Measuring time in the 17th century.

[Spinnor]

Suppose I'm alive and well and living in the 17th century and I want to make observations of times when Jupiter's moon Io disappears behind Jupiter. The best way to do this is to use the regular motion of the stars in the sky as a clock? What kind of accuracy could the best equipment of my day produce? I'm guessing the limit might be how well one could divide a large circle into equal parts?

Thanks for any help.

 

[mgb_phys]

It was probably not until Harrison that mechanical clocks were comparably accurate to the rotation of the Earth.
Tycho Brahe (died c1600) made measurements at about 1arc-min roughly the diffraction limit of the eye so instruments were at least this good

 

[Spinnor]

It was probably not until Harrison that mechanical clocks were comparably accurate to the rotation of the Earth.
Tycho Brahe (died c1600) made measurements at about 1arc-min roughly the diffraction limit of the eye so instruments were at least this good

From http://en.wikipedia.org/wiki/Minute_of_arc

"1 minute of arc is 1/21,600 of the amount of arc in a closed circle."

As there are 86400 seconds in a day this implies that time could be kept with a precision of about 86400/21600 = 4 seconds? !!!

Nice.

I think this means we need to measure angles to one part in 21600? If we accurately divide a circle with 21600 lines spaced a mm apart the circle would be almost 7 meters in diameter. I'm guessing the devices to measure angles in the sky were of this size?

Thanks for your knowledge.

 

[turbo]

It was probably not until Harrison that mechanical clocks were comparably accurate to the rotation of the Earth.

Since England's fortunes were tied to their dominance of the sea (military and commercial traffic) the solution to the longitude problem was paramount, and accurate mechanical timekeepers were critical to solving it. It's all well and good to have a local time on board a ship, but unless the time-keeping mechanism is dependable enough to reference to a standard (Greenwich observatory time, for instance) it is not possible to determine longitude well enough to navigate safely, even with very good charts. Latitude is trivial - longitude was a huge problem.

 

[mgb_phys]

As there are 86400 seconds in a day this implies that time could be kept with a precision of about 86400/21600 = 4 seconds? !!!

Not directly, you could measure relative spacing between stars - so you could then use the stars as a clock.

I think this means we need to measure angles to one part in 21600? If we accurately divide a circle with 21600 lines spaced a mm apart the circle would be almost 7 meters in diameter. I'm guessing the devices to measure angles in the sky were of this size?

Yes, they were architecture meets instruments.

 

[russ_watters]

IIRC Brahe essentially used a hole in the roof of his observatory as a sight and took measurements of stars that passed overhead. In this way, he was able to plot the positions of stars in a good fraction of the sky.

 

[Chronos]

Since England's fortunes were tied to their dominance of the sea (military and commercial traffic) the solution to the longitude problem was paramount, and accurate mechanical timekeepers were critical to solving it. It's all well and good to have a local time on board a ship, but unless the time-keeping mechanism is dependable enough to reference to a standard (Greenwich observatory time, for instance) it is not possible to determine longitude well enough to navigate safely, even with very good charts. Latitude is trivial - longitude was a huge problem.

That is an unfounded assertion. Longitude is no more difficult to cipher than latitude using a ship's compass.

 

[HallsofIvy]

That is an unfounded assertion. Longitude is no more difficult to cipher than latitude using a ship's compass.

Could you please explain that? How would you use a compass to determine longitude?

 

[turbo]

That is an unfounded assertion. Longitude is no more difficult to cipher than latitude using a ship's compass.

So that's why the British government established very generous (and increasing) prizes for inventors to some up with ways to determine longitude within 60, 40, and 30 nautical miles respectively? Google on "longitude prize" and revel in your "unfounded assertion".

 

[russ_watters]

That is an unfounded assertion. Longitude is no more difficult to cipher than latitude using a ship's compass.

