To find the Longitude by the Eclipses of Jupiter's Satellites.

The eclipses of the satellites are given in page III. of the month of the Nautical Almanac for mean time at Greenwich. There are two kinds of these eclipses-an Immersion, denoting the instant of the disappearance of the satellite by entering into the shadow of Jupiter, and an Emersion, or the instant of the appearance of the satellite in coming from the shadow. The immersions and emersions generally happen when the satellite is at some distance from the body of Jupiter, except near the opposition of Jupiter to the sun, when the satellite approaches near to his body. Before the opposition they happen on the west side of Jupiter, and after the opposition on the east side; but if an astronomical telescope is used which reverses the objects, the appearance will be directly the contrary. The configurations, or the positions in which Jupiter's satellites appear at Greenwich, are laid down every night, when visible, in page XII. of the month of the Nautical Almanac.

As these eclipses happen almost daily, they afford the most ready means of determining the longitude of places on land, and might also be applied at sea, if the observations could be taken with sufficient accuracy in a ship under sail, which can hardly be done, since the least motion of a telescope which magnifies sufficiently to make these observations, would throw the objects out of the field of view.

As these eclipses are given in the Nautical Almanac in mean time, it is necessary to regulate your watch to mean time ;* this is easily obtained from the apparent time by applying to the latter the equation of time taken from the Nautical Almanac, by adding or subtracting according to the directions in the column from whence the equation was taken; hence the error of a watch with respect to mean time may be ascertained.

The watch being thus regulated, you must then find nearly the time at which the eclipse will begin at the place of observation; this may be done as follows: Find from the Nautical Almanac the time of an immersion or emersion, and apply thereto the longitude turned into time, by adding when in east, but subtracting when in west longitude, the sum or difference will be nearly the mean time when the eclipse is to be observed at the given place. If there be any uncertainty in the longitude of the place of observation, you must begin to look out for the eclipse at an earlier period; and when the eclipse begins, you must note the time by the watch, and after applying the correction for the error of the watch, if there be any, you will have the mean time of the eclipse at the place of observation; the difference between this and the time in the Nautical Almanac, being turned into degrees, will be the longitude from Greenwich.

EXAMPLE.

Suppose that on the 21st of August, 1820, sea account, in the longitude of 127° 55′ W. by account, an immersion of the first Satellite of Jupiter was observed at 7h. 12m. 32s. P. M. mean time. Required the longitude?

which turned into degrees gives 128° 50′ W. for the longitude of the place of observation.

To find the Longitude by Eclipse of the Moon.

The determination of the longitude by an eclipse of the moon is performed by comparing the times of the beginning or ending of the eclipse, as also the times when any number of digits are eclipsed, or when the earth's shadow begins to touch or leave any remarkable spot on the moon's face; the difference of time between the like observations made at different places, turned into degrees, will be the difference of longitude of those places.

When the beginning or end of an eclipse of the moon is observed at any place, the longitude of that place may be easily found by comparing the time

In the Almanacs published before 1805, the apparent time of the eclipses was given instead of the

dean time.

of observation with the time given in the Nautical Almanac, for the difference between the observed time of beginning or ending, and the time given in the Nautical Almanac, will be the ship's longitude in time, which may be turned into degrees by Table XXI. Thus if the beginning of an eclipse of the moon was observed March 30, 1820, sea account, at 9h. 59 m. the time by the N. A. being March 29 or March 30, sea account, at 5h. 163m. their difference 4h. 43m. is the longitude of the place of observation=70° 45', which is east from Greenwich, because the time at the place of observation is greatest.

To find the Longitude by a perfect time-keeper or chronometer.*

It was before observed, that if a chronometer could be made in so perfect a manner as to move uniformly in all places, and at all seasons, the longitude might easily be deduced therefrom, by comparing the time shown by the chronometer, regulated to the meridian of Greenwich (or some other known meridian) with the mean time at the place of observation. For the difference of these times would be the difference of longitude between that meridian and the place of observation. The moderate price of good chronometers now, in comparison with their values many years since, together with the various improvements in their construction, have caused this method of determining the longitude to be much more used within a few years, than it was when the first editions of this work were published: we shall therefore explain more fully the use of this instrument, and the methods of regulation.

