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Evolution of the Marine
                     Chronometer

The development of the Marine Chronometer from
                 1714 to 1942
Clocks in Navigation
• The Earth’s poles are stationary and this allows the North-South
  position to be determined by the apparent height of a known star
  above the horizon. The North Star, Polaris, provides the most accurate
  reading.
• The East-West position is more difficult and eluded navigators for
  centuries.
• Early navigators found a North-South position and then sailed East or
  West until they made landfall. They estimated their position by dead
  reckoning of their speed on the sea.
• The use of local time with a precision clock showing the time at a
  known location allowed precise East-West position calculation.
    – The Earth rotates 360° in 24 hours
    – Each hour time difference equals 15° in longitude
Act of Queen Anne

•   As sea commerce developed in the 17th century many tragedies
    occurred with loss of lives and ships.
•   In 1707 Sir Cloudesly Shovel, returning from Gibraltar with
    his fleet, sailed in cloudy weather. After 12 days with no sight
    of land, they calculated they were west of the southern tip of
    England and decided to hold station. That night they ran
    aground on the Scilly Isles losing 4 ships and nearly 2,000
    men including the Admiral.
•   The one lone dissenter to the position calculation had been
    hanged the day before for mutiny.
•   The Act of Queen Anne provided a prize for a method of
    “discovering” the Longitude at sea.
     –   £10,000 for 1 degree (60 nautical miles)
     –   £15,000 for 40 minutes (40 nautical miles)
     –   £20,000 for ½ degree (30 nautical miles)
The International Competition
• The nation that could provide a commercial solution for
  the problem of the longitude would have a great advantage
  on the seas.
• The English had the Act of Queen Anne and the Longitude
  Board to spur interest.
• The French and Spanish governments offered similar
  prizes.
• Philip of Portugal had been a major influence in the earlier
  development of the use of the compass and North Star.
• The major competition in the 18th century was between the
  French and the English.
Harrison and the
                          Act of Queen Anne
• John Harrison built the first successful Marine
  Chronometer, H1 in 1735, in response to the £20,000 prize
  offered under the November 12th, 1713 Act of Queen Anne.
• His final development, in H4, completed in 1759, was a
  very different mechanism but was the first true Marine
  Chronometer capable of supporting world wide navigation.
• We are indebted to the work of Rupert Gould for the
  restoration of these pieces and the the publication of his
  magnificent book Marine Chronometer in 1923 that spurred
  the revival of interest in the topic of early chronometers.
Working
 Model
  of H1




          Harrison’s H1 was the first working Sea Clock
          This model is pictured in the Time Museum Catalog
Harrison’s H4
The Chronometer that
   won the Longitude
               Prize
The Chronometer Problem
Harrison formulated the requirements for a marine chronometer. This work
  followed a great deal of discourse that preceded it for 50 years or so.


• First, the machine must be insensitive to the amount of power
  available to drive the regulator.
• Second, the machine must be insensitive to the temperature.
• Third, the machine must operate reliably for long periods of time in
  harsh conditions.


These requirements became known as Harrison’s Principles and
guided the further work of both the English and French makers.
Power and Isochronism
• Harrison’s first problem can be solved in two ways.
   – The power from the driving force to the governor can be kept
     constant over time.
     Fuzees, detached escapements and remontoires were the main
     approaches to this problem.
     The elegant constant force escapements were the ultimate
     development of the remontoire concept.
   – The governor can be insensitive to the power used to drive it.
     Isochronal hairsprings were the main expression of this
     solution to the problem
Temperature
•   Harrison’s second problem was also approached from two directions.
    In a balance/spring oscillator the temperature problem is primarily due
    to changes in elasticity of the balance spring with temperature.
    – The compensation curb is a device that changes the effective length of
      the hairspring as a function of temperature
      This is the method Harrison used and was the dominant method for
      the first 30 years of development
    – The compensation balance is a device that changes the moment of
      inertia of the balance as a function of temperature.
      The first temperature compensating balance was developed by Leroy
      in 1765 and the common bi-metal form was patented by Arnold in
      1775 and improved by Earnshaw a few years later.

