Shore processes and shoreline development

Preface

The present work was born of a need experienced by the author in connection with his shoreline studies. In the course of a critical examination of the arguments supposed by many to demonstrate a progressive subsidence of the Atlantic coast of North America within historic time, it developed that in respect to certain of these arguments agreement between students of the problem could not be reached because there was not sufficient agreement as to what features are normally characteristic of a stable coast ; and what features are peculiar to coasts which are rising or subsiding. No work existed which combined with an extended analysis of the forces operating along the shore, a full and systematic discussion of the cycle of shoreline development and such further discussion of the modifying effects of changes of level as would enable one to differentiate stable, rising, and subsiding coasts.

It seemed necessary, therefore, to enquire somewhat fully into the fundamental principles of shore processes and shoreline development; for it would not be profitable to add to the already overburdened literature on changes of level another essay which should merely add quantitatively to the volume of evidence previously discussed by many earlier writers, and again assert as the correct interpretation of that evidence conclusions which some geologists and geographers accept and others reject. Profit could come from the study only in case the discussion of principles was such as to bring geologists and geographers into substantial agreement as to what shore features are, and what are not indicative of changes of level. Once this measure of agreement was reached, I could not doubt that a critical analysis of the arguments supposed to prove the progressive subsidence within historic time of the coast of southeastern Canada, the Atlantic coast of the United States, and certain other marginal areas of the continents, would demonstrate to the impartial and. critical student the inadequacy of those arguments. I therefore set myself the task of bringing together the results of shoreline studies published in different languages, of analyzing and criticising the conclusions reached iv PREFACE

where this might appear to be profitable, and of presenting a digest of those fundamental principles which should prove to be best established by the independent work of different students and best supported by my own field observations. At the seme time I purposed to develop somewhat fully certain important aspects of the physiography of shorelines which have hitherto received little consideration.

The magnitude of the task proved to be greater than anticipated, partly because of the wide divergence of expert opinion regarding the manner in which shore processes operate, and partly because of the great volume and scattered distribution of the writings dealing with the subject. It was, indeed, the desire to relieve others who might have occasion to study shore processes and shoreline forms, of the burden of duplicating the work involved in my undertaking which first suggested to me the desirability of placing on record, in compact form for their use, the results of my enquiry, even where these results did not relate to the original problem of coastal subsidence. The present volume is the concrete product of this desire to render a service to my fellow students.

The engineer will find in the chapters on waves and currents a summary of the widely conflicting opinions and observations relating to those most puzzling forces with which he has to deal. In the later chapters he will also find, I hope, not a few discussions of shore forms and of the method of their development which will prove useful to him in his work on marine engineering structures. The dynamic geologist will find in the first chapters an extended account of two of the forces of nature with which he is much concerned, and in the remaining chapters abundant illustrations of the manner in which those forces operate near the margins of the lands. The geographer will be mainly concerned with the last seven chapters where the forms of the shoreline receive a systematic treatment which, if not adequate, is at least somewhat more detailed and complete than any hitherto attempted. Throughout the volume the reader will note that repeatedly conclusions reached and principles established are briefly applied to the problem of changes of level; and he will understand that this is the thread, appearing now and then, which is to connect parts of the present study with a later volume devoted exclusively to the much mooted question of coastal subsidence.

PREFACE V

As a rule an advance summary precedes, and a brief resume concludes the text of each chapter. This will enable engineer, geologist and geographer to determine in some measure the extent to which matters pertinent to their respective fields are discussed. A bibliography, arranged alphabetically according to authors and placed at the end of the volume, supplements the list of references given at the close of each chapter. Finally, an index of authors and an index of subjects are provided in the form which it is hoped will prove most serviceable to the reader.

