¹Jones, Sir Harold Spencer (1948). The Development of Navigation. This Journal, 41, 1.Google Scholar

²Severin, T. (1987). Early Navigation: The Human Factor. This Journal, 41, 1.Google Scholar

³Practice of Navigation and Nautical Astronomy earned its author, Lieutenant Henry Raper, RN, the Gold Medal of the Royal Geographical Society. The book was issued in the Royal Navy as ship's stores. Hull was a Superintendent of Admiralty Charts. His edition, the nineteenth, at least contained a new chapter on the magnetic compass and its deviation, written by Captain W. Mayes, the famous Superintendent of Compasses at the Admiralty. The last edition appeared in 1920.Google Scholar

⁴ Columbus believed that the Eurasian continent extended 282° to the east and therefore could be found 780 to the west, that a degree was about 83 km, and that Japan was more than 2000 km offshore. Before Christ the Phoenicians had circumnavigated Africa, Hipparchus invented latitude and longitude, Eratosthenes calculated the circumference of the Earth probably within 1% (there is some doubt as to the length of his stade) and Poseidonius calculated a circumference which is much too small if he used the same stade. The science of antiquity was largely lost to western Europe during the middle ages but in 1410 the Geographike Huphegesis of Ptolemy was translated into Latin (printed in 1475). Ptolemy's famous map shows Asia extending much too far east and he quoted the figure of Poseidonius so he has been blamed for the misconception of Columbus but the matter is more complicated. Columbus knew of a ninth century Arab figure of 1° = 56 2/3 miles which is accurate in terms of an Arabic mile of 1975 metres but Columbus assumed an Italian mile of 1477 metres which make the Arabic figure agree roughly with Poseidonius if his stade was a tenth of a Roman mile. The final misconception comes from Marco Polo who flatly states ‘Cipangu (Japan) is an island far out to the eastward, some 1500 miles from the mainland ’. As poor Columbus despaired ‘ neither reason, nor mathematics, nor maps were any use to me ’.Google Scholar

⁵ In 1481, Pope Sixtus IV had allotted all the lands to be discovered south of the Canaries to Portugal. Islands discovered by Columbus in 1492 were south of the line but this was uncertain in 1493. The rules had to be changed quickly and the Pope was a Spaniard. The Portugese were dissatisfied and they had the stronger navy. In 1494, by the Treaty of Tordesillas (as amended in 1495) the dividing meridian was moved further west which had the effect of giving Brazil (not officially discovered until 1500) to the Portugese. In 1497 John Cabot, bearing the patent of His Most Catholic Majesty Henry Tudor, planted the English flag on Cape Breton Island (or possibly Labrador).Google Scholar

⁶ The Royal Society (of London for Improving Natural Knowledge) was founded in 1660, before the Académie Royale, but its objects were much more general.Google Scholar

⁷ Not everyone will agree. The King's intervention and its effectiveness are incontrovertible but the merits of Harrison's case are still controversial. James Newman certainly goes too farin describing Harrison as ‘ the victim of a series of unsurpassed chicaneries perpetrated by scientistsand politicians ’ (The World of Mathematicians, p. 779) but personally I am equally unconvinced by modern admirers of Nevil Maskelyne, fifth Astronomer Royal, father of the Nautical Almanac, arch-priest of lunar distances, arch-enemy of all mechanics and John Harrison in particular. For their point of veiw see Howse, D. (1985), Nevil Maskelyne, the Nautical Almanac and G.M.T. This Journal, 38, 159, and references thereunder.Google Scholar

⁸Morison, S. E. tells us (1942, Admiral of the Ocean Sea, Little, Brown) ‘the testimony of his(Columbus) own journals proves that the simple method of finding latitude from a meridional observation of the Sun … was unknown to Columbus. Polaris observations for latitude he madenot infrequently … but he never knew the proper correction to apply’. At that date, Polaris was much further from the pole than now, about 3 1/20, so the correction could exceed 200 n.m. The effect of this polar distance on the azimuth of Polaris was equally unrecognized by Columbus with consequent adverse effect on the accuracy of his DR and his estimate of magnetic variation. Columbus was not a skilled navigator by the best Portugese standards of his day.Google Scholar