        Both of these approaches were finally perfected with metallurgy in
        the early part of the 20th Century
Compensation
• Compensation Curbs                     • Early temperature compensation balances
                                           as pictured in Rees’ Encyclopedia
• Middle left was used by Harrison &
  Ferdinand Berthoud                     • The examples in the middle are from
                                           Arnold’s patents
• Lower left is commonly found on 19th
  Century French watches                 • The example at the top left is the Le Roy
                                           balance of 1765
Durability
• The major foes of durability were oil deterioration, rust and metal
  fatigue over time.
• Harrison addressed the problem with the use of lignum vitae laminated
  parts, anti-friction rollers and the Grasshopper escapement.
• Later Arnold used gold hairsprings to avoid rust
• Continuous improvements in steel during the 19th Century produced
  better and better hairsprings and mainsprings
• The production of Palladium Hairsprings by Paillard solved both the
  rust and magnetism problem introduced when iron replaced wood in
  the ships
• The final problem solved was the deterioration of oil. It finally fell to a
  group of Swiss chemists led by the Paul Ditisheim in the early 20 th
  Century
Working
 Model
  of H1




          Harrison’s H1 was the first working Sea Clock
          This model is pictured in the Time Museum Catalog
Harrison’s H4
The Chronometer that
   won the Longitude
               Prize
Larcum Kendall
• Harrison had a difficult time convincing the Board of Longitude to pay
  his prize money. (Eventually the King ordered parliament to pay him.)
• The board insisted in knowing all the secrets of how to make the
  machines before they would award the prize. They also believed the
  chronometer was too expensive.
• Harrison was reluctant to part with what he had learned and
  developed.
• He agreed to train another chronometer maker, Larcum Kendall, to try
  to convince the Board that “one skilled in the art” could make the
  chronometers.
• Kendall produced one copy of H4 and two more on a simplified
  design that had performance nearly equal to that of H4.
• Kendall’s K1 and K3 were used by Captain Cook on his voyages of
  discovery. K2 was in use by Capt. Bligh on the Bounty at the time of
  the mutiny and it remained on Pitcairn Island for the next 50 years.
Mudge’s Remontoire
• Thomas Mudge invented the lever escapement mechanism that was the
  dominant timekeeping mechanism in watches until the introduction of
  quartz electric watches.
• Mudge interrupted his career as a major maker of watches to pursue
  the prize for further improvements in Marine Chronometers.
• His “Green” and “Blue” represent the ultimate development of the
  remontoire concept.
• Mudge’s son commissioned several additional chronometers on his
  father’s design.
    – Kendall’s chronometers had been built for £250 and Kendall did not feel
      he could make a profit at that price so stopped production.
    – Thomas Mudge Jr. agreed to supply Mudge’s design for £150
    – Arnold and Earnshaw were prepared to sell their machines for £80
Mudge’s
                    Green
One of the pair of marine chronometers
developed by Mudge to compete for the
prize. The other was “Blue.”




Much of the material in this presentation is
“borrowed” from the book shown here
Pierre LeRoy and the
                             French School
• Pierre LeRoy invented the detent escapement in 1765.
• LeRoy’s thermometric compensated balance provided a
  theoretically perfect solution to the temperature
  compensation problem.
• LeRoy was in a fierce competition with Ferdinand
  Berthoud and both published extensive analyses of their
  work.
• The works of F. Berthoud, L. Berthoud, Breguet and Motel
  continued a tradition of highly artistic but impractically
  expensive chronometers.
Pierre Le Roy’s
Marine Chronometer
 Pierre LeRoy’s Chronometer had performance
 equal to that of H4 and was a theoretical as well as
 a practical success. It resides in the National
 Museum of Arts & Sciences in Paris.
Ferdinand Berthoud’s Montre
                     Marine

                   Berthoud made a
                   number of chronometers
                   that were larger
                   versions of Harrison’s
                   basic design. He later
                   made detent
                   chronometers as did his
                   nephew Louis
                   Berthoud.
Pocket Chronometer by Louis
                  Berthoud
Three Chronometers by Breguet
                       from Antiquorum “Art of Breguet”
Breguet and Arnold were close
friends. Breguet studied with
Arnold and later Arnold’s son,
John Roger studied with Breguet.
John Arnold and Thomas Earnshaw

• Arnold invented a practical pivoted detent chronometer several years
  after Leroy.
• Arnold invented the bi-metallic temperature compensation balance.
• Arnold invented the helical hairspring and terminal coils.
• Earnshaw conceived of using a flat spring in place of the pivot on the
  Arnold detent.
• Earnshaw conceived of laminating the brass and steel components of
  the bi-metallic balance.
• Arnold invented a less practical form of spring detent escapement.
  There was considerable controversy over who had precedence
Arnold Marine
 Chronometer
Large Arnold Pocket
       Chronometer
Arnold & Son Chronometer 1789
Earnshaw Pocket Chronometer
 “In the Grey”
Chronometer Escapement




