Sources, simplifications and validation

This page collects, from every chapter, what NavMuseum relies on and what it leaves out.

Evidence classes§

Historical claims carry one of four tags:

• documented supported by primary sources or well-established scholarship.
• reconstructed inferred by historians or practitioners from partial evidence.
• contested scholars disagree; treat as a hypothesis.
• illustrative a teaching model, not a claim about a specific historical practice.

How the numbers are checked§

The computational core (static/js/engine/ in the source repository) is pure functions with no drawing code. It is checked by its own unit tests and by an independent oracle suite written from published formulas and reference values without reading the core’s code. Both run on every change. The engine is also callable from the command line (node tools/engine.mjs), so anyone can check a number.

Simplifications, chapter by chapter§

Latitude from the sky§

• The figure treats Earth as a perfect sphere and the horizon as a geometric plane, with no atmosphere.
• The noon Sun in these figures is a point at the Sun’s centre, seen without refraction, and the declination is held fixed through the day.

Reading the world§

• The figure uses a geometric horizon at sea level, no atmospheric refraction, and equal 11.25° sectors for counting. It precesses star positions to 2026 and ignores proper motion.
• The figure assumes a perfectly vertical “up,” a spherical Earth, and no refraction. It shows one star at a time.
• Two monochromatic, long-crested swells add linearly; the canoe is treated as a point that feels the surface slope.
• One wind table for the whole Arabian Sea, twelve monthly states, and a rule that a square-rigged or lateen-rigged ship sails only when the wind is within 75° of astern.

Longitude is a clock problem§

• The polar view shows a spherical Earth turning at a constant rate under a Sun that sits still, with the “mean Sun” setting the time unless you tick the box.
• The figure treats chronometer error as a starting error plus a constant unallowed rate plus a random walk of daily rate changes, and treats latitude as perfectly known.
• The curve and the analemma use a low-precision solar theory (accurate to about 0.1 minute in the equation of time over 1900–2100) for the year 2026.
• The simulation fixes the ship in place, gives each sight an independent random error, and does not apply the small correction for the Sun’s changing declination between the two equal-altitude sights.
• The lunar theory here is the 60-term series from Meeus’s Astronomical Algorithms, accurate to about 10″, evaluated with a modern ΔT[17]. Local time comes from a separate time sight and is taken as exact.
• The figure treats Earth as a sphere, uses a single standard atmosphere, and ignores the flattening of the Sun’s and Moon’s discs by refraction near the horizon.

How a sextant works§

• The drawing shows a ray in the plane of the frame and idealized thin mirrors pivoting exactly on the index arm’s axis; the light paths are drawn at the instrument’s scale, as if the Sun were close above the frame.
• The calculator uses one standard refraction formula scaled for temperature and pressure, the almanac’s dip formula, a fixed solar semidiameter of 16.0′, and a spherical Earth for parallax.
• Each instrument is given one reading step, one random scatter, and (for the cross-staff) one systematic bias, chosen within the ranges discussed by historians of navigation, for one observer in a moderate sea.

From a sight to a fix§

• The ship steers a single course at a steady speed, and every source of error is constant for the whole passage: one current vector, one heading error, one speed error per possible voyage. The ellipse is the exact covariance of that model; the faint tracks are samples from it.
• The figure treats Ho as already corrected: the altitude of the Sun’s center above the true horizon, as if seen from Earth’s center, on a spherical Earth.
• The zoom uses an orthographic view centered on the ship, and the line is drawn as the great circle tangent to the circle of equal altitude at the ship.
• Deneb’s GHA and declination are taken from the almanac values quoted by Bowditch, and the AP and DR are fixed to his example.
• These sights have no error at all, so the lines meet in a point and the fix sits on the true position.
• All sights are simultaneous, the errors are Gaussian and independent with a known σ, and the bodies are idealized: placed at the altitudes and azimuths the controls ask for.
• The ship holds one course and speed between the sights, the sights themselves are perfect, and the current is constant.
• The stars carry real names but are placed at random azimuths and altitudes, and each sight has 1′ of random error and no systematic error.

