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U. S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 86 PLATE I APPARATUS ON CAMPUS OF UNIVERSITY OF CALIFORNIA. DEPARTMENT OF THE INTERIOR UNITED STATES ^GEOLOGICAL SURVEY GEORGE OTIS SMITH, DIRECTOR PROFESSIONAL PAPER 86 . THE TRANSPORTATION OF DEBRIS BY RUNNING WATER BY GROVE KARL GILBERT BASED ON EXPERIMENTS MADE WITH THE ASSISTANCE OF EDWARD CHARLES MURPHY WASHINGTON GOVERNMENT PRINTING OFFICE 1914 CONTENTS. Page. Preface.......................................... 9 CHAPTER II. Adjustment of observations........... 55 Abstract......................................... 10 Observations on capacity and slope............ 55 Notation......................................... 13 The observational series................. 55 CHAPTER I. The observations.................... 15 Errors................................... 56 Introduction................................. 15 Intake influences................. .^..... 56 General classification..................... 15 Outfall influences....................... 56 Stream traction.......................... 15 Changes in apparatus.................... 57 Outline of course of experimentation ...... 17 Rhythm................................. 58 Scope of experiments..................... 17 Slopes of de'bris and water surface........ 59 Accessory studies........................ 18 The logarithmic plots.................... 59 Flume traction.......................... 18 Selection of an interpolation formula. .... 60 Apparatus and material........!............. 19 The constant a and competent sloped...... 65 Experiment troughs...................... 19 Interpolation........................... 72 Water supply............................. 19 Precision............................... 73 The water circuit........................ 19 Duty.................................... 74 Discharge................................ 20 Efficiency............................... 75 Sand feed............................... 20 Observations on depth....................... 87 Sand arrester............................ 20 Mode of adjustment...................... 87 Settling tank............................ 21 Precision............................... 94 Gage for depth measurement............. 21 Mean velocity........................... 94 Level for slope measurement............. 21 Formratio............................... 94 Pitot-Darcy gage......................... 21 Graphic computation.................... 94 Sand and gravel.......................... 21 CHAPTER III. Relation of capacity to slope........ 96 Methods of experimentation................... 22 Introduction................................. 96 General procedure for a single experiment. 22 In channels of fixed width................... 96 Details of procedure..................... 22 The conditions..!..........,............. 96 Width of channel.................... 22 The sigma formula...................... 96 Discharge............................ 22 The power function and the index of rela- The feeding of sand................... 23 tive variation.......................... 97 The collection of sand............... 24 The synthetic index..................... 99 Determination of load................ 24 Application to the sigma function......... 99 Determination of slope............... 25 Variation of the index.................... 104 Contractor........................... 25 Formulation with constant coefficient..... 109 Measurement of depth............... 25 Effect of changing the unit of slope........ 112 Measurement of velocity.............. 26 Precision............................... 113 Modes of transportation...................... 26 Evidence from experiments with mixed Movement of individual particles......... 26 debris................................. 113 Boiling.............................. 26 Relation of index to mode of traction...... 115 Saltation........................... 26 In channels of similar section................. 116 Collective movement.................... 30 The conditions........................... 116 Units......................................:. 34 Sigma and the index..................... 117 Terms...................................... 35 The synthetic index..................... 119 Load.................................... 35 Summary............................... 120 Capacity................................ 35 Review.................................... 120 Competence.............................. 35 Duty and efficiency......................... 121 Discharge................................ 35 CHAPTER IV. Relation of capacity to form ratio..... 124 Slope.................................... 35 Introduction................................. ]24 Size of debris........................... 35 Selection of a formula....................... 124 Form ratio............................... 35 Maximum............................... 124 Duty and efficiency..................... 36 Capacity and width...................... 125 Symbols................................. 36 Capacity and depth...................... 127 Table of observations on stream traction. ..... 36 Capacity and form ratio................. 128 (cid:9)3 CONTENTS. Paga. Page. CHAPTER IV Continued. CHAPTER X. Review of controls of capacity........ 186 Discussion of experimental data.............. 130 Introduction................................. 186 Scope and method of discussion.......... 130 Formulation based on competence............ 