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puted in the same way as for the main river. The datum line was taken at the observed reading of January 7, 17.76 feet on the local gauge. In the reduction of the low-water observations (for field report see page 3120) the cross sections were plotted to a scale of 1 inch to 200 feet horizontal and 1 inch to 10 feet vertical. The transverse curves of velocity were plotted on the cross sections in terms of meter registrations, the scale being approximately 1 inch=1 foot velocity per second. Velocities were scaled from this curve every 200 feet, or, where the curve was irregular, 100 feet. Soundings were scaled every 50 feet. The end velocity stations were 30 or 40 feet from shore, and observed velocities were applied to end areas. The discharges were computed same as described for Helena high-water series. Since the velocities of discharges were low the rating observations, ranging from 0.86 to 4.80 feet, were selected for computing the rate of the meter (for results of reduction sce table). Datum line in the low-water series is taken at 2.80 feet on the local gauge. Fulton, Tennessee.-Velocities were measured with double floats, same as described for Columbus, Ky., and were also reduced in the same manner; only one discharge was observed.

Memphis, Tennessee.-The high-water discharge section was at the same place as in 1890, about 3,500 feet above the bridge. The low-water section was near Hopefield, and about 24 miles above the high-water section. (For field reports see page 3120.) In the high-water series the areas were computed from the soundings as taken, the distances apart being computed, and the discharges were found, in the usual manner, directly from the observed velocities. In the low-water series the cross sections were plotted and also the transverse curves of velocity, and from these plots velocities were scaled off every 100 and soundings every 50 feet; from these the discharges were computed in the same way as described for Helena high-water series. On the shallow side, the end velocity station was generally about 300 feet from shore, with a sounding of about 10 feet; two-thirds of this observed velocity was applied to the end area; on the deep side of the river the distance out was about 100 feet, and four-fifths of the observed velocity at this point was applied to the end area. For results of rating meter No. 34 see table of meter ratings. Datum line taken at 3.65 feet on the standard gauge at Memphis, which was the mean of 8 a. m. and 4 p. m. readings September 29, 1891.

Helena, Arkansas.-The high-water section, 1891, is about 7,200 feet below the wharf boat and at the same place as the low-water section of 1890; the high-water section of 1890 was about 900 feet below the wharf boat. The low-water section of 1891 is about 4,500 feet below the wharf boat. (For field reports see page 3120). For high-water observations the sounding and velocity stations were located on the section line by sextant angles and at irregular intervals across the river. The distances out were computed and the areas between soundings found; these areas were summed in a series of partial areas to correspond with the velocity stations, each partial area extending on either side of the corresponding velocity station half way to the next station. Each of these partial areas was multiplied by the registrations of the meter at the corresponding station, reduced to one second of time. These partial products were summed and multiplied by the value of the meter constant a. The total area was multiplied by the meter constant b; the sum of these two products is the total discharge in cubic feet per second. On the Arkansas side of the river the distance out of the first velocity station was generally 400 or 500 feet, except on three days, when it was about 300 feet. For the first 200 feet of this distance, or as far as the river bank proper, the water was only 4 feet deep, but it then became very deep, the sounding at the first velocity station being usually about 80 feet deep at 400 or 500 feet out. Where the distance out of the velocity station was about 400 feet or over, two-thirds of the observed velocity was applied over the end area as done heretofore in similar cases, the observations on the three days above mentioned agreeing well with this. On the Mississippi side of the river the last velocity station was generally 300 to 400 feet from shore, except on four days when the distance was about 200 feet. The mean of these four days was used as velocity at this distance for the other days.

The sounding at the last velocity station was about 22 feet.

The time the meter was run at each station varied from two to seven minutes, but was generally about two and a half minutes.

Since no observations were made for rating the meter this year, the equation y = 4.1419 +0.361 (in which y velocity in feet per second and x = = registrations of meter per second) was used in computing the present set of discharges; the values of the meter constants in this equation were derived from reduction in this office last season of rating observations of December 3 and 27, 1890.