The invisible lighthouse§

• The figure draws a perfect figure-eight on a flat chart, with the bearing measured from true north and the line of position drawn straight.
• The figure uses two perfectly perpendicular figure-eight patterns of equal strength, no fall-off of the A/N ratio with distance, a flat landscape, and Morse timing chosen for clarity. The cone of silence is drawn as a fixed circle.
• The figure works on a flat plane, propagates every signal in a straight line at the vacuum speed of light, ignores the emission delays, treats the two time differences as independent and draws the noise as Gaussian with a σ far larger than Loran-C achieved, so that the ellipse is visible.
• The figure enlarges the lanes, uses a single master–slave pair, a coarse wavelength exactly six times the fine one, and a coarse error that is Gaussian and independent of the fine one.

You have four satellites§

• The figure uses straight-line propagation at the vacuum speed of light, perfectly synchronised transmitters, and no measurement noise. Distances are scaled so a fraction of a millisecond is visible on a map.
• The figure uses a spherical, optionally rotating Earth, a perfect circular orbit known exactly, a stationary receiver, instantaneous frequency samples with an illustrative 3 Hz noise, and one carrier with no ionosphere.
• The constellation is illustrative: 24 satellites on circular orbits of radius 26,560 km, inclined 55°, six planes of four. The receiver has perfect satellite positions, no noise, and signals that travel instantly in an Earth-fixed frame.
• Every satellite has the same, independent, Gaussian ranging error and the linearised geometry is exact.
• Fault sizes are chosen to be visible on the chart, the spoofer is perfectly synchronised, and the consistency check is a textbook chi-square test with a known noise level.
• One horizontal axis, constant biases, no initial errors, and an independent radio fix whose error is redrawn at random each time.

