An Abstract of a Letter from Mr J. Flamsteed. Math. Reg. et F. of the R.S. Giving the Description et Uses of an Instrument for Finding the Distances of 4^s Satellits from His Axis, with the Help of the Table of Parallaxes and Catalogue of Eclipses; Printed in the Preceding Transactions

An Abstract of a Letter from Mr J. Flamsteed. Math. Reg. &c. of the R.S. giving the description & uses of an Instrument for finding the distances of its Satellites from his Axis, with the help of the Table of Parallaxes and Catalogue of Eclipses; printed in the preceding Transactions. See Tab. 2. Fig. 2. The little Circle in the middle represents the Planet Jupiter, the four concentric Circles the proper Orbits of his four Satellites, duly proportioned to the breadth of his body; the distances betwixt the parallel lines intersecting them, being each equal to one of his Semidiameters. The 4 divided Circles next without these, are distinguished into so many parts as there are days and hours in each Satellite's revolution; the Innermost of them serving for the first, or innermost Satellite; that next it, for the 2d, that next without this for the 3d, and the outermost for the 4th; above which is a small divided Arch of 15 degrees. By this with the aforementioned tables to find the distances of the Satellites from its Axis to a proposed time. 1. In the Table of Parallaxes of the Orb, find the Parallax to the time proposed, and note whether it be to be Added or Subtracted. 2. Extend the third from the center of the Instrument over the Parallax numbed in the small Arch: it cuts off in the 4 divided Circles, so many hours as each Satellite spends in passing from the Axis of the shadow to the Axis of its viewed from our Earth; these I call the Simple Parallactic Intervals, which if the Parallax was to be added, are also additionall, if to be Subtracted, Subductive. 3. To these Parallactic Intervals add the times of half the duration of the Eclipse of each Satellite, which for the 1st may be assumed 1h.10', for the 2nd 1h.30'. greater exactness being needless; but for the 3d, and 4th, when Eclipsed, (their Immersions into the shadow and emersion from it being commonly given in the Catalogue) take half the difference of these times at the next Eclipse to the time proposed, for the half duration, and add them to the Simple Parallactic Intervals, so have you them Augmented. But note that this year 1686, and so often as the 4th Satellit is not Eclipsed, (which is two years in every six) its Interval needs no augmentation, the Catalogue shewing the very time when it passes the Axis of the shadow. 4. Find in the Catalogue the times of the Eclipses of each Satellit next preceding the time proposed, and when the 4th is not Eclipsed, of its passing the Axis of the shadow, to which, if the Parallactic Intervals augmented were Additionall, add them to, if Subductive, Subtract them from, each the time of its proper Satellites Eclipse, so have you very near the Apparent times, when each Satellit last past over the Axis of \( z \) viewed from our Earth. 5. Subtract each of the times thus got from the time proposed: the Remainders are the Intervals of the Motion of each Satellit from \( z \)'s Axis. 6. Extend the thread from the Center over each of these Intervals of Motion numbered severally in the divided Circles belonging each to its proper Satellit, where it cuts the proper Orbit of that Satellit, whose interval was numbered in its peculiar Circle, it shews amongst the parallels, how many semidiameters of \( z \) that Satellit is distant from him, and on which side of him tis posited. Note further, that the thread as it lay extended over the parallax of the orb numbered in the small Arch, where it cut the several proper Orbits of each Satellit, shew'd amongst the Parallels, how many Semidiameters of \( z \) the center of the shadow was distant from the center of \( \theta \) viewed from our Earth. And that if the Parallax of the Orb were additionall, the shadow lies on the right hand from \( \theta \), if Subductive, on the left. To explain these precepts, I shall give two brief examples. Let it be then proposed to know how far each Satellit appears distant from \( \theta \) on the 26th of December this present year 1685, at 16\(^{h}\). 52'. p. m. when the 3\(^{d}\) Satellit falls into the Shadow; also on July the 16. 1686. at 10\(^{h}\). 00'. p. m. when there is no Eclipse. Vide Tab. 2. Fig 3. 1685. Dec. 26\(^{d}\). 16\(^{h}\). 52'. p. m. the Parallax of the Orb is 9°. 20'. additional. | Therefore. | 1 | 2 | 3 | 4 | |------------|---|---|---|---| | The simple Parallactic Intervals Add | 1. 05 | 2. 10 | 4. 25 | 10. 20 | | The half duration of the Eclipses to be Added. | 1. 10 | 1. 30 | 1. 18 | | | The Parallactic Intervals Augmented | 2. 15 | 3. 40 | 5. 43 | | | Last Immersions and \( \sigma \)'s in the Catalogue. Dec. | 25. 09. 37 | 25. 05. 47 | 19. 12. 58 | 16. 00. 30 | | Times of last passing Jupiters Axis Dec. | 25. 11. 52 | 25. 09. 27 | 19. 18. 41 | 10. 10. 50 | | Subtracted from the time proposed. Dec. | 26. 16. 52 | 26. 16. 52 | 26. 16. 52 | 26. 16. 52 | | Leaves the Intervals of Motion. Over which numbered in their peculiar circles, the third being severally laid, cuts the proper Orbit of each at their visible distances from Jupiter. | 1. 05. 00 | 1. 07. 25 | 6. 22. 11 | 16. 06. 02 | | Semid dext. | 6\(\frac{1}{2}\) Sin; 3. dext. | 4\(\frac{1}{2}\) dext. | Vide Tab. 2. Fig. 4. Again, 1686. July the 16. 10'. p. m. the Parallax of the Orb. is 10°. 46'. subductive. | Hence. | 1 | 2 | 3 | 4 | |--------|---|---|---|---| | The simple Parallactic Intervals sub. | 1. 12 | 2. 35 | 5. 10 | 12. 00 | | Half duration of the Eclipses add. | 1. 10 | 1. 30 | | | The Par- And the Satellites stand at the two proposed times as in the two Figures. In drawing of which, tho' I have considered their Latitudes from the line of their utmost Elongations passing through its center, yet I give no rules for determining it, the contrivances and directions necessary on that account, being too many and troublesome to be inserted here: my design is only to shew the Ingenuous observer, how to find at what distance from its each Satellite appears, that so he may not mistake one for another when he is to observe any of their Eclipses. But thus much I shall advise him, That from the beginning of the year 1686. for 3 years following, the Satellites, in the upper or remoter Semi-Circles of their Orbits from us, have South Latitude from the line of their utmost Elongations, passing over its center; in the under or nearer North, but continually decreasing till the end of 3 years, when they change for the contrary. That the Latitude of the 4th Satellite is never more than \( \frac{1}{5} \) Semidiameter of its, of the 3rd little more then half as much, of the two innermost still less. And that towards the end of the year, the 4th Satellite (which will then have passed uneclipsed near two years) will begin to fall into the Penumbra again, for which reason he may doe well to attend its transits at its first appearing, least perhaps it be really Eclipsed. The Observatory, Novemb. 17. 1685. V v v 2 A Re-