In order to secure the local mean time (L. M. T.) of a star’s transit, the G. M. T. of the star’s transit over the Greenwich meridian is found in the Nautical Almanac (p. 96) for the first day of the month and correct for the day by table on next page (N. A.). The ship’s mean time of transit will be the same, as both sun and star hold their relative positions as the star moves from Greenwich to the ship’s meridian except for the small retardation of the sun’s movement over the star’s movement. This is best found at the foot of page 2, Nautical Almanac, where the longitude in time gives the correction to be subtracted from (G. M. T.) of transit which will give the local mean time of transit at ship—the time to observe the star. An observation of a planet is similarly handled. The moon is somewhat unreliable owing to its rapid changes in position and the large corrections necessary to correct the altitude, and is consequently rather an unpopular body to observe. However, there are times when she might prove valuable in giving position when much needed.
In the case of the sun the time of transit is local apparent noon, by applying the longitude in time gives Greenwich apparent time of local noon, and corrected for equation of time gives Greenwich mean time of transit.
It is often necessary to report the latitude at noon very quickly to the master. This can be accomplished by calculating the problem to a point where the addition or subtraction of the observed altitude is all that is necessary to give the latitude. The corrections are applied in advance by the estimated altitude, and declination corrected by the estimated longitude. Art. 325, Bowditch, gives the constants to be used in four different situations.
Circum- or Ex-meridian Altitude
It frequently happens, especially in the higher latitudes, that an aggravating mass of cloud drives over the sun or other objects that you are chasing, with the tangent screw, and it is lost from view together with all hope of a meridian altitude. But such an unfortunate occurrence as the loss of the mid-day latitude may be averted by employing the Circum-meridian sight or Ex-meridian, as our English cousins call it.
The mariner accustomed to its use “shoots” the sun and notes the time by chronometer or watch. Or on cloudy days, he would be standing by, near apparent noon watching for a chance to catch a glimpse of the object through a rift of cloud, and thereby forestall the loss of his latitude.
The theory of this observation is extremely simple, being merely to add to the observed altitude, taken before or after apparent noon when the sun is being considered, the amount of rise or fall between the time of sight and the time of culmination, and proceed with this amended altitude as in an ordinary meridian altitude sight.
The use of this method of obtaining the latitude is restricted to certain limits. Those who use Bowditch Tables will find themselves restricted to 26 minutes from the time of transit and a declination of 63°, while Brent’s Ex-meridian Tables allow a greater scope and their limit of 70° of declination includes many stars that would be otherwise unavailable. A good guide is to never allow the number of degrees in the zenith distance to be exceeded by the number of minutes from noon. In very high altitudes circum-meridians are not to be recommended, and the higher the altitude, the more accurate must be the time used. This is plain when it is realized that the lower the sun’s altitude at noon, the more nearly its diurnal path approaches the line of the horizon; with the lessening curve of its course, comes a lessening rise near noon, hence less accuracy is needed in the exact time of sight from that of transit. In the tropics, however, where high altitudes of the sun prevail, the clouds do not offer such an element of bother as they do farther north or south, and there this problem as applied to the sun loses its popularity.
In practice the use of the tables of Bowditch makes this problem an exceedingly simple one, requiring but few figures. Table 27 contains the value of rise of the body for one minute, but as this rise varies as the square of the interval from noon, it becomes necessary to resort to another table (26) of constants for a multiplier, in lieu of the number of minutes from noon. That is, if we should multiply the amount of rise or fall for 1 minute by the number of minutes from noon, we would not be taking into account the decreasing rapidity of rise or the increasing rapidity of fall as the body approaches or leaves the meridian. But Table 26 provides a multiplier which reconciles this inequality and gives the proper correction to apply to the observed altitude.
This quantity is added in every case where the upper transit is observed but subtracted when a sight is taken below the pole where the conditions are reversed.