TABLE IV. A Table of the Sun's Equation. Sign o. Sign 1. Sign 2. | Sign 3. | Sign 4. Sign 5. Æ. Subj.Æ. Subs. Æ. Subj.Æ. Subj.Æ. Subs. Æ. Subs. A. Add. A. Add. Æ. Add. Æ Add Æ. Add. Æ. Add 11 Sign. 10 Sign. 9 Sign. 8 Sign. 17 Sign. 6'Sign, The T The Use of the Tables. the Ecliptick at any time, by O find the Sun's true Place in From the several Tables, collect the Years, Month, and Day of the Month, and also the odd Hours, if any be, and set them down, one under another, with the respective Longitudes and Anomalies answering thereto: Then add the several Longitudes and Anomalies together, and with the Sum of the Anomalies, enter (Table IV.) of Equations, which Æquation, Add to, or Substrait from, the Sum of the Longitudes, and the Sum or Remainder, shall be the Sun's true Place in the Ecliptick for the time proposed. How Time is to be computed. 1. Any Day begins upon its own Noon; so that the First Day of January, at 12 at Noon, is the common Term of the Old and New Years. Example. Let the true Place of the Sun in the Ecliptick be required, for the 16th Day of May, in the Year of our Lord 1703. at 5 in the Afternoon. First, Set down the Year 1703. then the Month and Day, May 16; and lastly, the Hours, 5, as is here due. Secondly, Look for 1703. (in Table I.) againft which stands 9 S... 10 D. 14 M. for the Longitude; and 6 S. 12 D. 46 M. for the Anomaly; both which set down as here you fee. Thirdly, Look for May 16. (in Table II.) against S. D. M. S. D. M. Year 1703. Hour 5 Mean Lon. Æquat. Add. which stands 4 S. 14 D. true Place. 3 M. for the Long. And 4S. 12 D. 2 M. for the Anomaly; both which fet under the for mer, as you fee. Fourthly, Look for 5 Hours (in Table III.) against which stands 12 Minutes, both for the Longit. and Anomal, both fet down, as you fee. Fifthly, Fifthly, Add all the Longitudes together, and they make 14 Sig. 04 Deg. 29 Min. (from which abate 12 Signs, and there remains only Two Signs.) - Also Add the Anomalies together, and they make to Sig. 25 Deg. 00 Min. Sixthly, (in Table IV.) Look for 10 Signs at the Bottom of the Table, and 25 Deg. in the laft Column towards the Right Hand, so against it, over 10 Signs, you shall find I Deg 6 Min. to be Added. Set them under the Mean Longitude, and add them to it, so will the Sum be 2 Sig. 05 Deg. 35 Min. And that is the true Place of the Sun in the Ecliptick, which is 35 Deg. diftant from the Equinoctial Point Aries. Note, that Signs o I 2 3 4 5 6 7 8 9 IO II In all the Problems in this Section, it is to be understood, That (in all the Spherical Schemes, or Figures following. Pole of the World. Equinoctial Circle, or Æquator. Parallels (or smaller Circles) of Declination of the Sun, or of a Star. Pole of the Ecliptick. Ecliptick. Parallels (or lesser Circles) of Altitude of the or Country. Vernal 2 Interfection of the Ecliptick and A- quator. of any Point of the Ecliptick. Prime Vertical Circle, or Azimuth of East and East Pole of the Meridian: Or the Place in the Horizon, where the Sun, or a Star, Rifes or Sets. Right Angle... Star. Side, Sun (and sometimes) Star. North Latitude, Declination, Amplitude. R. A. P. T. Right-angled O. A. P. T. Oblique-angled R. A. S. T. Right-angled O. A. S. T. Oblique-angled Plain Triangles. Plain Triangles. Aftrono Astronomical Problems. PROBLEM I. The Longitude, or Place of the Sun, in the Ecliptick, being given; To find, I 1. The Sun's Right Afcenfion. 2. The Sun's Declination. 4 3. The Angle of Position made by the Intersection of the N this Problem there is given the Sun's or a Star's Place, the Equinoctial, is required, I. By the Cœleftial Globe. Example. Let the Place of the Sun be in 29 Deg. of Taurus 8, (that is, 59 Deg. from the beginning of Aries V, which is the nearest Equinoctial Point.) The Globe being in any Position, (for in this Problem there is no regard to be had to the Latitude) count the Sun's Place in the Ecliptick upon the Ecliptick Circle, from r; and bring that Point to the Graduated Side of the Brass Meridian. Then, (1.) Will the Brass Meridian cut the Equinoctial Circle in 56 d. 46 m. counted also from r; and that is the Right Afcenfion. And, (2.) The Number of Degrees of the Brass Meridian, comprehended between the Equinoctial and Ecliptick Circles, will be 20 d. which is the Sun's Declination. -And, (3.) The Angle made by the Interfection of the Brass Meridian, and the Ecliptick Circle in the Point of the Sun's Place, will be 77 d. 23 m. which is the Angle of Position, in respect of the Meridian and Ecliptick. II. By Trigonometrical Calculation. 1 The Globe being in this Position, there is represented upon the Superficies thereof, Two Right-angled Spherical Triangles, fuch as are expressed in the Diagrams; and are there noted Fig. with OR and R; in which, the SidesrandXXVII. are Arches of the Ecliptick Circle, and is the Sun's Longitude: XXVIII, Hh2 The |