The many Equal Altitude observations that Lewis made while at Fort Mandan leave little doubt that he was concerned about his chronometer—and with good reason. The chronometer had stopped twice without apparent cause since leaving Camp Dubois (and twice before that), and one other time it had been allowed to run down. The Equal Altitude observations were the key to regulating the chronometer and determining its error on Local Time.
Observations for the meridian altitude of the sun and double altitudes of the sun for latitude and calculations for latitude from them could be made without knowing the precise Local Time. To make calculations for latitude by the sun's hour angle or calculations for longitude and magnetic declination, however, depended upon knowing the correct Local Time.
During the summer and early fall months of 1804, the chronometer's daily rate of loss had averaged about 28 seconds. The winter cold, however, must have made the lubricating oil in the chronometer more viscous, increasing its daily rate of loss. In the seventeen days between the observations on 20 January and 6 February, for example, the chronometer's loss on Mean Time was 12 minutes 35.7 seconds; a loss of 44.45 seconds per day.
Although no mention is made of it in the journals, the chronometer must have stopped again between 6 February and 23 February. At noon on the 6 February the chronometer was 1 hour 18 minutes 18.3 seconds slow on Mean Time, but at noon on the 23rd it was 2 hours 28 minutes 11.1 seconds slow on Mean Time. This difference of 1 hour 9 minutes 52.8 seconds (4 minutes 8.6 seconds per day) certainly is more than can be attributed to daily loss.
Some time between 23 February and the observation for Magnetic Declination on 25 March (again with no reference in the journals) the chronometer must have been reset either intentionally or accidentally, because it was 27 minutes 23.6 seconds fast on Local Mean Time. Later observations show that it continued to lose time, and was 24 minutes 26.3 seconds fast on 3 April, four days before the Expedition departed Fort Mandan.
The Equal Altitudes observation of the sun provided Lewis a means to check the time shown by his chronometer. Using his sextant and an artificial horizon (usually a tray filled with water), Lewis would measure the altitude of the sun in the morning, and the times of these measurements, as shown by the chronometer, were recorded. In the afternoon, when the sun was at the same altitude it had been for the morning observations, Lewis would again measure its altitude, noting the times shown by the chronometer. These data, after allowing for the sun's changing declination, would tell him what time the chronometer would have shown at noon. From another Equal Altitudes observation made the next day or some days later, Lewis could determine his chronometer's daily rate of loss.
These Equal Altitude observations, made during the winter especially when the temperature was well below freezing, presented a special problem for Lewis. He preferred to use water as a reflecting surface (artificial horizon), but unless he used warm water and made his observations very quickly, the water would freeze. On several occasions at Fort Mandan, therefore, he was obliged to use a mirror leveled with a spirit level for these observations, and he did not trust that he could make the surface perfectly horizontal as a water surface would be.
Despite the problems with the chronometer, because Lewis took so many (nine) observations of Equal Altitudes of the sun while at Fort Mandan, his observations for magnetic declination and most of his observations for longitude can be calculated and made to yield useful results.
|Date||Apparent Time||Mean Time||Interval||Loss per Day|
|1804 Dec 22||0:40:36.5 slow||0:39:43.4 slow||---||---|
|1805 Jan 15||0:52:01.8 slow||1:01:57.3 slow||24 days||55.58 seconds|
|1805 Jan 20||0:54:11.4 slow||1:05:42.6 slow||5 days||45.06 seconds|
|1805 Jan 28||0:57:48.6 slow||1:11:13.8 slow||8 days||41.40 seconds (observation error?)|
|1805 Feb 6||1:03:50.0 slow||1:18:18.3 slow||9 days||47.17 seconds|
|1805 Feb 23||2:14:29.2 slow||2:28:11.1 slow||---||---|
|1805 Mar 28||0:32:45.0 fast||0:27:34.6 fast||---||(observation error?)|
|1805 Mar 30||0:31:33.3 fast||0:26:58.9 fast||2 days||17.85 seconds (?)|
|1805 Apr 03||0:27:47.6 fast||0:24:26.3 fast||4 days||38.15 seconds|
Funded in part by a grant from the National Park Service, Challenge-Cost Share Program.