TO CAPT. A. PARTRIDGE OF THE CORPS OF ENGINEERS, WEST POINT, NEW YORK.
Monticello, October 12, 1815.
Sir,—I thank you for the statement of altitudes, which you have been so kind as to send me of our northern mountains. It came opportunely, as I was about making inquiries for the height of the White Mountains of New Hampshire, which have the reputation of being the highest in our maritime States, and purpose shortly to measure geometrically the height of the Peaks of Otter, which I suppose the highest from their base, of any on the east side of the Mississippi, except the White Mountains, and not far short of their height, if they are but of 4,885 feet. The method of estimating heights by the barometer, is convenient and useful, as being ready, and furnishing an approximation to truth. Of what degree of accuracy it is susceptible we know not as yet; no certain theory being established for ascertaining the density and weight of that portion of the column of atmosphere contiguous to the mountain; from the weight of which, nevertheless, we are to infer the height of the mountain. The most plausible seems to be that which supposes the mercury of barometer divided into horizontal lamina of equal thickness; and a similar column of the atmosphere into lamina of equal weights. The former divisions give a set of arithmetical, the latter of geometrical progressionals, which being the character of Logarithms and their numbers, the tables of these furnish ready computations, needing, however, the corrections which the state of the thermometer calls for. It is probable that in taking heights in the vicinity of each other in this way, there may be no considerable error, because the passage between them may be quick and repeated. The height of a mountain from its base, thus taken, merits, therefore, a very different degree of credit from that of its height above the level of the sea, where that is distant. According, for example, to the theory above mentioned, the height of Monticello from its base is 580 feet, and its base 610 feet 8 inches, above the level of the ocean; the former, from other facts, I judge to be near the truth; but a knowledge of the different falls of water from hence to the tide-water at Richmond, a distance of seventy-five miles, enables us to say that the whole descent to that place is but 170 or 180 feet. From thence to the ocean may be a distance of one hundred miles; it is all tide-water, and through a level country. I know not what to conjecture as the amount of descent, but certainly not 435 feet, as that theory would suppose, nor the quarter part of it. I do not know by what rule General Williams made his computations; he reckons the foot of the Blue Ridge, twenty miles from here, but 100 feet above the tide-water at Richmond. We know the descent, as before observed, to be at least 170 feet from hence, to which is to be added that from the Blue Ridge to this place, a very hilly country, with constant and great waterfalls. His estimate, therefore, must be much below truth. Results so different prove that for distant comparisons of height, the barometer is not to be relied on according to any theory yet known. While, therefore, we give a good degree of credit to the results of operations between the summit of a mountain and its base, we must give less to those between its summit and the level of the ocean.
I will do myself the pleasure of sending you my estimate of the Peaks of Otter, which I count on undertaking in the course of the next month. In the meantime accept the assurance of my great respect.