us. Which happening at Midnight, was of Courfe invifible to The next will happen as follows: To 17517 May 13. 11. 24. 8" Add 18 1769 10. 7.43.15 23.19. 7.23 From which fubtract as follows: For the Sun's Motion, May 13, or 2 N. S. fubtract That is, the twenty-fourth of May 1769, at fourteen Minutes and fix Seconds paft Six in the Morning, Old Style; but, by Reason of the Alteration of the Style, this Eclipfe will fall on the fourth of June, at the fame Time of the Day. The next Example fhall be of a total Eclipfe of the Moon, which happened on the twenty-third of February 1700, at twenty-four Minutes and forty-fix Seconds paft Seven in the Morning: To which adding eighteen Years, ten or eleven Days, (according as there have happened either five or four Leap-Days) feven Hours, forty-three Minutes, and fifteen Seconds, three times, we fhall have the three fucceffive correfpondent Lunar Eclipfes as follows: That is, the feventh of April, New Style, at thirty-four Minutes and thirty-one Seconds after Six in the Morning. To each of which adding or fubtracting the Time in the foregoing Tables, we fhall have the true Time of each Eclipfe: Thus, the firft Eclipfe happening on the twenty-third of February, Old Style, and the Anomaly of the Moon being then 7.8°, one being add, the other fubtract; their Difference being added, as that is the greater Part, gives the true Time: For the Sun's Motion, Feb. 23, or 12 N. S. add 29 ́· 43′′ 22.51 What is to be added or fubtracted for each of the other two is as follows: For the Sun's Motion, March 5, or February 22 } 23′. 21′′ New Style, add For the Anomaly of the Moon, 7'. 11°, fubtract 22} 21.50 21. 46" 14.39 For the Anomaly of the Moon, 7. 14°, fubtract To the mean Time of the 2d, 1718 March 5d. 3. 8'. 1" Add Gives the true Time, 6.52 1736 March 15.10.59.39 1754 April N.S. 6d. 18h. 34′. 31′′ and 7.7′′, i.e. 1.16 1754 April N. S. 6.18 18.35.46 The principal Alteration in this Period is with Regard to the Time of the Day, on Account of the feven Hours, fortythree Minutes, and fifteen Seconds; which not only makes a great 39 great Difference with Regard to the Places where thofe Eclipfes are vifible, but, in Solar Eclipfes, makes a more confiderable Alteration with Regard to the Time and Quantity; tho' Lunar Eclipfes are abfolutely the fame in all Places where they are visible. To remove these Inconveniences, Mr. Whiston propofed the putting three of thefe Cycles together, which he calls the grand Cycle for Eclipfes, in which the odd Hours and Minutes amount nearly to a whole Day: By which Means the Eclipfes will be brought to nearly the fame Time of the Day, in the fame Places, with only fifty Minutes Anticipation. This Cycle confifts of fifty-four Years and thirty-two or thirty-three Days, (that is, thirty-two Days when fourteen Leap-Days have intervened, and thirty-three Days when there has been but thirteen Leap-Days) abating fifty Minutes. This Cycle brings the Eclipfes to almoft the fame Time of the Day, and with nearly the fame Circumftances, and is therefore preferable to the fingle Cycle, especially for Solar Eclipfes: This has been already fhewn in the former Examples. Thus the Solar Eclipfe on the firft of May 1706, at Nine in the Morning, by the Addition of fifty-four Years and thirty-two Days, wanting fifty Minutes, (as there are fourteen Leap-Days) brings us to the fecond of June, Old Style; that is, the thirteenth of June 1760, at about Seven in the Morning. Thus alfo the great Eclipfe of the Year 1715 will happen in the Year 1769, within about two Hours of the fame Time of the Day. And the laft Example of the Lunar Eclipfe will be but little more than Half an Hour fooner than it happened in the Year 1700. Eclipfes of the Sun that are central, are either total, when the whole Body of the Sun is hid by the Moon; or annular, when the Moon's apparent Diameter, being less than the apparent Diameter of the Sun, cannot hide the whole Body of the Sun, but a Ring of Light is feen round the Moon's Body. Alfo the Duration of total Darknefs, in total Eclipfes of the Sun, is longer or fhorter, in Proportion as the apparent Diameter of the Moon exceeds that of the Sun. These Differences