Fig. LIX. CHA P. X. Of Direct South and North Declining Plains, and how SUCH Plains as do directly behold the s North the{ Southpoint of the Hrizon, but do Recline (or fall backwards) from the Zenith towards South the th {North}are called { South Direct Plains Reclining : So many Dgrees as the Reclination is: And of fuch Plains there are Six Varieties; Three of South, and Three of North Recliners: All which may be Reduced to New Latitudes, wherein they will be come Horizontal Plains: And confequently Dials (or Hour Lines) may be described upon them both by the Globe, Spherical Projection, and Trigonometrical Calculation, according to the Precepts delivered in the Fourth Chapter hereof. I. Of South Recliners Examples of all thefe Varieties of Reclining Plains, in the La I, Variety. Let there be a Direct South Plain in the Latitude of The Plains Reclination 120 deg. being less then 38 de.. 30 m.. the Complement of the Latitude of London; Subftract 20 deg. from 38 d. 30 m. the Remainder (or difference) 18 de. 30 m. is the New-Latitude. So that an Horizontal Dial made for that Latitude, fhall be a South Recliner 20 deg. in the Latitude of London. II. Variety. If a South Plain in the Latitude of 51 děg. 30 m. fhould Recline 60 deg. from the Zenith thereof: In what Latitude will that be an Horizontal Plain? The Reclination of the Plain 60 deg. being Greater than 38 deg. 30 m the Complement of the Latitude of London, Subftract 3& de. 20 m. from 60 deg. and the Remainder 21 deg. 30 m. is the Nem-Latitude: And an Horizontal Dial ́inade for the Latitude of. 212 Fig. 21 de. 30 m. fhall ferve for a South Dial Reclining 60 deg. in LIX. the Latitude of London. III. Variety. If a South Plain in the Latitude of London fhould Recline from the Zenith thereof 38 d. 30 m. Equal to the Complement of the Latitude of London. Then The Difference between the Complement of the Latitude of London and the Reclination being nothing; it fhews, the New-Latitude to be no Latitude, that is neither Pole hath any Elevation above fuch a Plain: And therefore a Dial for fuch a Plain muft be made in all refpects as an Erect Direct Eaft or Weft Dial is made, by the Precepts in Chapter VII. hereof: Only, the Hour-Line of VI there, muft be the Hour-Line of XII in this: And as the Stile there was equal to the diftance between Six and Three or Nine a Clock. So in this, it must be equal to the diftance between XII and IX or III. And may be either a Plate of that breadth; or a Wyre or Pin of that Length. II. Of North Recliners I. Variety. If a North Plain in the Latitude of 51 de. 30 m. fhould Recline from the Zenith 20 deg. In what Latitude will that be an Horizontal Plain? The Reclination 20 deg. being less than the Complement of the Latitude of London,38 de. 30 m. Add the Reclination 20-de. and the CoLatitude 38 deg. 30 m. together; their Sum 58 deg 30 m. is The New Latitude: And an Horizontal Dial for that Latitude shall be a North Plain Reclining 20 deg. in the Latitude of 51 de. 30 m. IL Variety. If a North-Plain in the Latitude of London, 51 deg. 30 m. fhould Recline from the Zenith 75 deg. In what Latitude will fuch a Plain be Horizontal? Add The Reclination 75 deg. being greater than 38 deg. 30 m. them together, and they make 113 deg. 30 min. which being above 90 deg. take the Complement thereof to 180 deg, which is 66 deg. 30 m. And that is the New-Latitude: So that an Horizontal Dial made for the Latitude of 66 de. 30 m. will be a North Plain Reclining 75 deg. in the Latitude of London 51 deg. 30 m. III. Variety. If a North Plain in the Latitude of London 51 de. 30 m. fhould Recline from the Zenith thereof 51 de. 30 m. In what Latitude will fuchi a Plain be Horizon- Fig. tal? Here, the Reclination 51 de. 30 m. is Equal to the Latitude of London And the Sum of the Reclination 51 de. 30 m. and the ; Complement of the Latitude 38 de. 30 m. Added together, their Sum is 90 deg. for The New-Latitude: And an Horizontal Dial made for that Latitude of 90 deg. (which is no other then a Circle divided into 24 