The 1779/80 Greenwich trial of John Arnold's pocket chronometer #36. Data taken from:
- Arnold, John. 1780. An Account kept during Thirteen Months in the Royal Observatory at Greenwich, of the Going of a Pocket Chronometer, made on a New Construction, by John Arnold, having his new-invented Balance Spring, and a Compensation for the Effects of Heat and Cold in the Balance. Published by Permission of the Board of Longitude. London: John Arnold, No. 2 Adam-Street, Adelphi. Accessed online (Jan. 2016) at: http://cudl.lib.cam.ac.uk/view/PR-UNCAT-00005
The data are time errors recorded in seconds, and go from March 26, 1779 to February 29, 1780. The report shows both frequency and time errors, which provides redundancy against errors. I entered both into a spreadsheet and checked them against each other; I found a handful of errors which I fixed to the best of my judgement. None of the errors amounted to more than 1.1 seconds, and they cancel out. (The errors are phase noise, not frequency noise, after all.)
The chronometer was compared to the transit clock (presumably George Graham's No. 3), which was rated to keep sidereal time, and the readings were corrected about once a week for mean time and the observed error of the transit clock. The transit clock's error was computed irregularly about every 7 days, and its rates were assumed to be constant between calibrations, so values for sampling periods lower than say 10 days are questionable.
There are a few gaps where Greenwich did not record rates for the watch for some days. In their analysis the way they handled this was to assume that the watch kept a perfectly steady rate during the gap. This can be seen as "flat" valleys or peaks in the daily rate chart. The gaps are all relatively short, so again, they likely don't contribute much to the result.
In any case, the most important thing about this data isn't the exact value of the deviation at any one sampling interval. What I'm interested in here is:
- The approximate inflection points the stability curve;
- The order of magnitude of the stability values.
So the TheoH chart suggests this watch could keep its initial rate to within about 30 seconds (2 standard deviations) for 40 days, but for periods longer than that its rates went on a random walk or a deterministic drift.
The data is taken from here:
The parameter that's of interest to us is "LOD" (length of day). This value is the excess length of each recorded mean solar day, relative to 86,400 atomic seconds. This value is thus a frequency error data series.