arife from the different real Distances of the Earth, Moon, and Sun: For, if, at the Time of a central Solar Eclipfe, the Earth be in the Aphelion, at the fartheft Distance from the Sun, the apparent Diameter of the Sun being then leaft, and the Moon in the Perigee, or nearest Distance, and of Course its apparent Diameter greateft, the total Darkness will be of longer Duration: On the contrary, the Earth in its Perihelion, the apparent Diameter of the Sun being then greatest greatest, and the Moon in her Apogee, in a central Solar Eclipfe, there can be no total Darkness; but the Eclipfe will be annular, that is, a Ring of the Solar Light will be seen round the Moon's Body. Therefore, if, at any central Eclipfe, the Earth is going from the Aphelion to the Perihelion, the Sun's apparent Diameter will gradually increase every Cycle; and, from the Perihelion, decrease 'till arrived at the Aphelion. The fame is the Cafe with Regard to the apparent Diameter of the Moon, which increases from the Apogee to the Perigee, and decreafes from the Perigee to the Apogee. Now, if the Moon's apparent Diameter be increafing, and the Sun's decreafing, the Eclipfes will every Cycle increase; but, if the Moon's apparent Diameter decreases, and the Sun's increases, there will be every Cycle lefs total Obfcurity, 'till the Eclipfe becomes annular: Laftly, if the Diameters of the Sun and Moon are both increafing, or both decreasing, the Eclipfes will be nearly the fame thro' a long Succeffion of Periods. The Situation of the Earth in its Orbit may be known by the Time of the Year; for the Earth is in its Aphelion about the thirtieth of June, and in the Perihelion about the thirtieth of December; and increases one Sign of Anomaly in about thirty Days, or nearly a Degree each Day. And, as to the Anomaly of the Moon, the Days fhe is in her Apogee and Perigee are noted in all Ephemerides; and her Motion of Anomaly being about thirteen Degrees a Day, that is, a Sign in fomewhat less than two Days and an Half, it will not be difficult to determine the Anomaly of the Moon when any Eclipfe happened by an old Ephemeris, without Aftronomical Tables, near enough for the Purpose of determining the Variations of any future Eclipfe, either as to their true Time of happening, by the Table above given, or the Increase or Decrease of the Obfcurity of central Eclipfes. Only obferve, that the Anomaly of the Moon is reckoned from the Apogee, and of the Earth from the Aphelion. Thus may the Full, Change, and Quarters of the Moon, and Eclipfes both of the Sun and Moon, be found by the single or grand Cycle, with little Trouble, to a good Degree of Exactness. And by the fame may alfo be found the Moon's Place in the Zodiac; for, the mean Motion of the Moon from the Sun exactly correfponding with thefe Periods, the Distance of the Moon from the Sun will vary very little thro' any fucceceding Period from what it was in a former. To find the Moon's Place in the Zodiac by the grand Cycle of fifty-four Years and thirty-two or thirty-three Days, abating fifty Minutes. Rule. From the given Time fubtract fifty-four Years and thirty-two or thirty-three Days, according as fourteen or thirteen Leap-Days have intervened; then, by an Ephemeris for that Year, take out the Moon's Place in the Zodiac for the given Day, and alfo the Sun's Place; from the Place of the Moon fubtract the Place of the Sun, adding twelve Signs if neceffary, and the Remainder is the Moon's Distance from the Sun; this being added to the Sun's Place for the given Day, gives the Moon's Place for the fame Day very nearly, making Allowance for the fifty Minutes. Exam. 1. The prefent Year 1753, January 1. This being fince the Alteration of the Style, eleven Days muft firft be fubtracted. Moon's Place Nov. 19, 1698, is m, 3°.19', i. e. 7° 3°. 19^ To which add Sum From which fubtract the Sun's Place the fame Remainder is the Moon's Distance from the Sun 12 That is, 6°. 50', the Moon's Place at ten Minutes after Eleven o'clock; to which adding 27' for the Moon's Motion in fifty Minutes of Time, gives 7°. 17' for the Moon's Place at Noon, on the firft of January 1753: And by White's Ephemeris it is 7°.22. |