About 8 a.m. on June 3, the Expedition began to move its camp to the junction point between the two rivers. Once there Lewis lost no time getting his sextant, artificial horizon and chronometer ready to take an Equal Altitudes observation of the sun. This observation was essential because, from it, the chronometer's error at local noon could be determined and, if its daily rate of loss was known, the average times of the Lunar Distance observations taken on June 2 could be corrected to true Local Time, as could those he planned to take that afternoon.
After completing the afternoon part of the Equal Altitudes observation, Lewis should have calculated his chronometer's error on local time. Other priorities, such as scouting the area near camp, probably kept him from doing so. The times recorded for the observation, however, show that the chronometer was 1h21m29.0s fast on Local Apparent Time and 1h23m46.6s fast on Local Mean Time.1
From the morning of June 4 until the evening of June 8, neither captain took any celestial observations. On June 9 Lewis began another set of Equal Altitude observations. After completing the PM observations he calculated that the chronometer, at noon, had been 1h19m45.7s fast on Local Mean Time.
If Lewis had calculated his chronometer's error on Local Mean Time for noon of June 3 and compared it with the error he had calculated for June 9 he would have discovered that its daily loss averaged about 42 seconds. This rate of loss is about 15 seconds per day greater than the average daily loss during the summer of 1804. This apparent high rate of loss should have prompted Lewis to take another Equal Altitudes observation of the sun on June 10 to see if that rate of loss was real or had resulted from an observational error or improper winding2. An error of 15 seconds in time produces an error of 3'45" in longitude or about 3 miles at 48° latitude.
It should be noted, however, that an error in longitude of as much as 15 arc minutes was not unusual from an observation for Lunar Distance in the early 1800s. Rather than take another Equal Altitudes observation, Lewis may have felt that it was more important to inform himself about the cache the men were digging and to get equipment ready for his trek to find the falls of the Missouri.
The chronometer's rate of loss on June 9, as calculated from observations made that day for which the sun's altitude and declination could be determined, shows that the chronometer was losing time at the rate of 22 seconds in 24 hours, not 42 seconds. The loss rate of 22 seconds per day was used to make the calculations for longitude and magnetic declination discussed in the respective sections that follow.
1. Mean Time (also called Mean Solar Time) is the time kept by a perfect watch or clock. The earth's annual motion around the sun produces what appears to be an irregularity in the length of time it takes for the earth to make one complete rotation. Time thus measured is called Apparent (solar) Time. Mean time is the measure of the mean (average) of all the earth's rotations during a year.
The Mean Time at any point on the earth is called its Local Mean Time. It is the correct Mean Time only for that meridian (longitude). Standard (Mean) Time is the time shown by a perfect timepiece set to one of the 24 standard meridians. Those meridians, spaced 15 degrees apart, begin at 0 degrees longitude and extend east and west around the globe.
2. Lewis usually wound the chronometer at noon. It is possible that whoever was detailed to wind the chronometer while Lewis was exploring the Marias, failed to wind it sufficiently, producing a higher than normal daily loss of time.
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