The Longitude Problem
For every 15° that one travels eastward, the local time moves one hour ahead. Similarly, travelling West, the local time moves back one hour for every 15° of longitude. Therefore, if we know the local times at two points on Earth, we can use the difference between them to calculate how far apart those places are in longitude, east or west. This idea was very important to sailors and navigators in the 17th century. They could measure the local time, wherever they were, by observing the Sun, but navigation required that they also know the time at some reference point, e.g. Greenwich, in order to calculate their longitude. Although accurate pendulum clocks existed in the 17th century, the motions of a ship and changes in humidity and temperature would prevent such a clock from keeping accurate time at sea. King Charles II founded the Royal Observatory at Greenwich in 1675 to solve the problem of finding longitude at sea. If an accurate catalogue of the 
positions of the stars could be made, and the position of the Moon then measured accurately relative to the stars, the Moon's motion could be used as a natural clock to calculate Greenwich Time. Sailors at sea could measure the Moon's position relative to bright stars and use tables of the Moon's position, compiled at the Royal Observatory, to calculate the time at Greenwich. This means of finding Longitude was known as the 'Lunar Distance Method'. In 1714, the British Government offered, by Act of Parliament, £20,000 for a solution which could provide longitude to within half-a-degree (2 minutes of time). The methods would be tested on a ship, sailing. A body known as the Board of Longitude was set up to administer and judge the longitude prize. They received more than a few weird and wonderful suggestions. Like squaring the circle or inventing a perpetual motion machine, the phrase 'finding the longitude' became a sort of catchphrase for the pursuits of fools and lunatics. Many people believed that the problem simply could not be solved. The longitude problem was eventually solved by a working class joiner from Lincolnshire with little formal education. John Harrison (1693-1766) took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. To solve the longitude problem, Harrison would have to devise a portable clock which kept time to an accuracy of one second a moth. The first real success was known as H1. 
Constructed between 1730 and 1735, H1 is essentially a portable version of Harrison's earlier precision wooden clocks. It is spring-driven and only runs for one day (the wooden clocks run for eight days). The moving parts are controlled and counterbalanced by springs so that, unlike a pendulum clock, H1 is independent of the direction of gravity. In 1736, Harrison and his timekeeper travelled to Lisbon aboard the ship Centurion to test the clock, and returned on the Orford. H1 performed well in the trial, keeping time accurately enough for Harrison to correct a misreading of the Orford's longitude on the return voyage. However, Harrison did not ask for a second trial but, instead, requested financial assistance from the Board of Longitude to make a second marine timekeeper. Larger and heavier than H1, H2 is of fundamentally the same design as H1. Harrison began work on H2 in 1737 but in 1740 realised its design was wrong. The bar balances did not always counter the motion of a ship, a deficiency that could be corrected if the balances were circular. Harrison requested more money from the Board to work on a third timekeeper. Harrison worked on his third timekeeper from 1740 to 1759. After 19 years of labour, it failed to reach the accuracy required by the Board of Longitude. 
H3 incorporated two inventions of Harrison's; a bimetallic strip, to compensate the balance spring for the effects of changes in temperature, and the caged roller bearing, the ultimate version of his anti-friction devices. Both of these inventions are used in a variety of machines nowadays. Despite these innovations, work on H3 seemed to lead nowhere and its ultimate role was to convince Harrison that the solution to the longitude problem lay in an entirely different design. In 1753, Harrison commissioned London watchmaker John Jefferys to make him a watch following Harrison's own designs. The watch was intended for Harrison's own personal use - to help with his astronomical observing and clock testing. No one in the 1750s thought of the pocket watch as a serious timekeeper. However, Harrison discovered with his new watch that if certain improvements were made, it had the potential to be an excellent timekeeper. In 1755, as well as asking for continued support for the construction of H3, he asked the Board of Longitude for support.
H4 is completely different from the other three timekeepers. Just 13 cm in diameter and weighing 1.45 kg, it looks like a very large pocket watch. Harrison's son William set sail for the 
West Indies, with H4, aboard the ship Deptford on 18 November 1761. They arrived in Jamaica on 19 January 1762, where the watch was found to be only 5.1 seconds slow! It was a remarkable achievement but it would be some time before the Board of Longitude was sufficiently satisfied to award Harrison the prize.
