Library Engineering Science Series THE HYDRAULIC PRINCIPLES GOVERNING RIVER AND HARBOR CONSTRUCTION ENGINEERING SCIENCE SERIES EDITED BY DUGALD C. JACKSON, C.E. PROFESSOR OF ELECTRICAL ENGINEERING MASSACHUSETTS INSTITUTE OF TECHNOLOGY FELLOW AND PAST PRESIDENT A.I.E.E. EARLE R. HEDRICK, Ph.D. PROCESSOR or MATHEMATICS, UNIVERSITY OF MISSOUBI MEMBER A.S.M.E. THE HYDRAULIC PRINCIPLES GOVERNING RIVER AND HARBOR CONSTRUCTION.. BY CURTIS McD. TOWNSEND COLONEL, UNITED STATES ARMY (RETIRED), MEMBER, AMERICAN SOCIETY OF CIVIL ENGINEERS, WESTERN SOCIETY OF ENGINEERS, ST. LOUIS SOCIETY OF ENGINEERS, ETC.; LATE PRESIDENT, MISSISSIPPI RIVER COMMISSION gorfe THE MACMILLAN COMPANY 1922 AU rights reserved FEINTED IN THE UNITED STATES OF AMEKICA Engineering Library COPYRIGHT, 1922, BY THE MACMILLAN COMPANY Set up and electrotyped. Published July, 1922, Press of J. J. Little & Ives Co. New York CONTENTS CHAPTER I PAGES INTRODUCTION 1-4 CHAPTER II THE FORMATION OF RIVERS ........ 5-14 The Ocean, the Origin of the Water Supply of Rivers The Sur- face Flow The Movement of Eroded Material The Subterra- nean Flow The Formation of an Alluvial Valley The Influence of Snow on the River's Discharge The Area of Deposition Glacial Action The Formation of the River Channel . CHAPTER III LAWS GOVERNING THE FLOW OF WATER IN RIVERS . . . 15-23 The Derivation of Hydraulic Formulas The Coefficient of Roughness Minimum and Maximum Critical Stages Diffi- culties of Applying Hydraulic Formulas to River Channels Modifications Due to the Velocity of Approach The Flow of Water in Bends The Effect of Obstacles on the Flow of Rivers The Flow Near the Mouths of Rivers. CHAPTER IV THE FLOW OF SEDIMENT IN NON-TIDAL RIVERS .... 24-34 Material in Solution Material in Suspension Relation of Slope to Degree of Saturation Movement of Material Along the River's Bed Sand Waves Proportion of Material in Suspen- sion and Moving as Sand Waves Movement of Material in Bends and in Straight Reaches Resultant River Sections The Radii of Curvature of Bends Deposition of Sediment Caused by Dikes Depth in Pools a Function of a River's Discharge; That on Bars of its Slope A Comparison of the Flow of Sediment in the Strait Con- necting Lake Huron and Lake Erie with that in the Mississippi River The Effect on Channel Depths of the Inclination of the Axis of the Bar to that of the Channel The Flow of a River Sum- marized. CHAPTER V A RIVER'S DISCHARGE AND FLOOD PREDICTION . . . 35-43 The Discharge Curve of Conduits and its Equation The 813606 VI CONTENTS PAGES Mean Discharge Curve of a River The Danger in its Application The Influence of a Tributary on the Discharge Curve The Effect of Changes in Slope Rate of Transmission of the Flood Wave Flood Prediction by Measuring Rainfall Variability of the Rainfall Computations of the Run-off Variations in Dif- ferent Months Prediction of Floods in the Department of Ardeche, France Flood Prediction by Discharge Measurement . Method Employed on the Elbe River Flood Prediction by Gauge Relations Method Employed on the Rhine River Method Employed on the Seine River Combinations of the Methods of Belgrade and Von Tein suggested for the Rivers of the United States. CHAPTER VI RIVER REGULATION ......... 44-54 Methods Proposed for Improving River Channels The Neces- sity for Obtaining Increased Depths in Rivers Parallel Longitudi 1 nal Dikes River Straightening The French Method of River Regulation M. Fargues' Laws The Proper Curve to be Given the Channel Discussion of the Effect of Straight Reaches on the Shape of the Bars The Height of Jetties and Dikes River Improvement not Susceptible of Rigid Mathematical Analysis The River Rhine Improved by Straightening. CHAPTER VII DIKE CONSTRUCTION AND BANK PROTECTION .... 55-66 Requirements of the French System of River Regulation A Rigid Adherence Not Necessary in the United States The Longi- tudinal Dike Replaced by Bank Revetment Permeable Dikes Substituted for Those of Stone and Gravel Danger of Destruc- tion of Permeable Dikes by Drift and Ice Retards Where Material in Suspension is Small, Dikes of Stone and Brush Neces- sary Dike Construction on the Rhine The Proper Location and Inclination of Spur-Dikes French and Italian Practice Ad- vantages of Permeable Dikes on the Concave Bank of a River Method of Bank Protection Generally Adopted in Europe The Blees Werke of the Rhine The Triangle Werke Channel Straightening on the Rhine as a Method of Protecting Banks Noblings Bank Revetment in the United States Concrete Mats Precautions to be Observed in Mattrass Construction Substitutes Suggested for Bank Protection. CHAPTER VIII RIVER IMPROVEMENT BY CANALIZATION , . . . . 67-88 The Effect of a Dam on a River's Regimen The Substitution of Movable Dams The Types of Movable Dams Dams Rarely Constructed of a Single Type The Drowning Out of Dams The CONTENTS Vll PAGES Types Ordinarily Used in the United States The Substitution of Concrete and Metal for Wood in Dam Construction Increase in the Heighth of Dams Due to the Development of Electrical Power Effect on the Stability of the Structures Foundations of Rock, Gravel, Sand and Clay Methods of Reducing Percolation Under Dams Protection from Overflow Protection of Banks from Percolation and Eddy Action The Location of Dams The Lateral Canal The Flow of Sediment in Pools A River Flowing through Glacial Drift More Readily Improved by Canalization Than One Flowing in an Alluvial Valley The St. Lawrence Valley versus the Mississippi Canalization versus Regulation The Lateral Canal versus a Canalized Bed The Reduction of Reservoir Capacity by the Deposition of Sediment Methods of Removing the Deposition The Sirhind Irrigation Canal in India Inclines, Lifts and Locks The Lock The Lock Gate Re- pairs to Lock Gates and Their Protection Filling and Emptying Locks The Width of Locks. CHAPTER IX DREDGING, REMOVAL OP OBSTRUCTIONS, BUOYS AND LIGHTS . . 89-97 A. DREDGING .......:.. 89-93 Dredging in Valleys Formed of Glacial Drift The Improvement of Rivers Emptying Into the Great Lakes The Lowering of Pools from Dredging Dredging in Canalized Rivers Below Dams The Limitations of Dredging in Rivers Carrying Large Amounts of Sedi- ment Dredging Required When it is Attempted to Straighten a River by Regulation Rate of Movement of Sand Waves Through Straight Reaches The Adaptability of Dredges to Various Kinds of Work Substitutes Proposed for Dredging. B. ROCK EXCAVATION . . .. . . . . . 94-95 By Coffer Dam By Lobnitz Crusher The Diving Bell Drill Barges Rock Removal at Hell Gate, New York Harbor and Blossom Rock, San Francisco Harbor. C. REMOVAL OF SNAGS . . . . . . . . 95-96 The Snag Boat The Removal of Trees from Caving Banks The Removal of Rafts from the Atchafalaya and Red Rivers. D. BUOYS, LIGHTS AND BEACONS . . . . . . 96-97 The Engineer Department Assists the Bureau of Lighthouses in Light and Buoy Location on the Western Rivers of the United States Methods of Marking a Channel Lighthouses Buoys Auxiliary Aids. CHAPTER X RESERVOIRS AND LEVEES AS A MEANS OF IMPROVING NAVIGATION . 98-106 RESERVOIRS < . . . , . . ' : . . 98-102 The Effect of Increasing the River's Discharge on Depths in Pools Vlll CONTENTS PAGES and Over Bars The Effect of a Constant Flow at a Given Stage The Changes in Depth in the Mississippi River as Its Discharge Increases Reservoir Construction at the Head Waters of the Mis- sissippi River Their Influence on Navigable Depths The Dif- ficulties in Practically Manipulating Reservoirs General Rules Observed in Operating the Reservoirs on the Upper Mississippi River. IMPROVING THE Low WATER CHANNEL BY CONFINING THE FLOOD DIS- CHARGE BETWEEN LEVEES 102-106 The Force Generated During Floods Its Relation to Useful Work Difficulty of Constructing Levees so as to Force the Flood Discharge to Follow the Low Water Channel The Use of Levees to Improve Navigation, Corollary of River Straightening Euro- pean Practice Improvement of the Danube River Comparison of the Improvement of the Danube and Rhone Rivers. CHAPTER XI FLOOD PROTECTION ......... 107-124 The Area of Erosion Forest Growth Terraces The Zone of Deposition Levees Retaining Dams Hydraulic Mining on the Tributaries of the Sacramento River The Raising of the River Bed from Deforestation and Drainage The Difficulties of the Problem The Claims of M. Proney and Herr Wex Recent Investigations The Yellow River of China The Protection of the Portion of a Valley where Deposition and Fill are in Unstable Equilibrium Mounds Forest Growth Storage Reservoirs Retarding Basis Enlargement of the River Section River Straightening and Cut-Offs Outlets Waste Weirs Improve- ment of the Sacramento River The Junction of the Red, Atchafalaya and Mississippi Rivers Levees Their Form and Dimensions Methods Employed in Levee Construction Flood Protection of the Miami River The Proper Method of Treat- ment of the Flood Waters of a Large River Basin. CHAPTER XII ESTUARIES 125-132 The Tidal Flow The Influence of the Form of the Estuary on the Tidal Flow Tidal Propogation The Bore The Effect of Tidal Oscillation on the Flow of Rivers The Movement of Silt in Estuaries The Difference in the Principles Governing the Im- provement of the Tidal and Non-Tidal Portions of a River The Objections to the Curved Trace in Estuaries Removal of Barriers to the Tidal Flow The Width of the Tidal Section Longitudi- nal versus Spur Dikes Dredging The Improvement of the River Clyde. CONTENTS IX CHAPTER XIII PAGES THE MOUTHS OF RIVERS . . . . . * . . 133-144 Ocean] Waves Their Height Their Oscillation Their Form Their Force Damage Caused to Breakwaters Damage to Cliffs Movement of Material by Wave Action on a Beach Effect of an Obstacle on the Flow of Sediment The Deposition at the Mouths of Rivers Deltas The Improvement of Deltas The Danube and the Mississippi Rivers The Rhone River Rivers whose Outlets Maintain Themselves The Improvement of the Entrance to New York Harbor Tidal Rivers Improved by Parallel Jetties Sluicing Basins The Malamocco Entrance to the Lagoon of Venice Converging Dikes The Employment of a Single Jetty The Improvement of the Mouth of Cape Fear River The Single Jetty at Sandusky Harbor The Reaction Break- water Wave Action Less Intense Against Jetties on River Bars than Against Harbor Breakwaters Mattrass Foundations. CHAPTER XIV HARBORS 145-153 The Location of Harbors Essential Elements of Harbor Con- struction Harbor Entrances Their Proper Form to Produce the Greatest Tranquillity The Width of Entrance The Exterior Breakwaters Employed on the Great Lakes to Reduce Wave Action within the Harbor Stilling Basins Rubble Mound Breakwaters Effect of Waves on their Sea Slopes The Paving of the Sea Slope The Substitution of Stone or Concrete in Large Masses for the Pavement General Dimensions of Breakwaters in the United States Breakwater Construction Dependent on the Character of the Quarry from which the Stone is Derived The Unpaved Breakwater More Effective in Dissipating the Wave Energy Vertical Breakwaters Causes of Failure of Early Masonry Types Advantages in the Substitution of Concrete for Masonry Verti- cal Breakwaters on Rubble Mounds The Failure of the Alderney Breakwater and that at Sandy Beach Harbor of Refuge, Mass. The Necessity of Protecting the Vertical Breakwater on a Vertical Mound by Wave Breakers of Concrete Blocks The Timber Crib Breakwater of the Great Lakes The Necessity for Tidal Basins in Europe The Advantages of the Piers Employed in the United States. CHAPTER XV THE ECONOMIES OF WATER TRANSPORTATION ... . . 154-166 The Determination of the Worthiness of an Improvement Re- quired Before Final Legislative Action Economies of River Navigation with Animal Traction Economies Produced by the Introduction of the Locomotive The Resistance to Motion of Boat and Car Economies Resulting from Enlarging Car and CONTENTS FAQ] Boat The Compound Condensing Marine Engine versus The Non- Condensing Locomotive Fuel Economy, and Labor Expenditure per ton Mile on Rail and River Overhead Charges Relative Costs of Constructing and Maintaining Rivers and Railroads Causes of Decline in Commerce on Western Rivers Car Ferries Influence of East and West Movement of Freight in the United States on Transportation by Rail and Water Recent Legislative Enactment Beneficial to Water Transportation The Effect of Delays in Loading and Unloading on the Cost of Transportation The Economic Limitations to the Size of Vessels The Relation of Density of Traffic to Ocean Transportation The Dimensions of Piers The Pier Shed Railroad Tracks on Piers The Effect of Tidal Fluctuation and Flood Heights on Loading Vessels. APPENDIX A . . ....... 167-172 Bibliographic Notes. APPENDIX B 173-179 Flood Prediction at the Mouth of the Ohio River Flood Pre- diction at the Mouth of the Missouri River Flood Prediction at the Mouth of the White River. (See also TABLES.) APPENDIX C. THE INFLUENCE OF FOREST ON STREAMS . . 180-182 Report of Meteorological Section of the Experimental Depart- ment of Forestry of Germany. TABLES 183-189 Table I. Computation of the Ohio River Floods at Cairo Table II. Computation of Mississippi River Floods at Cairo Table III. Computation of Missouri River Floods at St. Louis Table IV. Computation of Mississippi River Floods at the Mouth of White River. RIVER AND HARBOR CONSTRUCTION CHAPTER I INTRODUCTION During his professional career the writer has prepared numerous projects, and has answered many criticisms of the methods em- ployed in the improvement of rivers and harbors. The following pages are derived principally from these sources. In replying to complainants, the author came to the conclusion that there was a commendable interest among the American people in the sub- ject of the improvement of rivers and harbors, and a deplorable ignorance of the fundamental principles governing the flow of water in natural channels. Such is his apology for this pub- lication. The ordinary textbook on hydraulics treats principally of the flow of water in pipes and conduits, and the ordinary engineer is apt to consider a river as merely a large conduit governed by the same laws, ignoring the change in conditions arising from the fact that the walls of a pipe are not affected by the velocity of flow through it, while the channels of a silt-bearing stream expand or contract with every change in the volume of discharge. This fact is ig- nored also by many writers on river hydraulics, whose textbooks contain more_or less elaborate discussions of the formulas Q = VA, and V = C\/RS, which are authoritatively stated as guides for de- termining the depth in a contracted waterway. In a rock cut, these formulas give as accurate results as they do when applied to a sewer or to a pipe, but in the alluvium of the Mississippi or Missouri rivers, scour caused by the contraction produces a radical change in the hydraulic radius. Water flow- ing in a river channel is governed by the same immutable laws as when flowing in pipes, but these laws are so modified in the river by those governing the flow of sediment that effects are produced which are erroneously termed exceptions to general laws. For example if a given pipe is replaced by one of less diameter, the head (slope) must be increased to obtain the same discharge. 