Observations of Equal Altitudes to Check the Chronometer's Time
There are no journal entries to show that the chronometer's time had been checked since August 20. If it had not, it is understandable that the captains felt it imperative to discover the chronometer's error and rate of loss or gain. The reason for this is that the most critical element for determining the longitude is time. An Equal Altitudes observation, properly taken and corrected for the change in the sun's declination, can reveal a chronometer's error at Local Noon to within a second. It didn't matter if the chronometer stopped or ran erratically most of the time provided it ran uniformly between two Equal Altitudes observations a day or, perhaps, two apart during which a Lunar Distance observation was made.
Chronometer Error on Local Apparent and Mean Time
The captains made Equal Altitudes observations on September 30, October 3, and October 6. For noon of the given date the chronometer was too fast on Local Time as follows:
It would appear that the chronometer stopped sometime after the Equal Altitudes observation on September 30, but started runnin again before the observation on October 3. This conclusion is based on the tendency of the captains' chronometer to lose time–never gain time–so how could it be 6m 15.5s faster on Local Mean Time on October 3than it was on September 30.
Chronometer's Rate of Going
The chronometer lost 44.6 seconds on Mean Time between October 3 and October 6. This rate of loss of about 15 seconds per day is essentially the same as what Lewis recorded for 22 July 1804 when he described his navigational instruments. The uncertainty about the chronometer's error on Local Time for September 30 and its rate of loss between September 30 and October 3 produces some uncertainty about any longitude calculated from that day's Lunar observations, but there are ways around this problem.
Example of a calculation from Equal Altitudes observation with the sextant to determine the chronometer's error, October 3:
The time of 4:00:53 is from Moulton, 5:244. Thwaites has 4:00:05, but this is not possible.
Funded in part by the Idaho Governor's Lewis and Clark Trail Committee