A second trial of H4 was arranged and William departed for Barbados aboard the Tartar on 28 March 1764. As with the first trial, William used H4 to predict the ship's arrival at Madeira with extraordinary accuracy. The watch's error was computed to be 39.2 seconds over a voyage of 47 days, three times better than required to win the £20,000 longitude prize. The Board of Longitude, however, implied that the watch was a fluke and would not be satisfied unless others of the same kind could be made and tested. Harrison would be paid £10,000 as soon as he disclosed his secrets and handed over his mechanisms to the Astronomer Royal, with the remaining £10,000 being paid when other timekeepers of the same type, accurate enough to find longitude to within 30 miles, were made.
Although the performance of H4 during its second sea trial was three times better than the two minutes accuracy required to win the longitude prize, the Board of Longitude remained unconvinced. They stated that half of the prize money would be paid once Harrison had disclosed the workings of H4 to a specially-appointed committee. They also implied that H4's accuracy was a fluke and that copies of the watch should be made and tested. Finally, all four of Harrison's timekeepers should be handed over to the Board once he had received the £10,000. At first, Harrison refused to accept any of these proposals, but the Board was equally adamant. After several weeks, both John and William agreed to disclose the inner workings of H4. In August 1765, a panel of six experts gathered at Harrison's house in London and examined the watch. One week later, they were satisfied that the disclosure was complete and had signed a certificate to this effect. The Board then insisted that the four timekeepers should be handed over to them, and asked Harrison to recommend someone who could copy H4. Reluctantly, he recommended Larcum Kendall, a leading watchmaker who had probably contributed to the construction of H4, and finally received the first half of the longitude prize. In order to qualify for the second half of the prize, Harrison had to make at least two more watches and have them tested. The Board of Longitude insisted that he make these copies of H4 himself, but took the original away for testing at the Royal Observatory. Nevil Maskelyne, who had been appointed Astronomer Royal in 1765, remained unconvinced that a watch could be more reliable than the lunar distance method for finding Greenwich Time. John Harrison (now in his seventies) and William worked on a fifth timekeeper (H5), while Kendall made good progress on his copy of H4. Kendall's watch, now known as K1, was completed in 1769 and inspected in early 1770 by the same panel that had examined H4. William Harrison was also present and admitted that the copy was exceptional. The Board of Longitude was asked to consider H5 and K1 as the two copies of H4, but told John and William, in no uncertain terms, that both copies of H4 should be made by the Harrisons. John, now 79 years old, made an appeal to the highest authority in Britain. On 31 January 1772, an approach was made to King George III, via a letter to his private astronomer at Richmond, Dr Stephen Demainbray. William was summoned for an interview with the King himself, at which the King is said to have remarked Ò these people have been cruelly wronged..., and By God, Harrison, I will see you righted!Ó H5 was put on trial by the King himself in 1772, and performed superbly. The Board of Longitude, however, refused to recognise the results of this trial, so John and William petitioned Parliament. They were finally awarded £8,750 by Act of Parliament in June 1773. Perhaps more importantly, John Harrison was finally recognised as having solved the longitude problem. In the meantime, Captain Cook had set out on his second voyage of discovery with K1, Kendall's copy of H4. He returned in July 1775, after a voyage of three years, which ranged from the Tropics to the Antarctic. The daily rate of K1 never exceeded 8 seconds (corresponding to a distance of 2 nautical miles at the equator) during the entire voyage. It is not known for certain whether Harrison knew of this success, but Cook's voyage proved beyond doubt that longitude could be measured from a watch. John Harrison died almost one year after Cook's return, on 24 March 1776, in his house at Red Lion Square, London. It was his 83rd birthday.
