The Writings of Thomas Jefferson, Vol. 4 (of 9) / Being His Autobiography, Correspondence, Reports, Messages, Addresses, and Other Writings, Official and Private

by Thomas Jefferson

TO WILLIAM DUNBAR, ESQ.

Washington, March 13, 1804.

Dear Sir,—Your favor of January 28 has been duly received, and I have read with great satisfaction your ingenuous paper on the subject of the Mississippi, which I shall immediately forward to the Philosophical Society, where it will be duly prized. To prove the value I set on it, and my wish that it may go to the public without any imperfection about it, I will take the liberty of submitting to your consideration the only passage which I think may require it. You say, page 9, "The velocity of rivers is greatest at the surface, and gradually diminishes downwards." And this principle enters into some subsequent parts of the paper, and has too much effect on the phenomena of that river not to merit mature consideration. I can but suppose it at variance with the law of motion in rivers. In strict theory, the velocity of water at any given depth in a river is (in addition to its velocity at its surface) whatever a body would have acquired by falling through a space equal to that depth. If, in the middle of a river, we drop a vertical line, a e, from its surface to its bottom, and (using a perch, or rather a measure of 16.125 feet, for our unit of measure) we draw, at the depths, b c d e, (which suppose = 1.4 9.16 perch ordinates in the direction of the stream, equal to the odd numbers, 3, 5, 7, 9 perch, these ordinates will represent the additional velocities of the water per second of time, at the depth of their respective abscissæ, and will terminate in a curve, a f g h i,) which will represent the velocity of their current in every point, and the whole mass of water passing on in a second of time.[19] This would be the theory of the motion of rivers, were there no friction; but the bottom being rough, its friction with the lower sheet or lamina of water will retard that lamina; the friction or viscosity of the particles of which, again, with those of the one next above, will retard that somewhat less, the 2d retard the 3d, the 3d the 4th, and so on upwards, diminishing till the retardation becomes insensible; and the theoretic curve will be modified by that cause, as at n o, removing the maximum of motion from the bottom somewhere upwardly. Again, the same circumstances of friction and viscosity of the particles of water among themselves, will cause the lamina at the surface to be accelerated by the quicker motion of the one next below it, the 2d still more by the 3d, the 3d by the 4th, and so on downwards, the acceleration always increasing till it reached the lamina of greatest motion. The exact point of the maximum of motion cannot be calculated, because it depends on friction; but it is probably much nearer the bottom than top, because the greater power of the current there sooner overcomes the effect of the friction. Ultimately, the curve will be sensibly varied by being swelled outwardly above, and retracted inwardly below, somewhat like a k l m n o, in the preceding diagram.

Indulging corollaries on this theory, let us suppose a plane surface, as a large sheet of cast-iron, let down by a cable from a boat, and made to present its surface to the current by a long vane fixed on its axis in the direction of the current. Would not the current below, laying hold of this plate, draw the boat down the stream with more rapidity than that with which it otherwise moves on the surface of the water? Again, at the cross current of the surface which flows into the Chafaleya, and endangers the drawing boats into that river, as you mention, page 18, would not the same plane surface, if let down into the under current, which moves in the direction of the bed of the main river, have the effect of drawing the vessel across the lateral current prevailing at its surface, and conduct the boat with safety along the channel of the river?

The preceding observations are submitted to your consideration. By drawing your attention to the subject, they will enable you, on further reflection, to confirm or correct your first opinion. If the latter, there would be time, before we print a volume, to make any alterations or additions to your paper which you might wish. We were much indebted for your communications on the subject of Louisiana. The substance of what was received from you, as well as others, was digested together and printed, without letting it be seen from whom the particulars came, as some were of a nature to excite ill-will. Of these publications I sent you a copy. On the subject of the limits of Louisiana, nothing was said therein, because we thought it best first to have explanations with Spain. In the first visit, after receiving the treaty, which I paid to Monticello, which was in August, I availed myself of what I have there, to investigate the limits. While I was in Europe, I had purchased everything I could lay my hands on which related to any part of America, and particularly had a pretty full collection of the English, French and Spanish authors, on the subject of Louisiana. The information I got from these was entirely satisfactory, and I threw it into a shape which would easily take the form of a memorial. I now enclose you a copy of it. One single fact in it was taken from a publication in a newspaper, supposed to be written by Judge Bay, who had lived in West Florida. This asserted that the country from the Iberville to the Perdido was to this day called Louisiana, and a part of the government of Louisiana. I wrote to you to ascertain that fact, and received the information you were so kind as to send me; on the receipt of which, I changed the form of the assertion, so as to adapt it to what I suppose to be the fact, and to reconcile the testimony I have received, to wit, that though the name and division of West Florida have been retained; and in strictness, that country is still called by that name; yet it is also called Louisiana in common parlance, and even in some authentic public documents. The fact, however, is not of much importance. It would only have been an argumentum ad hominem. Although I would wish the paper enclosed never to be seen by anybody but yourself, and that it should not even be mentioned that the facts and opinions therein stated are founded in public authority, yet I have no objections to their being freely advanced in conversation, and as private and individual opinion, believing it will be advantageous that the extent of our rights should be known to the inhabitants of the country; and that however we may compromise on our Western limits, we never shall on the Eastern.

I formerly acquainted you with the mission of Captain Lewis up the Missouri, and across from its head to the Pacific. He takes about a dozen men with him, is well provided with instruments, and qualified to give us the geography of the line he passes along with astronomical accuracy. He is now hutted opposite the mouth of the Missouri, ready to enter it on the opening of the season. He will be at least two years on the expedition. I propose to charge the Surveyor-general N. of Ohio, with a survey of the Mississippi from its source to the mouth of the Ohio, and with settling some other interesting points of geography in that quarter. Congress will probably authorize me to explore the greater waters on the western side of the Mississippi and Missouri, to their sources. In this case I should propose to send one party up the Panis river to its source, thence along the highlands to the source of the Radoneas river and down it to its mouth, giving the whole course of both parties, corrected by astronomical observation. These several surveys will enable us to prepare a map of Louisiana, which in its contour and main waters will be perfectly correct, and will give us a skeleton to be filled up with details hereafter. For what lies north of the Missouri, we suppose British industry will furnish that. As you live so near to the point of departure of the lowest expedition, and possess and can acquire so much better the information, which may direct that to the best advantage, I have thought, if Congress should authorize the enterprise, to propose to you the unprofitable trouble of directing it. The party would consist of ten or twelve picked soldiers, volunteers with an officer, under the guidance of one or two persons qualified to survey and correct by observations of latitude and longitude, the latter lunar, and as well informed as we can get them in the departments of botany, natural history, and mineralogy. I am told there is a Mr. Walker in your town, and a Mr. Gillespie in North Carolina, possessing good qualifications. As you know them both, you can judge whether both are qualified, should two persons go, or which is best, should but one be sent, or whether there is any other person better qualified than either. Their pay would probably not exceed $1000 a year, to which would be added their subsistence. All preparations would be to be made at Natchez and New Orleans on your order. Instructions similar to those of Captain Lewis would go from here, to be added to by what should occur to yourself, and you would be the centre for the communications from the party to the government. Still this is a matter of speculation only, as Congress are hurrying over their business for adjournment, and may leave this article of it unfinished. In that case what I have said will be as if I had not said it.

There is such a difference of opinion in Congress as to the government to be given to Louisiana, that they may continue the present one another year. I hope and urge their not doing it, and the establishment of a government on the spot capable of meeting promptly its own emergencies. Accept my friendly salutations, and assurances of great esteem and respect.