We have given formulas for the determination of the rotation and the ellipticity of a wave that has propagated through a quartz sample in a waveguide. Taking into account the multiple reflections, calculations made with the help of a computer were compared with the experimental results. Dielectric constants of quartz are found to be 4.63 parallel and 4.51 perpendicular. Both results are believed to be correct to ± 0.7%.