Thomas Jefferson Papers

# To William Dunbar

Washington Mar. 13. 04.

Dear Sir

Your favor of Jan. 28. has been duly recieved, and I have read with great satisfaction your ingenious paper on the subject of the Missisipi, which I shall immediately forward to the Philosophical society, where it will be duly prized. to prove the value I set on it, & my wish that it may go to the public without any imperfection about it, I will take the liberty of submitting to your reconsideration 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 phaenomena of that river not to merit mature consideration. I cannot 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 it’s velocity at it’s surface) whatever a body would have acquired by falling thro’ a space equal to that depth. if, in the middle of a river we drop a vertical line a.e. from it’s surface to it’s bottom, and (using a perch, or rather a measure of 16.125 f. 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 stream1 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 abscissae, and will terminate in a curve a.f.g.h.i. which will represent the velocity of the current in every point, and the whole mass of water passing on in a second of time.* this would be the theory of the motion of rivers, were there no friction. but, the bottom being rough, it’s 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, & 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 & 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. & so on downwards, the acceleration always increasing till it reaches 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 inwardly2 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 it’s surface to the current by a long vane fixed on it’s 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 Chafalaya, and endangers the drawing boats into that river, as you mention pa. 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 it’s 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 recieved from you as well as others was digested together & 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 recieving 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 every thing I could lay my hands on which related to any part of America, and particularly had a pretty full collection of the English, French & 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 inclose you a copy of it. one single fact in it3 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 recieved the information you were so kind as to send me; on the reciept 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 recieved; to wit that tho’ the name & division of W. Florida have been retained, and in strictness that country is now called by that name, yet it is also called Louisiana in common parlance, & even in some authentic public documents. the fact however is not of much importance. it would only have been an argumentum ad hominem. altho’ I would wish the paper inclosed never to be seen by any body but yourself, & 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 & 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.

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, & the establishment of a government on the spot, capable of meeting promptly it’s own emergencies. Accept my friendly salutations & assurances of great esteem & respect.

Th: Jefferson

(); at foot of first page: “William Dunbar esq.” Enclosures: see The Boundaries of Louisiana, printed at 7 Sep. 1803 (Vol. 41:321-40), and Continuation of an Examination of the Boundaries of Louisiana, 15 Jan. 1804 (Vol. 42:280-4).

the chafalaya: Atchafalaya River.

For the published digest of communications on the subject of louisiana, see TJ to the Senate and the House of Representatives, 14 Nov. 1803 (Vol. 41:721).

For the publication in a newspaper attributed to Judge Elihu Hall bay that argued for the inclusion of West Florida within the boundaries of Louisiana, see Vol. 41:327, 328n, 619n.

i am told: TJ probably referred to a missing letter from Andrew Ellicott, dated 27 Feb. 1804, which he recorded in as received on 1 Mch. from Lancaster with the notation “Walker. Gillespie. Ellicott.” John Peter Walker and David Gillespie had assisted Ellicott on his survey of the southern boundary of the United States. After completing the field work, Walker went with Ellicott to Philadelphia to assist in preparing the maps of the expedition’s findings. Returning to Natchez by 1802, Walker subsequently worked as a surveyor and mapmaker for the Spanish government in Louisiana, Texas, and Mexico (Elizabeth A. H. John, “The Riddle of Mapmaker Juan Pedro Walker,” in Stanley H. Palmer and Dennis Reinhartz, eds., Essays on the History of North American Discovery and Exploration [College Station, Tex., 1988], 102-32; Vol. 42:378, 379n; Dunbar to TJ, 13 May; Appendix II).

1Preceding six words interlined.

2Word interlined.

3Preceding two words interlined.

4TJ here canceled “I believe Con.”

### Authorial notes

[The following note(s) appeared in the margins or otherwise outside the text flow in the original source, and have been moved here for purposes of the digital edition.]