It is surprising to us, in these advanced days of nautical science, to read of our adventurous ancestors of a century ago navigating their ships to all parts of the known and unknown world with nothing to guide them but their dead reckoning and the latitude crudely obtained by the method of meridian altitude. Many of our finest ships, as late as the first decade of the nineteenth century, sailed to China and back with no knowledge of their longitude save what the master guessed it to be. Even in later days much navigating has been done in the less lucrative trades by mariners who had no knowledge of the method of finding longitude. It required more time and distance to navigate by latitude and dead reckoning only, as it was not always safe to lay a course from an indefinite position directly for the coast. It was the custom in the old days to keep off soundings until on the latitude of the port of destination, then steer due west, and whatever the longitude might turn out to have been the master would sooner or later make the land in the vicinity of his port.
The first step in obtaining the latitude by meridian altitude is the measurement with the sextant of the sun’s altitude. This is done when it reaches its highest point in its course across the sky; this occurs when it bears due N. or S. true and this moment is local apparent noon. A few minutes before this time the image of the sun should be brought to the horizon, and by swinging the lower part of the instrument the image will be made to swing likewise in an arc; the lowest point of its lower edge (limb) should then be brought in contact with the horizon as closely as the circumstances will permit. The image will keep rising from the horizon, but by using the tangent screw it can be continually brought back to contact. At noon it will hang, and dip below; the reading of the sextant at this moment is the meridian altitude.
In working the problem three quantities are used and the navigator must be familiar with them:
The first is the zenith distance (z), which as its name implies is the sun’s (or stars) distance from the zenith. Zenith is 90° from the horizon, so the true altitude of the body subtracted from 90° is z the quantity desired.
The second element is the declination (d), which is the distance in degrees, minutes, seconds, of the body either north or south of the equator. This is taken from the Nautical Almanac.
The third and resulting quantity is the latitude, which is the distance in degrees, minutes, seconds, of the ship either north or south of the Equator.
The altitude observed taken with the sextant at noon is corrected for semi-diameter, parallax, dip, refraction and instrument error (if any exists). These corrections are explained in detail in Corrections for Observed Altitudes.
The declination of the sun is constantly changing between 23½° N. and 23½° S. This is given in the Nautical Almanac for each two hours of Greenwich mean time with the difference for each hour given for each day. So it becomes necessary to ascertain the declination at the moment of observation, namely, at local noon. This anywhere in the Atlantic will occur subsequent to Greenwich noon, as the sun (apparently) passes around the world from the eastward to the westward once a day—24 hours—which corresponds to 360° of longitude. The rate of travel is therefore equivalent to 15° in an hour. Hence if the sun crosses Greenwich meridian and five hours later crosses the meridian of the ship, say in 75° W., the interval is 75 divided by 15, or 5 hours. During this interval the sun has changed in declination northward or southward and should be picked out of the Almanac for 5 hours Greenwich mean time.
When the zenith distance and declination are at hand the latitude is obtained by a mere algebraic addition, which is, z + d = latitude; where, if the body bears south the z is marked +, if north it is marked -; if the declination is south it is marked - and if north it is +. The result of the addition if - indicates south latitude, if + north latitude. The meridian altitude of a star, planet or moon is found in a similar manner. The formula of z + d = latitude, having regard to signs named as above, is applicable to each. The declination and the correction of the observed altitude are picked out of the Almanac and Bowditch tables in a somewhat different manner peculiar to each body.
It is found by many navigators to be more convenient to observe a body for meridian altitude by time than in waiting for the “dip.” The altitude is taken at exactly local apparent noon in case of the sun and the time of meridian passage in the cases of other bodies. This expedient is especially desirable in observing stars, as the horizon is not as distinct and the “dip” not so easily detected as with the sun.