period in 1882 was on May 6, 1882, when it was 9 per cent. greater than on April 7, 1883; and that on May 6, 1882, the average slope between Lake Providence and Vicksburg was 10 per cent. greater than on April 7, 1883. Both stretches agree in indicating a less slope at Hays' Landing at the later than at the earlier date, and giving double weight to the first it would follow that the Hays' Landing slope was 9 per cent. less in 1883. May 6, 1882, the Lake Providence gauge read 32.85 feet, and it read 33.20 feet on April 7, 1883. There is no information to show that the riverbed had changed between 1882 and 1883, so that we must depend on gauge-readings and the slopes for the discharge at Hays' Landing on April 7, 1883. The gauge-readings are practically the same, the evidence adduced above is strong that the slope was much less at the later date. The conclusion then follows that on April 7, 18-3, the discharge at Hays' Landing was less than on May 5 or 6, 1882, when it was observed as 790,000 cubic feet. This value will, however, be taken for the discharge on April 7, 1883.

5. Having found 937,000 and 790,000 cubic feet per second as values for the discharges at Hays' Landing at the times of the maximum floods at Vicksburg in 1882 and 1883, those for the part of the river between Arkansas City and Cottonwood, 3 miles below Hays' Landing, where the return flow from the Yazoo swamp in 1882 began to come back into the river, may now be compared. Since no measures were made of the Yazoo return flow in either year, no reliable comparisons of discharges in the two years can be made between Cottonwood and Vicksburg, and the paper tends to confuse and mislead by neglecting this fact. March 20, 1882, the Hays' Landing observed discharge was 937,000 cubic feet per second. There was no escape between Hays' Landing and Cottonwood. The Mississippi River Commission Report for 1884 gives no escape into the Yazoo swamp between Hays' Landing and Arkansas City and (pp. 81-2) an escape of 82,000 cubic feet into the Tensas swamp between the same points. This, added to 937,000, gives 1,019,000 for the discharge at Arkansas City on March 19, 1882. Adopting the probably too large value, 790,000 cubic feet, previously obtained as the discharge at Hays' Landing on April 7, 1883, since the river from Hays' Landing to Arkansas City was below overflow stage, the same discharges may be assumed as approximations over the whole stretch. Tabulating the results for dates of maximum flood at Vicksburg in 1882 and 1883:

From this table it is seen that the return flow of the Yazoo swamp in 1882, at the time of the maximum Vicksburg flood on March 20, was superposed at Cottonwood and below on the main river, which had a larger discharge than at the corresponding maximum, April 7, 1883, by about 147,000 cubic feet.

The paper submitted by Major Suter gives the following table, in which the discharges for 1882 agree with those given in the preceding table, while for 1883 they differ widely.

The cause of the difference needs examination. It should be noted that the 668,000 and 905,000 cubic feet given in the last table as Vicksburg discharges are not such in fact, but are Vicksburg discharges minus Yazoo swamp return-flow, and hence they give no idea of the relative Vicksburg discharges in the two years.

To get the discharge at White River on April 7, 1883, the paper takes the Helena discharge for April 3, 1883, from the Helena discharge curve of 1882 as 740,000 cubic

feet, and then to get the discharge at White River on April 4 adds 224,000 cubic feet, derived by a very uncertain method, when a simple and pretty reliable one might have beer. used. At White River the Mississippi was about 6 feet below overflow stage on April 4, 1883, so that the White River swamp must have been almost entirely drained. Indeed, the Helena and Memphis guage curves show that the far larger St. Francis swamp was almost entirely drained by April 8. Hence, to obtain the discharge just below White River on April 4, 1883, as there was no escape and the only inflow was that of White River without swamp return-flow, which had probably ceased, it is only necessary to add the White River discharge for April 4. In the printed list of daily discharges this is given as 17,800 cubic feet, which added to 740,000 gives 758,000 cubic feet. Instead of 17,800 the paper adds 224,000, and hence makes all the discharges for 1883, given in the last table, about 200,000 cubic feet too large.