186 Sensitiveness and the index of relative vari- The form-ratio factor........................ 190 . ation.................................. 130 Duty and efficiency......................... 192 Control of constants by slope............. 131 The formula of Lechalas..................... 193 Control of constants by discharge......... 132 The formula.........................'.... 193 ;" Control of constants by fineness............ 133 Discussion.............................. 194 Special group of observations.............. 134 CHAPTER XI. Experiments with crooked chan Summary as to control by conditions..... 134 nels .......................................... 196 The optimum form ratio............:........ 135 Experiments................................ 196 Summary...:.'.'V...."............. 1.......... 136 Slope determinations......................... 196 CHAPTER V. Relation of capacity to discharge..... 137 Forms and slopes............................ 197 Formulation and reduction................... 137 Features caused by curvature................. 198 Measures of precision and their interpretation.. 142 CHAPTER XII. Flume traction.................... 199 Control of relative variation by conditions..... 143 The observations............................ 199 Duty and efficiency.............. 1. ^:....... 144 Scope................................... 199 Comparison of the controls of discharge and slope. 145 Grades of debris......................... 199 Controls of capacity..............'........ 145 Apparatus and methods................. 199 Controls of duty..................:...... 147 Processes of flume traction................ 200 Controls of efficiency..................... 148 Movement of individual particles.. . . 200 Summary.................................... 149 Collective movement................ 201 CHAPTER VI. Relation of capacity to fineness of Table of observations.................... 202 debris.......................................... 150 Adjustment of observations................... 203 Formulation................................ 150 Formulation............................ 203 Precision................................... 151 Precision............................... 206 Variation of the constant <f>.................... 153 Discussion.................................. 206 Index of relative variation................... 153 Capacity and channel bed................ 206 Duty and efficiency......................... 154 Capacity and slope....................... 208 Summary................................... 154 Capacity and discharge................... 209 CHAPTER VII. Relation of capacity to velocity.:.. 155 Capacity and fineness.................... 210 Preliminary considerations................... 155 Mixtures:............................... 212 The synthetic index when discharge is constant. 157 Capacity and form ratio................. 213 Mean velocity versus slope................... 158 Trough of semicircular cross section. ..... 214 The synthetic index when slope is constant.... 159 Summary................................ 215 The synthetic index when depth is constant... 160 Competence................................ 215 The three indexes............................. 160 Work of Overstrom and Blue.................. 216 Relative sensitiveness to controls.............. 162 CHAPTER XIII. Application to natural streams. ... 219 Competent velocity........................... 162 Introduction......:.......................... 219 CHAPTER VIII. Relation of capacity to depth...... 164 Features distinguishing natural streams........ 219 Introduction................................. 164 Kinds of streams........................ 219 When discharge is constant. ................. 164 Features connected with curvature of When slope is constant...................... 164 channel.............................. 220 Depth versus discharge....................... 165 Features connected with diversity of dis When velocity is constant.................... 165 charge. ............................... 221 The three conditions compared............... 166 Sections of channel...................... 222 Comparison of controls by slope, discharge, and The suspended load..................... 223 mean velocity............................. 167 The two loads........................... 230 CHAPTER IX. Experiments with mixed grades..... 169 Availability of laboratory results............. 233 Adjustment and notation..................... 169 .The slope factor.......................... 233 Mixtures of two grades......................... 172 The discharge factor...................... 233 Control by slope and discharge................ 175 The fineness factor....................... 235 Mixtures of more than two grades.............. 176 The form-ratio factor...................... 236 A natural grade............................. 177 Causes of superior mobility of mixtures........ 178 The four factors collectively.............. 236 Voids....................................... 179 The hypothesis of similar streams......... 236 Fineness................................... 180 Summary.-.............................. 240 Relation of capacity to fineness, for natural Conclusion................................... 240 grades.................................... 180 CHAPTER XIV. Problems associated with rhythm.. 241 Definition and measurement of mean fineness.. 182 Rhythm in stream transportation.............. 241 Summary................................... 184 Rhythm in the flow of water.................. 