Volume 13

Nautical Navigation and Survey at the Time of Cook's First Voyage to New Zealand

David Wilton


The Tuia 250 commemorations in the Hauraki- Coromandel area focused on the Mercury Bay area - understandably, as the Endeavour spent several days at that location. I conducted a brief study during 2018, focused on the western side of the Coromandel Peninsula, and this led to an article in The Treasury Journal. Although the Endeavour spent only two nights anchored in the Firth of Thames, the day-trip Cook and a small party undertook up the Waihou River in two small ship's boats, did have strong historical significance. While about 12-14 nautical miles (nm) up-river, the party went ashore and measured a large kahikatea tree. This effectively represented the birth of NZ's timber industry, as it resulted in ship's visits to collect kahikatea, and, later, kauri, to provide masts and spars for Royal Navy ships (see, for example at The Sailor's Grave).

My article led to public lectures, conducted in Thames and Paeroa, during November 2019 - almost exactly 250 years after the Firth of Thames visit took place. These included a section on navigation and survey methods used by Cook and crew, which seemed to be of interest to most attendees. I was encouraged to write it up as a separate article, which I have now done.

To distinguish, navigation is basically the methods used by a prospective traveler to get from A to B. Survey is recording the details of the journey between A and B, so that other prospective travelers can make the same journey without the uncertainty of the original journey. That recording is traditionally in the form of a chart (term used in nautical and aeronautical circles) or map (used in Army and most civilian circles). (I regard these terms as synonyms, and use them interchangeably.)


When conducting research on Cook's journeys and navigation and survey methods, some interesting, and sometimes puzzling, issues arose; mainly, but not limited to, the plethora of physical units used, pre-decimalisation.

An interesting concept which caused some initial confusion was that of the ‘Ship’s day’ – a 24-hour period commencing at midday (but using same times – e.g. ‘3 pm’). There were differences between days/dates in Journals, most notably those of Cook and Banks, the reason for which later transpired to be the nautical tradition of commencing the 'day' at midday.

Distance - a variety of metrics were used. Miles was used extensively in Cook's and Banks' Journals, but a question arose as to whether these were statute miles (1760 yards) or nautical miles (2025 yards; 1.85 km) - approximately a 15% difference between the two units. Another distance metric used was league, being three miles (statute or nautical) - originating from the distance a body of Roman troops could march in one hour. Close examination of Journals, and constructions on maps showed that nautical miles was the metric used, as opposed to statute, even by civilians such as Banks. A useful result is that 1 nautical mile (nm) represents 1 minute of arc (ie 1/60th of a degree) at the Earth’s equator.

Angles/bearings were measured in degrees, minutes (1/60th of a degree) and seconds (1/60th of a minute), as is still in vogue today. Measured bearings were magnetic (i.e. measured with a magnetic compass) but were marked on charts as true bearings. For this to be possible, the magnetic variation (aka magnetic declination) needed to be known.

This was very important for charting purposes, and apparently early navigators spent a significant amount of time calculating it, as there had been no-one in the area previously to work it out for them. True north is the direction of the sun at midday, and magnetic north is the direction that the compass needle pointed. A problem that was not well known by mariners in Cook's time was that magnetic north (i.e. the direction their compass needle pointed) was affected by large quantities of iron in the ship, so that the orientation of the ship was a factor when trying to calculate magnetic variation!

Magnetic variation has changed over time, and is different in different localities across the Earth's surface. A useful tool which predicts historic magnetic variation across the Earth's surface is at The NOAA website: Historical Magnetic Declination. The tool was developed by the US National Oceanographic and Atmospheric Administration (NOAA). It predicts that the magnetic variation in northern NZ was 12o East in 1769. At least one of Cook's charts (that of the 'River Thames', now Coromandel, area) shows the magnetic variation as 9o East. The reason for the discrepancy (from the NOAA tool's prediction) is not apparent - it could have been the iron-on-the-ship problem, or possibly the NOAA mathematical model has limitations. It is fair to say that Cook's 'true north' shown on his charts, aligns with true north on Google Earth, when the charts are imported as overlays.

Speed was measured in knots: 1 knot = 1 nautical mile per hour.

Depth was measured in fathoms: 1 fathom = 6 feet (2 yards; 1.83 metres).

