Lewis and Clark
on this site:

Asteroid 2822 Sacajawea:
The Photograph
The Tech Specs

The Mandan Moon
A Total Lunar Eclipse Almost Reprised

Coming Eventually:

Pompey's Pillar
Virtually Restored

Photos from the Trail:
"Scenes of Visionary Enchantment"



Internet Resources:
Lewis and Clark

University of Nebraska Press
Journals of the L&C Expedition

Charles G. Clarke's
A Biographical Roster...

PBS

National Park Service

The National L&C
Bicentennial Council




L&C's
Celestial Navigation:

Richard S. Preston's
American Philosophical Society analysis
(PDF)

Lewis and Clark
and the Mandan Moon



Totally Eclipsed Moon Beside Open Cluster Messier 44, "The Beehive"
January 20-21, 2000. (Click the image for a larger view.)

This eclipse was very nearly a replay of the total lunar eclipse of January 14-15, 1805, which Lewis and Clark observed in an attempt to establish the longitude of the Mandan Villages. The eclipse the boys on the boat watched took place about five lunar diameters to the right of the one shown above, just beyond the right edge of the photo.

Historical context:

The Lewis and Clark expedition spent the winter of 1804-1805 encamped in the Mandan Villages on the banks of the Missouri River in what is now central North Dakota.

The explorers used the total lunar eclipse of January 14-15, 1805, to determine the longitude of their winter camp which they called Fort Mandan. The longitude found by the eclipse observations was not particularly accurate, as Lewis soon realized. Not only was the beginning of the eclipse obscured by clouds, but so was the beginning of totality. Lewis lamented how poorly-defined some of the eclipse's stages were. The next day, while completing the longitude observation by shooting "equal angles" of the Sun to find local noon, Lewis's ill luck continued. The weather was too cold and windy for him to use his usual artificial horizon. In its place he used a less reliable horizon: a mirror adjusted with a spirit level. Worse, Lewis had to take this glass horizon down and set it up a second time for his afternoon sightings "lest the savages should pilfer it."

The longitudes derived for the Mandan Villages based on Lewis's observations of the two phases of the lunar eclipse in which he had the most confidence, the end of totality and the end of the eclipse, gave results that were significantly east of the position given years earlier by Canadian explorer, trapper, and map-maker David Thompson. Lewis's longitudes were 99o23'W and 99o27'W, while Thompson had found 101o14'W. Thompson was a much more experienced celestial navigator whose many sightings provided a firm underpinning for early maps of western Canada. (For the record, a GPS would have shown that the Mandan Villages were at longitude 101o27'W. Lewis's best measures were off by 94 and 98 statute miles.)

For a time, Lewis insisted that Thompson's position was the one in error, but he soon gave in and began using Thompson's longitude rather than his own.

The Experiment:

I had always suspected that Lewis's attempt was doomed from the first. Lewis could only have seen 2 or 3 lunar eclipses in his short life and had no good idea what to look for. Without some experience with lunar eclipses, how could he have coped with how vague the stages of a lunar eclipse are? I wanted to know how practical it was to use a lunar eclipse to find longitude.

In the winter of 2000, I decided to indulge the American fetish for retracing Lewis and Clark, this time from my own backyard. I used the eclipse of January 20-21, 2000, to determine the longitude of "Fort Cortner" which is where my wife and I have been encamped for some time in the township of Cajah's Mountain in western North Carolina.

As it turns out, this method can work quite well. I proved this much at least: two centuries on, it is still dangerous to second-guess Meriwether Lewis.

Eclipse Observations:

1st contact: 22:02:40 EST, Jan 20, 2000.
2nd contact: 23:03:30 EST, Jan 20, 2000.
3rd contact: 00:23:00 EST, Jan 21, 2000.
4th contact: 01:25:40 EST, Jan 21, 2000.

1st contact is the moment the dark, central portion of the Earth's shadow touches the Moon; 2nd contact is the beginning of totality; 3rd contact is the end of totality; and 4th contact is the moment the Earth's umbra passes off the face of the Moon. None are crisp. 1st contact is especially troublesome. 1st and 4th, 2nd and 3rd occur symmetrically around the time of mid-eclipse, so we can use them to derive the moment of mid-totality.

Mid-eclipse derived from 1st and 4th contact: 23:44:10
Mid-eclipse derived from 2nd and 3rd contact: 23:43:15
Mid-eclipse derived as the mean of these values: 23:43:42
Take that as the observed time of mid-eclipse.

This establishes that by my watch, the moment of central eclipse occured at 23:43:42 EST. Don't be troubled by the fact that I am using Eastern Standard Time (or any standard time) for this observation. All that matters is that I am able to measure the interval between mid-totality and the next transit of the Sun --local noon of the following day.

I could have set my watch to Greenwich Mean Time or to any arbitrary setting, to a mean or to a standard time zone or to something completely novel. It wouldn't matter if it had stopped now and then -- as the expedition's had -- and was no longer keeping good Philadelphia time.

All that is required is that it be permitted to run continuously between the eclipse observations and a well-observed noon transit of the Sun.

