observations of it can be taken at any time when it is visible, and from a convenient table given in the Nautical Almanac the altitude of the pole itself (which equals the latitude) is readily obtained.
Longitude at sea is in modern navigation always found by comparing local or ship mean time with Greenwich mean time, the latter being accurately known from the chronometers and the former from astronomical observations of suitably placed heavenly bodies. It may be assumed in all well found modern ships that on applying the known errors and accumulated rates to the times shown by the chronometers the Greenwich time at any instant is practically accurately known, and as the distance east or west of any place is merely the difference between the two local times at any instant expressed in degrees, so also is the distance east or west of Greenwich (longitude) the difference between time at place and Greenwich time at any one instant. The connexion between time and degrees depends upon the complete rotation of the earth in twenty-four hours, causing meridians 15° apart to pass under the same fixed point in the heavens at intervals of one hour, those east of Greenwich passing earlier and those west later, resulting in local time being in advance of Greenwich time in east longitude and vice versa in west longitude.
The errors and rates of gaining or losing of the chronometer referred to are known from observations made on shore prior to the beginning of the voyage with a sextant and artificial horizon, and these observations are capable of almost as great accuracy as those taken at fixed astronomical observatories. As this knowledge is absolutely essential every opportunity is taken at each principal port visited of either repeating such observations or obtaining the information from time balls dropped from observatories on shore at the Greenwich times indicated in the Time-ball pamphlet. Local or ship time can only be found with fair accuracy from calculations based on altitudes of heavenly bodies, when they are nearly east or west of the observer or technically on the prime vertical. Such times can be approximately seen from the azimuth diagrams or from tables of true bearings of heavenly bodies, and the error involved by uncertainty as to the position of the horizon can be greatly obviated in twilight or at night by taking the mean of results arising from nearly simultaneous observations of bodies bearing both east and west. In the usual case of determining time by observations of the sun the results arising from morning observations are compared with those similarly obtained in the afternoon. It will of course be remarked that should any unallowed-for error in the chronometer exist it will affect the resulting longitude by its full amount.
In considering the foregoing methods of astronomically fixing a ship’s position we notice that always when the two elements of latitude and longitude are determined at different times, and generally, as we shall presently see, when they are determined together (though usually for a shorter time) the navigator has to depend for some time on the accuracy of the course steered and estimated distance run; also when cloudy weather prevails he has to depend entirely on those elements for a knowledge of the ship’s position. The frequent astronomical observation of the error of the compass is therefore a most important and fortunately simple duty. In practice the error is found by a comparison between the compass bearing of a heavenly body and its true bearing, obtained either by calculation, or more generally from a graphic diagram (Weir’s azimuth diagram) or tables from which at practically any time when above the horizon the true bearings of the principal heavenly bodies are taken by inspection. These important observations are most accurately made when the body observed is bearing nearly east or west true, if not too high, but if clouds prevent observations at such times, fairly good results can be obtained by observing the compass bearing when the object is on the meridian (if not too high) and therefore lying north or south true.
The causes of the changing errors of a compass in an iron ship are described elsewhere (see Compass), but by making comparisons as above the navigator can at once ascertain what is termed the “total” error, and if he takes from that the portion of error due to the earth, or what is termed variation (known from a chart of such elements), the remaining error is that caused by the iron of the ship, technically known as deviation. The latter method of procedure has the great advantage of enabling the navigator to ascertain during a voyage whatever magnetic changes in the ship are taking place other than those he would expect to occur on change of position. The total error is that applied to compass courses.
Deviations greater than a few degrees are not merely inconvenient but in modern compasses produce unsteadiness or oscillation of the compass card, so that, especially in new ships, the skilful navigator reduces such errors by adjusting the compensating magnets when favourable occasions offer. Recognizing the great value of a sound knowledge of compass adjustment, the British Board of Trade have included this among the compulsory subjects of examination for the rank of master, thus following the example of the navy, where all navigating officers have to attend a practical course of study on the subject.
