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These being divided into two Setts os thrce Observatlons, each, ui%. Thetyth, xctb, and iad, and the lyth, xith, and xid, \ve shall have in theHrst tbree, c = i 3, and b~j, r — 3 days, s — 1 i and in the second,.c =

1 y, and b 7, r — 3, and s — a. Whence according to the Rule, the rythday at Noon the Sun wanted os the Tropick a Time Proportionate to oneday, as t1 c — s s b : to ite ■— zb s, that is, as 11 o : to 64 in the firstSett, 01* 107 : to 62. in the second Sett ; that is, t d . 17h. iy'. in the first:,or J d . i" h . 2.y'. in the second Sett: So that \ve may conclude the momentof the Tropick to have been, June icA I “K zo'. in the Meridian os Mar-seille;.

Now that these two Tropical Times thus obtaincd, will be found to con-sirm each others Exactneß from their near Agreement, appears by the Inter-val of Time between them, vi\. i d . i h . 30h leis than 136 Julian Years,whereof i d . i h . 8'. arifes from the Defect of the Length of the TropicalYcar from thc Julian, and the rest from the Progreifion of the Sun’s Apogxonin that time; so that no two Obscrvations made by the fame Observer in theCime place, can better answer each other, and that without any the least Arti-fice or Force in the management of them.

What were the Methods uscd by the Ancients to conclude the Hour of theTropicks, Ptolemy has no where delivered; but it were to have been wilhied,that they had been aware of this, that so we might have been more certainof the Moments of tne Tropicks we have received from them, which wouldhave been of singular use to determine the Question, VVhether the Sun’sApogaon be fixt in the Starry Heaven; or if it move, What is the true Mo-tion thereof ? It is certain, That if we take the Account of Ptolemy , theTropick seid to bc ohservqd by EuElemon and Meton, Junii 2.7. Mane, Ann.431. Ante Christum, can no ways be reconciled, without siipposing thc Obser-vation made the next day, or June 2.8. in the Morning. And Ptolemy % ownTropick, Observed m the third Year of Antoninus, Ann.\christ. 140. was cer-tainly on the 2.zd, and not the x4th day of June, as will appear to tholethat {hall duly consider and compare them with the Length. ot the Year de-duced from the diligent and concordant Observatlons of those two greatAstronomical Genii, Hipparchus and Albatani ; establifhed and confirmed bythe Concurrence of all the Modern Accuracy. For these Observations givethe Length of the Tropical Year, flieh as to Anticipate the Julian Accountonly one day in 300 Years ; but we are now secure, that the seid Period ofthe Sun’s Revolution does Anticipate very nearly 3 days in 400 Years ; sothat the Tables of Ptolemy founded on that Supposition, do Err about awhole Day in the Sun’s Place, for every 2.40 years. Which Principal Er-rour, in so Fundamental a Point, does Vitiate the whole Superstructure ofdie Almageß, and ferves to ConviB its Author of xoant of Diligence, or Fidelity,tr both.

But to return to our Method, the great Advantage we have hereby, is,That any very high Building serves for an Instrument, or the top of anyhigh Tower or Steeple, or eyen any high Wall whatsoever, that may be suf-ficient