In the real world (celestial navigation is as filled with the caveat "in the real world" as introductory physics is with "neglecting air friction"), it also matters that its "rate of going" is known, that is, the rate at which it gains or loses time. In my case, I was blessed with access to US Naval Observatory time, so the "rate of going" is moot -- my clock neither loses nor gains any time at all. But if it lost an hour a day, and I knew it lost an hour a day, then its imperfection could be taken into account. Lewis and Clark's chronometer lost 55.8 seconds a day -- but they knew this before setting out, and it would have been an easy correction to apply.

Observing Local Noon:

I found the moment of local noon the day after the eclipse by using the same tools and methods Lewis and Clark used:

First, I made an artificial horizon. I filled a cereal bowl with water (the temperature in North Carolina being more moderate than in North Dakota in 1805) and poured an ounce or two of vegetable oil on top to keep wind-riffles from constantly destroying the clear reflection of the Sun. Our dog Jack, that 4-legged savage, twice pilfered my artificial horizon, but I replaced it easily to complete the morning sighting. (Incidentally, I think this shows that the problem Lewis faced was wind, not cold; he could have replaced a frozen horizon as readily as I drunk one, but wind destroys the sharp reflection required. When is it windy in North Dakota? When is it not?)

Second, with a modern vernier sextant (identical in principle and in function to the sextant used by Lewis and Clark), I observed several altitudes of the Sun during the morning and then waited to observe the same altitudes in the afternoon. From each pair of equal angles, I could derive the time the Sun was at its maximum height -- the time of local noon. The mean of several pairs of equal angles yielded a time I could depend upon.

Third, I also observed the altitude of the Sun as it crossed the meridian so that I could easily calculate my latitude from that maximum altitude. (No, you can't just write down the time when the Sun appears highest and call that noon, because the heighest altitude of the Sun is indeterminate by several minutes. The Sun's altitude changes very slowly as it crosses the meridian.)


Finding Latitude:

The easy part comes first, then the infinitely more interesting problem of longitude.

The angle between the Sun and its reflection in the artificial horizon at its highest point was 68o25' or just a little more; call it 68o26'. This "double angle" is twice the Sun's actual altitude -- we're looking down at a reflection rather than straight ahead at a real horizon. So the Sun's observed altitude was half this angle, or 34o13'.

The Sun's declination -- that is, its distance north or south of the celestial equator -- was -19o50'. (I got this from precise ephemeris software; Lewis and Clark would have consulted a table of declinations and interpolated.) A moment of sketching circles and angles on the back of an envelope to see how declination relates to latitude (hints: the north star, at 90o declination is overhead at the north pole; a star at declination 0o will pass overhead at the equator), will convince you that the latitude of Fort Cortner follows directly:

90o - observed altitude + declination = latitude
90o - 34o13' + -19o50' = 35o57'

In the real world, this latitude needs to be corrected for atmospheric refraction. The refracting effect of the Earth's atmosphere raises the Sun's apparent place in the sky. At the Sun's observed altitude, this effect would amount to about 1 minute arc. It's the actual, geometric position of the Sun and not the observed, refracted position we care about. So after subtracting the slight correction for atmospheric refraction from my observed solar altitude we get 35o58' as my observed latitude.

Also in the real world, Lewis had to apply a correction for the known error in the sextant. I splurged on a good one soon after GPS receivers made them cheap, so no such correction is required.


Observations for Longitude:

First, we need to find the time the Sun was at its highest point. We have, by observation:

Morning
Double Angle
Afternoon
11:00:30
59o22'
14:14:24
11:02:00
59o35'
14:13:10
11:03:20
59o50'
14:11:45
12:19:30
68o04'
12:55:25
12:22:50
68o11'
12:50:05
12:25:30
68o16'
12:44:20
12:27:30
68o19'
12:42:00

Here's what the table represents. Take the second line as an example. At 11:02 AM, I observed the Sun and its reflection seperated by 59o35'. In the afternoon, I set the sextant to that value and waited for the Sun to descend to that height again. I recorded the time: 2:13:10 PM or 14:13:10. Local noon is the instant exactly midway between those two times. The difference between the observed times of equal altitudes was 3 hours, 11 minutes and 8 seconds. That's 11,468 seconds. Half that is 5,734 seconds, or 1 hour 35 minutes and 34 seconds. Adding that time to the time of the morning sight yields an observed time of local noon: 11:02:00 + 1:35:34 is 12:37:34.

I've calculated a time of local noon from each line of the table, then taken the mean of all the derived times. That mean is 12:36:44. Take that to be the time of local noon.

The interval from mid-eclipse (23:43:42 last night, or 16 minutes and 18 seconds before midnight) to the following noon (at 12:36:44) was 12:36:44 + 00:16:18 = 12h 53m 02s.

That's the only observational datum we need.


Finding the longitude of Fort Cortner:

First, consider what an observer at the prime meridian (in Greenwich, England) would see. We can calculate -- and so could almanacs of 1804-5 -- how much time elapsed between the time of mid-eclipse and the next noon at a known location, Greenwich in particular. From anywhere west of Greenwich, that interval would be longer (because observers west of Greenwich must wait for the Earth's rotation to bring them "to the same place," directly in line with the Sun and the axis of the Earth at local noon). The difference between the time that transpires at one place and the time that transpires at another place gives the difference in longitude between those two places. If one of those places is Greenwich, on the 0-degree "prime meridian" then the difference gives us our longitude directly. In fact, that difference in interval is our longitude, albeit in non-standard units.

