Every navigator has, at various times, been confronted with the situation where a badly needed observation of the sun or other body was rendered temporarily impossible due to an obscured horizon. It is then that one prays for a bubble sextant that may be used with satisfactory results on a surface craft. Under such circumstances the horizon, while obscured directly beneath the body, may be quite clear at the opposite sector. Such conditions are frequently met when a vessel has encountered hazy or intermittently foggy weather.
It often happens that at evening twilight, the star most desired for an observation is located above that sector of the horizon opposite the setting sun, where a good observation is rendered impossible due to a poor and rapidly disappearing horizon. Possibly an overcast sky during twilight has prevented any evening star sights, and, as is so often the case, several bright stars pop out after the horizon has disappeared. At the same time the full moon has illuminated the horizon with sufficient clarity for an observation on the opposite sector from the star which it is wished to observe.
Our present-day textbooks are silent as to the possibilities of taking an observation under the above noted conditions and the navigator will be inclined to curse his luck and hope for better conditions later.
The Back Sight
All is not lost, however, and if the navigator will avail himself of the possibilities of a "back sight," he will thereby be enabled to utilize what has otherwise appeared to be a hopeless situation and obtain an observation.
The back sight, as the name implies, is an observation made with the sextant while facing the horizon in the opposite direction to that of the body observed. A little practice will enable the observer to attain great proficiency in this observation and with results equal to the best that can be secured when facing the body observed in the conventional manner.
The manner of correcting the observed altitude to obtain the true is obviously somewhat different from the conventional way and the following rules apply: The observed altitude is first subtracted from 180° to give a sextant altitude similar to that which would have been obtained had the observer been facing the body in the conventional manner. As noted in the sample problem, the altitude corrections are then applied to obtain the true altitude, being applied in the usual manner with the exception of the dip which in the case of back-sight observations is always additive.
When observing the sun for a back sight, it will be found easier to make good contact with the opposite horizon if the upper limb is brought over and down. This will make the sun appear in the horizon mirror in the same relative manner as it does when observing the lower limb in the conventional manner, i.e., when facing the sun. An inspection of the accompanying sketch and sample observation should make this clear. Note that the corrections are applied as for the upper limb.
As far as can be determined, the possibilities of this sight are not described in any of the present-day textbooks, in which the practice of navigation is usually reduced to the barest essentials. However, the fore sight and back sight were fully described in the works on navigation published during the nineteenth century. When so described, a cautionary note was usually appended warning the observer not to use the back sight unless the altitude was over 60°, for which reason this sight was usually restricted to the meridian altitude observation. Upon casual inspection this cautionary warning appears to be superfluous until the reader recollects that the early sextant was in fact a sextant, i.e., its arc was one-sixth of a complete circle (60°) and its range of angular measurement was therefore 120°. Our present-day sextants (so-called) have arcs which are generally graduated to at least 180° making them in fact quadrants and it will be seen that they may thereby be used for the back sight with any altitude.
The following description of the back sight was taken from an English work on navigation published just prior to 1800;
The Back Observation is managed the same as the Fore Observation, only your back must be turned towards the sun, and the screens shifted to the back Horizon Glass, remembering to subtract the Sun’s Semi-Diameter (if the apparent lower limb be taken) and add the Dip, subtracting the Effect of Refraction, and you will have the Altitude of the Sun’s Centre.
The Sunrise-Sunset Sight
In none of the modern textbooks on navigation will there be found any mention or description of the sunrise-sunset sights. These observations were looked upon with considerable favor during the latter part of the nineteenth century and were treated at more or less length in the navigational textbooks of that period. The U.S. Steamboat Inspectors were still asking questions relating to these sights up to the time of the World
In the past the descriptions published of the sunrise-sunset sights were all worked out for longitude by means of the old chronometer or time-sight formula, and the inclusion of these sights had been dropped from the textbooks before the Marcq Saint-Hilaire methods had become popular. As far as can be determined, no description of these sights computed by means of modern methods has ever been published.
It is obvious that at sunrise and sunset, when the sun's center is in the visible horizon, it is unnecessary to use the sextant to measure its altitude for it may be found by suitably combining the refraction, dip, and parallax.
It is difficult if not impossible to estimate the exact time when the sun's center is in the visible horizon, but, for the purpose of this sight, it is quite a simple matter to observe and note the times of contact with the horizon of the upper or lower limb. The application of the necessary corrections then gives the true altitude of the sun's center. The true altitude will be found to have a negative value due to the excess of the dip and refraction over the other corrections.
The refraction for 0° (36'29") is obtained from Table 20A, Bowditch, the parallax from Table 16, Bowditch, the dip from Table 14, Bowditch, and the semi-diameter from the Nautical Almanac.
The old textbooks sometimes used a combined correction or constant composed of an average semi-diameter, dip, refraction, and parallax. This constant amounted to —21' for the lower limb and —53'for the upper limb, but as this was for a height of eye of 12 feet, its use on modern vessels with lofty bridges would result in considerable error in the line of position so obtained.
The particular value of the sunrise-sunset sight lies in the fact that the sextant is dispensed with; consequently, should that instrument be damaged, the navigator is not entirely dependent upon his dead reckoning. For this reason, such observations would be of particular value in the event of shipwreck should the life-boats have time but no sextant. However, a more frequent use for this observation may be found when obscured skies during the day have prevented the usual sights of the sun. It frequently happens that the sun’s upper or lower limbs may be observed when they come into contact with the horizon as the sun comes out from beneath the clouds just before setting.
After noting the time of contact, the observer may proceed with the calculation of the computed altitude by means of any method which he may elect, and, like the observed altitude, the result will have a negative sign if the zenith distance is greater than 90° as it invariably will be. When applying the true (observed) altitude to the computed altitude to obtain the altitude intercept, it must be recollected that we are now dealing with negative quantities and that the old rule of “true greater towards” no longer holds good. The rule now becomes, “If the observed (true) altitude is greater, the intercept is away.”
Should the D.R. position be in error by 50 miles or more, or should the observer use one of the short methods” employing an assumed position at some distance from the D.R. position, the zenith distance may be less than 90° which will cause the computed altitude to take a positive sign. When using any of the “short methods” which solve for the computed altitude directly and do not use the zenith distance, it will be found difficult, if not impossible, to give the proper sign to the altitude so found. The writer, therefore, suggests that the zenith distance be computed by means of the Marcq Saint-Hilaire cosine-haversine formula using logarithms. No difficulties will be experienced in looking up the functions inasmuch as the tabulated values are alike for both positive and negative angles.
Near the horizon the refraction changes very rapidly. At the horizon it is about 36' while at an altitude of 0.5° it is only 29'; so that, as the sun rises or sets, the bottom of its disc is raised 7' more than the top, and the vertical diameter is thus made apparently about 20 per cent shorter than the horizontal diameter. This distorts the disc into the form of an oval, flattened on the under side. If the sun rises or sets considerably distorted or elongated, it is evidence that the refraction is excessive.
The observer will find that a good marine glass will be an excellent aid in determining the exact time of contact of the upper or lower limb with the horizon.
The reader will note that the results obtained from a sunrise-sunset sight will give an approximately north-south line of latitude and declination), and hence the vessel’s approximate longitude. Under good conditions, the results obtained from an observation of the sun for a sunrise- sunset sight will be found to be surprisingly accurate.
The following observations were made at time of sunset of the sun’s lower and upper limb and illustrate the manner in which this sight is to be used. These observations were made at a known position and under ordinary conditions. An inspection of the results will indicate the dependence that may be placed upon this observation.