A Letter from Mr. Flamsteed concerning the Ecclipses of Saturns Satellit's for the Year Following. 1684 with a Catalogue of Them, And informations concerning Its Use

A Letter from Mr. Flamsteed concerning the Eclipses of Saturns Satellites for the year following 1684 with a Catalogue of them, and informations concerning its use. SIR, The rules of the following Catalogue of all the Eclipses of Jupiters Satellites in the following year extending much further than that of a few only visible with us, which you were pleased to think worthy a place in the September Transactions; I find myself necessitated to give you a larger account both of it, and its Original; which I hope will be as kindly entertain'd by you as that was. It has been my custome for some years past to make myself quarterly a small Ephemeris of the Eclipses of Jupiters Satellites visible with us, that so none of them might escape me unobserved when the weather permitted; having by this means obtained a good stock of observations of them of my own, besides what I had collected from the Works of Galileo, Hodierna, Borelli, the papers of Mr. Rooke late professor of Geometry at Gresham College, (happily preserved and kindly imparted to me by his once intimate freind, and one of my honoured Patrons, the Right Reverend Seth Lord Bishop of Sarum,) and the communications of my honour'd freinds and correspondents Monsieur Cassini, and Mr. Towneley. I found myself well furnished, as I thought, for the restitution of their motions, which as I have formerly told you I attempted last Summer, and accomplished with such success; that having seen only 2 of the predicted Eclipses of the first Satellite, I find neither of them differ above 2 Minutes from my calculations. I have also observed one of the third, not above 3 Minutes faulty, and another of the second erring but two; which makes me hope the inequality I suspected in this last, will not be found so large as I feared it might be: after I had finished the Tables of their Mean Motions, I let myself to Calculate others for finding the true times of their return to the Heliocentrical Conjunction of \( \theta \) in all places of his Orbits, with some other which I foresaw would be requisite for the easy Calculation of their Eclipses: having this in readiness, and being encouraged with the aforesaid good success, of my endeavours, I resolved to Calculate all the Eclipses of the following year 1684. and to impart them to the publick, if you consented, in the Tracts; they being much desired both at home and abroad, that so not only our freinds here, who have a respect for Novelties of this sort, but such foreigners also as are Studious of Astronomy and Geography, or those of our own people who Travail into remote Countries, and shall be accommodated with instruments for this purpose, may have the opportunity of foreknowing such appearances, as, if observed, will certainly shew the difference of Meridians betwixt them and us. And I must confess it is some part of my design, to make our more knowing Seamen ashamed of that refuge of Ignorance, their Idle and Impudent assertion that the longitude is not to be found, by offering them an expedient that will assuredly afford it, if their Ignorance, Sloth, Covetousness, or Ill-nature, forbid them not to make use of what is proposed. Those of them that pretend to a greater talent of Skill then others, will acknowledge that it might be attained by Observations of the Moon if we had Tables that would answer her Motions exactly; but after 2000 years experience (for we have some Observations of Eclipses much ancienter) we find the best Tables extant erring sometimes 12 Minutes or more in her apparent place, which would cause a fault of a half an hour, or \( 7\frac{1}{2} \) degrees in the longitude deduced by comparing her place in the heavens with that given by the Tables: I undervalue not this Method, for I have made it my businets, and have succeeded in it, to get a large stock of good Lunar Obser- Observations in order to the correction of her Theory, and as a ground work for better Tables; but the examination will be a work of a long time, and if we should happily afterwards attain what we seek, yet the Calculation will be so perplexed and tedious, that it will be found much more inconvenient and difficult than that I propose by observing the Eclipses of Jupiter's Satellites which however at present I must prefer. For I am persuaded, that the Eclipses of the first will scarcely be found above 4 Minutes of time different from my Calculation in the Catalogue, nor those of the third above twice as much; Now an error of 4 Minutes cannot cause a fault of more than one degree in the Longitude collected by comparing an observed Ingress