The momentous experimental discovery of the Faraday effect is briefly sketc
hed from a historical perspective, through the eyes of several well-known s
cientists. This effect and its generalization can be explained theoreticall
y by using the dispersion theory for waves propagating in an anisotropic me
dium. A wave of arbitrary initial polarization will ha ie its wave polariza
tion transformed continuously as it propagates. It is convenient to represe
nt this continuous polarization transformation by a locus in the polarizati
on-ratio plane. In a lossless medium, when both characteristic waves are pr
opagating, this locus is a circle. Five cases in a magneto-ionic medium hav
e been investigated for different propagation angles. The results are discu
ssed and illustrated.