New and Accurate Tables for the Ready Computing of the Eclipses of the First Satellite of Jupiter, by Addition Only. By the Reverend Mr James Pound, R. S. S.

being brought nearer to the distinct Base of the Object Glass; and an Eye less Convex, the office of a less Convex Eye-Glass: but with this difference, that the more Convex the Eye is, the easier may any part of the Object be found, and the larger and more lucid it will appear. I have seen Saturn's Ring very plain with an Object-Glass of little more than six Foot Radius, without an Eye-Glass. I have also found out a way for the Presbyte to make use of an Object-Glass, by placing their Eye nearer the Lens than its Focus, by so much as their Eye is flatter than a common Eye, so as to make (as it were) the Telescope of Galileo; the flat Eye serving as a common Eye arm'd with a Concave Lens. I have so fixed the Telescope, as to make a Presbyte read at a great distance a small Print. The truth of this may be easily demonstrated, if it be requir'd. If this Experiment be made at Sea with a very large Tube, big enough to put in the Head and move it about, and the Object-Glass be also large, it may not perhaps be difficult to observe the Eclipses of the Satellites of Jupiter, which I would recommend to the Consideration of those that would try for the Longitude by such like Observations. VI. New and accurate Tables for the ready Computing of the Eclipses of the first Satellite of Jupiter, by Addition only. By the Reverend Mr James Pound, R. S. S. In Numb. 214. of these Transactions, for the Months of Novem and Decem. 1694. we exhibited an Epitome of Mr Cassini's curious Tables then newly pub- lished, for computing the Eclipses of the first Satellite of Jupiter, without the help of any other Numbers. The ease of this Calculus gave great satisfaction to those that delight in Telescope observations; and has been of good use to encourage Astronomers to ascertain the Geographical Longitudes of many places, by help of these Eclipses; whose frequency seems to afford us the properest means for that purpose. But it being now 26 Years since those Tables were published, length of Time has discovered that this Satellite's motion is a small matter swifter than M. Cassini had supposed it; and the Reverend Mr. Pound being provided with all the Qualifications requisite for such a Work, has of late apply'd himself to rectify by frequent Observation what he found amiss in the aforesaid Calculus; and withal has put it into another Form yet much more easy and compendious, by bringing what M. Cassini had given us in odd Numbers, to the Millesimals of a Circle, both as to Numb. I. which he calls Numb. A. being the mean Anomalie of Jupiter in such parts; as also to Numb. II. or our Numb. B. which is the distance of the mean place of Jupiter, from the true place of the Sun, and which with the addition of the Equation of Numb. B. gives the true angle of Commutation in the same Millesimals of a Circle. And having deducted from the Epoches the greatest Equations both of Numb. A. and B. he restores them by