Sextant, Longitude and Time

choi

(1) Jacob Sweet, How Harvard Profited on Keeping Time; Harvard clocks linked the world—and made money. Harvard Magazine (published by Harvard Alumni Association), September-October, 2021
https://www.harvardmagazine.com/ ... ofited-keeping-time

Quote:

"It was easy to determine latitude based on the angle between the horizon and Polaris [if one is located in northern hemisphere], but figuring out longitude—the basis for time—required tougher calculations. One needed to know the position of the stars overhead and those same stars as viewed from Greenwich, England, along the prime meridian. 'You might say, "Okay, that's easy: we'll just take a clock with us from Greenwich time, compare it to the local time set by the rising sun…and make this calculation,’" ' says [(Harvard) Pellegrino University Professor Peter] Galison[, who directs the Collection of Historical Scientific Instruments (at Harvard)]. But clocks didn't travel well. Temperature variation, storage angle, and other factors threw them off.

"In 1839, President Josiah Quincy invited astronomer and clockmaker William Cranch Bond (Vita, September-October 2015, page 46) to live in Dana House (where Lamont Library now stands), which became the University's de facto observatory.

"Transatlantic telegraph cables improved timekeeping in the nineteenth century, but the United States did not yet have standardized time zones. Keeping the time straight in a single city was hard enough, and different cities kept different times.

"From 1872 to 1892, Harvard made a profit selling its exact time across the region. * * * While Harvard lost relevance in time standardization by the end of the [19th] century, it took decades for the United States to enact the 1918 Standard Time Act, which established Daylight Saving Time and official time zones across the country.   The astronomical regulator pictured [at the top of this Web page] was made in 1832 by Simon Willard Jr, another prominent clockmaker.

Note:
(a) The prime meridian or zero degree longitude passes through Greenwich, where Royal Observatory, Greenwich (ROG; 1675 (founded and construction began; after Paris observatory was founded an construction began in 1667) - 1998 (when Royal Observatory moved) stood.
(b) "One needed to know the position of the stars overhead and those same stars as viewed from Greenwich, England, along the prime meridian."

Though the Harvard article does not say it, the article alludes to lunar distance method (to determine time (both local and Greenwich Mean Time) and longitude.
(c) lunar distance method
(i) Chapter 7 Finding Time and Longitude by Lunar Distances. In Henning Umland, A Short Guide to Celestial Navigation. 1st published in 1997 and revised in 2004 (e Book).
www.titulosnauticos.net/astro/Chapter7.pdf

Quote:

"In celestial navigation, time and longitude are interdependent. Finding one’s longitude at sea or in unknown terrain is impossible without knowing the exact time and vice versa. Therefore, old-time navigators were basically restricted to latitude sailing on long voyages, i. e., they had to sail along a chosen parallel of latitude until they came in sight of the coast. Since there was no reliable estimate of the time of arrival, many ships ran ashore during periods of darkness or bad visibility. Spurred by heavy losses of men and material, scientists tried to solve the longitude problem by using astronomical events as time marks.

"The basic idea of the lunar distance method is easy to comprehend. Since the moon moves across the celestial sphere at a rate of about 0.5° per hour, the angular distance between the moon, M, and a body in her path, B, varies at a similar rate and rapidly enough to be used to measure the time. The time corresponding with an observed lunar distance can be found by comparison with tabulated values.

• There is no need to read the rest of this work.
(ii) Lunar Distance.
www.siranah.de/html/sail008i.htm
(1750-1850; "the position of the Moon relative to the celestial background, can be thought of as similar to the position of the hands of a clock relative to the dial")

dial (n): "a face of a clock, watch, or sundial that is marked to show units of time  <the dial of your dive watch>"
https://www.lexico.com/en/definition/dial
(iii) lunar distance (navigation)
https://en.wikipedia.org/wiki/Lunar_distance_(navigation)

Do not read text, which is not helpful. Do view the graphic. One may measure the angle between the moon and the celestial body, but how to measure altitudes of the moon and of the celestial body? The answer: by sextant also. The three numbers must be measured at the same time.
(iv) Frank Ward (based in Bristol, England), Longitude. Space.fm (the website since 2018; .the country code fm stands for Federated States of Micronesia), undated
https://www.space.fm/astronomy/earthmoonsun/longitude.html
("The Moon moves across the sky at 13° over 24 hours (0.5° an hour). A navigator would measure the altitude of a prominent star above the horizon. Then they would observe the angle between the moon and the star. They would consult an almanac containing tables of data based on Greenwich and work out their longitude using the difference")

choi

(2) Michael O'Donnell, When Every Minute Counts. Wall Street Journal, Aug 14, 2021 (in the Review section that appears every Saturday)
https://www.wsj.com/articles/abo ... ometers-11628868304
http://www.michael-odonnell.com/when-every-minute-counts/
(book review on David Rooney, About Time: A History of Civilization in Twelve Clocks. WW Norton & Co, 2021)

Quote:

"For generations, the Royal Observatory in Greenwich tested each of the British Navy’s chronometers. These precision instruments—deck clocks used to calculate longitude and thus fix a ship’s position at sea—helped ensure safe navigation. The observatory’s testing room hummed with activity: 'What a wonderful instance of the proof of our maritime power is this apartment!' exclaimed one 19th-century [English] astronomer. * * * In this way, clocks made empire.

