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Frémont and the Determination of Elevations

Previous to the commencement of the nineteenth century, not a single altitude had been barometrically taken in the whole of New Spain...Our knowledge of the configuration [of the Great Basin] is one of the chief points of Frémont's great hypsometrical investigations in the years 1842 and 1844.
Baron Friedrich Heinrich Alexander von Humboldt, Kosmos, 1845-62.
The Prussian Orden Pour le Mérite für Wissenschaften und Künste personally presented to Frémont by Baron von Humboldt in 1860.

Never before had anyone attempted to measure the Altitude of an American mountain with a barometer.
William H. Goetzmann, Army Exploration of the American West

Prefatory note:
Skip this and go straight to article

Since writing what follows in 1996, I have continued to read whatever I could find about mid 19th century hypsometrical technologies and understanding of meteorological phenomenon. Three works, in particular, which shed light on Frémont's understanding of hypsometrical principles are J. N. Nicollet's (U. S. Corps of Topographical engineers, and Frémont's mentor and teacher) Essay on Meteorological Observations, 1839; Major (Army Corps of Engineers) R. S. Williamson's On the Use of the Barometer on Surveys and Reconnaissances, 1868; General A. W.Greely's (Chief Signal Officer, U. S. Army) American Weather, 1888.

These three works illustrate the beginning of the development of an understanding about weather systems. Nicollet, French Legend of Honor member, eminent astronomer and mathematician, was the foremost surveyor and mapmaker of his day. He had introduced the use of the barometer in American survey work. Yet, his 1839 essay is primarily a series of questions about weather and suggestions for study and examination. It represents the state of the art at the time of Frémont's 2nd Expedition - the most ambitious and comprehensive survey of the West undertaken at the time.

Major Williamson's 1868 essay is particularly valuable as the work cited was all carried out on the West Coast. The stations referred to are San Francisco, Mt. Diablo, Sacramento, Strawberry, Hope Valley --all places that Frémont visited and mapped. Williamson was chiefly endeavoring to establish a system of determining barometric means for different locations. He refers to the variations of the barometer as horary (diurnal) versus abnormal oscillations. Of the latter, Williamson was concerned with local weather; the understanding of global weather systems was still such that Williamson says, "There is no apparent reason why the barometer should rise on a particular day rather than fall."
go Available on-line from the University of Michigan, the entire text of On the use of the Barometer on Surveys and Reconnaissances. Williamson, Robert Stockton, New York, D. Van Nostrand; London, Trübner & Co., 1868.

William H. Brewer (seated at right) was Chief assistant in the Whitney Survey. His letters of 1860 - 64, published in Up and Down California, Yale University Press, 1930, are of great interest. In weather, and therefore barometric hypsometry, the exceptions always outnumber the rules. All these men were competent and dedicated observers. If the results of their observations give results not agreeing with modern maps, it is only because their means of observing and reducing were inadequate. It is interesting to note, that in spite of years of progress, Frémont's 15,000' estimate (with sextant) in 1844 of the height of Mt. Shasta was closer to the actual 14,440' than Williamson's 18,000' estimate in 1862.
In the photo at right are shown the barometer cases slung over the shoulder, sextant, botany box, rock hammer, and rifle.

General Greely's work moves much closer to a modern understanding of the principles governing weather - where local weather is determined by fluctuations in the system of global forces and changes.

One further mention should be made regarding the referencing of the instruments. Frémont's instruments, barometers in particular, were referenced to those of Dr. Engleman at the observatory in St. Louis--the starting point of these surveys. But the barometers never made the return trip intact; all failed to survive the rigors of travel. Therefore, they could not be checked on the return to ascertain if they remained in agreement.

go At the bottom of this page is a kitchen experiment in the use of the thermometer in determining elevation.

go My views on the debated route and identity of the Rocky Mountain peak Frémont conquered in 1842. Includes the barometric readings taken on the ascent.

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Frémont and the Determination of Elevations
Copyright © 1996 (revised 2003) by Bob Graham

Throughout the reports of Frémont's first and second expeditions, elevations are given for points reached on the routes, of passes through the mountains, and of mountain peaks. The measurement of heights, with reference to sea- level, is called hypsometry. In becoming a topographical engineer, Frémont had received training under Joseph Nicollet, a pioneer in the application of this science in surveys. In order to trace the route of the expedition it is necessary to understand what was involved in making altitude determinations, and how much importance they must be given in deciding on a locality that is identified as being of some particular elevation.

