ΤΟ FIND THE TIME AT SEA BY THE MOON'S ALTITUDE. HAVING a chronometer which is pretty well regulated to Greenwich time, we can use the moon's altitude for finding the mean solar time at the ship, which is required in determining the longitude. For, in the present improved state of the Nautical Almanac, we can easily find the moon's right ascension and declination for that time at Greenwich, without the very troublesome operation of interpolating for the second and third differences, as was necessary in the former arrangement of that ephemeris. Even without a chronometer thus regulated, the time at Greenwich can be obtained, if we know the longitude of the ship, as well as the mean time at the place of observation, by a watch that will give it with a considerable degree of accuracy; because, by adding the longitude in time to the time by the watch, if the longitude be west, or subtracting it, if the longitude be east, we shall obtain the corresponding time at Greenwich. We must, however, always keep in mind, that the accuracy of an observation of this kind depends on the certainty with which the time at Greenwich is computed; because an error in this estimate affects the moon's right ascension and declination, which frequently vary rapidly, as may be seen by the inspection of the Nautical Almanac, where we shall find that in a minute of time the right ascension may vary more than 2', and the declination more than 15". When we wish to ascertain the time by this method, we must observe, with a fore observation, the altitude of the moon's round limb, and at the same instant the time by the watch or chronometer, which is supposed to be regulated to Greenwich time. With this time at Greenwich we must take from the Nautical Almanac the sun's right ascension, the moon's right ascension, the moon's declination, the moon's horizontal parallax, and the moon's semidiameter, to which we must add the augmentation from Table XV. To the observed altitude we must apply the correction of the moon's semidiameter, by adding it, if the lower limb be observed, or subtracting it, if the upper limb be observed; from this sum or difference we must subtract the dip of the horizon, and we shall obtain the moon's central altitude. To this we must add the correction for parallax and refraction, and we shall obtain the moon's correct altitude, which is to be used in the rest of the calculation. This correction for parallax and refraction can easily be found, as in page 171, by means of Table XIX., by subtracting the tabular number, corresponding to the altitude and horizontal parallax, from 59′ 42′′; the remainder will be the correction for parallax and refraction, to be used as above; and then we find the time by the following rule:— RULE. Add together the moon's correct altitude, the ship's latitude, and the polar distance; from the half-sum subtract the moon's correct altitude, and note the remainder; then add together the log. secant of the latitude, the log. cosecant of the polar distance, (rejecting 10 from each index,) the log. cosine of the half-sum, and the log. sine of the remainder; half the sum of these four logarithms will be the log. sine of half the hour angle; take out the corresponding time in the column marked P. M., in Table XXVII., and apply it to the moon's right ascension, by subtracting when the moon is east of the meridian, or adding when west of the meridian; the sum or difference will be the right ascension of the meridian. From the right ascension of the meridian (increased by 24 hours if necessary) subtract the sun's right ascension; the remainder will be the apparent time at the ship, and by applying to it the equation of time found in the Nautical Almanac, we shall get the required mean solar time at the meridian of the place of observation. EXAMPLE. When the mean time at Greenwich, by the chronometer, was, Nov. 294, 2h 52m astronomical account, the altitude of the moon's upper limb was observed, when west of the meridian, and found to be 60° 25′ 8′′, the latitude of the place 30° 20′ N, and the dip 4'. Required the mean time of observation. We have from the Nautical Almanac, for the time, Nov. 29d 2h 52m, the sun's right ascension, 16h 22m 45a; the moon's right ascension, 9h 26m 23'; the moon's declination, 20° 32′ 47′′ N., or polar distance, 69° 27′ 13′′; the moon's horizontal parallax, 54' 23'; the moon's semidiameter, 14′ 49′′ +Aug. Table XV. 14" = 15′ 3′′. Ds observed altitude, upper limb..... Dip....... D's central altitude..... Parallax and refraction = 59′ 42′′. Cor. Tab. XIX. 33′ 08′′ ....add D's correct altitude...... 