Stephenson:Neal:Quicksilver:75:sundial synchronization (Bill Seitz)
From the Quicksilver Metaweb.
"had to make a little cross-tick at the place the gnomon's shadow stood when Trinity's bell (always just a bit out of synchronization with the King's) rang each of the day's hours"
How did the Trinity's bell-ringer decide when to ring? Why was this different from when the King's (College?) bell was rung?
Any consistent errors in the Trinity bell timing would throw off Newton's curves one way; occasional errors would result in bumps.
In a sense, the Trinity bell was the instrument through which the sun's shadow was perceived. That seems like a crude assumption to accept, esp from someone who stuck a needle into his eye socket to test its instrumental workings...
Related thought: distinguishing TimeAsABasisForSynchronizedAction vs ElapsedTimeAsABasisForCalculatingRates
Here's a good webpage with images of Newton's sundial as well as a java app that attempts to reproduce it http://www.quns.cam.ac.uk/Queens/Images/sundial.html
different
Why was this different... ?
I don't think it would be possible for both of them to ring at precisely the same time -- the clocks in Newton's time weren't accurate enough.
Say the towers were about 300 meters apart (I really have no idea). Even if both clocks were calibrated using modern atomic clocks and GPS technology to make them ring at precisely the same time (in the Earth's reference frame), the speed of sound (about 300 meters per second) would make it sound to someone standing at the foot of one tower that the other tower was one second slow.
accurate time
How did the Trinity's bell-ringer decide when to ring? ...a crude assumption to accept
I agree. At first glance, one would expect the sun to be more accurate than the clocks -- we would explain away any difference between them as error in the clock.
Astronomical observations of the stars can give incredibly accurate measurements of time -- the relative motion of most stars (except the sun) is unobservable, and the rotation of the earth is incredibly constant. (My understanding is that it's still more accurate than most digital clocks today, other than atomic clocks or those closely synchronized to them).
I'm speculating here that perhaps Trinity's bell and King's bell were run by clockwork, periodically synchronized to the stars, so they never drifted more than, say, 10 seconds or so away from each other and from star time / average solar time / clock time.
The relative motion of the sun, however, is observable. The time from high-noon to high-noon the next day (in March and September) is about 22 seconds shorter than average. The time from high-noon to high-noon the next day (in June and December) is about 29 seconds longer than average.
These few seconds a day accumulate so that high noon occurs anywhere from 15 minutes before the bell rang to 15 minutes after the noon bells ring, depending on the time of the year. (The Equation_of_Time analemma tells exactly how many minutes to add to "solar time" to get "clock time", and exactly how this depends on the time of the year).
-- DavidCary