Computer ray tracing results are presented for lightning generated whistlers propagating in the Jovian Magnetosphere. The waves are launched from a point on the Jovian surface at 66 ¿ latitude and propagate approximately along L=6 out to near the equatorial plane and into the Io plasma torus. The magnetospheric model includes the Io torus centered at the magnetic equator. The torus model is an empirical fit of the density contours presented by Warwick et al. [1979>, and the electron density outside of the torus is an adaptation from Sentman and Goertz [1977>. The results clearly indicate that the whistlers propagate through the magnetosphere with very little dispersion until recaching the torus, at which time the dispersion starts to increase very rapidly. We find that the computed dispersions using the assumed electron density model are in excellent agreement with the observed whistler dispersions, thereby confirming the validity of the model. In addition to the ray path studies, the effect of Landau damping on whistler waves has been investigated as a function of the electron temperature within the torus. For a constant electron temperature of 105 ¿K only the lowest frequencies, ≲1.0 kHz, show appreciable attenuation after passing through the torus. But an increase in the electron temperature of only a factor of three results in a very large attenuation over the entire frequency range observed. This result suggests an upper limit for the electron temperature in the torus of a few times 105 ¿K.