Bibliography§

1. Polynesian Voyaging Society. 50 years ago today, Hōkūleʻa makes landfall in Papeʻete, Tahiti. hokulea.com, 2026. practitioner (cited in Reading the world)
2. Guy Ropars, Gabriel Gorre, Albert Le Floch, Jay Enoch and Vasudevan Lakshminarayanan. A depolarizer as a possible precise sunstone for Viking navigation by polarized skylight. Proceedings of the Royal Society A 468: 671–684, 2012. scholarship (cited in Reading the world)
3. W. E. May. A History of Marine Navigation. G. T. Foulis, Henley-on-Thames, 1973. Instruments from the cross-staff to the sextant, their use at sea and their practical accuracy. scholarship (cited in How a sextant works)
4. Thomas H. Sumner. A New and Accurate Method of Finding a Ship’s Position at Sea, by Projection on Mercator’s Chart. Thomas Groom & Co., Boston, 1843. Sumner’s own account of the December 1837 sight, quoted in full in Bowditch (2019) Vol. I §110. primary (cited in From a sight to a fix)
5. J. J. O’Connor and E. F. Robertson. Abu Arrayhan Muhammad ibn Ahmad al-Biruni (biography). MacTutor History of Mathematics, University of St Andrews. The lunar eclipse of 24 May 997 timed at Kath and at Baghdad (by Abu’l-Wafa) to find the longitude difference. reference (cited in Longitude is a clock problem)
6. R. Ch. Duval. Admiral Marcq de Blond de St. Hilaire. The Journal of Navigation 19 (2): 209–212, 1966. scholarship (cited in From a sight to a fix)
7. Samuel Eliot Morison. Admiral of the Ocean Sea: A Life of Christopher Columbus. Little, Brown, 1942. Columbus’s navigation by dead reckoning; his quadrant and astrolabe sights and their large latitude errors in 1492. scholarship (cited in How a sextant works)
8. G. R. Tibbetts. Arab Navigation in the Indian Ocean before the Coming of the Portuguese. Royal Asiatic Society, 1971. Includes a translation of Ibn Mājid's Kitāb al-Fawāʾid and discusses star-altitude units (iṣbaʿ). scholarship (cited in Latitude from the sky)
9. G. R. Tibbetts. Arab Navigation in the Indian Ocean before the Coming of the Portuguese. Royal Asiatic Society of Great Britain and Ireland, 1971. Translation and study of Ibn Mājid’s Kitāb al-Fawā’id; star altitudes in isba‘ (‘fingers’) and the instruments used to take them. scholarship (cited in How a sextant works)
10. G. R. Tibbetts. Arab Navigation in the Indian Ocean before the Coming of the Portuguese (translation of Ibn Mājid's Kitāb al-Fawāʾid). Royal Asiatic Society of Great Britain and Ireland (Oriental Translation Fund, n.s. 42), 1971. scholarship (cited in Reading the world)
11. Jean Meeus. Astronomical Algorithms, 2nd ed.. Willmann-Bell, 1998. Ch. 12 (sidereal time), 21 (precession), 25 (solar coordinates). The basis of this site's solar and precession code. reference (cited in Latitude from the sky)
12. Jean Meeus. Astronomical Algorithms, 2nd ed. (ch. 12 sidereal time, ch. 25 solar coordinates, ch. 28 equation of time, ch. 47 position of the Moon). Willmann-Bell, 1998. Source of the lunar series used here (accuracy about 10″ in longitude, 4″ in latitude) and of the solar theory and equation of time. standard (cited in Longitude is a clock problem)
13. Wikipedia contributors. Bellini–Tosi direction finder. Wikipedia, 2026. Overview of the radiogoniometer and its use on ships; used here only for the general account. reference (cited in The invisible lighthouse)
14. Seán McGrail. Boats of the World: From the Stone Age to Medieval Times. Oxford University Press, 2001. scholarship (cited in Reading the world)
15. Adolphe-Laurent-Anatole Marcq de Blond de Saint-Hilaire. Calcul du point observé. Revue maritime et coloniale, Paris, 1875. Secondary sources cite the volume number differently (46 or 56); cited here by title and year. primary (cited in From a sight to a fix)
16. Te Ara – the Encyclopedia of New Zealand. Canoe navigation. Manatū Taonga Ministry for Culture and Heritage. reference (cited in Reading the world)
17. Robert S. Richardson. Captain Thomas Hubbard Sumner, 1807–1876. Publications of the Astronomical Society of the Pacific 55 (324): 136–144, 1943. scholarship (cited in From a sight to a fix)
18. U.S. Department of Transportation, Volpe Center. Complementary PNT and GPS Backup Technologies Demonstration Report. USDOT, 2021. Field tests in March 2020 included two eLoran systems; concluded no single technology can back up GPS universally. standard (cited in You have four satellites)
