jl) :! + II. 10 .»','. (lit ■I — ','. 1 — :!. :i +0. i» (Jii'iinvicli .Ml. :t:( 1 - i:!.-J :!7. ','7 1 —0.7 +1.1 +0. H Saiiliajrii (i. -i '> + II. 1(1. iio .) -1.4 — ','.'i —II. (1 Wasliiii};ti)H ','11. OM 1 — lo. S(i 1.-.. (H» I -0.7 +1.1 -II. 1 •,>r, ('a|ic ' .■>:'.. I-,' 'i + II. --'o 4. ',"J — 1.'.' —i.-i — II. '.• Saiiliapri) i -.H. 1 '■i + 11. 1 4','. 1'^ .) — l.-i —-i.-i — •,'. •J7 WilliaiiistdWii 1 r>:i. :u + l-J.-,'7 M. i:i •} — I.I —',•..-. + 1.(1 (ii'ci iiwicli 1 w. -jri I - 14.01 :t(i. iiit I —0..-. +1.4 — l.-i Saiiti»f;(i . 1 1-.'. ;! '> + II.-' '■ii. .'.."> .j — 1.0 —-i.-i -l.it 'JS \Villia[iist. 7 1 + 11.:! I7.i»4 1 —0.4 -I.I +11. It \\'asliiiif,'t()ti 'J(i.7'.t 1 — 11.07 l(l.!t'.i 1 —11.4 +1.1 + 1.-J 'Jl» Williitinstdwn 4:1. ii(l •.> + 1-.'. 'Ii '.(!. 'i> >> —0.7 — '2. .'. +11. ;i ('ape •JT. (i7 •■i + 11.4- :ut. 17 'J — 0. ti -•,'.:! +0.0 Saiili»i;'(> l~. 1 1 + II.:! 'i-*. -i^t I —(I.:! —1.1 -\.-> Alliaiiy ;!:•. o;» 1 — 1-J. II 'i'. .-!! 1 — 0. :f +1.',' +0. it :i(i Williainstiiwn '.'.». i^it »i + I-,'..".!'. l','..-.o •J —0..-. —•,'..-> +0. 1 :ti Williainstiiwii ;!i>. II I -i- 1-.', lifi 4:i. .'.1 T —0.1 — l.:i +0.7 Capi' •,'!..")(■. •J + ll.li(i :!(■.. 7ii »» -II. 'J ■-','.:! + 1.1 Saiiliapo •Ji.i •J + 11..-. ■Xi. 14 .1 _(i. -J —•,'.:! + 1.1 Sept. 1 I'lilkdwa 4;!. 7-J ;! — ir>. -Jii •.i7.(l(i :i 0.(1 +4.!» +0..-. (',:p,. . . l."..(i(i :i + 11.7.-. ti7..-.;i Ii 0.0 —;{..-. +0.4 o Pulknvva . 4s. s:t ;i — 1(1.40 :w. :r. :( +0.:! +4.il —II. '2 Capi' •Jl.:!:t ;i 4- 11. -1 :w. 7.-. ;! +0.:! - :!. (1 — l.:i , .Mlian.v 4-.-J(i •J — 1-,'. .-.0 :<(>. 40 .J +>K-> +','..-. + 1.:! Wa^liiiip;toii 4-^. (i."> •> — 11.4- :i(i. .-. 1 .) +(i.'J +','.:! — I.:i ;i I'lilkowii 7.:!:t !l — Ki. .-.1 r.i. II :i +0.(1 +.->. + ].^ Cape ;i'.i.;i;t 1 + II.!!'.' '<•>. -i' 1 +0.',' —1.',' +11. 4 (ii4'i'tnvicli f. 4.-. •) — Il.7tl ,".:!. (ill .) +i>. 4 +:!. —0. 1 SaiitiafTd 47. :! 1 + II. s .-.ii. :!■,' 1 +0.-J - 1.',' +ll.!i Alliaiiv II. (i4 1 — l','..-.il .-.1). .-.7 1 +o.-,' +i.;i +0.5 VVasliiiipliiii 1 1 . •,'.'> — II.. -.11 r.ii. -i .. +0.4 +'-'.:! +0. ;t 4 WilliaiiislDWii :.-. -i.s I + Ii!. 0:1 1 •,'..-..-. i +(i.:i —1.3 +l.-i I'lilkowu . 4i.:!o :! — 1(1.(1',' •.'4. (1.-. :! +0. i' +.'..0 —II. 1 Capi' i:!.77 :i + 1','. 00 'J.-.. iw :! +!•.!• — :t. (1 +0.() Saiilia. 7 1 + 11. i> ;t7..'>o 1 +11.1! —\.-> -(1. 1 All.any 4','. (lit 1 — l'.>. (W :«!. s.-< 1 +0 It +1.:! +0. ', \Vasliiiiji;ti:ii 47. s:! — 11.(14 ;<7. ','it .. +0.(1 +'.'. :i +•,'.•-' T) Williamstowii 4-.'. fi7 1 + i:i. II r.r». :!7 1 --0.1 — i.:t —0.4 (Japo i.v!:t •> + Iti.iC i:!.7l 'J --0. H — ■.'. -4 +0.8 Saiitia;r<' ]ti.!> •> + 11.!) •27. (lit .. +0. H — -J. 1 •)^ Albany 4o.:i7 I — l'J.77 •i". I-' 1 +0.4 +1.:! +(T i\ Wasliinfjtdii 40. .VJ 2 — Il.7'i •^n. 7:! ■> +0. s +■,'. 3 —0. 1 (i AVillianisti>« 11 :!7.:i7 1 + i:(. li> .V,'. 14 I +o.r. -1.!! +1.6 \\'iisliinijtciti 4:.. '-'S — Il.rti :u.(ii + 1.0 +','.4 +1.1 t Saiitiaffo :tit. 4 ») + 1','. 1 .-.i.:« >_> + I.'J -','.4 —0.3 Alliiuiy w.m I — I'J.iM r.'i.(ii» 0=ln, +(i.(U, +i.:tT' +1.1 AND TlIK KLKMKNTS WIIICII DKI'KNO UPON IT. ir. IIKS r si;kii:s-c. iitiiiiii'il. 1* ; 1 t 11 r Diitr. OliMi'ivatory. 1! i _. 5 1 = J, a ' a^ Ki|iiatiii|is III riinilllinii ^Ivrii iili.scrvalii.iis. l.y till' n-z t '■/. ~ " - a 1 = 3 V = c il J'. - w Ju |H(lV». Sf|>t. t^ Williiiiiixtowii ii.i;i I + l:i.:ti •jr.. iw II. Ill, +11.7 (, — I.ISt- + l."7 ('ii|ii' .... 111. <>ii *» -f I-,'.-.'- ,'.;i. :i.'. 2 +1. 1 —2. .'. +11. - Siiiiliairo 11. 1 + 1 •-'.•.' •,•:!. It- 1 +11.7 -- 1. 2 + 0. 1 Alliaiiy :i( ;.•.'•.' — 111. II-.' •,M. •.'•.' 1 +11.7 + l".'l + l.i» \Vilsliil|i,'liiII . :«■.. 17 — II. '."7 •J.-.. 1 1 + 1.4 +•-'• 1 + 1.11 1) Allpiuiy 'jii. 11". — l:i. II '.1. 17 1 +(•.■' + 1.:! +2. .-. III \\ illiainsdiwii \i . :\o + i:!. 1- .'.4.:!l 2 +1.7 •2.7 + 1.1 I'lllUliVMl ■III. :)',» — l7.-.';i :w. 1-.' ;i +2. 7 +.-.. 1 +11.1 Li'iilt'ii .... r.r..7(i — 1. ■..!.:! III.-.' 2 +1.- +:i. 1 + 1..". • ilriiiw irli r»7, i'lfi - ir.. Ill 4'.'. ;i.-. 1 +11.11 + 1..-. +11. 2 Allmiiy aii.iJi — iii.'.'ii 1 7.. Ml 1 +'1.11 + 1.:! + 0.1 II Williiiiii.'itdwii ii.'.ii + 111. .Ml 1 .".7. :!n + 1.11 .) *■ — 11. - I.i'idi'ii .... ;i. 17 - I.-..7-J i 4-. 7-.' 2 +2.11 -\--\. 1 +2. .-. (tici-invirli ".. Ill — I.-.. Ml ; .Ml. 1(1 1 +I.II + i.r, +ii.r. 1',' I'lilkdWii ir.. 1.'. - 17.111 r.s. ;in +2. 2 +:i. .-. — 0. •'> lli'Miifrtiirs . . IT.'.l-i 17.. '.7 II. .Ml 1 +1. 1 + 1.^ +11.2 (.'iipi! .... .'.II. -1 + 1 •.•.:.■.' , :!. 17 :! +;!.:i It ^ — II. .'. Lciilcn .... •ji. r.i ii — i:..-i 1 .-.-4 SKL'OM) si;i;ii:.s. 1) ;;„, +:i. :u, + 'i:7r' + 1-1 + 1.0 Si'pt. i:t WilliaiM.^liiw 11 V'.".. 1»7 •> + IH.Il- 111. 14 0^2.1. — 1. 1 <■ ■.'.7t I'lilkiiwii 17. 'JC. \\ — 17. .V.I •,'1>. 