No two branches of science have been so much improved the last two centuries as chemistry, and the theory, and practice of navigation. The first may be considered the most entertaining, as furnishing a greater variety of objects for the employment of the mind; but the latter appears to have the advantage in usefulness. By navigation all portions of the world become connected, and constitute one great family.—The improvements in those branches of science were not in the first instance the result of reasonings founded upon theories; but on the contrary, experiments, and observations, produced the theories.—The late improvements in navigation on which I shall take the liberty of making some remarks, are principally owing to the improvement of the lunar theory, which has been effected by observations made for that purpose in different parts of Europe; and the accurate mode now practised for graduating astronomical, and other instruments; to which may be added, the use of Arnold’s watches.—

As commerce is a subject of primary importance, and depends upon navigation in a considerable degree for the certainty, despatch and facility with which it may be carried on, it must appear singular, that the legislature of our country has wholy neglected institutions for the improvemt of astronomy, and navigation, and yet attended to a military school.—In Europe we find observatories erected, and supported, by petty Dukes, and Princes, whose whole revenues would scarcely maintain six regiments of infantry, and yet in our commercial country, which produces a large revenue, and where observatories would be more useful, they are unknown.—

In order that observatories should be made immediately useful to navigation, they should be erected in the vicinity of large commercial sea-port towns, where the Masters of vessels might have their quadrants, and sextants examined, and their errors ascertained, and the going, of their time-keepers determined before they left the port.—A master of a vessel will always proceed with more confidence, and more expeditiously, when certain of the truth of his instruments, and the uniform going of his time-piece, the latter can only be determined with the necessary precision by the practical astronomer.—

Since my return from our southern boundary, I have had an opportunity of examining the going of two of Arnold’s watches, or chronometers, which for accuracy far exceeded my expectation: one of them would have made land within 30 Geographical miles, in a voyage of 5 weeks; and the other within 20 geographical miles during the same period.—On my voyage from West Florida by the way of the West Indies to St. Mary’s, I had but two Sailors, neither of whom knew the alphabet, and it was the first time I had ever been out of sight of land; but from a confidence in my watches, and instruments, ventured to navigate the vessel, and made land within an hour of the time expected, without ever once heaving the log during the passage.

If we suppose the voyages of 100 vessels from one of our ports, to be expedited 3 days each, from the improvement of the practise, and theory of navigation, and 10 persons allowed to each vessel, it would produce a clear saving of 4200 dollars at the rate seamen are now employed;—but this saving is of small importance, when compared to the1 safety of a vessel from her position at sea being accurately known.—

The whole annual expense of supporting an observatory after being furnished with the necessary instruments, would not exceed 3500 dollars, and if erected near to one of our large sea port towns, would probably be a saving of a much larger sum to the commercial interest of the place.

The immediate connection of observatories in Europe with navigation, appears to be neglected, except at Cadiz, where I am informed by Don Jose Joaquin de Farrar an ingenious Spanish gentleman, they are connected with great advantage to the commerce of that City: But in this country, where the bar, and profession of arms, are almost the only avenues which lead to honour, and to which consequence, and usefulness by general consent appear to be attached, such institutions I suspect would be supported with difficulty, even by the publick, unless joined to a maritime school for the navy.

I have accompanied this with a few more pages of my astronomical observations, and a proof sheet of the first plate, which contains the references in the method used to describe the prime vertical, mentioned in pages 51, and 52.: likewise a sketch of those parts of the Mobile, Alabama, and Tensaw Rivers, with the great swamp, over which we carried the line, as described in the 83d. and 84th. pages.

I feel a singular satisfaction in presenting you with this work as it comes from the press, not because you are the first Magistrate in a great, and free nation, but because to your knowledge of national policy, you add in a very uncommon degree, that of an intimate acquaintance with the arts, and sciences in general, and more capable than any other gentleman2 among us, of judging of its merit.—

The publication of the 5th. volume of the Transactions of our Philosophical Society will be delayed for want of the charts, or the copies of them annexed to the report respecting our southern boundary.—Those charts, are the originals, and I intended to have replaced them by copies done in a better style, but in this I have been disappointed.

I have the honour to be with great respect and esteem your friend and Hbl. Servt.