In any attempt to give proper credit for the aid rendered by others during the preparation of this volume the writer is much embarrassed. The work of preparation has extended over several years, during which time a number of students, colleagues and friends have been most generous in rendering valuable assistance. It would be impossible to make specific acknowledgments to all of them, so great is the measure of my indebtedness. Special thanks are due to my cousin, Miss Laura Dale Johnson, for assuming the labor of reading the proofs and seeing the book through the press during my absence; to Miss Florrie Holzwasser of the Department of Geology of Barnard College, and others among my graduate students, for assistance in reviewing and abstracting the literature relating to the subject in hand; and to Dr. A. K. Lobeck for preparing the five block diagrams showing successive stages in the development of a shoreline of submergence. Acknowledgments should be made to "The Geographical Review," "Science," the "Bulletin of the Geological Society of America," and the "Journal of Geology" for the use of certain material originally published in their pages. Many of the observations recorded in this volume were made in the course of a special Shaler Memorial Investigation of the problem of coastal subsidence undertaken with the support of the Shaler Memorial Fund of Harvard University; and observations on the New Jersey coast were obtained in connection with a study in progress for the Geological Survey of New Jersey under the direction of Dr. H. B. Kummel. It is a pleasure to express special obligations to Professor W. M. Davis for helpful criticism of the manuscript, and to acknowledge the debt which all physiographers owe to his studies of shoreline topography, which were the first to demonstrate the value of applying the idea of the cycle to the history of shore forms. To Professor Joseph Barrell, whose studies have to some extent paralvi PREFACE

leled certain of my own, I am indebted for many valuable suggestions and for his generous courtesy in giving to the manuscript a careful and critical reading, from the results of which I have greatly profited.

In conclusion it is but fair to acknowledge the author's keen appreciation of certain defects which the reader may discover in his perusal of the text. The volume goes to press under circumstances which absolutely prevent that careful attention to details which every work of this kind should receive. On entering the service of his country the writer was forced to choose between publishing his studies without the final supervision which he had hoped to give the proofs, and postponing publication indefinitely. In view of the uncertainties attending service in the zones of military operations, it has seemed wiser to allow the work to go to press, in the hope that the indulgent reader will not find the value of the volume materially affected by such errors in execution as the presence of the author alone could have prevented.

DOUGLAS WILSON JOHNSON.

On Board Troop Ship, April 3, 1918.

Contents

Page

List of Plates ix

List of Illustrations xiii

Chapter I

Advance summary, 1; Scope of subject, 2; Literature, 4; Waves of oscillation, 7; Origin, 7; Wave motion, 8; Wave form, 12; Wave height, 21; Wave length, 27; Wave velocity, 29; Waves of translation, 33; Earthquake and explosion waves, 38; Tidal waves, 41; Standing waves; seiches, 42; Boundary waves, 44; Resume, 45; References, 46.

Chapter II

Advance summary, 55; Wave energy, 55; Nature of wave attack, 57; Wave dynamometer, 62; Measurements of wave energy, 63; Damage by storm waves, 65; Conditions affecting wave energy, 72; Wave refraction, 74; Depth of wave action, 76; Resume, 83; References, 83.

Chapter III

Advance summary, 87; Types of currents, 88; Wave currents, 90; Tidal currents, 106; Seiche currents, 122; Wind currents, 123; Planetary currents, 128; Pressure currents, 130; Convection currents, 131; Salinity currents, 131; River currents, 136; Reaction currents, 138; Eddy currents, 139; Deflection of currents, 141; Resume, 148; References, 149.

Chapter IV

Advance summary, 159; Terminology of shores, 159; Plains, planes, and peneplanes, 164; Classification of shorelines, 169; I. Shorelines of submergence, 173; II. Shorelines of emergence, 186; III. Neutral shorelines, 187; IV. Compound shorelines, 190; Stages of shoreline development, 192; Resume, 192; References, 192.

Vlll CONTENTS

CHAPTER V Page

Shorelines of submergence, 199; Advance summary, 199; Initial stage, 201; Young stage, 203; Mature stage, 210; Old stage, 224; Validity of the theory of a marine cycle, 228; Correlation of the marine and fluvial cycles, 242; Independence of marine and fluvial cycles, 245; Comparative rapidity of marine and fluvial planation, 249; Probability of marine planation, 253; Interruptions and accidents during the marine cycle, 257; Shorelines of emergence, 258; Initial stage, 258; Young stage, 259; Mature and old stages, 262; Neutral shorelines, 262; Compound shorelines, 265; Resume, 267; References, 268.

Chapter VI

A. Shorelines of submergence, 272; Advance summary, 272; Initial stage, 272; Young stage, 275; Stages of development of shore details, 328; Relative importance of different marine forces in the formation of bars, forelands, etc., 333; Mature stage, 339; Old stage, 344; Resume, 345; References, 345.

CHAPTER VII Development of the Shoreline (Continued) 348

B. Shorelines of emergence, 348; Advance summary, 348; Initial stage, 348; Young stage, 350; Effect of progressive subsidence on lagoon history, 383; Effect of progressive elevation on lagcon history, 386; Offshore bars not an evidence of subsidence, 386; Mature stage, 389; Old stage, 390; Resume, 392; References, 392.

