# Popular Science Monthly/Volume 6/December 1874/Correspondence

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RIVER HYDRAULICS.
To the Editor of The Popular Science Monthly:
IN the July number of The Popular Science Monthly, there is an article entitled "The Hydraulics of Great Rivers," said to have been mainly derived from an account, in the April number of the Edinburgh Review, of a book called "The Parana, the Uruguay, and the La Plata Estuaries," by M. Révy, a member of the Institute of Civil Engineers of Vienna.
In that article there were so many statements calculated to give an erroneous impression to the reader, that it seemed to me some comment was called for. These statements I will examine in turn:
"At the point near Rosario, where the river is 4,787 feet wide, a series of measurements has been made by M. Révy, which constitutes the largest measurement of a river section yet effected. ... The average depth was 47 1/2 feet, and the greatest 72 feet, while the sectional area measured 184,858 feet."
In the "Report upon the Physics and Hydraulics of the Mississippi River," by Captain Humphreys and Lieutenant Abbot, of the Corps of Topographical Engineers, United States Army, published by Lippincott & Co., in 1861, by authority of the War Department, there are given the dimensions of 93 cross-sections of the Mississippi River, commencing at Columbus, Ky., and extending to Fort St. Philip, some 75 miles below the city of New Orleans. Two sections, one at Osceola, Ark., the other at Randolph, Tenn., measured by Lieutenant Abbot in 1858, are, respectively, 6,880 and 6,080 feet in width, 195,844 and 184,717 square feet in area, the maximum depths being 87 and 117 feet; while four of the other sections of the Mississippi exceed 243,000 square feet in area, which M. Révy gives as the measurement of the same Rosario section during the ordinary flood. The claim, therefore, of "the largest measurement of a river-section yet effected," is hardly a valid one. The language, "largest measurement yet effected," rather gives one the idea that it is a pretty difficult matter to measure the cross-section of a large river, whereas it is a comparatively simple operation. A sounding-party in a boat, and two observers at the extremities of a carefully measured base-line on shore with theodolites taking simultaneous observations on the sounding-boat, are all that is necessary to determine the section with great accuracy.
To quote again: "While, therefore, it is easy to measure the velocity of the surface-current, it is difficult, because of this retardation beneath, to determine the mean velocity or actual flow of the river. This has never been satisfactorily done before. Many experiments, with a view to the accomplishment of this end, have indeed been made by eminent men, but they have failed to establish the relationship between the depth of the stream and the velocity of the flow. M. Révy has established that the velocity of a river is directly proportionate to its depth, diminishing or increasing therewith."
It is indeed true that many eminent men have occupied themselves with this problem; but whether they have failed to establish the relation between the velocity and depth is another question, though they certainly failed to find the relation so extremely simple as that determined by M. Révy. In the Government publication referred to, there is an outline of the history of hydraulics applied to rivers, beginning with the contributions to the subject by Castelli, a pupil of Galileo, in 1628, and extending up to the date of the Report. And, by-the-way, Dr. Thomas Young, a portrait and biographical sketch of whom are in the same July number of The Popular Science Monthly, was a contributor to this subject. The numerous formula? of different investigators are given in the Report, all reduced to a uniform system of notation, but, are rather too complicated to be merely copied in a letter, without the ​accompanying remarks and discussions to render them intelligible.
Again: "It was determined by actual experiment that the greatest velocity of current is at the surface, and the least at the bottom; and that the increase of velocity 'is in the simple ratio of the distance from the bottom.' "
Taking this ratio as true, draw a vertical right line, to any convenient scale of equal parts, to represent the depth of the river at any given place. Then the velocities at different depths would be represented graphically by an inclined right line, the lower extremity coinciding with that of the vertical and the upper at a distance from the upper extremity of the vertical equal to the surface-velocity. Humphreys and Abbot did not find the relation so simple; they demonstrate that "the velocities at different depths below the surface, in a vertical plane, vary as the abscissæ of a parabola, whose axis is parallel to the water-surface," and that "the position of the axis in calm weather is about $^3$⁄$_{10}$ of the depth below the surface, whatever be the mean velocity of the river." In order to deduce the relation between the velocity and depth, the river-depth was divided into ten equal parts, and the velocity of each was determined by 222 observations; the mean velocity, which was 0.297 D (depth) below the surface, was 3.26 feet; the mean depth 82 feet.
Very many other points of interest are brought out in the Report; such as proving that the curve of surface-velocities is also a parabola, deducing the values of the parameters of these curves, showing how the curves are affected by winds, irregularities of the bottom, etc., etc. The conclusions were deduced from an immense number of observations taken at different times of the year, different stages of high and low river, and at numerous points, by a number of careful and trained observers. In the mathematical discussion of results, the most refined methods were employed.
The current-metre used by M. Révy, although it is stated that he improved it greatly, is open to grave objections, double floats being preferable in point of accuracy in determining the laws regulating the flow of water in river-channels. I have never used any of the patent current-metres, though I have seen and examined them; but I have used the double-floats often enough to be convinced of their utility. I have, however, used an instrument very similar in principle to the current-metre, one of the numerous patent deep-sea leads. This instrument registered depths in fathoms and quarters on an index-wheel turned by the rotation of a propeller, the latter being so arranged as to turn the index-wheel on going down, but, on being drawn up through the water, was thrown out of gear, so as not to unwind the register.
This lead I tested by over one hundred careful soundings, taken at depths ranging from six to fifty fathoms, simultaneous soundings being taken with the patent lead and an ordinary lead-line. The soundings given by the patent lead were so utterly unreliable that I discarded it, and used the ordinary lead-line for the entire work of some pretty extensive hydrographic surveys. To show that this is not merely my own individual opinion about this style of instrument, I will quote, from page 621, Report of the Chief of Engineers for 1870, the criticism of General Abbot upon the same class of instruments:
"In my opinion, founded on a somewhat close study of the subject, instruments of this class are pretty toys, which have contributed more to retard the progress of discovery in the science of river hydraulics than any other one cause. This is due principally to the fact that they register their results in a kind of cipher, to which we can by no means be sure that we possess the key. To translate a given number of revolutions of a submerged wheel into velocity per second, and by this means to detect laws whose existence is denoted only by differences of a few tenths of feet in this velocity, is so delicate an operation that errors in the coefficient have usually masked the laws."
The subject of river hydraulics is quite an intricate one, and not likely to be investigated by people generally. Therefore, an article on this subject in a magazine is apt to be read and its statements accepted with less of questioning than one upon almost any other scientific topic.
I have been a constant reader of The ​Popular Science Monthly from its commencement; I know that it has been the aim to make the science of the Monthly not only popular, but accurate, and that must be my apology for writing this letter.
* Very respectfully yours,
* Charles E. L. B. Davis,
* First-Lieutenant U.S. Engineers.