In computing datum areas the datum line is taken at 44.70 feet on the Helena gauge, and datum width at 5,800 feet; these were the observed stage and width March 26.

The other quantities tabulated have been found in the usual way, which has been fully described in previous office reports.

In the low-water series double floats were used; the method of reduction is similar to that described for Columbus, Ky. The float paths were plotted to a scale of 1 inch to 100 feet, and the cross sections to the same horizontal scale and to a vertical scale of 1 inch to 20 feet for soundings and 1 inch to 1 foot for velocities. The soundings were scaled off every 50 feet and the velocities every 100 feet, except where the curves were irregular, when one-half the distance was taken.

The distances out of the end velocity stations varied, but were generally less than 100 feet from shore; on the shallow side two-thirds of this observed velocity was applied to the end area and on the deep side four-fifths

The low-water section is about one-half mile above the high-water section. The datum line is taken in the low-water series at 4.73 feet on the standard Helena gauge, and the datum width as 1,656 feet, both as observed on September 30, 1891.

Robertsonville crevasse, 353.8 miles below Cairo.-Two sets of soundings and velocities were observed on the same day, both sets of soundings were combined in computing the area, but the velocities were applied separately, giving two discharges. In transmitting the field notes of these observations the district officer states: "The crevasse measurement is of doubtful accuracy on account of the existence of an eddy in the gap between the ends of the standing levee, in which the discharge section was located."

Arkansas City, Arkansas.-The discharge section intersects the Arkansas shore at the same point, and the Mississippi shore at a point 100 feet below the section of 1889 and 1890.

The soundings were at irregular intervals across the river, and were located on the range by transit angles, the transit being at the end of a 2,000-foot base on the Arkansas shore.

These soundings were plotted, after being corrected for error of lead line, and ordinates scaled from these cross sections every 50 feet, and tabulated for computing the areas; the discharges being computed in the same manner as described for Wilson Point.

The velocity stations were at fixed points 300 feet apart on the section, except Stations I and II, near the Mississippi shore. Until March 25 Station I was 90 feet from the bank, but after that date, on account of snags near the bank, velocities for Station I were generally taken 152 feet from bank, and only 12 feet below the surface, the depth at that point being about 40 feet. Velocities for several days were also observed at six-tenths depth 128 feet from the bank. The observer remarks that this was the "center of mass of the partial section." From these observations veloci- . ties were deduced for the point 90 feet from the bank at six-tenths depth. The observer estimates the velocity at the Mississippi bank to be five-tenths or six-tenths of that observed at 152 feet out. It was assumed that the mean velocity for 131 feet out was one-half the velocity observed at 152 feet from the bank.

From March 25 to April 20, inclusive, observations for Station II were taken at 376 feet instead of 330 feet from the bank, the latter being the regular distance. For these days velocities at 330 feet were deduced from velocities observed at 376 feet. Station XII was 96 feet from the Arkansas bank, and the velocity observed at this station was applied from the bank to midway between Stations XII and XI. On May 1 and 5 float observations were made for determining the direction of the current near the discharge section; the plots show the average direction of the floats to be about 10° 30' from a normal. This indicates that the velocity as observed on the cross section is about 1 per cent too large, but no correction has been made for this in the final reduction.

The velocities were observed with the Price current meters at six-tenths depth, and generally for five minutes at each station. Meters Nos. 4, 5, and 6 were used during the season; the results of the ratings are given on page 3143. For notes on these meters see under Wilson Point, and also report of Mr. Hoopes in Report Chief of Engineers, 1891, page 3660.

For measuring discharges the meters were used as follows: Meter No 4, March 25 and 27, May 2 to 7; meter No. 5, March 6 to 11, and March 28 to April 30; meter No. 6, March 12 to 24 and May 8 to 12, dates inclusive. The rating nearest in date was used for each discharge (except where meter was cleaned or altered), the same as at Wilson Point.

Meter No. 4 was rated March 26, but the results were so discordant they could not be used; the discharges measured with this méter March 25-27 are apparently worthless, and are not printed; the observer also rejected them on account of their discordance.