of the first Satellite into its shadow or emersion from it, with the time given in the Catalogue; and I hope it will scarce ever be found to err so much. But if the same Eclipse may be observed in two distant places at the same time, or compared with an observation of the same Satellite made within a Week elsewhere, the difference of Meridians will be had something better than by comparing two observations of the same phase of a Lunar Eclipse, made in distant places. For whereas it is somewhat difficult by reason of the Penumbra to determine the true time of the application of either of the Moon's limbs to the shadow, the Satellites' Eclipses, especially those of the first, are almost momentary. And whereas there can rarely happen 4 Eclipses of the Moon visible the same year, those of the Satellites happen so frequently, that there are more of them visible in one year than we count days in it, tho the Planet 72 lie hid under the Sun's rays every year a whole month together. I know our Navigators will object against this Method, that it is difficult to practice at Sea, because long Telescopes are required which the Motion of the Ship will not permit them to manage aboard, that it is hard to stinguish one Satellit from another, and that Tables or other contrivances for shewing their Mutual positions are here wanting; to which I answer. That if it be not practicable at Sea they cannot deny but it is at land; That the true longitude of remote Coasts from us are the first thing desired for the correction of their Charts; let them attempt these first, and I doubt not but the success will encourage them so much, that they will readily find means to put it in practice at Sea. That the French have used this method successfully both in Denmark and their own Country; That a Telescope of 14 foot long at most, or for need one 8 foot, with broad eye glasses, will be sufficient for this purpose; that the difficulty cannot be known till it be tried, and that use renders many things easy which our first thoughts concealed unpracticable. That the Satellites may be distinguished by their Magnitudes, the third from 7/ being the biggest, the first something less, the second yet less than the first, and the fourth or outermost the smallest. And to their last objection, that if I find this method heeded by them, I shall take care to publish easy Tables for finding their Configurations and Eclipses in good time. I delay it at present on no other account, then that by further Observations I may get a better knowledge of their Motions, for though these Satellites were discovered 74 years ago, yet have we no Observations of their Eclipses, that we may rely on, before Hodierne's, and the first of his is scarce 42 years old as yet: I hope nevertheless my present Tables will not err sensibly for half a dozen years further, and that in the mean time I may give them a further correction by the help of such Observations, as if God spare me life and health, I intend to make, whereby they may be rendered serviceable for a much longer time, without any considerable faults. As for the Catalogue itself I give in it first the Moneth, then the day, and to avoid mistakes I have prefixed the Planetary Character for the day of the week to each; then the Hour and Minute of the appearance; counted (after the Astronomical manner from Noone, and lastly the Number of the Satellit that is Eclipsed with an i after it when its ingress, an e when its emersion is the appearance observable at that time. And that it may be readily known which of these are visible in our Horizon I have marked them with a*betwixt the Number and the Letter. Thus in the sixth line of the Catalogue you find O6|12-29|4*i, which shews that on Sunday the sixth of that Moneth at 12h 29' after Noon, the fourth or utmost Satellit makes its ingress, and is Eclipsed in its shadow; and the Numbers under it |15-39|4*e| that the same day 15h 39' after Noone, or that on the 7th day at 3h 39' in the Morning, it again emerges from the shadow, and becomes visible betwixt it and the body, and the * added to them both, shews that both appearances are visible with us. If it be required to know whether any one of those invisible with us be visible in any other given place. Convert the difference of Meridians betwixt it and London into time. And if the place lie to the East of London, add it to, if to the West, subtract it from the time of the appearance at London, the Sun or difference accordingly shall be the true time of the Eclipse under that Meridian, at which if it be above the Horizon the Sun beneath it, the Eclipse is there visible, otherwise not. Or by the help of the Ephemerides of the Planets places and a terrestrial Globe, the space on it in which