But here, as in the case of thin films, the different lengths of the waves of light come into play. Red will require a greater thickness to produce the retardation necessary for extinction than blue; consequently when the longer waves have been withdrawn by interference, the shorter ones remain, the film of gypsum shining with the colours which the short waves confer. Conversely, when the shorter waves have been withdrawn, the thickness is such that the longer waves remain. An elementary consideration suffices to show, that when the directions of vibration of the prisms and the gypsum enclose an angle of forty-five degrees, the colours are at their maximum brilliancy. When the film is turned from this direction, the colours gradually fade, until, at the point where the directions of vibration in plate and prisms are parallel, they disappear altogether. (The best way of obtaining a knowledge of these phenomena is to construct a model of thin wood or pasteboard, representing the plate of gypsum, its planes of vibration, and also those of the polarizer and analyzer. Two parallel pieces of the board are to be separated by an interval which shall represent the thickness of the film of gypsum. Between them two other pieces, intersecting each other at a right angle, are to represent the planes of vibration within the film; while attached to the two parallel surfaces outside are two other pieces of board, which represent the planes of vibration of the polarizer and analyzer. On the two intersecting planes the waves are to be drawn, showing the resolution of the first polarized beam into two others, and then the subsequent reduction of the two systems of vibrations to a common plane by the analyzer. Following out rigidly the interaction of the two systems of waves, we are taught by such a model that all the phenomena of colour obtained by the combination of the waves, when the planes of vibration of the two Nicols are parallel, are displaced by the _complementary_ phenomena, when the planes of vibration are perpendicular to each other.)