17 :t 1..". +.-.. li — 11. (1 Hi'lsiiifjliii's 4f. .-"> •» — 17.117 :ii.-j 2 —I.ll +;i. .-. + l.:i ('iijif ','l.ii'> :! + |-i..".7 :i4.iii :t 1..-. +:i. 2 Lridcll .... .Ml. ^,'. :! — 1.'.. '.Ml 111.7.". :i —1..". + i'. -^ — 0. 11 Siiiitiiijro I.ll 1 + l-.'.4 Iil.ii:! 1 —11..". -1.2 II. 1 Wiisllill^rtdli V!-. >7 tj — I'.'. :m 111. 7li 2 -1.1' +•-'. .-. + 0..-. II WilliMIMSiO-.Vll .-,. :w :! + i:;.7l l-.',ll :; —1.;; — 1. 1 — 0. ll I'ulUiiwii •v'!l. '.Hi :i - 17. IIS ll.'.M :! —1.2 +:.. ;i - 1.0 Liiilcii .... :!'.l. 7ri •> — l.-..'.i'.l •24. ii-.i 2 II.- +:i. 2 +0,.-, Siiiitiil^'ii •17.0 T + i-'.r. ;".'.». .Ml 1 — II. 1 — 1.2 +11. II 1") Williiiiiisliiwu iVi.-.>l) •> -f i:i.7;» -.11(1 2 —11.7 .. w -II. 1 I'lilkiiwii •Si. lili •} -- 17.77 ."..-.".I 2 —II. 11 + :'!!.-. — 11. ll Liiiliii .... :t:!. !»7 ~i — HI. iw 1-. 14 1! —Il.lt + l--^ + 0. ■' Wasliiiicton . 1'.'. lit •) - I-J. H .".'.I.OI 2 — II. r. +2. .-. — I.:i III Williaiiistiiwii "..".. 7;i ;i + i:!.-;! 11. 4.". :! -11.7 -1. 1 —II. :i I'lilUiiwa . •,'7.llf< 4 — 17. -II 11. Hw' :; —11.11 +.V 1 — II. t; Li'iili'ii .... :w. -It; :i — 1(1. Ill •i-i. .".II :t — (1. ti + I.H +11.11 (ill't'llW iili tii.i;:! 1 — III. III! •.'l.lllt 1 —11.2 + 1.11 +11.4 Sanliiip" . .'.11. 1) 1 + I'.MI •.'. :i.-. 1 —11.2 — l.:i —11.2 17 Williaiiistiiwn li. Ilti a + l:i.>7 III. ss :'. —11.4 4. 1 —11.2 I'lilkiiwii . 411. -^f) 3 — 17. H4 2-.'. 4- :( — (1. :i +.-.. I + 0. 1 Ilclsinp;l'(irs 44. .^.8 1 - 17. IW 2.-.. 44 1 II. 1 + 1.- — 1.2 Li'iili'ii .... W. '.'a 1 — m.-ji :iii.7:t 1 -11. 1 +1.11 + 0.- (ill'fliwicll r..-.. r.-.> 1 — 111. 07 nil. '.'It 1 —II. 1 + 1.11 —11. 2 1 Sanfm^'ii . r». f) 1 + I -.Ml I-. IJ 1 —II. 1 — 1.:! +0.;! 18 I'lilkiiwii •,'. 44 li — 1-*. ii'J 4.".. Ill :s 11.0 +.-.. 1 + !•- i llflsiii},'('i)is .'■.. l»5 1 — IS. 111! 4s. Ill 1 11.11 + I.S +0.2 j t'api! .... :ti>.(i:! :j + I-.'. 711 51.-2 ;! 0. II — :i. s +11. 1 ! I.i'iili'n .... If.. 4H :; — 111. lil .V.I. si» :t 11.0 + 1. It — 0. -^ \Vusliiiii;tiiii . (1. :tii •J — 1-J.(l'.l 47. 1 H 2 11.0 +2. .". —1. 1 1!» Williaiii.stDWii r.:t. ti:{ :{ + i:i.ic. 7. iri :! +0.2 — 1.2 +1.11 • rulkdwa :m. i»7 :i - IS. (!'.» 1.".. 112 :! +11.:! +.-.. 4 —2. 11 , Ciii.i' .... III. It) :s + |-.'.7s 22.1111 :! +11. :i — :i. s +11.2 j Li'uli'ii .... 4^.7.-. 1 — Ifl.liS :tl.:!ii 1 +0. 1 + 1.11 — 1.0 ] Santiagi) .-.. :i 1 + l-.Ml ir..,".i 1 +0. 1 — l.ii — 1. 1 iill 1 Li'iili'ii .... •M. (1(( ;i - 111.11 lii.4li :i +o.(; + 1. 11 +11.7 8aiitiai;ii 411. 1 'i + I--'. 7 .'■.7. IIS v! +11.4 —2. ."> — :t. I yi Williamstown i:!.l>4 u + 14.1111 27. 47 2 +"■•'' — 2. S —ii.lt I'lilkiiwa . .>-. 17 :» — l-.-.'J nil. Ill :( +11. '.1 +.".. .". —11. 1 Albany r.". r.() 1 — I:!.'.i7 411. 2.'. 1 +:i.:i + 1.4 + 1.7 ' Washiuptou . •,'. 4-^ 1 — I-J.s.-. 4s. :!.", 1 +11. :i + l.:i — 1.2 'ii ' I'lilkowa . r.ii.4:i =' — IS. 27 :{|.:w O—Wui ■\-\.-i.ii +:.. .-.T — .'. :i 16 INVKSTKIATION OF TIIK DISTANCE OF THE Hl'N HKe'OND .SKIMKS— ('..ntiniiiMl. 7i , i ^ Hi Uiiti', ( •l).>ii'i\ iitdiy. ■~ 2. 1 i = 11 1 "y J- i Hi|iiatii.iiM III ciiiiilitiiiii (i^ivcu iilistu'valioiiM l.y tlic = E 2 1 z S ;2 s c ! 1^"^ l^ty. 1 i // Srpl. •,'•.• llilsiiiirriHs :.i. i-* 1 - i«. :t(i :ti.^'s 0—1 * (Jiriiiwicli (1. it:. 1 — It;. :i;i r.i. 1:1 1 +0. 1 +I.. I 1 + P.'. 7 j :t7.:io 1 +0..I -i.:t —0. .''. Alliiiiiv M. Iti 1 — 11.02 it'.t. :i-.' 1 +0.1 +1..1 + \.'i W,i.sliili;rtiiri r.i. 10 *> — IV. '.to 11.17 t> + 0.H +v'.ti +0.4 '.':i W'llluiiiisldwii ^t^.i^i't ;i + II.O'.! : I.'. 17 :t + 1.4 -l.-J +0.!l I'lilkonii 17. •I',> — |H.:fi '.*^. (II) *» + 1.0 +:i.7 o_ •) Clip!' '.':i. :w :i + I'.'.HI 1 ;t.'.. -ll 'i + 1..-. — ;i. H — 0.!l Lriilcn . II. <)i 1 — Itl.til 1 -i.-.. Hi 1 +0..-. +1.7 + 0. H ( ini'iiw ifli 1. II 1 — It!. IJ •1-. IC. 1 +0.,-, +1.1; + ».-i SllMtill^'"!! '.'■-'. '"^ 1 + I-.'. 7 :!.'.. 1 " 1 +0..-, — i.:t —0. :i Allmiiv r.ii. t;r> 1 — N.07 1 :i7. •,'.-. 1 +0..-. +1.1 +0.7 \\*MNliin(;tini .■.i.(ir> •) — |-.i.!t« :i!t. 11 + 1.0 +-.'.r. + i.r. ','1 Williiiiii^liiwii r.7. r.ii •> 1 4- l-J.o-i 11.77 + 1.1 —-i.rt +0.'. llil-iiiirliiis .-.1. iv 1 — |M.4(J :!••'. 1.'. T + 11. f. +I.H i).:, Ciipi' •.•:!. 7:1 :t + l-.'.sl ;!i;. ^> ;t + I.-1 -X'* +0. H l.rjili'll . . . . •J. i;t >. — 1(1. tltl 111. ■,'(! .. + I.V' +;!.;! + 1.0 Siiiili;i;;o M\. :t >. + |-.'.7 :i7.ol + 1.-,' -•.'.:. +0.1 All.iiiiv . . W. 7 1 I 1 — II. li :!'.!. 1-.' 1 +0.(i +1..1 +0.:, \VM'iiiiii(;l(iii r>:i.(;i '■i 1 — lii. Hit 4i.:i5 U=->nj + 1.2,1, +- ' 14.9:1 -•,'«:, -1. H:, — >.><:r' —0. :i lli'l>ill;;rcirs ! .".1. i- \ — I-..-.0 :ii:. lio 1 —0..'. + 1.^ +0.11 Cape . . . . : ','7. in; + l-J. K! 4l.o-.> — 1.0 —2. ti +0.;-. (in'i'liwicli '.Mi,-. • I — Iti. .-.1 i :.:!. ll-.' — 1.0 +:<. :i + 1.0 ."