( 2S7 )

Of this there are two Cases; the one, when the time of thc.second Observa-tion B is precisely in the middle between A apd C : In this Case, putring tfor tlte whole time between A and C, we shall have A c, the Interval of the

renjotest Observation A, front the Tropick, by the following Analogy.

As z /i c — b c : to z * c — j b c :: So is £ r, or A E : to A c, the time ofthe remotest Observation A, from the Tropick.

But the other Case, when the middle Observation is not exactly in themiddle between the other two Times, as at F, is lomething more operose,

and the whole Time from A, to C, being put — t, and from A, to F, = j,

and bc

z t c — zbs

the Time sbught.

To illustrate this Method of Calculation, it may porhaps be requilke tpgive you one or two Examples.

Ann. i 500. Bcrrutrd IValtcr in the month of June at Nuremberg , observet!the Chord of the Distance of tlte Sun from tlte Lenith, by a large Paml-Uflick. Instrument of Ptolemy, as follows:

June Z . 45467.June 9. 449 Z 4 -

June 16. 44990.

June 8. 44975.June 12. 4488z.June 16. ,44990.

June 8. 44975 -

June 12. 4488z.June 16. ,44990.

In both wbich Cases, the Middle Time is exactly in the middle between

Ute Extreams, and «herefore in the former three, ac — yzz, bc — 477,and r, the Time between being 14 days, by tlte first Rule, the Time of theTropick will bc found by this Proportion ; as 589 : to 827s :: So £ r, or7 days : to 9 days, zo h . 2'. Whence the Tropick, Ann. 1 500. is concludedto have fallen June 11 . 20* 1 . z 1 . In the lattcr three, a c is = 107, andl?c 15, and the whole Imerval of Time is 8 days = to t ; whence, as199 : to 2o6i : : so is 4 days to 46. zh. ^ • vhich taken from the i6thday .atNoon, leaves iid. ac* 1 . 23h for the Time of the Tropick, agreeingwhh the fortner to the third part of an Hour.

Agaio, Ann. I 6z6- Gajfendus at Marseilles , observed the Sunutier Sollticcby a Gnomon of 55 Foot high, in order to deterntinc the Proportion of tlteGnomon to the Solstitial Shade, and he bath lest us tbele Ohservations, whichmay ferve as an Example for the Second Rule.

June

St. N. fhadow Parts,whcrcof the Gnomon was 89428,

V 75 9

M m 2

These