Shadwell’s Manual for the Accurate Determination of Meridian Distances by Chronometer



After a long struggle with the Board of Longitude, English woodworker John Harrison was finally awarded, in 1773, the prize for meeting the requirements of the English Longitude Act of 1714 for finding a practical and useful means of determining longitude at sea (the Board of Longitude having being specifically set up to administer the Act). Nevertheless, it was not until the late 19th century that reliable marine timekeepers or chronometers started to emerge in quantity to enable general maritime use for finding longitude.

Also, by this time in the 19th century the (electric) telegraph had been invented and telegraph lines were starting to connect populous places. As described in this 2014 paper Australian Longitudes by “Wire and Wireless”, longitude by telegraph became an acceptable and accurate method of obtaining longitude as it allowed time differences to be measured…over any distance spanned by the telegraph.

Figure 1 : Depiction of Sydney Cove, circa 1831, showing the shipping in Circular Key and built-up Rocks area with Fort McQuarrie (left) the present site of the Sydney Opera House. The longitude of Fort Macquarie became the first principal meridian in Australia. This depiction was made during the voyage of Cyrille Pierre Théodore Laplace (1793–1875) a French navigator famous for his circumnavigation of the globe on board La Favorite (Brochure image).


While indeed the technology for finding longitude now existed, in 1855 then Captain Charles Shadwell first pointed out that unless a rigorous regime was maintained the whole methodology of marine timekeeping on any vessel might be flawed rendering any derived longitude(s) worthless.

Shadwell’s 1861 publication titled Notes on the Management of Chronometers and the Measurement of Meridian Distances, showed that the use of the new timekeepers or chronometers for finding longitude was, for the most part, unreliable (Shadwell’s 1861 edition was a revised version of his earlier 1855 first edition). Thus, he concluded that information from voyages regarding longitude is kept in a state of perpetual fluctuation, from which it is impossible that universal precision can ever be obtained.

The aim of Shadwell’s book was to condense the dispersed information about the application of chronometers to the accurate interpretation of differences of longitude and endeavour to supply naval officers, and others entrusted with the care of chronometers, with a manual of instruction how best to use them, and how to furnish systematic results in recording the meridian distances of the several places visited during their voyages.


Charles Frederick Alexander Shadwell

Admiral Sir Charles Frederick Alexander Shadwell, KCB FRS, was born the fourth son of Sir Lancelot Shadwell in 1814 and joined the Royal Navy in 1827.

A Lieutenant by 1838, in Castor he was present during operations off Syria in 1840. Between 3 December 1841 and 4 July 1846, Shadwell was a Lieutenant in Fly, commanded by Francis Price Blackwood, surveying the Torres Straits and northern coast of Australia. A Commander by 1846, in 1850 he was commanding HMS Sphynx and took part in the Second Anglo-Burmese War of 1852. Promoted Captain in February 1853, from 1 August 1856 to 2 January 1860, in Highflyer (from commissioning at Portsmouth), was present during the Second Anglo-Chinese War including the capture of Canton in December 1857, and attack on Peiho or Taku Forts on 25 June 1859, when a wound rendered him permanently lame. From 1861 he commanded HMS Aboukir and then from 1862 HMS Hastings (from commissioning) the flagship of Rear-Admiral Lewis Tobias Jones.

Appointed Captain-Superintendent of Gosport victualling yard and of the Royal Haslar Hospital in June 1864 Shadwell was promoted Rear-Admiral in January 1869 and later became Commander in Chief, China Station 1871-1874. On his posting to China he vacated his appointment as Naval aide-de-camp to the Queen, which he had received in March 1866. Promoted Vice-Admiral in April 1875, in 1877 he received the flag officers' pension for meritorious service.

Shadwell had been elected a Fellow of the Royal Society (FRS) in 1861 and in 1873 was gazetted a Knight Commander of the Bath (KCB) and later in 1878 made President of the Royal Naval College, Greenwich.

After Shadwell retired in 1879, he lived at Meadow Bank in Melksham in Wiltshire, dying unmarried in March 1886 at age 72.


Longitude from the observation of Lunar Distance

While John Harrison (1693-1776) was perfecting his timekeeper his nemesis, depending on whom you believe, Nevil Maskelyne (1732-1811) the then Astronomer Royal, accepted the chair of the Board of Longitude in 1765. With his background Maskelyne believed longitude could be found from the heavens with astronomy, as was latitude. This belief and being chair of the Board is reported to have clouded his judgement when it came to assessing other options for finding longitude. In Maskeleyne’s defence it is reported that while using Harrison's time piece H4 was considered more accurate for finding longitude, Maskelyne's method combined with his Tables was far cheaper. Maskelyne’s tables at then a few shillings against the many pounds for a timekeeper saw Maskeleyne’s method predominate for the next century.