If a chronometer is to be used on a voyage, it must be adjusted, and its rate of going ascertained, before sailing. This may be done by taking altitudes of the sun or some other heavenly body, and finding therefrom the apparent time of observation, by any of the methods before given in pages 154-161. To this time must be applied the equation of time, found in page II. of the month of the Nautical Almanac, or in Table IV. A (reduced to the moment of observation by means of Table VI. A) by adding the equation to, or subtracting it from, the apparent time, according to the directions given in or at the top of each column of the table, the sum or difference will be the mean time of observation, being the same time as would be shown by a chronometer whose motion is perfectly uniform. Comparing this mean time of observation with the time by the chronometer, shows how much it is then too fast or too slow for the meridian of the place of observation; and by repeating the operation on a future day, the rate of going may be ascertained. If it is found to gain or lose a few seconds or parts of a second per day, that allowance must be made on all future observations at sea. Thus, if on the 1st of June, 1824, at 5h. 10m. 20s. by the chronometer, the mean time, deduced from an observation of the sun's altitude, was 5h. 12m. 40s. the chronometer would then be too slow by the difference of those times 2m. 20s. and if on the 21st of June following the time by the chronometer was 4h. 15m. 35s. when the mean time was 4h. 18m. 17s. the chronometer would then be too slow by the difference of those times or 2m. 42s. and the rate would have varied in 20 days from 2m. 20s. to 2m. 42s. which is a difference of 22 seconds in 20 days, being 17 seconds per day, and this rate must be allowed on all future observations at sea, until a new regulation can be obtained, at some place whose longitude is known. It is best to have a considerable number of days interval between the two observations for fixing the rate, by which means it may be determined to tenths of a second, the absolute error of the observations being reduced in finding the daily rate, by dividing by the number of days. Thus if the above difference of 22 seconds had been erroneous 2s. and the true value 20s. the daily rate would be one second instead of 1s.1, varying only one tenth of a second, notwithstanding the observations on which the rate was established, contained an error of 2 seconds.

*The Chronometers most celebrated for correctness are those made by Mr. French, London, and for sale by JAMES LADD, No. 30 Wall-street, New-York, who mechanically understands that valuablę instrument. Proprietor.

Having regulated a chronometer, in the manner first mentioned, at a place whose longitude from Greenwich is known, it is easy to find how much it is too fast or too slow for the meridian of Greenwich, by allowing for the difference of meridians. Thus, if the above mentioned observation of June 1, was made in place in 740 west longitude, corresponding in Table XXI. to 4h. 5€m. the chronometer on that day would be too slow for Greenwich time by the sum of 4h. 56m.* and 2m. 20s. or 4h. 58m. 20s. In general it will be full as simple, when thus regulating a chronometer, at a place whose longitude is known, to reduce at once the mean time at the place of observation to the meridian of Greenwich, by adding the longitude if west, subtracting if east, the sum or difference will be the mean time of observation upon the meridian of Greenwich, the difference between this and the time given by the chronometer, shows how much it is too fast or too slow for Greenwich mean time. Thus by adding the longitude 4h. 56m. to the mean time of the above observation 5h. 12m. 40s. the sum 10h. 8m. 40s. is the mean time at Greenwich, from which subtracting the time by the chronometer 5h. 10m. 20s. the remainder 4h. 58m. 20s. is what the chronometer is too slow for Greenwich time, as was found before.

The chronometer having been thus regulated to Greenwich time, and the daily rate of its going ascertained, if this rate should remain unaltered, the time at Greenwich will be known by it, at any moment at sea, and if at that moment by any observation of the sun, moon, planet or a fixed star, the apparent time be found by any of the methods explained in pages 154-161, and the mean time at the ship deduced therefrom, by applying the equation of time, as above explained, then the difference between this mean time at the ship, and the mean time at Greenwich shown by the chronometer, will be the longitude, which may be turned into degrees and minutes by Table XXI. We shall explain by a few examples the preceding remarks.

EXAMPLE I.

Wishing to regulate a chronometer, in a place whose latitude is 51° 30' N.. and longitude 1140 E. from Greenwich, I observed Oct. 10, 1824, at 8h. 21m. A. M. sea account per chronometer, the altitude of the sun's lower limb, by a fair observation 13° 32', the correction for semi-diameter, parallax and dip being 12'. It is required to find the errror of the chronometer for mean time at Greenwich?

The apparent time of this observation, computed as in Example I. page 158, is 8h. 7m. 9s. A. M. corresponding to Oct. 9d. 20h. 7m. 9s. by the Nautical Almanac. From this subtract the longitude 114° turned into time 7h. 36m. by Table XXI. the remainder Oct. 9d. 12h. 31m. 9s. is the appaTent time at Greenwich. Now by Table IV. A, the equation of time for Oct. 9d. at noon is sub. 12m. 44s. with a daily increase of 16s. and this in Table VI. A, under 16s. and opposite to 12h. 31m. 9s. gives 9s. to be added to 12m. 448. (because it is increasing) the sum 12m. 53s. is the equation of time, which by the table is subtractive from the apparent time at Greenwich Oct. 9d. 12h. 31m. 9s. to obtain the mean time at Greenwich Oct. 9d. 12h. 18m. 18s. If the mean time at the place of observation is required, it would be found by subtracting the equation of time 12m. 53s. from the apparent time at the place of observation, 8h. 7m. 9s. and it would therefore be 7b. 54m. 16s.

EXAMPLE II.

May 10, 1824, at 5h. 30m. P. M. sea account per chronometer, in latitude 39 54', in a place whose longitude was known to be 17° 30 E. from Greenwich, the altitude of the sun's lower limb by a fore observation was 15° 45', the correction for dip, parallax and semi-diameter being 12'. It is required to find the error of the chronometer for mean time at Greenwich, and at the place of observation ?