CHAPTER VIII Development of the Shoreline (Continued) 395

C. Neutral and compound shorelines, 395; Neutral shorelines, 395; Compound shorelines, 400; Contraposed shorelines, 401; References, 403.

Chapter IX

Advance summary, 404; Origin of beach ridges, 404; Rate of beach ridge formation, 414; Beach ridges as records of changes of level, 439; Resume, 453; References, 454.

Chapter X

Advance summary, 458; Beach cusps, 458; Low and ball, 486; Ripple marks, 489; Rill marks, 512; Swash marks, 513; Backwash marks, 517; Sand domes, 518; Shore dunes, 519; Resume, 525; References, 525.

LIST OF PLATES

Page I. Storm waves breaking against seawall at Hastings, England . 1 4 II. Combing wave, showing water completing orbital movement although insufficient in quantity to fill the wave form 17

III. Waves breaking against seawall at Scarborough, England. . 19

IV. Storm wave striking face of seawall at Scarborough, England 59 V. Water forced vertically upward by wave breaking against

seawall at Scarborough, England 61

VI. Marine Cliff at Highland Light, Cape Cod, rapidly retreating under wave attack 64

VII. Shakespeare's Cliff near Dover, England 79

VIII. Wire fence undermined by wave attack and left hanging in

mid-air 73

IX. Cobblestones cast into a high ridge well above sealevel by •

storm waves 78

X. Cobblestones cast upon the beach from deep water through the combined effect of wave action and the buoyancy of

attached seaweeds 92

XI. Surf breaking on the shore of Cape Canaveral, Florida .... 95 XII. Winthrop Great Head, a wave-cliffed drumlin near Boston,

Massachusetts 98

XIII. Lowestoft Ness on the east coast of England 102

XIV. Giant sand ripples produced by strong ebb tide current in

the Avon River estuary near Windsor, Nova Scotia 110

XV. Salt marsh near Green Harbor, Massachusetts 112

XVI. Hornviken, a small fjord near North Cape, Norway, showing

typical oversteepened walls of a glacial trough 175

XVII. Idde Fjord near Fredriksten, Norway, showing rectangular

pattern characteristic of many fjord coasts 178

XVIII. The Naero Fjord, Norway, a partially submerged glacial

trough 180

XIX. Lake Loen, Norway, occupying a glacial trough and practically continuous with the upper part of Nord Fjord .... 183 XX. Stromstad Harbor, Sweden, showing characteristics of a

fiard coast 185

XXI. Northwestern coast of France near Fecamp, showing youthful cliff profiles on a mature shoreline of submergence . . . 200 XXII. Same view as Plate XXI, but at low tide, showing marine

cliff, wave-cut bench, and narrow beach at base of cliff . . 202 XXIII. Marine cliff cut in glacial drift near Plymouth on the Massachusetts coast 205

ix

X LIST OF PLATES

Page XXIV. Marine cliff cut in sand and clays of the coastal plain near

Beaufort, North Carolina 207

XXV. Marine cliff cut in sand dunes on the shore of Cape Canaveral, Florida 1209

XXVI. View near Rhuvaal, Islay, off the west coast of Scotland, showing former marine cliff and wave-cut bench, recently

elevated above sealevel 227

XXVII. Elevated marine cliff near Oban, Scotland 233

XXVIII. Marine cliff and wave-cut rock bench on the Pacific coast

south of Cape Flattery, Washington 236

XXIX. Marine peneplane and monadnock near Madura, east coast

of India 239

XXX. Base of monadnock in Plate XXIX, showing effects of

marine erosion 241

XXXI. Monadnock on marine peneplane of the east coast of India . 251 XXXII. Imposing marine cliff at North Cape, Norway 252

XXXIII. Rocky headland and drowned valley of a young shoreline of

submergence, near Clifton, Massachusetts 255

XXXIV. Stack or chimney in front of a young cliff on the coast of

France 277

XXXV. The Dogstone, near Oban, Scotland, a stack in front of a

marine cliff, now elevated 25 feet above sealevel 279

XXXVI. Fingal's Cave on the Island of Staffa, western Scotland. . . . 280 XXXVII. Ancient sea cave on an elevated shoreline of western Scotland, transformed into a stable 282