It is not known how the flow of the White and Arkansas rivers was distributed at their months. Their combined flow was but about 65,000 cubic feet at this date. If both rivers had discharged through White River mouth, but 65,000 cubic feet should then be added instead of 224,000 to give the discharge just below White River. On April 1 and 2 the combined discharge of the two rivers was still less, and these were the discharges which reached their mouths on April 4.

This explains the chief difference between the two tables and shows the error in the one last given.

It may be noted that on April 4, 1883, the Arkansas River discharge given in the printed list is 47,000 cubic feet. If this be added to the 758,000 cubic feet discharge at White River there results for the discharge at Arkansas City, April 5, 805,000 cubic feet, which differs but slightly from that derived from Hays' Landing and given in the first table as 790,000 cubic feet.

It is therefore seen that the method followed in the paper submitted by Major Suter would, if correctly applied, prove that the discharges at the time of the Vicksburg maxima in 1882 were much greater than those of 1883 above where the Yazoo swamp return-flow comes in.

6. An attempt will now be made to form an idea of the relation between the Yazoo swamp return-flows in the two years at the time of the greatest floods at Vicksburg, though from lack of data nothing precise can be obtained.

As those greatest flood heights result from this return flow, the return flow must be a maximum at about the time of the maximum height. In the Mississippi River Commission Report, 1884, may be found values of the observed escape into the Yazoo swamp in 1882 and 1883. They are respectively 782,000 and 546,000 cubic feet per second. In 1883 the observations were made near the maximum stage of the river, but in 1882, over the part where the greatest escape occurred, they were made at á stage from 1 to 2.2 feet below the maximum stage. Although the length of the crevasses would increase between the maximum stage and observations ten days or more later, it is not probable that this increase would balance the decreased flow due to a fall in the river surface, and it is probable that the 1882 observed escape should be increased to give the maximum value. If the value were increased it would make the ratio of maximum return flow to maximum escape smaller than that given below. Take, however, the observed value, 782,000 cubic feet.

Humphreys and Abbot, in 1858, obtained a discharge curve for Vicksburg. In 1885, the Mississippi River Commission obtained a discharge curve at Warrenton, just be low Vicksburg, for Vicksburg gauge readings varying from 4 to 41 feet. The ascending branches of the two curves agree remarkably well, and notwithstanding the occurrence of the Vicksburg cut-off between the two dates, this enables us at once to use Humphreys and Abbot's Vicksburg discharge curve to determine discharges now occurring.

On June 24, 1858, with Vicksburg gauge reading 48.2 feet (48.8 feet on our gauge), they observed a discharge of 1,244,000 cubic feet per second. As on March 20, 1852, our Vicksburg gange read 48.75 feet, we may take 1,244,000 cubic feet as the discharge on that day. At this time the escape into the Tensas swamp between Hays' Landing and Vicksburg (M. R. C. Rep., 1884, p. 82) was 269,000 cubic feet, which, added to 1,244,000, gives a sum of 1,513,000 feet. Subtracting the observed Hays' Landing discharge (937,000) there remains 576,000 as the flow from the Yazoo swamp on March 20, 1852. This is about three-fourths of the observed escape into the Yazoo swamp. Had the escape into the Yazoo swamp in 1883 lasted as long as that of 1882, we might roughly assume that the maximum outflow would also be about three-fourths of the 546,000 escape (or 408,000). But in 1882 the river at Helena was above 41 feet, which is the escape stage, for 114 days, while in 1883 it was above that stage but 60 days, the floods being at Helena of about the same height in the 2 years. The shorter duration of the 1883 flood must have failed to have filled the Yazoo basin as full, and must have given a return flow that was much less than 40,000 cubic feet. It does not seem improbable that the maximum return flow did not exceed one-half the maximum escape, or 273,000 cubic feet. Let us estimate for this value the discharge at Vicksburg on April 7, 1883. At Hays' Landing it was

790,000; adding 273,000 for the Yazoo swamp return-flow, there results 1,063,000, or 181,000 less than in 1882.

But there is a more reliable method. The ascending branch of Humphreys and Abbot's discharge curve at Vicksburg for 1858 gives for 43.8 feet, the gauge-reading of April 7, 1883, a discharge of 1,120,000 cubic feet per second, or 124,000 cubic feet less than on March 20, 1882, a value not differing widely from 1,063,000 cubic feet previously obtained.

