Yesterday about 12 o’clock I put the steamboat in motion, first with a paddle 8 inches broad 3 feet long with which I ran about one mile up the East River against a tide of almost one mile an hour, it being nearly high water. I then anchored and put in another paddle 8 inches wide 3 feet long, started again and then according to my best observations I went 3 miles an hour, that is two against a tide of one; another board of 8 inches was wanting which had not been prepared. I therefore turned the boat and run down with the tide of one mile, boat 3, equal four, and turned her round neatly into the berth from which I parted. She answers the helm equal to anything that ever was built. And I turned her twice in three times her own length. Much has been proved by this experiment; First, that she will when in complete order run up to my full calculations; Second, that my axles I believe will be sufficiently strong to run the engine to her full power; Third, that she steers well and can be turned with ease. The sum of the surfaces of the paddles were 8 feet, the Bow of the boat 9. My paddle boards should have been equal 12 feet which I was afraid to put on at first; they are now making. The engine having worked for the first time requires overhauling and new packing. The cold-water pump for condensing is 7 inches and a two foot stroke yet does not furnish sufficient cold water for complete condensation and vacuum. I am about making it 10 inches diameter; these connections with the finishing of the cabins will take me the entire week and I shall start on Monday next at 4 miles an hour. Yesterday I beat all the sloops that were endeavoring to stem tide with the slight breeze which they had; had I hoisted my sails I consequently should have had all their means added to my own. Whatever may be the fate of steamboats for the Hudson every thing is completely proved for the Mississippi, and the object is immense. Please to forward me 1000 or 1500 dollars as soon as possible. Yours truly, R. FULTON. Best respects to Mrs. Livingston. Addressed to Robt. R. Livingston, Esqr. Clermont, New York.