⁹ However, calculation using the Babylonian numerical systems is very tedious. The key to the perfected positional decimal system, as we know it, is the use and correct placement of a symbol for zero which is credited to the Hindus. It came very late. The earliest known inscription using the zero symbol as we do is ninth century A.D. The use of Roman numerals for accountancy did not die out in Europe until the eighteenth century. It has been argued that addition and subtraction, but not multiplication and division, is simpler with the Roman system than with our (Hindu) system.Google Scholar

¹⁰ Gerhard Kremer (latinized as Gerardus Mercator) has been called ‘the greatest of renaissance geographers’. The famous world map of 1569 shows, with more valour than discretion, the location of the meridian of demarcation. There are directions for measuring distance and an ‘Organum Directorium’ apparently for the construction of secants. The meridional parts are not accurate. Professor Taylor was not unfair when she wrote (in The Haven Finding Art), ‘it was a scholar's map of which navigators could make nothing’. Edward Wright's tables were published in his influential Certaine Errors in Navigation (1599). The most intriguing aspect of this curious history is Thomas Hariot's method of calculating meridionial parts which was, mathematically, ahead of its time. See George F. (1956) Hariot's meridionial parts. This Journal, 9, 66. Hariot understood Kepler instantly. Galileo apparently did not.Google Scholar

¹¹ Müller, Johann (1436—1476) called himself Regiomontanus because he was born in Köningsberg (as, in reverse, Mons is call Bergen in Flemish). De Triangulis was written in 1464 but not generallly published until after his death.Google Scholar

¹² Quoted by Professor H. W. Turnbull in The Great Mathematics, Methuen, 3rd ed, 1940. Logarithms were invented independently by Joost Pürgi in Prague but Napier has the prior claim. Henry Briggs went on to invent logarithms to the base 10, essential for nautical tables, and to produce a table of log sines to 14 decimal places.Google Scholar

¹³ See, for example, Tyrén, C. (1982). Magnetic Anomalies as a Reference for Ground-speed and Map-matching Navigation. This Journal, 35, 242.Google Scholar

¹⁴ Notably the Dutch polymath Simon Stevin whose influential navigation treatise Haven Vinding was translated into English by Wright.Google Scholar

¹⁵ For a general account and some further references see Fanning, A. E. (1986), Edmond Halley – Nautical Scientist, Navigation News 1, No. 2, p. 12.Google Scholar

¹⁶ Typically, each degree of error in measuring magnetic variation (subject to anomalies, deviation of the compass and errors in estimating true north) correspond to a position line error on Halley's own Atlantic isogonic chart of 1701 of 100—300 miles. In any case such position lines run roughly east—west on that chart between the tropic and 450 N.Google Scholar

¹⁷ Including Newton and Hooke.Google Scholar

¹⁸ For interesting speculations on the accuracy of altitude measurement at sea before the sextant see Forty, G. (1983/1986). This Journal, 36, 388 and 39, 259.Google Scholar

¹⁹ The third law is incomplete. Newton showed that the square of the period must also be inversely proportional to the sum of the masses of the Sun and the planet.Google Scholar

²⁰ Made in the last quarter of the sixteenth century in the observatories of the prodigious TychoBrahe. His principal quadrant had a diameter of 14 feet and the scale was graduated in minutes of arc.Google Scholar

²¹ The herculean metaphor is taken from Kepler himself ‘I essayed to clean the Augean stables and am left with a cart load of dung’.Google Scholar

²² These famous ephemerides are not, in fact, a product of the Académie Cassini was recruited from Bologna because of their fame. An interesting feature is the careful description of observational technique. Cassini went on to found a unique dynasty. He, his son, grandson and great grandson were successive directors of the Paris Observatory.Google Scholar

²³ Newton had done most of the work 20 years earlier with the major exception of the proof that the centre of gravity of a spherical shell is its geometric centre.Google Scholar

²⁴ This was the instrument which gave Captain Cook such excellent results.Google Scholar

²⁵ A formula given by Maskelyne in his ‘ Requisite Tables’ is vers LHA = (sin m − sin a) sec lsec d (where m is meridional altitude, a altitude, 1 latitude and d declination).Google Scholar

²⁶ There are of course the double altitude and the ex-meridian altitude methods but they would not have helped Captain Sumner.Google Scholar