The practical problem of finding both latitude and longitude at the same time is the most important of all in modern navigation, and is rapidly superseding other modes of ascertaining a ship’s position. The principle involved depends upon the fact that every heavenly body is at each particular instant of time directly overhead or in the zenith of some place on the earth. Thus, if we take the sun as an instance, it is noon at all places on the meridian of 60° W. when it is exactly 4 p.m. at Greenwich, and at the one spot on that meridian where the observer is as far north or south of the terrestrial equator as the sun is north or south of the celestial equator (declination) it will not only be noon but the sun will be immediately overhead and will have an altitude of 90°. This, therefore, at any instant defines the position where the sun is vertical; its latitude must equal the sun’s declination and its longitude in time equal the time since noon at Greenwich. Now at distance of 60 m. in every direction on the surface of the earth from the point thus defined the sun will have an altitude of 89° and in all directions at a distance of 1200 m. its altitude will be 70° (＝90°−20°), so that on a globe, by marking the position where at a certain instant the sun is vertical and taking that as a centre, a series of concentric circles may be drawn, on all points of each of which the sun’s altitude will be the same. When, therefore, at sea we measure with a sextant at any time the altitude of the sun (say 60° 10′) we at once know we are somewhere on the arc of a circle having for its centre the spot where the sun is vertical at that instant, and for radius a distance equal to 1790′ (＝90°−60° 10′). Such information, combined with the best and most recent knowledge we have of the ship’s latitude at the time, will of itself afford valuable information as to the position, but by making two such observations, separated by a sufficiently long interval for the position having the sun vertical to have moved considerably (owing to the rotation of the earth), we are able to consider with certainty that we must be at one or other of the widely separated intersections of two such circles, the movement of the ship in the interval between the two observations being duly allowed for. The dead reckoning affords information as to which of these intersections is the true position.
Now even on a large globe it would be practically impossible to obtain very accurate results from this problem by drawing such circles, but on a large scale chart (or ordinary squared paper) much greater accuracy is obtainable. The method commonly used on a Mercator chart involves two suppositions: (1) that the concentric circles we have referred to will be correctly represented as circles on the chart, and (2) that these are of such diameters, that a portion of say 100 m. of arc may be considered to be a straight line coincident with the tangent to the circle and therefore at right angles to the direction of the sun. Except in high latitudes (above 60°) Mercator’s projection fulfils the first condition sufficiently well for practical purposes, and, except when the altitude is greater than 70°, the second condition is also approximately true since the radii of such circles will exceed 1200 m.
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Fig. 7. |
Premising these conditions, suppose that on a certain day at 9 a.m. when the ship’s approximate position, known from previous observations and laid down on the chart, is supposed to be at A (fig. 7), an observation of the sun is made from which the longitude is calculated, the result being that on the supposition that the latitude of A is correct, the ship’s position is probably at B. Now by drawing a straight line ab through B at right angles to the true bearing of the sun at the time of observation (which is most readily known from the azimuth tables) we are obviously right in assuming the ship’s position to be somewhere on that line if we consider it as approximately an arc of a large circle having the place where the sun is then vertical as a centre, the direction of such place being indicated by an arrow.
If our supposed latitude be right the position will be at B, but if not correct it must still be on the line ab, and if near land or any danger the direction of this line, even if no subsequent observation be available, will often give most valuable information. If, while waiting for the sun to change its bearing, the ship runs from B to C, a line cd drawn through C parallel to ab will represent an arc on which the position lies when she is probably at C, which at this instant (10.30 a.m.) is the most probable position of the ship.
If another observation of the sun for longitude is now made and the resulting position is D (lying of course in the same latitude as C), on drawing through D a line ef at right angles to the bearing of the sun (indicated by an arrow) we are right in assuming the position to be somewhere on such an arc as is represented by this line.
Hence E, the intersection of the two arcs on which the position lies at the same instant, must be the true place when the last observation was taken at the supposed position D, the discrepancies being entirely due to the original unknown error in the assumed latitude of A, for had that been accurate the position on the original line ab would have been such that on laying off the course and distance from that position C would have coincided with E.
Errors in the assumed latitude of as much in many cases as 30 m. will often be found to produce no practical difference in the resultant position, but of course the accuracy of the longitude found is entirely dependent upon the chronometer, and in such cases as arise when the intersecting arcs make a small angle with each other great accuracy
