# Thomas Jefferson to Alden Partridge, 2 January 1816

# To Alden Partridge

Monticello Jan. 2. 16.1

Sir

I am but recently returned from my journey to the neighborhood of the Peaks of Otter, and find here your favors of Nov. 23 & Dec. 9. I have therefore to thank you for your meteorological table and the Corrections, of Colo Williams’s altitudes of the mountains of Virginia which I had not before seen; but especially for the very able extract on Barometrical measures. the precision of the calculations, and soundness of the principles on which they are founded furnish, I am satisfied, a great approximation towards truth, and raise that method of estimating heights to a considerable degree of rivalship with the trigonometrical. the last is not without some sources of inaccuracy, as you have truly stated. the admeasurement of the base is liable to errors which can be rendered insensible only by such degrees of care as have been exhibited by the Mathematicians who have been employed in measuring degrees, on the surface of the earth. the measure of the angles, by the wonderful perfection to which the graduation of instruments has been brought by a Bird, a Ramsden, a Troughton, removes nearly all distrust from that operation; and we may add that the effect of refraction, rarely worth notice in short distances, admits of correction by2 well established laws. these sources of error once reduced to be insensible, their geometrical employment is certainty itself. no two men can differ on a principle of trigonometry. not so, as to the theories of Barometrical mensuration. on these have been great differences of opinion, and among characters of just celebrity.

Dr Halley reckoned 1⁄10 I. of mercury equal to 90.f. altitude of the atmosphere:

Derham thought it equal to something less than 90.f.

Cassini’s tables | to 24° of the Barometer allowed | 676. toises of altitude; |

Mariote’s | to the same | 544. toises |

Scheuchzer’s | to the same | 559. toises |

Nettleton’s tables applied to a difference of .5975 of mercury, in a particular instance gave 512.17 f. of altitude, and Bouguer’s & DeLuc’s rules, to the same difference gave 579.5 f Sr Isaac Newton had established that at heights in Arithmetrical progression the ratio of rarity in the air would be geometrical; and this being the character of the Natural numbers and their Logarithms, Bouguer adopted the ratio in his mensuration of the mountains of S. America, and, stating in French lignes the height of the mercury at different stations, took their Logarithms to 5 places only, including the index, and considered the resulting difference as expressing that of the altitudes in French toises. he then applied corrections required by the effect of the temperature of the moment on the air and mercury. his process, on the whole, agrees very exactly with that established in your excellent extract. in 1776. I observed the height of the mercury at the base and summit of the mountain I live on, and, by Nettleton’s tables, estimated the height at 512.17 f. and called it about 500.f. in the Notes on Virginia. but calculating it since, on the same observations, according to Bouguer’s method with De Luc’s improvements, the result was 579.5 f. and lately I measured the same height trigonometrically, with the aid of a base of 1175.f in a vertical plane with the summit, and at the distance of about 1500. yards from the axis of the mountain, and made it 599.35 f. I consider this as testing the advance of the barometrical process towards truth by the adoption of the Logarithmic ratio of heights and densities; and continued observations and experiments will continue to advance it still more. but the first character of a common measure of things being that of invariability, I can never suppose that a substance so heterogeneous & variable as the atmospheric fluid, changing daily and hourly it’s weight & dimensions to the amount sometimes of one tenth of the whole, can be applied as a standard of measure to any thing with as much Mathematical exactness as a trigonometrical process. it is still however a resource of great value for these purposes, because it’s use is so easy, in comparison with the other, and especially where the grounds are unfavorable for a base; and it’s results are so near the truth as to answer all the common purposes of information. indeed I should in all cases prefer the use of both, to warn us against gross error, and to put us, when that is suspected, on a repetition of our process. when lately measuring trigonometrically the height of the peaks of Otter (as my letter of Oct. 12. informed you I was about to do) I very much wished for a barometer, to try the height by that also. but it was too far and too hazardous to carry my own, and there was not one in that neighborhood. On the subject of that admeasurement, I must premise that my object was only to gratify a common curiosity as to the height of those mountains, which we deem our highest, and to furnish an à peu près, sufficient to satisfy us in a comparison of them with the other mountains of our own, or of other countries. I therefore neither provided such instruments, nor aimed at such extraordinary accuracy in the measures of my base, as abler operators would have employed in the more important object of measuring a degree, or of ascertaining the relative position of different places for astronomical or geographical purposes. my instrument was a theodolite by Ramsden, whose horisontal and vertical circles were of 3½ I. radius it’s graduation subdivided by Noniuses to 3.′ admitting however by it’s intervals, a further subdivision by the eye to a single minute, with two telescopes, the one fixed, the other moveable, and a Gunter’s chain of 4. poles, accurately adjusted in it’s length, and carefully attended on it’s application to the base line. the Sharp, or Southern peak was first measured by a base of 2806.32 f. in the vertical plane of the axis of the mountain. a base then nearly parallel with the two mountains of 6589 f. was measured, and observations taken at each end, of the altitudes and horizontal angles of each3 apex, and such other auxiliary observations made as to the stations, inclination of the base Etc as a good degree of correctness in the result would require. the ground of our bases was favorable, being an open plain of close grazed meadow, on both sides of the Otter river, declining so uniformly with the descent of the river as to give no other trouble than an observation of it’s angle of inclination, in order to reduce the base to the plane of the horizon. from the summit of the sharp peak I took also the angle of altitude of the flat or Northern one above it, my other observations sufficing to give their distance from one another.