"Yet if timepieces could empower, they could also dominate. As David Rooney, a former curator at the Royal Observatory, writes in 'About Time: A History of Civilization in Twelve Clocks,' the British used timekeeping as one more tool of imperial repression. Colonial authorities marked noon each day at the Cape of Good Hope in South Africa by firing a cannon: hardly subtle. Some 100 British-built clock towers stood out over the landscape of India during the colonial period, reminding residents who was in charge.

"Mr Rooney writes. '* * * In Buddhism, time only exists in our minds—and perhaps our nostrils, as incense-burning clocks were used to mark the passage of time in Buddhist ceremonies in Korea, Japan and China for hundreds of years.” As mechanical timepieces appeared in the 13th century, replacing sundials and water clocks * * *

"Markets depend on timepieces. The oldest stock exchange in the world, in Amsterdam, featured a clock tower whose bell called traders together beginning in 1611. Today atomic clocks facilitate the regulation of high-frequency trading to the millionths of a second. In between, entwined with the story of capitalism itself, lies the history of modern horology, from pendulum clocks to the quartz timepieces (measuring the vibrations of a quartz crystal) that led to a crisis in traditional Swiss watchmaking in the 1970s. * * *

"Markets depend on timepieces. The oldest stock exchange in the world, in Amsterdam, featured a clock tower whose bell called traders together beginning in 1611. Today atomic clocks facilitate the regulation of high-frequency trading to the millionths of a second. In between, entwined with the story of capitalism itself, lies the history of modern horology, from pendulum clocks to the quartz timepieces (measuring the vibrations of a quartz crystal) that led to a crisis in traditional Swiss watchmaking in the 1970s.

Note:
(a) apartment (n): "3: British : a large and impressive room or set of rooms —usually plural"
https://www.merriam-webster.com/dictionary/apartment
(b) This WSJ review talks about a book on time or timepiece (watch or clock), but not about longitude.
"Amsterdam first established a stock exchange in 1602 to trade in shares of the Dutch East India Company [also formed that year]; it thus claims to be the world's oldest stock exchange." Oxford Reference, undated.
(c)
(i) Euronext Amsterdam
https://en.wikipedia.org/wiki/Euronext_Amsterdam
("Euronext Amsterdam"/ section 2 Building: building completed in 1611)
(ii) (written in) 2008.
https://www.beursgeschiedenis.nl/en/moment/the-gong/
("In December 2002, the end of floor trading [replaced by electronic trading] was affirmed with a stroke of the gong by Job Cohen, the then-mayor of Amsterdam. * * * Opening trading with a sound signal is an old custom. The first Koopmansbeurs (Merchants Exchange) of Henderick de Keyser already had a tower with a bell that sounded at the 'start and conclusion of the market.' The gong tradition, however, goes back even further to 1582, to be precise. That year, the Amsterdam city council tried to create order and regularity in trading, which then took place at the Nieuwe Brug, with introduction of the first regulations. * * * the exchange clerk [at Nieuwe Brug] sounded a bell to open the exchange")
(iii) Dutch-English dictionary:
* koopman (noun masculine): "a male merchant"
https://en.wiktionary.org/wiki/koopman  
   ^ koop (noun masculine): "a purchase"
https://en.wiktionary.org/wiki/koop
* beurs (noun feminine; from Latin [noun feminine] bursa [purse], from Ancient Greek búrsa): "1: purse; 3: bourse"
https://en.wiktionary.org/wiki/beurs
* nieuw (adj): "new"
https://en.wiktionary.org/wiki/nieuw
* brug (noun masculine or feminine): bridge
https://en.wiktionary.org/wiki/brug
(d)
(i) English dictionary:
* chrono- (prefix; from Ancient Greek [noun masculine] khrónos time)
https://en.wiktionary.org/wiki/chrono-
* horology (from Ancient Greek [noun feminine] hōra time)  
* gong (n; Malay & Javanese, of imitative origin)
https://www.merriam-webster.com/dictionary/gong
(ii) New Testament used three words for time (in English: kairos, chronos and hora), with nuances, which will be explained.
(iii) kairos (Ancient Greek noun masculine kairós): "a time when conditions are right for the accomplishment of a crucial action; the opportune and decisive moment"
https://en.wiktionary.org/wiki/kairos
(iv) DA Carson, The Gospel According to John. Grand Rapids, Michigan: William B Eerdmans Publishing Co (1991) at page 307
https://books.google.com/books?i ... ference&f=false
("The Greek word for 'hour' (hōra), often rendered 'time' in NIV [New International Version (Bible)] * * * Chronos, another word rendered 'time,' always focuses on the extent of time, not the point or specific hour of time (used in [Gospel of] John only in 5:6, 7:33, 12:35, 14:9). The word kairos, found in vv, 6, 8, unlike chronos but like hōra, refers in this Gospel to a point of time * * * ")