1 2 IL'iU RIVERS AND HARBORS " *" c Cl v>* > *,""*** * *' * In ii stream ^with, a mobile bed, however, if the channel is con- tracted and at the same time straightened, the resultant increase in velocity produces a scour which enlarges the hydraulic radius to such an extent as to reduce the slope through the contracted section. In the discussion of hydraulic problems, there is too great a tendency to draw conclusions from special cases without taking into consideration all the conditions which surround them. Thus, if one side of a hill is covered with trees and the other side is cul- tivated, the rapidity with which the snow melts is attributed to the forest growth, without taking into consideration the fact that one may have a southern exposure and the other a northern, and that the inclination of the sun's rays to the surface of the ground may have a greater effect in melting the snow than the surface covering. As another illustration, if one year's flood, attaining a height X at a locality A, produced a height Y at a point B further down a river, it often has been assumed that upon a repetition of the height X at A, the height F would recur at B unless there had been an enlargement or diminution of the river section between the two localities, thereby ignoring the influence of the discharge of the tributaries below B on the river's regimen. While harbors were improved before the Christian Era, and canals were constructed in the Middle Ages, the improvement of rivers is of recent origin, and owes its development to the invention of the steamboat. The early efforts to regulate rivers were gen- erally unsuccessful, and it is only within the past thirty years that the correct principles of river regulation have been evolved, principally by French and German engineers. There is a strong temptation for the author of a textbook to compile data from the works of earlier authors. An American unfamiliar with foreign languages is practically limited in his knowledge of European practice in river improvement to transla- tions of certain French and German works made by officers of the Corps of Engineers, U. S. Army, forty or fifty years ago, which are now out of print, and to the proceedings of the various navigation congresses. Some of our textbooks therefore quote with approval methods of river regulation long since abandoned by the nations in which they originated. For example, the proj- ect of 1882 for improving the Danube river, though vitally modi- INTRODUCTION 3 fied by the Austrian Government in 1899, is still given as an illus- tration of the proper method of improving a river. As this book has been derived principally from reports and addresses in advocacy of certain propositions, the author recog- nizes that he is prone to discuss a subject as a lawyer would pre- sent the evidence before a jury, and that he may at times give too great weight to his own views instead of judicially summing up the concensus of opinion among engineers. He has also failed to give proper credit to the numerous authors from whom he has derived his ideas. He makes no claim to originality, but his notes extend over an active professional life of forty years, and he has now forgotten the sources of much of his information. De Mas' Rivieres a Courant Libre, and Harcourt's Rivers and Canals and Harbours and Docks, are the foundations of the struc- ture; Jasmund's Die Arbeiten der Rheinstrom-Bauverwaltung , and the Report of the Italian Commission appointed in 1903 to in- vestigate the internal navigation of the valley of the Po, have been quoted freely. The student will also recognize extracts from Van Ornum's Regulation of Rivers, Thomas and Watts' Improvement of Rivers, Shield's Principles and Practice of Harbour Construction, and Wheeler's Tidal Rivers. The ANNALES DBS FONTS ET CHAUS- SEES, the transactions of the various engineering societies, the PROCEEDINGS OF THE PERMANENT ASSOCIATION OF NAVIGATION CONGRESSES, THE PROFESSIONAL MEMOIRS, CORPS OF ENGI- NEERS, U. S. A., and the REPORTS OF THE CHIEF OF ENGINEERS, U. S. ARMY, are mines of information on river and harbor con- struction. While a proper conception of the theory of engineering con- struction is necessary, a knowledge of existing practice is also indispensable. In river and harbor construction, every engineer- ing district affords data for an extensive treatise on that subject, and there is urgent need of a condensed work on American prac- tice in the improvement of estuaries, of the mouths of rivers, and of harbors, similar to Van Ornum's book on River Regulation, and Thomas and Watts' chapters on lock and dam construction in their book on Improvements of Rivers. A statement of the principles of river hydraulics within the limits of a single volume has required intense condensation and to attempt to illustrate the applications of these principles in practice would require a large addition to its pages. By request, 4 RIVERS AND HARBORS notes, indicated in the text by numbers, have been appended which, while not attempting to give a complete bibliography, will show the student where he can find practical applications of the prin- ciples discussed, and the pros and cons of subjects which may have been too positively stated in the text. These notes are of more value to officers of the Corps of Engineers and others who have access to the library of the Engineers School of the U. S. Army, or to the Congressional Library at Washington, D.C., than to the general reader, as the writer has found by experience that, ordinarily, libraries are limited in volumes on river hydraulics to the textbooks quoted above. CHAPTER II THE FORMATION OF RIVERS The origin of the water supply, of rivers and streams, is the ocean into which they in turn discharge. Aqueous vapor evapo- rated from its surface is carried by the winds over the land, where it condenses and is deposited as rain or snow. A certain portion of this precipitation returns to the sea over the surface of the ground, while another part is absorbed by the soil, and after a subterranean flow of variable duration appears on the earth's surface in springs. In this general flow of moisture from ocean to land and return, there are, however, numerous short circuits. Evaporation occurs not only from the surface of rivers and streams, but also from the soil itself, and in such quantities during summer months as to materially reduce the surface flow. Over large lakes, the evaporation may be sufficient to cause a local precipitation along their borders. The roots of trees and of other vegetation, under certain conditions, extract a large percentage of the water ab- sorbed by the soil, and return it to the atmosphere through their leaves, thus reducing the subterranean flow of streams. Also at the mouths of rivers there is frequently a large ebb and flow of salt water from the sea, due to tidal influences. The ratio of surface flow to absorption is dependent on the permeability of the soil, the surface covering, its surface slope, and the intensity and duration of the rainfall. A sandy soil absorbs more water than one whose principal ingredient is clay, and even rock, especially limestone, frequently contains permeable seams and crevices, which permit a large subterranean flow. A sandy soil in summer may absorb a rainfall which in early Spring would have flowed off its surface, due to its frozen condition. In forests, the decayed leaves and mosses create a humus which will absorb a large amount of water, but many kinds of vegeta- tion produce roots which seriously interfere with the flow of such waters in the underlying soil, retaining it in the humus as in a reservoir. The roots of Bermuda grass form a more impermeable 5 6 RIVERS AND HARBORS covering than those of wheat, corn or cotton. A root of an Osage orange tree may extend a long distance in a horizontal direction in its search for moisture and open up a sub-surface channel around it which ultimately may be destructive to a levee; while roots of other species of forest growth may retard such flow. The surface slope affects the degree of saturation of the soil. A hillside retains less water than a plain, since both the surface flow and the subterranean flow are accelerated by the slope. Even with porous soils, there is a period during every rainfall when the precipitation exceeds the capacity of the soil to absorb it and of the subterranean channels to remove it; the surplus water then flows on the surface. The surface flow is therefore a function of the intensity of the precipitation, the slope of the ground, and the roughness of its surface covering. During a light rainfall, in a plowed field, the degree of saturation and the velocity of the surface discharge is affected by the direction of the furrows. Vegetation materially retards the flow. In forests, fallen trees, branches, and brush may collect in heaps which create timber dams, similar to the rafts which formerly obstructed some of our western rivers. A heavy precipitation on a steep mountain slope produces such a volume and velocity of discharge as to create a powerful erosive action which not only removes particles of soil and its vegetable covering but, when concentrated in the channels of ravines, can move large boulders and forest growth. Every hillside is being degraded by this force, and it is assisted in its destructive work by frost, which disintegrates rock masses and renders them sus- ceptible to its action. 1 The material eroded from the hills is transported as far as the waters which dislodged it maintain the velocity they originally 1 Aa an example of the tran3portive force of rapidly moving water, the following personal experience of the writer may be cited. He was requested by the Insular Government of the Philippines to inspect a road which had just been completed in the valley of the Bug River, which flows in the mountainous regions of the province of Benguet, Island of Luzon. At a certain locality, in order to form a shelf on which to construct the roadway, a large amount of rock had been blasted from the mountain side and had fallen into the valley below. At the the time of the inspection, the channel of the river was so choked with debris that its flow, then insignificant, was through the dump pile. A few days afterward a rainfall of eighteen inches occurred in the valley, most of the pre- cipitation occurring within twenty-four hours. Three days after the storm, the writer made a return trip over the remnants of the road. The Bug River was again an insignificant stream, but the rock pile had disappeared, and the river was placidly flowing in its original bed. The debris was scattered through the lower valley, masses of rock weighing at least ten tons having been transported long distances. THE FORMATION OF RIVERS 7 acquired, but in the channels of streams flowing from a mountain peak to the sea the slope of the earth's surface rapidly diminishes. At first the concentration of the flow in gullies and ravines, by reducing the frictional resistance, will maintain the velocity ac- quired on the steeper slope, but as the ravine widens into a valley the carrying capacity of its waters is diminished and a deposition of the material transported occurs. With a reduction in the velocity, the boulders are first deposited, then successively smaller stones, gravel, and the heavier sands. The finer sands and clays are frequently transported long distances, a sufficient reduction in velocity not occurring to cause their deposition until the stream empties into a lake or sea. Since the velocity of flow varies in different parts of the cross- section of a torrential stream, as in other channels, finer material is deposited intermingled with the boulders. A boulder once at rest induces whirls and eddies which cause the settlement around it of sand and gravel, imbedding it in the channel so that a flood of greater intensity or longer duration is necessary to set it in motion again. In the disintegration of stratified rock masses, the fragments, even those of the size of gravel, are in the form of slabs when they are first detached, and they may be deposited overlapping one another so as to form a pavement which may oppose a great resistance to erosion so long as the current main- tains the direction that caused the deposition, yet a change in the direction of the flow attacking these slabs from the side instead of on the surface may destroy the pavement. For example, a gravel bar in a river may resist the flow of floods for ages, but if a dam is constructed on such a foundation, the percolation under it may first remove particles of sand and clay mixed with the gravel and thus create a channel through which the velocity of the discharge, though less than that of an unobstructed flood, may dislodge the gravel by reason of the change in direction of its attack. The imbedding of detritus in stream channels tends to reduce the area of deposition of the coarser materials to narrow limits. But as rock masses roll down a stream they impinge upon one another, producing a grinding effect which reduces the dimensions of the boulders, breaks the slabs into smaller pieces, converts stone into gravel and gravel into sand, and tends to give a spherical form to all the elements set in motion. This facilitates the 8 RIVERS AND HARBORS movement and causes a gradual reduction in the size of the ele- ments which form the deposits, the farther the debris is trans- ported from the zone of degradation. Since material rolling along a stream bed has a smaller velocity than the current, and since a heavy precipitation is of short duration, the movement of such material is intermittent and the distance traveled is relatively short during each storm; but material fine enough to be carried in suspension moves with the velocity of the stream, and is less subject to this intermittent deposition. The subterranean flow of waters is slow except through rock crevices, due to the obstructions which particles of the soil offer to its passage. It is governed by the same laws as is other flowing water, its velocity being a direct function of the head and an inverse function of frictional resistance. However, as will be explained in discussing the laws governing the flow of water, the ordinary hydraulic formulas are inapplicable to subterranean flow, for it has been found by experiment that the velocity varies approximately as the head instead of as the square root of the head. There is also a great diminution in the velocity, that in pipes for instance being ordinarily measured in feet per second, whereas that in ordinary soil is measured in feet per day. Since the permeable crust of the earth is of vast extent and is frequently of great depth, there exists an underground water- system of streams, rivers, and lakes similar to those which appear on the surface, but these underground streams flow with very much smaller velocity. Wherever the surface of the ground intersects the surface of one of these subterranean streams, springs appear. These springs increase the discharge of a river at all stages, and they are its principal sources of supply during low water. If this intersection takes place in the bed of a stream, the differ- ence of head of the underground waters and of the surface waters determines the rate of discharge; and when the head of the surface water is the greater, the surface stream may even dis- appear and be absorbed in the sub-surface flow. The failure to recognize this fundamental principle has caused large errors in estimating the capacity of reservoirs to store water and of