19. Wikipedia contributors. Decca Navigator System. Wikipedia, 2026. Chain 5B harmonics (master 6f = 85 kHz, purple 5f, red 8f, green 9f) and lane and zone widths on the baseline. reference (cited in The invisible lighthouse)
20. Jerry Proc. Decca Navigator: history. jproc.ca hyperbolic navigation archive, 2023. W. J. O'Brien's work from 1936; the D-Day chain; first civil chain 1946; lane identification; UK closure on 31 March 2000. practitioner (cited in The invisible lighthouse)
21. Thomas Gladwin. East Is a Big Bird: Navigation and Logic on Puluwat Atoll. Harvard University Press, 1970. scholarship (cited in Reading the world)
22. Air Force Historical Foundation. February 22, 1978. afhistory.org. reference (cited in You have four satellites)
23. History of Parliament Trust. Finding latitude in longitude: Parliamentary funding of early modern science and technology. The History of Parliament blog, 2014. The 1714 Act’s reward tiers and conditions. scholarship (cited in Longitude is a clock problem)
24. Richard Dunn and Rebekah Higgitt. Finding Longitude: How Ships, Clocks and Stars Helped Solve the Longitude Problem. Collins / Royal Museums Greenwich, 2014. A history of the Board of Longitude and of the many methods it considered; corrects the lone-genius story. scholarship (cited in Longitude is a clock problem)
25. Barry Schiff. Four-Course Radio Ranges. AOPA Pilot, 1997. A and N loops, legs about 3° wide, 200–400 kHz receivers, more than 400 ranges, the cone of silence, the last US ranges in Alaska. practitioner (cited in The invisible lighthouse)
26. European Space Agency. Galileo begins serving the globe. ESA, 2016. Galileo Initial Services declared 15 December 2016. primary (cited in You have four satellites)
27. Royal Air Force Museum. GEE Ground Transmitter Type T1365. RAF Museum collections, 2026. Gee's widespread introduction to Bomber Command from March 1942. museum (cited in The invisible lighthouse)
28. William H. Guier and George C. Weiffenbach. Genesis of Satellite Navigation. Johns Hopkins APL Technical Digest 18(2), 178–181, 1997. First-hand account of the Sputnik Doppler analysis and McClure's inversion, 17 March 1958. primary (cited in You have four satellites)
29. Defense Mapping Agency. Geodesy for the Layman (DMA TR 80-003), 1983. Astronomical, geodetic and geocentric latitude. reference (cited in Latitude from the sky)
30. Pratap Misra and Per Enge. Global Positioning System: Signals, Measurements, and Performance (2nd ed.). Ganga-Jamuna Press, 2006. Chapter 6: linearised least-squares position solution and dilution of precision. scholarship (cited in You have four satellites)
31. ESA Navipedia. GLONASS General Introduction. European Space Agency. Accessed November 2026. Brought to 24 operational satellites in 1995. reference (cited in You have four satellites)
32. U.S. government (National Coordination Office for Space-Based PNT). GPS Accuracy. GPS.gov (archived). Accessed November 2026. Smartphones typically within a 4.9 m radius under open sky; URE vs user accuracy; geometry, blockage, atmosphere, multipath. standard (cited in You have four satellites)
33. U.S. government (National Coordination Office for Space-Based PNT). GPS Space Segment. GPS.gov (archived). Accessed November 2026. About 20,200 km altitude, two orbits a day, six equally spaced planes, 24 baseline slots. standard (cited in You have four satellites)
34. Polynesian Voyaging Society. Hawaiian Star Lines and Names for Stars. Hōkūleʻa archive. States that some star names are traditional and others are new; house names devised by Nainoa Thompson. practitioner (cited in Reading the world)
35. Royal Museums Greenwich. How did astronomers including Nevil Maskelyne help solve the longitude problem?. Royal Observatory Greenwich. Maskelyne’s 1761 St Helena voyage (lunar longitude within 1½°); Bradley’s estimate of 1° with Mayer’s tables; the almanac for 1767 ready to print by the end of 1766. museum (cited in Longitude is a clock problem)
36. Richard B. Langley. Innovation column on the U.S. Federal Radionavigation Plan. GPS World, 1992. March 1992. Loran-C, Omega, VOR and DME principles, frequencies and FRP accuracy figures. scholarship (cited in The invisible lighthouse)
37. Gary C. Kennedy and Michael J. Crawford. Innovations Derived from the Transit Program. Johns Hopkins APL Technical Digest 19(1), 1998. Transit navigation service terminated on 31 December 1996. primary (cited in You have four satellites)