242 CONTENTS. Page. Page. CHAPTER XIV Continued. APPENDIX B. The discharge-measuring gate and its The vertical velocity curve.................. 244 rating......................................... 257 The moving field............................ 249 The gate..................................... 257 APPENDIX A. The Pitot-Darcy gage.............. 251 Plan of rating............................... 258 Scope of appendix............................ 251 Calibration of measuring reservoir............. 258 Form of instrument........................... 251 The observations.......................... .. 259 Rating methods............................. 252 INDEX. .......................................... 261 Rating formula............................... 253 TABLES. Page. Page. TABLE 1. Grades of de"bris...................... 21 TABLE 26. Values of m1} in Coc rf7"1, when slope is 2. Gate readings and corresponding dis constant............................ 128 charges............................. 23 27. Quantities illustrating the influence of 3. Data connected with changes in mode slope on the relation of capacity to form of transportation..................... 33 ratio................................ 132 4. Observations on load, slope, and depth.. 38 28. Quantities illustrating the influence of 5. Values of capacity generalized from Table discharge on the relation of capacity 4(G)............................... 61 to form ratio......................... 133 6. Data for the construction of curves in 29. Quantities illustrating the influence of figures 20 and 21 .................... 62 fineness on the relation of capacity to 7. Values of a in C=61(S-<;)n............ 66 form ratio........................... 133 8. Values of a, arranged to show variation 30. Quantities illustrating the influence of in relation to fineness of debris........ 68 slope and discharge on the,relation of 9. Experimental data on competent slope.. 69 capacity to form ratio ............... 134 10. Experimental data on competent dis- 31. Estimated ratios of depth to width to charge.............................. 70 enable a given discharge, on a given 11. Values of a, as adjusted for use in inter slope, to transport its maximum load. 135 polation equations................... 72 32. Data on the relation of capacity to dis 12. Adjusted values of capacity, duty, and charge .............................. 137 efficiency.......................... 75 33. Values of «, computed from data of b' Table 32............................ 140 13. Values of nt in d= ................. 89 Adjusted system of values of K. ......... 141 & u4. 14. Adjusted values of depth of current, with 35. Values of i3, arranged to show variation values of mean velocity and form ratio. 89 in relation to fineness............... 144 15. Values of i, in relation to slope......... 100 35. Comparison of ^ with i3................ 145 16. Values of;, in C=cS'i................. 109 37. Variations of ij and i3 in relation to dis 17. Values of i, for mixtures of two or more charge .............................. 146 grades.............................. 114 33 Variations of \ and i3 in relation to width. 146 18. Comparison of values of ir for mixtures 39. Variations of i^ and i3 in relation to fine and their components................ 115 ness ................................ 147 19. Values of it associated with the smooth 40. Variations of ij and iz in relation to slope. 147 mode of traction .................... 115 Variations of the ratio - ............ 148 20. Relations of ^ to discharge, debris grade, and channel width.................. 116 i,-l Variations of the ratio 148 21. Selected data showing the relation of ca L-l pacity to slope when the form ratio is 43. Yalues of capacity, arranged to illustrate constant............................ 117 the relation of capacity to grades of 22. Values of a corresponding to data in debris.............................. 150 Table 21............................ 118 44. Data connected with the plots in fig 23. Values of synthetic index under condi ure 50.............................. 151 tion that R is constant, and under con- ' 45. Values of 74, compared with slope, dis dition that w is constant............. 119 charge, and width................... 154 23a. Comparison of (parameters in C=&! 46. Values of IVQ .......................... 157 (S-a)n and E=f^ (S-a)nu. ....... 123 47. Means based on Table 46, illustrating the 24. Relation of capacity to width when control of IVQ by discharge, fineness, slope and depth are constant......... 126 and width.......................... 158 25. Values of capacity and depth for grade 48. Synthetic indexes, comparing the con (C), width 0.66 foot, and slope 1.0 per trol of capacity by mean velocity with cent............................... 128 the control by slope................. 158 CONTENTS. Page. Page. TABLE 49. Values of IVS- ........................ 159 TABLE 66. Relative speeds of coarse and fine de"- 50. Means based on Table 49, illustrating bris in flume traction .....:........... 200 the control of TVS by slope, fineness, . 67. Observations on flume traction, showing and width .......................... 159 the relation of load to slope and other 51. Values of Ira ......................... 160 conditions.......................... , 202 52. Means based on Table 51, illustrating the 68. Values of capacity .for flume traction, ad control of Iva by fineness and width.. 160 justed in relation to slope............. 