and acquires sufiicient velocity to pass the discharge. It consumes
*This assertion is strictly applicable only to such places as are origins of velocity; that
is, where the velocity, having received a check from one cause or another, takes a fresh start
toward acceleration. In other situations, the velocity may not correspond with slope at all,
but be governed by the momentum already acquired, as has been acutely observed by
Captain Leach, in his observations on the CarroUtou observations of 1879, where there was
actually in some instances a reverse slope (the river running up hill) for considerable dis-
tances. See Report of Mississippi River Commission for 1882, page 103; see also the low-
water observations of 1883, in the Report of the Mississippi River Commission for 1885.
204 STARLING ON MISSISSIPPI FLOOD HEIGHTS.
time in this eftbrt, and arrives at the lowe:- end of the lake behind the
regiilar period. The flood line at this point is at first lower than it
would have been in a confined stream, but it does not afterwards ma-
terially exceed the normal height.
Supjsose, instead of a lake which is i^art of the stream, a great emptv
reservoir, access to which is given by breaches in the banks or levees
which confine the main river. The surface of the river will be lowered
and stay lowered as long as the discharge into the reservoir progresses
uniformly with the increase of flood discharge of the river. After the
reservoir is filled, it will receive Avater at the ujiper end and discharge
it at the lower. It is obvious that the eff'ect uj^on the height of the
stream at and below the lower end of the reservoir will dei)end upon
the time and manner of return, and this will depend uiion which of the
three types above mentioned the reservoir most resembles. It actually
partakes of the nature of all three. At first the flow is over shallow and
obstructed ground, then is concentrated into water-courses becoming
deeper and deeper, and at the foot of the basin it approximates to an
unobstructed lake. If the contents of the reservoir can be held back
until the body of the flood has passed, the flood-line will be lower than
in a uniform stream. This, however, can hardly be the case when the
reservoir cannot be artificially closed, the water being free to follow the
impulse of gravity, and with a greater fall than in the river. If it be
poured in on top of the flood, it may be higher, for this reason. If
there were no crevasse or outlet, but the river were confined between
banks, it would be doing its full duty. While the crevasse or outlet
(presumably in the upper part of the basin) is open and the surface of
the main stream lowered, then the river is not doing its full duty. Now
suddenly return the water lately abstracted through a channel at the
lower end of the reservoir, while the flood is at its height. As the river
has been lately doing less than its duty, so now it will have to do more,
and the surface will be raised accordingly iintil it can pass the discharge.
Now what are the facts? At Cairo, in 1882,* the top of the rise of Feb-
ruary was not past but within 0.6 of its full height on the 4th of that
month. The outflow from the St. Francis was in full progress on the
7th, and reached its height on the 13th. The second rise was within
0.2 of its crest on February 26th. The return swell at Helena began on
the 3d of March, and was at its height from the 6th to the 10th. The
* Stages of the Mississippi River from Cairo to Carrollton.
STARLING ON MISSISSIPPI FLOOD HEIGHTS. 205
flood wave of 1883 was very strongly marked.* It stood at 52.08 at
Cairo on the 28th of February. The outflow from the St. Francis began
about the 2d of March and reached its maximum on the 8th. Now a
flood wave should take about three days to j)ass from Cairo to Helena.
It is clear, then, that the return flow catches the flood. Another proof
of this is that the river in all these instances had not fairly begun to fall
at Memphis when the return Avave overtook it at Helena.
This proof is not conclusive, because it does not show that the water
which was abstracted from above was returned suddenly enough to meet
the conditions of the hypothesis. It would api:)ear from the movement
of the gauge at Helena, that its return was sudden â€” for the river had
very nearly reached a stand in each case, showing that little, if any, had
returned before the great swell. After the swell had passed, however,
there was still a large mass that returned more slowly. At Helena, on.
the 15th of March, 1882, the quantity that was returning was estimated
at about 475 000 feet per second, the river being then on the decline.