60 06 05 26 34 60 32 39 Sum (being west of the merid.) gives right ascension of the meridian 11 29 59 Subtract the sun's right ascension. ..... .sub. 16 22 45 19 07 14 11 19 .Nov. 28d. 18 55 55 7 56 05 W It very frequently happens, that, a few minutes before or after taking the sun' meridian altitude for the determination of the latitude, we can observe the moon's altitude for the regulation of the time; and as the latitude by observation is then known accurately, without depending on the ship's run for any considerable length of ume, it will operate to render the regulation of the chronometer by the moon's altitude more accurate. In like manner, if we observe the latitude by the moon's meridian antitude, we can, at nearly the same time, take an observation of the sun's altitud late the cntonometer. TO FIND THE TIME AT SEA BY A PLANET'S ALTITUDE. We may use either of the large planets, Jupiter, Saturn, Mars, or Venus, for determining the time at sea; and the process is very nearly the same as that in the preceding section, where the moon's altitude is used. In this case, we must ascertain the time of observation, reduced to the meridian of Greenwich, either by a chronometer regulated to that meridian, or by knowing pretty nearly the mean time of observation at the ship, and the longitude; for by adding the longitude in time to th mean time at the ship by the watch, if the longitude be west, or subtracting the longitude if it be east, we shall obtain the corresponding time at Greenwich. With this time at Greenwich, we must take, from the Nautical Almanac, the sun's right ascension, the planet's right ascension, the planet's declination, or polar distance. The parallax and semidiameter might also be noticed, but the corrections from these quantities are so small that they may be neglected, as only amounting to a few seconds. Then from the observed central altitude of the planet we must subtract the dip and the refraction, and we shall obtain the planet's correct altitude.* these we may find the time by the following rule :— RULE. With Add together the planet's correct altitude, the ship's latitude, and the polar distance; from the half sum subtract the planet's correct altitude, and note the remainder; then add together the log. secant of the latitude, the log. cosecant of the polar distance, (rejecting 10 from each index,) the log. cosine of the half-sum, and the log. sine of the remainder; half the sum of these four logarithms will be the log. sine of half the hour angle; take out the corresponding time in the column marked P. M., Table XXVII., and apply it to the planet's right ascension, by subtracting from the right ascension when the planet is east of the meridian, or adding when west of the meridian; the sum or difference will be the right ascension of the meridian. From the right ascension of the meridian (increased by 24 hours if necessary) subtract the sun's right ascension; the remainder will be the apparent time at the ship; and by applying to it the equation of time, found in the Nautical Almanac, we shall get the required mean solar time, at the meridian of the place of observation. EXAMPLE I. In the latitude 42° 22′ N., and longitude 70° 15′ W., on May 26d 7h 18m 35o, astronomical time, by a watch which was very nearly regulated for mean time at the ship, observed the central altitude of the planet Jupiter, by a fore observation, and found it to be 32° 16' 23"; the planet being to the west of the meridian, and the dip 4' 8" Required the mean time of observation at the ship. Adding the longitude 4h 41m to the time by the watch, we get the mean time at Greenwich, May 26d 11h 59m 35; and with this time we get, from the Nautical Almanac, the sun's right ascension 4h 15m 04; Jupiter's right ascension 7" 8m 32s; Jupiter's declination 22° 48′ 39′′ N., or polar distance 67° 11' 21". * When very great accuracy is required, we may notice the parallax in altitude, which is found in Table X. A., and is to be added to the correct altitude computed by the above rule. We may also find the correction of refraction and parallax, by entering Table XVII. in the page corresponding to the horizontal parallax of the planet, and taking out the corresponding number, which, being subtracted from 60, gives the correction for parallax and refraction, at one operation. Sum (being west of meridian) gives right ascension of meridian... Subtract the sun's right ascension..... 