Latitude and Longitude The practice of representing geo-locations by latitude and longitude were developed by ancient Greek philosophers in the 2nd and 3rd centuries BC and originated shortly after the model of a near-spherical earth was adopted.

Figure 1: Schematic of the concepts of latitude and longitude
Source: Wikipedia.

Figure 2: A quadrant/sextant believed to have been used by Cook on his third voyage (1770s) .
Source: British National Maritime Museum

Measuring Latitude - an 'easy' problem in 1769.

In Cook's time, measuring latitude was a relatively easy problem - as long as the sky was clear enough to enable a sun sight at noon. To measure latitude, observers used an instrument called an octant (1/8th part of circle) or sometimes known as reflecting quadrant. (Cook used the term ‘quadrant’.) This was a general-purpose instrument for measuring angles – it had a 45o arc, but could measure angles up to 90o due to its reflecting mirror optics.

An observer would sight the sun at midday and measure its angle above the horizon. Adjustments would be made to allow for time of season and convert to latitude (the sun is higher above the horizon in summer, lower in winter).

This instrument was later superseded by the sextant (1/6 part of circle), which could measure angles up to 120o; sometimes necessary for celestial navigation, or measuring horizontal angles as part of a survey.

Figure 3: Schematic of an octant, showing how its optics functioned (Wikimedia Commons:Godfrey-octant)

Measuring Longitude - an 'easy' problem now; a 'hard' problem in 1769.

Post -1770, longitude is easily calculated by measuring the difference between local time and GMT – the difference represents 15o of longitude per hour and part thereof. However, at the time of Cook’s 1769 voyage there were no clocks that could keep accurate GMT over periods of weeks or months at sea.

Prior to the advent of suitable clocks, mariners calculated longitude by measuring the angle between the moon and certain stars, and used look-up tables:

Briefly, this involved observing the moon's angular distance from the sun, or from a suitable star; at the moment of observation, Greenwich time was obtained from tables which predicted the moon's motion and position in relation to other celestial bodies; then comparison with the local time gave the observer his longitude.
Using the tables that Maskelyne published, it would have taken between three and four hours to perform the necessary calculations. The improved tables in the Nautical Almanac, which was first published in 1767, gave the angular distances between the moon and each of a number of suitably placed bright stars and the sun, for every 3rd hour of Greenwich time for the whole year and reduced the computing time to perhaps under half-an-hour. (K.J. Snowden (1983)
From Captain Cook as a Hydrographer

The method produced results of varying accuracy and errors of half a degree were reasonably common. Although half a degree (30 minutes) difference in longitude may seem insignificant, it actually represents approx 50 km on the ground (as one minute of arc represents one nautical mile).

By Cook's second voyage, one accurate clock had actually been developed in England, which Cook ‘acquired’ for the voyage:

The first model [clock] finished by Kendall was an accurate copy of John Harrison's H4, cost £450, and is known today as K1. It was engraved in 1769, and was presented to the Board of Longitude on 13 January 1770, at which point he was given a bonus of £50. The original H4, the first successful chronometer, had an astronomical price of £400 in 1750, which was approximately 30% of the value of a ship.

James Cook and astronomer William Wales tested the clock on Cook's second South Seas journey aboard Resolution, 1772–75 and were full of praise after initial scepticism. "Kendall's watch has exceeded the expectations of its most zealous advocate," Cook reported in 1775 to the Admiralty. Cook also described it in his log as "our trusty friend the Watch" and "our never-failing guide the Watch". - Wikipedia.

Figure 4: Memorial to Larcum Kendall, a key figure in the development of an accurate clock, suitable for long sea voyages (Wikipedia).

Type image captioFigure 5: Kendall's 'K1' clock.
(From Royal Museums Greenwich)n here (optional)

Most of Cook's survey work around the NZ coast was conducted during his first voyage, which utilised the less-accurate celestial method of calculating longitude. The results, however, were still remarkably good, as will be described in a later section.

Measuring Depth

Figure 6: A sailor depth-sounding, by dropping a lead weight with a graduated line.
(From: Frontispiece catalogue

This activity was also known as ‘swinging the lead’ and came into use as a derogatory term for someone pretending to work, working very slowly, or claiming to be ill when they are not. In Cook's day, seamen would check the depth of water by dropping a lead weight, attached to a thin marked rope, to the bottom of a waterway. Some lazy sailors would take as long as possible about it. They would 'swing the lead' to and fro several times instead of just dropping it straight into the water.

