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The Motion of Venus, according to Weaver's Ephemeris
1744, from the twenty-first of December to the End, and
the Year 1745, from the firft of January to the twenty-ninth
of March inclufive, compared with the first three Months of
this prefent Year 1753, according to White's Ephemeris.
1745. 1753. 1745. 1753.
January. February February.
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1744. 1753. December. January.

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March.

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Mercury's Motion, according to Gadbury's Ephemerides, from the twenty-fecond of December 1673 to the twenty-firft of March 1674, (there having twenty Leap-Years intervened) compared with the first three Months of the prefent Year 1753, according to White's Ephemeris.

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Venus's Motion for the first three Months of the Year 1668, according to Wing's Ephemerides, compared with the first three Months of the Year 1747, according to Weaver's Ephemeris. But, there having been twenty Leap-Days betwixt January 1668 and January 1747, the fecond of January in the former correfponds with the first in the latter, which continues to the twenty-ninth of February 1668, which anfwers to the twenty-eighth in 1747.

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1668. 1747. February. January. in

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1668. 1747. March. March.

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The Differences appear, by thefe Examples, to be but small, and may be allowed for, according to what each Example fhews to be requifite. And, as to the Place of the Sun, that is well known to be the fame, taking a Cycle of four Years, on Account of the Leap-Years. So that the Sun's Place for four fucceffive Years will ferve for a Century, adding one Minute and thirty-fix Seconds for every Cycle of four Years. And when, at the End of a Century, the Leap-Year is omitted, the Cycle must be made four Years and one Day.

Of Mr. Whifton's Cycle for Eclipfes.

The moft ufeful Cycle for Eclipfes is that published by Pliny, of two hundred and twenty-three Lunations, which are made in eighteen Years, eleven Days, feven Hours, forty-three Minutes, and fifteen Seconds. By Reafon of a Mistake of a Figure in Pliny's Book, it being two hundred and twenty-two inftead of two hundred and twenty-three, this Cycle had been taken no Notice of. Moft of his Readers finding it, by Trial, to be a Mistake, enquired no farther. But the great Dr. Halley, prefuming on the Sagacity of Pliny, made farther Enquiry, and found out the Miftake. Perceiving the Ufefulness of this Cycle, he looked on it as a valuable Discovery, and, I fuppofe, intended to publish it to the World. In the mean Time, Mr. Whiston learning the Doctor had made a Discovery of a Cycle for Eclipfes, and that he called it the Chaldean Saros, he recollected that Pliny had made Ufe of that Word, and thence began to fufpect the Doctor had his Cycle from thence. On fearching Pliny, and finding the Number wrong, he foon found out the Miftake, as Dr. Halley had done before, and immediately published it. In this Cycle, the mean Motion of the Moon from the Sun is entire Revolutions, and the other mean Motions are nearly fo: Hence the Eclipfes of the Sun and Moon, in this Period, return with nearly the fame Circumftances, except what arifes from the Excefs above equal Days. I fhall fet down the mean Motions from Mr. Whiffon.

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From the mean Motion of the Apogee
Subtract that of the Moon in the Ecliptic

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Thus the Difference of the mean Motion of the Apogee from that of the Moon is but 2°. 51. 28", which is about of the whole Difference of 180°: That of the Node is but 28.44", or TT Part of the whole Difference: And the mean Motion of the Sun differs little more than of the entire Difference. Which Quantities, being but fmall, cannot occafion any great Variations in the Time or Circumftances of the Change or Full of the Moon, or even in Eclipfes, which will therefore return nearly the fame in different Periods.

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The Limits for Eclipfes are, for Lunar Eclipfes 11°. 40, or 700, on each Side of the Node; and for Solar Eclipfes 16.40', or 1000', on each Side. If we divide 700' by 28.16 we fhall have 25 for the Number of Periods after a central Eclipfe of the Moon in either of the Nodes, before the Moon gets clear of the Earth's Shadow entirely; that is, 450 Years, for 18, being multipled by 25, produces 450; and it is double that Time, or 900 Years, from the Moon's firft getting within the ecliptic Limits on one Side of the Node, before the gets clear on the other. And if 1000', the Limits of Solar Eclipfes, be divided by 28. 16, we fhall have 35 for the Number of Cycles after a central Eclipfe of the Sun in

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