( ?66 )

Tofini tbtS-St XIX. It nuy perhaps paß for a Paradox, if I fhould affert, That k Is anTroflcds&s ; Easier matter to be affured of the Moments of tbe Tropicks, or of the Timesb y Mr. Edm. of the Sun’s entrance into Cancer and Capricortt, than it is to observe the trueHallcy. Times of the Tquinoctials or Ingrels into Aries and Libra. . But I here de*

^ 1 sign to fhcw a Mcthod to find the Moment of the Tropkkj capable of allthe exactneß the mofl Accurate can desivf ; and that without any considera*tton of the Parallax of the Sun, ot the Hefractlons of the Air, of the greatestObliquity of the Ecliptick, or Latitude of the place : Ali which are required,to afeertain the Times of the Equinoctials from Observation; and which be»ing faultily alTumed, ha ve occafioncd an Error of near ihr« Hours in the'l imes of the Equinoctials deduced from the Tables of the Noble Tjcho Brakeand Kspler, the Vernal being so much later, and the Autumna! so much ear-lier than by the Calculus of these famous Authors.

Now before we proceed, it will be necessary to premife the following Lem-mata, Icrving to demonstrate this Method; vt\.

i. That the Motion of the Sun in the Ecliptick, about the Time of theT ropickj, is so nearly Equablc, that the Difference from Equality is not sensi-ble, from y gr. before the Tropick to y days aster, by rcason of the near-nels of the Apogtcn of the Sun to the Tropick of Cancer.

x. That for 5 Deg. before and aster the Tropicks, the Differences wherebythe Sun falls (bort of the Tropicks, are as the Versal Sines of the Sun’s Dirstance in Longitude from the Tropicks, which Versed Sines in Arches under 5Degrees, are beyond the utmost Nicety of Senie, as the. Squares of thoseAjches. From these two follow a third.

5. That for 5 days before and aster the Tropicks, the Declination of theSun falis fhort of the utmost Tropical Declination, by Spaces which are inDuplicate Proportion, or as the Squares of the Times by which the Sun iswanting of, or past, the Moment of the Tropick.

Hence, it is evident, That if the Shadows of the Sun* either in the Me-ridian, or any other Azimuth, be carefully observed, about the time of theTropicks, the Spaces whereby the Tropical Shade falls (hört of, or exceedsthole at other times, are always proportionable to the Squares of the Intervalsof Time between those Observations and. the true Time of the Tropick, andGonlequently if the Line, on which the L «imita of the Shade is raken, be madethe Axis, and the correlpondent Times from the Tropick Exp.ounded by Lines,be erected on their refpective Points in the Axis as Ordinäres, the exmemitiesof those Lines fliall touch the Curve of a Parabola •- Thus a , />, c, c,feeing supposed Points observed, the Lines a B, b C, c A, cF, are respectivelyProportional to the Times of each OWervation before or. aster the TropicalMoment in Cancer.

Thiß premised, we Ihall be able to bring the Problem of finding the true.( Ttme of the. Tropick by three Oblervatioas, to this Georaenical one :Kaving three Point» in a Parabola. A,. B, C, oc A, F, C, gi-sen, fogether vssitb theDirciiion of the Asis* to find the Distance of those Points from the Axis..