Navigation is usually defined as that maritime art by which a mariner is able to get his vessel safely and expeditiously from one place to another. When within sight of identifiable objects or land, a navigator can establish his position and thus check his progress by two or more simultaneous bearings of shore objects, or by horizontal or vertical sextant angles of two or more shore objects. These methods comprise that branch of the subject known as Coastal navigation.

The early assumption of pre-knowledge in Navigation is that the student has studied and has practical experience of Coastal Navigation, understands navigational charts, the principals of position definition by Lat. and Longitude and by range and bearing, and the terrestrial methods of position fixing including the running fix.

Despite widespread amateur belief to the contrary, it is fundamentally no more difficult than coastal navigation, and indeed, there is less to learn than in coastal navigation. It does not involve any special mathematical knowledge to grasp its underlying theory and its practice does not call for calculations any more advanced than simple arithmetic, principally simple addition. It is true that the structure of Astro-navigation is held together by mathematics and it is the man that compiles the Navigation Tables and N.A.‘s who must be the mathematician, not the navigator, who merely uses them. There is nothing to prevent anyone with no more than a schoolboy’s knowledge of arithmetic and geometry from becoming a competent Astro-navigator.

A sextant is a simple instrument but the use of it requires a lot of practice. In the 1960’s, navigation reached a high level of accuracy because the technology was there (good instruments – daily radio signals a stable platform aboard vessels) and because the will and interest of the seafarers were there as well.

In the Merchant Marine, no sextants were provided and a cadet/midshipman joining the fleet and wishing for promotion to 4th Mate had to work hard (10 hours/day) for six weeks to be able to acquire his own sextant. If he wished to discern the suspicion of approval in the eyes of his 1st Mate, he could not board with less than a Plath with a 6 x 30 telescope.

The day that his observations and calculations were good enough to be relied upon, he was ready for promotion. Some had the knack of it after a few months, some needed 6-8 months, and some still had problems a long time after this. The practice was all day long in his spare time, 10-12 shots in the morning or afternoon depending on his watch (watch was for working, not for practising). If he got the sympathy of the Officer of the Watch, they took sights together – the quickest way to find errors and learn from mistakes. Once the Sun was mastered, the boy spent every evening on the bridge shooting stars (cutting hours off his sleep)

The 3rd Mate took at least three Sun sights in his morning watch of 0800-1200; all Officers joined together for Noon; the 2nd took a last Sun around 1600; the Chief-Mate and 4th took a star at evening and at dawn. When you came on the bridge, the first sight you had was a battery of sextants, from three to five, ready for use. As in other trades before industrialisation, a very high level of skill and craftsmanship was achieved. The Sun was tracked between and behind clouds, the horizon between showers; a few seconds was enough to get a workable sight. The best Officers knew up to 70 stars; 30 stars were minimum.

Fig. 1-1. At Noon, when at least three Officers were observing, the senior officers always achieved the same results to within 1 min. Which means there was no, or negligible, personal error. The same could be said when more than one Officer took stars; they came to the same position within one sea mile.

A marine sextant should be heavy Plath, the telescope clean and adapted to the sight of the observer personal sextant. The way a person takes a sextant out of its box and keeps it in both hands will tell you who he is.  Most cadets had problems with technique:

Eyesight keeping (adapting telescope to the eye)    The way of kissing, light or too heavy.

Swinging body and sextant around spine, finding the vertical plane    Rocking the sextant to keep it vertical

Point’s ii and iii give big errors, i and iv very small ones.

Ship movements should have no influence on the quality of a sight. Rhythmic movements like rolling, pitching, heaving are compensated by the body – that is why they are seamen. Unexpected surging or yawing of the vessel can hamper and can make a sight very difficult; but then, so is reading and writing in such conditions. The wind can be a problem, but that is why a marine sextant should be heavy, having more inertia.