204 53. Comparison of synthetic indexes for ca 69. Comparison of capacities associated with pacity and mean velocity, under the different characters of channel bed.... 206 several conditions of constantdischarge, 70. Values of /! for flume traction........... 208 constant depth, and constant slope.... 161 71. Comparison of values of II for flume trac 54. Values of Ids......................... 164 tion with corresponding values for 55. Means based on Table 54, illustrating stream traction....................... 209 the control of las by slope, fineness, 72. Data illustrating the relation of capacity and width.......................... 165 for flume traction to discharge........ 209 56. Synthetic indexes comparing the control 73. Values of capacity for flume traction, of capacity by depth with control by illustrating the control of capacity by discharge........................... 165 fineness.............................. 210 57. Values of lav ......................... 165 74. Capacities for mixed grades and their 58. Means based on Table 57, illustrating the components......................... 212 control of lav by mean velocity, fine 75. Depths and form ratios of unloaded ness, and width..................... 166 streams.............................. 213 59. Comparison of synthetic indexes for ca 76. Capacities for flume traction in troughs pacity and depth under the several of different widths .................. 213 conditions of constant discharge, con 77. Data on flume traction in a semicylindric stant slope, and constant mean velocity 167 " trough............................ 1.. 214 60. Adjusted values of capacity for mixtures 78. Observations by Blackwell on velocity of two or more grades of d6bris....... 169 competent for traction................ 216 61. Capacities for traction, with varied mix 79. Values of n in Coc Vmn based on Blue's tures .of two grades............... r.. 172 experiments.."...................... 218 62. Percentages of voids in certain mixed 80. Velocities of streams with and without grades of debris ...................... 179 tractional loads....................... 230 63. Fineness of mixed grades and their com ponents............................. 180 81. Ratio of the suction at one opening of the 63a. Data on subaqueous dunes of the Loire. 194 Pitot-Darcy gage to the pressure at the 64. Comparison of slopes required for straight other............................... 254 and crooked channels................ 197 82. Values of KanduinH-H^KV" ..... 254 65. Grades of debris....................... 199 83. Values of A in V= A^H-I^........... 255 ILLUSTRATIONS. Page. Page. PLATE I. Apparatus on campus of the University FIGUKE 10. Longitudinal section illustrating the of California.................... Frontispiece. dune mode of traction.............. 31 II. Debris used in experiments............. 22 11. Longitudinal section illustrating the III. Rough surfaces used in experiments on antidune mode of traction........... flume traction........................ 200 12. Profiles of water surface, automatically FIGURE 1. Diagrammatic view of shorter experi recorded, showing undulations asso ment trough......................... 19 ciated with the antidune mode of 2. Diagram of water circuit.............. 20 traction............................ 33 3. The contractor........................ 25 13. Plot of a single series of observations of 4. Diagrammatic view of part of experi capacity and slope................. 55 ment trough with glass panels and 14. Logarithmic plot of a series of observa sliding screen....................... 27 tions on capacity and slope......... 56 5. Appearance of the zone of saltation.... 27 15. Diagrammatic longitudinal section of 6. The beginning of a leap, in saltation. . 28 outfall end of experiment trough, 7. Diagram of accelerations affecting a saltatory grain..................... 28 illustrating influence of sand arrester 8. Theoretic trajectory of a saltatory par on water slope..................... 57 ticle. ............................. 29 16. Diagrammatic longitudinal section of 9. Ideal transverse section of zone of sal debris bed and stream, in a long tation at side of experiment trough.. 30 trough............................. 57 CONTENTS. Page. Page. FIGURE 17. Diagrammatic longitudinal section of FIGURE 43. Eelation of capacity, C, to form ratio"," outfall end of trough, illustrating R. The variation of the function influence of contractor............. C=bi(l+aR)Rm with slope......... 131 18. Profiles of channel bed, illustrating 44. Relation of capacity, C, to form ratio, tractional rhythms associated with R. The variation of the function dunes of greater magnitude......... 58 C=b2(l-aR)Rm with discharge..... 132 19. Logarithmic graph of C=f(S), for grade 45. Relation of capacity, C, to form ratio, (G), w=0.66 foot, Q==0.734 ft.3/sec... 61 R. The variation of the function 20. Extrapolated curves of C=f(S) for vari C=6a(l-f*R)Rm with fineness of d6- ous tentative equations of interpola bris................................ 133 tion and for slopes greater than 2.4 46. Relation of capacity, C, to form ratio, per cent............................ 62 i-'-::R. The variation of the function 21. Extrapolated curves of C=f(S) for vari \ i'G=^(\ fxK)Rm with slope and dis ous tentative equations of .interpola charge. ............................ 134 tion and for slopes less than 0.8 per 47. Logarithmic plots of the relation of cent............................... 63 ;.-capacity to discharge................ 