-aiiliairo ■J". VJ ** + |-<.'.7 I 41..-.^ • > — 1.0 --.'. r. +•2. Alliatiy . . . i Eti." I7 : 1 — 14. Ill 4::. 91 T -II..-. + 1.4 +-2.0 Waslniifrton 1 .^•^. 111 1 t> — i:i.ii;i 1 4(i.-j;! »> — 0. .-> +-2.tJ +■2. -2 ■H'i W'illiaiiisldwii 7. !•.' 1 '* ■ + 11.01 •-'0. (i.-^ ~', -l.:t — 1.-2 —1.1 ' I'lilUdWu i .-.-.-Jit ! :t — 1-. 41 i :i9. :ti :i !.•,' +.^. -. —1.4 l.cicliU . . . . 1:!. 17 ;j — Iti. 7-J .-.7. mi :• —l.-J +.-.. +0.9 .'^arilia^o :!ii. ,-< • ) + l-.'.7 4'-. 7-J •> — II. s V. .') -i.ii Alliaiiy . . . :i. 1.-. I - 11. lit ,'.0. f^:! ii —II. 4 + 1.4 + i.ti Wasliiiif.'-liii] ti. 11 •) — i;(. (Hi ,-.:!. 1 1 .» — 0, 8 +-2.li — 0. r. J7 ^\■illi,•llrlslll^vIl i:!..^:! •> + 14.00 y.-. 09 •J —0.7 — -2. f' +1. 1 Piilkdua . . . .-.. 1,-. •> — l-.4(i 47.04 .) —0.(1 +:i.7 +0.1 1 Ii'Uiii^,''r(ir,s |0. -."J — !>..-.t! r.o. 74 0. (i +:i.7 —1.8 l.iiilcii . . . . •Ji.'-'-i ;; - Hi. 7.-. 4. >,-. li —0.9 +r>.o + 1.0 .""Miiiiat,''! ! i;;. :! 1 + I-.'. 7 .-.(i. or. I -0. :( —1.:! +0.7 .Mliaiiy ; ll.ii7 1 — 14. -,'1 .-)>. 78 1 — 0. :i + 1.4 +1.3 is Wllli.-llMSldWIl ! -JLiilt + i:!.ii-' :iii.'-'o *> —0..-. —-2. 8 +1.7 I'lilkdua . 1:!. .-.1 •J — M.4S ,-.,-.. k; •> —0.4 +;!.7 +0.2 Ijclsiiifrl'i'i-s ii.:il •1 — 1 H. .->r< .-.8, Si •j —II.. I +:{.7 (+li.-2) i .' 4.71 »> —0.4 —-2. r. + 1.0 Wasliiinrlon •-'■-'. HI 11 — 1:!. II 9. 1 1 I —II. -J + i.:{ —0.7 ',",t W'illiaiii.sliiwii 1 'Jit. r.:! »i + i:i.!t(i 44.04 \> — 0. '2 —2.r^ + 1.1 I'lilUiiwa ! V'l.K". :! — If'. 411 ■.'. 7-> :1 —0. :i +-,.ry — 1.9 llflsiii(;l'oM •,>:!. :io •.' — lH..-.il ti. 40 •> — 0. ^2 +:i.7 +:t.4 I.iiilcii . . . . ' :i7.o:! •> — Iti.71t •-'0. 4.-. 2 —0. -2 +:i. 4 --(t.4 \Va!-lMni;'toii [ :!o. \■^ \ — i:{. 14 Hi. :u 1 — (t. 1 + 1.:! —0.7 ; !0 Williainsluwii :!7. 1.-. a + 1:1.9:1 -.0.1 i7 2 0.0 —2.>i —0. 8 ; I'lilkiiwa . •,'7.77 •■i - 18.49 8.77 •2 0.0 +:!.7 — 1.0 Santiai,'!) .-.. 1 1 + i'2A\ 17.4;.' T 0.0 — i.:i — o.:i Got. 1 WiHiaiiislown i 11.17 •,' 1 + i:i.lio -).-.. 17 +0.-2 —-2.8 +1). 2 I'lilkowa i :to. lio :{ — 18.49 1-2.41 ii +0. :! +5. 5 +0. 9 l.riiltMl . . . . ! 47.41 2 — H!.80 •29. 78 •2 +0.-2 - -3. 4 -17 !> WilliaiMslowii 4:;. 44 3 + l:!.87 Til). (i7 Ti +0. (i —4.1 — .9 ^ Cajic . . . . s. 19 .i + IV-'.tiH •20. til :i +0.() —3.8 • -0. ri : Saiitiapii . ii.lt 1 + 1 •.».;-. 19.49 1 +0. 2 —1.-2 +(t.i ! Wiisliinfjtoii :tf.. r.7 1 -i:U5 •-':t. 70 0=:2a:x +0. 4A +2. (i:;-' +0. t! ^ AND THi; ELKMKNTS WIIICII FH'.I'KND I'I'OV IT. 17 v^ nilKD .-JKUIKS-C. (Iltiniled , >-3 "1-2 . 3 5 ?- Dnto. 01)Ht'rvatory. 31. d 1 ^ a r.ipiiiiioi M oC cnuditidii givei nliNel \ alioiiH. h.V till' "o-a ? '1 f ■- B C 2 '.% V -< r s V i r • 1H. H~i +0.7 1 Cftpi- .... l.lll o + l.'.fll Hi. 01 •J -fii. Oi — 2. .5 — 0.1 4 1 WilliiiiiiHtnwn :w. '.>v! • > -f- 13.78 47. I-.' o -j-ll. H —2.8 +0.8 I'lilkowii . M. (i7 \\ H.44 0. HI 3 + 1.2 +5. 5 —0. 1 Ili'lsinirl'iii's . . lit. HH 1 — II..M 3. ,'.0 1 +0.4 + 1.5 — 1.8 r. WillJlllMStOWll •->l. II 1! + 13.73 31.3.-. 3 + 1.4 I. 1 1.5 Ciipi' .... 41. Ill :t + l','.r)3 Wi. 07 3 + 1.5 —3.8 —2. 11 Leiden .... 1^-. C.-J 1 Hi. 73 1 . •»• 1 +0.5 + 1.7 —0,0 Smiliiipd . :t.i.(i 1 + \-<.\ 47. I-J 1 +0.5 1.2 +0.4 fi rulkiiwii . !•.>. i:i :t — 18.37 yi.oii 3 + 1.8 +5. 5 —0.2 llelsilipfors •1.".. oil 1 — I-.47 a7.ai 1 -t-0. r. + !.'< +0. Ciipe .... I7.f.l! :t + I-J.48 31.07 3 + 1.^ —3.7 +2. 8 Leiilon .... ri.'i. 77 ;! — Hi. 70 311. 12 3 + 1.'* +5. + 1.0 tSaiitiH|r<) . IV'.II 1 + !•,'. 3 24. 03 1 +ii.ii - 1.2 0.3 WiiHliinfrton 11.7(1 1 — 13. 10 27.77 0-_l(i, + lif, + I.3T' —0.8 FOLK' I'll SKKIKS. Oct. 7 hoicleii .... '.T). :t7 3 _ Il).(!(> 10.03 Ov-^304 -i.8,y, +5. On-' +0."8 Siiiitinffo 41. 1 1 + IV'.3 -.2. 117 1 —0.0 — 1.2 —0.4 Allmiiy 7. I\> 1 14. 17 r.4.71 1 —0.0 + 1.4 + 1.8 Wii.sliiii7. 7(i 1 — 13.0.'-. 10.111 1 —0. 5 + 1.3 +2. a 9 Williiinistown is.:i7 3 + 13. 4'J 31.28 3 — 1.3 —4.0 — 1.7 Ilelsiiifjldift r>:!. \n 1 18.31 34. 83 1 —0. 4 + 1.8 —0.8 Leiden .... •.'. Ill 3 — lti..'iti 45.00 3 — 1.2 +5.0 +0.2 WiLsliinpton 40. :{.") a — l3.oa 27. nil •1 —0.8 +2. r, + 1.3 10 WillianiHlowii 'l\. 'iS a + 13.4a 38. 02 *) —0.7 —2.7 + 1.8 Ciipu .... •J'.l. !».". 3 + l-J.'.'-J 42.08 3 -0. It —3.7 —0.3 Leiden .... 4. 87 3 It). .'lO 4i».OI 3 —0.9 +.5. + 1.11 Siiniiiipo 1 :!..'. a + 1-J.O 20.00 2 —0.0 -2. 4 + 1.0 11 Williiinistown 1i:i. If) a + 13.3.-. 3.-.. 7 I •) —0.5 -2. 7 +0. 5 I'ulkowa . 47. :«» 3 18.07 21t. 92 3 —0.0 +5.4 + 1.8 llel.singt'ors 4!). 7:5 a — 18.18 3-J. 42 o —0.4 +3.0 + 1.7 la Willianistown f<.;ii a + I3.a7 21.118 2 —0. 3 —2. 7 +0.8 I'ulkowa :to. iiCi 3 n.ti'j 12. 5i; 3 —0.3 +5. 4 0.3 Cll))!! .... r>. !)!» 3 + ia.o8 17.71 3 —0.3 —3. -1. 1 Santiiigo 44. 4 1 + II. it 5li. 00 1 -0. 1 — 1.2 —0.3 13 Willianistown 4-2.7I a + 13. 1'.) !'.0.7I •.) 0.0 —2. + 1.0 Ilelsiugfors 4. 