the result was, | the mean height | of the Sharp peak above | f |

ye surface of Otter R. | 2946.5 | ||

of the flat peak | 3103.5 | ||

the distance between the two summits | 9507.73 |

their rhumb N. 33° 50′ E. the distance of the stations of observation from the points in the bases of the mountains vertically under their summits was the shortest 19002.2 f. the longest 24523.3 f. these mountains are computed to be visible to 15. counties of the state, without the advantage of counter-elevations, and to several more with that advantage. I must add that I have gone over my calculations but once, and nothing is more possible than the mistake of a figure, now and then, in calculating so many triangles, which may occasion some variation in the result. I mean therefore, when I have leisure, to go again over the whole. The ridge of mountains of which Monticello is one, is generally low. there is one in it however, called Peter’s mountain, considerably higher than the general ridge. this being within a dozen miles of me North Eastwardly, I think, in the spring of the year, to measure it by both processes, which may serve as another trial of the Logarithmic theory. should I do this you shall know the result. in the mean time accept assurances of my great respect & esteem

Th: Jefferson

RC (NN); addressed: “Capt A. Partridge Norwich Windsor county Vermont”; franked; postmarked Milton, 3 Jan. PoC (DLC).

Edmond halley published his findings on the relationship between the height of mercury and altitude in “A Discourse of the Rule of the Decrease of the Height of the Mercury in the Barometer, according as Places are elevated above the Surface of the Earth,” Royal Society of London, Philosophical Transactions 16 (1686/92): 104–16. William derham found in his experiments that mercury in a barometer would drop 1⁄10 of an inch at an elevation of either 80 or 82 feet (“Part of a Letter of Mr. William Derham … Giving an Account of some Experiments about the Heighth of the Mercury in the Barometer, at Top and Bottom of the Monument,” Philosophical Transactions 20 [1698]: 2–4). For one version of the tables of Jacques Cassini, Edme Mariotte, and Johann J. Scheuchzer, see John G. Scheuchzer, “The Barometrical Method of measuring the Height of Mountains, with two new Tables shewing the Height of the Atmosphere at given Altitudes of Mercury,” Philosophical Transactions 35 (1727/28): 537–47. Thomas nettleton’s tables were published as “Observations concerning the Height of the Barometer, at different Elevations above the Surface of the Earth,” Philosophical Transactions 33 (1724/25): 308–12.