Maskeleyne’s method for finding longitude from astronomy, came in the form of an observation called Lunar Distances. To determine his longitude by this method, an observer had to measure the angle between the centre of the Moon and a listed star (the lunar distance) along with both their altitudes. Next, he had to calculate his own local time and correct the Moon’s position for the twin effects of parallax and refraction. From the Nautical Almanac the time at Greenwich when the Moon was at the same calculated position was then extracted. The difference between the Greenwich time and the observer’s local time, then gave the difference in longitude from the meridian of the Royal Observatory at Greenwich. To make the whole process as simple as possible, Maskelyne proposed the Board of Longitude publish a Nautical Ephemeris. What came to be called The Nautical Almanac and Astronomical Ephemeris was first prepared for the year 1767 and published in 1766. Some 2,000 copies (price 2 shillings and 6 pence) were printed. At the same time Maskelyne also published his Tables Requisite to be Used with the Astronomical and Nautical Ephemeris to serve as a handbook for navigators using lunar distances. These Tables Requisite, were published from time to time, and it is said that the 1781 edition sold 10,000 copies immediately on publication.

When published, The Nautical Almanac contained the lunar tables of German mathematician Tobias Mayer (1723-1762). In 1755 Mayer had submitted to the British government an amended body of manuscript tables, which James Bradley (1693-1762), Astronomer Royal from 1742-1762, compared with the Greenwich observations. Bradley found Mayer’s work to be sufficiently accurate to determine the moon's position to 5 seconds of arc, and consequently longitude at sea could be determined to within around half a degree of arc (50 kilometres approximately). In consideration of Mayer’s contibution to the finding of longitude at sea, his widow received from the Board of Longitude £3,000 (equivalent to £408,000 in 2018).

The Nautical Almanac for 1906 was the last to publish tables for the Lunar Distance method for finding longitude.


Shadwell’s Introductory Observations

The Lunar Distance method for finding longitude in conjunction with the tables of The Nautical Almanac had existed for some 100 years when Shadwell’s publication became available. Nevertheless, timekeepers had now become more reliable and readily available and Maskeleyne’s cheap alternative was now being challenged by the more accurate method. In this changing world, Shadwell’s opening chapter provided an overview of the then state of play with what he terms maritime geography.


The application of chronometers to the accurate determination of "Meridian Distances," or the differences of longitude of distant stations, has usually formed an important object in the scientific voyages of modern times, from those undertaken in the last century by the illustrious Cook, to those performed in our own day by more recent navigators.

The happy invention of the Electric Telegraph, the successful accomplishment of its submarine connexion, and its application to astronomical purposes, would seem to have completely and successfully solved the problem of differences of longitude of stations which are either situated on the same continent, or, if occupying insular positions, only separated by narrow seas; and there can be little doubt that, before long, the various observatories in the British Islands and on the Continent will, by its means, be accurately linked together, and their relative positions consequently determined to the last degree of mathematical correctness. Considered as base stations, they may then be viewed as forming salient points in a network of triangles described on the surface of our globe, to which minor places can afterwards be conveniently referred by geodetic means, so as ultimately to combine them in one comprehensive whole, hitherto unexampled for accuracy in the annals of geographical science.

From the very nature of its invention, however, and from the probable limits to its use, interposed by the difficulties of its submarine connexion, except in narrow seas, the application of the Electric Telegraph to the question of Terrestrial Longitude will doubtless be comparatively very limited; and it must still be to the successful appliance of the ordinary means at the disposal of the navigator that we must continue to look for the final solution of questions relating to the relative longitudes of outlying stations on the ocean, and their connexion with the fixed points on the great continents.

Fortunately, at a period when the successful application of the system of galvanic signals to astronomical purposes has given a great impetus to the final solution of the questions concerning the relative longitude of stations on land, the gradual improvements effected of late years in the construction of marine chronometers, and the yearly increasing extension of the application of steam to ocean navigation, seem at the same time to afford increased facilities to the Navigator for the improvement of Maritime Geography, as he will thus be enabled also to maintain an honourable rivalry with the Astronomer, and, like him, to contribute his fair share towards the ultimate perfection of geographical science.

