Matsuno's study investigates quasi-geostrophic motions in the equatorial region, focusing on wave behavior in a homogeneous, incompressible fluid layer with a free surface. The Coriolis parameter is proportional to latitude, and two wave types— inertio-gravity and Rossby waves—are identified. However, in the equatorial region, the distinction between these waves is unclear. The wave moves westward, and its frequency depends on wave number. As the wave number increases, the frequency approaches that of Rossby waves. The pressure and wind fields show mixed characteristics of the two wave types. Equatorial disturbances exhibit low-frequency wave trapping near the equator. Both inertio-gravity and Rossby waves have significant amplitudes near the equator, with a north-south extent of (c/β)^{1/2}, where c is the velocity of long gravity waves and β is the Rossby parameter. This expression matches Bretherton's result for inertio-gravity oscillations in a meridional plane. The study also examines "forced stationary motion" in the equatorial region, where periodic mass sources and sinks are introduced. High and low pressure cells form, split by troughs or ridges along the equator. A strong east-west current develops along the equator, intensified by the turning of circular flows in higher latitudes. The paper discusses the behavior of Rossby and gravity waves in the equatorial area, noting that for the lowest mode (n=0), the wave has a frequency that ranges between inertio-gravity and Rossby wave frequencies. The wave connects the two wave families, filling the frequency gap. The study also explores the trapping of waves in the equatorial area, noting that low-frequency waves are confined near the equator. This is due to refraction and the variation of inertio-gravity wave propagation velocity with latitude. Rossby waves, however, are not easily trapped due to their slower velocity. The paper concludes that there is no marked difference between Rossby and gravity waves for the lowest modes in the equatorial region. The concept of filtering is not applicable in the equatorial area due to the lack of a clear distinction between wave types. The study also discusses the validity of approximations in the context of tidal theory, showing that the equations used are an approximate form of Laplace's tidal equation near the equator. The solutions obtained are considered approximate solutions of the tidal equation under certain conditions. The study also examines forced stationary motion, showing that mass sources and sinks create pressure cells and strong east-west currents. The circulation pattern is influenced by the geostrophic balance between pressure and wind fields. The study concludes that the equatorial region's pressure or temperature fields can be opposite to external heatings. The paper also discusses the formal development of the theory for general stratified fluids, showing that the equations derived can be applied to stratified fluids under certain conditions.Matsuno's study investigates quasi-geostrophic motions in the equatorial region, focusing on wave behavior in a homogeneous, incompressible fluid layer with a free surface. The Coriolis parameter is proportional to latitude, and two wave types— inertio-gravity and Rossby waves—are identified. However, in the equatorial region, the distinction between these waves is unclear. The wave moves westward, and its frequency depends on wave number. As the wave number increases, the frequency approaches that of Rossby waves. The pressure and wind fields show mixed characteristics of the two wave types. Equatorial disturbances exhibit low-frequency wave trapping near the equator. Both inertio-gravity and Rossby waves have significant amplitudes near the equator, with a north-south extent of (c/β)^{1/2}, where c is the velocity of long gravity waves and β is the Rossby parameter. This expression matches Bretherton's result for inertio-gravity oscillations in a meridional plane. The study also examines "forced stationary motion" in the equatorial region, where periodic mass sources and sinks are introduced. High and low pressure cells form, split by troughs or ridges along the equator. A strong east-west current develops along the equator, intensified by the turning of circular flows in higher latitudes. The paper discusses the behavior of Rossby and gravity waves in the equatorial area, noting that for the lowest mode (n=0), the wave has a frequency that ranges between inertio-gravity and Rossby wave frequencies. The wave connects the two wave families, filling the frequency gap. The study also explores the trapping of waves in the equatorial area, noting that low-frequency waves are confined near the equator. This is due to refraction and the variation of inertio-gravity wave propagation velocity with latitude. Rossby waves, however, are not easily trapped due to their slower velocity. The paper concludes that there is no marked difference between Rossby and gravity waves for the lowest modes in the equatorial region. The concept of filtering is not applicable in the equatorial area due to the lack of a clear distinction between wave types. The study also discusses the validity of approximations in the context of tidal theory, showing that the equations used are an approximate form of Laplace's tidal equation near the equator. The solutions obtained are considered approximate solutions of the tidal equation under certain conditions. The study also examines forced stationary motion, showing that mass sources and sinks create pressure cells and strong east-west currents. The circulation pattern is influenced by the geostrophic balance between pressure and wind fields. The study concludes that the equatorial region's pressure or temperature fields can be opposite to external heatings. The paper also discusses the formal development of the theory for general stratified fluids, showing that the equations derived can be applied to stratified fluids under certain conditions.