139 22. The relation of a in C=f(S-a) to the 48. Ideal cross section of a stream in the ex- curvature of the logarithmic graph.. 65 < periment trough, illustrating the rela 23. Diagrammatic sections of laboratory tion of competent discharge to width. 140 troughs, illustrating relation of cur 49. Logarithmic plot of *=/(!>)........... 141 rent depth to trough width......... 67 50. Logarithmic plots of capacity,for trac 24. Ideal curve of competent slope in rela tion in relation to fineness of debris.. 150 tion to width of trough .............. 67 51. Average departures of original values 25. Logarithmic plot of competent slope in of capacity from system of -values relation to fineness of de'bris........ 69 readjusted in relation to fineness of 26: Illustration of the method used to ad ..debris.............................. 152 just values of capacity in relation to 52. Vertical velocity curve, drawn to illus slope by means of a logarithmic plot trate its theoretic character near the of observed values of capacity in re stream's bed......................... 155 lation to slope minus a............. 72 53.. Ideal profile of a stream bed composed 27. Observations of depth of current in re of de'bris grains..................... 155 lation to' slope..................... 87 54. Ideal curves of velocity in relation to 28. Logarithmic computation sheet, com depth, illustrating their relation to bining relations of capacity, mean the zone of saltation................ 161 velocity, form ratio, and slope...... 95 55. Tractional capacity for mixed debris, 29. Logarithmic locus of the exponential .in relation to proportions of compo equation.......................... 98 nent grades, with associated curves of 30. Locus of log j/=/(log x), illustrating the fineness and of percentages of voids.. 173 nature of the index of relative varia 56. Tractional capacities of components of tion. ............................... 98 mixed grades in relation to the 31. Variations of i, in relation to slope..... 105 percentages of the components in the 32. Variations of i, in relation to width of mixtures........................... 174 channel........................... 106 57. Curves of capacity in relation to slope 33. Variations of i, in relation to discharge. 107 for grade (A), grade (G), and mixtures 34. Variations of i, in relation to fineness of of those grades..................... 175 de'bris.............................. 108 58. Curves of capacity in relation to slope 35. Variations of exponents ilt jl; and k in for grade (B), grade (F), and mixtures relation to slope..................... 113 of those grades..................... 175 36. Variations of ij under conditions of uni 59. Curves of capacity in relation to slope form mode <5f traction and uniform for grade (C), grade (E), and mixtures slope............................... 116 of those grades..................... 176 37. Curves of C f(S) for three trough 60. Curves of capacity in relation to slope widths............................. 118 for a mixture of five grades, (C, D, E, 38. Illustration of the relation of capacity F, G). Comparison of mixture curves to width of channel and to form ratio, for three discharges and of mixture when slope and discharge are constant 124 curve with curves for component 39. Cross sections of stream channels....... 125 grades ............................ 176 40. Capacity for traction in relation to 61. Capacity-slope curves for related mix width of channel, when depth and tures and capacity-discharge curves slope are constant.................. 127 for mixture and component grades.. 177 41. Plot of equation (55).................. 129 62. Capacity-slope curves for a natural 42. Logarithmic plots of grade of d6bris, compared with curves 2\ ~ p m-t-1 130 for sieve-separated grades........... 178 CONTENTS. Page. Page. FIGURE 63. Curves showing the relations of various FIGURE 78. Modification of vertical velocity curve quantities to the proportions of fine when mean velocity is increased by and coarse components in a mixture of change of slope...................... 245 two grades of debris, (C) and (G).... 179 79. Modification of vertical velocity curve ' 64. Logarithmic plots of capacity in relation when mean velocity is increased by to linear fineness, for related mixtures change of discharge.................. 246 of debris........................... 181 80. Modification of vertical velocity curve 65. Curve illustrating the range and dis by changes in the roughness of the tribution of finenesses in natural and channel bed........................ 246 artificial grades of debris............. 181 81. Modification of vertical velocity curve 66. Typical curves illustrating the distri by addition of load to stream, with bution of the sensitiveness of capacity corresponding increase of slope...... 246 for traction to various controlling con 82. Modification of vertical velocity curve ditions............................ 191 by addition and progressive increase . 67. Plans of troughs used in experiments to of load............................. 246 83. Ideal longitudinal section of a stream, show the influence of bends on trac illustrating hypothesis to account tion................................ 196 for the subsurface position of the level 68. Contoured plat of stream bed, as shaped of maximum velocity.-.............. 248 by a current....................... 198 84. Diagrammatic plan of suggested mov 69. Curves illustrating the relation of ca ing-field apparatus................... 