In hazy weather, the 2nd Officer took a sight on the main deck, as low as possible, and in many cases, a reasonable fix was obtained. Poor fixes were attributed to the poor horizon (dip), sometimes taking the Sun through clouds or in a flash between two clouds. However, the experienced Officer had a very good idea of the quality of his sight.

The best sights were between 30° and 60° above the horizon. Below 15° there were some doubts, below 10°, it was not worth taking. Above 80° you needed a minimum of experience and at 89°, correct Noon positions were always possible. The vertical edge of the horizon glass will give no clue as it will not be discernible. However, no Officer should have doubt about the verticality of his sextant; that is why the kiss should be light. Sights were rounded to 1.m, calculations to one mile. This precision is more than enough for ocean navigation, and closing a danger to less than five miles (ocean) is poor seamanship. Coastal navigation is a different thing.

Choosing the correct shades for both mirrors could make the difference between a good and a poor sight. Astro positions by sextant were very accurate – less than a mile out. This was proved over and over again by correct landfalls within less than six miles. Officers (and ratings) were proud of their trade, and sights and calculations were regularly compared and analysed. Job satisfaction was the result of the lengthy application.

Satellite navigation systems were the beginning of the end of the art; dead reckoning became sloppy, radio signals were forgotten, chronometers were not wound. It was also the end of sea-sense; currents and meteorology were no longer studied.

The coming of GPS put an end to it all. The sextant (one per ship) is hidden in a lower drawer; the chronometer is not connected to its battery. Time is given by the GPS. If one day the satellites should be switched off, 99% of the ships would be lost. In the 1960’s and 1970’s, a good ship had at least two mechanical chronometers. The top was taken daily at the same time, and they were compared with each other. Some ships had lamps in the chronometers to keep them at an even temperature. If one of them stopped working it was a major event, and the Master informed. The daily rate was quite correct. Later battery-operated chronometers became available. To the general surprise of all, they were no better; only one was provided. With the coming of GPS, the younger Officers took time from the set; some were using their wristwatch (Seiko), which was often steadier than the chronometer! Older Captains lost their health. Nowadays a 2nd Engineer can get a position by pushing a button.

The last three decades has seen a revolution in water transport of the same importance as during the demise of the sailing ship the change from steam tramp to cargo liners, which occurred in the 50s. It is another trade, another job. Let us hope the new seamen obtain the same level of satisfaction and pride as we had. Seven sights in five minutes were the norm. With the introduction of a Global Positioning System (GPS) of satellites, worldwide coverage of the Earth’s surface is now possible. The ability to fix a vessel’s position with great accuracy, even when out of sight of land, is now available. Highly sophisticated satellite fixing systems are no longer beyond the electrical resources of small craft or the financial resources of their owners. In this modern age, Astro-navigation is now carried out as a ‘back-up system’ on large commercial vessels. 

More often that not, it is the ‘small-craft’ navigator who is keeping the art of navigation alive through his interest and belief in his own efforts.



If any celestial body (Sun, Moon, planet or star) and the sea horizon can be seen simultaneously at any position in the world, a position line can be established within 10-15 minutes. If two or more celestial bodies and the sea horizon can be observed nearly simultaneously a fix can be established and plotted on the chart within 20-30 minutes. Taking sights is the name given to the act of securing observations of celestial bodies at sea with a sextant.

The practical side of taking a sight consists simply of measuring the altitude of a celestial body, i.e. its angle of height above the sea horizon, at the same time noting the exact time either from a chronometer or from a good clock or watch keeping time to seconds and checked by radio time signals.

This practical operation takes only a minute or so; the rest of the time in establishing the position line or fix is occupied in working up the Sight, that is, simple calculations using Nautical tables and the N.A.

Proficiency at sea demands only two main qualifications: –

Familiarity in handling the sextant as an instrument – to enable observations to be made accurately and with confidence.

Familiarity with the reference books – The N.A. and the Tables – to ensure that the necessary data can be looked out quickly and with certainty.

