epeakIng of the liorucon we Always moan a mercurial horizon, except another in /specified. The glasses of the roof should be truly plane and parallel, but by reverting the horizon for half the observations any error of this kind is destroyed. The mercurial horizon in unfortunately heavy and inconvenient, and troublonome from Its tremors wherever there is any motion. Several subseltutes have been used!, Oil or treacle him leen adopted with good success where the nhaking from carriages, kc., has prevented the use of mercury. Sometime a piece of glass is act horizontal by a level applied to its surface, or by a fluid below it, ea as to get a reflecting rurface, but those generally absorb too much light to be used conveniently for stars, and are not very trustworthy. The lest subetituto aroma to be a piece of xpeculum metal, ground plane. and Laid horizontal by a level. It is certainly the brightest, and therefore the beet for stars, but it must be remembered that benisons which are nut stlfaegulated, by being fluid, are scarcely to be trusted ander a hot syn. Treughton'a reflecting circle is rather heavy, as d reading three veinier* for every observation is troublesome, especial y at night, but it is very accurate, and fewer (Amen-alb us are re, irel. Roe is* redeems circle may be male much smaller and !wiser, but demantla th most ceptutita workmanship, a greater uutal sr of obiervatleas, and mule !Western. The simple 'extant Is more manageable, but requires greater precautions and checks in ita use. But with any of these a skilful observer will get the latitude very nearly. Sextants are made of all sizes from 10 indica radius (which is probably not so good as 8 inches) down to the snuff-box sextant of 1 y inches radius. For travellers who cannot afford to carry much weight, the 3-inch sextant is very convenient. In a com munication to the Royal Astronomical Society, Mr. Laseell states, that with a 3-inch sextant made by Dollond, which packs up, stand, horizon, and all, in a box 4'3 inches square and 21 deep, he found that he could get the latitude within 10', and the time to P.0 by observations of stars. The horizon was of speculum metal, ground by himself, and set true by a level. The observations sent with the account completely justify Mr. Lassell's opinion, but one observer differs more from another in sextant observations than in any other class of astronomical instruments ; with the snuff-box sextant, altitudes may be got within I'. The state of the barometer and thermometer must be noted at the time of all observations for the latitude, in order to compute the true refraction. At the same time we may remark, that if the obeervatimui be balanced, that if the altitudes to the north have nearly corresponding altitudes to the south, the refraction still affect the observations like an instrumental error, and the variations depending on the barometer and thermometer will be quite insensible.
5. Observations of Polaris may be taken at any timo for the latitude, and there are tables for approximate reduction given in the Nautical Almanac' for each year.
6. At sea the sextant is the only instrument which can be used, and the latitude is generally got by observing the altitude of the sun's lower limb when on the meridian, above the sea horizon. This is rather a nude process, but the resulting latitudes are generally true to 1', or at worst to 2'. The moon, since 1S34, the date of the improved and extended ' Nautical Almanac,' may be very conveniently used for finding the latitude at sea, and the brighter planets and stars are often observable on the meridian. The latitude may also be deduced from two altitudes of the sun, and the time elapsed between the obser vations, or indeed from any two altitudes of two known celestial bodies, one of which is near the meridian, and the other distant from it, as persons not acquainted with spherical trigonometry may satisfy themselves on the celestial globe. There is a considerable difficulty in
seeing the sea horizon by night, which is somewhat reduced by getting as near the level of it as you am.
Determination of the Longitude.—The determination of the longitude of any place on the earth's surface, astronomically considered, resolves itself into two parts, the finding the time at the place of observation, and finding the time, at due same moment, on the first meridian (we shall always speak of Greenwich), or at any place thb longitude of which from Greenwich is well known. It will be more convenient to classify the methods of finding the longitude by the phenomena than by the instruments.
Determination of Time at the Place.-1. This is best and most easily done by a transit instrument, and the time, when found, is kept by a clock or chronometer. [Teeests.] The transit however is neither 11 very portable instrument, nor is a proper situation for it, we mean one (sufficiently steady, readily found.
2. The time can also be found from the altitude of the sun, or stars out of the meridian. Thum let 1. be the pole, z the zenith, and z m the zenith distance, ors ti the altitude of any heavenly body, the right amen non and declination of which are well known, end conse quently the polar distance r s. From these data and r z the co-latitudo of the place, the angle z re can be computed, callal the hour angle, and this, if the body be time sun, and to the west of the meridian, is the apparent time after noon ; or if the sun ho to the mat, the hour tangle is the apparent time before noon. Thin apparent tinie is easily reduced to mean time with the data of the ' Nautical Almanne.' M'hcu the object observed is a planet or star, the hour angle being added to the right ascension when the body is to the west, or subtracted from the right ascension when time body is cant, will give tho sidereal time, which can be reduced to mean solar Ulm, with only nn approximate knowledge of the longitude. The problem therefore of finding the time consists genemlly in observing the altitude or zenith distance of any known object, and determining the hour tangle from it. The repeating or alti tude and azimuth circles are very fit for this purpose, but the moat usual and portable inztrument in fl reflecting circle or sextant with its hurizon mud a chronometer. The observations of altitude ahould Ise nettle as much its pomade on the prime vertical, that is, when the object is mat or west. Again, to get rid of instrumental error, and also to save computation, the sun should to observed, when convenient and possible, at the same altitude morning and evening. We should also recommend when the sun is observed that both limbs should be observed without moving the index. For instance, if in the morning the sun were about 14° high, set the instrument to 30°, note the instant when the upper limb by reflection touches the upper limb seen in the horizon, read off the angle very carefully, wait till the lower limbs form their contact, and note the time. Then set to 31° 30' or 32° and proceed as before, and repeat the operation, having again set forward 1° 30' or 2°. The observer has then several checks without trouble, for the time in which the sun rises through a diameter will be sensibly equal or vary uniformly ; and in like manner the times of rising through 1° 30' or 2° will point out if any of the usual errors have been committed. lu the after noon the same process should be repeated in an inverse order, and the time of apparent noon deduced from each pair.* It is to be understood as a universal rule, that the index error is to be carefully determined, and the barometer and thermometer noted whenever observations of altitude for time or latitude are made.