adding as much to the Equations themselves, by which means they all become Affirmative, so that the whole computation is performed by Addition only. The Reader is supposed to be acquainted with the Method of M. Cassini's Calculus, which is at large explain'd in the aforesaid Transaction, Num. 214. For which reason this shorter Description may suffice at present. ### Epochæ Conjunctionum Primi Satellitis Cum Jove. | An. Jul. | Conjunct. | Num. A. | Num. B. | |----------|-----------|---------|---------| | 1719 | 6 11 13 | 872 | 396 | | 1720 | 20 22 40 | 956 | 310 | | | 21 5 2 | 44 | 229 | | | 22 19 14 | 11 | 125 | | | 23 9 25 | 38 | 209 | | 1724 | 1 18 5 | 42 | 293 | | | 2 8 17 | 10 | 377 | | | 26 16 57 | 13 | 462 | | | 27 7 8 | 41 | 546 | | | 28 21 20 | 8 | 630 | | | 29 1 6 | 0 | 12 | | 1730 | 20 11 39 | 799 | 468 | | | 31 10 23 | 7 | 883 | | | 32 0 34 | 34 | 967 | | | 33 9 14 | 38 | 52 | | 1734 | 1 17 54 | 41 | 136 | | | 2 8 6 | 9 | 220 | | | 3 22 17 | 36 | 305 | | | 4 6 57 | 40 | 389 | | | 5 21 9 | 7 | 473 | | 1739 | 11 20 35 | 557 | 708 | | | 1 1 32 | 2 | 642 | | | 2 10 12 | 6 | 726 | | | 3 23 33 | 810 | 454 | | | 4 9 3 | 37 | 895 | | 1744 | 2 23 15 | 4 | 979 | | | 3 7 55 | 8 | 63 | | | 4 22 6 | 35 | 148 | | | 5 12 18 | 3 | 232 | | | 6 29 30 | 316 | 947 | | 1749 | 11 9 34 | 400 | 866 | | An. Jul. | Conjunct. | Num. A. | Num. B. | |----------|-----------|---------|---------| | 1749 | 11 9 34 | 400 | 866 | | 1750 | 1 21 1 | 485 | 780 | | | 5 10 1 | 5 | 569 | | | 5 12 3 | 3 | 653 | | | 5 8 52 | 37 | 738 | | 1754 | 2 3 4 | 4 | 822 | | | 13 15 32 | 906 | 359 | | | 3 27 0 | 990 | 273 | | | 12 7 3 | 75 | 191 | | | 2 18 30 | 159 | 10 | | | 10 58 34 | 243 | 24 | | 1760 | 1 10 1 | 328 | 938 | | | 9 50 3 | 412 | 856 | | | 1 0 2 | 496 | 770 | | | 14 13 0 | 580 | 684 | | 1764 | 4 24 27 | 665 | 598 | | | 13 4 3 | 749 | 517 | | | 3 15 58 | 833 | 431 | | | 11 56 2 | 918 | 349 | | | 2 7 29 | 263 | | | 1769 | 10 47 33 | 86 | 182 | | | 0 59 0 | 171 | 96 | | | 15 10 28 | 255 | 10 | | | 5 21 56 | 339 | 924 | | | 14 2 0 | 423 | 842 | | 1774 | 4 13 27 | 508 | 761 | | | 12 53 31 | 592 | 675 | | | 3 4 58 | 676 | 589 | | | 11 45 1 | 761 | 507 | | | 1 56 28 | 845 | 421 | | 1779 | 16 7 | 56 | 929 | | | 56 7 | 929 | 335 | Revolutio Revolutiones Primi Satellitis Jovis in mensibus. | Januarii | N. | Nu. | |----------|----|-----| | D. h. | A. | B. | | 18 28 36| 0 | 5 | | 12 57 12| 1 | 9 | | 7 25 48 | 1 | 14 | | 1 54 24 | 2 | 18 | | 20 23 | 2 | 23 | | 14 51 36| 2 | 27 | | 9 20 12 | 3 | 32 | | 3 48 48 | 3 | 37 | | 22 17 24| 4 | 41 | | 16 46 | 4 | 46 | | 11 14 36| 4 | 51 | | 5 43 12 | 5 | 55 | | 0 11 47 | 5 | 60 | | 18 40 23| 6 | 64 | | 13 8 59 | 6 | 69 | | 7 37 35 | 7 | 73 | | 2 6 11 | 7 | 78 | | 20 34 47| 7 | 82 | | Februarii | N. | Nu. | |-----------|----|-----| | D. h. | A. | B. | | 0 20 34 47| 7 | 82 | | 15 3 23 | 8 | 87 | | 9 31 59 | 8 | 92 | | 4 0 35 | 9 | 96 | | 22 29 11 | 9 | 101 | | 16 57 47 | 9 | 105 | | 11 26 23 | 10 | 110 | | 5 54 59 | 10 | 114 | | Martii | N. | Nu. | |-----------|----|-----| | 4 12 23 | 14 | 155 | | 22 40 59 | 14 | 159 | | 17 9 