There is a good book on this that I had to read for a history of science/engineering class in college. I'll see if I still have it/look for it online. The story turbo-1 tells is correct. Here's the wiki on John Harrison:

John Harrison (24 March 1693 – 24 March 1776) was a self-educated English clockmaker. He invented the marine chronometer, a long-sought and critically-needed key piece in solving the problem of accurately establishing the East-West position, or longitude, of a ship at sea, thus revolutionising and extending the possibility of safe long distance sea travel in the Age of Sail. The problem was considered so intractable that the British Parliament offered a prize of £20,000 (comparable to £2.77 million / €3.52 million / $4.56 million in modern currency) for the solution.

http://en.wikipedia.org/wiki/John_Harrison

It is an interesting tidbit of history, not widely known, about how a pretty small (in modern terms) invention had an enormous impact on the course of history.

I also did a little celestial navigation in the navy....celestial navigation requires a good chronometer for accuracy of both latitude and longitude, but at least with latitude, a sextant will get you within about 100 miles without one by looking at polaris. But without a chronometer, you won't have any clue what your longitude is*. You could be literally anywhere and have no way to know.

*Columbus is treated in modern history to have been lucky and he was, but he was also regarded (in his time) as a magician when it came to dead reckoning. In his time, dead reckoning was the only way to determine your longitude and effort was taken to sail at constant latitude to avoid compounding the position error. The development of accurate cel-nav eliminated the need and kept ships from getting stuck in the doldrums in the middle of the atlantic, instead following the wind patterns.

edit: The book is referenced in the wiki: here's the Amazon link for it: https://www.amazon.com/dp/0140258795/?tag=pfamazon01-20

 

[D H]

That is an unfounded assertion. Longitude is no more difficult to cipher than latitude using a ship's compass.

I would think that someone with a user name like yours would have a much better knowledge of how the accurate measurement of time turned out to be the key to solving the longitude problem -- and how the use of clocks was viewed by the best minds of the time (Flamsteed, Hadley, Halley, Newton) as a crackpot idea.

The astronomers who dominated the Commissioners for the Discovery of the Longitude at Sea (aka the Board of Longitudes) were absolutely certain that the only way to determine longitude was through astronomical observations: "Without astronomy the longitude is not to be found" (Isaac Newton, personal correspondence, 1715) (http://articles.adsabs.harvard.edu/...=0&data_type=GIF&type=SCREEN_VIEW&classic=YES).

The Board placed artificial hurdles against use of clocks to solve the longitude problem and never did acknowledge that Harrison met the requirements. Harrison had to appeal to the King to receive the prize money.

 

[turbo]

Amateur astronomers sometimes have some pretty glaring gaps in the basics. Those who have studied the history of astronomy know that the kings of France, England, etc, did not fund Royal Observatories because they thought the stars were pretty or for the sake of scientific knowledge. The primary purpose of those observatories was the creation of charts and tables of the positions of stars, so that the data could be used for celestial navigation. THAT was a matter of national security, since it could make the difference between military dominance of the seas and successful, profitable shipping (which the royalty had their hands in) or ceding superiority to one's competitors. The charts and tables that the Royal Observatories produced were very accurate and precise (to the limits of existing technology), but they could not be used to accurately determine longitude until time-keeping devices became accurate enough to keep time properly at sea. If a star crosses the zenith at your position at sea, and you have a table that gives the time at which that star crosses the prime meridian, it's not that tough to take the time difference (local time vs Greenwich time for the transit, for instance) and calculate the longitudinal difference directly from the time.

As Russ pointed out, a huge advantage of not having to rely on dead-reckoning is that the ships' captains could take advantage of trade winds to cut their travel times. Not only would they be able to avoid known shoals and other shipping hazards, etc, but they would be able to seek out and exploit seasonal winds previously charted by themselves and other captains. Harrison's chronometers were worth every penny of the prize (though as DH points out, he had to fight for the prize until near the end of his life) and those clocks likely had a greater positive effect on naval navigation than any other improvement since, including GPS.

 

[turbo]

I, for one would be very interested in finding out how a captain of that era could calculate his longitude using a ship's compass, as Chronos asserts. I'm not holding my breath. "Unfounded assertions" seem to be the currency of the clueless who are dead-certain that they are right despite any supporting evidence.