In examining the earlier history of modern hydrography, and on inquiring into the circumstances which have hitherto impeded its progress towards final perfection, notwithstanding the zealous and useful labours of numerous scientific navigators, and the voluntary contributions of many intelligent commanders, two causes will, we apprehend, be found to have tended, although accidentally, to retard its satisfactory development; first, the practice of mixing up in one indiscriminate combination the astronomical data for the positive settlement of disputed positions, and the relative evidence afforded by chronometric measurements; and, secondly, a want of clearness of comprehension of the relative values of absolute and differential longitudes.

For instance, nothing is more common than to find, on examining even comparatively recent works on hydrography, that the data quoted for the settlement of a given position are of the most miscellaneous and incommensurable character : lunar observations, eclipses of Jupiter's satellites, occultations of stars by the moon, solar eclipses, and chronometric measurements by various authorities, from adjacent and independent points, all blended together in one crude and inharmonious result; or again, than to find chronometric determinations of a purely relative character, and often measured from two or more independent stations, confounded with absolute results.

Places are fixed absolutely by astronomical observations, or relatively by chronometers. This distinction must be clearly kept in view if ever we wish to arrive at final and conclusive results, and if we desire to avoid the perpetual oscillation of ideas which a mixture of the two principles is sure to entai [first person singular past historic of ‘enter’] on us.

Much has been done of late years towards simplifying the conclusions of maritime geography, by collecting from the records of astronomical and chronometric observations satisfactory details for the final establishment of several important fundamental positions.

…Many concurrent circumstances of a favourable nature, and peculiar to the present time, seem to be conducive to the more systematic application of chronometers on board ship to the objects of science in the measurement of differences of longitude. The mechanical construction of chronometers has attained a high and unexampled degree of perfection, these improvements having at the same time been accompanied by a very considerable reduction in their cost; so that chronometers are now no longer rare instruments only within reach of the wealthy; and in lieu of one solitary chronometer as formerly, it is now not unusual to find three or more good chronometers on board every ship. The more general diffusion of a good practical education among young officers, both in the royal and mercantile navies, at the same time renders them more capable of applying chronometers to the accurate purposes of science and better able to appreciate their results. The increasing application of steam machinery, moreover, to men of war, whereby the average duration of passages will be much shortened and return voyages greatly facilitated, and the extension of lines of ocean steam navigation by the great mercantile companies to all parts of the globe, seem to afford, simultaneously with the abovementioned circumstances, increased facilities for the systematic and careful measurement of chains of meridian distances.

If this view of this important question be correct, and the writer's partiality for a favourite subject has not caused him to take a too favourable view of present circumstances, it is important to consider whether the time has not arrived when it might be advisable to attempt to concentrate and condense in a practical form the necessary instructions for the guidance of those, who may be desirous of undertaking the accurate and systematic measurement of chronometric differences of longitude.

…Speaking generally, we apprehend that, unless from peculiarly favourable circumstances of previous service in a surveying ship, on a scientific voyage, or under a scientific chief, officers in general have no organised knowledge of the minutiae and details requisite to be attended to in the accurate measurement of meridian distances. No single book supplies the required information, and an officer furnished with some good chronometers, and desirous of advantageously employing them, has probably to grope his way as best he may, and devise a system for himself.

This want we propose to endeavour to remedy. With this object in view, in the following pages we shall endeavour to collect together and arrange various hints relating to the custody and management of chronometers on board ship, at present existing only in a traditional form, or to be found scattered amid many books often not easily accessible. The questions relating to errors and rates next engage attention; and subsequently, the formulae for the determination of meridian distances are discussed and arranged in an organised and systematic manner, worthy, it is hoped, of the present advanced state of hydrographic science.

…The utility of chronometric determinations, and the value of their results, as well as the possibility of their advantageous incorporation with the previous labours of others, much depends on the degree of care bestowed on the minute details of their manipulations. Many series of observations have often had their value materially impaired by the accidental neglect of some small particulars; and doubtless a few measurements executed with a due regard to accuracy of detail, are many times more valuable than much larger masses of observation reduced and recorded in a loose, uncertain, and unsystematic manner.

Chronometric determinations obtained with no special regard to accuracy, reduced approximately, and recorded vaguely, although perhaps formerly valuable contributions to our then knowledge, are unsuited at present to the existing condition of maritime geography.…As a contribution towards the improvement of geographical science, and in furtherance of the development of the above views, these pages have been undertaken : and if in the hands of scientific officers or intelligent travellers they are found at all conducive to the systematic realisation of this important subject, they will not have been written in vain, or the author's labour lost.


By contrast in an emerging Australia, at the time of Shadwell’s 1855 publication the name of Van Diemen's Land had just been changed to Tasmania, the Colony of Victoria had only been separated from the Colony of New South Wales for a few years, and the Colony of Queensland was yet to be determined.