35 | 15 | 164 | | 11 38 10 | 15 | 168 | | 6 6 46 | 16 | 173 | | 0 35 22 | 16 | 177 | | 19 3 58 | 16 | 182 | | 13 32 34 | 17 | 186 | | 8 1 10 | 17 | 190 | | 2 29 46 | 18 | 195 | | 20 58 22 | 18 | 199 | | 15 26 58 | 18 | 204 | | 9 55 34 | 19 | 208 | | 4 24 10 | 19 | 213 | | 22 52 46 | 20 | 217 | | 17 21 22 | 20 | 221 | | 11 49 58 | 20 | 225 | | 6 18 34 | 21 | 230 | Aprilis. Revolutiones Primi Satellitis Jovis in mensibus. | Aprilis | Maii | |---------|------| | D. h. | N. | Nu. | D. h. | N. | Nu. | | | A. | B. | | A. | B. | | 0 6 8 34 | 21 230 | | 16 6 42 9 | 31 343 | | | 2 0 47 10 | 21 235 | | 18 1 10 45 | 32 348 | | | 3 19 15 46 | 22 239 | | 19 19 39 21 | 32 352 | | | 5 13 44 22 | 22 244 | | 21 14 7 57 | 33 356 | | | 7 8 12 58 | 22 248 | | 23 8 36 33 | 33 361 | | | 9 2 41 34 | 23 252 | | 25 3 5 9 | 33 365 | | | 10 21 10 10 | 23 257 | | 26 21 33 45 | 34 369 | | | 12 15 38 46 | 24 261 | | 28 16 2 21 | 34 373 | | | 14 10 7 22 | 24 265 | | 30 10 30 57 | 35 378 | | | 16 4 35 58 | 25 270 | | Junii | | 17 23 4 33 | 25 274 | | | | | | 19 17 33 | 25 279 | | 0 10 30 57 | 35 378 | | | 21 12 1 45 | 26 283 | | 1 4 59 32 | 35 382 | | | 23 6 30 21 | 26 287 | | 2 23 28 8 | 36 386 | | | 25 0 58 57 | 27 292 | | 4 17 56 44 | 36 391 | | | 26 19 27 33 | 27 296 | | 6 12 25 20 | 36 395 | | | 28 13 56 9 | 27 300 | | 8 6 53 56 | 37 399 | | | 30 8 24 45 | 28 304 | | 10 1 22 32 | 37 403 | | | Maii | | 0 8 24 45 | 28 304 | | 11 19 51 8 | 38 408 | | | 2 2 53 21 | 28 309 | | 13 14 19 44 | 38 412 | | | 3 21 21 57 | 29 313 | | 15 8 48 20 | 38 416 | | | 5 15 50 33 | 29 317 | | 17 3 16 56 | 39 420 | | | 7 10 19 9 | 29 322 | | 18 21 45 32 | 39 425 | | | 9 4 47 45 | 30 326 | | 20 16 14 8 | 40 429 | | | 10 23 16 21 | 30 330 | | 22 10 42 44 | 40 433 | | | 12 17 44 57 | 31 335 | | 24 5 11 20 | 40 438 | | | 14 12 13 33 | 31 339 | | 25 23 39 56 | 41 442 | | | | | | 27 18 8 32 | 41 446 | | | | | | 29 12 37 8 | 42 450 | | Julii Revolutiones Primi Satellitis Jovis in mensibus. | Julii | N. | Nu. | Augusti | N. | Nu. | |-------|----|-----|---------|----|-----| | D. h. | A. | B. | D. h. | A. | B. | | 1 | 7 | 544 | 42 | 16 | 7 | 29 | 19 | 53 | 567 | | 3 | 1 | 342 | 42 | 18 | 1 | 57 | 55 | 53 | 571 | | 4 | 20 | 56 | 43 | 19 | 20 | 26 | 31 | 54 | 575 | | 6 | 14 | 31 | 43 | 21 | 14 | 55 | 7 | 54 | 580 | | 8 | 9 | 0 | 44 | 23 | 9 | 23 | 43 | 54 | 584 | | 10 | 3 | 28 | 44 | 25 | 3 | 52 | 18 | 55 | 588 | | 11 | 21 | 57 | 20 | 26 | 22 | 20 | 54 | 55 | 593 | | 13 | 16 | 25 | 55 | 28 | 16 | 49 | 30 | 56 | 597 | | 15 | 10 | 54 | 31 | 30 | 11 | 18 | 6 | 56 | 602 | | 17 | 5 | 23 | 7 | | | | | | | | 18 | 23 | 51 | 43 | | | | | | | | 20 | 18 | 20 | 19 | | | | | | | | 22 | 12 | 48 | 55 | | | | | | | | 24 | 7 | 17 | 31 | | | | | | | | 26 | 1 | 46 | 7 | | | | | | | | 27 | 20 | 14 | 43 | | | | | | | | 29 | 14 | 43 | 19 | | | | | | | | 31 | 9 | 11 | 55 | | | | | | | Septembris. | | | | | | | | |-------|----|-----|---------|----|-----|-----| | 1 | 5 | 46 | 42 | 56 | 606 | | 3 | 0 | 15 | 18 | 57 | 610 | | 4 | 18 | 43 | 54 | 57 | 615 | | 6 | 13 | 12 | 30 | 58 | 619 | | 8 | 7 | 41 | 6 | 58 | 624 | | 10 | 2 | 9 | 42 | 58 | 628 | | 11 | 20 | 38 | 18 | 59 | 632 | | 13 | 15 | 6 | 54 | 59 | 637 | | 15 | 9 | 35 | 30 | 60 | 641 | | 17 | 4 | 4 | 6 | 60 | 646 | | 18 | 22 | 32 | 42 | 60 | 650 | | 20 | 17 | 1 | 18 | 61 | 655 | | 22 | 11 | 29 | 54 | 61 | 659 | | 24 | 5 | 58 | 30 | 62 | 663 | | 26 | 0 | 27 | 6 | 62 | 668 | | 27 | 18 | 55 | 42 | 62 | 672 | | 29 | 13 | 24 | 18 | 63 | 677 | Octobris. Revolutiones Primi Satellitis Jovis in mensibus. | Octobris | N. | Nu. | Novembris | N. | Nu. | |----------|----|-----|-----------|----|-----| | D. h. | A. | B. | D. h. | A. | B. | | 1 7 52 54 | 63 | 681 | 16 8 16 29 | 74 | 799 | | 3 2 21 30 | 64 | 686 | 18 2 45 5 | 74 | 804 | | 4 20 50 6 | 64 | 690 | 19 21 13 40 | 75 | 808 | | 6 15 18 41 | 65 | 695 | 21 15 42 16 | 75 | 813 | | 8 9 47 17 | 65 | 699 | 23 10 10 52 | 76 | 817 | | 10 4 15 53 | 65 | 704 | 25 4 39 28 | 76 | 822 | | 11 22 44 29 | 66 | 708 | 26 23 8 4 | 76 | 827 | | 13 17 13 5 | 66 | 713 | 28 17 36 40 | 77 | 831 | | 15 11 41 41 | 67 | 717 | 30 12 5 16 | 77 | 836 | | 17 6 10 17 | 67 | 721 | Decembris | | | | 19 0 38 53 | 67 | 726 | | | | | 20 19 7 29 | 68 | 730 | 0 12 5 16 | 77 | 836 | | 22 13 36 5 | 68 | 735 | 2 6 33 52 | 78 | 840 | | 24 8 4 41 | 69 | 739 | 4 1 2 28 | 78 | 845 | | 26 2 33 17 | 69 | 744 | 5 19 31 4 | 78 | 849 | | 27 21 1 53 | 69 | 749 | 7 13 59 40 | 79 | 854 | | 29 15 30 29 | 70 | 753 | 9 8 28 16 | 79 | 859 | | 31 9 59 5 | 70 | 758 | 11 2 56 52 | 80 | 863 | | Novembris | | | | | | | 0 9 59 5 | 70 | 758 | 13 21 25 28 | 80 | 868 | | 2 4 27 41 | 71 | 762 | 14 15 54 4 | 80 | 873 | | 3 22 56 17 | 71 | 767 | 16 10 22 40 | 81 | 877 | | 5 17 24 53 | 71 | 772 | 18 4 51 16 | 81 | 882 | | 7 11 53 29 | 72 | 776 | 19 23 19 52 | 82 | 886 | | 9 6 22 5 | 72 | 781 | 21 17 48 28 | 82 | 891 | | 11 0 50 4 | 73 | 785 | 23 12 17 4 | 82 | 897 | | 12 19 19 17 | 73 | 790 | 25 6 45 40 | 83 | 900 | | 14 13 47 53 | 74 | 794 | 27 1 14 16 | 83 | 905 | | 30 14 11 28 | 84 | 914 | | | | PRIMÆ Prime Æquationes Conjunctionum Primi Satellitis cum Jove. | Num. A. | Æquat. Conjunct. Add. | Num. B. | Æquat. Conjunct. Add. | Num. A. | Æquat. Conjunct. Add. | Num. B. | Æquat. Conjunct. Add. | |---------|----------------------|---------|----------------------|---------|----------------------|---------|----------------------| | 0 | 39 | 8 | 15 | 128 | 12 | 7 | 26 | | 4 | 38 | 12 | 16 | 132 | 11 | 27 | 26 | | 8 | 37 | 16 | 16 | 136 | 10 | 47 | 26 | | 12 | 36 | 21 | 16 | 140 | 9 | 27 | 27 | | 16 | 35 | 26 | 16 | 144 | 9 | 31 | 27 | | 20 | 34 | 30 | 17 | 148 | 8 | 45 | 27 | | 24 | 33 | 35 | 17 | 152 | 8 | 19 | 27 | | 28 | 32 | 40 | 18 | 156 | 7 | 44 | 28 | | 32 | 31 | 45 | 18 | 160 | 7 | 0 | 28 | | 36 | 30 | 50 | 19 | 164 | 6 | 38 | 28 | | 40 | 29 | 56 | 19 | 168 | 6 | 7 | 28 | | 44 | 29 | 3 | 19 | 172 | 5 | 37 | 28 | | 48 | 28 | 10 | 20 | 176 | 5 | 8 | 29 | | 52 | 27 | 16 | 20 | 180 | 4 | 41 | 29 | | 56 | 26 | 23 | 20 | 184 | 4 | 15 | 29 | | 60 | 25 | 30 | 21 | 188 | 3 | 49 | 29 | | 64 | 24 | 38 | 21 | 192 | 3 | 24 | 29 | | 68 | 23 | 47 | 21 | 196 | 3 | 1 | 29 | | 72 | 22 | 56 | 22 | 200 | 2 | 40 | 30 | | 