There are extensive depth markings on Cook’s charts (including in rivers and inland waterways), indicating that depth-sounding was used extensively in navigation and surveying, especially in shallow waters. Cook's Journal entries imply that depth sounding was conducted to a depth of 150 fathoms (900 feet), presumably the maximum length of the line used.

Measuring Bearings/Angles

Figure 7: A nautical compass, as found in a ship's wheelhouse. Note the swiveling mounts (known as gimbals), which allows the compass face to remain horizontal when the ship rolls.
(From Penobscot Marine Museum)

Figure 8: US National Oceanographic and Atmospheric Administration (NOAA) model of historical magnetic variation, centred on the NZ region. The variation for northern NZ in 1769 (yellow line) is shown as 12 degrees East.
(From NOAA Historical Magnetic Declination.)

Bearings were measured with a magnetic compass, although sometimes an octant/sextant was used to give greater accuracy (because of the more detailed scale). As discussed previously, units were degrees/minutes/seconds. Magnetic variation (the angle between true north and magnetic north) was of critical importance.

Measuring Distance/Speed

To measure distance while under way, crews actually measured speed then multiplied by time, on any given course.

Figure 9: A ship's log, used for measuring speed through the water while under way (Wikipedia).

A chip log, also called common log, ship log, or just log, is a navigation tool mariners used to estimate the speed of a vessel through water. The word knot, meaning one nautical mile per hour, derives from this measurement method.

All nautical instruments that measure the speed of a ship through water are known as logs. This nomenclature dates back to the days of sail, when sailors tossed a log attached to a rope knotted at regular intervals off the stern of a ship. Sailors counted the number of knots that passed through their hands in a given time to determine the ship's speed. (Wikipedia)

The time interval was usually 30 seconds, determined using an ‘hour glass’-type timer. The interval between knots on the rope was about 50 ft.

The main problem with this method was that it measured speed relative to the water, not to the land. It didn’t work well in a river or estuary, for example, with current and tidal flows, which had to be estimated, or else disregarded. On the open sea, however, it was fairly accurate; probably to within about one or two knots.

Putting the Methods Together - the Running Survey

In the late 18th century, there were two main survey methods in use: triangulation, which was mainly for use on land or for coastal regions where land was readily accessible from a ship; and a running survey, which was conducted entirely from the ship, with no observations taken from land at all. The triangulation method was used by Cook early in his career, and is well described by the following:

Cook's early training and experience was in close association with military engineers, ... during the operations of the Louisburg, Quebec and Newfoundland campaigns, and it was they who taught him how to construct his marine surveys on a network of shore triangulation. These methods which he used for charting Newfoundland and where he worked from measured bases on land, are quite different to his charting of the Pacific where it was necessary to employ other techniques which I will mention later.
For the Newfoundland survey he took with him a very good outfit of instruments including a brass telescopic octant made by John Bird. He also took a theodolite, drawing instruments and some small station flags. The inclusion of the theodolite indicated that the survey would not be by a running traverse from the ship, but by the observation of angles from shore stations. The title of the chart of the coast from Point Ferolle to Cape Auguille, commences with the words "an exact trigonometrical survey". ...
Cook described in his journal his operations during the 1764 season and it gives us a good indication of his methods. He commenced his surveying in the north on July 14th. He went into the Bay Sacre, measured a base line and fixed some flags on the different islands. He completed the survey of the bay and the islands in six days. He then carried out a similar survey of Pistolet Bay, to the west, and by the end of the month he had completed the survey as far as Cape Norman, the latitude of which was fixed by meridional observation [sun sights at midday]. ... (K.J. Snowden (1983).
From Captain Cook as a Hydrographer

The methods used by Cook in the South Pacific, however, were mainly those of a running survey. This is a rough survey made by a vessel while coasting. Bearings to landmarks are taken at intervals as the vessel sails offshore, and are used to fix features on the coast and further inland. Intervening coastal detail is sketched in. The method was used by Cook, and subsequently by navigators who sailed under—or were influenced by—him, including Vancouver, Bligh and Flinders (Wikipedia).