250 pacity for flume traction to fineness 85. Longitudinal section of lower end of of debris........................... 211 receiver of Pitot-Darcy gage No. 3, 70. Diagram of forces...................... 224 with transverse sections at three 71. Interference by suspended particle points.............................. 251 with freedom of shearing............ 226 86. Cross section of prism of water in trough, 72. Suggested apparatus for automatic feed showing positions given to gage open of debris........................... 241 ing in various ratings................ 255 73. Modification of vertical velocity curve 87. Graphic table for interpolating values of by approach to outfall............... 244 74. Modification of vertical velocity curve A \nV=A -JH H1} for observations by approach to contracted outfall.. 245 made with gage 3b in different parts 75. Plan of experiment trough with local of a stream.......................... 256 contraction........................ 245 88. Arrangement of apparatus connected 76. Profile of water surface in trough shown with the rating of the discharge- in figure 75......................... 245 measuring gate..................... 257 77. Modification of vertical velocity .curve 89. Elevation and sections of gate for the by local contraction of channel...... 245 measurement of discharge........... 258 PREFACE. Thirty-five years ago the writer made a work as well as for the discussion of results study of the work of streams in shaping the here contained, while Mr. Murphy is responsible face of the land. The study included a for the experimental work. It must not be qualitative and partly deductive investigation understood, however, that in assuming responsi of the laws of transportation of d6bris by bility for the discussion I also claim sole credit running water; and the limitations of such for what is novel in the generalizations. Many methods inspired a desire for quantitative conclusions were reached by us jointly during data, such as could be obtained only by our association, and others were developed by experimentation with determinate conditions. Mr. Murphy in his report. These have been The gratification of this desire was long de incorporated in the present report, so far as ferred, but opportunity for experimentation they appeared to be sustained by the more finally came in connection with an investigation elaborate analysis, and specific credit is given of problems occasioned by the overloading of only where I found it practicable to quote certain California rivers with waste from from Mr. Murphy's manuscript. hydraulic mines. The physical factors of Mr. J. A. Burgess was for a short time a those problems involve the transporting capac scientific assistant in the laboratory, and his ity of streams as controlled by various condi work is described in another connection. tions. The experiments described in this Credit should be given to Mr. L. E. Eshleman, report were thus instigated by the common carpenter, and Mr. Waldemar Arntzen, mechan needs of physiographic geology and hydraulic ician, for excellent work in the construction of engineering. apparatus., I recall with sincere gratitude A laboratory was established at Berkeley, the cordial cooperation of several members of Cal., and the investigation became the guest the university faculty, and the investigation is of the University of California, to which it is especially indebted to the good offices and indebted not only for space, within doors and technical knowledge of Prof. S. B. Christy without, but for facilities of many kinds most and Prof. J. N. Le Conte. generously contributed. Portions of my manuscript were read by Almost from the beginning Mr. E. C. Murphy Dr. R. S. Woodward and Dr. Lyman J. Briggs, has been associated with me in the investigation and the entire manuscript was read by Mr. C. E. and has had direct charge of the experiments. Van Orstrand and Mr. Willard D. Johnson. Before the completion of the investigation I To these gentlemen and to members of the was compelled by ill health to withdraw from editorial staff of the Geological Survey I am it, and Mr. Murphy not only made the remain indebted for criticisms and suggestions leading ing series of experiments, so far as had been to the elimination of some of the crudities of definitely planned, but prepared a report. the original draft. This report did not include a full discussion of While the aid which my work has received the results but was of a preliminary nature, from many colleagues lias been so kindly and it being hoped that the work might be con efficient that individual mention seems invid tinued, with enlargement of scale, in the near ious, my gratitude must nevertheless be future. When afterward I found myself able expressed for valuable assistance by Mr. Fran- to resume the study, there seemed no im 9013 E. Matthes in the examination of foreign mediate prospect of resuming experimentation, literature, and for the unfailing encouragement and it was thought best to give the material and support of Mr. M. 0. Leighton, until comparatively full treatment. It will readily recently in charge of the hydrographic work be understood from this account that I am of the Survey. responsible for the planning of the experimental G. K. G.

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APPARATUS ON CAMPUS OF UNIVERSITY OF CALIFORNIA. TRANSPORTATION OF DEBRIS BY RUNNING WATER. BY The water circuit. by addition of load to stream, with study of the work of streams in shaping the.
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