Lemon Hill, half a mile above the Fairmount water-works of Philadelphia, was, 20 years ago, the most perfect specimen of the geometric mode in America, and since its destruction by the extension of the city, a few years since, there is nothing comparable with it, in that style, among us. All the symmetry, uniformity, and high art of the old school, were displayed here in artificial plantations, formal gardens with trellises, grottoes, spring-houses, temples, statues, and vases, with numerous ponds of water, jets-d'eau, and other water-works, parterres and an extensive range of hot-houses. The effect of this garden was brilliant and striking; its position, on the lovely banks of the Schuylkill, admirable; and its liberal proprietor, Mr. Pratt, by opening it freely to the public, greatly increased the popular taste in the neighborhood of that city.

On the Hudson, the show place of the last age was the still interesting Clermont, then the residence of Chancellor Livingston. Its level or gently undulating lawn, four or five miles in length, the rich native woods, and the long vistas of planted avenues, added to its fine water view, rendered this a noble place. The mansion, the greenhouses, and the gardens, show something of the French taste in design, which Mr. Livingston's residence abroad, at the time when that mode was popular, no doubt, led him to adopt. The finest yellow locusts in America are now standing in the pleasure-grounds here, and the gardens contain many specimens of fruit trees, the first of their sorts introduced into the Union.

Waltham House, about nine miles from Boston, was, 25 years ago, one of the oldest and finest places, as regards Landscape Gardening. Its owner, the late Hon. T. Lyman, was a highly-accomplished man, and the grounds at Waltham House bear witness to a refined and elegant taste in rural improvement. A fine level park, a mile in length, enriched with groups of English limes, elms, and oaks, and rich masses of native wood, watered by a fine stream and stocked with deer, were the leading features of the place at that time; and this, and Woodlands, were the two best specimens of the modern style, as Judge Peters' seat, Lemon Hill, and Clermont, were of the ancient style, in the earliest period of the history of Landscape Gardening among us.

There is no part of the Union where the taste in Landscape Gardening is so far advanced, as on the middle portion of the Hudson. The natural scenery is of the finest character, and places but a mile or two apart often possess, from the constantly varying forms of the water, shores, and distant hills, widely different kinds of home landscape and distant view. Standing in the grounds of some of the finest of these seats, the eye beholds only the soft foreground of smooth lawn, the rich groups of trees shutting out all neighboring tracts, the lake-like expanse of water, and, closing the distance, a fine range of wooded mountain. A residence here of but a hundred acres, so fortunately are these disposed by nature, seems to appropriate the whole scenery round, and to be a thousand in extent.

At the present time, our handsome villa residences are becoming every day more numerous, and it would require much more space than our present limits, to enumerate all the tasteful rural country places within our knowledge, many of which have been newly laid out, or greatly improved within a few years. But we consider it so important and instructive to the novice in the art of Landscape Gardening to examine, personally, country seats of a highly tasteful character, that we shall venture to refer the reader to a few of those which have now a reputation among us as elegant country residences.

Hyde Park, on the Hudson, formerly the seat of the late Dr. Hosack, now of W. Langdon, Esq., has been justly celebrated as one of the finest specimens of the modern style of Landscape Gardening in America. Nature has, indeed, done much for this place, as the grounds are finely varied, beautifully watered by a lively stream, and the views are inexpressibly striking from the neighborhood of the house itself, including, as they do, the noble Hudson for sixty miles in its course, through rich valleys and bold mountains. But the efforts of art are not unworthy so rare a locality; and while the native woods, and beautifully undulating surface, are preserved in their original state, the pleasure-grounds, roads, walks, drives and new plantations, have been laid out in such a judicious manner as to heighten the charms of nature. Large and costly hot-houses were erected by Dr. Hosack, with also entrance lodges at two points on the estate, a fine bridge over the stream, and numerous pavilions and seats commanding extensive prospects; in short, nothing was spared to render this a complete residence. The park, which at one time contained some fine deer, afforded a delightful drive within itself, as the whole estate numbered about seven hundred acres.

The plans for laying out the grounds were furnished by Parmentier, and architects from New York were employed in designing and erecting the buildings. For a long time, this was the finest seat in America, but there are now many rivals to this claim.

The Manor of Livingston, lately the seat of Mrs. Mary Livingston (but now of Jacob Le Roy, Esq.), is seven miles east of the city of Hudson. The mansion stands in the midst of a fine park, rising gradually from the level of a rich inland country, and commanding prospects for sixty miles around. The park is, perhaps, the most remarkable in America, for the noble simplicity of its character, and the perfect order in which it is kept. The turf is, everywhere, short and velvet-like, the gravel-roads scrupulously firm and smooth, and near the house are the largest and most superb evergreens. The mansion is one of the chastest specimens of the Grecian style, and there is an air of great dignity about the whole demesne.