choi

(3) Tristan Gooley, Time, Sun and Longitude. The Natural Navigator, July 12, 2013
https://www.naturalnavigator.com ... -sun-and-longitude/

Quote:

(i) "The sun rises in the morning and sets in the afternoon. When it is rising, the sun is east of you. When it is setting, the sun is west of you. When it is neither rising, nor setting it is neither east nor west of you, it has the same longitude as you do. This means that at this exact moment that the sun is highest in the sky [relative to you] * * *

(ii) "Let's say a friend told you that they were going on a touring holiday of the world, but you then said, 'Don't tell me exactly where yet. What I’d like you to do is this...

"Put a stick in the ground and mark the end of the shadows.

"When the shadow reaches its shortest length each day, this means the sun has reached its highest point and I'd like you to give me a telephone call.

"Now on the first day they kindly give up their holiday plans to mark shadows and your telephone goes at 11.00am GMT.

"You quickly do the mental arithmetic. Where your friend is the sun reached its highest point one hour before it did in Greenwich. One hour is 1/24th of a day, therefore they must be 1/24th of the way round the world from you, in the direction of the sun rising. 1/24th of 360 degrees is 15.

" 'You're 15 degrees east of Greenwich.' You reply.

(iii) "The sextant is just a fancy shadow stick in reverse. It may be quite a bit more accurate, but it is not much more complex in principle. All a sextant does is measure angles. Once the angle between your horizon and the sun stops growing [ie, atop you at 90 degrees], you know the sun is highest where you are, therefore it is your local midday.

"A chronometer keeps track of time at your home, or traditionally Greenwich for most navigators. By looking at the time on the chronometer when the sun is highest in the sky, there is no need to ‘phone a friend’. You can therefore work out your longitude on a ship at sea.

"The picture at the top shows the visible time signal that ships moored near Edinburgh used to set their chronometers. The [wooden, per en.wikipedia.org] ball on the Nelson Monument is raised halfway at 12.55, to give a warning to the ships’ navigators to get ready. It is raised all the way at 12.58 and then drops at 13.00 precisely. When it was foggy, the ships would listen to the gun fired at the Castle each day. Sound is not a bad second option, but it travels so much more slowly than light that it is prone to greater inaccuracies. (The gun has traditionally been fired at the Castle, not to keep tourists happy, but because the vibrations would harm the instruments at the Observatory.)

"Tourists take the time to come to Edinburgh, they take the time to listen out for the Castle gun and some even watch the ball drop from the Nelson Monument. But very few take the time to understand the relationship between the sun, time and the place they are.

Note:
(a) City Observatory
https://en.wikipedia.org/wiki/City_Observatory
(1776-2009; on Calton Hill in Edinburgh, Scotland)
(b) Edinburgh Castle
https://en.wikipedia.org/wiki/Edinburgh_Castle  
(since on Caste Rock (elevation 140m); table: Built  11th century through to the 21st century)
(c) City Observatory is separate from Edinburgh Castle by two miles in air distance.
So you need the precise time, say GMT, as a reference time. The local time at high noon is always 12 noon; however with GMT, you can not know the longitude of where you are.