                   Animation courtesy of
                      Volker Vyskocil
                      Klostergasse 1
                     D-41334 Nettetal
                         Germany
                    www.clockwatch.de
Brockbanks Peto
Cross Detent ca 1800
Practical Chronometers
• Dozens of English makers entered the competition in the
  early 19th Century for the annual prize chronometer to
  furnish to the Admiralty.
• The Kew trails spurred an intense competition that soon
  solved essentially all the problems of adjusting for
  isochronism and temperature.
Wm. Bond & Son Survey
William Bond & Son were influential
Boston clock and instrument makers.  Chronometer
Bond’s telegraphic chronometer was
used in the Coast and Geodetic
Survey. Many Bond instruments are
on display in Harvard University’s
Fogg Museum.
John Roger Arnold Chronometer
       w/ Prest’s Keyless Works
Kelvin & White 8 Day
A More Perfect Balance
• The remaining problem that plagued makers in the middle of the 19 th
  Century was the error in the middle temperature region. Even though
  this problem had been solved by LeRoy in 1765, the thermometer
  solution had not survived in practice.
• Many schemes were devised using stops and strangely shaped bi-
  metallic systems. Experiments were performed using glass for both the
  balance and the hairspring.
• The use of mercury thermometers for auxiliary compensation was re-
  invented in the 1870’s 100 years after LeRoy’s first use.
• However, the ultimate solution awaited the discovery of the nickel
  iron alloys Invar and Elinvar plus a host of other formulations in the
  early 20th century.
The Middle Temperature Problem

                                                                  Longer
•   The hairspring loses elasticity as the temperature                0.5




                                                                   Period (sec)
    rises (it also elongates slightly)
     – This causes the oscillation of the balance to slow down.                   0.4
     – A plain balance expands as the temperature rises which
       also causes the oscillation of the balance to slow down.
                                                                       0.3
•   A bi-metallic balance decreases its radius as the             Shorter
    temperature rises
                                                                  Longer
     – This causes the oscillation of the balance to speed up.
                                                                      0.5




                                                                   Period (sec)
•   Unfortunately, these two phenomena do not have
    the same shape because the inertia of the balance                             0.4
    goes by the square of the radius.
     – Therefore the period as a function of temperature will
                                                                       0.3
       only be correct at two temperatures
                                                                  Shorter
                                                                                        Temperature
Middle Temperature
          Balances
Kelvin & White w/
 Poole’s Auxiliary
Dent Staple Balance
The Golden Age 1880 to 1910


• Springers and Adjusters became the stars of the
  industry by the 1880s
• Kullberg, Johannsen, Walsh, and the Frodsham family
  took leadership of the British chronometer industry.
• Ditisheim, Paillard, and Nardin led the development of
  the Swiss chronometer industry.
• Lange began the development of a German
  chronometer industry in Glasshutte.
Fletcher Marine
  Chronometer
  w/ Airy’s Bar
Johannsen
Marine Chronometer
Johannsen
Deck Watch
The Decline of the
                    Chronometer Industry


• By the 1920’s lever wristwatches could compete and win
  the Kew trials
• The long peace from 1914 to 1933 and a large inventory of
  chronometers led to economic hard times
• The shortage of makers and the Atlantic blockade created a
  crisis during the Second World War
Jurgensen Conversion to
           Deck Watch
Hamilton WW I Deck Watch
WW II Revival

• The US Navy issued a request for mass produced Marine
  Chronometers at the beginning of WW II.
• Hamilton developed a new design loosely based on the Swiss Nardin
  ebauche using a newly designed balance, hairspring and detent.
• Elgin developed a new design with special features for maintainability
  using the proven Guillaume Balance
• The Elgin entry failed the purchase trials and was not used by the
  Navy. It was sold in small numbers for civilian use after the war.
• Large numbers of lever pocket watches were finished and adjusted for
  navigation use
Hamilton Marine Chronometer
Elinvar hairspring                   M21
Stainless steel “ovalizing” balance
Elgin Marine Chronometer
Steel hairspring
                                   Grade 600
Guillaume integral balance
Satellites and the Final Solution to
                       the Longitude Problem


• Global Positioning Satellite System is the ultimate solution
  to the navigation problem. The satellites allow the position
  of an observer to be determined by “triangulation” from a
  set of known objects in the sky.
• GPSS is oddly similar to one of the “insane proposals”
  brought to the Longitude Commission in the early 18th
  Century. The idea was to station ships across the ocean
  that would place flares in the sky for ships to observe and
  determine their position.

