How Captain Cook found his longitude

K1 chronometer, courtesy National Maritime Museum UK

K1 chronometer, courtesy National Maritime Museum UK

Yesterday afternoon (Tuesday 24 July 2007) Sydney Observatory staff farewelled the Director of the Director of the Powerhouse Museum, Dr Kevin Fewster. Dr Fewster has been appointed the Director of the National Maritime Museum at Greenwich UK that includes the Royal Observatory, Greenwich, the centre of time and space on Earth.

Naturally, the talk turned to time measurement and the wonderful Harrison clocks on show at Greenwich. Dava Sobel has ably told the story of the clocks and their maker John Harrison in the best-selling book Longitude.

Interestingly Captain James Cook on his first voyage did not have a chronometer on board his ship the Endeavour. H4 was still the only one then in existence and that was far too precious to send on a highly risky voyage. So how did Cook find the longitude, that is how far he was east or west of Greenwich? He used the method of lunar distances. In one of the great coincidences in the history of science two techniques of determining longitude at sea were developed at the same time, lunar distances and chronometers.

Lunar distances involve measuring the angular distances of stars from the Moon. More precisely three observations are made, of a star’s elevation above the horizon, of the Moon’s elevation of the horizon and of the angular separation between the star and the Moon. This is then repeated with another star. The measurements of angular distance are made with a sextant, an instrument based on the previously invented octant, but modified to be able to measure larger angles for use with lunar distances.


Sextant, image Nick Lomb

After taking the observations Cook had to do long and laborious calculations to establish the ship’s position. To assist he used the Nautical Almanac published at Greenwich. Unfortunately, at the start of the three year voyage in 1768 only the almanacs for 1768 and 1769 were available so they were the only ones he could take on the voyage.

For his subsequent voyages Cook did take chronometers. Kenneth Slessor has a wonderful poem, Five Visions of Captain Cook. The short extract below refers to two chronometers including K1, Larcum Kendall’s famous replica of H4, which is pictured at the top of this post:

Two chronometers the captain had,
One by Arnold that ran like mad,
One by Kendal in a walnut case,
Poor devoted creature with a hangdog face.
Arnold always hurried with a crazed click-click
Dancing over Greenwich like a lunatic,
Kendal panted faithfully his watch-dog beat,
Climbing out of Yesterday with sticky little feet.

14 responses to “How Captain Cook found his longitude

  • Why was Cooks longitude so far out at Princess Charlotte Sound, Cape Farewell and longitude of the east coast of Tasmania? There are reasonable assumptions for all the smaller errors and why are the reading of the 19th April 1770 deemed to be correct. Thankyou.

  • I was bequeathed an old Sextant from a dear friend. She said it was significant as it was used by one of the Captains who once sailed with Captain Cook.

    It’s a Brass Sextant with silver inscribed slide by Ainsley of South Shields. 1828.

    I would like to know it’s history.

    My friends father came from Germany and lived in New Zealand and had this, and Brass Telescope which she left to me when she died.

    Can anyone help me to discover the history of this piece please?

    • Vicki, Unfortunately Sydney Observatory doesn’t have the resources to help you with this research, but maybe another reader can help?

    • Chris, Yes he only had the Nautical Almanacs for two years. The Almanacs contained tables of the Moon’s position at several (Greenwich) times during the day, against which the Moon’s position (as observed on board ship) could be compared. But someone had to calculate the Moon’s position in the first place before publishing it! And that’s what Cook (or perhaps it was his officers and astronomer) had to do from 1770 – these calculations were particularly time-consuming and laborious.

  • It was scarcely a coincidence that the chronometer and lunar distances were developed around the same time. The British government’s Longitude Prize of 1714 was the spur.

  • Does anyone have a copy of Cook’s….(or Green’s) observed measurements for longitude? And his reduction of those observations?
    They should tell you exactly what method he used, as the calculation reductions for each are so different.

  • I adapted James Cook’s journal for 80 broadcasts, the HMB Endeavour was in Far North Queensland for 80 days. I also wrote an article ‘The Heavenly Clock’ explaining James Cook and Mr. Green’s fixing of their longitude and it wasn’t lunar. It was calculated from the emersion of the first satellite of Jupiter as suggested by Galilee Galileo who called it the Universal Clock. James Cook sailed west from England he sailed west around the globe and didn’t allow for the date line. On 29th June 1770 whilst in what became Cooktown Harbour, he and Mr. Green, his astronomer took measurements and compared the local time with an almanac they had for 1768 to arrive at ‘214 degrees 42.30 of longitude which this place is west of Greenwich’ which has been found to be 10 secs. short in the distance between Cooktown and Greenwich.

    • Irene, the method of finding “the longitude” by observing the eclipses of Jupiter’s moons was only one of the methods Cook used. As you note he used it during his enforced stay in the future Cooktown, after running aground on the reef. His journal entry for 29 June 1770 confirms this. He probably used the two-feet focal length reflecting telescope he had previously used for observing the Transit of Venus. However, he made those observations on land. The method was well known to be impossible on board a rolling ship and Maskelyne confirms this in his ‘Explanation and Use…’ notes in the Nautical Almanac. For most of his voyage Cook was finding his longitude by another method made viable by the Nautical Almanac – the Lunar distance method. Cook was an excellent navigator and surveyor!

    • Dear Irene….hope I will meet you in Cooktown next year July-Aug 2020 for Cook’s 250. We would love to hear you speak about your understanding of Cook and his first voyage. The Historical conference is Aug 1 2020.

  • James Cook (RN) must surely rate as the all time master navigator/mariner. Regarding his subsequent voyages, the original fixes for many places along the Eastern seaboard of Australia were checked against todays GPS co-ordinates. In most instances those fixes of the late 1700’s were within metres of the later GPS fixes…amazing and a testament to the man and his crew of the time.

    • James Cook was amazing. Another feather to his bow is that he and the crew were the first to compile a vocabulary of an Aboriginal language. All Aboriginal languages were oral until James Cook! Over 100 words of the Guugu Yimithirr language were taken back to England. David Hill’s brilliant book ‘1788 – The First Fleet’ adds a sequel to the story. When the first fleet were assembling Sir Joseph Banks as he then was, arranged for this vocabulary to be printed and bound and he presented it to Governor Philips just in case it was useful. I live quite close to the Guugu Yimithirr people and they are now studying their language.

      • Indeed the observation of Jupiter’s satellites had to be carried out on land. It was obviously more accurate than the lunar method and, as has been noted, it was 10 secs. out in some 14,000 miles. Must rank Cook as a mathematical genius alongside Eratosthenes who computed the circumference of the planet in 192 BC and gave us Lat. and Long. and so much more.

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