NAVIGATION 269 Finding the latitude by a meridian altitude of a star differs from a similar operation for the sun only in so far as there is no semi- diameter or parallax to be applied. Star observations are of great value after the sun has been obscured for one or more days, for which reason a navigator should know all the principal stars, so as to recognize them during a very partial clearance of the sky. The Nautical Almanac gives the positions of all the principal fixed stars. The apparent right ascension of a heavenly body is its angular dis tance from the true equinox, expressed by the abbreviation R.A. Sidereal time, given in page ii. of each month in the Nautical Almanac for mean noon each day, is the angular distance between the mean or imaginary position of the sun and the true equinox. Declination is the distance from the equinoctial or celestial equator. Mean time is that shown by a good clock, regulated upon the sup position that every day is of equal duration. Apparent time has reference to the time actually occupied by the sun between successive transits over any meridian. Equation of time is the difference between mean and apparent time. Sidereal time is measured by the transits of a star over any meridian. See ASTRONOMY. To find the time that any star will pass the meridian, subtract the sun s R.A. from that of the star ; or, in other words, find their distance apart as expressed in time by R.A. As an instance, on May 10, 1882, between 7 and 8 P.M. the sun s R.A. was 3 h 10 m and that of ollrsffi Majoris 10 h 56 m ; consequently the star will pass the meridian of the ship in 7 W. at 7 h 46 m . The knowledge of the longitude is only necessary for finding the Greenwich time (G.T.) and the sun s R.A. The same night, the R.A. of Vega (a Lyrae) being 18 h 33 m and that of the sun 3 h ll m , the star was 15 h 22 m after the sun, and would pass the meridian about 3 h 22 m A. M. of next day. To know which suitable star will pass the meridian after a certain hour, add that hour to the sun s R.A., the sum will be the R.A. of the meridian (decreased by twenty-four hours if necessary); the star table will then show the stars of that or greater R.A. Thus, on October 2, 1882, in 160 E. long., which bright star will pass the meridian after 10 P.M.? The difference of longitude in time being 1 O h 40 m E. , when the sun has passed the meridian ten hours it will evidently be forty minutes before noon at Greenwich, therefore the sun s R. A. will be 12 h 33 | m at the time named. As it will be 10 p. M. at ship, the R.A. of any star then on the meridian must be (12 11 33J m + 10 h ) 22 h 33| m . The first bright star found in the table having greater R.A. is Fomalhaut (a Pis. Aus.), the R.A. of which is 22 h 51 m , which is seventeen minutes more than the time sought ; consequently that star will pass the meridian of the ship at 10.17 P.M., and Markab (a Pegasi) eight minutes later. Another ship on the same day being in 90= 6 hours west, the sun s R.A. at her 10 P.M. would be 12 h 36 m , and Fomalhaut would pass her meridian at 10.15 P.M., two minutes earlier by apparent time ; the difference is due entirely to the change in the sun s position. All doubt will be removed, when finding the approximate time of a star s transit, if it be remembered that the sun (from which we reckon apparent time) indicates a position the R.A. of which is known ; therefore by adding any time which it may have passed the meridian the R. A. of another meridian in the sky is obtained, called the R.A. of the meridian at that moment. Having the true altitude of a star, and thus the Z. D. (zenith distance), we can determine the latitude without risk of mistake by remembering that the declination in the heavens corresponds with the latitude on the earth ; therefore a star will pass the zenith of every place whose latitude corresponds with its declination. If a star having north declination passes south of the observer, the zenith distance must be added to the declination, as the latitude is then the greater. If such a star pass north of the observer, his north latitude will be less than the star s declination, and the differ ence will be the latitude. The reverse holds good if the star has south declination and the observer is north of the equator. An old rule is also useful and simple : If the zenith distances be invariably marked north or south according as the observer is north or south of the object observed, and the declination placed under it marked north or south, add like signs and take the difference of the unlike; the latitude will take the name of that which preponderates. The oldest of all nautical observations is that of taking the height of the pole-star, a star which everybody should know whether at sea or on shore. If it were exactly at the pole the corrected altitude would be the latitude, but it is not so. During 1882 its mean declination has been 88 41 , therefore it describes a diurnal circle round the pole with a radius of seventy-nine minutes. It was once far from the pole, and now advances nearly nineteen seconds annually. The mean R.A. has been during 1882 about l h 16 m , increasing about 28 s annually. The time it passes the meridian above and below the pole can be found as has been before described; and 1 19 being subtracted from the upper transit or added to the lower one will give the latitude. The great consideration attached to the pole star