+Summary+ 54 CHAPTER III. THE WORK OF RUNNING WATER. +Rain and River Erosion+ 57 _Subaërial Erosion without Valleys_ 58 _The Development of Valleys_ 63 By the growth of gullies, 63. Limits of growth, 67. The permanent stream, 70. Other modes of valley development, 73. Structural valleys, 77. The courses of valleys, 77. The development of tributaries, 78. +A Cycle of Erosion. Its Stages+ 80 +General Characteristics of Topography Developed by River Erosion+ 92 +Special Features Resulting from Special Conditions of Erosion+ 92 Bad-land topography, 93. Special forms of valleys; canyons, 94. +The Struggle for Existence Among Valleys and Streams+ 100 Piracy, 103. +Rate of Degradation+ 105 Material in solution in river water, 107. +Economic Considerations+ 108 +Analysis of Erosion+ 110 _Weathering._ 110 _Transportation_ 115 Transporting power and velocity, 115. How sediment is carried, 116. _Corrasion_ 119 Abrasion, 119. Solution, 122. +Conditions Affecting the Rate of Erosion+ 123 _The Influence of Declivity_ 123 _The Influence of Rock_ 124 Physical constitution, 124. Chemical composition, 124. Structure, 125. _The Influence of Climate_ 127 +Effects of Unequal Hardness+ 132 Rapids and falls, 132. Rock terraces, 140. Narrows, 141. Other effects on topography, 142. Adjustment of streams to rock structures, 146. +Influence of Joints and Folds+ 150 Joints, 150. Folds, 154. +Effect of Changes of Level+ 161 Rise, 161. Sinking, 170. Differential movement, warping, 171.