4h 26" 06 7 08 32 11 34 38 4 15 04 Gives the apparent time at the ship...... Mean time at the ship...... .sub. 7 19 34 3 14 7 16 20 The time by the watch being 7h 18m 35', it is 59' too slow for apparent time and 2m 15 too fast for mean time. EXAMPLE II. January 5 15h 40m 24, 1836, astronomical mean time, at a place in tl e latitude of 24° 16' N., longitude 34° 56′ W. of Greenwich, observed the central altitude of the planet Saturn, by a fore observation, and found it to be 28° 15'; the planet being east of the meridian, and the dip 3' 41". Required the mean time of observation at the ship. Adding the longitude 2h 19m 44 to the time by the watch, we get the mean time at Greenwich, Jan. 5 18h 00m 08; and with this time we get from the Nautical Almanac the sun's right ascension 19h 5m 13; Saturn's right ascension 14" 10m 22"; Saturn's declination 10° 36′ 17′′ S., or polar distance 100° 36′ 17′′. Difference (being east of meridian) gives right ascension of meridian.. 10 41 02 Add 24h, and subtract the sun's right ascension... 19 (15 13 The time by the watch being 15h 40m 24', it was 4m 35 too fast for apparent time, TO FIND THE APPARENT TIME BY A STAR'S ALTITUDE. Correct the observed altitude for the dip and refraction, (the dip being generally 4 minutes when the observation is taken on the deck of a common-sized vessel;) find the ship's latitude at the time of observation, and the star's right ascension and declination in Table VIII.* Add together the star's correct altitude, the ship's latitude, and the polar distance; from the half-sum subtract the star's altitude, and note the remainder. Then add together the log. secant of the latitude, the log. cosecant of the polar distance, (rejecting 10 in each index,) the log. cosine of the half-sum, and the log. sine of the remainder; half the sum of these four logarithms will be the log. sine of half the hour angle; take out the corresponding time in the column marked P. M. (Table XXVII.) and apply it to the star's right ascension, by subtracting when the star is east of the meridian, or adding when west of the meridian; the sum or difference will be the right ascension of the meridian. From the right ascension of the meridian (increased by 24 hours if necessary) subtract the sun's right ascension, taken from the Nautical Almanac; the remainder will be the apparent time at the ship, and by applying to it the equation of time, we get the mean time at the ship. EXAMPLE I. Suppose that, on September 84 14" 19" 20",1836. astronomical time, as shown by a chronometer, regulated to mean time at Greenwich, when in the latitude of 7° 45′ S., and longitude of 29° 12′ E. from Greenwich, the altitude of the star Procyon, being then east of the meridian, was observed by a fore observation, and found to be 28° 16', and the dip 4'. Required the mean time of observation at the ship. By inspection in the Nautical Almanac, we find that, on the above-mentioned day Procyon's right ascension was 7h 30m 44', and the declination 5° 39 N., or polar distance 95 39 nearly, agreeing nearly with the result from Table VIII., corrected for the annual variations, &c. Sun's right ascension by Nautical Almanac, Sept. 8, at mean noon... 11h 07m 47• Correction, Table XXXI., for 14h 19m 10, mean time Sun's right ascension at the time of observation... Star's observed altitude...... 28° 16′ Dip 4', ref. 2, Table XII., sub. .....add 2. 09 11 09 56 6 *The right ascensions and declinations of the stars in Table VIII. are the mean values for January Ist, 1830, and must be reduced to the time of observation by means of the annual variation given in the same table. When very great accuracy is required, the right ascensions and declinations, thus obtained, must be corrected for the aberration and nutation, as explained in the precepts of Tables XLII XLIII; but in general these corrections may be neglected. These corrections are, however, all oticed in the places of 100 of the most noted fixed stars, given in the Nautical Almanac since the year 1834, for every ten days in the year; and when any of these stars are used, the places must be taken out, to the nearest day, from the Nautical Almanac, without any further correction, because the varia tions in ten days are very small. Thus, on July 29, 1836, Procyon's right ascension was 7h 30m 43′, north polar distance 84° 21′ 29′′, or 5° 38′ 31′′ N. declination, corresponding to 95° 38′ 41′′ south polar uistance. This additional table of the Nautical Almanac simplifies this kind of calculation considerably. The sun's right ascension and the equation of time are to be taken from the Nautical Almanac, for |