The paper by Taroh Matsuno discusses quasi-horizontal wave motions in the equatorial region of the atmosphere or ocean, focusing on a single layer of homogeneous, incompressible fluid with a free surface. The Coriolis parameter is assumed to be proportional to the latitude, leading to the emergence of two types of waves: inertio-gravity waves and Rossby waves. For the lowest mode, the distinction between these two types is not clear, as the wave moves westward and its frequency approaches that of the Rossby wave as the wave number increases. The pressure and wind fields exhibit a mixed character of both wave types, and the wave's characteristics change continuously with the wave number. This suggests that it is difficult to "filter out" gravity waves from large-scale motions. Another key finding is that low-frequency waves are trapped near the equator, with both inertio-gravity and Rossby waves having appreciable amplitude only in this region. The characteristic north-south extent of these waves is given by \((c/\beta)^{1/2}\), where \(c\) is the velocity of long gravity waves and \(\beta\) is the Rossby parameter. This expression is consistent with Bretherton's (1964) results for inertio-gravity oscillations in a meridional plane. The paper also explores "forced stationary motion" in the equatorial region, where mass sources and sinks are introduced periodically in the east-west direction. This leads to the formation of high and low pressure cells, which are split into two parts separated by troughs or ridges along the equator. A strong east-west current forms along the equator, directed from the source to the sink, and is intensified by the turning of circular flow in higher latitudes. Finally, the paper discusses the validity of the approximations used in the tidal theory, showing that the equations treated are an approximate form of Laplace's tidal equation valid near the equator. The solutions obtained are approximate free wave solutions of the tidal equation, and the lower the frequency of a free wave, the more resonant it is to the excitation.The paper by Taroh Matsuno discusses quasi-horizontal wave motions in the equatorial region of the atmosphere or ocean, focusing on a single layer of homogeneous, incompressible fluid with a free surface. The Coriolis parameter is assumed to be proportional to the latitude, leading to the emergence of two types of waves: inertio-gravity waves and Rossby waves. For the lowest mode, the distinction between these two types is not clear, as the wave moves westward and its frequency approaches that of the Rossby wave as the wave number increases. The pressure and wind fields exhibit a mixed character of both wave types, and the wave's characteristics change continuously with the wave number. This suggests that it is difficult to "filter out" gravity waves from large-scale motions. Another key finding is that low-frequency waves are trapped near the equator, with both inertio-gravity and Rossby waves having appreciable amplitude only in this region. The characteristic north-south extent of these waves is given by \((c/\beta)^{1/2}\), where \(c\) is the velocity of long gravity waves and \(\beta\) is the Rossby parameter. This expression is consistent with Bretherton's (1964) results for inertio-gravity oscillations in a meridional plane. The paper also explores "forced stationary motion" in the equatorial region, where mass sources and sinks are introduced periodically in the east-west direction. This leads to the formation of high and low pressure cells, which are split into two parts separated by troughs or ridges along the equator. A strong east-west current forms along the equator, directed from the source to the sink, and is intensified by the turning of circular flow in higher latitudes. Finally, the paper discusses the validity of the approximations used in the tidal theory, showing that the equations treated are an approximate form of Laplace's tidal equation valid near the equator. The solutions obtained are approximate free wave solutions of the tidal equation, and the lower the frequency of a free wave, the more resonant it is to the excitation.