any of these Eclipses will be visible may be found thus. First seek the true places of the Sun and Jupiter with his Latitude in the Ephemerides, whereby you may find their declinations and right ascensions either by the vulgar Tables or the Globe itself exactly enough for this Method. Bring London on the Globe to the Meridian, and detaining it there note what degree of the Equator is cut by it it From this subtract the time of the Eclipse after Noon converted into degrees and minutes, the remainder shews you the Longitude of that Meridian on the earth, where it is then Noon when the Satellit is Eclipsed; which, I therefore call the Meridional Longitude of the Eclipse. Bring this Meridional Longitude under the Meridian, and elevate the nearer Pole to the Sun as much as is his declination, keep the Globe in this position and if \( \theta \) be in Consequence of the Sun, draw a line on the Globe along the Eastern Horizon, it passes over all those places where the Sun is setting at that time, but if \( \theta \) be in Antecedence of the Sun, draw the said line on the Globe by the Western Edge of the Horizon, it passes over all those places where the Sun is then arising. Jupiter being in Consequence of the Sun add the difference of his and the Suns right ascensions to the Meridional Longitude aforementioned, bring the degree of the Equator answering their summe under the Meridian. Raise the Pole next Jupiter equal to his declination, and detaining the Globe in this position, draw a line again by the Eastern Horizon, the space intercepted betwixt this and the line of the Suns settings before described on the Globe, Comprehends all those places on the earth from Sun setting till \( \theta \) is set. But if \( \theta \) were in Antecedence of the Sun, Subtract the difference of his and the Suns right Ascentions from the Meridional Longitude, set the degree of the Equator answering the remainder under the Meridian, and elevate the Pole next Jupiter equal to his declination. Keeping the Globe in this position draw a line by the Western Edg of the Horizon, the space included betwixt this, and the line of the Suns risings contains all those places, on the Earth where this Eclipse is visible betwixt \( \theta \)'s rising and Sunrise. When any Eclipse of these is observed, the difference betwixt the noted time and that in the Catalogue, shall H h h 2 be be the difference of Meridians betwixt the place of the observation and London which lies so near the Meridian of the Observatory that the distance need not be accounted for. And this determination may be relied on, if the first or third Satellit were observed; but I dare not be so confident of the second and fourth for the reasons formerly given. However I shall make it my business to observe all such Eclipses of as many of them as shall be visible with us, that by comparing my observations with such as shall be made abroad, the error, if any, may be discovered and Corrected. When \( \mathcal{Z} \) is in Quartile of the Sun: the distance of the first Satellit from his next limb when it falls into his shadow, and is Eclipsed, is one Semidiameter of \( \mathcal{Z} \). Of the second, two or a whole Diameter nearly. Of the third, three. Of the fourth, five of his Semidiameters, or something better when the parallax of the Orbe is greatest. But these quantities diminish gradually as he approaches the \( \sigma \) or \( \phi \) of the Sun somewhat nearly but not exactly in the proportion of Sines. As the Sun removes from the \( \sigma \) of \( \mathcal{Z} \) the Ingresses of the Satellites into his shadow become observable. When he is about thirty degrees from it, the Emerisions of the fourth, and at sixty degrees of the third begin to be seen betwixt the shadow and body continuing so till the Sun be arrived within sixty degrees of the \( \phi \) of \( \mathcal{Z} \), when the Emerisions of the third fall behind his body, but the Emerisions of the fourth continue visible till he be less than thirty degrees distant from the \( \sigma \) at which time they also are hid behind him, all the appearances being made really to the right hand or in antecedence of \( \mathcal{Z} \), tho with inverting Telescopes, they appear to the contrary, the left. After the opposition of the \( \odot \) and \( \mathcal{Z} \) we begin to see the Emerisions of all the Satellites from the shadow, now on the left hand or in consequence of \( \mathcal{Z} \), but through inverting glasses on the right, when the ⊙ is near thirty degrees from the opposition of the Ingresses of the fourth, when sixty degrees from it of the third, begin to be observable betwixt the body and shadow, continuing so till the Sun arrive at the same or rather within something a wider