76 | 22 | 5 | 22 | 204 | 2 | 20 | 30 | | 80 | 21 | 15 | 22 | 208 | 2 | 1 | 30 | | 84 | 20 | 20 | 23 | 212 | 1 | 42 | 30 | | 88 | 19 | 37 | 23 | 216 | 1 | 25 | 30 | | 92 | 18 | 48 | 23 | 220 | 1 | 10 | 30 | | 96 | 18 | 0 | 24 | 224 | 0 | 58 | 30 | | 100 | 17 | 14 | 24 | 228 | 0 | 47 | 30 | | 104 | 16 | 28 | 24 | 232 | 0 | 36 | 30 | | 108 | 15 | 42 | 24 | 236 | 0 | 26 | 30 | | 112 | 14 | 57 | 25 | 240 | 0 | 18 | 30 | | 116 | 14 | 13 | 25 | 244 | 0 | 12 | 31 | | 120 | 13 | 30 | 25 | 248 | 0 | 7 | 31 | | 124 | 12 | 48 | 26 | 252 | 0 | 4 | 31 | | 128 | 12 | 7 | 26 | 256 | 0 | 1 | 31 | *Primeae* Prima Æquationes Conjunctionum Primi Satellitis cum Jove. | Num. A. | Equat. Conjunct. Adde. | Num. B. | Equat. Conjunct. Adde. | Num. A. | Equat. Conjunct. Adde. | Num. B. | Equat. Conjunct. Adde. | |---------|------------------------|---------|------------------------|---------|------------------------|---------|------------------------| | 512 | 42 17 | 640 | 70 26 | 768 | 77 40 | 896 | 61 48 | | 516 | 43 19 | 644 | 71 3 | 772 | 77 29 | 900 | 61 2 | | 520 | 44 21 | 648 | 71 3 | 776 | 77 18 | 904 | 60 15 | | 524 | 45 23 | 652 | 72 11 | 780 | 77 6 | 908 | 59 28 | | 528 | 46 25 | 656 | 72 42 | 784 | 76 51 | 912 | 58 39 | | 532 | 47 26 | 660 | 73 12 | 788 | 76 34 | 916 | 57 50 | | 536 | 48 27 | 664 | 73 42 | 792 | 76 15 | 920 | 57 1 | | 540 | 49 28 | 668 | 74 10 | 796 | 75 56 | 924 | 56 11 | | 544 | 50 28 | 672 | 74 36 | 800 | 75 36 | 928 | 55 20 | | 548 | 51 28 | 676 | 75 1 | 804 | 75 15 | 932 | 54 29 | | 552 | 52 27 | 680 | 75 25 | 808 | 74 52 | 936 | 53 38 | | 556 | 53 25 | 684 | 75 48 | 812 | 74 27 | 940 | 52 46 | | 560 | 54 23 | 688 | 76 8 | 816 | 74 1 | 944 | 51 53 | | 564 | 55 21 | 692 | 76 26 | 820 | 73 35 | 948 | 51 0 | | 568 | 56 17 | 696 | 76 43 | 824 | 73 8 | 952 | 50 6 | | 572 | 57 12 | 700 | 76 59 | 828 | 72 39 | 956 | 49 13 | | 576 | 58 7 | 704 | 77 13 | 832 | 72 9 | 960 | 48 20 | | 580 | 59 1 | 708 | 77 26 | 836 | 71 38 | 964 | 47 26 | | 584 | 59 4 | 712 | 77 38 | 840 | 71 6 | 968 | 46 31 | | 588 | 60 46 | 716 | 77 48 | 844 | 70 32 | 972 | 45 36 | | 592 | 61 38 | 720 | 77 57 | 848 | 69 57 | 976 | 44 41 | | 596 | 62 28 | 724 | 78 4 | 852 | 69 21 | 980 | 43 46 | | 600 | 63 17 | 728 | 78 9 | 856 | 68 45 | 984 | 42 50 | | 604 | 64 5 | 732 | 78 13 | 860 | 68 7 | 988 | 41 55 | | 608 | 64 53 | 736 | 78 15 | 864 | 67 29 | 992 | 41 0 | | 612 | 65 39 | 740 | 78 16 | 868 | 66 49 | 996 | 40 4 | | 616 | 66 24 | 744 | 78 15 | 872 | 66 9 | 1000 | 39 8 | | 620 | 67 7 | 748 | 78 12 | 876 | 65 28 | 1004 | 38 12 | | 624 | 67 49 | 752 | 78 9 | 880 | 64 46 | 1008 | 37 16 | | 628 | 68 30 | 756 | 78 4 | 884 | 63 3 | 1012 | 36 21 | | 632 | 69 10 | 760 | 77 58 | 888 | 62 19 | 1016 | 35 26 | | 636 | 69 49 | 764 | 77 50 | 892 | 62 34 | 1020 | 34 30 | | 640 | 70 26 | 768 | 77 40 | 896 | 61 48 | 1024 | 33 45 | Secundæ Secundae Æquationes Conjunctionum Primi Satellitis cum Jove. Addenda. | Num. | B. | Equ. | Equ. | Equ. | Equ. | Equ. | Equ. | Equ. | Equ. | |------|----|------|------|------|------|------|------|------|------| | | | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | | 