Lindzen's work on atmospheric tides led him to the study of planetary waves and the general circulation of atmospheres. By 1967, he had contributed a number of papers on the theory of waves in the middle atmosphere. In "Planetary waves on beta planes", he developed a beta plane approximation for simplifying the equations of classical tidal theory, whilst at the same time developing planetary wave relations. He noticed from his equations that eastward-traveling waves (known as "Rossby waves" since their discovery in 1939 by Carl-Gustav Rossby) and westward-traveling waves (which Lindzen himself helped in establishing as "atmospheric Kelvin waves") with periods less than five days were "vertically trapped." At the same time, an important paper by Booker and Bretherton appeared, which Lindzen read with great interest. Booker and Bretherton showed that vertically propagating gravity waves were completely absorbed at a critical level.