It is shown that the neglect of the terms in the differential equations of atmospheric oscillations which are quadratic in the velocities is not justified in the case of free oscillations for heights greater than 100 kilometers. This result is illustrated for two atmospheres of different temperature distributions where it is shown that at about 130 kilometers the neglected quadratic terms become equal to the retained linear terms and that they even exceed the latter at heights greater than 130 kilometers. A method is outlined for including the quadratic terms in the theory of atmospheric oscillations. The bearing of this result on atmospheric tides is discussed.

An analytical method is presented for obtaining turbulent temperature recovery factors for a thermally insulated surface in supersonic flow. The method is an extension of Squire's analysis for incompressible flow. The boundary layer velocity profile is represented by a power law and a similarity is postulated for squared-velocity the static-temperature-difference profiles.

Everyone is familiar with the daily changes of air temperature. The barometer shows that these are accompanied by daily changes of mass distribution of the atmosphere, and consequently with daily motions of the air. In the tropics the daily pressure change is evident on the barographs; in temperate and higher latitudes it is not noticeable, being overwhelmed by cyclonic and anticyclonic pressure variations. There too, however, the daily change can be found by averaging the variations over many days; and the same process suffices to show that there is a still smaller lunar tide in the atmosphere, first sought by Laplace. Throughout nearly two centuries these 'tides', thermal and gravitational, have been extensively discussed in the periodical literature of science, although they are very minor phenomena at ground level. This monograph summarizes our present knowledge and theoretical under standing of them. It is more than twenty years since the appearance of the one previous monograph on them - by Wilkes - and nearly a decade since they were last comprehensively reviewed, by Siebert. The intervening years have seen many additions to our know ledge of the state of the upper atmosphere, and of the tides there, on the basis of measurements by radio, rockets and satellites.

Advances in Geophysics