The datum line is taken at 41.73 feet on the standard gauge as tabulated; datum width taken as 3,416 feet, which was the observed width May 8. For reports on fieldwork see Report Chief Engineers, 1891, pages 3658 and 3660.

Wilson Point, Louisiana, low water of 1890, and high and low waters of 1891.-The discharge section used is 100 feet above the section used during high water of 1890. The soundings were at irregular intervals across the river; in 1890 these soundings

were located by transit angles from the end of a 1,600-foot base on the Louisiana shore; in 1891 they were located from the boat by sextant angles to 1,000-foot bases, one base on either shore, each base being used half way across the river. On April 30 the soundings were located simultaneously by the two methods, the transit on shore with 1,600-foot base, and the sextant in boat to 1,000-foot base; the results show a close agreement, the difference ranging from 0 to 39 feet, the latter being, however, exceptional, generally the difference not exceeding 6 feet; the mean difference of 94 sets, including the extreme case above noted, is 2.3 feet.

The distances out of the soundings were computed and cross sections plotted to a scale of 1 inch to 200 feet horizontal and 1 inch to 20 feet vertical. From these plots ordinates were scaled off at intervals of 50 feet, arranged so that every seventh scaled sounding coincided with a velocity station. These scaled soundings were tabulated and the partial areas computed.

The velocity stations were 300 feet apart (except Stations I and II, which were 250 feet) and always at the same place. The end velocity stations in the high-water observations were 88 and 154 feet from the Mississippi and Louisiana shores, respectively. In the low-water sets the distances from shore varied from 50 to 250 feet.

The velocity as observed at each station was applied to the corresponding partial area; this partial area extended on either side of the station half way to the adjacent stations. Each partial area was multiplied by the registrations per second of the meter at the corresponding station and the sum of these partial products was multiplied by the value of the meter constant a; to this product was added the area multiplied by the meter constant b, the sum being the total discharge per second. During the high water the entire banks between the main levees were overflowed. The field notes of this discharge over banks being incomplete, the field results were adopted and are given in the tabulation as made up by the observer, who evidently interpolated for days when it was not observed.

The Price current meter No. 6 was used for all the high-water observations except May 7, when No. 5 was used. No. 5 was also used for all the low-water observations. The meters were rated frequently and the results, derived from final reduction in this office by the method of least squares, are given in the appended table, page 3143. The table shows that the rates of the same meters are very different. In seeking to explain these differences Mr. T. C. J. Bailey, who was assistant to the surveyor, Mr. Richards, during time observations were taken, under date of January 4, 1892, writes: "The larger values of the coefficients a and b for meter No. 5 found at Huntington from those found at Wilsons Point, I think, are due to the fact that at the former place only the lower bearings were oiled, for fear of injuring the electrical connection, while at the latter place both bearings were oiled.

In the case of meter No. 6, both upper and lower bearings were oiled, except in the rating of May 8, 1891, when only the lower ones were. I have found that the stiffness of the oil used has a marked effect upon these coefficients. It has been our practice recently to use pure vaseline in the upper bearings and sperm oil in the lower, although I believe good sperm or watch oil to be preferable both above and below. Probably, however, the differences in the ratings are due more to unequally worn bearings than to any other cause. It is found that with the same impulse meter No. 6 spins different lengths of time at different inclinations, spinning the longest held with both axes horizontal, an indication of bad bearings. The base lines were checked before each rating, and being temporary could not now be remeasured."

From the foregoing, it appears that the meters were not always in the same condition, hence it was decided to use the rating for each discharge, nearest in date to that discharge observation. This was also done in the last low-water series, since a very marked difference appears in the rate of meter No. 5 after it was reported as being thoroughly cleaned.

The field notes of the low-water observations of 1890 were received in this office for reduction January 11, 1892, together with notes of a meter rating of January 19, 1891; this rating was used in computing the three discharges.

The meter was generally run for five or six minutes at each velocity station and at six-tenths depth for all the work. January 9, 1892, the third district officer, referring to these meters, states that he considers them unreliable and has ordered two new ones. (For field reports see Report Chief Engineers, 1891, page 3658.)

