PROBLEM VIII.

To rectify the Globe for the Latitude, Zenith, and Sun's place.

1. For the Latitude: Elevate the pole above the horizon, according to the latitude of the place.

2. For the Zenith: Screw the quadrant of altitude on the Meridian at the given degree of latitude, counting from the equator towards the elevated pole.

3 For the Sun's place: Find the sun's place on the horizon, and then bring the same place found on the ecliptic to the meridian, and set the hour index to twelve

at noon.

Thus, to rectify for the latitude of London on the 10th day of May, the globe must be so placed, that the north pole shall be 5 degrees above the north side of the horizon, then 51 will be found on the zenith of the meridian, on which the quadrant must be screwed. On the horizon the 10th of May answers to the 20th of Taurus, which find on the ecliptic, and bring it to the meridian, and set the index to twelve.

Rectify the globe for London, Petersburg, Madras, Pekin, Oporto, Venice, Quebec, Port Mahon, Vienna, Dantzic, and Corinth, for the 24th of February, 27th of June, and the 6th of August.

PROBLEM IX.

To find at what hour the Sun rises and sets any day in the year, and also upon what point of the Compass.

Rectify for the latitude and sun's place, (Prob. vIII) and turn the sun's place to the eastern edge of the hori zon, and the index will point to the hour of rising: then bring it to the western edge of the horizon, the index will shew the setting

Thus, on the 16th of March the sun rises a little after six, and sets a little before six in the evening.

What time does the sun rise and set at Petersburg, Naples, Canton, Dublin, Gibraltar, Teneriffe, Boston, and

Vienna, on the 15th of April, the 4th of July, and the 20th of November?

NOTE. On the 21st of March the sun rises due east, and sets due west; between this and the 21st of September, it rises and sets to the northward of these points, and in the winter months to the southward of them When the sun's place is brought to the eastern or western edge of the horizon, it makes the point of the compass upon which it rises or sets that day.

PROBLEM X.

To find the length of the day and night at any time in the

year.

Double the time of the sun's rising, which gives the length of the night: double the time of his setting, which gives the length of the day.

Thus on the 25th of May, the sun rises at London about four o'clock, and sets at eight. The length of the night is twice four, or eight hours: the length of the day is twice eight, or sixteen hours.

PROBLEM XI.

To find all the places to which a Lunar Eclipse is visible at any instant.

Find the place to which the sun is vertical at that time, and bring that place to the zenith, and set the index to the upper twelve, then turn the globe till the index points to the lower twelve, and the eclipse is visible to every part of the earth that is now above the horizon.

OF THE CELESTIAL GLOBE.

As the terrestrial globe, by turning on its axis, represents the real diurnal motion of the earth; so the celestial globe, by turning on its axis, represents the apparent motion of the heavens.

The nominal points of Aries and Libra are called the equinoctial points, because when the sun appears to be in either of them, the day and night are equal.

The nominal points of Cancer and Capricorn are called solstitial points, because when the sun arrives at either of them, he seems to stand still, or to be at the same height in the heavens, at twelve o'clock at noon, for several days together.

Definition. The latitude of the heavenly bodies is measured from the ecliptic north and south. The sun, being always in the ecliptic, has no latitude.

Def. The longitude of the heavenly bodies is reckoned on the ecliptic, from the first point of Aries, castward round the globe. The longitude of the sun is what is called, on the terrestrial globe, the sun's place.

PROBLEM I..

To find the Latitude and Longitude of any given Star.

Put the centre of the quadrant on the pole of the eclip. tic, and its graduated edge on the given star; then the arch of the quadrant, intercepted between the star and the ecliptic, shews its latitude: and the degree which the edge of the quadrant cuts on the ecliptic is the degree of it longitude.

Thus the latitude of Regulus is 0° 28′ N. and its longitude nearly 147°.

PROBLEM 11.

To find any place in the heavens, by having its latitude and longitude given.

Fix the quadrant, as in the last problem; let it cut the longitude given on the ecliptic; then seek the latitude on the quadrant, and the place under it is the place sought. Thus, if I am asked what part of the heavens that is, whose longitude is 66° 30' and latitude 5° 30′ S. I find it is that space which Aldebaran occupies.

Def. The declination of any heavenly body is measured upon the meridian from the equinoctial.

PROBLEM III.

To find the declination of the Sun or Stars.

Bring the sun or star to the brazen meridian, and then as far as it is in degrees from the equinoctial is its declination. Thus the sun's declination, April 19, is 11° 19' north. On the 1st of December it is 21° 54′ south.

What is the declination of the sun on the 10th of Feb. ruary; and the 15th of May ?

Def. The right ascension of any heavenly body is its distance from the first meridian, or that which passes through the first point of Aries, counted on the equinoctial

CONSTRUCTION OF MAPS.

There are four methods of representing the Earth's surface, viz. the Orthographic, the Stereographic, the Globular, and Mercator's Projections; all of which have their respective advantages and defec's. The two latter methods approach nearest the truth, and are most generally in use.

Globular Projection. The Globular Projection of the Sphere exhibits its surface by means of curve lines called Circles of Longitude, and Parallels of Latitude.

Mercator's Projection. Mercator's Chart exhibits the projection of the two hemispheres, laid down upon a plane, with all the circles of latitude and longitude projected into straight lines. The lines of longitudes are all equidistant, and parallel to each other; the lines of latitude are also all parallel, but not equidistant.

PROBLEMS.

1. To divide a given line into two equal parts.

Let A B, fig. 1, be the given line. With the points A and B as centres, with any distance in the compasses greater than half A B, describe the arcs intersecting each other in m and n.