Because Cook seldom had the time or the opportunity to go ashore to fix positions [in the South Pacific] by regular triangulation, the framework of his surveys was, of necessity, the astronomically determined positions of the ship and of coastal features. The scale of his charts had to be derived from the computed distances between fixes, to which the ship's dead reckoning, from compass and log, was adjusted.
Little time was wasted during the voyages. On the 1st voyage, he charted the coasts of New Zealand - some 2400 miles, in six months, and a further 2000 miles of the east coast of Australia in four months. Despite the speed with which the surveys were completed, their accuracy was quite remarkable. If we compare his chart of New Zealand with the modern chart, it shows that the errors in Longitude rarely exceed half a degree, except in the north of the South Island. (K.J. Snowden (1983).
From Captain Cook as a Hydrographer
Figure 10: Endeavour track off north eastern Coromandel, showing course of the ship.

Figure 11: Chart of the Coromandel Peninsula, showing area of maximum error - of the order of 4.5 nm (4.5 minutes of arc) on the east coast.

This track would have been mainly plotted by dead reckoning (i.e. measuring the direction of travel by magnetic compass, measuring the ship's speed through the water, and the time spent on each leg multiplied by the speed, gives the distance traveled during that leg. Latitude and longitude measurements were made whenever possible, and these were used to update the dead reckoning course. Bearings would also be taken to prominent features ashore, and these would be included on the working survey plot, which was compiled as the ship progressed. Note the compass rose and notation ‘Var.n – 9oE’ – the NOAA computer model predicted 12oE. Note also depth soundings; at least one per directional leg. The ship was presumably beating into strong westerly winds; hence the zig-zag course.

The Accuracy of Cook's NZ Charts

The 4.5 nm error noted in Fig 11 would have been due to the problem measuring longitude during the Endeavour voyage. Also apparent is a problem measuring distance on inland waterways - the Whitianga harbour and Mangrove River estuary is drawn about 2 or 3 times its actual size. This is probably due to difficulties noted previously about measuring distances with the chips log when there is a current and/or tidal surge. (A similar problem was apparent in the Waihou River - see previous article.) Often, distances would be estimated, in such circumstances.

It was not until the second voyage, in HMS Resolution, was well under way that Cook realised the significance of the longitudinal errors of the Endeavour voyage, and the improvement afforded by Kendall's clock.

Referring to Cook’s second voyage on HMS Resolution (at Ship Cove, Marlborough Sounds, November 1774), Hough comments:

‘Before they set sail, Wales [astronomer], with Kendall’s watch at hand, re-designated their longitude. Cook had previously been 40’ [40 minutes of arc] too far east. As a man who was conscientious and proud of his surveying skills, he experienced much chagrin … that his charts would have to be redrawn.’
- Richard Hough (1994) Captain James Cook.

Forty minutes of arc represents 40 nautical miles, (i.e. about 60 km), but the error wouldn’t be 40’ east consistently, so the charts from the Endeavour voyage couldn’t be redrawn, unless he re-circumnavigated NZ and did all the longitude readings again.

Beaglehole (1955) notes the following Cook entry for 10th November 1774, in the Journal of the Resolution and Adventure:

... Mr Wales having from time to time communicated to me the observations he had made in this Sound, for determining the Longitude, the mean results of which gives 174o 25' 07 1/2" East for the bottom of Ship Cove where the observations were made the Latitude of which is 41o 5' 56 1/2" South. In my Chart constructed in my former Voyage this place is laid down in 184o 54' 30" w equal to 175o 5' 30" East, the error of the Chart is therefore 0o 40' and nearly equal to what was found at Duskey Bay; by which it appears that the whole of Tavai­ Poenammoo, is laid down 40' too far East in the said Chart, as well as in the Journal of the Voyage; but the error in Eahei-no-mauwe is not more than half a degree or 30' because the distance between Queen Charlottes Sound and Cape Palliser has been found to be greater by 10' of Longitude than it is laid down in the Chart.
I mention these errors not from a supposition that they will much effect neither Navigation or Geography, but because I have no doubt of their existence, for from the multitude of observations which Mr Wales took the situation of few parts of the world are better ascertained than Queen Charlottes Sound. Indeed I might with equal truth say the same of all the other places where we have made any stay at. For Mr Wales, whose abilities is equal to his assiduity, lost no one observation that could possibly be obtained.1 Even the situation of such Islands as we past without touching at are by means of Mr Kendalls Watch determined with almost equal accuracy.
The preceding two sentences are a red ink revision of the following, which almost conveys the impression that Cook thought Wales was going a little too far in accuracy; but that as he had done so, his efforts must be mentioned. 'As Mr Wales had made so many observations in the Sound for determining the Longitude, I thought 1t was proper to say what the results were, otherwise I should hardly have mentioned these errors; from a supposition that few will think them of such consequence as to effect Navigation or Geography ...