Two weeks afterw^ard, the gauge still stood Avithin 2.5 of high watery
and the stream was not fairly within its banks till nearly the middle of
April; so it cannot be denied that a considerable portion of the return
flow follows after the crest of the rise. Let us see what can be learned
from the discharge and crevasse measurements.! At Hampton, 12
miles below Memphis, the maximum discharge was estimated at 1 210 000
feet. Maximum return flow from Memphis to Helena, including the
discharge of the St. Francis River, 548 639. Escape into the Yazoo
Basin above Helena, 268 795. Net estimated discharge at Helena,
1 490 639. Actual measured discharge, 1 562 240. J Now what should
have been the maximum discharge had the St. Francis Basin been
closed (leaving open the foot, of course, for drainage)? There passed
Columbus about 1 746 000 feet, of which nearly all was in the channel
and actually measured. The discharge of the St. Francis Piiver was
estimated at 52 000, but was evidently much greater. The observations
of 1883, taken under very similar circumstances, place it at a much
higher figure. It may easily have been as much as 80 000. Adopting,
however, the estimate first given, and deducting 268 795, as before, for
* See the hydrograph of this flood, in the paper on the Improvement of the Mississippi
Kiver. Transactions, VoL XX, March, 1889. Plate XIV.
t Report of the Mississippi Kiver Commission for 1884.
J Discharge observations at Helena in 1882, in the report of the Mississippi River Com-
mission for 1883.
206 STARLING ON MISSISSIPPI FLOOD HEIGHTS.
escape into the Yazoo Bottom, we have about 1 530 000 as the probable
net discharge at Helena. The difference between this and the actual
discharge is so small that it may well be regarded as within the limits of
error. So far, then, both reason and experience seem to point to the
conclusion that the closure of the St. Francis Basin would not have any
very marked effect either in increasing or diminishing the maximum
discharge at Helena. How, now, as to the flood height?
It is not only the quantity of water but the manner of its return that
has to be considered. It was abstracted from the river in such a manner
that it probably had an effect more or less decided in diminishing the
velocity. It is now thrust back into the channel a mere mass of brute
water, in a direction approximately perpendicular to the thread of the
current. Were it returned in a direction parallel to the current, by the
laws of collision the velocity of the united mass would be equal to their
combined momenta divided by the sum of their masses. As it is, the
velocity of the returning flood water, great or small, makes no dift'er-
ence, for its effect is null by its direction. Biit even were its direction
favorable, the velocity does not exceed one foot per second.* It may
easily be understood what its deadening effect must be. To 1 200 000
cubic feet of water moving with a velocity of 5.4 per second, add 300 000
with a velocity of zero, or even one foot. The resultant velocity will be
4.5. It is not proposed to use this method quantitatively, in ascertaining
the additional elevation that must thus be given at Helena, to communi-
cate the observed velocity of 6.7. The data are too crude for such a
liurpose. Moreover, the flow was not all projected in one body, nor at
Helena itself, but in all quantities, at various points in the vicinity of the
mouth of the St. Francis Eiver. Still the principle is rigorously accu-
rate, as is apparent to any one. The water of the stream has its own
duty to perform, in transporting its weight against the resistance of
friction. Give it an additional quantity, moving with the same velocity,
and its task is not increased. But impose upon it a burden, in the shajje
of an inert mass suddenly thrust upon it, and its labor will be increased
and its velocity lessened. It may be said that the returned water will
acquire its own velocity. So it will, in time. In the meantime it is
swelling the river to a height beyond that which it would have attained
had it never been withdrawn. Therefore, while it is very possible that
* See the observations of 1882 and 1883, in the Report of the Mississippi River Commis-
siou for 1884.
STARLING ON MISSISSIPPI FLOOD HEIGHTS. 207
the discharge of 1 560 000 would have taken jilace whether the St.
Francis Basin had been closed or not, it is certain that the gauge
height at Helena was higher than it would have been in that event.
It is to be remarked that this reasoning applies only to great floods.
In small floods, the movement of the overflow water is necessarily slow
and impeded. It takes a long time to fill the reservoir, and a long time
to empty it. The proportion of water permanently retained in the lakes
and depressions of the reservoir â€” such as the sunken lands of the St.
Francis Basin â€” is relatively large, compared with the whole. In fact,
there may be overflow enough to fill the basin and no more. Therefore,
in such a ease, a reservoir may be positively beneficial. Unfortunately
in small floods this beneficial influence is of no great moment.