is in consequence of the facility it affords, with very little calculation, for finding the latitude at all times when the star and horizon are visible. It is necessary to know the time at ship to the nearest minute. Apparent time is invariably kept on board ships at sea, corrected at noon each day. The change of longitude since noon must be roughly worked up in order to find the correct apparent time at ship, also the Greenwich time within half an^hour, for the purpose of finding from the Nautical Almanac the sun s R.A. at that time, which added to the time at ship will give the R.A. of the meridian, rejecting twenty-four hours if neces sary. With all nautical tables there is one for finding the latitude by the pole star, in which the correction is given for every ten minutes. Enter the table with the year and R. A. of meridian. Opposite the latter, or by proportion, will be found a correction + or - to be applied to the true altitude ; the result will be the latitude. The principle of this table is that when the R.A. of the meridian coincides with that of the star the whole mean distance of the star from^the pole for that year must be subtracted, while if the two R.A. s differ by exactly twelve hours the same distance must be added, as the star is then on the meridian below the pole. If the star is six hours from the meridian on either side no correction is necessary. At other points the correction varies as the cosine of the time angle between the pole star and the meridian. Thus the R.A. of the pole star being l h 16 m for 1882, and distance 79 minutes, the correction corresponding to five hours is thus found : 5h _ !h 16 m = 3h 44m. 79xcos3 h 44 m = ^ ^ rad. (Multiply the decimals taken from the logarithms of numbers by six, to bring them into seconds. ) As the star was less than six hours past the meridian the correction is - . A similar calculation having been made for every ten minutes of one quadrant, the result may be applied inversely to the one below it, and the remaining twelve hours written on the opposite side of the page with the sign + or - the reverse of the first column. It is evident from the above that the table may be easily dis pensed with ; also, as annual tables must be founded on the mean position of the star during that period, greater accuracy would be obtained by taking the R.A. and declination for the day required from the Nautical Almanac, and finding the corrections as above. A table for finding the latitude by the pole star when off the meridian is also given in the Nautical Almanac with instructions. It is used with sidereal and mean time ; also an allowance is made for the spheroidal figure of the earth. When the latitude found by any star observation at sea is within one mile of the truth it may be considered satisfactory. Latitude by the meridian altitude of the moon is obtained in a manner similar to that applied to the sun, but not so simple. First it is necessary to ascertain the approximate time of transit, by reference to p. iv. of each month in the Nautical Almanac. It is there given in mean time both for Greenwich and the anti podes ; to one of those periods apply the proportion due to the ship s longitude in time. It is necessary to guard against a false horizon often produced by clouds under the moon. Having obtained the meridian altitude, correct for errors of instrument and dip. From Nautical Almanac, p. iii., take the moon s semi- diameter (calculated from the centre of the earth) for the nearest noon or midnight, augmenting it by a table for the purpose, as it increases with the altitude (only a few seconds) ; add it if the lower limb were observed, and subtract the refraction due to that altitude. Take from the Almanac the horizontal parallax for the time of observation, correcting it for decrease in proportion to altitude by a table for the purpose, and add it to the apparent altitude. Tables generally give the parallax due to Q altitude, minus refraction, in one correction. Having the true altitude, take it from 90, and mark the zenith distance N. or S. as it is north or south of the moon. Take the declination for the nearest minute of Green wich time. It is now given for every hour (mean time), and the change in ten minutes. Place the re duced declination marked N. or S. under the zenith distance ; add if the signs are like, or take the differ ence if unlike, and the result will be the latitude. Ex-meridian Altitudes, It is important to be able to get the latitude when the sun may have been obscured from a few minutes before noon till some minutes after. Such observations near the meridian are called ex-meridian altitudes. When the sky is cloudy the observer should keep the watch in hand in order to secure the apparent time with the altitude nearest the meridian. If the sun be rising fast or declining fast, it will be better to work the sight with two latitudes, and with the assistance of the chrono meter, as described below. In a low latitude and less than half an hour from noon, the pamphlet by J. T. Towson, containing tables for the reduction of ex- "8- 16 - meridian altitudes, will be found very useful, as the correction or allowance for what the sun would further rise (or had risen) can be taken out entirely by inspection, which saves the labour of working four propositions. The principle is illustrated by fig. 16, which is projected with double the angle at P in order to make it more
