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whose poles are the poles of the world. The equator on the earth is the equinoctial, when referred to the heavens. Geocentric place of a Planet.-Its place in the heavens, as seen from the earth.

Latitude of a Planet.-Its distance from, measured by an arc of a circle, drawn perpendicular to, the ecliptic, north or south.

Longitude of a Planet, is its distance in the ecliptic from the first point of Aries as seen from the earth. Horizon. A great circle of the sphere, dividing the earth and the heavens into two equal parts, which are called the upper and lower hemispheres.

Nocturnal Arc.-The arc described by any celestial body from the time of its setting to its rising.

Nocturnal Horary Time, is one-sixth of the star's seminocturnal arc.

Oblique Ascension.-That point of the equinoctial which rises with the centre of any celestial body in an oblique sphere.

Decension.-That point of the equinoctial which sets with the centre of any celestial body in an oblique sphere.

-Sphere, is that position of the globe, when either pole is elevated less than 90°, and consequently the equator and its parallels cut the horizon obliquely.

Right Ascension.-That point of the equinoctial which comes to the meridian with the centre of the sun, a planet, or fixed star, computed from the first point of Aries, or it is that point which rises with any celestial body in a right sphere, and the point which sets with it in like manner, is called its right decension.

Sphere. Is that on which the equator and its parallels cut the horizon at right angles.

N.B. When we speak of the rising, setting, or culminating of any celestial body, we refer to those phenomena occasioned by the diurnal motion of the earth on its own axis, which is the true cause of the apparent motion of the stars from east to west.

Solstitial Points.-Cancer and Capricorn, and the equinoctial points, are the first points of Aries and Libra.

Zodiac.-A belt surrounding the heavens, in the middle of which runs the ecliptic. It contains twelve constella

tions,

Aries, 8 Taurus, Gemini, Cancer, & Leo, my Virgo, Libra, m Scorpio, Sagittarius, Capricornus, Aquarius, and Pisces, which are called the twelve signs of the Zodiac.

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Each sign is divided into 30 equal parts, called degrees, each degree into 60 equal parts, called minutes, and each minute into 60 seconds, and so on to thirds, fourths, fifths, &c.

Abreviations. Sextile; Quartile; A Trine; 8 Opposition; R.A. Right Ascension; A.D. Ascensional Difference; O.A. and O.D. Oblique Ascension and Decension; D.H.T. Diurnal Horary Time; N.H.T. Nocturnal Horary Time; Add; Subtract; = Equal to; < Angle; Long. Longitude; Lat. Latitude; Dec. Declination.

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The student should have a perfect knowledge of the following problems before he proceeds further in the calcula

tory departments of Genethliacal Astrology, as they form the basis on which this ancient science is founded.

Stereographic projection of the sphere, on the plane of the meridian, by a careful attention to which the construction of the following diagrams will be easily understood.

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NADIR.

Construction. With the chord of 60 degrees describe the circle Zenith H, Nadir H, and draw the diameter H H. Take the chord of 53 26, and set it from H to N; then through the centre of the circle draw N A S.

Perpendicular to NA S through A draw E A E. From the points Æ Æ, with the chord of 23.28, set off the points EE, and make n A s perpendicular thereto. Lay the tangent of 23. 28. from A towards N and S, through which points and WW describe the tropical circles D and v D vs. From A to B lay the tangent of 30 degrees, and from A to E that of 60 degrees, through which points and N S describe the circles NB S, NES, &c. The meridians of celestial longitude n K s and n I s

are described in a similar manner, laying the tangent of the required number of degrees, which in the above projection are 45 and 75, from A on the line A towards .

1st. Then will the circle Zenith H, Nadir H, represent the brazen meridian, having its North Pole elevated above the horizon 53. 26.

2d. N. is the North Pole, and S. the South Pole, and NA S the axis of the globe.

3d. Æ A Æ, the Equator. 4th. H H the Horizon.

5th. Zenith A the prime vertical passing through

0° Aries.

6th. A, the Ecliptic, n its north, and s its south Pole.

7th., the tropic of and v vs, the tropic of Capricorn.

8th. H N, the elevation of the North Pole above the horizon = to the latitude of the place.

9th. NE S-N BOS-N KE S, &c.-Meridians of terrestrial longitude.

10th. n K I s―n I ✶ s, &c. are meridians of celestial longitude.

11th. In the right angled triangle A B O-A O is the sun's longitude, or an arc of the Ecliptic, from the first point of Aries. A B, the sun's right ascension, or an arc of the equator, from the first point of Aries. B, the sun's declination, and the angle B A O, is the obliquity of the ecliptic, measured by the arc Æ, Ævs.

12th. In the right angled spherical triangle A B D, A B is the occasional difference, and B A D the complement of the latitude measured by the arc H Æ.

13th. Nn, the obliquity of the ecliptic, or difference between the poles of the equator and the ecliptic.

14th. n K, the complement of the star's latitude I K. 15th. N K, the complement of its declination E K. 16th. The angle N'n K, the complement of the star's longitude.

17th. The supplement of the angle n N K, measured by the arc E = the complement of the star's right

ascension.

N. B. The latitude, declination, &c. of the heavenly bodies are north or south, according as they are si

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