225

Of Dialing .

for the hour-line of IIII: and so of the rest.—The forenoon hour-lines are drawn the fame way, by the continua! addition of the tangents15 0 , 3°°> 45°> öcc. to 42 0 52' (=the tangent of KM) for the hoursof XI, X, IX, &c. as far as neceffary; that is, until there be sive hourson each side of the fubstile. The sixth hour, accounted from thathour or part of the hour on which the fubstile falls, will be alwaysin a line perpendicular to the fubstile, and drawn through theCenter C.

4. In all erect dials, CM, the hour-line of XII, is perpendicularto the horizon of the place for which the dial is to ferve : for thatline is the interfection of a vertical plane with the plane of theMeridian of the place, both which are perpendicular to the plane ofthe horizon: and any line HO, or bo , perpendicular to CM, willbe a horizontal line on the plane of the dial, along which line thehours may be numbered; and C M being fet perpendicular to thehorizon, the dial will have i t ts true position.

5. If the plane of the dia^had declined by an equal angle towardthe east, its defcription would have differed only in this, that thehour-line of XII would have fallen on the other side of the fubstile CL ,and the line HO would have a fubcontrary position to what it has i«this figure.

6. And thefe two dials, with the upper points of their stiles turned

toward the north pole, will ferve for other two planes parallel to

them ; the one declining from the north toward the east, and the

other from the north toward the west, by the fame quantity of

angle. The like holds true of ali dials in general, whatever be their

declination and obliquity of their planes to the horizon.

CASE II.

7. If the plane of the dial not only declines , but also reclines , or Fig. 3.inclines. Suppofe its declination from fronting the fouth S be equal

to the are § O on the horizon; and its reclination be equal to thearc Dd of the vertical circle HZ: then it is plain, that if thequadrant of altitude ZdD , on the globe, cuts the point D in thehorizon, and the reclination is counted upon the quadrant from Dto d the interfection of the hour-circle P R d, with the equinoctialW£>JB, will determine R d , the latitude of the place d, whofe horizonis parallel to the given plane at Z ; and Rg^ will be the difference inlongitude of the planes at d and Z.

G g Trigonos