38. International Meridian Conference. International Conference Held at Washington for the Purpose of Fixing a Prime Meridian and a Universal Day, October 1884: Protocols of the Proceedings. Gibson Bros., Washington (Project Gutenberg edition), 1884. primary (cited in Longitude is a clock problem)
39. U.S. Space Force, GPS Directorate. IS-GPS-200: Navstar GPS Space Segment / Navigation User Segment Interfaces. GPS.gov ICWG. Accessed November 2026. Constants (μ, ω_E, c), pseudorange model, Klobuchar obliquity factor, relativistic clock offset. standard (cited in You have four satellites)
40. J. J. O’Connor and E. F. Robertson. John Hadley (biography). MacTutor History of Mathematics, University of St Andrews. The reflecting octant of 1730–31, designed for use ‘where the motion of the objects’ makes ordinary instruments unsteady. reference (cited in How a sextant works)
41. Cambridge University Library. Kendall, Larcum, 1719–1790 (watchmaker): records in the Papers of the Board of Longitude. ArchiveSearch. K1, the Board’s copy of H4, and its performance on Cook’s second voyage (1772–75). primary (cited in Longitude is a clock problem)
42. U.S. Coast Guard. Loran-C User Handbook (COMDTPUB P16562.6). U.S. Coast Guard, 1992. History of Gee and Loran-A (ch. I); Loran-C signal format, GRI, emission and coding delays, accuracy and propagation corrections (ch. II–III). primary (cited in The invisible lighthouse)
43. Jerry Proc. Loran-C: closure. jproc.ca hyperbolic navigation archive, 2010. Reproduces the U.S. Coast Guard notices: U.S. Loran-C transmissions ended on 8 February 2010. practitioner (cited in The invisible lighthouse)
44. Wikipedia contributors. Lorenz beam. Wikipedia, 2026. Experimental installation at Berlin-Tempelhof in 1932; adopted by Deutsche Lufthansa in 1934. reference (cited in The invisible lighthouse)
45. U.S. Naval Institute. Lunar Observation Without Distance Tables. Proceedings of the U.S. Naval Institute, vol. 34 (December 1908), 1908. Notes that the British Nautical Almanac for 1907 left the lunar distances out. practitioner (cited in Longitude is a clock problem)
46. Smithsonian Magazine (Smart News). Mariner’s Astrolabe Recovered From Shipwreck Is World’s Oldest. Smithsonian Institution, 2019. Astrolabe from the Esmeralda (Vasco da Gama’s second voyage, sank 1503), dated about 1496–1501; mariner’s astrolabes came into use in the late 15th century. museum (cited in How a sextant works)
47. IEEE History Center. Milestones: Loran, 1940–1946. Engineering and Technology History Wiki, 2012. First permanent Loran pair (Montauk Point and Fenwick Island) by June 1942; station and receiver counts by 1945–46. scholarship (cited in The invisible lighthouse)
48. Polynesian Voyaging Society. Nainoa Thompson (biography and voyaging history). Hōkūleʻa archive. practitioner (cited in Reading the world)
49. Bradford W. Parkinson. NAVSTAR: Global Positioning System — an evolutionary research and development program. Proceedings of the Sixth Annual Precise Time and Time Interval (PTTI) Planning Meeting, NASA Goddard Space Flight Center, 1974. The program director's contemporary description of NAVSTAR and its concept-validation phase. primary (cited in You have four satellites)
50. J. J. O’Connor and E. F. Robertson. Nevil Maskelyne (biography). MacTutor History of Mathematics, University of St Andrews. The British Mariner’s Guide (1763) with Mayer’s tables; first Nautical Almanac (for 1767) published 1766. reference (cited in Longitude is a clock problem)
51. NOAA Global Monitoring Laboratory. NOAA Solar Calculator: calculation details. reference (cited in Latitude from the sky)
52. Trinity House. Notice to Mariners No. 27 of 2015: Enhanced Loran discontinued. Trinity House, 2015. The UK and Irish eLoran trial service, running since 31 October 2014, ended on 31 December 2015. primary (cited in The invisible lighthouse)
53. Homer. Odyssey, book 5, lines 270–277. primary (cited in Reading the world)
54. National Air and Space Museum Archives. Omega Navigational System Collection (NASM.2017.0038). Smithsonian Institution, 2017. Approved for development in 1968; six of eight stations operating by 1971; shut down in September 1997. museum (cited in The invisible lighthouse)
55. US Department of the Interior, Office of Insular Affairs. Pacific giant Mau Piailug dies on Satawal, 2010. primary (cited in Reading the world)