4r, 1 18.01 4.-.. 58 \ 0.0 + 1.8 -0.11 Capo .... :tri. !»i( 3 + la.oo 48. I!» 3 0.0 —3. +0. 1» 14 Leiden .... aii. 'jis a Ki.ai 11.31 >.> +0.2 +3. -J +1.1 Albany n-j. -a 1 — 13.80 31>.5I T +0. 1 + 1.4 +1.1 ir. I'lilkowa . 24.71 3 — 17.71 7. 33 3 +0.0 +5. 3 + 1.0 Capo .... f)'.*. -it; a + 11.8". 11.23 2 +0.4 -2. 4 +0.2 Greenwich :i:!. f 8 a l.'>. 9.-. 17.29 »> +0. 4 +3.2 — 1.3 Santiago . . !i7. r> a + 11.7 40. 11 2 +0.4 —a. 3 + 1.8 16 Pnlkowa . . 10. r.r. 3 17.60 59. 22 3 +o.<» +5. 3 +0.8 Leiden .... 1W.5I a - 10. 03 0. 72 2 +0.0 +3.2 +0. 5 17 \Vasliinp;tou . lo.lhJ 1 ia.o3 3. 3'J 1 +0.4 + 1.3 +0. 18 Wiliiamstown 'i.'ij)-i a + I-J.74 35. 35 2 + 1.0 —2. 5 + 1.2 Washington . \\->. 'i'i a la. 45 22. 18 2 + 1.0 +2. 5 — 1.2 19 Cape .... iVJ.Iil a + 11.55 10.44 2 --I.2 -2. 3 —1.4 Santiago . . . 13.0 a + 11.3 24. 83 n=2n< + L2A —a. 3jr' + 1.1 18 INVKSIKIATION OK TlIK DISTANCK OF IIIK HI'N nirii -iiMi.s. ■Si ~it . f^ K - 3 2 I>llt 1', Oli-ll\lll(il\V. .3 1 hi a ~ l'',c|iiatiiiiiN III' I'liiiditliin irivi'ii iilisi'i valiiiiii. liy till' s n i _/. ? i s V B* r *■ — c r 11 — ■z — ^_ _.^ '/j f"t; 1 '■ o.t. •jii Siipliiit;" •-'. 1 Vi -1- 11. :i III. 1- 0=".'i(, -i.Hr, —'■>. It.T' — 1.0 Wii^liili^'tnii ••'11. 1'.» >> — r»'. ys i:i. -;t *» -1. 1 +'.'. T) -{■0.0 '■i\ ('m|M' '.•:.:i'.' :i + ii!;f.' 111 1.(1.'. li — {.r* — n. .« --I.2 .j.» ^Vil^ulMl^ll'u II III. ."ill o + i-.'.:i:. .Ml. 1 111 *> 1. 1 — ','. .'> --2.2 ('lllll' IT.'.i'J :t + ll.'.':i .V.l.'.'l ll — I..-. -it.» +0.2 \\(lsllill).'lii|| I-.',.'.- •1 — I'J.ii'.i l.-l *> 1.0 +•-'. ■» +2.»i •j:i \\'illiMIII>lllWtl .'il.:i.-. •^ 4- 1 •.'.••.'.■. :i. 17 •* — d. 11 •.'. 1 -0. 11 ('(llll' .V.MU ;f + ll.i:i • i -.s fi — \.'i —It. II —0.8 Siiiiliii(.'(i . .Ml. -J >i + 11. (( i!-.'i — 0. s •) .J +0.0 Alliriiiy I-,'.:.-. 1 — V-i.'Xi 1. 1.'. 1 - (1.1 +1 Ti + 1.4 \V!i-liiiii;tip|i I','. (i!» 1 •- ll.l'K I.d.-. 1 — (1. 1 + 1.-.' + 1.0 'vM \\'illi;iMi>lii\\ n II..V. •J + l-.M.-. .Mi. Ill .. -(1.7 —•J. 1 — 0. H <'il|M' :;-. :i7 Ti + 11.111 111. -1 li — d. !l —It. It + 1.2 I.riilcll . ;!.•-". 1 *> - 1.-., 11 ■I-. '.17 >> — d. ti +ii.d + l. •i:!. '.K I -0. II —1. 1 +0. » \\ a.-liiii}.'lip|i ■il.iti 1 — 11. -s ■lit. .V,' 1 — 0. It + ".•-' +1.1 yri ('il|lC H. 7;t :i + Kl.'.t.'. r.>. -li li — d. (1 —It. It +d.4 Siiiiriiii;o .^7. !t 1 4- ic.'^ '.1. 7s 1 — (1. '.' -1. 1 + 1.1 '.'(■ Williiiinslnwii :l■■'.^l ;i + II.IM .■.l.-J7 li — d. 1 — li.d + 1.0 Lciiii'li . •l.'.. II.". o — 11. Kl :i(i. 0.". »i — d. 'i +lt.O -j-0. !• -i: Ciipr 17. f'.l ;! + 1(1.7.". •js. 7-J Ti 0.0 -II. •-' +0.2 Sniilia;;(i .^f . :, •» + K'.d Id. I'.i o 0.0 — •-'. 1 +2.2 Allmiiy •,'l.ti7 I -- I'.'.r.i '.1. .'.1 I 0. d + 1.11 +0.4 '.V ('ll|M' .">7. Ill ■,t + hu;.-. 7. Is II + O.Ii —It. '■> — 1.7 Alliiiiiy .">.■>. IMi .> — I-.'. Ill .i:i. If.' it +d.-J +■,'.-, +2. .-. \Vii~liiii(jliiii .'.:i. '.H .1 — 11. 11 .|:i. (k; .) +d.-,' +•,'. 11 + 1.0 ast Williiiiiisiiiwii .M. •,'.-. ft -f- ii.i;;t .".. Ill Il +d..^. —It. .'» —0.7 ( Jrciiiwicli :iH.iii .> - 11. -ji; •,':i. (Ki »> +d.'l +'.'.;• —0.2 SllMtilir^ci r.1.7 1 + 1(1.1 ■■!. •.'( 1 I + d.V.' — 1.0 +0.1 Wil^llillHtdll III. •.'■' 1 .- ii.:!;t (1. •,':! 1 +d.-i + 1.1 + 1.1! 30 \Villiaiiistiiwn l.:si 1! + 11.. -.:t 111. lid It +o.rt —It. .''. + 1.4 Cape t':i. •,'!• 1! + 1(1.17 lilt, s'.t It 4-0. 11 —It. 1 +0.7 Saiitiftgi) . .-.;t. >' 1 + 1(1. li •-'. 7li 1 + 0.li — 1.0 -1.4 AU'aii.v {•^. ii'.» 1 — I'^ll l.lllt 1 +o.ii + \.-2 + 1.7 Washinplciii 11. 1'.) «> - II. 'Jl d. 17 •J + 0.0 +'.'.'J + 1.0 :ii WilliillllSlOWIl .^is. 'j;» ;"i + ll.l'i Id. (IS I't +'M —It. i + 1.1 I'lilkciwa n.'j'.i 1! — 1.'.. .'id 'J(i. li'.l li + 1.--' + 1. r, + 1.« lli'lsiiijjliir.s :!7. ti.'. 1 — l.^C.l •Jl.-Jlt 1 + 0.1 + i.ti +2.2 CilJX' 1(1. 7s :t + 1(1. ;is •JI.7S li + l.--i —II. 1 + I.H Liiilcii . \>\K (i7 :i — 11.11 1(1. lid ;i + 1.'-' +4.2 +2.2 Saiiliajjd :!(>..'. 1 + 10. '.i •1(1. lit 1 +0.1 — 1.0 —0.2 \Vasliiiif,'toii . r. 1. IS »» — 11, oil ■Hi. 1»-' o +0. H +2. 2 + 1.1 Nov. 1 Williaiiistowu Xi. 'Jil ft + ii.:i-,' ■17. 1.-. it + 1.1 —II. 4 + 1.1> I'ulUiiwa . ' I-.'. '.Ml ;! — i.-..;ii .--.s. IS It + 1..^ +4.ti + 1.7 ('m|ic i 4:!.ii'j ;i + Id. ',".• Mi. dl It + i.r. —II. 1 — (l.l» Saiiliaijo :t.r, 1 + 10. -J lli.tl-J 1 +0..-. + 1.0 —0. 2 AUiany •,'v!. lid 1 — 11. SS 1V!.-J,-. 1 +0. .', + 1.2 + l.ri 2 lli'lsiiij;l'or.s '■i'jf-i .> - I.v,".t Id.s-i 2 + i.'J +11. 1 —l.S Capi' 'u. 1(1 11 + Id. •,'(! 7.71 'i + i.'.i —2. +0.8 Sniitiiigo i:i. 7 I + 10. 1 •_'l. •-'(■> 1 +0.(i — 1.0 +0. r. Wasliiiifrtmi . :!i.:i(; o — 10. s:, •i 1 . ( IS i> + i.'.i +2.2 +1.1 a Williainstiiwn 11. ii<) •> + 11.11 11.(1(1 >j + l.it o_ o -f-o. '.> ('a|if .".7.-j:i •J -j- l(». I'J ".. Ill* >> + 1.1 —2. —2.7 (iivcuwicli s. itC, T - in. 117 r.