0 | | 14 | 12 | 52 | 9 | 45 | 5 | 30 | 1 | 37 | 0 | 1 | 37 | 5 | 30 | 9 | 45 | 12 | 52 | | 4 | | 14 | 12 | 46 | 9 | 36 | 5 | 20 | 1 | 30 | 0 | 1 | 44 | 5 | 40 | 9 | 54 | 12 | 58 | | 8 | | 13 | 59 | 12 | 40 | 9 | 26 | 5 | 9 | 1 | 23 | 0 | 1 | 52 | 5 | 51 | 10 | 3 | 13 | 2 | | 12 | | 13 | 59 | 12 | 35 | 9 | 17 | 4 | 59 | 1 | 16 | 0 | 2 | 1 | 59 | 6 | 1 | 10 | 12 | 13 | 7 | | 16 | | 13 | 58 | 12 | 29 | 9 | 7 | 4 | 48 | 1 | 9 | 0 | 3 | 2 | 7 | 6 | 1 | 10 | 21 | 13 | 11 | | 20 | | 13 | 57 | 12 | 23 | 8 | 5 | 8 | 38 | 1 | 3 | 0 | 4 | 2 | 15 | 6 | 2 | 10 | 31 | 13 | 16 | | 24 | | 13 | 56 | 12 | 17 | 8 | 4 | 8 | 48 | 4 | 2 | 8 | 0 | 5 | 2 | 24 | 6 | 3 | 10 | 40 | 13 | 20 | | 28 | | 13 | 54 | 12 | 11 | 8 | 3 | 8 | 38 | 4 | 1 | 8 | 0 | 5 | 2 | 32 | 6 | 4 | 10 | 49 | 13 | 25 | | 32 | | 13 | 53 | 12 | 4 | 8 | 2 | 8 | 28 | 4 | 8 | 0 | 4 | 6 | 1 | 41 | 6 | 5 | 10 | 57 | 13 | 29 | | 36 | | 13 | 51 | 11 | 56 | 8 | 1 | 7 | 3 | 58 | 0 | 4 | 0 | 1 | 3 | 2 | 5 | 7 | 5 | 1 | 5 | 13 | 33 | | 40 | | 13 | 49 | 11 | 45 | 8 | 7 | 3 | 58 | 0 | 3 | 5 | 0 | 1 | 6 | 2 | 5 | 9 | 7 | 1 | 1 | 13 | 36 | | 44 | | 13 | 47 | 11 | 42 | 7 | 5 | 7 | 57 | 3 | 3 | 8 | 0 | 3 | 1 | 9 | 3 | 9 | 7 | 2 | 6 | 1 | 20 | 13 | 38 | | 48 | | 13 | 44 | 11 | 34 | 7 | 4 | 7 | 47 | 3 | 2 | 9 | 0 | 2 | 7 | 2 | 3 | 1 | 9 | 7 | 3 | 6 | 1 | 27 | 13 | 41 | | 52 | | 13 | 41 | 11 | 27 | 7 | 3 | 6 | 36 | 3 | 1 | 9 | 0 | 2 | 3 | 7 | 2 | 7 | 4 | 7 | 1 | 3 | 13 | 44 | | 56 | | 13 | 38 | 11 | 20 | 7 | 2 | 6 | 3 | 9 | 0 | 1 | 9 | 0 | 3 | 1 | 3 | 8 | 7 | 5 | 7 | 1 | 4 | 13 | 47 | | 60 | | 13 | 36 | 11 | 13 | 7 | 1 | 6 | 2 | 5 | 9 | 0 | 1 | 6 | 0 | 3 | 5 | 8 | 7 | 1 | 1 | 4 | 9 | 13 | 49 | | 64 | | 13 | 33 | 11 | 5 | 7 | 5 | 2 | 5 | 0 | 1 | 3 | 0 | 4 | 0 | 3 | 5 | 8 | 3 | 1 | 7 | 1 | 5 | 13 | 51 | | 68 | | 13 | 29 | 10 | 57 | 6 | 5 | 5 | 2 | 4 | 1 | 0 | 1 | 0 | 4 | 6 | 4 | 8 | 8 | 2 | 8 | 1 | 2 | 4 | 13 | 53 | | 72 | | 13 | 25 | 10 | 49 | 6 | 4 | 4 | 2 | 3 | 2 | 0 | 7 | 0 | 5 | 2 | 4 | 1 | 8 | 8 | 3 | 8 | 1 | 1 | 13 | 54 | | 76 | | 13 | 20 | 10 | 40 | 6 | 3 | 3 | 2 | 2 | 4 | 0 | 5 | 0 | 5 | 7 | 4 | 2 | 8 | 8 | 4 | 8 | 1 | 1 | 13 | 56 | | 80 | | 13 | 16 | 10 | 31 | 6 | 2 | 2 | 2 | 1 | 5 | 0 | 4 | 1 | 3 | 4 | 3 | 8 | 8 | 5 | 8 | 1 | 2 | 3 | 13 | 57 | | 84 | | 13 | 11 | 10 | 21 | 6 | 1 | 1 | 2 | 7 | 0 | 3 | 1 | 9 | 4 | 4 | 8 | 9 | 7 | 1 | 2 | 9 | 13 | 58 | | 88 | | 13 | 7 | 10 | 12 | 6 | 1 | 1 | 5 | 9 | 0 | 2 | 1 | 1 | 6 | 4 | 5 | 9 | 9 | 1 | 7 | 1 | 2 | 3 | 13 | 59 | | 92 | | 13 | 2 | 10 | 3 | 5 | 5 | 1 | 5 | 2 | 0 | 1 | 1 | 2 | 3 | 5 | 9 | 9 | 2 | 6 | 1 | 2 | 4 | 13 | 59 | | 96 | | 12 | 5 | 8 | 9 | 5 | 4 | 5 | 4 | 0 | 1 | 4 | 4 | 0 | 1 | 3 | 0 | 5 | 2 | 0 | 9 | 3 | 6 | 1 | 2 | 4 | 14 | 0 | | 100 | | 12 | 5 | 2 | 9 | 4 | 5 | 5 | 3 | 0 | 1 | 3 | 7 | 0 | 1 | 3 | 7 | 5 | 3 | 0 | 9 | 4 | 1 | 2 | 5 | 2 | 14 | 0 | Tertia | Tertiae Æquationes Addendae | Semidurationes Eclipsium Primi Satellitis Jovis | |-----------------------------|-----------------------------------------------| | **Nu.** | **Æquationes** | **Num.** | **Nu.** | **Semidurationes** | **Nu.** | **Semidurationes** | **Nu.