The constitution of Hamburg, although far from being free in the just acceptation of the term, has secured to the citizens enviable advantages, compared with many of the other states of Germany. We dine with Mr. Gossler to-morrow. (Here follows a minute account of the coins in common use in Hamburg.) _May 23d._ We dined with Mr. Gossler, the son, in the country; his father, to whom we had the letter, being now in England. Our host had resided in Boston, and about three years ago married Miss Bray of that city. She is related to the Elliott family, and is a sprightly, pleasant woman, who talks very well. Besides our host and hostess, the company consisted of Mr. William Gossler, their uncle, an old bachelor; Mr. Charles H. Carnegy, a young Scotchman who came in the packet with us from London; Mr. Wainwright, from Boston, also our fellow-passenger; Mr. Barry, and myself. We spent a very agreeable afternoon and evening. We received an invitation from Mr. Richard Parish to dine with him on Sunday at his country place, which we were obliged to decline, intending to leave for Lubeck on Saturday. _Thursday, May 24th._ In the morning, we visited Altona, a Danish town in Holstein adjoining Hamburg, and below it on the river. Its appearance is similar to that of the old part of Hamburg, though it contains some fine modern houses. The public walks are also pleasant here. The population is said to be 25,000. In the afternoon, we ascended the steeple of St. Michael’s, and had a fine view of the city. It is 480 feet in height. The church is a fine building. I observed in it an altar, at some distance from the pulpit, with an image above it of our Saviour on the cross. This in a Lutheran Church was new to me. Before I enter upon the business of the mission, some of the private letters which Mr. Buchanan wrote to his friends at home, during the summer of 1832, will be found to contain matters of interest. Whatever other accomplishments he possessed or wanted, he certainly wrote very agreeable letters. One of the first persons to whom he wrote, after his arrival at St. Petersburg, was General Jackson. [MR. BUCHANAN TO GENERAL JACKSON.] ST. PETERSBURG, June 22, 1832. DEAR GENERAL:—