 

[epenguin]

There is a good book on this that I had to read for a history of science/engineering class in college. I'll see if I still have it/look for it online.

edit: The book is referenced in the wiki: here's the Amazon link for it: https://www.amazon.com/dp/0140258795/?tag=pfamazon01-20

That book turned out to be a rave best-seller in UK surprisingly. I think there was also a Scientific American article on the subject. I remember reading that on the first voyage to the Caribbean I think, coming back home after months the Harrison clock was found to be only very slightly in error and quite accurate enough for its purpose. However, someone in the amazon review of the book claims it did not solve all problems immediately. There is a complicated method of calculating longitude involving observations of the moon that was still used by Captain Cook.

 

[mgb_phys]

There is a complicated method of calculating longitude involving observations of the moon that was still used by Captain Cook.

But it's hard to do from a ship's deck. The lunar libation method is used to check charts and chronometers when you can land somewhere for long enough.

he primary purpose of those observatories was the creation of charts and tables of the positions of stars, so that the data could be used for celestial navigation. THAT was a matter of national security,

Still applies today, the accurate empheris data needed for VLBI is secret until a few months after the data was taken because you also need it to launch ICBMs

 

[skeptic2]

That is an unfounded assertion. Longitude is no more difficult to cipher than latitude using a ship's compass.

I don't know to what Chronos is referring but it seems to me that with a compass and a knowledge of trigonometry, longitude can be determined if the ship doesn't sail due west or due east. For instance if a ship were to sail southwest (225 deg) and by knowing the change in one's latitude one could calculate the change in longitude. I wouldn't go so far as to say it is no more difficult though.

 

[mgb_phys]

Assuming there are no winds or currents

 

[russ_watters]

Assuming there are no winds or currents

That's what made good dead reckoning a real gift.

 

[skeptic2]

Unfortunately for Columbus not only did he probably not know trigonometry but because he first went to the Canary Islands for repairs, he sailed nearly due west to the new world.

 

[Vanadium 50]

There's a bit of a misunderstanding here.

There were mechanical clocks with very good accuracy pre-Harrison. What there weren't is portable mechanical clocks with very good accuracy.

The fundamental problem is accelerating a mechanical clock places forces on the mechanism, and these forces cause the machinery to run slower or faster. Harrison's insight (well, one of them) was that a clock whose center of gravity didn't move during a "tick" would be much less susceptible to this problem.

 

[mgb_phys]

There's a bit of a misunderstanding here.
There were mechanical clocks with very good accuracy pre-Harrison. What there weren't is portable mechanical clocks with very good accuracy.

Not invented by Harrison, but at around that time there were a few improvements like temperature compensation and new escapements that made high accuracy possible.

 

[Chronos]

http://www.historicalatlas.com/lunars/
I was, however, remiss in not acknowledging the longitude problem in pre-middle age navigation.

 

[mylko]

IIRC Brahe essentially used a hole in the roof of his observatory as a sight and took measurements of stars that passed overhead. In this way, he was able to plot the positions of stars in a good fraction of the sky.

Fascinating! Do you have a source? I've been looking for good sources about the methods that Brahe used to make his observations, but the only stuff I find is too unspecific.

 

[phyzguy]

From http://en.wikipedia.org/wiki/Minute_of_arc

I think this means we need to measure angles to one part in 21600? If we accurately divide a circle with 21600 lines spaced a mm apart the circle would be almost 7 meters in diameter. I'm guessing the devices to measure angles in the sky were of this size?

Thanks for your knowledge.

This site shows a photo of the equatorial armillary Tycho Brahe used for his observations.

http://www.sciencephoto.com/media/321250/enlarge

It says that it was 2.7 m in diameter - apparently the lines were more closely spaced than 1 mm.

 

[epenguin]

I'd forgotten this thread, what fun! Anyway Harrison was 18th C and the question was re 17th C. I suppose it was in connection with Romer's impressive estimate of the speed of light. So I don't know how they did it but they did it!