** | **Semidurationes** | **Nu.** | **Semidurationes** | | **A.** | **H.** | **A.** | **H.** | **A.** | **H.** | **A.** | **H.** | **A.** | **H.** | | 0 | 3 | 29 | 1000 | 0 | 15 | 9 | 250 | 17 | 0 | 500 | 15 | 9 | 750 | 17 | 46 | | 20 | 3 | 28 | 980 | 10 | 14 | 56 | 260 | 17 | 15 | 510 | 14 | 53 | 760 | 17 | 57 | | 40 | 3 | 25 | 940 | 20 | 14 | 44 | 270 | 17 | 31 | 520 | 14 | 39 | 770 | 18 | 7 | | 60 | 3 | 19 | 920 | 30 | 14 | 33 | 280 | 17 | 45 | 530 | 14 | 26 | 780 | 18 | 15 | | 80 | 3 | 12 | 900 | 50 | 14 | 13 | 290 | 17 | 57 | 540 | 14 | 15 | 790 | 18 | 22 | | 100 | 3 | 4 | 880 | 60 | 14 | 7 | 300 | 18 | 7 | 550 | 14 | 7 | 800 | 18 | 26 | | 120 | 3 | 4 | 860 | 70 | 14 | 4 | 310 | 18 | 15 | 560 | 14 | 3 | 810 | 18 | 28 | | 140 | 2 | 56 | 840 | 80 | 14 | 2 | 320 | 18 | 22 | 570 | 14 | 1 | 820 | 18 | 30 | | 160 | 2 | 46 | 820 | 90 | 14 | 0 | 330 | 18 | 27 | 580 | 14 | 0 | 830 | 18 | 28 | | 180 | 2 | 34 | 800 | 100 | 14 | 2 | 340 | 18 | 28 | 590 | 14 | 3 | 840 | 18 | 26 | | 200 | 2 | 22 | 780 | 110 | 14 | 3 | 350 | 18 | 29 | 600 | 14 | 7 | 850 | 18 | 22 | | 220 | 2 | 10 | 760 | 120 | 14 | 6 | 360 | 18 | 27 | 610 | 14 | 13 | 860 | 18 | 16 | | 240 | 1 | 57 | 740 | 130 | 14 | 12 | 370 | 18 | 24 | 620 | 14 | 23 | 870 | 18 | 8 | | 260 | 1 | 44 | 720 | 140 | 14 | 21 | 380 | 18 | 17 | 630 | 14 | 35 | 880 | 18 | 0 | | 280 | 1 | 30 | 700 | 150 | 14 | 31 | 390 | 18 | 9 | 640 | 14 | 49 | 890 | 17 | 50 | | 300 | 1 | 17 | 680 | 160 | 14 | 42 | 400 | 17 | 58 | 650 | 15 | 4 | 900 | 17 | 37 | | 320 | 1 | 5 | 660 | 170 | 14 | 55 | 410 | 17 | 46 | 660 | 15 | 19 | 910 | 17 | 22 | | 340 | 0 | 53 | 640 | 180 | 15 | 9 | 420 | 17 | 31 | 670 | 15 | 36 | 920 | 17 | 8 | | 360 | 0 | 41 | 620 | 190 | 15 | 23 | 430 | 17 | 14 | 680 | 15 | 54 | 930 | 16 | 55 | | 380 | 0 | 31 | 600 | 200 | 15 | 39 | 440 | 16 | 58 | 690 | 16 | 10 | 940 | 16 | 40 | | 400 | 0 | 22 | 580 | 210 | 15 | 55 | 450 | 16 | 40 | 700 | 16 | 28 | 950 | 16 | 23 | | 420 | 0 | 14 | 560 | 220 | 16 | 11 | 460 | 16 | 20 | 710 | 16 | 46 | 960 | 16 | 8 | | 440 | 0 | 8 | 540 | 230 | 16 | 26 | 470 | 16 | 2 | 720 | 17 | 2 | 970 | 15 | 54 | | 460 | 0 | 4 | 520 | 240 | 16 | 43 | 480 | 15 | 45 | 730 | 17 | 17 | 98 | 15 | 37 | | 480 | 0 | 2 | 500 | 250 | 17 | 0 | 490 | 15 | 26 | 740 | 17 | 33 | 990 | 15 | 22 | | 500 | 0 | 0 | 500 | 250 | 17 | 0 | 500 | 15 | 9 | 750 | 17 | 46 | 1000 | 15 | 9 | The Use of the foregoing TABLES. THE Eclipses of the first Satellite of Jupiter, as has been already said, afford the best means of determining the Longitude of places on the Land, where Telescopes of a convenient length may be used; thirteen of these Eclipses happening every 23 Days; but it is requisite that the Observer know near the matter when these opportunities offer themselves, least on the one hand he let them slip, or else grow weary by a too long attendance on them. Those therefore who are curious to observe them, may readily compute the times of the Immersions or Emersions of this Satellite, and that with great exactness, by the following very short Precepts, which admit of no Exception or Caution, viz. Out of the first Table take the Epoche for the Year, with its corresponding Numb. A and Numb. B; and to them add, out of the Tables of Months, the Day, Hour, Minute and Second, nearest less than the time of the Eclipse you seek for, together with its Num. A and B: the Sum of the times is the mean time of the middle of the Eclipse. 