Carlsrhue, the duke of Baden's capital and residence, is one of the neatest towns I have seen on the continent. The streets are broad, straight, and well-paved, and the buildings all of stone, painted cream-color. The chateau of the duke is in the form of a crescent, opposite a block of private houses in similar style, thus making an elegant circle, with a garden and orangery in the centre. In the rear of the chateau, is an extensive hunting-park. The whole of this duchy appears to be one level plain, not specially fertile; and there is little to remark in riding over it, except the extensive squadrons of geese, tended by the lasses like a flock of sheep, and the battalions of _ganders_, in the shape of the duke's soldiers. Our introduction to his Serene Lowness, the Rhine, did not give us the most favorable impression of his majesty. If one should see that part of the river between Switzerland and Mayence, and no more, he would pronounce its far-famed beauties all a joke. It passes here through this flat uninteresting duchy, the banks affording nothing more attractive than pine bushes, six feet high; and the river itself has lost its primitive attraction at Schaffhausen, for here it is of a brown muddy color, instead of its once transparent green. Occasionally, however, the monotony of the shores is relieved by a pretty town, which, the atmosphere being clear, and the view unobstructed, may be seen from a great distance. Among others, we passed Spires and Worms, noted for their cathedrals, which are very conspicuous objects from the river; and Manheim, a handsome town, with a fine palace, (now chiefly in ruins,) in the midst of a beautiful park. Near Manheim is Heidelberg, celebrated for its university, which is the oldest in Germany. These places are in the 'Grand Duchy' of Hesse-Darmstadt, which adjoins that of Baden. The boat stopped a short time at Manheim, and we went on shore to see the palace. It was dusk when we came in sight of the famous and very pretty town of Mayence, our steamer passing _through_ the bridge of boats over the Rhine, which was promptly opened to admit it. The spires, and domes of the town, as seen from the river, give it quite an imposing appearance. We stepped on the quay, with very little bustle, and without any obstruction or examination. The hotels near the river were all full, but we found good lodgings at the 'Trois Courounes' in the interior. I shall proceed to-morrow to Frankfort and Leipsic, with the intention of returning here to take the Rhine to Cologne. * * * * *