(!. •,';> l' +0.7 + 1.4 + 1.2 Saiiliapro i>. (t 1 + 10.0 IS. .1(1 1 +d.7 — 1.(1 —0. r. \Vasliiii;;ti)ii '2->. •>(•, 1 — ld.7:i l.">. (Mi 1 +0.7 + 1.1 +0. Ti 11 Helsiiifjt'ors (■>. :!•-' •j — I4.il(i 51.77 0— •.'n.^ + l.(i/i^ +H. Orr' -f-o. 8 AND TIIK KMIMKNTH WlllCll DKl'KNU UTON IT. ll» Tn'^itiiif? tlit'se t'(|iiiitioiiH \)\ the iiutli(Ml of lourtt si|Uaref<, wn linvt- fln' rulluwiii- iiuimal oqiiutiuiis; First scrii's. :ill '/|- ll.r),*,- .•li.l-:'+l8".5 = 0, - ll..V/|4.14.'->.S,j|+|ll.()r'-f 1 I .()«(>. SiH,'nlii| scricH, 308 'h+ V>.-2;ii+\:>21i:'+ »'"..'J=0, G.:^/j+ 41.I,J^- l!».".l-'- 1 .:i = 0. 122.7'/^— l!»!l,ir. + 71!».(l-' — 2') .;J = 0. Third scries. a.-n ":,+ 4.s,j;,+ (i7.9r'+ :t".!i = (), 4.8'/,+ :i:i.(i,J:,— 12.1-'— 7 .1=0, (17.!>«:,- l2.'l,V:, + .'';(;7.lr:'+|;i .0 = 0. FiiiirtI I scrii'i 192 '/,— 2;{.s,j,+ ^■,:>^-' + ^[".\ = ^), - 2;{.N,/,+ 217,?,,- no-'- !t .7 = 0, (J2.1'/,- 11.0,J,+ |--'7,!lr' + ;i8 .4 = 0. Filth srrics. 264 «,',+ 23.5,5r,— s;J.2r' + 7/)".l=0, 23.5«s+ 45.4,Jr,+ 20.4-'+ 7 ..5 = 0, — 83.2'/s+ 2(J.4,5,+:{7^s.2-' + ;iS .0 = 0. The scpiinito Holution of oach worios of oquntioiis ^i:;ivos tiif folio win;.,' results: First seriofl - - Second series - Third series Fourth aeries - Fifth series - - «, = — 0.167; «.^=— 0.020; the scpii- rate Hums of residuals and multipliers for each series of e(iuatioiis, with tho tiual rueau residual : Willimnstowii. Piilkuwii, lli'lsiiii;t"is. First series . . . + !!.(» •J.-) — •-'. '.t 2(1 - II. 1 1 Second st>rips + '■i. ti 2:! — K :t 2H +(l.l» t'> Third serii's . . + •^••l -2'> — :>.', 1« +(i.:t 1 Eourtli series . + -i.:, It) — (1.5 "'■J —1.:! 4 Fifth series . + -'. 1 •,»:i + 1.1 (} —(!.>' .'■. Sum .... +1 .-..•.> li> — l(i. 1 111 — I.ll -,':! \ Cape + 2..^. + r,.,-, + (1.4 — :!.4 — 7.() 11 :i4 Leiden. First series . Second series . Third series . . . Fourtli series . Fifth series . Sum .... + :?. 4 7 — (1. 1 2:i — ().;t 14 + i.:i Ki — - 2. 1 7 — -i. <■) 114 + (i.4 ()7 Greeuwu h — ;{. 1 () +(!.(> -fll. 1^ — 1.;» 4 o •> —(1. 1 :! Santiaf fO. 2:! 11 11 14 i All>iiiiy. „ -11.4 - 4.9 -f-2.8 + 2.1 — X 4 1 + ^. 1 12 4- H.'.t 4 -i 4.7 :j • 4- 2.9 ;» -j- .'>.(■) () -14. H (is +2."). 2 28 ■ - 1 Wiishington. +•-»■ •) 14 — ('. H i:t —II ,'» 11 +<» 2 7 4-'' 1(> 4-. 4 ±0. 07 ±:j.o - 3.7 ±0. 18 ±5.7 -14.8 ±0. 08 ±4.3 +25. 2 ±0.15 ±4.9 + t;.i ±0. 08 Actual mean. +0. 14 —0. 17 —0. 04 —0. (12 +0. 10 —0. 22 —0. 22 +0. 90 +0. 10 It will be seen that the actual exceeds the probable residual in seven cases out of the nine, 80 that the probability in favor of systematic dinerences is very great. In the case of Albany the evidence in favor of extraordinary systematic difference is indisputable, the observed polar differences being nine-teutha of a secuud less than those of the other northern Oli.sorvatorioa 22 INVKSTKiATION OF TIIK DLSTANCK OF TllK SUN tlirou^''li(iiit tlif ("iitirt" xM-ii's. 'I"lii>- jiicat iliscr('|iaiic_v >;'ivfs rise to tlie (|iierition wlu'ther the oliscrvatiiiiis fxliiliitini;- tlicm nii;;ht imt to In- cdiisiiliM-ed iis aiViH-toil witli some ahiioriiial source of error, and rcjei'tcil I'lilirely; or, in oIIilt words, \vlu'tli(!r tliat standard to wliicli the tlireo Hoiithcrn Ohscrvatories is coniiiarahle, is more likely to be the mean of all the northern Obser- vatories, ineludiii;; Alliany. or only the mean of those five which ajj,-ree widl between them- selves. RejeetinL;- Albany alto^'ether, tlu; final e(|nation in -' would be, a|i|iro.\iniately, •io74-' = -f)7". The resultin,!j,- [w.-iilax would, tiierelore, be ^' .8G(J, the Albany observa tioifs entt'ring into the final n-snlt for paridlax with a wcij^ht of oidy one-fiftieth that of all the others. I think we ina\ consider them eiilithd to this weight notwithstanding- their discordance, and shall, there* fore, considci' tfic jiarallax already deduced the most probable result of the meridian ol)servations. OwiiiL;-, however to tlu' evidence of constant errors, the |)r()bable error of the result must be increased to 0".<)"J(l, .uiviim', as the parallax from meridian observations of Mars, made in 18G2, accordinj;' to Winnec!l(ir Ptn-allti.r from Ohf*'" ('S-i!] + r-: i^iii (X-|--V)+ I'tc. The powers of «52 are to he developed in like manner. In developing the square of mh, 1 lind no ffruis which will sensilily alTcct the parallactic inequality. The latter will therefore depend altou'etlier in tin; f)llowin^' terms in Hansen's u(h: — ll".692 8in (—§•' + ('» — f/)') producin;,'' the cncflicicut ((".till, — 12l".;iG8siii (ir— i'-' + f..- — (//) " " 12]".;J(;s, — V'.6Uii\n(2g — <;'+o, — ,„') ()".0S!). The total value of the theoretical coellicients is therefore 12'2".09*^, whicli, heinj; midtipliecl bv l.