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All night above their rocky bed, They saw the stars march slow;
The wild Sierra overhead, The desert's death below.
Frémont: The Pass of the Sierra, John Greenleaf Whittier, 1856

Watching the Heavens change
copyright Bob Graham 2002

February 24, 1844. Frémont: We rose at three in the morning, for an astronomical observation, and obtained for the place a latitude of 38° 46' 58"; longitude 120° 34' 20" . The sky was clear and pure, with a sharp wind from the northeast, and the thermometer at 2° below the freezing point.

That determination of latitude was made from observations of polaris--the north star. Why on earth would someone, after an exhausting day of traveling for miles down a steep mountain covered with ice and snow, get up at three in the morning and stand shivering in the cold to shoot polaris? Hadn't it been there all night? And wouldn't it still be there for hours yet before dawn. Why not after dinner, or before breakfast, instead of getting out of a warm sack in the middle of the night?
go This place was 41-mile Tract on Highway 50 near Strawberry.

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July 13, 2000. Near Carson Pass in the Sierra Nevada.
At about 11 p.m., by the light of a nearly full moon, I climbed up to Frémont's 1844 winter "Long Camp" to spend the night. I set down my sleeping bag right where you see Frémont's men in the snow hole. I had discovered this campsite in 1996 by following Frémont's narrative from the report of the expedition of 1843-44 and from his determination of latitude from polaris observations made on the night of February 14, 1844.

go See the Long Camp then and now.

As I lay there and looked at the same moonlit mountains and the stars above that they had seen in 1844, it came to me that the one thing that had changed the most in 156 years was the one thing that I hadn't expected to change--the stars.

NOTE: I have since learned that in 1872, in one great quake the Sierra rose 3', and moved NNW 20' in a few seconds. But still well within the resolution of Frémont's coordinates and determined elevation.

Here I have colorized Charles Preuss's 1844 drawing of the place and added a moon and a flickering fire.
Cozy, huh? You can almost hear the wolves howling at the moon. If you have the QuickTime plugin for your browser you can: start the player here.

Because of precession (wobble of earth's pole), in Frémont's day polaris was nearly 1.5 degrees from the celestial pole. Today it is only approximately 1 degree from that pole. Going back further in California history, polaris was nearly 3 degrees from the pole in 1579 when Francis Drake spent 37 days on the coast making repairs to his ship. Having spent as much time as I have following the trail of Frémont and the wake of Drake, it is almost as if I have been watching it move!

But why did Frémont get up at such an ungodly hour to look at a star that was there to see throughout the hours of darkness?

Edward Wright, in CERTAIN ERRORS IN NAVIGATION, 1590 wrote, "I must for the present only give the mariner warning that he not trust to it [the Pole-Star reading], being very erroneous, and grounded on two false positions." What was the problem with polaris?

Part of the problem, in a time before optics, was in determining just how far polaris actually was from the celestial pole. In Drake's time, various tables had put it at from 4°9' (Cortes) to about 3° (Bourne). That would be the maximum correction a sighting would require if the star was above or below the pole--without correction a sighting would be off that much (a lot!).

There is a way around this. When polaris is left or right of the celestial pole (exactly 9 or 3 on a virtual clock dial) the error is zero. If one has time, one waits until the handle of the Big Dipper and Cassiopia on the opposite side are horizontal to polaris, and at that time the altitude of polaris is the latitude. This is the sort of rule-of-thumb published in survival manuals. The other way around is a little nocturnal-like device (go See a nocturnal.) such as this one published by Martin Cortes about 1545. One is instructed to hold it up before him, facing polaris, and then to rotate the arm to configure it to match the current position of the Little Dipper. The correction is then read off the dial. The illustration is showing a bit more than 3°, but notice that it is calibrated for a maximum of 4° 9'--way too much. This prompted Edwin Wright's 1599 admonition about relying on polaris sighting.

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Of course, in the mid 19th Century, Frémont had the advantages of very accurate instruments and tables of ephemerides which give the polaris correction for any day, hour, minute, and second that the sighting might be made. So why three in the morning? From his Ephereris he would have been able to calculate the time during the hours of darkness that that position would require no correction--a direct reading of latitude. But that was not what he wanted; he wanted to know the time of the position requiring the maximum correction. Frémont was after a precise determination, and because he was not absolutely sure of his Greenwich Time, he wanted the apparent change of position to be at its slowest--adding or subtracting the correction in the process of the reduction of the reading presented no difficulty at all.