Think of it like this: for each observer, -- one in Greenwich and another at Fort Cortner -- mid-eclipse "starts the clock" and the next passage of the Sun across the meridian stops it. The eclipse occurs at the same moment for all observers everywhere on Earth, but the passage of the Sun across the observer's meridian depends entirely upon the observer's longitude. The difference between the interval as seen from Greenwich and the interval as seen by me is the longitude of Fort Cortner. Simple, no? (I'm not kidding -- it is simple if you think about it long enough and stay clear about each step means. At this point it is customary to get out an apple, a melon, and an electric light bulb, and whirl around with them while spinning the apple on the tip of your finger. I leave that as an exercise for the reader.)

By the tables, mid-totality in Greenwich occured at 04:43:31 GMT. Noon, on the prime meridian, is 12:00:00 GMT. But the "M" is for "mean" and "mean" is for "mean sun" and what is measured with sextants is not mean time but solar time. The difference between mean and solar time is given by the "equation of time" and on January 21, the difference amounts to 10m50s. In the real world, this complication arises because the Earth's orbit around the Sun is not a perfect circle but an ellipse. The speed of the Sun's motion across the sky varies slightly. It varies on a yearly cycle in step with the Earth's distance from the Sun. In northern-hemisphere winter, the Earth is nearest the Sun and races in its orbit a little faster than usual. In summer, the situation is reversed. This excess angular rate of revolution in winter takes away just a little from the motion of the Sun across the Earth's sky, so the Sun seems to cross the meridian a little later than it otherwise would. On January 21, the delay is 10 minutes and 50 seconds. An observer on the prime meridian would see the Sun cross the meridian at 12:10:50 GMT, not at straight up 12:00:00 "noon."

So, for any hypothetical observer in Greenwich, the interval between the middle of the eclipse and the next passage of the Sun across the meridian was:

(time of noon) - (time of mid eclipse) = interval
12:10:50 - 04:43:31 = 7h 27m 19s.

For an observer at Fort Cortner --Me!-- the actual, honest-to-god observed interval was 12h 52m 45s.

The difference between these two intervals is:

12:53:02 - 07:27:19 = 5h 25m 43s

5h 25m 43s is the observed longitude of Fort Cortner, though it is given in non-standard units. We need only convert from hours, minutes and seconds into degrees -- the angular distance the Earth rotates in that amount of time -- and that will be the longitude in its more usual form.

The key to this conversion is that the Earth spins exactly 15 degrees in one hour. In 5:25:43 the Earth spins 81.43o, so I am 81o26' west of Greenwich.

Checking the results:

It appears from this longitude and from the latitude derived earlier that I live somewhere between King's Creek, North Carolina, and the Cedar Rock Country Club. While that is true in a socio-economic sense, I happen to know that geographically Fort Cortner lies in the township of Cajah's Mountain. My derived latitude and longitude put me out on NC Highway 18, a day's modest hike east of where I live. In particular, by reference to a USGS map, I know the following:

My actual position: 35o52'N 81o32'W
My derived position: 35o58'N 81o26'W
Error in Latitude: 6.9 statute miles
Error in Longitude: 5.6 statute miles (!)
Total error: 8.8 miles.

The error in latitude shows that I am a novice with a sextant; a skilled navigator with an ocean horizon should get this measurement to within a couple of miles, every time.

The small error in longitude shows that the method can work (actually, it worked so well that I must have gotten lucky). My position is about twenty times more accurate than Lewis managed using the same method under much more arduous conditions. It's twice as accurate as the position Alexander Mackenzie derived through observations of the moons of Jupiter upon reaching the Pacific Coast of Canada in 1793. It's about as accurate as the positions recorded throughout Canada by the excellent frontier navigator David Thompson with incomparably more skill and experience.

To my surprise, the Mandan Moon could have been used to determine a reasonably accurate longitude for Lewis and Clark's winter camp. There was nothing futile about the attempt. Clouds, cold, and the need to reset a mechanical horizon seriously undermined Lewis's efforts, but they were not, in principle, ill-conceived.

David Cortner
Connelly's Springs, NC

Addendum:

In the November 2001 issue of We Proceeded On, the Journal of the Lewis and Clark Trail Heritage Foundation, Robert Bergantino provides an authoritative reduction of the Captains' lunar eclipse observations. They were better than Lewis knew. On the one hand, Bergantino addresses mistakes made in the field analysis of the observations (he corrects the Captains' sums), while I have been concerned with the other hand: the pragmatics of obtaining and using the observations.



The details of Lewis and Clark's observations of the eclipse of January 14 - 15, 1805, including the comparison of positions with those found by David Thompson, come from The Journals of the Lewis and Clark Expedition, Vol 3., editted by Gary E. Moulton, University of Nebraska Press, 1987. See the links at left for online access to the Journals.