();}57;i gives 126". IG for the actual value of the parallactic inequality dediieeil by Ifansen from the observati ms of Greenwich and Dorjiat, ami adopted in his tables. The Monthly Notices of the Royal Astrononiieal Society for May, 18(!7, contain a short abstract of a paper by Mr. Stone, in whicii he deduces from •2,07.') Cireenwich observations the value I2.5".;{r). This resnlt I shall accept as the definitive restdt nf the Circenwicli observations. The Wasliinfi'ton observations of the Moon, troin 1H(I2 to 18(1.'), inclusive, an' re;,Mdarly compared with Hansen's tables. I have discussed those maile within two days of tlie time of maximum and minimum parallactic inequality, on the supposition that thi; ellect of errois in the other inequalities will destroy each other in the course of the four ye.irs. Thus, the following corrections to Hansen's parallactic inequality are ol)taiiied for the s(!V(;ral years: 18G2, ISGIJ, 1SG4, 18G.>, •) ■> . — •■-' ) ') •> . -2.0 ; -2.0. These results are still subject to correction for adojtted senn'-iliai.ieter of ^[oon. Seven transits of both limbs of the nearly full Moon were observed during tin; above period. The it.ean cor- rection to Hansen's s(?rai-diameter was zero. If. then, we suppose this same semi-diameter applicable to the Moon at her first and last (juartcrs, the coeflicient of parallactic ine(piality will be 126".46— 2".]0=12l".;{6. But the same semi-diameter will not be applicable, because! one-lialf the oliservations for parallactic ine(iuality are made while the Sun is above the horizon, and a considerable fraction of the remaining half are made (hiring twilight, while thos(> on which the semi-diameter depends are made at midnight, when the brilliancy of the Moon is such as to excite the eye to a dis- agreeable extent. Prom the experiments of Dr. Robinson,* and the researches of Mr. IJreen,t and other data, it .seems that the eflect of this brilliancy is to in(M-ease the afqiarent semi- diameter of the Moon by about 2". About one-half of the observations being thus aOected^ the correction to the parallactic inequality from this cause ought to be about -|-l".(). ' Memoirs Royal Astronomical Society, vol. v. tGreeuwidi ObHerv»tions IVir IstM, Aj)poiidix. 24 INVESTIGATION OF THE DISTANCE OF THE SUN To obtain an iiidcpi'iiilt'iit (Ictcrniiiiiitioii of this (•(irr"ftioii, 1 liavo niado a f:;oiieral com- l)arison of tlio apiiariMit errors ol Hansen's lables in rii^^iit as(;(3nsion, wlien tiio ol)servati()n8 wore tnado durinj^ daylijilit witli the eorrespondin;^ errors when tiioy wero made at nij^ht. The selected ni^lit honrs were, on the averaj^e. a very litth; nearer to midnight than the day hours were to noon. Th(! results were; lor tlie apparent errors of the tables in right ascension: .V Hefore sinit«'t — O.lfj'l Alter l)ri>;lit (layliglit in the evening — 0.0f)3 iJcforc liriglit (layliglil in the morning -f 0.091 Alter sunri.-i>t >Ie la Lii'ie, tome II, p. 847. Mr. Delaunay was good enough to communicate the formulsR lor F ill aJvuncf of tho volume. i AND I'HK KLKMKNTS WHICH DEPKNU ll'ON IT. 25 WImt. ,T;=: ciiiislaiit ot -iA..v piirail.ix. //—^iiiiiss III' llif .Mimii. Adiiptcil \iiliir, ^^' .. /'::;= fuiistant nl' liiliiii- |iaialla\. = .'! I 'J'J". i. //'=: ratio III iin'aii iiMlinii~ nl Sim ami Mimii. /''. a lat'tiir wlmsr vahu , a rn nil in;;- In i>i'lailiia\ ' ^ tlicnrv. is rii|-iiii''l as Inllnws: 'I'crins iiiililililird 1)V />/ O.l.SMJ.i in' ■ - .()(;")(){> " m' A):i2t\:^ ///'--- .OOSS") m'' .(i(i;;^-j in" - - .0(11. !(; ///■ .(KKKil IligliiT trniis, ; iiy iiidiu'tiini 1 .()()0:J!t 'I'otal valiif iif F .-ill-.':; VVliciico, snlar parallax I'mm paiallactic iiiri|iiality of tlic .Mnnn =. S".S38 L 0",()rj.>. As a test of tlio tlieory, this nvsull, may liu rnmparcil with that of Hansen, in tlie Monthly Notices, vol. 24. From a value of the Moon's mass -J~, and the parallaetie ineipiality of his tables, (12«".4G,) ho finds for the solar 8".'J16. Alterintr the result to corres|)ond to the data of the prcsont paper, it will be S".Si4. agreeing" satisfactorily with the theory of Delannay. S 8. Solar Poralldx from t/ic Ohstrvcd Linuir lujnoflon nf lltr A'arf/i coinhincil with the Mdsft of thr Moon. — In constructinp; his tables of the Sim, L'' Verrier inv(;stigated the lunar inequality of the earth from 35 years of Greenwich, 42 of P' , i.s, and 17 of Konigsbery observations, with the result* G''.50, and a probable error of aboiit 0".03. To complete tlie investigation, 1 have added the results of 14 years of Greenwich and T) years of Washington observations. The results for the separate years are as follows; GrcenivU'h OhsirrnlionN. n II ti II iMol. (Jiir. = + 0.;J.'