XXXVIII. Wave-cut arch on the northwest coast of France 284

XXXIX. Third Cliff near Scituate, Massachusetts, showing small

landslide due to wave erosion of cliff base 286

XL. Bay-head or pocket beach near Rye, New Hampshire 288

XLI. Deltas of cobblestone formed by overwash of storm waves

near Marblehead, Massachusetts 305

XLII. Tombolo connecting the former island of Marblehead with

the Massachusetts mainland 314

XLII I. Hanging valleys on the chalk coast of southeastern England, where waves cut back the shore faster than the streams

can deepen their valleys 342

XLIV. Former offshore bar near Wrightsville, North Carolina, rising above the marsh surface back of the present offshore bar 353

XLV. Surface of a salt marsh near Boston, Massachusetts, which overlies a peat deposit 20 feet deep composed of remains

of high-tide vegetation 384

XLVI. Contraposed shoreline south of Rye Beach, New Hampshire. 402 XLVII. Ancient beach ridge (center of view) connecting former

island in distance with one in foreground 406

XLVIII. Ancient series of dune ridges on Cape Canaveral, truncated at right angles by a later series in the foreground, on one member of which the man is sitting 415

LIST OF PLATES xi

Page XLIX. Shingle beach ridges of the Dungeness cuspate foreland,

England 421

L. Shingle beach ridges on the island of Riigen, Germany .... 425 LI. Forested dune ridges on the Darss cuspate foreland, Germany, showing marked inequality in altitude of crestlines 427 LII. Road-cut through an old dune ridge at the back of the

present shore at Daytona, Florida 432

LIII. Successive curving beach ridges and swales forming lines of

growth on Cape Canaveral 441

LIV. Level surface of Skanor peninsula, southwestern Sweden. 448 LV. Beach cusps of gravel on the shore of Carmel Bay, California 452 LVI. Giant sand cusps on Melbourne Beach, Florida, truncated

J by wave erosion 464

LVII. Cusps on Nantasket Beach, Massachusetts 468

LVIII. Beach cusps on the west coast of Porto Rico, near Melones

Point 472

LIX. Sandstone slab showing fossil oscillation ripples 490

LX. Current ripples formed by an ebbing tide 492

LXL Current ripples on the shore of Nantasket Beach, Massachusetts 493

LXII. Giant current ripples near Annisquam, Massachusetts, showing irregular pattern due to interference of wave and

LXIII. Current ripples near Windsor, Nova Scotia 503

LXIV. Current ripples modified by later oblique wave or current

action 506

LXV. Plaster cast of interference ripple mark formed by two

systems of waves crossing nearly at right angles 507

LXVI. Rill marks on a sandy beach 511

LXVII. Plaster cast of swash marks left by four successive waves

on the sandy shore of Lake Erie 514

LXVIII. Cast of backwash marks 515

LXIX. Plaster cast of backwash marks 516

LXX. Shore dunes of the Holland coast near Katwijk 520

LXXI. Shore dunes near Scheveningen, Holland 521

LXXII. Dune of barchane form overwhelming trees on the Provincelands of Cape Cod 522

LXXIII. Shore dunes near Cape Henry, Virginia, migrating iniand

over the forest 524

LIST OF ILLUSTRATIONS

Frontispiece. Wave-cut bench and marine cliff bordering Desecheo Island, Porto Rico, recently elevated above sealevel. Fig. Page

1. Diagram showing the motion of water particles in an oscillatory

wave 9

2. Diagram showing the elliptical orbits of water particles in shallow-

water waves, and the decrease in size of orbits with increasing depths 10

3. Diagram showing theoretical form of a cycloidal wave, and the

rapid decrease in size of the orbits (through which the water particles move) with increasing depth 12

4. Theoretical profiles of three trochoidal waves having different sized

orbits (solid-line profile and broken-line profile), or different spacing of orbits (broken-line profile and dotted-line profile). 13

5. Diagram showing how two regular series of waves of different

heights and lengths combine to form an irregular series 26

6. Diagram showing movement of water particles in a wave of trans-

lation 34

7. Diagram showing how oscillatory waves breaking on a subaqueous

terrace produce waves of translation 37

8. Diagram to illustrate the movement of water particles in standing

1 waves, such as the seiche . . 43

9. Boundary wave formed by local air current over liquids of different

densities 44

10. Diagram showing movement of water particles in overlying fresh

water and underlying salt water during the passage of boundary waves from left to right 44

