New-York is destined to be the brightest star in the American galaxy. This state commands the means of vast improvements and extension of inland navigation. To the natural advantages for navigation which (the most beautiful river that geography records,) the Hudson affords, may be added further improvements to those already made at the head of its tide waters for the benefit of Albany, Troy, Lansinburgh, and Waterford; and these extended up the river to Fort Edward. If clearing out the rocks and stones in the bed of the river-sinking the channel on the small rifts-damming and locking the falls at Fort Miller, Saratoga, and the rift at Waterford would not effect the necessary improvements, a capacious canal could be thrown from Fort Edward to Waterford, and continued almost the whole distance on the west bank of the river; a distance of forty miles. This communication could be continued to Lake Champlain, by cutting a canal from Fort Edward to Skeensborough, or the head of South Bay. I have no information of the balance of waters between the two points, except what is drawn by inference from the maps, and by presumption. From the latter, I conceive the head of water which gives current to Lake Champlain and Chamblee River, into the St. Lawrence, is greater than from Fort Edward to tide waters in the Hudson. If this be fact, a draft could be obtained from the lake for the supply of the canal-but when looking at the head and course of Wood Creek, there is a probability that the Hudson, at Fort Edward, is the highest. Admit it, then the supply of the canal must be gained from the Hudson by taking it out at the head of Glen's Falls, or by tapping (and if the surrounding hills require it, to tunnel also) the head of Lake George, which could conveniently be thrown on the highest ground between the two points. The distance would be about fifteen or twenty miles. These would open an important communication between Lake Champlain and the tide waters of the Hudson.

The several branches of the Susquehannah and the Tioga which take their rise in, and traverse a part of the state, would merit a consideration also.

In turning our attention to the westward, an immense field opens to view. To the Genesee canal and its appendages already spoken of-there could be a continuation of water communication to the north-western extremity of our territory, with several valuable diver gent branches. From Buffalo (the contemplated head of the Genesee Canal) the navigation to the straits of St. Marie is already complete. These straits might be improved by sinking its rapids, or by damming and locking them, which would complete the navigation into Lake Superior.

The improvement of the Fox and Ouisconsing rivers, with a canal to connect them at or about their portage, supplied by the most elevated stream, would open a communication between Lake Michigan and the Mississippi 1150 miles from its mouth.

Another important improvement could be effected by tapping Lake Michigan and throwing a canal into the Plein river, the west branch of the Illinois, thence down that river into the Mississippi 1180 miles from its mouth. The evenness of the land between the Plein and Michigan, gives a certainty to its feasibility, and a probability of its being completed by a canal of ten-at furthest twenty miles. With the necessary improvements in the river below the canal, the navigation of this branch could be made of equal dimensions with the Genesee Canal.

To render the route of transportation from Buffalo to the Mississippi, by the Illinois, of its greatest value, another improvement would become essential-a cut across the promontory between Lakes Erie and Michigan at their heads. Here, indeed, the course of waters (the rivers taking their rise near Lake Erie, and falling into Lake Michigan) appears to preclude the idea-but Michigan disemboguing its waters through Huron and the straits, into Erie, establishes the fact that the former lies something higher than the latter, and the project is forbidden only by the unevenness of the intermediate ground, of which I have not been able to acquire particular information.

As the importance of this improvement may not immediately strike the perception of the reader, I will make a brief statement of it. It would require the distance of 180 or 190 miles. From the head of it, across the lake to Chicago, about 50 miles, making 240 miles from the head of Lake Erie. This would make the distance from Buffalo to Chicago 540 miles, which by the present route through Lake Huron, &c. is 1200, with a difference of 300 miles of north latitude.

The distance from New-York by this route, to the Mississippi, would be-to Albany, 165to Buffalo, 300-to Chicago, 540-to the mouth of the Illinois, about 425-to the mouth of the Missouri, 20 miles, making 1450 miles; of which 165 would be tide waters-350 dead waters-445 down, and but 490 up stream of current waters; and the most of that regulated by canals. Whereas, from the mouth of the Mississippi to the mouth of the Missouri is 1160 miles, with its whole distance up the stream of current waters. This would evidently give the port of New-York a share of the trade in supplying the Missouri with foreign merchandise, and with a participation in its fur trade, which, however, would return with the current of the Mississippi-while the other improvements would secure to that port the entire command of both over all our North-western territory.

Unless this improvement be found practicable and become effected, it is doubtful whether the port of New-York will be able to enter into competition with that of New-Orleans for the Missouri trade-for the increased distance of the route through Lake Huron, &c. and the sometimes dangerous navigation of that lake, with the more lengthy interruptions by frost, would materially enhance the charges of transport-nor could it well be substituted by a connection between and improvement of the rivers Miamee of the lakes and Saint Joseph, for their courses are indirect and their branches too small for any other purpose of improvement but the benefit of their own shores.

Valuable improvements could be made by canalling the portages between, and improving the beds of several rivers between Lake Erie and Ohio River-between the Miamee of the lakes and the Wabash; also between the former and the great Miamee-between Sandusky and the latter; and the Scioto-and between the Cayuga and the Muskingum. The route between the Sandusky and the Scioto is the best of these in the natural state.

Another important acquisition to the commerce of the port of New-York presents itself to view-if the necessary improvements can but be found practicable-but it yet remains to be ascertained, whether a draft can be had on the waters of Lake Erie, and thrown into any one of the branches of the Ohio. The portage of Chatauque Lake, and the Presque Isle, are the only places which offer a prospect at present. Of these, the latter is the most promising. The tapping at Presque Isle would of course be thrown into the French Creek, which is already one of the best navigable streams, for its size, in the United States.

The land is level along the portage to La Boeuf, and should the French Creek be something higher at this place than the lake at Presque Isle, the canal could be continued down its stream until it gained a draft. Should this be found impracticable, the only alternative is the Chatauque Lake, with a less probability of success. But were they to fail, we have an inferior substitute left us, by damming the mouth of the Chatauque and raising it several feet, for the purpose of opening it occasionally to facilitate the navigation of its outlet during the summer droughts.

This would give a route of transport from New-York to Buffalo, 465-to Presque Isle, 90-to Pittsburgh (by land 125, add for the bends of the river 40,) is 165, making 720 miles and about the half of it up stream, and is 80 miles more than twice the distance from Philadelphia to Pittsburgh over land, with a very mountainous road.

Could the capital improvement of commanding a draft on the waters of Lake Erie be effected, it is obvious that it would give to the port of New-York, the supply trade for all the shores of the Ohio, and its northern branches, until it was met by arrivals from NewOrleans.

This fertile country would make able remittances for its importations.

HERCULES.