Edit: child post points out the Longitude Board's examination of Harrison's watches for finding the longitude at sea was much earlier than the publication of Harrison's book. Wikipedia page has the time-line.
Its worth noting that this recreation uses materials and fabrication techniques not available at the time, too. So there is still no definitive proof that it would have worked.
For those who might be wondering why it's not every 24 hours, or 86400 seconds, look up "Sidereal Day".
The Shortt-Synchronome clock  was the most accurate pendulum clock, known to have an error of less than 1 second per year. It was used in 1926 to detect tiny seasonal changes in the Earth's rotation rate. An evaluation of the clock in 1984 revealed it was even more accurate than thought --- it was in fact accurate to within 1 second per 12 years, the discrepancy being due to "the slight changes in gravity due to tidal distortions in the solid Earth caused by the gravity of the Sun and Moon."
Harrison's claim of 1 second error in 100 days is clearly in the same order of magnitude as the Shortt-Synchronome's known error rate of 1 second per year in 1926, and thus would have been also affected by the tiny seasonal changes in the Earth's rotation rate.
If the main purpose of the clock was to measure longitude by observing the position of the stars, "only as accurate as the Earth's rotation is consistent" is as good as you could possibly need.
However, the situations are actually pretty different. If you look into the study of the Shortt-Synchronome clock, you'll see it's actually talking about the gravitational effects of the sun and moon on pendulums. The Harrison clocks had no pendulums.
The Shortt-Synchronome is still a pretty amazing clock, though.
> The Harrison clocks had no pendulums.
Alternately, you could use astronomical angle measurements. You can get quite accurate measure if you don’t move around.
(The reason determining time was difficult on ships is that you need to know precisely where the ship is to figure out the time from the stars, or precisely what time it is to figure out position.)
For more info about the number of seconds in a solar day, see this awesome Wikipedia page: http://en.wikipedia.org/wiki/Leap_second
Edit: here is a link to some accuracy measurement. I have no idea what the record is, but these ones were getting down to 30 seconds ish. http://www.sage.unsw.edu.au/currentstudents/ug/projects/o%27...
One thing it shows is the irrepressible drive of human curiosity.
Harrison designed this clock, like most of his clocks, to run without lubrication, eliminating another source of variability. It's a beautiful piece of mechanical design.
The Smithsonian Institution used to have a very nice collection of important high-precision clocks, which they kept set and running. They seem to have been retired from public display.
Harrison apparently spent his whole life building these clocks and fighting to secure the prize given a hostile council of astronomers who had pre-decided that an astronomical method put forth by some learned man would win, not some pathetic carpenter. Every demonstration he made, they would decide they required some higher standard of proof, or some rule had changed which invalidated the demonstration. He became extremely bitter at the process. His son spent much of his life attempting to validate the timepieces in naval voyages. Harrison was only awarded part of the prize on his deathbed after intervention by a sympathetic sovereign and also the death of some of the strong personalities on the Board.
Thief of Time (from the Discworld series by Terry Pratchett)
I wonder if we will look back on the forward thinkers of today (Stallman, Assange et. al) in 50 years and regret the scepticism which we throw their way today.
I'm reminded of AskReddit threads, where people ask "what will people 100 years look back on our time and think was crazy?" and the top responses are always relatively uncontroversial (e.g. "people will look back and wonder how we could have banned gay marriage").
I wonder if there have been any good discussions, on HN or Reddit or somewhere, that focus on that question from the perspective of "what kinds of things will people believe in in the future, things for which I'll be on the 'wrong side of history'?"
I'm a meat eater, and don't intend to stop. That's the best thing I can think of where I expect to be seen as horrible 100 years from now.
In the case of current online communities, I hope the current habit of picking one comment someone made, or one photo they took, and the whole internet attacking them for it, will be seen as unacceptable. (I'm not talking about people doing things genuinely terrible, but doing things which lots of people do every day, but then one person, for some reason, gets into the public sphere for it).
I believe the self-reflection you're referring to is pretty much impossible to cultivate in an online community. Especially one that has entered into the public sphere, like a default sub-reddit.
If what you say goes against a pillar of the culture of the community (or offends a sizable portion of said community), you're likely to get castigated, and maybe even outcasted. From the perspective of a moderator, perhaps the best thing to do is to cull the excess negativity and triumphant navel-gazing that perennially afflicts the more idealogical forums.
But the fact that some geniuses were laughed at
does not imply that all who are laughed at are
geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers.
But they also laughed at Bozo the Clown.
-- Carl Sagan