We now see why it was that the velocity at Helena and Arkansas City
-was so little affected by the slope as compared with stations above, as
Mhoon's and the mouth of Wliite River. Between those stations and
the principal ijoints there was interi^osed the disturbing influence of the
volume of returning water from the swamp and tributary. Had we
chosen a station like Hays' Landing, we would have found that the
velocity at high water sympathized with the slope as compared from
above rather than with that from below, because this time the disturb-
ing influence is on the lower side, between Hays' and Vicksburg (see
Plate XLY), and compare the slope Greenville-Hays' (unfortunately
defective) with the slope Hays' -Vicksburg. The slope Lake Provi-
dence-Hays' (not plotted on the jjlate) corresponds closely to the slope
Hays'-Yicksburg, showing that the velocity at Hays' is affected more
by momentum than by slope. The change really occurs about Ashton.
The data for the Yazoo Basin are much less satisfactory than for the
St. Francis. "\Ye lack the important advantage of places like Columbus
at the head of the basin and Helena at the foot, where the discharges
were measured. Furthermore, the phenomena along that front were
greatly complicated by the large escajje over the Tensas front, directly
oi^posite. The method of reasoning, however, is exactly the same.
The case of the Yazoo Basin is stronger on account of its perfect
system of drainage, and the greater quantity of clear and unobstructed
The entrance of tributaries into the main stream is governed by the
same laws. If the angle of impact be favorable and the velocities of the
two streams equal, the flood wave resulting will be of uniform height â€”
208 STARLING OX MISSISSIPPI FLOOD HEIGHTS.
that is, its crest will be parallel to the surface of the main stream so
long as the supply continues unaltered. Bat if the velocities are un-
equal, then one or the other stream will contribute material faster than
the resultant velocity will carry it off, and there Avill be a rise at the
point of junction, "flattening out" as it proceeds down stream.
It is high-water conditions that now interest us, and at such times
the entrance of the tributary waters into the Mississippi is always
modified by discharge into an intermediate reservoir. As the Arkansas
and White Rivers are the most important contributors to the flood
waters of the Lower Mississippi, we will speak particularly of them.
These streams interosculate near their mouths, and i>our their discharge
through two channels, but principally through the mouth of "White
River. It has been observed, many years ago,* that tributaries fre-
quently manifest, at their mouths, the same tendency that the main
stream does at its debouchement into the sea, namely, to form deltas.
The cause is the same â€” the discharge into a stagnant basin â€” and the
explanation is well known.
The Wuite River Basin is an oblong area, of an average width of
perhaps 13 or 14 miles, from the ujalands of Arkansas on the one
side to the Mississippi levees on the other, and about fifty miles
long from its head, just below Helena, to the Cypress Creek lins of
levees, which is the beginning of the Arkansas and Louisiana system
along the Tensas Front. The upper portion of the White River Front-
is protected by levees, and one or two limited areas are encircled by
embankments built at private expense. This basin is filled by overflow
from the Mississippi at high stages. Previously to the reconstruction
of the line of levees along the bank of Cypress Creek (known as the
Opossum Fork Levee) the lower end of the White River Basin was
open and discharged directly into the Tensas Basin, i^ouring down a
vast body of overflow, which has been variously estimated, but was.
always considered by the Louisiana people, whom it affected, as of great
extent and consequence. In 1885 and 188G the line just alluded to was
rebuilt, but suffered numerous bi-eaches in the latter year. In 1887 it
was successfully held, and it is now both high and strong. Considered
merely as a reservoir it might be thought that the influence of the
White River Basin would be inappreciable on account of its compara-
* See a very interesting and able pamphlet by Colonel Albert Stein, on the Improvement
of the Mississippi River, printed at Philadelphia iu 1842, page 5.
STARLING ON MISSISSIPPI FLOOD HEIGHTS. 209"
lively small extent. It does not take long to fill it â€” and it miglit be
supposed tlicit the discharge of the main river -would pass freely tlirongb
the overflow as between banks of water. So doubtless it would were
the swamp water absolutely stagnant. But this it is not. It keep*
flowing from the main river at the upper part of the basin, and into the-
river at the lower part. Therefore a part of the work of the river is
spent in overcoming the resistances thus intruded into the system..
This efiect should be perceptible in an increased elevation at Arkansas
City and a slightly delayed high water at that point. These phenomena
are usually so complicated with those arising from the inflow of the
tributaries that it is not easy to verify such reasoning by the test of
fact. It is tolerably certain that some efi'ect is jirodueed, but it is hard
to say how much.