TJ obtained the rules of Pierre Bouguer and Jean André Deluc for estimating heights barometrically from the entry on barometers in the Dictionnaire de Physique (Paris, 1793; forming part of the Encyclopédie Méthodique [Paris, 1782–1832; no. 4889]), and he copied his resulting notes into his Weather Memorandum Book, 1776–1821 (DLC). Sir isaac newton discussed the relationship between height and air density in The Mathematical Principles of Natural Philosophy, trans. Andrew Motte (London, 1729; repr. London, 1803; no. 3721), 2:57–60. Bouguer published his mensuration of the mountains of South America in La Figure de la Terre, Déterminée par les Observations de Messieurs Bouguer, & de la Condamine (Paris, 1749; no. 3804).

lignes are equal to a twelfth of an inch ( ). TJ’s 15 Sept. 1776 calculation that Monticello was 512.17 feet in height can be found in his Weather Memorandum Book, 1776–1821 (DLC). In his Notes on the State of Virginia, TJ described Monticello’s summit as being 500.f in “perpendicular height above the river which washes its base” ( , 76). à peu près: “approximation.”

1. Reworked from “15.”

2. TJ here canceled “known laws.”

3. TJ here canceled “peak.”

# Index Entries

- altitude; barometers used to calculate search
- altitude; calculations for Peaks of Otter search
- altitude; of Monticello search
- altitude; of Peter’s Mountain search
- barometers; altitude calculated with search
- Bird, John; scientific-instrument maker search
- Bouguer, Pierre; and barometric calculation of altitude search
- Bouguer, Pierre; La Figure de la Terre search
- Cassini, Jacques Dominique de; and barometric calculation of altitude search
- Davis, William; editsThe Mathematical Principles of Natural Philosophy (I. Newton; trans. A. Motte) search
- Deluc, Jean André; and barometric calculation of altitude search
- Derham, William; and barometric calculation of altitude search
- Dictionnaire de Physique search
- Encyclopédie Méthodique search
- Halley, Edmond; and barometric calculation of altitude search
- Jefferson, Thomas; Travels; to Peaks of Otter search
- Jefferson, Thomas; Writings; Notes on the State of Virginia search
- La Figure de la Terre (P. Bouguer) search
- Mariotte, Edme; and barometric calculation of altitude search
- mathematics; logarithms search
- mathematics; trigonometry search
- meteorological observations; by A. Partridge search
- Monticello (TJ’s estate); altitude of search
- Motte, Andrew; translatesThe Mathematical Principles of Natural Philosophy (I. Newton; ed. W. Davis) search
- Nettleton, Thomas; and barometric calculation of altitude search
- Newton, Sir Isaac; and barometric calculation of altitude search
- Newton, Sir Isaac; The Mathematical Principles of Natural Philosophy (ed. W. Davis; trans. A. Motte) search
- Notes on the State of Virginia (Thomas Jefferson); and altitude of Monticello search
- Partridge, Alden; and calculation of altitude search
- Partridge, Alden; letters to search
- Partridge, Alden; meteorological observations search
- Peaks of Otter, Va.; altitude of search
- Peaks of Otter, Va.; TJ visits search
- Peter’s Mountain (Southwest Mountains); altitude of search
- physics; barometric calculation of altitude search
- Ramsden, Jesse; scientific-instrument maker search
- Ramsden, Jesse; theodolite of search
- Royal Society of London; transactions of search
- Scheuchzer, Johann J.; and barometric calculation of altitude search
- scientific instruments; barometers search
- scientific instruments; theodolites search
- Southwest Mountains; altitude of search
- surveying; and chain search
- The Mathematical Principles of Natural Philosophy (I. Newton; ed. W. Davis; trans. A. Motte) search
- theodolite search
- Troughton, Mr.; scientific-instrument maker search
- Williams, Jonathan; and altitude calculations search