²⁷ H. O. 249. It was the first publication to be reviewed in this Journal. During the second world war the air forces of the UK, USA, Germany and Japan all had pre-computed tables of some form and pre-computed graphs and tables had been used in the air for two decades before H. O. 249 appeared. Charles Cotter has argued persuasively that the development of improved methods in the nineteenth century was retarded by the examination system. Navigators did what they were taught. They were taught to pass examinations. When the civil aircraft navigator (first class) examinations were restarted after the World War II, methods developed for air use were not allowed in the examination room and the candidate was required to show speed and accuracy in the use of nautical tables he would never see again. The drag effect of the examination system endured for a century.Google Scholar

²⁸ Reflectors were fitted to Merseyside lights as early as 1763 but it was Fresnel's invention of the dioptric lens in 1822 which made high definition beams of light possible. The electric arc lamp at Dungeness in 1862 has been quoted as the first commercial use of electric light but electric light had been used experimentally from 1858 at South Foreland which in 1922 became the first electric filament light.Google Scholar

²⁹ By Dr Herman An schutz-Kaempfe aboard the battleship Deutschland. Einstein himself advisedon a later improvement to Anschutz gyrocompasses.Google Scholar

³⁰ Despite the distinguished achievements of Sir George Airy, seventh Astronomer Royal, the most conspicuous exception must be Lord Kelvin with his interest in tides and soundings, and self-interest in compasses. Harmonic analysis of tides, incidentally, employs a theorem derived by Fourier in 1822, a comparatively rare example of nineteenth century pure mathematics being applied to nineteenth century navigation. Kelvin’ tidal predictor was a notable early analog computer. Kelvin also interested himself in sight reduction and pioneered short methods but he fell short of inventing the intercept method.Google Scholar

³¹ In 1959 a British industrialist, Henry Kremer offered a prize for the first man-powered flight over a one mile figure of eight course. It was not won until 1977 (by Bryan Allen in Gossamer Condor). The illustration is of Musculair an advanced ‘third generation’ craft designed in Munich flown on this occasion by Holger Rochelt.Google Scholar

³² We need not be as reverent to Great Men of Science as those historians who indignantly record that Galileo was sentenced to recite penitential psalms once a week but — to a man — fail to tell us that Galileo passed this dreadful duty on to his daughter!Google Scholar

³³ Leo X, Clement VII, Paul III. Only Martin Luther and his friends denounced the ideas of Copernicus. It may not have helped Galileo that whereas the work of Copernicus was fulsomely dedicated to the pope of the day, The Simpleton in Galileo's Dialogue was believed by contemporaries to be modelled on the pope of their day.Google Scholar

³⁴ Eugene Paul Wigner, Nobel prizewinner.Google Scholar

³⁵ Newton was a closet heretic whose doubts about the Trinity were only discovered after his death but on the metaphysics of physical science he was all that Pope Urban VIII could ever have desired. He did not believe in the reality of gravity: ‘That one body may act upon another through a vacuum … is to me so great an absurdity’; and to Bentley, ‘ You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me'. His words in the first book of the Principia I nowhere take it upon me to define the kind or the manner of any action, the causes or the reason thereof sound like the Preface to the De Revolutionibus of Copernicus more than a century earlier. Kepler agreed with Galileo. ‘ It is a most absurd fiction, he wrote ‘that natural phenomena can be explained by false causes’. He was wrong. He also attributed this opinion to Copernicus despite the Preface. We will never know. Kepler studied papers of Copernicus that are lost for ever and we cannot say either that Copernicus approved the Preface (which he certainly did not write) or had the courage of his convictions, if any.Google Scholar

³⁶ Herbert, Nick (1985). Quantum Reality. Anchor Press/Doubleday.Google Scholar

³⁷ A mind imperfectly cleansed of the Greeks apparently!Google Scholar

³⁸ Dampier, Sir William (1929). Natura enim non nisi parendo vincitur. A History of Science. Cambridge University Press.Google Scholar

³⁹ Hülsmeyer's British patent, accepted 22 09 1904, is headed ‘Hertzian-wave Projecting and Receiving Apparatus Adapted to Indicate or Give Warning of the Presence of a Metallic Body, such as a Ship or a Train, in the Line of Projection of such Waves’. Hülsmeyer demonstrated his ‘ Telemobiloskop’ on 18 May 1904 at Cologne but despite his indefatigability and press coverage which extended as far as the New York Times, he could not interest naval authorities in Germany, Britain or anywhere else.Google Scholar

