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n Introduction and Acknowledgments vii Methods of Map Analysis and Definitions of Trrms 1 Map accuracy 1 Methods of obtaining quantitative data from maps 1 Properties measured from maps 2 Derived quantities 4 Problems of Field Study 7 Methods of field observation 7 Observed watershed properties 7 General plan of field measurements Ö Measured properties 8 Climatic Data 13 General Description of Basins 15 Basins in Arizona 15 Basins in Colorado 16 Basins in New Mexico 18 Basins in Utah 20 Methods of Statistical Analysis 23 Appropriateness of statistical methods 23 Regression and correlation analysis of paired variables 24 Final multivariate analysis 24 Inferences Drawn from Results of Statistical Tests 27 Restrictions on inferences 27 Results of analysis of variance and covariance tests 27 Results of simple correlation and regression analyses 29 Relations among planimetric properties of basins 30 Relation of valley-side slopes to other basin characteristics 30 Texture of topography as affected by climatic and mantle characteristics 33 Generalizations on investigative procedures 35 Summary of Conclusions 37 References Cited 39 Appendices I Derivations of relations among geometrical elements of valleys 41 II Index maps of study areas 45 IT! Derivation of relation between diameter of imprint and volume of imprint, :. used in soil strength test 47 IV Maps and drainage nets of study areas 49 V Two-variable correlation and regression analyses A. Correlation tables of re", ions analyzed by grouped-data methods .... 63 B. Scatter plots and regressions of selected relations; ungrouped data ... 71 VI A. Analyses of variance 77 B. Determination of the effect of gullying and trenching on drainage density, by the analysis of covariance 80 VII Solution of normal equations relating drainage density to soil properties and climate elements by the Doolittle method 83