I had the honor duly to receive your letter of the 3d of January 1816—Containing your Calculation of the Altitudes of the Peaks of Otter—for which, and for your observations relative to the Barometer be pleased, Sir, to accept my unfeigned acknowledgements. I now take the liberty, Sir, to enclose you for your examination the Copy of a letter I wrote about five years ago, to Genl Williams relative to the Method adopted by Mr Robbins, for determining1 the initial velocities of Military Projectiles by means of the Ballistic Pendulum, but concerning which I never obtained the Genls opinion. To this I have annexed a table containing the Results of some Experiments which I made at this Place about two years ago, (on the Ice of the River) upon the principles contained in this letter. You will oblige me, Sir, by taking the trouble to examine my objections to Mr Robbins method, and also the method which I have proposed in the 2nd part of the letter, and giving me your opinion upon the Subject. Since I last wrote you I have calculated from barometrical observation the Altitudes of the high-lands of Nave-Sink near Sandy-Hook and likewise the Altitude of Hemp Stead Harbour Hill said to be the highest land on Long-Island. I have also made some observations for the purpose of testing practically, the Accuracy of the Method of measuring heights by the Barometer, by applying it to the determining of very small altitudes. The results obtained from these observations and also the Altitudes2 of the High lands of Navesink and of Harbour-Hill, I will do myself the honor in a few days to enclose you.—