It is seen, then, that whether the Vicksburg discharges at top of floods in 1882 and 1883 are determined from the 1858 discharge curve, or from the Hays' Landing discharge curve with the inflow and outflow between Hays' Landing and Vicksburg added, the results are practically the same, namely, that the Vicksburg discharge was about 150,000 cubic feet less April 7, 1883, than on March 20, 1882.

Collecting the preceding results, we have the following table, giving the excesses of discharge in 1882 over those in 1883, at and immediately prior to the top of the floods at Vicksburg in the two years.

There are, of course, considerable uncertainties in these values, for such uncertainties are unavoidable with our scanty data. They are much more reliable than those in the paper, and they explain the observed facts without resorting to the improbable and unproven assumption that the relation between gauge-readings and discharges was widely different in 1883 from that in 1882, in consequence of the building of levees.

7. From this discussion it is seen (1) that at the top of the flood at Vicksburg, March 20, 1882, the Mississippi River, between Cottonwood, where the Yazoo swamp return-flow began to enter it, and Arkansas City, was discharging much more water than at the top of the flood about April 7, 1883; (2) that the return flow from the Yazoo swamp was greater in 1882; (3) that the flow past Vicksburg was greater in

1882.

I therefore repeat the second conclusion in my paper of March 15, 1884, viz, that "the theory that levees built in 1882-83 reduced the flood heights at Vicksburg in 1883, as compared with 1882, is not needed to account for the facts."

8. The paper submitted by Major Suter makes an estimate of the difference of discharges at points between White River and Vicksburg both inclusive at dates (allowing three days for flow from White River to Vicksburg) immediately following those of the Helena maximum gauge-readings of March 9, 1882, and of March 8, 1883. The conclusions drawn are, that in the two years at these dates, at White River the discharges were equal, the gauge being .3 foot lower in 1883.

It may be noted that the list of daily discharges p:epared under Major Suter's direction gives at the mouth of White River a discharge for the Mississippi on March 9, 1882, exceeding that on March 8, 1883, by 135,000 cubic feet, or differing by 135,000 cubic feet from the value here taken. At Arkansas City the discharge was 349,000 cubic feet greater in 1883; gauge .7 higher. At Lake Providence the discharge was 378,000 cubic feet greater in 1883; gange 1.2 lower. At Vicksburg the discharge was 566,000 cubic feet greater in 1883; gauge 3.5 lower.

The Yazoo return flow is not included in either year.

Such results are astounding if reliable. Unfortunately, they only furnish one more example of the ease with which figures and assumptions can be made to prove anything.

It will be at once noticed if the assumption that equal gauge-readings give equal discharges had been made for Arkansas City instead of for the mouth of White River, all these quantities would have been reduced by 349,000 cubic feet.

As Arkansas City is below White River and Arkansas River, and below the flows of their swamps, instead of being like the White River station near the rivers and in the midst of their swamp return flow, it would have been probably a safer place at which to make assumptions as to equality of discharge. But the fact that, as one point or the other is chosen for the assumption, the results are changed by 349,000 cubic feet, shows sufficiently how uncertain those results are. It can not be assumed in advance that the relation between gauge-reading3 and discharges at Arkansas City has been widely changed by the construction of levees in 1882-'83, since that change is the very thing which is to be proven

9. Leaving these general considerations, some errors in computations in this paper and uncertainties in results will be examined. The value 319,000 cubic feet given for the escape into the Yazoo swamp between White River and Arkansas City will be corrected to 294,000 cubic feet if escapes 18, 19, and 20 (M. R. C. Report 1884, pp. 57-58) are included as they should be. The paper takes 117,000 cubic feet as the Tensas escape in 1882, between White River and Arkansas City. The Mississippi River Commission Report, 1884, pp. 78–80, gives an observed inflow from White River to Cypress Creek of 98,000 cubic feet, and an observed escape of 64,000 cubic feet back of Arkansas City, leaving a net inflow of 34,000 cubic feet, and differing from 117,000 cubic feet escape given in the paper by 151,000 cubic feet. If the estimated escape for the maximum stage (86,000) were used, it would only change the 34,000 net inflow to 12,000 cubic feet, leaving the value in table in error by 129,000 cubic feet according to the observations of 1882. Taking the observed net inflow (34,000 cubic feet) from the 294,000 cubic feet found above, there remains 260,000 cubic feet for the net escape in 1882, between White River and Arkansas City. The paper gives 466,000 cubic feet.