11. Stevenson's wave dynamometer , . . c 62

12. Diagram to illustrate the process of wave refraction, whereby wave

attack is concentrated on headlands , 75

13. Section of beach slope showing by dotted lines the so-called zig-zag

path of debris particles during beach drifting and by solid lines

the parabolic paths actually followed 94

14. Parabolic paths of large and small particles of debris subject to

beach drifting , 96

15. Parabolic paths followed by debris particles impelled by tne com-

bined action of on-shore swells and oblique wind waves 97

16. Diagram to illustrate relation of beach drifting to wind directions 100

17. Parabolic paths of debris particles subject to beach drifting 101

18. Elliptical orbit of water particle during passage of the tide wave

over a sloping seabottom 106

19. Course followed by a nearly submerged float under the influence

of tidal currents in New York harbor , „ . . . . . 116

xiii

XIV LIST OF ILLUSTRATIONS

Fig. Page

20. Theoretical course calculated by Parsons for the float whose actual

course is shown in Figure 19 118

21. Eddy currents in the Gulf of Honduras and Mosquito Gulf 140

22. Elements of the shore zones during an early stage of development . 160

23. Elements of the shore zones in an advanced stage of development. 162

24. Embayed coastal plain of Chesapeake Bay region, showing example

of ria shoreline 174

25. A typical section of the fjord coast of Norway, showing angular

pattern attributed to fault-control 177

26. Mississippi Delta 187

27. Delta of the Tiber 188

28. Niger Delta 189

29. Initial stage of a fault shoreline 190

30. Coast of North Carolina, showing one type of compound shoreline. 191

31. Compound shoreline due to faulting and partial submergence of up-

throw block 191

32. Stages in the development of the shore profile of a shoreline of sub-

mergence . 201

33. Successive profiles of equilibrium on a retrograding shore 211

34. Profiles of equilibrium off the Madagascar coast as plotted from

charts by Barrell 212

35. Stages in the development of the shore profile of a shoreline of sub-

mergence 213

36. Variations in the beach profile of equilibrium due to variations in

the different shore forces 218

37. Mature and old shore profiles of a shoreline of submergence 224

38. San Clemente Island off the coast of southern California, showing

series of uplifted wave-cut terraces 229

39. Cross-section of the western coast and continental shelf of Norway. 232

40. Stages in the reduction of a land mass 256

41. Overlapping of marine deposits upon the abrasion platform of a

slowly subsiding land mass 258

42. Elements of the profile of a shoreline of emergence 258

43. Stages in the development of the shore profile of a fault coast .... 264

44. Profile of a shoreline of emergence 266

45. Shoreline of submergence, initial stage 273

46. Shoreline of submergence in Chesapeake Bay region 274

47. Early youth of a shoreline of submergence, showing crenulate shore-

line 275

48. Crenulate shoreline of the southwest coast of Ireland 276

49. Young shoreline of submergence near Idzuhara, Japan, showing

crenulate stage 278

50. Young shoreline of submergence, showing types of beaches, bars,

spits, and forelands 283

51. Initial unorganized condition of currents along a young shoreline

ot submergence compared with organized condition which obtains when the stages of submaturity or maturity are reached . . . 285

