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Present day understanding of the hydrologic cycle is limited by the fact that little data have been compiled concerning mass movements of water in the atmosphere. As a result, relationships between precipitation, evapotranspiration, and runoff have been obscured. The role of the atmosphere in the hydrologic cycle is discussed, and the relationship of the hydrologic cycle to the air mass cycle is clarified. Taking the Mississippi Watershed as an example, quantitative estimates are prepared of the percentage of precipitation occurring from, and of evapotranspiration occurring into, maritime and continental air masses. These estimates are based upon quantitative studies for selected stations within the watershed. Pilot balloon and radiosonde data are utilized to determine the total flux of moisture in maritime and in continental air into the Mississippi Watershed. From these data a complete balance of the hydrologic cycle for the Mississippi Watershed is prepared. The results of this investigation are then used in analyzing the various phases of the hydrologic cycle. It is shown that only a small percentage of the maritime moisture advected over the continents is ever precipitated; that in spite of this fact most precipitation occurs from maritime air and is derived directly from oceanic sources; and that the modification of the evapotranspiration regime even over a widespread area can have comparatively little direct effect on the average quantity of precipitation recorded over that or neighboring regions.

The problem of flow through rotating channels of almost arbitrary cross-section is considered. It is shown that when the ratio of the Rossby number and the Reynolds number is small (ε = Ro/Re [Lt ] 1) and when the Reynolds number is not too large (Re [Lt ] ε−1): (1) the viscous effects are important only in thin boundary layers along the channel walls; (2) the flow in the interior is geostrophic; and (3) the inertia effects may be neglected everywhere. Solutions for the geostrophic region and the boundary layers are obtained and are combined to give the complete velocity field. Experimental results for a circular conduit are presented which are in good agreement with the theory.

A generalized Ekman flow is obtained for the boundary layer of a semi‐infinite, rotating homogeneous fluid with lateral variation in the horizontal velocity components far from the boundary surface. The fields of motion considered include uni‐directional motion with lateral shear, symmetric and elongated eddies, and cols. A solution for the first of these cases is obtained to fifth order; for the others, to second order. In all cases the magnitude of the vertical velocities induced by convergence in the boundary layer is greater for systems with negative relative vorticity than for systems with positive relative vorticity. The result differs substantially from first‐order theory, for which the magnitude of the vertical velocity is proportional to the relative vorticity. A number of meteorological applications are considered.