56. Claudio Aporta et al.. Pan Inuit Trails Atlas. reference (cited in Reading the world)
57. Cambridge University Library and Royal Museums Greenwich. Papers of the Board of Longitude, 1714–1828 (digitised). Cambridge Digital Library. primary (cited in Longitude is a clock problem)
58. Aratus. Phaenomena, lines 37–44 (ed. and trans. D. Kidd). Cambridge University Press, 1997. primary (cited in Reading the world)
59. Federal Aviation Administration. Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter on navigation. FAA, 2023. VOR radials as magnetic courses from the station; DME slant range. standard (cited in The invisible lighthouse)
60. Fred Espenak and Jean Meeus. Polynomial Expressions for Delta T (ΔT). NASA Goddard Space Flight Center, 2006. ΔT = TT − UT used to evaluate the lunar theory at a given UT. standard (cited in Longitude is a clock problem)
61. R. G. Stuart. Probabilities in a Gaussian Cocked Hat. The Journal of Navigation 72 (6): 1496–1512, 2019. Derives the probability that a given cocked hat contains the true position and relates it to the average of 25 %. scholarship (cited in From a sight to a fix)
62. ESA Navipedia. Relativistic Clock Correction. European Space Agency. Accessed November 2026. Satellite clocks set to 10.22999999543 MHz instead of 10.23 MHz; periodic eccentricity term. reference (cited in You have four satellites)
63. Neil Ashby. Relativity and the Global Positioning System. Physics Today 55(5), 41–47, 2002. Fractional offset 4.4645 parts in 10¹⁰; uncorrected errors of more than 11 km in a day. scholarship (cited in You have four satellites)
64. Neil Ashby. Relativity in the Global Positioning System. Living Reviews in Relativity 6, 1, 2003. scholarship (cited in You have four satellites)
65. Claudio Aporta. Routes, trails and tracks: trail breaking among the Inuit of Igloolik. Études/Inuit/Studies 28(2), 2004. scholarship (cited in Reading the world)
66. European Union Aviation Safety Agency. Safety Information Bulletin 2022-02R3: Global Navigation Satellite System Outage and Alterations Leading to Communication / Navigation / Surveillance Degradation. EASA, 2024. Increase in jamming and spoofing since February 2022; spoofing harder to detect. standard (cited in You have four satellites)
67. Joseph Needham et al.. Science and Civilisation in China, vol. 4 pt 1 (Physics) and pt 3 (Civil Engineering and Nautics). Cambridge University Press, 1962. Part 3 published 1971. scholarship (cited in Reading the world)
68. U.S. government (National Coordination Office for Space-Based PNT). Selective Availability. GPS.gov (archived). Accessed November 2026. standard (cited in You have four satellites)
69. Whipple Museum of the History of Science. Sextant, by John & Edward Troughton (catalogue entry). University of Cambridge. Mayer’s reflecting circle tested at sea by Captain John Campbell, who found it awkward and had John Bird make a 60° arc: the sextant. museum (cited in How a sextant works)
70. Lionel Casson. Ships and Seamanship in the Ancient World. Princeton University Press, 1971. scholarship (cited in Reading the world)
71. The White House, Office of the Press Secretary. Statement by the President regarding the United States' decision to stop degrading Global Positioning System accuracy. Clinton White House archive (NARA), 2000. 1 May 2000; degradation discontinued at midnight; civil users 'ten times more accurate'. primary (cited in You have four satellites)
72. David Titterton and John Weston. Strapdown Inertial Navigation Technology (2nd ed.). IET, 2004. Schuler-loop error propagation for accelerometer and gyro biases. scholarship (cited in You have four satellites)
73. Ettore Bellini and Alessandro Tosi. System of directed wireless telegraphy (US Patent 943,960). United States Patent Office, 1909. Filed 1 October 1907, granted 21 December 1909: fixed crossed aerials with a rotating coil. primary (cited in The invisible lighthouse)
74. National Geospatial-Intelligence Agency. The American Practical Navigator (Bowditch), Pub. No. 9. NGA, 2019. Chapters on navigational astronomy, the noon sight and Polaris sights. reference (cited in Latitude from the sky)
