As 24 hours, diminished by this sum or difference, when the planet's motion is greater than the sun's, or increased by it, when the sun's motion is the greater, Is to 24 hours, So is the difference between the sun's* and planet's right ascension at noon to the time required. For a Star. Take the increase of the sun's right ascension in 24 hours, and add to it 24 hours; then say, As this sum Is to 24 hours, So is the difference between the sun's* and star's right ascension To the time required. Examples. On July 1st, 1767, the sun's right ascension when on the meridian of Greenwich, was 6h 40′ 25′′; and on July 2d, it was 6h 44' 33": also the moon's right ascension was 159° 2' ; and on July 2d, it was In the latter part of both these rules, the sun's right ascension is to be taken from the planet's or star's right ascension; and if their right ascensions should be less than the sun's, they must be increased by 94 hours, before you subtract. At what time will the star Arcturus come to the meridian of Greenwich on the 1st of Sept. 1787 ? Sun's R.A. 1 Sep. 10h 41′ 59′′ Star's R.A. 14h 6' 6" As 24h 3 38 24h:: 3 24' 1: 3" 28′ 31", the time required. PROBLEM XI. To find the altitude of the sun, or any other celestial body. This consists in the simple application of the quadrant to a celestial body, in the same manner as I have already shewn with respect to terrestrial objects. The quadrant being adjusted as it should be in all cases previous to its use, the celestial body must be viewed through the sights, and the plumb-line will shew its altitude on the graduated limb of the instrument. If the observation be made on the sun, the dark glass must be used to defend the eye, or the luminous spot formed by the small hole must be made to fall on the centre of the cross immediately beneath the eye-hole. The sun having no visible point to mark out its centre, you must take the altitude either of the upper or lower limb. If the lower limb be observed, you must add the sun's semidiameter thereto, in order to find the altitude of the sun's centre. If the altitude of the upper limb be observed, the semidiameter must be subtracted. The mean semidiameter of the sun is 16 minutes, which for common observation may be taken as a constant quantity, for the greatest deviations from this quantity scarcely exceed a quarter of a minute. When greater accuracy is aimed at, the semidiameter may be taken from the Nautical Almanack. The observed altitude of the sun's lower limb being 18° 41', add thereto 16 min. for the sun's semidiameter, and you obtain 18° 57', the central altitude. The apparent altitudes of all the heavenly bodies are increased by refraction, except when they are situated in the zenith. An observed angle of a star, or any other object in the heavens, must be diminished a small quantity, to be taken from the table of refractions. Where greater exactness is required, a small quantity is to be added to the error occasioned by parallax, or the difference between the altitude of an object as seen from the centre and the surface of the earth. That from the centre is the true altitude, and the greatest, except at the zenith, where parallax vanishes; consequently the apparent altitude of the sun is to be augmented by a small quantity taken from the table of the sun's parallax. June 6, 1788, the apparent altitude of the sun's lower limb was observed to be 62° 19′; required the H H |