52. Sand spits on the shore of Port Orchard, Washington 287

LIST OF ILLUSTRATIONS XV

Fig. Page

53. Simple spit and compound recurved spit at entrance to Port

Moller, Alaska 289

54. Successive stages in the development of one type of compound re-

curved spit 291

55. Compound recurved spit enclosing Toronto Harbor 293

56. Development of the Cape Cod shoreline 294

57. Development of Sandy Hook spit 296

58. Lagoons and ridges of the Presque Isle compound recurved spit.. . 299

59. Spits built by converging currents 300

60. Spits converging to form a bay bar on the Alaskan coast 300

61. Bay-mouth bars on the Marthas Vineyard coast 301

62. Bay-mouth bar on the Marthas Vineyard coast 302

63. Bay-head bar near Duluth 303

64. Mid-bay bar in Hempstead Harbor, Long Island 304

65. Winged headland near Sag Harbor, Long Island 306

66. Offsets, overlaps, and stream deflection „ . 308

67. Looped bar on shore of Shapka Island, Alaska 310

68. Renard Island near Seward, Alaska, showing embankment growing

from island toward mainland 311

69. Inner Iliasik Island, Alaska, showing embankment which may be

upbuilding toward the surface simultaneously along its entire

length 311

70. Single tombolo connecting former island of Marblehead with the

mainland 312

71. Former island of Big Nahant tied to Little Nahant, and the latter

to the mainland by single tombolo 313

72. Duxbury and Saquish Neck tombolos uniting former islands with

the mainland of Massachusetts near Plymouth 316

73. Monte Argentario, Italy, tied to the mainland by a double tombolo 317

74. Morro del Puerto Santo, Venezuela, a Y-tombolo 318

75. Former islands, many of which were wholly or completely eroded by

wave action, and the resulting debris used by the waves to build

a complex tombolo tying the remaining islands to the mainland. 319

76. Nantasket Beach, Massachusetts, the complex tombolo formed by

wave erosion of the islands shown in Fig. 75, with deposition of the debris to give connecting beaches uniting the remaining

islands with each other and with the mainland at the south. 320

77. A strongly recurved spit on the Washington coast, about to become i

a cuspate bar 321

78. Cuspate bars on the Narragansett Bay shore 321

79. Cuspate bar, showing enclosed marsh near Providence, Rhode

Island 321

80. Cuspate bar originally built as a tombolo tying to the mainland an

island since removed by wave erosion 321

81. Cuspate bars on the shores of Port Discovery, Washington 323

82. Cuspate foreland near Port Townsend, Washington 324

83. Types of cuspate foreland bars 324

84. The former Cape Canaveral, now known as False Cape 326 xvi LIST OF ILLUSTRATIONS

Fig. Page

85. Marsh bars on the Delaware Bay shore 327

Comparison of text figures to facilitate correlations of successive

stages in the development of a shoreline of submergence 331

86. Lake Balaton (Platten Lake), showing position of cuspate bar . . . 337

87. Shoreline of submergence, submature stage 340

88. Shoreline of submergence, mature stage 341

89. Valleuses on the northwest coast of France 343

115. Offshore bar and lagoon of the Long Island coast, showing distribu-

tion of tidal inlets 371

16. Offshore bar and lagoon of the New Jersey coast 371

17. Tidal delta at Ocracoke Inlet, North Carolina coast 375

18. Stages in the development and retrogression of an offshore bar. 376

119. Stages in the normal history of an offshore bar, due account being

taken of the effect of migrating inlets 378

120 . Diagram showing how wave erosion of a lobate delta may transform

it into an arcuate delta (broken line) 396

121. Fault shoreline bordering a scarp which dies out toward the right 397

122. Similar to Fig. 121, except that the fault traversed a little dissected

plain of faint relief 398

123. Successive stages in the retrogression of a fault shoreline bordering

rocks of varying resistance 399

124. Compound shoreline, combining essential features of a shoreline of

submergence and a fault shoreline 40]

LIST OF ILLUSTRATIONS XV11

Fig. Page

125. Stages in the formation of a contraposed shoreline 403

126. Cuspate delta of the Tagliamento River, Italy, showing parallel

beach ridges 410

127. Successive stages in the development of Ro'ckaway sand spit, Long

Island 417

128. Diagram of cliffed headland and associated beach ridge plain, show-

ing that one series of ridges truncating another does not necessarily imply a longer lapse of time than an equal number of

parallel ridges 418

129. Ridges of the Cape Canaveral cuspate foreland 420

130. The Dungeness cuspate foreland, showing shingle beach ridges and

swales 423

131. Dune ridges of the Darss cuspate foreland, Germany 429

132. Dune ridges of the Swinemunde tombolo 434

133. Beach ridges indicating coastal emergence 446

134. Beach ridges indicating coastal submergence . 447

135. Hypothetical case in which beach ridges on a rising coast may give

a false indication of stability 449

136. Hypothetical case in which beach ridges on a sinking coast give a

false indication of stability 450

137. Types of beach ridges formed on a stable coast 451

138. Beach ridges of equal height 'separated by swales of different depths

due to variations in spacing of ridges 453

139. Diagram illustrating Branner's theory of beach cusp formation . . . 461

140. Diagram illustrating Branner's theory of the formation of unequally

spaced beach cusps 461

141. Variations in the form of beach cusps 465

142. Partially eroded older cusps and respaced later series 466

143. Normal and inverted beach cusps 473

144. Artificial beach cusps 476

145. Beach cusps (after Jefferson) showing compound cusps at right. . . 484

146. Oscillation ripples -. 491

147. Current ripples 494

148. Vortices involved in the formation of current ripple mark 497

L49. Sand dome 518