At the time, besides triangulation, elevations could be measured in two, interrelated ways. Basic to both methods was the barometer, which measures the weight of the column of air above it--the higher the barometer is carried, the less the air there is above it, and the less that air weighs. The standard barometer at that time, as it still is today, was the mercury barometer. It is a simple, but precisely made, device consisting of a glass tube about three feet long, sealed at one end, which is filled with pure mercury, and inverted into a cistern also filled with mercury. The mercury flows out of the tube into the cistern, leaving a vacuum in the top of the tube, until it reaches equilibrium with the weight of the atmosphere pressing down on the surface of the mercury in the cistern. The height of the column of mercury in the tube is then precisely measured on an attached scale with reference to the surface of the mercury in the cistern. At mean sea level, and at 32°f, and at mean atmospheric pressure, the column will stand at 29.922" above the surface of the mercury of the cistern, and the altitude would be zero feet. Mercury is used because it is heavy; water can be used, but the instrument needs to be nearly 30 feet tall. Within a few years of , the anneroid barometer would also be used in determining elevations, but because it is not a direct reading instrument, it must always be referenced to the mercury barometer.

The type of barometer used in survey work was a portable device called a mountain barometer. By carefully tipping the tube, the mercury would move to the top of the tube, filling it, and the bottom of the cistern is raised to keep it there. It could then be moved safely without spilling, or allowing air to enter the tube that would render it useless. It was transported in a wooden case to protect it from breaking.

go A description of Frémont's barometers, including a remarkable field repair in 1842.

If a barometer is taken to the top of an elevation above the level of the sea, the column of mercury will no longer stand at about 30", as it did at sea level, but at some lesser height--say, 27.50". You then know that you have ascended into the column of air, that is the atmosphere, and that there is not as much of it above you as there had been at sea level. But, how far up have you gone?

The mathematics for determining the elevation based on the reading of the barometer can be very complicated. Compensations must be made for the mean temperature (density) of the air column, if it is other than 32°f; for the humidity of the air column; and for the latitude (local acceleration of gravity); and even for the expansion and contraction of the metal of the brass scale. A simplified formula for elevations under 20,000' standardizes all the above to:

Z= 62,900 log10 P0/P, where Z=altitude in feet, P=pressure at the upper limit in any units, and P0=pressure in same units as above corresponding to zero altitude.

go A program for use in HP programable calculators, and an Excel spreadsheet.

Using this formula, the 27.50"Hg that was recorded on the mountain in the example above comes out to 2359' elevation above mean sea level. But, only if the pressure at sea level was still at 30". If the sea-level pressure had changed, and it's always changing, then the elevation wouldn't be 2359', but something else. And if you cannot know what the pressure is at sea-level, and sea-level not far removed laterally, and at the same time you measure the upper level, you can't know what 27.50'Hg means; except, that it might be between about 1825' and 2693'. These are extremes, and most of the time you would be much closer to the actual elevation.

The problem with the results of these computations is that they must always be referenced to sea level. The atmospheric pressure is constantly changing--it is as changeable as the weather. So, how do you know what the current sea level pressure is? In 1844 you could not know if you were out of signal-distance from the sea, or some other point that had previously been surveyed and referenced to the sea. So you had to use a mean--an average pressure that been established over long periods of observation. For the West Coast this mean has a high of 30.05" in January, and a low of 30.00" in April, but the range in these months, in the course of a few days, can be nearly an inch, from as low as 29.4" to as high as 30.35". If one had the time, means can be established by many observations at one station taken over a period of days, months, and years. This was how you would carry out a topographical survey. But, you hadn't time for that on an exploratory expedition, so, at best, only a general indication of relative elevations of routes, mountain ranges, and passes could be obtained.

Mountain barometers are fragile things when packed on mules traveling in rough terrain. Frémont had two on this expedition that were calibrated in St. Louis before starting out: a siphon barometer (of the type invented by Guy Lusak) by Bunten, of Paris, and a cistern barometer (similar to Fortin's design) by Frye and Shaw, of New York. Both were broken before he reached the Sierra Nevada; however, there is another way to determine elevation above the sea that he could still use.

