Abstract: In order to explain the structures of low-frequency atmospheric wavetrains the theory for propagating in a slowly varying medium is applied to the planetary waves. Using the ray tracing techniques, this paper discusses the effect of the variations of the warenumber Ks on the variations of ray and the bifurcations of wavetrains nearby latitudes where the ray parallels to the latitude circle. The amplitude variations along the ray path are also discussed. It is pointed out that the phenomena of the wavetrain bifurcations obviously exist nearby the latitudes where Ks has the extremism, and wave amplitude is the maxima near the latitude during propagating. They agree with observational and numerical model results. The limitation of the great circle theory is also discussed.