Accordingly, in the same memoir, Fresnel offered his first attempt at a wave theory of chromatic polarization. When polarized light passed through a crystal lamina, it was split into ordinary and extraordinary waves (with intensities described by Malus's law), and these were perpendicularly polarized and therefore did not interfere, so that no colors were produced (yet). But if they then passed through an analyzer (second polarizer), their polarizations were brought into alignment (with intensities again modified according to Malus's law), and they would interfere. This explanation, by itself, predicts that if the analyzer is rotated 90°, the ordinary and extraordinary waves simply switch roles, so that if the analyzer takes the form of a calcite crystal, the two images of the lamina should be of the same hue (this issue is revisited below). But in fact, as Arago and Biot had found, they are of complementary colors. To correct the prediction, Fresnel proposed a phase-inversion rule whereby one of the constituent waves of one of the two images suffered an additional 180° phase shift on its way through the lamina. This inversion was a weakness in the theory relative to Biot's, as Fresnel acknowledged, although the rule specified which of the two images had the inverted wave. Moreover, Fresnel could deal only with special cases, because he had not yet solved the problem of superposing sinusoidal functions with arbitrary phase differences due to propagation at different velocities through the lamina.