drain- age ditches to discharge it. Variations in precipitation cause a rise and fall of the surface of these underground waters, similar to the floods in rivers. On account of the sluggishness of the flow and the great reservoir capacity of THE FORMATION OF RIVERS 9 the permeable strata, a long period of time may elapse before these changes manifest themselves on the earth's surface. For example, at the head waters of the Mississippi River, a yearly minimum rainfall does not produce a minimum stream flow until the low water season of the year succeeding its occurrence. The water which filters through soils for long distances carries little material in suspension, but it may contain a large amount of soluble matter, which, by evaporation of the water, may produce deposits of considerable extent. If the head of the sub- surface flow exceeds one-tenth of the distance it travels, however, the water may acquire sufficient force to remove particles of the soil, which is an important consideration in designing levees and other structures whose foundations rest on permeable material. While subterranean flow is the principal source of a river's water supply during low water, the higher stages of the river are created by the addition thereto of surface flow. Hence a river's stage becomes a function of the relative amount of the precipitation that is absorbed by the ground and by the surface flow, but it is modified by the reservoir capacity of the channel, and by evaporation. A lake tends to diminish a river's maximum discharge and to increase the minimum discharge. If the pre- cipitation is greater during the winter and early spring than during the summer and early fall, evaporation will diminish the low water flow. But in localities where the conditions are re- versed, evaporation will reduce the discharge during the summer high stages, particularly where reservoirs expose a large surface to the action of winds and of the sun's rays. During extreme low stages, the velocity of the discharge is usually insufficient to move the heavier material along the stream bed and only a small amount of fine material capable of being carried in suspension flows into the stream. As the discharge in- creases, however, the capacity of a stream to transport solid material rapidly increases, though the amount and character of the material transported is more dependent on the character of the soil on which the rain falls than on the capacity of the river channel to carry it away. The surface flow from a prairie contains a large amount of fine sand and clay which is readily carried in suspension, while the detritus from a rocky hillside consists principally of gravel and coarse sand which is rolled along the river bed. 10 RIVERS AND HARBORS Material that is in suspension while moving with the velocity of the water is also deposited when this velocity is reduced for any cause. As a stream's discharge increases, low lands are gradually submerged, and since the velocity of the overflow is much less than that of the main stream, there is a deposit of sediment, which is greatest where the change in velocity first occurs, and gradually diminishes as the amount of material in the water is reduced by the deposition. By this means a silt-bearing stream builds up its bank, producing the characteristic of alluvial valleys that the ground close to the river channel during medium stages of the water is higher than the land more distant. The rainfall in such valleys, instead of flowing directly into the river, flows away from it and toward the area of deposition from the bordering hills, where (augmented by the discharge from the hills) it creates a stream which gradually attains sufficient volume to erode a channel through the ridge which forms the banks of the main river and thereupon discharges into the river. As these silt deposits have been made during geological eons of time, they frequently attain great depth, and the main river which has been depositing sediment in its bed as well as on its banks may be flowing on a ridge, its thalweg having a higher elevation than the surface of the ground at the foot of the hills that limit its valley. The alluvium thus formed is readily eroded whenever it is attacked by water flowing with a greater velocity than that which deposited it, and a change in the direction of the current even at medium or low stages may cause the banks to cave. For this reason also the closure of a crevasse in a levee line on such alluvial soils as are found in the Mississippi Valley becomes a difficult problem, if the water is flowing through it with a depth exceeding six feet. When the precipitation takes the form of snow, it neither enters the soil nor flows off its surface immediately. The density of a snow covering varies from that of ice, when it falls as sleet or hail, to a light fluffy substance which is exceedingly porous when first deposited but which is liable to be drifted by winds into large snow banks where it becomes more compacted. A light rain followed by freezing weather may convert the surface of porous snow into a crust of impervious ice. When snow is exposed to the melting effect of the sun's rays, its transformation into water is gradual, on account of its latent THE FORMATION OF RIVERS 11 heat, and its run-off resembles that from a spring; but if exposed to a warm rain or warm winds, unless a crust of ice exists which will protect it from percolation, the snow becomes saturated with water, which, absorbing the latent heat, suddenly melts it. The resulting flow is added to that of the delayed precipitation, and the entire mass starts with destructive violence on its path to the sea. A layer of ice also prevents soil percolation, and thus in- creases surface flow. The combination of a layer of sleet formed in early winter, making an impervious crust on a hillside, and covered later with a thick coating of porous snow melted in the spring by a heavy fall of rain, will produce a most destructive flood. Freezing weather largely reduces surface flow by converting the water into ice, but even with the surface flow thus diminished, high stages may occur in a stream on account of the formation of ice gorges. The precipitation at any locality is very variable, not only in the amount which falls per day, per month, and per year, but even in averages of ten-year intervals. Thus in the records of precipi- tation at New York City, a period of ten years can be selected in which the average rainfall exceeds forty-eight inches per annum, and another in which it is only thirty-five inches. There is also a great variation in the amount and intensity of the rainfall at different localities in the same basin. Even within the limits of a city there may be a marked difference in the discharge of sewers during the same storm, due to this cause. The discharge of a river which drains a large area is affected not only by the variation in the amount of precipitation but also by the difference in the time required by both the subterranean and the surface flows to empty into it. In a stream that derives its waters from a single hill, extreme variations in high and low water are frequent; but as the drainage area increases, the probability of the superposition of either the extreme high or low stages of the various tributaries which form the main stream diminishes, since the shorter tributaries or those with the steeper slopes deliver their maximum or minimum discharge earlier than those of greater length or those of gentler slope. The subterranean flow is similarly retarded. The reservoir capacity of the river bed also tends to diminish the maximum discharge and to increase the minimum discharge, because a large amount of water is expended in filling the bed as 12 RIVERS AND HARBORS the river rises, and runs out as it falls, the duration of the stage being thereby increased, and the maximum or minimum discharge correspondingly modified. Both high and low stages may be so prolonged, however, that the reservoir capacity of the channel is exhausted, but the longer the river and the greater its drainage area, the less frequently either extreme high or low water occurs. As a result, a river, even at low stages, flows on its lower reaches with sufficient velocity to cave its banks and create a channel proportionate to its volume in the fine sediment which has been deposited there. The degradation of the hills and the filling of the valleys has continued for geological ages, gradually raising the surface of the ground in the valley of a river and increasing its length by deposits at its mouth. During the period, the water which has been transporting this material has been creating and maintaining a channel through the deposits, so that at the present time it has been found by observation that, while the beds of streams near their head waters are slowly rising, an unstable equilibrium exists between the forces which are filling and those which are excavating the channel, at a relatively short distance from their sources. At certain stages at a given locality the river bed may be enlarged and at other stages a fill may occur. If high stages predominate, for several years, the capacity of the high-water channel may be increased, and during a series of low-water seasons the capacity may be diminished. But when former conditions recur, while there may be numerous local changes, the same channel capacity of the river as a whole will be reestablished, unless the forces of nature have been modified in the interim by the works of man. Under these conditions, the average discharge of solid matter over the banks of a river and at its mouth equals the average amount it receives. The areas of deposition at the head waters of a stream have an effect on the supply of solid material to a river, similar to the effect of a lake on the supply of its fluid contents. During a storm they retain a large amount of the heavier debris, gradually delivering it to the river during minor floods. They thus act like huge rock crushers, grinding the larger fragments which pass through them into small particles. When they emerge from the area of deposition these particles are readily moved by the current which exists on the lower portions of the stream. THE FORMATION OF RIVERS 13 While the valleys of most of the rivers of the United States have been formed as explained above, there are some which have been created by glacial action. Moving ice also has a powerful erosive effect, and the eroded material, when once imbedded in a glacier, may be carried long distances before being deposited. Its area of deposition is the moraine at the foot of the glacier where the ice is being melted by the sun's rays, and where there is formed a heterogeneous pile of boulders, stone, sand, gravel, and clay, far different from the graded material found in alluvial valleys. As the glacier recedes, the eroded valley is paved with a similar heterogeneous mixture. The glacier also excavates deep holes in its valley which later become lakes. When the glacier finally disappears, and the erosion of the hills is resumed by water derived from precipitation, a different condition exists than in those valleys which owe their formation through geological ages to such precipitation alone. At the foot of the hills limiting the valley, areas of deposition are formed which gradually encroach on the valley, but the water escaping from these areas flows into the existing lakes and there deposits its solid matter. Emerging from the lakes it flows as a clear water stream of diminished velocity and passes over the surface of ground that had been eroded by a force far greater than it possesses. Its sinuosities and depth become functions, not of its discharge, but of the character of the deposits left by the glacier. Instead of having steep slopes at its source gradually diminishing toward its mouth, it is liable to flow with gentle slopes in its upper reaches until it comes to obstructions deposited by the glacier, over which it flows in rapids, not having sufficient force to excavate its channel through them. As such a stream carries little sediment, it is in- capable of building up its banks and the rain which falls in its valley, instead of flowing from the river to the foothills, as in alluvial streams, has a reverse flow. In such valleys, the lakes are gradually filling and are being converted into marshes, and in future geological ages they will be transformed into valleys similar to those first described. In certain valleys, the transformation is more complete than in others, and there is found a foundation of glacial drift covered by a relatively thin layer of alluvial deposits. A glacier has a powerful erosive effect on rock, but is very eccentric in its action, occasionally leaving rock ridges extending 14 RIVERS AND HARBORS across its valley which the clear water of the river which forms on the glacier's disappearance is unable to remove. In the upper valleys of streams formed by water derived from precipitation, deep canyons may be excavated through rock by the erosion of the de- bris which is being carried down them. In the area of deposition of an alluvial valley, as in one formed by glacial action, the channel formed by a stream is dependent on the eccentricities of the deposition of debris. A flood carries the sand, gravel, and boulders down the ravines and spreads them in a fan-shaped mass across their entrances. As the flood subsides, pools will be scoured out where the deposit is of sand and gravel, and between the pools the water will flow in shallow ripples over material it is incapable of moving. Such a channel is not per- manent but is liable to be obliterated by the deposits from the next flood, and a new channel may be formed where, due to some freak of nature, material more readily moved is found. But as the detritus becomes broken up into smaller particles in its passage through the area of deposition, it becomes more amen- able to the action of the stream currents, and the channel assumes a more stable form. There is still a large amount of material being carried down the river during floods, but after each flood there is a greater tendency for the stream to return to the channel it formerly occupied at similar stages. The pools develop in the bends of the stream, and are separated by bars of heavy material. In other words, the sediment flows in accordance with certain laws, and it is as important to comprehend clearly these laws as it is to comprehend those of the flow of water (1). CHAPTER III LAWS GOVERNING THE FLOW OF WATER IN RIVERS The Chezy formula * and those derived from it, such as Bazine's, Farming's, and Kutter's, are the result of careful experiments from which numerical values have been deduced for empirical coefficients which render the formulas of great assistance in solv- ing hydraulic problems, but they have the defect of all empirical formulas that great caution must be exercised in applying them where conditions differ from those of the experiments. These formulas as a class were first derived from the flow of water in pipes and conduits, and it was attempted to concentrate in a coefficient c all the_variations of the flow which prevented v from being equal to Vrs. It was soon observed, however, that c was a variable function of both r and s, and tables were prepared giving values of the coefficient for changes in both these quan- tities. It was also found by experiment that the condition of the enveloping surface affected the velocity of the discharge, a smooth iron or vitrified clay conduit discharging more water in a given time than a brick one of the same diameter and laid to the same slope. Changes in the value of the coefficient then became necessary to provide for the change in velocity due to the rough- ness of the surface of the material composing the conduit. The frictional resistance of a liquid flowing over a solid sub- stance is slight and affects only the thin layer that is in contact with the solid. In a large conduit, such resistance is negligible and the retarding effect of a rough surface on the flow is due, not to such frictional resistance, but to the eddies which it creates in the liquid itself and which absorb a portion of the energy that would otherwise be expended in producing a velocity of discharge through the conduit. Hence the term coefficient of roughness does not give a proper conception of this force. The velocity may be such as to develop frictional resistance only. There exist two critical stages, as they have been termed, a minimum stage when the velocity is so low that eddy action is 1 v = cVrs in which = the velocity; c = a variable coefficient; r = the hydraulic radius; and s = the slope. 