Both these qualifications come rapidly with experience:


Until comparatively recent years there was only one method of working up or reducing a sight – the long method involving a knowledge and application of spherical trigonometry. The growing need for a quick and simple method of sight reduction, however, has resulted in the publication in recent years of sets of nautical tables.

The term Inspection Tables applies to a table giving direct solutions to the Astronomical triangle (to be described in this ‘Ocean Navigation’), thus obviating the necessity for mathematical formulae and calculations. In themselves, inspection tables are by no means a modern invention, since the great Astronomer Cassini prepared the first navigation inspection tables in about 1770.

These early tables never became popular, largely because the tedious interpolation involved in their use. Seamen have never taken kindly to interpolation, and when triple interpolation is needed, as in these early tables, most seamen preferred to solve their Astronomical triangles using direct methods of spherical trigonometry.

Following the introduction of the intercept method of sight reduction devised by Commandant Marc St. Hilaire of the French Navy in 1875, attention was directed to the task of designing inspection tables with improved methods of interpolation. The first inspection tables designed for use with the intercept method were those published in 1907 under the authorship of the RN. Instructor, Frederick Ball, and were followed in 1917 by Davis Altitude-Azimuth Tables.

The relative difficulty of interpolation in both these sets of tables, as with the earlier inspection tables, spelt their doom, and they are seldom used now.

In 1946, a comprehensive set of inspection tables in nine volumes was published by the U.S. Hydrographic Office under the title Tables of Computed Altitude and Azimuth but generally known by the book reference HO. 214. The corresponding British tables, known as H.D. 486, were published in six volumes and formed at the time the most comprehensive set of sight reduction tables in existence.

An interesting and valuable set of sight reduction tables, known as, Sight Reduction Tables for Air Navigation or AP. 3270, designed and prepared jointly by the N.A. Office of the U.S. Naval Observatory and H.M. N.A. Office was first published in 1953. These tables are in three volumes and in general principle similar to HD. 486 but being designed essentially for air navigation, where the requirements for accuracy are much less severe than for sea navigation, they are not so precise.

The real breakthrough in connection with inspection tables came in 1967 with the publication of Sight Reduction Tables for Marine Navigation in the United States as HO. 229. The Hydrographer of the Navy, under the reference NP 401, published these tables in Britain in 1971. The concept, design, development, and preparation of these new tables are the results of the collaborative efforts and joint accomplishments of the U.S. Naval Oceanographic Office, The U.S. Naval Observatory, and Her Majesty’s N.A. Office, Royal Greenwich Observatory.

In producing this new work the aim was to provide the mariner with tables, which, with convenient methods of observation and altitude correction, the highest precision possible is attainable with the absolute minimum of interpolation. The enormous task of compiling such tables only became possible with the advent of electronic data processing coupled with automatic photo composing for offset printing.

These new tables, HO. 229 (NP. 401) appear in six volumes each of more modest dimensions than the former HO. 214 (HD. 486) tables, the subdivision being by way of Lat., as follows: –

Being the finest and most comprehensive set of high precision tables for marine navigation available today HO. 229 (NP. 401) has been selected as the basis for the tabular method of sight reduction to be described in this ‘Ocean Navigation Study’

Volume 4 (Lat. 45° to Lat. 60°) was chosen as being the most appropriate single volume on which to base text, examples and problems, as these latitudes cover the British Isles. This volume is the most usual volume with which to start a collection of the full set of tables.

The tabular method of sight reduction is the term given to the use of inspection tables to reduce a sight taken with a sextant to a form suitable for plotting on a chart as a position line, as opposed to the direct method of sight reduction by spherical trigonometry. As already stated, no mathematics beyond a facility for simple arithmetic is required for the Tabular method, but in order to be able to understand and use the inspection tables, it is necessary to have knowledge of the basic theory of nautical Astronomy.

This will be explained in the ensuing text of this ‘Ocean Navigation Study’, and no more theory will be introduced than is necessary for its application to practical Astro-navigation using the NP. 401 Inspection Tables

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