{; iiii'(|, =(i.87. IS.JS. Cur. = + 0.01 ; iiicip =(;.l-"i. \H[)2. — o.i;_j; G.ii. isr.n. +0.21 ; g.().'). is/;;!. 4-0 -^.'i; 0.79. lS(iO, +0.1(i; (J.(JO. l^io4. —0.11; (i.:r,i. isiij. -o.:jo; <;.io. is.jo. +0.0;{; G.47. JSO-;;. +0.i!2; 6.70. 18,5(i. -|-0.;J!>; G.8:j. j ISG-i. +'».ll; G.tio. 1857. -O.IO: <;.;J1. 1S61. -0.0:>; (i.lH. Resulting value of the lunar inecpudity, 6".56±0".04. ' Animli's cl<> rOliscrviitiiin' Iiii|iiiiiil ili- I'liris, Miiiiijiri-s, tome i\, p. Kill. 4 ■_*() IMVKSIKJAI lO\ OF TlIK 1 US lANCK OK Till; Sl'N // iislii mititit Oliy( vrnfiiiHS, // It n It JsCI-'-j. (',,!■. ——(1.0 I ; iu,'(|. =:(i.:!7. |S(il. ("i.r =— 0.01 ; ini'i|. =f).10. ISC,;;. 4-0..'",: (i.(;s. isi;,-,. +n.lS; g..')0. Ki'i-nltiuu' viiliic nl' ihc lMii;ir iinMiualit}", iV'.ra I o".o;. Il w ill lir seen \\\,\[ till' I'dlldU iiin' Viiliics <)l' tlic taln.Lr cocllicicnt have Ix'cii used in ulitain- iiiii' llic in('i|iialily fniiii ihr (•(iircctidii given liy tin' (iliscrvations; // ( Jim (iiwifli, I *>.)l-lsr):) - (5 ;j I |s,vl-lS(;o (i.ll iMil-lfSO:! (J..') I isoi (;..')0 AVa.^iliiii;.'!!!!! (i..)! Il i- ncci'.-'^ary fo explain Imw tlu'.-.-irveil positions 1)1' the Snn, l>y a e()ni])aris()n nl' the "Apfiai-enf Erroi's " within three days of tin' nia.xinia and niiniinti values ol' lunar ineipiality. The next sto|) is to find the valiu? of the ineipiality actually contained in tlie eplienieris. The latter is, until lS(j.'>, that dedu(;ed tVniii Carlini's Tallies and pnldished each year in the IJritish Xaiitical Almanac. Hv induction from Cai'lini's Talde V, it appeared that his value ol' tlu' ineipiality was O"..")!. Afterward, 1 ioiind that in a |ireceiling vohune of the " KiVemerides "' lie had deduced the value ()".').'{7 Irom theory, and probaldv the table was constructed from this value. If, ttii'ii, the ephomeris ('orres|u)nded exactly with the tables, this would be the value to which the corrections correspond. l>iit on jingc V of oa(di voluini^ of tlio Nautical Almanac from 1854 fo ISOO. inclusive, it is slated that "The Longiliide and Radius-Vector have been computed accurately from the Tables lor the .Moan Noon ol e\ery (Jth day of the year, and iiitiM'polated with 'oiii-lh dill'erences for each day." Now, since the lunar inequality goes through its period in a month, its successivo orders of dill'erences for eat'li sixth day will bo divergent, and interpolation with fourth dilTer- eiiccs will result in the interpolated iiie(iuidity lieing generally too small numerically. To find how much too small. a<'tual trial was resorted to. A number of six-day series of values of tiio ine(|uality was taken from Carlini's 'I'able V, interpolated to days near the maxima and minima, and compared with the corresponding tabulai' values. Th(> result showed that the interpolated values were, on the average, numerically too siuall by 0". 10."). .^iiico one-sixth of tho values would be accurate, the actual tliminutioii of Carlini's iiiei|Uality would be (>".6n7, reducing it to O".!'). From 1S5S forward, the Sun's positions given in the American K|)h(>meris art; deduced from Hansen's 'I'ables, in which the value of the lunar inequality is S ". 1 1 . Comparing thes(! positions with the corresponding ones of the N:ioti'. -ftLOn^: ; •>■■' +(1.(1.1: -f 0.01 : Mean, -f 0.02 : giving, for the v.due of the inequality actually cnntained in the N.iutical .Almanac Eplietneris. (•".4.'{. The mean of this and tiie former result is 6". 44, which was considered the must prob- able value of the quantity in question. AND TIIK Kl.KMKMS WHICH Dl'.l'I'.Nlt ri'ON 11'. 27 Witlinut the limits ol' tlic scwcii yciirs, 18r)4-'GO, tlic (•'iiiipiihitions i\\' tlu^ N'aiilic;il AIiiciiiik; iiro prohiiltly ut sulllcicntly short iiit(>rs-;ils fo avulil |iic n-nir of intcf|) 'lilion. For ISIM, licVorritM-'s Sohir TaliK's wrrc ailoptiMl, (li(> value of i he lunar t'i|iiatioii in wliifli is ()".;")(). We liavo, tluMi, tlio foljowin;: tlirco valiuvs of tlic (|iiiutity soii^li' for, (IciIiu'imI from obsi'rviitions: Knim (in'finvicli, I'iiris.aiid lvc>iiii;^lii'r..'» I I (\M', {\.'