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Le chronomètre de marine à travers les âges

  • 1. Evolution of the Marine Chronometer The development of the Marine Chronometer from 1714 to 1942
  • 2. Clocks in Navigation • The Earth’s poles are stationary and this allows the North-South position to be determined by the apparent height of a known star above the horizon. The North Star, Polaris, provides the most accurate reading. • The East-West position is more difficult and eluded navigators for centuries. • Early navigators found a North-South position and then sailed East or West until they made landfall. They estimated their position by dead reckoning of their speed on the sea. • The use of local time with a precision clock showing the time at a known location allowed precise East-West position calculation. – The Earth rotates 360° in 24 hours – Each hour time difference equals 15° in longitude
  • 3. Act of Queen Anne • As sea commerce developed in the 17th century many tragedies occurred with loss of lives and ships. • In 1707 Sir Cloudesly Shovel, returning from Gibraltar with his fleet, sailed in cloudy weather. After 12 days with no sight of land, they calculated they were west of the southern tip of England and decided to hold station. That night they ran aground on the Scilly Isles losing 4 ships and nearly 2,000 men including the Admiral. • The one lone dissenter to the position calculation had been hanged the day before for mutiny. • The Act of Queen Anne provided a prize for a method of “discovering” the Longitude at sea. – £10,000 for 1 degree (60 nautical miles) – £15,000 for 40 minutes (40 nautical miles) – £20,000 for ½ degree (30 nautical miles)
  • 4. The International Competition • The nation that could provide a commercial solution for the problem of the longitude would have a great advantage on the seas. • The English had the Act of Queen Anne and the Longitude Board to spur interest. • The French and Spanish governments offered similar prizes. • Philip of Portugal had been a major influence in the earlier development of the use of the compass and North Star. • The major competition in the 18th century was between the French and the English.
  • 5. Harrison and the Act of Queen Anne • John Harrison built the first successful Marine Chronometer, H1 in 1735, in response to the £20,000 prize offered under the November 12th, 1713 Act of Queen Anne. • His final development, in H4, completed in 1759, was a very different mechanism but was the first true Marine Chronometer capable of supporting world wide navigation. • We are indebted to the work of Rupert Gould for the restoration of these pieces and the the publication of his magnificent book Marine Chronometer in 1923 that spurred the revival of interest in the topic of early chronometers.
  • 6. Working Model of H1 Harrison’s H1 was the first working Sea Clock This model is pictured in the Time Museum Catalog
  • 7. Harrison’s H4 The Chronometer that won the Longitude Prize
  • 8. The Chronometer Problem Harrison formulated the requirements for a marine chronometer. This work followed a great deal of discourse that preceded it for 50 years or so. • First, the machine must be insensitive to the amount of power available to drive the regulator. • Second, the machine must be insensitive to the temperature. • Third, the machine must operate reliably for long periods of time in harsh conditions. These requirements became known as Harrison’s Principles and guided the further work of both the English and French makers.
  • 9. Power and Isochronism • Harrison’s first problem can be solved in two ways. – The power from the driving force to the governor can be kept constant over time. Fuzees, detached escapements and remontoires were the main approaches to this problem. The elegant constant force escapements were the ultimate development of the remontoire concept. – The governor can be insensitive to the power used to drive it. Isochronal hairsprings were the main expression of this solution to the problem
  • 10. Temperature • Harrison’s second problem was also approached from two directions. In a balance/spring oscillator the temperature problem is primarily due to changes in elasticity of the balance spring with temperature. – The compensation curb is a device that changes the effective length of the hairspring as a function of temperature This is the method Harrison used and was the dominant method for the first 30 years of development – The compensation balance is a device that changes the moment of inertia of the balance as a function of temperature. The first temperature compensating balance was developed by Leroy in 1765 and the common bi-metal form was patented by Arnold in 1775 and improved by Earnshaw a few years later. Both of these approaches were finally perfected with metallurgy in the early part of the 20th Century