15 16 RIVERS AND HARBORS not developed, and a maximum stage in which mere occurs the greatest retarding eddy action the velocity can create (1). This maximum stage is dependent on the form assumed by the particles producing the roughness. Both below the minimum critical stage and above the maximum critical stage there is a tendency for the flow to follow rectilinear lines instead of producing eddies. As an illustration, suppose that a straight channel be excavated through rock and that the sides and bottom be left as blasted. If the slope is gentle, a small discharge will flow through the cut without a serious disturbance of the water surface. As the dis- charge and its velocity increase, boils and eddies begin to appear, which attain a maximum at a certain stage. Above this stage the eddies gradually disappear on the surface, having been limited to certain distances from the bottom and sides of the cut, beyond which the current tends to flow in straight lines. On the con- trary, if the same discharge flows in a channel of sand which has been deposited in sand waves, the minimum critical stage is not attained so soon, i.e., the water flows tranquilly at low stages, but at the velocity of a maximum discharge, the water moving up the surface of the ridges continues on the same path to the water surface and boils and eddies of great magnitude result. Furthermore the length and height of the sand wave affect its capacity to reduce velocity. Sand waves deposited during low water, though composed of the same material and more frequent in number, have a lower coefficient of roughness during floods than those deposited during high stages. As the experiments from which the ordinary formulas were de- rived were for ordinary flow between the critical stages described above, their application to either extremely low or extremely high velocities should be made with caution. The subterranean flow of water is so slow that it is below the minimum critical stage, and the velocity has been found to vary almost directly as the head. The same rule applies to the discharge of small pipes. With brass pipes of a diameter as great as two inches under low heads a formula v 1M crs has been found to be appli- cable. Hazen and Williams have proposed a formula with a variable exponent for v as a substitute for the ones generally employed, and this is theoretically more exact. When it is attempted to apply these formulas to river channels, as in the experiments of Kutter, serious difficulties arise. The FLOW OF WATER IN RIVERS 17 formulas were derived from uniform flow in conduits or pipes which had the same hydraulic radius in different sections, and uniform slope. Such conditions do not exist in rivers, for no two cross-sections of a river have the same area, and the area of the same cross-section changes from day to day. Moreover, the slopes are exceedingly variable, being not only steeper over bars than in pools, but frequently varying on opposite sides of the same pool. Finally, the coefficient of roughness varies from section to section, being greater on a gravel bar than in a sandy pool. In applying a formula it is therefore necessary to consider long reaches of the river, obtaining a mean hydraulic radius and a mean slope. If it is attempted to apply the formula to a short stretch which happens to have a uniform section and slope, the velocity of approach becomes a disturbing factor, the propelling force being not the difference in head at .the two extremities of the section, but that created by slopes further upstream. Even a strong wind influences the discharge of a river, since it raises or lowers the thread of maximum velocity. At the mouths of rivers, tides may have sufficient force (on account of the funnel- shaped form of the estuary) to cause a flow in a reverse direction to the low-water slope; when the tides introduce salt water into the channel, they produce a most complicated flow, incapable of mathematical analysis. It is therefore advisable when discussing questions of river hydraulics to determine by actual measurements the various ele- ments entering a formula. When this is impracticable, the reader is cautioned to employ a liberal coefficient of safety, bearing in mind that most mathematical computations are applicable to average conditions, and that in treating such questions as floods, and depths of channel during extreme low water, it is not the average but the exceptional that has to be considered. In a pipe the velocity of flow is determined by the head. In a river the living force of the water also must be considered. When the flow of water in a pipe is suddenly checked, the pressure on its surface is merely increased, as the water has no means of escape. But in a river, when the flow is restricted at any locality, the force of the approaching water causes an elevation of the con- tracted section corresponding to the pressure existing in the pipe. A rapid current impinging perpendicularly on a river bank may 18 RIVERS AND HARBORS reverse the river slopes. This was forcibly illustrated in the Mississippi River at Vicksburg after the Centennial Cut-off of 1876. The old river bed around the island created by the cut-off then became the harbor of Vicksburg and was connected to the river during certain stages at both its upper and lower ends. The flow through the cut-off during high stages impinged on the Vicksburg bank with sufficient force to cause such a local elevation of the water surface as to create an upstream current through Vicksburg harbor until the river fell to about mid-stage, and caused a heavy deposit of sediment, necessitating the closing of the upper entrance to the harbor and the diversion of the Yazoo river into it to restore and to maintain its navigability. At the outlets of rivers the tidal wave frequently has a force far exceeding that produced by the natural slope of the river and causes a rising of the river's waters in excess of that existing in the ocean. The impetus of the outflowing tides may also lower the river level below that of low water in the ocean. The flow of water in bends has such a vital effect on a river's regimen that it merits a more careful analysis than it ordinarily receives in textbooks on hydraulics. While there have been numerous experiments upon the retardation of flow caused by bends in pipe, the subject usually is dismissed with the statement that the loss of head in bends is equivalent to adding a certain amount to the length (2) . It is more fully discussed in an article by M. R. H. Gockinga on La Pente Transversale et son Influence sur VEtat des Rivieres (ANNALES DBS FONTS ET CHAUSS^ES, 1913, p. 112). In a straight paved conduit the filaments of water flow in straight lines, with the exception of those near its bed, which are disturbed by the roughness of the material with which they come in contact. The thread of maximum velocity lies in the vertical plane passing through the deepest section, and the variations of velocity of the filaments of water in that plane will conform to the arc of a parab- ola whose apex is near the water surface. A similar curve will determine the variations in velocities from the plane of maxi- mum velocities to the sides of the conduit. In a cross-section the water surface will be horizontal. If the flow is uniform, the longitudinal surface slope will conform to that of the conduit. If a circular curve be introduced into the conduit, however, there is a derangement of this regularity of flow. The inertia of FLOW OF WATER IN RIVERS 19 the water resists the change of direction, and there is an elevation of the water surface on the concave side of the conduit and a corresponding lowering on the convex side. The mid-stream longitudinal slope remains the same, but there has been created a transverse slope in the bend which causes a marked difference of head on the opposite sides. The cross-section of the water surface becomes a curved line. For the case in which the cross-section of the conduit is trapezoidal, Mr. Gockinga deduced the equation where V denotes the longitudinal velocity, R denotes the radius of curvature of the axis of the conduit in meters, and x and y are coordinates of a point on the surface referred to a system of rec- tangular axes through the intersection of the axes of the conduit and the water surface. For a trapezoidal conduit whose width is 200 meters and whose radius is 500 meters, and whose depth is such that a longitudinal slope of 0.0001 produces a velocity of one meter per second, he computes a difference of head of 4 centimeters on opposite sides of the conduit, i.e. a transverse slope twice that of the longitudinal. These theoretical computations have been confirmed by obser- vations on the Mississippi River, where differences of head of about 1 foot have been observed on opposite banks of bends, with mean mid-section longitudinal slopes of about 0.4 foot per mile. Under such conditions the thread of maximum velocity no longer cor- responds with the mid-stream section, but approaches the concave bank. When two bodies of water whose surfaces have different ele- vations, are connected by a pipe, there is a flow through the pipe from the one having the greater head, which will continue until the heads are equalized. The velocity of the flow through the pipe is a function of the difference of head. If a variation in head exists in different parts of a lake, which usually results from a wind blowing over its surface, the same tendency to restore the normal levels is created, but since the force of the wind is com- pelling the surface water to travel in the same direction as the wind, the return flow is along the lake bed. This rises to the surface where the lake level is lowest, thereby giving the water a curvi- linear path (3) . Under certain conditions this subsurface flow may attain great 20 RIVERS AND HARBORS force. The vertical piers constructed on the Great Lakes have to be protected by heavy rip-rap in depths of thirty feet to prevent scour from this cause. In a river, the centrifugal force created by bends produces a similar action, but the curvilinear path of the water in a lake is modified in a river by the motion of the water downstream, due to the longitudinal slope. Hence the water in a river assumes a helicoidal motion. The motion of translation downstream is re- tarded, but in the circumference of the helicoid the filaments of water have acquired a velocity much greater than that which exists in a straight reach due to the longitudinal slope alone. The dimensions of the helicoid are functions of the longitudinal slope and the radius of curvature of the bend. They conform to the section in which the water flows only when it is permitted to construct its own path, i.e., in a stream in its natural state. Beyond the sphere of its flow, eddies are produced which also interfere with the motion downstream. The helicoidal flow of water in bends was practically demon- strated by Professor James Thompson before the Institution of Mechanical Engineers of Glasgow in 1879, and the direction and velocity of such currents on the Dnieper River were measured by M. Leliavski, as described in a paper presented to the Sixth In- ternational Navigation Congress held at the Hague in 1894. From the results of his experiments, Leliavski came to the con- clusion that in a bend, surface currents converge toward the concave bank, along which a stream of water flows to the bottom of the river, thence move to the convex side in divergent currents, and then gradually rise to the surface. He found not only that these currents have sufficient force to cause caving of banks of clay, sand, or gravel, but he found evidences also that they had caused erosion in the lava rock which forms the bed of the river at the Dnieper rapids. The greatest depth was found where the greatest number of surface filaments of water converge on the concave bank. If the radius of curvature of the bend is uniform, this point occurs at some distance below the middle of the bend. The influence of a circular bend, moreover, affects the straight sections of a conduit for a considerable distance above and below it. Below the bend, it is evident that a considerable distance is required to transform the helicoidal motion again into a recti- linear motion, since this transformation depends on the inertia FLOW OF WATER IN RIVERS 21 and the frictional resistance of the particles of water. Above the bend there is a similar back-water effect, since the surface of the cross-section cannot suddenly change from a horizontal to an in- clined line, i.e. the transition must be gradual. The helicoidal motion of the water therefore begins considerably above the bend, attains its maximum velocity when the transverse slope adjusts itself to the radius of curvature, then remains constant to the end of the curve, and then gradually diminishes. The locus of the maximum velocity moves away from the axis of the conduit in a corresponding manner and there is a disturbance in the longi- tudinal velocity of flow in the straight sections as well as in the curve. In a paved conduit the location of the thread of maximum velocity is of minor importance, but as this line is also the one of greatest scour, it determines the navigable channel, and river regulation consists principally in its proper location and main- tenance. Another question which requires more elucidation than is con- tained in the ordinary textbooks is the effect of obstacles on the flow of water. It is recognized that the sudden expansion and contraction of a conduit entails a loss of head, due to the eddies formed, but the paths followed by the water in passing the ob- stacles have received little consideration. In a straight conduit not susceptible to erosion, if a vertical dike extending above the water surface be constructed perpendicular to one of its sides, the reduction of the area of cross-section will cause a local elevation of the water surface, reducing the slope above the obstacle and increasing it below. This elevation, while extending