The paper assumes an escape of 117,000 cubic feet into the Tensas swamp March 10, 1883, between White River and Arkansas City. But (M. R. C. Report, 1884, p. 99), the escape was observed between Cypress Creek and Arkansas City at the maximum stage, which was bat.7 foot below that of 1882, as 22,000 cubic feet. The inflow of the Arkansas and its swamps was not measured, but must have much exceeded this, giving a net inflow March 10, 1883, in place of the escape of 117,000 cubic feet taken in the paper. In the absence of information assume that the net inflow between White River and Arkansas City was the same in 1832 and 1883. As there was no escape into the Yazoo swamp here it follows that the escape on the stretch was 294,000 cubic feet greater on March 11, 1882, than on March 10, 1833, in place of the 349,000 cubic feet given in the paper.

On March 19, 1882, the observed net escape into the Yazoo swamp between Arkansas City and Lake Providence, or Hays' Landing, was nothing, and March 15, 1883 it was 6,700 cubic feet. For this distauce the observed escape into the Tensas swamp was 83,000 March 20-30, 1882, and 107,000 March 13, 1883 (M. R. C. Report, 1884, pp. 81, 97, 100.) Hence the observed net escape was 31,000 cubic feet greater in 1883 than in 1832, and it gives an excess of observed escape in 1882 over 1833 between White River and Hays' Landing of 263,000 in place of 378,000 given in the paper. In 1852 the return flow from the Yazoo Swamp extended up to Cottonwood, which is but three miles below Hays' Landing. As this return flow amounted to several hundred thousand cubic feet per second, and as nothing is known of its distribution between Cottonwood and Vicksburg, nothing can be known of the net difference of escapes or discharges during the floods of 1882 and 1883 between these points. At Cottonwood the difference of escapes would be the same as at Hays' Landing, or 263,000 cubic feet, and there are no inflow data for estimating the differences between this point and Vicksburg.

The paper, however, by omitting the inflow from the Yazoo swamp, and by including the escape into the Tensas swamps, between Hays' Landing and Vicksburg, obtains the purely illusory result of 566,000 cubic feet as the excess of escape at Vicksburg in 1882. The paper is written in so vague a way that it is difficult to be sure what it really means. It says the excess of discharge at Vicksburg in 1883 was 566,000 cubic feet. This can not be true, for the Yazoo return flows are neglected in both years, and they differed widely in 1832 and 1883. If the paper intended to compare in the two years the river flow above where the Yazoo return flow comes in, it should not have made the error of including 247,000 cubic feet escape into the Tensas swamp below Cottonwood in 1882. The estimated value 566,000 therefore represents no difference of river flow which really existed and is purely illusory.

In fine, on the assumption that at White River the discharges were equal on March 10, 1882, and March 9, 1883, it is seen that an excess of discharge in 1833 over that of 1-82 results on dates one or two days later than those at White River; (1) of 294,000 for Arkansas City in place of 349,000 given in the paper; (2) of 263,000 at Hays' Landing, or Lake Providence, in place of 378,000; and (3) of 263,000 at Cottonwood, in place of 566,000 at Vicksburg.

Thus far only errors of computation have been considered; defects and uncertainties in metho is also need examination. Notwithstanding much smaller differences of discharge than those given in the paper have been found, yet the uncertainties in the methods are such that even these changed results have no value as proof of the theory that for equal gauge-readings discharges were much larger in 1883 than in 1882. In the paper (1) the assumption is that at the dates chosen, when the gauge-readings at White River differed by but .3 foot, the discharges were equal. Now, the White River gange is in the immediate vicinity of two large tributaries and their swamp flow, which must give varying slopes; there is no discharge curve there, and it can not be assumed, if we had one, that it would be more regular than those observed at Helena and Lake Providence, where, during the overdow stage at nearly ENG 88-140

At

equal gauge-readings, differences of discharge of about 300,000 cubic feet occur. Helena, March 13, 1882, gauge 46.5, the observed discharge was 1,562,000 cubic feet. At Helena, March 29, 1882, gauge 44.6, the observed discharge was 1,259,000 cubic feet, the river being in a falling stage on both dates, while on March 2, 1882, the gauge-reading was 1 foot lower than March 13, and the discharge was 320,000 cubic feet less. Errors of 200,000 cubic feet or more are then possible in the assumption of equal discharges at White River on March 10, 1882, and March 9, 1883.

