The paper by Robert E. Horton, "Erosional Development of Streams and Their Drainage Basins; Hydrophysic Approach to Quantitative Morphology," explores the quantitative aspects of stream and drainage basin development. The author introduces a set of tools to analyze the development of landforms, particularly drainage basins and their stream networks, from a hydrophysical perspective. Key concepts include: 1. **Stream Orders**: Streams are classified into orders based on the number of tributaries they receive. The main stream is of the highest order, and unbranched tributaries are of the 1st order. 2. **Drainage Density**: This measures the average length of streams per unit area and is used to characterize the degree of drainage development within a basin. 3. **Length of Overland Flow**: This is the length of flow of water over the ground before it collects in streams. It is crucial for understanding the hydrologic and physiographic development of drainage basins. 4. **Stream Frequency**: This is the number of streams per unit area. 5. **Composition of Drainage Net**: This refers to the numbers and lengths of streams and tributaries of different sizes, regardless of their pattern. 6. **Laws of Drainage Composition**: Two fundamental laws are presented: - **Law of Stream Numbers**: The number of streams of different orders in a basin follows an inverse geometric series. - **Law of Stream Lengths**: The average lengths of streams of different orders follow a direct geometric series. 7. **Total Length of Streams**: The total length of streams of a given order is influenced by the bifurcation ratio and stream-length ratio. 8. **Channel-Storage Capacity**: This is a significant factor in modulating flood intensities and is determined by the stream length and cross-sectional area. 9. **General Equation of Composition of Stream Systems**: This equation combines all the physiographic factors that determine the composition of a stream system, providing a quantitative generalization of Playfair's law. 10. **Relation of Size of Drainage Area to Stream Order**: The order of the main stream in a basin increases with the logarithm of the drainage area, but other factors like bifurcation and stream-length ratios can also influence this relationship. The paper also discusses methods for determining these factors from topographic maps and provides examples to illustrate the application of these concepts. The work aims to provide a quantitative framework for understanding and predicting the development of stream systems and drainage basins.The paper by Robert E. Horton, "Erosional Development of Streams and Their Drainage Basins; Hydrophysic Approach to Quantitative Morphology," explores the quantitative aspects of stream and drainage basin development. The author introduces a set of tools to analyze the development of landforms, particularly drainage basins and their stream networks, from a hydrophysical perspective. Key concepts include: 1. **Stream Orders**: Streams are classified into orders based on the number of tributaries they receive. The main stream is of the highest order, and unbranched tributaries are of the 1st order. 2. **Drainage Density**: This measures the average length of streams per unit area and is used to characterize the degree of drainage development within a basin. 3. **Length of Overland Flow**: This is the length of flow of water over the ground before it collects in streams. It is crucial for understanding the hydrologic and physiographic development of drainage basins. 4. **Stream Frequency**: This is the number of streams per unit area. 5. **Composition of Drainage Net**: This refers to the numbers and lengths of streams and tributaries of different sizes, regardless of their pattern. 6. **Laws of Drainage Composition**: Two fundamental laws are presented: - **Law of Stream Numbers**: The number of streams of different orders in a basin follows an inverse geometric series. - **Law of Stream Lengths**: The average lengths of streams of different orders follow a direct geometric series. 7. **Total Length of Streams**: The total length of streams of a given order is influenced by the bifurcation ratio and stream-length ratio. 8. **Channel-Storage Capacity**: This is a significant factor in modulating flood intensities and is determined by the stream length and cross-sectional area. 9. **General Equation of Composition of Stream Systems**: This equation combines all the physiographic factors that determine the composition of a stream system, providing a quantitative generalization of Playfair's law. 10. **Relation of Size of Drainage Area to Stream Order**: The order of the main stream in a basin increases with the logarithm of the drainage area, but other factors like bifurcation and stream-length ratios can also influence this relationship. The paper also discusses methods for determining these factors from topographic maps and provides examples to illustrate the application of these concepts. The work aims to provide a quantitative framework for understanding and predicting the development of stream systems and drainage basins.