⁴⁰CQD. The more urgent rhythm of SOS came later. In 1899 the East Goodwin lighthouse was struck in fog by a steamship and successfully signalled its distress by Marconi equipment tothe South Foreland lighthouse. In 1900 experimental equipment of the neglected Russian pioneer Alexandr Popov installed on an icebreaker was instrumental in saving 27 lives.Google Scholar

⁴¹ As an indication of the pace of civil development dictated more by safety and economic considerations than pure science, fully automatic landing was demonstrated in 1945 by a Boeing 247D but in regular passenger carrying airline service, the first good weather automatic landing was in 196 c and the first landing in Cat 3 conditions was in 1972; by BEA Tridents equipped with the British autoland system in both cases. For this system see Charnley, W. J. (1959). Blind Landing. This Journal, 12, 115.Google Scholar

⁴² Notable milestones include Lorentz, SBA, BABS, SCS51, ILS.Google Scholar

⁴³ The intention was that night fighters should be ‘ vectored’ on a converging track by ground controllers equipped with radar uncluttered by ground returns. The failure of the enemy to cooperate by holding his course led to the situation I have described.Google Scholar

⁴⁴ However, it must be said that the term magnetron to describe a vacuum tube in which plate current is controlled by a magnetic field goes back to 1921 and A. L. Samuel of the Bell Telephone Laboratory applied for a patent on a multi-cavity anode in 1934. At about that time a magnetron operating in a co cm band developed commercially by Phillips of Holland proved useful to the early development of radar in Germany.Google Scholar

⁴⁵ Nearly 4000 in the National Defence Research Council Radiation Laboratory (opened in1940), the remainder in the US Signal Corps Laboratory, the Aircraft Radio Laboratory, the Naval Research Laboratory and other establishments. The peak 1945 manning at the British Telecommunications Research Establishment at Malvern was about 3000. The gift of the multi-cavity magnetron to Germany was made involuntarily when an H2S was recovered, virtually intact, in 02 1943 from the wreckage of an RAF bomber near Rotterdam. There is a story that the details were sent to Japan by submarine, an interesting voyage at that date.Google Scholar

⁴⁶ Probability theory has its roots in attempts by renaissance mathematicians at theories of games of chance but Jacob Bernoulli's Theorem (published posthumously in 1713) is the beginning of mathematical probability in the modern sense. Statistics, in the sense of the organization and analysis of an array of numerical facts, and the deduction of rational conclusions from those facts began, so far as the writer is aware, with papers by two Londoners. John Graunt's Observations upon the Bills of Mortality (1662) and Edmond Halley's Estimate of the degrees of mortality of mankindwith an attempt to ascertain the price of annuities (1963). Both titles are abbreviated. Halley's paper invents actuarial science and, en passant, the theory of investment, which even today is not always correctly applied to the cost-effectiveness of navigation systems. Halley even uses the term present value in the modern way to describe discounted future cash.Google Scholar

⁴⁷ The name gyroscope means literally viewing the turning. It was given by Leon Foucault who demonstrated Sang's principle in 1852. There is no reason to believe Foucault knew of Sang'spaper any more than that Sang had read the key paper of Coriolis published in the Journal del’Ecole Polytechnique a year before his own lecture. There are times when things are in the air.Google Scholar

⁴⁸ Another example of how navigational science now applies new technology to old ideas. Sagnac is credited with demonstrating in 1913 the shift of interference fringes when a system of mirrors reflecting two light beams travelling in opposite directions around the system is rotated but the idea must be much older than that.Google Scholar

⁴⁹ For a recent summary of INS see Smith, S. G. (1986). Developments in Inertial Navigation. This Journal, 39, 401.Google Scholar

⁵⁰Fanning, A. E. (1986). Steady as She Goes. HMSO.Google Scholar

⁵¹ The everyday experience that the pitch (frequency) of a sound is affected by the relative velocity of the source was formalized and extended to light in a paper written by C. J. Doppler in 1842. The first discussion of the application of the Doppler effect to radio navigation in theJournal is six papers by various authors in vol. 11 (1958). See also Journal Index.Google Scholar