In all the earlier series at this place, the readings tabulated under "local gauge" are elevations of the water surface, at the discharge section, above a plane at the same elevation as the zero of the Lake Providence gauge, which is 89.62 feet above the Cairo datum plane, survey Mississippi River.

It appears from levelings to bench marks in April, 1892, that a change was made in the local guage in 1890, which affected the readings beginning with the low water of that year; this error has been corrected in the tabulation for the low-water series, but the high-water series was already computed and printed, and since the error only affected the datum quantities, no correction has been made. Therefore, to re

duce the local gange readings of this high-water series to agree with the low-water series, and also with former publications, subtract 0.25 of a foot. The datum line has been take at 41.83 feet on the local gauge as tabulated. The datum width has been taken as 3,788 feet, and the slope of the banks assumed to be uniform down to 10.5 feet on the local gauge, at which height the width has been taken as 3,632 feet for computing the datum areas of the last low-water series.

On October 19 the subsurface floats were run to determine the direction of the current near the discharge section. The results showed the general direction of the current to be about 129 from a normal, the deflection being all in the same direction. This would indicate that the discharges, as computed from meter observations on the section are about 2 per cent too large; no correction, however, has been applied for error from this source.

The observer attributes the deflection of the current to the presence of bars above and below the discharge section.

Louisiana Bend, Louisiana.-One discharge was measured here October 19, 1891; the velocity stations were from 150 to 300 feet apart. The reduction was made in the same way as for Wilson Point.

Natchez, Mississippi.—The velocity and sounding stations were coincident and always at the same places. They were located on the section by means of fixed signals on shore, and from April 4 a sextant was used in addition to the range signals. The distance between stations varied from 98 to 233 feet; the end stations were about 60 and 80 feet from shore.

The Price meter No. 25 was run at each station for two and three minutes. At Stations 4 to 9, covering the deepest part of the river, the meter was at two-tenths depth, and at stations nearer shore was at from three-tenths to six-tenths, except on one day when Stations 1 and 2 were taken at seven-tenths depth. The note book contains a table of coefficients to reduce velocities at different depths to velocity at six-tenths depth, which was stated to be derived from observations of Mr. Price in 1883. This table was used in the final reduction and is as follows: To reduce velocities to six-tenths depth multiply by the following co-efficients.

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Since the sounding and velocity stations were coincident, the mean of the velocities, as observed or reduced, at two consecutive stations, was applied to the included area. The discharges so obtained were corrected approximately by the same formula as in 1889 and 1890; the correction was from + 2,000 to +3,000 cubic feet per second for a total discharge. Four-fifths of the velocities observed at the end stations was applied to the end areas. The datum line was taken at 46.50 feet on the gauge, and the datum width as 2,135 feet; both as observed on April 11.

The rating of meter No. 25, March 25, 1891, was used, see table of ratings for values. The rating of March 8, 1890, y = 3.9515x +0.393, was used for meter No. 23. Mr. B. J. Oliveira was observer until April 3; after that Mr. G. Ed. Mott was the observer. Slope observations were made at time of discharge measurements, but the level connections between the gauges was not made until March and April, 1892. The results are given in the accompanying slope table.

Red River Landing, Louisiana.-The discharge section was at the same place as in 1889 and 1890.

The velocity and sounding stations were coincident and at the same places on the section. Stations were 200 feet apart except near the shore they were 100 feet apart. The end stations were about 80 and 100 feet from shore in the high-water series, in the low-water series the station nearest the left bank was about 330 feet from shore, the sounding at that point being only about 7 feet, at the other side the distance out was about 116 feet.

The meters were run for three minutes at six-tenths depth; meter No. 23 being used for high water, and No. 25 for low-water series. For No. 23 the results of rating of March 8, 1890 (y = 3.9515 x +0.393), were used. For No. 25 same values as for Natchez were used.

The discharges were computed in the manner described for Natchez. The formula correction varied from about 300 to +800 cubic feet per second for each total discharge.