Water boils at 212°f. at a sea-level pressure of 29.922"Hg. At higher elevations, the atmospheric pressure being less, water boils at a lower temperature, which is why it takes longer to boil an egg at Lake Tahoe than it does in Sacramento. At Lake Tahoe, on average, water boils at only about 201°f. By measuring the temperature of boiling water, consulting a Steam Table, and interpolating between the listed figures, the temperature can be converted to tension in inches of mercury ("Hg). From that point, the same computations used in barometrical observations can be used. This was the method resorted to in determining elevations during the part of the expedition of 1843-44 while crossing the Sierra.

There are many difficulties associated with using a thermometer to measure the boiling point of water. When thermometers are calibrated, the bulb is not actually submerged in the water, but is suspended in a column of steam. If the method used to measure the boiling water is not the same as that used in the manufacture of the thermometer, the results will be different. The water boiled must be pure; melted snow would do, but anything dissolved in the water (like mule cooking) would lower the boiling point and falsely indicate a higher elevation than otherwise. Two years later, in 1845, Victor Regnault would invent a portable Hypsometer (at right) for making accurate boiling-point measurements, in the same manner in which thermometers are calibrated. But Frémont could have had no such device, and must have actually entered the bulb of the thermometer into a pot of boiling water over the campfire.

Good thermometers are also inherently less accurate than good barometers. In any collection of thermometers, it is actually unusual to find any that agree. The bore of the tube must be perfectly uniform throughout the length of the scale, and thermometers are calibrated from only two fixed-points--32°f. and at 212°f. All points in between are arrived at by equally dividing the intervening space. Due to small variations in bore, these divisions may not be accurate throughout the range of the instrument. It was presumed, but was not always the case, that the fixed-point calibration for the boiling point was made at an atmospheric pressure corresponding to that of mean sea level.

Thermometers, glass being a fluid, age--especially in the first year or so after manufacture. Eventually they don't register the same as when they were made. They must then be re-calibrated, re-scaled, or replaced. No details of the thermometers carried on the expedition are given, but it is recorded in the expense account that five thermometers (types unspecified) were purchased from Frye and Shaw, in New York, and there would also have been thermometers attached to the cases of both barometers. A comparison of the readings of the thermometers attached to the two barometers carried on Frémont's Expedition of 1842 shows a variation of from .7 to 6.5°f, within a range of only 54-83.5°f. Without being able to reference to current sea level atmospheric conditions a mean pressure must be used.

The biggest problem with the results of Frémont's calculations is that, for some reason, he merely subtracted the observed boiling point from 212°f. and multiplied the difference by the constant factor of 644'. This cannot produce accurate results, as the pressure exerted by the column of air is not linear; it is logarithmic. One wonders if the Topographical Bureau wasn't just a little behind the times.

What does this all mean in regards to locations mentioned in the report? At the pass where they crossed, what does "The temperature of boiling water [197.5°f] gave for the elevation of this encampment, 9,338 feet above the sea." really mean? Must a pass that high be found where they might have crossed? Some seem to have thought so.

This elevation was determined by subtracting 197.5°f from 212°f and then multiplying the remainder by 644'. Simple, but the method is wrong. Had he used steam tables to convert the 197.5°f. to inches of mercury, he would have found the equivalent to be 22.27Hg. By using more tables, or a formula, he would have determined the elevation to be 8,374' at a mean sea-level pressure of 30.05'Hg--the mean for their position in February. Using a step-system table of that period, a similar result of 8,346'el. is obtained.

However, Carson Pass, where they crossed, is actually about 8,600'--not something less than 8,400'. To make things come out right, the sea-level barometer would have had to be standing at 30.5'Hg. But a pressure of over 30.3' Hg is unusual, so only part of the discrepancy can be accounted for. Each degree below the boiling point of 212°f, at this general altitude, we must add about 550 feet. But an error of a fraction of a degree, due to the thermometer itself, or the method of taking the measurement, can account for this discrepancy.