This phenomenon is most readily observable in the rising and setting of the sun. It appears to jump up fast at daybreak, hang in the sky at noon, and plunge rapidly to the horizon at sunset. The sun does not, of course, actually speed up and slow down in its transit of the sky. (Yes, I accept that it is really the earth that rotates, but I get dizzy thinking that way.) A simple diagram (rise over run) will graphically demonstrate the reason for the apparent rate of change. Notice how rapidly the sun rises in the sky in the first hour between 6:00 and 7:00 and how little it rises between 11:00 and Noon. It is just the reverse in the afternoon hours. And it is exactly the same with polaris.

So on February 24. 1844 Frémont and Kit Carson did get up at 3:00 a.m., The determination of latitude is very good. You can go there and find the only place they could have stood to take this sighting. The canyon itself is used as the second line of position, because of problems he had been having with the chronometer. His longitude determinations on this part of the journey are off by over 20 miles. Not bad, considering that it had stopped altogether near Bridgeport, and he had been able to re establish Greenwich Time this well from telescopic observations of the moons of Jupiter. Twenty miles is good enough to make a landfall at sea. He later was able to refine this time to make very good determinations of longitude on the return leg of the expedition.
go See the place.

The results are shown on this page from the Astronomical Tables of his Report. The altitudes are doubled, because he used an artificial horizon in his sextant sightings.

go What is an artificial horizon

Polaris was also used to establish the latitude of his "Long Camp" (above) near Carson Pass at the crest of the Sierra Nevada in the winter of 1844. He recorded it on February 14, after having climbed 10,000' Red Lake Peak earlier in the day to be the first man to record having seen Lake Tahoe. That night, taking 10 sightings of polaris, he determined his latitude to be 38° 41' 03". In 1996, with a GPS receiver, I located the campsite by walking along that line of latitude. Since then, the DOD has removed Selective Availability from the GPS signal; currently, I make the latitude to be N38° 41' 02" longitude W119° 57' 18" el. 8087' (EPE=6'). Not bad!

Frémont has particularly touched my imagination. What a wild life, and what a fresh kind of existence! But, ah, the discomforts! Henry Wadsworth Longfellow

go A climb from Long Camp and the sighting of Lake Tahoe from Red Lake Peak on February 14, 1844.

go DETERMINATION OF LATITUDE BY FRANCIS DRAKE ON THE COAST OF CALIFORNIA IN 1579
go AN EXPERIMENT IN THE DETERMINATION OF LATITUDE: This is a followup to the proceeding article, in which the conclusions made therein are put to practical test that may be repeated by anyone wishing to go to the trouble.
go A DAY AT THE COVE: An actual on-site demonstration of the determination of latitude with an astrolabe at Campbell Cove before a group of interested spectators.
go See a comparison of the TABLES OF SOLAR DECLINATION by Martin Cortes with those of William Bourne.

Dunkerque, December 30, 1795.

"Precision is painstaking work. It demands precautions, stratagems planned like war. [Jean-Baptiste-Joseph] Delambre used astronomical theory to prepare his observations. He verified the verticality of his [Borda's repeating] circle by three different methods. He drew up formulas to correct his data for refraction and temperature. He estimated in advance the best precision he could expect. And only then did he begin his sightings of Polaris, a star particularly suitable for assessing latitude because its proximity to the pole meant that its angular height as it crossed the celestial meridian would, with only minimal correction, supple the angular distance of the observer from the equator.--or, in other words, his latitude.

"His thirty-eight observations of Polaris as it transited the celestial meridian below the pole gave him a latitude of 51° 3' 16.66", which shifted by a minuscule 0.06 seconds when he removed his least reliable data. The two hundred results for its transit above the celestial pole were trickier, due to the cloud cover, and differed by one full second with the earlier results. But when he excluded the less reliable data, the difference narrowed to within .5 seconds (or some twenty-five feet). It was another demonstration of the repeating circle's precision, as well as a testament to Delambre's preparation, skill, and integrity."
Ken Alder, The Measure of All Things

Frémont of his mentor Joseph N. Nicollet on the survey of the upper Mississippi and Missouir Rivers in 1839.

"In all this stir of frontier life Mr. Nicollet felt no interest and took no share; horse and dog [the hunt] were nothing to him...To him an astronomical observation was a solemnity, and required such decorous preparation as an Indian makes when he goes to where he thinks there are supernatural beings. 'C'est toujours comme ca chez vous,' he said. Instead of occupying your mind with these grand objects, you give your attention to insect things [biology]."


©1999, 2007
Bob Graham