Meridian Distances

The Meridian Distance or difference of longitude in time between any two places, is obtained chronometrically by comparing the errors on local mean time shown by a chronometer at the two places in succession; the error at the first place being corrected by the known rate of the chronometer in the interval, so as to give the state of the watch at the moment of the second observation. The errors of the chronometers being thus known simultaneously at the two places, their difference represents the meridian distance or difference of longitude in time, between them.


Figure 2 : Example of using a marine chronometer to find longitude.

A meridian is another name for a line of longitude. Meridians run from pole to pole and are notated from 0 (zero) degrees thru Greenwich England to 180 degrees east and west. A Meridian Distances is just the difference in longitude between two meridians of longitude. Meridians are related to time by the spinning motion of the earth such that 360 degrees equals 24 hours. As depicted in Figure 2 above, the Meridian Distance between longitudes 0 and 30 degrees west is two hours of time as there are 15 degrees of arc per hour of time. From this relationship between time and longitude it can be seen that time needed to be measured to decimals of a second as 0.1 second of time equated to 1.5 seconds of longitude or about 40 metres of distance, if very precise longitude was required. 

A ship would generally carry several chromometers from different makers, scientific vessels many more. On Cook’s second voyage when he departed in July 1772, Larcum Kendall's No.1 (K1) and John Arnold's No.3 timekeepers went with him on Resolution, and John Arnold's Nos.1 and 2 timekeepers went in Tobias Furneaux's Adventure (K1 was a copy of John Harrison's fourth timekeeper (H4)). Cook on his third voyage of 1776-1780 again took K1 in his own ship while Larcum Kendall's No.3 (K3) went in Discovery. Table 1 below lists the twelve chromometers aboard HMS Fly employed surveying the coast of Australia from March 1842 to April 1846. Circa 1825, Heinrich Christian Schumacher (1780-1850) is reported to have carried eighty-six (86) ship’s chromometers over European roads of the time in an effort to establish the longitude differences between Greenwich, Copenhagen, Altona and other places.


Table 1 : Chronometers of HMS Fly employed surveying on the coasts of Australia, during a period of four years,

from March 1842 to April 1846.


Serial Number

























Parkinson & Frodsham



Porthouse (Pocket)









Parkinson & Frodsham (Pocket)


All these chronometers were the property of Her Majesty's Government, except Chronometer C, which belonged to Captain Blackwood.

Z was employed as the standard; C was also frequently taken on shore for the purposes of astronomical observation.

The other chronometers (excepting A and B) were never moved from the chronometer room, from the time they were received on board at Devonport, in March 1842, till the ship's return there in June 1846, except when the Fly was hove down for repairs at Sydney in October 1845.

Chronometers A and B having stopped on various occasions were repaired at Hobart and Sydney. The continuity of their performances was thus interrupted.

The rates were always determined by observations, made on shore, with the artificial horizon, and usually by the method of equal altitudes.


The chronometer considered most reliable in running consistently ie not fast one day and slow the next or gain or lose time unpredictably would be selected as the standard against which all the other chronometers would be rated (compared). These rates would be recorded and used to adjust the time interval given by a particular chronometer. The adjusted time interval was thus considered to be equal to the time interval given by that chronometer had it been able to be theoretically read at both places at the same instant. The time interval or meridian distance obtained from all chronometers should then be the same. It was from this time interval that the meridian distance and hence longitude was derived.

Importantly the chronometers were used to measure time intervals rather than tell absolute time. While simple mathematics could be used to determine average rates of time gained or lost, Shadwell suggested that when opportunity allowed the rates of time gained or lost should be calculated using the Method of Least Squares. The value so derived by this method would minimise the sum of the squares of the differences between this value and the observed values for every single observation.

Additionally Shadwell noticed, as happened on scientific and related voyages, observations on the sun, stars, moon and planets were used to modify the timed meridian distance. Unless all the pertinent data was provided regarding such observations then the validity of the resultant longitude could be difficult to verify. 

