all stages of water, and derived the mean of each set, to the number of many hundreds of observations.*

9. The result shows a mean surface velocity at high water of 2.61 miles per hour, at Carrollton, and 2.60 miles per hour at Vidalia; respectively, 3.80 and 3.82 feet per second of time. The one was derived from 176 observations, and the other from 70 observations. At low water, Carrollton, 1.45 miles per hour, or 2.11 feet per second; at Vidalia, 1.54 miles per hour, or 2.25 feet per second.

10. (Vide tables B. C. E.) The mean velocity for mean water, as derived from thirty years' observation, is 2.26 miles per hour, or 2.95 feet per second.

11. The velocities at various depths are not easily obtained. The irregularities of bottom and sides in the channel, and their continually shifting nature, give so many lateral and vertical directions to portions of the current, as very much to equalize the current velocity, at all depths. Besides, the largeness of the volume renders friction much less influential than is usually computed to fluents. Accordingly, in sounding, I have found the lead, when thrown in great depths, to be drifted down stream, as fast as the boat from which it was thrown, so that my soundings were made vertically, by letting the boat drift while the lead was descending.

I have allowed, with some hesitation, one-eighth for retardation from friction, which is 12 1-2, instead of 15 per cent., the rate usually allowed. This is a liberal allowance at high water, but at low water, it is small enough, as we shall probably see. (Vide table B, 1, 2.)

12. It is remarkable that the high water sections at Vidalia and Carrollton, 275 miles apart, should be the same; but much. more remarkable, that observations should have given so precisely the same mean velocity, 2.60 and 2.61 miles per hour. This is what should have been expected from observations of the utmost exactness on the hypothesis I assume, that the Atchafalaya, Lafourche and Plaquemine, carry off as much as Red River introduces.

13. Rise and Fall of the River.---The range of the river is, at Vidalia, as above stated, 51 feet; and at Carrollton 15 feet. These are the extremes not often reached. In 1829 and in 1819, the river was 51 feet below the mark of 1828, and this latter mark is the highest for thirty years, at all known points

It may, and probably will be objected, that floating drift-wood is not a relia ble index to the current's velocity, because of atmospheric friction and accidental disturbances. Some care was always taken in selecting bodies least liable to these objections, and calm days invariably chosen. The estimated distances, too, are liable to be erroneous, but when the objects timed are very numerous, the errors arising from estimating distances from shore may be assumed to cancel each other. Let those who have better observations offer them, I pretend only to approxima tions.

on the river, up to the year 1849, when the water reached in several places the same point as in 1828. In 1815 the water rose at Vidalia two inches higher than in 1828, and was said to be the highest water since 1770. Mr. Hutchings thinks the water mark was made in 1770, which was still visible in his recollection, fully one foot higher than any mark since reached. Governor Sargeant records this tradition, in 1809, when there was a flood higher than for forty years. The accompanying table or scale, L, will show the relative height in different years for forty years, and the date of culmination. These are from a register kept of actual rise and fall for thirty years, and from other sources reliable. The range of high water marks is three feet at Carrollton-1839, April 8th-the highest water of the year being three feet four inches below high water. Low water marks have a much greater range; the lowest mark of 1844 being seven feet above the lowest known.

14. The median line or curve of rise and fall for thirty years, 1817 to 1847, reaches an elevation just one foot seven inches below the mark of 1849. This is in the last week of April, which proves to be the mean time of highest water. The lowest water by the same mean is on the 1st of October, and is three feet six inches above the lowest mark. It will be observed that this table has been reduced to Carrollton, or 15 feet range in rise and fall; but the dates have not been altered.They should be reckoned a week or ten days later for Carrollton than for Vidalia. The mean height of this line for the whole thirty years is 7,222 feet below highest mark. (See plate M for the four median lines, three of ten years each, and one of thirty years.)

15. Recapitulation.-We have shown the "rate of fall"" depth, breadth, velocity, and rise and fall of the water. From these we may compute the rate of discharge at all stages, and the mean rate for thirty years. And the quantity by these data is 12,250,000,000,000 cubic feet per annum, or 447,199 cubic feet per second. (See table D, 1, 2, 3, 4.)

It is worthy of especial observation, that the mean for the three sets of ten years shows a lower level of discharge at each consecutive ten. (See table C.)

16. Sediment.-The experiments of Professor J. L. Riddell show the sedimentary matter transported by the Mississippi to bear a proportion in bulk to the whole quantity discharged of one to three thousand.† At this rate, the cubic contents would

To those accustomed to the woods which have been long inundated it will not be surprising that water marks remain many years, possibly half a century. The water mark of 1828 is perfectly visible over a large portion of our alluvion, and is, in the woods above Bayou Sara, two and a half inches above the highest mark of 1849. I examined this matter most thoroughly.

†The experiments made by Andrew Brown, Esq., of Natchez, Mississippi, and

be, by my measurements, as above, equal to 4,083,333,333 cubic feet. The sediment, then, would cover twelve miles square one foot deep.

Application of Statistics and Principles.

17. Reasoning a priori, the following inductions and conclusions seem unavoidable:

a. The channel of the river is made by the abrasive force of its waters. A greater force would produce a greater channel; and a less force a less channel.

b. The greater the channel, the less the liability to overflow. c. Concentration of force increases abrasive power, and diffusion of force reduces it.

d. Levees confine and concentrate the waters, concentrate and increase the force, therefore increase the abrasion, therefore the capacity of the channel.

e. Outlets diffuse the waters, reduce the abrasive force, and therefore reduce the capacity of the channel.

f. If the channel be already greater than necessary for its servitudes, it would be safe to relieve it of some of its grooving force by outlets.

g. If the channel be too small for its servitudes, it would be wise to increase the channel making power, by closing outlets. 18. The Mississippi river discharges a given quantity annually, and this is divided into daily supplies, with a maximum here, in April and May. It can produce no more.

a. If this supply be discharged with a greater velocity, it must maintain a lower level, even if the channel remain unchanged; for there can be no more than the supply to be discharged, and hence the volume discharged in a month or year must remain the same.

b. A greater force, with the same volume, implies a greater velocity.

c. Therefore, the levees which confine the waters and concentrate the force, increase the velocity and depress the level of discharge.

