An Extract of Mr. Flamsteads Letter of April. 19. 1673. Containing Some More Accurate Observations of His Own, about Jupiter's Transets Near Some Fixed Stars; Useful for Determining the Inclination of That Planet to the Ecliptique

An Extract of Mr. Flamsteeds Letter of April, 19. 1673, containing some more accurate Observations of his own, about Jupiter's Transits near some Fixed Stars; useful for determining the Inclination of that Planet to the Ecliptique. SIR, The inclosed Paper contains some Observations of Jupiter, which being made from a more convenient Station, than I commonly have used, are more accurate than my former ones: And, the Planet being in a fit place of his Orbit, they are the most useful for determining his Inclination to the Ecliptique, that we can again expect this six years, or perhaps before he returns again to this place. Had the Latitudes of the Fix't Stars of Tycho's constitution been exact and coherent, we should easily have determined the precise quantity of this Inclination and those regular Inequalities we find in this and in all the other Planets, which are found irrepresentable by numbers, only by reason of some latent errors in the Places and Latitudes of the Fixed. It would be a task deserving the pains and accuracy of the Learned Cassini, and of all others that have good Observatories and Instruments, to endeavour the Restoring of the Fix't Stars, especially of those that are near the Ecliptique. Had I only a convenient place for observing, a ready Assistant, and other necessary accommodations, I should not doubt in a few nights to rectify many of Tycho's errors; and to add some Stars to his Catalogue, as well visible to the bare eye, (yet omitted,) as Telescopical ones. I have made lately some Observations of the utmost Elongations of the three Inmost Satellites; which I find greater than Signor Cassini states them, but almost the very same with Mr. Townley's. But I have just cause to suspect some Excentricity in the third; for I find (except I mistook in my measures, which, I think, I could not possibly do,) its Elongation greater on the one hand of Jupiter than on the other. I intend, at another opportunity, to make more Tryals as carefully as I can, either to confirm or destroy this observation. Ob- Observationes ipsæ Joh. Flamstedii. Quam tibi Jovis, prope Fixas transeuntis, observationes jam antea Clarissime Oldenburghi, impertit, ejus in Tabulis motus fieri tardiores quam in coelo, (quod & Horroccio pridem suboluerat,) evidentissime ostenderint: Latitudines etiam observate, minores semper supputatis, vel satis non promotum Nodi locum, vel justo latiorum Planis orbite Jovis inclinationem constitutam, videbantur innuere. Nodus, numeris Rudolphinis promotorem coeli us positi, à suis se observationibus reperire scribit Clar. Cassinus: Orbitæ minorem esse aliquantulum inclinationem ad Eclipsicam, quam statuit Keplerus (si Fixarum latitudinibus, in catalogo Tychonica exaratis, fidendum est;) ab observationibus infrà descriptis ostendam. Anno instanti 1673. Martii 13. st. Jul. vesperi, Jupiter Aphelius, pronus ad phasim Acronicam, & limitem orbite Boreum paululum transgressus, Retrogradatus incessit versus 9° in mx lucis 4°, è qua (alto eo sex circiter gradus) limbi ejus remotissimi distantiam, septempedali tubo & microscopio Towleianó cepi 45° = 52° - 34°. Martii 17 die D°, circa hora dimidia post exortum Jovis, ejus, eodem tubo, limbi remotissimi à Fixa cepi iterum distantiam 20° = 23° - 54°. Martii 20. die V°, è loco multùm commodiori, sequentes habui observationes. Primam breviori tubo, digitorum tantum 85, reliquas longiori, videlicet. 164. fig. V. Fig. 2. | Fix. alt | hor. sup | Limbi ph. | Centri | |----------|----------|-----------|--------| | 0° | | | | | 1° | | | | | 2° | | | | | 3° | | | | | 4° | | | | | 5° | | | | | 6° | | | | | 7° | | | | | 8° | | | | Inde ad diem 26. nubes & pluvia, continua fere, Jovis omnem observationem prohibuere; huic tamen vesperi, caelo prater spem facto sereno, alto 2°. 15° - 40°, limbi sui remotioris à Fixa distantiam, eodem minori tubo, dimensus sum 42° = 48°. 