# Local Time

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Fair and cool weather greeted Clark at Station Camp on the morning of November 17. Because Lewis still had not returned from exploring the coast west of that camp, Clark took it upon himself to make the AM observations for Equal Altitudes of the sun. Lewis returned to camp about 1 PM, but it probably was Clark who completed the PM Equal Altitude observations. After correcting for two mistakes that Clark's assistant made in reading the chronometer that morning, these observations give the chronometer error at solar noon.

## Table 4. Chronometer Error on Local Time

Date Error on Local Apparent Time Error on Local Mean Time
November 17, 1805, noon: 15m 56s slow 1m 19s slow

Adverse weather prevented the captains from taking celestial observations for longitude until November 24. To make reliable longitude calculations from the Lunar Distance observations, accurate time is needed for those observations. If the expedition's chronometer had kept perfect time or always had run at a steady rate, the time of the Lunar Distance observations could be projected reliably from November 17 to the observations on the 24th. The captains knew that their chronometer did not run at a steady rate; they also knew that sometimes it stopped. They needed another observation or set of observations from which the true time could be calculated to find the chronometer's error on Local Time.

On the morning of November 24, the captains began taking observations for Equal Altitudes of the sun and completed them a few minutes later. Clouds, however, blocked the sun in the afternoon, preventing the captains from taking the PM observations. Although Clark recorded the times for the AM observations, he—perhaps thinking that without the PM observations the AM data were unuseable—failed to record the sun's altitude for the AM observations. If Clark HAD recorded the sun's altitude for the AM observations, a good value for the chronometer's error could have been calculated despite the missing PM data. As such, this Equal Altitudes observation cannot be used to help determine the time of the Lunar Distance observations.

Shortly before the AM Equal Altitudes observation on November 24, the captains took an observation of the sun for Magnetic Declination. Clark dutifully recorded the chronometer times and sun's magnetic bearing and its altitude. Unfortunately, Clark failed to record whether Lewis had observed the sun's upper limb, its lower limb or its center. If Clark had recorded this information, the chronometer's error on Local Time for this observation easily could have been calculated by using Robert Patterson's Problem 3, Form III. In November, at the latitude of Station Camp and time of day this observation was made, the sun's altitude increases by one semidiameter in a little more than two minutes. Calculations for the time of the observation made assuming the altitude recorded was for the lower limb would differ by more than four minutes from those made assuming the altitude was for the upper limb—and four minutes makes a difference of one degree of longitude.

Does this mean that the observations the captains made for longitude are unuseable?

No . . . times for the Lunar Distance observations still can be approximated, but the confidence level for the accuracy of the longitudes derived is not high.

The method I used to determine the time for the longitude observations is lengthy, but could have been made by mathematicians of the early 1800s. It is summarized as follows:

1. Determine the chronometer error at Local Apparent Noon on November 17 from the Equal Altitudes observations taken that day (this value is shown in Table 4, above).
2. Calculate the Local Apparent Time of the observation for Magnetic Declination; assume that it was the upper limb that was observed (see discussion, below and Magnetic Declination, below),
3. Subtract the average chronometer time of the Magnetic Declination observation from the calculated time of theobservation average; this gives the minutes and seconds that the chronomieter is slow on Local Apparent Time,
4. Determine the Equation of Time for the observation for Magnetic Declination and subtract it from the chronometer's error on Local Apparent Time; this gives the minutes and seconds that the chronometer is slow on Local Mean Time,
5. Subtract the result of Step 1 from the result of Step 4; the result is the minutes and seconds of Mean Time that the chronometer lost between the two observations,
6. Divide the result of Step 5 by the number of hours of Mean Time that elapsed between the two observations; this gives the chronometer's hourly rate of loss on Local Mean Time, which will essentially be that for Local Apparent Time for the date in question.
7. Find the difference in time between the Lunar Distance observation average and that of the Magnetic Declination average, multiply the result by the result of Step 6; this gives the number of additional seconds that the chronometer has lost since the observation for Magnetic Declination,
8. To the result of Step 8, add the number of minutes and seconds that the chronometer was slow on Local Apparent Time for the observation for Magnetic Declination (this value was found in Step 3); this gives the chronometer's total error on Local apparent Time for the Lunar Distance observation with the sun,
9. Add the result of Step 8 to the chronometer time of the Lunar Distance observation with the sun; this gives the calculated Local Apparent Time of the observation average.
10. Repeat Steps 7-9 for the Lunar Distance observation with Markab.

Between the mouth of Ohio River and Camp Chopunnish the captains made twenty-eight observations of the sun for Magnetic Declination. Of these, they specifically recorded only one as being of the sun's center. For five observations, including that of November 24, 1805, they did not specify which limb was observed. Eleven of the observations they recorded as being of the sun's upper limb and eleven were of the sun's lower limb. For those observations of the sun's lower limb, however, the lowest sun altitude was more than 2° higher than the lowest of the three sightings made on November 24. Inasmuch as the sun on November 24 was only about 11° above the horizon for the average time of the three timed observations for Magnetic Declination, it is not likely that the captains observed the sun's lower limb. Good observation practice suggests that the captains observed the upper limb.

The chronometer's daily rate-of-loss of about 33 seconds per day while at the mouth of Snake River lends additional support to the interpretation that Lewis observed the sun's upper limb for the Magnetic Declination observation of November 24.

1. Given a clock time of 12 noon on November 17, one could designate that time Day 17.5; similarly, 9 PM on that day could be called Day 17.875. Decimal time is useful when comparing chronometer loss rates over several days, especially when used with linear regression capabilities on modern hand-held calculators.

Funded in part by a grant from the National Park Service's Challenge-Cost Share Program