75. Nathaniel Bowditch; National Geospatial-Intelligence Agency. The American Practical Navigator (Bowditch), Pub. No. 9, 2019 edition, Volume I. National Geospatial-Intelligence Agency, Springfield, Virginia, 2019. Ch. 1 (history, Sumner’s account, sight reduction tables, the log), ch. 9 (dead reckoning and plotting symbols), ch. 14 §1409 (sextant accuracy), ch. 18 (sight planning, twilight, azimuth spread), ch. 19 (sight reduction, the Deneb worked example of 9 March 2016, LOP approximation error, running fix). standard (cited in From a sight to a fix)
76. Nathaniel Bowditch; National Geospatial-Intelligence Agency. The American Practical Navigator (Bowditch), Pub. No. 9, 2019 edition, Volume II: Navigational Errors. National Geospatial-Intelligence Agency, Springfield, Virginia, 2019. Mathematics for Navigation, ch. 3: systematic and random errors (§302–304), error ellipses (§305), most probable position (§311), mistakes (§312), the cocked hat as a guide to accuracy (§313). standard (cited in From a sight to a fix)
77. National Geospatial-Intelligence Agency. The American Practical Navigator (Bowditch), Pub. No. 9, ch. 16–20 (time, the almanacs, sight reduction). NGA, 2019. standard (cited in Longitude is a clock problem)
78. David W. Waters. The Art of Navigation in England in Elizabethan and Early Stuart Times. Hollis & Carter, 1958. scholarship (cited in Latitude from the sky)
79. D. Hoffleit and W. H. Warren Jr.. The Bright Star Catalogue, 5th revised ed. (VizieR V/50). Yale University Observatory, 1991. Star positions and magnitudes used in every sky view. reference (cited in Latitude from the sky)
80. G. G. Bennett. The Calculation of Astronomical Refraction in Marine Navigation. Journal of Navigation 35 (2): 255–259, 1982. R = cot(h + 7.31/(h + 4.4)) arcminutes for apparent altitude h in degrees. standard (cited in How a sextant works)
81. UNESCO Local and Indigenous Knowledge Systems (LINKS). The Canoe Is the People: Indigenous Navigation in the Pacific. UNESCO, 2005. Educational multimedia centred on Satawal. museum (cited in Reading the world)
82. G. J. Marcus. The Conquest of the North Atlantic. Boydell Press, 1980. Discusses the Landnámabók sailing directions. scholarship (cited in Reading the world)
83. John Hadley. The Description of a New Instrument for Taking Angles. Philosophical Transactions of the Royal Society 37 (420), 1731. Read to the Royal Society on 13 May 1731. primary (cited in How a sextant works)
84. Roger Mola. The Evolution of Airway Lights and Electronic Navigation Aids. U.S. Centennial of Flight Commission, 2003. Four-course range introduced 1928 and standardized 1929; VOR tests from 1944; Victor airways by 1952; system-wide DME from 1961. scholarship (cited in The invisible lighthouse)
85. Walter Blanchard. The Genesis of the Decca Navigator System. Journal of Navigation 68(2), 2015. scholarship (cited in The invisible lighthouse)
86. E. G. R. Taylor. The Haven-Finding Art: A History of Navigation from Odysseus to Captain Cook. Hollis & Carter, 1956. Portuguese latitude practice, the Rule of the North Star and the Regiments. scholarship (cited in Latitude from the sky)
87. Bureau International des Poids et Mesures. The International System of Units (SI Brochure), 9th edition. BIPM, 2019. The speed of light in vacuum is fixed at exactly 299 792 458 m/s. standard (cited in The invisible lighthouse)
88. W. E. May. The Last Voyage of Sir Clowdisley Shovel. Journal of Navigation 13 (3): 324–332, 1960. Analysis of the surviving logbooks of the fleet; errors in latitude, compasses, currents and charts, not longitude alone. scholarship (cited in Longitude is a clock problem)
89. Royal Museums Greenwich. The loss of Sir Cloudesley Shovell’s ships on the Isles of Scilly, 22 October 1707 (collection object and catalog note). National Maritime Museum. Catalogue note: the cause ‘remains the subject of debate’ and the link to the 1714 Act has ‘no hard evidence’. museum (cited in Longitude is a clock problem)
90. Rupert T. Gould. The Marine Chronometer: Its History and Development. J. D. Potter, London, 1923. Standard account of the H4 trials: about 5 s error on arrival at Jamaica (1762); 39 s, under 10 miles, at Barbados (1764). scholarship (cited in Longitude is a clock problem)
91. HM Nautical Almanac Office and US Naval Observatory. The Nautical Almanac (annual): explanation of the altitude correction tables; dip = 1.76′√h (h in meters). UKHO / USNO. standard (cited in How a sextant works)
92. HM Nautical Almanac Office and US Naval Observatory. The Nautical Almanac (annual): Polaris tables and sight-reduction explanation. standard (cited in Latitude from the sky)