The author has imported Cook's chart of the entire coastline of NZ into GE, and geo-referenced it as an overlay (Fig 13).

Figure 12: Cook's chart of NZ imported into Google Earth as an overlay, and geo-referenced.

Looking from a large scale (Tasman Sea) perspective, the coastline, as charted by Cook, has a very close correlation to the actual coastline (highlighted in yellow). By zooming and inspection, the author has determined that the largest errors occurred around the Cook Strait area; i.e. central NZ.

Figure 13: TUMONZ map of Cook Strait area, showing Ship Cove and other prominent coastal landmarks.

Figure 14: GE view of the Cook Strait area, showing a few of the longitudinal errors of Cook's chart from the Endeavour voyage.

The maximum error noted was 42 nm (42 degrees of arc) at Cape Farewell. However, Cook was philosophical, in that it was a 'best efforts' running survey, conducted in a relatively short timeframe. As noted by Snowdon:

It is obvious however that Cook was dissatisfied with the methods he was forced to adopt, and he would have preferred to have spent much more time in each area, to have landed more frequently, and thus to have produced charts with more detail and greater accuracy. Whilst making a sketch survey of an island in the New Hebrides in August 1774, he noted in his journal "The word survey is not to be understood here in its literal sense". Another entry referred to his chart of New Zealand in these terms: 'The coast as it is laid down from Cape Saunders to Cape South, and even to Cape West is no doubt in many places very erroneous as we hardly ever were able to keep near the shore and were sometimes blown off altogether'. (Snowdon, 1983)

In spite of the sailing difficulties (particularly, weather), short timeframe, deficiencies of measurement methods used at the time, and operating in a potentially hostile environment, the resulting charts are considered to be of remarkably high quality. They were used for many decades by mariners around the NZ coast, and Tessa Duder notes that one small section was only superseded by RNZN hydrographers in the 1980s. Snowdon's summary is considered appropriate:

In closing I can do no better than remind you of some of the words inscribed on Cook's monument at Chalfont-St-Giles in Buckinghamshire.
'To the memory of Captain James Cook, the ablest and most renowned navigator this or any other country has produced'. (Snowdon, 1983)

Author's Note: This article is based on two public lectures I gave, in Thames and Paeroa, during November 2019; to commemorate the visit by HMS Endeavour to the Firth of Thames and Waihou River, 19-21 November 1769. A section of the talks included navigation and surveying methods of the time, and the accuracy of Cook's charts. At the time of the lectures, I was unaware of Tessa Duder's excellent book: First Map: How James Cook Charted New Zealand Aotearoa, and any similarities between this article and the book are purely coincidental (apart from one citation, near the end of the article).


  1. Endeavour Journals: National Library of Australia.
    [Includes Journals of Cook, Banks, Parkinson, and ‘Summary’ report by Hawkesworth (1773)]
  2. Beaglehole, J. C. (Ed.) (1955). The Journals of Captain James Cook on his voyages of discovery: Vol. 1. The Voyage of the Endeavour 1768-1771, University Press for the Hakluyt Society, Cambridge.
  3. Ibid, Vol 2. The Voyage of the Resolution and Adventure 1772 - 1775.
  4. Beaglehole, J. C. (Ed.) (1962). The Endeavour Journal of Joseph Banks, Halstead Press, Sydney.
  5. Begg, A. C. and Begg, N. C. (1969). James Cook in New Zealand: Part 1 The Voyage of the Endeavour 1768-1771, Government Printer, Wellington.
  6. David, A. (Ed.) (1988). The Charts and Coastal Views of Captain Cook's Voyages: Volume 1 The Voyage of the Endeavor 1768-1771, Hakluyt Society, London.
  7. Hawkesworth, J. (1773). Account of the Voyages in the Southern Hemisphere, London.
  8. Hough, R. (1994), Captain James Cook, Hodder and Stoughton, London.
  9. Kitson, A. (1911). The Life of Captain James Cook: About Captain Cook, On-line edition.
  10. Snowdon, K.J. (1983), Captain Cook as a Hydrographer (Presentation to CCSU Meeting, 1983).


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