Datum line taken as formerly, at 48.50 feet on the standard gange, datum width assumed to be 3,995 feet at that height and 3,860 feet at 24 feet on the gauge, for computing datum areas.

The discharge over bank was on line of discharge section on the right bank and partly around the end of an old levee; the discharge was all between the main Ïevees.

Mr. G. Ed. Mott was observer until April 2 and on April 20; Mr. W. G. Price was observer from April 7 to 16; Mr. B. J. Oliveira was observer during low water. The slope-gauge observations were made in April, 1891, and the level connections made in March, 1892, by Mr. G. Ed. Mott.

Simmesport, Louisiana.-The high-water discharge section was at the same place as in 1889 and 1890, that is, about 700 feet below Dam No. 3. The observer states that the low-water section is about midway between Dams Nos. 1 and 3.

The sounding and velocity stations are coincident and mainly 100 feet apart; near the shores they are about 50 feet apart.

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Price meter No. 23 was used for all discharges, except April 27, when No. 25 was used; for rating of No. 25 see table. For meter No. 23, the equation y 3.9515x+ 0.393 was used for the high-water discharges, and y 4.1701 x + 0.188 for the lowwater discharges; these are derived from rating observations of March 8, 1890; the first using all the observations, and the second using a group of the lowest velocities, since the river velocities were very low, during low water being less thán 1 foot per second, while the lowest velocity observed in the rating was 1.6 feet per second.

The meters were run at six-tenths depth except on April 13, when the meter was at four-tenths depth; to reduce this to six-tenths depth, .013 of the observed velocity was deducted.

The time of an observation was three minutes at each station, except in a few cases, when the time was six minutes. The discharges have been computed in the same manner as described for Natchez. The formula correction was from 0 to + 1,200 cubic feet per second for the high-water discharges; no correction was applied to the low-water discharges. The high-water datum line is taken at 32.30 feet on the standard Simmesport gange and the datum width as 885 feet. The low-water datum line is taken at 0.1 foot on standard Simmesport gauge, the low-water readings, as tabulated, are taken from the standard record, since the gauge record in the field book was incomplete; the low-water datum width is taken at 752 feet, as observed. October 16, 1891.

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Mr. G. Ed. Mott was the observer from March 9 to 30 and on April 17; Mr. W. G. Price was observer from April 4 to 15; Mr. R. Y. Briggs was observer April 27 and October 16 to November 20.

Slope was observed at the time of high-water discharges, and the level connections made by Mr. Mott after the water had receded.

Carrollton, Louisiana.-The sketch of discharge section accompanying the field notes shows the Carrollton section at apparently the same place as in 1890; discharges were also measured at Henry Clay avenue, which is about 2 miles below the regular section and about one-quarter mile below the lower end of the Ames Crevasse; for field report of Mr. William Garvin, assistant engineer, see Report Chief Engineers, 1891, page 3715.

The sounding and velocity stations are coincident, and at the Carrollton station from 30 to 200 feet apart; mainly being 100 or 200 feet apart.

At Henry Clay avenue they are 100 feet apart. The end stations are about 100 and 180 feet from shore at Carrollton, and 56 and 85 feet at Henry Clay avenue. Price meter No. 22 was run at six-tenths depth and for two minutes at each station; see table of meter ratings for values of constants.

The discharges have been computed in the same way as at Natchez. The formula correction was from + 1,200 to + 2,500 cubic feet per second for each total discharge at Carrollton and from + 500 to +2,100 at Henry Clay avenue. Four-fifths the velocity observed at the end stations was applied to the end areas, except at the Carrollton station 180 feet out, for which two-thirds velocity was used.

At Carrollton the datum line is taken at 13.54 feet and datum width at 2,365 feet; at Henry Clay avenue the same datum line is taken and datum width at 2,080 feet, the standard Carrollton gauge being used for both sections in the tabulation.

The observer attributes the large variations in discharges obtained at Henry Clay avenue, to the eddies or irregularities in the current produced by the crevasse.

When not otherwise stated, results given in this appendix are derived from final reduction at the office of the secretary, Mississippi River Commission.

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