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the Horizontal Distance be the greater, then the Plane declines towards the contrary Coast.
Note, All Declination is from North or South towards East or Weft, and must never exceed go Degrees.
To find the Plane's Reclination from the Zenith.
The Reclination of a Plane is the Quantity of the Arch of that Vertical or Azimuth Circle (which is perpendicular to the Plane, and contained between the z Zenith and the Plane.
>R Angle Z V A, to find which do thus ; on the Plane draw the Horizontal Line A B, which cross at Right Angles with the Line CD; to this Line C D apply a square Staff or Ruler CF; and to that Part of it which hangs off the Plane, as at F, apply a Quadrant as FER, then the Thread and Plummet E P will form an Angle P EF= AV Z ; consequently the Degrees on the Limb of the Quadrant between F and P are the Degrees of the Plane's Reclination, which was fought.
To find the Latitudes, in which a South Direct Reclining Plane shall become an Erect or Horizontal
In this Problem there be three Varieties. For the Reclination may
be either 1. Lefs, 2. Equal to, 3. Greater than the Pole. I shall illustrate each with a proper Scheme. Variety 1. Admit in
B В the Latitude of London a Plane declines from
А the Zenith 30° oor 'cis
P required to find the La Æ titude in which it will be an Erect, and an Hori-zontal one?
In the Scheme let Zb. be the Zenith of London, Lat. 51° 32'; P the L North, and S the South Pole, Æ Q the Equator,
N and HO the Horizon. And let A B be the Plane, given reclining from the Zenith 30° oo'. Then parallel to the Plane A B draw a Tangent to the Meridian, as CD; perpendicular to which draw the Diameter EF, and cross this at Right Angles with the Diameter I G; to the Point G draw the Tangent K L ; then shall the Tangents CD, and K L be, the Horizontal, and erect South Plane, required in the Latitude E and G. But because NTG=VAB = Plane's Reclination = 30°, therefore. QG = 81° 32' is the Latitude in which it will be an erect Plane, and is always ( in this Case ) equal to the Sum of the given Latitude and Reclination. The Complement of which GS = Æ E = 89 28' is the Latitude in which it is an Horizontal Plane, as required ; and in this Case, is always equal to Difference of Co-Latitude and Reclination.
Variety 2. If the Reclination of the Plane be equal to that of the Pole, viz. 38° 28', then it is evident from the Scheme, that the point in the Equinoctial Æ, is that on which such a Plane would be Horizontal. But that point having no Latitude, the Pole would have no Elevation above it ; and fo a Dial described thereon, must be in the Manner of a direct East or West Dial.
Variety 3. Suppose the Plane AB recline from the Zenith 50° oo', which is greater
P than the Poles Reclination. Then CD and LK will be the Hori. zontal and erect Planes 'LH in the Latitudes E and G: But Æ E = P I = 509 oo' - 38° 28' =119 32' = the Latitude for the Horizon
K tal Plane CD; And
N its Complement 78° 28' is the Latitude of the erect Plane ĽK; as required.
To find the Latitudes in which a Direct North Reclining Plane shall be an Horizontal or erect Plane.
Practice. Herë arë likewise three Varieties, for a Plane may recline from the Zenith Less, Equal to, or More than the Equinoctial.
Variety 1. Suppose at London a North Plane reclines from the Zenith 30% oor ; Quere in what Latitudes it will be an Horizontal and erect Plane? VOL. II.
In this Cafe C D will be the Horizontal Plane in the Latitude E ; Now Q E = 20 +0E = 38° 28' + 300 00' = 68° 287 the Latitude for the Horizontal Plane, which here is always equal to the Sum of the Co-Latitude and Reclination, the Complement of which 2. G = 21° 32' =Æ I, is the Latitude in which it will be an erect Plane.
C Variety 2. Admit the Reclination of a Plane be equal to that of the Equinoctial ; 'tis plain in this case the Point P,
H that is, the Pole it felf, will be the Latitude in which such a Plane will be Horizontal, and the erect Plane of Confe
S quence can have no Latitude as being in the Equinoctial it felf.
Variety 3. Suppose a North Plane recline 700 oo', Quere in what Latitudes it will be Horizontal and Erect? Here Æ EN AZ
B В + ZH-ZI= 51
TA 32' 4 900 = 71° 32' the Lati-. tude for the Horizontal Plane ; which is alway ( in this case ) equal to H the Latitude and Co-Re
I clination. Also its Complement EP=180 281 = 2G is the Latitude of the Erect Plane, as required.
To find the Latitude in which a South Reclining Plane Declining East, shall be an Ereet Plane ; and also what Declination it shall there have.
Suppose a Plane in the Latitude of London 51° 32', decline from the South Eastward 35° 00', and recline from the Zenith 18° 30'; In what Latitude shall it be an upright or erect Plane, and what Declination shall it there have ? In the Scheme ad
C joined, let S WNE represent the Hori
N zon; A B the Interfection of the Plane therewith ; CD the Meridian, or Vertical Line of the Plane ; A
B S N the Meridian of the Place ; W E the prime Vertical of East and Weft ;
S AHB the Reclining Plane ; P the Pole ; WP E the Hour Circle of Six; Q the Pole of the Reclined Plane ; and A QB a Circle of Declination passing through the fame ; and W Æ E the Equinoctial.
The Scheme being thus prepared, we are first to find Æ O, or the Arch of the Meridian contained between the Equinoctial and the Reclining Plane, that being the Latitude fought.
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