2. With Num. A thus collected take out the first Æquation of the Conjunctions; as also the Æquation of Num. B. always to be added to Num. B. before found. 3. With Num. B so equated, take out the second Æquation of the Conjunctions; and in the last Table, the third Æquation, as also the Semi-duration of the Eclipse answering to Num. A. 4. To the mean time of the middle of the Eclipse, add all those three Æquations; the Sum shall be the true equated time of the middle of the Eclipse sought. 5. If Num. B. equated be less than 500, subtract the the Semiduration, and you will have the time of the Immersion, or if it be more than 500, adding the same, it will give the time of the Emerion. But Note, the times thus found are equal time, still to be reduced to the Apparent: and that in the Bissextile Year, after February, one Day is to be deducted from the Day of the Month. The less skilful may perhaps be pleas'd with an Example or two, which may serve them to imitate. Let it be required to find the time of the Immersion of this Satellite into Jupiter's shadow, November the 9th 1719. in the Morning. The Work stands thus, | D. h. | Nu. A. | Nu. B. | |-------|--------|--------| | 1719. | 1. 6.11.13 | 872 | 396 | | Novemb. | 7.11.53.29 | 72 | 776 | | Conj. Med. | 8.18.4.42 | 944 | 172 | | Æquat. I. | 51.53 | 10 | Æq. B. | | Æquat. II. | 10.26 | 182 | B. Æquat. | | Æquat. III. | 3.26 | | 8.19.10.27 1. 6.33 Semidur. Subft. Novemb. 8.18.3.54 So that by this Calculus, on the ninth of Novemb. at 4 Minutes after 6 in the Morning, equal Time, may be seen the Immersion of this Satellite into Jupiter's shadow. Another Example shall be of the Emerion on the fifth of April 1720. viz. Hence it appears that at one Minute after Midnight following the fifth of April, equal Time, will happen the Emersion required. Nor do we doubt but that the Event will very nearly answer. Lastly, it may not be amiss here to inform the Reader, that we have learnt, by the experience of many Years Observation, that the second inequality of this Satellite proceeds from the progressive Propagation of Light, and is common to all the rest of the Satellites: Light, being found to proceed in about seven Minutes of time as far as from the Sun to the Earth, whether with an equable motion or otherwise is still a question. For this reason we have added a Third Equation, whereby to account for the greater distance of Jupiter from the Earth in Aphelio than in Perihelio, as the Second Equation answers to the greater distance of the Planet when near the Conjunction of the Sun, than when near his Opposition. FINIS. London: Printed by W. and J. Innys, Printers to the Royal Society, at the Princes-Arms at the West Corner of St. Paul's Church-Yard. 1719.