Now as to the efi'ect of the tributary waters. Though the basin is
full at high water time, and freqiiently "backs up" the tributary, yet
the latter does not by any means lose its identity on this account, nor
is its velocity merged in that of the lake-like expanse. In 1882, when
the Mississippi was only a little past its extreme height, and the White
and Arkansas Eivers were comparatively low, yet the current at the
l^rinciijal common mouth was 4 feet per second, and at the secondary-
mouth (that of the Arkansas) more than 2 feet.* No better illustration-
could be desire! of the conservation of acquired velocity, maintaining
itself against slope. What the high water velocities of these streams-
may be I do not know. The obliquity at which the White Eiver meets-
the Mississippi, as shown by the maps, is apparently favorable, and'
the flood-line presents few indications of any prominence of waves at
that point. In fact, White Kiver is not a striking illustration of the-
rule commonly laid down that the oscillation at the mouths of tribu-
taries is excessive, as compared with that at intermediate points. The
reason of this no doubt is that in this situation the tributary presents
itself at a favorable inclination, and little engorgement is produced;,
and its effects are separated from those of the reservoirâ€” the latter being
most prominent below. It is otherwise with the Arkansas. The re-
turn flow from the basin is discharged between the mouth of the latter
river and Cypress Creek, just above Arkansas City.
Nevertheless the range between high and low water is still greater
* Report on the White River Front for 1882, in Report of Mississippi River Commission
for 1884, page 76.
210 STARLING ON" MISSISSIPPI FLOOD HEIGHTS.
than at the intermediate points; and the rule as laid down is generally
correct. A great part of this excessive oscillation is very justly
attributed by the Mississippi Kiver Commission to the depression of
low water at the former localities.* At Helena I have noticed, as no
doubt others have done, that the mean bed of the river, which at
moderate stages is about on a level with the zero of the gauge, at low
"water is ten feet or so below it. This phenomenon is not of universal
occurrence, though whether it is confined to the mouths of tributaries I
cannot say. It seems, however, to characterize such situations. See
Plate XLVI, which shows the difference between the mean depth and
the gauge reading at Helena in 1882 and 1884-85, at Hays' Landing
in 1882, at xVrkansas City in 1884-85, and at Warrenton (just below
Vicksburg) in 1884-85, thus giving the depression of the mean bottom
beneath the zero of the gauge. This depression is probably caused by
the scour from the discharge of the tributary, the effects of which are
generally most conspicuous at low water.
But a considerable portion of the oscillation must be attributed to
excess of height as well as of depth. The phenomenon known as the
" flattening out" of flood waves is well recognized ; and it occurs most
frequently with waves from tributaries. It will not do to ascribe this to
an absolute diflference of discharge between the mouth of the tributary
and the station below ; that is, to say that the flood wave being short
and sharp, and the layers thereof traveling with difl"erent velocities, a
high water above for one day is equivalent to a lower water below for
two days â€” for the same thing is observed for prolonged high stages,
where the discharge is necessarily equalized for great distances. The
true explanation unquestionably is the same as that given for the
excessive elevation of the returning flood water at Helena ; that is, that
it is projected into the main stream with an unfavorable velocity and
direction, and an engorgement must result until increased height gives
the requisite velocity â€” which height will be less as the velocity becomes
accelerated by the fallâ€” and the higher and sharper the wave, the
quicker and more decided the "flattening out."
It is probable that a great part of the excess in height here alluded
to is due to the influence of the reservoir rather than of the tributary.
The actions of the two are usually inextricably intermixed. It is
â™¦ See Report of the Mississippi lUver Commissiou for 1881, page IG.
STARLING ON" MISSISSIPPI FLOOD HEIGHTS. 211
certain that the largest tributariesâ€” the "^Miite and Arkansas â€” show
much less excess in height than the St. Francis and Yazooâ€” and this
may rationally be attril)uted to the smallness of the White River Basin
as compared to the others.
The attentive observer will not fail to remark that even at the time
of its greatest upward oscillation, the flood- line at the mouth of White
River is very little elevated.* In fact, leaving out minor variations, the
slope Helena- White River is materially greater than the slope White
River- Arkansas City. In the typical year 1887 these slopes were 0.37
and 0.30. These relations are altered by the conduct of the tributaries.
