At morning twilight at about 03:17 (Zone -11) on 04th Dec in D.R. Posn. Lat. 46º 04.0 S., Longitude 158º 44.0 E., three celestial bodies were observed commencing with a meridian altitude of *Procyon as it was seen to be approaching the meridian, Brg. N. The observation of *Procyon gave Lat. 46º 02.0 S. at 3d. 16h. 15m. 36s., while the other two observations were as follows: –

Chosen Position (C.P.) G.M.T. Body, Intercept, True Bearing

46º S., 158º 27.3 E. 16h. 16m. 48s. Jupiter10.8 TOWARDS 046º T.

46º S., 158º 58.8 E. 16h. 17m. 52s.

* Rigel 5.3 TOWARDS 308º T.

The plot for Ex. No. 1 is shown on the ASTRO-NAVIGATION STUDY PLOTTING SHEET EX. NO. 1. Since the D.R. Position is Lat. 46º 04.0 S., Long. 158º 44.0 E., the central parallel of Lat. was designated Lat. 46º S., the left-hand meridian Long. 158º E., the central meridian Long 158º 30.0 E. and the right-hand meridian Long. 159º E. Latitudes and distances. were measured from the 46º Lat. scale at the right of the plotting sheet (i.e., the first vertical line from the left-hand side of the scales), remembering that since we are in S. Lat., the Lat. will increase downwards on the plotting sheet. Longitudes can be read directly from the scale along the bottom of the plotting sheet.

The meridian altitude of *Procyon resulted in a Lat. 2′ N. of the D.R. Lat., and this was plotted as a meridian altitude position line, the shorter arrow indicating that the body was bearing N.. The second observation, that of the planet Jupiter, was calculated from the chosen or assumed position 46º S., 158º 27.3 E. (marked CP1) and the intercept of 10.8 laid off towards the true bearing of Jupiter in an 046º T. direction from this position, the position-line being drawn in at right angles to the true bearing and of sufficient length to cut the mer. alt. position line from *Procyon.  The third observation. that of the star *Rigel. chosen because its azimuth was such as to form a good cut with the other two (three stars separated in azimuth 120º would be ideal). was calculated from the chosen or assumed position 46º S., 158º 58.8 E. (marked CP2). The intercept of 5.3 was therefore laid off from this position in a 308º T. direction (the true bearing of *Rigel) and the position line was drawn in at right angles to this so as to cut the two previous position lines.

The three-position lines result in the small triangle familiar enough to coastal navigators and known as a cocked hat. Theoretically, of course, the position lines should meet at an exact point and the fact that they sometimes do does not necessarily mean that an error in calculation has been made.

The measurement of altitudes with a sextant is necessarily a matter of experience and judgement and small errors introduced at this stage will reflect in the final result, and even the most experienced navigators are limited by the stability of the platform on which they stand (their vessel’s deck – which can be extremely unstable on occasions at sea). and by meteorological conditions such as the necessity to make a snap observation of a body as it momentarily becomes visible between clouds or a poorly defined horizon.

In Astro-navigation, providing a cocked hat is reasonably small, the observed position can usually be accepted as being the centre of the triangle, as in Ex.
No.1.the observed position or fix has been taken to be:

Lat 46º 01.0 S., Long. 158º 49.0 E.

If, after working and plotting three position lines from three celestial bodies, it becomes obvious that one of the position lines is in error (unless one of them is so far out as to make it evident which one of them needs correction) then it may well be any one of the three, and the only resort is to rework them. It all the calculations are found to be correct, then one of the sextant readings must have been either badly observed or incorrectly recorded, but the question still remains – which one?  In this case, another set of observations is the only solution. This is a good argument in favour of observing four altitudes – the fourth only to be worked in case of error in one of the other three.


On a vessel bound from Guernsey to Plymouth on a Cse 310º T. D.R. Posn. Lat. 49º 47.0 N., Longitude 02º 54.0 W., a Mer. Alt. of Venus ♀was combined with an observation of the Sun in order to obtain an observed position. The Mer. Alt. of Venus ♀(brg. S.) at 15h. 26m. 55s. G.M.T. gave Lat. 49º 45.9 N., while the Sun observation at 15h. 28m. 23s. G.M.T., worked from assumed position 50º N., Longitude 03º 20.3 W., gave an intercept of 9.3 AWAY from Sun’s true bearing 253º T.

The plot for Ex. No. 2 is shown on the ‘Ocean Navigation’ Plotting Sheet Ex. No.2. In this case the central parallel of Lat. was designated Lat. 50º N. the right-hand meridian Longitude02º 30.0 W., with the central meridian 03º 00.0 W. and the left-hand meridian 03º 30.0 W. Latitudes and distances were measured from the 50º Lat. scale to the right of the plotting sheet (i.e., the fifth vertical line from the left-hand side of the scales). Again, longitudes can be read directly from the scale at the bottom of the plotting sheet, remembering to read this scale from right to left in this case because we are in W. Longitude.