(4) The above sounds good, but in reality not precise.
(a) longitude by chronometer
https://en.wikipedia.org/wiki/Longitude_by_chronometer   (section 1 Noon sight for Longitude: "It is impossible to determine longitude with an accuracy better than 10nmi by means of a noon sight. * * * At noon the sun's change of altitude is very slow, so determining the exact time that the sun is at its highest by direct observation is impossible * * * By taking a sextant reading within 15 to 30 minutes prior to local noon (culmination) and noting the time, then leaving the sextant set to the same angle and subsequently observing the moment in time at which the sun passes through the sight tube on its descent from its highest altitude between a half-hour and hour later, the two times can be averaged to obtain a longitude sufficiently accurate for navigation (within 2nmi)" )  (citation omitted).
(b) nautical mile
https://en.wikipedia.org/wiki/Nautical_mile


(5)
(a) sextant
https://en.wikipedia.org/wiki/Sextant
(used in "celestial navigation. * * * The principle of the instrument was first implemented around 1731 by John Hadley (1682–1744) and Thomas Godfrey (1704–1749), but it was also found later in the unpublished writings of Isaac Newton (1643–1727).  In 1922, it was modified for aeronautical navigation by Portuguese navigator and naval officer Gago Coutinho. * * * The frame of a sextant is in the shape of a sector which is approximately 1⁄6 of a circle (60°), hence its name (sextāns, sextantis is the Latin word for 'one sixth'")

Quote:

"Most sextants also have filters for use when viewing the sun

"Star and planet sights are normally taken during nautical twilight at dawn or dusk, while both the heavenly bodies and the sea horizon are visible.

• There is no need to read the rest of text. Do view the animation whose caption reads: "Using the sextant to measure the altitude of the Sun above the horizon[.]"  Please do not read the rest of the text, which I could not understand.
(b) Latin-English dictionary:
* sextāns (noun masculine; from numeral sex six): "a sixth"
https://en.wiktionary.org/wiki/sextans
* sexus (noun masculine): "sex, gender"  (Ultimately from this Latin word comes the English noun sex.)
https://en.wiktionary.org/wiki/sexus

(c) How a Sextant Works. PBS, undated.
https://www.pbs.org/wgbh/nova/sh ... te/escapeworks.html
(d) Navigation by Sextant. PBS, undated
https://www.pbs.org/wgbh/nova/shackleton/navigate/escapenav.html

two consecutive paragraphs:

"Finding latitude is easy enough. The first thing you need to do is measure the angle [with a sextant] between the horizon and the sun when the sun is at its highest point, which is right around noontime on your watch [but an ordinary mechanical watch is not reliable at sea; a quartz watch is (reliable)]. A quick look at your trusty tables tells you which line of latitude the sun should be above on that particular day. For example, let's say it's noon on December 21 [winter solstice], and the sun is directly overhead. Well, on that day the sun is above the Tropic of Capricorn, so your latitude would have to be 23.5 degrees S.

" * * * Now if you have a chronometer (this is just a fancy name meaning 'extremely accurate clock'), you can find your longitude. Let's say that the sun is directly overhead and your chronometer, which was set to noon when you were at 0 degrees, says it's 3 o'clock. This means that three hours ago the sun was overhead at this latitude at 0 degrees longitude. In those three hours, the sun moved 15 degrees 3 times, or 45 degrees. So you're at 45 degrees West. Of course, the fact that the sun was directly overhead (which very rarely happens) made it especially convenient for finding your longitude, but you could have found your longitude anyway, with the help of your tables.

• trusty (adj): "TRUSTWORTHY, DEPENDABLE"
https://www.merriam-webster.com/dictionary/trusty
• "the fact that the sun was directly overhead (which very rarely happens)"

The sun over one's head happens if and only of he is located between Tropic of Cancer 北回归线 and Tropic of Capricorn 南回归线, AND in season. Outside this zone, the sun willneer appear over the head. I have observed for decades that sun in Massachusetts never does even on summer solstice.

(c)
(i) Chronometer. Encyclopaedia Britannica, undated
https://www.britannica.com/technology/chronometer
("the word [chronometer] was originally employed in 1779 by the English clock maker John Arnold to describe his sensationally accurate pocket chronometer “'no. 1/36.' * * * [Englishman] constructed four marine timekeepers, the fourth of which effectively won him the reward of £20,000 offered in 1714 by the British government for any means of determining a ship's longitude within 30 geographical miles (about 34.6 miles, or 55.7 km) at the end of a six weeks’ voyage. * * * The modern chronometer is, broadly speaking, a large, well-made watch but with a detached chronometer escapement, suspended in gimbals (a set of rings connected by bearings) poised so as to remain horizontal whatever the inclination of the ship.  The modern chronometer is, broadly speaking, a large, well-made watch but with a detached chronometer escapement, suspended in gimbals (a set of rings connected by bearings) poised so as to remain horizontal whatever the inclination of the ship")
(ii) How Does a Marine Chronometer Work. Sep 8, 2017
https://sailorinsight.com/how-does-a-marine-chronometer-work/
("With the advent of satellite navigation, GP and integrated navigation systems very accurate GMT can be obtained from any of thm and hence ib nidern ships the chronomeeter tends to take a backseat. However, at least one chronometer is carried on board ships and they are required to be maintained")