The manner of Collecting the equal Anomalies from thefe T ABLES, is thus : First, Exfcribe the Epocha which belongs to that Year which moft nearly precedeth the Year wherein you feel the Place of a*ny Planet. Secondly, Under that Epocha (or number) write the Motions belonging to fo many Tears, Months and Days, as are compleatly expired fince the Tear of the Epocha; all which Numbers muft be taken out of their proper Tables, and fet orderly one under another; which the disjunction of the Numbers will give Direction enough how to do. - Thirdly, All thefe Numbers must be added into One; and their Sum fhall give the Anomaly for the Time propofed And if the Sum rife to be above a whole Circle, or 3.60 Degrees; you must then caft 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 feverally; as is done in the Example following. CHA P. 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 Biffextile, or Leap-Year. Fift, Out of the Table of Tears, exfcribe the Apocha for 1700: And under it 4 Tears and 7 Tears, (which together inake 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 pleat 15. Thus is the first part of your Work performed. Secondly, Repairing to your Tables, you fhall find the Anomaly of the Earth which ftands against 1700, to be 194.26 de. and the Anomaly of h to be 83.88 deg. both which fet in their proper Columns under and h, against 1700. Alfo, Take out of their proper Tables, the Anomalies belonging to 4 Tears and 7 Tears; and write them in their proper Columns againft their refpe Etive Times: As 359.96 deg. for the, and 48.86 deg. for h which fet down against 4 Tears: Do the like for 7 Tears: And for the Month of April, which must be taken out of the Table of Months in the Leap-Tears, becaufe 1712 will be Leap-Tear: 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 exfcribed out of the Tables, and fet orderly one under another; you muft add them toge ther, and you fhall 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 O Reduced But, the Anomaly of h being lefs than 360 deg. needs no fuch Réduction. And thus have you computed the Anomalies of the and, for the 16th Day of May, in the Year 1712 at Noon. CHAP. IV.. How the Degrees of Anomaly of the Earth, Planets (found as before) in their Orbit's; duced to Degrees in the Ecliptick.. F fire. or any of the are to be Re- OR the performance hereof, the following Table is fubfervient, for it will readily (by infpection only) anfwer your de A Anomalies in their Orbits. A TABLE, fhewing fhewing 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. The Ufe of the Table. The Table confifts of Seven Columns: In the firft, 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, k, 4, 6, 2, 9, you have the Degrees, and Ico Parts of the Ecliptick which anfwer thereunto. So that if you feek the Degrees of Anomaly of any Planet (found as by the former Table) in the firft Column, you fhall find against thofe Degrees of Anomaly, the Sign, Degree, and 100 Part of the Ecliptick anfwerable thereunto. -- So in the foregoing Example of the Earth and Saturn h, where the Anomaly of the Earth was found to be 328, and of Satwin 223 (neareft)- Now, if you look for thefe Numbers in the firft Column of this Table, you fhall find, that against 330, (which is the nearest Number to 328) in the Earths Column, 8.02 de. And that Degree of the Ecliptick anfwers to 330 deg. of the Earths Anomaly in its Orbit Alfo, againft 220 in the firft Column (which is the nearest to 223, the Anomaly of Saturn) you shall find in the Column for Saturn, 11.93 deg. And that Degree of the Ecliptick anfwers 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 firft Column, the Degrees in the other Columns for the Planets give thofe Signs and Degrees of the Ecliptick, of every Tenth Degree of Anomaly: And therefore you must make Proportion (which how to perform, we fuppofe to be known) and therefore in our Example. |