The Background and History of Navagation
The need for celestial or astro-navigation is being questioned more and more as GPS sets become cheaper and in common use. GPS is here to stay, is very "user friendly", reliable and extremely accurate. Astro-nav is not user friendly, not very accurate and can only be used in ships when both celestial bodies and the horizon are simultaneously visible. Its use is promoted because it is the only system available to the mariner crossing oceans that does not rely on electronics. It requires a sextant, an accurate timepiece, a nautical almanac and a set of mathematical tables plus, of course, the knowledge of how to use them. Total electronics failures have been reported in yachts suffering lightening strikes, even spare portable GPS sets, switch-off and in the locker have been affected. Further, it is a fundamental of navigation never to rely absolutely on one system. Those students entering the course as the start of a professional career at sea require this knowledge for career advancement. Those, whose reasons may be mostly recreational, normally find the subject challenging and rewarding. Believe it or not most students enjoy it!!
Why do we sail when it is far more convenient and simple to motor?? Because we find it more aesthetically pleasing; we like it. Same with astro!
The Instruments
Mariners have been determining their position using celestial navigation with varying degrees of accuracy for many years. Over time a variety of different instruments have been employed.
The Marine Quadrant
Gunter's marine quadrant was in use from around 1450 to 1650. Originally the quadrant was made from a quarter circle of wood, brass or copper with a graduated scale marked on the 
circumference from 0º to 90. The celestial body is sighted across the two projections. Altitude is given directly by reading off where the plumb line cross the scale along the curved edge.
The Cross Staff
The cross-staff was used by ancient astronomers to measure angular separation between celestial objects. It also served a secondary function of aiding to determine distances, latitudes and heights of terrestrial objects such as hills, mountains and islands. The earliest recorded use of this object was by the German mathematician, cartographer and navigator Martin Behaim, and this was in the 1480s.
In simple terms, the cross-staff is a cross made from two pieces of wood, one long and the other short, with the shorter piece being movable. The longer piece comprises a long, squarish staff, made of hardwood, while the shorter length, also called the crosspiece or transom is made of the same material and it slides along the staff. The staff is then held up to the eye level and viewed. The crosspiece is adjusted so that the celestial object is just visible above the upper part of the crosspiece.
The cross-staff was simple to construct, light and portable, making it a handy and cheap navigational tool. It did frustrate some who were trying to measure the sun's altitude in the sky, as that required them to look into the sun. Of course, this problem was soon overcome by the use of smoked glass for the crosspiece. Navigators were also susceptible to parallax errors.
Marine Astrolabe
The history of the astrolabe begins more than two thousand years ago. The principles of the astrolabe projection were known before 150 B.C., and true astrolabes were made before A.D. 400. The astrolabe was highly developed in the Islamic world by 800 and was introduced to Europe from Islamic Spain (Andalusia) in the early 12th century. It was the most popular astronomical instrument until about 1650, when it was replaced by more specialized and accurate instruments.
The Mariner's Astrolabe, which was popular in the late 15th and early 16th centuries, was a simple brass ring, graduated in degrees with a rotating alidade for sighting the Sun or a star. The ring was cast brass, quite heavy and cut away to keep it from blowing around in the wind. It was not a very good instrument and errors of four or five degrees were common.
The Astrolabe was used by lining up the star through the two sighting holes on the movable adlidade, the zenith distance of the body could then be read directly from the graduated scale.
The Kamal
This extremely simple instrument appeared in the Middle Ages and was still in use in 1875 in the Indian Ocean. A Kamal is a small recantgualr piece of wood with a notch cut in the centre of one side. A fixed length of cord is stretched between the observers teeth and the middle of the board. The cord length is adjusted to match the altitude of of the Pole Star at the destination port, making it possible to navigate along a parallel of latitude.
The Sextant
All of the instruments described above were at best accurate to 1º (in other words 60nautical miles). The modern marine sextant is a precision optical instrument enabling observer to achieve high levels of accuracy.
