I have often felt the difficulty of illustrating, by means of Airy's Wave Machine, and various other complex instruments of a similar character, the composition of plane polarised rays into a single elliptically or circularly polarised one; the difficulty arising chiefly in showing separately, but in close succession, to the audience the two vibrations which are to be compounded, and their resultant. Lissajoux's apparatus would exactly answer the purpose if we had tuning-forks vibrating 10 or 15 times a second, its sole defect being the extreme rapidity with which differences of phase are run through; and, in fact, I have tried metronome pendulums with mirrors attached to them; but I have since found the following arrangement to be much more satisfactory. It consists simply in using plane mirrors rotating about axes very nearly perpendicular to their surfaces.