being continually applied. The moon's distance from the sun is obtained by the solution of a quarantal triangle; the data may be seen in Example I.

This is one of the most useful and celebrated problems in Astronomy. We shall give a few examples adapted to the year 1834.

2. Regulus.

*'s A.R=149° 53′ 1′′ · 6 D's A.R-114° 16′ 40′′-5

Dec. 12° 46′ 30′′ · 1 N. =

Distance

Dec. 23° 10′ 12′′ ·8 N.

35° 19′ 2′′·5.

3. a Aquila. July 16th, 1834. Midnight.

*'s A.R=295° 40′ 42′′ · 5

D's A.R=245° 7′ 56′′ ·9

Dec. 19° 41' 9"-9 s.

Distance 57° 9′ 5′′-7.

=

* Apparent time at Greenwich.

6. Antares. Dec. 22nd, 1834. Midnight. ✶'s A.R=244° 48′ 47′′ · 6 D's A.R=176° 23′ 50′′·1

Dec. 26° 3′ 21′′ s.

Dec. 7° 16′ 37′′ N.

Distance 74° 12′ 21′′.8.

SECTION XII.

ON THE LONGITUDE.

(170.) Longitude of a place upon the earth may be defined to be the angle at the pole formed by the meridian of the place and the first meridian. This angle is measured by the corresponding arc of the equator, and may be expressed either in degrees or in time. When the sun is on the meridian of any place to the west of Greenwich, or in west longitude, he has evidently passed the first meridian, and the time at Greenwich is afternoon: on the other hand, when it is apparent noon at a place in east longitude, the sun has not yet arrived at the first meridian. Hence this problem, which is of the utmost importance in Nautical Astronomy, consists in finding what o'clock it is at two places under different meridians at the same instant. The most obvious method, apparently, of effecting this, would be to determine the time at the place of the observer, which can readily be done by the sun's altitude (155.), and comparing it with a chronometer previously regulated to shew Greenwich time; the

difference in time would thus be known, and consequently the longitude of the observer. But notwithstanding the plausibility of this plan, it is found to be liable, in practice, to errors which no precaution can altogether guard against. Chronometers must always be subject to variations from many obvious causes, and perpetually liable to accidents; so that an entire reliance upon them at sea would frequently be attended with fatal consequences. They are, however, of the utmost importance when constantly verified by some method, more regular in its operation, and less under the influence of accidents.

(171.) The method universally agreed upon as the most practical and certain, is by lunar distances. As the distance of the moon from the fixed stars which are situated near her path varies about half a degree every hour, her change of place is sufficiently great to be perceptible in a small portion of time. In the Nautical Almanac are given the distances of the moon from the sun, and from certain stars, for every third hour of Greenwich time; and, as her motion is sufficiently uniform for the purpose, the time for any intermediate distance is obtained by a simple proportion. Now if the distance of the moon from a certain star be observed at any place, with the corresponding time, a reference to the Nau

tical Almanac, which, in this case, stands in the stead of a perfect chronometer, will show the time at Greenwich when the same distance or event took place: hence the difference of time between the two places becomes known. But owing to the observed distance not being the true distance, the problem is extended to the solution of two spherical triangles.

(172.) Let Z (fig. 33.) be the zenith of the observer, Z▷ the apparent zenith distance of the moon, ZO that of the sun, and the apparent or observed distance between them. Now all the heavenly bodies are affected by refraction, which elevates them above their true places. And the bodies in our system are depressed below their true places by parallax.

The effects of refraction and parallax are greatest in the horizon, and vanish at the zenith. The parallax of the moon, owing to her proximity to the earth, is greater than the refraction; and hence the true altitude of this body will always be greater than the apparent altitude. On the other hand, the parallax of the sun is less than the refraction, and therefore the true altitude will be less than the apparent altitude. But as these effects operate only in a vertical direction, the angle at the zenith will remain unaltered.