  • 11. Compensation • Compensation Curbs • Early temperature compensation balances as pictured in Rees’ Encyclopedia • Middle left was used by Harrison & Ferdinand Berthoud • The examples in the middle are from Arnold’s patents • Lower left is commonly found on 19th Century French watches • The example at the top left is the Le Roy balance of 1765
  • 12. Durability • The major foes of durability were oil deterioration, rust and metal fatigue over time. • Harrison addressed the problem with the use of lignum vitae laminated parts, anti-friction rollers and the Grasshopper escapement. • Later Arnold used gold hairsprings to avoid rust • Continuous improvements in steel during the 19th Century produced better and better hairsprings and mainsprings • The production of Palladium Hairsprings by Paillard solved both the rust and magnetism problem introduced when iron replaced wood in the ships • The final problem solved was the deterioration of oil. It finally fell to a group of Swiss chemists led by the Paul Ditisheim in the early 20 th Century
  • 13. Working Model of H1 Harrison’s H1 was the first working Sea Clock This model is pictured in the Time Museum Catalog
  • 14. Harrison’s H4 The Chronometer that won the Longitude Prize
  • 15. Larcum Kendall • Harrison had a difficult time convincing the Board of Longitude to pay his prize money. (Eventually the King ordered parliament to pay him.) • The board insisted in knowing all the secrets of how to make the machines before they would award the prize. They also believed the chronometer was too expensive. • Harrison was reluctant to part with what he had learned and developed. • He agreed to train another chronometer maker, Larcum Kendall, to try to convince the Board that “one skilled in the art” could make the chronometers. • Kendall produced one copy of H4 and two more on a simplified design that had performance nearly equal to that of H4. • Kendall’s K1 and K3 were used by Captain Cook on his voyages of discovery. K2 was in use by Capt. Bligh on the Bounty at the time of the mutiny and it remained on Pitcairn Island for the next 50 years.
  • 16. Mudge’s Remontoire • Thomas Mudge invented the lever escapement mechanism that was the dominant timekeeping mechanism in watches until the introduction of quartz electric watches. • Mudge interrupted his career as a major maker of watches to pursue the prize for further improvements in Marine Chronometers. • His “Green” and “Blue” represent the ultimate development of the remontoire concept. • Mudge’s son commissioned several additional chronometers on his father’s design. – Kendall’s chronometers had been built for £250 and Kendall did not feel he could make a profit at that price so stopped production. – Thomas Mudge Jr. agreed to supply Mudge’s design for £150 – Arnold and Earnshaw were prepared to sell their machines for £80
  • 17. Mudge’s Green One of the pair of marine chronometers developed by Mudge to compete for the prize. The other was “Blue.” Much of the material in this presentation is “borrowed” from the book shown here
  • 18. Pierre LeRoy and the French School • Pierre LeRoy invented the detent escapement in 1765. • LeRoy’s thermometric compensated balance provided a theoretically perfect solution to the temperature compensation problem. • LeRoy was in a fierce competition with Ferdinand Berthoud and both published extensive analyses of their work. • The works of F. Berthoud, L. Berthoud, Breguet and Motel continued a tradition of highly artistic but impractically expensive chronometers.
  • 19. Pierre Le Roy’s Marine Chronometer Pierre LeRoy’s Chronometer had performance equal to that of H4 and was a theoretical as well as a practical success. It resides in the National Museum of Arts & Sciences in Paris.
  • 20. Ferdinand Berthoud’s Montre Marine Berthoud made a number of chronometers that were larger versions of Harrison’s basic design. He later made detent chronometers as did his nephew Louis Berthoud.
  • 21. Pocket Chronometer by Louis Berthoud
  • 22. Three Chronometers by Breguet from Antiquorum “Art of Breguet” Breguet and Arnold were close friends. Breguet studied with Arnold and later Arnold’s son, John Roger studied with Breguet.
  • 23. John Arnold and Thomas Earnshaw • Arnold invented a practical pivoted detent chronometer several years after Leroy. • Arnold invented the bi-metallic temperature compensation balance. • Arnold invented the helical hairspring and terminal coils. • Earnshaw conceived of using a flat spring in place of the pivot on the Arnold detent. • Earnshaw conceived of laminating the brass and steel components of the bi-metallic balance. • Arnold invented a less practical form of spring detent escapement. There was considerable controversy over who had precedence
  • 25. Large Arnold Pocket Chronometer
  • 26. Arnold & Son Chronometer 1789
  • 27. Earnshaw Pocket Chronometer “In the Grey”