across the entire cross-section, will be greatest near the side of the conduit above the dike, due to the greater retardation of the longitudinal velocity at that locality, and the least on the opposite side. This difference of head will induce a flow toward the points of lower elevation and the locus of the thread of maximum velocity will be diverted from the straight line it followed when the conduit was unobstructed. For a certain distance above the dike, back-water effects will produce a difference of elevation on opposite sides of the conduit, and a helicoidal motion will be imparted to the water similar to that in bends. Below the dike conditions are suddenly reversed. The water behind the dike has lost its longitudinal velocity and tends 22 RIVERS AND HARBORS to sink to a lower level than formerly existed, while on the opposite side the elevation has increased. A portion of the water flowing around the obstacle seeks to fill this void, but because it has a high longitudinal velocity as it passes the dike, it forms an eddy of a very complicated flow but with a large spiral component with a vertical axis. In experiments on the Rhine it (4) was found that this spiral eddy attacked the bank at a distance below the dikes equal to about two and one-half times its length. Another component has a quasi-helicoidal flow diagonally toward the op- posite side, which also converts some of the longitudinal velocity into eddy currents. If a similar dike is constructed on the opposite side of the conduit in the same cross-section, the water surface between the dikes assumes a curved form, higher at the extremities of the dikes than in mid-stream. The locus of maximum velocities divides into two lines diverging upstream from the axis of the conduit to the ends of the dikes, and gradually returning to the middle section below them. Two powerful eddies are produced behind the dikes, but the remainder of the flow tends to follow lines more rectilinear than those which exist when only one obstruction is formed. There is also eddy action above a dike, but its nature and extent is a function of the inclination of the dike to the direction of the current. If the dike is inclined sufficiently downstream, it has an action similar to that of a curve and a tendency to scour de- velops along its face. This tendency is diminished as the dike is given a greater inclination upstream. If the dike be submerged there is a tendency toward the crea- tion of a jump in the water surface over it. A very complicated flow results. The overflow produces a powerful scouring effect immediately below the dike, and interferes with the eddy action around its end. On a concave bank, a dike causes a curvature of the line of maxi- mum velocity, but it cannot ordinarily overcome the centrifugal force created by the bend and the line soon returns to its normal position. The discharge of a tributary does not immediately mingle with the water of the main stream, but flows beside it until bends and obstacles (by their helicoidal and eddy action) interfere with the regularity of flow. FLOW OF WATER IN RIVERS 23 Near the mouths of rivers, a very complicated flow frequently results from the difference in density of fresh and salt water. The water of the inflowing tide has a greater specific gravity than that of the river discharge. At certain periods of the tide the salt water flows up the river along its bed, while the fresh water is flowing out above it. On account of irregularities in the river bed, there may also be an upstream surface flow in certain por- tions of a river section with a downstream flow in others, until the inertia of the moving water is overcome and the salt and fresh waters have an opportunity to mingle. CHAPTER IV THE FLOW OF SEDIMENT IN NON-TIDAL RIVERS Material is transported down a river in solution, in suspension, and by being rolled along its bed. The material in solution is carried to the mouth of the river without deposition unless there is excessive evaporation. Streams flowing in valleys formed by glacial action not infrequently carry more material in solution than in suspension, as is demonstrated by the observations of the Geological Survey on the Mississippi River at Minneapolis, where the mean of the observations shows 200 parts per million in solu- tion and 7.9 parts per million in suspension. In a river flowing in an alluvial valley, the reverse is the case except occasionally at extreme low water, and the amount of ma- terial carried in suspension is primarily dependent on the character of the soil of the watershed from which it flows and on the intensity of the rainfall. The western tributaries of the Mississippi River carry a greater amount of sediment per unit of volume of water, termed the degree of saturation, than its eastern tributaries, and (for the same discharge) the degree of saturation is greater in summer than in the winter, due to the frozen condition of the soil in winter. The light clays and sands which are carried in sus- pension become intimately mixed with the water as it flows over the soil and (moving with the velocity of the water) are carried to the river's mouth unless the velocity is checked, as in the flow through a lake. In a, watershed whose soil contains a large amount of clay and is of a relatively uniform character over the drainage area, the degree of saturation rapidly increases with an increase in the discharge. In the Mississippi system of rivers, however, the Missouri carries so much more sediment in suspension than any of the other tribu- taries that it determines the degree of saturation of the main stream, and a flood from the Missouri River carries more material in suspension to the Gulf than one from the Ohio, although the amount of water flowing from the latter in floods largely exceeds that from the former. When material carried in suspension has once been deposited, 24 SEDIMENT IN NON-TIDAL RIVERS 25 and is afterwards eroded, -only a comparatively small portion is again placed in suspension. The original deposit contains a large amount of water, and assumes gentle slopes, but it becomes more compacted and is capable of maintaining a steeper slope when additional deposition occurs. If the river falls to such a stage that the deposit is above the water surface, and the water is drained from it, the binding force of its clay contents may be sufficient to enable the material to assume a vertical slope, and thus produce the steep banks found above low water in the concave bends of alluvial streams. Below the water surface, the adhesive force of the clay diminishes, and the water contents of the deposit increase. When such a bank is eroded, there is a local deepening of the river bed, and an increase in the under-water slopes, which cause large masses to slide into the river. These masses do not mingle with the water sufficiently to be carried in suspension. When rain falls on a plowed field every drop of water picks up a load of clay or sand which it can transport; but a mass of water which acts on a concave bank moves a mass of earth too heavy to float, and which therefore is rolled along the river bed. There is also a relation between a river's low-water slope and the amount of sediment it carries; the greater the amount of sediment, the steeper becomes the slope. This is particularly noticeable at the junction of two streams. If a river carries relatively little sediment, its slope above the junction with a turbid stream is less than that of the tributary, and increases below it. If the reverse is the case, the slope of the main stream above the junction is increased, and below it more nearly conforms to that of the tributary. Exceptions to the rule result from the geological formation of non-erosive beds in the vicinity of the junction. For example, the upper Mississippi carries less sediment than the Minnesota, its first large tributary, but the falls of St. Anthony above the junc- tion and the rapids produced by the detritus from the falls create an exceptional condition. The rule is illustrated by the following instances: The waters of the next large tributary, the St. Croix River, have been clari- fied during their passage through Lake St. Croix, and the mean slope of the Mississippi above their junction is about 0.4 foot per mile, below it 0.2 foot. At the junction with the Chippewa, which transports a large amount of coarse sand and but little 26 KIVERS AND HARBORS finer material, the low-water slope through Lake Pepin is zero, and immediately below the mouth of the Chippewa 0.9 feet per mile. At the mouth of the Wisconsin, which also carries large amounts of sand during floods, the slope of the main river above it is 0.1 foot, and below 0.6 foot per mile. The western tributaries of the river below have sufficient material in suspension to maintain an average slope of 0.4 foot per mile to the Illinois River, with the exception of the Rock Island and DesMoines rapids. The Illinois River carries little sediment, and the slope above its junction ex- ceeds 0.4 foot per mile; below it a gentler slope is observed as far as the Missouri River. Below the Missouri River a slope exceed- ing 0.8 foot per mile is created, gradually reducing to 0.6 foot, and below the junction with the Ohio still gentler slopes exist for a considerable distance. These phenomena are usually explained by the assumption that they are caused by the relative degree of saturation of the two streams, and that when their waters mingle they are capable of increasing their capacity for transporting material in suspension, the less turbid waters increasing their load from material eroded from the bed of the river ( 1 ) . Observations by the Mississippi River Commission fail to confirm this assumption. At the junction of the Missouri and upper Mississippi it was noted that the waters of the two rivers have a tendency to flow side by side without mingling, the waters of the upper Mississippi following the Illinois bank of the river and the waters of the Missouri the opposite bank. At low stages of the Missouri, this tendency continues considerably beyond the portion of the river having a steep slope. Boils and eddies cause a gradual mixing of the waters, and during certain high stages, at the first concave bend below the junction which occurs on the Missouri bank, there is a decided movement of the water of the upper Mississippi across the channel on the surface, and an opposite bottom flow of Missouri River water, which is exhibited in the observations of sediment taken at that locality. A more logical explanation of the changes of slope at the mouths of tributaries is to be found in the deposition of material in sus- pension, and its conversion into sand waves which are moved along the river bed. As the crests of floods of rivers rarely coincide, when a clear-water stream empties into a turbid river there will be a period during a high stage of the tributary when its discharge will act as a dam on that of the main river, diminishing the SEDIMENT IN NON-TIDAL RIVERS 27 velocity of flow above the junction and causing a deposit of ma- terial carried in suspension which will reduce the river's cross- section. Below the junction its added waters will tend to enlarge the cross-section. When the tributary falls to its normal relation to the main stream, the velocity above the junction is increased and the deposits tend to scour, being slowly rolled along the bottom as sand waves instead of being carried in suspension with the velocity of the current. There is a tendency for this scoured material to deposit in the enlarged section below the junction, but before the equilibrium can be established a second rise occurring in the tributary causes a repetition of the process. If the main stream is less turbid than the tributary, a flood in the latter flows into an enlarged section and consequently deposits sediment due to a reduction in velocity. As the tributary falls, the main stream has an increased burden in removing the deposits below the junction, a work it also fails to accomplish before a second rise occurs in the tributary. The serious problem in river regulation is the movement of material along the river bed. In straight reaches it moves in sand waves which are functions of the velocity of the current and of the depth of water, being greatest when for any cause the current is suddenly increased. At such a time, the most rapid erosion of the bottom takes place. Conversely, the movement of material is least when the velocity of the current is suddenly decreased, since the greatest deposit of sedimentary matter occurs at that time. The sand waves have an irregular motion downstream, and the maximum size and rate of progress is attained when the stage of the river is at its highest and is nearly stationary, their height, length, and rate of motion being dependent on their location with reference to the line of maximum velocity. The waves have the least dimensions and slowest rate of travel at low water. They move downstream by material being pushed or rolled up their flat anterior slope and dropped over their crest, where it remains until the wave has progressed far enough downstream to expose it again to the action of the current, to be again rolled or pushed forward. The amount of material thus moving is greatest in high water, or when the velocity for any cause has been suddenly ac- celerated. Changes in the form of waves are gradual, the waves 28 RIVERS AND HARBORS retaining their form and individuality as long as the velocity of the current remains nearly uniform. They disappear by the deposition of sediment carried in suspension, if the velocity is suddenly decreased, and again make their appearance when the velocity approaches uniformity for any length of time. On the lower Mississippi River, sand waves have been observed that have a length of 1000 feet, a height of 22 feet, and a maximum rate of travel of 40 feet per day. At New Orleans the amount of material transported in sand waves during a year was estimated at less than 1 per cent of that carried in suspension, at Lake Provi- dence Reach about 10 per cent. In some of the tributaries of the upper Mississippi, the amount rolled along the river bed largely exceeds the amount carried in suspension. This variation in the relation of material rolled along the bed to that in suspension is due to the relative sizes of the particles in different portions of the river bed. At New Orleans a large amount of material was observed inter- mittently in suspension, the ratio of the material in suspension at the water surface to that near the bed being in some cases 1 to 1.83. Furthermore, a difference in the degree of saturation of floods from the Ohio and the Missouri rivers respectively could readily be observed, notwithstanding the enormous caving of banks which occurs during every flood below the mouth of the Ohio River. At St. Louis it was observed that some of the material from the bed did not sufficiently mingle with particles of water to remain in continuous suspension until it reached the sea, but was " detached for a time by some energetic impulse and described a longer or shorter path, moving in or out with the surrounding water "(2). In bends, the helicoidal flow impressed upon the water affects the motion of sand waves, and every eddy also changes their form to some extent. The axis of maximum flow in bends