The Sextant
The figure opposite shows the typical structure of the modern sextant and the table below gives a brief description of the component parts. Essentially the sextant enables you to measure the angle between two rays of light, one from the observers eye to the horizon and the other to the body being observed.
| Arc scale |
Indicates the number of degrees of an angle. |
Index arm |
Pivots at one end to allow the attached index mirror to reflect an object onto the horizon glass and swings along the arc scale on the other end to indicate what the angle measures. |
| Micrometer drum |
Rotates to make fine adjustments when measuring angles and indicates minutes of a degree of angle. It is attached to the lower end of the index arm. One complete rotation moves the index arm 1° along the arc scale. The drum has 60 graduations, each representing 1' of arc. |
| Vernier scale |
Indicates tenths of a degree of angle. It is attached on the index arm adjacent to the micrometer drum and has 10 graduations, each representing 0.1' of arc. |
| Index mirrior |
Reflects objects onto the horizon glass. |
| Horizon glass |
Allows the observer to view one object directly on one side while observing a second object reflected next to it. The half of the horizon glass next to the frame is silvered to make that portion of the glass a mirror; the other half is clear glass. |
| Telescope |
Directs the line of sight of the observer to the horizon glass and magnifies the objects observed. |
| Filters |
Protects the observer's eyes when viewing the Sun. |
| Release levers |
Disengages the index arm from the arc scale to allow the index arm to move freely. |
Disposition of Celestial Bodies
The Sun is the basis for all life on Earth. It is a small star (a yellow dwarf star) generating light and heat and it is the body around which the Solar System orbits. The nine planets in the system orbit in concentric circles (really ellipses) in a more or less flat plane and our earth is the third one out from the sun.
Those between the Earth and the Sun are called inferior planets (Venus and Mercury). Those further out than the Earth are superior planets (Mars, Saturn, Jupiter. Uranus, Neptune, Pluto)
All planets shine reflected sunlight; so, like the moon, the inferior planets will have Òfull moonÓ and Ònew moonÓ characteristics and will therefore vary in brightness. The superior planets will always be in the Òfull moonÓ phase and their brightness will depend on their distance from Earth. Some planets are enormous; Jupiter is 1320 times the volume of Earth whereas tiny Pluto is 0.1 times and is so far away that it is several thousand times fainter than the smallest object visible to the eye. The figure below shows the relative sizes of the planets within our solar system.
Orbiting Earth is the moon. To give proportion to this, the moon is about 250,000 miles from earth and the sun about 93,000,000 miles. It might help to consider the Sun to be a ball one metre in diameter and the Earth the size of a pea; in these proportions the Earth would be the length of a rugby pitch away from the Sun. Due to a combination of size and distance only four planets can be easily seen and these are the ones used for navigation. Venus, the brightest of all stars and planets, is 67,200,000 miles from the Sun; Mars 141,700,000 miles; Jupiter, 483,700,000 miles and Saturn 885,200,000 (see table below). Their distance from Earth varies with their dispositions in their orbits.
Miles (millions) |
km (millions) |
Astronomical unit (AU)1 |
36.0 |
57.9 |
0.387 |
3.2 |
67.2 |
108.2 |
0.723 |
6.0 |
93.0 |
149.6 |
1.000 |
8.3 |
0.238 |
0.383 |
0.003 |
1.3 |
141.7 |
228.0 |
1.524 |
12.7 |
483.7 |
778.4 |
5.203 |
43.3 |
885.2 |
1424.6 |
9.523 |
79.5 |
1785.5 |
2873.5 |
19.208 |
159.7 |
2796.8 |
4501.0 |
30.087 |
250.4 |
3694.6 |
5945.9 |
39.746 |
332.1 |
1. An Astronomical Unit is a unit of length used in measuring astronomical distances within the Solar System equal to the mean distance from Earth to the Sun, approximately 150 million kilometres (93 million miles).
Although light is considered, for all practical purposes, to be instantaneous, it has a finite speed of travel of c.162,000 nautical miles per second and thus light emitted by the Sun takes nearly 9 minutes to arrive at Earth. Compare this distance with those of the stars: the light of the nearest star takes 4 years to travel here and that of the furthest star used for navigation 5,000 years. So it is possible that some stars may have ceased to exist thousands of years ago but their light is still travelling so we can still see it!! For example, if the North Star (Polaris) had disappeared in 630AD we would have only noticed in 2003!
In normal distance terms a light year is 5,2000,000,000,000 n.miles These vast distances defy comprehension by normal minds and, fortunately, have little to do with their use for navigation apart from one important point. With the exception of the moon, all other celestial bodies are so far removed from Earth that rays of light emitted by them can be considered to travel in parallel lines. It is of fundamental importance that this is understood.
