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 enquiries for the height of the White mountains, of N. 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 Missisipi, except the White mountains, and not far short of their height if they are but of 4885. 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 the barometer divided into horizontal lamina of equal thicknesses. 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 it’s base, thus taken, merits therefore a very different degree of credit from that of it’s height above the level of the sea, where that is distant. according, for example, to the theory abovementioned, the height of Monticello from it’s base is 580. feet, and it’s base 610 f–6 I above the level of the ocean. the former, from other facts, I judge to be near the truth: but a knolege of the different falls of water from hence to the tide-water at Richmond, a distance of 75. 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 100. miles. it is all tidewater, and thro’ 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 Genl Williams made his computations. he reckons the foot of the Blue ridge, 20 miles from hence, 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 different1 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 it’s base, we must give less to those between it’s 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 mean time accept the assurance of my great respect.

Th: Jefferson