The manner of Collecting the equal Anomalies from these T ABLES, is thus : First, Exscribe the Epocha which belongs to that Year which *most nearly precedeth the Year wherein you feek the Place of any Planet. Secondly, Under that Epocha (or number) write the Motions belonging to so many Tears, Months and Days, as are compleatly expired fince the Tear of the Epocha; all which Numbers must be taken out of their proper Tables, and fet orderly one under ano*ther; which the disjunction of the Numbers will give Direction enough how to do. Thirdly, All these Numbers must be added into One; and their Sum shall give the Anomaly for the Time proposed - And if the Sum rise to be above a whole Circle, or 3.60 Degrees; you must then cast away the number of 360 as oft as you - may, and the remaining Number inuft be taken for the Anomaly. Fourthly, Thefe things are to be done both in the Earth and the Planet severally; as is done in the Example following. CHAP. III. How to Collect the Anomalies of Saturn and the Earth, for the 16th Day of May, at Noon, in the Year of Chrift 1712, being Bissextile, or Leap-Year. Finft, Out of the Table of Tears, exscribe the Apocha for 1700 : And under it 4 Tears and 7 Years, (which together make 11 compleat Tears :) Under them exfcribe April Compleat (putting B to it, for that it is a Leap-Tear :) And under that exfcribe Days Com plect 15. Thus is the first part of your Work performed. Secondly, Repairing to your Tables, you shall find the Anomaly of the Earth which stands against 1700, to be 194.26 de. and the Anomaly of h to be 83.88 deg. both which fet in their proper Columus under and h, against 1700. Also, Take out of their proper Tables, the Anomalies belonging to 4 Tears and 7 Years; and write them in their proper Columns against their refpe. Etive Times: As 359.96 deg. for the, and 48.86 deg. for h; which fet down against 4 Years: Do the like for 7 Years: And for the Month of April, which must be taken out of the Table of Months in the Leap-Tears, because 1712 will be Leap-Year: And for the 15 Days, take the Anomalies anfwering to them out of the Table of Anomalies for Days. Thirdly, all the Anomalies being thus exscribed out of the Tables, and set orderly one under another; you must add them together, and you shall find the Sum of the Anomaly to be 1047.45 deg. And the Anomaly of h to be 222.76 deg. But, because the Sum of the Earths Anomalies is above 360, you must take that Number, as oft as you can (which is twice, viz. 720 deg.) and the Remainder 327.45 deg. is the Anomaly of the Reduced: But, the Anomaly of h being less than 360 deg. needs no such Reduction. And thus have you computed the Anomalies of the and, for the 16th Day of May, in the Year 1712 at Noon. How the Degrees of Anomaly of the Earth, or any of the Planets (found as before) in their Orbit's; are to be Re-duced to Degrees in the Ecliptick. / Fr COR the performance hereof, the following Table is subservient, it will readily (by inspection only) answer your de fire. : Anomalies in their Orbits. A TABLE, shewing what Point of the 'Ecliptick anfwers to any Degrees of Anomaly, that the Earth, or any of the other Planets is found to have in its own Orbit. 130 15. 408 2. 26 13.42 1: 60 12:20 3:35 -140 15016.08 24.01 4.90 24:48 29: 62 2.42 160 16. 27 5. 12 15.82 6:27 12: 558 14:18 16. 29 26.80 1805 7.00 27.50 7.32€ 0: 350 2:82 15:00 190 17.37 8.72 18.84 12:44 210 5 2.050 0.998 10.74 6:24 12 3: 23 29.82 24:42 23:09 0:29 17:82 13: 34 13: 90 22. 74 Π 2.22 26:55 240 8.80 २. ८८ 12. 758 10:07 3:50呎 8:25 19:05 24.00 3.30 II 1:00 23: 60 29:05 9.075 4.02 13.33 10: 90 3:62 8:35 13.84 23.20 20:55 13:60 17:05 1 23. 49 2.90 29:90 23:57 25: 26 22.455 9:01 3:50 3:07 21: 89 13:42 10:52 330 8.027 0.34 10:44 5:17 340 17.69 9.60 19:66 13:62 350 7.00 27.50 7:82 035 W 23:32 3:23 13:09 23: 60 2:82 17: 73 24:72 1: 52 8:26 14: 951 The The Ufe of the Table CHAP. V. The Table confifts of Seven Columns: In the first, towards the Left-hand, is placed the Degrees of Anomaly, from 1 to 360, by every 10th Degree. And in the other Six Columns noted at the Head with , h, 4, 8, 2,, you have the Degrees, and IcO Parts of the Ecliptick which answer thereunto. So that if you seek the Degrees of Anomaly of any Planet (found as by the former Table) in the first Column, you shall find against those Degrees of Anomaly, the Sign, Degree, and 100 Part of the Ecliptick anfwerable thereunto. So in the foregoing Example of the Earth and Saturn, where the Anomaly of the Earth was found to be 328, and of Saturn 223 (nearest) Now, if you look for these Numbers in the first Column of this Table, you shall find, that against 330, (which is the nearest Number to 328) in the Earths Column, 7 8.02 de. And that Degree of the Ecliptick answers to 330 deg. of the Earths Anomaly in its Orbit----- Also, against 220 in the first Column (which is the nearest to 223, the Anomaly of Saturn) you shall find in the Column for Saturn, Ω 11.93 deg. And that Degree of the Ecliptick answers to 320 deg. of Saturns Anomaly in his Orbit: And fo of any other. But in the Ufe of this Table you are to note, That there being but every Tenth Degree of Anomaly in the first Column, the Degrees in the other Columns for the Planets give those Signs and Degrees of the Ecliptick, of every Tenth Degree of Anomaly: And therefore you must make Proportion (which how to perform, we suppose to be known) and therefore in our Example. The Use of the Theories, and by them to find the Places of the Earth and Planets, both in Longitude and Latitude, &c. for any time proposed. As for MARS and the EARTH, on the 18th of October 1705. T HE Orbits of the EARTH and MARS being defcribed in the Theory, as is before shewed how to do; First, Collect the equal Anomalies for the Earth and Mars, for the Time proposed, and their Reductions to the Ecliptick, as is here done. The Equal Anomalies of the Earth and Mars, for the 18th Day of October 1705 at Noon. Secondly, The Equal Anomaly of the Earth, reduced to the E-cliptick, being in 5. 12 de. of Taurus, lay a Ruler to the Centre O, and 5.12 deg. 8, (as atc) and where it crosseth the Orbit of the Earth, make, for that is the Place of the Earth in his Orbit at that time. Thirdly, The Equal Anomaly of MARS, reduced to the Eclip-tick Circle, being in 17.68 deg. of Libra: Lay a Ruler to the Centre |