Although the student may certainly discover the chief events of his life by the foregoing methods; yet as some persons may deem this work incomplete without it, we will give the problems for calculating these celestial arcs.

Directions termed zodiacal, are nothing more than the intercepted arcs between certain significators, as before observed; and are easily calculated by a skilful arithmetician.

Problem 1. To find the right ascension of a star, without latitude.

Rule. - -Add the co-sine, of its longitudinal distance from the nearest equinoctial point, to the arithmetical complement of the cosine of its declination, the sum will be the co-sine of its right ascension from that point whence the distance was taken.

If the star be in or , the arc thus found will be the R. A.

But if it be in or , it must be subtracted from 180°. If in or , it must be added to 180°. If in or , the arc thus found must be subtracted from 360°.

Problem 2. - To find the R. A. of a star, with latitude.

Rule. - As the co-sine of the star's declination is to the cosine of its longitudinal distance, so is the co-sine of its latitude to the co-sine of the right ascension required.

The R. A. may also be easily found by Astronomical tables, which are easily procured. In those, it is already calculated.

Problem 3. - To find the Ascensional Difference.

Rule. - Add the tangent of the latitude of the birth-place, to the tangent of the declination, the sum will be the sine of the Ascensional Difference.

Problem 4. - To find the Semi-diurnal arc of a star.

Rule. - If the star have north declination, add the ascensional difference to 90o. If south, subtract it from 90°; the remainder is the required arc.

Problem 5. - To find the Semi-nocturnal arc of a star.

Rule. - Subtract the Semi-diurnal arc from 180°, it will give the Semi-nocturnal arc required.

Problem 6. - To find the Oblique Ascension or Oblique De-scension of a star.

Rule. - If the star have north declination, subtract the Ascensional Difference from the R. A.; the remainder is the Oblique Ascension. If south declination, add it instead of subtracting.

If the star have north declination, add the Ascensional Difference to the R. A.; and if south subtract it; the remainder is the true Oblique Descension required.

Problem 7. - To find the pole of a star, or celestial house, in any figure.

Rule 1. - As the semi-arc is to 90°, so is its distance in R. A. from the meridian or fourth house, to the difference between its circle of position, and that of the meridian; which difference subtracted from its right distance, will give its true Ascensional Difference under its own pole.

Rule 2. - To the sine of this ascensional difference, add the co-tangent of its, declination; the sum will be the tangent of its pole.

Problem 8. - To direct a significator to any part of the heavens, or any star, conjunction, or aspect, without latitude.

Rule. - Find the true Oblique Ascension or Descension of the star, under its own celestial pole, and subtract this from the true Oblique Ascension or Oblique Descension of the conjunction or aspect, taken under the same pole; the remainder is the true celestial arc of direction.

Problem 9. - To direct a significator with latitude.

From the true Oblique Ascension or Descension of the aspect, taken as before; under the pole of the significator, subtract that significator's true Oblique Ascension or Oblique Descension under its own pole. The remainder is the arc of direction.