Perhaps the major issue Shadwell had with existing procedures was that the chronometers were not protected against changes in temperature nor was temperature a consideration when Meridian Distances were extracted. Shadwell provided an example from Harrison's timekeeper after its second trial voyage to the West Indies in 1764. Harrison had provided the British Admiralty before the voyage, with the equivalent of a calibration certificate for his timekeeper. The certificate showed the expected rate of the timekeeper at every ten degrees of temperature from 42° to 82°F. After the voyage Harrison’s timekeeper was found to have gained 54 seconds during the 156 day journey and thus it met the Admiralty’s criteria. If, however, as Shadwell points out allowance be made for the variation of the thermometer, as stated by him [Harrison] before his departure, it will be found to have lost only 15 seconds. Shadwell goes on to say that English navigators appear to have been as equally unmind­ful of the refinements of temperature corrections…. No allusion is made to the subject in the account of Cook's voyages, nor does the matter seem to have engaged the attention of the commanders of our various scientific voyages, and hydrographic expeditions, during the present century, in any practical degree; although the failures and anomalies which sometimes presented themselves in chronometric measurements, have often been attributed to excessive or irregular fluctuations of temperature.


Figure 3 : Relative sizes of Harrison’s H1 to H4 with far right Kendall’s K1; overall approximately a 90% reduction in size.


The Determination of the Errors and Rates of Chronometers

Having discussed accommodating the chronometers aboard ship, their winding and the minimisation of environmental effects, Shadwell moves on to describe how the errors and rates of the ship’s chronometers can be determined. The three modes, summarised below he stated, are available to officers serving on board ship, and within compass of the means ordinarily at their disposal.


Transit observations

Such observations were generally only undertaken by ships on scientific voyages or surveying duties where they were supplied with the appropriate instrumentation. Thus such instrumentation will very rarely be found among the apparatus employed on board ships engaged in the ordinary duties of the service.

Those requiring a sextant

At sea, altitudes observed with a sextant using the sea horizon, even under the most favourable circumstances, were liable to be impacted by; the inaccuracy of the contact with the celestial object; the uncertain effects of refraction on the appearance of the horizon; and errors arising from an inaccurate estimation of the correction for dip (of the horizon). Thus while the simplest and most convenient kind of astronomical observations available for the determination of time were those which could be made with a sextant, the observations must be made on land using an artificial horizon.

Observations made on shore with a sextant and artificial horizon allow contact with the celestial object to be made with great precision, while the effects of refraction and estimation of dip are negated. Please refer to Figure 4 below where the use of an artificial horizon is shown.

The best artificial or mercurial horizon comprised a shallow trough filled with mercury, and screened from the wind when necessary, by a glass cover. The mercury was stored in a bottle and decanted into the trough for use and then poured back into the bottle when the observations were completed. While it was best to avoid using the glass cover, if its use was unavoidable, error due to imperfection in, or non-parallelism of, the surface of the glass had to be minimised. This was achieved by marking the glass cover and trough so that the cover could always be placed over the trough in exactly the same position. Any errors introduced by the cover would then be equal for all observations. Alternatively, the cover could be reversed during the obser­vations; half the observations being made with the cover in one position, and half in the other position, thus neutralising any errors.

The sextant used for such observations should not be indifferently hacked about for other purposes; it is of great importance that an observer should be able to place reliance on the trustworthiness of his instrument, and on the stability of its index error. If, therefore, he has the command of more than one instrument, the best may be suitably reserved for the finer kinds of observation, such as lunars at sea, and determining the latitude and time on shore; and the other one to the common observations required in the ordinary navigation of the ship at sea.

Care should be taken, especially in tropical climates, that the sextant is not unnecessarily exposed to the action of the sun's rays, and, when not actually in use during the pauses between the observations, it should be kept in the shade, or screened with a handkerchief : nothing tends to ruin sextants more, than unnecessarily roasting them in the sun.

The methods of observation for the determination of time was either equal or corresponding altitudes or single or independent altitudes. Equal or cor­responding altitudes observations were preferred as any errors in knowing the latitude of the place of observation, the declination of the celestial object observed, and its altitude as recorded by the observer and his sextant were negated.

The celestial objects observed was either the sun or stars. The sun was the most convenient, and generally preferred.

Preconcerted signals

Such signals refer to where the precise moment of mean time at a place was indicated by the fall of time-balls, the display of signal-flags, the flashes of guns, etc as well as any special measures which may occasionally be devised between different ships for the intercomparison of their chronometers.

As well as understanding the signal(s) and what it/they represented, regarding the local time, arrangements must be in place aboard ship to transmit that instant from where the phenomenon was observed on the ship’s deck to its chronometer room.


Figure 4 : Diagrams showing the use of an artificial horizon;

(top) at sea the altitude of the celestial body with reference to the sea/sky horizon must be corrected for the dip of the horizon;

(bottom) the observer views the celestial body both directly and reflected from the artificial horizon

removing the need to account for dip and being able to determine the sea/sky horizon.


After discussing all these issues and then resolving them with procedures, relevant mathematical formulae and worked examples, Shadwell then sets out his Manual.


Second and final part next month.