19. By reference to the diagram M and table C, we shall find these inductions, a priori, sustained by the facts.

a. From the year 1817 to 1827, there were no considerable levees above the mouth of Concordia coast, say 250 miles. And from 1837 to 1847, we may regard the system of levees as in full operation, for a long distance above and below the point of observation at Vidalia.

b. During the first ten years (1817 to 1827) the mean height

read before the American Association for the promo ion of Science, by Dr. Dickeson, give a much larger proportion of sediment; but from the manner of conducting the experiments and obtaining the water tested, I rely upon the results of Dr. Riddell in preference.

of the river's surface was, for the year, 6 inches above the mean height of the following ten years (1827 to 1837), while levees were being constructed; and 9 inches higher than the mean height of ten years (1837 to 1847), under the levee system. This relates to the mean annual height, and reduced to the range of Carrollton.*

c. But the mean high water mark of these decennial periods is in like manner reduced, being 4.4 inches lower, in the second, than the first period, and 6 inches lower in the third period.

d. But we have from the dates of highest water a very unexpected result—namely, the date of highest water is later in the second and third periods than in the first.

The mean dates of culmination are for Vidalia, April 26, April 30, and May 15, for the three periods, in their order, and the mean of the 30 years is on May the 7th.

e. The common impression, that levees produce earlier high waters, would appear to be unfounded; and this is the conclusion which it seems to me would be arrived at, from section 18, a, b, c, because the supply cannot be increased or hurried before the rains and thaws of the spring, and our levees can have little effect in hastening the dates of highest water at any point within the influence of levees. The mean dates of culmination, as given here, then, only prove to me, that the periods observed are too short to obtain a fair mean, when the range is from March 12th to July 16th.

20. Cut-offs. By application of the principles and reasonings to facts, we shall find:

a. That a cut-off shortens the channel, increases the declivity, accelerates the velocity, strengthens the channel-making power, abrades the banks and bottom with more vigor, and ultimately produces a lower mean level than before the cut cut

off.

b. Accordingly, the effect of Shreeve's cut-off at the mouth. of Red River, presented in 1844† these phenomena, namely,— At the cut-off, the water was 3 feet or more lower than the water-mark of 1828. Twenty miles above, it was 30 inches lower, 40 miles up, it was 14 inches lower; at Vidalia, 60 miles above, it was 7 1-2 inches lower, and at Water-Proof, 90 miles, it was 3 inches lower, and at points above Water-Proof, it was regarded as equal to 1828.

c. At Morganza, it was 18 inches lower, and at New Orleans and at Carrollton full 8 inches lower than in 1828.

The difference of mean height at Vidalia would be more properly considered. The six inches at Carrollton was about 20 inches at Vidalia, and the 9 inches equal to 30 inches, where the range is 51 feet.

In all these comparisons I regard the river as having been of the same height> when not locally affected in the years 1823, 1828, 1844, and 1849.

These facts were determined by myself at the time, and since, and carefully noted.

d. We may conclude, hence, that the effect was perceptible about 100 miles above, and at least 200 miles below a cut-off, abridging the distance of current 18 miles, and 3.54 feet to the fall of water, thence to the Gulf; and that it showed a reduction of high-water level both above and below the cut-off.

21. The Raccourci cut-off has been too recently made, for a full illustration of the effects. Some have already been severely felt. It shortened the distance 28 miles, with a fall at high water of 4.5 feet. The effects in draining the district above it have been realised as anticipated. Its effect at Vidalia was about 4.5 inches, and expired at a distance of about 100 miles. Below it has not had time to produce the new channel due to its acceleration, and has raised the water probably in a slight degree, but not to the mark of 1828, at Bayou Sara, by 2.5 inches. By the best information I can obtain, the difference is about two inches in the bend above Carrollton.By changing points of greatest force, and by increase of that force, it has committed great ravages upon the banks, both above and below the cut-off. It will require but two or three years more, judging from past experience, to adapt the new channel to the new channel maker, when the whole will be discharged at a lower level than before the cut-off.

22. The matter, as a question of hydrostatics, is settled that a cut-off will reduce the level of discharge on both sides; and the question of policy reduced to one of cost from abrasion of banks. This should be well weighed, before making a cut-off, from the suddenness with which a new force is applied. Levees are extended so gradually, that the consequences are slow in being felt, and may be guarded against.

23. Regimen of Rivers.-It has recently been advanced by Dr. Riddell, that the river has some normal regimen, and that the effects of a cut-off were, to continue the carving in the bends of the river, until its channel shall obtain its former length, and regain its normal regimen.

a. I am not aware of any law or laws of currents, whether sediment bearing, or clear, which will warrant such doctrine. Inert matter can certainly have no choice of greater or less velocity.

b. The greater the momentum, of course, the greater the to remove obstacles and all bends are obstacles. power c. The weaker a fluent, the easier diverted from its course, and hence the tortuousness of streams with little fall.

d. The aggregate tendency of a river, with alluvial banks, of uniform power to resist abrasion, is to straighten its channel.

e. No banks are uniform in this respect, and hence no stream