2. If a Direct North Plane recline to the Equator, the Dial will be a Polar one. See Prob. 11. 3. Admit a Direct North Plane recline more than the Equinoctial, fuppofe 70° 00′, in Latitude 51° 32!;

This Dial might be made as the last; but for Variety's fake, I have chose to use two Methods; and therefore the Dial here above is made by a Projection of the Sphere and Plane together on the given Latitude. Whence alfo the Reafon of the Trigonometrical Calculation doth appear.

PROBLEM XX.

To defcribe Hour-Lines on a Direct Eaft or West Reclining Plane.

Practice.

1. Suppose in Latitude 51° 32' a Direct East Plane recline 40° 00'. Then by Prob. 9, you reduce it to

the

the new Latitude 38° 28', and new Declination 50°

by Prob. 17. The Dial fo made will alto fit this Eaft reclining Plane, and is fuch an one as you fee above.

2. Suppofe in the fame Latitude a Direct West Dial recline as much; then is fuch a Dial made alfo by Projection of the Sphere and Plane on the given Latitude, as has been before taught, and is evident in the Scheme following; and the Method by Calculation is evident also in each of thofe Projections.

Note,

Note, In either Dial if the Hour-Lines are drawn through the Center, you conftitute an Eaft and West Incliner, defigned here by the dotted Lines.

You must also obferve in fixing these fort of Dials, to place the Hour-Line of XII precifely parallel to the Horizon, as in all Erect South or North Planes, it is perpendicular thereto.

PROBLEM XXI.

To defcribe Hour-Lines on South Reclining Planes, declining East or West.

Practice.

1. Admit there is a South Plane declines to the East 35° 00', and reclines from the Zenith of London

18° 30'.

By

By Prob. 7, 'twas fhewn that in Latitude 73 451 this would be an erect South Plane declining Eastward 32° 57'; therefore a Dial made for this new Latitude

and Declination, (by Prob. 17,) will be a Dial fitting this reclining Plane. But the new Latitude being fo great, 'tis easier to make this Dial by Projection of the Sphere on the Horizon of the given Latitude, as taught in Prob. 18, Cafe 3. By drawing the reclined Plane AH C, and referring the various Interfections of the Hour-Circles therewith to the Primitive, by a Ruler

Ruler laid from the Pole 2 to each of them; then by a Ruler laid on the Center Z to the Marks XXXX, &c. draw the Hour-Lines required. See the Figure.

2. Suppofe the foregoing Plane recline equal to the Pole; then (by Prob. 7) the Reclination Z H is Q 33 04', and the new Declination E Q is 28° 43′, which (in this Cafe) is alfo equal to the Plane's Difference of Longitude. Alfo in the Triangle Z HP Rightangled at H, there is given Z P = 38° 28', and the Angle at 35° 00'; whence we fhall find the Dif tance of the Subftile from the Meridian HP La = 20° 54'.