In the chilly pre-dawn hours of July 28, moisture-laden air from the rain that fell the previous evening developed into fog. Before sunrise the fog had gathered and thickened over the streams and wetlands. There it clung, gray and damp, until the sun topped the hills and mountains to the northeast and began to burn it off. By about 8 a.m. the fog was gone and the sun stood alone in a clear sky. This was an invitation to Lewis to take the Equal Altitudes observations that could yield his chronometer's error on Local Time. Lewis began these observations about 8:40 by his chronometer when the sun's upper limb reached an altitude of 72°08'15"1 as measured by his sextant with the artificial horizon. About a minute and a half later the sun's center reached that same altitude, then its lower limb. With these times noted, the AM part of the observations was complete.
Storm clouds began moving into the Three Forks area from the west by early afternoon. By the time the sun had descended nearly to the altitude observed for it that morning, clouds were drifting near it. Lewis, however, was able to observe the sun's lower limb when it had descended to a sextant altitude of 72°08''15" above the horizon. When the sun's center reached that altitude, clouds partially blocked it, and Lewis considered this observation: "doubtful." A minute and a half later when the sun's upper limb should have reached that altitude, clouds completely obscured it: "lost by clouds" Lewis wrote. He, therefore, may have doubted the usefulness of the Equal Altitude observation made that day. On July 29, Lewis again took Equal Altitude observations of the sun. Observing conditions that day were near-perfect.
Despite the interference from afternoon clouds on July 28, the Equal Altitude observations for that day provide all the information needed to determine the chronometer's error on Local Time. The chronometer's error could be found by two different methods: 1) standard Equal Altitudes calculation and 2) that outlined in Patterson's Astronomy Notebook (1803) which Lewis carried.
- The three AM observations were reliable. This is shown by the time interval between them (1m 33s and 1m 32s). Despite the afternoon clouds, the time interval between when the lower limb and center reached the altitude of the AM observations was 1m 35. This difference is well within the acceptable range for these observations. The chronometer times for the sun's center, AM and PM, thus, can be used to make the standard Equal Altitudes calculation for chronometer error.
- As noted above, the interval times for the AM observation were highly consistent, indicating a quality observation. Lewis also had obtained the sun's altitude for that observation. By making a good estimate of his longitude, he could obtain a reasonable approximation of the sun's declination. Then, by the method outlined in Patterson's Astronomy Notebook (Problem 3, Form III), he could have calculated the true time of the observation.
Either method would have provided Lewis with the chronometer's error. Method 1 would have given Lewis the time that the chronometer would have shown at Local Apparent Noon, and from this he could have determined its error on Local Apparent Time and Local Mean Time at noon. Method 2 would have given Lewis the Local Apparent Time of the AM observation, and from this he could have determined its error both on Local Apparent Time and Local Mean Time for that observation.
Lewis would still need to know how many seconds per day his chronometer is losing. The Equal Altitudes observation that he took on July 29 not only would have provided him with the chronometer error on Local Time for that noon, but by subtracting the noon error on the 29th from that determined for noon the 28th (or for the time of the AM Equal Altitudes observation), he could have determined the chronometer's daily rate of loss both on Local Apparent Time and Local Mean Time. This done, Lewis has the time information he would have needed to make his calculations for longitude and magnetic declination.
|Date 1805||Error at Local Noon
Local Apparent Time
|Error at Local Noon
Local Mean Time
|July 28||0h 33m 39.5s fast||0h 27m 35.4s fast|
|July 29||0h 33m 11.0s fast||0h 27m 08.2s fast|
|Daily loss||0h 00m 28.5s||0h 00m 27.2s|
The calculations for the chronometer's daily rate of loss, shown above, were made from Lewis's Equal Altitudes observations. Lewis's chronometer, however, seems to have had an irregular diurnal rate of loss. Calculations made for the time of the AM and PM Equal Altitude observations on July 28 and July 29,2 show a rate of loss of about 1 minute per day. These rates, however, require that the chronometer's loss rate slow to only 15.6 seconds per day between the PM observation on July 28 and the AM observation on July 29.3
When the time of the lunar observations are calculated from the noon-noon chronometer errors for July 28 and 29, they are 5, 6 and 9 seconds earlier, respectively, than those calculated from the AM and PM Equal Altitudes observations (using latitude, and sun's declination and altitude). At 4 minutes per degree of longitude this makes a longitude difference of 1'15", 1'30" and 2'15", respectively. The effect of these time differences on the calculated magnetic declination is less than that which most magnetic compasses can distinguish.
Lewis knew that his chronometer lost time at varying rates. If he had the opportunity, and the weather cooperated, he should have taken Equal Altitudes observations before and after Lunar Distance observations. If expedition priorities prevented his taking an Equal Altitudes observation the next day after a Lunar Distance observation, he could have taken an observation such as that noted in Method 2, above.
1. The altitude of the sun actually was about 35°58'45". This altitude is derived from 78°08'15—8'45" (sextant's index error) = 71°59'30" ˜ 2 (because of the use of an artificial horizon) = 35°59'45" minus about 1' for the combined effects of refraction + parallax = 35°58'45".
3. It is possible that Lewis changed his practice of winding the chronometer at noon—at least on those days when he took Equal Altitude observations—until after the PM observation was completed so as not to affect the chronometer's rate. Lewis recorded that the chronometer "went from 3 to 4 seconds slower in the last 12 h, than she did the first 12 h. after being wound up [emphasis added]." Moulton, Journals, 2:412.
Funded in part by a grant from the National Park Service, Challenge-Cost Share Program.