distance from the ⊙ of ⊙. Therefore all the Eclipses from the beginning of the year till the ⊙ of the Sun and Jupiter on the twenty fifth of February are made in antecedence of ⊙ but appear through the inverting Telescope on the left hand of him, afterwards till the ⊙ in August they are made in Consequence but through the same glasses appear on the right. But when he Emerges again from the Sun in September they are made, and appear as in the beginning of the year. After which time the Latitude of the fourth Satellit becomes so great that it escapes the shadow and body both of ⊙ and suffers no more Eclipses by either of them according to my Tables this year; it will be therefore worth the while for those who are accommodated with good glasses to look for the following Conjunctions of the fourth Satellit with the Axis of the shadow, of which that on November the nineteenth is visible with us. For if its Latitude be any thing less than I esteem-ed, it may be Eclipsed. The Conjunctions of the 4th Octob. ⊙ 17°-07'-53 Satellit with the Axis of the Nov. ⊙ 3°-01'-47 shadow when it suffers no E- clipses 1684. are Decem. ⊙ 6°-13'-24 ⊙ 23°-07'-13 Next Next year I intend (God willing) to give you the like Catalogue with corrections if I find them requisite, something earlier that so our freinds abroad may have timely notice and be incited to mind and observe these appearances. J. F. The Observatory at Greenwich, Dec. 18. 1683. A Catalogue of the Visible Eclipses of the Satellites, shewing the apparent times of their Ingresses into Shadow and Emergences, from it under the Meridian of the Observatory in the year 1684. Calculated from new Tables of their Motions. by John Flamsteed M.R. & R.S.S. | Year | Month | Day | Hour | Minute | Second | Description | |------|-------|-----|------|--------|--------|-------------| | 1684 | Jan. | 1 | 13-03 | * | | | | | Feb. | 2 | 23-30 | * | | | | | Mar. | 3 | 7-3 | * | | | | | Apr. | 4 | 19-05 | * | | | | | May | 5 | 1-58 | * | | | [Continued table with more entries] | M7 | June b | July b | Aug. b | |----|--------|--------|-------| | 12 | 18-21 | c | 4-3 | 22-30 | c | 1-0-38 | | 19-06 | 1 | 11-14 | 3 | 4-05 | 2 | 19-07 | | 21-02 | c | 14-18 | 3 | 16-58 | 1 | 4-3-48 | | 3 | 18-09 | 2 | 20-27 | 1 | 5-11-27 | 1 | 3-36 | | 19-20 | 3 | 3-14-55 | 1 | 6-17-23 | 2 | 5-2-01 | | 22-25 | 3 | 4-17-47 | 2 | 7-5-55 | 1 | 6-8-05 | | 4 | 2-51 | * | 5-7-10 | 4 | 7-04 | 3 | | 6 | 7-19 | 1 | 8-41 | 4 | 10-05 | 3 | | 7 | 7-27 | 2 | 9-24 | 1 | 8-19-18 | 4 | | 8 | 1-47 | 1 | 7-3-52 | 1 | 20-18 | 4 | | 9 | 20-16 | 1 | 8-7-04 | 2 | 9-0-24 | 1 | | 10 | 20-45 | 2 | 15-12 | 3 | 10-5-41 | 2 | | 23-18 | 3 | 18-15 | 3 | 18-52 | 1 | | 11 | 2-24 | 3 | 22-20 | 1 | 12-13-21 | 1 | | 14-45 | 1 | 10-16-49 | 1 | 13-19-59 | 2 | 13-10-01 | | 13 | 9-14 | 1 | 11-20-21 | 2 | 14-7-50 | 1 | | 14 | 10-03 | 2 | 12-11-17 | 1 | 11-03 | 3 | | 15 | 3-43 | 1 | 14-5-46 | 1 | 14-03 | 3 | | 16 | 22-11 | 1 | 15-9-39 | 2 | 16-2-19 | 1 | | 17 | 23-21 | 2 | 19-1-13 | 3 | 17-9-16 | 2 | | 18 | 3-17 | 3 | 22-12 | 3 | 20-47 | 1 | | 19 | 13-05 | 4 | 17-18-43 | 1 | 19-15-16 | 1 | | 20 | 11-08 | 1 | 18-22-56 | 2 | 20-22-34 | 2 | | 21 | 12-38 | 2 | 19-13-11 | 1 | 21-9-45 | 1 | | 22 | 5-30 | 1 | 21-7-39 | 1 | 22-4-14 | 1 | | 24 | 0-05 | 1 | 22-1-13 | 4 | 24-1-53 | 2 | | 25 | 2-55 | 2 | 23-6-8 | 3 | 25-13-27 | 4 | | 26 | 7-16 | 3 | 23-2-09 | 1 | 26-17-11 | 1 | | 27 | 10-20 | 3 | 2-1-03 | 3 | 28-1-11 | 2 | | 28 | 13-02 | 1 | 24-20-36 | 1 | 11-4-01 | 1 | | 29 | 7-30 | 1 | 26-1-31 | 2 | 22-02 | 3 | | 31 | 1-59 | 1 | 28-9-33 | 1 | 31-14-29 | 2 | *Septembretto Z sub radijs Solis latet.* | Octo. | Nov. | Dec. | |-------|------|------| | 1684 | | | | ♀ 1 | 7-08 | ☉ 2 | | | 21-21| 3 | | ♀ 3 | 11-21| 4 | | | 15-59| 6 | | | 10-18| 8 | | | 0-40 | 4-47 | | | 11-08| 9 | | | 23-16| 11 | | ♀ 10 | 13-58| 13 | | | 17-44| 15 | | | 12-13| 17 | | | 3-16 | 19 | | | 6-41 | 21 | | | 15-07| 23 | | | 1-10 | 25 | | ♀ 17 | 16-33| 27 | | | 19-39| 29 | | | 14-07| 31 | | | 5-51 | 33 | | | 8-35 | 35 | | ♀ 22 | 19-04| 37 | | | 3-04 | 39 | | ♀ 24 | 19-08| 41 | | | 21-32| 43 | | | 16-00| 45 | | | 8-24 | 47 | | | 10-28| 49 | | | 23-01| 51 | | | 4-57 | 53 | | | 21-41| 55 | | | 23-25| 57 | | | 1-10 | 1 | | | 19-43| 3 | | | 21-03| 5 | | | 14-10| 7 | | | 8-37 | 9 | | | 21-26| 11 | | | 8-38 | 13 | | | 10-20| 15 | | | 23-36| 17 | | | 21-33| 19 | | | 16-00| 21 | | | 22-31| 23 | | | 1-19 | 25 | | | 10-27| 27 | | | 12-50| 29 | | | 4-55 | 31 | | | 23-22| 33 | | | 2-06 | 35 | | | 17-42| 37 | | | 2-24 | 39 | | | 5-12 | 41 | | | 12-17| 43 | | | 15-22| 45 | | | 6-45 | 47 | | | 1-12 | 49 | | | 4-36 | 51 | | | 19-39| 53 | | | 6-19 | 55 | | | 9-06 | 57 | | | 14-06| 59 | | | 17-51| 61 | | | 8-34 | 63 | | | 3-01 | 65 | | | 7-67 | 67 | Descript Dec. 11. 1683. Iii Joh.