Fig. To find the Side Y X, or the Distance of the Sign of the XIth Houfe from the Vernal Equinox. By Cafe IV. of R. A. S. T. XLVIII. But it will be fufficient to count the Signs of the Oriental Houfes: For those which are oppofite to them, (as the IVth to the Xth, the Vth to the IXth, &c.) are counted as many Degrees and Minutes as the others; but of an Oppofite Sign. Example, Let it be required to Erect a Scheme of the Heavens, The Place of the Sun then was in 27 d. 54 m. x. The Time 16 h. 5 m. turned into Degrees, gives 241 d. 15 m. D. M. The Oblique XII 29 29. II 45 8 But because the IVth House is oppofite to the Xth House, it will have as many Degrees and Minutes upon the Cufpis thereof, but of the oppofite Sign, viz. II, and the Vth the fame as the XIth, viz. 15 d. 15 m. of the oppofite Sign, п. The VIth 1 d. oo m. The VIIth 29 d. 27 m. of. The VIIIth 28 d. 46 m. of m. The IXth 11 d. 45 m. of m. As may be seen in the Ereled Fig. XLIX. I. PROB. II. How to Direct any Point of an Erected Scheme to any other Point. THE HE Point that is Directed is called, otherwife, the First Fig Place, or Significator: But that to which we direct it, XLIX. the Second Place, or the Promiffor: But the Significators are directed whither they tend: Directed, that is, Going according to the Series of the Signs; but Retrograde in Antecedens, or against the Succeffion of the Signs. 2. Let Fig. L. III. IV. 2. Let the Pofition made by any direct Significator, or by the Promiffor to which the Retrograde is Directed, be called the Horizon of a Star: And it is either a right one, paffing through both the Poles, as the Meridian; or an Oblique one, having One of the Poles elevated. 3. The Oblique one is, fometimes, the fame as the Horizon of the Place; and confequently, the Elevation of the Pole is the fame: But, when it is different (which moft commonly happens) you must first enquire how much One of the Poles is Elevated above the Horizon of the Star: But if a Star be Oriental, North,) Fig. I. Occidental, With Decli-South, As in Fig. II. In the Triangle POS, or PHS, for the Situation of the Star above or below: There is Given, 1. The Side P O, or P H, the Elevation of the Pole at London, 51 d. 30 m. 2. The Side P S, the Complement of the Star's Decli nation. 3. The Angle S P O, comprehended between them (whofe Measure is the Arch of the Equator, which is intercepted between the Sides PO (PH) PS: One of which being produced, fhews the Right Afcenfion of the Star; the other, the Right Afcenfion of Imum Cali. Required, The Angle P OS, or P HS. By Cafe III. of R. A. S. T. Again, In the Triangle R P O, or R P H, (which are in different Hemifpheres, when O or H (before found) are greater than a Quadrant or 90 d.) There is Given, (1. PO or P H, the Elevation of the Pole. befides the 2. The Angle O or H, before found, (which Right Angle if it exceeds a Quadrant, is Complement to 180 d. at R, To find R P, The Elevation of the Pole above the Horizon of the 4. Having found the Elevation (by the Third beforegoing) then look COriental, the Afc. Fig. L. when the Horizon hath any Star that is Occidental, the Obl. I. II. both of the Significator and Promiffor. Defcenfion 5. Having Promiffor, to whom the Afcenfion or Defcenfion found out the Retrograde is Directed, for the Horizon of the Star: Let the Right one, or the Oblique one, be fubftracted from the like Afcenfion or Defcenfion of the other Star (adding 360 d. if Need be) the Remainder is the Ark of Direction fought for. PROB. III. The Ark of Direction of any Significator being given, To find how far it will reach. Converfe of the foregoing. Therefore look for the Elevation of the Pole above the Horizon of a Dire Significator,as before, and at that Elevation you will get (by the 3d.) S the Oblique {Defcenfion} Occidental, S } to which Defcenfion add the given Ark of Direction, fo will Afcenfion Afcenfion. you get the Oblique Denon To which find what Degree of the Ecliptick anfwers (being counted from the Elevation of the Pole above the Horizon of the Significator) which is the very Place to which the Ark is Direded, and to which the Significator will come. But fubftract the Ark of Diredion given, from the Right Afcen- fion of the Retrograde Significator, and there will remain the Degree of the Equator, which is found out by the Retrograde Significator, by Direction, tending to the Promiffor: The Circle of Pofition paffing through this Degree (which ought well to be obferved) will be the Horizon of the Promiffor: Above which, find the Elevation of the Pole, as before: For, if that Degree fall North, Fig. I. 2 Eastern Part of Heaven, the Weftern } on the South, Fig. II. S the Significator inclining unto the North, Fig. III.2 in the Triangle For III. IV. Fig. L. For the Situation of the Degree obferved, whether Above of Below. From the given Angles, as above, (the Angle P being counted in the Equator, not from the Right Afcenfion of the Significator, but from that Degree which hath, oftentimes, been taken notice of, as that at the Medium or Imum Cali) I feek for the Angle Oor H. And moreover, in the other Triangle, R P, the very Eleva tion of the Pole above the Horizon of the Promissor: At this Elevation of the Significator, if you obferve that Degree Oriental ? Afcenfion. you will gain the Oblique Denon. From which take the given Ark of Direction, and the Remainder will be the Oblique Afcenfion, to which the Degree of the Ecliptick anfwers, (but it must be counted from the Elevation of the Pole above the Horizon of the Promiffor) and is the very Place, to which the Significator will come, by this Ark of Direction given. Defcenfion, The End of the Aftronomical Problems. A N |