Equal Parts, for the Hours; and a Wyre erected perpendicularly, of any Length for the Stile.). Thefe are all the Varieties of South and North Reclining Plains, Reduced to New Latitudes, wherein they will become Horizontal Plains: So that neither Trigonometrical Calculation, Geometrical Projection, or Operation by the Globe, need be. here Repeated, they being all the fame as in the IVth Chap-ter hereof.. Re Note alfo: That in making of any of thefe North or South Reclining Dials, you have made alfo A Direct Northor South Dial inclining from the Zenith towards the Horizon so many Degrees as is the clination. So that when you have made a South-Dial Reclining from the Zenith 60. deg. (as is the Second Variety of South Recliners in this Chapter) you have made alfo a North Dial inclining to the Ho-rizon 60 degrees, either by drawing of the Hour-lines: and Stile through the Centre; or by turning the Reclining Dial about upon the Hour-line of VI. And then, as the North Pole is elevated upon the South Recliner, fo much will the South Pole be, elevated above the North Incliner, &'c.. LIX.. Of Direct Eaft or Weft Reclining Dials, and how Hour-lines may be defcribed upon them. A S all Direct North and South Reclining Dial Plains were Re-duced to New-Latitudes wherein they would be. Horizontal Plains; and therefore made by the Directions given in the CHAP. IV. hereof: So all Dired Eaft or Weft Reclining Dial Plains 290 Fig. Plains in any one Latitude, may be Reduced to Ered, or Upright, LIX. Declining Plains in another Latitude: and therefore may be made by the Precepts delivered in the VIIIth. CHA P. hereof. Either, I. How to Reduce any Direct Eaft or Weft Reclining Dial Plain And EXAMPLE, Suppose then, that a Direct Eaft or Weft Plain, in the Latitude RULE. The Complement of the known Latitude, is (always) The New- The Complement of the Reclination is (always) The Declination So that if an Eaft or Weft Dial, fhould Recline 40 deg. in the Latitude of 51 d. 30 m. That will be An Upright Plain, Declining 50 deg. in the Latitude of 38 de. 30 m For, .38 de. 30 m. being the Complement of the Latitude of London 51 d. 30 m. is the New-Latitude: And 50 deg. being the Complement of 40 de. the Plains Reclination, is the Declination in the New-Latitude. So that, if (according to the Precepts delivered in the VIIIth. CHA P. hereof) you make an Upright Dial for the Latitude of 38 de. 30 min. to Decline 50 deg. Such a Dial will ferve for an Eaft or Weft-Dial Reclining 40 de. in the Latitude of (London) 51 de. 30 m. Thus for the Making of the Dial. But in the placing of the Dial (thus made) upon the Reclining Plain, this Difference is to be obferved: For, Whereas in all Upright Declining Plains, the Meridian, or Hour-line of XII is always Perpendicular to the Horizon of the Place for which it is made. But But this Declining Plain when it, is applyed to the Reclining Plain, Fig. the Hour-line of XII. muft lie Parallel to the Horizon of the Place, LX. as in the Figure. And here Note, that all Eaft Recliners in the known Lati- ners. And Note farther; That upon all Eaft and Weft Reclining And Laftly, Note that when you have made an Eaft or Weft CHAP. XII. Of Dial Plains that do both Decline and Recline: How HESE Plains may alfo be Reduced to New-Latitudes and T New Declinations, where they may stand as Upright Decli mers: And fo Dials may be defcribed on them, by the Directions in the VIIIth. CHA P. hereof: And to find the New-Latitude, and New Declination of any fuch Plain, The Rules following will direct. EXAMPLE. Suppofe that in the Latitude of London, 51 d. 30 min: A South Plain fhould Decline towards the Eaft or Weft 24 deg. 20 min. And alfo Recline from the Zenith 54 deg. 'I. To find the New-Latitude The Canon for Calculation. As the Radius, Sine 90 de. Is to the Co-fine of the Old Decl. 24 de. 20 m. So is the Co-Tangent of the Reclination 54 d. To a Fourth Tangent, viz. 33 de. 30 m. 10. 9.959596 9.861261 9.820857 This Fourth Tangent being thus found, the Rules following are to be obferved. |