(From the New York Express.] Boundaries of the United States, as fixed by the Treaty of the 3d Nov., 1783.

To the Editors :-It may be observed that the boundaries of the United States remained unchanged from what they were fixed by the Treaty of the 34 of November, 1783, in 1793, and the parts were, et the latest dates, us follows; Commending at the N E. angle of Maine,

and thence along the Eastern border of the then territo, y to the Atlantic Ocean.. Thence, by general courses. disregarding incurves along the atlantic Ocean, from Passam quosdy Bay to St. Croix River. Thence along the Southern boundary to the Mississippi River..

Thence along Southwestern border from the mouth of the Rio Grande to Pacific Ocean at San Diego.....

Thence along the Pacific Ocean to the S raits of St. Jean de Fuca..

250

Western boundary, along the Mississippi, &o, to the N. W angle.

1,400

And thence along the inflexions of the Northern boundary to the N. E. angle of Maine. 1,800

5,500

Entire boundary, in 1793, miles... Note-Rejecting minor numbers, Geographers, after the ratification of the Treaty of 1783, estimated with sufficient accuraoy the area within this perimeter at one million of square miles. The subsequent acquisition of Louisiana, Florida, and the great intermediate space westward of Louisiana to the Pacific Ocean, gave to the United States its existing limits, as shown in the annexed table: Table of the Existing Boundaries, commencing at the Mouth of St. Croix River. From the mouth of St. Croix River, along the Atlantic Ocean to Florida Point.. From Florida Point along the Gulf of Mexioo to the mouth of the Mississippi River.. From the mouth of the Mississippi to that of the Rio Grande..........................

Thence eastward along N. latitude 49 to Lake of the Woods......

1,400

650

400

900

700

1,400

1,300

1,400

Thence along former Northern or Canadian.. 1,800 And thence along the Atlantic Ocean to the mouth of St. Croix River...64-4

1,650

Entire existing boundary in 1851...... 9,450 We find that by these tabular elements the present aggregate of outline exceeds the former, as they existed in 1793, not materially differing from two to one. The most important contrast is not, however, in the outline, but in relative contents. One million of square miles demand, if laid down in a square, one thousand miles, each side. But if the sides are doubled, the quantity is quadrupled. Estimated by the comparative Rhumbs, the joint surface added to the territory of the United States since 1793, rather exceeds two millions of square miles. It is, therefore, safe to allow, that within the existing perimeter of the United States there are three millions of square miles. Therefore, while the outline has nearly doubled, the contents have trebled

It may, indeed ought to be, observed, that the maritime outline, as given in the tables herewith included, are general distances, and irrespective of the inner curves of bays or inlets. Of the whole aggregate, 3,700 miles are along maritime coasts, to which, if due allowance is made for inland curves, the entire outline would exceed eleven thousand miles, with the Atlantic border facing Europe and Africa, and the Pacific coast fronting eastern Asia. Neither recorded history or existing national limits present a parallel. WILLIAM DARBY.

Washington, July 22.

The above, furnished by Dr. Darby, an old geographer and statistician, of Washington, gives the reader hardly a fair outline of the extension of the boundaries of the country. It is eertain, however, that the 5,500 miles of boundary in November, 1793, the date of the laying of the corner stone of the old capitol, by George Washington, have grown, under the acquisitions of fifty-eight years (to the laying of the corner stone of the new or extended capitol, by President Fillmore) to 9,450 miles. This is the external boundary, without the indentations of rivers, bays, coves, inlets, which would many times multiply these nine or ten thousand miles.