whose horizon is parallel to that surface. Thus it appears that SP, which is the co-latitude of London, is the latitude of the place whose horizon is represented by the plane ADCB: for, let the south pole of the globe be elevated 38 degrees above the southern point of the horizon, and the point Aries be brought to the brass meridian; then, if the globe be placed upon a table, so as to rest on the south point of the wooden horizon, it will have exactly the appearance of Fig. 5, Plate II.; the wooden horizon will represent the opaque plane ADCB, the south point will be at B, and the north point at D, under London, the east point at C, and the west point at A. Hence, we have the following

Rule for performing the problem.-If the place be i north latitude, elevate the south pole to the complement of that latitude: bring the point Aries to the brass meridian; then, supposing meridians to be drawn through every 15° of longitude, eastward and westward fron the point Aries (as is generally the case ;) observe where these meridians intersect the horizon, and note the number of degrees between each of them; the arcles between the respective hours will be equal to these de grees. The dial must be numbered XII at the brass meridian, thence XI, X. IX, VIII, VII, VI, towards the west, for morning hours; and I, II, III, IV, V, VI, towards the east, for evening hours. As the sin cannot shine longer upon such a dial as this, than from VI in the morning to VI in the evening, the hourlines need not be extended any father.

Example. To make a vertical dial for the latitude of London.

Elevate the south pole 383 degrees above the horizon, ar bring the point Aries to the brass meridian; then the meridians will intersect the horizon, reckoning from the south towards theeast. in the following degrees; 9° 28′, 19° 45', 31° 54′, 47° 9′,56° 49′, and 90°, for the hours I, II, III, IV, V, VI; or, if you cant from the east towards the south, they will be 0°, 23° 18', 49′ 51', 58° 6', 70° 15', 80° 32', for the hours VI, V, IV, III, II, I. The distances from XII to VI in the forenoon are exactly the sme as the distances from XII to VI in the afternoon. The following table, calculated by spherical trigonometry, contains not only the hour arches, but the halves and quarters from XII to VI.

The above table is calculated exactly in the same manner as that in the preceding problem, using the complement of the latitude instead of the latitude.

The student will recollect, that the time shewn by a sun-dial is nt the exact time of the day, as shewn by a watch or clock (see Detnitions 55, 56, and 57, pages 12 and 13.) A good clock measures time equally, but a sun-dial (though used for regulating clocks and watches) measures time unequally. The following table will shew to the nearest minute how much a clock should be faster or slower than sun-dial; such a table should be put upon every horizontal sun-dal.

Hour Angles.

Hour Arches.

Dials may be constructed on all kinds of planes, whether horizontal or inclined: a vertical dial may be made to face the south, or any point of the compass; but the two dials already described are the most useful. To acquire a complete knowledge of dialling, the gnomonical projection of the sphere, and the principles of spher ical trigonometry, must be thoroughly understood; these prelimi nary branches may be learned from Emerson's Gnomonical Proje.co tion, and Keith's Trigonometry. The writers on dialling are very numerous; the last and best treatise on the subject is Emerson's.

CHAPTER II.

Problems performed by the Celestial Globe.

PROBLEM LXV.

To find the right ascension and declination of the sun,*

or a star.

Rule. Bring the sun or star to that part of the brass meridian which is numbered from the equator towards the poles; the degree on the brass meridian is the declination, and the number of degrees on the equinoctial, between the brass meridian and the point Aries, is the right ascension.

OR, Place both the poles of the globe in the horizon, bring the sun or star to the eastern part of the horizon; then the number of degrees which the sun or star is northward or southward of the east, will be the declination north or south; and the degrees on the equinoctial, from Aries to the horizon, will be the right ascension.

Examples. 1. Required the right ascension and declination of a Dubhe, in the back of the great Bear? Answer. Right Ascension 162° 49′, declination 62° 48′ N. 2. Required the right ascensions and declinations of the following stars ?

y, Algenib, in Pegasus. B, Rigel, in Orion.

Scheder, in Cassiopeia., Bellatrix, in Orion. B, Mirach, in Andromeda., Betelguese, in Orion. a, Acherner, in Eridanus., Canopus, in Argo Navis. a, Menkar, in Cetus.

B, Algol, in Perseus.
a, Aldebaron, in Taurus.
a, Capella, in Auriga.

a, Procyon, in the Little Dog.
y, Algorab, in the Crow.
a, Arcturus, in Bootes.
, Vendemiatrix, in Virgo.

* The right ascensions and declinations of the moon and the plan. ets, must be found from an ephemeris; because, by their continual change of situation, they cannot be placed on the celestial globe, as the stars are placed.

PROBLEM LXVI.

To find the latitude and longitude of a star.*

Rule. Place the upper end of the quadrant of altitude on the north or south pole of the ecliptic, according as the star is on the north or south side of the ecliptic, and move the other end till the star comes to the graduated edge of the quadrant; the number of degrees between the ecliptic and the star is the latitude; and the number of degrees on the ecliptic, reckoning eastward from the point Aries to the quadrant, is the longitude.

Or, Elevate the north or south pole 664° above the horizon, according as the given star is on the north or south side of the ecliptic; bring the pole of the ecliptic to that part of the brass meridian which is numbered from the equinoctial towards the pole; then the equinoctial will coincide with the horizon; screw the quadrant of altitude upon the brass meridian over the pole of the ecliptic; keep the globe from revolving on its axis, and move the quadrant till its graduated edge comes over the given star: the degree on the quadrant cut by the star is its latitude; and the sign and degree on the ecliptic cut by the quadrant shew its longitude.

Examples. 1. Required the latitude and longitude of a Aldebaran in Tauras?

Answer. Latitude 5° 28′ S. longitude 2 signs 6° 53′; or 6a 53' in Gemini.

2. Required the latitudes and longitudes of the following stars?

Markab, in Pegasus. B, Scheat, in Pegasus.

Ja, Vega, in Libra.
Rastaben, in Draco.

Fomalhaut, in the S. Fish.ja, Antares, in the Scorpion.

Ja, Arcturus, in Bootes.

18, Pollux, Gemini.

8, Rigel, in Orion.

* The latitudes and longitudes of the planets must be found

from an ephemeris.

M m