The Mer. Alt. position line for Venus ♀(bearing S.) was first drawn in the vicinity of the D.R. position through Lat. 49º 45.9 N. Next, the chosen or assumed position for the Sun observation was marked (C.P.) and the intercept of 9.3′ laid off AWAY from the true bearing (253º T.) of the Sun, i.e., in an 073º T. direction. The Sun’s position line was finally drawn in at right angles to the intercept and of sufficient length to cut the Mer. Alt. position line of Venus ♀at the required observed position

Lat. 49º 45.9 N., Long. 02º 58.4 W.

When two observations are made within a minute or two of each other, they may as a rule be considered simultaneous sights. The interval between them being comparatively small and the distance run between sights being so short, there is normally no need to transfer one of the position lines to compensate for it. It is as well to remember, however, that 1 knot is equivalent to 100ft. per minute, and that at 6 knots a vessel will travel 1 cable (or one-tenth of a nautical mile) in 1 minute, or ¼ mile in 2½ minutes, and if true accuracy is required one of the position lines (if two have been obtained) should be transferred either forwards or backwards along the vessel’s track to cut with the other one at a common time. If three or more position lines have been obtained then all except one should be transferred by appropriate amounts so that they cut one another at a common time.

On slow-moving vessels when the run between sights is negligible, no such adjustment is normally necessary unless the accuracy of the position required is critical because the vessel is near danger. There are occasions, however, when an unexpected delay occurs between observations; it may be necessary to wait for a cloud to clear the next celestial body to be observed, or something may happen on deck to absorb the navigator’s time for a moment or two. In these cases the time between observations may necessitate one or more of the position lines being run-on so that they all cut at a common time. Similarly a fast-moving vessel may cover an appreciable distance between sights, and earlier position lines must be run-on accordingly or all position lines adjusted to a particular time, in order to obtain an accurate observed position. It is usual to record the log reading at the time of recording of all sights to enable position lines to be transferred according to the distance run between sights, or to enable the D.R. to be updated. The next example shows how such adjustments are made.


On a fast powerboat at 16:50 (Zone +2) in D.R. Posn. Lat. 50º 07.0 N., Longitude 30º 47.0 W., Course 070º T., speed 25 knots, observations gave the following results: –

C.P.                                  G.M.T.                    Body             Intercept      True Bearing

50º N., 30º 46.0 W.       18h. 46m. 13s.       Moon.           5.0 AWAY        192º T.

50º N., 30º 18.1 W.       18h. 47m. 55s.       Jupiter        11.0 AWAY      162º T.

50º N., 30º 27.8 W.       18h. 49m. 33s.     *Aldebaran    11.0 AWAY      090º T.

Find the Observed Position at 16:50 (Zone +2)

The plot for Ex. No. 3 is shown on the OCEAN – NAVIGATION COURSE PLOTTING SHEET EX. NO. 3. In this case the central parallel of Lat. was designated Lat. 50º N. the right-hand meridian Longitude 30º 00.0 W., the central meridian Longitude 30º 30.0 W., and the left-hand meridian Longitude 31º 00.0 W. Latitudes and distances were again measured from the 50º Lat. scale, and Longitude taken directly from the scale at the foot of the plotting sheet.

From the G.M.T.’s of the observations, it was seen that the first observation (of the Moon) was actually made at 1646¼ (Zone time). The position, however, was required for 1650, so that the Moon’s P/L must be run on for 3¾ minutes at 25 knots ( = 1.6 miles) similarly, Jupiter’s P/L must be run on for 2 minutes ( = 0.8′ mile), and *Aldebaran’s P/L for ½ minute ( = 0.2′ mile). In practice it is simplest to draw each run-on from the chosen or assumed position before drawing in the intercept, so from the C.P. for the Moon (50º N. 330º 46.3 W.) a short line of length 11.6′ was drawn in the direction of the powerboat’s Course (070º T.) to position A, then the Moon’s intercept was drawn for 5.0′ away from the true bearing of 192º T. and the Moon’s position line (drawn as a transferred P/L with two arrowheads at each end) drawn in at right-angles to the intercept. 

The C.P. for Jupiter (50º N. 30º 18.1 W.) was run on 070º T. for 0.8′ to B before drawing the 11.0′ intercept away from the true bearing of Jupiter (162º T.) and, at right-angles to this, Jupiter’s transferred P/L to cut the Moon’s P/L. Finally the C.P. for *Aldebaran (50º N., 30º 27.8 W.) was run on 070º T. for 0.2′ before measuring the intercept 11.0′ westwards (i.e. from the true bearing of 090º T.) and plotting *Aldebaran’s P/L in a N-S direction. In this case, all three position lines cut at the same point, and the vessel’s position at 16:50 (Zone +2)

Lat. 50º 05.7 N. Long.. 30º 44.5 W.


A Double Sight, will be remembered. is one in which the position line obtained from the observation of a celestial body is run-on along the vessel’s course to be combined with a later observation either of the same body (when its azimuth has changed sufficiently for its position line to give a good angle of cut with the previous one) or of another body whose azimuth is suitable, in the same way as a running fix in coastal navigation.