(2) The assumption that escapes into the Yazoo swamp for different dates and different gauge-readings are the same as at the dates on which they were observed is liable to give large errors. The widths of crevasses change, and even with the same river stage escape velocities may change as the country back of the levee fills up. Between White River and Vicksburg errors of 100,000 cubic feet or more may be introduced in these ways into estimates of relative escapes in the two years and by errors of observation. Our knowledge of the net escape or inflow between White River and Arkansas City in 1882, 1885, and 1884, also is very small. In 1882 a net inflow of 34,000 cubic feet was observed at a stage 3 feet below the maximum which was at Arkansas City 47.1 feet. In 1883 the inflow above Cypress Creek was not observed; the escape from there to Arkansas City observed was 22,000 cubic feet, the Arkansas City gauge reading 46.3 feet; in 1884 the observed escape into the Tensas swamp between Cypress Creek and Arkansas City was 211,000 cubic feet for gauge equal 46.4 feet, while the inflow between Cypress Creek and White River was not observed. In 1882, the estimated escape at maximum stage back of Arkansas City was 86,000 cubic feet. So far as the observations in 1882 and 1883 go they indicate in both years a net inflow on the west bank between White River and Arkansas City; that the paper submitted by Major Suter estimates on the contrary an outflow of 117,000 cubic feet per second in both 1832 and 1883 (while containing an error of computation in not including the inflow in 1884 between Cypress Creek and White River) is simply evidence of our ignorance of the true values. Under this head there may be an uncertainty of 100,000 cubic feet.

It appears, then, that the values 294,000, 263,000, and 263,000 previously obtained by the method of the paper for excesses of discharge about March 10, 1883, over about March 11, 1882, are subject to one possible error of 200,000 cubic feet each, and to two of 100,000 cubic feet each, these values being rough approximations. Hence the uncertainties in these values for the differences of discharges for the two years may equal the values themselves, and therefore no safe conclusions can be based on those values, even after they have been largely reduced by corrections.

10. Having shown that the methods followed in the paper to obtain the differences of discharge in the two years at dates immediately following the Helena maxima of those years are subject to errors too great to give any value as proof to the results, a different method will be applied to estimate those differences.

Humphreys and Abbot's discharge curve for 1858, as already stated, is strongly corroborated by the Warrenton discharge curve of 1885. The 1858 curve may then be safely used for present discharges. On March 13, 1882, the Vicksburg gauge read 46.5 or 45.9 on Humphreys Abbot's gauge. From the 1858 discharge curve the corresponding discharge is 1,150,000 cubic feet per second, while in the same way 1,100,000 cubic feet result for a gauge-reading of 42.4 on March 12, 1883. On March 12, 1882, the Hays' Landing discharge may be taken as 982,000 cubic feet, the observations giving a discharge of 982,000 cubic feet for a gauge-reading of 37.64 feet on March 13, 1882. What was the discharge March 11, 1883, when the Hays' Landing gauge (derived from Lake Providence) read 36.0 feet? The Hays' Landing discharges in 1882 give for gauge-readings near this value: February 2, 1882, gange equal 35.85, discharge equal 942,000 cubic feet; March 29, 1882, gauge equal 36.06, discharge equal 915,000 cubic feet.

What value shall be taken as the discharge March 11, 1883? As in a preceding case a discharge in 1882 should be selected for which slopes are nearly equal as well as gauge-readings, to those of March 11, 1883:

From this table it is seen that February 2, 1882, the slopes above and below Hays' Landing agreed on the whole more nearly with those of March 11, 1883, than did those of March 29, 1882, and hence that the discharge of February 2, 1882, proba.