* If the longitude had been east, it would have been subfractive.

This is to be added if the ship's longitude is rest.

The apparent time of this observation, computed as in Example II. page From this sub156, is May 9d. 5h. 34m. 26s. by the Nautical Almanac. tract* the longitude 17° 30', turned into time, 1h. 10m. by Table XXI. the remainder May 9d. 4h. 24m. 26s. is the apparent time at Greenwich, By Table IV. A, the equation of time for May 9th. at noon is sub. Sm. 48s. with a daily increase of 3s. and this in Table VI. A, under 3s. and opposite 4h. 24m. 26s. is 1s. which added to 3m. 48s. (because it is increasing) gives the equation of time, at the moment of observation, sub. Sm. 49s. Subtracting this, according to the direction in the table, from the apparent time at Greenwich May 9d. 4h. 24m. 26s. leaves the mean time at Greenwich May 9d. 4h. 20m. 37s. Subtracting the same equation Sm. 49s. from the apparent time at the place of observation 5h. 34m. 26s. gives the mean time at the place of observation 5h. 30m. 37s. The difference between the mean time at Greenwich 4h. 20m. 37s. and the time by the chronometer 5h. 30m. is 1h. 9m. 23s. which is the time the chronometer is too fast for Greenwich mean time.

EXAMPLE III.

Suppose that July 27, 1820, sea account, the apparent time was found by an altitude of the sun to be 1h. 5' 8" P. M. when by a watch well regulated to mean Greenwich time, the time was 4h. 3' 8" P. M. Required the longitude?

Apparent time.......
Equation of time add.

1h. 5' 8"
68

Suppose that May 14, 1820, sea account, the apparent time was found by an altitude of the sun to be 4h. 3′ 5′′ P. M. when the time by the watch was 2h. P. M. the watch being too slow for mean Greenwich time 11′ 9′′. Required the longitude?

Time per watch
Watch error add

2h. 0' 0"

11 9

Time at Greenwich 2 11 9 P. M.

EXAMPLE V.

Suppose that on June 14, 1820, sea account, in a place whose longitude from Greenwich was known, a number of observations were taken to ascertain the going of the watch; and it was found that on that day it was 10 too slow for mean Greenwich time, and lost time 2" per day; and that on July 14, 1820, sea account, the time per watch was 6h. 0' 6" P. M. when, by an observed altitude of the sun, the apparent time was 1h. 16′ 10′′ P. M. Required the longitude?

To regulate a Chronometer by Lunar Observations.

It sometimes happens that a chronometer is by accident suffered to run down when at sea, in which case it can be regulated, by means of a great number of lunar observations, which must be taken with the greatest care, and with objects on different sides of the moon. These observations may be made on the same day, or on several successive days, finding by each observation how much the chronometer is too fast or too slow for Greenwich time, and taking the mean result for the error at the mean time of observation.

In the last example some of the observations made the chronometer too slow, and others too fast; these are marked with different signs + and -, the sum is to be found, noticing the signs in the algebraical manner, as taught in the introduction to the appendix of this work.

It has lately been discovered that chronometers generally go faster on board of a vessel than when on shore; this variation has been sometimes found to be as much as 14 seconds per day, though in general not more than 1 or 2 sez conds. It is suspected that this arises from the attraction of the iron in the vessels, the chronometer having acquired a small degree of magnetism. To remedy this inconvenience it has been recommended to keep the chronometers always in the same place on board the ship, and to regulate them when thus placed, before leaving the port, or by means of lunar observations (after the above manner) when at sea. Thus, in the first of the above examples, the chronometer was 2m. 9s. too fast for Greenwich time April 9, 1820, suppose now by a set of lunar observations made April 30, 1820, it was found to be fast 2m. 30s. the variation would be 21s. in 21 days, which is 1 second per day for the acceleration of the chronometer.

It has also been found that chronometers generally gain by an increase of density of the air, and lose by a decrease of density. The firing of guns on board a vessel will sometimes alter the rate of going, unless the instrument be well suspended, or held in the hand during the firing. Any sudden jar will sometimes alter the rate. The imperfection of the oil used will after sometime impair the instrument. Finally, the mechanism used to correct the change of temperature of the air may not do it completely, and some error may arise from this source. Notwithstanding these various causes of error, it is wonderful to observe how accurately some of those chronometers perform their office.

To find the Longitude by a Variation Chart.

In the year 1700, Dr. Halley proposed to find the longitude by a chart he published, on which the lines of the variation of the compass were drawn ; and since that time several similar charts have been published for the same purpose; but the difficulty of determining the variation, combined with other causes, will probably prevent this method from being sufficiently accurate to be generally useful.

The method of using this chart is as follows: On the parallel of latitude which you are in, find the observed variation, and that point will be the place of observation.

A chart, on which the lines of the dip of the magnetic needle arc mark ed, might be used in the same manner for determining the longitude.

Bb