The first position line is plotted in the same way as described previously for simultaneous sights. It must now be transferred along the vessel’s estimated course made good by an amount equal to the vessel’s estimated distance made good in the time interval between the first and second observations. At first, it might appear immaterial from which point on the first P/L the vessel’s course is plotted, since any point chosen will produce the same transferred P/L at the end of the run.

Consider, however, the position line in fig. 22-4 which has been drawn with an intercept of 30 miles from an assumed or C.P.

The vessel’s position must lie somewhere on this position line but it is clear from the figure that the C.P. from which the intercept was plotted is a great deal further away from the P/L than the navigators original D.R. or E.P..

Suppose it is now required to transfer this P/L to combine with a second P/L later, and that the vessel’s course is 280º T. Had the vessel’s course been plotted from position J. that point on the P/L nearest to the E.P., it would be obvious that the vessel was standing into danger. If, however, the course is plotted from position A, the intersection of the intercept and the position line, the navigator might well be misled into believing that the vessel will pass a safer distance from danger.

Obviously, this problem will not arise if the vessel is a long distance from land or any possible submerged hazards, but when in the vicinity of any dangers or about to make a landfall it is recommended that having plotted the first position line in the normal manner from the assumed or C.P., the vessel’s E.P. is then plotted and a perpendicular dropped on to the position line from the E.P. to obtain the point J., and the vessel’s course plotted from point J in order to transfer the position line.

Fig. 22-5 illustrates this general principle incorporated into the plot for the most common of all Double Sights – a morning Sun position line combined with a noon Sun meridian altitude.

The morning Sun position line was plotted in the normal way from the C.P. used for working the sight. Then the vessel’s D.R. or E.P. at the time the sight was taken was plotted, and a perpendicular dropped on to the position line at J. Next the estimated course and distance made good between the morning observation and the time of meridian altitude was plotted from J to give the second D.R. or E.P. through which the first P/L was transferred parallel to its original direction. Finally, the Sun’s meridian altitude position line was plotted to cut the transferred P/L at the vessel’s observed position at noon.


At 0647 (Zone +3) in E.P. Posn. Lat 00º 09.0 N., Longitude 51º 55.0 W. during morning twilight an observation of Venus ♀gave an intercept of 18.2 AWAY, Venus bearing 137º T., using an assumed position on the Equator in Longitude 51º 48.9 W. Later in the day, a meridian altitude of the Sun at 12:23 (Zone +3) gave Lat. 00º 20.7 N. If the vessel is estimated to have made good a course of 282º T. at 6.3 knots between the observations, find her position at the time of the Sun’s meridian altitude.

The plot for Ex. No. 4 is shown on the OCEAN-NAVIGATION STUDY PLOTTING SHEET, EX. NO. 4. Here the central parallel of Lat. was designated Lat. 0º (the Equator). the right-hand meridian Longitude 51º 40.0 W., the central meridian Longitude 52º 10.0 W. and the left-hand meridian 52º 40.0 W. Since the base parallel is the Equator, where the Lat. and Longitude scales are equal, the Longitude scale can in this case be used for all measurements of Lat., distance and Longitude.

The assumed position for working the Venus ♀sight was first plotted in Lat. 0º 00.0. Longitude 51º 48.9 W. then the intercept of 18.2 drawn away from Venus bearing of 137º T. and a position line drawn in at right angles to this. Next, the vessel’s E.P. was plotted and a perpendicular dropped on to the Venus ♀position line.

At this point, in practice at sea, the time of the Sun’s Mer. Pass. would have to be calculated before the run between sights could be found.

Since the calculation for the time of Mer. Pass. (see Lesson 4) uses the Longitude at the time of passages and this is not known at this stage, the calculation must be done in two steps. A first approximation in obtained by using the vessel’s DR. or E.P. Longitude (52º W. in this case), given a G.H.A. of 52º with which to extract the approximate time of the Sun’s Mer. Pass. from the N.A., and let us suppose this is 15h. 18m. G MT or Zone time 1218 (Zone +3). The run from the Venus ♀sight to the time of Mer. Pass. (06:47 – 12:18) is 5.5 hours at 6.3 kts. or 34.6, which, if plotted from point J, gives a Longitude at 1218 of 52º 34.0 W. Using this E.P. Longitude, a more accurate time of the Sun’s meridian altitude can be calculated, and in this case was found to be 12:23 (Zone +3).

The run to the time of Mer. Pass. should therefore have been 5.6 hours (06:47 – 12:23) at 6.3 kts. or 35.3, so this was plotted from point J on the plotting sheet to give the 12:23 (Zone +3) E.P. in Lat. 01º 22.0 N., Longitude 52º 34.5 W. through which Venus ♀’ transferred position line was drawn. Finally, the meridian altitude position of the sun was drawn in a 090º~ 270º direction through the observed Lat. of 00º 20.7 N. and the 12:23 observed position marked? where the two position lines intersect. By measurement from the common scale, the observed position was found to be: –

Lat.. 00º 20.7 N. Long. 52º 36.0 W.

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