is diverted from the axis of the channel which it occupies in straight reaches toward the concave bank, and causes an erosive action on that bank, which is intensified by the transverse slope created in the bend combining with the longitudinal slope. The material scoured from the bank,together with that brought down the river in sand waves, is diverted from the direction followed in straight reaches to a diagonal path across the river. It forms a sand bar extending downstream a distance from the origin of scour SEDIMENT IN NON-TIDAL RIVERS 29 which is dependent on the original slope of the river and on the radius of curvation of the bend. This sand bar usually forms the convex bank throughout the curved section; but when the river changes its section to one that is straight or has a curvature in the opposite direction, the intensity of the helicoidal velocity gradually diminishes; the water no longer has sufficient energy to transport the material across the river, and deposits it in a bar extending across an unimproved channel in a diagonal direction, so that the length of its crest largely exceeds the river's width. A dam is thus soon created which reacts on the local slopes and velocities, diminishing those above the bar, and increasing those of the water passing over it. This process continues until the velocity in the pool above the bar is insufficient to produce scour, or until an equilibrium is established between the material brought to the bar and that which passes over it. On a rising river the tendency is to produce the equilibrium by an elevation of the crest of the bar and by a reduction of velocities in the pool. On a falling river there is a tendency to scour a channel through the bar and to attain the equilibrium by the resulting increase of velocity over it. While the movement of sand waves in straight reaches is a slow process, averaging about forty feet per day when the river current has a mean velocity of six feet per second, the movement of the particles of sand which form them is much more rapid, and the elevation of the crest of the bars also rapidly increases with a rise of the river stage. On the Mississippi River the rise of some of the bars is at the rate of one-half the change of stage. On the Rhone River a ratio of one to five has been observed. On a falling river there is a similar scouring of the bar. The rate of rise and fall of the crests of bars, however, varies greatly in different reaches of the same river, being dependent not only on the velocity of the water and the radius of curvature of the bend, but also on the eddies formed, on the character of the material moved, and on its distribution on the bar. On a falling river the channel tends to form across the bar along the line of the deposited material which is most susceptible to erosion; and since the coarser material of sand waves is usually found in the line of greatest velocity, the location of the channel across bars on an unregulated river usually differs on rising stages from that which is created on falling stages. The divergence of the thread of maximum velocity toward the 30 RIVERS AND HARBORS concave bank of a bend tends to produce a triangular cross-section in pools, and the slope of the concave bank becomes a function of the radius of curvature and of the character of the soil of the bank. If this soil is readily eroded, the amount of material falling into the stream is greater than the helicoidal flow can transport. In that case, the thalweg depths are reduced, and gentler slopes obtain, than those when material of greater resistance to scour is encountered. In the fine sediment of the lower Mississippi, slopes of one (vertical) to three (horizontal) are not infrequent even in sharp bends. Coarse sands will assume slopes of one to two. If the concave bank is composed of rock, a nearly vertical slope may exist. On a bar there is a tendency to a trapezoidal form until a channel is scoured through the bar during a falling river. The radius of curvature of a bend, while it is primarily a function of the material that composes the bank, is also affected by the volume of the discharge, and by the slope. In a river flowing through glacial drift, the variations in the soil are the determining factor in the river's course. In an alluvial valley, however, the greater the discharge, and the gentler the slope, the longer becomes the radius of curvature in the bends, though it is modified by conditions that exist in the bank. Thus in the Mississippi River below St. Paul, the radius of curvature of the bends varies from 1500 to 4500 feet, while in the bends above Greenville, Mississippi, it varies from 8000 to 15,000 feet. Similarly, at low water a river tends to flow with curves of less radius than in flood stages, when its volume has been very largely increased. This tendency to a change of curvature at different stages has an injurious effect on the river's regimen, causing a variation in the location of the thread of maximum velocity, transferring the caving from one bank to the opposite one, and making a fill at high stages where the river strives to create its channel during low water. When the low-water channel has excavated sharp bends, the volume of water during floods may be too great to conform to the path that the radius of curvature strives to create and a large flow follows a chord of the bend, frequently with sufficient velocity to scour a secondary channel and to produce an eddy action at its junction with the current along the bend, which will form large deposits of sediment. A powerful scouring effect is also produced on the portion of the bank on which it impinges. SEDIMENT IN NON-TIDAL RIVERS 31 An interesting example of the influence of discharge on the form of the river bed is afforded by the Atchafalaya River (3). Originally the Atchafalaya was obstructed by an accumulation of snags and drift called a raft, which limited the amount of water which could flow through it at both high and low stages. The removal of the raft and the construction of levees along its banks has largely increased its discharge both at high and at low water. As a result the river has attempted to enlarge its section, but instead of retaining its old sinuosities and forms it has created new ones, cutting a channel through bars on convex points, and thus attempting to adjust its curvature to its discharge. In the Illinois River where the low-water discharge has been increased from about 1000 second-feet to over 5000 second-feet by the flow from Lake Michigan through the Chicago sanitary drainage canal, a corresponding change in the radius of curvature of its bends is also taking place. When a dike is constructed in a river, the resulting disturbance of the slope causes the shape and the distribution of the sand waves to change. In the reduced section the increased slope scours a deeper channel, and the scouring effect is most intense at the end of the dike. The eddy below the dike deposits material in its vertex and has a gradually reducing scouring effect along its outer elements, which tends to create a channel extending from the end of the dike toward the bank to which it is connected. A second channel tends to form diagonally across the river toward the opposite bank, on account of the helicoidal motion generated in that direction. When these currents lose the force imparted to them by the obstruction, a bar with a curved crest is formed, which incloses both channels. The navigable channel of the river is determined by the scour across this bar, which occurs on a falling river, and which may be toward either bank, dependent on the local character of the deposits in the bar. Above the dike, a deposit is formed from sand waves by eddy action and from material in suspension by a reduction of the velocity. Along the face of the dike, there is a narrow channel due to eddy action, if the dike makes an acute angle with the direction of flow, and a pronounced scour if it is inclined downstream. Observations in the Mississippi River indicate that in alluvial rivers depths in pools are a function of the river's discharge, while depths over bars vary with the slope. For the same slope, the 32 RIVERS AND HARBORS depth in pools increases with the discharge. For the same dis- charge, the depth over bars increases as the slope diminishes. However, a slight increase in the depth over bars accompanies an increased discharge. These conditions may be reversed, however, in rivers flowing through glacial drift, as is forcibly illustrated by a comparison of the regimen of the lower Mississippi River with that of the St. Clair River, of Lake St. Clair, and of the Detroit River, which connect Lake Huron and Lake Erie. In the lower Mississippi River wherever steep slopes exist, shoals occur, and wherever the slope is reduced to 0.2 foot per mile, a channel of ample depth for navigation exists. In the connecting waters between Lake Huron and Lake Erie, the greatest depths are formed where the slopes are relatively steep, and when the slope becomes less than 0.1 foot per mile the natural crossings are extremely shallow. During storms from a northerly quadrant a large amount of sand, gravel, and shingle is transported along the shores of Lake Huron, a portion of which enters the St. Clair River. An insignifi- cant amount of this material is in suspension. The sand waves in- stead of being propagated along the river bed as in alluvial rivers, enter the mouth of the St. Clair River along its banks, and contract the river instead of shoaling it. The steep slope and swift current which are thus created scour out the finer material and pave the banks with a deposit of gravel and shingle which protects them from scour as efficiently as a revetment. As the slope diminishes further downstream, coarse sand is deposited, in an enlarged river section of less depth. The finer sands are carried to Lake St. Clair, where the slope is inappreciable, and a bar is then formed through which channels originally existed having depths varying from two to six feet. At the foot of Lake St. Clair, there is a similar movement of sand into the Detroit River during northerly storms, which, though less in amount than in Lake Huron, has been sufficient during geological ages to form a bar at the mouth of the Detroit River similar to that at the mouth of the St. Clair River. The formation of these lake bars is similar to the delta forma- tions of rivers in tidal seas, and also resembles the deposit which occurs where an alluvial river overflows its banks. They are highest where the water first leaves the confined bed. SEDIMENT IN NON-TIDAL RIVERS 33 Both in alluvial rivers and in those formed by glacial action, however, the pools tend to form in the bends and the bars in the straight reaches between them. If the forces acting in a bend produce a diagonal bar in the reach below it, and if the bar has a long crest line when compared with the river's cross-section, the water flows over the bar in a thinner sheet than it does when the bar is located more nearly at right angles to the axis of the channel. This dispersion of the water prevents so great a scour during falling stages as results from a more concentrated flow, and there exists a shoal crossing that obstructs low-water navigation. The modern science of river regulation consists in converting such poor crossings into good ones by so directing the river currents as to cause the bars to assume a position more nearly at right angles to the axis of the river than they do in a state of nature. From what precedes, the flow of a river may be summarized as follows : In every river bed the uplands are being continuously eroded, and the material thus removed is being deposited in the valleys or transported by the streams to a sea or lake, and is gradually being reduced in size the further it is removed from the zone of erosion. In an alluvial river the heavier material is being slowly and intermittently rolled along the river bed, while lighter sands and clays are transported long distances in suspension. The water supply causing these changes flows over steep slopes with great velocity through the zone of erosion, but its slope and veloc- ity are gradually diminished toward the river's mouth. At the sources of rivers there are great variations between the high-water and the low-water discharge, but the longer the river and the greater the drainage basin, the smaller the ratio of the high-water discharge to the low-water discharge becomes, although they both increase. Through the area of deposition, a river's bed is gradually rising. Its channel is not fixed, but is liable to a change in location after every flood. Below this area, the river assumes a sinuous course, with pools formed in its bends and bars in its straight reaches. The crests of these bars rise and fall with the rise and fall of the river. The slope of a river is not uniform, but is steeper over the bars than in the pools. The material carried in suspension tends to be deposited whenever the velocity is reduced. The material that rolls along the river bed moves in sand waves, or is 34 RIVERS AND HARBORS intermittently in suspension. The movement of the water is periodic. The movement of material follows the periods of the movement of the water, but in place of being continuous is intermittent; "its journey to the sea is effected by a series of etapes" 1 (4). 