93. Robert J. Danchik. The Navy Navigation Satellite System (TRANSIT). Johns Hopkins APL Technical Digest 5(4), 1984. Operational since 1964; released to industry July 1967; 150 and 400 MHz; orbits of about 600 nautical miles. primary (cited in You have four satellites)
94. Lionel Casson. The Periplus Maris Erythraei: Text with Introduction, Translation, and Commentary. Princeton University Press, 1989. primary (cited in Reading the world)
95. Anthony R. Constable and William Facey (eds). The Principles of Arab Navigation. Arabian Publishing, 2013. scholarship (cited in Reading the world)
96. William J. H. Andrewes (ed.). The Quest for Longitude: Proceedings of the Longitude Symposium, Harvard University, 1993. Collection of Historical Scientific Instruments, Harvard University, 1996. scholarship (cited in Longitude is a clock problem)
97. John Davis. The Seamans Secrets. Thomas Dawson, London, 1594. Describes the back-staff (Davis quadrant). primary (cited in How a sextant works)
98. Polynesian Voyaging Society. The Star Compass. Hōkūleʻa Worldwide Voyage learning resources. practitioner (cited in Reading the world)
99. Science Learning Hub – Pokapū Akoranga Pūtaiao. The star compass – kāpehu whetū. University of Waikato. museum (cited in Reading the world)
100. GPS World. The System: Celebrating 20 Years of GPS. GPS World, 2015. Air Force Space Command declared Full Operational Capability on 27 April 1995; formally announced 17 July 1995. reference (cited in You have four satellites)
101. American Philosophical Society. Thomas Godfrey (member biography). APS Members Biographies. Philadelphia glazier who devised a reflecting quadrant independently around 1730; James Logan pressed his claim (Phil. Trans. 38, 1733–34). reference (cited in How a sextant works)
102. Zoe Craig. Time machines: chronometers from the collection. Royal Museums Greenwich. Earnshaw’s simplified, reproducible chronometer; by the 19th century chronometers essential on naval and surveying ships; 22 carried on the second Beagle voyage. museum (cited in Longitude is a clock problem)
103. Michael A. Lombardi. Time Signal Stations. NIST Time and Frequency Division. First regularly scheduled US Navy radio time broadcasts from the Boston Navy Yard on 9 August 1904; Eiffel Tower signals from 23 May 1910. reference (cited in Longitude is a clock problem)
104. Elliott D. Kaplan and Christopher J. Hegarty (eds.). Understanding GPS/GNSS: Principles and Applications (3rd ed.). Artech House, 2017. scholarship (cited in You have four satellites)
105. Edwin Hutchins. Understanding Micronesian navigation. In D. Gentner and A. Stevens (eds), Mental Models, Lawrence Erlbaum, 1983. scholarship (cited in Reading the world)
106. University of Texas at Austin. UT Austin Researchers Spoof Superyacht at Sea. UT News, 2013. Invited demonstration, June 2013, aboard the White Rose of Drachs in the Mediterranean. primary (cited in You have four satellites)
107. Ben Finney. Voyage of Rediscovery: A Cultural Odyssey through Polynesia. University of California Press, 1994. scholarship (cited in Reading the world)
108. Joseph Genz, Jerome Aucan, Mark Merrifield, Ben Finney, Korent Joel and Alson Kelen. Wave navigation in the Marshall Islands: comparing indigenous and Western scientific knowledge of the ocean. Oceanography 22(2): 234–245, 2009. scholarship (cited in Reading the world)
109. David Lewis. We, the Navigators: The Ancient Art of Landfinding in the Pacific (2nd ed.). University of Hawaiʻi Press, 1994. First edition ANU Press, 1972. Based on voyages with Micronesian and Polynesian navigators, including Hipour of Puluwat. scholarship (cited in Reading the world)
110. Richard Easton. Who invented the Global Positioning System?. The Space Review, 2006. Argues GPS is essentially the Navy's TIMATION; quotes Parkinson's contrary view. Partisan in a contested debate. scholarship (cited in You have four satellites)
111. Royal Museums Greenwich. Who was John Harrison? (Harrison’s clocks and the longitude problem). Royal Observatory Greenwich. H1 to Lisbon 1736; the £500 of 1737; H3 begun 1740; the Jamaica (1761) and Barbados (1764) trials; the Longitude Act of 10 May 1765. museum (cited in Longitude is a clock problem)
112. China Daily. Xi officially announces commissioning of BDS-3 navigation system. China Daily Hong Kong, 2020. Commissioned 31 July 2020 in Beijing. reference (cited in You have four satellites)