Near Sutter's Fort, on March 10, 1844, Frémont recorded the boiling point of water at 211.6°f., and the weather as "brisk S. wind; sky nearly clear", at 4:20 P.M. But, on the 11th, "light rain". He did not calculate or record the elevation, which, using his formula of 644' per 1°f. below 212°f., would have yielded a result of 257', which he knew that was at least 200 feet too high. Under mean atmospheric conditions in March (30"Hg), water at Sacramento should boil at about 211.8°f. If his thermometer and observation were correct, and the water did boil at precisely 211.6°f, it would indicate that the barometer was standing at about 29.77"Hg. That would account for the weather change the following day. This illustrates the problems with the published elevations of the Reports. Throughout most of the crossing, they had unusually good weather, or the Report could never have been written.

A note in concluding: All of the barometric observations taken on the 1st and 2nd expeditions were conventionally reduced using established protocol and algorithms and to the only base data available--Dr. George Engelmann's observatory at St. Louis.
But, on the 2nd expedition when boiling point observations were made following the breakage of the barometer, the means of reduction seemed to have eluded Frémont and Engelmann.
The means was at hand; steam tables. These would convert the observed temperature to tension in "Hg, and the reductions could then have been carried on in the same identical way that the barometric observations were reduced.
They did not seem to make this connection in theory. Surely, Nicollet (a student of Laplace), who had trained both Frémont and Engelmann, could have directed them; but Nicollet had recently died.
The method to which they resorted was some published rule-of-thumb of 644' per 1°f below 212°f.
I know this because I back-figured all the determinations and they all came ot evenly to this 644' constant. Many of these rules were published at the time, the constant varying depending on the intended, very limited, range of elevations encountered.

In the case of Frémont's observations for elevation made in the Sierra crossing, the data is just fine, but you cannot track him by it, because his method was wrong. However, once the site from which the observation was made is located, and the actual elevation known, the Frémont data becomes very valuable as an historical climatological record.

Only sixteen years after Frémont crossed the Sierra, in the years 1860--1864, Major Robert S. Williamson of the Army Corps of Engineers set up observation stations in San Francisco, Mt. Diablo, Sacramento, Strawberry, Hope Valley, and east slope stations at Carson City and Fort Churchill--all places that Frémont visited and mapped on his 1844 crossing. Twice daily records were made over this four year period. Major Williamson's On the Use of the Barometer on Surveys and Reconnaissances was published in 1867. He was endeavoring to establish a system of determining barometric means for these different locations. Williamson was concerned with local weather; the understanding of global weather systems was still such that Williamson says, "There is no apparent reason why the barometer should rise on a particular day rather than fall."

This can be contrasted with the following thoroughly modern description of the mechanics of the climate of California written by Frémont in his 1848 Geographical Memoir Upon Upper California.

It [Sierra Nevada] is a grand feature of California, and a dominating one, and must be well understood before the structure of the country and the character of its different divisions can be comprehended.

It divides California [here as a more global reference which includes the Great Basin] into two parts, and exercises a decided influence on the climate, soil, and the productions of each.

Stretching along the coast, and at a general distance of 150 miles from it [here again, the large picture], this great mountain wall receives the warm winds, charged with vapor, which sweep across the Pacific ocean, precipitates their accumulated moisture in fertilizing rains and snows upon its western flank, and leaves cold and dry winds to passage on to the east. [now called the Rain Shadow]

Hence the characteristic differences of the two regions [today's state of California and the Great Basin]--mildness, fertility, and a superb vegetable kingdom on one side, comparative barrenness and cold on the other.

Thus December, on one side of the mountain, was winter, and on the other side it was spring.

go Frémont's contributions to meteorology.

Considering the then state of the science, that his barometers had been broken, and the impossibility of his reducing any measurement to sea level, Frémont's ingenuity under very difficult conditions yielded results as good as, and as useful as, any other method.

EXAMPLE: Sacramento, March 10th, 1844 - Frémont records the boiling point of water at 211.6°f., and the weather as "brisk S. wind; sky nearly clear", at 4:20 P.M. But, on the 11th, "light rain". He did not calculate or record the elevation, which, using his formula of 644' per 1°f. below 212°f., would have yielded a result of 257' el.--he knew that was at least 200 feet too high. Under mean atmospheric conditions in March (30"Hg), our water should boil at about 211.8°f. If his thermometer and his observation were correct, and the water did boil at precisely 211.6°f., it would indicate that the barometer was standing at about 29.77"Hg. That would account for the weather change (rain) the following day. This illustrates the problems with the published elevations of the Reports. Throughout most of the crossing, they had unusually good weather (a high-pressure ridge), or the Report could never have been written.

