In discussing wave motions along a strong jet of westerlies, we can no longer neglect the variation of west wind with latitude, and therefore must consider the possibility of having a phase velocity whose value is between the maximum and minimum west-wind velocities. The study of wave motions is thus extended from the very long and slowly moving or retrograding waves into the realm of ordinary waves and cyclone waves and it is found that, for nondivergent barotropic motion, the condition for the presence of neutral and amplified waves with a phase velocity whose value is between the maximum and minimum wind velocity in the belt is the existence of critical points where the absolute vorticity has an extreme value. If no such point exists, then all perturbations must be damped. When this condition is satisfied, both amplified (unstable) and neutral waves can be expected. The wave moving with a velocity equal to the current velocity at the critical point is neutral while those with a velocity less t... Abstract In discussing wave motions along a strong jet of westerlies, we can no longer neglect the variation of west wind with latitude, and therefore must consider the possibility of having a phase velocity whose value is between the maximum and minimum west-wind velocities. The study of wave motions is thus extended from the very long and slowly moving or retrograding waves into the realm of ordinary waves and cyclone waves and it is found that, for nondivergent barotropic motion, the condition for the presence of neutral and amplified waves with a phase velocity whose value is between the maximum and minimum wind velocity in the belt is the existence of critical points where the absolute vorticity has an extreme value. If no such point exists, then all perturbations must be damped. When this condition is satisfied, both amplified (unstable) and neutral waves can be expected. The wave moving with a velocity equal to the current velocity at the critical point is neutral while those with a velocity less t...