the Horizontal Distance be the greater, then the Plane declines towards the contrary Coaft.

Note, All Declination is from North or South towards Eaft or Weft, and must never exceed 90 Degrees.

PROBLEM IV.

To find the Plane's Reclination from the Zenith.

Practice.

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 Zenith and the Plane.

Z

Sugpofe VAC BD be a Reclining Plane, the Quantity V of its Reclination will be the Angle Z VA, to find which do thus; on the Plane draw the Horizontal Line A B, which cross at Right Angles

B

with the Line CD; to this Line C D apply a fquare Staff or Ruler C F; 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 E FAVZ; confequently the Degrees on the Limb of the Quadrant between F and P are the Degrees of the Plane's Reclination, which was fought.

PROBLEM V.

To find the Latitudes, in which a South Direct Reclining Plane fhall become an Erect or Horizontal

one.

Practice.

Practice.

In this Problem there be three Varieties. For the Reclination may be either 1. Lefs, 2. Equal to, 3. Greater than the Pole. I fhall illuftrate each with a proper Scheme.

Variety 1. Admit in the Latitude of London a Plane declines from the Zenith 30° oo' 'tis required to find the Latitude in which it will be an Erect, and an Horizontal one?

In the Scheme let ZD. be the Zenith of London, Lat. 51° 32'; P the L. North, and S-the South Pole, E Q the Equator, and HO the Horizon.

And let AB be the Plane, given reclining from the Zenith 30° 00'. Then parallel to the Plane AB draw a Tangent to the Meridian, as CD; perpendicular to which draw the Diameter E F, and cross this at Right Angles with the Diameter I G; to the Point G draw the Tangent K L; then fhall the Tangents C D, and KL be the Horizontal, and erect South Plane, required in the Latitude E and G. But becaufe NTG VAB Plane's Reclination 30°, therefore 2G 81° 32′ is the Latitude in which it will be an erect Plane, and is always (in this Cafe) equal to the Sum of the given Latitude and Reclination. The Complement of which GSEE 89 28' is the Latitude in which it is an Horizontal Plane, as required; and in this Cafe, is always equal to Difference of Co-Latitude and Reclination.

Variety

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 fuch 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 Eaft or Weft Dial. VI -B

Variety 3. Suppose the Plane AB recline from the Zenith 50° oo, which is greater than the Poles Recli

IN

its Complement 78° 28' is the Latitude of the erect Plane LK; as required.

PROBLEM VI.

To find the Latitudes in which a Direct North Reclining Plane fhall be an Horizontal or erect Plane.

Practice.

Here are likewife three Varieties, for a Plane may recline from the Zenith Lefs, Equal to, or More than the Equinoctial.

Variety 1. Suppofe at London a North Plane reclines from the Zenith 30° 00; Quere in what Latitudes it will be an Horizontal and erect Plane?

VOL. II.

U u

In

In this Cafe CD will be the Horizontal Plane in the Latitude E; Now Q E = 20 +0 E = 38° 28′+ 30° 00' 68° 28′ the Latitude for the Horizontal Plane, which here is always equal to the Sum of the Co-Latitude and Reclination, the Complement of which 2G 21° 32'

=

in this Cafe the Point P, H
that is, the Pole it felf,
will be the Latitude in
which fuch a Plane will
be Horizontal, and the
erect Plane of Confe-
quence can have no La-

B

C

E

L

G

S

K

titude as being in the Equinoctial it felf.

Variety 3. Suppofe a North Plane recline 70° 00', Quere in what Latitudes it will be Horizontal and

Erect?

PROBLEM VII.

To find the Latitude in which a South Reclining Plane Declining Eaft, fhall be an Erect Plane; and alfo what Declination it fhall there have.

Practice.

Suppose a Plane in the Latitude of London 51° 32o, 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 fhall it there have?

WPE the Hour Circle of Six; 2 the Pole of the Reclined Plane; and AQB a Circle of Declination paffing through the fame; and WE 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.

VOL. II.

Uu 2

Now