1 This expression etapes can appropriately be translated in its military meaning: a day' march, with its stoppages for rest and refreshment. CHAPTER V A RIVER'S DISCHARGE FLOOD PREDICTION For water flow in a conduit a curve can be constructed which gives the relation between the height of the water surface and the discharge. This curve can be expressed mathematically by the equation 2m +1 (A) Q where Q is the discharge, c is a constant, s is the slope, d is the greatest depth, and m is an exponent varying with the shape of the conduit. The exponent m is 1 when the sides are vertical, between 1 and 2 when the side-wall is a curve concave to the water surface, 2 when the side-wall is triangular in shape, and greater than 2 if the side-wall is composed of convex curves that form a cusp at the deepest part (1). If the slope remains uniform at different stages, the equation can be reduced to the form 2m +1 (B) Q=c'drT- which represents some parabolic curve. The exponent of d varies with the shape of the conduit. Such a curve is frequently em- ployed to express the relation between the stage and the discharge of a river, but it is liable to give erroneous results as ordinarily used. As a river changes its stage, its slope does not remain constant, but is greater on a rising river than on a falling river. Instead of having the parabolic form of equation (B) shown in Fig. 1 by the line AB, the curve assumes the complex form given by equation (A). If a relation between height and slope could be expressed mathematically, the relation (A) would be represented graphically by some such curve as XBY, which is a curve of two branches, one for a rising river and one for a falling river. Since the slope is dependent, not on the actual rise and fall of the river, but on the rate of rise and fall, which is a varying quantity, a mathematical relation between the stage and the slope cannot be obtained, and the line XBY merely limits an area in which the discharge for a 35 36 RIVERS AND HARBORS given height will be found. The exact value of the discharge depends on the rate of rise or fall. Not only is the slope of a river perpetually changing, but also the area of the cross-section of the river varies as sand waves are propagated downstream in an unimproved section, or as the bed rises and falls in a section that has been regulated. These changes in the area of the cross-section occur irregularly and cannot be expressed mathematically in terms of the stage. Hence the curve of discharge, instead of being capable of representation by a para- bolic curve, degenerates into a tangled skein within the area XBY, Fig. 1. If numerous discharges are measured indiscrimi- nately on rising and falling stages, however, the mean of the dis- charge observations will produce a line A B, which should always be characterized as the mean discharge curve. When only a few discharge observations have been made, those at low stages may have been taken on a rising river and those at high stages on a falling river, or vice versa, producing for the mean discharge curve the line abed, or the line a'b'c'd'. If these lines are extended beyond the sphere of the actual observa- tions, as has often been done, the resulting errors are large, es- pecially if the curves are extended as straight lines, according to a practice which is usual. A river's slope may be affected also by the inflow from a tributary below the discharge station; and if the discharge measurements are taken during a sudden rise or fall of the tributary, still greater perturbations in the discharge curve occur, as represented in Fig. 1 by the lines abef and a'Ve'f. The reader is cautioned particularly against extending a mean discharge curve, no matter how accurately it has been determined up to a bank-full stage, to unmeasured discharges at flood stages. When a river overflows its banks, there is a violent change in its regimen which will be reflected in the mean discharge curve unless the river's flow be restrained by levees. The reason that the slope of a river is more dependent on the rate of its rising and falling than on the actual stage is that the river bed possesses a reservoir capacity. On a rising river, a certain portion of the flow is expended in filling the bed, and the maximum discharge at a lower station is diminished by the amount of water thus expended. On a falling river, the water thus stored has to escape, and the discharge becomes greater at the lower A RIVERAS DISCHARGE FLOOD PREDICTION 37 station on account of this excess flow. Hence the time required for a rise or a fall becomes an important factor in determining 3 Ml V v> li FIG. 1 the difference in elevation of the water surfaces at the two stations. If a river rises slowly, its slope will be gentler than if it rises rapidly. A tributary can perform the work of filling the river bed, and 38 RIVERS AND HARBORS thus affect the slope and the discharge at the lower station. Moreover, if one rise rapidly follows another down the river, the delay resulting from the filling and emptying of the pools will cause the second rise to overtake the first and add its waters to it. On the long rivers of the United States, the rapidity of the rise and fall sometimes has a large effect on the slope and the discharge. Thus the crest of a flood of fifty feet in the Ohio River at Cincinnati may cause a variation of from thirty to fifty feet in the heights of floods at Cairo due to this cause, and Humphreys and Abbot cite a case where the maximum discharge of a flood-wave on the Mississippi River was reduced on this account by 400,000 second-feet in its passage from Columbus, Ky., to Natchez, Miss. (2). The rate of transmission of a flood is a variable quantity that changes with the river's slope and with the area of land subject to overflow. The investigations of von Tein on the Rhine and its tributaries would indicate that, for the basin of the Rhine, with the possible exception of the Moselle, the rate of transmission is a function of the stage; and he has deduced an equation for the time of transmission of the flood-wave in terms of the stage and the distance, which he applies to the portion of the Rhine between Waldshut and Caub for stages between 2 meters and 5.50 meters. He submits a table of the rates of transmission of certain flood- waves, which shows that the flood of September, 1893, whose elevation was 220 centimeters on the Waldshut gage, was trans- mitted to Kehl, 189 kilometers, in 20 hours, while the crest of the flood of June, 1876, rising to 667 centimeters on the gage, required 54 hours to pass over the same distance (3). On the Mississippi River at midstage, the rate of propagation of the flood-wave is a function of the slope. Between Cairo and the mouth of White River (392 miles) , the slope is about 0.4 foot per mile, and the time of transmission of a flood-wave is about five days. From the mouth of Red River to Fort Jackson (274 miles), the slope is about 0.1 foot per mile and the time of transmission is about one day. Above a bank-full stage, however, on account of the time required to fill and empty the basins at the mouths of the St. Francis, White, and Arkansas rivers, the time required for the crest of the flood-wave to be transmitted from Cairo to the mouth of the White River varies from 5 to 10 days, while it is not affected below the mouth of Red River, If a crevasse occurs in A RIVER'S DISCHARGE FLOOD PREDICTION 39 the levees of the St. Francis basin, the maximum flood at the mouth of the White River may occur two weeks after the flood passes Cairo. On the Ohio River the rate of transmission of the flood-wave is about 75 miles per day; on the Missouri and on the Tennessee it is about 100 miles per day. The rate does not exceed 4 kilometers per hour on the Saone or on the Seine below Paris, while it attains 6 kilometers per hour on the Garonne, and 8 to 10 kilometers per hour, or over, on the Rhone and on the Danube (4). The time of transmission of the flood-wave of the Ohio from Cincinnati to Cairo is about six days, but the floods from the Cumberland, the Tennessee, and the upper Mississippi may so combine with it that the flood attains its maximum at Cairo ten or twelve days after the crest of the flood passes Cincinnati. There can also be such a combination of the discharges of the different rivers that the maximum flood height at Cairo will occur four days after that at Cincinnati. During the so-called June rise of the Missouri River, the dis- charge of the upper Mississippi frequently determines the height of the flood at Cairo. If the crest of a flood-wave from the Ohio River arrives at that locality at a later date, it merely prolongs the flood stage. One of the most difficult problems the engineer can be called upon to solve is the prediction of flood heights. Such predictions are required not only for the benefit of navigation, but also for agriculture. They are also a necessity for the preservation of the life and property of communities in valleys subject to overflow. Many attempts have been made to predict flood heights by measuring the rainfall over the river's basin, and by computing therefrom the river's discharge. These attempts have met with little success, since the difficulties attending this method of pre- diction are practically insurmountable. The extreme variability of the rainfall would necessitate the establishment of an enormous number of rain-gages to record accurately the precipitation over a river's basin. The rain on a mountain peak differs from that in a valley; that over forests differs from that over cleared land; that over a city differs from that over the surrounding country; and even the records of rainfall in a gage on the roof of a building may differ materially from that of one established in a neighbor- ing street- With measurements of precipitation In only a few 40 RIVERS AND HARBORS large cities of the basin, a very inadequate conception of the rain- fall of the entire area drained by the river is obtained. The computation of the run-off leads to other difficulties. A geological survey may be made of the valleys and the permeability of the soil classified under certain conditions. The conditions are constantly changing, however. A rainfall preceded by a drought may be entirely absorbed by the soil, while if the ground has been saturated by preceding rains, the run-off may be a large percentage of the precipitation. If a field is plowed preparatory to planting a crop in the spring, its absorbing power largely exceeds that of the same field when the crop is being gathered in the fall. If a calm cloudy day succeeds a rainfall, the amount of water evapo- rated from the earth's surface is much less than when the sky is clear and a strong wind is blowing. The great flood of 1912 in the lower Mississippi River was almost entirely due to a moderate rainfall in the Middle Western States, which fell on a soil which had become impermeable by its being covered with a layer of sleet formed earlier in the season. An attempt has been made to provide for these variations by means of a different coefficient for the run-off for different months of the year. Thus on the German river Main, it is estimated by von Tein that in January 55% of the precipitation flows over the surface, in February 55%, in March 68%, in April 45%, in May 23%, in June 15%, in July 13%, in August 15%, in September 17%, in October 20%, in November 30%, and in December 33%. The evaporation varies from 40% to 55%, the absorption by plants from 0% to 28%, and the absorption by the soil from 0% to 40%. Von Tein employs these figures to determine the amount of the rainfall necessary to produce a flood in different seasons of the year. They are of little value in determining the height that the flood will attain. The water flowing down the hillsides moves with much greater velocity than that collected in the swamps and marshes of the valley, so that the determination of the percentage of the precipi- tation that will enter the river from the various portions of the basin at the same time becomes a very intricate problem. The Burkli-Ziegler equation and those of a similar nature have been deduced from average conditions in an area, and are of value in determining the dimensions of sewers and drains. But it cannot be too strongly emphasized that floods result from exceptional A RIVER'S DISCHARGE FLOOD PREDICTION 41 conditions. In order to be of value, a flood prediction must differentiate between the exceptional and the average. While it is impracticable to determine the absolute height of the flood by the methods referred to, they may afford early in- formation when a large flood is threatening, and for this purpose an attempt at great accuracy is not desirable. A few rain-gages in impermeable torrential valleys of the basin will give indices of the flood which may be obscured if the attempt is made to combine with them the rain records of more permeable portions with gentler slopes. In the prediction of floods in the Department of Ardeche, France, where this method is employed, a flood warn- ing is issued when the rainfall in 48 hours attains over 250 milli- meters in the mountainous valleys (5). Another method of flood prediction is by measuring the dis- charge at the origin and at various stations established on the tributaries, and computing the discharge at the lower station from these measurements. This method has been employed on the Elbe (6). It removes many of the difficulties resulting from at- tempting to determine the discharge from the precipitation. The process consists in determining the mean discharge curve at the different stations by numerous discharge measurements. From the curves are taken the discharge at such a time that the sum of the discharge of the main river and of its tributaries will be a maximum at the lower stations, and from its discharge curve the height the flood will attain is determinined. On account of the reservoir capacity of both the river and its tributaries on the dis- charge, the proper time to make the computation is difficult to determine and it frequently happens from this cause that the computed discharge at the lower station does not conform to the measured discharge. On the Elbe, the flood is derived from three tributaries which have a tendency to deliver their maximum dis- charge to the main river simultaneously, so that the computation is much simpler than would usually obtain in rivers. A third method of flood prediction is based upon a study of the relations that exist between the heights of the gages on the river and on its tributaries. This method seeks to obtain corrections for the perturbations caused by the tributaries and to add them to a standard flood-wave propagated down the main stream. On the Rhine, where this method of prediction has been employed extensively, there is first determined a primary flood-wave, that 42 RIVERS AND HARBORS is to say, the wave which would be produced if the tributaries did not exist, the relations between the stages attained by the primary flood at different stations being shown both graphically and by equations of the form h 2 = ahi+b, in which a and 6 are constant, while h is contained between certain limits. The equations employed between Waldshut and Maxau (above the Neckar river) are in meters: 7^ = 1.01 tat +1.28 1.72 Japan, S. Shima. Transac- tions of the American Society of Civil Engineers, Vol. LIV, Part A, p. 237. 10. Principles and Practices of Harbour Construction, by William Shields, F.R.S., p. 178. 11. Same p. 205. 12. Breakwater at Sandy Bay, Cape Ann, Mass., by Col. E. Creighill, Corps of Engineers, U. S. Army, Professional Memoirs Corps of Engineers, U. S. Army, and Department at Large, Vol. VIII, p. 587. 13. Cost of Crib Construction, Brief Methods of Preparing Estimate, by J. A. M. Liljencrantz, Journal of Western Society of Engineers, VoL IV, p. 361. 14. Concrete Steel Caissons, their Development and Use for Breakwaters, Piers and Revetments, by W. V. Judson, Journal of the Western Society of Engineers, 1909. CHAPTER XV 1. Freight Train Resistance Its Relation to Car Weight, Bulletin 43, University of Illinois. 2. Influence de la Capacite" des Bateaux sur les Frais de Transports par Canaux par M. Galliot, Inspecteur General des Ponts et Chaussees, Annales des Ponts et Chaussees, 1920. 3. Utilization of the Navigation of Large but Shallow Rivers. Xllth Inter- national Congress of Navigation, No. 48, Philadelphia, 1912. 