30°. Notio etiam proxima sequente, Jovem à Fixa plus remotum vidit; sed accuratae metiri distantiam, nubium, coeli locum subterrensum, spissities haud permisit; Ad Ad Planetarum locum ex his annotationibus eliciendum, structis supputationibus, invenio | hor. | 8 | 16 | hora | 8 | 50 | |------|---|----|------|---|----| | Angulum parallacticum | 34° 44' | 37° 30' | | Centrum 4° à Fixa distitit | 9° 28' | 9° 39' | | Altitudinum differentia erat | 4° 17' | 4° 36' | | Ergo, Angulus erat positionis | 80° 06' | 78° 21' | | Et Jupiter in antecedentia Fixa | 1° 38' | 1° 55' | | cum latitudine minori | 9° 19' | 9° 18' | Fixa mihi locus, accepto motu anno 50", erit ≈ 13° 37' 11"; quem vult author Carolinus 13° 33' 47" latitudine ejus Borea 10° 45' Locos ergo versus Jovis erit mihi, | h. | 8 | 16 | 13 | 35 | 33 | |----|---|----|----|----|----| | Latitudo vera | {1° 35' 40½" | 1° 35' 42" | Jovis tunc locus in Ephemeride Heckeri est ≈ 13° 22', justo minor, jam 14' min. Motus retrogradus est 8' min. Propereea scrupulis hora 34' recessit Planetae scrupulos secundos 11" fere; nostra observatio dat 17"; qua exigua differentia ejus praecisionem admodum commendat. At Fixae concessio loco Carolino, prodibit 4° locus ≈ 13° 32' 09". qui ab istis Tabulis eruatur 13° 27' 32", à caelis suis deficiens 4° 37" latitudo ab iis supposita reperietur 1° 37' 21", caelos exsuperans 1° 4'". Loco sic Planetarum latitudine, & Tabularum à caelis deviationibus perceptis, nec commodissima observationis ulteriorem summumque fructum perdamus, Orbitae jovialis ad Terrestres orbitae Planum inclinationem indecernere conabimus. Huic equidem inveniende, una cum loco Solis, ejusdem, Jovis, & Terrae intermutua distantia postulantur: quas à Tabulis quibusvis probatoribus tutissime bariere licet: Ego Tabulis utor plerumque Carolinis, quippe quas, usus nonnumquam deviantes, coelorum motibus propius annuentes, accuratiiores, & faciliores catervis omnibus comperii, ex quibus ad 8 h. - 16 p.m. deponendi; Solis locum verum | V 10° 40' 18" | |-----------------|----------------| | distantiam à Terra | 100084 | | Jovis à Sole distantiam | 544921 | | à Terra | 444952 | Fam in appositâ figura 3. sint, S Sol, T Terra, Π Planeta, SE Radius Eclipticae, ad Π orbitam proferens, & angulus Π TS, visa Planeta à Terra Latitudo 1° 35' 40½". Ex datis (in triangulo Π ST) angulo, Π TS, visa latitudinis ad Circulum complemente 3 Π S, Φ Π T, Planeta à Sole & Terra distantias, ut supra, repertis, eruetur angulus Π SE, latitudo sive Inclinatio Planeta à Sole conspecta, I° 18' 7". Jovis. Jovis locus Geo-centricus erat \( \approx 13^\circ 35'33'' \); ab iis ergò datis \( \varphi \) Terra à Sole distantias, inveniatur locus Helio-centricus planetæ \( \approx 13^\circ 03'33'' \), è quo subdatis figillati iis nodi locis, quos autores, quorum nomina in segmenti tabella exaravimus, assumferunt, annexa produnt argumenta Latitudinis; è quibus videre est, nullis plus foveam à limite promortum haberi quam \( 6^\circ 29'56'' \), nec minus quam \( 3^\circ 58'59'' \), qua quantavis videatur differentia, in maxima orbita inclinatione investiganda, errorem scrupulis secundis \( 23'' \) majorem inferre nequit. Iste nodi locus, quem Clarissimus Cassinus elegit, mihi etiam aliquantulum justo promotor videtur, magis tamen catenis variis de causis, placet: sumptis propterera, in Triangulo \( \varphi A \delta \), argumento latitudinis \( \varphi A 94^\circ 18'33'' \), & inclinatione \( \varphi A 1^\circ 18'07'' \), erretur Angulus inclinationis plani orbitæ Jovialis ad Eclipticam \( 1^\circ 18'20'' \); quem statuunt Keplerus \( 1^\circ 19'00'' \), Streetius \( 1^\circ 20'00'' \). Bullialdus & Wingius \( 1^\circ 21'48'' \); omnes, justo nonnull majorem. V. § 4. Tantamque esse inclinationem, vel saltem non majorem, cum hefterna noctis, tum Mensum Februarii, Martii & Maii Anni elapsi observationes suadent. Interea vero non disfumandum, posse & majorem (scilicet \( 1^\circ 20'20'' \)) à transitu \( \varphi \) prope \( 8^\text{th} \) \( \text{m} \), Anno 1649. Maii 29 & 30, St. Juliano, Bononiae & Majorcae à Ricciolo * & *vid.Almag.Novum Muto, viris dotissimis, observato, demonstrari: id part. I. pag. 710. quod nobis (si quidem orbitarum inclinationes ab omnibus invariabiles habentur,) videtur innuere, errorem vel huic, vel illis Fixarum latitudinibus à Tychone assignatis, inesse aliquem: qua propterera donec accuratius restituantur, à praecisa hujus inclinationis quantitate determinanda merito nos arcet: Hoc tanquam, quoniam fixarum ea latitudines etiam immutables reperiuntur, ausim affirmare; Angulum maximæ inclinationis plani orbitæ Jovialis ad Eclipticam minorem esse scrupulis \( 26'40'' \) quam latitudo stellæ \( 9^\text{th} \) lucis \( 4^\text{th} \), qua Tychoni dicitur, ultima quatuor in sinistra ala Virginis: qua propterera si quando corretta dabitur, eadem certa dabitur inclinatione. J.F. Derbix, Apr. 16. 1673.