  • 28. Chronometer Escapement Animation courtesy of Volker Vyskocil Klostergasse 1 D-41334 Nettetal Germany www.clockwatch.de
  • 30. Practical Chronometers • Dozens of English makers entered the competition in the early 19th Century for the annual prize chronometer to furnish to the Admiralty. • The Kew trails spurred an intense competition that soon solved essentially all the problems of adjusting for isochronism and temperature.
  • 31. Wm. Bond & Son Survey William Bond & Son were influential Boston clock and instrument makers. Chronometer Bond’s telegraphic chronometer was used in the Coast and Geodetic Survey. Many Bond instruments are on display in Harvard University’s Fogg Museum.
  • 32. John Roger Arnold Chronometer w/ Prest’s Keyless Works
  • 33. Kelvin & White 8 Day
  • 34. A More Perfect Balance • The remaining problem that plagued makers in the middle of the 19 th Century was the error in the middle temperature region. Even though this problem had been solved by LeRoy in 1765, the thermometer solution had not survived in practice. • Many schemes were devised using stops and strangely shaped bi- metallic systems. Experiments were performed using glass for both the balance and the hairspring. • The use of mercury thermometers for auxiliary compensation was re- invented in the 1870’s 100 years after LeRoy’s first use. • However, the ultimate solution awaited the discovery of the nickel iron alloys Invar and Elinvar plus a host of other formulations in the early 20th century.
  • 35. The Middle Temperature Problem Longer • The hairspring loses elasticity as the temperature 0.5 Period (sec) rises (it also elongates slightly) – This causes the oscillation of the balance to slow down. 0.4 – A plain balance expands as the temperature rises which also causes the oscillation of the balance to slow down. 0.3 • A bi-metallic balance decreases its radius as the Shorter temperature rises Longer – This causes the oscillation of the balance to speed up. 0.5 Period (sec) • Unfortunately, these two phenomena do not have the same shape because the inertia of the balance 0.4 goes by the square of the radius. – Therefore the period as a function of temperature will 0.3 only be correct at two temperatures Shorter Temperature
  • 36. Middle Temperature Balances
  • 37. Kelvin & White w/ Poole’s Auxiliary
  • 39. The Golden Age 1880 to 1910 • Springers and Adjusters became the stars of the industry by the 1880s • Kullberg, Johannsen, Walsh, and the Frodsham family took leadership of the British chronometer industry. • Ditisheim, Paillard, and Nardin led the development of the Swiss chronometer industry. • Lange began the development of a German chronometer industry in Glasshutte.
  • 40. Fletcher Marine Chronometer w/ Airy’s Bar
  • 43. The Decline of the Chronometer Industry • By the 1920’s lever wristwatches could compete and win the Kew trials • The long peace from 1914 to 1933 and a large inventory of chronometers led to economic hard times • The shortage of makers and the Atlantic blockade created a crisis during the Second World War
  • 45. Hamilton WW I Deck Watch
  • 46. WW II Revival • The US Navy issued a request for mass produced Marine Chronometers at the beginning of WW II. • Hamilton developed a new design loosely based on the Swiss Nardin ebauche using a newly designed balance, hairspring and detent. • Elgin developed a new design with special features for maintainability using the proven Guillaume Balance • The Elgin entry failed the purchase trials and was not used by the Navy. It was sold in small numbers for civilian use after the war. • Large numbers of lever pocket watches were finished and adjusted for navigation use
  • 47. Hamilton Marine Chronometer Elinvar hairspring M21 Stainless steel “ovalizing” balance
  • 48. Elgin Marine Chronometer Steel hairspring Grade 600 Guillaume integral balance
  • 49. Satellites and the Final Solution to the Longitude Problem • Global Positioning Satellite System is the ultimate solution to the navigation problem. The satellites allow the position of an observer to be determined by “triangulation” from a set of known objects in the sky. • GPSS is oddly similar to one of the “insane proposals” brought to the Longitude Commission in the early 18th Century. The idea was to station ships across the ocean that would place flares in the sky for ships to observe and determine their position.

Editor's Notes

  1. Columbus thought he had found the orient because he believed he had sailed 180 ° of longitude rather than the 75° he had actually sailed. Galileo had calculated the times of eclipses of the 4 major moons of Jupiter, so a land based observer with a good telescope could determine the longitude by observing the local time of the eclipses. This was the primary technique used to establish the longitude of a new location such as an island or a new continent.