>2l) \ ovs.;. Altli(Mi;j,li flie aocidiJiitiil errors of tin; oliservutioiis on wliicli \\\'\< rcsnlt ilt'iicnds arc (piito liif^o, the observations have this invaluable (^liararteristie, that tlh-y secin to b ; |)erfi'ctlv i'ree from any eiiiise of systematic eri'or. Amoni;' all the <'onstant sources of (>rror to which ob- Kcrviitioiis of the Sun ;irc liable, I can think of noni! whicii can systematically chanats with the first and hist (juarters of the Moon. If there are none, the precision of the determination of the lunar equation will go on increasing indelinitely with the number of observations. The next stt'p is to determine the mass of tiio Moon. The most precise determination is obtained by a comparison of the const, mts of precession and nutation, which i;-ives the ratio of "* the disturbiiif^ forces of the Sun and Moon in chan<;iiig tin; dirct'tion of the earth's axis of rotation. The value of this ratio will Ite (le(luced fn/ui tl\e t'xhaustivc memoir of Serret*, afttu- reconstructing his expression for SJ so as to include tin; terms of tin; tiiird order with respect to the inclination and eccentricity of the Moon's orliit, which he has neglected. This is etfected by substituting the (Expression I 1 + i!'-"^ I sill f cos )■ for c in his value of .V. Let ns i)ut //zrmass of the Moon, that of the Earth being unity. ^)=sine of its parallax, in seconds. M = inass of the Siui. e = ratio of disturbing forces of Sun and .\b)on. / = disturbing force of the Sun. f< = luni-solar [)r!£. Peters' a concluded value of the constant of nutation is N=9".223. 'Animlt's lit' roh.sciviitoire Impcriul ili' I'.'iris, vol. \, |). :!'.i;i 2H INVKSl'ICATION OK PUK niSIANTK (»l" IIIK SI'N TIk! Viilun nf llir liiiii ■>' ill r nirf('--i(p|i ilrrivcil IV.iiii Sinnc's -(Mh-imI |)ri"'rssii)ii, uilli tlir iiiii>-i III' VuiiiiM coiK-liKlcd liy lii'N'cnicr, IVniii his iiivr-i i-atiiHis cil' llio molinii of thai phiiiut, is (I = :,!)". -.i'lS. Snlistiliitiiij;' these vahies dI' ii ami N in tho alinve ei|iiatii>iis. \vu liml Id;,' >r;=l..r(Nl.S, In;; / =l.-j:{SOS. 1.1^' ; =:n.:);!'.i-i(i. I N|.()f> DeveliipiiiL:' the hui^'itiide and paralhix of tlir .Mumi sd as lo inehide ihe varial ion, and (lie e()iTes|Miiidint:' term in the parallax, we lind l'=l.()(IN() 1+/'/' .;.;i.i|.,-_. t»r. T= .oKiKH r (-')■ SiiusI ilnlini;' the \-aliie nl !', already I'.amd iroin nliservatmn, we have rr = S".S()9. Till! must uiirertaiii data whieli enter intn this re-:ult are the ennstaiit of nutation, with the I'e.-ultin^" mass nt' ihd Moon, and the lunar eipiation nT i!io earth. 'I'he. [)rol)al)le error of tlie nutation eiiiislant is perhaps -v',- of its whole ainniint, which would involve an error of --';-- in tho resultiuL;' mass of the Moon a?id solar parallax, or. of U".OH: in the latter. The unc(;rtaiiit y of the other faetor involves a prohalde error of 0".0,!1, so that the total jiroliahh' error of tho result is ((".OiU. TraiisU of Whuh In 17(!!t. — The results of Powalky's discussion* will be accepted. He linds -= 8". S32±0".0'2!. l>ut eonsidorin^- that the longitude of the ohsorvinj;- station at San Jose is uncertain, he arbitrarily chanji-es it by lOv.. which increases the [larallax to 8".S(i, which he considers the most probidile value. That so >mall a change in the longitude of a single station should change the parallax so largely, shows that the piobable error 0".021 iiiust be illusory. I think 0".()-l a more likely value of this element. i^ 10. C<>i)cbi^\\:i - - 8.N,0r)rl: .020; \vf. =:2,5. FroDi miinwiifric ofisrrraf ions of Mar.i, 18(j2 - 8.812:h .040; G Fro)n jiiirdlUiiiic invqindili/ iii a cniisidriai imi <>{' all tho results, it is (•(HicIikKmI tliat in tin' prcsi'iit >lali' ol astroiiomiiMJ sciiMioi' tln' niosi priiliabji- Viilu(5 of till) menu t;(|iiatiirial hori/.oiil.it paralliix ol' tlio Sun is W'.HIW, witii a prohalilu error of |-()"(il;i, forrospoiuliiin' to a mdaii (listaii(M> oi' '.) hiLvinj; e(pi;il \vei--|it with tlii> aliove imiicIiiiIimI value. § 11. Conclusions irspicHiu/ the (Ulfcniil Kl; 7. j=a.i74. N=<)".:.MO I 0"011, a value of the constant of nutation rather more probable, and more easily obtained than any derived from direct observation. The advanta^•e of the theoretical mode of deriviiiL; this con- stant arises from the fact that an error in the adopted mass of the Moon produces an error of less than one-third its proportignate amount in the resulting constant of nutation. The theory does not apj)ear to be subject to any objection arising from our ignorance of the physical constitution of the iuterit)r of the Marth. From the data of §G, Delaunay's thecu-y gives i'or the parallactic ineijuality of the Moon 12r>".(j;{4:0".19. Taking the constant of aberration as 20". 445 1, we have for the velocity of light 18.5,600 mile.'* per Hecoiul. This is slightly greater than the result of Foucault's experiments with the revolving mirror. Adopting that determination, the constant of aberration would ite increased about 0".03. But tho distance of tho Sun and the terrestrial determination of the velocity of light are both uncertain to an amount greater than this increase, which is therefore altogether unre- liable. The constant of aberration must be found by direct observation. lA y? ■J*- ^v- — • -iv ii iTj^ -.. ^ ^ s