The aneroid, or holosteric, barometer did not exist in reliable form at the time of Frémont's expeditions. They began to be used in survey work in the 1850s, but because they are not a direct reading instrument, only as an adjunct to the mercury barometer; they must be frequently referenced to the mercury barometer, or to a known elevation. My own 1920s Short & Mason 2 1/2 inch Tycos barometer is shown at right.

go Hypsometrical results from the 1855 Sierra Nevada wagon road survey by George H. Goddard and Sherman Day.

An Experiment in the use of the thermometer in determining elevations.
Frémont, Fort Laramie, July 1842--We had the misfortune to break here a large thermometer, graduated to show fifths of a degree, which I used to ascertain the temperature of boiling water, and with which I had promised myself some interesting experiments in the mountains. We had but one remaining, on which the graduation extended sufficiently high; and this was too small for exact observations.

August 7, 2001.

I recently obtained a 220° Taylor lab thermometer on ebay. Today I rigged a Rube Goldberg-ish sort of hypsometer on the kitchen range, and measured the boiling point at 213° f.
Using Fremont's faulty rule-of-thumb conversion, I found that he would have calculated -644 feet elevation today--the elevation is actually about 25".
Corrected for sea level, the barometer was standing at 30.49"hg, which corresponds to 30.64 at my actual elevation.
Using my own go calculator program and spreadsheet, which use the equasions above, I came up with an elevation of 51'. My actual elevation is nearer to 25', but quite good results, as this thermometer is graduated only in whole degrees.
So, the easiest way to find out how high up you are, is to start out knowing how high up you are.

Another way (in an extremity).

Frémont, Platte River, August 24, 1842--We had no thermometer to ascertain the temperature [of the hot spring], but I could hold my hand in the water just long enough to count two seconds.

I'm not planning to experiment with this one, but it demonstrates Frémont's determination to collect data using any method at his disposal. He no-doubt intended to repeat the experiment later with a thermometer.

go Another hypsometrical experiment, by none other than Mark Twain!

The mountain barometer.
go Frémont's methods of determining coordinates.
A history of Frémont 's training in mathematics, navigation, and mapmaking.
Find out how correcting errors in the published coordinates in Frémont's 1845 Report led to the discovery of his "Long Camp" site.
Or, to see a study of the determination of latitudes by Francis Drake, and how the errors in those determinations point to the actual location of his 1579 California landfall.

A brief bibliography:

Blodget, Lorin, Climatology of the United States and the Temperate Latitudes of the North American Continent, J. B. Lippincott and Co., Philadelphia: 1857.

Bowditch, Nathaniel, Ll. D., The New American Practical Navigator, E. and G. W. Blunt, New York, 23rd Edition, 1853.

Eaton, Herbert N, A.M., et. al., Aircraft Instruments, The Ronald Press Company, New York, 1926.

Frémont, Brevet Captain J. C., Report of The Exploring Expedition to the Rocky Mountains in the Year 1842, and to Oregon and North California in the Years 1843-'44, Printed by order of the Senate of the United States, Gales and Seaton, Washington. 1845.

Greely, Gen. A. W., American Weather, Dodd, Mead & Company, New York, 1888.

Knight, Edward H., Knight's American Mechanical Dictionary, J. B. Ford and Company, New York, 1874-1879.

Negretti & Zambra, A Treatise on Meteorological Instruments, London, 1864.

Nicollet, J. N., Essay on Meteorological Observations, Printed by order of the War Department, Washington, 1839.

Middleton, W. E. Knowles, A History of the Barometer, The Johns Hopkins Press, Baltimore, 1964.

Middleton, W. E. Knowles, A History of the Thermometer, The Johns Hopkins Press, Baltimore, 1966.

Smithsonian Meteorological Tables [Based on Guyot's Meteorological and Physical Tables] Second Edition (1893) - Smithsonian Miscellaneous Collections - 1032.

Williamson, R. S., On the Use of the Barometer on Surveys and Reconnaissances; part I, Meteorology in its Connection with Hypsometry; part II, Barometric Hypsometry; D. Van Nostrand, New York, 1868.
go Entire text now available online!

Plympton, George W., The Aneroid Barometer; Its Construction and Use, D. Van Nostrand Company, New York, 1884.

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Bob Graham