4. Wharf Equipment, by Ray S. MacElwee, Ph.D., Professional Memoirs Corps of Engineers, U. S. Army, and Department at Large, Vol. X, p. 820. APPENDIX B EXAMPLES OF FLOOD PREDICTION Cairo at Junction of Ohio and Mississippi Rivers The problem can be stated as follows : When the crest of a flood passes Cincinnati on the Ohio River, what height will be recorded on the gage at Cairo, at the mouth of the Ohio, six days thereafter? The data available for its solution are the gage readings at Cincinnati, 498 miles above Cairo on the Ohio River, at Chatta- nooga, 509 miles above Cairo on the Tennessee, at Nashville, 246 miles above Cairo on the Cumberland, and at St. Louis, 191 miles above Cairo on the Mississippi, on the date the crest of the flood passes Cincinnati. Gage records at these places are avail- able for a period of over forty years. If there are plotted the gage heights of the flood at Cairo six days after the flood-wave passes Cincinnati, using the height at Cincinnati as abscissae, a curve can be drawn giving the mean gage relation between the two localities, as shown hi Fig. 4. This curve shows merely that the mean of all the floods that have passed Cincinnati at a given height has attained a height at Cairo as shown by the curve. Thus a flood of fifty feet at Cincinnati will produce a mean flood height at Cairo of 41.9 feet. But in order that the flood at Cairo shall actually attain that height, average conditions must obtain, not only in the slope of the Ohio River, but in the discharge of the tributaries. Similarly, by plotting the heights which the Cairo gage recorded the day the crest of the flood passed Cincinnati, a curve is obtained which indicates the mean difference in gage heights between Cairo and Cincinnati on that date. On the Ohio River this curve is parallel to the curve of mean gage relations and about 5 feet be- low it, i.e., if on the day the crest of the flood passes Cincinnati, the Cairo gage reads 5 feet less than that shown by the curve of mean gage relations, the river slope is normal and the crest of the flood at Cairo six days thereafter will conform to that shown by the curve if there are no perturbations from the tributaries. If, 173 174 RIVERS AND HARBORS FIG. 4 APPENDIX B FLOOD PREDICTION 175 however, on the day the crest of the flood passes Cincinnati, the reading of the Cairo gage is higher or lower than 5 feet below that indicated by the curve of mean gage relations, the crest of the flood will exceed or be less than the height shown by the curve and by an amount in this particular case found to be equal to one- half the difference. The tributaries will also have a disturbing influence unless they also conform to average conditions, and similar curves have been constructed also for each tributary giving the average height it has attained when the crest of the flood passed Cincinnati. If the actual heights differ from the mean, corrections have to be ap- plied, which for the upper Mississippi River at St. Louis are found to be db 1/6 the difference, for the Tennessee River at Chatta- nooga 1/15, and for the Cumberland River at Nashville 1/20. There remains, however, a large area of country (over 50,000 square miles) drained by the numerous rivers emptying into the Ohio between Cincinnati and the mouths of the Cumberland and Tennessee rivers which affects the computations. The Wabash is the largest of these rivers. Employing its flow as an indicator for the others as M. Belgrand utilized certain tributaries of the Seine in his flood predictions for Paris, it is found that when the Wabash River at Mt. Carmel, 221 miles from Cairo, is rising or falling more than six inches a day, the height of the Cairo flood is increased or diminished about one foot. The data for the Wabash River have been published by the Mississippi River Com- mission during the past twenty years only, so that the correction can be but partially applied in the tables. As it requires only from two to three days for the flood-wave to be transmitted from St. Louis and Nashville to Cairo, and about five days for it to be transmitted from Chattanooga, the readings of the gages on the day the crest of the flood passes Cincinnati are not those which produce the crest of the flood at Cairo. They should be increased or diminished by the rise or fall during the interval which must elapse before their waters will be in con- junction with the crest of the Ohio River flood. To obtain ac- curate results at Cairo a flood prediction therefore is required at these localities, and the rise or fall during the preceding day for this reason is added to or subtracted from their readings. This ordinarily gives, within a few feet, the height of the wave in the river which affects the flood crest at Cairo, but occasionally 176 RIVERS AND HARBORS an error of from 5 to 10 feet in the gage readings occurs from the resulting faulty predictions, causing an error from 0.5 foot to one foot in the flood height at Cairo, as is shown in the last column on Table 1. There is, however, an exception to the rule which must be care- fully guarded against. If the river is falling at Cairo, while it is rising at Cincinnati, it usually indicates that a flood from some of the other rivers is passing Cairo, on which that of the Ohio River is merely a perturbation. If the flood originates in the upper Mississippi River, which is normally the case, its height at Cairo can be determined by a similar set of curves shown in Fig. 4 with St. Louis the controlling gage. The prediction can be made only three days in advance, and the heights of the gages at Cincinnati and Chattanooga used are those recorded three days prior to the crest of the flood at St. Louis. Theoretically the readings of the gages at Evansville on the Ohio River, 179 miles from Cairo, and at Johnsonville on the Tennessee, 141 miles from Cairo, on the day the flood passes St. Louis, are preferable to the ones employed on those rivers, but the records of these gages were not available when the computations were first made and have been published only recently in the daily bulletins of the Weather Bureau. The gage at Cairo also may fall while that at Cincinnati is rising, due to an ice gorge in the Ohio River, as in January, 1918. Such irregularities are incapable of computation. If the main flood-wave passing Cincinnati begins to fall, and within two or three days a perturbation from one of the upper tributaries causes a second slight rise, the computations should be based on the main rise. Before the flood reaches Cairo the per- turbation will be absorbed in the general flood and merely prolong its duration. St. Louis at the Junction of the Mississippi and Missouri Rivers A similar set of curves has been deduced (shown in Fig. 5) for determining the height of a flood at St. Louis three days after its crest passes Kansas City, 388 miles above the mouth of the Missouri River, with perturbations of the upper Mississippi com- puted from the gage at Hannibal, and of the Illinois River from that at Peoria. APPENDIX B FLOOD PREDICTION 177 FIG. 5 178 RIVERS AND HARBORS There are, however, three important tributaries of the Missouri River, between Kansas City and its mouth, on which regular gage stations should be established and maintained for a number of years, to enable accurate predictions of the floods at St. Louis to be made; i.e., the Grande River, draining 7185 square miles, the Osage, draining 15,375 square miles, and the Gasconade, 3553 square miles. The floods in these rivers are sometimes very vio- lent, the rivers rising twenty feet in a day, and with a moderate flood in the Missouri River, their effect singly or combined may be large. There is no satisfactory indicator of their combined action. Hermann on the Missouri River, 103 miles from its mouth, gives an invariable warning that there is an abnormal flow in the Missouri River, by a rise of over two feet on the day the crest of the flood passes Kansas City, and it also measures the extent of the rise, but on the same day the flood passes St. Louis and therefore too late to be of value in predicting floods. During the years 1915, '16, and '17, the Weather Bureau published the gage readings at Chillicothe on the Grande River, 62 miles from its mouth, and at Arlington on the Gasconade, 108 miles from its mouth. It has also occasionally published the readings at Bagnelle, 70 miles from the mouth of the Osage River. These limited observations clearly indicate that if continuous records were published for a number of years at the same stations on these rivers, a satisfactory flood prediction could be made for St. Louis for lower stages than those indicated in Table 3. Mississippi Floods at the Mouth of White River An application of the same principles has been made at the mouth of White River, as shown in Table 4, with Cairo as the origin of floods, 393 miles above it, and for the tributaries using the gages at Little Rock on the Arkansas River, 174 miles from its mouth, and Jacksonport on the White River, 264 miles from its mouth. In this case the time of transmission of the flood is variable, it is about 5 days for floods in the Mississippi less than 40 feet in height, about 10 days for those over 45 feet. If a crevasse occurs in the levee line in the St. Francis Basin it may be increased to two weeks. In the table, the computations are based on the transmission of the flood from Cairo to the mouth of White River in 5 days, for floods not exceeding 42 feet in height, APPENDIX B FLOOD PREDICTION 179 and in 10 days for those exceeding 46 feet. Between 42 feet and 46 feet, the results for a movement of the flood wave in both 5 and 10 days are given. On account of the frequency of breaks in the levee line, prior to 1910, the computations are confined to the past ten years. APPENDIX C INFLUENCE OF FORESTS UPON STREAMS Verbal Note Foreign Office No. II S 7540 81331 Referring to the Verbal Note of the 27th ult., the Foreign Office begs to transmit to the Embassy of the United States of America the enclosed copy of an expert opinion on the influence of forests upon streams, rendered by the instructor in the Academy at Eberswalde, Professor Dr. Schubert. The Royal Prussian Minister of Agriculture, at whose instiga- tion the above-mentioned opinion was given, has no further ma- terial on hand. But more detailed information on the subject may be found in a paper on the drainage from forests, read by Professor Dr. Vater of Tharandt, a separate impression of which, from the report of the 49th meeting of the Sachsischen Forst- verein in Marienberg i. S. 1905, was published in Freiberg i. S. 1905 by Craz & Gerlach (Sch. Stettner), and in the report by Mr. Hermann in the "Forstliche Rundschau" of 1906, p. 45, published by S. Neumann in Neudamm. Berlin, November 7th, 1908 To the Embassy of the United States of America. Copy from S 7540. Meteorological Section of the Experimental Department of Forestry. Discussions about the influence of the destruction of forests and the drainage of swamps upon the course and the water-supply of streams, for which the representatives of the different countries had submitted reports, took place at the Congress on navigation at Milan in 1905. The views in regard to the action of forests 180 APPENDIX C FORESTS 181 were rather divided, and the members finally contented themselves with the following joint resolution: "The Congress expresses the wish that those Governments which have not done so before, may now issue distinct and rig- orous instructions about the conservation of the forests still ex- tant, about the protection of the mountain districts and about the afforestation of waste lands, so as to avoid the damage to navigable water-courses, resulting from the formation and the movement of alluvial detritus. " Interesting numerical results were embodied in the report by M. E. Lauda, Director of Public Works and Chief of the Hydro- graphical Central Bureau in Vienna, containing measurements as to precipitation and drainage of the Bistritzka and the Seniza creek-basins. Both these valleys show great similarity in regard to area, shape of surface, and permeability of soil, the last named of which they possess only in a moderate degree. There is also no marked difference in the angle of their banks and in their eleva- tion above sea-level. The two localities are about 20 kilometers distant from one another. The Bistritzka creek flows in a di- rection from east to west, the Seniza creek from south to north. In both valleys meadows and pastures are in preponderance of the tilled ground. But while these conditions are fairly similar, the area of forest in the district of the Bistritzka is about 1.8 times greater than that in the district of the Seniza. The annual precipitation is nearly equal for both valleys, that of the Bistritzka basin being a trifle heavier in summer. Highest elevation Area of district above sea-level in square Area of forest, Drainage, (in meters) kilometers per cent per cent Bistritzka . . 912 63.8 48 28 Seniza ... 923 74.0 27 42 The drainage, in proportion to the precipitation, from the heavier timbered district is considerably smaller, amounting to only two- thirds of that of the other valley. In wide districts, during the dry period of summer, the propor- tion of drainage was of the same inconsiderable quantity of about 5 per cent. An article by F. Umfahrer, on the report cited above and on the transactions of the congress on navigation, is to be found in the 182 RIVERS AND HARBORS " Oesterreichische Wochenschrift fur den offentlichen Baudienst" (Austrian Weekly Magazine for Public Works), XII, 1906, p. 176. According to the measurements, taken by the Prussian State- institution for Hydrology (Prussische Landesanstalt fur Gewas- serkunde) , it appears that in a number of river basins in Northern Germany the proportion of drainage for the heavier timbered districts is generally larger than that for those poorer in forests. From a comparison of several affluents of the Vistula the follow- ing values are derived: Precipitation Forest, Drainage, in millimeters per cent per cent Ferse, Dreweuz .... 540 17.5 27.0 Brahe, Schwarzwasser . . 555 30.1 34.1 There the permeability of the ground plays an essential part, being greater in wooded localities possessing a more sandy soil, and naturally increasing the amount of drainage. The forests in the lowlands of Northern Germany alter the drainage in a sense exactly opposite to that of the results of the Austrian experiments and so we shall have to agree to the opinion of G. Keller that the influence of the forests on the drainage pro- ceedings is being hidden by other causes more powerful in their effects. EBERSWALDE, 1908. Signed: PROF. DR. T. SCHUBERT. TABLES 184 RIVERS AND HARBORS ++ rHtNOSMCO^C^GOOO^OSlO^OOOrH^i-Ji-HrHCOp^OSrHOOOrHCO 1 ^ rH Tji r-5 CN* ' r-5 r-5 r-5 " "r-5r-5 '^^^ * ' ,-J ' rH CN * *r-5 _ + + I I + I + I + + + + + + I + + + + + + I I I I +11 p pop p p p p p r-5 i I rH rH rH rHrH r-5 i I I ++ I I I + ++ +++ i i + i 7+++ i ++++++++ i ++++ i ++ i +^ 1 77 i +7 i +j^++++ ' ' ++ ' j, ' + ' ' '"'++ 1 i i +++ iTi + i i + 1 MI i++i i + 1 i ++++7 i i o ++ I I I ! _[" + I ++++ I ++++++ l l l ++ i + i i 1+1 i ++++++7+++ i ++++ i i i 7+ i*_ ~ COCO CO rH r-i rH <*< " " CN rH rH rH " t>^ r-i rH " CO rH ,J I l + l I ++ I I I I + + + I I I I I ++ I I I I ++ I I CQCMrH r-lrHCQ rH(MrH(MCNrH(N(M(MCOCOi-li-HIM(MrHl-H rHrH rH * QJ CO OS rH rH 6 i i ++ 1 i ^ i j^++ 1 4,^++ ' ' ! + ' +++ ' i + cto ^'c6O^c6r-5l6cN^C^^rHrHlOlOi-5cdrHOSOCDOSOb^lOrHo6cOr-5r-5 rHCNrHCMrH | rH -^ <> iO CO t>I Ci CO CO "^ <*< * CO p pop ~p p p rH r-5 r-5 rH i 5 rH r-5 + I + + + + I rc^ + 111 ++ I I I I ++J.J. I ++++ I ++ I ++++ I '++++++ I CO(irlo"tlirtclJ 5 o"ictooJliii: t l C !,^co^ Fj^ rH ^ O O O CTOi" 3% c^ % $% CV rH CO C. C^rHC^ O5CJr^O O5 O^ Oi MISSOURI RIVER FLOODS 187 1 1 + 1 1 1 1 1 +++ 1 +++ 1 + 1 1 + 1 8 Tf M 188 RIVERS AND HARBORS + I- ++ I I I I ++ I I I I I I + I I ++++ I I 3. *-* S W O5QO 00 ^ CO OOCO *f O5 MISSISSIPPI RIVER FLOODS 189 co" _; i o i> H ; TjJ CD t^ CO b- 00 RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (510)642-6753 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date. DUE AS STAMPED BELOW OCT161997 12,000(11/95) YC 33157 ^---^____ ^-^ 813606 -fC/^ UNIVERSITY OF CALIFORNIA LIBRARY