Thus in the two rises of 1885, the slopes Helena- White River were
respectively 0.35 and 0.33 â€” the slopes White River-Arkansas City 0.30
and 0.32. This brings to our attention the fact formerly adverted to
that volume exercises a most important influence on velocity â€” one diffi-
cult indeed to submit to calculation, but very potent notwithstanding.
It was remarked long ago by the Italian engineers, who had to wrestle
with the same problems as ourselves, that the introduction of affluents
into a stream was followed by a flattening of the sloj^e below the junc-
tion.! In spite of this adverse influence, the velocity goes on increasing.
In 1S85, at the height of the January rise, the greatest velocity at
Helena was 4.96â€” at Arkansas City, 5.37. During the April-May rise,
the velocities were probably about 4.7 and 5.4.
It must be remembered that points intermediate between tributaries
are also places of small discharge, where the "waste-weir" system has
had fuU play. It is not j^ossible that flood heights should be excessive
where there is perpetual escape over the banks and no return, as along
the Tensas Front, and the deterioration of the channel acts in further-
ance of the same end â€” so that in such places the flood height is lowered
and the low-water mark raised â€” a process precisely the reverse of that
which takes place at the mouths of tributaries.
It is hoped that the irregularities in the flood-line are sufficiently
accounted for, and the laws which govern the movements of the flood-
waters sufficiently discussed. We may now proceed to the practical
question as to the flood heights to be expected in the future, under the
changed conditions which have occurred since the epoch of the great
floods, and such other changes as may be reasonably anticii^ated.
* See Plates XLII and XLIII.
t See Frisi on Rivers and Torrents (En3li8h translation, page 115).
212 STARLING OX MISSISSIPPI FLOOD HEIGHTS.
In the present paper it is not intended to go higher than Helena.
An investigation of high-water heights above that point would require
an accurate local knowledge, and may be undertaken by those better
While the closure of the St. Francis Front may be regarded as a
â– certainty at some time in the future, it is not imminent. Whatever
progress is made in that direction may be expected to effect a re-
duction m the high-water mark at Helena. But it is a matter of
absolute uncertainty how great this progress may be. Therefore we
â€¢cannot count upon it at all, and our reasoning must proceed as though
the existing state were to be maintained.
In 1884-85 the closure of the Yazoo Front was completed. In 1886
there came a considerable flood, not so great as 1882, 1883 or 1884, but
sufficient to fill the St. Francis Bottom to its fall capacity. That year
the Helena gauge attained a height of 48.1 â€” 0.9 higher than in 1882.
It is of great consequence to us to know the discharge in 1886, but
unfortunately the data with which to determine it are very scanty. It
was not measured anywhere.* The gauge at Cairo stood at 0.85 less
than in 1882; at Columbus, 0.07 less;t at New Madrid, 0.85 less. The
.slight engorgement at Columbus indicates that the velocity was some-
what less than in 1882 â€” else why so great a gauge-height for a less flood?
By comparing the observation of March 4th, 1882, when the slope
Cairo-Columbus was almost exactly the same,| and allowing for the in-
crease in mean depth, a probable velocity is found of 7.91, and a dis-
<;harge of 1 497 213.
In 1882, at the observation stage, when the Cairo gauge was 3. 19 feet
below the high water mark of 1886, the escape over the banks, which
passed the latitude of Columbus, was estimated at 48 311 â€” at the maxi-
mum stage it was 89 000â€” so for 1886 it may fairly be estimated at 78 000 â€”
or say, altogether, for the whole discharge past Columbus, at 1 575 000.
This should nearly all have been concentrated and passed New Madrid
in the channel, as against 1 746 000 in 1882â€” and the estimate seems
to be reasonable. The discharge of the St. Francis, which appears to
* This was not the fault of the Mississippi River Commission, but was the result of the
failure of appropriations by which the most valuable labors of that body were subjected to
serious and long continued interruption.
t Mean of the Columbus and Belmont gauges.
I There is no station below with which to compire it. Even at New Madrid there is
no daily record for 1882.
STARLING ON MISSISSIPPI FLOOD HEIGHTS. 213